Mr.Chen Teaches art at the community center . to prepare for a water painting class, he bought w new water palettes. he put an equal number of the new palettes on each of the 6 tables in his classes. write an expression to show how many new watercolor palettes are on each table.

The potential function for the given vector field f is φ = (3/2)xyz. To find it, we integrated the given equations with respect to their variables and found a constant of integration that makes them consistent.

To find a potential function f for the given vector field f, we need to find a scalar function φ such that the gradient of φ is equal to f. That is,

∇φ = f

So, we need to find a scalar function φ such that

∂φ/∂x = yz

∂φ/∂y = x²z

∂φ/∂z =x²y

Integrating the first equation with respect to x, we get

φ = xyz + g(y,z)

where g(y,z) is the constant of integration with respect to x. Now, we differentiate φ with respect to y and z and compare with the given equations to find g(y,z). We get

∂φ/∂y = xz + ∂g/∂y = x²z

∂φ/∂z = xy + ∂g/∂z = x²y

Integrating these two equations with respect to y and z, respectively, we get

g(y,z) = x²yz/2 + h(z)

g(y,z) = x²yz/2 + h(y)

where h(z) and h(y) are constants of integration. To make the two equations consistent, we set h(z) = h(y) = 0. Therefore, the potential function f for the given vector field f is

φ = xyz + x²yz/2

or

φ = (3/2)xyz

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Part A:

The arithmetic sequence will be approximately,

42 , 36 , 30 , 24 , ....

Given,

The graph of amount of money a movie earns each week after its release where n is the number of weeks after opening, and a(n) is earnings (in millions).

Now,

After reading the graph carefully it can be judged that the the graph is decreasing linearly. Thus the sequence can be framed as,

42 , 36 , 30 , 24 , ....

here the common difference is 6.

Part B:

The movie will earn $16 million in approximately 3.5 -4 weeks.

As from the graph we can see that the earnings will further decline to $15 million in 3.5 weeks.

So for $16 million the required time will be 3.5 to 4 weeks.

Part C:

The movie will approximately earn

Arithmetic sequence,

41 , 34 , 27 , 20..

Complete the sequence,

42 , 36 , 30 , 24 , 18 , 12 , 6 , 0

For total earning,

Add the earning of the respective weeks.

$(42 + 36 + 30 + 24 + 18 + 12 + 6 + 0) million = $168

Hence the total earning of the movie is approximately $168 million.

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The  equation of the tangent line to the curve x(t) = 2/t, y(t) = t^2 + 1 at the point (2, 2) is y = -x + 4.

To find the equation of the tangent line to the curve x(t) = 2/t, y(t) = t^2 + 1 at the point (2, 2), we need to find the slope of the curve at that point and then use the point-slope form of a linear equation.

First, we need to find the derivative of y with respect to x:

dy/dx = (dy/dt) / (dx/dt)

To find dy/dt and dx/dt, we differentiate y(t) and x(t) with respect to t:

dy/dt = 2t
dx/dt = -2/t^2

So, we have:

dy/dx = (dy/dt) / (dx/dt) = (2t) / (-2/t^2) = -t^3

Now, we can find the slope of the tangent line at the point (2, 2) by plugging in t = 1:

dy/dx = -1

Therefore, the slope of the tangent line is -1.

Next, we use the point-slope form of a linear equation:

y - y1 = m(x - x1)

where (x1, y1) is the point on the curve where the tangent line intersects it, and m is the slope of the tangent line.

Since the point (2, 2) lies on the curve, we have x1 = 2 and y1 = 2. Plugging in the slope and the point, we get:

y - 2 = -1(x - 2)

Simplifying, we get:

y = -x + 4

Therefore, the equation of the tangent line to the curve x(t) = 2/t, y(t) = t^2 + 1 at the point (2, 2) is y = -x + 4.

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The ideal graphical depiction for the state's 13-year-old population's heights would be a histogram.

A histogram is a sort of bar graph that shows how continuous or discrete data are distributed. It is made up of bars that stand in for various data ranges or intervals, with the height of each bar indicating the frequency or relative frequency of the data included inside that range.

It is possible that the data acquired contains a variety of different heights because the nutritionist received information from a random sample of 400 pediatricians. The dietitian can see the height distribution and spot any trends, clusters, or gaps in the data by utilizing a histogram. This graphical representation makes it possible to see how all the state's 13-year-old population is distributed.

Therefore, the best graphical representation would be a histogram.

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The calculated value of the commission percentage is 4%

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

Hourly rate = $15

Commission = x%

So, the function of the earnings is

f(x) = x% * 1400 + Hourly rate * Number of hours

This gives

When the total earning is 176, we have

x% * 1400 + 15 * 8 = 176

This gives

x% * 1400 + 120 = 176

So, we have

x% * 1400= 56

Divide

x = 4

Hence, the commission percentage is 4%

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The 95% confidence interval for b1 is approximately (0.197, 0.703).

The 95% confidence interval for the slope estimate (b1) is given by:

b1 ± t(alpha/2, n-2) * s(e) / (sqrt(SSX) * sqrt(1 - r^2))

where:

t(alpha/2, n-2) is the t-score with alpha/2 probability (alpha = 0.05 for 95% confidence level) and n-2 degrees of freedom

s(e) is the standard error of the estimate for the regression

SSX is the sum of squared deviations of the predictor variable from its mean

r is the correlation coefficient between the predictor and response variables

Substituting the given values, we have:

b1 ± t(0.025, 7) * 2.16 / (sqrt(2.25*8) * sqrt(1 - 0.45^2))

= 0.45 ± 2.365 * 2.16 / (2.121 * 0.676)

= 0.45 ± 1.253

Therefore, the 95% confidence interval for b1 is approximately (0.197, 0.703). So, the answer is (d) (0.11, 0.79).

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Answer: B.) 32

Step-by-step explanation:

Because the triangles are similar, you can use proportions to find GH. 10/15 is 2/33, so triangle GEH is 2/3 the size of triangle DEF.
2/3 of 21 is 14, so GH = 14. 8 + 10 + 14 = 32

Based on the given diagram 1 to 5, each picture represent a number, diagram 5 is 661.

Based on the diagram;

Diagram 1;

90 = 30 + 30 + 30

Each picture in diagram 1 represents 30

Diagram 2:

1 × 1 × 0 = 0

Diagram 3:

30 ÷ 1 = 30

Diagram 4:

22 × 1 - 1 = 21

Hence,

Diagram 5:

1 + 30 × 22 + 0

Using PEMDAS

P = parenthesis

E = Exponents

M = Multiplication

D = Division

A = Addition

S = Subtraction

1 + 30 × 22 + 0

= 1 + 660 + 0

= 661

Ultimately, diagram 5 equals 661.

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tan theta=1/√3

2×1/√3/1-1/3

=2/√3÷2/3

=√3

Answer:

2

Step-by-step explanation:

tanθ+

tanθ

1

=2

Squaring both sides, we get

⇒(tanθ+

tanθ

1

)

2

=4

⇒tan

2

θ+

tan

2

θ

1

+2.tanθ.

tanθ

1

=4

⇒tan

2

θ+

tan

2

θ

1

+2=4

⇒tan

2

θ+

tan

2

θ

1

=2

Hence, the answer is 2.

The correct function for the graph of dotted line is,

⇒ y = -  (x - 2)² + 3

We have to given that;

The function f (x) = x² is shown in image.

Here, The dotted graph is translation of f (x) = x² by 3 units up, 2 units right and jus opposite to f (x) = x²

Hence, The correct function for the graph of dotted line is,

⇒ y = -  (x - 2)² + 3

Thus, After translation, The correct function for the graph of dotted line is,

⇒ y = -  (x - 2)² + 3

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Transcription is the process of creating mRNA from a gene. RNA polymerase binds to the gene and synthesizes mRNA by adding complementary nucleotides according to base-pairing rules: A with U, G with C. This forms a single-stranded mRNA molecule with a sequence complementary to the gene.

In transcription, the gene's DNA double helix unwinds, and RNA polymerase attaches to the promoter region of the gene. The RNA polymerase moves along the DNA strand, reading the nucleotides, and adds complementary RNA nucleotides. Adenine (A) pairs with uracil (U) instead of thymine (T) in RNA, while guanine (G) pairs with cytosine (C). This process continues until the RNA polymerase reaches the terminator sequence, signaling the end of transcription. The result is a single-stranded mRNA molecule with a sequence complementary to the gene, ready for translation into proteins.

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The number of gallons needed to fill 3/4 of the bathtub is 123 gallons. Option C.

To calculate the number of gallons of water needed to fill 3/4 of the bathtub, we need to find the volume of 3/4 of the rectangular prism-shaped bathtub and then convert that volume into gallons.

Given dimensions of the bathtub:

Width = 30 inches

Length = 60 inches

Depth = 21 inches

Volume of the bathtub = Width × Length × Depth

Volume = 30 inches × 60 inches × 21 inches

Volume in cubic feet = (30 inches × 60 inches × 21 inches) / ([tex]12^3[/tex])

Volume of 3/4 of the bathtub = (3/4) × [(30 inches × 60 inches × 21 inches) / ([tex]12^3[/tex])]

Now, to convert the volume from cubic feet to gallons, we multiply by the conversion factor of 7.48 gallons per cubic foot:

Volume in gallons = (3/4) × [(30 inches × 60 inches × 21 inches) / ([tex]12^3[/tex])] × 7.48

Volume in gallons ≈ 123 gallons

Therefore, the approximate number of gallons of water needed to fill 3/4 of the bathtub is 123 gallons.

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For the 2-parameters, m and n, both the functions [tex]m^{ln(n)}[/tex] and [tex]n^{ln(m) }[/tex] have the same θ-complexity.

In order to find the θ-complexity of the function,

We let, f(m,n) = [tex]m^{ln(n)}[/tex]  , and g(m,n) = [tex]n^{ln(m) }[/tex] ;

To simplify, we take "ln" for both sides,

we get,

ln(f(m,n)) = ln([tex]m^{ln(n)}[/tex]),

ln(f(m,n)) = ln(n)×ln(m),    ...equation(1)

and for g(m,n),

We have,

ln(g(m,n)) = ln([tex]n^{ln(m) }[/tex] ),

ln(g(m,n)) = ln(m)×ln(n),     ...equation(2)

On comparing both equation(1) and equation(2), we observe that both f(m,n) and g(m,n) are reducible to exactly same forms, thus, f(m,n) = g(m,n);

Therefore, both functions have same θ-complexity.

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The given question is incomplete, the complete question is

Suppose we have two parameters, m and n, with m → ∞ and n → ∞, perhaps at different rates independent of one another. Which has larger θ-complexity: [tex]m^{ln(n)}[/tex] or [tex]n^{ln(m) }[/tex] ?

Answer:

Step-by-step explanation:

The depth underground would be represented by 260. This integer is the opposite of 60, the

above ground height.

Based on the information, the correct answer is: reflect over the x-axis, vertically stretch by a factor of 3, and then shift down 1 unit.

The graph of function g is a reflection of the graph of the parent function f(x) = x over the x-axis. This is because the y-values of the points on the graph of g are the negative of the y-values of the corresponding points on the graph of f.

The graph of function g is also vertically stretched by a factor of 3. This is because the distance between any two points on the graph of g is 3 times the distance between the corresponding points on the graph of f.

The graph of function g is also shifted down 1 unit. This is because the y-values of the points on the graph of g are 1 less than the y-values of the corresponding points on the graph of f.

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Consider the graph of function g below. A diagonal curve declines from (negative 3, 8), (negative 2, 5), (negative 1, 2), (0, negative 1), (1, negative 4), (2, negative 7), and (3, negative 10) on an x y coordinate plane. Determine which sequences of transformations could be applied to the parent function f(x) = x to obtain the graph of g.

reflect over the y-axis, vertically stretch by a factor of 3, and then shift down 1 unit

reflect over the x-axis, vertically stretch by a factor of 3, and then shift down 1 unit shift right 1 unit,

reflect over the x-axis, and then vertically stretch by a factor of 3 shift right 1 unit, reflect over the y-axis, and then vertically stretch by a factor of 3 shift down 1 unit,

reflect over the x-axis, and then vertically stretch by a factor of 3 shift left 2 units, reflect over the x-axis, and then vertically stretch by a factor of 3

Olive will need to buy 8 bags of stone to fill the acquarium.

First, we need to find the volume of the aquarium.

Since the aquarium is rectangular, we can use the formula:

volume = length x width x height

where height is the depth of the stone layer we want to add. In this case, the height is 2 inches.

volume = 24 in x 12 in x 2 in

volume = 576 cubic inches

Now we need to find how many cubic inches of stone we need. We know that we want to add a 2-inch layer of stone, and the aquarium is 24 in x 12 in, so:

stone volume = 24 in x 12 in x 2 in

stone volume = 576 cubic inches

To find the number of bags we need, we can divide the stone volume by the volume of one bag:

bags = stone volume/bag volume

bags = 576 cubic inches / 75 cubic inches per bag

bags ≈ 7.68

Since we can't buy a fraction of a bag, we need to round up to the nearest whole number. Olive will need to buy 8 bags of stone.

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The value of x in this triangle is approximately 5.83.

We can use the Pythagorean theorem to find the value of x.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

In this triangle, the hypotenuse is x, and the other two sides have lengths 3 and 5. So we have:

x² = 3² + 5²

x² = 9 + 25

x² = 34

Taking the square root of both sides, we get:

x = √34

So, the value of x in this triangle is approximately 5.83.

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The interval of convergence is (6,8). The interval of convergence, we need to test the endpoints x = 6 and x = 8.

To find the radius of convergence, we can use the formula:

R = 1/lim sup |an|^(1/n)

Here, an = (x-7)^n(n^3+1)

Taking the limit superior of |an|^(1/n), we get:

lim sup |an|^(1/n) = lim sup |(x-7)^n(n^3+1)|^(1/n)

= lim sup |x-7|(n^3+1)^(1/n)

= |x-7| lim sup (n^3+1)^(1/n)

Now, we know that lim (n^3+1)^(1/n) = 1, so:

lim sup (n^3+1)^(1/n) = 1

Therefore, we have:

R = 1/lim sup |an|^(1/n) = 1/lim sup |x-7|(n^3+1)^(1/n) = 1/|x-7|

Thus, the radius of convergence is R = 1/|x-7|.

To find the interval of convergence, we need to test the endpoints x = 6 and x = 8.

When x = 6, we have:

∑(x-7)^n(n^3+1) = ∑(-1)^n(n^3+1)

= -1 + 2 - 3 + 4 - 5 + ...

which diverges by the alternating series test. Therefore, the series diverges when x = 6.

When x = 8, we have:

∑(x-7)^n(n^3+1) = ∑1^(n)(n^3+1)

= ∑n^3 + ∑1

= (1/4)(n(n+1))^2 + n

which diverges by the p-series test. Therefore, the series diverges when x = 8. Thus, the interval of convergence is (6,8).

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ANSWER

A 153/225 = 17/25 =0.68=68%

B 225/153 = 25/17 =1.47=147%

C 153/225 = 51/75 =0.51=51%

D 225/153 = 75/51 =0.75=75%

The radius of convergence for the series [tex]\sum_{n=1}^{\infty}[/tex] xⁿ/(n3ⁿ) is 3.

Given the series is,

[tex]\sum_{n=1}^{\infty}[/tex] xⁿ/(n3ⁿ)

So, here the n th term is given by

aₙ = xⁿ/(n3ⁿ)

Then the (n + 1) the term of the series is given by,

aₙ₊₁ = xⁿ⁺¹/((n + 1)3ⁿ⁺¹)

Now, the value is,

aₙ₊₁/aₙ = (xⁿ⁺¹/((n + 1)3ⁿ⁺¹))/(xⁿ/(n3ⁿ)) = (n/(n + 1))*(x/3)

Now the value of the limit is given by,

[tex]\lim_{n \to \infty}[/tex] |aₙ₊₁/aₙ| = [tex]\lim_{n \to \infty}[/tex] |(n/(n + 1))*(x/3)| = [tex]\lim_{n \to \infty}[/tex] |x/3|*|1/(1 + 1/n)| = (|x|/3)*(1/(1 + 0) = |x|/3

So, now [tex]\lim_{n \to \infty}[/tex] |aₙ₊₁/aₙ| < 1 gives

|x|/3 < 1

|x| < 3

-3 < x < 3

Hence, the radius of convergence = 3.

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C, that reddish orangish line, it's pointing upwards, so as X increases, Y increases too.

Answer:

Step-by-step explanation:

its c girly

Answer:

Answer is as follows

Step-by-step explanation:

a. The probability of choosing a blue marble can be found by dividing the number of blue marbles by the total number of marbles in the jar. So the probability of choosing a blue marble is:

P(blue) = 4/18 = 2/9

b. Similarly, the probability of choosing a green marble is:

P(green) = 4/18 = 2/9

c. There are no black marbles in the jar, so the probability of choosing a black marble is 0.

Answer:

Blue marbles: [tex]\frac{2}{9}[/tex]

Green marble: [tex]\frac{2}{9}[/tex]

Black marble: [tex]0[/tex]

Step-by-step explanation:

It is given that a jar contains 4 blue, 4 green, 7 yellow, and 3 red marbles, for a total of 18 marbles in all. To solve for probability, you will put the part of what you are solving for (in this case, a certain color marble) over the whole (which includes all colors of the marble together).

a. What is the probability of choosing a blue marble?

It is given to us that there are 4 blue marbles total in the given jar. Therefore, the fraction of blue marbles/all marbles will be 4/18.

You may be asked to simplify. Simplify fractions by dividing common factors. The common factor in this case will be 2:

[tex]\frac{(\frac{4}{18})}{\frac{2}{2}} = {\frac{2}{9}[/tex]

[tex]\frac{2}{9}[/tex] is your probability for blue marbles.

b. What is the probability of choosing a green marble?

It is given to us that there are 4 green marbles total in the given jar. Therefore, the process will be the same as blue, meaning that your answer is 2/9 simplified:

[tex]\frac{\frac{4}{18}}{\frac{2}{2}} = \frac{2}{9}[/tex]

[tex]\frac{2}{9}[/tex] is your answer.

c. What is the probability of choosing a black marble?

There are no black marbles in the given set (the colors being blue, green, yellow, and red). Therefore, within the given set, there will be no chance of obtaining a black marble.

[tex]0[/tex] is your answer.

~

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The larger hospital to more closely match the population value

The binomial distribution, is a probability distribution that describes the number of successes (in this case, female births) in a fixed number of independent trials (in this case, the number of babies born in a week) when the probability of success is constant (in this case, 0.5).

Use the expected value of the binomial distribution to calculate the number of female births we expect in each hospital in a week, assuming that the probability of a baby being female is 0.5.

Here we have

Akron ohio is served by two hospitals.

In the larger hospital, about 50 babies are born each day, and in the smaller hospital, about 25 babies are born each day in the U.S about 50% of all babies born are girls.

Here can use the binomial distribution to calculate the expected number of female births in each hospital in a week, assuming that the probability of a baby being female is 0.5.

For the larger hospital, we expect 50 x 7 to be born in a week.

Hence, the expected number of female births = 0.5 x 350 = 175.

For the smaller hospital, we expect 25 x 7 to be born in a week.

Hence, the number of female births is therefore 0.5 x 175 = 87.5.

Since the expected number of female births in the larger hospital is closer to the population value of 50%, we expect the larger hospital to more closely match the population value.  

Therefore,

The larger hospital to more closely match the population value

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The sample size needed to obtain a 99% confidence interval with a margin of error of 0.05 for the true proportion of homes in the city that are heated by oil is 666.

To calculate the required sample size, we need to use the formula n = [tex](z^2 * p * q) / e^2[/tex], where z is the z-score for the desired confidence level (2.58 for 99% confidence), p is the estimated proportion of homes heated by oil, q is 1-p, and e is the desired margin of error (0.05).

Using the information given in the question, we can estimate p as 0.5 (assuming equal probability of homes being heated by oil or other means) and q as 0.5. Plugging these values into the formula, we get n = [tex](2.58^2 * 0.5 * 0.5) / 0.05^2[/tex], which simplifies to n = 665.64. Therefore, we would need a sample size of at least 666 homes to obtain a 99% confidence interval with a margin of error of 0.05 for the true proportion of homes in the city that are heated by oil.

Thus, the answer is 666.

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The container can fit 1600 cube-shaped boxes.

To find out how many cube-shaped boxes can fit into the larger container, we need to calculate the volume of the larger container and divide it by the volume of each cube-shaped box.

The volume of the larger container can be calculated by multiplying its length, width, and height:

Volume of the larger container = 4 ft · 1 1/4 ft · 2 ft

We need to convert the mixed fraction 1 1/4 to an improper fraction:

1 1/4 = (4 · 1 + 1) / 4 = 5/4

Volume of the larger container = 4 ft · (5/4) ft · 2 ft

= (20/4) ft · (5/4) ft · 2 ft

= 50/4 · 2 ft

= 100/4

= 25 ft³

Now let's calculate the volume of each cube-shaped box.

Since all edges are equal to 1/4 ft, the volume can be calculated as the cube of the edge length:

Volume of each cube-shaped box = (1/4 ft)³

= 1/4 ft · 1/4 ft · 1/4 ft

= 1/64 ft³

Finally, we can divide the volume of the larger container by the volume of each cube-shaped box to find out how many boxes can fit:

Number of cube-shaped boxes = (Volume of the larger container) / (Volume of each cube-shaped box)

= 25 / 1/64

= 25 × 64/1

= 1600

Therefore, the container can fit 1600 cube-shaped boxes.

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f(x)= x³− 6x²− 15x the maximum value of f on the interval [0,6] is 0

f(x) = x³− 6x²− 15x

F(x) = 3x² - 12x - 15

For maximum value f'(x) = 0

3x² - 12x - 15 = 0

3x² + 3x - 15x -15 = 0

3x(x + 1)-15(x+1)=0

(3x-15)(x+1) = 0

x = -1 and x = 5

f(x) is decreasing (-∞,-1) ∪ (5,∞)

f(x) is increasing (-1,5)

x ∈ [0,6]

f(0) = 0

f(6) = 6³ - 6(6)² -15(6)

f(6) = -90

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Yes, given explanation is correct.if the calculated test statistic is less than -1.645 then the null hypothesis can be rejected.

For test the claim that the proportion of people who smoke is less than 22.5%.

A one-tailed test of hypothesis can be used. Specifically, a one-sample z-test for a proportion can be used where:

Null hypothesis: p ≥ 0.225 (the proportion of people who smoke is equal to or greater than 22.5%)

Alternative hypothesis: p < 0.225 (the proportion of people who smoke is less than 22.5%)

The test statistic for the one-sample z-test for a proportion is calculated as:

z = (p - P0) / √[(P0 × (1 - P0)) / n]

where p is the sample proportion, P0 = the hypothesized proportion under the null hypothesis and n = The sample size.

If the calculated test statistic falls in the rejection region which is determined by the chosen significance level (e.g., alpha = 0.05) then the null hypothesis can be rejected and it can be concluded that there is evidence to support the claim that the proportion of people who smoke is less than 22.5%.

For a one-tailed test with alpha = 0.05, the critical value is -1.645.

Hence, if the calculated test statistic is less than -1.645 then the null hypothesis can be rejected.

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Let

Now

Charge:-

Pay:-

Now earning:-

Answer:

Y = 1.5x + 5

Step-by-step explanation:

To model the amount of money the florist earns for each delivery, we can break it down into the different components involved.

This can be represented by the term "+10".

This can be represented by the term "+2x", where x represents the number of miles.

This can be represented by the term - ( 0.50x + 5 )

Y = 10 + 2x - (0.50x + 5)

Simplify.

Y = 10 + 2x - 0.50x - 5

Combine like terms.

Y = 1.5x + 5