I will give brainlyist to who ever answers it.



A family with travel 475 miles on the Road trip which inequality can be used to find all possible values of T the time it would take to reach their destination if they travel in an average speed of at least in miles per hour

Using the linear model, we can predict that a 100 mg dose of the experimental drug would cause a change in the patient's blood pressure of 540 mmHg.

An equation is a mathematical statement that expresses the equality of two expressions. It consists of two expressions, one on the left side and one on the right side, which are connected by an equals sign (=). Equations are fundamental to mathematics, and are used to solve many problems. In addition, equations can also be used to describe physical laws, such as Newton's law of gravity.

10 + 2(20) + 3(30) + 4(100)

= 10 + 40 + 90 + 400

= 540 mmHg

The linear model suggests that a 100 mg dose of the experimental drug would cause a change in the patient's blood pressure of 540 mmHg. This can be seen by using the linear equation 10 + 2x + 3x + 4x. Here, the first coefficient of 10 represents the change in blood pressure for a 10 mg dose, the second coefficient of 2 represents the change in blood pressure for each additional 10 mg dose, the third coefficient of 3 represents the change in blood pressure for each additional 20 mg dose, and the fourth coefficient of 4 represents the change in blood pressure for each additional 30 mg dose.

For example, if the patient was given a 40 mg dose, the equation would be 10 + 2(20) + 3(30), which would yield a change in blood pressure of 140 mmHg. Similarly, if the patient was given a 50 mg dose, the equation would be 10 + 2(20) + 3(30) + 4(10), which would yield a change in blood pressure of 190 mmHg.

Therefore, using the linear model, we can predict that a 100 mg dose of the experimental drug would cause a change in the patient's blood pressure of 540 mmHg.

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The linear model predicts that a 100 mg dose of the investigational drug will raise the patient's heart rate by 540 mmHg.

A mathematical statement that expresses the equality of two expressions is known as an equation. It comprises of two expressions that are joined together by the equals sign (=), one on the left side and one on the right. Equations are essential to mathematics and are frequently used to resolve issues. Moreover, equations can be utilised to explain natural laws like Newton's law of gravity.

10 + 2(20) + 3(30) + 4(100)

= 10 + 40 + 90 + 400

= 540 mmHg

The linear model predicts that a 100 mg dose of the investigational drug will raise the patient's heart rate by 540 mmHg.

Using the linear equation 10 + 2x + 3x + 4x, this may be observed. In this case, the first coefficient of 10 denotes the change in blood pressure for a dose of 10 mg, the second coefficient of 2, the change for each additional dose of 10 mg, the third coefficient of 3, the change for each additional dose of 20 mg, and the fourth coefficient, the change for each additional dose of 30 mg.

For instance, if the patient received a dose of 40 mg, the equation would be 10 + 2(20) + 3(30), resulting in a 140 mmHg change in blood pressure. The calculation would be 10 + 2(20) + 3(30) + 4(10) if the patient received a 50 mg dose, which would result in a 190 mmHg change in blood pressure.

As a result, we can infer from the linear model that a 100 mg dose of the experimental medication would result in a 540 mmHg change in the patient's blood pressure.

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The correct equation to determine the number of people (p) who can go to the amusement park is: 100.25 = 13.75p + 17.75.

Here's the step-by-step explanation:

1. The total amount they have to spend is $100.25.
2. The cost of parking is $17.75, which is a one-time expense.
3. The cost of admission per person is $13.75.

To find out how many people can go, you need to account for both the parking cost and the cost of tickets for each person. Therefore, the equation is:

100.25 (total amount) = 13.75p (cost per person times the number of people) + 17.75 (cost of parking)

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48 pound mass will stretch the spring approximately 12.31 inches.

If the spring's force is directly proportional to how far it is stretched, we can express this relationship mathematically as follows:

F = kx

Where

We can use the first value of the spring scale to determine k:

39 = k(10)

k = 3.9

Now, using this value of k, we can calculate how far the spring is stretched when a 48-pound mass is applied:

F = kx

48 = 3.9x

x = 48/3.9

x = 12.31

Therefore, a 48 pound mass will stretch the spring approximately 12.31 inches.

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Answer:

11.17, my answer needs to be 20+ characters soooooooo

Answer:

3 cm.

Step-by-step explanation:

Let's use the formula for the perimeter of a rectangle, which is P = 2l + 2w, where P is the perimeter, l is the length, and w is the width.In this case, we have:P = 16 cm (given)

l = k cm (given)

w = 5 cm (given)Substituting these values into the formula, we get:

16 cm = 2(k cm) + 2(5 cm)

Simplifying, we get:

16 cm = 2k cm + 10 cm

Subtracting 10 cm from both sides, we get:6 cm = 2k cm

Dividing both sides by 2, we get:

3 cm = k

Therefore, the value of k is 3 cm.

The possible amount of time for Dinah to drive 420 miles on the highway is between 6 & 7 hours.

To get the possible time, we need to consider the range of speeds she can drive at.

Because she must drive at least 60 miles per hour and at most 70 miles per hour, we can calculate the possible time ranges using "Time = Distance / Speed"

At 60 miles per hour:

= 420 miles / 60 miles per hour

= 7 hours

At 70 miles per hour:

= 420 miles / 70 miles per hour

= 6 hours.

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The correct arrangement of problem is explained below and their solution are as follows:

(1) Zaira will arrive at her grandmother's house at 9:00 am.

(2) The total distance covered by bus is 207.5 km.

(3) The average-speed of the train was 28 km/h.

Part (1) : The Problem is : Zaira goes to her grandmother's house. If she leaves home at 6:00 in the morning, she cycles 30 km at a steady speed of 10 km. What time will she arrive?

Solution:

Zaira cycles at a steady speed of 10 km, she will cover the distance of 30 km in 30/10 = 3 hours.

So, she will arrive at her grandmother's house at 6:00 + 3:00 = 9:00 am.

Part (2) : Problem : A bus had an average speed of 65 kph for 1.5 hours in the morning. It had average speed of 55 kph for 2 hours in afternoon. What was total distance covered by bus?

Solution:

The distance covered by the bus in the morning can be calculated as:

Distance = Speed × Time = 65 kph × 1.5 hours = 97.5 km,

The distance covered in the afternoon can be calculated as:

Distance = Speed × Time = 55 kph × 2 hours = 110 km

So, total-distance covered by bus is = 97.5 km + 110 km = 207.5 km.

Part (3) : Problem : A train left Station X at 9:00 a.m. and arrived station Y at 9:30 a.m. The distance between the two stations is 14 km. What was  average speed of train?

Solution:

The time taken by the train to cover the distance of 14 km can be calculated as:

Time = Arrival Time - Departure Time = 9:30 am - 9:00 am = 0.5 hours

The average speed of the train = Distance/Time = 14 km/0.5 hours = 28 km/h;

Therefore, the average speed of the train was 28 km/h.

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The given question is incomplete, the complete question is

Directions: Arrange the sentences in the box to form a problem. Then solve each problem.

(1) If she leaves home at 6:00 in the morning

What time will she arrive?

Zaira goes to her grandmother's house

She cycles 30 km at a steady speed of 10 km

(2) I had an average speed of 55 kph for 2 hours in the afternoon

What was the total distance covered by the bus

A bus had an average speed of 65 kph for 1. 5 hours in the morning.

(3) What was the average speed of the train?

The distance between the two stations is 14 km

A train left Station X at 9:00 a.m. and arrived station Y at 9:30 a.m. ​

Part A: The mean of the data is approximately 5.79. Part B: The median is 6.5. Part C: The mode of the data is the set of values {5, 9}.

In statistics, mean is a measure of central tendency that represents the average of a set of numbers. The mean is calculated by adding up all the values in a data set and dividing by the total number of values.

The formula for calculating the mean of a set of n numbers is:

mean = (x1 + x2 + ... + xn) / n

where x1, x2, ..., xn are the individual values in the data set.

Part A:

To find the mean of the data, we need to add up all the values and divide by the total number of values:

3 + 4 + 4 + 5 + 5 + 5 + 6 + 7 + 7 + 8 + 8 + 9 + 9 + 9 = 81

There are 14 values in the data set, so we divide the sum by 14 to get:

81/14 ≈ 5.79

Therefore, the mean of the data is approximately 5.79.

Part B:

To find the median of the data, we need to arrange the values in order from lowest to highest:

3, 4, 4, 5, 5, 5, 6, 7, 7, 8, 8, 9, 9, 9

There are 14 values, so the median is the middle value. Since there is an even number of values, we need to find the average of the two middle values, which are 6 and 7. Thus, the median is:

(6 + 7)/2 = 6.5

Therefore, the median of the data is 6.5.

Part C:

To find the mode of the data, we need to look for the value(s) that occur most frequently. From the stem plot, we can see that the values 5 and 9 occur three times each, while all other values occur either once or twice. Therefore, the mode of the data is:

5 and 9

Thus, the mode of the data is the set of values {5, 9}.

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A reasonable prediction for the number of times the spinner will land on the number 3 is 3 times.

Since the spinner has 8 congruent sections and is spun 24 times, we can use probability to make a reasonable prediction for the number of times it will land on the number 3.

1. Calculate the probability of landing on the number 3 for a single spin:
Since there are 8 congruent sections, the probability of landing on the number 3 is 1/8.

2. Determine the expected number of times the spinner will land on the number 3:
To do this, multiply the probability of landing on the number 3 (1/8) by the total number of spins (24).
Expected number of times = (1/8) * 24

3. Simplify the expression:
Expected number of times = 3

So, a reasonable prediction for the number of times the spinner will land on the number 3 is 3 times.

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Answer: less than

Step-by-step explanation:

The cost to alter each dress is $25 and each suit is $30 based on the given set of relations.

Let us represent the dresses as x and suit as y. Forming the equation for both customers.

Cost of one dress × number of dress +

Cost of one suit × number of suit = total cost

2x + y = 80 : equation 1

x + 3y = 115 : equation 2

Multiply equation with 1

6x + 3y = 240 : equation 3

Subtract equation 2 from equation 3

6x + 3y = 240

- x + 3y = 115

5x = 125

x = 125/5

x = $25

Keep the value of x in equation 2 to find the value of y

25 + 3y = 115

3y = 115 - 25

3y = 90

y = 90/3

y = $30

Hence, the altering cost of each is $25 and $30.

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The complete question is -

A tailor charges set amounts for alterations on dresses and suits. One customer has 2 dresses and 1 suit altered for a total of $80. Another customer has 1 dress and 3 suits altered for a total of $115. How much does it cost to alter each dress?

A z-score of 0 means that the sample proportion is equal to the population proportion. Therefore, after using sampling distribution we can conclude that we agree with Aiden's expectation that the percentage for this sample will be 45%.

Based on the given information, we can assume that the population proportion of students who brought a can of food to contribute to the canned food drive is 0.45. Aiden picks a representative sample of 25 students, and he expects the percentage for this sample will be 45%.

We can use the sampling distribution formula to calculate the expected sample proportion:

SE = sqrt[p(1-p) / n]

where p is the population proportion, n is the sample size, and SE is the standard error.

Plugging in the values, we get:

SE = sqrt[0.45(1-0.45) / 25] = 0.0984

Next, we can use the normal distribution to find the z-score corresponding to a sample proportion of 0.45:

z = (0.45 - 0.45) / 0.0984 = 0

A z-score of 0 means that the sample proportion is equal to the population proportion. Therefore, we can conclude that we agree with Aiden's expectation that the percentage for this sample will be 45%.

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Answer: 344cm²

Step-by-step explanation:

7x7=49

49x5=245

3x2=6

49-6=43

245+43=288

5x2=10 10x2=20

5x3=15 15x2=30

288+30+20+6=344

V = ∫2πx f(y) dy volume of the solid

a. The integral of dz is simply z + C, where C is the constant of integration. So the result of integrating dz is:

∫ dz = z + C

b. To find the integral of (C^2 + I∫sin(x))/(1+cos(x)) dx, we can use the substitution u = 1 + cos(x), du/dx = -sin(x), and dx = du/(-sin(x)). Then we have:

∫(C^2 + I∫sin(x))/(1+cos(x)) dx = ∫(C^2 + I∫sin(x))/u (-du/sin(x))
= -I∫(C^2 + I∫sin(x))/u du
= -I(C^2ln|u| + I∫ln|u| sin(x) dx) + C'
= -I(C^2ln|1+cos(x)| - I∫ln|1+cos(x)| sin(x) dx) + C'

where C' is the constant of integration.

c. To find the volume of the solid obtained by rotating the shaded region about the x-axis or the y-axis, we need to use the method of cylindrical shells or disks, respectively.

If we rotate the region about the x-axis, we can use the formula:

V = ∫2πy f(x) dx

where f(x) is the distance from the x-axis to the function y(x) that defines the region. If we have a function y(x) = g(x) - h(x) that defines the region between two curves, then f(x) = g(x) - h(x) and the limits of integration are the x-values where the two curves intersect.

If we rotate the region about the y-axis, we can use the formula:

V = ∫2πx f(y) dy

where f(y) is the distance from the y-axis to the function x(y) that defines the region. If we have a function x(y) = g(y) - h(y) that defines the region between two curves, then f(y) = g(y) - h(y) and the limits of integration are the y-values where the two curves intersect.

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The derivative of the given function is:

y' = (8x – 9) e⁻⁴ - 16x (4x - 9) e⁻⁴

Find the derivative?

To find the derivative of the given function y= (4x² – 9x) e⁻⁴, we need to use the product rule of differentiation. The formula for the product rule is:

(fg)' = f'g + fg'

Where f and g are two differentiable functions. Applying this formula, we get:

y' = (4x² – 9x)' e⁻⁴ + (4x² – 9x) (e⁻⁴)'

The first term on the right-hand side can be simplified using the power rule and the constant multiple rule of differentiation:

(4x² – 9x)' = 8x – 9

The second term on the right-hand side requires the chain rule of differentiation. Let u = -4x, then we have:

(e⁻⁴)' = (e^u)' = e^u (-4) = -4e⁻⁴x

Substituting these results back into the expression for y', we get:

y' = (8x – 9) e⁻⁴ + (4x² – 9x) (-4e⁻⁴x)

Simplifying this expression, we get:

y' = (8x – 9) e⁻⁴ - 16x (4x - 9) e⁻⁴

Therefore, the derivative of the given function is:

y' = (8x – 9) e⁻⁴ - 16x (4x - 9) e⁻⁴

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The speed of the faster car is 90 kph and the speed of the slower car is 45 kph.

We are given that two cars are starting together and they travel in the same direction. Let one car be car A and the other car B. Speed of car B is twice the speed of car A. Let r be the rate of speed of car A and 2r be the rate of speed of car B.

We know that these two cars are 225 km apart. We will use the formula distance = speed * time. Let the distance car A travels after 5 hours be 5r. So, the distance traveled by car B after 5 hours will be 5(2r) = 10r.

Since car B is faster, it will have traveled farther after 5 hours. Therefore,

Distance traveled by car B - distance traveled by car A = 225

10r - 5r = 225

5r = 225

r = 45 kph

and

2r = 90 kph

Therefore, car A is traveling at 45 kph and car B is traveling at 90 kph.

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Answer: 8

Step-by-step explanation:

CF looks like the radius of the circle.

ED looks like the diameter.

.: ED = 2 x CF = 2 x 4 = 8

.: ED = 8

Answer:

The length of ED, or the diameter, is 8

Step-by-step explanation:

As the other person explained, CF is the radius, as the radius is from the centermost point to the edge.  I also see that ED is the diameter, as the diameter is from edge to edge, going through the centermost point.  Therefore, since the diameter is double the radius, we can solve this with the following equation:

2 * r = d, where r is radius and d is diameter.

2 * 4 = d

8 = d

The base of her ladder should be 12 feet from the house.

A Pythagorean theorem is a useful theorem which can be applied so as to determine the length of the missing side of a right angled triangle. It states that:

/Hyp/^2 = /Adj/^2 + /Opp/^2

So that from the information given in the question, let the distance from the base of her ladder and the house be represented by x;

/Hyp/^2 = /Adj/^2 + /Opp/^2

20^2 = x ^2 + 16^2

400 = x^2 + 256

x^2 = 400 - 256

      = 144

x = 144^1/2

  = 12

x = 12 feet

Thus, Allison should place the base of her ladder 12 feet to the house.

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The total area of the given figure is 12 units²

In the given figure, we have 3 shapes. One is rectangle and the other two are triangles. We can find areas of all three shapes and add to find the total area.

Finding area of the triangle ABC,

base of the triangle ABC = 4 units

height of the triangle ABC = 4 units

Area of the triangle ABC = 1/2 x base x height = 1/2 x 4 x 4 = 8 units²

Finding area of the triangle CDE,

base of the triangle CDE = 2 units

height of the triangle CDE = 2 units

Area of the triangle CDE = 1/2 x base x height = 1/2 x 2 x 2 = 2 units²

Finding area of the rectangle,

length of the rectangle = 2 units

breadth of the rectangle = 1 unit

Area of the rectangle = length x breadth = 2 x 1 = 2 units²

So, total area of the given figure = 8 units² + 2 units² + 2 units² = 12 units²

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The final step when solving the given math problem is:

Take the fifth root of both sides: x = [tex]((y^2)/19)^(^1^/^5)[/tex]

To solve √19x^5 for x, follow these steps:

Isolate the square root term: [tex]\sqrt{19x^5}[/tex] = y (Let y be the other side of the equation)

Square both sides: [tex](y^2) = 19x^5[/tex]

Divide both sides by 19: [tex](y^2)/19 = x^5[/tex]

Take the fifth root of both sides: x = [tex]((y^2)/19)^(^1^/^5^)[/tex]

The square root of a number is a value that, when multiplied by itself, gives the original number. It is denoted by the symbol √ and can be found using mathematical operations.

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Answer:

2 7/24 gallons

(sorry if its wrong)

Answer:

Read

Step-by-step explanation:

If Alex can stack exactly 16 cookies with a diameter of 5 cm inside a cylindrical container with the same diameter, then the height of the cylinder will be equal to the height of 16 cookies stacked on top of each other, which is 16 multiplied by the height of one cookie.

The diameter of each cookie is 5 cm, so the radius is 2.5 cm. The volume of each cookie is πr²h, where r is the radius and h is the height, so the volume of one cookie is:

V1 = π(2.5 cm)²h

The volume of 16 cookies will be:

V16 = 16π(2.5 cm)²h

Since the volume of the cylindrical container is 100% cm³, we have:

V16 = Vcyl

where Vcyl is the volume of the cylindrical container. Therefore:

16π(2.5 cm)²h = Vcyl

The height of 16 cookies stacked on top of each other is 16 times the height of one cookie, so:

h = 16(1 cm) = 16 cm

Substituting this value into the equation above and solving for the radius, we get:

r = √(Vcyl / (16πh)) = √(100 cm³ / (16π(16 cm))) ≈ 1.03 cm

The surface area of the cylindrical container is given by the formula:

A = 2πr² + 2πrh

Substituting the values we found for r and h, we get:

A = 2π(1.03 cm)² + 2π(1.03 cm)(16 cm) ≈ 142 cm²

Therefore, the surface area of the container is approximately 142 square centimeters. Rounded to the nearest square centimeter, the answer is 142 square centimeters.

The surface area of the given cylindrical container is 290 cm².

The volume of a cylinder is given by the formula:

V = πr²h

where r is the radius of the cylinder and h is its height.

We know that the volume of the cylindrical container is 100π cm³ and that it has the same diameter as the cookies, which is 5 cm.

Since the diameter of the container is 5 cm, its radius is 2.5 cm.

We can rearrange the formula for volume to solve for

h = V/πr²

h = 100π/π(2.5)²

h = 16

So, the height of the container is 16 cm.

To find the surface area of the container, we can use the formula:

A = 2πrh + 2πr²

where r is the radius of the container and h is its height.

Substituting the values we have, we get:

A = 2π(2.5)(16)+2π(2.5)²

A = 92.5π

A ≈ 290.45

Rounding to the nearest square centimeter,

A = 290

Thus, the surface area of the container is 290 cm².

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The statements is true of this categorical proposition is: It is a standard-form categorical proposition because it is a substitution instance of this form: some s are not p option A.

A proposition or statement that is categorically affirmed or denied of all or part of the topic is known as a categorical proposition in syllogistic or classical logic. Hence, there are four fundamental types of categorical propositions: "Every S is P," "No S is P," "Some S is P," and "Some S is not P."

Every man is mortal, for instance, is an A-proposition since these forms are denoted by the letters A, E, I, and O, respectively. In particular, being declarations of reality rather than logical connections, they contrast significantly with hypothetical propositions, such as "If every man is mortal, then Socrates is mortal," which categorical propositions are to be differentiated from and enter into as integral words.

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Answer:

Therefore, the product of 23.5 and 2.3 is 54.05.

Step-by-step explanation:

To determine the product of 23.5 and 2.3, we can use the following steps:

Align the numbers vertically with the ones digit of the second factor (2.3) under the tenths digit of the first factor (3 in 23.5).

   23.5

 x 2.3

 -----

Multiply the ones digit of the second factor by the first factor and write the result below, shifted one place to the right.

   23.5

 x 2.3

 -----

    71

Multiply the tenths digit of the second factor by the first factor and write the result below, shifted two places to the right.

   23.5

 x 2.3

 -----

    71

   470

Add the two partial products together.

   23.5

 x 2.3

 -----

    71

   470

 -----

   54.05

Therefore, the product of 23.5 and 2.3 is 54.05.

Answer:

m = -3

Step-by-step explanation:

We Know

Slope = rise/run or (y2 - y1) / (x2 - x1)

Pick 2 points (0,15) (2,9)

We see the y decrease by 6, and the x increase by 2, so the slope is

m = -6/2 = -3

So, the slope of the line representing the data is -3.

Answer:

  x = 3  or  x = 12

Step-by-step explanation:

You want the possible values of x that make it true that ...

  (x +1)²/(x -2) = 16 +(x -3)/(x -2)

The given division expression can be written in terms of quotient and remainder as  ...

  p/q = a +r/q   ⇒   p = aq +r

Here, this means ...

  (x +1)² = 16(x -2) +(x -3)

  x² +2x +1 = 16x -32 +x -3

  x² -15x = -36

  x² -15x +56.25 = 20.25 . . . . . complete the square

  (x -7.5)² = 4.5²

  x = 7.5 ± 4.5 . . . . . . . . . . . . . take the square root, add 7.5

  x = 3 or 12

__

Additional comment

The given quotient-remainder equation has a vertical asymptote at x = 2. When we write it as f(x) = 0, the graph of f(x) is symmetrical about the point (2, -11).

Answer: -12x + 16

Step-by-step explanation:

To find the difference between (−5x+6) and (7x−10), we need to subtract the second expression from the first. So we have:

(−5x+6) - (7x−10)

To subtract the second expression, we can distribute the negative sign to all the terms inside the parentheses:

-5x + 6 - 7x + 10

Then we can combine the like terms:

-12x + 16

Therefore, the difference between (−5x+6) and (7x−10) is -12x + 16.

The probability that the mean weight of the sample of horses would differ from the population mean by greater than 18lbs if 41 horses are sampled at random from the large stable is approximately 0.131 or 13.1%.

Suppose the horses in a large stable have a mean weight of 807lbs and a variance of 5776. We want to find the probability that the mean weight of a sample of 41 horses would differ from the population mean by greater than 18lbs.

Step 1: Calculate the standard deviation of the population.
Standard deviation (σ) = √variance = √5776 = 76lbs.

Step 2: Calculate the standard error of the mean.
Standard error (SE) = σ / √n = 76 / √41 ≈ 11.88lbs, where n is the sample size (41 horses).

Step 3: Calculate the z-score for the difference of 18lbs.
z = (difference - 0) / SE = (18 - 0) / 11.88 ≈ 1.51

Step 4: Find the probability corresponding to the z-score.
Using a z-table, we find that the probability corresponding to a z-score of 1.51 is approximately 0.9345.

Step 5: Calculate the probability of the mean weight differing by more than 18lbs.
Since we are looking for the probability of the mean weight differing by more than 18lbs (in either direction), we need to consider both tails of the distribution.
P(z > 1.51) = 1 - 0.9345 = 0.0655
P(z < -1.51) = 0.0655 (since the distribution is symmetric)

Total probability = P(z > 1.51) + P(z < -1.51) = 0.0655 + 0.0655 = 0.1310

So, the probability that the mean weight of the sample of horses would differ from the population mean by greater than 18lbs if 41 horses are sampled at random from the large stable is approximately 0.131 or 13.1%.

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There are approximately 0.1480 standard deviations (or 3.7 screws) to the right of the mean when there are 1009 screws in the box.  When the automatic filling device delivers 1065 screws to the box, there are approximately 2.6 standard deviations (or 65 screws) to the left of the mean.

To answer this question, we need to use the normal distribution formula.

a. To find how many units to the right of 1000 is 1009, we need to calculate the z-score:

z = (X - μ) / σ

where X = 1009, μ = 1000, and σ = 25.

z = (1009 - 1000) / 25 = 0.36

Using a standard normal distribution table or calculator, we can find that the probability of getting a z-score of 0.36 or higher is 0.3520.

To convert this probability to units to the right of the mean, we subtract it from 0.5 (which represents the area to the left of the mean):

units to the right = 0.5 - 0.3520 = 0.1480

Therefore, there are approximately 0.1480 standard deviations (or 3.7 screws) to the right of the mean when there are 1009 screws in the box.

b. To find the X value that is 2.6 units to the left of the mean, we can rearrange the formula:

X = μ - zσ

where z = -2.6 (since we want units to the left of the mean) and μ and σ are the same as before.

X = 1000 - (-2.6) * 25 = 1065

Therefore, when the automatic filling device delivers 1065 screws to the box, there are approximately 2.6 standard deviations (or 65 screws) to the left of the mean.

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The cost of points for this mortgage is $3,510 rounded to the nearest dollar if Julie pays 2.25 points.

Cost of house =  $225,000.

Mortgage amount =  $156,000

Fixed-rate = 4.5%

Bank offer rate = 4.25%

Points to pay = 2.25 points

If we assume that one point is equal to 1%, then 2.25 points are equal to 2.25% of the loan amount.

The cost of points for the mortgage can be calculated by the product of the loan amount by 2.25%.

Cost of points = 0.0225 × $156,000

Cost of points = $3,510

Therefore, we can conclude that the cost of points for this mortgage is $3,510 rounded to the nearest dollar.

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