A ball will be thrown upward from a height of 20 meters above the ground, with an initial velocity of 15 meters per second. Its distance from the ground, d, is a function of the time in seconds since the ball was thrown, t. This function is graphed below. How many seconds after the ball is thrown will it be 20 meters from the ground again ?

a) The mean of the random variable is 2.610 (rounded to 2 decimal places).

b) The variance of the random variable is 1.880 (rounded to 3 decimal places).

c) The standard deviation of the random variable is 1.372 (rounded to 3 decimal places).

d) The probability that a randomly selected student has a parent involved in 4 activities is 0.260 (rounded to 3 decimal places).

To compute the variance of the random variable, we need to calculate the squared deviation of each value from the mean, weighted by their respective probabilities, and then sum them up.

b) Variance [tex](\sigma^2)[/tex] of the random variable:

Variance is given by the formula[tex]Var(X) = \sum [(X - \mu)^2 \times P(X)],[/tex] where X represents the values of the random variable, μ is the mean, and P(X) is the probability.

Using the given data:

X: 0 1 2 3 4

P(X): 0.053 0.117 0.258 0.312 0.26

μ (mean): 2.610

Calculating the squared deviations for each value:

[tex](0 - 2.610)^2 \times 0.053 = 14.152[/tex]

[tex](1 - 2.610)^2 \times 0.117 = 0.291[/tex]

[tex](2 - 2.610)^2 \times 0.258 = 0.148[/tex]

[tex](3 - 2.610)^2 \times 0.312 = 0.122[/tex]

[tex](4 - 2.610)^2 \times 0.26 = 1.429[/tex]

Summing up the squared deviations:

Var(X) = 14.152 + 0.291 + 0.148 + 0.122 + 1.429 = 16.142

Therefore, the variance of the random variable is 16.142.

c) Standard deviation (σ) of the random variable:

The standard deviation is the square root of the variance.

Taking the square root of the variance calculated above:

Standard deviation (σ) = √(16.142) ≈ 4.020 (rounded to 3 decimal places)

d) Probability of a randomly selected student having a parent involved in 4 activities:

The probability of a specific value occurring in a discrete probability distribution is given by the corresponding probability value.

From the given data:

P(X = 4) = 0.26

Therefore, the probability that a randomly selected student has a parent involved in 4 activities is 0.26 (rounded to 3 decimal places).

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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: if it's true that 10 > 7 (P), then it's also true that 10 > 5 (Q).

Step-by-step explanation: In the context of logic and truth tables, p → q can be read as "if p then q." You've provided the truth values for the combinations of p and q, which I'll summarize here:

If p and q are both False (F), then p → q is True (T).

If p is True (T) and q is False (F), then p → q is False (F).

If p is False (F) and q is True (T), then p → q is True (T).

If p and q are both True (T), then p → q is True (T).

Given your propositions:

P: 10 > 7

Q: 10 > 5

P is True because 10 is indeed greater than 7. Q is also True because 10 is greater than 5.

Therefore, we're in the fourth case of your truth table: both p and q are True, so p → q is also True.

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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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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Answer:

  125/384 ≈ 0.32552

Step-by-step explanation:

You want the area between the curves y = 5x and y = 8x².

The difference between the curves is ...

  f(x) = 5x -8x² = x(5 -8x)

This difference is zero when ...

  x = 0

  5 -8x = 0   ⇒   x = 5/8

The area will be the integral of f(x) with the limits 0 and 5/8:

  [tex]\displaystyle \text{area}=\int_0^\frac{5}{8}{(5x-8x^2)}\,dx=\dfrac{5}{2}\cdot\left(\dfrac{5}{8}\right)^2-\dfrac{8}{3}\cdot\left(\dfrac{5}{8}\right)^3\\\\\\\text{area}=\left(\dfrac{5}{8}\right)^2\left(\dfrac{5}{2}-\dfrac{8}{3}\cdot\dfrac{5}{8}\right)=\dfrac{25}{64}\cdot\dfrac{5}{6}=\boxed{\dfrac{125}{384}}[/tex]

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Answer:

V = (4/3) × 3.14 × 14³ = 11,310.08 cubic feet

Work Shown:

d = diameter = 28

r = radius = d/2 = 28/2 = 14

V = volume of a sphere

V = (4/3)*pi*r^3

V = (4/3)*3.14*(14)^3

V = 11,488.2133 cubic feet approximately

The info "weighs almost 8 tons" is never used. It is likely an intended distraction. All we need is the radius of the sphere to get its volume.

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:  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

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:

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

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

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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Answer:

Expected winnings = $1.33

Expected profit or loss = -$2.67

Step-by-step explanation:

Winning Probability Prize Value

Yes   1/150         $200

No         149/150         $0

Expected winnings of one raffle ticket:

Expected winnings = (Probability of winning x Prize value) + (Probability of losing x Prize value)

Expected winnings = (1/150 x $200) + (149/150 x $0)

Expected winnings = $1.33

If a raffle ticket costs $4, the expected profit or loss of one raffle ticket can be calculated as:

Expected profit or loss = Expected winnings - Cost of ticket

Expected profit or loss = $1.33 - $4

Expected profit or loss = -$2.67

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.

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 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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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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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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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

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 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.

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

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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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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Answer:

d

Step-by-step explanation:

Answer: y = 550x

Step-by-step explanation:

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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