Rewrite without rational exponents, and simplify, if possible.

X^1/3

Answer:

b

Step-by-step explanation:

x + 5y = 4x - 3y ( subtract 4x from both sides )

- 3x + 5y = - 3y ( subtract 5y from both sides )

- 3x = - 8y ( multiply both sides by - 1 )

3x = 8y → b

the ship is approximately 398.4 feet from the base of the lighthouse.

We can see that the angle of depression from the top of the lighthouse to the ship is 27°. This means that the angle between the horizontal and the line from the top of the lighthouse to the ship is also 27°.

We want to find the distance from the ship to the base of the lighthouse, which we can call x. We can use the tangent function to relate the angle and the distances:

tan(27°) = opposite / adjacent

n this case, the opposite side is the height of the lighthouse, 189 ft, and the adjacent side is x, the distance from the ship to the base of the lighthouse. So we can solve for x:tan(27°) = 189 / x

x = 189 / tan(27°)

x ≈ 398.4 ft

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The variance of Billy's grades obtained from his test scores is 15.76

The variance is a measure of variability or spread a dataset. The variance can be calculated from the sum of the square of the differences of the data points from the mean divided by the number or count of the data points.

The variance of Billy's test scores can be calculated by finding the mean or the average of the scores, then finding the sum of the squares of the differences of each score from the mean as follows;

The mean score = (89 + 88 + 93 + 90 + 81)/5 = 88.2

The square of the differences of the values from the mean can be calculated as follows;

(89 - 88.2)² = 0.64, (88 - 88.2)² = 0.04, (93 - 88.2)² = 23.04, (90 - 88.2)² = 3.24, and (81 - 88.2)² = 51.84

The sum of the square of the differences is therefore;

0.64 + 0.04 + 23.04 + 3.24 + 51.84 = 78.8

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A. The system of equations in standard form is: 4x + 5y = 540 and 3x + 5y = 440.

B. The y-intercept of the equation representing the prices on Saturday night is 108, and the y-intercept of the equation representing the prices at the matinee on the second day is 88.

A) Let's define the variables:

Let x represent the number of children attending.

Let y represent the number of adults attending.

On Saturday night:

The equation for the revenue generated on Saturday night is:

4x + 5y = 540 (since children's tickets cost $4 and adults' tickets cost $5, and the total revenue is $540).

Matinee on the second day:

The equation for the revenue generated at the matinee is:

3x + 5y = 440 (since children's tickets cost $3 and adults' tickets still cost $5, and the total revenue is $440).

Therefore, the system of equations in standard form is:

4x + 5y = 540

3x + 5y = 440

B) Let's rewrite the system of equations in slope-intercept form:

On Saturday night:

4x + 5y = 540

Rearranging the equation, we get:

5y = -4x + 540

Dividing both sides by 5, we get:

y = (-4/5)x + 108

The y-intercept of this equation is 108.

Matinee on the second day:

3x + 5y = 440

Rearranging the equation, we get:

5y = -3x + 440

Dividing both sides by 5, we get:

y = (-3/5)x + 88

The y-intercept of this equation is 88.

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a) the Central Limit Theorem conditions are met. b) The 95% confidence interval for the proportion of adults who believe in protecting the rights of those with unpopular views is approximately 0.7934 to 0.8466.

c) . A 90% confidence interval would be wider than the 95% interval

To verify the Central Limit Theorem (CLT) conditions, we need to check the following:

1. Random Sampling: The survey states that 800 adults were randomly selected, which satisfies this condition.

2. Independence: We assume that the responses of one adult do not influence the responses of others. This condition is met if the sample is collected using a proper random sampling method.

3. Sample Size: To apply the CLT, the sample size should be sufficiently large. While there is no exact threshold, a common rule of thumb is that the sample size should be at least 30. In this case, the sample size is 800, which is more than sufficient.

Therefore, the Central Limit Theorem conditions are met.

b. To find a 95% confidence interval for the proportion of adults who believe in protecting the rights of those with unpopular views, we can use the formula for calculating a confidence interval for a proportion:

CI = p ± z * √(p(1-p)/n)

where:

- p is the sample proportion (82% or 0.82 in decimal form).

- z is the z-score corresponding to the desired confidence level. For a 95% confidence level, the z-score is approximately 1.96.

- n is the sample size (800).

Calculating the confidence interval:

CI = 0.82 ± 1.96 * √(0.82(1-0.82)/800)

CI = 0.82 ± 1.96 * √(0.82*0.18/800)

CI = 0.82 ± 1.96 * √(0.1476/800)

CI = 0.82 ± 1.96 * √0.0001845

CI ≈ 0.82 ± 1.96 * 0.01358

CI ≈ 0.82 ± 0.0266

The 95% confidence interval for the proportion of adults who believe in protecting the rights of those with unpopular views is approximately 0.7934 to 0.8466.

c. A 90% confidence interval would be wider than the 95% interval. The reason is that as we increase the confidence level, we need to account for a larger margin of error to be more certain about the interval capturing the true population proportion. As a result, the interval needs to be wider to provide a higher level of confidence.

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The monthly PMI Payment for Christina's loan is $37.50.The correct answer is option B.

To determine Christina's monthly PMI (Private Mortgage Insurance) payment, we need to find the corresponding interest rate for her loan-to-value (LTV) ratio. The LTV ratio is calculated by dividing the loan amount by the property value.

The loan amount can be calculated by subtracting the down payment from the property value:

Loan amount = Property value - Down payment

           = $170,000 - $20,000

           = $150,000

Now we can calculate the LTV ratio:

LTV ratio = Loan amount / Property value * 100

         = $150,000 / $170,000 * 100

         = 88.24%

Since Christina is obtaining a 30-year mortgage, we need to look at the interest rates for LTV ratios between 85.01% and 90%. According to the table, the interest rate for this range is 0.30%.

To calculate the PMI payment, we multiply the loan amount by the PMI rate and divide it by 12 months:

PMI payment = (Loan amount * PMI rate) / 12

           = ($150,000 * 0.30%) / 12

           = $450 / 12

           = $37.50

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The Probable question may be:
Christina is buying a $170,000 home with a 30-year mortgage. She makes a $20,000 down payment.

Use the table to find her monthly PMI payment

Base to loan% = 95.01% to 97%,90.01% to 95%,85.01% to 90%,80.01% to 85%.

30-year fixed-rate loan = 0.55%,0.41%,0.30%,0.19%

15-year fixed-rate loan = 0.37%,0.28%,0.19%,0.17%.

A. $51.25

B. $37.50

C. $23.75

D. $42.50

Answer:

Step-by-step explanation:

1) 2x+ 4 = 10

2x = 6

x = 3 (3 is the answer)

2) we have to substitute y with 3 and z with 4

3.75*3 + 6.50*4 ≥ 50

11,25 + 26 ≥ 50

37.25 ≥ 50

so the answer is no, because the total will be $37.25

3)  12k + 2 < 12

12k < 10

k < 5/6

3/4 < 5/6  so the answer is true

4) we have to try the options

a)  3*4 + 4*2 + 6 = 26

12 + 8 + 6 = 26

26 = 26 (true)

b) 3*5 + 4*6 + 6 = 26

15 + 24 + 6 = 26

45 = 26 (false)

c) 3*4 + 4*3 + 6 = 26

12 + 12 + 6 = 26

30 = 26 (false)

d) 3*3 +4*5 + 6 = 26

9 + 20 + 6 = 26

35 = 26 (false)

so the answer is x=4 , y=2

5) 3a + 4 ≥ 13

3a ≥ 9

a ≥ 3

so the answer is {3,4.5,5}

Answer:

y=-1/4-6

Step-by-step explanation:

Answer:

0.4 or 6/15

3×2 is 6

leaving 6/15 or 0.4

Answer:

x = 0.77 to the nearest hundredth.

Step-by-step explanation:

5^3x = 42

3x ln 5 = ln 42

3x = ln42 / ln 5 = 2.3223

x = 2.3223 / 3 = 0.7741

Answer:

5:4

Step-by-step explanation:

60/48

=> Dividing numerator and denominator by 12,

=> 5/4 = 5:4

Answer:

Step-by-step explanation:

The ratio of 60:48

Answer:

The answer to this problem is 0.0013.

Answer:

7. 14

15. 30

28. 56

32. 64

18 36

x 2x

1/2y. y

2x. 4x

x+3 2x+9

Step-by-step explanation:

each out is double the in

Answer:

Option A is the correct answer

Step-by-step explanation:

BA - BD = DA and BC - BE = EC

Answer:

C) 1/16

Step-by-step explanation:

2*2*2*2=16

Therefore, 2^(-4)=1/16.

Answer:

C) \(\frac{1}{16}\)

Step-by-step explanation:

2⁻⁴

2⁴ = 2 × 2 × 2 × 2 = 16

\(\frac{1}{16}\)

The parent function for the given function is y=\(x^\frac{1}{3}\).

The given function is \(f(x)=\sqrt[3]{27x-81}\).

The parent function of a family of functions is the simplest one that satisfies the definition of that particular type of function. For example, the simplest linear function would be y = x which is the parent function of the linear family of functions.

The parent function y=\(x^\frac{1}{3}\), horizontally shrink by a factor of 27 shift 3 units to the right.

Therefore, the parent function for the given function is y=\(x^\frac{1}{3}\).

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Answer:

  x = 9 inches

Step-by-step explanation:

You want the value of x in the similar triangles shown.

Corresponding sides are proportional. This means the ratio of the horizontal side of the triangle to the vertical side is the same for both.

  6/4 = (6+x)/10

  15 = 6 +x . . . . . . . . multiply by 10

  9 = x . . . . . . . . . subtract 6

The measure of x is 9 inches.

__

Additional comment

You could also write the proportion ...

  6/4 = x/(10 -4)

  x = 36/4 = 9 . . . . . . . multiply by 6

You can see this if you draw a horizontal line through the figure at the top of the side marked 4 in.

<95141404393>

The amount of the last payment that Elroy will make is $710, which includes the $200 monthly payment and a balance of $510.

The last payment amount is the result of the mathematical operations of subtraction and multiplication.

The first mathematical operation was the subtraction of the down payment from the total cost of the video game system.

Using multiplication, the monthly payments are determined to be $3,400 for 17 months.  This is subtracted from the remaining balance to obtain the last payment amount.

The cost of a custom video game/virtual sound system = $4,210

Down payment = $100

The remaining balance for monthly payment = $4,110 ($4,210 - $100)

Payment period = 18 months (1¹/₂ years)

Monthly payments = $200

Payment for the first 17 months = $3,400 (17 x 200)

Last payment = $710 ($4,110 - $3,400)

Thus, if Elroy makes the minimum monthly payment of $200 till the last payment, then he will pay $710 to settle the account.

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He made a $100 down payment and agreed to pay the entire purchase off in 1 1/2 years The minimum monthly payment is $200 if he makes the minimum monthly payment up until the last payment what will be the amount of his last payment?

Answer:66.871

Step-by-step explanation:

The mean=67

The population standard deviation=9.9

Let the minimum score representing grade D above the bottom 10% is x1.

so

P(x<x1)=0.10

P(Z<z)=0.10

z~=-1.48

Two angles whose sum is 180° are called supplementary angles. The measure of ∠UPS is 151°.

Two angles whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line. Those two angles are two pairs of supplementary angles. That means, that if supplementary angles are aligned adjacent to each other, their exterior sides will make a straight line.

Since ∠4 and ∠5 form a line, therefore, the two lines are supplementary to each other. Thus, the sum of the two angles can be written as,

∠4 + ∠5 = 180°

(3x + 7) + (9x - 43) = 180

3x + 7 + 9x - 43 = 180

3x + 9x + 7 - 43 = 180

12x - 36 = 180

12x = 180 + 36

12x = 216

x = 216 / 12

x = 18

Now, the measure of ∠UPT can be written as,

∠UPT = ∠4

∠UPT = 3x + 7

         = 3(18) + 7

         = 54+7

         = 61°

Further, since the ∠UPS is formed of ∠UPT and ∠TPS, therefore, we can write,

∠UPS = ∠UPT + ∠TPS

         = 61° + 90°

         = 151°

Hence, the measure of ∠UPS is 151°.

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Answer: 6 possibilities.

Carol, Beryl, and Darryl

Carol, Darryl, and Beryl

Darryl, Carol, and Beryl

Darryl, Beryl, and Carol

Beryl, Darryl, and Carol

Beryl, Carol, and Darryl

Hope this helps :)

The grams of cocoa does it contains is 36.57 grams

From the question, we have the following parameters that can be used in our computation:

Weight of the chocolate bar = 69

Proportion = 53%

This implies that

Grams of cocoa = weight of the chocolate bar * Proportion

Substitute the known values in the above equation, so, we have the following representation

Grams of cocoa = 53% * 69

Evaluate the products

Grams of cocoa = 36.57

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Answer:

28x−6

Step-by-step explanation:

Okay 2 sides of equal lenght so

2(6x-4)+2(8x+1)=

12x-8+16x+2

28x-6

Answer:    8.3 or C  

Eplanation: This is because a half life is 50 percent of a normal life so 50 percent divided by 6 is 8.3

\(8.3\)% is the approximate decay rate of the element after the first day.

What is Radioactive decay ?

Radioactive decay is the process by which an unstable atomic nucleus loses energy by radiation. A material containing unstable nuclei is considered radioactive. Three of the most common types of decay are alpha decay, beta decay, and gamma decay, all of which involve emitting one or more particles.

What is decay rate?

The rate of decay, or activity, of a sample of a radioactive substance is the decrease in the number of radioactive nuclei per unit time.

According to question, a radioactive element has a half-life of six days.

A half- life is \(50\)% of a normal life.

So, the approximate decay rate of the element after the first day

\(=\frac{50}{6}\)% \(=8.3\)%

Hence, we can conclude that \(8.3\)% is the approximate decay rate of the element after the first day.

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Answer:

\(a \cdot b = 1\)

Step-by-step explanation:

\( a = 5i + 7j \)

\( b = -4i + 3j \)

\( a = a_xi + a_yj \)

\(b = b_xi + b_yj\)

\( a \cdot b = a_xb_x + a_yb_y \)

\( a \cdot b = (5)(-4) + (7)(3) \)

\( a \cdot b = -20 + 21 \)

\(a \cdot b = 1\)

Answer:

\(\boxed{-20i^2 -13ij+21j^2}\)

Step-by-step explanation:

\(\sf Plug \ in \ the \ values.\)

\((5i+7j) \cdot (-4i+3j)\)

\(\sf Expand \ brackets.\)

\(5i(-4i+3j)+7j(-4i+3j)\)

\(-20i^2 +15ij+-28ij +21j^2\)

\(\sf Combine \ like \ terms.\)

\(-20i^2 -13ij+21j^2\)

1 From the given information, no determination can be made as to whether the parallelogram is a rhombus, a rectangle, or a square.

2 The reason for the determination made in the previous step is A. From the given information, no determination can be made as to whether the parallelogram is a rhombus, a rectangle, or a square.

The diagonals of a parallelogram bisect each other, but this is true for all parallelograms, regardless of whether they are squares, rectangles, or rhombuses.

Therefore, the given information is not sufficient to determine whether the parallelogram is a rhombus, a rectangle, or a square.

In conclusion, from the given information, no determination can be made as to whether the parallelogram is a rhombus, a rectangle, or a square.

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Answer:

-2

Step-by-step explanation:

We can find the slope for two points

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

    = ( 12 - 4)/(-6- -2)

   = 8/( -6+2)

   = 8/-4

   = -2

1. Cluster sampling / Multistage sampling

2. Stratified sampling

3. Multistage sampling

Stratified sampling

1. Cluster sampling / Multistage sampling

Explanation:Brianna can use cluster sampling and multistage sampling in this case because the number of social media posts students make per month is constant. As a result, the resulting cluster will be heterogeneous, and this method is less expensive and time consuming.

2. Stratified sampling

Explanation: Josh can use stratified sampling in this case. Because clinical depression differs by gender, he can create strata based on the gender of the students.

3. Multistage sampling

Explanation: Emily must use a multistage sampling technique to collect the students attending four-year colleges in the Boston metropolitan region to determine the average amount of time students spend at the library each semester in this case.

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Answer:

it's E

Step-by-step explanation:

Because the 1 is closer to 0

Given the word problem, we can deduce the following information:

1. The function has zeroes at 3,4, and -4 and passes through the point (2,24) has a value of 120.

To determine the cubic polynomial function, we let the values of x be:

x=3

x=4

x=-4

Since we the polynomial function is cubic, it would be like this:

To determine a or the constant, we let P(x)=24 and x=2:

Next, we plug in P(x)=120 and a=-4 into P(x)=a(x-3)(x-4)(x-5):

We can further simplify this into standard form. So,

The graph would be:

The root or the x-intercept would be found at x=0.78553.

Therefore, the answer is x=0.78553.