The equation for a projectile's height versus time is h(t)=-16t^2+Vt+h. A tennis ball machine serves a ball vertically into the air from a height of 2 feet, with an initial speed of 110 feet per second. Which equation correctly models the ball’s height as a function of time?

If f(x)= √(x−1) and g(x)=12x+5, then the value of (f∘g)(2) is 2√7.

What is function?

In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range.

To find the value of (f∘g)(2), we first need to evaluate g(2), and then use the result as the input for f.

So,

g(2) = 12(2) + 5 = 24 + 5 = 29

Now, we use the value g(2) = 29 as the input for f:

f(g(2)) = f(29)

Since f(x) = √(x-1), we have:

f(29) = √(29-1) = √28 = 2√7

Therefore, the value of (f∘g)(2) is 2√7.

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The solution of equation is (2, 3).

We have,

x= 3y -7.........(1)

y= x + 1.........(2)

Solving equation (1) and (2) we get

y = 3y - 7 + 1

y - 3y = -7 + 1

-2y = -6

y = -6/(-2)

y = 3

and, x = 3(3) - 7

x = 9 - 7

x = 2

Thus, the solution of equation is (2, 3).

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Answer:

-78, -5/6, -0.2001, 20%

Step-by-step explanation:

The first step is to convert all of the numbers into the same form. In this case, it is easiest to use decimal form.

-5/6 = -0.8333...

-0.2001

20% = 0.2

-78

-78 is the smallest by far

-0.8333... is the next smallest

-0.2 is next

and 0.2 is the largest

Answer: n^6-25

Step-by-step explanation:

Use the distributive property to obtain: n^6-5n^3+5n^3-25

Simplify: n^6-25

Answer: n^6-25

The product of the given expression [tex](n^{3} + 5) (n^{3} - 5)[/tex] will be the second option  [tex]n^{6} - 25[/tex].

This is a simple math problem that can be solved using algebraic identities. Algebraic identities are mathematical formulas that hold true regardless of the value assigned to each of the variables. They can be used to resolve equations and simplify expressions.

In the above question, we have used the following identity:

[tex](a^{2} - b^{2} ) = (a + b) (a - b)[/tex]

In the given question, a = [tex]n^{3}[/tex] and b = 5

So putting values in the identity, we get

[tex][(n^{3})^{2} - 5^{2}] = (n^{3} + 5) (n^{3} - 5)[/tex]

On solving the left side of the equation, we get

[tex]n^{6} - 25[/tex] which is our answer to the given question.

Note: [tex](n^3)^2 = n^6[/tex] because the powers get multiplied.

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The distance you live from the library, would be 6. 4 miles.

Assigning the distance between your house and where you can find books as x miles, we could approximate that initially you cycled 0.75x miles before retracing your route back a third of what had already been travelled; converting to 0.25x mile. Thus, at this stage, you will have covered an accumulated distance of 0.5x - taking into account earlier computations.

Realizing that borrowing such book would be unnecessary, you rode back to the library from whence you started- making it 3.2 miles. As you have advanced some length by travelling a cumulative distance of 0.5x from your private residence on previous trial, only another 0.5x miles stands between you and the target place after spinning around anew.

The equation is:

0. 5 x = 3. 2

x = 3. 2 / 0. 5

x = 6. 4 miles

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The 95.44% confidence interval for the mean score, μ, of all students taking the test is 59.6 to 86.4.

A confidence interval is a range of values that is calculated from a sample of data. It provides a level of certainty, usually expressed as a percentage, that a population parameter lies within this range. It is used to estimate a population parameter, such as a mean, a proportion, or a difference between two means.

The 95.44% confidence interval for the mean score, μ, of all students taking the test can be calculated using the formula:
Confidence Interval = overbar(x) ± (1.96 x (σ/√n))
where overbar(x) is the mean score on the aptitude test, σ is the standard deviation of the population (15 in this case), and n is the sample size (5 in this case).
Plugging in the given values, we get:
Confidence Interval = 73 ± (1.96 x (15/√5))
= 73 ± (1.96 x 3)
= 73 ± 5.88
Therefore, the 95.44% confidence interval for the mean score, μ, of all students taking the test is 59.6 to 86.4.

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Answer:

We can use the vector addition property to find the coordinates of the points M, N, and I.

Let

[tex]\bold{ A = (x_1, y_1), B = (x_2, y_2), C = (x_3, y_3), and\: D = (\frac{x_2+x_3}{2}, \frac{y_2+y_3}{2})}[/tex]

To find M, we use the fact that MA + MB = 0. Therefore, we have:

MA = -MB

A - M = -(B - M)

A - M = -B + M

2M = A + B

M =[tex]\frac{A + B}{2}[/tex]

So, the coordinates of point M are

[tex]\bold{(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})}[/tex]

To find N, we use the fact that 3NA + NC = 0. Therefore, we have:

3NA = -NC

3A - N = -(C - N)

3A - N = -C + N

4N = 3A + C

N =[tex]\frac{ 3A + C}{4}[/tex]

So, the coordinates of point N are [tex]\bold{(\frac{3x_1+x_3}{4},\frac{ 3y_1+y_3}{4})}[/tex]

To find I, we use the fact that IM + 2IN = 0. Therefore, we have:

IM = -2IN

M - I = -2(N - I)

M - I = -2N + 2I

3I = M + 2N

I = [tex] \frac{(M + 2N)}{3} [/tex]

Substituting the values of M and N that we found earlier, we get:

I = (A + B + 2(3A + C)/4)/3

Simplifying this expression, we get:

I = [tex]\frac{(7A + 2B + 2C)}{12}[/tex]

So, the coordinates of a point I are[tex]\bold{(\frac{7x_1+2x_2+2x_3}{12}, \frac{7y_1+2y_2+2y_3}{12}).}[/tex]

The residual plot shows that the regression equation is a good model of the data because it shows a random scatter of points around a horizontal line at zero, with no pattern or trend

A residual plot is a scatter plot of the residuals against the predictor variable(s) or the fitted values. It is used to verify whether the regression equation fits the data well.

In the event that the residual plot shows a random scatter of points around a horizontal line at zero, with no pattern or trend, it shows that the regression equation is a good model of the data.

On the other hand, supposing the residual plot shows a pattern or trend, such as a curve, a U-shape, or a funnel shape, it shows that the regression equation is a bad model of the data.

Therefore, from the graph given, the residual plot shows that the regression equation is a good model of the data.

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Answer:

The given expression is a polynomial:

f(x) = x^2 + 7x - 9 + 2x - 1

Combining like terms, we get:

f(x) = x^2 + 9x - 10

The degree of the polynomial is 2, since the highest power of x is 2.

Answer: 2

Step-by-step explanation:

(7+2x)(9+2x)= 143 (area= length x width)

63+14x+18x+4x^2=143

4x^2+32x−80=0

x^2+8x−20=0

(x−2)(x+10)=0

x = 2 or -10

Since the length of the walkway can't be negative, the answer is 2.

We can begin by focusing on c on one side of the equation to help us solve it. Craig's height is 44 as a result.

A mathematical equation is a claim that two expressions are equivalent. It is divided into two sections, the left and the right, by the equal sign (=). Equation's left and right sides each have the potential to include variables, constants, and operators.

Finding the value(s) of the variable(s) necessary to make an equation true is the aim of equation solving. Algebraic techniques like simplification, substitution, and elimination can be used to solve equations.

An equation can be used to represent the following sentence:

c + 24 = 68

Craig's height is represented by c in this equation. The equal sign (=) is used to symbolise the phrase "is 68," while the phrase "is 24 more than Craig's height" is symbolised by c + 24. The formula for the problem can be solved to find the value of c, which corresponds to Craig's height.

We can begin by concentrating c on just one side of the equation in order to solve it:

c + 24 - 24 = 68 - 24

c = 44

Therefore, Craig's height is 44.

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The difference in the length of dogs jump is 24 inches.

Given that, Mackenzie's dog can jump [tex]2\frac{1}{2}[/tex] =5/2 feet off the ground. Jordyn's dog can jump 1/2 foot off the ground.

We know that, 1 feet = 12 inches

Here, 5/2 feet = 5/2 ×12

= 30 inches

1/2 foot = 1/2 ×12

= 6 inches

Now, difference = 30-6 = 24 inches

Therefore, the difference in the length of dogs jump is 24 inches.

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According to given information, the arc length of a partial circle is 14.67 units.

A partial circle is a portion of a circle, usually defined by an angle that is less than 360 degrees.

To find the arc length of a partial circle, we need to know the measure of the central angle, θ, in radians.

Let's say that the central angle of the partial circle is 2π/3 radians, which corresponds to an angle of 120 degrees.

Then, the arc length, denoted by L, can be calculated using the formula:

L = rθ

where r is the radius of the circle.

Plugging in the values we have, we get:

L = 7(2π/3)

L = (14/3)π

Using 3.14 for π, we get:

L ≈ 14.67 units (rounded to two decimal places)

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The image is attached of the graph of the inequality y < 4x - 5.

What is the inequality equation?

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).

To graph the inequality y < 4x - 5 using the slope-intercept form, follow these steps:

Rewrite the inequality in slope-intercept form, y = mx + b, where m is the slope of the line and b is the y-intercept.

y = 4x - 5

Plot the y-intercept on the y-axis.

The y-intercept is -5, so plot the point (0, -5).

Use the slope to find a second point on the line.

The slope is 4, so start at the y-intercept and move up 4 units and to the right 1 unit to find the point (1, -1).

Draw a dashed line through the two points.

Since the inequality is y < 4x - 5, use a dashed line to indicate that the line itself is not part of the solution.

Shade the region that satisfies the inequality.

To do this, pick a test point that is not on the line and plug its coordinates into the inequality. If the inequality is true for that point, shade the region that contains the test point. If the inequality is false for that point, shade the region that does not contain the test point.

Let's use the test point (0, 0). Plug its coordinates into the inequality to get:

0 < 4(0) - 5

This simplifies to 5 < 0, which is false. Therefore, we need to shade the region that does not contain the test point.

Since the inequality is y < 4x - 5, we need to shade the region below the dashed line.

Label the shaded region with the inequality symbol.

The inequality is y < 4x - 5, so label the shaded region below the dashed line with the symbol "<".

hence, The image is attached of the graph of the inequality y < 4x - 5.

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An equation that could represent P(x) include the following: A. P(x) = (x + 1)(x - 2)²

In Mathematics and Geometry, the graph of a polynomial function touches the x-axis at zeros, roots, solutions, x-intercepts, and factors with even multiplicities.

Also, the graph has a zero of multiplicity 2 at x = 2 and zero of multiplicity 1 at x = -1;

x = 2 ⇒ x - 2 = 0.

(x - 2)²

x = -1 ⇒ x + 1 = 0.

(x + 1)

In this context, an equation that represent the polynomial function is given by:

p(x) = a(x - 2)²(x + 1)

By evaluating and solving for the leading coefficient "a" in this polynomial function based on the y-intercept (0, 4), we have;

4 = a(0 - 2)²(0 + 1)

4 = a4

a = 4/4.

a = 1

Therefore, the required polynomial function is given by:

p(x) = (x - 2)²(x + 1)

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Answer:

Area of the shape is 244.98cm² is B

Step-by-step explanation:

Area of shape=Area of semi circle+Area of trapezoid

A=1/2 πr² + 1/2(a+b)h

A=1/2×3.142×7² + 1/2(14+18)10.5

A=1/2×3.142×49 + 1/2×32×10.5

A=76.98+168

A=76.98+168

A=244.98cm²

Answer:

After half hour=30 min you have 2×2500=5000 bacteria so you can use this into your equation to write:

and:

Apply the natural logarithm ln to both sides and get:

so  in units of

so your equation is now:

1] it t= 50 min substituting you get:

bacteria

2] if t= 8 h = 480 min you get:

bacteria

Step-by-step explanation:

1. The force they must apply is 2256.3 N

2. The amount of work done = 3835.71 J

3. The work done using the ramp = 4500 J

4.  The efficiency of the ramp = 85.24%

5. When the people use inclined ramp, they don't have worry about the gravitational force that is acting on the piano. The trade off with with less force, the ramp is able to cover more distance.

1. To find force applied, used the formula; F = mg

230 x 9.8N

=2256.3N

2. To find the amount of work done, we use the formula;

W = Fd

2256.3 x 1.7 m

= 3835.71J

3. o calculate the work done using the ramp, you use the same formula you used in step 2

300N x 15m

= 4500J

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Answer:

[tex]\frac{11}{24}[/tex] yards

Step-by-step explanation:

[tex]\frac{1}{8}[/tex] + [tex]\frac{1}{3}[/tex]  we need a common denominator which is 24

[tex]\frac{1}{8}[/tex] x [tex]\frac{3}{3}[/tex] = [tex]\frac{3}{24}[/tex]

[tex]\frac{1}{3}[/tex] x [tex]\frac{8}{8}[/tex] = [tex]\frac{8}{24}[/tex]

[tex]\frac{3}{24}[/tex] + [tex]\frac{8}{24}[/tex] = [tex]\frac{11}{24}[/tex] yards

Helping in the name of Jesus.

Answer:  x = 6 and y = -5.

Step-by-step explanation: Multiply the second equation by -2 to eliminate the y term:

-2(x + y) = -2(1) -> -2x - 2y = -2

Add the resulting equation to the first equation to eliminate the y term:

2x + y = 7

-2x - 2y = -2

0x - y = 5

Solve for y:

-y = 5

y = -5

Substitute y = -5 into either of the original equations and solve for x:

x + y = 1

x + (-5) = 1

x = 6

Therefore, the solution to the system of equations is x = 6 and y = -5.

The solution to the simultaneous equations is x = 2 and y = -4. To obtain these values,  18 = 7x - y  is rearranged to y = 7x - 18, and then substituted into 3x + y = 2  to obtain the value of x and y.

Rearranging equation (1) to make y the subject

18 = 7x - y

Add y to both sides

18 + y = 7x

Subtract 18 from both sides

y = 7x - 18

Using the answer to part a) to solve the simultaneous equations

Substitute the expression for y from equation (1) into equation (2)

3x + (7x - 18) = 2

Simplify

10x - 18 = 2

Add 18 to both sides

10x = 20

Divide both sides by 10

x = 2

Substitute x = 2 into equation (1) to find y

18 = 7(2) - y

18 = 14 - y

Subtract 14 from both sides

4 = -y

Multiply both sides by -1

-4 = y

Therefore, the solution to the simultaneous equations is x = 2 and y = -4.

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Answer:

[tex]\$1342.64[/tex]

Step-by-step explanation:

We can represent the value [tex]A[/tex] of a quantity [tex]P[/tex] compounded continuously for [tex]t[/tex] years at [tex]r[/tex] rate of interest as:

[tex]A = P\cdot e^{rt}[/tex]

This formula uses the mathematical constant [tex]e[/tex] (approx. 2.72), which is the theoretical limit for continuous compounding.

Plugging the given values into the formula:

[tex]A = \$900 \cdot e^{(0.04 \, \cdot \, 10)}[/tex]

We can now solve for [tex]A[/tex].

↓ simplifying [tex]e[/tex]'s exponent

[tex]A = \$900 \cdot e^{0.4}[/tex]

↓ plugging into a calculator

[tex]A \approx \$1342.64222788[/tex]

↓ rounding to the nearest cent

[tex]\boxed{A \approx \$1342.64}[/tex]

a. The proportion of students have scores less than 380 is 11.51%.

b. The proportion of students have scores greater than 639 is 8.23%.

1. Using the z-score formula:

We can calculate that score of 380 corresponds to a z-score of -1.2 since z = (x - μ) / σ.

Using a standard normal distribution table, we find that:

2. Similarly, a score of 639 corresponds to a z-score of 1.39.

Using a standard normal distribution table, we find that:

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Start at 0 on the number line and move 18 yards to the right to represent Jenna throwing the disc to Karl. Then move 11 yards to the right to represent Karl throwing the disc to Alice the result shows that.

To represent Jenna throwing the disc to Karl, we need to move 18 yards to the right on the number line. This is because Jenna threw the disc directly to Karl, so the distance between them is 18 yards. Therefore, we can start at 0 on the number line and move 18 yards to the right to represent Jenna throwing the disc to Karl.

To represent Karl throwing the disc to Alice, we need to move 11 yards to the right from Karl's position on the number line. This is because Karl threw the disc 11 yards in the same direction as Jenna threw it to him.

So, we can start at Karl's position on the number line (which is 18 yards to the right of 0) and move 11 yards to the right to represent Karl throwing the disc to Alice.

Overall, to represent the entire throwing sequence from Jenna to Karl and then to Alice, we can start at 0 on the number line and move 18 + 11 = 29 yards to the right.

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Answer:

  x° = 36°

Step-by-step explanation:

You want to find the angle between a secant and a tangent to a circle, where the intercepted arcs are 126° and 54°.

The angle at D, labeled x°, is half the difference of the intercepted arcs:

  x° = (126° -54°)/2 = 72°/2

  x° = 36°

__

Additional comment

The same relationship applies for the angle between two secants.

This is easy to prove by considering triangle ADE. Angle DAE is half of arc CE. The exterior angle to the triangle at E is half of arc AE. That exterior angle is equal to the sum of the remote interior angles at D and A:

  AE/2 = x° + CE/2   ⇒   x° = (AE -CE)/2

Answer: ∠BDA

Step-by-step explanation:

Complementary: Either of two angles whose sum is 90°.

Starting Angle: ∠BDC

Possible Complement: ∠BDA

Answer: ∠ACD

Step-by-step explanation:

Complementary angles are angles which have a sum of 90 degrees when added together.

Angle ∠ADB is 90°

So ∠BDC and another angle should give you ∠ADB

The angle that when added to ∠BDC give you ∠ADB is ∠ACD

Answer: 92.5

Step-by-step explanation:

Answer:

w = 92.5

Step-by-step explanation:

You cannot use Law of Sine in this case.

Use Law of Cosine.

They gave you 2 side length and one angle.

plug in your values into the equation and solve for w.

Let just use u, v, & w: Let u be 25 and v be 84.

[tex]w^2 = u^2 + v^2 - 2*u*v*cos(W)[/tex]

[tex]w^2 = 25^2 + 84^2 - 2*25*84*cos(102)[/tex]°

[tex]w^2=625+7056-4200*cos(102)[/tex]

[tex]w^2=7681-4200*(-0.2079116908)[/tex]

[tex]w^2=7681+873.2291014[/tex]

[tex]w^2=8554.229101[/tex]

[tex]w=\sqrt{8554.229101}= 92.48907558[/tex]

Joelle gave a total of 300 yards of ribbon in all

Let's assume that the total amount of ribbon Joelle has is "x" yards.

We know that 24 yards of ribbon is 8% of her total amount of ribbon. So we can write an equation:

0.08x = 24

To solve for x, we divide both sides of the equation by 0.08:

x = 24 ÷ 0.08

x = 300

Therefore, Joelle has a total of 300 yards of ribbon.

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Answer:

Step-by-step explanation: the answer is 300 just divide and you’ll get the answer that simple