Answer:
using the trigonometry identities
Cos ∅ = Adj/Hyp
where ∅ = 73°
Cos 73 = 8.6/x
X × Cos 73 = 8.6
x = 8.6/0.2923
x = 29.421 ≈ 29.4
What are the ordered pair solutions
for this system of equations?
y = -x² + 2
y = x
First, set the equations equal to each other and
move everything to one side.
A:-x²+x+2=0
C:-x² + 2 = x
B:x²+x-2 = 0
D:x²+x+2=0
To find the ordered pair solutions, we need to solve the system of equations by setting them equal to each other:
-x² + x + 2 = x
Simplifying:
-x² + 2x + 2 = 0
We can solve for x using the quadratic formula:
x = (-2 ± sqrt(2^2 - 4(-1)(2))) / (2(-1))
x = (-2 ± sqrt(12)) / (-2)
x = 1 ± sqrt(3)
So the x-values of the ordered pair solutions are:
x = 1 + sqrt(3)
x = 1 - sqrt(3)
To find the corresponding y-values, we can substitute these x-values into either equation. Let's use y = x:
When x = 1 + sqrt(3):
y = 1 + sqrt(3)
When x = 1 - sqrt(3):
y = 1 - sqrt(3)
select the correct answer. of the students in gianna's math class, 28% of the students have Gianna's favorite book, and 36% of the students have seen the movie version of the book. she finds that 20% of the students have both read the book and seen the movie version. what is the probability that a randomly chosen student in gianna's math class has read her favorite book or seen the movie version of the book? (a) 44%, (b)64%, (c)24%, (d)84%.
As a result, the probability that a randomly selected student in Gianna's probability maths class has read or seen the movie adaptation of her favourite book is 44%.
What is probability?Probability is a measure of how likely an event is to occur. It is represented by a number between 0 and 1, with 0 representing a rare event and 1 representing an inescapable event. Switching a fair coin and coin flips has a chance of 0.5 or 50% because there are two equally likely outcomes. (Heads or tails). Probabilistic theory is an area of mathematics that studies random events rather than their attributes. It is applied in many fields, including statistics, economics, science, and engineering.
solve this problem,
P(A or B) = P(A) + P(B) - P(A and B)
P(A) = 28%
P(B) = 36%
P(A and B) = 20%
Using the formula, we can find:
P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) = 28% + 36% - 20%
P(A or B) = 44%
As a result, the probability that a randomly selected student in Gianna's maths class has read or seen the movie adaptation of her favourite book is 44%.
As a result, the right answer is (a) 44%.
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Set up a proportion and solve for x
Thus value of x in the given the proportion is 7.
How to find the value of x?Here, both triangles are congruent due to sss congruency,
Thus,
6 : 12
6k = 12
k = 12/6
k = 2
Also, The expressions are
(x+2) : 3x - 3
(x+2)k = 3x - 3
(x+2)2 = 3x - 3
2x + 4 = 3x - 3
3x - 2x = 4 + 3
x = 7
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Find the area of this shape pls help
Answer:
Area = 63.2 cm²
Step-by-step explanation:
To find the area of the given shape, we can split it into two shapes: a trapezium and a rectangle (as shown in the attached diagram).
Doing so gives us a rectangle with a length of 10 cm and a breadth of 2.8 cm at the bottom of the shape. Therefore its area:
Area = length × breadth
= 10 cm × 2.8 cm
= 28 cm²
We also get a trapezium, whose area can be found using the following formula:
[tex]\boxed{\mathrm{Area = \frac{1}{2} \times (a + b) \times h}}[/tex]
where:
• a, b ⇒ length of the parallel sides of trapezium
• h ⇒ distance between the parallel sides a and b
From the diagram attached below, we can see that the two parallel sides have lengths of 10 cm and 6 cm. Moreover, the distance between the parallel sides is 7.2 - 2.8 = 4.4 cm.
Therefore, using the above formula and information, we can calculate the area of the trapezium:
Area = [tex]\frac{1}{2}[/tex] × (6 + 10) cm × 4.4 cm
= [tex]\frac{1}{2}[/tex] × 16 cm × 4.4 cm
= 35.2 cm²
Now that we have the areas of the rectangle and trapezium, we can find the area of the whole shape simply by adding those two areas:
Area of shape = 28 cm² + 35.2 cm²
= 63.2 cm²
Therefore, the area of the given shape is 63.2 cm².
The length of a radius of a circle, measured in centimeters, is represented by the expression x + 1.5. The diameter of the circle is 9 2/5
cm.
What is the value of x?
Enter your answer as a decimal or mixed number in simplest form in the box.
X =
Answer:
The value of x of a circle with radius x + 1.5 and diameter of 9 2 / 5 cm is 7.9 cm
Radius of a circle
Radius of a circle is half of the diameter of a circle. The radius extend from the centre of the circle to the circumference.
Mathematically,
radius = 1 / 2 (diameter)
Therefore,
radius = (x + 1.5) cm
diameter = 9 2 / 5 cm = 47 / 5 cm
let's find x with the relationship above.
Therefore,
x + 1.5 = 47 / 5
subtract 1.5 from both sides
x + 1.5 - 1.5 = 9.4 - 1.5
x = 7.9 cm
Step-by-step explanation:
The outside of a closed glass display case measure 22 inches by 15 inches by 12 inches. The glass is half an inch thick. how much air is contained in the case?k
Answer:
V_air = V_inside = 2,600 cubic inches.
Step-by-step explanation:
To find the amount of air contained in the display case, we need to subtract the volume of the glass from the volume of the outside dimensions.
The volume of the outside dimensions of the display case is:
V_outside = 22 * 15 * 12 = 3,960 cubic inches
The glass is half an inch thick, which means it adds 1 inch to each dimension of the display case. Therefore, the inside dimensions of the display case are:
22 - 2(1) = 20 inches
15 - 2(1) = 13 inches
12 - 2(1) = 10 inches
The volume of the inside dimensions of the display case is:
V_inside = 20 * 13 * 10 = 2,600 cubic inches
The volume of the glass is the difference between the outside and inside volumes:
V_glass = V_outside - V_inside = 3,960 - 2,600 = 1,360 cubic inches
Therefore, the amount of air contained in the display case is:
V_air = V_inside = 2,600 cubic inches.
in triangle ABC AC =10 in. ,BC =2.5 in., and m angle C =63°. what is the area of triangle ABC?
The area of triangle ABC is approximately 11.14 square inches.
What is the area of triangle ABC?To find the area of triangle ABC, we can use the formula:
Area = 1/2 * AC * BC * sin(C)
where the base is BC and the height is the perpendicular distance from A to BC.
To find the sine 63, we can use the sine of angle C:
sin C = sin(63)
Therefore, the area of triangle ABC is:
Area = 1/2 * 10 * 2.5 * sin(63)
When evaluated, we have
Area ≈ 11.14 square inches
So, the area of triangle ABC is approximately 11.14 square inches.
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I really need help please help
Answer:
Question 7 is correct.
205,000 (For Question 8)
Step-by-step explanation:
First, we need to find the value of x.
We need to subtract 1995 from 2010 to find out how many years would have passed.
This gives us 15, which is our x value.
Next, we need to solve for y.
We multiply 2000 by 15 to get 30,000.
Then, add 175,000 to 30,000 to get 205,000. That leaves us with the equation y = 205,000.
The Y value is equivalent to the population in 2010.
A student is solving the equation 3(x−12)=9x . Which describes a first step the student could use to solve the equation correctly? Responses The student can distribute 3 on the left side of the equation, resulting in 3x−36=9x . The student can distribute 3 on the left side of the equation, resulting in 3 x − − 36 = 9 x . The student can distribute 3 on the left side of the equation, resulting in 3x−12=9x . The student can distribute 3 on the left side of the equation, resulting in 3 x − − 12 = 9 x . The student can divide both sides of the equation by 3 , resulting in x−12=6x . The student can divide both sides of the equation by 3 , resulting in x − − 12 = 6 x . The student can divide both sides of the equation by 3 , resulting in x−4=3x .
Step-by-step explanation:
The correct first step the student could use to solve the equation 3(x-12)=9x is to distribute 3 on the left side of the equation, resulting in 3x - 36 = 9x.
This is because the distributive property states that a(b + c) = ab + ac. In this case, we have 3(x - 12), so we can distribute the 3 by multiplying it by both terms inside the parentheses: 3(x - 12) = 3x - 36.
Then, we can simplify the equation by subtracting 3x from both sides: -36 = 6x. Finally, we can solve for x by dividing both sides by 6: x = -6.
Therefore, the correct option is: "The student can distribute 3 on the left side of the equation, resulting in 3x−36=9x."
The first step in solving the equation 3(x−12)=9x is to distribute the 3 on the left-hand side of the equation. You multiply each term inside the parentheses by 3, resulting in a simplified equation: 3x - 36 = 9x.
Explanation:If you're aiming to solve the equation 3(x−12)=9x, the initial step would be to distribute the 3 into the parentheses on the left side of the equation. This is achieved by multiplying each term inside the parenthesis by 3. Here's the process in detail:
Step 1: Start with the initial equation, which is 3(x−12)=9x.
Step 2: Remove the parentheses by distributing 3, resulting in 3x - 36 = 9x.
This is a viable initial step because now you have simplified equations on both sides, which helps you to get closer towards isolating the variable x.
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Complete this proof using SSS.
Given: ∆ABD and ∆DCB; AB ≅ DC and AD ≅ BC Prove: ∆ABD ≅ ∆DCB
STATEMENTS
1. ∆ABD and ∆DCB; AB ≅ DC; AD ≅ BC
2. BD ≅ BD
3. ___
REASONS
1. ___
2. ___ Prop. of ≅
3. SSS
Answer (Please mark as brainliest):
STATEMENTS
∆ABD and ∆DCB; AB ≅ DC; AD ≅ BC
BD ≅ BD
∆ABD ≅ ∆DCB
REASONS
Given
Reflexive Property of Congruence
By SSS, since AB ≅ DC, AD ≅ BC, and BD ≅ BD.
Therefore, ∆ABD ≅ ∆DCB by SSS.
15) Find mMP
12x + 3
P
M
45°
S
R
3x + 12
Answer:
Determine the lengths of sides and measures of angles in a right triangle by ... 9 = 12x. Cross Products Property. 9 = 3x. Subtract 9x from each side. 3 = x.
In a circle, an angle measuring
radians intercepts an arc of length
. Find the radius of the circle in simplest form.
The formula to find the length of an arc of a circle is given by L = rθ, where L is the length of the arc, r is the radius of the circle, and θ is the angle measured in radians and the radius of the circle is 2.
To find the length of the arc, we use the formula L = rθ. Substituting the given values, we get:
L = rθ
L = r( [tex]\frac{\pi}{2}[/tex]) or ( [tex]\frac{\pi}{2}[/tex])r
We are also given that the length of the arc is 1π, so we can write:
( [tex]\frac{\pi}{2}[/tex])r = 1π
Simplifying this equation, we get:
r = (1π) ÷ ( [tex]\frac{\pi}{2}[/tex])
r = 2
We can say that the length of an arc that is intercepted by an angle of [tex]\frac{\pi}{2}[/tex] radians is equal to half the circumference of the circle. Since the length of the arc is given as 1π, we can find the radius of the circle by dividing 1π by [tex]\frac{\pi}{2}[/tex], which gives us 2.
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The complete question is:
In a circle, an angle measuring [tex]\frac{\pi}{2}[/tex] radians intercepts an arc of length 1π. Find the radius of the circle in simplest form.
Write the equation of the line in slope-intercept form.
Answer:
y = (- 3/4)x + 8---------------------
Slope-intercept form is:
y = mx + b, where, m - is the slope, b - is the y-interceptUse two points on the line:
(0, 8) and (4, 5)The first point represents the y-intercept, b = 8.
Find the slope, using the slope equation:
m = (y₂ - y₁)/(x₂ - x₁)m = (5 - 8)/(4 - 0) = -3/4Substitute the found values to get the equation of the line:
y = (- 3/4)x + 8Airplanes are sometimes used to fight fires. A certain airplane can deliver 4x10^4 liters of water in one trip. How much water can this airplane deliver in 38 trips?
Write your answer in scientific notation.
Answer:
1.52×10⁶ liters of water
Step-by-step explanation:
38(4×10⁴)
an angle measure 14.6 degrees more than the measure of its supplementary angle. what is the measure of each angle?
The measure of the angles are 82. 7 degrees and 97. 3 degrees
What are supplementary angles?Supplementary angles are simply described as those angles whose sum is equal or equivalent to 180 degrees.
Note that pair of angles on a straight line are supplementary to each other.
From the information given, we have that;
Let the angle of one be x
Then,
Angle 1 = x
Angle 2 = 14. 6 + x
Equate the angles
x + 14. 6 + x = 180
collect the like terms, we get;
2x = 180 - 14. 6
subtract the values
2x = 165. 4
x = 82. 7 degrees
Then, the second angle = 82. 7 + 14. 6 = 97. 3 degrees
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QUESTIONS
WHALE CAN FLY FASTER THAN A
CROW?
TRUE
FALSE
Answer: False
Step-by-step explanation: A whale can't fly
Answer:
False
Step-by-step explanation:
Because a whale cannot fly
find the value of 8w+6 given that -7w+1=8
Answer: -2
Step-by-step explanation:
-7w + 1 = 8
Subtract 1 from both sides
-7w + = 7
Divide -7 from both sides
w = -1
then
8(-1) = -8
-8 + 6 = -2
What is the interquartile range (IQR) of the data set represented by this box
plot?
0
10
A. 55
B. 37
OC. 24
D. 12
← PREVIOUS
18 25 37
20
30
40
49 55
50
60
The interquartile range (IQR) of the data set represented by this box plot is 24.
What is IQR and how it is find?The interquartile range, or IQR, can be determined in four easy steps: Sort the facts in ascending order of importance. locate the centre. Do the lower and higher half of the data's median calculations. Upper and lower median differences make up the IQR.
We must determine the difference between the third quartile (Q3) and the first quartile (Q1) in order to determine the interquartile range (IQR) of the data set depicted by this box plot.
We can see from the box plot that the range of the box is 18 to 49, which implies that Q1 is 25 and Q3 is 49. Therefore,
IQR = Q3 - Q1 = 49 - 25 = 24
So, none of the choices provided are the correct response. The data collection represented by this box plot has an IQR of 24, which is 24.
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Complete question:
What is the interquartile range (IQR) of the data set represented by this box plot?
A. 55
B. 37
C. 24
D. 12
Use the spinner below.
P(>7) =
The probability of landing on a number greater than 7 is 4÷12 or 1÷3, which is approximately 0.333 or 33.3%.
What is Probability ?
Probability is a branch of mathematics that deals with the study of random events or outcomes. It is a measure of the likelihood or chance of an event occurring, expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
If the spinner has 12 sections labeled with the numbers 1 through 12, then the probability of landing on a number greater than 7 would be:
There are 12 equally likely outcomes when the spinner is spun.
Out of these 12 outcomes, 4 are greater than 7: 8, 9, 10, and 11.
Therefore, the probability of landing on a number greater than 7 is 4÷12 or 1÷3, which is approximately 0.333 or 33.3%.
So P(>7) = 1÷3 or 0.333 or 33.3%.
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What is the probability that out of 175 chicks hatched on Peeper Farm, at
least 90 will be female? Assume that males and females are equally probable,
and round your answer to the nearest tenth of a percent.
OA. 3.5%
OB. 99.7%
C. 38.1%
D. 88.7%
Determine any data values that are missing from the table, assuming that the data represent a linear function. x y 1 6 2 10 3 a. 6 c. 16 b. 15 d. 14 Please select the best answer from the choices provided
The missing data value in the table of values is y = 14
Determining the missing data valuesWe can use the two given data points (1,6) and (2,10) to find the equation of the linear function that represents the data.
First, we can use the slope formula to find the slope of the line:
slope = (change in y) / (change in x) = (10-6) / (2-1) = 4/1 = 4
Next, we can use the point-slope formula to find the equation of the line using one of the given points. Let's use (1,6):
y - 6 = 4(x - 1)
We can simplify this equation to slope-intercept form (y = mx + b) by solving for y:
y = 4x + 2
Now we can use this equation to find the missing data value when x = 3:
y = 4(3) + 2 = 14
Therefore, the missing data value is y = 14, and the correct answer is (d) 14.
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To make blackberry jam, you must cook blackberries until they become juice. If 4 cups of blackberries give you 1 1/3 cups of juice, find the constant of proportionality of juice to blackberries.
I don't need sleep, I need answers.
The constant of proportionality of juice to blackberries is 3. This means that for every cup of blackberries, you will get 1/3 cup of juice.
Describe Constant of proportionality ?The constant of proportionality is a mathematical term used to describe the relationship between two quantities that are directly proportional to each other. When two quantities are directly proportional, they vary in proportion to each other such that if one quantity doubles, the other also doubles. The constant of proportionality is the number that relates the two quantities together.
To find the constant of proportionality, we need to divide the amount of juice by the amount of blackberries.
Let x be the amount of blackberries required to make 1 cup of juice. Then we have:
4 cups of blackberries = 1 1/3 cups of juice
Divide both sides by 1 1/3 cups of juice:
4 cups of blackberries / (4/3) cups of juice = 3 cups of blackberries / cup of juice
So the constant of proportionality of juice to blackberries is 3. This means that for every cup of blackberries, you will get 1/3 cup of juice.
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One child can complete her homework twice as fast as her partner. When working together, both children can complete the homework in 45 minutes. If they work by themselves, how long will it take each child to complete the homework?
HINTS: 1) Let t = the time needed for the faster child to complete the homework.
2) Portion of the homework completed=rate ×time (P=rt)
3) When a child works alone the portion of the work completed is all the homework. That is (P=1)
1) The rate at which the faster child is working is ___________ Write an algebraic expression.
2) The rate at which the slower child is working is ___________Write an algebraic expression.
3) The part of the homework was done by the faster child in 45 minutes is ___________Write an algebraic expression.
4) The part of the homework was done by the slower child in 45 minutes is ___________ Write an algebraic expression.
5) The time taken by the faster child to do the homework by herself is _______________Give your answer in minutes.
6) The time taken by the slower child to do the homework by their self is _______________Give your answer in minutes.
1. The rate at which the faster child is working is 1/t.
2.The rate at which the slower child is working is 1/(2t)
3.The homework done by the faster child in 45 minutes is (1/t) * (3/4), since both children can complete the homework in 45 minutes.
4.The part of the homework done by the slower child in 45 minutes is (1/(2t)) * (3/4),
5.Thus, t=30 minutes, which is the time taken by the faster child to do the homework by herself.
6. Thus, 2t=90 minutes and t=45 minutes, which is the time taken by the slower child to do the homework by herself.
What is time?Time is a concept used to describe the progression of events from the past, through the present, and into the future. It is a measure of duration or an interval between two events, and it is often represented in units such as seconds, minutes, hours, days, weeks, months, and years.
1. Let t = the time needed for the faster child to complete the homework.
The faster child completes the homework twice as fast as the partner. Therefore, the rate at which the faster child is working is 1/t.
2.The rate at which the slower child is working is 1/(2t) since the slower child takes twice as long as the faster child to complete the homework.
3.The part of the homework done by the faster child in 45 minutes is (1/t) * (3/4), since both children can complete the homework in 45 minutes. In 45 minutes, the faster child completes 3/4 of the homework because she is working at a rate of 1/t, while the slower child is working at a rate of 1/(2t).
4.The part of the homework done by the slower child in 45 minutes is (1/(2t)) * (3/4), since both children can complete the homework in 45 minutes. In 45 minutes, the slower child completes 3/4 of the homework because she is working at a rate of 1/(2t), while the faster child is working at a rate of 1/t.
5.Let's use the equation P=rt, where P=1 (since the entire homework is done by one child alone) and r=1/t (since the faster child completes the homework in t time). Thus, t=30 minutes, which is the time taken by the faster child to do the homework by herself.
6.Similarly, we can use the equation P=rt, where P=1 (since the entire homework is done by one child alone) and r=1/(2t) (since the slower child takes twice as long as the faster child to complete the homework). Thus, 2t=90 minutes and t=45 minutes, which is the time taken by the slower child to do the homework by herself.
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The perimeter of a rectangular garden is 372 m
If the width of the garden is 88 m, what is its length?
Answer:
Let L be the length of the rectangular garden. We know that the perimeter of a rectangle is given by: P = 2L + 2W where P is the perimeter, L is the length, and W is the width. In this case, we are given that the perimeter is 372 m and the width is 88 m. Substituting these values into the equation, we get: 372 = 2L + 2(88) Simplifying and solving for L, we get: 372 = 2L + 176 2L = 196 L = 98 Therefore, the length of the rectangular garden is 98 m.
Answer: L = 98 m
Step-by-step explanation:
The perimeter of a rectangle can be found with this formula:
P = 2W + 2L
➜ P is Perimeter
➜ W is Width
➜ L is Length
We will input known values and solve for the length. To solve, we will use multiplication and inverse operations.
372 m = 2(88 m) + 2L
372 m = 176 m + 2L
196 m = 2L
L = 98 m
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A boat is heading towards a lighthouse, whose beacon-light is 136 feet above the
water. From point A, the boat's crew measures the angle of elevation to the beacon,
6°, before they draw closer. They measure the angle of elevation a second time from
point B at some later time to be 19°. Find the distance from point A to point B.
Round vour answer to the nearest foot if necessary.
Answer:
Rounding to the nearest foot, the distance from point A to point B is 719 feet.
In a large population, 91% of the households have cable tv. A simple random sample of 196 households is to be contacted and the sample proportion computed. What is the probability that the sampling distribution of sample porportions is less than 87%?
a) 0.2786
b) 0.7214
c) 0.0126
d) 0.0252
e) 0.9748
Answer:
Step-by-step explanation:
B. Now, look at the list of verbs in part A. Select the correct subject pronoun for each verb.
11) ___ escribimos
A. ustedes
B. nosotros
If you bet $5 in a Pick 4 lottery game, you either lose $5 or gain $9,995. (The winning prize is $10,000, but your $5 bet is not returned, so the net gain is $9,995.) The game is played by selecting
a four-digit number between 0000 and 9999. What is the probability of winning? If you bet $5 on 1234, what is the expected value of your gain or loss? What is the probability of winning?
Answer:
the expected value of your gain or loss is a net loss of $0.5006.
The probability of winning is 1/10,000 = 0.0001.
Step-by-step explanation:
There are 10,000 possible four-digit numbers between 0000 and 9999. Only one of those numbers is the winning number. Therefore, the probability of winning the Pick 4 game is:
Probability of winning = 1/10,000 = 0.0001
If you bet $5 on 1234, there are two possible outcomes:
-You lose $5 with probability 0.9999
-You gain $9,995 with probability 0.0001
The expected value of your gain or loss is the sum of the products of each outcome and its probability:
Expected value = (-$5 x 0.9999) + ($9,995 x 0.0001)
Expected value = -$0.5006
Answer:
Step-by-step explanation:
(Need help please and thank you!)
Answer:
Step-by-step explanation:
F
x=weeks
5=inital
y=total money saved
Given that sin(x)
A. 4
B.
11
NEF=
7
11
C. 11
7
D. 11
4
=
7
11'
find cos (90-x).
The value of cos (90 - x ) = sin (x) = 7/11.
option B.
What is the value of cos (90 - x)?In trigonometry identity, we know that sin(x) = opposite / hypotenuse. Therefore, we can draw a right triangle with an angle x and opposite side 7 and hypotenuse 11.
Using the Pythagorean theorem, we can find the adjacent side of the triangle:
adjacent² = hypotenuse² - opposite²
adjacent² = 11² - 7²
adjacent² = 120
adjacent = √(120)
adjacent = 2 √(30)
Now, we can use the definition of cosine to find cos(90 - x):
cos(90 - x) = sin(x)
Therefore, cos(90 - x) = 7/11.
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$1000 is deposited in an account with a 8.5% interest rate, compounded continuously. What is the balance after 5 years?
By answering the presented question, we may conclude that the balance interest after 5 years is approximately $1,484.71.
what is interest ?In mathematics, interest is the amount of money gained or payable on an original investment or loan. You can use either simple or compound interest. Simple interest is calculated as a percentage of the initial amount, whereas compound interest is calculated on the principal amount plus any previously earned interest. If you invest $100 at a 5% annual simple interest rate, you will get $5 in interest per year for three years, for a total of $15.
for calculating the balance
[tex]A = Pe^(rt)\\[/tex]
this formula,
[tex]A = 1000e^(0.085*5)\\A = 1000e^(0.425)\\[/tex]
A ≈ $1,484.71
the balance after 5 years is approximately $1,484.71.
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Answer:1529.59
Step-by-step explanation:
1000e^(.085)5