the slope of the line is below 2. use the coordinates of the labeled point to find a point-slope equation of the line.

The value of the radius of the circle 'r' will be 14 units.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as

H² = P² + B²

The tangent and radius of the circle intersect at the right angle. Then the value of 'r' is given as,

QT² = QS² + ST²

(r + 36)² = r² + 48²

r² + 72r + 1296 = r² + 2304

72r = 1008

r = 14

The value of the radius of the circle 'r' will be 14 units.

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The total profit that is earned is 4512.5

100 - q = 0

q = 100

Maximization is where q = 0

MR = mc

100 - q = 5

such that q = 95

Price would be  100 -0.5(95)

= 100 - 47.5

= 52.5

Profit earned would be

= 95*52.5 -5*95

= 4512.5

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Answer:

60

Step-by-step explanation:

asked google

Answer:

60

Step-by-step explanation:

5: 5 10 15 20 25 30 35 40 45 50 55 60 65 70

12: 12 24 36 48 60 72 84

The probability of choosing a 5 and then a 6 is 1/49

From the question, we have the following parameters that can be used in our computation:

The tiles

Where we have

Total = 7

The probability of choosing a 5 and then a 6 is

P = P(5) * P(6)

So, we have

P = 1/7 * 1/7

Evaluate

P = 1/49

Hence, the probability of choosing a 5 and then a 6 is 1/49

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Question

You randomly choose one of the tiles. Without replacing the first tile, you choose a second tile. Find the probability of the compound event. Write your answer as a fraction or percent rounded to the nearest tenth. The probability of choosing a 5 and then a 6

The z-score for an individual midge that spends 12. 7 days in its larval stage is -0.636

Given,

The mean number of days that the midge Chaoborus spends in its larval stage = 14.1 days

Standard deviation = 2.2 days

We have to find the z-score for an individual midge that spends 12. 7 days in its larval stage;

Now,

z score = (x - μ) / σ

Here,

x = 12.7

Mean, μ = 14.1

Standard deviation, σ = 2.2

Then,

z score = (x - μ) / σ = (12.7 - 14.1) / 2.2 = -0.636

That is,

The z-score for an individual midge that spends 12. 7 days in its larval stage is -0.636

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Answer:

y = 7x -9

Step-by-step explanation:

This is a linear equation.

The change in y over the change in x is 9.  The y-intercept will be (0, -9).

If you follow the pattern as x is -1 and you go up 1 to zero, the the y goes up 7 from -16 to get -9

Answer:

y = 7x - 9

Step-by-step explanation:

y = 7x - 9

Let checks

-16 = 7(-1) - 9

-16 = -16

-23 = 7(-2) - 9

-23 = -23

So, y = 7x - 9 is the correct answer.

The value of the double integral is I = 0.

To calculate the double integral ∬ √(4+12ry) dA dy, we need to determine the limits of integration for each variable and then evaluate the integral.

Assuming the region of integration is not specified, we'll integrate over the entire xy-plane.

The integral can be rewritten as follows:

I = ∫∫ √(4 + 12ry) dA dy

Since there are no specific limits given, we'll integrate from negative infinity to positive infinity for both variables.

I = ∫(-∞ to ∞) ∫(-∞ to ∞) √(4 + 12ry) dx dy

To solve this integral, we'll integrate with respect to x first and then with respect to y.

∫(-∞ to ∞) ∫(-∞ to ∞) √(4 + 12ry) dx dy = ∫(-∞ to ∞) √(4 + 12ry) [x] dx dy

Evaluating the integral with respect to x:

∫(-∞ to ∞) √(4 + 12ry) [x] dx dy = ∫(-∞ to ∞) [x√(4 + 12ry)]|(-∞ to ∞) dy

Since the limits of integration for x are from negative infinity to positive infinity, the term [x√(4 + 12ry)] evaluates to 0. Therefore, the integral becomes:

I = ∫(-∞ to ∞) 0 dy

Integrating a constant value of 0 over the entire y-axis yields a result of 0.

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Answer:

f(x)=-5x+1x=−5x+1, find f(6)

f(6)= -5(6)+1(6)=-5(6)+1

F(6)=-24,-29

Answer:

the dispersion of something that was originally localized

Step-by-step explanation:

that's the definition of the word diaspora.

Answer:

All the given measurements of the right triangles are correct

Step-by-step explanation:

Check the three diagram and determine the three sides of the right triangle that correspond to Pythagoras triple.

For the first triangle:

12² + 5² should be equal to  13²

144 + 25  =  13²

169 = 13²

Thus, 5, 12 and 13 corresponds to three sides of right triangle.

For second diagram;

24² + 7² should be equal to 25²

576 + 49 = 25²

625 = 25²

Thus, 7, 24 and 25 corresponds to three sides of right triangle.

For third diagram;

3² + 4² should be equal to 5²

9 + 16 = 5²

25 = 5²

Thus, 3, 4 and 5 corresponds to three sides of right triangle.

The transformation of the rectangles ABCD and ABCD is for the 90-degree clockwise rotation about the origin and a translation of 7 units down.

Here the transformed rectangle is  the result of two steps, including the steps of  rotation and  translation from the x-y axis, near the origin.

Here change is in such a way that,  the first rotation is a 90 clockwise rotation about the origin, where the vertex c is near to the origin,  again there is a translation of 7 units down, considering the rotated rectangle As A'B'C'D'. here the proper explanation of the process is shown in the image attached.

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The given quadratic function `f(x) = -3x² - 6x` has a maximum value of `-9`, which is obtained at the point `(1, -9)`.

A quadratic function can either have a maximum or a minimum value depending on the coefficient of the x² term.

If the coefficient of the x² term is positive, the quadratic function will have a minimum value, and if the coefficient of the x² term is negative, the quadratic function will have a maximum value.

Given function is

f(x) = -3x² - 6x.

Here, the coefficient of the x² term is -3, which is negative.

Therefore, the function has a maximum value, and it is obtained at the vertex of the parabola

The vertex of the parabola can be obtained by using the formula `-b/2a`.

Here, a = -3 and b = -6.

Therefore, the vertex is given by `x = -b/2a`.

`x = -(-6)/(2(-3)) = 1`.

Substitute the value of x in the given function to obtain the maximum value of the function.

`f(1) = -3(1)² - 6(1) = -3 - 6 = -9`.

Therefore, the given quadratic function `f(x) = -3x² - 6x` has a maximum value of `-9`, which is obtained at the point `(1, -9)`.

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Answer:

it's 37/40

I just took the quiz

Answer:

A

Step-by-step explanation:

Given:

\(8-3x > 2(3x-5)\)

Simplify by distributing:

\(8-3x > 6x-10\)

Add 10 to left side and add 3x to the right side:

\(18 > 9x\)

The conclusion regarding the publisher's claim is that it is incorrect if the potential advertiser rejects the null hypothesis. A newsletter publisher believes that less than 65% 65 % of their readers own a personal computer. For marketing purposes, a potential advertiser wants to confirm this claim. After performing a test at the 0.02 0.02 level of significance, the advertiser decides to reject the null hypothesis.

What is a null hypothesis?

The null hypothesis is a fundamental idea in inferential statistics that represents the null assumption. It's frequently utilized to compare datasets and decide whether any differences between them are real or just by chance.

It is also called H0. It is the default theory that no difference exists between two tested populations or data sets.

A hypothesis test is a way of deciding whether the data supports or disproves the null hypothesis. If the null hypothesis is incorrect, it is referred to as a Type I error. If it is true and the data leads to its rejection, it is known as a Type II error.

Thus, after performing the test at the 0.02 level of significance, if the potential advertiser decides to reject the null hypothesis, the publisher's claim is incorrect.

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=======================================================

Explanation:

The triangles are similar, allowing us to form a proportion

The vertical sides pair up on one side, the horizontal sides pair up on the other side. Divide in the same order.

QV/RT = VS/TS

5/3 = x/12

12*5 = 3x ... cross multiply

60 = 3x

3x = 60

x = 60/3

x = 20

VS = 20

Answer:

35

Step-by-step explanation:

Hi!

The answer is 12!

19-7=12

Answer:

A

Step-by-step explanation:

If the triangles ΔABC≅ΔDEF then the congruent to side BA is ED.

The dimensions of the sides and angles of two or more triangles determine whether they are congruent. A triangle's size and shape are determined by its three sides and three angles, respectively. If pairs of corresponding sides and corresponding angles are equal, two triangles are said to be congruent. They are the exact same size and form. Triangles can satisfy a wide variety of congruence requirements.

From the ΔABC ≅ ΔDEF we observe that the corresponding segment to BA in triangle DEF is ED.

Hence, if the triangles ΔABC≅ΔDEF then the congruent to side BA is ED.

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Assuming the results of two patients are independent events, the probability that  neither one of them will be successfully cured is 0.04.

The success rate of a medical treatment means the probability the treatment will cure the patient.

Let the two patients are patient A and patient B.

From the problem:

P(A_success) = 0.8

P(B_success) = 0.8

Which means:

P(Afailed) = 1 - 0.8 = 0.2

P(Bfailed) = 1 - 0.8 = 0.2

The probability of two independent events is:

P (A∩B) = P(A) . P(B)

Therefore,

P(Afailed ∩ Bfailed) = P(Afailed) . P(Bfailed)

                                = 0.2 . 0.2 = 0.04

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A is rational

B and C are irrational

A: √50x^2 and d: √72x^2 are like radicals.

Like radicals are square roots with the same coefficient outside the radical. For example, √50x^2 and √72x^2 can be simplified to √2 * √25x^2, which makes them like radicals. Simplifying the expressions helps to see if they are alike.

Expressions such as √32x and √18n cannot be simplified to have the same coefficient outside the radical and hence, they are not like radicals.

In conclusion, only √50x^2 and √72x^2 are like radicals after simplification.

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Answer:

A&D

Step-by-step explanation:

Got it right on edge

The probability that you will walk at least 2 dogs this week is 0.74

The probability that you will walk at most 2 dogs this week is 0.41

The probability that you will walk 3 dogs this week is 0.23

The probability that the number of dogs you will walk this week is not less than 5 is 0.18

The expected number of dogs you will walk this week is 2.83

The expected value of x is 11.29

The variance of dogs you will walk this week is 3.2811

The standard deviation of dogs you will walk this week is 1.8113

X: Random variable denoting how many dogs you walk this week.

Table attached at the end of solution

a) Probability that you will walk at least 2 dogs this week

\(P(x \geqslant 2) & =1-P(x < 2) \\\)

= 1 - [P(x = 0) + P(x = 1)]

= 1 - [0.14 + 0.12]

= 1 - 0.26

\(P(x \geqslant 2) &\) = 0.74

b) What is the probability that you will walk at most 2 dogs this week

P(x < 2) = P(x = 0) + P(x = 1) + P(x = 2)

= 0.14 + 0.12 + 0.15

P(x < 2) = 0.41

c) Probability that you will walk 3 dogs this week

P(x = 3) = 0.23

d) Probability that the number of dogs you will walk this week is not less than 5

\(P(x \geqslant 5) &\) = P(x = 6) + P(x = 7) + P(x = 5)

= 0.08 + 0.01 + 0.09

= 0.09 + 0.09

= 0.18

e) Expected number of dogs you will want this week

F(x) = \(\sum_i p_i x_i\)

E(x) = 0 × 0.14 + 1 × 0.12 + 2 × 0.15 + 3 × 0.23 + 4 × 0.18 + 5 × 0.09 + 6 × 0.08 + 7 × 0.01

E(x) = 2.83

f) Expected value of \($x^2$\)

\(E\left(x^2\right) & =\sum_1 p_i x_i^2 \\\)

= 0 × 0.14 + 1 × 0.12 + 4 × 0.15 + 9 × 0.23 + 16 × 0.18 + 25 × 0.09 + 36 × 0.08 + 49 × 0.01

\(E\left(x^2\right) &\) = 11.29

g) Variance of dogs you will walk this week

\(V(x) & =E\left(x^2\right)-[E(x)]^2 \\\)

\(& =11.29-(2.83)^2 \\\)

= 3.2811

h) Standard deviation of dogs you will walk this week

SD (x) = \(\sqrt{3.2811} \\\)

= 1.8113

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You start a dog-walking business. Define X to be a random variable denoting how many dogs you walk

this week. The probability mass function (pmf), f(x), of X is defined as follows:

Table attached at end of the solution

(a) What is the probability that you will walk at least 2 dogs this week?

(b) What is the probability that you will walk at most 2 dogs this week?

(c) What is the probability that you will walk 3 dogs this week?

(d) What is the probability that the number of dogs you will walk this week not be less than 5 ?

(e) What is the expected number of dogs you will walk this week?

(f) What is the expected value of \($X^2$\) ?

(g) What is the variance of dogs you will walk this week?

(h) What is the standard deviation of dogs you will walk this week?

If the histogram shows a bell-shaped curve and the normality test (if performed) supports the normality assumption, it appears safe to assume that the normality condition is satisfied for the wood pieces prepared for the lab session, considering them as an SRS of all similar pieces of Douglas fir.

To determine if the normality condition is satisfied, you can follow these steps:

1. Organize the data: Collect the measurements for the characteristics of the wood pieces in your sample (such as density, strength, etc.) and organize them in a list or a table.

2. Create a frequency distribution: Calculate the frequencies of the different measurements and arrange them in a frequency distribution table.

3. Plot a histogram: Using the frequency distribution, create a histogram to visually represent the data. The x-axis represents the measurements and the y-axis represents the frequency.

4. Evaluate the shape of the histogram: Examine the shape of the histogram to determine if it resembles a normal distribution. A normal distribution is characterized by a bell-shaped curve, which is symmetrical around the mean value.

5. Conduct a normality test (optional): If you want to statistically confirm the normality of the data, you can perform a normality test, such as the Shapiro-Wilk test or the Kolmogorov-Smirnov test.

For the wood pieces manufactured for the lab session, using them as an SRS of all comparable pieces of Douglas fir, it is acceptable to infer that the normality criterion is satisfied if the histogram displays a bell-shaped curve and the normality test (if performed) confirms the normality assumption.

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Answer:

12.5

Step-by-step explanation:

:0.4 ( 3b + 10 ) = 19 Equation Step 2:1.2b + 4 = 19 Multiply Step 3:1.2b = 15 Subtract 4 on ... the number of hours of renting a lawn mower and the total amount spent to rent the lawn mower? ... What is the output got each input ⚠️⚠️ my last one help ⚠️⚠️.

as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solving for "y", let's do so.

\(\stackrel{f(x)}{y}~~ = ~~\cfrac{4x}{x-9}\implies \stackrel{\textit{quick switcheroo}}{x~~ = ~~\cfrac{4y}{y-9}}\implies xy-9x=4y\implies -9x=4y-xy \\\\\\ -9x=y(4-x)\implies \cfrac{-9x}{4-x}=y\implies \cfrac{9x}{x-4}=\stackrel{f^{-1}(x)}{y}\)

how to test algebraically? well, for any (a,b) pair in f(x), its inverse will have another pair but (b,a), hmmm let's plug hmmm say

f(10) = 40, and f⁻¹(40) = 10.

we could plug more values in each, same pair will come up.

as far as testing them graphically, Check the picture below.

Answer:

95% confidence interval for the difference between the proportions of women and men who follow a regular exercise program

(-0.1740 , 0.1672)

Step-by-step explanation:

Step(i):-

Given A survey found that 31 of 60 randomly selected women

First sample proportion

                \(p_{1} = \frac{x_{1} }{n_{1} } = \frac{31}{60} = 0.5166\)

Second sample proportion

               \(p_{2} = \frac{x_{2} }{n_{2} } = \frac{38}{73} = 0.520\)

Level of significance = 0.05

Z₀.₀₅ = 1.96

Step(ii):-

95% confidence interval for the difference between the proportions of women and men who follow a regular exercise program

\(((p_{1} ^{-}-p^{-} _{2} - Z_{0.05} S.E(p_{1} ^{-} - p^{-} _{2} ), (p_{1} ^{-}-p^{-} _{2} +Z_{0.05} S.E(p_{1} ^{-} - p^{-} _{2} ))\)

where

\(Se(p_{1} - p_{2} ) = \sqrt{\frac{p_{1} (1-p_{1} )}{n_{1} }+\frac{p_{2}(1-p_{2} }{n_{2} } }\)

\(Se(p_{1} - p_{2} ) = \sqrt{\frac{0.5166 (1-0.5166 )}{60 }+\frac{0.520(1-0.520 }{73 } } = 0.08706\)

95% confidence interval for the difference between the proportions of women and men who follow a regular exercise program

\(((p_{1} ^{-}-p^{-} _{2} - Z_{0.05} S.E(p_{1} ^{-} - p^{-} _{2} ), (p_{1} ^{-}-p^{-} _{2} +Z_{0.05} S.E(p_{1} ^{-} - p^{-} _{2} ))\)

((0.5166-0.520-1.96(0.08706) , 0.5166-0.520+1.96(0.08706))

(-0.1740 , 0.1672)

Final answer:-

95% confidence interval for the difference between the proportions of women and men who follow a regular exercise program

(-0.1740 , 0.1672)

Answer:

1.99 per notebook

Step-by-step explanation:

I did have an explanation here but someone *cough* *cough* laurenercsp6fpli  deleted all my answers for no reason. But I did the math and I assure you that the answer is correct.

Therefore, the estimated difference between the cube roots of 343 and 345.1 is approximately 0.0189.

To estimate the difference between the cube roots of 343 and 345.1 using linear approximation, we can use the fact that the derivative of the function f(x) = ∛x is given by f'(x) = 1/(3∛x^2).

Let's start by calculating the cube root of 343:

∛343 = 7

Next, we'll calculate the derivative of the cube root function at x = 343:

f'(343) = 1/(3∛343^2)

= 1/(3∛117,649)

≈ 1/110.91

≈ 0.0090

Using the linear approximation formula:

Δy ≈ f'(a) * Δx

We can substitute the values into the formula:

Δy ≈ 0.0090 * (345.1 - 343)

Calculating the difference:

Δy ≈ 0.0090 * 2.1

≈ 0.0189

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