Aisha and Jordan start by making a floor plan for their treehouse. They decide to build a porch on one side of the treehouse. Floor Plan : 10. 5 Ft (Length) by 6 Ft (wide) - Withing the plan the porch is 1. 25 Ft by 6 Ft
Make a grid and shade to find the area of the porch. (I can do the math but not sure how to make the grid)

When a swimming coach needs to choose a team for a relay race then the number of ways they can arrange 444 of the 666 swimmers is 3.53×\(10^{1735}\)

There are a total of 444\(C_{444}\) (or 6.64 x \(10^{847}\)) ways to select 444 swimmers from the pool of 666.

Once the swimmers have been chosen, they need to be arranged in a strategic sequence.

This can be done in 444! (or 5.34 x \(10^{906}\)) ways.

Therefore, the total number of unique ways to arrange 444 of the 666 swimmers is

6.64 x \(10^{847}\) x 5.34 x \(10^{906}\)

3.53 x \(10^{1735}\)

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Therefore, the equation x^3 - 15x + c = 0 has at most one root in the interval (-2, 2).

To show that the equation x^3 - 15x + c = 0 has at most one root in the interval (-2, 2), we can use the concept of the Intermediate Value Theorem and Rolle's Theorem.

Let's assume that the equation has two distinct roots, denoted as a and b, in the interval (-2, 2). Without loss of generality, we assume a < b.

Since the function is continuous on the closed interval [-2, 2] and differentiable on the open interval (-2, 2), we can apply Rolle's Theorem. According to Rolle's Theorem, there exists a point c in the open interval (a, b) such that the derivative of the function at c is zero.

Consider the derivative of the function f(x) = x^3 - 15x + c:

f'(x) = 3x^2 - 15

Setting f'(c) = 0, we have:

3c^2 - 15 = 0

c^2 - 5 = 0

c^2 = 5

Taking the square root of both sides, we get:

c = ±√5

Now, let's consider the function values at the endpoints of the interval (-2, 2):

f(-2) = (-2)^3 - 15(-2) + c = -8 + 30 + c = 22 + c

f(2) = (2)^3 - 15(2) + c = 8 - 30 + c = -22 + c

If c = √5, then f(-2) = 22 + √5 and f(2) = -22 + √5.

If c = -√5, then f(-2) = 22 - √5 and f(2) = -22 - √5.

In either case, the function values at the endpoints have different signs. This implies that there exists at least one value, say k, in the interval (-2, 2) such that f(k) = 0, according to the Intermediate Value Theorem.

However, we assumed at the beginning that there are two distinct roots in the interval (-2, 2), denoted as a and b. This contradicts our finding that there is at most one root in the interval. Hence, our assumption of having two distinct roots is false.

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Answer:

Use sine:

Answer:

yeah the answer is one of those just pick one

Answer:

step 3

Step-by-step explanation:

when you multiply an even amount of negative numbers you will always get a positive result thus the answe would be 16.6 + 4.15 as in positive numbers

The purpose of using prefix in the metric system is to properly sale the basis of the unit so large numeric values can be used effectively.

If the metric system is not properly prefixed it can lead to various inconsistencies in the the numeric values. for example if you go to a computer store and you do not know the scale like (kb, mb, gb, tb) you will get quite confused about what is the sales representative saying

Consider you went to a store to get sugar and you do not know the metric system say(gram, kg, mg) you would not know how much sugar you need directly by taking it in your hands.

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Answer: There would 20-gon

The correct answer is x = -1 and the remainder of the division is -22.

Kayla proceeds to the correct answer by using the remainder theorem which states that if a polynomial f(x) is divided by x-a, then the remainder is equal to f(a). In this case, Kayla evaluates the numerator of the rational expression when x = -1, since -1 is the value that makes x+1 equal to zero, which is the factor of the divisor (x+1).

Evaluating the expression, she gets a remainder of -22. Therefore, the correct answer is x = -1 and the remainder of the division is -22.

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Answer:

This would be Helium(He)

Step-by-step explanation:

Its Helium because the bohr model in the picture has 2 electrons.

On the periodic table, it says that Helium has 2 protons which are also equal to electrons

Answer:

The answer is (He) also known as Helium!

Answer:

Which function has an inverse that is a function?

Answer:

I don't either sorry, but try many different techniques and double. heck your answers multiple times when you find them, I'm not sure what else you should do

The vertices of the solution region are:

(2, 1)

(3, 0)

(1, 2)

(1, -1)

To graph the system of inequalities, we can first graph each individual inequality and then shade the regions that satisfy all four inequalities.

The graph of the first inequality, 5x - 3y >= -7, is:

The graph of the second inequality, x - 2y >= 3, is:

The graph of the third inequality, 3x + y >= 9, is:

The graph of the fourth inequality, x + 5y <= 7, is:

Now, we can shade the region that satisfies all four inequalities:

The vertices of the solution region are:

(2, 1)

(3, 0)

(1, 2)

(1, -1)

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The slope of the equation c=450+28g represents the increase in cost per additional guest.

Typically, a line's slope provides information about the steepness and direction of the line. Finding the difference between the coordinates of the locations will allow you to quickly compute the slope of a straight line connecting two points, (x1,y1) and (x2,y2). The letter "m" is frequently used to signify slope.

We can see that the preceding equation is in the slope-intercept format, where m denotes the line's slope and b is its y-intercept or starting point.

In this case, the slope is 28 dollars per additional guest. This means that for every additional guest, the cost of the banquet increases by $28.

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Answer:

A=28.27units2

Step-by-step explanation:

im not positive on this but you can try

There is a 1/2 probability that both spinners will produce an odd number.

The probability is equal to the variety of possible outcomes.

The total number of outcomes that could occur.

For instance, there is only one way to receive a head and there are a total of two possible outcomes, hence the probability of flipping a coin and getting heads is 1 in 2. (a head or tail). P(heads) = 12 is what we write.

So, assume that:

Both the spinners have 1 positive number and 1 odd number.

Probability formula:

P(E) = Favourable events/Total events

Now, calculate as follows:

P(E) = Favourable events/Total events

P(E) = 2/4

P(E) = 1/2

Therefore, there is a 1/2 probability that both spinners will produce an odd number.

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Answer:

8400

Step-by-step explanation:

The smallest whole number that is divisible by both 112 and 525 is their LCM.

112 = 2 × 2 × 2 × 2 × 7

525 = 3 × 5 × 5 × 7

Therefore, LCM = 2 × 2 × 2 × 2 × 3 × 5 × 5 × 7 = 8400

So it is 8400.

Hope it helps.

If you have any query, feel free to ask.

Given the equation of the function f(x)

We will divide f(x) by the factor (x-2)

We can use the long division or the synthetic division

We will use the long division as shown in the following figure:

So, the answer will be as follows:

The volume of the statue is approximately 270 ft³.

To calculate the volume of a cone, we use the following formula:

Volume = (1/3)πr²h

where:

π is approximately equal to 3.14

r is the radius of the base

h is the height of the cone

In this case, we know that the diameter of the base is 12 ft, so the radius is 6 ft. We also know that the height is 9 ft.

First, we need to find the radius of the base. The diameter of the base is 12 ft, so the radius is half of that, or 6 ft.

Next, we need to find the height of the cone. It is given to us as 9 ft.

Now that we know the radius and height, we can plug them into the formula for the volume of a cone:

Volume = (1/3)πr²h

= (1/3)(3.14)(6²)(9)

= 270 ft³

Therefore, the approximate volume of the statue is 270 ft³.

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Answer:

X = 21 / 4 (21 over 4)

Step-by-step explanation:

First, we combine like terms:

5x−11=x+10

Step 2: Subtract x from both sides.

5x−11−x=x+10−x

4x−11=10

Step 3: Add 11 to both sides.

4x−11+11=10+11

4x=21

Step 4: Divide both sides by 4.

4x/4 = 21/4

x= 21 / 4

Please give me brainliest of this helped you! Thanks!

The gradient vector field of function f(x,y) is given as follows:

grad(f(x,y)) = (1 + 3xy)e^(3xy) i + 3x²e^(3xy) j.

Suppose that we have a function defined as follows:

f(x,y).

The gradient function is defined considering the partial derivatives of function f(x,y), as follows:

grad(f(x,y)) = fx(x,y) i + fy(x,y) j.

In which:

The function in this problem is defined as follows:

f(x,y) = xe^(3xy).

Applying the product rule, the partial derivative relative to x is given as follows:

fx(x,y) = e^(3xy) + 3xye^(3xy) = (1 + 3xy)e^(3xy).

Applying the chain rule, the partial derivative relative to y is given as follows:

fy(x,y) = 3x²e^(3xy).

Hence the gradient vector field of the function is defined as follows:

grad(f(x,y)) = (1 + 3xy)e^(3xy) i + 3x²e^(3xy) j.

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Answer: 6347.218

Step-by-step explanation:

Answer:6,347.218

Step-by-step explanation:

look at the thousandths place and then look at the number next to it if the number was 5 and above the answer would be 6,347.219 but in this situation it's not so you would keep everything the same but subtract the 0.0004

Answer:

\(z=\frac{931-1131}{\frac{333}{\sqrt{30}}}=-3.290\)  

Now we can calculate the p value using the alternative hypothesis:

\(p_v =P(z<-3.290)=0.0005\)  

Since the p value is lower than the significance level of 0.05 we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly less than 1131

Step-by-step explanation:

Information given

\(\bar X=931\) represent the sample mean

\(\sigma=333\) represent the population standard deviation

\(n=30\) sample size  

\(\mu_o =1131\) represent the value to check

\(\alpha=0.05\) represent the significance level

z would represent the statistic

\(p_v\) represent the p value

System of hypothesis

We want to verify if the true mean is less than 1131, the system of hypothesis would be:  

Null hypothesis:\(\mu \geq 1131\)  

Alternative hypothesis:\(\mu <1131\)  

The statistic is given by:

\(z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}\) (1)  

Reaplacing we got:

\(z=\frac{931-1131}{\frac{333}{\sqrt{30}}}=-3.290\)  

Now we can calculate the p value using the alternative hypothesis:

\(p_v =P(z<-3.290)=0.0005\)  

Since the p value is lower than the significance level of 0.05 we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly less than 1131

Answer:

$750

Step-by-step explanation:

2500 divided by 100 = 25 and 25 x 30 = 750

Sorry if im wrong

The price for 2500 pencils is $750.

The unitary technique involves first determining the value of a single unit,  followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

We have,

A box of 100 personalized pencils costs $30.

So, cost of 1 pencil = $30 / 100 = 3/10

Now, the price to buy the 2500 pencils

= 2500 x 3/10

= 250 x 3

= $750

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Answer:

The distance is 36 miles.

Step-by-step explanation:

distance in either direction = d

total time = 5

time going = t

time returning = 5 - t

speed = distance/time

going:

speed = distance/time

18 = d/t

d = 18t       Eq. 1

returning:

speed = distance/time

12 = d/(5 - t)

60 - 12t = d

d =  60 - 12t     Eq. 2

Eq. 1 and Eq. 2 form a system of equations.

d = 18t

d = 60 - 12t

Since d = d, then 18t must equal 60 - 12t

18t = 60 - 12t

30t = 60

t = 2

d = 18t = 18(2) = 36

The distance is 36 miles.

Answer: Juan

Step-by-step explanation: Because if you divide 27 by 30 that makes 0.9 which if you multiply by a hundred you have 90 which means that Kim scored 80% and Juan scored 90%.

Answer:

what percent of interest does Jerry have?

A. The lifetime of the new model of washing machine can be modelled by a gamma distribution with mean 8 years and variance 16 years.

B. (a) The probability density function (pdf) of the lifetime of the new model of washing machine can be expressed as f(x) = x^(α-1) * e^(-x/β) / (β^α * Γ(α)), where α = mean^2 / variance = 4 and β = variance / mean = 2. The pdf can be written as f(x) = x^3 * e^(-x/2) / (8Γ(4)).

(b) Let X be the lifetime of a washing machine. Then, P(X > 5) = ∫_5^∞ f(x) dx. Using this, we can find the probability that a single washing machine will last beyond the warranty period. The probability that at least 7 out of 10 washing machines will last beyond the warranty period is given by the binomial distribution with n=10 and p=P(X>5).

Thus, P(X>5) = ∫_5^∞ f(x) dx ≈ 0.1435, and P(at least 7 out of 10 last beyond warranty period) = 1 - ∑_(k=0)^6 (10 choose k) * p^k * (1-p)^(10-k) ≈ 0.0877. Therefore, the probability that at least 7 out of 10 washing machines will last beyond the warranty period is approximately 0.0877.

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a.  The probability density function (pdf) of the lifetime of this new model of washing machine is f(x) = (1/Γ(α)) * (β^α) * (x^(α-1)) * exp(-βx).

b.  The probability that at least 7 of the 10 washing machines will have a lifetime beyond the warranty period is ) ≈ 0.0877.

(a) To specify the probability density function (pdf) of the lifetime of the new model of washing machine, which follows a gamma distribution, we need to consider the mean and variance parameters provided.

The gamma distribution is defined by two parameters: shape (α) and rate (β). In this case, we can calculate the values of α and β using the mean and variance information given.

The mean (μ) of a gamma distribution is given by μ = α/β, and the variance (σ^2) is given by σ^2 = α/β^2.

From the given information, we have:

Mean (μ) = 8 years

Variance (σ^2) = 16 years^2

We can set up the following equations to solve for α and β:

μ = α/β

σ^2 = α/β^2

Rearranging the equations, we get:

α = μ^2 / σ^2

β = μ / σ^2

Substituting the given values, we have:

α = 8^2 / 16 = 4

β = 8 / 16 = 0.5

Therefore, the pdf of the lifetime of the new model of washing machine, which follows a gamma distribution, is:

f(x) = (1/Γ(α)) * (β^α) * (x^(α-1)) * exp(-βx)

where Γ(α) is the gamma function.

(b) We want to calculate the probability that at least 7 out of the 10 washing machines will have a lifetime beyond the warranty period, which is 5 years.

Let's denote X as the random variable representing the lifetime of a washing machine, which follows the gamma distribution as specified in part (a).

To find the probability that at least 7 out of 10 machines will have a lifetime beyond the warranty period, we need to calculate the cumulative distribution function (CDF) for X, evaluated at x = 5, for the distribution of the sum of 10 independent random variables following the gamma distribution.

P(X > 5) = 1 - P(X ≤ 5)

Using the CDF of the gamma distribution, we can calculate the probability for a single machine:

P(X ≤ 5) = ∫[0 to 5] f(x) dx

However, calculating the exact value of this integral can be complex. Alternatively, we can use numerical methods or statistical software to calculate the probability.

Using a software or calculator with gamma distribution functions, input the parameters α and β derived in part (a), and find P(X ≤ 5). Then, subtract it from 1 to get the desired probability:

P(X > 5) = 1 - P(X ≤ 5) = ) ≈ 0.0877.

The e probability that at least 7 out of the 10 washing machines will have a lifetime beyond the warranty period is ) ≈ 0.0877.

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