What is the surface area of the pyramid? 12ft 10ft 10ft

Answer:

Approximately 34% of people sleep between 6 and 7.5 hours per night

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 6

Standard deviation = 1.5

The normal distribution is symmetric, which means that 50% of the measures are below the mean and 50% are above.

What percentage of people sleep between 6 and 7.5 hours per night

6 is the mean.

7.5 is 1 one standard deviation above the mean.

By the Empirical Rule, of the 50% of the measures that are above the mean, 68% are within 1 standard deviation of the mean(between 6 and 7.5).

0.5*0.68 = 0.34

Approximately 34% of people sleep between 6 and 7.5 hours per night

Answer:

probability of the event E = 1/5

Step-by-step explanation:

We are given;

Sample space, S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10},

Number of terms in sample S is;

n(S) = 10

We are given the event; E = {1, 2}

Thus, number of terms in event E is;

n(E) = 2

Now, Probability = favorable outcomes/total outcomes

Thus, the probability of the event E is;

P(E) = n(E)/n(S)

P(E) = 2/10

P(E) = 1/5

Answer:

(a) The value of E (X) is 4/7.

    The value of V (X) is 3/98.

(b) The value of P (X ≤ 0.5) is 0.3438.

Step-by-step explanation:

The random variable X is defined as the proportion of surface area in a randomly selected quadrant that is covered by a certain plant.

The random variable X follows a standard beta distribution with parameters α = 4 and β = 3.

The probability density function of X is as follows:

[tex]f(x) = \frac{x^{\alpha-1}(1-x)^{\beta-1}}{B(\alpha,\beta)} ; \hspace{.3in}0 \le x \le 1;\ \alpha, \beta > 0[/tex]

Here, B (α, β) is:

[tex]B(\alpha,\beta)=\frac{(\alpha-1)!\cdot\ (\beta-1)!}{((\alpha+\beta)-1)!}[/tex]

            [tex]=\frac{(4-1)!\cdot\ (3-1)!}{((4+3)-1)!}\\\\=\frac{6\times 2}{720}\\\\=\frac{1}{60}[/tex]

So, the pdf of X is:

[tex]f(x) = \frac{x^{4-1}(1-x)^{3-1}}{1/60}=60\cdot\ [x^{3}(1-x)^{2}];\ 0\leq x\leq 1[/tex]

(a)

Compute the value of E (X) as follows:

[tex]E (X)=\frac{\alpha }{\alpha +\beta }[/tex]

         [tex]=\frac{4}{4+3}\\\\=\frac{4}{7}[/tex]

The value of E (X) is 4/7.

Compute the value of V (X) as follows:

[tex]V (X)=\frac{\alpha\ \cdot\ \beta}{(\alpha+\beta)^{2}\ \cdot\ (\alpha+\beta+1)}[/tex]

         [tex]=\frac{4\cdot\ 3}{(4+3)^{2}\cdot\ (4+3+1)}\\\\=\frac{12}{49\times 8}\\\\=\frac{3}{98}[/tex]

The value of V (X) is 3/98.

(b)

Compute the value of P (X ≤ 0.5) as follows:

[tex]P(X\leq 0.50) = \int\limits^{0.50}_{0}{60\cdot\ [x^{3}(1-x)^{2}]} \, dx[/tex]

                    [tex]=60\int\limits^{0.50}_{0}{[x^{3}(1+x^{2}-2x)]} \, dx \\\\=60\int\limits^{0.50}_{0}{[x^{3}+x^{5}-2x^{4}]} \, dx \\\\=60\times [\dfrac{x^4}{4}+\dfrac{x^6}{6}-\dfrac{2x^5}{5}]\limits^{0.50}_{0}\\\\=60\times [\dfrac{x^4\left(10x^2-24x+15\right)}{60}]\limits^{0.50}_{0}\\\\=[x^4\left(10x^2-24x+15\right)]\limits^{0.50}_{0}\\\\=0.34375\\\\\approx 0.3438[/tex]

Thus, the value of P (X ≤ 0.5) is 0.3438.

Answer:

x ≈ 6.7 ft

Step-by-step explanation:

We are going to use tan∅ to find our answer:

tan66° = 15/x

xtan66° = 15

x = 15/tan66°

x = 6.67843 ft

Answer:

  5.03

Step-by-step explanation:

Answer:

5.03 = AC

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp/ adj

tan 40 = AC /6

6 tan 40 = AC

5.034597787 = AC

To the nearest hundredth

5.03 = AC

Answer:

a) 8.2962

b) 6.3956

c) 3.845

Step-by-step explanation:

Z-score:

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 question, we have that:

[tex]\mu = 5.6, \sigma = 2.6[/tex]

(a) What response represents the 85th ​percentile? ​

This is X when Z has a pvalue of 0.85. So X when Z = 1.037.

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

[tex]1.037 = \frac{X - 5.6}{2.6}[/tex]

[tex]X - 5.6 = 2.6*1.037[/tex]

[tex]X = 8.2962[/tex]

(b) What response represents the 62nd ​percentile?

This is X when Z has a pvalue of 0.62. So X when Z = 0.306.

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

[tex]0.306 = \frac{X - 5.6}{2.6}[/tex]

[tex]X - 5.6 = 2.6*0.306[/tex]

[tex]X = 6.3956[/tex]

​(c) What response represents the first ​quartile?

The first quartile is the 100/4 = 25th percentile. So this is X when Z has a pvalue of 0.25, so X when Z = -0.675.

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

[tex]-0.675 = \frac{X - 5.6}{2.6}[/tex]

[tex]X - 5.6 = 2.6*(-0.675)[/tex]

[tex]X = 3.845[/tex]

Answer:

1937.98

Step-by-step explanation:

In the given question, to find the value to be added per year we will use the formula

P= A. r/n/ (1 +r/n)ⁿ - 1

Here A = 50,000

r (rate of interest) = 5 % or 0.05.

n = 1

t = 17

P = value deposit per year

therefore, P = (50,000 X 0.05)/ (1 +0.05)¹⁷ - 1

P =   2500 / 2.29- 1

= 1937.98 $.

therefore, person has to deposit 1937.98 $ per month.

Answer:

The 95% confidence interval for the difference between means is (-25.5, -14.7).

Step-by-step explanation:

We have to calculate a 95% confidence interval for the difference between means.

The sample 1 (Method 1), of size n1=63 has a mean of 52.2 and a standard deviation of 15.92.

The sample 2 (Method 2), of size n2=93 has a mean of 72.3 and a standard deviation of 17.96.

The difference between sample means is Md=-20.1.

[tex]M_d=M_1-M_2=52.2-72.3=-20.1[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{15.92^2}{63}+\dfrac{17.96^2}{93}}\\\\\\s_{M_d}=\sqrt{4.023+3.468}=\sqrt{7.491}=2.74[/tex]

The critical t-value for a 95% confidence interval is t=1.975.

The margin of error (MOE) can be calculated as:

[tex]MOE=t\cdot s_{M_d}=1.975 \cdot 2.74=5.41[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=M_d-t \cdot s_{M_d} = -20.1-5.41=-25.5\\\\UL=M_d+t \cdot s_{M_d} = -20.1+5.41=-14.7[/tex]

The 95% confidence interval for the difference between means is (-25.5, -14.7).

Answer:

Negative Coterminal: -5π/4

Positive Coterminal: 11π/4

Step-by-step explanation:

The easiest way to find specific (not infinite) coterminal values is to ±2π. When you subtract 2π, you will get a negative coterminal. When you add 2π, you will get a positive coterminal. Keep in mind though that a tan∅ or cot∅ only needs ±π, not ±2π.

Answer:

[tex]3^{7} = 2187[/tex]

Step-by-step explanation:

The base of the log, 3, would be the base of the exponent. The =7 would be the exponent itself, so now we have [tex]3^7[/tex]. The log of 2187 would be the = for the exponential form, so we have [tex]3^7 = 2187[/tex] as our final answer.

Answer:

y = 2x+4

Step-by-step explanation:

First we need to find the slope using two points

(-2,0) and (0,4)

m = (y2-y1)/(x2-x1)

m = (4-0)/(0--2)

   = 4/+2

   = 2

we have the y intercept  which is 4

Using the slope intercept form of the line

y = mx+b where m is the slope and b is the y intercept

y = 2x+4

Answer:

Step-by-step explanation:

The question is incomplete. The complete question is:

It is known that the number of hours a student sleeps per night has a normal distribution. The sleeping time in hours of a random sample of 8 students is given below. 7.4, 6.2, 8.5, 6.3, 5.4, 5.5, 6.3, 8.3 Compute a 98% confidence interval for the true mean time a student sleeps per night and fill in the blanks appropriately. We have 98% confidence that the true mean time a student sleeps per night is between _____ and ____ hours. (Keep 3 decimal places)

Solution:

Mean = (7.4 + 6.2 + 8.5 + 6.3 + 5.4 + 5.5 + 6.3 + 8.3)/8 = 6.7375

Standard deviation = √(summation(x - mean)²/n

Summation(x - mean)² = (7.4 - 6.7375)^2 + (6.2 - 6.7375)^2 + (8.5 - 6.7375)^2 + (6.3 - 6.7375)^2 + (5.4 - 6.7375)^2 + (5.5 - 6.7375)^2 + (6.3 - 6.7375)^2 + (8.3 - 6.7375)^2 = 9.97875

Standard deviation = √(9.97875/8

s = 1.12

Confidence interval is written in the form,

(Sample mean - margin of error, sample mean + margin of error)

The sample mean, x is the point estimate for the population mean.

Margin of error = z × s/√n

Where

sample standard deviation

number of samples

From the information given, the population standard deviation is unknown and the sample size is small, hence, we would use the t distribution to find the z score

In order to use the t distribution, we would determine the degree of freedom, df for the sample.

df = n - 1 = 8 - 1 = 7

Since confidence level = 98% = 0.98, α = 1 - CL = 1 - 0.98 = 0.02

α/2 = 0.02/2 = 0.01

the area to the right of z0.01 is 0.01 and the area to the left of z0.01 is 1 - 0.01 = 0.99

Looking at the t distribution table,

z = 2.998

Margin of error = 2.998 × 1.12/√8

= 1.19

the lower limit of this confidence interval is

6.738 - 1.19 = 5.548

the upper limit of this confidence interval is

6.738 + 1.19 = 7.928

We have 98 % confidence that the true mean time a student sleeps per night is between 5.548 hours and 7.928 hours.

Answer:

x = 3.6

Step-by-step explanation:

By the Postulate of intersecting chords inside a circle.

[tex]x \times 5 = 3 \times 6 \\ 5x = 18 \\ x = \frac{18}{5} \\ x = 3.6 \\ [/tex]

Answer:

a) P(x > 43) = 0.9599

b) P(x < 42) = 0.0228

c) P(x > 57.5) = 0.03

d) P(x = 42) = 0.

e) P(x<40 or x>55) = 0.1118

f) 43.42

g) Between 46.64 and 53.36.

h) Above 45.852.

Step-by-step explanation:

When the distribution is normal, we use 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 question, we have that:

[tex]\mu = 50, \sigma = 4[/tex]

a) x>43

This is 1 subtracted by the pvalue of Z when X = 43. So

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

[tex]Z = \frac{43 - 50}{4}[/tex]

[tex]Z = -1.75[/tex]

[tex]Z = -1.75[/tex] has a pvalue of 0.0401

1 - 0.0401 = 0.9599

P(x > 43) = 0.9599

b) x<42

This is the pvalue of Z when X = 42.

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

[tex]Z = \frac{42 - 50}{4}[/tex]

[tex]Z = -2[/tex]

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

P(x < 42) = 0.0228

c) x>57.5

This is 1 subtracted by the pvalue of Z when X = 57.5. So

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

[tex]Z = \frac{57.5 - 50}{4}[/tex]

[tex]Z = 1.88[/tex]

[tex]Z = 1.88[/tex] has a pvalue of 0.97

1 - 0.97 = 0.03

P(x > 57.5) = 0.03

d) P(x = 42)

In the normal distribution, the probability of an exact value is 0. So

P(x = 42) = 0.

e) x<40 or x>55

x < 40 is the pvalue of Z when X = 40. So

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

[tex]Z = \frac{40 - 50}{4}[/tex]

[tex]Z = -2.5[/tex]

[tex]Z = -2.5[/tex] has a pvalue of 0.0062

x > 55 is 1 subtracted by the pvalue of Z when X = 55. So

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

[tex]Z = \frac{55 - 50}{4}[/tex]

[tex]Z = 1.25[/tex]

[tex]Z = 1.25[/tex] has a pvalue of 0.8944

1 - 0.8944 = 0.1056

0.0062 + 0.1056 = 0.1118

P(x<40 or x>55) = 0.1118

f) 5% of the values are less than what X value?

X is the 5th percentile, which is X when Z has a pvalue of 0.05, so X when Z = -1.645.

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

[tex]-1.645 = \frac{X - 50}{4}[/tex]

[tex]X - 50 = -1.645*4[/tex]

[tex]X = 43.42[/tex]

43.42 is the answer.

g) 60% of the values are between what two X values (symmetrically distributed around the mean)?

Between the 50 - (60/2) = 20th percentile and the 50 + (60/2) = 80th percentile.

20th percentile:

X when Z has a pvalue of 0.2. So X when Z = -0.84.

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

[tex]-0.84 = \frac{X - 50}{4}[/tex]

[tex]X - 50 = -0.84*4[/tex]

[tex]X = 46.64[/tex]

80th percentile:

X when Z has a pvalue of 0.8. So X when Z = 0.84.

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

[tex]0.84 = \frac{X - 50}{4}[/tex]

[tex]X - 50 = 0.84*4[/tex]

[tex]X = 53.36[/tex]

Between 46.64 and 53.36.

h) 85% of the values will be above what X value?

Above the 100 - 85 = 15th percentile, which is X when Z has a pvalue of 0.15. So X when Z = -1.037.

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

[tex]-1.037 = \frac{X - 50}{4}[/tex]

[tex]X - 50 = -1.037*4[/tex]

[tex]X = 45.852[/tex]

Above 45.852.

Answer:

First of all expand the terms

2x(1-x)³ = 2x( 1 - 3x + 3x² - x³)

Multiply by 2x

You will get

2x - 6x² + 6x³ -2x⁴

Differentiate each of the terms using differentiation rules

You will get

2 - 12x + 18x² - 8x³

So the final answer is

- 8x³ + 18x² - 12x + 2

Hope this helps.

Answer:

Step-by-step explanation:

Given that;

the following procedure for accomplishing our task are:

1. Flip the coin.

2. Flip the coin again.

From here will know that the coin is first flipped twice

3. If both flips land on heads or both land on tails, it implies that we return to step 1 to start again. this makes the flip to be insignificant since both flips land on heads or both land on tails

But if the outcomes of the two flip are different i.e they did not land on both heads or both did not land on tails , then we will consider such an outcome.

Let the probability of head = p

so P(head) = p

the probability of tail be = (1 - p)

This kind of probability follows a conditional distribution and the probability  of getting heads is :

[tex]P( \{Tails, Heads\})|\{Tails, Heads,( Heads ,Tails)\})[/tex]

[tex]= \dfrac{P( \{Tails, Heads\}) \cap \{Tails, Heads,( Heads ,Tails)\})}{ {P( \{Tails, Heads,( Heads ,Tails)\}}}[/tex]

[tex]= \dfrac{P( \{Tails, Heads\}) }{ {P( \{Tails, Heads,( Heads ,Tails)\}}}[/tex]

[tex]= \dfrac{P( \{Tails, Heads\}) } { {P( Tails, Heads) +P( Heads ,Tails)}}[/tex]

[tex]=\dfrac{(1-p)*p}{(1-p)*p+p*(1-p)}[/tex]

[tex]=\dfrac{(1-p)*p}{2(1-p)*p}[/tex]

[tex]=\dfrac{1}{2}[/tex]

Thus; the probability of getting heads is [tex]\dfrac{1}{2}[/tex] which typically implies that the coin is fair

(b) Could we use a simpler procedure that continues to flip the coin until the last two flips are different and then lets the result be the outcome of the final flip?

For a fair coin (0<p<1) , it's certain that both heads and tails at the end of the flip.

The procedure that is talked about in (b) illustrates that the procedure gives head if and only if the first flip comes out tail with probability 1 - p.

Likewise , the procedure gives tail if and and only if the first flip comes out head with probability of  p.

In essence, NO, procedure (b) does not give a fair coin flip outcome.

Answer:

Step-by-step explanation:

The question lacks the required diagram. Find the diagram attached.

From the diagram, it can be seen that point U is the midpoint of T and V. This means that TU = UV

Given TU=8x+11 and UV=12x−1

8x+11 = 12x -1

8x-12x = -1-11

-4x = -12

x = 3

Since TU = 8x+11

TU = 8(3)+11

TU = 24+11

TU = 35

Also UV = 12x-1

UV = 12(3)-1

UV = 36- 1

UV = 35

TV = TU+UV

TV = 35+35

TV = 70

Answer:

  7

Step-by-step explanation:

The number of cells in a tile is 4. If colored alternately, there are 3 of one color and 1 of the alternate color. To balance the coloring, an even number of tiles is needed. Hence the board dimensions must be multiples of 4.

In the given range, there are 7 such boards:

  4×4, 8×8, 12×12, 16×16, 20×20, 24×24, and 28×28

Answer:

[tex]solution \\ 3(5x) + 8(2x) \\ = 3 \times 5x + 8 \times 2x \\ = 15x + 16x \\ = 31x[/tex]

hope this helps...

Good luck on your assignment...

The expression  [tex]3(5x) + 8(2x)[/tex] in simplest form is 31x.

To simplify the expression [tex]3(5x) + 8(2x)[/tex], we can apply the distributive property:

[tex]3(5x) + 8(2x)[/tex]

[tex]= 15x + 16x[/tex]

Combining like terms, we have:

[tex]15x + 16x = 31x[/tex]

Therefore, the expression [tex]3(5x) + 8(2x)[/tex] simplifies to [tex]31x.[/tex]

To learn more on Expressions click:

https://brainly.com/question/14083225

#SPJ6

Answer:

7.5 pounds

Step-by-step explanation:

30/4=7.5 :)

Answer:

C =81.64 cm

Step-by-step explanation:

The circumference is given by

C = 2* pi *r

The radius is 13

C = 2 * 3.14 * 13

C =81.64 cm

Answer:

[tex]= 81.64cm \\ [/tex]

Step-by-step explanation:

[tex]c = 2\pi \: r \\ = 2 \times 3.14 \times 13 \\ = 81.64cm[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

see below

Step-by-step explanation:

y = -sqrt(x) +1

We know that the domain is from 0 to infinity

The range is from 1 to negative infinity

Answer:

b

Step-by-step explanation:

e2020

Answer:

The full name of the place is the "Danat Jebel Dhanna".  The Jebel Dhanna is currently located in the Abu Dhabi.  It is said that it is one of the most best beach in the UAE, they also say that it is the biggest resort, of course, with a bunch of hotels.

hope this helps ;)

best regards,

`FL°°F~` (floof)

Answer:

B

Step-by-step explanation:

Answer:

there will be 9 id no. which it contains

Answer:

Domain: All real numbers or (negative infinity, positive infinity)

Range: [0, positive infinity)

Step-by-step explanation:

Domain; Since all values of x would work for this equation, simply any number could be plugged in. That means the domain would stretch to infinity because  there are an infinite amount of inputs and outputs

Range; Even though we have an infinite amount of domain, when we plug in a negative x, anything inside the absolute value will turn positive. Therefore, no output (y) value will ever go below zero, and we have [0, positive infinity).

Answer:

  The line of g(x) is steeper and has a lower y-intercept.

Step-by-step explanation:

Doubling the function expands it vertically by a factor of 2. Everything is twice as far from the x-axis as it was. The line becomes steeper, and the y-intercept moves twice as far away. It was at -1, now is lower, at -2.

The line of g(x) is steeper and has a lower y-intercept.

Answer:

the length of his shadow on the building is decreasing at the rate of 0.525 m/s

Step-by-step explanation:

From the diagram attached below;

the man is standing at point D with his head at point E

During that time, his shadow on the wall is y = BC

ΔABC and Δ ADE are similar in nature; thus their corresponding sides have equal ratios; i.e

[tex]\dfrac{AD}{AB} = \dfrac{DE}{BC}[/tex]

[tex]\dfrac{8}{12} = \dfrac{2}{y}[/tex]

8y = 24

y = 24/8

y = 3 meters

Let take an integral look  at the distance of the man from the building as x, therefore the distance from the spotlight to the man is  12 - x

∴

[tex]\dfrac{12-x}{12}=\dfrac{2}{y}[/tex]

[tex]1- \dfrac{1}{12}x = 2* \dfrac{1}{y}[/tex]

To find the derivatives of both sides ;we have:

[tex]- \dfrac{1}{12}dx = 2* \dfrac{1}{y^2}dy[/tex]

[tex]- \dfrac{1}{12} \dfrac{dx}{dt} = 2* \dfrac{1}{y^2} \dfrac{dy}{dt}[/tex]

During that time ;

[tex]\dfrac{dx}{dt }= 1.4 \ m/s[/tex]   and y = 3

So; replacing the value into above ; we have:

[tex]-\dfrac{1}{12}(1.4) = - \dfrac{2}{9} \dfrac{dy}{dt}[/tex]

[tex]\dfrac{dy}{dt} = \dfrac{\dfrac{ 1.4} {12 } }{ \dfrac{2}{9}}[/tex]

[tex]\dfrac{dy}{dt} = {\dfrac{ 1.4} {12 } }*{ \dfrac{9}{2}}[/tex]

[tex]\dfrac{dy}{dt} =0.525 \ m/s[/tex]

Thus; the length of his shadow on the building is decreasing at the rate of 0.525 m/s

Answer: D

Step-by-step explanation:

Sometimes, it is hard to see which function fits g(x). We are given the point (4,1). Luckily, the point lies on g(x). We can plug in (4,1) into the g(x) equations and see which best fits.

A. Incorrect

[tex]1=4(4)^2[/tex]

[tex]1=4(16)[/tex]

[tex]1\neq 64[/tex]

B. Incorrect

[tex]1=\frac{1}{4} (4)^2[/tex]

[tex]1=\frac{1}{4} (16)[/tex]

[tex]1\neq 4[/tex]

C. Incorrect

[tex]1=(\frac{1}{2}(4))^2[/tex]

[tex]1=(2)^2[/tex]

[tex]1\neq 4[/tex]

D. Correct

[tex]1=(\frac{1}{4}(4))^2[/tex]

[tex]1=(1)^2[/tex]

[tex]1=1[/tex]