A catapult hurls a pumpkin from a height of 32 feet at an initial velocity of 96 feet per second. the function h(t)=-16t^2+96t+32 represents the heights of the pumpkin h(t) in terms of time t. what is the max height the pumpkins will reach and what time will it reach that height?

Answer:

[tex]x < -6[/tex]

Step-by-step explanation:

[tex]~~~~~~3x-2 > 5x+10\\\\\implies 5x+10 < 3x-2\\\\\implies 5x < 3x-2-10\\\\\implies 5x < 3x-12\\\\\implies 5x-3x < -12\\\\\implies 2x < -12\\\\\implies x < -\dfrac{12}2\\\\\implies x < -6[/tex]

The value of f⁻¹(f⁻¹(7)) is 10

The expression is given as:

f⁻¹(f⁻¹(7))

We start by solving the inner expression f⁻¹(7).

The above means that we determine the x value when y = 7.

So, we have:

f⁻¹(7) = 14

Substitute f⁻¹(7) = 14 in f⁻¹(f⁻¹(7))

f⁻¹(14)

Next, we determine the x value when y = 14

f⁻¹(14) = 10

Hence, the value of f⁻¹(f⁻¹(7)) is 10

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Answer:

20

10

Step-by-step explanation:

The key features are (a) both f(x) and g(x) include domain values of [3, ∞) and range values of (0, ∞), and both functions are positive for the entire domain.

The functions are given as:

f(x) = 3x

[tex]g(x) = \sqrt{x -3}[/tex]

Next, we enter the above equations in a graphing calculator.

From the graphing calculator, we have:

By comparing the above highlights, the true statement between functions g(x) and f(x) is option (a)

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Since we know it's quadratic, the n-th term will follow the pattern

[tex]x_n = an^2 + bn + c[/tex]

for some unknown coefficients a, b, and c.

Given that [tex]x_1=-1[/tex], [tex]x_2=2[/tex], and [tex]x_3=7[/tex], we have the following conditions on these coefficients:

[tex]\begin{cases} a + b + c = -1 \\ 4a + 2b + c = 2 \\ 9a + 3b + c = 7 \end{cases}[/tex]

Solve this system to get a = 1, b = 0, and c = -2. Then

[tex]\boxed{x_n = n^2 - 2}[/tex]

To solve the system, use elimination.

[tex](4a + 2b + c) - (a + b + c) = 2 - (-1) \implies 3a + b = 3[/tex]

[tex](9a + 3b + c) - (a + b + c) = 7 - (-1) \implies 8a + 2b = 8 \implies 4a + b = 4[/tex]

[tex](4a + b) - (3a + b) = 4 - 3 \implies a = 1 \implies b = 0 \implies c = -2[/tex]

Answer:

[tex]\displaystyle\frac{5}{36}[/tex]

Step-by-step explanation:

Probability is used to find how likely an outcome is to happen. Probability can be expressed as a fraction with the total outcomes as the denominator and the number of successful outcomes (what you want to happen) as the numerator.

Sample Size

The sample size is the number of possible outcomes. In this case, the sample size will be the total number of coins. To find the sample size we need to add together all of the coins.

This means that the sample size is 12. For this type of probability, the sample size will serve as the denominator for each probability.

Replacement

In the question, it is stated that coins are replaced. This means that the sample size will not change at any point. So, the denominator will be the same for every probability.

Creating Probability Fractions

We are looking for the probability of getting a quarter and nickel, so we need to find the fractions that represent both situations.

First, let's find the quarter. As stated in the first paragraph, the number of successful outcomes is the numerator. There are 4 quarters, so 4 is the number of successful outcomes. Therefore, 4 will be the numerator. Then, 12 will be the denominator because 12 is the sample size.

Next, we need to find the probability of a nickel. Since there are 5 nickels, there are 5 successful outcomes. Then, the sample size is still 12 because there is replacement.

Complex Probability

Now we have the probability of both a quarter and nickel alone. However, this question asks about the probability of both, so this is an example of complex probability. To find complex probability, you have to multiply each probability together.

To reach the final answer we have to simplify the answer.

This means that the probability of pulling a quarter and then a nickel is 5/36.

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3200\\ r=rate\to 7.75\%\to \frac{7.75}{100}\dotfill &0.0775\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &13 \end{cases} \\\\\\ A=3200\left(1+\frac{0.0775}{1}\right)^{1\cdot 13}\implies A=3200(1.0775)^{13}\implies A\approx 8444.51[/tex]

The value of a dependent variable is dependent on the value of an independent variable. The correct option is C.

Even though everything can be almost always related to its reason, when we talk about two related things, there might happen that one of those things is dependent on other.

The complete question is:

A telephone company charges a $0.25 connection fee, then $0.10 per minute for long distance calls. Which statement is true regarding this situation?

A. The rate of change is $0.25 and minutes are the independent variable.

B. The rate of change is $0.25 and minutes are the dependent variable.

C. The rate of change is $0.10 per minute and minutes are the independent variable

D. The rate of change is $0.10 per minute and minute are the dependent variable.

The cost of making a call is the sum of the cost of connection fee which is one time fee and cost $0.25, and the cost charged for a minute which depends on the number of minute for which the call is been established. Therefore, the total cost can be written for a x minute call is,

Total Cost = $0.25 + $0.10(x)

Since the total cost is dependent on x, therefore, x which is the minute is the independent variable. The rate of change is $0.10 per minute and minutes are the independent variable.

Hence, the correct option is C.

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Answer:

Option C

Step-by-step explanation:

Any evening time on a 24 hour clock will be that hour add 12 :

3:50 pm =

3:50 + 12:00 = 15:50

Option C must be the answer

Hope this helped and brainliest please

Answer:

c.1550 hrs

Step-by-step explanation:

It Is military time to it stays going for 12:00 to 13:00 14:00 15:00 and so on

Hope This Helped

Answer:

200

Step-by-step explanation:

(24 x 100) / 12

Answer = 200

To solve this problem you multiply 24 by 100 and then divide the total by 12 as follows: (24 x 100) / 12

Answer:

  about 51.77%

Step-by-step explanation:

The probability you will roll a 2 is the complement of the probability you will not roll a 2.

__

A die has 6 faces, one of which is labeled with 2. The probability of rolling a 2 on any given roll is 1/6, so is 1-1/6 = 5/6 that a 2 will not be rolled. Sequential rolls of the die are presumed to be independent, so the probability of 4 rolls not showing a 2 at any time is ...

  p(no 2) = (5/6)^4 = 625/1296

The probability that at least one 2 will show up on at least one roll is the complement of this value:

  p(some 2) = 1 -625/1296 = 671/1296 ≈ 0.517747

The chance you will roll at least one 2 is about 51.77%.

The quadratic equation that has a root of 6 and 2 is x^2 - 8x + 12 = 0

The roots are given as:

x = 6 and x = 2

Rewrite as:

x - 6 = 0 and x - 2 = 0

Multiply both equations

(x - 6)(x - 2) = 0 * 0

Evaluate the product

x^2 - 6x - 2x + 12 = 0

Evaluate the difference

x^2 - 8x + 12 = 0

Hence, the equation that has a root of 6 and 2 is x^2 - 8x + 12 = 0

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Answer:

x=-2

Step-by-step explanation:

x+7=5

To find x, we subtract 7 from both sides, to get x+7-7=5-7

x=5-7

x=-2

Hope this helped!

Answer:

x = -2

Step-by-step explanation:

in order to find x u need to subtract 7 from 5 to get -2. therefore your answer is -2

i love you when you call me se

The measure of ∠P to the nearest 10th of a degree is 84.8°

From the question, we are to determine the measure of ∠P

From the law of cosines, we can write that

[tex]cos \ P=\frac{o^{2}+q^{2}-p^{2} }{2oq}[/tex]

From the given information,

o = 500 cm

p = 600 cm

q = 380 cm

Putting the parameters into the formula, we get

[tex]cos \ P=\frac{500^{2}+380^{2}-600^{2} }{2\times 500 \times 380}[/tex]

[tex]cos \ P =\frac{34400}{380000}[/tex]

[tex]cos \ P =0.0905[/tex]

P = cos⁻¹(0.0905)

P = 84.8076

P ≅ 84.8°

Hence, the measure of ∠P to the nearest 10th of a degree is 84.8°

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Answer:

x>-12

Step-by-step explanation:

We want to the equation so that x is the only thing on the left-hand side.
-x/8 < 1.5 (multiply both sides by 8)
-x < 12

Now, whenever you multiply or divide by a negative when dealing with an inequality, you have to switch the sign.
x > -12.

Answer:

H

Step-by-step explanation:

every "|" is equal to 0.1

so you count 5 points which will get you to H which is 0.5

Answer:

(3,4)

Step-by-step explanation:

Hello!

To find the maximum value, we can find the vertex of the graph.

Since the coefficient of x² is negative, the graph opens downwards, meaning that the vertex would be the highest point.

To solve for the vertex, we can convert it to vertex form.

The vertex is (3,4)

Answer:

a. 1

Step-by-step explanation:

The question requires us to find the value of the function g(x) when x is -3.

g(x)= -2x -5

This means that for the function of g, when the input value is x, the output value is -2x -5.

For g(-3), x takes on the value of -3. We can thus evaluate the value of g(-3) by replacing x by -3 in the expression -2x -5.

g(-3)

= -2(-3) -5

= 6 -5

= 1

Therefore, a is the correct option.

Additional:

Here is another question on functions which you might wish to check out.

Let x, y, z denote the costs of milk, Serrano ham, and olive oil, respectively. Form the related system of equations and solve.

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{ \left\{\begin{matrix} 24x+6y+12z =156 \\ \ \qquad \qquad \quad \ z=3x \\ \qquad\ 4x+4z=y \end{matrix}\right.\ \Longrightarrow\ y=16x } \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{ 156=24x+6(16x)+12(3x)=156x\Longrightarrow x=1 } \end{gathered}$}[/tex]

         [tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{ y= 16\qquad z=3 } \end{gathered}$}[/tex]

Milk costs 1 a liter, Serrano ham 16 a kilogram and olive oil 3 a liter.

Using a trigonometric identity, it is found that the values of the cosine and the tangent of the angle are given by:

The identity that relates the sine squared and the cosine squared of the angle, as follows:

[tex]\sin^{2}{\theta} + \cos^{2}{\theta} = 1[/tex]

In this problem, we have that the sine is given by:

[tex]\sin{\theta} = \frac{1}{3}[/tex]

Hence, applying the identity, the cosine is given as follows:

[tex]\cos^2{\theta} = 1 - \sin^2{\theta}[/tex]

[tex]\cos^2{\theta} = 1 - \left(\frac{1}{3}\right)^2[/tex]

[tex]\cos^2{\theta} = 1 - \frac{1}{9}[/tex]

[tex]\cos^2{\theta} = \frac{8}{9}[/tex]

[tex]\cos{\theta} = \pm \sqrt{\frac{8}{9}}[/tex]

[tex]\cos{\theta} = \pm \frac{2\sqrt{2}}{3}[/tex]

The tangent is given by the sine divided by the cosine, hence:

[tex]\tan{\theta} = \frac{\sin{\theta}}{\cos{\theta}}[/tex]

[tex]\tan{\theta} = \frac{\frac{1}{3}}{\pm \frac{2\sqrt{2}}{3}}[/tex]

[tex]\tan{\theta} = \pm \frac{1}{2\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}}[/tex]

[tex]\tan{\theta} = \pm \frac{\sqrt{2}}{4}[/tex]

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Answer:

2/8

Step-by-step explanation:

there is the 4 sections of a spinner and 2 sides on the coin when you lay it out that leaves 2 opportunities to spin a 3 or a 4 and flipping heads

Answer:

1080

Step-by-step explanation:

Answer:

Here is the answer...hope it helps:)

Answer:

14 students

Step-by-step explanation:

You didn't include a graph, so I looked up the question to find the graph you are likely talking about.

If this graph does not match, ignore my answer (although the question is exactly the same so I'm guessing it might be the same)

{even if different , conceptually, here is what you do: }

Receiving at least 10 messages includes those who receive 10 messages.

Each X represents 1 student. So, 3 students received exactly 10 messages.

3 (who received 10)

2 (who received 15)

4 (who received 20)

5 (who received 25)

+________

14 students

14 students received ≥ 10 messages

(≥ means greater than or equal to,

< is less than (less < more)

> is greater than (more > less)

the line under includes the value _ (same or more ≥ than this value ;  same or less ≤ than this value)

hope this helps you !!

The solution to the given inequality is x < 9

Inequality are expressions not separated by an equal sign, Given the inequality

5x + 15< 60

Subtract 15 from both sides

5x < 60 - 15

5x < 45

Divide both sides by 5

5x/5 < 45/5

x < 9

The number line that describes the solution is attached

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The corresponding angles of triangle ABC and its image are congruent

The transformation rule is given as:

A rotation of 180 degrees about the origin

The rotation transformation is a rigid transformation.

This means that it does not alter the side lengths and the angle measure of the shape being rotated

Hence. the corresponding angles of triangle ABC and its image are congruent

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Answer:

it takes 2 seconds to do one situp

it takes 2 seconds to do one pushup

to do 14 pushups, it takes 28 seconds.

to do 12 situps it takes 24 seconds

to do 12 pushups, it takes 24 seconds

BRAINLIEST PLEASE!

hope this helps :)

Step-by-step explanation:

14x + 12y = 52

12x + 12y = 48

^^^ this is an inequality that we can make.  

x stands for pushups

y stands for situps

if we subtract the second equation from the first, we get

2x = 4

x = 2

now we can place x in one of the equations to solve for y

12(2)+12y=48

24 + 12y = 48

12y = 24

y = 2

Answer:

[tex]\frac{1247}{100}[/tex], or 12.47

Step-by-step explanation:

I looked this up on my scientific calculator. I hope this helps! :)

Answer:

1296

Step-by-step explanation:

times each number by 6

example: 1x6=6 6x6=36 36x6=216 216x6=1296

Hi student, let me help you out! :)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

We are asked to fill in the missing number in the sequence

[tex]\star~\mathrm{(~~),216,36,6,1}[/tex]

[tex]\triangle~\fbox{\bf{KEY:}}[/tex]

Since every number is divided by 6, we need to multiply 216 times the common ratio, 6:

[tex]\star~\mathrm{216\times6}[/tex]

Simplify!

[tex]\star~\mathrm{1296}[/tex]

Hope it helps you out! :D

Ask in comments if any queries arise.

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