Evaluate the following expression.
7^0 =

Answer:

5

Step-by-step explanation:

To calculate a 95% confidence interval for the mean weight of all Utah County Fair pigs, we use the formula:

Confidence Interval = Sample Mean ± Margin of Error

Given:

Sample Mean (x) = 195

Standard Deviation (σ) = 18

Sample Size (n) = 100

The margin of error can be calculated using the formula:

Margin of Error = (Z * σ) / √n

For a 95% confidence level, the Z-value for a two-tailed test is approximately 1.96.

Margin of Error = (1.96 * 18) / √100

= 3.528

Therefore, the confidence interval is:

(195 - 3.528, 195 + 3.528)

(191.472, 198.528)

The correct answer is (191, 199).

Question 4: If the sample size is increased from 100 to 200, the margin of error will decrease in size. The margin of error is inversely proportional to the square root of the sample size. As the sample size increases, the margin of error becomes smaller, resulting in a more precise estimate.

Question 5: To find out how many pigs must be sampled to have 90% confidence in the results with a margin of error of 6.8, we can use the formula:

Sample Size (n) = (Z^2 * σ^2) / E^2

Given:

Confidence Level (1 - α) = 90% (or 0.9)

Margin of Error (E) = 6.8

Standard Deviation (σ) = 18

For a 90% confidence level, the Z-value for a two-tailed test is approximately 1.645.

Sample Size (n) = (1.645^2 * 18^2) / 6.8^2

= 3.379

Therefore, the minimum number of pigs that must be sampled is approximately 4 (rounded up to the nearest whole number).

The correct answer is 5.

function\(\(f(x)=2x+8\)\) We are to find \(\(f(x+h)\) and \(\dfrac{f(x+h)-f(x)}{h}\)\)First,

let's calculate \(\(f( x +h )\)To find \(f(x +h)\),\)

substitute\(\((x +h)\) for \(x\) in \(f(x)\)\)and simplify.

The resulting function is\(\(f(x +h)\).\)

\(\(f(x+ h)=2(x +h)+8=2x+2h+8\)\)

Now, let's calculate\(\(\dfrac{f(x +h)-f(x)}{h}\)\)

Using the definition of derivative formula,

we know

\(\(\dfrac{f(x+h)-f(x)}{h}\)\)is equal to the derivative of the function.

\(\(f(x)=2x+8\)\)

\(\[\dfrac{f(x+h)-f(x)}{h}=\dfrac{2(x+h)+8-2x-8}{h}\]\)

\(\[\dfrac{f(x+h)-f(x)}{h}=\dfrac{2x+2h+8-2x-8}{h}\]\[\dfrac{f(x+h)-f(x)}{h}=\dfrac{2h}{h}\]\)

Cancel the h's on both the numerator and denominator,

we get

\(\[\dfrac{f(x+h)-f(x)}{h}=2\]\)

Answer:

\[\begin{aligned}&

\(f(x+h)=2x+2h+8\\\dfrac{f(x+h)-f(x)}{h}=2\end{aligned}\]Given, {h}=10x+5h-2\]\)

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Answer:

-3

Step-by-step explanation:

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8

Answer:

About 6,018 students

Step-by-Step Explanation:

0.0089 x 6,072 = 54.0408

6,072 - 54.0408 = 6017.9592

6017.9592 can be rounded to 6,018

The time the bus should arrive at School Road from Hope Street is 08 : 04.

The time of the latest bus that Jo can catch from the Bus Station is 07 00.

The time the bus takes to travel from the bus station to School Road is 14 minutes.

The table shows that when a bus leaves for School Road from Hope Street,  at 07 54, it will arrive on School Road at 08 04.

The time it takes from the bus station to School road is:

= Arrival time at school road - Departure time from Bus station

= 08 04 - 07 50

= 14 minutes

If Jo wants to be in school road at 8 am by the latest, she needs to leave before :

= 8 am - 14 minutes

= 07 46

The only bus leaving before this time is the 0700 bus from the Bus Station.

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The standard deviation of those data will be 9. Then the correct option is D.

It is the measure of the dispersion of statistical data. Dispersion is the extent to which the value is in a variation.

The standard deviation is given as

\(\sigma = \sqrt{\dfrac{1}{N} \Sigma (x_1 - \bar{x})^2}\)

Suppose you gather some data and calculate that ∑ (Xi – X)² = 81. Further, you know that N = 9.

Then we have

\(\sigma = \sqrt{\dfrac{1}{9} \times 81}\)

On simplifying, we have

σ = √9

σ = 3

Thus, the correct option is D.

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The amount of heat required to raise the temperature of the water from 20°C to 90°C is 585.92 kJ.

The specific heat capacity of water is 4.184 J/g°C. To calculate the amount of heat required to raise the temperature of the water from 20°C to 90°C, we will use the following formula:

Q = m x c x ∆T

Q = amount of heat required (in Joules)

m = mass of water (in grams)

c = specific heat capacity of water (in Joules/gram°C)

∆T = change in temperature (in °C)

Converting the mass of water from kg to g:

m = 2 kg x 1000 g/kg = 2000 g

∆T = (90°C - 20°C) = 70°C

Substituting the values into the formula:

Q = 2000 g x 4.184 J/g°C x 70°C = 585,920 J

The amount of heat required to raise the temperature of the water from 20°C to 90°C is 585,920 J.

Convert into kilojoules (kJ)

To convert the amount of heat from Joules to kilojoules, we will divide the answer by 1000.

585,920 J / 1000 = 585.92 kJ

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The missing lengths  in the triangles are h = 3/2√2 and b = 4√3

Triangle a and b

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

A special right triangle

For a right triangle with an angle of 45 degrees

The measure of the leg is

h = Hypotenuse/√2

So, we have

h = 3/√2

Evaluate

h = 3/2√2

For the other triangle, we have

sin(60) = b/6

So, we have

b = 6/sin(60)

Evaluate

b = 4√3

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The number of ounces of meat were used is 52 ounces.

Given that, a sandwich shop serves 4 ounces of meat and 3 ounces of cheese on each sandwich.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

There are 7 ounces of combined meat and cheese in each sandwich (4+3 =7)

Number of sandwiches can make with 91 ounce of meat and cheese

= 91/7

= 13 sandwiches

Number of ounces of meat = 13 × 4 = 52 ounces

Number of ounces of cheese = 13 × 3 = 39 ounces

Therefore, the number of ounces of meat were used is 52 ounces.

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The MP curve initially rises to its maximum value because of the specialized nature of the fixed capital, where each additional worker's productivity rises due to the marginal product of the fixed capital.

Production Function: q = f(L,K) = 20L + 25K + 5KL - 0.03L² - 0.02K²

Given, K = 5, i.e., capital is fixed. Therefore, the total product of labor, average product of labor, and marginal product of labor are:

TPL = f(L, K = 5) = 20L + 25 × 5 + 5L × 5 - 0.03L² - 0.02(5)²

= 20L + 125 + 25L - 0.03L² - 5

= -0.03L² + 45L + 120

APL = TPL / L, or APL = 20 + 125/L + 5K - 0.03L - 0.02K² / L

= 20 + 25 + 5 × 5 - 0.03L - 0.02(5)² / L

= 50 - 0.03L - 0.5 / L

= 49.5 - 0.03L / L

MP = ∂TPL / ∂L

= 20 + 25 - 0.06L - 0.02K²

= 45 - 0.06L

The following diagram illustrates the TP, MP, and AP curves:

Figure: Total Product (TP), Marginal Product (MP), and Average Product (AP) curves

The production function demonstrates increasing marginal returns due to specialization when L is low enough, i.e., when L ≤ 750. The marginal product curve initially increases and reaches a maximum value of 45 units of output when L = 416.67 units. When L > 416.67, MP decreases, and when L = 750 units, MP becomes zero.

The MP curve's initial increase demonstrates that the production function displays increasing marginal returns due to specialization when L is low enough. This is because when the capital is fixed, an additional unit of labor will benefit from the fixed capital and will increase production more than the previous one.

In other words, Because of the specialised nature of the fixed capital, the MP curve first climbs to its maximum value, where each additional worker's productivity rises due to the marginal product of the fixed capital.

The APL curve initially rises due to the MP curve's increase and then decreases when MP falls because of the diminishing marginal returns.

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Three of the system of equations has no solution and one have Infinite solutions.

Given are system of equations, we need to solve them,

A) 5(11x + 4) - x = 61x + 20

55x+20-x = 61x+20

55x = 62x [no solution]

B) 7(5x + 10) - x = 34x + 74

35x + 70 - x = 34x+74

34x + 70 = 34x + 74

70 = 74 [no solution]

C) 6x + 8 + x = 7x + 6

7x + 8 = 7x +6 [no solution]

D) 5(x − 12) + 3x = 8x - 60

5x-60+3x = 8x-60

8x-60 = 8x-60 [Infinite solutions]

Hence, three of the system of equations has no solution and one have Infinite solutions.

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Answer:

A (2,-1)

Step-by-step explanation:

-1 = 3(2) -7

5(2) - (-1) = 11

Answer:

Step-by-step explanation:

Given,

Parallel sides of the trapezium = 3in, 7in

Height of the trapezium = 5in

Therefore,

Area of the trapezium

\( = \frac{1}{2} \times sum \: of \: parallel \: sides \times height\)

\( = \frac{1}{2} \times (7 + 3)in \times 5in\)

\( = \frac{1}{2} \times 10in \times 5in\)

= 5in × 5in

\( = {25in}^{2} \)

Hence,

Area if the trapezium is 25 square inches (Ans)

The answer to the question is x = 15. This can be calculated using the following logic:

From the given data, we know that 15 people like all three fruits. Therefore, out of the 100 customers, 85 customers like one or more of the three fruits.

We also know that 22 people like mangoes and bananas, 33 people like mangoes and kiwi fruits, and 27 people like bananas and kiwi fruits. Therefore, the total number of customers that like mangoes is 55 (22 + 33).

Since 85 people like one or more of the three fruits, and 55 of those people like mangoes, then x (the number of people who like only mangoes) must be 30 (85 - 55).

However, we know that 15 people like all three fruits. Therefore, the actual number of people who like only mangoes must be 15 (30 - 15).

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Answer:

36

Step-by-step explanation:

 72 different kinds of sandwiches can be made using 6 different types of bread, 4 different types of meat, and 3 different types of toppings

Given :

A sandwich shop offers 6 different types of bread, 4 different types of meat, and 3 different types of toppings

bread = 6 , meat=4, toppings=3

Sandwich is made of 1 type of bread, 1 type of meat, and 1 topping.

To find the number of combinations we multiply all the possible types we have

Number of combinations of sandwiches = \(6 \cdot 4 \cdot 3=72\)

There are 72 different kinds of sandwiches.

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Answer:

x has infinity solutions

Step-by-step explanation:

5 (1 + x) = 5x +5

first you distribute the 5 to the 1 and x

5 + 5x = 5x + 5

then you subtract 5x from both sides

5 = 5

5 is equal to 5

so there are infinity solutions

hope this helps

Answer:

y = -8

Step-by-step explanation:

All we need to is substitute for x and solve for y.

y = 8 - 2x

y = 8 - 2(8)

y = 8 - 16

y = -8

Best of Luck!

The three statements are correct about any business organization is

a) The ultimate goal of a business is to make profits.

b) Customer loyalty has little impact on a business’s revenue.

c) Customer service adds to a business’s profitability in the long run.

What is Revenue?

Revenue is the entire amount of money made through the sale of products and services that are essential to the business's core operations. Sales or turnover are other terms used to describe commercial revenue. Some businesses make money from royalties, interest, or other fees.

Concept:

The process of identifying and grouping the work to be done, defining and allocating responsibility and authority, and building relationships in order to enable individuals to collaborate most effectively in order to achieve goals is known as organization.

The organizational process gives workers the ability to make choices that benefit their development. They are constantly prepared to take on new difficulties. This circumstance may support the growth of the company. This contributes to the enterprise's growth by enhancing its earning potential.

Over time, providing good customer service increases a company's profits.

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Answer:

the number of words made = w

the number of tiles not used = t

the points earned from words made = 10w

the points taken away from tiles not used = 3t

(srry if this is wrong but I believe it's correct)

(a) The mean of Z in case (a) is -60 and the variance is 400.

(b) The mean of Z in case (b) is 280 and the variance is 3600.

(c) The mean of Z in case (c) is 60 and the variance is 65.

(d) The mean of Z in case (d) is -20 and the variance is 65.

(e) The mean of Z in case (e) is 80 and the variance is 505.

To find the mean and variance of the random variable Z for each case, we can use the properties of means and variances.

(a) Z = 40 - 5X

Mean of Z:

E(Z) = E(40 - 5X) = 40 - 5E(X) = 40 - 5 * 20 = 40 - 100 = -60

Variance of Z:

Var(Z) = Var(40 - 5X) = Var(-5X) = (-5)² * Var(X) = 25 * Var(X) = 25 * (4)² = 25 * 16 = 400

Therefore, the mean of Z in case (a) is -60 and the variance is 400.

(b) Z = 15X - 20

Mean of Z:

E(Z) = E(15X - 20) = 15E(X) - 20 = 15 * 20 - 20 = 300 - 20 = 280

Variance of Z:

Var(Z) = Var(15X - 20) = Var(15X) = (15)² * Var(X) = 225 * Var(X) = 225 * (4)² = 225 * 16 = 3600

Therefore, the mean of Z in case (b) is 280 and the variance is 3600.

(c) Z = X + Y

Mean of Z:

E(Z) = E(X + Y) = E(X) + E(Y) = 20 + 40 = 60

Variance of Z:

Var(Z) = Var(X + Y) = Var(X) + Var(Y) = (4)² + (7)² = 16 + 49 = 65

Therefore, the mean of Z in case (c) is 60 and the variance is 65.

(d) Z = X - Y

Mean of Z:

E(Z) = E(X - Y) = E(X) - E(Y) = 20 - 40 = -20

Variance of Z:

Var(Z) = Var(X - Y) = Var(X) + Var(Y) = (4)² + (7)² = 16 + 49 = 65

Therefore, the mean of Z in case (d) is -20 and the variance is 65.

(e) Z = -2X + 3Y

Mean of Z:

E(Z) = E(-2X + 3Y) = -2E(X) + 3E(Y) = -2 * 20 + 3 * 40 = -40 + 120 = 80

Variance of Z:

Var(Z) = Var(-2X + 3Y) = (-2)² * Var(X) + (3)² * Var(Y) = 4 * 16 + 9 * 49 = 64 + 441 = 505

Therefore, the mean of Z in case (e) is 80 and the variance is 505.

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Answer:

20 times 4

Step-by-step explanation:

suricce area

To calculate the slope use the

gradient formula

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

∣

∣

∣

2

2

m

=

y

2

−

y

1

x

2

−

x

1

2

2

∣

∣

∣

−−−−−−−−−−−−−−−−−

where m represents the slope and

(

x

1

,

y

1

)

,

(

x

2

,

y

2

)

2 coordinate points

here the 2 points are (10 ,-8) and (7 ,-8)

let

(

x

1

,

y

1

)

=

(

10

,

−

8

)

and

(

x

2

,

y

2

)

=

(

7

,

−

8

)

⇒

m

=

−

8

−

(

−

8

)

7

−

10

=

0

−

3

=

0

A slope of zero indicates that the line is horizontal, parallel to the x-axis and passes through all points in the plane with the same y-coordinate.

For the 2 given points both y-coordinates are - 8 and so the equation of the line is

y=-8

.

If you note this fact then it can be stated that the slope is zero without using the gradient formula.

graph{y-0.001x+8=0 [-20, 20, -10, 10]}

Answer:

\(\frac{-7}{17}\)

Step-by-step explanation:

To find the slope simply use the rise over run.

The change in y value (rise) from (7,1) to (-10,8) is y=1-8

The change in x value (run) from (7,1) to (-10,8) is y=7-(-10)

As a fraction this can be modeled by \(\frac{1-8}{7-(-10)}\)

\(\frac{-7}{17}\) is the slope as it is rise over run and cannot be simplified further.

Answer:

i think the answer is c

Step-by-step explanation:im just guessing but if it is wrong then im sorry

Answer:

25,36,49,64,81,100

................................

Answer:

Your answer is 1, 4, 9, 16, 25, 36, 49, 64, 81, 100.

Step-by-step explanation:

1 - 4  

+ 3

4 - 9

+ 5

9 - 16

+ 7

+9, +11, +13, +15, +17, +19...

Answer:

Step-by-step explanation:

x can take on values as small as 0, as large as 8 and all values in between.  The third answer choice is the correct one.

Answer:

It's A.

Step-by-step explanation:

I took the test.

The equation of line which has slope -3/4 and passes through a point (-5,4) is given by          

y = -3/4x  +1/4

We have been given,

                       Slope = m = -3/4

                       Point = (x1,y1) = (-5,4)

The general slope-intercept form is given as,

              y = mx + c

                 where m = slope

                               c = intercept

Further, the formula to find the equation of line when we have been given one point and the slope is as follows,

            (y-y1) = m(x-x1)            (1)

Now putting the required value in equation (1) we will get,

       (y-4) = -3/4(x+5)

        y-4 = -3/4x – 15/4

         y = -3/4x – 15/4 + 4

         y = -3/4x  +1/4

Thus, the equation of line which has slope -3/4 and passes through a point (-5,4) is given by          

y = -3/4x  +1/4

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Answer: $24 after 4 years

Step-by-step explanation:

1.5% = 0.015

Take 400 times 0.015 = $6 per year

6 times 4 = $24 after 4 years

The rate of change of weight of the rabbit in pounds per week is 0.5 pounds per week.

To calculate the rate of change of weight of Samuel's rabbit in pounds per week, we need to look at how much the weight of the rabbit changes as the number of weeks since birth increases by one. This is also known as the slope of the linear relationship between the number of weeks and the weight of the rabbit.

Looking at the table below, we can see that when the rabbit is born (week 0), it weighs 0.5 pounds. As the number of weeks since birth increases by one, the weight of the rabbit increases by 0.5 pounds. This pattern continues for each subsequent week, with the weight of the rabbit increasing by 0.5 pounds each time.

| Number of Weeks Since Birth | Weight of Rabbit (in pounds) |
|-----------------------------|------------------------------|
|              0              |             0.5              |
|              1              |             1.0              |
|              2              |             1.5              |
|              3              |             2.0              |
|              4              |             2.5              |
|              5              |             3.0              |

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The type of experiment design described in the scenario is: B) Stratified.

In this design, the population is divided into homogeneous groups (in this case, males and females) called strata. Then, within each stratum, participants are randomly assigned to different treatment groups (treatment and control groups).

This approach ensures that each stratum is represented equally in both treatment groups, allowing for comparisons within each group and reducing potential confounding variables.

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