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A 95% confidence interval for the population mean reduction in cholesterol level is (19.78, 28.22) mg/dl, based on a sample mean of 24 mg/dl and a standard deviation of 15 mg/dl.

Using the information, we can compute a confidence interval  for the population mean decrease in cholesterol level as follows:

1. Calculate the standard error of the mean:

standard error = standard deviation/sqrt(sample size)

= 15/sqrt(50)

= 2.12

2. Calculate the margin of error using a t-distribution with (n-1) degrees of freedom at 95% confidence level:

margin of error = t_(n-1, 0.025) * standard error

= t_(49, 0.025) * 2.12 (using a t-table)

= 2.009 * 2.12

= 4.26

3. Calculate the confidence interval by subtracting and adding the margin of error to the sample mean:

CI = sample mean +/ - margin of error

= 24 +/ - 4.26

= (19.74, 28.26)

In this manner, we can say with 95% certainty that the true mean reduction in cholesterol level following one month of drug of the new medication is between 19.74 mg/dl and 28.26 mg/dl. Since the lower limit reaches the confidence interval (19.74 mg/dl) is greater than 20 mg/dl, we can reason that there is persuading proof that the new medication is powerful in lessening cholesterol level following one month of purpose.

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The variance of the sample is 17.05. However, none of the given options matches with this value. The closest option is option (d) 16.5.

Variance is a measure of the spread or variability of a set of data. It is the average of the squared differences from the mean. The formula for variance is:

Variance = (sum of squared deviations from the mean) / (number of observations - 1)

where the squared deviation from the mean is the difference between each data point and the mean of the data set, squared. The variance is useful in statistical analysis and can provide information about the distribution of the data. A higher variance indicates that the data is more spread out, while a lower variance indicates that the data is clustered more closely around the mean.

In the given question,

To find the variance of the sample, we can use the formula:

Variance = [(sum of squared deviations from the mean)/ (number of observations - 1)]

First, we need to find the squared deviation of each observation from the mean, which is the difference between each observation and the mean, squared:

(3-5.4)² = 5.76

(5-5.4)² = 0.16

(12-5.4)² = 43.56

(3-5.4)²= 5.76

(2-5.4)²= 12.96

Next, we need to sum up these squared deviations:

5.76 + 0.16 + 43.56 + 5.76 + 12.96 = 68.2

Then, we divide the sum of squared deviations by the number of observations minus 1:

Variance = 68.2/(5-1) = 17.05

Therefore, the variance of the sample is 17.05. However, none of the given options matches with this value. The closest option is option (d) 16.5.

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Answer:

17

Step-by-step explanation:

The number of vertical angles are 6

The number of linear angles are 6

The value of x is 20

Vertical angles are defined as a pair of non-adjacent angles that are formed by the intersection of two straight lines.

Four angles are created from this intersection.

Linear angles are defined as those angles that are formed when two lines intersect each other at a single point.

Note that supplementary angles are angles that sum up to 180 degrees.

Then, we have;

<1 + <5 = 180

substitute the angles

2x + 10 + 5x + 30 = 180

collect the like terms

7x = 180 -40

7x = 140

Make 'x' the subject

x = 20

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The value of x in the given digram using trigonometry to the nearest tenth is 7.15.

In planar geometry, an angle is a form created by two rays or lines that terminate in the same place. The name "angle" comes from the Latin "angulus," which means "corner". The vertex and the two rays, which are referred to as the sides of an angle, are the shared termini of two rays.

Given an angle and the length of the adjacent side, we are to determine the value of the hypotenuse using cos.

Cos = adjacent / hypotenuse

cos 33 = 6 /x

x = 6 / cos 33

x = 6 / 0.83867

x = 7.15

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The man had $1.60 at first.

What is an equation?

An equation is a statement that shows that two expressions are equal. It contains an equals sign "=" and may include variables, constants, coefficients, and mathematical operations such as addition, subtraction, multiplication, and division.

Let's assume the man had x amount of money at first.

Then he spent 1/8x on a package of cigarettes and 3 times as much, or 3/8x, on a meal.

So he spent a total of 1/8x + 3/8x = 1/2x of his money.

If he had 80 cents left, that means he spent x - 0.8.

So we can set up an equation:

1/2x = x - 0.8

Solving for x:

1/2x - x = -0.8

-1/2x = -0.8

x = (-0.8)/(-1/2)

x = 1.6

Therefore, the man had $1.60 at first.

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Answer:

10

Step-by-step explanation:

We can use the distance formula to find the distance between the two points:

Distance = √((x2 - x1)^2 + (y2 - y1)^2)

Plugging in the coordinates of A and B, we get:

Distance = √((-2 - 6)^2 + (-1 - 5)^2)

Distance = √((-8)^2 + (-6)^2)

Distance = √(64 + 36)

Distance = √100

Distance = 10

Therefore, the distance between A(6, 5) and B(−2, −1) is 10 units.

Answer: The equation for the 7th grade is y = 5x + 7, where y is the total number of items collected and x is the number of days. The initial value is 7 and the slope is 5.

The equation for the 8th grade is y = 8x + 20, where y is the total number of items collected and x is the number of days. The initial value is 20 and the slope is 8.

Therefore, the 8th grade has a greater slope (8) compared to the 7th grade (5). The 8th grade also has a greater initial value (20) compared to the 7th grade (7).

Step-by-step explanation:

Answer:

The answer would be 80.

Step-by-step explanation:

First you want to add 16 and 24.

Next you want to multiply that answer by 2.

Then you have your answer and I hope this helps

Answer:

64 %

Step-by-step explanation:

To change a fraction to a percent, we need the denominator as 100.

16        4

----  * -----

25       4

64

-----

100

Percent means out of 100, so the percent is 64 %

Answer:

graph A is the correct graph.

The graph of the function is plotted by graph A

Graphs behave differently at various x-intercepts. Sometimes the graph will cross over the x-axis at an intercept. Other times the graph will touch the x-axis and bounce off.

Identify the even and odd multiplicities of the polynomial functions' zeros.

Using end behavior, turning points, intercepts, and the Intermediate Value Theorem, plot the graph of a polynomial function.

The graphs cross or are tangent to the x-axis at these x-values for zeros with even multiplicities. The graphs cross or intersect the x-axis at these x-values for zeros with odd multiplicities

Given data ,

Let the function be represented as f ( x )

Now , the value of f ( x ) is

f ( x ) = ( x - 2 ) ( x + 5 )

To find the x-intercepts (or zeros) of the function f(x) = (x - 2)(x + 5), we need to set the function equal to zero and solve for x.

f ( x ) = ( x - 2 ) ( x + 5 ) = 0

This product is zero if and only if one of the factors is zero. So we can set each factor equal to zero and solve for x.

x - 2 = 0 or x + 5 = 0

x = 2 or x = -5

Hence , the x-intercepts of the function are x = 2 and x = -5 and the graph is plotted

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The volume of the cheese is approximately 135 cubic centimeters.

To calculate the volume of the cheese, we can use the formula:

Volume = Mass / Density

Given that the mass of the cheese is 216 grams and the density is 1.6 g/cm³, we can plug these values into the formula:

Volume = 216 g / 1.6 g/cm³

Now, we need to convert the units so that they are consistent. Since density is given in grams per cubic centimeter (g/cm³), we need to convert the mass from grams to cubic centimeters.

1 gram is equal to 1 cubic centimeter, so:

Volume = 216 cm³ / 1.6 cm³

Now, divide:

Volume ≈ 135 cm³

The volume of the cheese is approximately 135 cubic centimeters.

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After addressing the issue at hand, we can state that  As a result, the square value of x to three significant figures is 5.03 cm.

According to Euclidean geometry, a square is an equilateral quadrilateral with four equal sides and four equal angles. It is also referred to as a rectangle with two neighbouring sides of equal length. A square is an equilateral quadrilateral because it has four equal sides and four equal angles. Square angles are 90-degree or straight angles. Furthermore, the diagonals of the square are evenly spaced and split at a 90-degree angle. a neighbouring rectangle with two equal sides. a quadrilateral with four equal-length sides and four right angles. A parallelogram with two adjacent, equal sides forming a right angle. A rhombus with straight sides.

The Pythagorean theorem can be used to find the square's diagonal:

2x2 = diagonal2 = x2 + x2 = 2x2[tex]x * \sqrt = diagonal = sqrt(2x2) (2)[/tex]

Because the diagonal equals the circle's diameter, the radius is half of the diagonal:

x * \sqrt(2) / 2 = radius

We can now use the formula for the area of a circle to calculate x:

[tex]\pi * radius2 = area[/tex]

[tex]\Pi * (x * sqrt(2) / 2)2 = 56[/tex]

[tex]56 = pi * (x^2 / 2)[/tex]

[tex]x^2 = 112 / pi[/tex]

x = 5.027 (rounded to 3 significant figures) (rounded to 3 significant figures)

As a result, the value of x to three significant figures is 5.03 cm.

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Using the information provided, we can construct a 90% confidence interval for the mean number of hours a student studies per week as follows: (15.34, 16.66).

The given problem involves estimating the mean hours of studying per week for a population of students using a confidence interval. A simple random sample of 55 students is taken, and the sample mean is computed to be 16 hours per week. The population standard deviation is assumed to be known to be 3.1 hours per week. Using the formula for a confidence interval for the population mean with known standard deviation and a significance level of 0.10 (corresponding to a 90% confidence level), the lower and upper bounds of the interval are calculated to be 15.19 and 16.81 hours per week, respectively. This means that we can be 90% confident that the true mean hours of studying per week for the population of students lies within this interval

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Complete question:

A professor wants to estimate how many hours per week her students study. A simple random sample of 55 students had a mean of 16 hours of studying per week. Construct a 90% confidence interval for the mean number of hours a student studies per week. Assume that the population standard deviation is known to be 3.1 hours per week. Round to two decimal places.

The surface area of the cylinder in terms of π is 15.98π in².

What is surface area ?

Surface area is the measure of the total area that the surface of a three-dimensional object covers. In other words, it is the sum of the areas of all the faces or surfaces of the object. For example, the surface area of a rectangular prism is the sum of the areas of its six rectangular faces.

To find the surface area of the cylinder, we need to find the area of each of its faces and add them up.

The cylinder has two circular faces, each with a diameter of 3.4 inches. The formula for the area of a circle is A = πr², where r is the radius of the circle. The radius of each circle is half of the diameter, so r = 1.7 inches. Therefore, the area of one circular face is:

A1 = π(1.7 in)² = 9.05π in²

Since there are two circular faces, their total area is:

A1_total = 2 × A1 = 18.1π in²

The cylinder also has a rectangular face, which is the curved surface between the two circular faces. The height of this rectangle is given as 3 inches. The length of this rectangle is the same as the circumference of one of the circular faces, which is πd (where d is the diameter). Therefore, the length of the rectangle is:

L = πd = π(3.4 in) = 10.64 in

The area of the rectangular face is:

A2 = L × h = 10.64 in × 3 in = 31.92 in²

Therefore, the total surface area of the cylinder is:

A_total = A1_total + A2 = 18.1π in² + 31.92 in² = 49.02π in²

Rounding to two decimal places, we get:

A_total ≈ 15.98π in²

So the answer is: 15.98π in².

Therefore, the surface area of the cylinder in terms of π is 15.98π in².

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Answer: 15.98π in²

Step-by-step explanation:

did test and it is right

According to the image, we can see that 3 rectangles are half-shaded= 1.5 units²,

A square is a quadrilateral with four equal sides and four equal angles that is a regular quadrilateral. The square's angles are at a straight angle or 90 degrees. The square's diagonals are also equal and split at a 90-degree angle.

A rectangle with two opposite sides that have the same length can also be referred to as a square.

P.S: Rectangle attached in image.

According to the image, we can see that 3 rectangles are half-shaded.

This means that:

Half-shaded square + Half-shaded square + Half-shaded square

=> 0.5 + 0.5 + 0.5

=> 1.5 units²

Check:

To check our answer:

3 x 0.5 = Area of rectangle

=> 1.5 units² = Area of rectangle

Hence, our explanation is correct.

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The estimated total percentage of the company that exercised at least 3 times a week is approximately 20.5%.

Using the Hansen-Hurwitz dropout plan (method), the estimated total percentage of the company that exercised at least 3 times a week is approximately 20.5%. This can be calculated by multiplying the response rate of the survey (4860/6480) by the response rate of the sample (7/80).

The response rate of the survey is 0.7479 and the response rate of the sample is 0.0875. To get the estimated total percentage of the company that exercised at least 3 times a week, you would multiply these two numbers together to get 0.205 (0.7479 x 0.0875 = 0.205).

So, the percentage is 20.5%.

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The algebraic expression that represents the sentence "N increased by 25%" is 0.25N.

Hence the correct option is A.

This means that N is multiplied by 0.25 or 1/4. To find the result of N increased by 25%, you simply need to multiply N by 0.25 and add the result to the original value of N. The option A, 0.25N, represents this concept in a clear and concise manner.

The other options (B, C, and D) are either incomplete or incorrect. It is important to understand the concept of percentage increase and how it is represented algebraically, as it is a common operation in many mathematical and real-life scenarios, such as calculating interest rates, growth rates, and inflation rates.

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Answer:

72.25π cm²

Step-by-step explanation:

C = 2πr

17π cm = 2πr

Divide both sides by 2π.

8.5 cm = r

r = 8.5 cm

A = πr²

A = π × (8.5 cm)²

A = 72.25π cm²

Bi-weekly gross paycheck based on 40 hours a week at a rate of $18.25 per hour is $1,460.

What is multiplication ?

Multiplication is a basic arithmetic operation that involves combining two or more numbers to find their product or the total number of items when a certain number is repeated a certain number of times. In multiplication, the numbers being combined are called factors, and the result is called the product.

To calculate your bi-weekly gross paycheck, you need to multiply your hourly rate by the number of hours you work per week and then multiply that by 2 to account for two weeks in a pay period.

Hourly rate: $18.25

Weekly hours: 40

Bi-weekly hours: 40 x 2 = 80

Bi-weekly gross paycheck: Hourly rate x Bi-weekly hours

Bi-weekly gross paycheck: $18.25 x 80 = $1,460

Therefore, your bi-weekly gross paycheck based on 40 hours a week at a rate of $18.25 per hour is $1,460.

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The cost of the plan for the limited talk and text is $50 with an additional cost of $22.99 for each gigabyte of data.

Generally, a mathematical function means a rule that gives value of a dependent variable that corresponds to specified values of one or more independent variables. It can take an input from many variables but will  always give the same output, unique to that function.

We are given that "H(g) = 22.99g + 50", where H represents the cost, in dollars, and g represents the number of gigabytes of data. The main answer is based on the given function where the constant term of 50 represents the cost of the plan for limited talk and text, and the coefficient of 22.99 represents the additional cost for each gigabyte of data used.

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The total cost of the mirror based on its area is obtained as $9.80.

What is area?

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.

The area of the bathroom mirror can be found by multiplying its length and width -

Area = Length × Width

Area = 5 feet × 4 feet

Area = 20 square feet

Since the mirror sells for $0.49 per square foot, we can find the total cost of the mirror by multiplying the area of the mirror by the cost per square foot -

Total Cost = Area × Cost per square foot

Total Cost = 20 square feet × $0.49 per square foot

Total Cost = $9.80

Therefore, the total cost of the bathroom mirror will be $9.80.

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Answer: To calculate the amount of the element remaining after 16 minutes, we can use the formula:

A = P * (1 - r)^t

where:

A = amount remaining after time t

P = initial amount

r = rate of decay per unit time (as a decimal)

t = time elapsed

In this case, we have:

P = 420 grams

r = 0.118 per minute

t = 16 minutes

Substituting these values into the formula, we get:

A = 420 * (1 - 0.118)^16

A ≈ 123.82 grams

Rounding this answer to the nearest tenth of a gram, we get:

A ≈ 123.8 grams

Therefore, approximately 123.8 grams of the element remain after 16 minutes.

Answer:

information provided:

ordinary annuity = $650

Number of periods (n) = 20 years

Interest rate (r)= 11 percent

After calculating we get, x-intercept is (-8/3, 0), y-intercept is (0, -16), slope is -6, f(3) = (-34) and So when f(x) = 110, x = -21.

To find the characteristics of the linear function 30x + 5y = -80:

To find the x-intercept, we set y = 0 and solve for x:

30x + 5(0) = -80

30x = -80x = -8/3

So the x-intercept is (-8/3, 0).

To find the y-intercept, we set x = 0 and solve for y:

30(0) + 5y = -80

5y = -80y = -16

So the y-intercept is (0, -16).

To find the slope, we solve for y in terms of x by rearranging the equation to slope-intercept form, y = mx + b:

30x + 5y = -80

5y = -30x - 80y = -6x - 16

So the slope is -6.

To find f(3), we substitute x = 3 into the equation and solve for y:

30(3) + 5y = -80

90 + 5y = -80

5y = -170y = -34

So f(3) = (-34).

To find x when f(x) = 110, we substitute y = 110 into the equation and solve for x:

30x + 5(110) = -80

30x + 550 = -80

30x = -6

30x = -21

So when f(x) = 110, x = -21.

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Answer:

10(15h-125)

Step-by-step explanation:

In this question, h is represented for hours. we want to see how much money sally will have after 10 weeks. We know each hour she makes $15 per h. This will look like 15h. We also know her bills cost $125 each week so we have to subtract 125 from 15h which the equation will now look like

15h-125.

Now we want to know how much she will have after 10 weeks so we will now the equation will look like 10(15h-125).

Answer: Pls I don't know this

Step-by-step explanation:

Pls I don't mean to hurt your feelings but my brother knows this and I have sent it to him

The safe distance between the supports to carry the load of 1500 pounds is found to be 8 meters.

One kind of proportionality relationship is inverse proportion. If two quantities remain inversely related, one will increase while the other will decrease.

The area of a circle is proportional to its radius, which serves as an illustration of direct proportion.

The equation for inverse proportion of the weight carried along with distance is:

P = 5400 /D

P is load in pounds (lb)

D is the safe distance.

Then, distance to carry 1500 lb of load is:

1500 lb = 1500*0.45 kg

1500 lb = 675 kg

675  = 5400 /D

D = 5400/675

D = 8 meters

Thus, safe distance between the supports to carry the safe load of 1500 pounds is found to be 8 meters.

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The solution to the system of equations is (3, -7).

To find the solution of these two equations, we need to find the values of x and y that satisfy both equations simultaneously.

We can set the two equations equal to each other to get:

-5x + 8 = x/3 - 8

Multiplying both sides by 3, we get:

-15x + 24 = x - 24

Simplifying, we get:

-16x = -48

Dividing both sides by -16, we get:

x = 3

Now that we know x = 3, we can substitute it into either of the original equations to find y. Let's use the equation y = -5x + 8:

y = -5(3) + 8 = -7

Therefore, the solution to the system of equations is (3, -7).

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Answer:

A. 450 trucks

Step-by-step explanation:

Given

Answer
A. 450 trucks

Answer:

d = [tex]\frac{2}{5}[/tex]

Step-by-step explanation:

[tex]\frac{3}{2}[/tex] = 5d - [tex]\frac{1}{2}[/tex]

multiply through by 2 to clear the fractions

3 = 10d - 1 ( add 1 to both sides )

4 = 10d ( divide both sides by 10 )

[tex]\frac{4}{10}[/tex] = d , then

d = [tex]\frac{2}{5}[/tex]