Two exponential functions, F and G, are shown in the figure below where G is a transformation of F.
Which of the rules given below shows the transformation of F?

Answer:

64

Step-by-step explanation:

When you have 105+x=169

x=64

If you do 169-105 you get 64

64+105=169

Answer:

- \(\frac{\sqrt{2+\sqrt{3} } }{2}\)

Step-by-step explanation:

using the half angle formula

cos(\(\frac{x}{2}\) ) = ± \(\sqrt{\frac{1+cosx}{2} }\)

cos195° = cos(180 + 15)° = - cos15°

then

cos15° = cos (\(\frac{30}{2}\) ) = \(\sqrt{\frac{1+cos30}{2} }\) = \(\sqrt{\frac{1+\frac{\sqrt{3} }{2} }{2} }\) = \(\sqrt{\frac{2+\sqrt{3} }{4} }\) = \(\frac{\sqrt{2+\sqrt{3} } }{2}\)

then

cos195° = - cos15° = - \(\frac{\sqrt{2+\sqrt{3} } }{2}\)

Answer:

Step-by-step explanation:

Answer& Step-by-step explanation:

To multiply powers of the same base, add their exponents.

5d³ / 3f

The probability of either getting a blue card or a green card is 0.648. The probability of either getting a blue card or a green card or a yellow card is 1.0. The probability of getting both a blue card and a green card is 0.277.

Probability is a measure or quantification of the likelihood or chance of an event occurring. It is used to describe and analyze uncertain or random situations.

Given, that the box is filled with 123 blue cards, 234 green cards, and 53 yellow cards.

Total number of cards = 123 + 234 + 53 = 410

The probability of getting a blue card = 123/410
The probability of getting a green card = 234/410
The probability of either getting a blue card or a green card is given by:
P(Blue or Green) = P(Blue) + P(Green) - P(Blue and Green)
= 123/410 + 234/410 - (123*234)/(410*410)
= 0.3 + 0.348 - 0.054
= 0.648

The probability of getting a yellow card = 53/410
The probability of either getting a blue card or a green card or a yellow card is given by:
P(Blue or Green or Yellow) = P(Blue) + P(Green) + P(Yellow) - P(Blue and Green) - P(Green and Yellow) - P(Blue and Yellow) + P(Blue and Green and Yellow)
= 123/410 + 234/410 + 53/410 - (123×234)/(410×410) - (234×53)/(410×410) - (123×53)/(410×410) + 0
= 0.3 + 0.348 + 0.129 - 0.054 - 0.039 - 0.019
= 1.0

The probability of getting both a blue card and a green card is given by:
P(Blue and Green) = (123×234)/(410×410)
= 0.054

Therefore, the probability of either getting a blue card or a green card is 0.648. The probability of either getting a blue card or a green card or a yellow card is 1.0. The probability of getting both a blue card and a green card is 0.277.

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Answer:

\(g(x) = 8x\)

Step-by-step explanation:

Given:

\(f(x) = x\)

\(Stretch\ factor = 8\)

Required:

Equation of the new function.

Let the new function be represented by \(g(x)\)

The interpretation of this question is that;

\(g(x) = f(x * 8)\)

Multiply 8 by x

\(g(x) = f(8x)\)

If

\(f(x) = x\)

then

\(f(8x) = 8 * x\)

Multiply 8 by x

\(f(8x) = 8x\)

Recall that

\(g(x) = f(8x)\)

Substitute \(f(8x) = 8x\) in the above expression

\(g(x) = 8x\)

Hence, the equation of the new function when stretched by a factor of 8 is \(g(x) = 8x\)

Yes, a normal approximation can be used for a sampling distribution of sample means from a population with a known mean (μ) of 50 and a known standard deviation (σ) of 9, when the sample size (n) is 25. The central limit theorem allows us to make this approximation because it states that as the sample size increases, the sampling distribution of the sample mean approaches a normal distribution, regardless of the shape of the population distribution.

The central limit theorem is a fundamental concept in statistics that states that as the sample size increases, the sampling distribution of the sample mean approaches a normal distribution, even if the population distribution is not normal. This approximation holds true as long as the sample size is reasonably large, typically considered to be above 30.

In this case, the sample size is n=25, which is relatively small but still reasonably large enough to apply the normal approximation due to the moderate sample size. Since the population mean (μ) and standard deviation (σ) are known (μ=50 and σ=9), we can calculate the standard error of the mean (SE) using the formula SE = σ/√n.

SE = 9/√25 = 9/5 = 1.8

The central limit theorem allows us to approximate the sampling distribution of the sample means as a normal distribution with a mean equal to the population mean (μ=50) and a standard deviation equal to the standard error of the mean (SE=1.8). Therefore, we can use the normal distribution to estimate probabilities and make inferences about the sample means in this case.

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Answer:

366 cm^3

Step-by-step explanation:

V = lwh

1st rectangle (L) = 3 x 6 x 15 = 270 cm^3

2nd rectangle (R) = 6 x 4 x 4 = 96 cm^3

270 + 96 = 366 cm^3

Hope this helps

Answer:

110.9° = 111°

Step-by-step explanation:

Given ∆ABC, where

length of side AB = 15 cm,

length of side AC = 7 cm

length of side BC = 11 cm

Required:

Size of largest angle in ∆ABC

SOLUTION:

The size of the largest angle in the triangle is the angle that has the largest side length opposite it.

Therefore, the largest angle in ∆ABC = <C, which has a side length of 15 cm opposite it.

=>Find the angle of C using the Law of Cosine

Cos C = (a² + b² - c²)/2ab

Cos C = (11² + 7² - 15²)/2*11*7

Cos C = (121 + 49 - 225)/154

Cos C = -55/154

Cos C = -0.3571

C = Cos-¹(-0.3571)

C = 110.9° ≈ 111°

To determine whether the series is convergent or divergent, we can use the integral test.

First, we note that the function f(x) = ln(x^2+3/8x^2+7) is continuous, positive, and decreasing for x ≥ 1.

Then, we take the integral of f(x) from 1 to infinity:

∫_1^∞ ln(x^2+3/8x^2+7) dx

We can evaluate this integral using integration by parts:

u = ln(x^2+3/8x^2+7)    dv = dx
du/dx = (2x)/(x^2+3/8x^2+7)    v = x

∫_1^∞ ln(x^2+3/8x^2+7) dx = [xln(x^2+3/8x^2+7)]_1^∞ - ∫_1^∞ (2x)/(x^2+3/8x^2+7) dx

We know that the limit of xln(x^2+3/8x^2+7) as x approaches infinity is infinity, so the first term evaluates to infinity.

For the second term, we can use the substitution u = x^2 to get:

∫_1^∞ (2x)/(x^2+3/8x^2+7) dx = ∫_1^∞ (2du)/(u+3/8u+7)

We can then use partial fractions to write the integrand as:

(2du)/((u/8)+7/8) - (2du)/(u+7)

We can now evaluate the integral:

∫_1^∞ (2du)/(u+3/8u+7) = [2ln(u/8+7/8)]_1^∞ = 2ln(∞/8+7/8) - 2ln(1/8+7/8) = ∞

∫_1^∞ (2du)/(u+7) = 2ln(u+7)]_1^∞ = ∞ - 2ln(8) = ∞

Since both integrals diverge, the original series diverges by the integral test. Therefore, the answer is divergent.

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The probability of mission success if at least 11 of the 16 patrol boats must operate for the duration of the 20-hour mission if each boat has a failure rate of 1 failure per 100 hoursis 99.5%. Hence, the correct option is (A).

To determine the probability of mission success, we'll need to calculate the probability of failure for each boat and then use the binomial probability formula.

Here are the steps:

1. Calculate the probability of failure for each boat during the 20-hour mission: Since each boat has a failure rate of 1 failure per 100 hours, the probability of failure for each boat in 20 hours is 20/100 = 1/5 or 0.2.

2. Calculate the probability of success for each boat: The probability of success for each boat is 1 - probability of failure = 1 - 0.2 = 0.8.

3. Use the binomial probability formula to find the probability of at least 11 boats operating successfully:
P(X ≥ 11) = 1 - P(X ≤ 10), where X is the number of successful boats.

4. Calculate P(X ≤ 10) using the binomial probability formula:

P(X ≤ 10) = ∑[C(16, k) × (0.8)^k × (0.2)^(16-k)], where k ranges from 0 to 10, and C(16, k) is the binomial coefficient or the number of ways to choose k successes from 16 boats.

5. Calculate 1 - P(X ≤ 10) to get the probability of mission success.

After performing the calculations, the probability of mission success is found to be approximately 99.5%, which corresponds to option A.

So, the probability of mission success, given that at least 11 of the 16 patrol boats must operate for the duration of the 20-hour mission and each boat has a failure rate of 1 failure per 100 hours, is approximately 99.5%.

Hence, option (A) is correct.

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Answer:

Q2) JN and LP

Q3) FJ and JM

Therefore , the solution of the given problem of equation comes out to be  option c is correct 2y = f(x) .

The equal letter (=) is used to signify equivalence between the statements in a mathematical formula. Using mathematical equation, which are declarations of reality, it is shown that many mathematical variables are equivalent. For instance, the equal sign in the equation

y + 6 = 12 divides the values 12 or b + 6 into two halves. The number of words that each side of a symbol corresponds to can be measured. Typically, a symbol's meaning is at odds with itself.

Here,

Given :

Every point on the graph in red is 1/2 away from the x-axis as that of the equivalent position on the graph in black.

Therefore, the vertically scale factor is equal to 1/2:

=> y = (1/2)f(x)

This problem can be solved by multiplying it by two and yields the following solution:

=> 2y = f(x)

thus , option c is correct

Therefore , the solution of the given problem of equation comes out to be  option c is correct 2y = f(x) .

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Answer:

19/28 or about 68%

Step-by-step explanation:

7 + 12 + 9 = 28

7 + 12/28

19/28

Answer:

They should bring 30 gallons

Step-by-step explanation:

Brainliest please :)

Elizabeth ought to have gotten $2.70 back in change. The information provided makes it impossible to calculate the amount saved by purchasing 40 T-shirts at the lower cost.

We need to add up the price of the sandwich, chips, drink, and tax, then deduct that sum from the amount of cash Elizabeth provided the cashier to determine how much change she should have received. Here is how to calculate it:

Cost of sandwich + chips + drink + tax = $3.75 + $2.20 + $0.80 + $0.55 = $7.30

Amount given to cashier = $10.00

Change = Amount given - Cost of items = $10.00 - $7.30 = $2.70

Therefore, Elizabeth should have received $2.70 in change.

Regarding the second question, there is no information provided about the prices of T-shirts or the better price at which they were bought, so it is not possible to calculate how much is saved by buying 40 T-shirts at a better price.

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The radius of the circular with maximum volume with the sum of the height and circumference is 30 centimeters is 20 centimeters.

The volume of a circular cylinder refers to the amount of space in the cylinder.

The relationship between the radius (r) and height (h) is given as: sum of the height and circumference is 30 centimeters.

r + h = 30

substract r from both sides

h = 30 - r

Volume of cylinder = πr²h

Substitute h = 30 - r into the equation

Volume of cylinder = πr²h

= π × r² × (30 - r)

= 30πr² - πr³

Differentiate the equation

Volume of cylinder = 60πr - 3πr²

Set the equation to 0

60πr - 3πr² = 0

60πr = 3πr²

Divide both sides by πr

60 = 3r

divide both sides by 3

r = 60/3

r = 20 centimeters

In conclusion, the radius of circular cylinder with the maximum volume is 20 centimeters

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For a taxable income of $1,80,900, the effective tax rate is 21.11%.

Marginal tax is the tax rate applied to an individual’s last dollar of income. It is the additional tax that must be paid on any additional income earned. In other words, it is the tax rate that applies to an individual’s income after all deductions. For example, if an individual’s income is $50,000 and the marginal tax rate is 25%, then the individual must pay an additional $12,500 in taxes on top of the $25,000 in taxes already paid on their $50,000 income.

Marginal tax rates are progressive, meaning that as an individual’s income increases, the marginal tax rate will increase as well. The marginal tax rate is important to understand because it helps individuals determine how much additional income they will need to earn in order to make up for the taxes they will have to pay on that income. It is also important to understand how marginal tax rates can affect tax planning strategies.

To determine the effective tax rate for a taxable income of $180,900, calculate the sum of the marginal tax rates for each tax bracket that the $180,900 falls into. The taxable income of $180,900 is greater than $89,075 and less than $170,050. The marginal tax rates for these two tax brackets are 22% and 24%, respectively. The sum of the marginal tax rates is 46%. Divide the sum by the taxable income of $180,900 to get the effective tax rate of 21.11%. Round the final answer to the nearest hundredth to get 21.11%.

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The value of x in the triangle WXY is 19 degrees

An equation shows how two or more numbers and variables are related to each other.

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

The triangle XYZ and the line YZ such that lie YZ and XW are parallel lines

Using the above as a guide, we have the following:

∠ZYW = ∠XWY (alternate angles are equal)

∠XWY = 2x (Given)

So, we have

∠XWY + ∠XYW + ∠YXW = 180° (the sum of angles in a triangle)

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

2x + (3x - 5) + 90 = 180

Open the brackets and solve

5x - 5 = 90

Evaluate the like terms

5x = 95

Divide both sides by 5

x = 19°

Hence, the value of x is 19°

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Answer: 1, 2, 4, 8 and 16

Step-by-step explanation:

The possible solution set for the system is (- 1, 4) and (4, - 1).

Given are the equations as -

x + y = 3

x² + y² = 17

Refer to the graph of the function attached. The points of intersection represents the possible solution set.

Therefore, the possible solution set for the system is (- 1, 4) and (4, - 1).

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Answer:

show the a pic

Step-by-step explanation:

the proceeds from the loan are $5,599.92.

the effective rate charged by the bank is approximately 25%.

To find the proceeds from the loan, we need to calculate the amount that Paul and Senoy Moede receive after the bank deducts the discount.

The formula to calculate the proceeds is:

Proceeds = Principal - Discount

Where:

Principal = $7,200 (the amount of the note)

Discount = Principal * Discount Rate * Time

Given:

Discount Rate = 25%

Time = 320 days

First, let's calculate the discount:

Discount = $7,200 * 0.25 * (320/360)

        = $7,200 * 0.25 * 0.8889

        = $1,600.08

Now, let's find the proceeds:

Proceeds = $7,200 - $1,600.08

        = $5,599.92

Therefore, the proceeds from the loan are $5,599.92.

To find the effective rate charged by the bank, we can use the following formula:

Effective Rate = (Discount / Principal) * (360 / Time)

Given:

Discount = $1,600.08

Principal = $7,200

Time = 320 days

Effective Rate = ($1,600.08 / $7,200) * (360 / 320)

             = 0.22223 * 1.125

             = 0.24999875

To convert this into a percentage, we multiply by 100:

Effective Rate = 0.24999875 * 100

             = 24.999875

Rounding to the nearest percent, the effective rate charged by the bank is approximately 25%.

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Answer:

a if both are right triangle

Step-by-step explanation:

if both are right triangles is the correct answer. Three sides and three angles together create a triangle. Here, Ryan and Kathy drew triangles with the same angle. We can say that two triangles are similarly based on certain rules.Ma

Answer:

9

Step-by-step explanation:

81= 1,3,9,27,81

72= 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36,72

9 is the most common so GCF will be 9.

Answer:

See below.

Step-by-step explanation:

81 - 1,3,9,27,81

72 - 1,2,3,4,6,8,9,12,18,24,36,72

The GCF is 9.

-hope it helps

The inverse of the equation is f-1(x) = -3 + 1/2[√(x + 8)]

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

g(x) = 4(x + 3)^2 - 8

Express as

y = 4(x + 3)^2 - 8

Swap x and y

This gives

x = 4(y + 3)^2 - 8

So, we have

(y + 3)^2 = (x + 8)/4

This gives

y + 3 = 1/2[√(x + 8)]

Make y the subject

y = -3 + 1/2[√(x + 8)]

Hence, the inverse is f-1(x) = -3 + 1/2[√(x + 8)]

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Answer:

-3 x 10

Step-by-step explanation:

the first one is 5

The populations from which the samples are obtained must be normally distributed.

Sampling is done correctly. Observations for within and between groups must be independent.

The variances among populations must be equal (homoscedastic).

Data are interval or nominal.