We have the iterated integral:
∫
�
=
0
2
∫
�
=
1
5
5
(
�
+
�
)
(
2
−
�
2
)
�
�
�
�
∫
y=0
2
∫
x=1
5
5(x+y)(2−y
2
)dxdy
To convert this to polar coordinates, we need to express $x$ and $y$ in terms of $r$ and $\theta$. Since the region of integration is defined by $0 \leq y \leq 2$ and $1 \leq x \leq 5$, we see that $1 \leq r \leq 5$ and $0 \leq \theta \leq \pi$. Then we have:
�
=
�
cos
�
and
�
=
�
sin
�
x=rcosθandy=rsinθ
The Jacobian of the transformation is $\frac{\partial(x,y)}{\partial(r,\theta)} = r$, so we have:
\begin{align*}
\int_{y=0}^{2} \int_{x=1}^{5} 5(x+y)(2-y^2) ,dx,dy &= \int_{\theta=0}^{\pi} \int_{r=1}^{5} 5(r\cos \theta + r\sin \theta)(2 - r^2\sin^2 \theta) ,r,dr,d\theta \
&= \int_{\theta=0}^{\pi} \int_{r=1}^{5} 10r^2\cos \theta ,dr,d\theta + \int_{\theta=0}^{\pi} \int_{r=1}^{5} 10r^2\sin \theta \cos \theta ,dr,d\theta \
&\quad + \int_{\theta=0}^{\pi} \int_{r=1}^{5} 5r^3\sin \theta ,dr,d\theta - \int_{\theta=0}^{\pi} \int_{r=1}^{5} 5r^5\sin^3 \theta ,dr,d\theta \
&= \int_{\theta=0}^{\pi} \left[ \frac{10}{3}r^3\cos \theta \right]{r=1}^{r=5} ,d\theta + \int{\theta=0}^{\pi} \left[ \frac{5}{2}r^3\sin^2 \theta \right]{r=1}^{r=5} ,d\theta \
&\quad + \int{\theta=0}^{\pi} \left[ \frac{5}{4}r^4\sin \theta \right]{r=1}^{r=5} ,d\theta - \int{\theta=0}^{\pi} \left[ \frac{5}{6}r^6\sin^4 \theta \right]{r=1}^{r=5} ,d\theta \
&= \int{\theta=0}^{\pi} \frac{1240}{3}\cos \theta + \frac{60}{2}\sin^2 \theta + \frac{155}{4}\sin \theta - \frac{2480}{6}\sin^4 \theta ,d\theta \
&= \left[ \frac{1240}{3}\sin \theta - \frac{60}{2}\frac
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Alice drops a rock off a building that is 64 feet tall. If the equation for height as a function of time is: y = -16+2 + 400 where t is time in seconds and y is height in feet, how many seconds will it take for the drone to hit the ground? Now, set the equation equal to zero and solve.
By using Algebraic methods It will take 5 seconds for the rock to hit the ground when dropped from a building that is 64 feet tall, given the equation y = -16t^2 + 400.
The equation is y = -16t^2 + 400, where y represents the height of the rock in feet and t represents the time in seconds.
To find out how many seconds it will take for the rock to hit the ground, we need to set the equation equal to zero because the ground is at a height of zero.
0 = -16t^2 + 400
Now, we can solve for t using Algebraic methods.
First, we can subtract 400 from both sides of the equation:
-400 = -16t^2
Next, we can divide both sides by -16:
25 = t^2
Finally, we can take the square root of both sides:
t = ±5
Since we can't have negative time, we know that it will take 5 seconds for the rock to hit the ground.
So, to summarize, it will take 5 seconds for the rock to hit the ground when dropped from a building that is 64 feet tall, given the equation y = -16t^2 + 400.
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Find the volume of the triangular prism with a height of 2.8, width of 4.2, and a length of 8.
Answer:
Step-by-step explanation:
The formula for this is:
V = (1/2) x b x h x l
b= base
h=height
l=length
V= (1/2) x 4.2 x 2.8 x 8
so...I think the volume could be 47.04m^3?
PRO TIP: If you want to solve anything with volume, just write down every single formula they have for volume or area. It is good to memorize formulas like that.
The volume of the triangular prism with a height of 2.8, width of 4.2, and a length of 8 is 46.96 cubic unit.
The base area of the triangular cross-section must be multiplied by the prism's height to determine its volume. The triangle cross-section in this instance has a base of 4.2 and a height of 8.
The following is the formula to determine a triangle's area:
(Base * Height) / 2 = Area
When the values are plugged in, we get:
Base = 4.2
Size = 8
Area = (4.2 * 8) / 2 = 33.6 / 2 = 16.8
Next, increase the prism's base area by its height:
Volume = Base Area * Height = 16.8*2.8 = 46.96
The triangular prism therefore has a 46.96 cubic unit volume.
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what is the lower quartile of the numbers 1 5 6 6 7 7 8 8 8 8 9 9 18 20 20 20 20 20 24 32 50 50 68 100
To find the lower quartile of a set of numbers, we need to determine the value that separates the lowest 25% of the data from the rest. In the given set of numbers, the lower quartile can be found by arranging the data in ascending order and identifying the value at the 25th percentile.
First, let's arrange the data in ascending order: 1 5 6 6 7 7 8 8 8 8 9 9 18 20 20 20 20 20 24 32 50 50 68 100.
To find the lower quartile, we need to determine the position of the 25th percentile. Since there are 23 data points, the 25th percentile corresponds to the value at the (25/100) * 23 = 5.75th position.
Since the position is not a whole number, we need to find the value between the fifth and sixth data points. The fifth data point is 7, and the sixth data point is also 7. Therefore, the lower quartile is 7.
The lower quartile represents the value below which 25% of the data lies. In this case, 25% of the data points are less than or equal to 7. It indicates that a quarter of the values in the dataset are smaller than or equal to 7, while the remaining 75% are larger.
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suppose we want to select a set of 4 coins from a box containing 6 different pennies and 8 different dimes. how many of the possible sets contain 2 pennies and 2 dimes?
Answer:
420 possible sets------------------------
Use a combination formula.
We want to select 2 pennies from a set of 6 and 2 dimes from a set of 8.
The number of ways to do this is:
C(6,2) * C(8,2) = (6!/(2!4!)) * (8!/(2!6!)) = 15 * 28 = 420Therefore, there are 420 possible sets of 4 coins that contain 2 pennies and 2 dimes.
i don't get it pls i need help pls pls pls
Answer:
IDONTKNOW but your answer might be 35 .
Step-by-step explanation:
i think the answer is
5 x 7
So basically you have 4 and 3 so you want to multiply that and idontrealyknow the rest. eh sorry idontknow i tried.
You spin a spinner that is equally divided into 9 parts. 3 parts are white, 3 parts are black, and 3 parts are yellow.
What is the probability of the spinner not stopping at a black section? Write your answer as a percent rounded to the nearest whole number.
(Thank you!!)
Answer:
6/9 67%
Step-by-step explanation:
Answer:
2/3
Step-by-step explanation:
66,6% are 2/3 -> 67%
From the 9 parts are 6 left - > 9/6 = 2/3
Kai uses an entire can of paint on a square backdrop for the school play. The label on the can states that one can covers 27 m2 of wall surface. Estimate the backdrop’s side length, to one decimal place.
Subtract the polynomials
(3x² + 2x − 5) – (4x² – 3x − 4)
A:-7x²+5x-9
B:7x²-x-9
C:x²-x-9
D:-x²+5x-1
please helpppp asap
Answer:
-x² + 5x - 1
Step-by-step explanation:
separate the x², the x, and the constants (numbers without any x).
3x² - 4x² = -x²
2x - -3x = 2x + 3x = 5x
-5 - -4 = -5 + 4 = -1.
we have -x² + 5x - 1
Rey is checking the distance between two rooms on a blueprint. The
blueprint uses a scale in which 3 inches equals 4 feet. If the distance
on the blueprint is 11 inches, how far is it between the rooms, in feet?
Your answer can be exact or rounded to two decimal places.
doris needs to renew her real estate license for the first time, and she's already completed 20.5 hours of continuing education. how many additional hours of ce does she need to complete?
Doris needs to complete a total of 30 hours of continuing education to renew her real estate license for the first time. As she has already completed 20.5 hours of CE, she needs to complete an additional 9.5 hours of CE.
It's important to note that continuing education requirements vary by state and licensing board, so it's always a good idea to check with the relevant authorities to ensure you meet all the requirements for license renewal. Real estate agents are typically required to complete a certain number of continuing education hours within a specific time frame in order to maintain their license and stay up-to-date with industry developments and best practices. This is important to ensure they are equipped with the necessary knowledge and skills to provide quality services to their clients.
In summary, Doris needs to complete an additional 9.5 hours of CE to meet the 30-hour requirement for renewing her real estate license for the first time.
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analysis is a form of horizontal analysis that can reveal patterns in data across periods. it is computed by taking the (analysis period amount/base period amount) x 100.multiple choice question.ratiotrendmodified horizontal
The type of analysis described in the statement is ratio analysis.
Ratio analysis is a tool used to evaluate the financial performance of a company by comparing different financial ratios over time or between companies. It involves calculating different ratios such as liquidity ratios, profitability ratios, and solvency ratios and comparing them across different periods to identify trends or patterns in the data. The ratio analysis formula mentioned in the statement is used to calculate the percentage change in a ratio between two periods, with the base period amount serving as the denominator.
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If each serving of the stew will contain pound of meat, how many servings of the stew can the club
make?
Enter your answer in the box.
The number of servings of the stew the club can make is 24
Calculating the servings of the stew the club can make?From the question, we have the following parameters that can be used in our computation:
The dot plot
From the dot plot, we have
Total = 4/8 * 2 + 6/8 + 1 * 3 + 1 2/8 * 1
Evaluate
Total = 6
Each serving can take 1/4 pounds
So, we have
Total = 6/(1/4)
Evaluate
Total = 24
Hence, the servings of the stew the club can make is 24
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a box of baseballs cost $66.12. what equation represents the cost,c, of n boxes
Hello !
c = the cost
n boxes = 66,12n
c = 66,12n
if $\&x$ is defined as $\&x = x + 5$ and $\#x$ is defined as $\#x = x^2$ , what is the value of $\#(\&4)$?
The value of $\#(\&4)$ is 81. We first evaluated $\&4$ using the definition given, which gave us the value 9. Then, we substituted this value into the definition of $\#x$ to find the final answer of 81.
To find the value of $\#(\&4)$, we first need to evaluate $\&4$. Using the given definition of $\&x$, we have:
$$\&4 = 4 + 5 = 9$$
Now, we can substitute this value into the definition of $\#x$:
$$\#(\&4) = \#9 = 9^2 = 81$$
Therefore, the value of $\#(\&4)$ is 81. We first evaluated $\&4$ using the definition given, which gave us the value 9. Then, we substituted this value into the definition of $\#x$ to find the final answer of 81.
To find the value of #(&4), let's first compute &4.
According to the definition, &x = x + 5. So, &4 = 4 + 5 = 9.
Now we need to find the value of #9. The definition of #x is x², which means #9 = 9² = 81.
Therefore, the value of #(&4) is 81.
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how to find the first term of arithmetic sequence given the number of terms, the last term and the common differnece
To find the first term of an arithmetic sequence, use the formula: first term = last term - (number of terms - 1) * common difference.
To find the first term of an arithmetic sequence given the number of terms, the last term, and the common difference, you can use the following formula
First term = Last term - (Number of terms - 1) * Common difference
Here's how to use this formula
Identify the number of terms, the last term, and the common difference of the arithmetic sequence.
Plug these values into the formula.
Simplify the formula using order of operations (PEMDAS) to find the first term.
For example, let's say we have an arithmetic sequence with 10 terms, a last term of 50, and a common difference of 5. Using the formula above, we get
First term = 50 - (10 - 1) * 5
First term = 50 - 9 * 5
First term = 50 - 45
First term = 5
Therefore, the first term of the arithmetic sequence is 5.
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In a scatter plot, if all data points were aligned along a 45° angle, your correlation would be:
A) Of medium strength
B) Of weak strength
C) Perfect
D) 0
E) None of the above
Answer:
C) Perfect correlation
Perform the following area application.
Compute the number of vinyl tiles, measuring 8 in. each side, needed to tile a kitchen measuring 24 ft. by 18 ft.
__________tiles
To find the number of vinyl tiles needed to tile a kitchen measuring 24 ft. by 18 ft. with tiles measuring 8 in. each side, we need to convert all measurements to the same units.
First, we need to convert the kitchen measurements from feet to inches:
- 24 ft. = 24 x 12 = 288 in.
- 18 ft. = 18 x 12 = 216 in.
Next, we need to divide the length and width of the kitchen by the length of each tile to find the number of tiles needed in each direction:
- Length: 288 in. ÷ 8 in. = 36 tiles
- Width: 216 in. ÷ 8 in. = 27 tiles
Finally, we multiply the number of tiles needed in each direction to find the total number of tiles needed:
- Total tiles: 36 tiles x 27 tiles = 972 tiles
To tile a kitchen, it is important to accurately calculate the number of tiles needed to ensure that there is enough material to complete the job. In this case, we converted all measurements to the same units and then used division and multiplication to find the total number of tiles needed.
To tile a kitchen measuring 24 ft. by 18 ft. with vinyl tiles measuring 8 in. each side, we need a total of 972 tiles.
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Find the volume of the following solids.
The base of the solid is the region between the curve y=2√sin x and the interval [0,π] on the x-axis. The cross-sections perpendicular to the x-axis are
a. equilateral triangles with bases running from the x-axis to the curve.
b. squares with bases running from the x-axis to the curve.
To find the volume of the solid with equilateral triangular cross-sections, we need to integrate the area of each equilateral triangle over the interval [0,π]. The area of an equilateral triangle with side length s is given by (s^2√3)/4. Since the triangles have bases running from the x-axis to the curve y=2√sin x, their side lengths will be 2√sin x. Therefore, the volume is given by the integral:
V = ∫[0,π] (2√sin x)^2√3/4 dx
Simplifying, we get:
V = √3∫[0,π] sin x dx
Using the substitution u = cos x, we get:
V = √3∫[-1,1] √(1 - u^2) du
Using the formula for the integral of the half-circle, we get:
V = (√3/2)π
Therefore, the volume of the solid is (√3/2)π.
To find the volume of the solid with square cross-sections, we need to integrate the area of each square over the interval [0,π]. Since the squares have bases running from the x-axis to the curve y=2√sin x, their side lengths will be 2√sin x.
Therefore, the volume is given by the integral:
V = ∫[0,π] (2√sin x)^2 dx
Simplifying, we get:
V = 4∫[0,π] sin x dx
Using the identity ∫sin x dx = -cos x + C, we get:
V = -4cos x ∣[0,π]
Since cos π = -1 and cos 0 = 1, we get:
V = -4(-1 - 1) = 8
Therefore, the volume of the solid is 8.
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Factorise the following
1.1. 6a-21
1.2.
[tex]6 {x}^{2} + 9x[/tex]
Answer:
1.1. 3(2a-7)
1.2. 3x(2x+3)
Step-by-step explanation:
Put the common factor on the outside of the parentheses.
1.1. 6a-21
The lowest common factor for 6a and -21 is 3.
3(2a-7)
1.2. [tex]6x^{2} +9x[/tex]
The lowest common factor for [tex]6x^{2}[/tex] and 9x is 3x.
3x(2x+3)
find the length of the curve y=ln(cosx) from 0 to pi/3
To find the length of the curve y = ln(cos(x)) from 0 to π/3, we can use the arc length formula for a curve defined by a function y = f(x):
L = ∫[a to b] √(1 + (f'(x))²) dx.
In this case, the function is y = ln(cos(x)). Let's first find the derivative:
y' = d/dx ln(cos(x)).
Using the chain rule, we have:
y' = -tan(x).
Now we can calculate the arc length:
L = ∫[0 to π/3] √(1 + (-tan(x))²) dx.
Simplifying the integrand, we have:
L = ∫[0 to π/3] √(1 + tan²(x)) dx.
Using the trigonometric identity tan²(x) + 1 = sec²(x), we can rewrite the integrand as:
L = ∫[0 to π/3] √(sec²(x)) dx.
Taking the square root of sec²(x), we have:
L = ∫[0 to π/3] sec(x) dx.
Integrating sec(x), we get:
L = ln|sec(x) + tan(x)| [0 to π/3].
Evaluating the integral at the upper and lower limits, we have:
L = ln|sec(π/3) + tan(π/3)| - ln|sec(0) + tan(0)|.
Simplifying further, we have:
L = ln|2 + √3| - ln|1 + 0|.
Since ln|1| = 0, the second term on the right-hand side becomes 0, and we are left with:
L = ln|2 + √3|.
Therefore, the length of the curve y = ln(cos(x)) from 0 to π/3 is ln|2 + √3|.
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Alang and his children went into a restaurant where they sell hamburgers for $7.50 each and drinks for $2.50 each. Alang has $95 to spend and must buy a minimum of 18 hamburgers and drinks altogether. If Alang decided to buy 15 drinks, determine the maximum number of hamburgers that he could buy
Alang can buy at most 10 hamburgers if he buys 15 drinks.
How to solve for the maximum number that can be boughtLet's say Alang buys x hamburgers. Then, he must buy (18 - x) drinks to meet the requirement of buying a minimum of 18 hamburgers and drinks altogether.
The cost of x hamburgers is 7.5x dollars.
The cost of (18 - x) drinks is 2.5(18 - x) = 45 - 2.5x dollars.
The total cost must be less than or equal to $95:
7.5x + (45 - 2.5x) ≤ 95
Simplifying and solving for x, we get:
5x ≤ 50
x ≤ 10
So Alang can buy at most 10 hamburgers if he buys 15 drinks.
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Cher has a motorcycle worth $11,357. She has $605 in cash, and
$1,811 in her savings account. Her only debt is the ken she took out
to buy the motorcycle. If Cher's net worth is $3,934, what is the
Amount of the loan?
The amount of the loan Cher took out to buy the motorcycle is $9839.
Here, we have,
To find the amount of the loan, we need to calculate Cher's total assets and then subtract her total liabilities (debts).
Given:
Value of motorcycle = $11,357
Cash = $605
Savings account = $1,811
Net worth =$3,934
Total assets = Value of motorcycle + Cash + Savings account
Total assets = $11,357 + $605 + $1,811
Total assets = $13,773
To find the amount of the loan, we subtract the total assets from the net worth:
Loan amount = Total assets - Net worth
Loan amount = $13,773 -$3,934
Loan amount = $9839
Hence, The amount of the loan Cher took out to buy the motorcycle is $9839.
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help please. thank you bro.
The area of the small and large sectors are about 11,760 feet² and 23,520 feet² respectively.
We have to given that;
A circle is shown in image.
Here, We have;
For small sector,
Angle = 120 deg
Radius = 14 feet
Since, Area of sector of circle is,
⇒ A = 1/2 (θr²)
Hence, For small sector,
Area = 1/2 (120 × 14²)
Area = 11,760 feet²
For large sector is,
Area = 1/2 (θr²)
Area = 1/2 (360 - 120) × 14²
Area = 1/2 × 240 × 14²
Area = 23,520 feet²
Thus, The area of the small and large sectors are about 11,760 feet² and 23,520 feet² respectively.
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if a car is speeding down a road at 50 miles/hour ( mph ), how long is the stopping distance d50 compared to the stopping distance d25 if the driver were going at the posted speed limit of 25 mph ?
The stopping distance of D40 is 2.56 times the stopping distance of D25.
Given that are two initial velocities: 40 mph and 25 mph, with which the car's stopping distance is D40 and D25.
The final velocity for both is 0 mph (as the car to a stops).
We need to compare the stopping distance D40 to the stopping distance D25.
Use the third equation of motion for both cases to get the comparison.
The equation is given by:
[tex]v^2 - u^2 = 2as.[/tex]
Case 1)
[tex]0 - 40^2 = 2a(D40)[/tex]
Case 2)
[tex]0 - 25^2 = 2a(D25)[/tex]
Comparing the obtained expressions.
[tex]\frac{40^2}{25^2} = \frac{2a(D40)}{2a(D25)}[/tex]
[tex]2.56 = \frac{D40}{D25}[/tex]
[tex]2.565 \times D25 = D40[/tex]
Hence the stopping distance of D40 is 2.56 times the stopping distance of D25.
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Jan creative a pattern using the rule ""add 3."" Bill creates a pattern using the rule ""add 6."" Which describes the relationship between Jan sand Bill’s patterns?
Jan created a pattern using the rule "add 3," and Bill created a pattern using the rule "add 6." In arithmetic sequences, the nth term is given by the formula a + (n-1)d, where a is the first term and d is the common difference between any two consecutive terms.
The common difference is the difference between each pair of consecutive terms in a sequence. Because Jan's pattern has a common difference of 3, the nth term in her sequence is given by a + (n-1)3, and because Bill's pattern has a common difference of 6, the nth term in his sequence is given by a + (n-1)6.The nth term in both Jan and Bill's sequence is a linear function of n. The slope of a line is the common difference between any two consecutive terms in a sequence.
As a result, the slopes of Jan and Bill's patterns are 3 and 6, respectively. In general, two patterns are in a linear relationship if their slopes are constant multiples of one another. In this case, Bill's pattern is the result of multiplying Jan's pattern by a factor of 2. As a result, their patterns have a linear relationship. Answer: The patterns have a linear relationship because Bill's pattern is the result of multiplying Jan's pattern by a factor of 2.
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Finding an angle measure given a triangle and parallel lines
Answer:
We have congruent alternate interior angles.
39° + 96° + x° = 180°
135° + x° = 180°
x = 45
can you help me with math
Answer:
B
Step-by-step explanation:
203.95 is equal to 4 of the tickets plus 11.95
You can write this as
203.95=4(price of ticket)+11.95
4(price of ticket)=192
Divide by 4
The price of a ticket is 48.
The equation would be 11.95+48t because its 48 times the amount of ticket plus the service fee.
a net for the gift box.
14 m
15.65 m
15.65 m
I
I
7m
15 m
1
14 m
what do u need help with
Pincushion circumference=8
If circumference of circle is 8 units then the radius of circle is 1.27 units
The circumference of the circle is 8 units.
We have to find the radius of the circle.
The formula for circumference of cirlce is two times of pi and radius.
Circumference = 2πr.
Where r is the radius of the circle.
The value of radius we have to find.
The circumference is 8 units.
Plug in the values of circumference to find r:
8=2×3.14 r
When 2 is multiplied with three point one four we get six point two eight.
8=6.28 r
Divide both sides by 6.28:
r = 8/6.28
When eight is divided by six point two eight we get one point two seven.
r=1.27 units
Hence, the radius of circle is 1.27 units when circumference is 8 units.
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Complete question
If circumference of circle is 8 units then find the radius of circle?
Which one of the following statements is true? A. If 4 3 h = 12 , then h = 16 . B. If − 2 5 r = − 20 , then r = − 50 . C. If 1 2 = − 3 7 q , then q = − 1 1 6 . D. If 3 8 = 24 c , then c = 9 .
The only True statement is B: If −2/5r = −20, then r = −50
We can solve each equation to determine which statement is true.
A. If 4/3h = 12, then h = 16.
To solve for h, we can multiply both sides of the equation by 3/4:
4/3h * 3/4 = 12 * 3/4
h = 9
Therefore, statement A is false.
B. If −2/5r = −20, then r = −50.
To solve for r, we can multiply both sides of the equation by -5/2:
-2/5r * -5/2 = -20 * -5/2
r = 50
Therefore, statement B is true.
C. If 1/2 = −3/7q, then q = −116.
To solve for q, we can multiply both sides of the equation by -7/3:
1/2 * -7/3 = -3/7q * -7/3
q = 21/3 = 7
Therefore, statement C is false.
D. If 3/8 = 24c, then c = 9.
To solve for c, we can divide both sides of the equation by 24 * 8/3:
3/8 * 3/24 * 8/3 = 24c * 3/24 * 8/3
c = 1/3 * 8
c = 8/3
Therefore, statement D is false.
Therefore, the only true statement is B: If −2/5r = −20, then r = −50.
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