AREA OF TRAPEZOID PLS ANSWER ASAP

The probability that a student chosen randomly from the class passed the test or completed the homework is 20/27.

The probability that a student chosen randomly from the class passed the test or completed the homework is calculated as follows:

Let the probability that a student completed the homework be P(B).

Also, let the probability that a student passed the test be P(A)

P(A or B) = P(A) + P(B) - P(A * B)

From the data table:

The number of students who passed the test = 18

The number of students who completed the homework = 17

The number of students who both passed the test and completed the homework = 15.

Total number of students = 27

P(A) = 18/27

P(B) = 17/27

P(A*B) = 15/27

Therefore,

P(A or B) = 18/27 + 17/27 - 15/27

P(A or B) = 20/27

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We can solve the quadratic equation 2x² - 8x + 5 = 0 by using the quadratic formula, which states that for an equation of the form ax² + bx + c = 0, the solutions are given by:

x = (-b ± sqrt(b² - 4ac)) / 2a

In this case, a = 2, b = -8, and c = 5. Substituting these values into the formula, we get:

x = (-(-8) ± sqrt((-8)² - 4(2)(5))) / (2(2))

x = (8 ± sqrt(64 - 40)) / 4

x = (8 ± sqrt(24)) / 4

x = (8 ± 2sqrt(6)) / 4

Simplifying the expression by factoring out a common factor of 2 in the numerator and denominator, we get:

x = (2(4 ± sqrt(6))) / (2(2))

x = 4 ± sqrt(6)

Therefore, the solutions to the equation 2x² - 8x + 5 = 0 are:

x = 4 + sqrt(6) or x = 4 - sqrt(6)

The model approximates the volume, V, in liters, of air in the lungs during a five-second respiratory cycle using the equation V = -0.0374t + 3 + 0.1525t^2 + 0.1729t.

The given equation represents a mathematical model for estimating the volume of air in the lungs during a respiratory cycle. It is a quadratic equation with three terms: -0.0374t, 0.1525t^2, and 0.1729t.

The term -0.0374t represents the linear decrease in volume over time, indicating that the volume decreases by 0.0374 liters for every second of the respiratory cycle.

The term 0.1525t^2 represents the quadratic relationship between volume and time squared, indicating that the rate of change of volume with respect to time is influenced by the square of time.

The term 0.1729t represents the linear increase in volume over time, indicating that the volume increases by 0.1729 liters for every second of the respiratory cycle.

Overall, this model provides an approximation of the volume of air in the lungs during a five-second respiratory cycle, taking into account both linear and quadratic relationships with time.

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Megha's total movement involves biking 20km north, 30km east, 20km south, and 30km west, resulting in a displacement of zero as she ends up back at her starting point.

Given that,

Megha bikes 20km north.

Megha then bikes 30km east.

After that, Megha bikes 20km south.

Lastly, Megha bikes 30km west.

Megha stops after completing the above movements.

Megha's displacement can be calculated by finding the straight-line distance between her starting point and ending point.

In this case,

She initially bikes 20km north, then 30km east, followed by 20km south, and finally 30km west.

Let's break it down:

The north and south distances cancel each other out, as she ends up back at her starting point vertically.

The east and west distances also cancel each other out, as she ends up back at her starting point horizontally.

Hence,

Megha's displacement is zero. She has returned to her original position.

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Answer:

Markets behave the same way as individual customers because markets are made up of individual consumers.

Step-by-step explanation:

Hose will take about 63.7 minutes to fill the pool and the the depth of the water is increasing at a rate of about 0.0079 feet per minute.

First, let's find the volume of the pool. The pool is in the shape of a cylinder with a height of 4 feet and a diameter of 16 feet, so its radius is half of the diameter, or 8 feet. The volume of a cylinder is given by

V = πr^2h

Plugging in the values, we get

V = π(8 ft)^2(4 ft)

V = 256π cubic feet

Next, let's convert the flow rate to cubic feet per minute. One gallon is equal to 0.1337 cubic feet, so the flow rate is

30 gallons/min x 0.1337 ft^3/gallon = 4.011 ft^3/min

Finally, we can use the formula

time = volume/flow rate

Plugging in the values, we get

time = 256π ft^3 / 4.011 ft^3/min

time ≈ 63.7 minutes

So it will take about 63.7 minutes to fill the pool.

Let's use the formula for the volume of a cylinder again to relate the volume of the water in the pool to its depth

V = πr^2h

We can solve this formula for h

h = V/πr^2

Taking the derivative of both sides with respect to time, we get

dh/dt = d/dt (V/πr^2)

The radius of the pool does not change, so we can treat it as a constant and take it out of the derivative

dh/dt = (1/πr^2) dV/dt

We know the flow rate is constant at 4.011 cubic feet per minute, so the rate of change of the volume of water in the pool is

dV/dt = 4.011

Plugging in the values, we get

dh/dt = (1/π(8 ft)^2) (4.011 ft^3/min)

dh/dt ≈ 0.0079 ft/min

So the depth of the water is increasing at a rate of about 0.0079 feet per minute.

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Answer:

7.6 cm

Step-by-step explanation:

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]

[tex]a^{2}[/tex] + [tex]6.5^{2}[/tex] = [tex]10^{2}[/tex]

[tex]a^{2}[/tex] + 42.25 = 100 Subtract 42.25 from both sides

[tex]a^{2}[/tex] = 57.57

[tex]\sqrt{\a^{a} }[/tex] = [tex]\sqrt{57.57}[/tex]

a ≈ 7.6

Helping in the name of Jesus.

Answer:

7.6 cm

Step-by-step explanation:

a^2+ b^2=c^2

a^2+6.5^2=10^2

a^2+42.25=100 subtract 42.25 from both sides

a^2=57.57

a=√57.57

a=7.6 cm

57 students most likely got heads between 45 and 60 times.

To determine the number of students who got heads between 45 and 60 times, we'll use the normal distribution properties. First, we need to calculate the z-scores for 45 and 60:

Z = (X - μ) / σ

For 45 heads:
Z1 = (45 - 50) / 5 = -1

For 60 heads:
Z2 = (60 - 50) / 5 = 2

Next, we need to find the probability that a student falls between these z-scores. We can do this by looking up the z-scores in a standard normal distribution table or using a calculator. The probabilities corresponding to these z-scores are:

P(Z1) = 0.1587
P(Z2) = 0.9772

Now, subtract P(Z1) from P(Z2) to get the probability of a student's result falling between 45 and 60 heads:

P(45 ≤ X ≤ 60) = P(Z2) - P(Z1) = 0.9772 - 0.1587 = 0.8185

Finally, multiply this probability by the total number of students (70) and round to the nearest whole number:

Number of students = 0.8185 * 70 ≈ 57

So, approximately 57 students most likely got heads between 45 and 60 times.

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A score of at least 183 is required to stay out of the bottom 1.5%. To find the minimum score required to receive the award, we need to determine the z-score corresponding to the top 3% of students.

Since the distribution is normal, we can use the standard normal distribution table to find the z-score. From the table, we find that the z-score corresponding to the top 3% is approximately 1.88.

Therefore, we can use the formula z = (x - μ) / σ, where μ = 400 and σ = 100, to find the minimum score required: 1.88 = (x - 400) / 100

Solving for x, we get: x = 1.88(100) + 400 = 488. Therefore, a score of at least 488 is required to receive the award.

To find the minimum score required to stay out of the bottom 1.5%, we need to determine the z-score corresponding to the bottom 1.5%.

From the standard normal distribution table, we find that the z-score corresponding to the bottom 1.5% is approximately -2.17. Therefore, we can use the same formula as before to find the minimum score required: -2.17 = (x - 400) / 100.

Solving for x, we get: x = -2.17(100) + 400 = 183. Therefore, a score of at least 183 is required to stay out of the bottom 1.5%.

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Answer:

#1        (176 - x)°

#2       m∠3 = m∠4 = 90°

Step-by-step explanation:

If a pair of parallel lines are cut by a transversal, there are several angles that are either equal to each other or are supplementary(angles add up to 180°).

For the specific questions...
For #1.

Angles ∠1 and ∠2 are supplementary angles since they are adjacent to each other and lie on the same straight line

Therefore
m∠1 + m∠2= 180°

Given m∠1 = (x + 4)° this becomes

(x + 4)° + m∠2 = 180°

m∠2 = 180° - (x + 4)°

= 180° - x° - 4°

= (176 - x)°

For #2

∠3 and ∠4 are supplementary angles so m∠3 + m∠4 = 180°

If m∠3 = m∠4 each of these angles must be half of 180°

So
m∠3 = m∠4 = 180/2 = 90°

The number of dolphins that will be there in the year 2100 is 1003, under the condition that in the Gulf of Mexico has been decreasing at a rate of 4% every 10
years.

Here the population of dolphins in the Gulf of Mexico in 2020 was 4,670.The rate of decrease is 4% every 10 years.
Therefore, the population would  decrease by 4% every 10 years.
We want to evaluate the population in 2100, which is  80 years from now, which is eight 10-year periods.
Now, we have to calculate the population after eight 10-year periods.
Each period would decrease the population by 4%.
Hence, the population after eight periods is
4670 × (1 - 0.04)⁸
= 4670 × (0.96)⁸
= 1003

Then, if things progress like this, the population of dolphins in the Gulf of Mexico in the year 2100 will be close to 1000.
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The statement is true as 3/9 and 7/18 represent the same part of the whole.

A sentença é falsa. As frações 3/9 e 7/18 não são equivalentes, pois não representam a mesma parte do todo. Para determinar se duas frações são equivalentes, é necessário simplificar as frações e verificar se os resultados são iguais.

No caso das frações 3/9 e 7/18, podemos simplificar ambas dividindo o numerador e o denominador pelo máximo divisor comum (MDC).

A fração 3/9 pode ser simplificada dividindo ambos por 3, resultando em 1/3. Já a fração 7/18 não pode ser simplificada ainda mais. Portanto, as frações 3/9 e 7/18 não são equivalentes, pois não representam a mesma parte do todo.

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Answer:

[tex]A = 68.75 \text{ square inches}[/tex]

Step-by-step explanation:

First, we need to identify the trapezoid's dimensions:

base 1 = 16

base 2 = 11.5

height = 5

Then, we can plug these values into the trapezoid area formula:

[tex]A = \dfrac{b_1+b_2}{2} \cdot h[/tex]

[tex]A = \dfrac{16 + 11.5}{2} \cdot 5[/tex]

[tex]A = \dfrac{27.5}{2} \cdot 5[/tex]

[tex]A = \dfrac{137.5}{2}[/tex]

[tex]\boxed{A = 68.75 \text{ square inches}}[/tex]

To find the coordinates of point P on the line, we can solve for x and y in the equation X-7 - Y + 2 = 2 + 6 = 5. Adding 7 to both sides, we get X - Y + 2 = 12. Subtracting 2 from both sides, we get X - Y = 10. We can choose any value for x, and then solve for y using this equation. For example, if we choose x = 0, then y = -10.

So the coordinates of point P on the line could be (0, -10, z), where z is any real number.

To find a vector v parallel to the line, we can take two points on the line and find the vector between them. For example, we could use the points (0, -10, 0) and (1, -9, 0). The vector between these points is (1-0, -9-(-10), 0-0) = (1, 1, 0).

So a vector v parallel to the line is v = (1, 1, 0).
To find the coordinates of a point P on the line and a vector v parallel to the line, we first need to rewrite the given equation in a more standard form. The equation provided seems to be incorrect, but let's assume it's meant to be in the format of Ax + By = C, then we can proceed as follows:

1. Identify the normal vector of the line (A, B): Since the given equation is X - Y = 3 (combining the constants), the normal vector is (1, -1).

2. Determine the direction vector of the line, which is perpendicular to the normal vector. One possible direction vector is the one obtained by swapping the components and negating one of them, so v = (1, 1).

3. To find a point P on the line, we can choose a value for either x or y and solve for the other coordinate. Let's choose x = 0, then we have 0 - Y = 3, which gives Y = -3. Therefore, P(x, y) = (0, -3).

In summary, the point P on the line is (0, -3), and a vector v parallel to the line is (1, 1).

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The Laplace transform of f(x)= (-2x-3)/4 is (-2L{x}-3L{1})/4, where L{x} is the Laplace transform of x and L{1} is the Laplace transform of 1.
Hi! The Laplace transform of a given function f(t) is denoted by L{f(t)} and is defined as the integral of f(t) multiplied by e^(-st), where s is a complex variable. For the function f(x) = (-2x - 3)/4, the Laplace transform can be calculated as follows:

L{f(t)} = L{(-2t - 3)/4}

To find the Laplace transform, we will treat the function as two separate parts:

L{(-2t - 3)/4} = (-2/4) * L{t} + (-3/4) * L{1}

The Laplace transforms of t and 1 are well-known:

L{t} = 1/s^2
L{1} = 1/s

Now, substitute these transforms back into our expression:

L{f(t)} = (-1/2) * (1/s^2) + (-3/4) * (1/s)

L{f(t)} = -1/(2s^2) - 3/(4s)

And that's the Laplace transform of f(x) = (-2x - 3)/4.

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When k = 0, both sides of the equation equal 0:
3cos(0) = 4(0)sin(0)
3 = 0

There are no other values of k for which the equation holds true, the only value of k that satisfies the given equation is k = 0.

To find the value(s) of k for which u(x, t) = e^(-3)sin(kt) satisfies the equation Ut = 4Uxx, we first need to calculate the partial derivatives with respect to t and x.
[tex]Ut = ∂u/∂t = -3ke^(-3)cos(kt)Uxx = ∂²u/∂x² = -k^2e^(-3)sin(kt)[/tex]
Now, we will substitute Ut and Uxx into the given equation:

[tex]-3ke^(-3)cos(kt) = 4(-k^2e^(-3)sin(kt))[/tex]
Divide both sides by e^(-3):

[tex]-3kcos(kt) = -4k^2sin(kt)[/tex]

Since we want to find the value(s) of k, we can divide both sides by -k:

3cos(kt) = 4ksin(kt)

Now we need to find the k value that satisfies this equation. Notice that when k = 0, both sides of the equation equal 0:

3cos(0) = 4(0)sin(0)
3 = 0

Since there are no other values of k for which the equation holds true, the only value of k that satisfies the given equation is k = 0.

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Answer: Yes those are correct good job

Step-by-step explanation:

Answer:

El coeficiente del término 23x^5 es 23.

Step-by-step explanation:

Answer:

D(6,4).

Step-by-step explanation:

The shape ABCD is a square.

By definition, the diagonals are equal.

The diagonal from A to C is 6 units long. Therefore, you should get your point D by drawing across from B to the right by 6.

D(6,4).

The distance that shows how much farther (in km) from the sun is Saturn than Venus is: [tex]1.2 * 10^9[/tex] km.

According to the table, the distance of Saturn from the Sun is [tex]1.4 * 10^{9}[/tex] and the distance of Venus from the Sun is [tex]1.1 * 10^{8}[/tex] .

Now to determine how much further from the Sun is Saturn than Venus, we will subtract the distance of the planet with the higher distance span from the one with the lower distance.

So our calculation will go thus:

[tex]1.4 * 10^9 - 1.1 * 10^8 = \\140000000 - 11000000 = 1290000000\\= 1.29 * 10^9[/tex]

From the calculation above, we can see how much further from the sun, is Saturn than Venus.

Complete Question:

The table shown below gives the approximate distance from the sun for a few different planets. How much farther (in km) from the sun is Saturn than Venus? Express your answer in scientific notation.

_______km

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To determine whether the series น k2 sk converges, we can use the Integral Test. Let f(x) = x2, then f'(x) = 2x. Since 2x is continuous, positive, and decreasing on [1,∞), In summary, the series Σ (1/k^2) converges, while the series Σ (2 + (-1)^{5k}) does not converge.

∫1∞ f(x) dx = ∫1∞ x2 dx = lim (t → ∞) [1/3 x3]1t = ∞
Since the integral diverges, the series น k2 sk also diverges.
b. To determine whether the series 2+(-1){ 5k converges, we can use the Alternating Series Test. The series has alternating signs and the absolute value of each term decreases as k increases. Let ak = 2+(-1){ 5k, then:
|ak| = 2+1/32k ≤ 2
Also, lim (k → ∞) ak = 0. Therefore, by the Alternating Series Test, the series 2+(-1){ 5k converges.

a. For the series Σ (1/k^2) (denoted as น k2 sk), we can use the p-series test. A p-series is a series of the form Σ (1/k^p), where p is a constant. If p > 1, the series converges, and if p ≤ 1, the series diverges. In this case, p = 2, which is greater than 1. Therefore, the series Σ (1/k^2) converges.
b. For the series Σ (2 + (-1)^{5k}), we can use the alternating series test. An alternating series is a series that alternates between positive and negative terms. In this case, the series alternates because of the (-1)^{5k} term. However, the series does not converge to zero as k goes to infinity, since there is a constant term 2. Therefore, the series Σ (2 + (-1)^{5k}) does not converge.
In summary, the series Σ (1/k^2) converges, while the series Σ (2 + (-1)^{5k}) does not converge.

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Answer: 4.5

Step-by-step explanation:

The area of the shaded region is (9/500)π.

To find the area shaded below in circle K, we first need to find the radius of the circle.

Let O be the center of the circle, and let N be the midpoint of segment LM. We can draw a radius ON to segment LM such that it is perpendicular to LM, and then draw another radius OL to point L. This forms a right triangle LON with the hypotenuse equal to the radius of circle K.

Since segment LM is given to have a length of 11/9π, we can find the length of LN by dividing it in half:

LN = (11/9π)/2 = 11/18π

We can then use trigonometry to find the length of OL:

sin(55°) = OL / LN

OL = LN sin(55°)

OL = (11/18π) sin(55°)

Next, we can use the Pythagorean theorem to find the length of ON:

ON² = OL² + LN²

ON² = [(11/18π) sin(55°)]² + [11/18π]²

ON ≈ 1.022

Therefore, the radius of circle K is approximately 1.022.

The area of the shaded region can now be found by subtracting the area of sector LOM from the area of triangle LON:

Area of sector LOM = (110/360)π(1.022)² ≈ 0.317π

Area of triangle LON = (1/2)(11/18π)(1.022) ≈ 0.326π

Area of shaded region = (0.326π) - (0.317π) = (9/500)π

So the area of the shaded region is (9/500)π.

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The cost of purchasing 2 pounds of sliced ham and 3 pounds of sliced turkey from the meat counter is $30.95.

The table provided shows the purchases made by two customers at a meat counter. To determine how much you will pay for 2 pounds of sliced ham and 3 pounds of sliced turkey, you need to first look at the prices listed in the table. For sliced ham, the price per pound is $4.99, and for sliced turkey, the price per pound is $6.99.

To calculate the cost of 2 pounds of sliced ham, you can multiply the price per pound ($4.99) by the number of pounds (2), which gives you a total cost of $9.98. Similarly, to calculate the cost of 3 pounds of sliced turkey, you can multiply the price per pound ($6.99) by the number of pounds (3), which gives you a total cost of $20.97.

Therefore, the total cost for 2 pounds of sliced ham and 3 pounds of sliced turkey would be $9.98 + $20.97 = $30.95.

In conclusion, by using the prices listed in the table, it is possible to determine the cost of purchasing 2 pounds of sliced ham and 3 pounds of sliced turkey from the meat counter. It is important to remember to multiply the price per pound by the number of pounds needed for each item, and then add the costs together to get the total price.

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To find the volume of the cone, we first need to find its radius. Since the pyramid is contained within the cone such that the vertices of the base of the pyramid are touching the edge of the cone, the diagonal of the square base of the pyramid is equal to the diameter of the base of the cone. The diagonal of the square base of the pyramid is:

d = √(10^2 + 10^2) = √200 = 10√2 cm

Therefore, the diameter of the base of the cone is 10√2 cm, and the radius is 5√2 cm.

The volume of the cone can be calculated using the formula:

V = (1/3)πr^2h

where r is the radius of the base of the cone and h is the height of the cone.

Substituting the given values, we get:

V = (1/3)π(5√2)^2(20)

V = (1/3)π(50)(20)

V = (1/3)(1000π)

V = 1000/3 * π

Using 3.14 as the decimal approximation for π, we get:

V ≈ 1046.35 cubic centimeters

Therefore, the volume of the cone is approximately 1046.35 cubic centimeters. The answer is A.

The exact value of the double integral ∫∫D 2xy dA is 0.

To evaluate the double integral ∫∫D 2xy dA, where D is the region between the circles of radius 2 and 5 centered at the origin that lies in the first quadrant, we need to use polar coordinates.

In polar coordinates, the region D is defined by 2 ≤ r ≤ 5 and 0 ≤ θ ≤ π/2. The double integral can be expressed as:

∫∫D 2xy dA = ∫θ=0^(π/2) ∫r=[tex]2^5 2r^3[/tex] cosθ sinθ dr dθ

Solving the inner integral with respect to r, we get:

∫r=[tex]2^5[/tex] 2[tex]r^3[/tex] cosθ sinθ dr = [r^4 cosθ sinθ]_r=[tex]2^5 = 5^4[/tex] cosθ sinθ - [tex]2^4[/tex] cosθ sinθ

Substituting this result into the double integral expression and solving the remaining integral with respect to θ, we get:

∫∫D 2xy dA = ∫θ=0^(π/2) (5^4 cosθ sinθ - 2^4 cosθ sinθ) dθ

= [5^4/2 sin(2θ) - 2^4/2 sin(2θ)]_θ=0^(π/2)

= (5^4/2 - 2^4/2) sin(π) - 0

= (5^4/2 - 2^4/2) * 0

= 0

Therefore, the exact value of the double integral ∫∫D 2xy dA is 0.

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In the expansion of the given expression, (2a - 5b)², the coefficient of ab is -20

From the question, we are to determine the coefficient of ab in the expansion of the given expression.

The given expression is

(2a - 5b)²

To determine the coefficient of ab, we will expand the expression

Expand the expression

(2a - 5b)²

(2a - 5b)(2a - 5b)

Applying the distributive property, we get

2a(2a - 5b) -5b(2a - 5b)

Distribute the expression outside

4a² - 10ab - 10ab + 25b²

Simplify the expression

4a² - 20ab  + 25b²

Hence, the coefficient of ab is -20

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it would take approximately 2,749 hours for a rocket traveling at 3.35×10⁴ kilometers per hour to travel from Earth to Mercury.

what is approximately ?

Approximately means "about" or "roughly". It is used to indicate that a number or value is not exact, but rather an estimate or approximation. When a value is given as approximately a certain number

In the given question,

To calculate the time it would take a rocket traveling at 3.35×10⁴ kilometers per hour to travel from Earth to Mercury, we need to divide the distance between Earth and Mercury by the speed of the rocket:

Time = Distance / Speed

Distance = 9.21×10⁷kilometers

Speed = 3.35×10⁴ kilometers per hour

Time = 9.21×10⁷ km / (3.35×10⁴ km/h)

Time = 2,748.66 hours

Rounding this value to the nearest whole number of hours gives:

Time = 2,749 hours

Therefore, it would take approximately 2,749 hours for a rocket traveling at 3.35×10⁴ kilometers per hour to travel from Earth to Mercury.

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We know that the westbound car has traveled 24 miles.

When the northbound car has traveled 18 miles and the straight-line distance between the two cars is 30 miles, you can use the Pythagorean theorem to determine the distance the westbound car has traveled. The theorem states that a² + b² = c², where a and b are the legs of a right triangle and c is the hypotenuse.

In this case, the northbound car's distance (18 miles) represents one leg (a) and the westbound car's distance represents the other leg (b). The straight-line distance between the cars (30 miles) represents the hypotenuse (c). The equation can be set up as follows:

18² + b² = 30²

Solving for b:

324 + b² = 900
b² = 900 - 324
b² = 576
b = √576
b = 24

So, the westbound car has traveled 24 miles.

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The shows that Luther can expect the speed to be 51 miles/hour when he throws 80 pitches and 64 miles/hour when he throws 54 pitches.

The average speed of Luther's pitches when he throws 80 pitches will be:

y = -0.511x + 91.636

= -0.511(80) + 91.636

= 50.756

= 51

Also, the number of pitches that Luther can throw when the speed is 64 miles per hour will be:

y = -0.511x + 91.638

64 = -0.511x + 91.638

0.511x = 91.638 - 64

0.511x = 27.636

x = 54

Therefore, the number of pitches will be 54.

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Answer:

Because the absolute value of the correlation coefficient, 0.9672, is very close to 1, Luther can be very confident in the predictions.

Step-by-step explanation: Edmentum Answer