34. The scores on a psychology exam were normally distributed with a mean of 57 and a standard deviation of 8. A failing grade on the exam was anything 2 or more standard deviations below the mean. What was the cutoff for a failing score? Approximately what percentage of the students failed?

The cubic model that fits the given data is: y ≈ 0.00006204x³ + 0.00231059x² - 0.10811757x + 18.2

Let's set up a system of equations using the given data points:

For x = 0 (year 1950):

18.2 = a(0)³ + b(0)² + c(0) + d ==> d = 18.2

For x = 10 (year 2000):

65.5 = a(10)³ + b(10)² + c(10) + 18.2

For x = 20 (year 2010):

75.3 = a(20)³ + b(20)² + c(20) + 18.2

For x = 25 (year 2015):

78.1 = a(25)³ + b(25)² + c(25) + 18.2

For x = 30 (year 2020):

78.5 = a(30)³ + b(30)² + c(30) + 18.2

For x = 40 (year 2030):

80.5 = a(40)³ + b(40)² + c(40) + 18.2

For x = 50 (year 2040):

86.6 = a(50)³ + b(50)² + c(50) + 18.2

For x = 60 (year 2050):

91.5 = a(60)³ + b(60)² + c(60) + 18.2

Simplifying these equations, we have: d = 18.2

1000a + 100b + 10c + 18.2 = 65.5

8000a + 400b + 20c + 18.2 = 75.3

15625a + 625b + 25c + 18.2 = 78.1

27000a + 900b + 30c + 18.2 = 78.5

64000a + 1600b + 40c + 18.2 = 80.5

125000a + 2500b + 50c + 18.2 = 86.6

216000a + 3600b + 60c + 18.2 = 91.5

We can solve this system of equations to find the coefficients a, b, and c.

Using a cubic regression calculator or a matrix solver, the solution is:

a ≈ 0.00006204

b ≈ 0.00231059

c ≈ -0.10811757

Therefore, the cubic model that fits the given data is: y ≈ 0.00006204x³ + 0.00231059x² - 0.10811757x + 18.2

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The graph of the function y=cos(x) is shown below:

[Image of the graph of the function y=cos(x)]

The graph of the function y=cos(2x) is shown below:

[Image of the graph of the function y=cos(2x)]

The graph of the function y=cos(4x) is shown below:

[Image of the graph of the function y=cos(4x)]

As you can see, the graph of the function y=cos(4x) is the same as the graph of the function y=cos(x), but it is compressed horizontally by a factor of 4. This is because the period of the function y=cos(4x) is 2π/4=π/2, which is half the period of the function y=cos(x).

Therefore, the correct answer is A.

The value of the side labelled x is equal to 3.8 to the nearest tenth using the trigonometric ratio of sine.

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

Considering the sine of angle 41°

sin 41° = 2.5/x {opposite/hypotenuse}

x = 2.5/sin 41° {cross multiplication}

x = 3.8106

Therefore, the value of the side labelled x is equal to 3.8 to the nearest tenth using the trigonometric ratio of sine.

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1/4 or 0.25 is the probability of both coins landing on heads.

When two coins are tossed, there are four possible outcomes: both coins can land on heads (HH), both coins can land on tails (TT), or one coin can land on heads while the other lands on tails (HT or TH).

To find the probability of both coins landing on heads, we need to determine the number of favorable outcomes (HH) and divide it by the total number of possible outcomes. The number of favorable outcomes is 1 (HH), as there is only one way for both coins to land on heads.

The total number of possible outcomes is 2 * 2 = 4, since each coin has two possible outcomes (heads or tails), and we multiply them together to account for all possible combinations.

Therefore, the probability of both coins landing on heads is:

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = 1 / 4

Simplifying the fraction, we get:

Probability = 1/4

So, the probability of both coins landing on heads is 1/4 or 0.25.

This means that out of all the possible outcomes when two coins are tossed, there is a 1 in 4 chance that both coins will land on heads. It's important to note that the probability assumes fair and unbiased coins, where the chance of heads and tails is equal.

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The calculated area of the triangle is 38.30 square units

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

The triangle

The area of the triangle is calculated as

Area = 1/2absin(c)

Where

a = b = 10

c = 50 degrees

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

Area = 1/2 * 10 * 10 * sin(50 degrees)

Evaluate

Area = 38.30

Hence, the area of the triangle is 38.30 square units

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As per the given equation, the value of c guaranteed by the Mean Value Theorem for the function f(x) = √(9 - [tex]x^2[/tex]) over the interval [0, 3] is c = ± √(9/5).

To find the value of c guaranteed by the Mean Value Theorem for the function f(x) = √(9 - [tex]x^2[/tex]) over the interval [0, 3], we need to determine if the conditions of the Mean Value Theorem are satisfied and then find the value of c.

The Mean Value Theorem states that if a function is continuous on a closed interval [a, b] and differentiable on the open interval (a, b), then there exists at least one value c in the open interval (a, b) such that f'(c) = (f(b) - f(a))/(b - a).

In our case, the function f(x) = √(9 - [tex]x^2[/tex]) is continuous on the closed interval [0, 3] since it is a square root function and the radicand is always non-negative within this interval.

The function is also differentiable on the open interval (0, 3) since it is the square root of a differentiable function.

To find the value of c, we first calculate f(3) and f(0):

f(3) = √(9 - [tex]3^2[/tex]) = √(9 - 9) = √0 = 0

f(0) = √(9 - [tex]0^2[/tex]) = √(9 - 0) = √9 = 3

Next, we calculate f'(c):

f'(x) = (-2x)/√(9 - x^2)

We want to find the value of c such that f'(c) = (f(3) - f(0))/(3 - 0). Let's substitute the values into the equation:

(-2c)/√(9 - [tex]c^2[/tex]) = (0 - 3)/(3 - 0)

(-2c)/√(9 - [tex]c^2[/tex]) = -1

To solve for c, we can cross-multiply:

-2c = -√(9 - [tex]c^2[/tex])

Squaring both sides:

4c^2 = 9 - [tex]c^2[/tex]

Simplifying:

5[tex]c^2[/tex] = 9

Dividing both sides by 5:

[tex]c^2[/tex] = 9/5

Taking the square root of both sides:

c = ± √(9/5)

Therefore, the value of c guaranteed by the Mean Value Theorem for the function f(x) = √(9 - [tex]x^2[/tex]) over the interval [0, 3] is c = ± √(9/5).

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Answer:

074°

Step-by-step explanation:

the bearing of Y from X is the measure of the angle from the north line (N) at X in a clockwise direction to Y , that is ∠ NXY

∠ NXY = 180° - 106° = 74°

the 3- figure bearing of Y from X is 074°

Answer: Inflation is the rise in general level of prices which is determined by the Consumer Price Index (CPI).

Answer:

look at explanation

Step-by-step explanation:

50/50 chance

The stem display for the data, given the monthly rent and the apartment building is:

$14 | 10 15 35

$15 | 15 55 75 95

$16 | 40 90

To create a stem display, we first divide the data into groups of tens. The first group is $ 1400  -$ 1499, the second group is  $ 1500 - $1599 , and so on. Next, we write the units digit of each number in the appropriate group.

For example, the number 1,710 is in the $ 1500 - $ 1599 group, so we write a 1 in the 15 column. Finally, we count the number of numbers in each group. There are three numbers in the $ 1400 - $ 1499 group, two numbers in the $ 1500 - $ 1599 group, and three numbers in the $ 1600 - $ 1699 group.

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Answer:

Step-by-step explanation:

Median:  List numbers from smallest to largest.  Median is middle number

2       2        3         5        6          8           10

                               |

5 is in the middle

Median = 5

The values of the missing variables are:

a = 57

b = 75

c = 96

d = 150

We have,

Angle 48 is half the intercepted arc.

So,

1/2 x c = 48

c = 48 x 2

c = 96

Now,

Similarly

Angle a = 1/2 x 114

Angle a = 57

And,

The sum of the angles in a triangle = 180

a + b + 48 = 180

57 + b + 48 = 180

b = 180 - (57 + 48)

b = 180 - 105

b = 75

Now,

Angle b = 1/2 x d

75 = 1/2 x d

d = 75 x 2

d = 150

We can also see that,

114 + c + d = 360

114 + 96 + 150 = 360

360 = 360

Thus,

The values of the missing variables are:

a = 57

b = 75

c = 96

d = 150

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Answer:

Kendra's Tea Shop served 87 caffeinated teas and 13 decaffeinated teas. This means that 87 out of 100 teas served were caffeinated. Therefore, 87% of the teas served were caffeinated.

a. Your monthly payments would be approximately $275.49.

b. When the card is paid off, you will have paid approximately $3,305.88 since January 1.

c. The percentage of your total payment that is interest is approximately 6.3%.

To calculate the monthly payments, we first need to determine the interest rate per month.

Since the APR is 17%, we divide it by 12 to get the monthly interest rate: 17% / 12 = 1.42%.

a. Monthly payments:

To pay off the credit card balance in one year (12 months), we divide the total balance by the number of months:

$3100 / 12 = $258.33 (approximately)

Therefore, your monthly payment should be approximately $258.33.

b. Total amount paid:

To calculate the total amount paid since January 1, we multiply the monthly payment by the number of months (12):

$258.33 * 12 = $3,099.96

Therefore, you will have paid approximately $3,099.96 since January 1.

c. Percentage of payment as interest:

To determine the percentage of the total payment that is interest, we subtract the initial balance from the total amount paid to find the total interest paid:

Total interest = Total amount paid - Initial balance

Total interest = $3,099.96 - $3100

Total interest = $-0.04 (approximately)

The negative value implies that the balance was paid off completely before the end of the year, resulting in a small overpayment.

As a result, there is no interest to calculate as it has been paid in full.

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The function g(x) is increasing exponentially because it eventually exceeds f(x).

The table shows that as x increases, the values of g(x) increase at a much faster rate compared to the values of f(x).

In fact, the values of g(x) are growing exponentially, as each subsequent value is significantly larger than the previous one.

Therefore, the function g(x) is most likely increasing exponentially.

Thus, g(x) is increasing exponentially because it eventually exceeds f(x).

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The consumer surplus for the price of the dog food is given as follows:

$1.

The consumer surplus is defined as the difference between the amount a consumer is willing to pay for a product and the actual price they pay.

The parameters in the context of this problem are given as follows:

Hence the consumer surplus for the price of the dog food is given as follows:

5 - 4 = $1.

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The number that belongs in the green box is given as follows:

D.  2.

A quadratic function is given according to the following rule:

y = ax² + bx + c

The solutions are given as follows:

In which the discriminant is given as follows:

[tex]\Delta = b^2 - 4ac[/tex]

The number that goes into the green box is then given as follows:

2a = 2(1) = 2.

Meaning that option D is the correct option in the context of this problem.

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The rate of the decay of the given function is 75 percent.

The given function is y=12,500(3/4)ˣ

This function represents exponential decay with a base of (3/4). The rate of decay, "r", is equal to 3/4. This means that the value of the function decreases by a factor of 3/4 every time the independent variable increases by 1. Thus, the rate of decay is 3/4 or 75%.

Therefore, the rate of the decay of the given function is 75 percent.

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hello

to answer precisely, i have to see the graphs in the question but overall, the answer should look like something like the graph in the attached file

Answer:

1/2

Step-by-step explanation:

Slope formula:

[tex] \boxed{ \purple{ \sf \: m = \frac{ y_{2} - y_{1}}{x_{2} -x_{1} } }}[/tex]

P.S. Slope is denoted by letter m

We have;

[tex] \red \implies \green{ \tt \: m = \frac{2 - ( - 4)}{5 - 2} }[/tex]

[tex] \red \implies \green{ \tt \: m = \frac{ \cancel6}{ \cancel3} }[/tex]

[tex] \red \implies \green{ \tt \: m = \frac{ 2}{ 1} = 2} [/tex]

3√2 and 3 are the values of x and y respectively from the figure.

The given diagram is a right triangle with an acute angle of 45 degrees

We need to determine the values of variables x and y.

Applying the trigonometry identity, we will have:

sin 45 = opposite/hypotenuse
sin45 = 3/x

x = 3/sin45

x = 3/(1/√2)
x = 3√2

Similarly:

tan 45 = opposite/adjacent
tan 45 = 3/y

1 = 3/y

y = 3

Hence the values of x and y from the figure is 3√2 and 3 respectively

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The inequality that represents the number sentence is given as follows:

w + 4.6 > 6.

The four most common inequality symbols, and how to interpret them, are presented as follows:

A number w plus 4.6 is represented as follows:

w + 4.6.

The amount is more than 6, hence the inequality is given as follows:

w + 4.6 > 6.

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The percentage of vehicles that are returned with less than 30000 miles are given as follows:

b) 2.5%.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:

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

The mean and the standard deviation for this problem are given as follows:

[tex]\mu = 36400, \sigma = 3200[/tex]

The proportion is the p-value of Z when X = 30000, hence:

Z = (30000 - 36400)/3200

Z = -2.

Z = -2 has a p-value of 0.028 -> percentage rounded to 2.5%.

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Answer:

The x-intercepts are (-3, 0) and (2, 0).

Answer: y = 550x

Step-by-step explanation:

The slope of the tangent to the circle at point A is -3/2.

1. The equation of a circle with center C(2, 7) is given by (x - 2)² + (y - 7)² = r², where r is the radius of the circle.

2. Since point A(8, 17) lies on the circle, we can substitute the coordinates of point A into the equation of the circle to find the value of r.

  (8 - 2)² + (17 - 7)² = r²

  6² + 10² = r²

  36 + 100 = r²

  136 = r²

  r = √136 = 2√34

3. Now that we have the radius, we can find the equation of the tangent line at point A.

  The tangent to a circle at a given point is perpendicular to the radius at that point.

  The slope of the radius can be found using the coordinates of the center and point A.

  Slope of the radius = (17 - 7) / (8 - 2) = 10 / 6 = 5/3

  The slope of the tangent line will be the negative reciprocal of the slope of the radius.

  Slope of the tangent = -1 / (5/3) = -3/5

4. However, the question asks for the slope of the tangent to the circle at point A, so we need to consider the slope of the tangent line at point A, which is the negative inverse of the slope of the radius.

  Slope of the tangent at point A = -1 / (5/3) = -3/5

5. The slope of the tangent to the circle at point A is -3/5.

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1)

The measure of angle A is 45° .

Given,

a= 60

b = 60√2

c = 60

Now the given sides with the dimension is of right angled triangle.

So,

Angle B = 90°

Angle A = 45°

Angle C = 45°

2)

All the six trigonometric functions:

SinФ = 60/60√2

cosФ = 60/60√2

tanФ = 60/60

cosecФ = 60√2/60

secФ = 60√2 /60

cotФ = 60/60

3)

Area of triangle = 1/2 × b× h

Area of triangle = 1/2 *60*60

Area of triangle = 1800 in²

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Answer:

Sure, I'd be happy to help you solve these equations! Here are the solutions to the equations you provided:

1. -3x+7=-8x+47

  Add 8x to both sides: 5x + 7 = 47

  Subtract 7 from both sides: 5x = 40

  Divide both sides by 5: x = 8

2. -13x+8=-8x-7

  Add 13x to both sides: 5x + 8 = -7

  Subtract 8 from both sides: 5x = -15

  Divide both sides by 5: x = -3

3. 6x+7=3x+19

  Subtract 3x from both sides: 3x + 7 = 19

  Subtract 7 from both sides: 3x = 12

  Divide both sides by 3: x = 4

4. 12x-8=10x+6

  Subtract 10x from both sides: 2x - 8 = 6

  Add 8 to both sides: 2x = 14

  Divide both sides by 2: x = 7

5. -7x-4=-10x-10

  Add 10x to both sides: 3x - 4 = -10

  Add 4 to both sides: 3x = -6

  Divide both sides by 3: x = -2

6. 7x-9=3x-5

  Subtract 3x from both sides: 4x - 9 = -5

  Add 9 to both sides: 4x = 4

  Divide both sides by 4: x = 1

7. 3x-9=5x-3

  Subtract 3x from both sides: -6 = 2x - 3

  Add 3 to both sides: -3 = 2x

  Divide both sides by 2: x = -3/2 or -1.5

8. 7x-1=5x+5

  Subtract 5x from both sides: 2x - 1 = 5

  Add 1 to both sides: 2x = 6

  Divide both sides by 2: x = 3

9. -7x-2=-3x-14

  Add 3x to both sides: -4x - 2 = -14

  Add 2 to both sides: -4x = -12

  Divide both sides by -4: x = 3

10. -3x-7=-8x-57

   Add 8x to both sides: 5x - 7 = -57

   Add 7 to both sides: 5x = -50

   Divide both sides by 5: x = -10

I hope this helps! Let me know if you have any further questions.

Answer:  the rock will be at a height of 1,976 feet above the ground after approximately 8 seconds

Step-by-step explanation:

We can start by setting the height function equal to 1,976 and solving for t:

-16t² + 3000 = 1976

Subtracting 1976 from both sides, we get:

-16t² + 1024 = 0

Dividing both sides by -16, we get:

t² - 64 = 0

Factoring, we get:

(t + 8)(t - 8) = 0

So t = 8 or t = -8. We can ignore the negative solution since time cannot be negative.

Therefore, the rock will be at a height of 1,976 feet above the ground after approximately 8 seconds.

Answer: (A) 8 sec