someone help me with this asap thank you

Answer:

228

Explain your answer:

Answer:

A = 228 ft²

Step-by-step explanation:

The area (A) of a trapezoid is calculated as

A = \(\frac{1}{2}\) h (b₁ + b₂ )

where h is the height and b₁, b₂ the parallel bases

here h = 12 and b₁ = 14, b₂ = 24 , then

A = \(\frac{1}{2}\) × 12 × (14 + 24) = 6 × 38 = 228 ft²

Answer:

Length of the side of the square is 12 cm.

Step-by-step explanation:

Given information:

\(\text{side}_1 = 8a \text{ cm (side of a rectangle)}\\\text{side}_2 = 7a \text{ cm (side of a rectangle)}\\P_\text{rec} = 42 + P_\text{sq} \text{ cm } (P_\text{rec} \text{ is perimeter of the rectangle and } \\P_\text{sq} \text{ is the perimeter of the square)}\\\text{side}_\text{sq} = 4a \text{ cm (side of a square)}\)

Our mission is to find the length of the side of the square. We know that the side of the square is 4a cm, so to be able to answer we have to find the value of a first.

Step 1: Finding the value of a

Key to finding the value of a is the perimeter of the rectangle. Notice that we can calculate the perimeter of the rectangle in two different ways.

One way was given in the question:
\(P_\text{rec} = 42 + P_\text{sq}\)

We want equations in terms of a, so we can calculate a. Perimeter of the square can be calculated as:

\(\text{perimeter}_\text{square} = 4 \times \text{side}\)

Substituting the values in equation:

\(P_\text{sq} = 4 \times 4a\\P_\text{sq} = 16a\)

Therefore the first equation for perimeter of the rectangle becomes:

\(P_\text{rec} = 42 + P_\text{sq}\\\fbox{\begin{test}P_\text{rec} = 42 + 16a\end{test}}\)

For the second way we use formula for the perimeter of rectangle which is:
\(\text{perimeter}_\text{rectangle} = 2 \times \text{width} + 2 \times \text{length}\)

Substituting the values in equation:
\(P_\text{rec} = 2 \times 7a + 2 \times 8a\\P_\text{rec} = 14a + 16a\\\fbox{\begin{test}P_\text{rec} = 30a\end{test}}\)

Now let's equate both perimeters of the rectangle.

\(P_\text{rec} = P_\text{rec}\\42+16a = 30a\\42 =14a\\3 = a\)

Step 2: Find the length of the side of the square

It's given that side of the square is 4a cm. All we have to do is substituting a with its value, which we got in the previous step.

\(\text{side}_\text{sq} = 4a\\\text{side}_\text{sq} = 4(3)\\\text{side}_\text{sq} = 12 \text{ cm}\)

The function \(f(x) = x^2 - c^2\) for x < 6 and f(x) = cx + 45 for x ≥ 6 is continuous on (-∞, ∞) for all values of c except for c = 0.  Consider the definition of continuity.

A function is continuous at a point if the limit of the function as x approaches that point exists and is equal to the value of the function at that point.

For x < 6, the function \(f(x) = x^2 - c^2\) is a polynomial function and is continuous for all values of c since polynomials are continuous everywhere.

For x ≥ 6, the function f(x) = cx + 45 is a linear function. Linear functions are also continuous everywhere, regardless of the value of c.

However, at x = 6, we have a point of discontinuity if c = 0. When c = 0, the function becomes f(x) = 45 for x ≥ 6. In this case, the function has a jump discontinuity at x = 6 since the limit as x approaches 6 from the left is not equal to the value of the function at x = 6.

In conclusion, the function  \(f(x) = x^2 - c^2\) for x < 6 and f(x) = cx + 45 for x ≥ 6 is continuous on (-∞, ∞) for all values of c except when c = 0.

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The complete question is:

For What Value Of The Constant C Is The Function F Defined Below Continuous  on (−[infinity],[infinity])?

f(x)= { x² - c², x < 6

      { cx + 45, x ≥ 6

Answer:

Quotient is an answer to a division problem.

For example: 12 ÷ 2 = 6, the quotient is 6.

Reciprocal is the opposite of the fraction. When you put the numerator in the place of the denominator and vice versa.

For example: the reciprocal of 2/3 is 3/2. When divided, the two fractions cancel each other out.

To evaluate each integral in terms of areas, we need to understand that the integral represents the area under the curve of a function, f(x), between two points on the x-axis.

Let's discuss each integral:

(a) ∫₀⁸ f(x) dx: This represents the area under the curve of f(x) from x = 0 to x = 8. The integral calculates the accumulated area along this interval.

(b) ∫₀²⁰ f(x) dx: Similarly, this represents the area under the curve of f(x) from x = 0 to x = 20. It's a broader interval than (a), so it covers more area under the curve.

(c) ∫²⁰²⁸ f(x) dx: This integral represents the area under the curve of f(x) between x = 20 and x = 28. It's important to note that the interval is now shifted to the right compared to (a) and (b).

(d) ∫¹²²⁸ f(x) dx: This integral calculates the area under the curve of f(x) from x = 12 to x = 28. The interval here is larger than in (c), covering more area under the curve.

(e) ∫¹²²⁸ |f(x)| dx: This integral evaluates the area under the absolute value of f(x) from x = 12 to x = 28. The absolute value ensures that negative function values contribute positively to the area calculation, preventing any cancelation of areas.

(f) ∫₀⁸ f(x) dx: This integral is the same as (a), representing the area under the curve of f(x) from x = 0 to x = 8.

Each integral evaluates the area under the curve of f(x) for different intervals on the x-axis, providing insights into the total accumulated area in those intervals.

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The time that it would take Justin to charge the batter to 100% on both devices will be 111.67 minutes

It takes about 36.67 minutes to charge the Nintendo Switch entirely.

The iPad has a residual battery life of 40%, which means it must gain an additional 60% percent increase in energy.

Since we understand that the tablet powers up by approximately 12 percentage points every quarter of an hour, the estimated duration for one hundred percent charging is close to 75 minutes.

Consequently, Justin must energize both gadgets and will need nearly 111.67 minutes or almost two hours to accomplish this task completely.

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Answer:

4

Step-by-step explanation:

You just need to find the common factors, then find the largest in them.

Answer:

the very last one because none of the x values can be the same and it has two 0 in the x values

Step-by-step explanation:

Answer:

42 minutes

Step-by-step explanation:

6x7=42

Answer:

1) 3 people do 4 walls in 32 minutes

We make the assumptions that all people work at the same rate and each person starts and finishes at the same time. Since there are 3 people, each person does 1/3 of the total work. Therefore each person finishes their portion of the job in 32 minutes

2) 3 * 1/3 = 1 person does 4 * 1/3 = 4/3 walls in 32 minutes

The unit rate (the rate for 1 person to do 1 wall) is as follows

3) 1 person does 4/3 * 3/4 = 1 wall in 32 * 3/4 = 24 minutes

Since we need 4 people to do 7 walls then 1 person needs to do 1/4 of the work. So the following is true

4) 4 * 1/4 = 1 person does 7 * 1/4 = 7/4 wall

As we said before in #3

1 person does 1 wall in 24 minutes

So we conclude

5) 1 person does 1 * 7/4 = 7/4 walls in 24 * 7/4 = 42 minutes

And finally

6) 1 * 4 = 4 people do 7/4 * 4 = 7 walls in 42 minutes

No, it is simply the likelihood that the interval would include the population of the important quantity. Even though it is unlikely, it is possible that the 95% confidence interval does not include the desired population size.

The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval.

You have a 5% probability of being incorrect with a 95% confidence interval. You have a 10% probability of being incorrect with a 90% confidence interval. A 95% confidence interval is narrower than a 99% confidence interval (for example, plus or minus 4.5 percent instead of 3.5 percent).

No, it is simply the likelihood that the interval would include the population of the important quantity. Even though it is unlikely, it is possible that the 95% interval does not include the desired population size.

No, it is merely the chance that the population of the significant quantity would be present during the interval. Although uncommon, there is a chance that the target population size is not included in the 95% interval.

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Answer:

this should do it

Answer:

13.7

Step-by-step explanation:

Using cosine formula:

AB^2 = AC^2 + BC^2 - 2*AB*BC*cosC

AB^2 = 15^2 +12^2 -2*15*12*cos60

AB = 13.7 in

We have proved the statement (Vn ∈ Z) (2 | n² iff 2 | n).

To prove the statement (Vn ∈ Z) (2 | n² iff 2 | n), we will consider both directions separately.

Direction 1: If 2 divides n², then 2 divides n.

Assume that 2 divides n². This means that there exists an integer k such that n² = 2k.

Taking the square root of both sides, we have √(n²) = √(2k).

Since n is an integer, we know that n ≥ 0. Therefore, we can write n = √(2k).

To show that 2 divides n, we need to prove that there exists an integer m such that n = 2m.

Substituting the value of n from above, we have √(2k) = 2m.

Squaring both sides, we get 2k = 4m².

Dividing both sides by 2, we have k = 2m².

Since m² is an integer, let's denote it as p, where p = m².

Now, we can rewrite the equation as k = 2p.

This shows that 2 divides k, which means 2 divides n.

Direction 2: If 2 divides n, then 2 divides n².

Assume that 2 divides n. This means that there exists an integer m such that n = 2m.

To prove that 2 divides n², we need to show that there exists an integer k such that n² = 2k.

Substituting the value of n from above, we have (2m)² = 2k.

Expanding the equation, we get 4m² = 2k.

Dividing both sides by 2, we have 2m² = k.

Since m² is an integer, let's denote it as p, where p = m².

Now, we can rewrite the equation as 2p = k.

This shows that 2 divides k, which means 2 divides n².

In both directions, we have shown that if 2 divides n², then 2 divides n, and if 2 divides n, then 2 divides n². Therefore, we have proved the statement (Vn ∈ Z) (2 | n² iff 2 | n).

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(a) The firm is operating in the long run, and its supply function is determined by the profit maximization condition.

(b) The firm's input demand functions can be derived from the profit function, and their degree of homogeneity is 1/2. Changes in input prices will impact the firm's input demand.

(c) The market supply function can be derived by aggregating the supply functions of all 40 firms operating in the market.

(d) Given the market conditions and demand function, the total market supply can be calculated.

(a) The firm is operating in the long run because it has the flexibility to adjust its inputs and make decisions based on market conditions. The firm's supply function is determined by maximizing its profit, which is achieved by setting the marginal cost equal to the market price. In this case, the supply function for each firm can be derived by taking the derivative of the profit function with respect to the price of output (p).

(b) The input demand functions for the firm can be derived by maximizing the profit function with respect to each input price. The degree of homogeneity of the input demand functions can be determined by examining the exponents of the input prices. In this case, the degree of homogeneity is 1/2. Changes in the input prices will affect the firm's input demand as it adjusts its input quantities to maximize profit.

(c) The market supply function can be derived by aggregating the individual supply functions of all firms in the market. Since there are 40 identical firms, the market supply function can be obtained by multiplying the supply function of a single firm by the total number of firms (40).

(d) To determine the total market supply, we substitute the given market conditions and demand function into the market supply function. By solving for the market quantity at a given market price, we can calculate the total market supply.

In conclusion, the firm is operating in the long run, and its supply function is determined by profit maximization. The input demand functions have a degree of homogeneity of 1/2, and changes in input prices impact the firm's input demand. The market supply function is derived by aggregating the individual firm supply functions, and the total market supply can be calculated using the given market conditions and demand function.

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The circumference of the circle with radius 3 miles is 18.85 miles.

All points on a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.

The following are some of the circle's crucial characteristics:

The radius of the circle is 3 miles

Circumference of the circle 2π(radius) = 2*π*3 = 18.85 miles.

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Answer:

21

Step-by-step explanation:

Area of a parallelogram is Area = Base times Height. (A=B*H). here Base is 3 and Height is 7 so 7*3=21. 21 cm^2 is the answer.

(a) The probability of having two Tails given that at least one of the coins landed Tails is 1/2.

(b) The probability that both coins are from an "I" state is 6/1225, which simplifies to 2/245.

(c) The probability that one of the coins tossed was the Illinois quarter, given that you do not see the name "Illinois", is 49/75.

(d)

Therefore, the PMF of X is:

P(X=0) ≈ 0.4265

P(X=1) ≈ 0.5135

P(X=2) ≈ 0.0565

P(X=4) ≈ 0.0035

(a) To find the probability of having two Tails given that at least one of the coins landed Tails. Let B be the event that both coins landed Tails. Then, the probability we are looking for is P(B|A) = P(B and A)/P(A).

using complement rule: P(A) = 1 - P(neither coin landed Tails) = 1 - P(both coins landed Heads) = 1 - (1/2) * (1/2) = 3/4.

using conditional probability formula: P(B and A) = P(B|A) * P(A) = P(Tails on second coin | Tails on first or second coin) * P(Tails on first or second coin) = (1/2) * 3/4 = 3/8.

Therefore, P(B|A) = P(B and A)/P(A) = (3/8)/(3/4) = 1/2.

(b) There are 50 coins in total, so the sample space has size 50 choose 2 = 1225. There are 4 states whose name begins with "I", so the number of ways to choose two coins from those states is 4 choose 2 = 6. Therefore,

(c) Let B be the event that one of the coins tossed was the Illinois quarter.Then, P(B) = 1/2.

using formula: P(A and B) = P(B|A) * P(A) = P(B and A).

using law of total probability: P(B and A) = P(B and neither coin is Illinois) + P(B and one coin is Illinois) = (48/50) * (1/2) + (1/50) * (1/2) = 49/100.

Therefore, P(B|A) = P(B and A)/P(A) = (49/100)/(3/4) = 49/75.

(d)The number of ways to choose two coins from these states is 7 choose 2 = 21. Let X be the total number of G's in the state names for the two coins that were tossed. Then, X can take on the values 0, 1, 2, 3, or 4.

To find the PMF of X, we need to calculate P(X = k) for each value k.

The probability of getting a sum of 0 G's is therefore:

P(X=0) = 42C2 / 50C2 ≈ 0.4265

The probability of getting a sum of 1 G is therefore:

P(X=1) = 2(6C1 × 44C1 + 6C2) / 50C2 ≈ 0.5135

The probability of getting a sum of 2 G's is therefore:

P(X=2) = 6C2 / 50C2 ≈ 0.0565

The probability of getting a sum of 4 G's is therefore:

P(X=4) = 1 / 50C2 ≈ 0.0035

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The slope of the new road is zero.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

Take points from the Graph (5, 0) and (5, 4).

Slope of a line = m = tanθ

where θ is the angle made by the line with the x−axis.

For a line parallel to y−axis ,θ= π/2.

​

∴m = tan π/2 = undefined

The new road will therefore have 0° of inclination if it is perpendicular to D street because if they are perpendicular and D street is vertical, the new road is level and has 0° of inclination.

An horizontal line now has zero slope.

The new road has a zero slope as a result.

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Answer:

undefined

Step-by-step explanation:

you can't divide zero by zero

Answer:

0/0 is not possible, bcs u can't divide anything by 0

Step-by-step explanation:

SO ANSWER IS INFINITY OR NOTT POSSIBLE

Answer:

C (-∞, ∞)

Step-by-step explanation:

For graphs like these this will always be the domain as its 'arms' will continue to go further in x values

Answer:

C

Step-by-step explanation:

The maximum number of sheets of paper that can fit in the tray is 625 of a printer paper tray is 5 cm deep one sheet of paper is 8x10 to the power of -3 cm thick

To determine the maximum number of sheets of paper that can fit in the tray, we need to find the total thickness of the paper.

Since one sheet of paper is 8x10^-3 cm thick, if we have n sheets of paper, the total thickness will be:

total thickness = n * 8x10^-3 cm

And since the tray is 5 cm deep, the maximum number of sheets of paper that can fit in the tray is given by:

n = 5 / (8x10^-3) = 5 / 0.008 = 625

So, the maximum number of sheets of paper that can fit in the tray is 625.

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Answer:

1.32/100

Step-by-step explanation:

(1.32×100)/(1×100) = 132/100

It can be written as 132%= 132/100 or 132/100

4. To simplify 132/100 to its lowest terms, find LCM for the 132 and 100

4 is LCM for 132 and 100.

5. Divide numerator and denominator by 4

132/100=(132/4)/(100/4)=33/25.

33/25 is a simplest fraction for the decimal point number 1.32.

Answer:

132/100

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

I don’t rly know how to write this as a mixed number

Answer:

No, it is not a function.

Step-by-step explanation:

Vertical line test. A function can only have one output, y, for each unique input, x.

Answer:

y = -3(x + 2)^2 + 10.

Step-by-step explanation:

y = –3x2 – 12x – 2

Divide first 2 terms by -3:

y = -3(x^2 + 4x) - 2            Now complete the square on x^2 + 4x:-

y = -3(x^2 + 4x + 4 - 4) - 2

y = -3[(x + 2)^2 - 4] - 2

y = -3(x + 2)^2 + 12 - 2

y = -3(x + 2)^2 + 10.

The number of bacteria will double after 15.93 hours, or approximately 15 hours and 56 minutes.

The given exponential growth equation for N(t) is N(t) = 10000011.

To solve the problems related to it, we need to follow these steps:a) What is the number of bacteria at t = 0 hours?

We need to plug in t = 0 in the given equation of N(t) to find out the number of bacteria at t

= 0 hours.

N(0) = 10000011

= 1

Therefore, the number of bacteria at t = 0 hours is 1.b) When will the number of bacteria double?

Give the exact solution in the simplest form. Do not evaluate.

We know that the formula for the exponential growth function is given by the equation y = abx.

Here, x is the number of units of time passed, a is the initial value of y, b is the growth factor, and y is the final value of the function. We can use this formula to find out the time when the number of bacteria doubles.To find out the time when the number of bacteria doubles,

we can set y = 2 and s

olve for x.2 = abx

Since we are given that

N(t) = 10000011, we can write the above equation as:

2 = 10000011 * bxTaking the natural logarithm of both sides,

ln 2 = ln 10000011 + ln bx

Simplifying,

ln 2 - ln 10000011 = ln b + x ln b

Using a calculator, we get,

ln b = ln 2 - ln 10000011ln b

≈ -20.723

Using the properties of logarithms, we get,

x = [ln 2 - ln 10000011] / ln bSubstituting the value of ln b,

we get,x ≈ 15.93

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Answer:

what do you want us to tell you

Step-by-step explanation:

i would guess c but i'm not 100% sure

By using the given information about the matrix a, the trace and determinant, and the algebraic multiplicities of its eigenvalues to solve for the eigenvalues of a.

To solve this problem, we can start by using the fact that the trace of a matrix is equal to the sum of its eigenvalues. Since tr(a) = 3, we know that the sum of the eigenvalues of a is 3.

Next, we can use the fact that the determinant of a matrix is equal to the product of its eigenvalues. Since det(a) = -80, we know that the product of the eigenvalues of a is -80.

Let λ1 and λ2 be the two distinct eigenvalues of a, with algebraic multiplicities m1 and m2, respectively. Then we have:

λ1 + λ2 = 3 (from tr(a) = 3)

λ1λ2 = -80 (from det(a) = -80)

We can solve this system of equations to find the values of λ1 and λ2:

λ1 = 8, m1 = 2

λ2 = -5, m2 = 1

To see why these values are correct, note that the algebraic multiplicities must add up to the size of the matrix (which is 3 in this case). We have m1 + m2 = 2 + 1 = 3, so this condition is satisfied.

Therefore, the eigenvalues of a with their algebraic multiplicities are λ1 = 8 (with multiplicity 2) and λ2 = -5 (with multiplicity 1).

In conclusion,  by using the given information about the matrix a, the trace and determinant, and the algebraic multiplicities of its eigenvalues to solve for the eigenvalues of a.

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