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Question 12

A recent conference had 750 people in attendance. In one exhibit room of 70 people, there were 18 teachers and 52 principals. What prediction can you make about the number of principals in attendance at the conference?

There were about 193 principals in attendance.
There were about 260 principals in attendance.
There were about 557 principals in attendance.
There were about 680 principals in attendance.

Question 13

A college cafeteria is looking for a new dessert to offer its 4,000 students. The table shows the preference of 225 students.


Ice Cream Candy Cake Pie Cookies
81 9 72 36 27


Which statement is the best prediction about the number of cookies the college will need?
The college will have about 480 students who prefer cookies.
The college will have about 640 students who prefer cookies.
The college will have about 1,280 students who prefer cookies.
The college will have about 1,440 students who prefer cookies.

Question 14

A random sample of 100 middle schoolers were asked about their favorite sport. The following data was collected from the students.


Sport Basketball Baseball Soccer Tennis
Number of Students 17 12 27 44


Which of the following graphs correctly displays the data?
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44

Question 15

The line plots represent data collected on the travel times to school from two groups of 15 students.

A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 4, 6, 14, and 28. There are two dots above 10, 12, 18, and 22. There are three dots above 16. The graph is titled Bus 47 Travel Times.

A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 8, 9, 18, 20, and 22. There are two dots above 6, 10, 12, 14, and 16. The graph is titled Bus 18 Travel Times.

Compare the data and use the correct measure of center to determine which bus typically has the faster travel time. Round your answer to the nearest whole number, if necessary, and explain your answer.

Bus 18, with a median of 13
Bus 47, with a median of 16
Bus 18, with a mean of 13
Bus 47, with a mean of 16

The value of x Clare will get as a wrong solution using the wrong diagram would be: x = 32.

She should replace the 2 with x in the diagram she drew, which will give the right solution as: x = 17.

The diagram Clare drew to match the algebraic equation, 2x + 16 = 50, is shown in the diagram attached below.

The diagram is however incorrect. The value of x she will get using the diagram would be:

2 + x + 16 = 50

Add like terms

x + 18 = 50

Subtract 18 from each side

x = 50 - 18

x = 32

To fix the diagram, she should remove 2 and replace it with x. Thus, the new value of x would be:

2x + 16 = 50

2x = 50 - 16

2x = 34

x = 17

In summary, the value of x Clare will get as a wrong solution using the wrong diagram would be: x = 32.

She should replace the 2 with x in the diagram she drew, which will give the right solution as: x = 17.

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There are 40,320 different ways the race with 8 runners can be completed.

To determine the number of different ways a race with 8 runners can be completed, we can use the concept of permutations.

In a race with no tie, the order in which the runners finish matters. We want to find the number of permutations of 8 runners.

The formula to calculate permutations is given by n!, where n represents the number of items being permuted.

In this case, there are 8 runners, so the number of different ways the race can be completed is:

8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320.

Each permutation represents a unique arrangement of the runners crossing the finish line. By considering the order of finish for each runner, we account for all possible outcomes in the race.

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Answer:

The endpoint would be  (-5, -15).

Step-by-step explanation:

:)

Probability is a measure that indicates the chances of an event happening. It's calculated by dividing the number of desired outcomes by the total number of possible outcomes. In this case, we'll calculate the probability that a customer is at least 30 but no older than 50. Suppose the variable X represents the age of a customer.

Then we need to find P(30 ≤ X ≤ 50).To solve this problem, we'll use the cumulative distribution function (CDF) of X. The CDF F(x) gives the probability that X is less than or equal to x. That is,F(x) = P(X ≤ x)Using the CDF, we can find the probability that a customer is younger than or equal to 50 years old and then subtract the probability that the customer is younger than or equal to 30 years old, which gives us the probability that the customer is at least 30 but no older than 50 years old.Using the given data, we know that the mean is 40 and the standard deviation is 5.

Thus we can use the formula for the standard normal distribution to find the required probability, Z = (x - μ) / σWhere Z is the standard score or z-score, x is the age of the customer, μ is the mean and σ is the standard deviation. Substituting the values into the formula, we get:Z1 = (50 - 40) / 5 = 2Z2 = (30 - 40) / 5 = -2

We can use a z-table or calculator to find the probabilities associated with the standard scores. Using the z-table, we find that the probability that a customer is less than or equal to 50 years old is P(Z ≤ 2) = 0.9772 and the probability that a customer is less than or equal to 30 years old is P(Z ≤ -2) = 0.0228.

Therefore, the probability that a customer is at least 30 but no older than 50 years old is:P(30 ≤ X ≤ 50) = P(Z ≤ 2) - P(Z ≤ -2) = 0.9772 - 0.0228 = 0.9544This means that the probability that the customer is at least 30 but no older than 50 is 0.9544 or 95.44%.

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The probability that a randomly selected car with no 4-wheel drive has third-row seats is given by: Option B: 0.4

Suppose that there are finite elementary events in the sample space of the considered experiment, and all are equally likely.

Then, suppose we want to find the probability of an event E.

Then, its probability is given as

\(P(E) = \dfrac{\text{Number of favorable cases}}{\text{Number of total cases}} = \dfrac{n(E)}{n(S)}\)

where favorable cases are those elementary events who belong to E, and total cases are the size of the sample space.

For two events A and B, by chain rule, we have:

\(P(A \cap B) = P(B)P(A|B) = P(A)P(B|A)\)

where P(A|B) is probability of occurrence of A given that B already occurred.

For this case, the table given is:

Entries                          4-wheel drive        No 4-wheel drive        Total

Third Row Seats                  18                                12                        30

No Third Row Seats             7                                28                        35

Total                                     25                               40                        65

Let we take

A = event that a randomly selected car has no-4 wheel drive

B = event that a randomly selected car has third row seats

The total ways a car can be selected = 65 = n(S)

Total ways A can happen = n(A) = 40 (from the table).

Similarly, n(B) = 30

P(A) = n(A)/n(S) = 40/65

P(B) = n(B)/n(S) = 30/65

P(A∩B) = n(A∩B)/n(S) = 12/65

As by chain rule, we have:

P(A∩B) = P(A)P(B|A) = P(B)P(A|B)

We need P( A randomly selected car has three seats given that the selected car is with no 4-wheel drive)

which is symbolically P( B | A)

Thus, we use: P(A∩B) = P(A)P(B|A)

or

\(12/65 = (30/65)(P(B|A))\\\dfrac{12/65}{30/65} = P(B|A)\\\\P(B|A) = \dfrac{12}{30} = \dfrac{2}{5} = 0.4\)

Thus, the probability that a randomly selected car with no 4-wheel drive has third-row seats is given by: Option B: 0.4

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Answer:

b.  0.4

Step-by-step explanation:

took the test

Answer:

1719-1051.50 +667.50

667.50/44.50 =15

Step-by-step explanation:

The first equation is to find out how much money they have after buying the bus. The second equation is to find out how many people can come on the trip. So the amount of people that can come on the trip is 15 persons

a. Inductive Reasoning: The statement "I see fireflies in my backyard every summer" is based on observations and generalizing from past experiences.

b. Deductive Reasoning: The statement "If A = B and B = A" is an example of a logical deduction.

a. Inductive Reasoning: The statement "I see fireflies in my backyard every summer" is an example of inductive reasoning. By observing fireflies in the backyard during past summers, a pattern or trend is recognized. This pattern leads to the generalization that fireflies are likely to appear in the backyard during summer. Inductive reasoning involves drawing conclusions based on repeated observations and generalizing from those observations to make a prediction about future events. Therefore, when stating, "This summer, I will probably see fireflies in my backyard," it is an application of inductive reasoning, relying on the assumption that the pattern observed in the past will continue in the future.

b. Deductive Reasoning: The statement "If A = B and B = A" exemplifies deductive reasoning. Deductive reasoning relies on established rules, principles, or premises to draw logical conclusions. In this case, the statement refers to the concept of equality in mathematics. The principle of equality states that if A is equal to B, and B is equal to A, then they are interchangeable and represent the same value. Deductive reasoning allows us to deduce that A and B are equivalent based on the given premise. It involves applying logical reasoning and established principles to arrive at a specific conclusion.

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Answer:

No solution.

Step-by-step explanation:

Answer:

The coordinates of the point S could be;

A. (-1, -1)

Step-by-step explanation:

The given parameters are;

The ratio of the length of the line RS to the length of the line RT = 1:2

The coordinates of point R = (2. 5)

The coordinates point T = (-4, -7)

Therefore, we have;

\(\dfrac{The \ length \ of \, RS}{The \ length \ of \, RT} = \dfrac{1}{2}\)

\(\therefore {The \ length \ of \, RS} = \dfrac{1}{2} \times The \ length \ of \, RT\)

The length of the line RT = √(((2 - (-4))² + (5 - (-7))²) = 6·√5

Therefore, we have;

\({The \ length \ of \, RS} = \dfrac{1}{2} \times 6\cdot \sqrt{5} = 3 \cdot \sqrt{5}\)

When the coordinates of the point S = (-1, -1), we have;

The length of the line RS = √(((2 - (-1))² + (5 - (-1))²) = √45 = 3·√5

Therefore, the coordinates of the point S could be (-1, -1)

The determinant of the given matrix is 24, and the inverse (if it exists) is [1/6 -1/24; 0 1/4].

To evaluate the determinant of a matrix, you can use the formula:

det(A) = ad - bc

where A is a 2x2 matrix [a b; c d]. In this case, the given matrix is:

[6 1; 0 4]

Using the formula, we can find the determinant:

det(A) = (6 * 4) - (1 * 0)
      = 24 - 0
      = 24

Now, to find the inverse of a 2x2 matrix, you can use the formula:

A^(-1) = (1/det(A)) * adj(A)

where A^(-1) is the inverse matrix, det(A) is the determinant of A, and adj(A) is the adjugate of A.

The adjugate of a 2x2 matrix [a b; c d] is given by:

adj(A) = [d -b; -c a]

Using the formula, we can find the adjugate:

adj(A) = [4 -1; 0 6]

Finally, we can find the inverse by multiplying the adjugate by the reciprocal of the determinant:

A^(-1) = (1/24) * [4 -1; 0 6]
      = [1/6 -1/24; 0 1/4]

Therefore, the determinant of the given matrix is 24, and the inverse (if it exists) is [1/6 -1/24; 0 1/4].

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Yes, each vector in R4 can be written as a linear combination of the columns of matrix A.

To explain this, first, we must convert matrix A into its reduced row echelon form. This is done by performing row operations so that the leading (i.e. leftmost non-zero) entry in each row is a 1.

By doing this we can see that the columns of the matrix A form a basis for R4, which means that any vector in R4 can be written as a linear combination of the columns of A.

To be more specific, we can show that the columns of A span R4 by showing that the columns are linearly independent. To do this, we solve the equation Ax = 0, where x is the vector of unknowns. We can see that the only solution to this equation is x = 0, which implies that the columns of A are linearly independent and therefore span R4.

This means that any vector in R4 can be written as a linear combination of the columns of A. In other words, any vector in R4 can be expressed as a linear combination of the columns of A, which means that the columns of A span R4.

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The complete question is attached below.

H0: mean=1.45

H1: mean< 1.45

=-3.175

The result is significant at p < .01.

Reject Null Hypothesis

the mean level of exhaust emitted for this model reduces emissions

A)

Null hypothesis:

H0: mean=1.45

Alternative hypothesis:

H1: mean< 1.45

b)

estimate - the value we hypothesize standard error test statıstıc - t-statisticS

\(\begin{gathered}\text { test statistic }=\frac{\text { estimate }-\text { value we hypothesize }}{\text { standard error }} \\\text { t-statistic }=\frac{\bar{x}-\mu_o}{s / \sqrt{n}}\end{gathered}\)

t=1.21-1.45/0.4/sqrt(28)

=-3.175

c)

t=-3.175

df=28-1=27

alpha=0.01

The P-Value is .001863.

The result is significant at p < .01.

d)

p=0.001

< alpha of 0.01

Reject Null Hypothesis

e)

there is sufficient evidence

the mean level of exhaust emitted for this model reduces emissions

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Answer:

-Divide the value of the function at x=2 by the value of the function at x=1, and then subtract the result from 1.

Step-by-step explanation:

hope this help

pick me as the brainliest dont report me please

Answer:

28.5 ft^3

58.3 m^3

Step-by-step explanation:

volume of a pyramid = 1/3 x length x width x height

Perimeter of a pyramid = 4 x length

10.1 = 4 x length

length = 10.1 / 4 = 2.525

1/3 x (2.525 x 2.525 x 13.4) = 28.5 ft^3

1/3 x (6.1 x 6.1 x 4.7) = 58.3 m^3

the tenth is the first number after the decimal place. To convert to the nearest tenth, look at the number after the tenth (the hundredth). If the number is greater or equal to 5, add 1 to the tenth figure. If this is not the case, add zero

9514 1404 393

Answer:

  0.296

Step-by-step explanation:

8/27 is the repeating decimal 0.296296296...(3-digit repeat)

The ten-thousandths digit is 2, so rounding the number simply truncates it at the thousandths place.

  8/27 ≈ 0.296

Answer:

0.296

Step-by-step explanation:

The arc length of x = 0.5y² for 0 ≤ x ≤ ½ is 1.14779.

Arc length is the distance between two points along a section of a curve.

To determine the arc length of x = 0.5y² for \(0 \leq  x \leq  \frac{1}{2}\) without a calculator, we need to use the formula for arc length:
\(L = \int_{a}^{b}\sqrt{[1 + (dy/dx)^2]} dx\)

In this case, we need to express y in terms of x, so we can find dy/dx:
x = 0.5y²
y = ±√(2x)

Since we are only interested in the curve for \(0 \leq  x \leq  \frac{1}{2}\), we can take the positive root:
y = √(2x)

Next, we need to find dy/dx:
dy/dx = \(\frac{d}{d x}(\sqrt{2 x})\)
dy/dx = \(\frac{1}{\sqrt{2x}}\)

Now, we can plug this into the formula for arc length:
\(L = \int_{0}^{1/2}\sqrt{[1 + (dy/dx)^2]} dx\)
\(L = \int_{0}^{1/2} \sqrt{[1 + (1/2x)]} dx\)
\(L = \int_{0}^{1/2} \sqrt{\frac{2x+1}{2x} } dx\)

Integrating and substituting the limits, we get:

L= 1.14779.

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The linear programming model would include equation for profit will be Z = 0.85X + 0.9Y and production constraints are 0.3X <= Y <= 0.6X; demand constraints are X <= (5000 + 3A) and Y <= (4000 + 5B); and cost constraint are 0.6X + 0.85Y + A + B <= 16,000.

Optimal values of X, Y, A, and B that maximize profit (Z) can be determined by using Excel Solver.

The linear programming model for the given problem is shown below:

Let X be the number of jars of applesauce produced. Y be the number of bottles of apple juice produced.

The objective function will be to maximize profit, which can be calculated by the following equation:

Profit = revenue - cost

Revenue can be calculated by multiplying the number of units produced by their respective selling prices. Cost can be calculated by multiplying the number of units produced by their respective production costs. The equation for profit will be:

Z = 1.45X + 1.75Y - (0.6X + 0.85Y)

Z = 0.85X + 0.9Y

The marketing manager estimates that the demand for applesauce is a maximum of 5,000 jars, plus an additional 3 jars for each $1 spent on advertising. The maximum demand for apple juice is estimated to be 4,000 bottles, plus an additional 5 bottles for every $1 spent on promoting apple juice. The maximum amount of money that can be spent on production and advertising is $16,000.

Therefore, we can write the constraints as follows:

Production constraints:

0.3X <= Y <= 0.6X

Demand constraints:

X <= (5000 + 3A)

Y <= (4000 + 5B)

Cost constraint:

0.6X + 0.85Y + A + B <= 16,000

Where A and B are the amounts spent on advertising for applesauce and apple juice, respectively.

To solve the model by using the computer, we can use any software that solves linear programming problems.

One such software is Microsoft Excel Solver. We can set up the problem in Excel as follows:

Cell C9: 0.85X + 0.9Y

Cell C12: 0.6X + 0.85Y + A + B

Cell C13: $16,000

Cell C15: 0.3X

Cell C16: XCell C17: 0.6X

Cell C18: 5000 + 3A (for applesauce)

Cell C19: Y

Cell C20: 4000 + 5B (for apple juice)

Cell C21: A

Cell C22: B

We then use Excel Solver to find the optimal values of X, Y, A, and B that maximize profit (Z).

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Answer:

depends how much they cost each

Answer:

its b

Step-by-step explanation:

18 times 20 = 360 and  subtract 6 = 354.

Answer:

4x+2=22

4x=22-2

4x=20

x=20/4

x=5

Answer:

x = 5

Step-by-step explanation:

First step - subtract 2 from both sides:

4x + 2 - 2 = 22 - 2 which simplifies to 4x = 20

Second step - divide both sides by 4:

4x ÷ 4 = 20 ÷ 4 which simplifies to x = 5

Answer:

24 I guess sooooo nsksbsj

Answer:

Step-by-step explanation:

Xét tam giác DAB có: P là trung điểm AD, M là trung điểm AB

=> MP là đường trung bình của tam giác DAB => MP//BD và MP=\(\frac{1}{2}\)BD  (1)

Xét tam giác DBC có: N là trung điểm DC, Q là trung điểm BC

=> QN là đường trung bình của tam giác DBC => QN//BD và QN=\(\frac{1}{2}\)BD  (2)

Từ (1) và (2) => vecto MP song song cùng chiều với vecto QN

và độ dài MP = độ dài QN = \(\frac{1}{2}\)BD

=> vecto MP = vecto QN

Tương tự xét các tam giác DAC và tam giác ABC => vecto MQ = vecto PN

110 additional miles he will have to drive .

To calculate : additional miles qiang will have to drive

Let the additional no. of miles he has to drive be x .

⇒ Total Distance = 15 + x

    Total Time ( in hrs ) = ( 15 / 30 ) + ( x / 55 ) = ( 1 / 2 ) + ( x / 55 )

The equation becomes ,

[ ( 15 + x ) ] / [ ( 1 / 2 ) + ( x / 55 ) ] = 50

On simplification we get ,

15 + x = 25 + ( 10x / 11 )

x = 110

Therefore , 110 additional miles he will have to drive .

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The calculated measure of angle y is 60 degrees

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

The figure

From the figure, we can see that

The shape can be divided into two triangles such that

Each triangle is an equilateral triangle

The measure of an angle in an equilateral triangle is 60 degrees

using the above as a guide, we have the following:

y = 60

Hence, the value of y is 60 degrees

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The three dimensions of a three-dimensional shape are length, width, and height.  Length refers to the distance between two endpoints of a shape in a straight line. Width is the distance between two opposite sides of a shape, perpendicular to the length.  Height is the distance from the base of the shape to the highest point on the shape.

A drawing of a cube can help illustrate these dimensions. The length of a cube is the distance between opposite corners, the width is the distance between the opposite sides, and the height is the distance from the base to the top corner. A three-dimensional shape has three dimensions: length, width, and height, which determine its overall form and position in space. A three-dimensional shape has three dimensions, which are length, width, and height. These dimensions define the size and position of the object in space.  you can visualize a three-dimensional shape such as a cube or a rectangular prism, where the length, width, and height are the three dimensions that make up the shape.


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The expression that means the same as the given expression is w ÷ 5

From the question, we are to determine which of the given expressions means the same as w/5

To do this, we will simplify each of the given expressions if possible

This expression cannot be simplified further

This expression cannot be simplified further

This expression can be written as w/5

This expression can be written as 5w

This expression cannot be simplified further

This expression can be written as 5/w

Hence, the expression is w ÷ 5

Here is the complete question:

Which Of the expressions below means same as w/5

w + 5

w - 5

w ÷ 5

5 × w

5 - w

5 ÷ w

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