Using the standard domain for the sine function, which of the following expressions corresponds to the (1 point) composite function
sin(arccosx)
? Review Guidelines: If you guessed the answer to this question, or did not answer it correctly, go back and review the composition of trigonon Composition of Trigonometric Functions lesson.
(0pts) x 2
+1
​
(0pts) x 2
−1
​
(0pts) 1−x
​
(1pt)
1−x 2
​

The correct answer is II. Rescales the distribution by dividing by the standard deviation.  This transformation does not change the shape or skewness of the distribution and does not create outliers.

Standardizing a distribution means converting it into a standard normal distribution with a mean of 0 and a standard deviation of 1.

This is achieved by subtracting the mean from each value and then dividing by the standard deviation.

Standardizing does not shift the distribution, change its skewness or symmetry, or create outliers.

Standardizing a distribution involves transforming the original data so that it has a mean of 0 and a standard deviation of 1.

This transformation is useful because it allows for comparisons between variables that may be measured on different scales, and it simplifies the interpretation of statistical results.

Standardizing does not change the shape or skewness of the distribution, nor does it create outliers.

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Answer:

 (4 ft)(2 1/2 ft)(1 3/4 ft) = 17 1/2 ft³

The volume of the box is 17 1/2 cubic feet.

Step-by-step explanation:

The volume of a box, or any cubic object, is the product of its length, width, and height. In this case, the box is 1/2 ft long, 1/4 ft wide, and 3/4 ft high, so its volume is 1/2 × 1/4 × 3/4 = 3/32 cubic feet.

The volume of a cubic object like a box is determined by the product of its length, width, and height. For this box, those measurements are 1/2 ft, 1/4 ft, and 3/4 ft respectively. Multiply those values together to calculate the volume:

1/2 ft × 1/4 ft × 3/4 ft = 3/32 cubic feet

So, the volume of the box is 3/32 cubic feet.

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Answer:

C. 2A/b

Step-by-step explanation:

multiply both sides by 2

2A = bh

divide both sides by b

2A/b = h

The probability that the average number of months since the last examination in a sample of 150 patients is 14 or larger is practically 0, which means it is highly unlikely to occur by chance.

Now that we know the mean and standard deviation of the distribution of the sample mean, we can standardize the variable using the standard normal distribution formula:

Z = (x - μ) / (σ/√n)

where Z is the standard normal variable, x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

Substituting the values we obtained, we get:

Z = (14 - 12) / (0.237)

Z = 8.43

To find the probability that the sample mean is 14 or larger, we need to find the area under the standard normal distribution curve to the right of Z = 8.43.

This can be done using a standard normal distribution table or a calculator. The probability turns out to be practically 0.

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Answer:

C

Step-by-step explanation:

We'll have to use trigonometry for this.

First, note that in right triangle ABC, if we look from the perspective of angle A, the opposite side is x, the adjacent side is y, and the hypotenuse is 18.

In order to find x, then, we must use sine, which is opposite/hypotenuse. So:

sin(A) = sin(60) = opposite/hypotenuse = x/18

sin(60) is equal to (√3)/2, so multiplying both sides by 18 gives:

[(√3)/2] * 18 = 9√3

Already, we can tell that the answer is likely C, but let's find y to make sure.

We will use cosine to find y because cos = adjacent/hypotenuse.

cos(A) = cos(60) = adjacent/hypotenuse = y/18

cos(60) = 0.5, so multiplying both sides by 18 gives:

0.5 * 18 = 9

So, y = 9.

Thus, C is our answer.

~ an aesthetics lover

Answer:

C

Step-by-step explanation:

Using the cosine/ sine ratio in the right triangle and the exact values

cos30° = \(\frac{\sqrt{3} }{2}\) and sin30° = \(\frac{1}{2}\) , then

cos30° = \(\frac{adjacent}{hypotenuse}\) = \(\frac{BC}{AC}\) = \(\frac{x}{18}\) = \(\frac{\sqrt{3} }{2}\) ( cross- multiply )

2x = 18\(\sqrt{3}\) ( divide both sides by 2 )

x = 9\(\sqrt{3}\)

----------------------------------------------------------

sin30° = \(\frac{opposite}{hypotenuse}\) = \(\frac{AB}{AC}\) = \(\frac{y}{18}\) = \(\frac{1}{2}\) ( cross- multiply )

2y = 18 ( divide both sides by 2 )

y = 9

Thus

x = 9\(\sqrt{3}\) and y = 9 → C

Answer:

a) x^3y2

b) 6x^2y^3

Step-by-step explanation:

because 3 x's and 2 y's are being multiplied.

You can put a hidden exponent of 1 to each variable without an exponent, and the value will remain the same.

Merely add the exponents of the values with the same base number, or coefficient. —> like terms

X^1 times X^1 times X^1 is X^3, and Y^1 times Y^1 is Y^2.

Our final answer is X^3 Y^2.

Like the first expression, we can add a hidden exponent to each VARIABLE, not number.

2 times 3 is 6, and X^1 times X^1 is X^2, and Y^1 times Y^1 times Y^1 is Y^3.

Our final answer is 6X^2 Y^3.

Answer:

amplitude = |-4| =4

period = 2 pi/3

phase shift = pi / 3

midline = 2

Step-by-step explanation:

f(x)=-4 cos (3x-pi)+2

The equation is in the form

f(x) = a cos (bx -c) +d  where |a| is the amplitude

period  is 2 pi /b

phase shift:  c/b

midline = d

amplitude = |-4| =4

period = 2 pi/3

phase shift = pi / 3

midline = 2

The present value of $13,000 discounted back 5 years at a semi-annual compound rate of 9% can be calculated by the formula:PV = FV / (1 + r/m)^(m*t)Here, PV stands for Present Value FV stands for Future Valuer stands for the interest rate (9%)m is the number of times the interest is compounded (semi-annually, so m = 2)t is the number of years (5)

After substituting the values in the formula, we get:PV = 13,000 / (1 + 0.045)^10PV = 13,000 / 1.55709768854PV = $8,349.58. We can use the concept of present value (PV) and future value (FV) to solve this question. When the cash flow is considered at different points of time, the money's value changes with the time value of money. The time value of money takes into consideration the amount of interest that could be earned on the sum of money if invested. Present value (PV) is a mathematical concept that represents the current worth of a future sum of money, taking into account the time value of money and the given interest rate. PV is calculated by using a discount rate that is determined by the interest rate and the length of time between the present and future payment dates. Future value (FV) is a mathematical concept that represents the future worth of a present sum of money, taking into account the time value of money and the given interest rate. FV is calculated by using a compound interest rate that is determined by the interest rate and the length of time between the present and future payment dates. To calculate the present value of $13,000 discounted back 5 years at a semi-annual compound rate of 9%, we can use the formula PV = FV / (1 + r/m)^(m*t), where PV is the present value, FV is the future value, r is the interest rate, m is the number of times the interest is compounded per year, and t is the number of years. In this case, we know that FV is $13,000, r is 9%, m is 2 (since it is compounded semi-annually), and t is 5. After substituting these values into the formula, we get PV = $8,349.58. Therefore, the present value of $13,000 discounted back 5 years at a semi-annual compound rate of 9% is $8,349.58.

Therefore, the present value of $13,000 discounted back 5 years at a semi-annual compound rate of 9% is $8,349.58.

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a, b, and c are collinear points. b is the midpoint of ac .

The coordinate of c is 3. So, the coordinate of point c is 3.

If b is the midpoint of ac, it means that the coordinates of a, b, and c lie on the same line and b is exactly halfway between a and c.

Given that the coordinate of a is -8 and the coordinate of b is -2.5, we can determine the coordinate of c as follows:

The distance from a to b is equal to the distance from b to c. Since b is the midpoint, the distance from a to b is half of the distance from a to c. Mathematically, we can express this relationship as:

|a - b| = |b - c|

Substituting the given coordinates, we have:

|-8 - (-2.5)| = |-2.5 - c|

Simplifying further:

| -8 + 2.5 | = |-2.5 - c|

| -5.5 | = |-2.5 - c|

Since the absolute value of a number is always positive, we can drop the absolute value signs:

5.5 = 2.5 + c

Now we solve for c:

5.5 - 2.5 = c

3 = c

Therefore, the coordinate of c is 3. So, the coordinate of point c is 3.

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In mathematics, the place value chart is a tool that helps students understand the value of digits in a number. It is a visual representation of how digits are grouped and arranged to represent numbers. The place value chart is arranged in columns, with each column representing a different place value.

The place value chart starts with the ones place, also called units place. This is the rightmost column and it represents the ones digit in a number. The next column is the tens place, which represents the tens digit in a number. The hundredth place represents the hundreds digit and so on. Each column is ten times larger than the previous one.

A place value chart can be used to understand the value of a digit in a number.

Place value chart also helps to understand decimal numbers, which are numbers that have a decimal point. The decimal point separates the whole numbers from the fractional numbers. Each place to the right of the decimal point represents a smaller value.

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Based on the sample of 400 Canadians, we can be 95% confident that the true proportion of Canadians who would rather retire in the US is between 50.16% and 59.84%. We can use the formula for a confidence interval for a proportion: CI = p ± z*√(p(1-p)/n)



Using the information given in your question, we can plug in the values: p = 220/400 = 0.55
z = 1.96
n = 400
Plugging these values into the formula, we get: CI = 0.55 ± 1.96*√(0.55(1-0.55)/400)
CI = 0.55 ± 0.049
CI = (0.501, 0.599)
Therefore, we can say with 95% confidence that the true proportion of Canadians who would rather retire in the US is between 0.501 and 0.599. This confidence interval was calculated using three key pieces of information: the sample proportion, the z-score for 95% confidence, and the sample size.

To calculate the 95% confidence interval for the true proportion of Canadians who would rather retire in the US, we first need to find the sample proportion (p-hat). In this case, p-hat is 220/400, which equals 0.55. Next, we use the formula for the 95% confidence interval, which is: p-hat ± Z * √(p-hat * (1-p-hat) / n). Here, Z is the critical value for a 95% confidence interval (1.96), and n is the sample size (400). Now, let's plug in the values: 0.55 ± 1.96 * √(0.55 * (1-0.55) / 400). This gives us: 0.55 ± 1.96 * √(0.2475 / 400), which simplifies to 0.55 ± 1.96 * 0.0247. Finally, we calculate the interval: 0.55 ± 0.0484. This results in a confidence interval of (0.5016, 0.5984).

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picture answer

HOPE IT HELPS!!!

The terms through degree four of the Maclaurin series is \(f(x)=x+x^{2} +\frac{5x^{3} }{6} +\frac{5x^{4} }{6} +.....\).

In this question,

The function is f(x) = \(\frac{sin(x)}{1-x}\)

The general form of Maclaurin series is

\(\sum \limits^\infty_{k:0} \frac{f^{k}(0) }{k!}(x-0)^{k} = f(0)+\frac{f'(0)}{1!}x+\frac{f''(0)}{2!}x^{2} +\frac{f'''(0)}{3!}x^{3}+......\)

To find the Maclaurin series, let us split the terms as

\(f(x)=sin(x)(\frac{1}{1-x} )\) ------- (1)

Now, consider f(x) =  sin(x)

Then, the derivatives of f(x) with respect to x, we get

f'(x) = cos(x), f'(0) = 1

f''(x) = -sin(x), f'(0) = 0

f'''(x) = -cos(x), f'(0) = -1

\(f^{iv}(x)\) = cos(x), f'(0) = 0

Maclaurin series for sin(x) becomes,

\(f(x) = 0 +\frac{1}{1!}x +0+(-\frac{1}{3!} )x^{3} +....\)

⇒ \(f(x)=x-\frac{x^{3} }{3!} +\frac{x^{5} }{5!}+.....\)

Now, consider \(f(x) = (1-x)^{-1}\)

Then, the derivatives of f(x) with respect to x, we get

\(f'(x) = (1-x)^{-2}, f'(0) = 1\)

\(f''(x) = 2(1-x)^{-3}, f''(0) = 2\)

\(f'''(x) = 6(1-x)^{-4}, f'''(0) = 6\)

\(f^{iv} (x) = 24(1-x)^{-5}, f^{iv}(0) = 24\)

Maclaurin series for (1-x)^-1 becomes,

\(f(x) = 1 +\frac{1}{1!}x +\frac{2}{2!}x^{2} +(\frac{6}{3!} )x^{3} +....\)

⇒ \(f(x)=1+x+x^{2} +x^{3} +......\)

Thus the Maclaurin series for \(f(x)=sin(x)(\frac{1}{1-x} )\) is

⇒ \(f(x)=(x-\frac{x^{3} }{3!} +\frac{x^{5} }{5!}+..... )(1+x+x^{2} +x^{3} +......)\)

⇒ \(f(x)=x+x^{2} +x^{3} - \frac{x^{3} }{6} +x^{4}-\frac{x^{4} }{6} +.....\)

⇒ \(f(x)=x+x^{2} +\frac{5x^{3} }{6} +\frac{5x^{4} }{6} +.....\)

Hence we can conclude that the terms through degree four of the Maclaurin series is \(f(x)=x+x^{2} +\frac{5x^{3} }{6} +\frac{5x^{4} }{6} +.....\).

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Answer:

I can't help you sorry

Step-by-step explanation:

oops

The area of the kite is 40 square meters, calculated by using the area of a kite formula.

To calculate the area of a kite, you need to know the lengths of both the diagonals. Once you have those values, you can use the following formula to find the area:

Area = (d1 x d2) / 2

where d1 and d2 are the lengths of the diagonals.

Here is an example of how to use this formula:

Let's say you have a kite with diagonals of 8 meters and 10 meters. To find the area, you would use the formula:

Area = (8 x 10) / 2

Area = 40 square meters

So the area of the kite is 40 square meters.

There are also many online calculators available that can help you find the area of a kite if you enter the values of the diagonals.

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a.  4 is an extraneous root. , b. 0 is an extraneous root. , c. -3 is an extraneous root. , d. -13.21 is an extraneous root. , e. 9.22 is an extraneous root.

To solve the equation, we can begin by finding a common denominator for the fractions on the left-hand side. The common denominator is (x + 3)(x - 4). We can then rewrite the equation as follows:

[4x(x - 4) + 3(x + 3)] / [(x + 3)(x - 4)] = 5

Expanding and simplifying the numerator, we have:

[4x^2 - 16x + 3x + 9] / [(x + 3)(x - 4)] = 5

Combining like terms, we obtain:

(4x^2 - 13x + 9) / [(x + 3)(x - 4)] = 5

To eliminate the fraction, we can cross-multiply:

4x^2 - 13x + 9 = 5[(x + 3)(x - 4)]

Expanding the right-hand side, we get:

4x^2 - 13x + 9 = 5(x^2 - x - 12)

Simplifying further:

4x^2 - 13x + 9 = 5x^2 - 5x - 60

Rearranging the equation and setting it equal to zero, we have:

x^2 - 8x - 69 = 0

To solve this quadratic equation, we can factor or use the quadratic formula. Factoring the equation may not yield rational roots, so we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For the equation x^2 - 8x - 69 = 0, we have a = 1, b = -8, and c = -69. Substituting these values into the quadratic formula, we get:

x = (-(-8) ± √((-8)^2 - 4(1)(-69))) / (2(1))

= (8 ± √(64 + 276)) / 2

= (8 ± √340) / 2

= (8 ± 2√85) / 2

= 4 ± √85

So, the possible solutions for x are x = 4 + √85 and x = 4 - √85.

Now, let's check which of the given options (a, b, c, d, e) are extraneous roots by substituting them into the original equation:

a. 4: Substitute x = 4 into the equation: 4(4)/(4 + 3) + 3/(4 - 4) = 5. This results in a division by zero, which is undefined. Therefore, 4 is an extraneous root.

b. 0: Substitute x = 0 into the equation: 4(0)/(0 + 3) + 3/(0 - 4) = 5. This also results in a division by zero, which is undefined. Therefore, 0 is an extraneous root.

c. -3: Substitute x = -3 into the equation: 4(-3)/(-3 + 3) + 3/(-3 - 4) = 5. Again, we have a division by zero, which is undefined. Therefore, -3 is an extraneous root.

d. -13.21: Substitute x = -13.21 into the equation and evaluate both sides. If the equation does not hold true, -13.21 is an extraneous root.

e. 9.22: Substitute x = 9.22 into the equation and evaluate both sides. If the equation does not hold true, 9.22 is an extraneous root.

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Answer:

D

Step-by-step explanation:

Substitute n = 1, 2, 3, 4, 5 into the explicit formula

a₁ = \((-2)^{0}\) = 1

a₂ = \((-2)^{1}\) = - 2

a₃ = \((-2)^{2}\) = 4

a₄ = \((-2)^{3}\) = - 8

a₅ = \((-2)^{4}\) = 16

The first 5 terms are 1, - 2, 4, - 8, 16

Answer:

4x-16

Step-by-step explanation:

luckily for you, there is no need to distribute a factor in this equation. yay! :)

combine like terms:

(x-10) + (3x-6)

3x + x = 4x

-10+(-6) = -10-6 = -16

hope this helped, and good luck with algebra! :)

Answer:

c

Step-by-step explanation:

Suki has around 0.9 more hours until the tank will be out of gasoline.

To determine how many more hours until the tank will be out of gasoline, we need to calculate the rate at which Suki is using gasoline based on her current location and the distance she has traveled.

From 2 p.m. to 3 p.m., Suki traveled a distance of 8 miles east and 15 miles north. This forms a right-angled triangle, and we can use the Pythagorean theorem to find the total distance traveled:

Distance = √(8² + 15²) ≈ 17.0 miles

Since Suki's boat averages 6 miles per gallon of gasoline, we can calculate the amount of gasoline used in this one-hour trip:

Gasoline used = Distance / Gas mileage = 17.0 miles / 6 miles/gallon ≈ 2.8 gallons

Now, we can determine how many more hours until the tank will be out of gasoline. Suki's tank holds 8 gallons, and she used approximately 2.8 gallons in one hour. So, the remaining gasoline in the tank is:

Remaining gasoline = Tank capacity - Gasoline used = 8 gallons - 2.8 gallons ≈ 5.2 gallons

To find the time it takes to consume the remaining gasoline, we divide the remaining gasoline by the fuel consumption rate:

Time = Remaining gasoline / Gas mileage = 5.2 gallons / 6 miles/gallon ≈ 0.87 hours

Rounded to the nearest tenth, it will take approximately 0.9 hours for the tank to be out of gasoline if Suki continues at the same rate.

Therefore, Suki has around 0.9 more hours until the tank will be out of gasoline.

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The probability of exactly one successes in five trials  is 0.20

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

The probability is calculated as

P(x) = nCx * p^x * (1 - p)^(n -x)

Where

n = 5

p = 5%

x = 1

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

P(1) = 5C1 * (5%)^1 * (1 - 5%)^(5 -1)

Evaluate

P(1) = 0.20

HEnce, the probability value is 0.20

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To calculate the wavelength of a radio wave, we can use the formula: wavelength = speed of light / frequency  the wavelength of the radio wave used by this radio station is approximately 3.41 meters.

The speed of light is a constant value, approximately 3.00 × 10^8 meters per second.

Given that the frequency of the radio station is 8.81 × 10^7 Hz, we can substitute these values into the formula:

wavelength = (3.00 × 10^8 m/s) / (8.81 × 10^7 Hz)

Performing the calculation, the wavelength of the radio wave used by this radio station is approximately 3.41 meters.Therefore, the wavelength of the wave used by this radio station for its broadcast is approximately 3.41 meters, with three significant figures.

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Answer:

49.12 ft squared

Step-by-step explanation:

1/2(6*8) = 24

1/2(16)pi = 8pi = 25.12

total: 49.12

Answer:

a) 17.5%

b) $150,000

c) 27°

Step-by-step explanation:

Angles around a point add up to 360°.

Therefore, to find the percentage of the portion of the pie chart, divide the degree of the portion by 360° and multiply by 100%

Assuming that Real Estate is half of the circle, and Mutual Funds are a quarter of the circle.

a)  Government Bonds = (63° ÷ 360°) x 100% = 17.5%

b) Crypto Currency = 90° - 63° = 27°

Therefore, (27° ÷ 360°) x 100% = 7.5%

7.5% of $2,000,000 = 0.075 x $2,000,000 = $150,000

c) Crypto Currency = 90° - 63° = 27°

#a

Find percentage (whole is 360°)

#2

Angle of crypto=180-(90+63)=180-153=27°

Percentage:-

Total

#c

Found in second part

Answer: The answer is D.

Step-by-step explanation:

Multiply the art supplies with their assigned prices, then combine like terms.

Given data:

The given triangles is shown.

The expression for the corresponding parts is,