If the null hypothesis states that there is no difference between the mean net income of retail stores in Chicago and New York City, then the test is two-tailed.

Answer:

2.7

Step-by-step explanation:

50(6x4)+50(6x5)

50x24+50x30

1200+1500=2700

2700÷1000=2.7

Answer:

he runs 300 meters every time he runs, so in the first week he runs 1200 meters this week he runs 1500 meters so all together he ran 2700 meters in two weeks

Step-by-step explanation:

Hope this helps! :)

If Bob only fixes 50 computers, his total loss is $3,750.

The total loss results from the negative difference between the total revenue and the total costs.

The total costs consist of variable and fixed costs.

The result is a loss when the total costs exceed the total revenue.  This result becomes a profit or income when the total revenue exceeds the total costs.

Equipment = $5,000

Premises = $6,000

Advertising = $4,000

Total fixed costs = $15,000

Variable cost per unit = $25

Selling price per unit = $250

Total number of computers fixed = 50

The total variable cost for 50 units = $1,250 (50 x $25)

The total costs (fixed and variable) = $16,250

The sales revenue for 50 units = $12,500 (50 x $250)

Loss = $3,750 ($12,500 - $16,250)

Thus, Bob will incur a total loss of $3,750 if he fixes only 50 computers based on his fixed and variable costs.

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Therefore, the degree of the resulting polynomial is m + n when two polynomials of degree m and n are multiplied together.

What is polynomial?

A polynomial is a mathematical expression consisting of variables and coefficients, which involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents. Polynomials can have one or more variables and can be of different degrees, which is the highest power of the variable in the polynomial.

Here,

When two polynomials are multiplied, the degree of the resulting polynomial is the sum of the degrees of the original polynomials. In other words, if the degree of the first polynomial is m and the degree of the second polynomial is n, then the degree of their product is m + n.

This can be understood by looking at the product of two terms in each polynomial. Each term in the first polynomial will multiply each term in the second polynomial, so the degree of the resulting term will be the sum of the degrees of the two terms. Since each term in each polynomial has a degree equal to the degree of the polynomial itself, the degree of the resulting term will be the sum of the degrees of the two polynomials, which is m + n.

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a) To calculate the standard error of the mean number of inclusions, we divide the sample standard deviation by the square root of the sample size. In this case, the sample mean number of inclusions is 31.0635, and the sample standard deviation is 2.0996. The sample size is 30. Therefore, the standard error of the mean number of inclusions can be calculated as follows:

Standard Error = Sample Standard Deviation / √Sample Size

Standard Error = 2.0996 / √30 Standard Error ≈ 0.3836 (rounded to four decimal places) b) To estimate a 95% confidence interval for the mean number of inclusions per tourmaline gem, we can use the formula: Confidence Interval = Sample Mean ± (Critical Value × Standard Error) The critical value corresponds to a 95% confidence level, which is 1.96 for a large sample size. Using the standard error calculated in part (a) as 0.3836 and the sample mean of 31.0635, the confidence interval can be calculated as: Confidence Interval = 31.0635 ± (1.96 × 0.3836)

Confidence Interval ≈ 31.0635 ± 0.7521 Confidence Interval ≈ (30.3114, 31.8156) (rounded to four decimal places) Therefore, we can estimate with 95% confidence that the mean number of inclusions per tourmaline gem lies between approximately 30.3114 and 31.8156.

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Answer: B (The cost of a notebook is $0.75, and the cost of a folder is $0.25.)

Step-by-step explanation:

No need for explanation. i know i’m right!!

Recall that two equations in standard form represent parallel lines if they are as follows:

Where A>0, and all the coefficients are integers.

Therefore the equation of a parallel line to the given line is as follows:

Since the parallel line passes through (15,4) then:

Simplifying the above result we get:

Therefore:

Solving the above equation for y we get:

Answer: Last option.

Answer:

D

Step-by-step explanation:

The slope of the the straight line equation 3x+5y=11 is (−35)Hence the slope of the line parallel is same to the given line i.e,(−35) We can write the equation in the following form slope intercept form i.e, y=mx+cHere c=−6 and m=−35The answer is y=−35x−6⇒5y=−3x−30⇒3x+5y=−30Hope it helps...Thanks you...

Answer:

make 10 cheese

Step-by-step explanation:

u take 100 and divide by 10

Answer: The volume of the solid is -31π square units.

Step-by-step explanation:

To find the volume of the solid which lies above the xy-plane and underneath the paraboloid

z=4-x²-y²,

The first step is to sketch the graph of the paraboloid:

graph

{z=4-x^2-y^2 [-10, 10, -10, 10]}

We can see that the paraboloid has a circular base with a radius 2 and a center (0,0,4).

To find the volume, we need to integrate over the circular base.

Since the paraboloid is symmetric about the z-axis, we can integrate in polar coordinates.

The limits of integration for r are 0 to 2, and for θ are 0 to 2π.

Thus, the volume of the solid is given by:

V = ∫∫R (4 - r²) r dr dθ

where R is the region in the xy-plane enclosed by the circle of radius 2.

Using polar coordinates, we get:r dr dθ = dA

where dA is the differential area element in polar coordinates, given by dA = r dr dθ.

Therefore, the integral becomes:

V = ∫∫R (4 - r²) dA

Using the fact that R is a circle of radius 2 centered at the origin, we can write:

x = r cos(θ)

y = r sin(θ)

Therefore, the integral becomes:

V = ∫₀² ∫₀²π (4 - r²) r dθ dr

To evaluate this integral, we first integrate with respect to θ, from 0 to 2π:

V = ∫₀² (4 - r²) r [θ]₀²π dr

V = ∫₀² (4 - r²) r (2π) dr

To evaluate this integral, we use the substitution

u = 4 - r².

Then, du/dr = -2r, and dr = -du/(2r).

Therefore, the integral becomes:

V = 2π ∫₀⁴ (u/r) (-du/2)

The limits of integration are u = 4 - r² and u = 0 when r = 0 and r = 2, respectively.

Substituting these limits, we get:

V = 2π ∫₀⁴ (u/2r) du

= 2π [u²/4r]₀⁴

= π [(4 - r²)² - 16] from 0 to 2

V = π [(4 - 4²)² - 16] - π [(4 - 0²)² - 16]

V = π (16 - 16² + 16) - π (16 - 16)

V = -31π.

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To express a product as a sum or difference containing only sines or cosines, we can use trigonometric identities such as the sum and difference identities. These identities allow us to rewrite products involving sines and cosines as sums or differences of sines or cosines.

Let's consider an example:

Suppose we have the product cos(x)sin(x). We can rewrite this product using the double angle identity for sine:

cos(x)sin(x) = (1/2)sin(2x)

In this case, we have expressed the product as a sum of sines.

Similarly, if we have the product sin(x)cos(x), we can use the double angle identity for cosine:

sin(x)cos(x) = (1/2)sin(2x)

In this case, we have also expressed the product as a sum of sines.

In summary, to express a product as a sum or difference containing only sines or cosines, we can use trigonometric identities like the double angle identity for sine or cosine. By applying these identities, we can rewrite the product in terms of sums or differences of sines or cosines.

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a. the costs of non-compliance, enforcement, prevention and evaluation are -75 d/p, -$7500, $17500 and $5000 respectively

b. The percentage of effort devoted to each component is:

a) To calculate the costs of non-compliance, enforcement, prevention, and evaluation, we need to determine the deviations in effort for each component and multiply them by the corresponding cost per person-day.

Non-compliance cost:

Non-compliance cost = Actual effort - Predicted effort

To calculate the actual effort, we need to sum up the effort for each component mentioned:

Actual effort = Plan development + Software development + Reviews + Tests + Training + Methodology

Actual effort = 25 + 75 + 20 + 30 + 20 + 5 = 175 d/p

Non-compliance cost = Actual effort - Predicted effort = 175 - 250 = -75 d/p

Enforcement cost:

Enforcement cost = Non-compliance cost * Cost per person-day

Assuming a cost of $100 per person-day, we can calculate the enforcement cost:

Enforcement cost = -75 * $100 = -$7500 (negative value indicates a cost reduction due to underestimation)

Prevention cost:

Prevention cost = Predicted effort * Cost per person-day

Assuming a cost of $100 per person-day, we can calculate the prevention cost for each component:

Plan development prevention cost = 25 * $100 = $2500

Software development prevention cost = 75 * $100 = $7500

Reviews prevention cost = 20 * $100 = $2000

Tests prevention cost = 30 * $100 = $3000

Training prevention cost = 20 * $100 = $2000

Methodology prevention cost = 5 * $100 = $500

Total prevention cost = Sum of prevention costs = $2500 + $7500 + $2000 + $3000 + $2000 + $500 = $17500

Evaluation cost:

Evaluation cost = Total project cost - Prevention cost - Enforcement cost

Evaluation cost = $25000 - $17500 - (-$7500) = $5000

b) To calculate the percentage of effort devoted to each component out of the total cost, we can use the following formula:

Percentage of effort = (Effort for a component / Total project cost) * 100

Percentage of effort for each component:

Plan development = (25 / 250) * 100 = 10%

Software development = (75 / 250) * 100 = 30%

Reviews = (20 / 250) * 100 = 8%

Tests = (30 / 250) * 100 = 12%

Training = (20 / 250) * 100 = 8%

Methodology = (5 / 250) * 100 = 2%

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Answer:

  2.7 < x < 12.3 meters

Step-by-step explanation:

You want to know the possible lengths of the third side of a triangle, given that two sides are 7.5 m and 4.8 m.

The triangle inequality requires the sides of a triangle have the relationship ...

  a + b > c

for any assignment of side lengths to the letters a, b, c. In effect, this means the length of a third side must lie between the sum and the difference of the other two sides.

  7.5 -4.8 < x < 7.5 +4.8

  2.7 < x < 12.3 . . . . . meters

The probability of having one white ball is 1/20 or approximately 0.05.

To find the probability of selecting one white ball out of three balls, you need to know the number of white balls in the box and the total number of balls in the box. You also need to know whether the balls are being selected randomly or not.

Assuming that there is only one white ball in the box and the rest are some other color, and that the balls are being selected randomly.

The probability of selecting one white ball out of three would be:

Probability = (number of ways to select one white ball out of three) / (total number of ways to select three balls)

Since there is only one white ball, there is only one way to select one white ball out of three. The total number of ways to select three balls out of six is 6 choose 3, which is equal to 20.

Therefore, the probability of selecting one white ball out of three would be

Probability = (number of ways to select one white ball out of three) / (total number of ways to select three balls)

Probability = 1/20

Probability = approximately 0.05.

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In the expression 10p + 3q + 2  we have total three terms -  

10p, 3q and 2.

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation.

Given in the question is a expression as follows -

10p + 3q + 2

In order to identify the number of terms in this expression, it is important to keep in mind that the terms of an expression are separated from one another by the following → + (Addition),  - (Subtraction). In some cases, (equal to) '=' , (less than) '<' , (greater than) '>' are also used

There are total 3 terms as -

10p, 3q and 2.

Therefore, in the expression 10p + 3q + 2  we have total three terms -  

10p, 3q and 2.

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Since Sophie can grade 11 papers per hour

Since she worked for 5 hours, then

Multiply 11 by 5 to find the number of the graded papers

Since the total number of papers is 86, then to find the number of the remaining papers subtract 55 from 86

There were 31 paper Sophie has to grade after working 5 hours

i) Swornima's annual income is: Rs 6,24,000.

ii) The tax rebate for Swornima is: Rs 12,400.

iii) Swornima should pay Rs 0 as her annual income tax after applying the 10% rebate.

(i) The parameters given are:

Monthly basic salary = Rs 48,000

Dashain allowance (1 month's salary) = Rs 48,000

The Total annual income is expressed by the formula:

Total annual income = (Monthly basic salary × 12) + Dashain allowance

Thus:

Total annual income = (48000 × 12) + 48,000

Total annual income = 576000 + 48,000

Total annual income = Rs 624000

(ii) We are told that she is entitled to a 10% rebate on her income tax.

10% rebate on income has Income tax slab rates in the range:

Rs 500001 to Rs 700000

Thus:

Income taxed at 10% = Rs 624,000 - Rs 500,000

Income taxed at 10% = Rs 1,24,000

Tax rebate = 10% of the income taxed at 10%

Tax rebate = 0.10 × Rs 124000

Tax rebate = Rs 12,400

(iii) The annual income tax is calculated by the formula:

Annual income tax = Tax on income from Rs 5,00,001 to Rs 7,00,000 - Tax rebate

Annual income tax = 10% of (Rs 624,000 - Rs 500,000) - Rs 12,400

Annual income tax = 10% of Rs 124,000 - Rs 12,400

Annual income tax = Rs 12,400 - Rs 12,400

Annual income tax = Rs 0

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Answer:

The proportion of the pooled samples is 0.54.

Step-by-step explanation:

We have that:

70% of men own cats.

The proportion of men in the sample is:

\(\frac{170}{170+190} = 0.4722\)

40% of women own cats.

The proportion of women in the sample is: 1 - 0.4722 = 0.5278

Proportion of the pooled samples

\(p = 0.7*0.4722 + 0.4*0.5278 = 0.54\)

The proportion of the pooled samples is 0.54.

The three friends spent:Jan spent $30.5, Danetta spent $18.5, and Elaine spent $37.

Let's denote the amount Jan spent as J. Danetta spent $12 less than Jan, so her expenditure is J - $12. Elaine spent twice as much as Danetta, so her expenditure is 2(J - $12). The total expenditure of the three friends is $86. By setting up an equation using these values, we can find the individual expenditures of each friend.

Let's denote the amount Jan spent as J. According to the given information, Danetta spent $12 less than Jan, so her expenditure can be expressed as J - $12. Similarly, Elaine spent twice as much as Danetta, so her expenditure can be expressed as 2(J - $12).

The total expenditure of the three friends is stated as $86. We can set up the equation J + (J - $12) + 2(J - $12) = $86 to represent the sum of their expenditures. Simplifying this equation, we have 4J - $36 = $86.

By rearranging the equation, we find 4J = $122, which implies J = $30.5. Therefore, Jan spent $30.5.

Using this value, we can calculate the expenditures of the other two friends. Danetta spent J - $12, which is $30.5 - $12 = $18.5. Elaine spent twice as much as Danetta, so she spent 2($18.5) = $37.

In summary, Jan spent $30.5, Danetta spent $18.5, and Elaine spent $37.

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Answer:

b

Step-by-step explanation:

Answer:

The answer is B. since the m on the bottom is negative you are taking it away. You basically just combine your variables to make the equation.

Step-by-step explanation:

Answer: B

Step-by-step explanation:t+4+3−2.2t

Add 4 and 3 to get 7.

t+7−2.2t

Combine t and −2.2t to get −1.2t.

−1.2t+7

The surface area of the cylinder is 785 cm²

A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface.

A cylinder consist of two circular bases. The volume of a cylinder is expressed as πr²h.

The surface area of a cylinder is expressed as;

SA = 2πr( r+h)

Where r is the radius and h is the height of the cylinder.

radius = diameter /2

= 10/2 = 5cm

height = 20cm

Therefore;

SA = 2 × 3.14 × 5( 5+20)

SA = 31.4 × 25

SA = 785 cm²

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Answer: b) (-1,-6)

use the slope equation y2-y1 divided by x2-x1

or just use a slope calculator like i did <3

anyways i hope this helps :)

The volume of the display case is 2161 1/8 cubic inches.To find the volume of a rectangular prism-shaped display case, we multiply its length, width, and height.

Given that the display case is 30 1/2 inches wide, 10 1/2 inches long, and 32 1/4 inches tall, we can calculate the volume as follows:

Volume = Length * Width * Height

Using the given measurements:

Volume = 10 1/2 inches * 30 1/2 inches * 32 1/4 inches

To simplify the calculation, we can convert the mixed numbers to improper fractions:

Volume = (21/2) inches * (61/2) inches * (129/4) inches

Next, we multiply the fractions:

Volume = (21/2) * (61/2) * (129/4) = 17289/8

The resulting fraction, 17289/8, is an improper fraction. To convert it back to mixed number form:

Volume = 2161 1/8 in³.

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Given :

To Find :

Solution :

We know that,

\( \qquad \sf{ \pmb{(Hypotenuse ) {}^{2} = (Base) {}^{2} + (Perpendicular) {}^{2} }}\)

Substituting the given values in the formula :

\( \qquad\sf{ \dashrightarrow{ ( BC ) {}^{2} = (AB) {}^{2} + (AC ) {}^{2} }}\)

\( \qquad\sf{ \dashrightarrow{ ( BC ) {}^{2} = (6) {}^{2} + (8 ) {}^{2} }}\)

\( \qquad\sf{ \dashrightarrow{ ( BC ) {}^{2} = 36 + 64 }}\)

\( \qquad\sf{ \dashrightarrow{ ( BC ) {}^{2} = 100 }}\)

\( \qquad\sf{ \dashrightarrow{ BC {} = \sqrt{100} }}\)

\( \qquad\sf{ \dashrightarrow{ BC {} = 10 }}\)

⠀

Step-by-step explanation:

-3x^2  + 12

-3  (x +0) ^2  + 12     is the   Vertex form of the parabola

                                    vertex is   0,12

                                        the vertex's  x coordinate is the axis of symmetry :

                                                 x = 0

a) The logistic equation for this problem is L dP/dt = P(1 - P/L), where L = 2000 and Po = 100.

b)  The maximum reproduction rate is 0.03465 times the current population.

a. The logistic equation for this problem is:

L dP/dt = P(1 - P/L)

where L is the carrying capacity of the lake, P is the current population, and dP/dt is the rate of change of the population over time.

We know that at t = 0, P = 100, and one year later at t = 1, P = 200. So we can use this information to find k, which is the growth rate coefficient:

P(t) = L / (1 + (L / Po - 1) * exp(-kt))

200 = L / (1 + (L / 100 - 1) * exp(-k))

200 = L / (1 + (L - 100) * exp(-k))

200 + 200L - 20000 = L * (1 + (L - 100) * exp(-k))

200L -\(L^2\) * exp(-k) + 200L * exp(-k) - 10000 * exp(-k) = 0

\(L^2\) - 400L + 5000 = (L - 200)^2 - 30000

\((L - 200)^2\) = 35000

L = 200 + sqrt(35000) ≈ 223.6

So L ≈ 223.6, and we can use this to find k:

2000 = 223.6 / (1 + (223.6 / 100 - 1) * exp(-k))

20000 + 2000L - 2236 = L * (1 + (L - 100) * exp(-k))

2236 - \(L^2\)  * exp(-k) + 2236 * exp(-k) - 100 * exp(-k) = 0

\(L^2\) - 4472L + 220000 = 0

(L - 2000)(L - 100) = 0

So either L = 2000 or L = 100. We know that L ≠ 100, since we know that the population stabilizes at 2000 after a long time. Therefore, L = 2000, and we can solve for k:

k = -ln((L / Po - 1) / (1 + (L / Po - 1))) / t

k = -ln((2000 / 100 - 1) / (1 + (2000 / 100 - 1))) / 1

k ≈ 0.0693

Therefore, the logistic equation for this problem is:

L dP/dt = P(1 - P/L)

dP/dt = 0.0693P(1 - P/2000)

b. The maximum reproduction rate occurs when the population is halfway to the carrying capacity, or P = L/2. At this point, the equation becomes:

dP/dt = 0.0693P(1 - 0.5)

dP/dt = 0.03465P

Therefore, the maximum reproduction rate is 0.03465 times the current population. For example, if the current population is 1000, the maximum reproduction rate is 34.65 fish per year.

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Full Question : Logistic Equation: L dP dt P(1-2). P() = L - Po Po 1+ 4e ki Where A 1. Fish population in a lake grows according to the logistic law. The initial population of 100 fish and year later it was 200. After a long time fish population stabilized at 2000.

a. Write down the logistic equation for this problem.

b. What is the maximum reproduction rate (fish/year)?

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

\(y = \stackrel{\stackrel{m}{\downarrow }}{\cfrac{5}{7}}x+1\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\)

so for the parallel line we're really lookikng for the equation of aline whose slope is 5/7 and that it passes through (-5 , 6)

\((\stackrel{x_1}{-5}~,~\stackrel{y_1}{6})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{5}{7} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{ \cfrac{5}{7}}(x-\stackrel{x_1}{(-5)}) \implies y -6= \cfrac{5}{7} (x +5) \\\\\\ y-6=\cfrac{5}{7}x+\cfrac{25}{7}\implies y=\cfrac{5}{7}x+\cfrac{25}{7}+6\implies {\Large \begin{array}{llll} y=\cfrac{5}{7}x+\cfrac{67}{7} \end{array}}\)

now, keeping in mind that perpendicular lines have negative reciprocal slopes

\(\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{5}{7}} ~\hfill \stackrel{reciprocal}{\cfrac{7}{5}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{7}{5}}}\)

so for the perpendicular line we're really looking for the equation of a line whose slope is -7/5 and that it passes through (-5 , 6)

\((\stackrel{x_1}{-5}~,~\stackrel{y_1}{6})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{7}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{- \cfrac{7}{5}}(x-\stackrel{x_1}{(-5)}) \implies y -6= -\cfrac{7}{5} (x +5) \\\\\\ y-6=-\cfrac{7}{5}x-7\implies {\Large \begin{array}{llll} y=-\cfrac{7}{5}x-1 \end{array}}\)