The measure of weights of 15 students is normally distributed with a sample mean of 6 and standard deviation of 5. Find the 95% confidence interval for the mean.

The value of the function F(3) will be 1/125. It is obtained by putting the value 3 in the place of x.

A connection between independent variables and the dependent variable is defined by the function. Functions help to represent graphs and equations.

A function is represented by the two variables one is dependent and another one is an independent function. The relation between them is shown as y if dependent and x is the independent variable.

F(x)=(1/5)ˣ

F(3)=(1/5)³

F(3)=1/125

Hence, the value of the function F(3) will be 1/125.

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Answer:

1

Step-by-step explanation:

4-3 = 1

Answer:

1

Step-by-step explanation:

4-3=1

If you had 4 lollipops and you gave your friend 3 lollipops, how many would you have? 4-3=1 You could try it out at home.

The total money spent on a pass and lunch for each student is $850.14.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division.

here,

As mentioned in the question, Passes for 28 pupils and 4 teachers cost the school $778.88 and the school also spends $241.64 on lunch for kids only.

Total number of person  = 28 + 4
                                     = 32
Cost per pass = 778.88 / 32
                     = $24.34
Total passes of students = 25 × 24.34 = 608.5
Total spend on lunch of student = 241.64
Total spend on lunch = 241.64 + 608.5 = $850.14

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The sequence that shows the numbers in order from least to greatest is D. 2.14 < 2.8 < 3.16227766017.

The sequence that shows the numbers in order from least to greatest is D. 2.14 < 2.8 < 3.16227766017.What is the meaning of the inequality symbols?The inequality symbols are mathematical symbols that are used to compare two values.

They indicate the relationship between two values that are not equal to each other. Here are the inequality symbols:

< (less than)≤ (less than or equal to)> (greater than)≥ (greater than or equal to)What is the meaning of the sequence?

A sequence is a set of numbers arranged in a particular order. The order of the numbers in a sequence can be from smallest to largest or largest to smallest.

The sequence D. 2.14 < 2.8 < 3.16227766017 is arranged from smallest to largest because the first number in the sequence, 2.14, is the smallest, and the last number in the sequence, 3.16227766017, is the largest.

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The order of the opperations to simplify this expression is:

1. Parenthesis: Solve the operations to remove the parenthesis.

As:

2. Sum the similar terms: -1 -12:

Or:

Answer:

Option 2.

Step-by-step explanation:

Find the domain by finding where the function is defined. The range is the set of values that correspond with the domain.

Domain: \((- \infty} ,0)\) ∪ \((0, \infty} )\)

Range: \((- \infty} ,0)\)∪\((0, \infty} )\)

Answer:

Option 2.

Step-by-step explanation:

X is a number greater than the equality. Therefore the arrow will go to the bigger side. It also is not equal to the equality hence the cirle is open.

Answer:

I feel ya. It's the second one. Have a nice day.

Step-by-step explanation:

Answer:

Step-by-step explanation:

a+b-4c-a-4b-c=1-12, -3b-5c=-11

a+4b+c-a+3b+2c=12+5, 7b+3c=17

3(-3b-5c)+5(7b+3c)=3(-11)+5(17)

-9b-15c+35b+15c=-33+85

26b=52

b=2, making 7b+3c=17 become

14+3c=17

3c=3

c=1, making a+b-4c=1 become

a+2-4(1)=1

a-2=1

a=3

(a,b,c)=(3,2,1)

Probability helps us to know the chances of an event occurring. The number of times Tamika should expect the spinner to land on green or yellow is 60.

Probability helps us to know the chances of an event occurring.

\(\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}\)

Total number of sections on the spinner = 5

Number of sections with green or yellow sections = 2

Number of trials = 150

Now, the number of times Tamika should expect the spinner to land on green or yellow is,

Expected Number of lands on green or yellow = 150 × (2/5) = 60

Hence, the number of times Tamika should expect the spinner to land on green or yellow is 60.

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The expression becomes: p^(1/2) = p^(1/2 * 1) = p^(1/2) Now we can simplify p^(1/2) as p^1/2 which equals the square root of p.

The property of exponents that must be applied to the expression p^(1/2) to derive p as the result is the Power of a Power Property.

The Power of a Power Property states that when a power is raised to another power, the exponents are multiplied.

For instance, consider the expression p^(1/2). We can apply the Power of a Power Property to this expression as follows: p^(1/2) = (p^(1/2))^1 By applying the Power of a Power Property, the exponent (1/2) is multiplied by the exponent 1, giving a result of 1/2.

Therefore, the expression becomes: p^(1/2) = p^(1/2 * 1) = p^(1/2)Now we can simplify p^(1/2) as p^1/2 which equals the square root of p.

So we have derived p as the result using the Power of a Power Property.

In summary, we must apply the Power of a Power Property to the expression p^(1/2) to derive p as the result.

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Answer:

55R^3

Step-by-step explanation:

V= L X H X D

V= 4 X 5.5 X 2.5

V=55

The value of d when h is 500m is approximately 1,813m

Give the heights above the ground (hm) after it has dropped expressed as:

h = 3/8(d-480),

If h = 500m, then;

500 = 3/8(d - 480)

Cross multiply

500*8 = 3(d - 480)

4000 = 3(d - 480)

Expand to have:

4000 = 3d - 1440

3d = 5440

d = 1,813.3m

Hence the value of d when h is 500m is approximately 1,813m

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Answer:

44

Step-by-step explanation:

vertical angles

Answer:

1/3 foot longer

Step-by-step explanation:

2/3-1/3=1/3

Answer:

Step-by-step explanation:

45 cm + 30 cm x 2 = AREA

Answer:

y = 3x - 11

Step-by-step explanation:

(3, -2) and (5, 4)

m = 4+2/5-3

m = 6/2

m = 3

y = 3x + b

4 = 3(5) + b

4 = 15 + b

b = -11

y = 3x - 11

Answer:

sorry I only know the first page but i couldn't just comment it because of the squares

in order

\((3bc)^{2}\)

\((10mn^{3})^{2}\)

The surface area of the complex solid is 530 square yards.

In this problem we need to determine the surface area of the complex solid, that is, the sum of the area of all faces of the solid. The area formulas required to find the surface area is:

A = w · h

Where:

The surface area of the complex solid is:

A = 2 · (11 yd) · (3 yd) + 2 · (4 yd)² + (12 yd) · (11 yd) + (12 yd) · (3 yd) + (12 yd) · (7 yd) + 2 · (4 yd) · (12 yd) + (12 yd) · (7 yd)

A = 66 yd² + 32 yd² + 132 yd² + 36 yd² + 84 yd² + 96 yd² + 84 yd²

A = 530 yd²

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Answer:

105/136 ≈ 0.772

Step-by-step explanation:

There are 3 socks and 2 colors, so they are either all the same color or 2 will be different colors.

P(different colors)

= 1 − P(same color)

= 1 − ₁₀C₃/₁₇C₃ − ₇C₃/₁₇C₃

= 1 − 120/680 − 35/680

= 1 − 155/680

= 1 − 31/136

= 105/136

≈ 0.772

The value of x for which the two lines are parallel is given as follows:

x = 60º.

We have two parallel lines that are cut by a transversal, and the two angles are between the parallel lines and on the same side of the transversal, meaning that they are consecutive interior angles.

Consecutive interior angles are supplementary, meaning that the sum of their measures is of 180º, hence the value of x can be found as follows:

x + 2x = 180

3x = 180º

x = 180º/3

x = 60º.

The figure is given by the image presented at the end of the answer.

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Answer:

Rhombus and/or Square

Maureen's pension would be $50,035.20.

What is Percentage?

To compute a percentage, divide the value by the entire amount and multiply the result by 100. A percentage is a quantity or ratio that is stated as a fraction of one hundred. The percent sign, "%," is frequently used to represent it.

First, we need to calculate the average of Maureen's three highest salaries:

Average = (107,000 + 107,800 + 108,198) / 3

Average = 322,998 / 3

Average = 107,666

Next, we need to calculate 1.56% of this average:

Percentage = 1.56% * 107,666

Percentage = 1,667.84

Finally, we multiply this percentage by the number of years worked to find the pension:

Pension = 30 * 1,667.84

Pension = 50,035.20

So, Maureen's pension would be $50,035.20.

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Answer:

(a) To find the mean of the data set, sum up all the values and divide by the total number of values.

44 + 44 + 54 + 54 + 65 + 39 + 54 + 44 = 398

Mean = 398 / 8 = 49.75

Rounded to one decimal place, the mean of this data set is 49.8.

(b) To find the median of the data set, i need to arrange the values in ascending order first:

39, 44, 44, 44, 54, 54, 54, 65

The median is the middle value in the sorted data set. In this case, we have 8 values, so the median is the average of the two middle values:

(44 + 54) / 2 = 98 / 2 = 49

Rounded to one decimal place, the median of this data set is 49.0.

(c) To determine the modes of the data set, identify the values that appear most frequently.

In this case, the mode refers to the value(s) that occur(s) with the highest frequency.

From the data set, i see that the value 44 appears three times, while the value 54 also appears three times. Therefore, there are two modes: 44 and 54.

The value of b degrees (angle ABF) is 37 degrees.

A right-angled triangle is a type of triangle that has one angle that measures exactly 90 degrees, which is also known as a right angle. The side opposite to the right angle is called the hypotenuse, while the other two sides are called legs.

The Pythagorean theorem is a fundamental relationship that holds true for all right-angled triangles, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. This theorem can be used to calculate the length of any of the sides of a right-angled triangle, provided that the lengths of the other two sides are known.

Since angle ABC is a right angle, we know that angle ABF and angle CBF are complementary angles (their measures add up to 90 degrees). Therefore, we can find the measure of angle ABF by subtracting the measure of angle CBF from 90 degrees.

To find the measure of angle CBF, we need to use the fact that angles BCF and ECF form a linear pair (they are adjacent angles that add up to 180 degrees). Therefore, angle CBF has a measure of:

CBF = 180 degrees - ECF

To find the measure of angle ECF, we can use the fact that angles AEF and CEF form a linear pair. Therefore, angle ECF has a measure of:

ECF = 180 degrees - AEF

Substituting this into the previous equation, we get:

CBF = 180 degrees - (180 degrees - AEF) = AEF

So, angle CBF has a measure of AEF, which is 53 degrees according to the diagram. Therefore, angle ABF has a measure of:

ABF = 90 degrees - CBF = 90 degrees - 53 degrees = 37 degrees

Therefore, the value of b degrees (angle ABF) is 37 degrees.

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To find f(g(x)), we substitute g(x) in place of x in the function f(x).

f(g(x)) = f(5x/(1-x)) = (5x/(1-x)) / (5 + (5x/(1-x))) = 5x / (1-x+5-5x) = 5x / 6 - 4x/6 = x/6

To find g(f(x)), we substitute f(x) in place of x in the function g(x).

g(f(x)) = g(x/(5+x)) = (5(x/(5+x))) / (1 - (x/(5+x))) = 5x / (5+x-x) = 5x/5 = x

Therefore, f(g(x)) = x/6 and g(f(x)) = x.

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Answer:

When the water level is at the "-4" mark on the pole, the river is 4 feet  below the flood stage.

Step-by-step explanation:

Given

\(Flood\ stage = 0\)

Required

What does -4 represents

From the question, we can deduce that:

\(Above = +ve\ intervals\)

\(Below = -ve\ intervals\)

-4 belongs to the "below" category.

Hence, -4 mark represents 4 feet below the flood stage

Let X and Y be IID Unif(0, 1). the distance between X and Y.Expected value: 0 and Standard deviation: \($\sqrt{\frac{1}{3}}$\)

Expected value:

E(X-Y)

= E(X) - E(Y)

= 0 - 0

= 0

Standard deviation:

Var(X-Y) = Var(X) + Var(Y) = 1 + 1 = 2

SD(X-Y) = \($\sqrt{2}$\)

= \($\sqrt{\frac{1}{3}}$\)

The expected value of X-Y is the difference of the expected values of X and Y, which are both 0 since they are both IID Unif(0, 1). The variance of X-Y is the sum of the variances of X and Y, which are both 1. Since the standard deviation is the square root of the variance, the standard deviation of X-Y is the square root of 2.

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The solution to the compound inequality expression given as 5x + 7 ≤ -3 or 3x - 4 ≥ 11 is x ≤ -2 or x ≥ 5

Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal

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

5x + 7_< -3 or 3x - 4 _> 11

Rewrite the above compound inequality properly

So, we have the following representation

5x + 7 ≤ -3 or 3x - 4 ≥ 11

Evaluate the like terms in the above expression

So, we have the following representation

5x ≤ -10 or 3x ≥ 15

Divide both sides of the expression  by the coefficient of x

So, we have

x ≤ -2 or x ≥ 5

Hence, the solution is x ≤ -2 or x ≥ 5

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