To find the rate of change of the volume when the radius is 12 inches, we can use the formula for the volume of a sphere:
V = (4/3) * π * [tex]r^3[/tex]
To find the rate of change of the volume, we need to take the derivative of the volume function with respect to time (t) using the chain rule. The derivative of the volume function with respect to time will give us the rate of change of the volume.
dV/dt = (dV/dr) * (dr/dt)
where dV/dt is the rate of change of the volume, dV/dr is the derivative of the volume with respect to the radius, and dr/dt is the rate of change of the radius.
Given that the radius is increasing at a rate of 5 inches per minute (dr/dt = 5), we can substitute this value into the formula.
Now, let's calculate the derivative of the volume with respect to the radius (dV/dr):
dV/dr = d/dt [(4/3) * π[tex]* r^3[/tex]] = (4/3) * π * [tex]3r^2[/tex]= 4π[tex]r^2[/tex]
Substituting the values into the formula for the rate of change of the volume:
dV/dt = (dV/dr) * (dr/dt) = 4π[tex]r^2[/tex]* 5 = 20π[tex]r^2[/tex]
When the radius is 12 inches (r = 12), we can plug this value into the formula to find the rate of change of the volume:
dV/dt = 20π[tex]r^2[/tex] = 20π(1[tex]2^2[/tex]) = 20π * 144 = 2880π
Therefore, when the radius is 12 inches, the rate of change of the volume is 2880π cubic inches per minute.
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Angela purchased a car using a simple interest loan. The loan had an interest rate of 5% and was for three years. Angela paid $450 in interest. The principal amount of the loan was for $
Answer:
$3000
Step-by-step explanation:
Given data
Rate=5%
Time=3 years
Simple interest= $450
We know that the expression for simple interest is
SI=PRT/100
Substitute
450=P*5*3/100
cross multiply
P*15= 45000
Divide both sides by 15
P= 45000/15
P=$3000
Hence the principal amount is $3000
12. Use Russian Peasant Multiplication to perform the following problem. Explicitly show your addition. 49 x 65
Using the Russian Peasant Multiplication, 49 x 65 is 3,185.
What is the Russian Peasant Multiplication?The Russian Peasant Multiplication method converts the problem into binary (base 2) multiplication from base 10 by halving the numbers on the first column repeatedly till the second number doesn't become 1 and doubling the numbers on the second column.
Then, add up the numbers in the second column that correspond to odd numbers in the first column to get the result.
49 65
÷ 2 24 130 x 2
12 260
6 520
3 1,040
1 2,080
Add:
65, because we ignored 1 when we divided 49 by 2
1,040, because we ignored 1 when we divided 3 by 2
2,080
= 3,185
Check:
49 x 65 = 3,185
Based on the Russian Peasant Multiplication method, the product of 49 x 65 is 3,185.
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A variable needs to be eliminated to solve the system of equations below. Choose the
correct first step
— 5х + бу = 41
7x - 6y = -43
Answer:
6y-6y, cancel it out to find x first.
-5x+6y=41
7x-6y=-43
2x=-2
Step-by-step explanation:
i hope this helps :)
Answer:
Step-by-step explanation:
The first step is to add the 2 equations This will eliminate the y terms
( + 6y + -6y = 0).
So you are then left with 2x = -2
A cube. Point B is the top right point of the top face. Point A is the bottom left point of the bottom face and point C is the top right point of the bottom face. Diagonals are drawn from B to A and from A to C. Side B C is 10 inches long, and Side A B is StartRoot 300 EndRoot inches long. What is the length of Side A C? 14 in. StartRoot 200 EndRoot in. StartRoot 290 EndRoot in. 20 in.
Answer:
the answer is b
Step-by-step explanation:
i just did the assignment
Answer:
b
Step-by-step explanation:
Genoude towing test at the 0.10 vel tance by temperative contested to Put Assure at the comptes were obland de condendy ang simple random samping Test whether PPSample data are 30, 256, 38, 31 (a) Determine the rulanternative hypotheses. Choose the correct answer below OAH, versus H P = 0 OCH PD, versus HDD) OBH PP, VOUS HP) OD HIPP versus HDP (b) The fest statistics found to two decimal places as needed (c) The P values Round to three decimal places as needed) Test meil hypothesis. Choose the correct condusion below OA Roth null hypothesis because there is not suit evidence to conclude that, (b) The test statistic Zo is (Round to two decimal places as needed.) (c) The P-value is (Round to three decimal places as needed.) Test the null hypothesis. Choose the correct conclusion below. O A. Reject the null hypothesis because there is not sufficient evidence to conclude that p, p2. OC. Do not reject the null hypothesis because there is not sufficient evidence to conclude that p, #P2. OD. Reject the null hypothesis because there is sufficient evidence to conclude that p, p2.
The given problem involves hypothesis testing in statistics. The correct conclusion will depend on whether the null hypothesis is rejected or not.
(a) The null and alternative hypotheses can be determined as follows: OAH (One-sample test for proportion): P = 0 (H0) versus H P ≠ 0 (HA).
(b) The test statistic, denoted as Zo, needs to be computed using the given sample data.
(c) To determine the P-value, the calculated test statistic is compared to the appropriate distribution (e.g., standard normal distribution) based on the chosen significance level.
(d) Based on the P-value and the predetermined significance level, the null hypothesis is either rejected or not rejected. If the P-value is less than the significance level, the null hypothesis is rejected. Otherwise, the null hypothesis is not rejected.
The conclusion will depend on whether the null hypothesis is rejected or not and should be stated accordingly.
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Shana is doing a craft project
using yarn and sticks. She
has 3 green yam pieces and
7 blue yam pieces. She has 3
times as many sticks as yarn
pieces. Write an expression.
Plz help
Answer:
3(5 + 7)
Step-by-step explanation:
Shana is carrying our a craft project
She is making use of yarns and stuck
She has three green yarn pieces and seven blue yarn pieces
She has three times as many yarn pieces
Therefore the expression can be represented as follows
3(5 + 7)
A cylindrical soup can has a diameter of 3 in. and is 6.2 in. tall. Find the volume of the can.
Answer:
b
Step-by-step explanation:
3. Given a normal distribution of test scores from that same statistics class where the mean is 80 and the standard deviation is 7.5, determine BY HAND what percent of the scores were 78 or less. Also, what percent of scores were 85 or better?
The percent of the scores that were 85 or better is 25.14%.
The percent of the scores that were 78 or less is 39.25%.
The percent of the scores that were 85 or better is 25.14%.
Given a normal distribution of test scores from that same statistics class where the mean is 80 and the standard deviation is 7.5, we are to determine what percent of the scores were 78 or less and what percent of the scores were 85 or better.
Below are the steps to determine what percent of the scores were 78 or less.
Step 1: Determine the Z-score
To determine the Z-score, we use the formula
Z = (X - μ) / σ
Where X is the score, μ is the mean and σ is the standard deviation
Z = (78 - 80) / 7.5
Z = -0.27
Step 2: Use the Z-table to determine the percentage
Using the Z-table, we can find the percentage of scores that lie below Z = -0.27 which is 0.3925 or 39.25%
Therefore, the percent of the scores that were 78 or less is 39.25%.
Below are the steps to determine what percent of the scores were 85 or better.
Step 1: Determine the Z-score
To determine the Z-score, we use the formula Z = (X - μ) / σ
Where X is the score, μ is the mean and σ is the standard deviation
Z = (85 - 80) / 7.5
Z = 0.67
Step 2: Use the Z-table to determine the percentage
Using the Z-table, we can find the percentage of scores that lie above Z = 0.67
Which is 0.2514 or 25.14%
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can someone answer this one too?
Answer:
1
Step-by-step explanation:
put x = 3
8(1/2³) = 8/8 = 1
Please help me with the question
Answer:
the tree is 8ft long
Step-by-step explanation:
beans
The equation below has infinitely many solutions.
-3 (x – 3) – 1 = ax + b
True
False
Answer:
False
Step-by-step explanation:
A recent Gallup poll found large differences in the type of household chores done by wives and husbands.1 Wives still do most of the indoor household chores. Husbands still tend to do more work outside and with family cars. The simulated data in this problem are based on the results of this poll.
Suppose we wish to demonstrate that there is a difference between the proportions of wives and husbands who do laundry at home. From a random sample of 66 randomly selected wives, we observe 44 who do laundry at home. From a random sample of 46 husbands, we observe 18 who do laundry at home.
Test the claim that the proportion of wives, p1 , who do laundry at home is different from the proportion of husbands, p2 , who do laundry at home. Use a 1% significance level.
Answer : There is enough evidence to suggest that a higher proportion of wives do laundry at home compared to the proportion of husbands who do laundry at home.
Explanation:
The null hypothesis is that the proportion of wives and husbands who do laundry at home is the same. The alternative hypothesis is that the proportion of wives and husbands who do laundry at home is different.
Mathematically, null and alternative hypotheses are given below. H0: P1 - P2 = 0H1: P1 - P2 ≠ 0 where P1 is the proportion of wives who do laundry at home and P2 is the proportion of husbands who do laundry at home. Let α = 0.01 be the significance level. Therefore, α/2 = 0.005 and the Zα/2 value for the two-tailed test is ±2.58.
The point estimate of the difference in the proportions is:Point estimate, PE = P1 - P2 = (44/66) - (18/46) = 0.6667 - 0.3913 = 0.2754
The standard error of the difference in the proportions is: SE = sqrt{(P1(1 - P1)/n1) + (P2(1 - P2)/n2)} = sqrt{[(44/66)(22/66)/65] + [(18/46)(28/46)/45]} = 0.1033
The test statistic is given by:Z = (PE - 0) / SE = 0.2754 / 0.1033 = 2.6641
Since the absolute value of the test statistic is greater than the Zα/2 value, we reject the null hypothesis and conclude that the proportion of wives who do laundry at home is different from the proportion of husbands who do laundry at home at a 1% significance level. Therefore, there is enough evidence to suggest that a higher proportion of wives do laundry at home compared to the proportion of husbands who do laundry at home.
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Number of participants = 274 Number of groups = 5 SSD = 1 SSW = 192 What is the mean squares within?
The mean squares within is 0.7130044843.
The formula to calculate the mean squares within is given below:
Mean squares within (MSW) = SSW / (n - k), where n = Total number of observations, k = Total number of groups.
Here, Number of participants = 274, Number of groups = 5, SSD = 1, SSW = 192.
Now, the value of n and k can be calculated using the formula given below:
n = Number of participants = 274, k = Number of groups = 5.
Let's substitute the values in the formula of mean squares within:
Mean squares within (MSW) = SSW / (n - k)
MSW = 192 / (274 - 5)
MSW = 192 / 269
MSW = 0.7130044843
Hence, the mean squares within is 0.7130044843.
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Please help Sammy buys light bulbs in pack of 8 for $20. The shipping cost is $10 regardless of the number of packs bought. Billy has only $120 to spend.
Answer:
5
Step-by-step explanation:
Los primeros días de enero, el representante del mercado recibió cierta cantidad de di-
nero, hizo una operación y se dio cuenta que habían pagado 15 personas. ¿Cómo puede
saber la cantidad recibida?
15
425
El ejercicio completo con las opciones de respuesta está a continuación:
Los primeros días de enero el representante del mercado recibió cierta cantidad de dinero,hizo una operación y se dio cuenta que habían pagado 15 personas,cómo puede saber la cantidad recibida?
a.Multiplicando el dividendo por el divisor
b. Sumando el dividendo con el cociente y el residuo
c.Multiplicando el divisor por el cociente y sumando el residuo
d.Multiplicando el dividendo por el cociente y sumando el residuo
Answer:
La opción c es la respuesta correcta
Step-by-step explanation:
El valor de 15 corresponde al cociente es decir al total de personas que pagaron;el ejercicio nos da el valor del divisor que es 425 ; para saber cual es la cantidad exacta recibida debemos multiplicar el divisor por el cociente y si hay residuo sumarlo; el ejercicio nos queda de la siguiente manera:
425 x 15 = 6.375 (la cantidad recibida fue de 6.375)
[tex]\frac{6375}{425}[/tex] = 15 (comprobación de la división para obtener el cociente con valor de 15)
If the unit rate is constant, what are the total sales for 12 pounds of asparagus?
20 Points!!! Pls help me out with this, and please no links.
Answer:
7
Step-by-step explanation:
Answer: your answer is B
Step-by-step explanation:
Im so sorry if im wrong, have a good day!
Gardening Jessica is planting a garden. It has the shape of a right triangle. She wants 3
plants for each square meter of area. How many plants does she want in the garden?
Answer:
28
Step-by-step explanation:
plants in the garden = area of the garden / number of plants per square meter
the garden is in the shape of a triangle
A triangle is a three-sided polygon with three edges and three vertices. the sum of angles in a triangle is 180 degrees
Area of a triangle = 1/2 x base x height
(1/2) x 24 x 7 = 84 meters^2
plants in the garden = 84/3 = 28
Priya has planted a garden shaped like a right triangle. One leg of the triangle is 5 meters long, and the angle formed by it and the hypotenuse is 50°. If Priya wants to build a fence around her garden, how many meters of fence will she need? Round your answer to the nearest meter.
Answer:
19
Step-by-step explanation:
:)
The amount of fence that Priya would need (in meters) is 19 meters approximately.
What are the six trigonometric ratios?Trigonometric ratios for a right angled triangle are from the perspective of a particular non-right angle.
In a right angled triangle, two such angles are there which are not right angled(not of 90 degrees).
The slant side is called hypotenuse.
From the considered angle, the side opposite to it is called perpendicular, and the remaining side will be called base.
From that angle (suppose its measure is θ),
[tex]\sin(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of Hypotenuse}}\\\cos(\theta) = \dfrac{\text{Length of Base }}{\text{Length of Hypotenuse}}\\\\\tan(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of base}}\\\\\cot(\theta) = \dfrac{\text{Length of base}}{\text{Length of perpendicular}}\\\\\sec(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of base}}\\\\\csc(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of perpendicular}}\\[/tex]
For this case, we've to find the length of the fencing she needs to cover her garden.
Length of fencing needed = Perimeter of the considered right triangle = sum of its sides' lengths
Using the image attached below, from the perspective of angle A which is of 50 degrees from inside, we get:
|AB| = base length = 5 meters (given)|BC| = perpendicular length = p meters (say)|AC| = hypotenuse length = h meters (say)Using tangent ratio,[tex]\tan(m\angle A) = \tan(50^\circ) = \dfrac{p}{5}\\\\p = 5 \tan(50^\circ) \approx 5.96 \: \rm m[/tex]
Using sin ratio,[tex]\sin(m\angle A) = \sin(50^\circ) = \dfrac{p}{h}\\\\h = \dfrac{p}{\sin(50^\circ)} \approx \dfrac{5.96}{\sin(50^\circ)} \approx 7.78 \: \rm m[/tex]
Thus, perimeter of the triangle = 5 + p + h ≈ 18.74 m ≈ 19 m
Thus, the amount of fence that Priya would need (in meters) is 19 meters approximately.
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Arrange in ascending order 19,654 67,923 67,397 91,945
Answer:
19654,67397,67923,91945
Step-by-step explanation:
Ascending order mean arrange the number from smaller value to bigger value
Answer:
19654,67397,67923,91945
plz mark me as brainliest
Michelle counted 40 green cars and 20 silver cars in the parking lot. If
the number of green cars stays the same, how many more silver cars
would need to be added so the ratio of green cars to silver cars is 1 to 3?
Answer:
100 more silver cars
Step-by-step explanation:
Right now the ratio of silver cars to green cars is 20:40 or 1:2, but if you add a hundred more silvers cars the ratio would 120:40 or 3:1.
If You Have NO Explanation Than Don't Answer.
Answer: Option C
Step-by-step explanation:
C because 6+1=1+1+1+1+1+1+1
Answer:
C
Step-by-step explanation:
We want to find which model shows two equal expressions. We know that the value of x is 6. That being said, on the left side of each equation, plug in 6 for every "x" you see. Then, add the values on both sides. If they're equal, that's your answer.
For example:
In choice A, we see two x's, so we plug in 6 for them both and add them. That's 12 on the left side. On the other side of the equation, we have 7 "1" boxes, which simply just means add them, so that's 7 on the other side. 12 does not equal 7, therefore A is not the answer. However, for choice C, we are given x, which we know is 6, and a "1" box, which simply means 6 + 1, which is 7. On the other side of this equation, we have 7 "1" boxes, so that's 7. The equation becomes 7 = 7, which is true, so that is our answer.
What is the slope of the line through the points (-2, -1) and (4, 3)?
2/3
2/5
5/2
Answer:
The slope is A. 2/3
HOPE THIS HELPS!!!!
evaluate each of the following
205 x 195
Answer:
39,975
Step-by-step explanation:
There u go
Answer:
39,975
Step-by-step explanation:
Caculater
tomen puntos
toy aburridoooo
Answer:
aww thank you
pls mark brainliest
Step-by-step explanation:
Let f(x) = 9+√2-3. Find f(x).
The value of the function f(x) = 9 + √2 - 3 is a constant and can be simplified as f(x) = 6 + √2.
The given function f(x) = 9 + √2 - 3 is an expression that does not depend on the variable x. Therefore, it represents a constant value.
To evaluate the function, we can simplify the expression by combining like terms:
f(x) = 9 + √2 - 3
Combining the constants 9 and -3, we have:
f(x) = 6 + √2
Thus, the value of the function f(x) is a constant, which is 6 + √2.
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Find the radius of convergence, R, of the series. Σ (-7) Vn 00 ya n=1 R= Find the interval, I, of convergence of the series.
The series converges for x values within the interval (-29/7, -27/7), and the radius of convergence is 1/7.
How do we calculate?We apply the ratio test to our series:[tex]|7^(^n^+^1^)[/tex] (x + 4)[tex]^(^n^+^1^)^) / √(n+1)] / [( (x +7^n 4))^n\sqrtn]|[/tex]
We take the limit as n approaches infinity:lim(n→∞) |[tex]7(x + 4) / √(n+1)| = |7(x + 4)|[/tex]
For the series to converge, |7(x + 4)| must be less than [tex]1.|7(x + 4)| < 1-1 < 7(x + 4) < 1-1/7 < x + 4 < 1/7-29/7 < x < -27/7[/tex]
In conclusion, the interval of convergence is (-29/7, -27/7), and the radius of convergence is the half-length of the interval, which is 1/7.
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PLEASE HELP ME OUT! QUICK POINTS FOR YOU!
All information needed can be found in the image below
Thank you in advance.
Answer:
3.14 units squared
Step-by-step explanation:
A = pi r^2
A = pi (1) ^2
A = pi = 3.14
(Radius = diameter / 2)
Triangle ABC below has a right angle C and a height CD. (A height in a triangle connects its vertex and the opposite side, and is perpendicular to that side.)
If AC is 3 units long and BC is 4 units long, what is the length of AD?
can you show the picture please?
Two sides of a triangle measure 5
units and 3 units. The perimeter
of the triangle is 12 units. What is
the measure of the third side?
Answer:
4 units
Step-by-step explanation:
5+3=8
12-8=4