peaches at the farmers market cost 2.70 per pound is it proportional

\(-2x+6=12\\2x=-6\\x=-3\)

Answer: 1 \(\frac{1}{2}\)

Step-by-step explanation: Turn the mixed fraction into improper fraction, which is 9/4 and 15/4. Subtract 15/4 and 9/4 to get 3/2. Convert 3/2 into mixed number to get 1 1/2

hope it helps!!

The Probability that a randomly selected senior is both in the band and on the honor roll is 8/25.

To find the probability that a randomly selected senior is both in the band and on the honor roll, we need to divide the number of seniors who are in both categories by the total number of seniors.

Given:

Total number of seniors = 200

Number of seniors in the band = 32

Number of seniors in the band or on the honor roll = 64

Let's calculate the probability using these values:

Probability = Number of seniors in both categories / Total number of seniors

Probability = 64 / 200

To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 8:

Probability = (64 ÷ 8) / (200 ÷ 8)

Probability = 8 / 25

Therefore, the probability that a randomly selected senior is both in the band and on the honor roll is 8/25.

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Answer:

1, 2  

Step-by-step explanation:

Given parameters;

   Endpoints  = (-3, 3) and (5, 1)

Unknown:

The midpoint of the segment = ?

Solution:

 The midpoint between two endpoints is given as;

         x\(_{m}\), y\(_{m}\) =( \(\frac{x_{1} + x_{2} }{2}\) , \(\frac{y_{1} + y_{2} }{2}\))

       x and y are coordinates

x₁  = -3

x₂ = 5

y₁ = 3

y₂ = 1

        x\(_{m}\), y\(_{m}\)  = \(\frac{-3 + 5}{2}\), \(\frac{3+ 1}{2}\)

       x\(_{m}\), y\(_{m}\) = 1, 2  

The form that most quickly reveals the y intercept is

The y intercept is (0, 21/2)

The y-intercept is the point where a function or a curve intersects the y-axis. In other words, it is the value of the dependent variable (y) when the independent variable (x) is equal to zero.

In the form,  f(x) = 1/2 x² - 5x + 21/2 it is easier to see that eliminating x by plugging in 0 leaves 21/2 which is the y intercept

hence we can easily say that the y intercept is (0, 21/2)

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After answering the presented question, we may conclude that  the solution of the expressions are as follows.

In mathematics, you can multiply, divide, add, or subtract. An expression is constructed as follows: Number, expression, and mathematical operator A mathematical expression (such as addition, subtraction, multiplication, or division) is made up of numbers, variables, and functions. It is possible to contrast expressions and phrases. An expression or algebraic expression is any mathematical statement that has variables, integers, and an arithmetic operation between them. For example, the phrase 4m + 5 has the terms 4m and 5, as well as the provided expression's variable m, all separated by the arithmetic sign +.

the solution of the expressions are as follows -

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The values of ab, b - c, and c/d are 6, -1, and 4 respectively when a = 2, b = 3, c = 4 and d = 1.Using BODMAS rule, we can simplify the given expression.ab - c/d = 24

Given ab-c/d has a value of 24.Now, we have to find the value ofab, b - c, and c/d.Multiplying d on both sides, we getd(ab - c/d) = 24dab - c = 24d...(1)Now, we can find the value of ab, b - c, and c/d by substituting different values of a, b, c and d.Value of ab when a = 2, b = 3, c = 4 and d = 1ab = a * b = 2 * 3 = 6.

Value of b - c when a = 2, b = 3, c = 4 and d = 1b - c = 3 - 4 = -1Value of c/d when a = 2, b = 3, c = 4 and d = 1c/d = 4/1 = 4Putting these values in equation (1), we get6d - 4 = 24dSimplifying, we get-18d = -4d = 2/9

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You invested $3000 at 3% annual interest rate, and the remaining amount of $4000 - $3000 = $1000 was invested at 4% annual interest rate.

Let's assume you invested an amount, x, at 3% annual interest rate. This means the amount invested at 4% annual interest rate would be $4000 - x.

To calculate the interest earned from the investment at 3%, we multiply x by 3% (0.03). Similarly, the interest earned from the investment at 4% is calculated by multiplying ($4000 - x) by 4% (0.04).

According to the given information, the total interest earned from both investments is $130. So we can set up the equation:

0.03x + 0.04($4000 - x) = $130

Simplifying the equation:

0.03x + 0.04($4000 - x) = $130

0.03x + $160 - 0.04x = $130

-0.01x = $130 - $160

-0.01x = -$30

x = -$30 / -0.01

x = $3000

Therefore, you invested $3000 at 3% annual interest rate, and the remaining amount of $4000 - $3000 = $1000 was invested at 4% annual interest rate.

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Answer:

e-5=2f

take '-5' to the other side where '2f' is

e=2f+5

The matrix representation of the problem can be written as: ε = [ε1 ε2 ε3]'

The matrix representation of the linear regression problem can be expressed as Y = Xβ + ε, where Y is the n x 1 vector of the dependent variable (Yi),

X is the n x k matrix of the independent variables (xi),

β is the k x 1 vector of coefficients, and

ε is the n x 1 vector of errors.

In this case, n = 3 (number of observations), k = 2 (number of independent variables) and the matrix representation of the problem can be written as:

Y = Xβ + ε

Y = [0.3 0.8 -0.3]

X = [1 1 1; 1 2 0.1]

β = [β0 β1]'

ε = [ε1 ε2 ε3]'

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The solutions to the system of equations are x = 2 and 4

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

f(x) = x - 3

g(x) = 1/(x - 3)

The solution to the system of equations implies that

f(x) = g(x)

So, we have

x - 3 = 1/(x - 3)

Cross multiply the equation

This gives

(x - 3)² = 1

So, we have

x - 3 = ±1

Add 3 to both sides

x = 3 ± 1

So, we have

x = 2 and 4

Hence, the solutions to the system of equations are x = 2 and 4

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Answer:

10

Step-by-step explanation:

If you multiply the width with the length and height , you will get nine, then add that lonely brick on top to get ten

the equation of the line tangent to the curve y at x = 3 is y = 36x - 102.  The slope of the tangent line to the curve y at x = 3 is 36.

The equation of the line tangent to the curve y at x = 3 can be written using the point-slope form of a line, which is:

y - y1 = m(x - x1)

where m is the slope of the line, (x1, y1) is a point on the line, and m and (x1, y1) are known. In this case, m = 36 and (x1, y1) = (3, y). Substituting these values into the equation above, we get:

y - y = 36(x - 3)

y = 36x - 102

So the equation of the line tangent to the curve y at x = 3 is

y = 36x - 102.

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Answer:

With 99 %  confidence, it can be said that the population mean driving distance to work ​ (in miles) is between the​ interval's endpoints [19.91 miles, 31.49 miles] .

Step-by-step explanation:

The complete question is: In a random sample of  six  ​people, the mean driving distance to work was  25.7 miles and the standard deviation was  6.7  miles. Assuming the population is normally distributed and using the​ t-distribution, a  99​%  confidence interval for the population mean  mu  is  left parenthesis 14.7 comma 36.7 right parenthesis  ​(and the margin of error is  11.0​).

Through​ research, it has been found that the population standard deviation of driving distances to work is  5.5 .  Using the standard normal distribution with the appropriate calculations for a standard deviation that is​ known, find the margin of error and construct a  99 ​%  confidence interval for the population mean  mu .

Interpret the results. Select the correct choice below and fill in the answer box to complete your choice.  ​(Type an integer or a decimal. Do not​ round.)  

A.  nothing ​%  of all random samples of  six  people from the population will have a mean driving distance to work​ (in miles) that is between the​ interval's endpoints.

B.  With  nothing ​%  ​confidence, it can be said that most driving distances to work​ (in miles) in the population are between the​ interval's endpoints.

C.  It can be said that  nothing ​%  of the population has a driving distance to work​ (in miles) that is between the​ interval's endpoints.  

D.  With  nothing %  confidence, it can be said that the population mean driving distance to work ​ (in miles) is between the​ interval's endpoints.

We are given that in a random sample of  six  ​people, the mean driving distance to work was  25.7 miles and the standard deviation was  6.7  miles.

Through​ research, it has been found that the population standard deviation of driving distances to work is  5.5 .

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

                             P.Q.  =  \(\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }\)  ~  N(0,1)  

where, \(\bar X\) = sample mean driving distance to work = 25.7 miles

             \(\sigma\) = population standard deviation = 5.5 miles

            n = sample of people = 6

             \(\mu\) = population mean driving distance to work

Here for constructing a 99% confidence interval we have used a One-sample z-test statistics because we know about the population standard deviation.

So, 99% confidence interval for the population mean, \(\mu\) is ;

P(-2.58 < N(0,1) < 2.58) = 0.99  {As the critical value of z at 0.5% level

                                                      of significance are -2.58 & 2.58}  

P(-2.58 < \(\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }\) < 2.58) = 0.99

P( \(-2.58 \times {\frac{\sigma}{\sqrt{n} } }\) < \({\bar X-\mu}\) < \(2.58 \times {\frac{\sigma}{\sqrt{n} } }\) ) = 0.99

P( \(\bar X-2.58 \times {\frac{\sigma}{\sqrt{n} } }\) < \(\mu\) < \(\bar X+2.58 \times {\frac{\sigma}{\sqrt{n} } }\) ) = 0.99

99% confidence interval for \(\mu\) = [ \(\bar X-2.58 \times {\frac{\sigma}{\sqrt{n} } }\) , \(\bar X+2.58 \times {\frac{\sigma}{\sqrt{n} } }\) ]

                                            = [ \(25.7-2.58 \times {\frac{5.5}{\sqrt{6} } }\) , \(25.7+2.58 \times {\frac{5.5}{\sqrt{6} } }\) ]

                                            = [19.91, 31.49]

Therefore, a 99% confidence for the population mean is [19.91, 31.49] .

The margin of error here is = \(2.58 \times {\frac{\sigma}{\sqrt{n} } }\)

                                             = \(2.58 \times {\frac{5.5}{\sqrt{6} } }\)  = 5.793

With 99 %  confidence, it can be said that the population mean driving distance to work ​ (in miles) is between the​ interval's endpoints [19.91, 31.49] .

The total number of 512 portions will be made the recipe that contains 5 fluid ounces each.

The soup recipe gives 20 gallons.

As we know one gallon produces 128 fluid ounces.

There are 20 gallons produced.

So the number of fluid ounces produced will be 20*128= 2560

Given in the question each portion contains 5 fluid ounces.

Then there is a total of 2560 numbers of fluid ounces.

So the number of portions will be = number of fluid ounces/ number of fluid ounces in each portion=  2560/5= 512

Therefore the total number of 512 portions will be made the recipe that contains 5 fluid ounces each.

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The equation of the line that passes through the point (-1, 3) with a slope of 1 is y = x + 4.

To find the equation of a line that passes through the point (-1, 3) with a slope of 1, we can use the point-slope form of a linear equation.

The point-slope form of a linear equation is given by:

y - y1 = m(x - x1)

where (x1, y1) represents the coordinates of a point on the line, and m represents the slope of the line.

Using the given point (-1, 3) and slope 1, we substitute these values into the point-slope form equation:

y - 3 = 1(x - (-1))

Simplifying:

y - 3 = x + 1

Now, we can rewrite the equation in the standard form:

y = x + 4

Therefore, the equation of the line that passes through the point (-1, 3) with a slope of 1 is y = x + 4.

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Answer:

Your answer is correct

Step-by-step explanation:

Use the rules of exponents to simplify the expression.

To raise a power to another power, multiply the exponents.

Multiply 6 by 2.

The correct option is the third.

The walkway is 11 feet 6 inches long.

To find the length of the walkway, we need to add the lengths of the two boards.

The first board is 6 feet 11 inches long, which can be written as 6 + 11/12 feet using the fact that there are 12 inches in a foot.

The second board is 5 feet 7 inches long, which can be written as 5 + 7/12 feet.

Now we can add the lengths of the two boards:

6 + 11/12 feet + 5 + 7/12 feet

= 11 + 6/12 feet

=11 + 1/2 feet

Therefore, the walkway is 11 feet 6 inches long.

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On factoring the polynomial 6z² + 6z the values for length and width are obtained as 6z and z + 1.

What is a polynomial?

Polynomial is formed composed of the phrases Nominal, which means "terms," and Poly, which means "many." An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.

We can factor the polynomial 6z² + 6z by taking out the greatest common factor, which is 6z -

6z² + 6z = 6z(z + 1)

This means that the area of the wall is equal to 6z(z + 1) square meters. Since the area of a rectangle is given by the product of its length and width, we can write -

6z(z + 1) = length × width

Therefore, the possible expressions for the length and width of the wall are -

length = 6z

width = z + 1

or

length = z + 1

width = 6z

Both of these expressions give a product of 6z(z + 1), which is equal to the area of the wall.

We can switch the roles of length and width, so there are two possible expressions for the dimensions of the wall.

Therefore, the length is 6z and width is z + 1.

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Answer:

N = 5

Step-by-step explanation:

Answer:

n=5

Step-by-step explanation:

The circumference of the pool is 26.38 meters

The radius, r is given as:

r = 4.2

The circumference, C is calculated using:

\(C =2\pi r\)

This gives

C =2 * 3.14 * 4.2

Evaluate

C = 26.38

Hence, the circumference of the pool is 26.38 meters

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Step-by-step explanation:

In mathematics, the absolute value |x|, is the non-negative result of x without regard to its sign.

An absolute function, can never have a negative result.

By this alone, you can solve the question because the inequality is false, and therefore there are zero solutions.

Please see the attachment of f(x) = |x - 7|.

When you look at the graph, you can easily confirm that there is no value which can result in a negative y- coordinate like -2. In fact, that is the whole purpose of any absolute value or function. The result of an absolute function can never be negative.

Answer:

The measure of CD is 46

Step-by-step explanation:

From the midpoint theorem, we have,

FG = (1/2)CD

so,

\(13+5x=(1/2)(-3x+52)\\So,\\2(13+5x)=-3x+52\\26+10x=-3x+52\\13x=52-26\\13x=26\\x=26/13\\x=2\)

Now,

\(CD = -3x+52\\since \ x=2\\we \ get\\CD=-3(2) +52\\CD=-6+52\\CD=46\)

Answer: It snowed 3.5 inches on Monday and Tuesday combined.

Step-by-step explanation: 3 + 0.5 = 3.5 inches of snow

Hope this helped!

Answer:

k = -0.1

Step-by-step explanation:

An ordered pair is in the form (x,y)  We can use the x and y from the point (-30,3) to find k

y = kx  We will replace x with -30 and y with 3

3 = (-30)k  divide both sides by -30

-0.1 = k  or \(\frac{-1}{10}\) in the fraction form

To find the distance between Basti and Cian, we can use the law of sines in triangle ABC. The law of sines states that the ratio of the length of a side to the sine of the opposite angle is constant for all sides and their corresponding angles in a triangle.

Let's label the distance between Basti and Cian as "x". We know that the measure of angle ABC is 50 degrees and the measure of angle BAC is 60 degrees. We also know that Ali is exactly 150 ft away from Basti.

Using the law of sines, we can set up the following equation:

sin(50°) / 150 = sin(60°) / x

To solve for "x", we can rearrange the equation:

x = (150 * sin(60°)) / sin(50°)

Using a calculator, we can evaluate the expression:

x ≈ (150 * 0.866) / 0.766

x ≈ 168.4 ft

Therefore, the distance between Basti and Cian is approximately 168.4 ft.

Answer:

The answer is -3/4.

Answer: -3/4

Step-by-step explanation:

The line is pointing downwards, making it negative and having a negative slope. The line goes down 3, over 4, so its slope is -3/4.

A. The null hypothesis H₀ and the alternative hypothesis H₁ are:

H₀: μ = 35 minutes       H₁: μ > 35 minutes

B. If the consultant decides not to reject the null hypothesis, she might be making a Type II error.

C. A Type II error would be failing to reject the hypothesis that μ is = to 35 minutes when, in fact, μ is 43 minutes.

A Type II error occurs when the null hypothesis is false, but the test does not reject it.

In this case, the consultant would be concluding that the mean shopping time is 35 minutes, when in fact it is greater than 35 minutes.

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