A soccer ball on the ground is kicked with an initial velocity of 37 feet per second at an elevation angle of 70°. Which
parametric equations represent the path of the soccer ball?

Answer:

x^2 = (28)^2 + (45)^2

= 784 + 2025

= 2809

x = 53

The equation of the line is y = (1/3)x - 6.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

The equation of a line is y = mx + c.

Now,

m = 1/3

And,

(-6, -8) = (x, y)

So,

y = mx + c

-8 = 1/3 x -6 + c

-8 = -2 + c

-8 + 2 = c

c = -6

Now,

y = mx + c

y = (1/3)x - 6

Thus,

The equation of the line is y = (1/3)x - 6.

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Answer:

my best guess would be H

Step-by-step explanation:

I hope this helped and if you have more details that could help me get to a more appropriate answer pls comment them and I'll do my best to help but like I said with what you provided my best guess would be H

Answer:

94.88 cubic units

Step-by-step explanation:

Volume of the prism = Area of base * Height

[tex] = 5( \frac{1}{2} \times 2.75 \times 4) \times 3.45 \\ \\ = 5 \times 2.75 \times 2 \times 3.45 \\ \\ = 10\times 2.75 \times 3.45 \\ \\ = 94.875 \\ \\ \approx 94.88 \: cubic \: units[/tex]

Answer:

5 gallons

Step-by-step explanation:

3/4 + 6/8 + 20/8 + 1

6/8 + 6/8 + 20/8 + 8/8

40/8 = 5 gallons

Answer:

99 oak trees

Step-by-step explanation:

Given data

Ratio= 8:3

Number of pine tree= 264

Let the number of oak trees be x

Let us apply the part to part method

8/264= 3/x

cross multiply

264*3= 8x

792=8x

x= 792/8

x=99 oak trees

The owner of the tree farm planted 99 oak trees.

An equation is an expression used to show the relationship between two or more numbers or variables.

Given that a farmer plants pine trees and oak trees in a ratio of 8:3. If 264 pine trees are planted, let y represent the total number of trees hence:

264 = (8/11) * y

y = 363 trees

Number of oak trees = (3/11) * 363 = 99 trees

Therefore the owner of the tree farm planted 99 oak trees.

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The level of confidence that can be attributed to the interval estimate is approximately 97%. This means that we can be 97% confident that the true average amount of money spent by Australian students on subscription-based entertainment platforms falls within the range of $32,468 to $37,224.

To determine the level of confidence for the interval estimate, we need to consider the t-distribution and the degrees of freedom associated with the sample size.

Since the sample size is 48, the degrees of freedom would be 48 - 1 = 47. Using a t-distribution table or calculator, we can find that with 47 degrees of freedom, a confidence level of approximately 97% corresponds to a t-value of 2.682.

Since the interval estimate is not explicitly provided, we can assume it to be the range between $32,468 and $37,224.

We have that the t-value is associated with a two-tailed test, the level of confidence for this interval estimate is approximately 97%.

Therefore, we can attribute a confidence level of 97% to this interval estimate, indicating that we can be 97% confident that the true average amount of money spent by Australian students on subscription-based entertainment platforms falls within the given range.

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Answer:

The probability that the mean of this sample of home purchases is between 173 and 174 homes

P(173≤X≤174) = 0.0936

Step-by-step explanation:

Step(i):-

Given that the mean of the Population = 175

Given that the standard deviation of the Population = 6

Let 'x⁻' be the mean of the random sample

Given that  x₁⁻ = 173

[tex]Z_{1} = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } } = \frac{173-175}{\frac{6}{\sqrt{60} } } =-2.58[/tex]

Given that  x₂⁻ = 174

[tex]Z_{2} = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } } = \frac{174-175}{\frac{6}{\sqrt{60} } } = -1.29[/tex]

Step(ii):-

The probability that the mean of this sample of home purchases is between 173 and 174 homes

P(X₁≤X≤X₂)      = P(Z₁≤Z≤Z₂)

                       = P(Z≤Z₂) - P(Z≤Z₂)        ( both values 'Z' values are negative)

                       = 0.5 -A(Z₁) - (0.5 -A(Z₂))

                      = |A(Z₂) -A(Z₁)|

P(173≤X≤174)     =   | A(2.58)-A(1.29)|

                  = 0.4951 - 0.4015       (∵ from normal table)

                = 0.0936

Final answer:-

The probability that the mean of this sample of home purchases is between 173 and 174 homes

P(173≤X≤174) = 0.0936

The statement is False.

Let A = {1,3,5,7). B = {5, 6, 7, 8). C = {5, 8} D = (2,5,8), and U = {1,2,3,4,5,6,7,8).

To determine whether the expression DCB is true or false, we need to know the content of these sets.

To determine the content of DCB:

DCB contains all elements of D, all elements of C, and all elements of B except those that are already in D and C.

D = {2,5,8} C = {5, 8} B = {5,6,7,8}

DCB = {2,5,8,6,7}

Thus, DCB is false because not all elements in D are in B, and all elements in D are not in B.

Therefore, the answer is option B.False; all elements in D are not in B.

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Answer:

You need the minimum cost for renting the meeting room given the following info

Reservation Fee = $18

Hourly Rate = $5

The renter wants to keep the cost below $58

So the cost will vary with the time, t you use the inequality below

5t + 18 ≤ 58

You can solve this to get that minimum

You can check you answer by graphing it.

I hope this helps!<3

Answer:

22

Step-by-step explanation:

according to your question

The multiplicative inverse of 2a + 2 is 2a + 1.

To show that the polynomial p(x) = x² + 1 ∈ Z3[x] is irreducible, we can examine its factors. Since Z3 is a field with three elements {0, 1, 2}, we can substitute each value into p(x) to check for roots. However, none of the elements satisfy p(x) = 0. Therefore, p(x) has no linear factors.

Next, we consider the extension Z3(a) = {0, 1, 2, a, 1+a, 2+a, 2a, 1+2a, 2+2a} = Z3[x]/(p(x)), where a is a zero of p(x). In this field, we can perform addition and multiplication modulo 3.

Addition table:

+ | 0  1  2  a  1+a  2+a  2a  1+2a  2+2a

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

0 | 0  1  2  a  1+a  2+a  2a  1+2a  2+2a

1 | 1  2  a  1+a  2+a  2a  1+2a  2+2a  0

2 | 2  a  1+a  2+a  2a  1+2a  2+2a  0  1

a | a  1+a  2+a  2a  1+2a  2+2a  0  1  2

1+a | 1+a  2+a  2a  1+2a  2+2a  0  1  2  a

2+a | 2+a  2a  1+2a  2+2a  0  1  2  a  1+a

2a | 2a  1+2a  2+2a  0  1  2  a  1+a  2+a

1+2a | 1+2a  2+2a  0  1  2  a  1+a  2+a  2a

2+2a | 2+2a  0  1  2  a  1+a  2+a  2a  1+2a

Multiplication table:

* | 0  1  2  a  1+a  2+a  2a  1+2a  2+2a

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

0 | 0  0  0  0  0  0  0  0  0

1 | 0  1  2  a  1+a  2+a  2a  1+2a  2+2a

2 | 0  2  1  2a  1+2a  2+2a  a  2+a  1+a

a | 0  a  2a  1+2a  2+a  1+a  2+2a  2  1

1+a | 0  1+a  1+2a  2+a  2  a  1  2+2a  2a

2+a | 0  2+a  2+2a  1+a  a  2  1+2a  1  2a

2a | 0  2a  a  2+2a  1  1+2a  2  2+a  1+a

1+2a | 0  1+2a  2+a  2  2+2a  1  2a  a  1+a

2+2a | 0  2+2a  1+a  1  2a  2  1+a  1+2a  a

To find the multiplicative inverse of 2a + 2, we search for an element in the multiplication table that, when multiplied by 2a + 2, results in 1. In this case, the multiplicative inverse is 2a + 1.

Note: The addition and multiplication tables are constructed by performing arithmetic modulo 3 in the field Z3(a) using the given elements.

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The probability of X > 15.14 is approximately 0.0344 or 3.44%.

To find the probability of X > 15.14, we need to calculate the area under the normal distribution curve to the right of 15.14.

First, we need to standardize the value 15.14 using the formula:

Z = (X - [tex]\mu[/tex]) / o

where Z is the standardized value, X is the given value, [tex]\mu[/tex] is the mean, and o is the standard deviation.

In this case:

Z = (15.14 - 11.5) / 2

  = 3.64 / 2

  = 1.82

Next, we need to find the area under the standard normal distribution curve to the right of Z = 1.82. This can be done using a standard normal distribution table or a calculator.

Using a standard normal distribution table, we find that the area to the right of Z = 1.82 is approximately 0.0344.

Therefore, the probability of X > 15.14 is approximately 0.0344 or 3.44%.

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Answer:

angel a is 65 degrees

Step-by-step explanation:

40+2x+10=180

40-40+2x+10-10=180-40-10

2x=130

x=65

checking:

65 + 10 + 40 = 75 + 40 = 115

115+65=180

180=180

Given, Jada walks at a speed of 3 mph and Elena walks at a speed of 2.8 mph.Both Jada and Elena start walking along a walking trail at the same time.

Let us determine the distance covered by both of them.Distance travelled by Jada in 3 hours is:Distance = Speed × Time= 3 mph × 3 hours= 9 miles Distance travelled by Elena in 3 hours is:Distance = Speed × Time= 2.8 mph × 3 hours= 8.4 miles Thus, Jada will walk 0.6 miles farther than Elena after 3 hours.

To determine how far Jada will walk after 3 hours, we need to calculate the distance traveled based on her speed.

Jada walks at a speed of 3 miles per hour (mph), so we can calculate her distance using the formula:

Distance = Speed × Time

Plugging in the values, we have:

Distance = 3 mph × 3 hours

Distance = 9 miles

Therefore, Jada will walk a distance of 9 miles after 3 hours.

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The given information is as follows:

Jada walks at a speed of 3 mph and Elena walks at a speed of 2.8 mph. If they both begin walking along a walking trail at the same time.

Therefore, Jada will walk 9 miles after 3 hours.

The distance covered by Jada after 3 hours can be calculated as follows:

Distance = Speed x Time

Since Jada walks at a speed of 3 mph, the distance covered by her in 3 hours can be calculated as:

Distance covered by Jada = 3 mph x 3 hours

= 9 miles.

Therefore, Jada will walk 9 miles after 3 hours.

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The solution to the equation -3x^2 + 2x + 4 = -x - 3 is x = -2.44 and x = 3.12. Therefore, the correct option is A.

To solve the equation -3x^2 + 2x + 4 = -x - 3, we can rewrite it as a quadratic equation by combining like terms: -3x^2 + 3x + 7 = 0. This equation represents a quadratic function in the form of ax^2 + bx + c = 0, where a = -3, b = 3, and c = 7.

Using a graphing calculator, we can plot the function and find the x-intercepts, which represent the solutions to the equation. The intersection feature of the graphing calculator can help determine the coordinates of the points where the graph intersects the x-axis. Rounding to the nearest hundredth, we find that the solutions to the equation are x = -2.44 and x = 3.12.

Therefore, the correct answer is option A: x = -2.44 and x = 3.12.

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Answer:

$2100 will be his new salary

Step-by-step explanation:

Well since a 5 percent raise is basically 105% of his pay, we can multiply 105% with 2000

since its a percent in decimal form its 1.05

1.05*2000=2100

$2100 is his new salary

In triangle ABC, which is similar to triangle WYZ, the angles whose cosine equals are angle B and angle Z.

To determine the angles whose cosine equals, we need to consider the corresponding angles in similar triangles. In similar triangles, corresponding angles have the same measure, but the side lengths may be different. Since triangle ABC is similar to triangle WYZ, angle B in triangle ABC corresponds to angle Z in triangle WYZ. Similarly, angle Z in triangle ABC corresponds to angle B in triangle WYZ. Therefore, angle B and angle Z are the angles in the respective triangles whose cosine equals.

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Answer:

1.2

Step-by-step explanation:

There are 2 lines in the middle of the circle. Im guessing by you saying "The line in the middle" You must mean the radius your trying to find the diameter so, the radius is half of the diameter so to find the diameter you do the radius x 2 in this case 3/5x2 equals 1.2 :)

I Hope this helps!!

Answer:

d

Step-by-step explanation:

..........

Answer:

d

Step-by-step explanation:

e d g e

To construct a proof of the conclusion "-(∀x) (S(x) ∧ P(x))" from the given premises "-(3x) (P(x) ∧ M(x))" and "(3x) (M(x) ∧ S(x))," we can use a proof by contradiction.

We will assume the negation of the conclusion and derive a contradiction. Here's the proof:

Therefore, we have derived a contradiction, which allows us to conclude that the negation of the assumption is false. Thus, we can conclude:

-(∀x) (S(x) ∧ P(x))

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12.50 dollars per hour

Answer:

$12.50

Step-by-step explanation:

Hi,

Cassie: 250 / 20 = 12.5

Marli: 312.50 / 25 = 12.5

Brad: 350 / 28 = 12.5

Each worker makes $12.50 per hour.

I hope this helps :)

Answer:

Finding the equation using the two points is: y=3x-8

The slope is: m=3

The slope and y-intercept is: 3, (0,-8)

Step-by-step explanation:

I put all of these answers because i was basically fully confused by the wording of this question.. Sorry.

The system represented by the graph is y ≤ 1/2x + 3 and y < -2x + 8

The point (4, 0) is not a solution to the system

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

The graph

On the graph there are two inequalities and they are calculated as follows:

A linear equation is represented as

y = mx + c

Where

c = y when x = 0

So, we have

y = mx + 3

y = mx + 8

Using the points on the graphs, we have

y = mx + 3 ⇒ -6m + 3 = 0 ⇒ m = 1/2

y = mx + 8 ⇒ 4m + 8 = 0 ⇒ m = -2

So, we have

y = 1/2x + 3

y = -2x + 8

Represent as inequalities

y ≤ 1/2x + 3

y < -2x + 8

From the graph the point (4, 0) is out of the shaded region

This means that the point (4, 0) is not a solution to the system

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Answer:

horizontal

vertical

diagonal

Step-by-step explanation:

I guess I only know those.hope it helps you

Answer:

9

Step-by-step explanation:

8/12=6/x

cross multiply to get 9

To determine the angle of the ramp, we can use trigonometry and calculate the inverse tangent (arctan) of the ratio of the height to the length of the ramp.

Given a ramp length of 2.5 meters and a height of 30 centimeters (0.3 meters), the angle of the ramp is approximately 6.87 degrees. The angle of the ramp can be found using the formula: angle = arctan(height/length). By substituting the values, we get angle = arctan(0.3/2.5).

Using a calculator or math software to evaluate the arctan of this ratio, we find that the angle is approximately 6.87 degrees. This means that the ramp has a relatively gentle incline, indicating a low slope or gradient. Knowing the angle of the ramp can be useful in various applications, such as construction, accessibility planning, or determining the safety of the slope for specific purposes.

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y=-2x^2-8x-4

-2x^2-8x=4

divide by negative 2

x^2+4x=-2

complete the square

(x+2)^2=-2+4

(x+2)^2=2

x+2=±[tex]\sqrt{2}[/tex]

x=-2±[tex]\sqrt{2}[/tex]

nearest hundreths,

x=-0.59

x=-3.41