If f(x) = x2 and g(x) = 3x + 1, then g(f(2))= ?

The length of time the ball was in the air is 4 seconds.

To find the maximum height of the ball and the time at which it reaches this height, we need to first determine the vertex of the parabolic function h(t) = -16t² + 48t + 64.

The vertex of the parabola is given by the formula:

t = -b / (2a)

where a = -16 and b = 48 are the coefficients of the quadratic function. Substituting these values, we get:

t = -48 / (2(-16)) = 1.5

So the time at which the ball reaches its maximum height is t = 1.5 seconds. To find the maximum height, we substitute this value back into the function:

h(1.5) = -16(1.5)² + 48(1.5) + 64 = 112

Therefore, the maximum height of the ball is 112 feet, and this occurs at t = 1.5 seconds.

To find the length of time the ball was in the air, we need to find the times at which the ball hits the ground. The ball hits the ground when its height is zero, so we need to solve the equation h(t) = 0 for t:

-16t² + 48t + 64 = 0

Dividing by -16, we get:

t² - 3t - 4 = 0

Factoring, we get:

(t - 4)(t + 1) = 0

Therefore, the ball hits the ground at t = 4 seconds and t = -1 second. Since time cannot be negative,

we only consider the positive root t = 4. So the ball is in the air for the time between t = 0 and t = 4 seconds.

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Answer:

the second table on the bottom

Step-by-step explanation:

To be a function the points have to pass the horizontal line test.

When you plot the graph of a function, then draw a horizontal line across the graph. If the horizontal line touches the graph only once, then the function does have an inverse function.

Based on the given task content; C(4) is the cost a guest will pay for staying 4 nights.

The correct answer option is option B.

C(n) = 98n + 32

where

C(4) = 98n + 32

= 98(4) + 32

= 392 + 32

C(4) = 424

In conclusion, C(4) is the cost a guest will pay for staying 4 nights.

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Answer:

Number of Nickels is 12

Number of Dimes is 9

Number of Quarters is 15

Step-by-step explanation:

Given that there are a total of 36 coins, which consists of nickels, dimes, and quarters.

That is, when we sum the numbers of nickels, dimes, and quarters, we have 36.

Let number of nickels be N

Let number of dimes be D

Let number of quarters be Q

Then

N + D + Q = 36 .................................(1)

- There are three fewer quarters than nickels.

This implies that

N = Q - 3 ..............................................(2)

Or

Q = N + 3 .............................................(3)

- There are six more dimes than quarters.

This implies that

Q = D + 6 .............................................(4)

Comparing (3) with (4), we see that

N + 3 = D + 6

N - D = 6 - 3

N - D = 3 ................................................(5)

Using (3) in (1)

N + D + (N + 3) = 36

2N + D = 36 - 3

2N + D = 33 ..........................................(6)

Solving (5) and (6) simultaneously

From (5): D = N - 3

From (6): D = 33 - 2N

=> N - 3 = 33 - 2N

N + 2N = 33 + 3

3N = 36

N = 36/3 = 12..........................................(7)

Using (7) in (6)

2(12) + D = 33

24 + D = 33

D = 33 - 24

D = 9 ........................................................(8)

Using (7) and (8) in (1)

12 + 9 + Q = 36

21 + Q = 36

Q = 36 - 21 = 15.......................................(9)

Therefore,

Number of Nickels, N = 12

Number of Dimes, D = 9

Number of Quarters, Q = 15

(b) An equilateral triangle has 3-fold rotational symmetry, while (d) A cube has 4-fold rotational symmetry.

Rotational symmetry refers to the property of an object where it looks the same after it has been rotated a certain number of degrees around a central point. The number of times an object looks the same after a full rotation is called its order of rotational symmetry.
(a) An isosceles triangle has no rotational symmetry because it will not look the same after any degree of rotation around its center.

An isosceles triangle has no rotational symmetry. This is because it will not look the same after any degree of rotation around its center. For example, if you rotate an isosceles triangle by 180 degrees, it will be upside down and look completely different.
An equilateral triangle has 3-fold rotational symmetry. This means that it will look the same after being rotated 120 degrees and 240 degrees around its center. To see this, imagine drawing an equilateral triangle and marking its center. If you rotate the triangle 120 degrees around the center, each vertex will be in the same position as before, and the triangle will look the same. Similarly, if you rotate it 240 degrees, it will look the same as the original triangle.

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The coordinates of the vertices of the image include the following:

W' = (5, -2).

X' = (7, -4).

Y' = (3, -5).

In this exercise, we would have to dilate the coordinates of the pre-image (triangle WXY) by using a scale factor of 1/3 centered at the point (4, -1) by using this mathematical expression:

(x, y)  →  (k(x - a) + a, k(y - b) + b)

For coordinate W, we have;

Coordinate W = (7, -4)  →  (1/3(7 - 4) + 4, 1/3(-4 - (-1)) + (-1))

Coordinate W = (2, 4)  →  (1/3(3) + 4, 1/3(-3) - 1)

Coordinate W' = (5, -2).

For coordinate X, we have;

Coordinate X = (13, -10)  →  (1/3(13 - 4) + 4, 1/3(-10 - (-1)) + (-1))

Coordinate X = (2, 4)  →  (1/3(9) + 4, 1/3(-9) - 1)

Coordinate X' = (7, -4).

For coordinate Y, we have;

Coordinate Y = (1, -13)  →  (1/3(1 - 4) + 4, 1/3(-13 - (-1)) + (-1))

Coordinate Y = (2, 4)  →  (1/3(-3) + 4, 1/3(-12) - 1)

Coordinate Y' = (3, -5).

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The interval estimate for the true population proportion is 45.25% to 64.75% and we can conclude that the majority of the community supports water rationing

The given parameters are:

The error margin is calculated using:

\(E = z * \sqrt{\frac{p* (1 - p)}{n}}\)

Where z is the critical value.

At 95% confidence level, the critical value is:

z = 1.96

So, we have:

\(E = 1.96 * \sqrt{\frac{0.55 * (1 - 0.55)}{100}}\)

Evaluate

\(E = 1.96 * \sqrt{0.002475}\)

Evaluate

E = 0.0975

Hence, the error margin is 0.0975

This is calculated using:

I = p ± E

So, we have:

I = 0.55 ± 0.0975

Expand

I = (0.55 - 0.0975, 0.55 + 0.0975)

Evaluate

I = (0.4525, 0.6475)

Express as percentage

I = (45.25%, 64.75%)

Hence, the interval estimate for the true population proportion is 45.25% to 64.75%

From the simulation,

The values are approximately the interval estimates.

i.e.

45.25% ≈ 45% and 64.75% ≈ 65%

Hence, we can conclude that the majority of the community supports water rationing

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(x+2)/3 = (3x-2)/6

6(x+2) = 3(3x-2)

6x+12 = 9x-6

12+6 = 9x-6x

18 = 3x

x = 6

The amount of money in Iris's checking account can be modeled by a linear function of the form:

y = mt + b

where y is the amount of money in the account, t is the time (measured in years), m is the rate of interest, and b is the initial amount in the account.

In this case, we have m = 0.04 (since the interest rate is 4% per year) and b = 180 (since that's the initial amount in the account). Therefore, the linear function that models the amount of money in Iris's checking account at any time t is:

y = 0.04t + 180

For example, if t = 5 (years), then the amount of money in Iris's checking account is 0.04 * 5 + 180 = 198 dollars.

And

Check

Hence

Or

Option C

Answer:

1/64

Step-by-step explanation:

\( \frac{ {8}^{2} }{ {8}^{4} } = \frac{1}{ {8}^{4 - 2} } = \frac{1}{ {8}^{2} } = \frac{1}{64} \\ \)

Given a sample with a mean of 145 lb, a size of 16, and a standard deviation of 16 lb, we can analyze the sample using statistical measures such as the mean and standard deviation to understand the characteristics of the data.

The mean, also known as the average, is calculated by summing up all the values in the sample and dividing by the sample size. In this case, the mean is 145 lb.
The standard deviation measures the dispersion or spread of the data points around the mean. It quantifies the variability within the sample. A higher standard deviation indicates a greater spread of values. In this case, the standard deviation is 16 lb.
These statistical measures help us understand the central tendency and variability of the sample data. The mean of 145 lb indicates the average weight within the sample, while the standard deviation of 16 lb suggests that the weights in the sample are spread out around the mean. This information can be useful for making comparisons, identifying outliers, or conducting further statistical analysis.

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The total number of eigenvectors for an n x n matrix is equal to the sum of the multiplicities of its distinct eigenvalues,

which is at most n.

The reason why a 2x2 matrix can have at most two distinct eigenvalues is because the characteristic equation for a

2x2 matrix is quadratic. This means that there can be at most two distinct solutions for the eigenvalues.

As for an n x n matrix, the reason why it can have at most n distinct eigenvalues is because the characteristic equation

for an n x n matrix is of degree n.

This means that there can be at most n distinct solutions for the eigenvalues. Additionally, the maximum number of

eigenvectors that can be associated with each distinct eigenvalue is equal to the multiplicity of the eigenvalue.

Therefore, the total number of eigenvectors for an n x n matrix is equal to the sum of the multiplicities of its distinct

eigenvalues, which is at most n.

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Answer:

R72. 80

Step-by-step explanation:

1KG = R36, 40

2KG = R36.40 X 2

= R72. 80

Given:

Atul has \(\dfrac{2}{3}\) lb of candy.

Jose has \(\dfrac{3}{5}\) lb of candy.

Maria has \(\dfrac{1}{2}\) lb less than Jose.

To find:

How many more pounds of candy does Atul have than Maria?

Solution:

Since, Maria has \(\dfrac{1}{2}\) lb less than Jose, therefore

Maria has = \(\dfrac{3}{5}-\dfrac{1}{2}\) lb

Maria has = \(\dfrac{6-5}{10}\) lb

Maria has = \(\dfrac{1}{10}\) lb

Difference between the candies Atul and Maria have.

Difference = \(\dfrac{2}{3}-\dfrac{1}{10}\) lb

Difference = \(\dfrac{20-3}{30}\) lb

Difference = \(\dfrac{17}{30}\) lb

Therefore,  Atul have \(\dfrac{17}{30}\) lb of candy more than Maria.

Answer:

C. p

Step-by-step explanation:

Given the expression p - q = 0

We are to find the value of q

Substract p from both sides;

p - q - p = 0 - p

-q = - p

Multiply both sides by -1

-(-q) = -(-p)

q = p

Hence the correct solution is q = p

Answer:

x=9

Step-by-step explanation:

2x + 10 =28 <---- subtract by 10

2x = 18          < divide by 2

x = 9

Answer:

B and E

Here's how to do it.

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Info given

We have a total of people given (82). We also know that we have 54 children of under 12 years and under some children were under 3 years

We define x as the number of children under 3 years.

We want to find C for the total cost. We don't have the unitary prices but we can assume it as C1 (over 3 and lower than 12) and C2(adults) for children and adults.

Solution:

With C the total amount collected and C1 and C2 described above.

Answer:

Step-by-step explanation:

Answer is B

Step-by-step explanation:

T  |  0   |   1    |  2   |  3   |

C  | 24  |  21  |  18  |  15  |

Rule:

To find a rule, we need to find 2 things- what T is multiplied by and what is added.

To find what it is multiplied, we need to see the increase or decrease in C for every T. In this equation, there is a decrease of 3, so we multiply T by -3.

To find what is added, we go to 0 T and find the corresponding number. When T is 0, C is 24 so we add 24.

We write a rule as:  y = mx + c, or in this case, c = mt + a

So the rule is c = -3x + 24

The value of the expression 3^5 is 243

The expression is given as:

3 exponent 5

This can be properly represented as:

3^5

Expand the expression

3^5 = 3 * 3 * 3 * 3 * 3

Evaluate the exponent

3^5 = 243

Hence, the value of the expression 3^5 is 243

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Answer:

Hi there.....

Step-by-step explanation:

This is ur answer......

1, 3, 5, 7, 9, 11, 13, 15.................39

Therefore the total sum = 400

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Answer:

400

Step-by-step explanation:

These are the first 20 odd numbers

1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 + 25 + 27 + 29 + 31 + 33 + 35 + 37 + 39

Put them in a calculator and you get: 400

To calculate the gain on the sale of the office furniture, we need to determine the asset's book value and compare it to the sale price.

First, let's calculate the accumulated depreciation on the furniture. The furniture was purchased on January 1, 2014, and the straight-line depreciation method is used over 10 years with a salvage value of $80,200.

Depreciation per year = (Cost - Salvage Value) / Useful Life

Depreciation per year = ($746,800 - $80,200) / 10 years

Depreciation per year = $66,160

Next, we need to calculate the accumulated depreciation for the period from January 1, 2014, to May 1, 2021 (the date of the sale). This is approximately 7.33 years.

Accumulated Depreciation = Depreciation per year × Years

Accumulated Depreciation = $66,160 × 7.33 years

Accumulated Depreciation = $484,444.80

Now, we can calculate the book value of the furniture:

Book Value = Cost - Accumulated Depreciation

Book Value = $746,800 - $484,444.80

Book Value = $262,355.20

Finally, we can calculate the gain on the sale:

Gain on Sale = Sale Price - Book Value

Gain on Sale = $300,000 - $262,355.20

Gain on Sale = $37,644.80

Therefore, the gain that should be recognized on the sale of the office furniture is approximately $37,644.80.

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The gain that should be recognized on the sale of the office furniture is $84,080.

The gain is calculated by subtracting the equipment's book value from the sale price. This gain will be reported on the company's income statement. Here is how to calculate the gain:First, find the equipment's book value using the straight-line method of depreciation.

Straight-line depreciation is calculated by taking the difference between the equipment's original cost and its salvage value, and then dividing it by the number of years the equipment is used. The annual depreciation expense is then multiplied by the number of years the equipment is used to find the equipment's book value at the end of its useful life.

For this question, the book value of the equipment at the time of sale is:Cost of equipment: $746,800Salvage value: $80,200Depreciable cost: $746,800 - $80,200 = $666,600Annual depreciation: $666,600 ÷ 10 years = $66,660Book value at the end of 2020: $666,600 - ($66,660 x 7) = $156,420

Next, subtract the equipment's book value from the sale price to find the gain:Sale price: $300,000Book value: $156,420Gain: $143,580Finally, round the gain to the nearest dollar:$143,580 ≈ $143,580.00So the gain that should be recognized on the sale of the office furniture is $84,080.

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Answer: On the 20th day, he will give $5242.88

Step-by-step explanation: This is a geometric series with elements:

initial value (\(a_{0}\)) = 0.01

ratio = 2

At the twentieth day means the 20th term, i.e. n = 20.

To determine that term, use the formula: \(a_{n} = a_{0}.r^{n-1}\)

Substituing terms:

\(a_{20} = 0.01.2^{20-1}\)

\(a_{20} = 0.01.2^{19}\)

\(a_{20} = 0.01.524288\)

\(a_{20} = 5242.88\)

Then, on the 20th day, your uncle gave to you $5242.88

The population of birds to increase by 50% in 31.25 years.

The differential equation for the population of birds is:

dp/dt = 0.016P

where P is the population of birds and t is time in years.

To obtain the time it takes for the population to increase by 50%, we need to solve for t when P increases by 50%.

Let P0 be the initial population of birds, and P1 be the population after the increase of 50%.

Then we have:

P1 = 1.5P0 (since P increases by 50%)

We can solve for t by integrating the differential equation:

dp/P = 0.016 dt

Integrating both sides, we get:

ln(P) = 0.016t + C

where C is the constant of integration.

To obtain the value of C, we can use the initial condition that the population at t=0 is P0:

ln(P0) = C

Substituting this into the previous equation, we get:

ln(P) = 0.016t + ln(P0)

Taking the exponential of both sides, we get

:P = P0 * e^(0.016t)

Now we can substitute P1 = 1.5P0 and solve for t:

1.5P0 = P0 * e^(0.016t

Dividing both sides by P0, we get:

1.5 = e^(0.016t)

Taking the natural logarithm of both sides, we get:

ln(1.5) = 0.016t

Solving for t, we get:

t = ln(1.5)/0.016

Using a calculator, we get:

t ≈ 31.25 years

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A total of 55.86 minutes have gone by since Greg started his run on the treadmill.

If Greg has completed 57% of his run, it means he has 43% of his run remaining.

To find out how many minutes have gone by, we can use proportions.

Let's say x is the total number of minutes Greg needs to complete his run:

x = 57% * 98 minutes

Evaluate

x =  minutes

Therefore, approximately 55.86 minutes have gone by since Greg started his run on the treadmill.

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Answer:

\(x = 180 - \frac{y}{2}\)

Step-by-step explanation:

Our goal here is to isolate \(x\) on one side of the equals sign

\(360 = 2x + y\)

Here we have 2 terms on the right side of the equals sign, \(2x\) and \(y\)

in order isolate the \(x\) term we must subtract \(y\)

However, if we subtract \(y\) from one side of the equation we must also do the same to the other side to a maintain balanced equation.

\(360 = 2x + y\)
\(-y\)           \(-y\)

\(360 - y = 2x\)

Now to remove "2" from \(2x\) we must do the opposite of multiplication, which is division.

\(\frac{360}{2} - \frac{y}{2} = \frac{2x}{2}\)

simplify.

\(180 - \frac{y}{2} = x\)

The quotient of this division problem option A: 18 r89.

To find the quotient of the division problem 13,391 ÷ 739, we divide the dividend (13,391) by the divisor (739). The quotient represents the whole number result of the division, and any remaining value is the remainder.

Performing the division, we have:

First, we determine how many times 739 can be divided into 13,391 without exceeding it. We find that 739 can be divided into 13,391 eighteen times. We write this as the first part of the quotient:

      18

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

739 | 13,391

      739

We have a remainder of 89, which means we couldn't divide 89 further by 739 without exceeding it. Hence, we write the remainder after the division symbol:

 ----------

       6,651

      5,913

 ----------

         738

Remember, when performing division, the quotient represents the whole number result obtained from dividing the dividend by the divisor, and the remainder represents what is left after the division.

The division process shows that the quotient is 18 (OA) with a remainder of 738. Therefore, the correct answer is OA: 18 r89.

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