How many cubes with side lengths of 1/4 cm does it take to fill the prism?

[tex]9^{2}+a^{2}=15^{2} \\144=a^{2}\\a=12[/tex]

Answer:

a) 0.0537 = 5.37% probability that the mean number of minutes of daily activity of the 6 mildly obese people exceeds 420 minutes

b) 0.9871 = 98.71% probability that the mean number of minutes of daily activity of the 6 lean people exceeds 420 minutes

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mildly obese:

Mean 376 minutes and standard deviation 67 minutes, which means that [tex]\mu = 376, \sigma = 67[/tex]

Sample of 6

This means that [tex]n = 6, s = \frac{67}{\sqrt{6}} = 27.35[/tex]

Lean

Mean 520 minutes and standard deviation 110 minutes, which means that [tex]\mu = 520, \sigma = 110[/tex]

Sample of 6

[tex]n = 6, s = \frac{110}{\sqrt{6}} = 44.91[/tex]

A) What is the probability that the mean number of minutes of daily activity of the 6 mildly obese people exceeds 420 minutes?

This is 1 subtracted by the pvalue of Z when X = 420, using the mean and standard deviation for mildly obese people. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{420 - 376}{27.35}[/tex]

[tex]Z = 1.61[/tex]

[tex]Z = 1.61[/tex] has a pvalue of 0.9463

1 - 0.9463 = 0.0537

0.0537 = 5.37% probability that the mean number of minutes of daily activity of the 6 mildly obese people exceeds 420 minutes.

B) What is the probability that the mean number of minutes of daily activity of the 6 lean people exceeds 420 minutes?

This is 1 subtracted by the pvalue of Z when X = 420, using the mean and standard deviation for lean people. So

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{420 - 520}{44.91}[/tex]

[tex]Z = -2.23[/tex]

[tex]Z = -2.23[/tex] has a pvalue of 0.0129

1 - 0.0129 = 0.9871

0.9871 = 98.71% probability that the mean number of minutes of daily activity of the 6 lean people exceeds 420 minutes

Answer:

23 days

Step-by-step explanation:

We would first determine the volume of the tank. This gives information on the amount of water it can carry

WE divide the volume by the amount of water the town uses per day

Volume of a sphere = [tex]\frac{4}{3}[/tex]πr³

n = 3.14

r == radius

radius = 1/2 x diameter

radius = 26/2 = 13 meters

volume = (4/3) x (3.14) x (13^3) = 9198.106667 m^3

How long the tank would last = 9198.106667 / 400 = 23 days

Given:

The two points are P (-1,0) and S (-1,7).

To find:

Whether the line PS is vertical, horizontal or neither.

Solution:

We have, two points P (-1,0) and S (-1,7).

Slope of the line PS is:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\dfrac{7-0}{-1-(-1)}[/tex]

[tex]m=\dfrac{7}{0}[/tex]

[tex]m=\infty[/tex]

We know that the slope of a vertical line is [tex]\infty[/tex].

Since the slope of the line PS is [tex]\infty[/tex], therefore PS is a vertical line.

Answer:

50% because there are only 2 colors

Step-by-step explanation:

Answer:50%

Step-by-step explanation:

The probability is 50% or 1/2 because there's only 2 types of jelly bean in the jar unless either one has more amount than the other's

Answer:

Hi! Just for your safety do not click on the link in the other answer!

The answer to your questions is (5,0) Or another way to express it is 5.

Step-by-step explanation:

To find the x-intercept substitute 0 in for y and solve for x.

※※※※※※※※※※※※※※

⁅Brainliest is greatly appreciated!⁆

- Brooklynn Deka

Hope this helps!!

Answer:

$ 56 .0000

Step-by-step explanation:

.......... ....... ....... ........ .....

Answer:

-2

Step-by-step explanation:

Plug y=0 into the equation and solve the resulting equation 0=3x+6 for x

Answer:

No, Andre is not correct.

Step-by-step explanation:

I believe Andre is not correct because each 1 on the left balances with a 1 on the right. So taking away the two 1s on the left only leaves the hanger balanced if two 1s are removed on the right. This leaves on the left and three 1s on the right, so x=3. This is like x+2=5 if you subtract 2 from the x side then you get x=3. Hope this helps!

Answer:

Step-by-step explanation:

radius = 9.3 units

Diameter = 2 × radius

= 2 × 9.3

= 18.6 units

Answer:

6.26 automobile registrations

Step-by-step explanation:

Given

[tex]y=0.3949x-778.7[/tex] --- [function, missing from the question]

Required

The expected number in 1988

To do this, we substitute 1988 for x in: [tex]y=0.3949x-778.7[/tex]

[tex]y = 0.3949 * 1988 - 778.8[/tex]

[tex]y = 785.0612 - 778.8[/tex]

[tex]y = 6.2612[/tex]

[tex]y \approx 6.26[/tex] --- approximated to the nearest hundredth

Answer:

R = 3.813% per year.

Step-by-step explanation:

To find out how many of the 39 practice trials would be faster than 62 seconds, we need to calculate the proportion of trials that fall within the range of more than 62 seconds.

We can use the z-score formula to standardize the values and then use the standard normal distribution table (also known as the z-table) to find the proportion.

The z-score formula is:

z = (x - μ) / σ

Where:

x = value (62 seconds)

μ = mean (61 seconds)

σ = standard deviation (1.5 seconds)

Calculating the z-score:

z = (62 - 61) / 1.5

z ≈ 0.6667

Now, we need to find the proportion of values greater than 0.6667 in the standard normal distribution table.

Looking up the z-score of 0.6667 in the table, we find the corresponding proportion is approximately 0.7461.

To find the number of trials faster than 62 seconds, we multiply the proportion by the total number of trials:

Number of trials = Proportion * Total number of trials

Number of trials = 0.7461 * 39

Number of trials ≈ 29.08

Rounding to the nearest whole number, approximately 29 of the 39 practice trials would be faster than 62 seconds.

#SPJ1

Answer:

OOO

Step-by-step explanation:

Answer:

x=1, y=-5

Step-by-step explanation:

4(1)+2y=-6

2y=-10

y=-5

or

-3x-2(-5)=7

-3x=-3

x=1

Hope this helps!

Answer:

2r + 6 = 16

r = 5

Answer:

23 nights

Step-by-step explanation:

What does "Proportional" Mean? Proportional means that the ratio is the same throughout.

Step One: First, to set this up, we will put the 16 centimeters for the numerator and then the 8 nights on the bottom. The bottom is the independent variable because we can't physically change the number of nights. 16/8.

Step Two: Now, we have to scale this up to 46. Because the 46 is the centimeters, we have to do 46/16 to see how much we need to scale it by: 46/16= 2.875.

Step Three: Lastly, we can multiply 8 by 2.875 to see how many nights it took: 8 times 2.875 is 23 nights.  

Answer:

The cost of labor per hour is $105.

The expression is 4x + 77 = 497

Step-by-step explanation:

The expression is 4x + 77 = 497, where 4x represents the cost of labor per hour, 77 is the cost of the parts, and 497 is the total.

4x + 77 = 497

4x + 77 - 77 = 497 -77

4x = 420

4x/4=420/4

x = 105

Answer:

0.16

Step-by-step explanation:

rewrite 16 percent in the terms of per 100 or over 100.

16% = 16 over 100 or,

16% = 16/100

16 over 100 is the same as 16 divided by 100. So completeing the division we get:

16 ÷ 100 = 0.16

Thus, the answer is 0.16

hope this helps you :)

Answer:

A

Step-by-step explanation:

Answer:

(-5, -1)

Step-by-step explanation:

Moving towards the right makes a number more positive for x and moving down makes numbers more negative for y

Answer:

-9

Step-by-step explanation:

Hello! So, we need to find log_6 1/6. The definition of log is the power that you need to multiply that number by to get the next number. 1/6=6^-1, so our equation would be:

-1=x/9, so x is clearly -9.

Have a nice day.

~cloud

Answer:

You are correct

Step-by-step explanation:

[tex]log_{6} \frac{1}{6} =\frac{x}{9}[/tex]

[tex]log_{6} 6^{-1} =\frac{x}{9}[/tex]

[tex](-1)log_{6}6=\frac{x}{9}[/tex]

[tex]-1=x/9[/tex]

[tex]-9=x[/tex]

Hope that helps :)

Answer:

136

Step-by-step explanation:

The formula  to find the surface area is 2(wl+hl+hw)

W= 3

H= 8

L= 4

wl= 3*4 = 12

hl= 8*4= 32

hw= 8*3 = 24

12+32+24= 68

68 * 2 = 136

9514 1404 393

Answer:

  $3633.96

Step-by-step explanation:

The monthly payment is given by the amortization formula:

  A = P(r/12)/(1 -(1 +r/12)^(-12t))

monthly payment for principal P at annual rate r for t years.

  A = $672096(0.04/12)/(1 -(1 +0.04/12)^(-12·24)) = $3633.96

The monthly payment for the mortgage is $3633.96.

Answer:

f=5/8x^2+-3/2Divide both sides by two

Step-by-step explanation:

Hope that helped

Answer:

The null hypothesis will be that the average annual donor income is less or equal to $ 100,000

Step-by-step explanation:

The claim is mostly treated as alternate hypothesis .

In this question the claim is given as the average annual donor income has increased therefore it is written as

Ha: u > 100,000

The null hypothesis is reverse of the alternate hypothesis

H0: u ≤ 100,000

The null hypothesis will be that the average annual donor income is less or equal to $ 100,000