The base of a rectangular box measures 3 feet by 4 feet. What is the height in feet of the box if the volume is 48 cubic feet

Answer:

7

Step-by-step explanation:

THe Triangle Inequality Theorem states that the sum of the two least sides of a triangle must be greater than the third side. In this case, 2 and 6 are less than 10, 3 and 6 are less than 10, 6 and 10 are greater than 16, so the only number left is 7. The sum of seven and six is greater than ten so seven would be the correct answer.

Question:

Triangle D E F. Side D F is 6 inches, side F E is 10 inches, and side E D is question mark.

Which could be a possible length of side DE?

2 in.

3 in.

7 in.

Answer:

C.) 7 in.

Step-by-step explanation:

To calculate the perimeter of a triangle, add the length of its sides. For example, if a triangle has sides a, b, and c, then the perimeter of that triangle will be P = a + b + c. Remember the formula for finding the perimeter of a triangle. For a triangle with sides a, b and c, the perimeter P is defined as: P = a + b + c. What this formula means in simpler terms is that to find the perimeter of a triangle, you just add together the lengths of each of its 3 sides. Since all the three sides of the triangle are of equal length, we can find the perimeter by multiplying the length of each side by 3. 20 + 20 + 20 = 3 × 20 = 60 cm. Thus, the perimeter of an equilateral triangle is 3 times the length of each side. Area of a two-dimensional shape is the space occupied by the shape.

Have a Nice day! <3

Answer:

1/5 - 60 or b

Step-by-step explanation:

The expression that shows 20% of 60 is 1/5 * 60

The expression is given as:

20% of 60

Express of as *

20% * 60

Express the percentage as fraction

20/100 * 60

Simplify the fraction

1/5 * 60

Hence, the expression that shows 20% of 60 is 1/5 * 60

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Answer:

[tex]\displaystyle \frac{dy}{dx} = \frac{66}{x}[/tex]

General Formulas and Concepts:

Calculus

Differentiation

Derivative Property [Multiplied Constant]:                                                           [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]

Derivative Property [Addition/Subtraction]:                                                         [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle y = 66 \ln x + 135[/tex]

Step 2: Differentiate

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

The measure of the portion of Earth that can be seen from an airplane 5.7 miles above the ground is approximately 0.163 degrees, when rounded to the nearest tenth. This is found using the formula for the angle subtended by an arc, and then converting from radians to degrees.

To solve this problem, we can use the properties of a circle, since the Earth is approximately spherical in shape. The formula to calculate the angle subtended by an arc (BD⌢) on the Earth's surface is as follows: θ = 2 * arcsin((distance_to_object)/(2 * radius_of_earth)).

So inserting the given values:

We get: θ = 2 * arcsin((5.7)/(2 * 4000)). This will give you an answer in radians, to convert this to degrees multiply by 180/π. In this case, the answer is approximately 0.163 degrees, rounded to the nearest tenth.

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Answer:

The histogram of the sample incomes will follow the normal curve.

Step-by-step explanation:

According to the Central Limit Theorem if we have an unknown population with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.

In this case the researches wants to determine the monthly gross incomes of drivers for a ride sharing company.

He selects a sample of n = 200 drivers and ask them their monthly salary.

As the sample selected is quite large, i.e. n = 200 > 30, the central limit theorem can be applied to approximate the sampling distribution of sample mean by the Normal distribution.

Thus, the histogram of the sample incomes will follow the normal curve.

Answer:

95.44% probability that a sample of 100 steady smokers spend between $19 and $21

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 normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, 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.

In this problem, we have that:

[tex]\mu = 20, \sigma = 5, n = 100, s = \frac{5}{\sqrt{100}} = 0.5[/tex]

What is the probability that a sample of 100 steady smokers spend between $19 and $21

This is the pvalue of Z when X = 21 subtracted by the pvalue of Z when X = 19. So

X = 21

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

By the Central Limit Theorem

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

[tex]Z = \frac{21 - 20}{0.5}[/tex]

[tex]Z = 2[/tex]

[tex]Z = 2[/tex] has a pvalue of 0.9772

X = 19

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

[tex]Z = \frac{19 - 20}{0.5}[/tex]

[tex]Z = -2[/tex]

[tex]Z = -2[/tex] has a pvalue of 0.0228

0.9772 - 0.0228 = 0.9544

95.44% probability that a sample of 100 steady smokers spend between $19 and $21

To find the probability that a sample of 100 steady smokers spend between $19 and $21, calculate the Z-score and use a standard normal distribution table or calculator. The probability is approximately 0.3413.

To find the probability that a sample of 100 steady smokers spend between $19 and $21, we can use the Z-score formula. The Z-score is calculated as the difference between the sample mean and the desired value (in this case, $20), divided by the population standard deviation, multiplied by the square root of the sample size.

Z = (x - μ) / (σ / √n)

Plugging in the values we have:

Z = (21 - 20) / (5 / √100) = 1

We can then use a standard normal distribution table or a calculator to find the probability associated with a Z-score of 1. The probability of obtaining a Z-score of 1 or less is approximately 0.8413. Since we want the probability between $19 and $21, we subtract the probability of getting a Z-score of less than 1 from the probability of getting a Z-score of less than or equal to 0. This gives us:

Probability = 0.8413 - 0.5000 = 0.3413

Answer:

186

Step-by-step explanation:

definition: a_n = a_1 + f × (n-1)

Common difference is 11

The sum of all numbers up through the 17th: 1666

Answer: 824

Step-by-step explanation:

This is problem on progression.

Considering the series/ sequence,

10, 21, 32, 43, 54, ........

To find the 75th term, we first of all find which of the sequence is it, is it, Arithmetic or Geometric sequence .

Now fro this, it is an AP sequence because, when the first term us subtracted from the second term and the common difference added to the second term it produces the third term and so on, . Haven't gotten this, we now apply the formula for finding the number if terms in an AP.

Tn = a + (n - 1 )d, where n = number of terms we are computing for = 75, a = first term = 10, and d = 21 - 10 = 11.

Now substitute for those values in the formula above

T75 = 10 + ( 75 - 1 )11

= 10 + 74 × 11

= 10 + 814

= 824.

Answer:

The standard error of the mean (SE) is of 0.326lb.

Step-by-step explanation:

The standard error of the mean is given by the following formula:

[tex]SE = \frac{s}{\sqrt{n}}[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

In this problem, we have that:

[tex]s = 4.3, n = 174[/tex]

Then

[tex]SE = \frac{s}{\sqrt{n}} = \frac{4.3}{\sqrt{174}} = 0.326[/tex]

The standard error of the mean (SE) is of 0.326lb.

Answer:

6

Step-by-step explanation:

The line in the middle of the box is the median

Answer:

$1.50 per can

Step-by-step explanation:

6/4 = 1.5

to check your answer, do 1.50*4, and you get $6

hope this helps :)

Answer:

The unit rate is $1.50 per can.

Step-by-step explanation:

Price: $6

Number of Cans Purchased at This Price: 4

$6/4 cans=$1.50 per can

Answer: 54 stitches

Step-by-step explanation:

12/2=6

6 stitches= 1 inch

X stitches=9 inches

X=54 stitches

Answer:

16

Step-by-step explanation:

Number = x

(3/4 of x) - (1/2 of x) = 4

3x/4 - x/2 = 4

3x - 2x / 4 = 4

x/4 = 4

x = 16

Answer:

The 99% confidence interval for the mean amount spent daily per person at the theme park is between $52.81 and $134.05.

This means that we are 99% sure that the true mean amount spent daily per person at the theme park is between $52.81 and $134.05.

Step-by-step explanation:

We have the sample standard deviation, so we use the t-distribution to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 40 - 1 = 39

99% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 39 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.99}{2} = 0.995[/tex]. So we have T = 2.7079

The margin of error is:

M = T*s = 2.7079*15 = 40.62

In which s is the standard deviation of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 93.43 - 40.62 = $52.81.

The upper end of the interval is the sample mean added to M. So it is 93.43 + 40.62 = $134.05

The 99% confidence interval for the mean amount spent daily per person at the theme park is between $52.81 and $134.05.

This means that we are 99% sure that the true mean amount spent daily per person at the theme park is between $52.81 and $134.05.

Answer:

Step-by-step explanation: convert feet to inches then multiply all 3 numbers. 264 x 699x13 = 2398968. Then decide that by 12 the amount of inches in a foot and get 199,914 ft^3

Answer:

[tex]I_o = 10^{-12} \frac{W}{m^2}[/tex] represent the minimum audible intensity by the humans

[tex] I= 10^{-7} \frac{W}{m^2}[/tex] represent the intensity for the dinner conversation

And replacing this into the formula we got:

[tex] dB = 10 log_{10} (\frac{10^{-7}}{10^{-12}})= 10 log_{10} (100000) = 50 dB[/tex]

So then the best answer for this case would be:

O 50 Db

Step-by-step explanation:

For this case we can use the following equation for decibels:

[tex] dB = 10 log_{10} (\frac{I}{I_o})[/tex]

Where:

[tex]I_o = 10^{-12} \frac{W}{m^2}[/tex] represent the minimum audible intensity by the humans

[tex] I= 10^{-7} \frac{W}{m^2}[/tex] represent the intensity for the dinner conversation

And replacing this into the formula we got:

[tex] dB = 10 log_{10} (\frac{10^{-7}}{10^{-12}})= 10 log_{10} (100000) = 50 dB[/tex]

So then the best answer for this case would be:

O 50 Db

The approximate loudness of a dinner conversation with a sound intensity of 10^-7 is -50Db

Given the general expression for calculating the  loudness, L, measured in decibels (Db), of sound intensity, I as:

L = 10log(I0/I)

Given the following parameters

I0 = 10^-12 Wb/m²

I = 10^-7 Wb/m²

Substitute

L = 10log(10^-12/10^-7)
L = 10log(10^-5)
L = -5(10)log10
L = -50Db

Hence the approximate loudness of a dinner conversation with a sound intensity of 10^-7 is -50Db

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Answer:

a) The company should expect to replace 11.51% of its batteries.

b) 35 months.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

[tex]\mu = 43.8, \sigma = 6.5[/tex]

(a) If Quick Start guarantees a full refund on any battery that fails within the 36-month period after purchase, what percentage of its batteries will the company expect to replace?

This is the pvalue of Z when X = 36. Then

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

[tex]Z = \frac{36 - 43.8}{6.5}[/tex]

[tex]Z = -1.2[/tex]

[tex]Z = -1.2[/tex] has a pvalue of 0.1151.

The company should expect to replace 11.51% of its batteries.

(b) If quick Start does not want to make refunds for more than 10% of its batteries under the full refund guarantee policy, for how long should the company guarantee the batteries (to the nearest month)?

The warranty should be the 10th percentile, which is X when Z has a pvalue of 0.1. So it is X when Z = -1.28.

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

[tex]-1.28 = \frac{X - 43.8}{6.5}[/tex]

[tex]X - 43.8 = -1.28*6.5[/tex]

[tex]X = 35.48[/tex]

To the nearest month, 35 months.

Final answer:

To calculate the percentage of batteries that will be expected to be replaced within the 36-month period, we need to find the area under the normal distribution curve from 0 to 36.

Explanation:

In this question, we are given information about the average life of a Quick Start car battery, which follows a normal distribution with a mean of 43.8 months and a standard deviation of 6.5 months.

(a) To calculate the percentage of batteries that will be expected to be replaced within the 36-month period, we need to find the area under the normal distribution curve from 0 to 36. We can use the z-score formula to standardize the value of 36 and then use a standard normal distribution table to find the corresponding area. The percentage of batteries that will be expected to be replaced is the same as the percentage of batteries that fall within the range of 0 to 36 months.

Answer:

The height of the triangle, h, is 8 m

Step-by-step explanation:

The formula for the area of a triangle of base b and height h is A = (1/2)(b)(h).

Here b = 15 m and A = 60 m^2.  We want the measure of the height, h.

First we solve the area equation (above) for h:  2A = bh, or h = 2A/b,

and then substitute the given values for b and A:

       2(60 m^2)

h = ------------------ = 8 m

          15 m

The height of the triangle, h, is 8 m

Answer:

Answer is 8 because I did the quiz on my online school.

Hope it helps

Answer:-19/7

Step-by-step explanation:

f varies directly as m

f=k x m

When f=-19,m=14

-19=k x 14

k=-19/14

Relationship is f=-19m/14

When m is 2

f=(-19x2) ➗ 14

f=-38 ➗ 14

f=-19/7

Answer:

B. The x-value is between 3 and 4.

C. The y-value is between –2 and –1.

D. The x-value is positive.

Step-by-step explanation:

I did the Assignment on Edg.

The true options are: The x-value is between 3 and 4, the y-value is between –2 and –1 and the x-value is positive.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

From the graph, we have the following highlights

The point of intersection of the two lines is in the fourth quadrant.

The value of x is between 3 and 4.

The value of y is between -1 and -2.

x is positive, and y is negative.

x is not an integer.

x is between 3 and 4, while y is between -1 and -2

Hence, the true options are: The x-value is between 3 and 4.

the y-value is between –2 and –1 and the x-value is positive.

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Answer:

D = 24

Step-by-step explanation:

The given quadratic equation is [tex]y=x^2-8x+10[/tex].

It is required to find the value of the discriminant. The value of discriminant  of any quadratic equation is given by :

[tex]D=b^2-4ac[/tex]

Here, a = 1, b = -8 and c = 10

On plugging all the values, we get :

[tex]D=(-8)^2-4\times 1\times 10\\\\D=24[/tex]

So, the value of discriminant for y is 24.

Answer:

x=-6

Step-by-step explanation:

y=2x + 5

y= x -1

Plug in the equation for y

x-1=2x+5

Combine like terms

-1=x+5

-6=x

Hope this helps! Please mark brainliest :)

Answer:

Domain: { -3,1,6}

Step-by-step explanation:

The domain is the input values

Domain: { 6,1,-3,-3}

We usually put them in numerical order and we do not list the same value twice

Domain: { -3,1,6}

Answer:

The null and alternative hypothesis are:

[tex]H_0: \pi=0.1\\\\H_a:\pi<0.1[/tex]

The test statistic for this hypothesis test is z=-1.15.

The​ P-value for this hypothesis test is P-value=0.124.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that less than 10 percent of the test results are wrong.

Step-by-step explanation:

This is a hypothesis test for a proportion.

The claim is that less than 10 percent of the test results are wrong.

Then, the null and alternative hypothesis are:

[tex]H_0: \pi=0.1\\\\H_a:\pi<0.1[/tex]

The significance level is 0.05.

The sample has a size n=317.

The sample proportion is p=0.079.

[tex]p=X/n=25/317=0.079[/tex]

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.1*0.9}{317}}\\\\\\ \sigma_p=\sqrt{0.000284}=0.017[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.079-0.1+0.5/317}{0.017}=\dfrac{-0.019}{0.017}=-1.153[/tex]

This test is a left-tailed test, so the P-value for this test is calculated as:

[tex]P-value=P(z<-1.153)=0.124[/tex]

As the P-value (0.124) is greater than the significance level (0.05), the effect is  not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that less than 10 percent of the test results are wrong.

Answer:

a = 6.3mm

Step-by-step explanation:

Use Pythagoras theorem here

[tex]a^{2} + b^{2} = c^{2}[/tex]

Rearrange for a by subtracting [tex]b^{2}[/tex] from both sides of the equation

[tex]a^{2} + b^{2} -b^{2} = c^{2} -b^{2}[/tex]

Simplify

[tex]a^{2} = c^{2} -b^{2}[/tex]

Substitute in our numbers and solve for a

[tex]a^{2}[/tex] = [tex]8.3^{2} - 5.4^{2}[/tex]

[tex]a^{2}[/tex] = 68.89 - 29.16

[tex]a^{2}[/tex] = 39.73

a = [tex]\sqrt{39.73}[/tex]

a = 6.3mm

Final answer:

To find the length of leg a when b = 5.4 mm and c = 8.3 mm in a right triangle, we use the Pythagorean theorem a^2 + b^2 = c^2. We solve for a, yielding a ≈ 6.3 mm (rounded to the nearest tenth).

Explanation:

The student is asking how to find the length of leg a in a right triangle where the lengths of leg b and the hypotenuse c are given. Since b = 5.4 millimeters and c = 8.3 millimeters, we can use the Pythagorean theorem to find leg a.

First, we'll apply the theorem: a2 + b2 = c2. To solve for a, we rearrange it: a2 = c2 - b2.

Substitute the given values:

a2 = c2 - b2
= 8.32 - 5.42
= 68.89 - 29.16
= 39.73

Now, we take the square root of both sides to find a:

a =
√39.73

≈ 6.3 millimeters (rounded to the nearest tenth)

Therefore, the length of leg a is approximately 6.3 millimeters.

Answer:

5/8 mile is less than 1 mile

Step-by-step explanation:

in this question, one could assume a mile is 8/8

5/8<8/8

Answer:

  0.0833

Step-by-step explanation:

There are 7C6 = 7 ways to choose 6 hazelnuts from the 7 present.

There are 9C6 = 84 ways to choose 6 nuts from the 9 present.

The probability of choosing 6 hazelnuts from the 9 present is ...

  7/84 = 1/12 = 0.0833...(repeating)

The probability of interest is 0.0833.

____

Comment on the notation

The notation nCk means n!/(k!(n-k)!). It is the number of ways k items can be chosen from n items without regard to order. It can be pronounced "n choose k."

Answer:

We must pick at least 8 individual boots to be sure of picking at least one matching pair as explained from the pigeon hole principle.

Step-by-step explanation:

From pigeonhole principle, if k is a positive integer and k + 1 or more objects are placed into k boxes, then there is at least one box containing 2 or more objects.

Now, since we have 7 pairs of similar looking boots, thus, number of single boots we have will be;

Number of single boots = 7 x 2 = 14

Now, if we select 7 boots from the 14,then there's a possibility of selecting exactly 1 from each pair. Thus, we will not get a matching pair.

Whereas if we select 8 boots from the 14 single boots, then by the pigeon hole principle, at least 2 of the boots will need to be from the same pair. Hence we can pick at least 8 individual boots to be sure of picking at least one matching pair.

To ensure getting a matched pair from a pile of 7 pairs of boots, you would need to pick eight individual boots. This is based on the counting principle in mathematics where in the worst-case scenario, each boot you pick could be from a different pair.

The question is about probability and counting principles in mathematics, specifically about how to identify a matched pair of boots from a pile of similar looking pairs. In the pile, there are seven pairs of boots, which means there are 14 individual boots from seven different pairs.

Now, if you randomly pick one boot, it could be from any pair. If you pick a second boot, it could also be from any pair, including the same pair as the first one. But to be sure that you get a matched pair, you will have to pick up eight boots. This is because, in the worst-case scenario, you might pick seven different boots each from a different pair. Once you pick the eighth boot, it is guaranteed to match one of the earlier seven because there are only seven pairs.

The minimum number of individual boots that you must pick to be sure of getting a matched pair is eight.

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Answer:

The correct option is (A).

Step-by-step explanation:

The p-value is well defined as the probability, [under the null hypothesis (H₀)], of attaining a result equivalent to or more extreme than what was truly observed.

From the provided options we can guess that the hypothesis was defined as follows:

H₀: There is no difference in the mean number of partners, i.e. μ₁ - μ₂ = 0.

Hₐ: There is difference in the mean number of partners, i.e. μ₁ - μ₂ ≠ 0.

The test is two tailed mean difference test.

A z-test or a t-test can be used to conclude the result.

In this case the p-value can be defined as the probability of obtaining a test statistic value equal to or more extreme that the results obtained from the sample, when the difference between the mean number of partners is 0.

Thus, the correct interpretation of the​ p-value is provided by statement (A).

The p-value represents the likelihood of obtaining a test statistic as extreme as our observed data, assuming the null hypothesis is true. The null hypothesis usually posits there's no difference or effect. A small p-value would suggest rejecting the null hypothesis in favor of the alternative hypothesis, indicating a significant effect or difference.

The correct interpretation of the ​p-value is: The p-value is the probability of getting a test statistic equal to or more extreme than the sample result if there is no difference in the mean number of partners.

In other words, the p-value measures how likely you are to get the observed data if the null hypothesis is true. The null hypothesis typically represents a theory that there is no effect or no difference between the groups you're comparing. Hence, if there's no difference in the mean number of partners (which is our null hypothesis here), then the p-value tells how likely we are to observe a test statistic as extreme as our sample result.

For example, if the p-value is very small, it might be less than our significance level (commonly 0.05 or 5%). In such a case, we have evidence to reject our null hypothesis in favor of the alternative hypothesis. The alternative hypothesis generally represents a theory that there is an effect or a difference between the groups. So, in this case, a small p-value would indicate a statistically significant difference in the mean number of partners.

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Willy is using a systematic sampling method by selecting every tenth person entering the school to understand milk consumption habits after cereal.

When Willy selects every tenth person who enters the school to determine what percent of students drink the milk after they finish their cereal, he is using a systematic sampling method. This type of sampling involves selecting subjects at regular intervals from an ordered list.

It's a form of probability sampling where the first unit is selected randomly and the subsequent units are selected using a fixed periodic interval.

In the context of the situation provided, this method could potentially provide a more representative sample compared to methods like convenience sampling, but there could be inherent biases if there are underlying patterns in the student arrivals at school that correlate with milk drinking habits after cereal.

Answer:

2^-84

Step-by-step explanation:

First simplify inside the parentheses

2^-10 / 4^2

Rewriting 4 as 2^2

2^-10 / 4^2^2

We know that a^b^c = a^(b*c)

2^-10 / 2^(2*2) = 2^-10 / 2^4

We know that a^b / a^c = a^(b-c)

2^-10 / 2^4 = 2^(-10-4) = 2^-14

Replace the term in side the parentheses with 2^-14

2^-14 ^7

We know that a^b^c = a^(b*c)

2^(-14*7)

2^-84