Answer: V ≈ 927,587
Step-by-step explanation:
Formula for volume of a sphere:
V = [tex]\frac{4}{3}[/tex]πr³
Substitute the known value for radius:
V = [tex]\frac{4}{3}[/tex]π(60.5ft)³
Simplify:
V ≈ 927,587
the numerator of a certain fraction is nine less than the denominator. if the fraction reduces to (1/7), what is the numerator of the fraction?
The numerator of the fraction is 2.
The fraction can be written as 2/7, and since the numerator is nine less than the denominator, when the fraction reduces to (1/7) it means that the numerator must be 2.
To solve this problem, first determine what is given in the question: a fraction with a numerator that is nine less than the denominator, and that reduces to (1/7).
Using this information, the goal is to determine the numerator of the fraction.
To do this, simply subtract nine from the denominator and the result will be the numerator. In this case, the denominator is 7, so subtracting 9 from 7 gives us 2, which is the numerator of the fraction.
Therefore, the numerator of the fraction is 2.
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Find the volume of the solid by subtracting two volumes.
The solid in the first octant under the plane z = x + y, above the surface z = xy, and enclosed by the surfaces x = 0, y = 0, and x2 + y2 = 4
The volume of the solid is 1.5 cubic units. From the solid in the first octant under the plane z = x + y, above the surface z = xy, and enclosed by the surfaces x = 0, y = 0, and x2 + y2 = 4
To find the volume of the solid by subtracting two volumes, we need to find the limits of integration for x, y, and z.
From the given information, we know that the solid is in the first octant and is enclosed by the surfaces x = 0, y = 0, and x2 + y2 = 4. Thus, the limits of integration for x and y are 0 to 2 since the radius of the circle x2 + y2 = 4 is 2.
Next, we need to find the limits of integration for z. To do this, we need to set the two given equations equal to each other:
xy = x + y
xy - x - y = 0
Using partial fraction decomposition:
xy - x - y = (x - 1)(y - 1) - 1
So, we have:
(x - 1)(y - 1) = z - 1
Thus, the limits of integration for z are 1 to 3.
Now, we can set up the integral to find the volume:
V = ∫∫∫ dV
V = ∫0^2 ∫0^(2 - x) ∫1^(x + y) dz dy dx
Evaluating this integral, we get the volume of the solid as 1.5 cubic units.
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Assume that Canada imports more goods and services than it exports. Which of the following is true of the Canadian balance of payments accounts??
The correct answer is C. Could you please explain in detail why the trade balance must be negative, and why A and E is wrong. Thx!!!25. Assume that Canada imports more goods and services than it exports. Which of the following is true of the Canadian balance of payments accounts? (A) The current account balance must be negative. (B) The current account balance must be positive (C) The trade balance must be negative. (D) The financial account (formerly called capital account) balance must be negative (E) The financial account (formerly called capital account) balance must be positive
The trade balance must be negative.
If Canada imports more goods and services than it exports, the trade balance must be negative.
Here's a step-by-step explanation of why this is true and why options A and E are wrong:
1. The trade balance is calculated as the value of exports minus the value of imports. If imports are greater than exports, the trade balance will be negative (C). This m that Canada is seen spending more on goods and services from other countries than it is receiving from the sale of its own goods and services to other countries.
2. The current account balance includes the trade balance, but also considers other transactions such as income from investments and transfers like foreign aid. While it is possible that a negative trade balance could be offset by other positive inflows, we do not have enough information to determine whether the current account balance must be negative (A) or positive (B). Therefore, we cannot definitively say that A or B is true.
3. The financial account (formerly called capital account) balance records the net change in ownership of financial assets, such as stocks and bonds, between a country and the rest of the world. A negative financial account balance means that a country's residents are purchasing more foreign assets than foreign residents are purchasing of that country's assets. A positive financial account balance means the opposite. Since we only have information about the trade balance and not the financial transactions, we cannot determine whether the financial account balance must be negative (D) or positive (E).
Based on the information given, we can only conclude that the trade balance must be negative (C) if Canada imports more goods and services than it exports.
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Justin weighs 15 pounds less then greg weighs, haft of greg weight is 75 pounds less then justins weight how much does each of them weigh
By setting up equations and solving for the variables, we found that Greg weighs 180 pounds and Justin weighs 165 pounds.
Let's start by assigning variables to represent Justin and Greg's weights. Let J represent Justin's weight and G represent Greg's weight.
We are given that Justin weighs 15 pounds less than Greg, which can be written as:
J = G - 15
We are also given that half of Greg's weight is 75 pounds less than Justin's weight. We can write this as an equation:
(1/2)G = J - 75
We can simplify this equation by substituting the first equation (J = G - 15) for J:
(1/2)G = (G - 15) - 75
Now we can solve for G, which represents Greg's weight:
(1/2)G = G - 90
Subtracting G from both sides gives:
(1/2)G - G = -90
Multiplying both sides by 2 gives:
G - 2G = -180
Simplifying gives:
-G = -180
Dividing both sides by -1 gives:
G = 180
So we have found that Greg weighs 180 pounds. We can use the first equation (J = G - 15) to find Justin's weight:
J = 180 - 15
J = 165
Therefore, Justin weighs 165 pounds.
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v=[2;0;-1]; >> w=[1;3;3]; >> x=[6;1;-3]; >> y=[1;0;2]; >> z=[2;-15;-1];Exercise 5.1 Enter the following vectors into MATLAEB 6 a. List all maximal orthogonal subsets of the above set. That is, group the vectors v, w, x, y, and z in as many ways as possible so that all the vectors in your group are orthogonal to each other and none of the vectors outside the group are orthogonal to all the vectors in the group. For example, the set fw, x) contains two vectors that are orthogonal to each other and none of the other vectors are orthogonal to both of these at the same time. But this is only one example, there are more What is the maximum number of nonzero orthogonal vectors that you could possibly find in R3? What about R? Explain b. Take the largest orthogonal subset and normalize all the vectors in that set as follows: >> V-v/norm(v) This code replaces v with itself divided by its size-so we get a vector pointing in the same direction but with length 1. The above code normalizes v, so you'll have to normalize the other vectors in your orthogonal subset as well, replacing v with the appropriate letter. Store the resulting vectors in MATLAB as columns of a matrix W. Enter them in alphabetical order from left to right
As a question-answering bot, I cannot provide the solution of this question as it requires the use of MATLAB software which cannot be done in this platform. However, I can provide a general overview and steps that can be followed to solve the problem. List all maximal orthogonal subsets of the above set. That is, group the vectors v, w, x, y, and z in as many ways as possible so that all the vectors in your group are orthogonal to each other and none of the vectors outside the group are orthogonal to all the vectors in the group. The maximal orthogonal subsets of the above set are: {v, y}, {w, x}, {z}b. Take the largest orthogonal subset and normalize all the vectors in that set as follows: >> V-v/norm(v) This code replaces v with itself divided by its size-so we get a vector pointing in the same direction but with length 1. The above code normalizes v, so you'll have to normalize the other vectors in your orthogonal subset as well, replacing v with the appropriate letter. Store the resulting vectors in MATLAB as columns of a matrix W. Enter them in alphabetical order from left to right.The largest orthogonal subset is {w, x}. The normalized vectors are w/norm(w) and x/norm(x). Store the resulting vectors in MATLAB as columns of a matrix W and enter them in alphabetical order from left to right. The resulting matrix would be: W = [1/√19 6/√19; 3/√19 1/√19; 0 -3/√19]Note: This solution is based on the assumption that the vectors are given in column form.
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Clara's family has lunch at a restaurant. The total bill is 67.58. The bill includes 6% tax and 18% tip on the pre-tax amount. How much was the bill before tax and tip.
Answer:
$54.50
Step-by-step explanation:
$67.58 after 6% tax and 18% tip
Let x = pretax and pre-tip amount.
The amount of tax is 0.06x.
The amount of tip is 0.18x.
The total amount is x + 0.06x + 0.18x = 1.24x.
The amount after tax and tip is $67.58.
1.24x = 67.58
x = 67.58/1.24
x = 54.5
Answer: $54.50
Tyler has 3 times as many books as Mia.
a. How many books does Mai have have if Tyler has: 15 books? 21 books? x books?
b. Tyler has 18 books. How many books does Mai have?
According to the equation, Mia has 7 books if Tyler has 21 books and Mia has 6 books if Tyler has 18 books.
What is equation?
An equation is a mathematical statement that indicates the equality of two expressions. It typically consists of two parts: the left-hand side and the right-hand side, separated by an equal sign (=).
a. If Tyler has 15 books, we can set up the equation:
Tyler = 3 x Mia
15 = 3 x Mia
Dividing both sides by 3, we get:
Mia = 5
Therefore, Mia has 5 books if Tyler has 15 books.
If Tyler has 21 books, we can set up the same equation:
Tyler = 3 x Mia
21 = 3 x Mia
Dividing both sides by 3, we get:
Mia = 7
Therefore, Mia has 7 books if Tyler has 21 books.
If Tyler has x books, the equation would be:
Tyler = 3 x Mia
x = 3 x Mia
Dividing both sides by 3, we get:
Mia = x/3
Therefore, Mia has x/3 books if Tyler has x books.
b. If Tyler has 18 books, we can set up the equation:
Tyler = 3 x Mia
18 = 3 x Mia
Dividing both sides by 3, we get:
Mia = 6
Therefore, Mia has 6 books if Tyler has 18 books.
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How many tons of cardboard does it take to make boxes for 250 million tubes of toothpaste if the weight of one box is 0.51 oz.?
Answer:
3,984.375 tons
Step-by-step explanation:
First, let's convert the weight of one box from ounces to tons:
0.51 oz = 0.51/16 = 0.031875 lbs
1 lb = 0.0005 tons (since 1 ton = 2000 lbs)
0.031875 lbs = 0.031875 x 0.0005 = 0.0000159375 tons
Next, let's calculate the total weight of cardboard needed for 250 million boxes:
Total weight of cardboard = weight of one box x number of boxes
Total weight of cardboard = 0.0000159375 tons x 250,000,000
Total weight of cardboard = 3,984.375 tons
the gregorian year averages 365.242500 days in length. the tropical year is 365.242199 days. how many years must pass until the gregorian and tropical years are out of step by exactly one day? group of answer choices
Therefore, it would take about 3322 years for the Gregorian and tropical years to be out of step by exactly one day.
What is length?Length is a physical quantity that describes how long or how far apart two points or objects are from each other in space. It is typically measured in units such as meters, feet, or inches, and is one of the basic dimensions used to describe the size and position of objects in the physical world.
given by the question.
The difference between the length of the Gregorian year and the tropical year is:
365.242500 - 365.242199 = 0.000301
This means that every year, the Gregorian calendar gains 0.000301 days on the tropical year. To be out of step by exactly one day, the Gregorian calendar needs to gain one full day on the tropical year, which would take:
1 / 0.000301 = 3322.26 years.
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Austin wants to pour 50.94 grams of salt into a container. So far he has poured 39.2 grams. How much more salt should Austin pour
Using arithmetic operation it is obtained that Austin should pour 11.74 more grams of salt to reach his desired amount of 50.94 grams.
What is arithmetic operation?
A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.
To determine how much more salt Austin should pour, we need to subtract the amount of salt he has poured from the total amount he wants to pour -
Use the arithmetic operation of subtraction.
Total amount of salt = 50.94 grams
Amount of salt poured so far = 39.2 grams
Therefore, the amount of salt that Austin still needs to pour is obtained by the expression -
50.94 grams - 39.2 grams = 11.74 grams
Therefore, Austin should pour 11.74 more grams of salt.
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the stopping distance s of a car varies directly as the square of its speed v. if a car traveling at 40 mph requires 80 ft to stop, find the stopping
If a car traveling at 40 mph requires 80 feet to stop, the stopping distance S of a car varies directly as the square of its speed v and is equal to 180 feet.
Given, the stopping distance S of a car varies directly as the square of its speed v. So the relation can be represented as,
S ∝ v2
Here, the constant of proportionality is k.
S = kv2 ——— (1)
Given, when the speed v = 40 mph, stopping distance s = 80 feet.
Therefore, from equation (1), we have
80 = k × 402
k = 80/1600
k = 0.05
Hence, the relation between the stopping distance S and the speed v of the car can be given as
S = 0.05v2
To find the stopping distance S of the car at speed v = 60 mph, substitute v = 60 in the above equation.
S = 0.05 × 602
S = 0.05 × 3600
S = 180 feet
Therefore, the stopping distance of a car traveling at 60 mph would be 180 feet.
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Casper has a balloon with a diameter of
6 inches that is seven times the volume of
his brother's balloon. What is the
volume of Casper brother's
approximate
balloon?
Answer:
The volume of a sphere is given by the formula:
V = (4/3)πr^3
where r is the radius of the sphere.
Since the diameter of Casper's balloon is 6 inches, the radius is 3 inches. Therefore, the volume of Casper's balloon is:
V1 = (4/3)π(3 inches)^3 = 113.1 cubic inches (approx.)
We know that Casper's balloon is seven times the volume of his brother's balloon. Let's call the volume of his brother's balloon V2. We can set up an equation:
V1 = 7V2
Substituting the value of V1, we get:
113.1 cubic inches = 7V2
Dividing both sides by 7, we get:
V2 = 16.2 cubic inches (approx.)
Therefore, the approximate volume of Casper's brother's balloon is 16.2 cubic inches.
A coin is tossed 300 times, and gets heads for 200 times, tails for 80 times.What is the probability of getting a tales
Answer:
Step-by-step explanation:
Head: 220 times, tail 80 times. Find the probability of occurrence of each of events. 2.
Spaceship Earth is a major tourist at Epcot. It is a sphere whose volume is
approximately 65, 417 m³. What is the approximate circumference of Spaceship
Earth? Use π = 3. 14. Round to the nearest whole number. Do not label.
The approximate circumference of Spaceship Earth is approximately 138.02 meters.
What is circumference of a circle?A circle's perimeter is known as its circumference. It is the circumference of the circle as a whole. A circle's circumference is calculated by multiplying its diameter by the constant. This measurement of a circle's diameter is necessary for someone crossing a circular park or for enclosing a circle. The units for the circumference, which is a linear variable, are the same as those for length.
The volume of the sphere is given as:
V = (4/3)πr³
Substituting the values:
[tex]r = (3(65,417)/4(3.14))^{(1/3)} = 21.96 meters[/tex]
The circumference of the circle is:
C = 2πr
Substituting the value of r:
C = 2(3.14)(21.96) = 138.02 meters
Hence, the approximate circumference of Spaceship Earth is approximately 138.02 meters.
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Two ships are near a buoy in the open ocean. One ship is 20 km due north of the buoy, and the other ship is 13.5 km due east of the buoy.
Enter a number in the box to correctly complete the statement. Round the answer to the nearest tenth.
In this instance, the buoy forms the right corner of a triangle made up of the two ships and the buoy. To the closest tenth, the distance between the two ships is roughly [tex]24.1[/tex] km.
What is the distance between two object?To find the distance between the two ships, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the legs
(the sides that form the right angle) is equal to the square of the length of the hypotenuse (the side opposite the right angle).
In this case, the two ships and the buoy form a right triangle, with the buoy at the right angle.
Let d be the distance between the two ships, x be the distance of the northern ship to the buoy and y be the distance of the eastern ship to the buoy. Then we have:
[tex]d^2 = x^2 + y^2[/tex]
Substituting the given values, we get:
[tex]d^2 = (20 km)^2 + (13.5 km)^2[/tex]
[tex]d^2 = 400 km^2 + 182.25 km^2[/tex]
[tex]d^2 = 582.25 km^2[/tex]
[tex]d ≈ 24.1 km[/tex]
Therefore, the distance between the two ships is approximately 24.1 km, rounded to the nearest tenth.
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Max set a goal to decrease his original 60-minute swim time by 30% during the triathlon.
the amount of change: 18 minutes <----- correct answer
Triathlon swim time: 42 minutes <--------- Correct Answer
Everything is correct here, Don't forget to correctly read the answers, otherwise, you'll accidentally get it wrong. Thank me later :)
Max's swim time during the triathlon would be 42 minutes.
What is percentage?Rather than being stated as a fraction, a percentage is a piece of a whole expressed as a number between 0 and 100. Nothing is zero percent; everything is 100 percent; half of something is 50 percent; and nothing is zero percent. You split the part of the whole by the whole and multiply the result by 100 to get the percentage.
According to question:To calculate this, we first need to find out how much Max's original swim time will decrease by 30%. We can do this by multiplying his original swim time by 0.3:
60 minutes x 0.3 = 18 minutes
This means that Max will decrease his original swim time by 18 minutes during the triathlon.
To find out Max's new swim time during the triathlon, we need to subtract the amount of time he will decrease from his original swim time:
60 minutes - 18 minutes = 42 minutes
Therefore, Max's swim time during the triathlon would be 42 minutes.
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an architect needs to make a scale drawing of a home. the width w of the home in the drawing, In inches, is given by the equation w/0.6=9.5. what is the width of the home in the scale drawing?
Answer: 5.7 inches
Step-by-step explanation:
To find the width of the home in the scale drawing, we can use algebra to solve for w.
First, we can simplify the equation w/0.6 = 9.5 by multiplying both sides by 0.6:
w/0.6 * 0.6 = 9.5 * 0.6
w = 5.7 inches
Therefore, the width of the home in the scale drawing is 5.7 inches.
which of the following is the most likely to call up mental images of specific sights, sounds, tastes, or smells?
This connection makes smells particularly powerful in triggering memories and emotions.
The sense of smell is the most likely to call up mental images of specific sights, sounds, tastes, or smells. This is because the olfactory system, which is responsible for the sense of smell, is closely linked to the brain's limbic system, which is involved in emotions and memory. This connection makes smells particularly powerful in triggering memories and emotions.
The olfactory system, which is responsible for the sense of smell, is unique in its connection to the brain's limbic system, which is involved in processing emotions and memory. When we smell something, the odor molecules enter our nose and are processed by specialized sensory neurons in the olfactory epithelium. These neurons then send signals to the olfactory bulb, which is located in the brain and is the first site of olfactory processing.
From there, the olfactory information is sent to several brain regions, including the amygdala and hippocampus, which are both part of the limbic system. The amygdala is involved in processing emotions and is responsible for generating feelings of pleasure, disgust, or fear in response to smells. The hippocampus, on the other hand, is involved in forming new memories and is responsible for encoding information about the context in which a smell is experienced.
The strong connection between the olfactory system and the limbic system makes smells particularly powerful in triggering memories and emotions. For example, the scent of freshly baked bread may evoke memories of childhood mornings spent in the kitchen with a loved one, while the smell of a certain perfume may remind you of someone special. Additionally, certain smells may elicit strong emotional responses, such as the smell of smoke triggering feelings of panic and fear in someone who has experienced a fire.
Overall, the sense of smell is closely linked to our emotional and memory centers, making it a powerful tool for triggering mental images of specific sights, sounds, tastes, or smells.
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of the last 16 people at a carnival booth, 6 won a prize. what is the experimental probability that the next person at the booth will win a prize?
Answer:
Step-by-step explanation:
big cheeze
Answer: 3/8
The given information is as follows: Out of the last 16 people, 6 people won a prize. We need to calculate the experimental probability of the next person winning the prize. To calculate experimental probability, we use the formula of experimental probability is given as: Experimental probability = Number of favorable outcomes / Total number of outcomes.
The given information tells us that out of the last 16 people, 6 people won a prize. It means that the number of favorable outcomes is 6. So, the experimental probability of winning a prize = Number of favorable outcomes / Total number of outcomes. Total number of outcomes is 16.
Therefore, Experimental probability = 6 / 16. Let's simplify this fraction. We can divide the numerator and denominator by 2.6/16 = 3/8Therefore, the experimental probability of the next person winning a prize is 3/8.
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The ratio of ounces to pounds is 16:1. A veterinarian is treating a dog that weighs 46 pounds. To calculate the correct amount of medicine, the vet must convert the dog's weight
ounces. Which ratio shows the conversion to ounces?
The correct option is c: 46lb x (16 oz / 1lb). Thus, amount of medicine given for the weight of dog in ounce is 736 ounce.
Explain about the unit conversion?The same attribute is expressed using a unit conversion, but in a different measurement unit. For example say, time can be mentioned in minutes rather than hours, and distance can be expressed in kilometres, feet, or any other measurement unit instead of miles.
Measurements are frequently offered in one set of measurements, like feet, but are required in another set, like chains. A conversion factor is a mathematical equation that facilitates an equal exchange of feet for chains.
Given data:
ratio of ounces to pounds = 16:1
16 ounce / 1 pound
Let the weight of dog in ounce be 'x'.
weight of dog in pounds = 46 pounds.
ratio : x ounce / 46 pounds
Equating both ratios:
16 ounce / 1 pound = x ounce / 46 pounds
Cross multiplying:
x = 16*46 ounce
x = 736 ounce
The correct option is c: 46lb x (16 oz / 1lb)
Thus, amount of medicine given for the weight of dog in ounce is 736 ounce.
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Complete question is-
The ratio of ounces to pounds is 16:1. A veterinarian is treating a dog that weighs 46 pounds. To calculate the correct amount of medicine, the vet must convert the dog's weight
ounces. Which ratio shows the conversion to ounces?
The full question is attached.
Jared's class took a survey to see how many students owned a trampoline. Of the 23 students in the class, 21 students said they owned a trampoline. If you chose a student at random from Jared's class, what is the probability that the student does not own a trampoline?
Answer:
There are different ways to approach this problem, but one possible method is:
Define the event A as "the student owns a trampoline".
Find the probability of A: P(A) = 21/23, because 21 out of 23 students said they owned a trampoline.
Find the probability of the complement of A, which is "the student does not own a trampoline". We can denote this event as A', and it is equivalent to "the student is one of the 2 students who did not say they owned a trampoline". Therefore, P(A') = 2/23.
Check that P(A) + P(A') = 1, because the student either owns a trampoline or does not.
Answer the question: the probability that the student does not own a trampoline is P(A') = 2/23, or approximately 0.087 or 8.7% (rounded to one decimal place).
Therefore, the answer is: the probability that the student does not own a trampoline is 2/23, or approximately 0.087 or 8.7%.
number 5 goes through the device and the result is 25 . what would a possible rule for machine B be ?
Answer: multiplied by 5 or squared
Step-by-step explanation:
If the number 5 goes in and 25 is the result, the rule could be multiplying by 5 or squaring the number that goes in (input).
5 x 5 = 25
5^2 = 25.
Enlarge shape A by scale factor 3.5 with centre of enlargement (8, -7).
What are the coordinates of the vertices of the image?
Thus, the vertices of the larger square have the following coordinates: (-6, 7), (1, 7),(1, 0), and (-6 ,0).
Explain about the scale factor?The ratio of the scale of an original thing to a new object that is a representation of it but of a variable size is known as a scale factor (bigger or smaller).
The procedures below can be used to increase form A by a scale factor of 3.5 with the centre of enlargement at (8,-7).
Transform the square so that its origin is where the centre of enlargement is (0,0).
To do this, we deduct each vertex's coordinates from the centre of enlargement (8,-7):
A = (4 - 8, -3+ 7) = (-4, 4)
B = (6 -8, -3 + 7) = (-2, 4)
C = (6 - 8, -5 + 7) = (-2, 2)
D = (4 - 8, -5 + 7) = (-4, 2)
Multiply the coordinates of the each vertex by the scaling factor (3.5) to enlarge the translated square:
A = (-14, 14)
B = (-7, 14)
C = (-7, 7)
D = (-14, 7)
By adding those coordinates of the centre of the enlargement (8,-7) to each vertex, move the square from its larger state back to its original one:
A = (-14 + 8, 14-7) = (-6, 7)
B = (-7 + 8, 14-7) = (1, 7)
C = (-7 + 8, 7-7) = (1, 0)
D = (-14 + 8, 7-7) = (-6 ,0)
As a result, the vertices of the larger square have the following coordinates: (-6, 7), (1, 7),(1, 0), and (-6 ,0).
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I need to figure out the height of the house using these measurements.
She's standing 11 feet from the house, her eyes are 5 feet from the ground, and the angle of elevation for the house is 125 degrees. Please help quickly. I also need to show my work for this problem.
The height of the house with an angel of elevation 25° from the line of sight of the observer is equal to 10 ft to the nearest foot.
What is an angle of elevationThe angle of elevation is the angle between the horizontal line and the line of sight which is above the horizontal line.
The height of the house is the sum of length from her eyes to the ground and the perpendicular length from her eyes to the top of the house.
we shall represent the perpendicular length from her eyes to the top of the house with x so that;
tan 25° = x/11 {opposite/adjacent}
x = 11 × tan 25°
x = 5.1294
height of the house = 5 ft + 5.1294 ft
height of the house = 10.1294 ft
Therefore, the height of the house with an angel of elevation 25° from the line of sight of the observer is equal to 10 ft to the nearest foot.
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Possible question:
Figure out the height of the house using these measurements. She's standing 11 feet from the house, her eyes are 5 feet from the ground, and the angle of elevation to the top of house is 25 degrees.
4. Mrs. Green made lunch for her
family. She made turkey sandwiches
and cheese sandwiches. She also
made coconut cookies and oatmeal
cookies. Which list shows all the
possible combinations if a person
picked one sandwich at random and
one cookie at random?
All of these are the combinations that might be made if a person chose a sandwich and a biscuit at random.
What do you mean by probability?The possibilities of the result of any random event is known as probability. This phrase refers to determining the likelihood that any given occurrence will occur.
Turkey & cheese sandwiches and two varieties of cookies are available (coconut and oatmeal). As a result, there seem to be 2 x 2 = 4 different sandwich and biscuit combinations from which to pick.
The following four pairings are possible:
sandwich with turkey and a coconut biscuit
Oatmeal cookies and a turkey sandwich
Coconut cookies and a cheese sandwich
Oatmeal cookies with a cheese sandwich
So all of these are the combinations that might be made if a person chose a sandwich and a biscuit at random.
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assume that 90 million households in the u.s. turn on their televisions at 8:00 p.m. on a sunday night, and the total number of u.s. tb households is 119.9 million. calculate the households using television (hut) figure.
The households using television (HUT) figure is 75.06%.
The households using television (HUT) figure is a measure of the percentage of households that have turned on their televisions at a particular time. It is calculated by dividing the number of households watching TV by the total number of households and multiplying by 100%.
In this case, we are given that 90 million households in the US turned on their televisions at 8:00 p.m. on a Sunday night. The total number of US households is 119.9 million. Using this information, we can calculate the HUT figure as follows
Households using television (HUT) = (Number of households watching TV / Total number of households) x 100%
HUT = (90 million / 119.9 million) x 100%
HUT = 75.06%
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The following equation represents the volume of a rectangular prism with a width of w inches:
V=2w³-7w²+3w
a. What is the volume if the width is 5 inches?
b. Factor this polynomial completely and describe what each factor means in terms of the dimensions of the rectangular prism.
c. If the width is 5 inches, what are the other dimensions? How does this relate to your answer to part a?
d. Graph the polynomial on a graphing calculator or an online graphing application. What are the x-intercepts? What do these mean in terms of the situation?
e. What are the domain and range in terms of the situation? Justify your answers.
Answer:
a. To find the volume when the width is 5 inches, we plug in w=5 into the equation:
V = 2w³ - 7w² + 3w
V = 2(5)³ - 7(5)² + 3(5)
V = 250 - 175 + 15
V = 90
Therefore, the volume is 90 cubic inches.
b. To factor the polynomial, we can first factor out a w:
V = w(2w² - 7w + 3)
Then we can factor the quadratic expression in parentheses:
V = w(2w - 1)(w - 3)
Each factor represents a dimension of the rectangular prism:
w is the width
2w - 1 is the length
w - 3 is the height
c. If the width is 5 inches, we can use the factorization from part b to find the other dimensions:
length = 2w - 1 = 2(5) - 1 = 9 inches
height = w - 3 = 5 - 3 = 2 inches
This means that the rectangular prism has dimensions 5 inches by 9 inches by 2 inches. We can also use the dimensions to calculate the volume:
V = 5 × 9 × 2 = 90 cubic inches
This is the same as the answer from part a.
d. The graph of the polynomial is:
Graph of the polynomial
The x-intercepts are approximately 0.5 and 3. These correspond to the widths at which the volume is 0, which means the rectangular prism has zero volume. In other words, the x-intercepts represent the points where the rectangular prism collapses into a flat shape.
e. The domain of the function is all real numbers, since we can plug in any width w and get a corresponding volume. The range of the function is also all real numbers, since the volume can be any positive or negative value depending on the width. Specifically, the range is (-∞, ∞).
Need the answer to this ASAP!!
The distance between points F and G is 12.806 units. The coordinates of F are (6,6) and the coordinates of G are (16,14).
What is distance?Distance in a graph is a measure of the difference between two points. It is calculated as the shortest path between two points in a graph, usually measured in terms of the number of edges that must be traversed to get from one point to the other. Distance can also be measured in terms of the number of vertices that must be crossed to get from one point to the other.
The distance between two points F and G in the graph can be calculated using the distance formula.
The distance formula states that the distance between two points (x1, y1) and (x2, y2) =√ (x2-x1)² + (y2-y1)²
Therefore, to calculate the distance between points F and G, we will use the distance formula.
The coordinates of F are (6,6) and the coordinates of G are (16,14).
Substituting these values into the distance formula, we get the following:
Distance = √(16 - 6)² + (14 - 6)²
Distance = √100 + 64
Distance = √164
Distance = 12.806
The distance between points F and G is 12.806 units.
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Questions 3-6
The answer of the given question are, (3) the speed of the plane in still air is 135 km/h and the speed of the wind is 23 km/h. (4) the price of a senior citizen ticket is $8 and the price of a child ticket is $14. (5) the number is 43. (6) the speed of the boat in still water is 12 mph and the speed of the current is 9 mph.
What is Variable?In mathematics, variable is symbol or letter that represents value that can change or vary in given context or problem. Variables are often used in mathematical equations and formulas to express relationships between different quantities or to describe patterns and trends.
3). assume the speed of plane in still air "p" and speed of the wind "w". We can set up two equations based on the given information:
p + w = 158 (since the plane is flying with the wind)
p - w = 112 (since the plane is flying against the wind)
Adding the two equations together eliminates the w variable:
2p = 270
So p = 135 km/h. To find w, we can substitute this value into one of the original equations:
135 + w = 158
w = 23 km/h
Therefore, speed of plane in still air is 135 km/h and speed of the wind is 23 km/h.
4). Let's call the price of a senior citizen ticket "s" and the price of a child ticket "c". We can set up two equations based on the given information:
3s + 1c = 38
3s + 2c = 52
Subtracting first equation from the second eliminates the s variable:
c = 14
Substituting the value into first equation gives:
3s + 1(14) = 38
So 3s = 24 and s = 8
Therefore, the price of a senior citizen ticket is $8 and the price of a child ticket is $14.
5). Let's call the tens digit of the number "t" and the ones digit "u". We know that:
t + u = 7 (since the sum of the digits is 7)
10u + t - (10t + u) = 9 (since reversing the digits increases the number by 9)
Simplifying the second equation gives:
9u - 9t = 9
Dividing by 9 gives:
u - t = 1
Now we can solve for t in terms of u:
t = u - 1
Substituting the into first equation we get:
u - 1 + u = 7
So 2u = 8 and u = 4
Therefore, the number is 43.
6). Let's call the speed of the boat in still water "b" and the speed of the current "c". We know that:
b + c = 210/10 = 21 (since distance = rate × time)
b - c = 210/70 = 3 (since distance = rate × time)
Adding the two equations eliminates the c variable:
2b = 24
So b = 12 mph. Substituting the value into one of original equations gives:
12 + c = 21
So c = 9 mph.
Therefore, the speed of the boat in still water is 12 mph and the speed of the current is 9 mph.
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The triangle shown is rotated about line m.
A triangle with side lengths of 6 centimeters, 8 centimeters, and 10 centimeters is shown. The triangle is rotated about line m at the side with length 8 centimeters.
What is the approximate base area of the resulting three-dimensional figure?
Area of a circle: A = πr2
38 sq. cm
113 sq. cm
201 sq. cm
314 sq. cm
The resulting three-dimensional figure has a base area of 50.27 square centimetres. Option (D) 314 sq. cm is the correct answer (rounded to the nearest whole number).
When a triangle is rotated 360 degrees around one of its sides, it forms a cone with a base equal to the rotated side's length and a height equal to the perpendicular distance from the cone's apex to the rotated side.
In this case, the rotated side is 8 cm long. The Pythagorean theorem can be used to calculate the perpendicular distance from the apex of the cone to the rotated side. Heron's formula can be used to calculate the triangle's height:
s =(6+8+10)/2 = 12
(s(s-6)(s-8)(s-10)) = (12(6)(4)(2)) = 243
The triangle's height is:
h = 2 * Area / 8 = 3√3
The radius of the cone's base is 8/2 = 4 cm. As a result, the volume of the cone is as follows:
V = (1/3) * π * r^2 * h = (1/3) * π * 4^2 * 3√3 ≈ 50.27 cm^3
The resulting three-dimensional figure has the same base area as a circle with a radius of 4 cm, which is:
A = π * r^2 = π * 4^2 ≈ 50.27 cm^2
As a result, the resulting three-dimensional figure has an approximate base area of 50.27 square centimetres. Option (D) 314 sq. cm is the correct answer (rounded to the nearest whole number).
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Answer: answer is d) 314 sq. cm
Step-by-step explanation: hope this helps!