Wallpaper was applied to one rectangular wall of a large room. The dimensions of the wall are shown below. If the total cost of the wallpaper was $771.12, what was the cost, in dollars, of the wallpaper per square foot?

The probability of getting one marble of each color will be 0.044.

The probability of an event is a figure that represents how probable it is that the event will take place. In terms of percentage notation, it is stated as a number between 0 and 1, or between 0% and 100%. The higher the probability, the more probable it is that the event will take place. A random event's recurrence is the subject of this area of mathematics. The range of the number is 0 to 1. The degree to which something is likely to happen is essentially what probability means. You will discover the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution.

In this question,

Total number of balls=4+5+6=15

probability of red ball= 4/15

probability of white ball = 5/14  (Since the number of balls are decreasing

probability of blue ball= 6/13

probability of getting one marble of each color= 4/15×5/14×6/13    

                                                                              = 0.044

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Answer:

70

Step-by-step explanation:

Hello there! Let's work this through:

Firstly, we might want to simply 2 1/2 into 5/2, for simplification.

So, we now have 4 * 7 * 5/2

Simplifying we have \(\frac{4*7*5}{2}\)

We see that we can easily simplify 4/2 into 2 * 7 * 5

Further simplifying we get 10*7

Last bit and we get our answer of 70

From here we get 2

Answer:

1*3 = 1+7(3) = 22

5*22 = 5+ 7(22) = 159

159 is your answer.

hope this helps!

The value of expression 5 × ( 1 × 3 ) is, 159.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

⇒ m × n means (m + 7n).

Now, We can find the value of 5 × ( 1 × 3 ) as,

⇒ 5 × ( 1 × 3 )

⇒ 5 × (1 + 7×3)

⇒ 5 × (1 + 21)

⇒ 5 × 22

⇒ 5 + 7 × 22

⇒ 5 + 154

⇒ 159

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a) True, b) False, c) False, d) True, e) False, f) False, g) True

a) The statement is true. The symbol "∅" represents the empty set, which does not contain any elements. Since 0 is not an element of the empty set, the statement "0 ∈ ∅" is false.

b) The statement is false. The symbol "{0}" represents a set containing the element 0. The empty set, represented by "∅", does not contain any elements. Therefore, the empty set is not an element of the set {0}.

c) The statement is false. The symbol "{0}" represents a set containing the element 0. However, the empty set, represented by "∅", does not contain any elements. Therefore, the set {0} is not a subset of the empty set.

d) The statement is true. The empty set, represented by "∅", does not contain any elements. Every set is a subset of the empty set, including the set {0}.

e) The statement is false. The symbol "{0}" represents a set containing the element 0. In this case, {0} is not an element of itself. Therefore, the statement "{0}∈{0}" is false.

f) The statement is false. The symbol "{0}" represents a set containing the element 0. In this case, {0} is not a proper subset of itself. Therefore, the statement "{0}⊂{0}" is false.

g) The statement is true. The symbol "{∅}" represents a set containing the empty set. In this case, {∅} is a subset of itself because it contains the element ∅. Therefore, the statement "{∅} ⊆ {∅}" is true.

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The point estimate of the proportion of the population adults who think that today's children will be better off than their parents is 0.24.

The point estimate of P, is defined as the proportion of successes in the sample.

P' = X/N ; where X = number of successes; N = total trials.

Here, N = 1000

According to the Child outlook file, number of "yes" = 240.

Hence, P' = 240/1000

P' = 0.24

Therefore, the point estimate of the proportion of the population adults who think that today's children will be better off than their parents is 0.24.

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Answer:

B

Step-by-step explanation:

The color of your eyes doesn't depend on your shoe size, and your shoe size doesn't depend on the color of your eyes. All the other examples have a clear independent and dependent variable.

Answer:

8.4

Step-by-step explanation:

Since we want to minimize the average, the integers should be made as small as possible. So, we have 4 integers:

1, 2, 3, 4

However, the median must be 10. The next two integers must have an average of 10 - and since the integers are distinct, we should use:

9, 11

From there, we use the smallest integers (that are still above 11) possible:

12, 13, 14, 15

The average of these 10 integers is 84/10, or 8.4.

The median is still 10, because (9+11)/2 is 10.

Answer:

8 (or 8.4)

Step-by-step explanation:

First, the problem states the words: Distinct and positive.

That means that the smallest number we can use is 0.

We can make 10 blanks for 10 numbers for us to fill in.

_ _ _ _ _ _ _ _ _ _

Since 10 is an even number, and the median is not one single number, it will be the middle of the two numbers.

In this case, our two numbers are the 5th and 6th blank.

Any two numbers can be used, as long as they are the same actual value from 10.

Let us first put in the numbers we can, which are the numbers before the two middle blanks.

0,1,2,3, _ _ _ _ _ _

To find the median between two numbers, we can do:

(a+b) divided by 2 = median

We can use the smallest following number, 4. Then the 6th number will have to be 16 for 10 to be in the middle.

Also try the largest possible number for the 5th blank, 9. Then the 6th number will be 11.

4+16 and 9+11 both equal 20, and 20 divided by 2 is 10. So both of these work.

Now let's place the other numbers in for these two equations.

0,1,2,3,4,16,17,18,19,20

0,1,2,3,9,11,12,13,14,15

If we add the numbers of each together, we get:

0,1,2,3,4,16,17,18,19,20=100

0,1,2,3,9,11,12,13,14,15= 80

If we now divide each sum by 10 (to find the average) we get:

10

8

Since both of these were the most we could go, one with the 5th number as small as possible and one with the 5th number as large as possible.

Since the smaller answer we got was 8, the answer must be 8.

(I believe 0 is a positive integer because it doesn't carry a negative sign. If 0 is not a positive integer, the answer is 8.4. Use the same process

Answer:

36

Step-by-step explanation:

the pattern is adding the number to every whole number less than it. So if the start was 8, it would go 8+7+6+5+4+3+2+1, which is 36

✌

we have the points

A (1,-2) and B(5,3)

Find out the point (x,y) that divide the segment AB in a ratio 2:3

that means

AX/XB=2/3

step 1

Find out the horizontal distance AB

ABx=5-1=4 units

Find out the vertical distance AB

ABy=3-(-2)=5 units

step 2

we have that

the horizontal distance between A and x is

AX/XB=2/3

AX=(2/3)XB -----> equation 1

AX+XB=4 -----> equation 2

substitute equation 1 in equation 2

(2/3)XB+XB=4

(5/3)XB=4

XB=12/5

XB=2.4

the x-coordinate of X is

x=5-2.4=2.6

Find out the y-cpoordinate

AX=(2/3)XB -----> equation 1

AX+XB=5 ------> equation 2

substitute equation 1 in equation 2

(2/3)XB+XB=5

5/3(XB)=5

XB=3

the y-coordinate of X is

y=3-3=0

answer is

the coordinate of the point is (2.6,0)

Answer:

60 mph

Step-by-step explanation:

Each way of the trip is 240 miles.

The round trip is 2 × 240 miles = 480 miles

The first half of the trip, 240 miles, was made at a speed of 30 mph.

s = d/t

st = d

t = d/s

t = 240 miles / 30 mph = 8 hours

The first part of the trip took 8 hours.

The entire round trip is 240 miles × 2 = 480 miles

The speed for the entire trip is 40 mph.

480 miles / 40 mph = 12 hours

12 hours - 8 hours = 4 hours

The return trip takes 4 hours.

The return trip is 240 miles.

s = d/t = 240 miles / 4 hours

s = 60 mph

Answer: 60 mph

Answer:

x = ± 2/3

Step-by-step explanation:

9x^2 = 4

Divide each side by 9

9/9x^2 = 4/9

x^2 = 4/9

Take the square root of each side

x = ±sqrt(4/9)

x = ± 2/3

9x^2=4

/9       /9

x^2=4/9

sqrt both sides

x=+/-\(\sqrt{4/9}\)

x=+/-(\(\frac{\sqrt{4} }{\sqrt{9} }\))

x=+/-2/3

Answer:

x=2/3, x=-2/3

Answer:

its a function because each input (X) only has one output (y)

domain (3,-1,7,0)

range (2)

Step-by-step explanation:

Answer:

Kay sold 6 boxes and Ayan sold 19 boxes

Step-by-step explanation:

Let x = number of boxes Kay sells

y = number of boxes Ayan sells

Then the equations will be:

\(x+y = 25\\x = y-13\)

We can solve the system by using substitution method

Putting x = y-13 in equation 1

\(y-13+y = 25\\2y -13 = 25\\2y = 25+13\\2y = 38\)

Dividing both sides by 2

\(\frac{2y}{2} = \frac{38}{2}\\y = 19\)

Putting y = 19 in equation 2

\(x = y-13\\x = 19-13\\x = 6\)

Hence,

Kay sold 6 boxes and Ayan sold 19 boxes

The dimensions of the box that will minimize the cost of manufacturing it: base = 9.04 in and y = 3.01 in

And the minimum cost is 32.65 cents

Let us assume that x represents the base side of the box, and y represents the height of the box.

The volume of the box would be:

V = x²y

246 = x²y        ........(1)

The cost of the material for the base is 0.2 cents per square inch, and the cost of the material for the sides is 0.3 cents per square inch.

Since this box has 4 sides and 1 base, the total cost would be,

C = (0.2 × x² × 1) + (0.3 × 4 × xy)

C = 0.2x² + 1.2x(246x⁻²)              (from (1) y = 246x⁻²)

C = 0.2x² + 295.2 x⁻¹

Consider derivative with respect to x,

dC/dx = 0.4x - 295.2 x⁻²

Consider dC/dx = 0

So,  0.4x - 295.2 x⁻² = 0

0.4x³ =  295.2

x³ = 738

So, x = 9.04

So, the value of y would be:

y = 246 x⁻²

y = 246 × (9.04)⁻²

y = 3.01

So, the minimum cost would be:

C = (0.2 × 0.04² × 1) + (0.3 × 4 × 9.04 × 3.01)

C = 32.65

Therefore, the minimum cost is: 32.65 cents

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To find the midpoint, we must take the sum of both values and then divide by two.

In this case, our values are -6 and 14

-6 + 14 = 8

8 / 2 = 4

B is located at 4 on the number line.

Answer: x=23

Step-by-step explanation:

X-8=15. Add 8 to both sides. The 8 cancels on the left side because -8 +8 is 0 leaving x. 15+8=23 meaning x=23.

Answer:

On the first one, they took half of the original number then added it to the original to get the sides of the bigger shape.

Step-by-step explanation:

Answer: I just did this in my math class, so I'll try to help you the best I can.  I uploaded the pdf below with step by step solutions to each problem. I also wrote some background information you need to know in order to solve the problems.

Step-by-step explanation:

Hope This Helps!

The point X on the line PQ is marked at 1.5 cm from P, and on the line AB is marked at 4.5 cm from A.

Given that AB and PQ are lines of length 6 cm.

PX: XQ = 1:3

We are required to mark where point X would be on the line, with a cross.

First, we need to find the length of PX and XQ.

Let's assume that PX = x cm and XQ = 3x cm.

Now, PX + XQ = 6 cm

So, x + 3x = 6cm4x = 6cmx = 6/4cmx = 1.5cm

So, PX = 1.5cm and XQ = 3 × 1.5cm = 4.5cm.

To mark the point X on line PQ:

Draw a line PQ of length 6 cm.

Now, measure 1.5 cm from P on PQ and mark a point.

Name it as X. This point X is the point where the ratio

PX: XQ = 1:3.

The required marking of point X on line PQ is shown below:

Image obtained from Brainly

On the other hand, to mark the point X on line AB:

Draw a line AB of length 6 cm.

Now, measure 4.5 cm from A on AB and mark a point. Name it as X. This point X is the point where the ratio

PX: XQ = 1:3.

The required marking of point X on line AB is shown below:

Image obtained from Brainly

Thus, point X on the line PQ is marked at 1.5 cm from P, and on the line AB is marked at 4.5 cm from A.

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In this problem, we are dealing with a random variable related to people's opinions on a new building project. We are given four options for the correct wording of the random variable and need to determine the correct one. Additionally, we are asked to calculate probabilities associated with the number of people who favor the new building project, ranging from exactly 4 to at most 6.

a) The correct wording for the random variable is "rv = the number of people who are in favor of a new building project." This wording accurately represents the random variable as the count of individuals who support the project.

b) To calculate the probability that exactly 4 people favor the new building project, we need to use the binomial probability formula. Assuming the probability of a person favoring the project is p, we can calculate P(X = 4) = (number of ways to choose 4 out of 10) * (p^4) * ((1-p)^(10-4)). The value of p is not given in the problem, so this calculation requires additional information.

c) To find the probability that less than 4 people favor the new building project, we can calculate P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3). Again, the value of p is needed to perform the calculations.

d) The probability that more than 4 people favor the new building project can be calculated as P(X > 4) = 1 - P(X ≤ 4) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)).

e) The probability that exactly 6 people favor the new building project can be calculated as P(X = 6) using the binomial probability formula.

f) To find the probability that at least 6 people favor the new building project, we can calculate P(X ≥ 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10).

g) Finally, to determine the probability that at most 6 people favor the new building project, we can calculate P(X ≤ 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6).

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Answer:

True

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

Answer:

Step-by-step explanation:

Step one:

given data

the cost of the laptop= $800

initial payment= $200

monthly payment = $60

let the number of months be x

the expression for the situation is the function for the equation of line

y=mx+c

Step two:

the expression for the situation is

800=200+60x

solve for x

800-200=60x

400=60x

divide both sides by 60

x=400/60

x=6.7

Approximately 7 months

Step-by-step explanation:

all regular polygons have (n-2)*180 this formula can use here. n= no of sides

Answer:

M = (n-2)*180 degrees for polygons with n sides.

Step-by-step explanation:

As already noted, there is no description of the polygon in question.  However, the formula for the sum of the measure of the interior angles of a regular polygon is M = (n-2)•180 where n is the number of sides.  A triangle has 3 sides, so M = (3-2)*180 = 180 degrees.

A hexagon has 6 sides, so M = (6-2)*180 = 720.

The answer would be -2.

Step-by-step explanation:

The line crosses through the - 2.

Answer:

y intercept would be -2

Step-by-step explanation:

y intercept means at what point first crosses the line at the y axis. \

That would be -2

To find the equation of a line with the same y-intercept as the line y - 8x + 11 = 0, we can isolate the y variable. Rearranging the equation, we get y = 8x - 11. Therefore, the line that has the same y-intercept is y = 8x - 11.

For a line parallel to the equation 1x - 1y = 4, we need to determine the slope of the given line. Rewriting the equation in slope-intercept form, we have y = x - 4. The slope of this line is 1.

Since parallel lines have the same slope, the desired line will also have a slope of 1.Combining the information from both conditions, the equation of the line that satisfies both requirements is y = x - 11. The slope of this line is 1/1 or 1, which means that for every unit increase in x, y will also increase by 1.

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Answer:

the fish has a final elevation of negative 2

Step-by-step explanation:

The value of give operation is =[[0,-4,-28][20.4.-32]]

A rectangular or square array of numbers or variables that are arranged in rows and columns is known as a matrix in mathematics. Elements or entries are the names for individual things in a matrix.

The application of matrix plays a major role in Mathematics, as well as in other fields. It helps in solving linear equations. Matrices are extremely valuable objects that can be found in a wide range of applications. The application of matrices in mathematics is used in a wide range of scientific fields as well as mathematical areas. Engineering mathematics is used in almost every aspect of our lives. In this article, we are going to learn what is a matrix, different matrix operations and the application of matrices in detail.

Some of the matrix's rows and columns define how big it is. A matrix of "m" rows and "n" columns is written as "m*n," where "m" and "n" are the dimensions of the matrix.

We have, c=-4

\(A=\left[\begin{array}{ccc}2&1&1\\-1&0&3\\\end{array}\right] \\\\and , B=\left[\begin{array}{ccc}-1&0\\3&1\\\end{array}\right]\)

first, compute the cA.

\(=(-4)\left[\begin{array}{ccc}2&1&1\\-1&0&3\\\end{array}\right] \\\\cA=\left[\begin{array}{ccc}-8&-4&-4\\4&0&-12\\\end{array}\right] \\\\Now, BcA=\left[\begin{array}{ccc}1&2\\-1&3\\\end{array}\right] \left[\begin{array}{ccc}-8&-4&-4\\4&0&-12\\\end{array}\right] \\\\\\=\left[\begin{array}{ccc}0&-4&-28\\20&4&-32\\\end{array}\right]\)

The complete question is-

Perform the indicated operation,c=-4,

\(A=\left[\begin{array}{ccc}2&1&1\\-1&0&3\\\end{array}\right] \\\\and , B=\left[\begin{array}{ccc}-1&0\\3&1\\\end{array}\right]\)

B(cA)=?

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Using the inscribed angle theorems, the measure of the indicated angles are:

1. m∠BOA = 30°

2. m∠BDA = 15°

3. m∠BCA = 15°

Based on the inscribed angle theorems, the following relationships are established:

Given:

Intercepted arc BA = 30°

1. ∠BOA is central angle

Thus:

m∠BOA = 30° (inscribed angle theorems)

2. ∠BDA is inscribed angle.

m∠BDA = 1/2(30) = 15° (inscribed angle theorems)

3. m∠BCA = m∠BDA  = 15° (inscribed angle theorems)

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Answer and Step-by-step explanation:

In a polygon, when a shape is similar but dilated, the angles are still congruent.

Also, turn the pentagon QRSTP counterclockwise 90 degrees so it is upright and looks like pentagon ABCDE (making it easier to read).

A. The measure of angle P is 124 degrees, as it matches up with angle E.

B. To find the length of side r, we need to find the scale factor. We do this by looking at the given side on pentagon QRSTP (side RS) and match it with its similar side of pentagon ABCDE (side BC)

To find the scale factor, you divide the side of the bigger shape by the side of the smaller shape. For us, this results in the scale factor being 2.

Now, the similar side to r is side ED. We need to divide 7.5 by 2 to find r.

When doing so, we get r to be 3.75.

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