In a scale drawing of a house, 2 inches : 5 feet. The actual kitchen of the house will be 17 feet long. How long will the drawing of the kitchen be?​

Answer: (3⁴)⁵ simplifies to 3^20

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To simplify an exponentiation expression, we need to use the following rule: (a^m)^n = a^(m*n). In this case, we have (3⁴)⁵, which can be rewritten as (3^4)^5. Applying the rule, we get:

(3^4)^5 = 3^(4*5)

(3^4)^5 = 3^20

Therefore, (3⁴)⁵ simplifies to 3^20.

Answer: \(3^{20}\)

Step-by-step explanation:

An exponential rule states that \((a^{b} )^{c}\) = \(a^{bc}\)

So \((3^{4} )^{5}\) = \(3^{(4)(5)}\) = \(3^{20}\)

Answer:

6\(x^{2}\) - 19x + 15

Step-by-step explanation:

(2x - 3) (3x - 5)

2x(3x-5) - 3 (3x-5)

6\(x^{2}\) - 10x - 3 (3x - 5)

6\(x^{2}\) - 10x - 9x + 15

6\(x^{2}\) - 19x + 15

Answer:

6x² - 19x + 15

Step-by-step explanation:

(2x - 3)(3x - 5)

each term in the second factor is multiplied by each term in the first factor, that is

2x(3x - 5) - 3(3x - 5) ← distribute parenthesis

= 6x² - 10x - 9x + 15 ← collect like terms

= 6x² - 19x + 15

The value of x that satisfies the given conditions is 6. Let's solve the problem step by step.

We are given that the apples are shared in the ratios 1:3:x, where x > 3. This means that the total number of parts in the ratio is 1 + 3 + x = 4 + x.

To find the number of apples in each person's share, we divide the total number of apples (60) by the total number of parts in the ratio (4 + x):

Number of apples in each part = Total number of apples / Total number of parts

= 60 / (4 + x)

Now, we are given that the number of apples in Carol's share is 18 more than the number of apples in Betty's share. Therefore, we can set up the equation:

Number of apples in Carol's share = Number of apples in Betty's share + 18

Using the ratios, we can express the number of apples in each person's share:

Number of apples in Betty's share = 3 * (Number of apples in Abbie's share)

Number of apples in Carol's share = x * (Number of apples in Abbie's share)

Substituting these values into the equation, we get:

x * (Number of apples in Abbie's share) = 3 * (Number of apples in Abbie's share) + 18

Simplifying the equation, we have:

x * (60 / (4 + x)) = 3 * (60 / (4 + x)) + 18

To solve for x, we can multiply both sides of the equation by (4 + x) to eliminate the denominators:

x * (4 + x) * (60 / (4 + x)) = 3 * (4 + x) * (60 / (4 + x)) + 18 * (4 + x)

Simplifying further:

60x = 3 * 60 + 18 * (4 + x)

60x = 180 + 72 + 18x

42x = 252

x = 6

Therefore, x = 6.

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Answer:y-1 5/4(x-1)

Step-by-step explanation:

Answer:

y-1 5/4(x-1)

Step-by-step explanation

Answer:

\(x = 1.3788\)

Step-by-step explanation:

Use the sin rule

\(Sin (50) = \frac{Q}{H} \\0.7660=\frac{x}{1.8} \\x=0.7660 *1.8\\x = 1.3788\)

Hope this helps you..

Let me know if you have any other questions :-)

The vertices of the hyperbola are the x-intercepts of the hyperbola

The equation of the hyperbola is \(\frac{y^2}{400} -\frac{x^2}{81} = 1\)

The equation of a hyperbola is represented as:

\(\frac{(y - k)^2}{a^2} -\frac{(x - h)^2}{b^2} = 1\)

The vertices are (20,0) and (-20,0).

So, the center of the hyperbola is:

(h,k) = (0,0).

Also, we have:

a = 20

This gives

\(\frac{(y - 0)^2}{a^2} -\frac{(x - 0)^2}{b^2} = 1\)

Evaluate

\(\frac{y^2}{a^2} -\frac{x^2}{b^2} = 1\)

Substitute 20 for a

\(\frac{y^2}{20^2} -\frac{x^2}{b^2} = 1\)

\(\frac{y^2}{400} -\frac{x^2}{b^2} = 1\)

The length of the conjugate axis is:

l = 18 units

So, we have:

\(b = \frac{18}2 = 9\)

The equation becomes:

\(\frac{y^2}{400} -\frac{x^2}{9^2} = 1\)

\(\frac{y^2}{400} -\frac{x^2}{81} = 1\)

Hence, the equation of the hyperbola is \(\frac{y^2}{400} -\frac{x^2}{81} = 1\)

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Answer:C

Step-by-step explanation:

I HAVE GOT YOU!!!

Answer:

Answer is C

Step-by-step explanation:

Answer:

284 children

60 adults

Step-by-step explanation:

Answer:

Your answer is C

Step-by-step explanation:

You should look at the exponent. Once you figure out the difference between the two exponents then you get your answer.

Answer:

for 18 x is 6 and for 20 it is 11

Step-by-step explanation:

For 18, since -1+2x and 5+x is the same thing, set up and equation. WE can simplify to -1+x=5 and then we get x=6

For 20, 18 is 11 since 18=-4+2x. If we simplify we get 22=2x then we can use algebra to say that x=11

Hope this helps :)

Answer:

18.) x = 6

20.) x = 11

Step-by-step explanation:

18.)

We know that line segments FC and ED are parallel to each other so they are congruent to each other:

-1 + 2x = 5 + x

-1 + x = 5

x = 6

20.)

We know that line segments DE and CF are parallel to each other so they are congruent to each other:

18 = -4 + 2x

22 = 2x

22/2 = x

11 = x

Hope this helps!

If these conditions are met, the sampling distribution of x will be approximately normally distributed. This is helpful in statistical analyses, as it allows us to make inferences about the population mean using the properties of the normal distribution.

The sampling distribution of x (the sample mean) will be approximately normally distributed if certain conditions are met. These conditions are based on the Central Limit Theorem (CLT), which states that:

1. The sample size (n) is large enough, typically n > 30. This ensures that the sampling distribution of x becomes more normally distributed as the sample size increases.
2. The population from which the sample is drawn is either normally distributed or the sample size is large enough to compensate for non-normality.

The sampling distribution of x overbarx (the sample mean) will be approximately normally distributed if certain conditions are met. These conditions include:
1. The population distribution must be normal or approximately normal.
2. The sample size should be large (typically n > 30).
3. The samples should be randomly selected from the population.

If these conditions are met, the sampling distribution of x will be approximately normally distributed. This is helpful in statistical analyses, as it allows us to make inferences about the population mean using the properties of the normal distribution.

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Answer:

That's too many questions in one.

Step-by-step explanation:

Step-by-step explanation:

No because he had 14 and needs 16

\( \frac{1 + 6}{x - 4} = 1\)

\(x - 4 = 7\)

\(x = 11\)

Answer:

AB=CD=10,AD=BC=29

Step-by-step explanation:

11111111111

Answer:

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

AD and AB are adjacent sides hence their sum is half the perimeter:

And we are given that AD is 9 more than twice AB:

Substitute this into first equation:

Find AD by substituting the value of AB:

So the side lengths are:

Answer: I think it’s B (25)

Step-by-step explanation:

Answer:

Using the sine rule,

36/sin(50)=20/sin(R)

46.9=20/sin(R)

Sin(R)=46.9/20=0.43

R=Sin¯¹(0.43)=25.2°=25°

R=25°

Answer:

8 gallons

Step-by-step explanation:

To answer this question :

1 PINT = 0.125 Gallons

1 x 0.125 = 0.125

total gallons of water = 64 x 0.125 = 8 gallons

Solution

- The question would like us to solve the following inequality:

- The solution is given below:

- Thus, we need to put the solution in both Set-builder notation and Interval notation. This is done below:

Set-builder notation:

Interval notation:

Answer:

First, for end behavior, the highest power of x is x^3 and it is positive. So towards infinity, the graph will be positive, and towards negative infinity the graph will be negative (because this is a cubic graph)

To find the zeros, you set the equation equal to 0 and solve for x

x^3+2x^2-8x=0

x(x^2+2x-8)=0

x(x+4)(x-2)=0

x=0   x=-4   x=2

So the zeros are at 0, -4, and 2. Therefore, you can plot the points (0,0), (-4,0) and (2,0)

And we can plug values into the original that are between each of the zeros to see which intervals are positive or negative.

Plugging in a -5 gets us -35

-1 gets us 9

1 gets us -5

3 gets us 21

So now you know end behavior, zeroes, and signs of intervals

Hope this helps

Answer:

The degree of the function is odd and the leading coefficient is positive – so the function goes to negative infinity as x goes to negative infinity and to positive infinity as x goes to positive infinity. The zeroes are –4, 0, and 2, all with multiplicity 1. The function is negative from negative infinity to –4 and from 0 to 2. The function is positive from –4 to 0 and from 2 to infinity.

Step-by-step explanation:

sample response on edge 2022

1) The value of function is,

⇒ (2x − 3)

2) The value of function is,

⇒ (5x + 7)

We have to given that;

Functions are,

f(x) = (x + 7) (2x − 3) and g(x) = (x + 7).

Hence, We get;

⇒ f (x) / g (x)

⇒ (x + 7) (2x − 3) / (x + 7)

⇒ (2x − 3)

And, Functions are,

f(x) = (5x+7) (-3x+11) and g(x) = (-3x + 11).

Hence, We get;

⇒ f (x) / g (x)

⇒ (5x+7) (-3x+11) / (-3x + 11).

⇒ (5x + 7)

Thus, 1) The value of function is,

⇒ (2x − 3)

2) The value of function is,

⇒ (5x + 7)

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1) The condition for the combined estimator to be unbiased is a + b = 1. 2) The values of a and b that minimize the variance of the combined estimator subject to the condition of unbiasedness are: a = m/(n + m) and b = n/(n + m).

(1) To find the conditions that make the combined estimator unbiased, we need to have:

E(üm+n) = u,

where u is the true population mean.

Using the linearity of expectation and the fact that Xn and Ym are i.i.d, we have:

E(üm+n) = E(aXn + BÝm)

= aE(Xn) + BE(Ým)

= au + bu,

where u is the true population mean.

For the combined estimator to be unbiased, we need au + bu = u, which simplifies to:

a + b = 1.

Therefore, the condition for the combined estimator to be unbiased is a + b = 1.

(2) To find the values of a and b that minimize the variance of the combined estimator subject to the condition of unbiasedness, we need to minimize the expression:

Var(üm+n) = Var(aXn + BÝm)

= a^2Var(Xn) + B^2Var(Ým) + 2abCov(Xn, Ým),

where Cov(Xn, Ým) is the covariance between Xn and Ým.

Using the fact that Xn and Ym are i.i.d and have the same variance σ^2, we have:

Var(Xn) = Var(Ym) = σ^2/n.

Using the fact that Xn and Ym are independent, we have:

Cov(Xn, Ým) = 0.

Therefore, the expression for the variance simplifies to:

Var(üm+n) = a^2(σ^2/n) + B^2(σ^2/m).

Subject to the condition a + b = 1, we can write:

b = 1 - a.

Substituting this into the expression for the variance, we get:

Var(üm+n) = a^2(σ^2/n) + (1 - a)^2(σ^2/m).

To minimize this expression, we differentiate it with respect to a and set the derivative equal to zero:

d/dx [a^2(σ^2/n) + (1 - a)^2(σ^2/m)] = 2a(σ^2/n) - 2(1 - a)(σ^2/m) = 0.

Solving for a, we get:

a = m/(n + m).

Substituting this value of a into the expression for b, we get:

b = n/(n + m).

Therefore, the values of a and b that minimize the variance of the combined estimator subject to the condition of unbiasedness are:

a = m/(n + m) and b = n/(n + m).

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Answer:

42×15=x.....................

Step-by-step explanation:

:)

Option B, Justice is one of four ethical concepts. The definition states that there must be fairness in all medical judgments.

Four ethical principles: autonomy, benevolence, harmlessness, and justice. Each of these principles serves a specific purpose, but all four work together to empower you as healthcare professionals and ensure that your patients receive high-quality, ethical care.

The literal concept of autonomy and the medical concept of autonomy diverge and intersect. Charity is an act of compassion or mercy. The activities of all healthcare workers should always be positive. Of the four principles of medical ethics, harmlessness is the most important.

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Answer:

8

Step-by-step explanation:

Let's call the center of the middle circle J, and the center of the third circle K.

Draw a line from J to the line AD such that the line is perpendicular to AD.

This forms a right triangle that is similar to the triangle ΔADK.

Writing and solving a proportion:

x / DK = AJ / AK

x / 5 = 15 / 25

x = 3

Now, draw lines from J to B and C.  We now form two congruent right triangles, where the hypotenuse is 5 and the shared leg is 3.

That means these are both 3-4-5 triangles.

Therefore, BC = 4 + 4 = 8.

The best answer from the options that proves that the residual plot shows that the line of best fit is appropriate for the data is: ( Statement 1 ) Yes, because the points have no clear pattern

X         Given     Predicted     Residual value

1            3.5           4.06             -0.56

2           2.3           2.09             0.21

3            1.1            0.12               0.98

4           2.2           -1.85              4.05

5          -4.1            -3.82            -0.28

The residual value is calculated as follows using this formula: ( Given - predicted )

1) ( 3.5 - 4.06 ) = -0.56

2) ( 2.3 - 2.09 ) = 0.21

3) ( 1.1 - 0.12 ) = 0.98

4) (2.2 - (-1.85) = 4.05

5) ( -4.1 - (-3.82) = -0.28

Residual values are the difference between the given values and the predicted values in a given data set and the residual plot is used to represent these values .

attached below is the residual plot of the data set

hence we can conclude from the residual plot attached below that the line of best fit is appropriate for the data because the points have no clear pattern ( i.e. scattered )

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Answer:

A: Yes, because the points have no clear pattern.

Step-by-step explanation:

Edge quiz 100%

The probability mode for the given value is created. The expected value and standard deviation of prospective winnings are -$0.28 and $18.33. The expected value and standard deviation if the game is played five times are -$1.40 and $40.99. The probability that the person running the game makes a profit is 0.561.

Probability is a way to determine how likely something is to happen. It is computed by dividing the frequency of the event by the total number of outcomes. The formula then becomes P(X) = frequency of the event÷total number of outcomes.

The product of the probabilities determines the likelihood that two or more occurrences will coincide. This is given by, P(A and B) = P(A)P(B).

a) To create a probability model follow the steps. Let X is an occurrence of an event.  The table is attached here.

b)  The expected value is calculated using the formula, E(X) = μ = ∑ x P(x).

\(\begin{aligned}E(X)=\mu&=x_1p_1+x_2p_2+x_3p_3\\&=40\left(\frac{1}{6}\right)+0\left(\frac{5}{36}\right)+(-10)\left(\frac{25}{36}\right)\\&=-\$ 0.28\end{aligned}\)

Also,

\(\begin{aligned}E(X^2)&={x_1}^{2}p_{1}+{x_2}^{2}p_{2}+{x_3}^{2}p_{3}\\&=(40)^2\frac{1}{6}+(0)\frac{5}{36}+(-10)^2\frac{25}{36}\\&=(1600)\frac{1}{6}+(0)\frac{5}{36}+(100)\frac{25}{36}\\&=266.67+69.44\\&=336.11\end{aligned}\)

And the standard deviation is calculated using the formula, σ=√Var[X].

\(\begin{aligned}\sigma=\sqrt{\text{Var}(X)}&=\sqrt{E(X^2)-E(X)^2}\\&=\sqrt{336.11-0.08}\\&=\sqrt{336.03}\\&=\$18.33\end{aligned}\)

c) The expected value and standard deviation for playing the game 5 times are calculated as follows.

The expected value is,

\(\begin{aligned}5\times E(X)&=5(-\$0.28)\\&=-\$1.40\\\end{aligned}\)

The standard deviation is,

\(\begin{aligned}\sigma&=\sqrt{5\times\tex{Var}(X)\\&=\sqrt{5\times336.03\\&=\sqrt{1680.15}\\&=\$40.99\end{aligned}\)

d) The dice rolling is random and the winning chance is independent. The probability the person running the game makes a profit (P(x<0)) is given by,

The population mean, μ(Y) = -$0.28

The standard deviation for a population of 100 is,

\(\begin{aligned}\sigma&=\sqrt{\frac{\text{Var}(X)}{n}}\\&=\frac{18.33}{\sqrt{100}}\\&=1.83\end{aligned}\)

The z-score for mean winning is,

\(\begin{aligned}z&=\frac{x-\mu}{\sigma}\\&=\frac{0-(-0.28)}{1.83}\\&=0.153\end{aligned}\)

For a person to make a profit, the mean winning of the player should be less than the z-score. Then,

The P-value from the z-table, P(z<0.153)=0.5608

The answer is 0.561.

The complete question is -

You pay $10 and roll a die. If you get a 6, you win$50. If not, you get to roll again. If you get a 6 this time, you get your $10 back. a) Create a probability model for this game. b) Find the expected value and standard deviation of your prospective winnings. c) You play this game five times. Find the expected value and standard deviation of your average winnings. d) 100 people play this game. What’s the probability the person running the game makes a profit?

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EXPLANATION

We can affirm that the length of the adjacent leg is 5 units and the length of the hypotenuse is 8 units.

As given, the length of the third side is 6.245 units.

Now, computing sin A give us the following expression:

The solution is 1249/1600