A. For any number of monthly calls "x" greater than 200, Plan 1 is more economical than Plan 2.
Meaning of the answer to part A:The answer to part a means that if a customer expects to make more than 200 local calls per month, it is more economical for them to choose Plan 1 over Plan 2. For example, if a customer makes 250 local calls per month, Plan 1 would cost $28 while Plan 2 would cost $20 ($12 + $0.08 x 250), so Plan 1 would be the better choice for them. However, if a customer expects to make fewer than 200 local calls per month, then Plan 2 would be more economical for them, as they would pay less than $28 per month.
What is the break-even point for the two billing plans offered by the telephone company?The break-even point is the number of monthly calls for which the total cost of Plan 1 is equal to the total cost of Plan 2.
This occurs when the inequality $16 < $0.08x is satisfied, which simplifies to 200 < x.
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If something is $125 with a sale for $87.50, what percent off was the sale?
well, the amount off from the original 125 is just 125 - 87.50 = 37.50.
now, if we take 125(origin amount) as the 100%, what's 37.50 off of it as a percentage?
[tex]\begin{array}{ccll} Amount&\%\\ \cline{1-2} 125 & 100\\ 37.50& x \end{array} \implies \cfrac{125}{37.50}~~=~~\cfrac{100}{x} \\\\\\ 125x=3750\implies x=\cfrac{3750}{125}\implies x=30[/tex]
To determine what percent off the sale for something was, we need to use the formula for percent off calculation.
What is percent off? The percent off is used to refer to the reduction in price or value of something. The percent off calculation is used to determine the amount of discount in percentage of the original price or value.
What is the formula for percent off calculation? The formula for percent off calculation is as follows:
percent off = (discount / original price) x 100, where,discount = original price - sale price
original price = $125 sale price = $87.50
Substitute the given values into the formula and simplify.
percent off = (discount / original price) x 100percent off =
(($125 - $87.50) / $125) x 100percent off
(37.50 / 125) x 100percent off
⇒ 0.3 x 100percent off = 30%
Therefore, the percent off the sale was 30%.
Which of the following expressions is equal to 9? 4 x (one-half x 6) ÷ 3 6 ÷ (one-fourth x 3 x one and one-fourth) 8 + (one-third x 6) ÷ 5 10 − (one-fifth x 10) + 1
The expression that is equal to 9 is 10 − (one-fifth x 10) + 1.
What are arithmetic operators?Basic mathematical procedures known as arithmetic are used to calculate using numbers. Addition, subtraction, multiplication, and division are the four fundamental arithmetic operations. Finding the sum of two or more numbers is done using addition, finding the difference between two numbers is done using subtraction, finding the product of two or more numbers is done using multiplication, and finding the quotient of two numbers is done using division. There are more operations outside these four, such as square root and exponentiation (increasing a number to a power) (finding the root of a number).
For the given expressions we have:
4 x (one-half x 6) ÷ 3 = 4 x 3 ÷ 3 = 4 --> not equal to 9
6 ÷ (one-fourth x 3 x one and one-fourth) = 6 ÷ (3/4 x 5/4) = 6 ÷ (15/16) = 96/15 --> not equal to 9
8 + (one-third x 6) ÷ 5 = 8 + 2 ÷ 5 = 8.4 --> not equal to 9
10 − (one-fifth x 10) + 1 = 10 - 2 + 1 = 9 --> equal to 9
Hence, the expression that is equal to 9 is 10 − (one-fifth x 10) + 1.
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Can someone help me ASAP it’s due tomorrow. I will give brainliest if it’s all done correctly. Show work.
The probability of the spinner landing on blue and rolling an even number on a six-side die is 1/6.
What is probability?
The probability of the spinner landing on blue is 2/6, which simplifies to 1/3.
The probability of rolling an even number on a six-sided die is 3/6, which simplifies to 1/2.
To find the probability of both events occurring together, we multiply the probabilities:
P(blue and even number) = P(blue) x P(even number)
P(blue and even number) = (1/3) x (1/2)
P(blue and even number) = 1/6
Therefore, the probability of the spinner landing on blue and rolling an even number on a six-side die is 1/6.
What is spinner?
A spinner is a device or a toy used to randomly select or generate a value or outcome. It consists of a circular board or disc, often divided into sections of different colors or with different values or symbols, and a pointer or arrow that is spun around the disc to land on a particular section. Spinners are commonly used in games, educational activities, and statistical experiments to create random outcomes or to simulate probability distributions.
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Complete question is: The probability of the spinner landing on blue and rolling an even number on a six-side die is 1/6.
Answer:
Step-by-step explanation:
The probability of the spinner landing on blue is 2/6, which simplifies to 1/3.
The probability of rolling an even number on a six-sided die is 3/6, which simplifies to 1/2.
To find the probability of both events occurring together, we multiply the probabilities:
P(blue and even number) = P(blue) x P(even number).
P(blue and even number) = (1/3) x (1/2).
P(blue and even number) = 1/6.
Therefore, the probability of the spinner landing on blue and rolling an even number on a six-side die is 1/6.
explain clearly why we cannot have the combination of a yes to practical significance, and a no to statistical significance.
It is not possible for a study to have practical significance without statistical significance because statistical significance provides evidence that the observed effect is unlikely to have occurred by chance.
The Practical significance and statistical significance are two different concepts that are often used in hypothesis testing.
The Statistical significance refers to the probability that the observed results of a study occurred by chance, given a particular level of significance or alpha.
The Practical significance refers to whether the observed effect size is large enough to be meaningful in a real-world context.
It is possible for a study to have statistical significance without practical significance. For example, a study may find a statistically significant difference between two groups, but the difference may be so small that it is not meaningful in practice.
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A field is shaped like a trapezoid with the dimensions shown in the image.
7.2 meters
13.4 meters
There are 320 laying hens living in this field. What is the bird population density?
A Approximately 4 hens per square meter
More than 5 hens per square meter
c. Approximately Sens per square meter
Less than 2 hens per square meter
B
D
10.6 meters
Answer:
C. Approximately 3 hens per square meter
When the pressure is 2.6 g/m² then the depth is 3.9 m.
What is proportionality?The term proportionality describes any relationship that is always in the same ratio. The number of apples in a crop, for example, is proportional to the number of trees in the orchard, the ratio of proportionality being the average number of apples per tree.
Given that
the pressure varies directly with the depth. When the pressure is 320 g/m² the depth is 480 m.
We need to find the depth if the pressure is 2.6 g/m².
So, here we will use the concept of proportionality,
Let the unknown depth be x,
So,
320 / 480 = 2.6 / x
2 / 3 = 2.6 / x
2x = 7.8
x = 3.9
Hence when the pressure is 2.6 g/m² then the depth is 3.9 m.
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complete question:
Pressure varies directly with the depth. When the pressure is 320 grams per square meter the
depth is 480 meters. What is the depth, in meters, when the pressure is 2.6 grams per square
meter? (Round to the nearest tenth)
A 1.7 grams
B 1.9 grams
C 3.7 grams
D 3.9 grams
By the definition of a parallelogram, ab∥dc. ad is a transversal between these sides, so ∠a and ∠d are angles. because ab and dc are , the same-side interior angles must be by the same-side interior angles theorem. therefore, ∠a and ∠d are supplementary.
In a parallelogram, The statement "angle A and angle D are supplementary" is not correct.
The same-side interior angles theorem states that if a transversal intersects two parallel lines, then the same-side interior angles are supplementary. However, in this case, we are dealing with a parallelogram, which has two pairs of parallel sides.
When we say that "ab||dc", we are stating that side AB is parallel to side DC. We cannot assume that side AD is a transversal between these two sides, as it could intersect the sides at some other angle. Therefore, we cannot conclude that angle A and angle D are angles.
However, we do know that opposite angles in a parallelogram are congruent. Therefore, we can conclude that angle A is congruent to angle C, and angle B is congruent to angle D.
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PLEASE HELP ILL GIVE BRAINLIEST
The angles that form a linear pair is 6 and 8.
option C.
What are linear pair angles?
Linear pair angles are two adjacent angles formed by two intersecting lines. These two angles are always supplementary, which means that their sum is equal to 180 degrees. In other words, if we add the measure of one angle to the measure of the other angle, we will get a total of 180 degrees.
A linear pair of angles can be easily identified by observing the angles formed when two straight lines intersect each other. For example, if line AB intersects line CD at point E, then the two pairs of adjacent angles formed are:
∠AED and ∠DEB∠CEB and ∠BEDEach pair of adjacent angles in a linear pair is supplementary, which means that ∠AED + ∠DEB = 180 degrees and ∠CEB + ∠BED = 180 degrees.
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Given rectangle JKLM below, JN = 44.
If MN = -2x + 2, solve for x.
The solution for x is -21 when rectangle JKLM below, JN = 44.
If MN = -2x + 2,
What is the rectangle?
A rectangle is a geometric shape with four sides and four right angles. It is a quadrilateral in which opposite sides are equal in length and parallel to each other, and adjacent sides are perpendicular to each other.
To solve for x, we can use the given information that JN = 44 and MN = -2x + 2 in the rectangle JKLM.
Since JN is a side of the rectangle and is equal to 44, and MN is also a side of the rectangle and is equal to -2x + 2, we can set up the equation:
JN = MN
44 = -2x + 2
Now we can solve for x:
Add 2x to both sides:
44 + 2x = 2
Subtract 2 from both sides:
44 + 2x - 2 = 0
42 + 2x = 0
Subtract 42 from both sides:
42 + 2x - 42 = 0 - 42
2x = -42
Finally, divide both sides by 2 to isolate x:
2x / 2 = -42 / 2
x = -21
Hence, the solution for x is -21.
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of the 13,500 savings accounts in a bank, 4,675 belong to people younger than 40 years old. the bank president would like to increase her institution's marketing strategy to younger customers, so she is examining the population proportions in order to create a statistical study. find the population proportion, as well as the mean and standard deviation of the sampling distribution for samples of size n
Population proportion: The proportion of people aged under 40 who have savings accounts is the population proportion. This can be calculated as follows:Population proportion = (number of savings accounts belonging to people under 40) / (total number of savings accounts).
Population proportion = 4675/13500Population proportion = 0.3463 (rounded to four decimal places)Mean and standard deviation of the sampling distributionFor a given sample size, the mean and standard deviation of the sampling distribution can be calculated as follows:
Mean of sampling distribution = population proportionStandard deviation of sampling distribution = sqrt[(population proportion * (1 - population proportion)) / n]where n is the sample size.For this question, the sample size is not given, so we cannot calculate the mean and standard deviation of the sampling distribution.
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PLEASE HELP!
The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in seconds:
Part A: During what interval(s) of the domain is the water balloon's height increasing?
Part B: During what interval(s) of the domain is the water balloon's height staying the same?
Part C: During what interval(s) of the domain is the water balloon's height decreasing the fastest? Use complete sentences to support your answer.
Part D: Use the constraints of the real-world situation to predict the height of the water balloon at 16 seconds. Use complete sentences to support your answer.
step-by-step explanation:
Part A. We can see that within only for a 0-2 second interval, the height of the water balloon increases from 60ft to approximately 80ft.
Part B. In two intervals, 2-4 seconds to approximately 80 ft and 10-14 seconds to 0 ft.
Part C. Between 4 and 6 seconds, the water balloon height changes from approximately 80ft to 40ft, whereas between 6-8 seconds and 8-10 seconds, the height only changes by 20ft.
Part D. According to the graph, we can suppose that the water balloon was thrown up, and after beginning to fall, at 10 seconds touched the floor, so in 16 seconds kept staying on the floor, at 0ft.
Hope it helps.
[tex]\text{-B$\mathfrak{randon}$VN}[/tex]
DUE TODAY PLEASE HELP WELL WRITTEN ANSWERS ONLY!!!!
Here is a wheel with radius 1 foot. List three different counterclockwise angles the wheel can rotate so that point P ends up at position Q.
Below are the three angles listed out in both radians and degrees:
pi/2 radians (or 90 degrees)5π /2 radians (or 450 degrees)9π /2 radians (or 810 degrees)What is the rotation?Let us assume that point P is initially at the topmost point of the wheel, and Q is directly to the right of P.
When the wheel rotates counterclockwise, point P moves along a circle with radius 1 foot, centered at the center of the wheel. To end up at position Q, point P needs to move a quarter of the way around the circle, or pi/2 radians. Therefore, one angle that the wheel can rotate is pi/2 radians (or 90 degrees).
Another angle that the wheel can rotate is 5*pi/2 radians (or 450 degrees), which corresponds to rotating the wheel counterclockwise almost all the way around the circle, but stopping just short of completing a full rotation.
A third angle that the wheel can rotate is 9*pi/2 radians (or 810 degrees), which corresponds to rotating the wheel counterclockwise almost twice around the circle, but stopping just short of completing two full rotations.
Therefore, Note that there are a lot of many other angles that the wheel can rotate to end up at position Q, but these three examples give an idea of the possibilities.
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The graph of quadratic function g is shown on the grid.
Which statements are best supported by the graph of g?
Select THREE correct answers.
The correct option for the quadratic function g are-
The x-intercept are- (-4,0) and (2,0)The coordinates of y-intercept are (0, -8)The coordinates of the vertex are (-1, -9).Explain about the quadratic function?Mathematical expressions with a two as the highest power are called quadratic functions. A function or numerical statement of degree two is a quadratic function. This indicates that two is the function's highest power.
The examples are all of degree 2. Hence, two is their highest power. A quadratic function must have a highest power of two.The correct option for the given quadratic function g from the graph are-
The x-intercept are- (-4,0) and (2,0)The coordinates of y-intercept are (0, -8)The coordinates of the vertex are (-1, -9).Correction for the incorrect statements:
The axis of symmetry is (x = -1)The function has the minimum value of -9.Know more about the quadratic function
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Allison gas a poster that is 15 in by 18 in. what will the dimension of the Poster be if she scales it down by a factor pf 1/3
The new dimensions of the poster will be 5 in by 6 in.
What is scaling?In mathematics, scaling is the process of adjusting a geometric form or figure's size by a predetermined factor or ratio. With scaling, a shape's dimensions are all multiplied by the same quantity. Depending on whether the scaling factor is more than 1 or less than 1, respectively, scaling can either make the form larger or smaller. In addition to science, engineering, and computer graphics, scaling is frequently utilised in trigonometry, geometry, and other areas of mathematics.
Given that the scale factor = 1/3.
Thus, the new dimensions are:
New length = 15 in x (1/3) = 5 in
New width = 18 in x (1/3) = 6 in
Hence, the new dimensions of the poster will be 5 in by 6 in.
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An Electronic store donated a percentage of every sale to charity. The total sales were seven dollars, 150, of which the store donated $429 What percentage of seven dollars, 150 was donated to charity?
Answer:
6.00 %
Step-by-step explanation:
Percent = amount donated/total sales × 100 %
= 429/7150 × 100 %
= 6.00 %
The store donated 6.00 % of its sales to charity.
Point B has coordinates (5,1). The x-coordinate of point A is 2. The distance between point A and point B is 5 units. What are the possible coordinates of point A?
According to the solution we have come to find that, The possible coordinates of point A are (2,-2) and (2,4).
what is geometry?Geometry is a branch of mathematics that deals with the study of spatial relationships and properties of objects. It is concerned with the study of shape, size, position, and relative orientation of objects, as well as their properties such as angles, lines, curves, surfaces, and solids. Geometry is used extensively in various fields, including architecture, engineering, physics, astronomy, and computer graphics. The study of geometry involves using logic and reasoning to analyze and solve problems related to shapes and spatial relationships. It is an important subject that has practical applications in many areas of everyday life.
To find the possible coordinates of point A, we need to use the distance formula and the fact that the x-coordinate of point A is 2.
The distance formula is:
d = √((x2 - x1)² + (y2 - y1)²)
where (x1, y1) are the coordinates of point A, (x2, y2) are the coordinates of point B, and d is the distance between the two points.
We know that the distance between point A and point B is 5 units:
5 = √((5 - 2)² + (1 - y1)²)
Squaring both sides:
25 = (5 - 2)²+ (1 - y1)²
Simplifying:
9 = (1 - y1)²
Taking the square root of both sides:
3 = 1 - y1 or 3 = y1 - 1
Solving for y1 in each case:
y1 = -2 or y1 = 4
Therefore, the possible coordinates of point A are (2,-2) and (2,4).
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I NEED HELP ON THIS ASAP! IT'S DUE TODAY!!!
Answer:
b = 8.485
c = 23.995 ≈ 24
Step-by-step explanation:
Part b:
[tex]\sqrt{(10-4)^2+(9-3)^2}[/tex]
√(36 + 36)
= 8.485
Part c:
Base = [tex]\sqrt{(6-2)^2+(1-5)^2}[/tex]
Base = 5.656
Area = Base x Height x 0.5
Area = 5.656 x 8.485 x 0.5
Area = 23.995 ≈ 24
$1000 is deposited in an account with a 8.5% interest rate, compounded continuously. what is the balance after 5 years?
Answer:
$1529
Step-by-step explanation:
The formula for continuous compounding is:
A = Pe^(rt)
Where:
A = the final amount (balance) in the account
P = the initial principal (deposit)
e = Euler's number (approximately 2.71828)
r = the annual interest rate (as a decimal)
t = the time period (in years)
Plugging in the given values, we get:
A = 1000e^(0.0855)
A = 1000*e^0.425
A = 1000*1.529
A = 1529
Therefore, the balance after 5 years with continuous compounding at 8.5% interest rate is $1529.
Make p the subject of m=3n+2p
Answer:
[tex]n = \frac{m - 2p}{3} \\ \\ p = \frac{m - 3n}{2} [/tex]
Step-by-step explanation:
[tex]1. \: m - 2p = 3n \\ 2. \: \frac{m - 2p}{3} \\ 3. \: n = m - 2p \\ \\ 1. \: m - 3n = 2p \\ 2. \: \frac{m - 3n}{2} = p \\ 3. \: p = \frac{m - 3n}{2} [/tex]
Help me solve this please.
Write the equation of the line of reflection between the points (-9, 12) and (17, -78) in point-slope form
The equation of the line of reflection is y = (−13 / 45)x − (1376 / 45) in point-slope form.
EquationsTo find the equation of the line of reflection between the points (-9, 12) and (17, -78), we first need to find the midpoint of the line segment joining these two points, which will lie on the line of reflection. The midpoint formula is:
[(x₁ + x₂) / 2, (y₁ + y₂) / 2]
Using the coordinates of the two given points, we get:
[(−9 + 17) / 2, (12 − 78) / 2] = [4, −33]
So, the midpoint is (4, −33).
Next, we need to find the slope of the line of reflection. This is equal to the negative reciprocal of the slope of the line passing through the two given points, since the line of reflection is perpendicular to this line. The slope of the line passing through the two given points is
m = (y₂ − y₁) / (x₂ − x₁) = (−78 − 12) / (17 − (−9)) = −90 / 26 = −45 / 13
So, the slope of the line of reflection is:
m' = −1 / m = −13 / 45
Finally, we can use the point-slope form of the equation of a line, with the midpoint we found as the point and the slope we calculated as the slope which is
y − (−33) = (−13 / 45)(x − 4)
y + 33 = (−13 / 45)x + (52 / 45)
or
y = (−13 / 45)x − (1376 / 45)
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Question 5(Multiple Choice Worth 2 points)
(Factoring Algebraic Expressions MC)
Rewrite x^² - 2x³y³ using a common factor.
Ox²y(xy-2xy²)
Ox²²(x²-2xy)
O 2xy²(x²-x²y)
O 2xy(x³y-x²y)
[tex]x^4y^2-2x^3y^3\\\\x^2y^2(x^2-2xy)[/tex]
Answer is the second one.
Sandra is selling root beer in 300 mL bottles. She makes 2 batches of root beer. Each batch makes 3.2 L of root beer. How much root beer will she have left over, after filling her bottles?
Step-by-step explanation:
3.2 liters divided by 300 ml / bottle is
3200 ml / 300 ml/bottle = 10 2/3 bottles
10 full bottles plus 2/3 of a bottle left over
2/3 bottle * 300 ml/bottle = 200 ml left over
a continuous random variable x has the following sample frequency distribution: value frequency 0 73 between 0 and 70 37 between 70 and 200 182 between 200 and 500 232 what is the mean from this sample?
As per the mentioned informations and values provided, the mean from this sample frequency distribution is calculated to be approximately 160.50.
To find the mean from the given sample frequency distribution, we need to first calculate the midpoint for each class interval, then multiply it by the corresponding frequency, sum all of these products, and finally divide by the total frequency.
Using the formula: mean = (sum of midpoint x frequency) / (sum of frequency)
Midpoint for the first interval = (0 + 70) / 2 = 35
Midpoint for the second interval = (70 + 200) / 2 = 135
Midpoint for the third interval = (200 + 500) / 2 = 350
Now we can calculate the sum of midpoint x frequency:
35 x 73 + 135 x 37 + 350 x 182 + 232 x 500 = 84,166
The total frequency is the sum of all frequencies: 73 + 37 + 182 + 232 = 524
Finally, we can calculate the mean:
mean = (sum of midpoint x frequency) / (sum of frequency) = 84,166 / 524 ≈ 160.50
Therefore, the mean from this sample frequency distribution is approximately 160.50.
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Here is a point at the tip of a windmill blade. The center of teh windmill is 6 feet off the ground and the blades are 1.5 feet long. Write an equation giving the height h of the point P after the windmill blade rotates by an angle of a. Point P is currently rotated π/4 radians from the point directly to the right of the center of the windmill.
the height of point P after the windmill blade rotates by an angle of a is approximately 1.1908 feet.
What is Trigonometric Functions?
Trigonometry uses six fundamental trigonometric operations. Trigonometric ratios describe these operations. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions. The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities. Using trigonometric formulas, the sine, cosine, tangent, secant, and cotangent values are calculated for the perpendicular side, hypotenuse, and base of a right triangle.
To find the height h of point P, we can use the sine function, which relates the opposite side of a right triangle (in this case, the height h) to the hypotenuse (in this case, the length of the windmill blade, which is 1.5 feet). The angle between the opposite side and the hypotenuse is the complement of the angle of rotation a, which is π/4 radians minus the angle between the ground and the windmill blade, which is arctan(6/1.5) or approximately 1.3258 radians.
So, the equation for the height h of point P after the windmill blade rotates by an angle of a is: h = 1.5 sin(π/4 - arctan(6/1.5))
Therefore, the height of point P after the windmill blade rotates by an angle of a is approximately 1.1908 feet.
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Bridget is creating a new board game called Tri-Tri-Again to enter a contest at the local game shop. She is making the game board in the shape of a triangle. The base of the triangle is 1
1
4
feet long, and its height is 2
1
2
feet.
What is the area of the game board?
Write your answer as a whole number, proper fraction, or mixed number.
The area of the Tri-Tri-Again board game is 3 1/8 square feet.
To calculate the area of a triangle, we need to know the length of its base and its height. In this case, Bridget's Tri-Tri-Again board game is in the shape of a triangle with a base of 1 1/4 feet and a height of 2 1/2 feet. To find the area of the triangle, we can use the formula for the area of a triangle, which is 1/2 x base x height.
We first convert the mixed numbers to improper fractions. The base is 5/4 feet and the height is 5/2 feet. We can then substitute these values into the formula to get:
Area of triangle = 1/2 x 5/4 feet x 5/2 feet
Area of triangle = 25/8 square feet
We can simplify the answer by dividing the numerator and denominator by the greatest common factor of 25 and 8, which is 1. This gives us:
Area of triangle = 25/8 square feet
Area of triangle = 3 1/8 square feet
Therefore, the area of the Tri-Tri-Again board game is 3 1/8 square feet.
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(2x+3)(3x+6) as a trinomiol
Answer: [tex]6x^{2}[/tex] + 24x + 18
Step-by-step explanation: To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.
A brother and a sister are in the same math class. There are 9 boys and 8 girls in the class. One boy and one girl are randomly chosen. What is the probability that the brother and sister are chosen? Write your answer as a fraction in simplest form.
The probability is ?
Answer:
1/72
Step-by-step explanation:
There are a total of 17 students in the class, and we want to choose one boy from 9 and one girl from 8 without replacement. The total number of ways to choose two students from the class is:
17C2 = (17!)/(2!15!) = (1716)/(21) = 136
To choose a boy and a girl, we can choose the boy in 9 ways and the girl in 8 ways, for a total of 9*8 = 72 ways.
Now, since the brother and sister are both in the class, there is only one way to choose them together. Therefore, the probability of choosing the brother and sister is:
1/72
So the probability is 1/72, written as a fraction in simplest form.
The length of a rectangle is equal to
three times its width. If the perimeter of
the shape is equal to 56 feet, what is the
length and what is the width?
Answer:
the length of the rectangle is 21 feet.
Step-by-step explanation:
Let's use "w" to represent the width of the rectangle. According to the problem, the length is three times the width, so we can use "3w" to represent the length.
The perimeter of a rectangle is given by the formula:
Perimeter = 2(length + width)
Substituting the expressions for length and width, we get:
56 = 2(3w + w)
Simplifying the right side, we get:
56 = 2(4w)
56 = 8w
w = 7
So the width of the rectangle is 7 feet. To find the length, we can use the expression we derived earlier:
length = 3w = 3(7) = 21
Therefore, the length of the rectangle is 21 feet.
Sylvia is 56 3/4 inches tall Bill is 1/3 8 inches taller than Sylvia and Jane is 1 1/5 inches taller than bill how tall is Jane
The required Jane is approximately 59.28 inches tall.
How to find the height of the jane?Height is a measurement of vertical distance, either in terms of vertical extent (how tall an object or person is) or in terms of vertical position (how high a point is). "The height of that building is 50 meters" or "The height of an airplane in flight is approximately 10,000 meters" are two examples.
Sylvia's height can be represented as:
Sylvia’s height =56[tex]\frac{3}{4}[/tex] inches
Bill is [tex]\frac{1}{3}$[/tex] of 8 inches taller than Sylvia, which means that Bill's height is:
[tex]$\begin{align*}\text{Bill's height} &= \text{Sylvia's height} + \frac{1}{3} \times 8\ \text{inches} \&= 56 \frac{3}{4}\ \text{inches} + \frac{8}{3}\ \text{inches} \&= 58 \frac{7}{12}\ \text{inches}\end{align*}[/tex]
Jane is [tex]1 \frac{1}{5}$[/tex] inches taller than Bill, which means that Jane's height is:
[tex]$\begin{align*}\text{Jane's height} &= \text{Bill's height} + 1 \frac{1}{5}\ \text{inches} \&= 58 \frac{7}{12}\ \text{inches} + 1 \frac{1}{5}\ \text{inches} \&= 59 \frac{17}{60}\ \text{inches}\end{align*}[/tex]
Therefore, Jane is approximately 59.28 inches tall.
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distributive property
7(r+3)+2(r-2)?
1. 7r+3+2r-2
2. 7r+21+2r-4
3. 7r+21-2r-2
4. 7r+3+2r-4
Step-by-step explanation:
ans is 2 nd option
first bracket multiply with 7 and second multiply with 2 multiply the sign also carefully.