Enter the correct answer in the box.
The function f(x) = 7x + 1 is transformed to function g through a horizontal compression by a factor of What is the equation of function g?
Substitute a numerical value for k into the function equation.

Approximately 15.87% of the bowlers in the Capital Three bowling tournament performed better than Dr. Baker.

Standard deviation (σ) = √(variance) = √(121) = 11

Now, we can calculate the z-score for Dr. Baker's average of 169 using the formula:

z = (X - μ) / σ

z = (169 - 158) / 11

z = 11 / 11

z = 1

Dr. Baker's z-score is 1, meaning his performance is one standard deviation above the mean.

The area to the left (or the cumulative probability) is approximately 0.8413

1 - 0.8413 = 0.1587

Approximately 15.87% of the bowlers in the Capital Three bowling tournament performed better than Dr. Baker.

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Answer:

441cm^2

Step-by-step explanation:

84 divided by 4 is 21

21cm*21cm is 441cm^2

The probability that at least 2 students feel like they can do better in their math class is E. 0.9130.

To find the probability that at least 2 students feel like they can do better, we need to calculate P(X >= 2). This can be done using the cumulative distribution function (CDF) of the binomial distribution:

P(X >= 2) = 1 - P(X < 2) = 1 - P(X = 0) - P(X = 1)

Using the binomial probability formula, we can calculate:

P(X = 0) = (5 choose 0) * 0.6^0 * 0.4^5 = 0.01024

P(X = 1) = (5 choose 1) * 0.6^1 * 0.4^4 = 0.07680

Therefore,

P(X >= 2) = 1 - 0.01024 - 0.07680 = 0.91296

Rounding this to four decimal places, we get: 0.9130

Therefore, the answer is option E: 0.9130.

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Answer:

x = 68

Step-by-step explanation:

X + 22 = 90 degrees

90 - 22 = 68 degrees

Step-by-step explanation:

first of all, remember, the sum of all angles in a triangle is always 180°.

now, we see that both bottom angles are 45°.

that means

180 = 45 + 45 + top-angle

90° = top-angle

aha ! we are dealing with a right-angled triangle, that is also isoceles (both legs are equally long, because the angles with the baseline are equal).

via Pythagoras

c² = a² + b²

where "c" is the Hypotenuse (the side opposite of the 90° angle), "a" and "b" are the legs.

in our case both legs are 7×sqrt(2) units long.

so,

baseline² = (7×sqrt(2))² + (7×sqrt(2))² = 49×2 + 49×2 =

= 98 + 98 = 196

baseline = sqrt(196) = 14 units

x is now the height of this triangle, and because of the isoceles form, it splits the baseline exactly in half.

so, one side of the baseline from x is 14/2 = 7 units.

and now Pythagoras for that sub-triangle :

(7×sqrt(2))² = 7² + x²

98 = 49 + x²

49 = x²

x = sqrt(49) = 7 units

the area of the triangle is

baseline × height / 2

in our case

14 × 7 / 2 = 7×7 = 49 units²

The angle of depression that the paper airplane is flying down at 55. 78 degrees

Note that the different trigonometric identities in mathematics are;

These identities also have their ratios are;

sin θ = opposite/hypotenuse

cos θ = adjacent//hypotenuse

tan θ = opposite/adjacent

From the information given, we have;

Using the cosine identity

Adjacent = 9 feet

Hypotenuse = 16 feet

Substitute the values

cos θ = 9/ 16

divide the values

cos θ = 0. 5625

θ = 55. 78 degrees

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Answer:

55.8° (nearest tenth)

Step-by-step explanation:

The angle of depression is the angle between the horizontal line of sight at the top of the treehouse and line of sight to the sandbox (the flight path of the paper airplane). (See attached diagram).

To find the angle of depression, we can use the cosine trigonometric ratio. The cosine of an angle is equal to the ratio of the length of the side adjacent the angle to the length of the hypotenuse.

[tex]\boxed{\begin{minipage}{9 cm}\underline{Cosine trigonometric ratio} \\\\$\sf \cos(\theta)=\dfrac{A}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]

In this case, the length of the side adjacent the angle of depression is equal to the distance between the base of the tree and the sandbox, so A = 9 ft. The hypotenuse is the distance the airplane flies through the air, so H = 16 ft.

Substitute these values into the cosine ratio and solve for θ:

[tex]\cos (\theta)=\dfrac{9}{16}[/tex]

[tex]\theta=\cos^{-1}\left(\dfrac{9}{16}\right)[/tex]

[tex]\theta=55.7711336...^{\circ}[/tex]

[tex]\theta=55.8^{\circ}\; \sf (nearest \; tenth)[/tex]

Therefore, the angle of depression that the paper airplane is flying down at is 55.8° (nearest tenth).

To determine which of the given fractions is a multiple of 1/9, we need to check if each fraction can be written as the product of 1/9 and another integer.

3/9 = 1/3, which is not a multiple of 1/9

4/9 cannot be simplified further and is therefore a multiple of 1/9

9/12 can be simplified to 3/4, which is not a multiple of 1/9

9/10 cannot be simplified further and is therefore a multiple of 1/9

2/9 cannot be simplified further and is therefore a multiple of 1/9

9/9 = 1, which is not a multiple of 1/9

Therefore, the fractions that are multiples of 1/9 are 4/9, 9/10, and 2/9.

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Answer:

1st one is 6.9 X 10^6

2nd one is 2 x 10^5

Step-by-step explanation:

The proportional relationship between x and y is shown by the table:

x   7  14  28   35

y  1     2    4     5

A connection among two factors that changes proportionally is referred to as a proportional relationship. If y=kx, where k is just the proportionality constant, can be used to represent two quantities, x and y, then they are said to be proportional.

From the given options, consider the table:

x   7  14  28   35

y  1     2    4     5

As per proportional relationship.:

y=kx

k = y/x (must be same in all cases)

k = 1/7

k = 14/2 = 1/7

k = 4/28 = 1/7

k = 5/35 = 1/7

As all the k value for the given values of x and y are found equal.

Thus, the proportional relationship between x and y is shown by the table:

x   7  14  28   35

y  1     2    4     5

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The answer for the given expression is =1/128[35-56cos2x+28cos4x-8cos6x+cos8x]

What is trignomatric functions?

All trigonometric identities are built upon the foundation of the six trigonometric ratios. Some of their names are sine, cosine, tangent, cosecant, secant, and cotangent. The adjacent side, opposite side, and hypotenuse side of the right triangle are used to define each of these trigonometric ratios.

What is multiple angles?

If angle A is taken as a given, then many angles are 2A, 3A, 4A, etc. The many angle formulas employ the double and triple angles formulas. Sine, cosine, and tangent are the often utilised trigonometric functions for the multiple angle formula.

Answer is attached as a image must check:

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We can rewrite sin⁸x in terms of first powers of the cosines of multiple angles as:

sin⁸x = 1/128 (35 - 4cos²x + 40cos⁴x - 64cos⁶x + cos⁸x)

Trigonometric functions raised to powers can be rewritten using double-angle, half-angle, and Pythagorean identities in power lowering formulas. Equations can be made simpler using them, and trigonometric expressions can be precisely determined.

We can use the power-reducing formulas to rewrite sin⁸x in terms of cosines of multiple angles as follows:

sin²x = 1 - cos²x   (first power-reducing formula)

sin⁴x = (sin²x)² = (1 - cos²x)²

      = 1 - 2cos²x + cos⁴x   (second power-reducing formula)

sin⁶x = (sin⁴x)(sin²x)

      = (1 - 2cos²x + cos⁴x)(1 - cos²x)

      = 1 - 3cos²x + 3cos⁴x - cos⁶x   (third power-reducing formula)

sin⁸x = (sin⁶x)(sin²x)

      = (1 - 3cos²x + 3cos⁴x - cos⁶x)(1 - cos²x)

      = 1 - 4cos²x + 6cos⁴x - 4cos⁶x + cos⁸x

Now we can substitute the expression for sin⁸x into the given expression and simplify it:

1/128 (35 - 56 cos2x + 28 cos4x - 8 cos6x + cos8x)

= 1/128 (35 - 56(2cos²x-1) + 28(4cos⁴x-3cos²x) - 8(8cos⁶x-8cos⁴x+cos²x) + cos⁸x)

= 1/128 (35 - 112cos²x + 56 + 112cos⁴x - 84cos²x - 64cos⁶x + 64cos⁴x - 8cos²x + cos⁸x)

= 1/128 (35 - 4cos²x + 40cos⁴x - 64cos⁶x + cos⁸x)

Therefore, we can rewrite sin⁸x in terms of first powers of the cosines of multiple angles as:

sin⁸x = 1 - 4cos²x + 6cos⁴x - 4cos⁶x + cos⁸x

     = 1/128 (35 - 4cos²x + 40cos⁴x - 64cos⁶x + cos⁸x)

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The ratio of the areas is given as follows:

1:5.8.

The ratio of the areas is obtained applying the proportions in the context of the problem.

When a prism is dilated by a scale factor of k, we have that:

Hence the ratio of the areas is the cubic root of the ratio of the volumes squared, thus, as the ratio of the volumes is of 1:14, we have that:

(14²)^(1/3) = 5.8.

Hence:

1:5.8.

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the formula for the exponential function N(t) is N(t) = 14 * 59in power (t/6), where N is the population at time t and t is the time in hours, days, or any other unit of time as long as it is consistent with the time unit used in the formula

How to solve the question?

Let N(t) be the exponential function we are trying to find, where N is the population at time t.

From the given information, we know that when t=0, N(0) = 14, which is the initial value of N.

We also know that when t is increased by 6, N is multiplied by 59. In other words,

N(t+6) = 59N(t)

We can use this relationship to express N(t+6) in terms of N(t) by substituting N(t+6) with 59N(t) in the above equation, giving us:

59N(t) = N(t+6)

Now, we can use this equation to solve for N(t) in terms of N(0) by repeatedly substituting N(t) with 59N(t-6), 59²N(t-12), 59³N(t-18), and so on.

N(t) = 59  in power (t/6) * N(0)

Using the initial value of N(0) = 14, we get:

N(t) = 14 * 59 in power (t/6)

Therefore, the formula for the exponential function N(t) is N(t) = 14 * 59^(t/6), where N is the population at time t and t is the time in hours, days, or any other unit of time as long as it is consistent with the time unit used in the formula

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Answer:

The answer for Surface area is 332m²

Step-by-step explanation:

S.A=area of 2 triangle +Area of 2 rectangle +Area of rectangle

S.A=2×1/2×4×3 + 2(20×5) + 20×6

S.A=12+2(100)+120

S.A=12+200+120

S.A=212+120

S.A=332m²

According to the given condition. The inequality that matches this graph is option B) x ≥ -5.

An inequality equation is a mathematical statement that compares two expressions using an inequality symbol such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).

The inequality that matches this graph is option B, "x ≥ -5". The graph represents a solid dot at x = -5 and a shaded region to the right of x = -5, including x = -5. This means that x can take on any value greater than or equal to -5, so the inequality can be written as x ≥ -5.

Therefore, According to the given condition. The inequality that matches this graph is option B) x ≥ -5.

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Answer:

  (a)  52°

  (b)  128°

Step-by-step explanation:

You want the angle whose sine is 0.79 (a) in the interval [0, 90°], and (b) in the interval [90°, 180°].

The inverse sine function is used to find the angle when its sine is known.

  sin(x) = 0.79

  x = arcsin(0.79) ≈ 52°

x ≈ 52° in the domain 0 ≤ x ≤ 90°.

The sine function is symmetrical about x = 90°, so other angles for which sin(x) = 0.79 can be found as 180° -x.

  180° -52° = 128°

x = 128° in the domain 90° ≤ x ≤ 180°.

__

Additional comment

The attachment shows the angles and that their sine is 0.79. Note that the calculator is set to Degrees mode.

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Answer:

-9.5.

Step-by-step explanation

To find a reasonable value for n, we need to use the given data points and the equation of the line. We can plug in any pair of x and y values into the equation and solve for m or b. For example, using (4, 2), we get:

2 = m(4) + b

Solving for b, we get:

b = 2 - 4m

Now we can plug in another pair of x and y values, such as (7, 4.5), and use the value of b we just found:

4.5 = m(7) + 2 - 4m

Solving for m, we get:

m = 0.5

Now we have the slope and the y-intercept of the line. The equation is:

y = 0.5x + 2 - 4(0.5)

Simplifying, we get:

y = -1.5x + 4

To find n, we need to plug in x = 9 and solve for y:

y = -1.5(9) + 4

y = -9.5

Answer:

A nonlinear line is a line that is not straight. So the answers for these question include B and D

B and D  are not straight lines and they are increasing

Step-by-step explanation:

Hope this helps! =D

Mark me brainliest! =D

Suppose you are driving a car with the velocity function represented by the following equation: f(x)= 2x^3-3x^2-12x+1. The derivative would be: f'(x) = 6x^2 - 6x - 12

To find the acceleration of the car at a particular moment, we would need to calculate the derivative of the velocity function f(x). In this case, the derivative would be:

f'(x) = 6x^2 - 6x - 12

The result of this calculation would give us the instantaneous acceleration of the car at a given time x.

In terms of the car's motion, a positive value for f'(x) would indicate that the car is accelerating, while a negative value would indicate that the car is decelerating. The magnitude of the value would indicate the rate of change of the car's velocity, with larger values indicating a more rapid change.

Translated question "A derivative problem from everyday life using the following function: f(x)= 2x^3-3x^2-12x+1"

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The parametric equations graph as a portion of a parabola. The initial point is (5,0), and the terminal point is (3,4). The vertex of the parabola is (2,9). Arrows are drawn along the parabola to indicate motion right to left.

Parametric equations are a way of expressing a set of equations that define the coordinates of a point in terms of a third variable (parameter) that varies over a certain range. In the given problem, the parametric equations:

x(t) = 2 - t

y(t) = (t+3)²

To visualize the graph of these equations, we can substitute different values of t and plot the corresponding points (x(t), y(t)) on a coordinate plane. Since t ranges from -4 to 0, we can choose a few values of t such as t=-4, t=-2, and t=0 to get the corresponding points.

When plotted these points, a portion of a parabola that opens upwards. The vertex of the parabola is at the point (3, 4) where x=2-t and y=(t+3)² intersect. The initial point of the graph is when t=-4, which gives the point (6, 1) and the terminal point is when t=0, which gives the point (2, 9). The arrows are drawn along the parabola to indicate the direction of motion, which is from right to left in this case.

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To find the ratio of edge lengths of two triangles given their area ratio, we need to take the square root of the area ratio.

To find the ratio of edge lengths of two figures given their volume ratio, you need to use the fact that volume is proportional to the cube of the edge length.

If we have two figures, Figure A and Figure B, with edge lengths a and b respectively, and their volumes are in the ratio of V(A) : V(B) = k, then we can set up the following equation:

(Volume of A) / (Volume of B) = (a^3) / (b^3) = k

We can then solve for the ratio of edge lengths:

a / b = (k)^(1/3)

Therefore, to find the ratio of edge lengths given the volume ratio, we need to take the cube root of the volume ratio.

This method works for any shape, as long as the volume formula for that shape involves the cube of the edge length. For example, this method works for cubes, rectangular prisms, cylinders, spheres, and so on.

For triangles, however, we cannot use this method directly because the volume of a triangle is not a function of its edge length. Instead, we can use similar triangles to find the ratio of their edge lengths.

If we have two similar triangles, with corresponding sides in the ratio of a : b, then their areas are in the ratio of (a^2) : (b^2). We can use this fact to find the ratio of their edge lengths:

a / b = sqrt(Area of first triangle / Area of second triangle)

So, to find the ratio of edge lengths of two triangles given their area ratio, we need to take the square root of the area ratio.

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Answer:

There are three steps to find IQR

1. Know how the IQR is used. Essentially, it is a way of understanding the spread or "dispersion" of a set of numbers. The interquartile range is defined as the difference between the upper quartile (the highest 25%) and the lower quartile (the lowest 25%) of a data set.

2. Understand quartiles. To visualize a quartile, chop a list of numbers into four equal parts. Each of these parts is a "quartile."[2] Consider the set: 1, 2, 3, 4, 5, 6, 7, 8.

1 and 2 are the first quartile, or Q1

3 and 4 are the second quartile, or Q2

5 and 6 are the third quartile, or Q3

7 and 8 are the fourth quartile, or Q4

3. Learn the formula. In order to find the difference between the upper and lower quartile, you'll need to subtract the 25th percentile from the 75th percentile.

The formula is written as: Q3 – Q1 = IQR.

Answer:

the answer would be 2.5

Explanation:

The formula for finding the interquartile range takes the third quartile value and subtracts the first quartile value. Equivalently, the interquartile range is the region between the 75th and 25th percentile (75 – 25 = 50% of the data).

Step-by-step explanation:

a1 = 2

a2 = 10

d = a2 - a1 = 10 - 2 = 8

a15 = a + 14d = 2 + 14(8) = 2 + 112 = 114

Answer:

2, 10, 18, 26, 34, 42, 50, 58, 66, 74, 82, 90, 98, 106, 114

Step-by-step explanation:

all you do is add 8 each time

Answer:

Let s be the number of smartphones.

81 = .45s, so s = 180

Answer:

36.45

Step-by-step explanation:

You make 45 into a percentage, which is 0.45%. Then, multiply 0.45 by 81 and you get 36.45. Hope this helps! And if you’re incorrect I deeply apologize. I tried my best and I’m 95% sure that I’m correct.

Answer:

I would say probability.

Graph cookies and coffee, slope -2. Ben buys 2 cookies and 2 coffees. To optimize, allocate budget where MU per dollar is equal.

A budget is a financial plan that outlines expected income and expenses over a certain period. It helps individuals or organizations manage their money and make informed decisions about spending and saving.

Consumption refers to the use of goods and services by individuals, households, or organizations. It is an essential part of the economy and can be influenced by factors such as income, preferences, and prices.

According to the given information:

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1. the APR for this loan is 6%.

2.  the unearned interest is $118.83.

3.  the monthly payment necessary to amortize the $80,000 mortgage at 6% annual interest for 25 years is $506.69.

APR = (finance charge / loan amount) / number of years * 100%

In this scenario, the loan amount is $2400 and the finance charge is $288. Since it's a two-year loan, the number of years is 2

APR = (288 / 2400) / 2 * 100%

APR = 0.06 * 100%

APR = 6%

b.

Number of payments = 4 years * 12 months/year = 48

If the loan is paid off in 3 years instead of 4 years, the number of payments made is:

Number of payments made = 3 years * 12 months/year = 36

Substituting these values into the formula, we get:

Unearned interest = (1426 / 48) * (48 - 36)

Unearned interest = $118.83

3.

To find the monthly payment necessary to amortize a mortgage, we need to use the formula:

M = P * (r / (1 - (1 + r)^(-n)))

where M is the monthly payment, P is the principal (loan amount), r is the monthly interest rate, and n is the total number of payments (in months).

In this scenario, the loan amount is $80,000, the annual interest rate is 6%, and the loan term is 25 years. To find the monthly interest rate, we divide the annual interest rate by 12 (since there are 12 months in a year):

Monthly interest rate = 6% / 12 = 0.005

To find the total number of payments, we multiply the number of years by 12:

Number of payments = 25 years * 12 months/year = 300

Substituting these values into the formula, we get:

M = 80000 * (0.005 / (1 - (1 + 0.005)^(-300)))

M ≈ $506.69

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Answer:d. The inequality that represents "c is between 1/7 and 1/5" is:

1/7 ≤ c ≤ 1/5

e. The inequality that represents "p is not greater than -6" is:

p ≤ -6

f. The inequality that represents "the negative of m is not less than -2" is:

-m ≥ -2

Note that we need to flip the inequality when we multiply or divide both sides by a negative number, which is the case in part (f).

Step-by-step explanation:

Answer:

B. 314 m²

Step-by-step explanation:

Area of circle = π · r²

r = 10 m

π = 3.14

Let's solve

3.14 x 10² = 314 m²

So, the area of the circle is B. 314 m²

The truth set of the inequality is all values of x greater than -9. In interval notation, this can be written as (-9, ∞)

Multiply both sides by -2 (and reversing the direction of the inequality because we are multiplying by a negative number) gives:

x > -2*(5/2 + 2)

x > -5 - 4

x > -9

Therefore, the truth set of the inequality is all values of x greater than -9. In interval notation, this can be written as:

(-9, ∞)

Below is the complete question:

Find the truth set of x*(-1/2) < 5/2 + 2

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By using the partial sum of series is

[tex]a_{n} = 5^{(-n-1) } - (n+1)5^{(-(n+1))}[/tex]

and summation n=1 to infinity of [tex]a_{n}[/tex] is =6 .

To obtain the formula for the nth term of the series and its total, we must first discover the formula for the series' general term.

The formula for the series' nth partial sum is as follows:

[tex]sn = 6 - n*5^{-n}[/tex]

The nth term of the series can be obtained by subtracting the (n+1)th and nth partial sums, i.e.,

a = sn+1 - sn

When we substitute the formula for sn, we get:

[tex]a_{n} = [6 - (n+1)5^{(-(n+1))} ] - [6 - n5^{(-n)} ]\\a_{n} = 5^{(-n-1) } - (n+1)5^{(-(n+1))}[/tex]

As a result, the formula for the series' nth term is:

[tex]a_{n} = 5^{(-n-1) } - (n+1)5^{(-(n+1))}[/tex]

To calculate the series total, take the limit of the nth partial sum as n approaches infinity:

lim(n->inf) lim(n->inf) sn [6 - n*5^(-n)]

lim(n->inf) [n*5(-n)] = 6

= 6 - 0

= 6

As a result, the series' sum is 6.

As a result, the formula for the nth term in the series is:

[tex]a_{n} = 5^{(-n-1) } - (n+1)5^{(-(n+1))}[/tex]

And the series' total is:

a = sum(n=1 to inf) = 6

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