A food truck sells two types of meals: a hamburger for $5 and a
salad for $7. Yesterday, the food truck sold a total of 152 meals for a
total of $904.

Proof: If mn is even, then either m = 2k/n or n = 2k/m for an integer k, meaning either m or n must be even.

The following is a direct proof:

The proof shows that if m and n are integers and mn is even, then either m must be even or n must be even. The proof starts by assuming that m and n are integers and that mn is even. It then proceeds to show that one of the factors, either m or n, must also be even.

The proof uses the definition of an even number, which is a number that is divisible by 2, to conclude that if mn is even, then there must be an integer k such that mn = 2k. From this equation, the proof derives the expressions m = 2k/n or n = 2k/m. Since k is an integer, it follows that either m or n must be even, since the result of dividing an integer by another integer is also an integer.

The proof concludes by stating that if mn is even, then either m must be even or n must be even, based on the logical reasoning provided in the proof.

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Answer:

1.35

Step-by-step explanation:

10.80 divided by 8

n = 1.35

Answer:

12

Step-by-step explanation:

1+1+1+1+1+1+1+1+1 x 2 x 2= 12

Answer:

12

Step-by-step explanation:

pls tell me if wrong have a good day/night<3

The expression for 4 difference than the sum of g and 5 is  4- (g+ 5).

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:

Given:

4 difference than the sum of g and 5

writing the mathematical expression for the above we get

sum of g and 5

= g+ 5

and, 4 difference than the sum of g and 5

= 4- (g+ 5)

= 4- g- 5

= -g- 1

Hence, the expression is (-g-1).

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[tex]5x^2-x+9[/tex] when x is equal to 3

Substitute for x with the given value(3):

[tex]5(3)^2-3+9[/tex]

[tex]5(9)-3+9[/tex]

[tex]45-3+9[/tex]

[tex]=\boxed{51}[/tex]

Answer:

it equals 231

Step-by-step explanation:

Answer:

-5 <= x < 3

Step-by-step explanation:

The left end of the inequality is -5 with a closed circle so it has an equal sign with it

The right end of the inequality is 3 with an open circle so it will not have an equals sign.

The line is in the middle of the points so the variable is in the middle.

-5 <= x < 3

Answer:

[tex] - 5 \leqslant y < 3[/tex]

The table that represents f⁻¹(x) in the attached figure

A relation is a function if it has only One y-value for each x-value.

we know that, If (x,y) is a solution of f(x)

then (y,x) is a solution of f⁻¹(x)

In this problem, the ordered pairs in the table that represent f(x) are

(-2,11),(-1,8),(0,5),(1,2),(2,-1)

therefore, The ordered pairs that represent f⁻¹(x) are

(11,-2),(8,-1),(5,0),(2,1),(-1,2)

Hence, the table that represents f⁻¹(x) in the attached figure

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Answer:

Step-by-step explanation:

You want an equation and its solution for the scenario in which Kimberly scored 35.08 points in four gymnastic events, the same number in each event. You want to know her score in each event.

If p represents the number of points that Kimberly scored in each event, her point total is ...

  4p = 35.08

Dividing by the coefficient of p gives the solution:

  p = 35.08/4 = 8.77

Kimberly scored 8.77 points in each event.

Answer:

A flood is mainly caused by rapid water flowing through a certain area and drought is when there is little to no water.      

I hope this helped:)

Answer:

answer is sister's.

Step-by-step explanation:

sisters mean more than one sister.

sisterses isn't a word.

sisters' also isn't a word.

sister's is a word and it means that she has possession of something or that she owns something.

The sum of the expression is 5r - 3.7s + 5.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows:

Expression: (Math Operator, Number/Variable, Math Operator)

Given the expression,

(-0.3s - 2) + (5 - 3.4s) + (5r + 2)

-0.3s -2 + 5 - 3.4s + 5r + 2

arranging the variables and constants,

(-0.3s - 3.4s) + 5r + (- 2 + 5 + 2)

apply operations,

-3.7s + 5r + 5

5r - 3.7s + 5

Hence the simplified expression is 5r - 3.7s + 5.

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The mid-point of segment AB is X. Ray XY is perpendicular to segment AB. Point L is on ray XY. By congruence of triangle, statements (C) point L is equidistant from point A and B.

If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance.

Given that, The mid-point of segment AB is X. Ray XY is perpendicular to segment AB. Point L is on ray XY.

Draw the line segment AL and BL.

In Δ AXL and Δ BXL

AX is equal to BX

XL is common in both Δ

∠AXL is equal to ∠BXL because both are right angle.

So, Δ AXL ≅ Δ BXL

So AL = BL

So we say that point L is equidistant from point A and B.

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The sampling distribution  of the sample proportion is approximately normal when the sample size (n) is large and the population proportion (p) is close to 0.5.

This can be mathematically expressed as follows:

[tex]n*p > 10 and n*(1-p) > 10[/tex]

To illustrate, let's say we are sampling from a population with a proportion of 0.3. For the sampling distribution to be approximately normal, the sample size (n) must be larger than 33.3 (n > 33.3). This is because [tex]33.3*0.3 = 10 and 33.3*0.7 = 23.3[/tex].

In other words, the sample size (n) must be large enough so that the product of the sample size (n) and the population proportion (p) is greater than 10 and the product of the sample size (n) and the population proportion (1-p) is also greater than 10. This ensures that the sampling distribution of the sample proportion is approximately normal.

To sum up, the sampling distribution of the sample proportion is approximately normal when the sample size (n) is large and the population proportion (p) is close to 0.5.

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Answer:

To obtain the fraction first we need to obtained the number. The number can be identified by using algebraic expression.

The fraction is .

Given:

The given fraction is .

Let the numerator is  .

The numerator is 18 less than denominator is  , the fraction is .

Write the algebraic expression as per question to find the number.

Calculate the fraction.

Thus, the fraction is  .

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Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

assume top a, bottom b

so a/b =2/5

so a=2/5b

b=a+18 = 2/5b+18

so 3/5b = 18

b = 30

a=12

The sequence is neither arithmetic nor geometric because it does not have a common difference or a common ratio

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

a = (2n)² n

For a sequence to be an arithmetic sequence, the sequence must have a common difference

For a sequence to be a geometric sequence, the sequence must have a common ratio

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

The sequence is neither because it does not have a common difference or a common ratio

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The linear equation that shows how the wind power would need to grow to make this goal is y = 25x + 15

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

(x, y) = (0, 15) and (5, 90)

A linear equation is represented as

y = mx + c

Where

c = y when x = 0

So, we have

y = mx + 15

Using the other point, we have

5m + 15 = 90

So, we have

5m = 75

Divide by 5

m = 25

So, the equation becomes

y = 25x + 15

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Complete question

Using the two data points from Exercises 1 and 2, write a linear equation that shows how the wind power would need to grow to make this goal. Use years for the independent variable and terawatt hours for the dependent variable. Let year 0 represent year 2012, (0, 15) and (5, 90)

The area of the composite figure is 54 in².

The perimeter of the composite figure is 35 in.

A rectangle is a two-dimensional shape where the length and width are different.

The area of a rectangle is given as:

Area = Length x width

We have,

The composite figure has 3 shapes.

Triangle and 2 rectangles.

Now,

Base = 3 in

Height = 4 in

Area of the triangle.

= 1/2 x base x height

= 1/2 x 3 x 4

= 6 in²

Now,

Length = 5 in

Width = 4 in

Area of the rectangle.

= length x width

= 5 x 4

= 20 in²

Now,

Length = 4 in

Width = 7 in

Area of the rectangle.

= length x width

= 4 x 7

= 28 in²

Now,

Area of the composite figure.

= 6 + 20 + 28

= 54 in²

Now,

The perimeter of the composite figure.

= 12 + 7 + 4 + 3 + 5 + 4

= 35 in

Thus,

The area is 54 in².

The perimeter is 35 in.

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The hourly rate that they are paid is $24 per hour

An equation is an expression that uses mathematical operations to show the relationship between numbers and variables. Types of equations are linear, quadratic, cubic and so on.

Let us assume that all of them are paid the same amount of money per hour.

Let x represent the amount of money each is paid per hour.

Joshua worked five hours, Katleho worked for three hours and Pevashnee worked for four hours if they paid R288. Hence:

5x + 3x + 4x = 288

12x = 288

x = 24

Their hourly rate is $24 per hour

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The values of the solution for the triangle is A = 55°, a = 10. 1, b = 12. 3, B = 86.01°, c = 7.68 and C = 39°

The sine rule is used to show the relationship between the sides and angles of a triangle. It is given as:

a/sinA = b/sinB = c/sinC

Where A, B, and C are the angles and a,b, and c are the opposite sides to the angles.

1)

A = 55°, a = 10. 1, b = 12. 3

10 / sin(55) = 12.3 / sinB

B = 86.01°

A + B + C = 180° (angle in triangle)

55 + C + 86 = 180

C = 39

10 / sin(55) = c / sin(39)

c = 7.68

The values of the solution for the triangle is A = 55°, a = 10. 1, b = 12. 3, B = 86.01°, c = 7.68 and C = 39°

The complete question is-

Use the Law of Sines to solve (if possible) the triangle. If two solutions exist, find both. Round your answers to two decimal places. (If a triangle is not possible, enter IMPOSSIBLE in each corresponding answer blank. ) A = 55°, a = 10. 1, b = 12. 3

Case 1

B

C

c

Case 2

B

C

c

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The value of j in the triangle is 8.66 feet

The complete question is added as an attachment

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

The right triangle

The value of j can be calculated using the following

tan(60) = j/5

So, we have the following representation

j = 5 * tan(60)

Evaluate

j = 5√3

This gives

j = 8.66

Hence, the value is 8.66 feet

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Answer:

Step-by-step explanation:

25 because when you take 2x times 3x +1

Height from window = 450ft  the tomato passes your window after 2 seconds and hits the ground 5 seconds after it was thrown. neglect air resistance

Time taken to get from window to ground = 2 secs

V0, initial speed of tomato from drop point = 0 ft/s

Acceleration due to gravity = 32.2 ft/s

When the tomato gets to the observer at the window, its initial speed is no longer 0ft/s but an unknown value, u.

We can apply one of the equations of linear motion to then find this initial velocity at the window using the other parameters given i.e.  

s = ut + [tex]\frac{1}{2}[/tex] [tex]at^{2}[/tex]

= 450ft

t = 2 secs

a = g = 32.2ft/sec

=> 450 = (u*2) + (1/2 * 32.2 * 2^2)

450 = 2u + 64.4

2u = 450 – 64.4

2u = 385.6

=> u = 192.8ft/s

Now that we know this initial velocity, we can use another equation of linear motion to find the height distance between the drop point and the window for the resistance

[tex]v^{2}[/tex] - [tex]u^{2}[/tex] = 2gs

where s = distance between drop point and window

v = 192.8ft/s

u = 0ft/s;

=> [tex]192.8^{2}[/tex] - 0^2 = 2*32.2*s

37171.84 = 64.4s

=> s = 37171.84/64.4

s = 577.20ft

Hence, distance from drop point to the ground, H, will be the addition of s and the height from the window to the ground:

=>H = 577.20 + 450

H = 1027.2ft

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A national opinion poll found that 44% of all American adults agree that parents should be given vouchers good for education at any public or private school of their choice.

The result is based on a small sample, and it is important to note that opinions can change quickly as more people become aware of the issue and as more information becomes available.

While the poll results are encouraging for proponents of school choice and educational vouchers, it is important to recognize that opinions can be subject to change. As the debate over school choice continues, more individuals may become aware of the issue and may form different opinions as they learn more about the issue.

Furthermore, more information and details about the issue may become available which could lead to individuals changing their opinions based on the new information. Additionally, opinions may also differ based on geographical location, as different areas may have different opinions on the issue. All of these factors should be taken into account when assessing the current opinion on educational vouchers.

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The required point (-2, 1/2) lies in the second quadrant of the coordinate plane.

Coordinate, is represented as the values on the x-axis and y-axis of the graph. while the coordinate x is called abscissa and the coordinate of the y is called ordinate.

The point (-2, 1/2) lies in the second quadrant of the coordinate plane.

In the second quadrant, the x-coordinates are negative and the y-coordinates are positive. Since the x-coordinate of the point (-2, 1/2) is negative and the y-coordinate is positive, it lies in the second quadrant.

Thus, the point (-2, 1/2) lies in the second quadrant of the coordinate plane.

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Answer:

Step-by-step explanation:

5h + 3h + 4h = R288

12h = R288

h = R24

Josh, 5 hours at R24/hour = R120

Katleho, 3 hours at R24/hour = R72

Pevashnee, 4 hours at R24/hour = R96

Check your work: 120 + 72 + 96 = 288

Converting the raw data into a 'frequency' distribution is often a first step in making the data more manageable and easier to assess.

A scatterplot is the most helpful graph for demonstrating the connection between two quantitative variables.

Data are listed in rising or decreasing numerical order in a raw data listing. The stem-and-leaf presentation gives more depth than the frequency distribution since it may explain individual data values as well as indicate how many are in each group, or stem.

Bins should have the same width and be mutually exclusive and exhaustive.

A scattergram is a graphical representation of the linkages or correlations that exist between two numerical variables (or covariables), which are shown as points (or dots) for each pair of scores. A scattergraph depicts the intensity and direction of the covariables' connection.

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The probability of x = 1 is 0.2,x = 2 is 0.3, x = 3 is 0.5

Let X be a random variable with the following probability mass function:

f(x) =

x = 1: 0.2

x = 2: 0.3

x = 3: 0.5

This is indeed a probability mass function because the values of f(x) are all greater than or equal to 0, and the sum of the values of f(x) is equal to

To calculate the probability of x = 1, we can use the formula for probability mass functions: P(X = x) = f(x).

Therefore, the probability of x = 1 is 0.2.

To calculate the probability of x = 2, we can use the same formula: P(X = x) = f(x).

Therefore, the probability of x = 2 is 0.3.

To calculate the probability of x = 3, we can use the same formula: P(X = x) = f(x).

Therefore, the probability of x = 3 is 0.5.

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complete question

What is the probability of x = 1, x = 2, and x = 3?

Answer:

(-6x-2)(2x+4)

-12x+24x-4x+6

=8x+6

The inverse matrix is (b) [tex]\left[\begin{array}{ccc}-19&9&-7\\15&-7&6\\-2&1&-1\end{array}\right][/tex]

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

x + 2y + 5z = 14

3x + 5y + 9z = -1

x + y - 2z = 6

When represented as a matrix, we have

[tex]\left[\begin{array}{ccc}1&2&5\\3&5&9\\1&1&-2\end{array}\right][/tex]

The determinant is calculated as

D = 1 * (5 * -2 - 9 * 1) - 2 * (3 * -2 - 9 * 1) + 5 * (3 * 1 - 5 * 1)

Evaluate

D = 1

This means that the matrix is invertible

Next, we calculate the cofactor elements

5 * -2 - 9 * 1 = -19

3 * -2 - 9 * 1 = -15

3 * 1 - 5 * 1 = -2

2 * -2 - 5 * 1 = -9

1 * -2 - 5 * 1 = -7

1 * 1 - 2 * 1 = -1

2 * 9 - 5 * 5 = -7

1 * 9 - 5 * 3 = -6

1 * 5 - 2 * 3 = -1

So, we have

   [tex]\left[\begin{array}{ccc}-19&-15&-2\\-9&-7&-1\\-7&-6&-1\end{array}\right][/tex]

Next, create the adjoint or the adjugated matrix

[tex]A = \left[\begin{array}{ccc}-19&15&-2\\9&-7&1\\-7&6&-1\end{array}\right][/tex]

Transpose the adjoint

[tex]A^T = \left[\begin{array}{ccc}-19&9&-7\\15&-7&6\\-2&1&-1\end{array}\right][/tex]

Divide by the determinant

[tex]A^T = \left[\begin{array}{ccc}-19&9&-7\\15&-7&6\\-2&1&-1\end{array}\right][/tex]

Hence, the inverse is (b) [tex]\left[\begin{array}{ccc}-19&9&-7\\15&-7&6\\-2&1&-1\end{array}\right][/tex]

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