Question 12
A school survey found that 18 out of 30 students prefer pizza to hamburgers. If the school has 400
students, which is the best prediction of the total number of students who prefer pizza? (Hint: Write and
solve a proportion.)

(a) Expected number of repairs per year is 0.33 (b) Standard deviation of number of repairs per year is 0.749, (c) The mean and standard deviation of annual expense are $136.55 and $26.217 respectively.

Standard deviation is a measure in statistics which measures the amount of deviation a set of data has with respect to their mean.

(a) Expected number of repairs for the freezer per year is the sum of the product of number of repairs to their probability.

E(Repairs) = (0 × 0.80) + (1 × 0.11) + (2 × 0.05) + (3 × 0.04)

                 = 0.33

(b) Standard deviation of number of repairs per year can be calculated as,

SD(Repairs) = \(\sqrt{[(0 - 0.33)^{2}(0.8)]+[(1-0.33)^{2}(0.11)] + [(2-0.33)^{2}(0.05)]+[(3-0.33)^{2}(0.04)] }\)

= √ (0.5611)

= 0.749

(c) Mean of the restaurant's annual expense with service contract is,

Mean = Expected cost = $125 + ($35 × 0.33) = $136.55

Standard deviation of the restaurant's annual expense with service contract is,

SD = \(\sqrt{35^{2}(0.5611) }\) = 35 × 0.759 = 26.217

Hence the expected number of repairs is 0.33, standard deviation of number of repairs is 0.749, mean and standard deviation of annual expense is $136.55 and $26.217 respectively.

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Answer:

No

Step-by-step explanation:

When \(x=2\), \(y=-6(2)=-12\), not \(4\).

Answer:

The graph represents a linear function because there is a constant rate of change.

Step-by-step explanation:

Linear functions have constant rate of change,

For any two points (x1, y1) and (x1, y2), rate of change remains constant, it also represents a straight line.

We know this constant as the slope of line passing through these points

\(\dfrac{y_2 - y_1}{x_2 - x_1} = m\)

Therefore, we can say that The graph represents a linear function because there is a constant rate of change.

Hopefully this answer helped you!!

Answer:

Maybe 60

Step-by-step explanation:

I don't know just please guess sorry but can you mark as brainiest.

Answer:

1

Step-by-step explanation:

i think

z = 20°

Hope it helps! Please do comment if you have any query.

Thank you

Answer:

118.3

Step-by-step explanation:

The formula for the area is a triangle is base*height/2

Area = 18.2*13/2 = 118.3

Answer:

118.3

1/2b×h

1/2(13)x18.2

6.5×18.2

118.3m^2

In mathematics, "\(a^2\)" denotes the square of a number or variable "a." It is calculated by multiplying "a" by itself.

4For example, if "a" is 5, then a^2 would be 5*5, which equals 25. When "a" represents a positive number, its square is always positive.

If "a" is negative, its square is still positive since a negative multiplied by a negative results in a positive.

In geometrical terms, if "a" represents the length of the side of a square, then a^2 represents the area of that square. This notation is part of the general concept of exponentiation.

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The Question in English

What does a^2 mean in mathematics

Answer:

3(x-3)(x+3)

Step-by-step explanation:

First, factor out 3 from the expression: 3(x²-9)

Second, use a²-b²=(a-b)(a+b) to factor the expression: 3(x-3) · (x+3)

In a proportional relationship between two quantities, the constant of proportionality, often denoted by the letter "k," represents the value that relates the two quantities. The equation y = kx is the standard form for expressing a proportional relationship, where "y" and "x" are the variables representing the two quantities.

Here's a breakdown of the components in the equation:

y: Represents the dependent variable, which is the quantity that depends on the other variable. It is usually the output or the variable being measured.

x: Represents the independent variable, which is the quantity that determines or influences the other variable. It is typically the input or the variable being controlled.

k: Represents the constant of proportionality. It indicates the ratio between the values of y and x. For any given value of x, multiplying it by k will give you the corresponding value of y.

The constant of proportionality, k, is specific to the particular proportional relationship being considered. It remains constant as long as the relationship between x and y remains proportional. If the relationship is linear, k also represents the slope of the line.

For example, if we have a proportional relationship between the distance traveled, y, and the time taken, x, with a constant of proportionality, k = 60 (representing 60 miles per hour), the equation would be y = 60x. This equation implies that for each unit increase in x (in hours), y (in miles) will increase by 60 units.

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The solution to this system of equations is dependent.

Dependent matrix is a matrix where one or more rows can be expressed as a linear combination of the other rows. This means that the rows are not linearly independent, and there is redundancy in the information they provide.

A dependent matrix has less than full rank, which means that the rank of the matrix is less than the number of rows or columns. In a dependent matrix, one or more variables can be expressed in terms of the other variables, and the system of equations represented by the matrix has infinitely many solutions.

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When computing the given expressions for f(x) = 3x - 1, we find that f(3 + 1) = 15, f(3) + f(1) = 8, f(3-1) = 5, f(3) = 8, f(1) = 2, and f(3-1) = 5.

To find f(3 + 1), we substitute the value of 3 + 1 into the expression for f(x): f(3 + 1) = 3(3 + 1) - 1 = 12 - 1 = 11.

Next, to calculate f(3) + f(1), we substitute the values of 3 and 1 into the expression for f(x) separately and add them together: f(3) + f(1) = (3 * 3 - 1) + (3 * 1 - 1) = 8.

For f(3-1), we substitute the value of 3 - 1 into the expression for f(x): f(3-1) = 3(3-1) - 1 = 5.

Since f(3) and f(1) are both defined as 3x - 1, they have the same value: f(3) = f(1) = 8.

Finally, to compute f(3) f(1), we multiply the values of f(3) and f(1) together: f(3) f(1) = (3 * 3 - 1)(3 * 1 - 1) = 5.

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Answer:

y= x ^3 - 4x

Step-by-step explanation:

Regroup terms.

y=x^3 +2x−6x

Simplify x^3 +2x−6x  to x^3 −4x.

AAAAANNNNNnnNNND the answer  is

y= x^3 - 4x

IN GRAPH

Answer:

102 cups of water

Step-by-step explanation: If you need 34 cups of water for every 2 cups of flour, you can cut the 6 in half to get 3. 3 times 34 is 102.

The U.N. Resolution 1373 further enhanced the President's "imperial" powers under President George W. Bush by providing him with the authority to take necessary actions to protect American national security.  

Additionally, it permitted the use of force to deter terrorism and included measures to prevent terrorist financing and money laundering. Resolution 1373 reinforced the Presidential powers in various ways. Firstly, it authorized the President to utilize all appropriate military power to prevent and respond to acts of international terrorism. It allowed the President to seize and freeze assets that are believed to belong to terrorist groups, and it required states to stop providing sanctuary for terrorists and dismantle terrorist networks. Additionally, it permitted the President to take necessary measures to ensure that terrorists were not allowed to enter or transit their territories. Finally, Resolution 1373 obliged all states to cooperate fully in the struggle against terrorism by sharing information about terrorist activities with other states and exchanging financial and travel information.

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Answer:

B

Step-by-step explanation:

To make it easy

Answer:

12.60.

Step-by-step explanation:

12.00 × 5%=.6

,6 + 12.00= 12.60

Step-by-step explanation:

the given speed is

63 cm / 2 days

1 m = 100 cm

therefore, m = cm/100.

so,

63 cm = 0.63 m

1 day = 24 h

therefore,

2 days = 24×2 = 48 h

so, we have a speed of

0.63 m / 48 h

we need to get the speed of meters in 1 hour.

so, we need to do a normal fraction operation.

e.g. when we have 43/10, but we want to have 1 in the denominator (bottom part).

what do we do ? well, we divide top and bottom (to keep the total value of the fraction unchanged) by 10 and get

4.3/1 = 4.3

we do the same with

0.63 m / 48 h

as we want to have only 1 hour in the denominator.

we divide top and bottom by 48 :

0.63/48 / 1 h = 0.013125 m/h ≈ 0.01 m/h

A. statistically significant difference in the mean blood hemoglobin levels between breastfed infants and formula-fed infants at α = 0.05.

B. the 95% confidence interval for the difference in population means between breast-fed infants and formula-fed infants is (−0.06, 1.18).

C. Both the hypothesis test and the confidence interval lead to the same conclusion that there is a difference in the mean blood hemoglobin levels between the two feeding regimens.

What is null hypothesis?

In statistics, the null hypothesis (H0) is a statement that assumes that there is no significant difference between two or more groups, samples, or populations.

(a) To test the hypothesis that there is a difference in the population means between breast-fed infants and formula-fed infants, we can use a two-sample t-test with equal variances. The null hypothesis is that the population means are equal, and the alternative hypothesis is that they are not equal. Using α = 0.05 as the significance level, the critical value for a two-tailed test with 40 degrees of freedom is ±2.021.

The test statistic can be calculated as:

t = (x1 - x2) / (Sp * √(1/n1 + 1/n2))

where x1 and x2 are the sample means, Sp is the pooled standard deviation, and n1 and n2 are the sample sizes. The pooled standard deviation can be calculated as:

Sp = √(((n1 - 1) * s1² + (n2 - 1) * s2²) / (n1 + n2 - 2))

where s1 and s2 are the sample standard deviations.

Plugging in the values from the table, we get:

t = (13.3 - 12.4) / (1.776 * √(1/23 + 1/19)) = 2.21

Since the absolute value of the test statistic is greater than the critical value, we reject the null hypothesis and conclude that there is a statistically significant difference in the mean blood hemoglobin levels between breastfed infants and formula-fed infants at α = 0.05.

(b) To construct a 95% confidence interval for the difference in population means between breast-fed infants and formula-fed infants, we can use the formula:

(x1 - x2) ± tα/2,Sp * √(1/n1 + 1/n2)

where tα/2,Sp is the critical value of the t-distribution with (n1 + n2 - 2) degrees of freedom and α/2 as the significance level.

Plugging in the values from the table, we get:

(x1 - x2) ± tα/2,Sp * √(1/n1 + 1/n2)

= (13.3 - 12.4) ± 2.021 * 1.776 * √(1/23 + 1/19)

= 0.56 ± 0.62

Therefore, the 95% confidence interval for the difference in population means between breast-fed infants and formula-fed infants is (−0.06, 1.18).

(c) The hypothesis test and the confidence interval both lead to the conclusion that there is a difference in the mean blood hemoglobin levels between breast-fed infants and formula-fed infants. In part (a), we rejected the null hypothesis that the population means are equal, which means we concluded that there is a difference. In part (b), the confidence interval does not contain 0, which means we can reject the null hypothesis that the difference in means is 0 at the 95% confidence level.

Therefore, both the hypothesis test and the confidence interval lead to the same conclusion that there is a difference in the mean blood hemoglobin levels between the two feeding regimens.

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Answer:

16.2 U.S. Dollars  -  I hope this helps! :D

Step-by-step explanation:

Answer:

60 degrees

Step-by-step explanation:

ACD and ACB are complementary angles. Find ACB=30 degrees. Subtract 30 from 90 degrees. ACD=60 degrees.

Answer:

ACD=60

BCA=30

BCD=90

90-30=60

Considering the equations for the length of each segment, the numerical length of line ln is of 17 units.

Line segment ln is divided by the point m, hence the length of the line can be written according to the following equation:

ln = lm + mn.

The measures are given as follows:

Hence, using the equation we can solve for x, as follows:

ln = lm + mn.

4x + 9 = 2x + 7 + 3x

5x + 7 = 4x + 9

x = 2.

Hence the numerical length of line ln is given by:

ln = 4x + 9 = 4(2) + 9 = 8 + 9 = 17 units.

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There is no "best approximate solution" for this system of linear equations since no solution exists.

The given system of linear equations is y = -1 and y = 1. These are two horizontal lines parallel to the x-axis, where one line is located at y = -1 and the other at y = 1.

When we solve this system of equations, we find that there is no common solution for the variables x and y. The lines y = -1 and y = 1 do not intersect, meaning there is no point that satisfies both equations simultaneously.

On a graph, these two lines will appear as parallel lines running horizontally at different heights on the y-axis. They will never cross or intersect.

Therefore, there is no "best approximate solution" for this system of linear equations since no solution exists.

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Answer:

Step-by-step explanation:

The inequality as per question:

Its solution is:

It means on the number line a closed circle is at 80 and shaded area is to the right

Correct choice is C

Answer:

C! "A number line going from 78 to 82. A closed circle is at 80. Everything to the right of the circle is shaded."

Step-by-step explanation:

Good Luck!!!!

To solve the equation in part a and determine the mystery weight, we used the following properties of equality:

Addition property: This property states that if we add the same number to both sides of an equation, the equality is preserved. In this case, we added 23 grams to both sides of the equation to isolate the variable.

Subtraction property: This property states that if we subtract the same number from both sides of an equation, the equality is preserved. In this case, we subtracted 8 grams from both sides of the equation to isolate the variable.

Multiplication property: This property states that if we multiply both sides of an equation by the same number, the equality is preserved. In this case, we multiplied both sides of the equation by 3 to isolate the variable.

Division property: This property states that if we divide both sides of an equation by the same number (excluding 0), the equality is preserved. In this case, we divided both sides of the equation by 2 to isolate the variable.

By using these properties of equality, we were able to manipulate the equation and isolate the variable to determine the mystery weight.

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Answer:

Reflection only and rotation then translation.

Step-by-step explanation:

im not sure

Answer:

look at the picture below

Step-by-step explanation:

Edna should leave at 2:07 PM in order to arrive at Jake's party by 2:30 PM

To determine the time Edna should leave, we need to subtract the travel time from the desired arrival time.

If Edna needs to be at Jake's party at 2:30 PM and it takes her 23 minutes to drive there, she should leave 23 minutes before 2:30 PM.

To calculate the departure time, we subtract 23 minutes from 2:30 PM:

2:30 PM - 23 minutes = 2:07 PM

Therefore, Edna should leave at 2:07 PM in order to arrive at Jake's party by 2:30 PM

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