The total area, in square feet, of a rectangular stage that has been widened by x feet is represented by 1,900 + 76x. Use the distributive property to factor the expression. What does each factor in the equivalent expression tell you about the stage?

Since M and N are independent events, [tex]P(M)=P(M|N)=0.71[/tex]

Step-by-step explanation:

Two events A and B are said to be independent when the probability of A happening does not depend on whether B has happened or not.

In other word, this condition can be rewrite as follows:

[tex]P(A|B)=P(A)[/tex]

where

[tex]P(A|B)[/tex] is the probability of A happening  given that B has happened

[tex]P(A)[/tex] is the probability of A happening

In this problem, we have:

- M and N are independent events: so M does not depend on whether N occurs or not

Therefore,

[tex]P(M)=P(M|N)[/tex]

- Also, we know that

[tex]P(M|N)=0.71[/tex]

Therefore, it follows that

[tex]P(M)=0.71[/tex]

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The probability of getting the number 4 and the multiple of 5 is 1 / 4.

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability = Number of favourable outcomes / Number of samples

Given that an adventure game has a number cube with 12 equal-size faces. Each face is labelled with a number from 1 to 12.

The probability will be calculated as:-

Number of favourable outcomes = { 4, 5 , 10 } = 3

Number of samples = 12

Probability = 3 / 12

Probability  = 1 / 4

Therefore, the probability of getting the number 4 and the multiple of 5 is 1 / 4.

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The required simplified expression for 0.2(5x – 0.3) – 0.5(–1.1x + 4.2) is 1.55x - 2.16.

What is simplification ?

Simplification means reducing the expression in a simpler form using various operations. It eliminates unnecessary diversiry and variety.

The given expression is

0.2(5x – 0.3) – 0.5(–1.1x + 4.2)

or, 0.2 [5x + (–0.3)] + (–0.5)(–1.1x + 4.2) x – 2.16

Now,Let us expand the bracket-

0.2*5x - 0.2*0.3 - 0.5(-1.1x) - 0.5*4.2

Further,

x - 0.06 + 0.55x - 2.1

therefore,

x + 0.55x - 0.06 - 2.1

⇒ 1.55x - 2.16

Hence,the required simplified expression for 0.2(5x – 0.3) – 0.5(–1.1x + 4.2) is 1.55x - 2.16.

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Answer:

1.55 is the answer on edge

Answer:

C & D

Step-by-step explanation:

Social Science and Math/CS do represent 1/4 of the total majors.

Furthermore, Science and Social Sciences represent half of the majors.

Therefore, C & D are true.

Combining Science and Social Science represent half the intend majors. Therefore, option D is the correct answer.

Given that, a dean polled the sophomore class about their intended majors, then created this graph based on the data.

A pie chart is a type of a chart that visually displays data in a circular graph. It is one of the most commonly used graphs to represent data using the attributes of circles, spheres, and angular data to represent real-world information.

From the given pie chart,

More students intend to majors in science

Less students intend to majors in Maths/CS

1/4 of students intend to major in other subjects.

Combining Science and Social Science represent half the intend majors. Therefore, option D is the correct answer.

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Answer:

The greatest possible number of boxes that is needed to pack the items with no leftovers is 24.

Step-by-step explanation:

Given:

Number of rice bags = 72

Number of blankets =48

Number of water cases = 24

To Find :

The greatest possible number of boxes that the items can be packed into so that there are no leftover = ?

Solution:

we can find the greatest possible number of boxes that is required by finding the HCF(Highest common factor) of(24,48,72)

Finding the HCF (Highest common factor):

The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24

The factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

The factors of 72 are: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

24 is the greatest common factor

Hence 24 will the number boxes required

[tex]\dotfill[/tex]

To find the value of the given function, substitute x = 12 instead of x and evaluate.

Given function:

[tex]\sf f(x)=\cfrac{2}{3} x+14[/tex]

Substitute 12 for x:

[tex]\sf f(12)=\cfrac{2}{3}\times12+14[/tex]

Convert 12 to a fraction to make multiplying easier:

[tex]\sf f(12)=\cfrac{2}{3}\times\cfrac{12}{1}+14[/tex]

[tex]\sf f(12)=\cfrac{2\times12}{3\times1}+14[/tex]

[tex]\sf f(12)=\cfrac{24}{3}[/tex]

[tex]\sf f(12)=8[/tex]

>>> Therefore, the value of the function is 8.

The value of  [tex]\( f(x) = \frac{2}{3}x + 14 \)[/tex] is 22.

To find the value of f(12), you simply need to substitute (x = 12) into the function f(x) and evaluate it:

Given: [tex]\( f(x) = \frac{2}{3}x + 14 \)[/tex]

Substituting x = 12:

[tex]\[ f(12) = \frac{2}{3} \times 12 + 14 \][/tex]

Now, let's calculate:

[tex]\[ f(12) = \frac{2}{3} \times 12 + 14 \]\[ = \frac{2}{3} \times 12 + 14 \]\[ = 8 + 14 \]\[ = 22 \][/tex]

So, [tex]\( f(12) = 22 \)[/tex].

Final answer:

The pencil is 11 centimeters shorter now than when it was new, which is determined by subtracting the current length (8 centimeters) from the original length (19 centimeters).

Explanation:

The subject of this question is Mathematics. The question involves calculating the length by which a pencil has become shorter, which is a basic arithmetic problem dealing with subtraction.

To find how much shorter the pencil is now compared to when it was new, we subtract the current length of the pencil from its original length. Given that the new pencil was 19 centimeters long and now measures 8 centimeters, the calculation would be:

Original length - Current length = Length difference

19 cm - 8 cm = 11 cm

Therefore, the pencil is 11 centimeters shorter now than when it was new.

The unit of measurement is particularly important here to provide clarity and accuracy to the measurement. For example, while measuring the length of a classroom, you might use meters or feet, but for small objects like a pencil, centimeters or inches are more appropriate.

Answer:

F(a) =2a^2+4a+5

Step-by-step explanation:

just put x= a

Answer:

45

Step-by-step explanation:

The sum of angle in a straight line is 180

=> 3n + (4n - 15) + 90 = 180

3n + 4n + 75 = 180

7n = 180 - 75 = 105

n = 15

Angle ZLQK = 4n - 15 = 4*15 - 15 = 60 - 15 = 45

The volume of the solid is 540 mm

Step-by-step explanation:

The volume a rectangular prism is calculated as the product of its length, width and height.

Mathematically, V=l*w*h where l is length of the prism, w is width and h is the height

Given that the dimensions of the rectangular prism as;

Length=15 mm

Width= 6 mm

Height = 6 mm

V=15*6*6= 540 mm

The vertex is [tex](-1,1)[/tex]

Explanation:

The equation is [tex]f(x)=2x^{2} +4x+3[/tex]

To find the vertex, we need the equation in the form of [tex]f(x)=a (x-h)^{2}+k[/tex]

Dividing each term by 2 in the equation [tex]f(x)=2x^{2} +4x+3[/tex]

[tex]f(x)=2(x^{2} +2x+\frac{3}{2} )[/tex]

Now, completing the square by adding and subtracting 1, we get,

[tex]f(x)=2(x^{2} +2x+1-1+\frac{3}{2} )[/tex]

The first three terms can be written as [tex](x+1)^{2}[/tex],

[tex]f(x)=2[(x+1)^{2}+\frac{1}{2} ][/tex]

Multiplying 2 into the bracket, we get,

[tex]f(x)=2(x+1)^{2} +1[/tex]

This equation is of the form [tex]f(x)=a (x-h)^{2}+k[/tex]

Now, we shall find the vertex [tex](h,k)[/tex]

Thus, [tex]h=-1[/tex] and [tex]k=1[/tex]

Thus, the vertex is [tex](-1,1)[/tex]

[tex]\frac{8}{35}[/tex] of all claims were paid in the second month.

Step-by-step explanation:

Step 1; In the first month [tex]\frac{3}{7}[/tex] of all expenses were paid. So to find the expenses that were not paid in the first month we subtract [tex]\frac{3}{7}[/tex] from 1 i.e. 1-[tex]\frac{3}{7}[/tex]= [tex]\frac{4}{7}[/tex]. So in the first month  [tex]\frac{4}{7}[/tex] of total expenses were not paid.

Step 2; In the second month [tex]\frac{2}{5}[/tex] of the remaining claims were paid i.e. [tex]\frac{2}{5}[/tex] of the remaining claims which is  [tex]\frac{4}{7}[/tex] of the total claims. So to find out the number of claims paid in the second month it's just a case of multiplying [tex]\frac{2}{5}[/tex] with [tex]\frac{4}{7}[/tex].

Fraction of all claims paid in second month = [tex]\frac{2}{5}[/tex]  * [tex]\frac{4}{7}[/tex]= [tex]\frac{8}{35}[/tex].

Example; If $ 70,000 was the total claim amount, [tex]\frac{3}{7}[/tex] of that which equals $30,000 was paid in the first month. So $40,000 was still to be paid. In the second month [tex]\frac{2}{5}[/tex] of $40,000 was paid which equals $16,000 paid in the second month which is [tex]\frac{8}{35}[/tex] of total claims i.e. $70,000

Answer:

see the explanation

The solution's table in the attached figure

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]

Let

y ----> the price

x ----> the weight

Find the value of the proportionality constant for each ordered pair in each table

[tex]k=\frac{y}{x}[/tex]

If all the values of k are equal, then the table represents a proportional relationship between the variable x and the variable y

Table 1

For x=1.5 lb, y=$4.50 ---->  [tex]k=\frac{4.5}{1.50}=3[/tex]

For x=2 lb, y=$9.00 ---->  [tex]k=\frac{9.00}{2}=4.5[/tex]

The values of k are different

therefore

The table not represent a proportional relationship

Table 2

For x=10 g, y=$0.50 ---->  [tex]k=\frac{0.50}{10}=0.05[/tex]

For x=15 g, y=$0.55 ---->  [tex]k=\frac{0.55}{15}=0.04[/tex]

The values of k are different

therefore

The table not represent a proportional relationship

Table 3

For x=0.5 Kg, y=$0.75 ---->  [tex]k=\frac{0.75}{0.5}=1.5[/tex]

For x=5 g, y=$7.50 ---->  [tex]k=\frac{7.50}{5}=1.5[/tex]

The values of k are equal

therefore

The table represent a proportional relationship

Table 4

For x=1 oz, y=$2.00 ---->  [tex]k=\frac{2}{1}=2[/tex]

For x=2 lb, y=$4.00

Convert lb to oz

Remember that

1 lb=16 oz

so

2 lb=2(16)=32 oz

For x=32 lb, y=$4.00 ---->  [tex]k=\frac{4}{32}=0.125[/tex]

The values of k are different

therefore

The table not represent a proportional relationship

Answer:

[tex]42x + 49 \\ = 7(6x + 7)[/tex]

hope this helps..!

This is a combinatorial geometry problem involving the probability of forming a triangle with an integer area from randomly selected lattice points within a square grid. It requires analyzing the properties of lattice point triangles and applying combinatorial mathematics.

The problem given discusses the selection of random points within a square on a coordinate system to form a triangle, and it questions the probability of the triangle's area being an integer. This involves combinatorics, geometry, and number theory within the field of mathematics. To approach the problem of calculating the probability that the area is an integer, one must consider the distribution of lattice points and use combinatorial analysis.

Area of a triangle with vertices at lattice points can be expressed using the formula derived from the determinant of a matrix. The triangle's area, if non-degenerate, can be half of the odd integer, which upon doubling to remove the half, leaves an integer area. Thus, the problem reduces to a combinatorial question concerning lattice points, selected at random, and forming a triangle whose twice the area is an odd integer.

However, a direct count of the favorable vs. total possibilities may be complex due to the large number of possible point combinations and the chance of degenerate triangles (where the area is zero). Thus, a systematic probabilistic and combinatorial approach is necessary to resolve this question, likely involving a careful analysis of the geometric configurations and properties of integer triangles on a lattice grid.

Answer:

28) 120 x 20y

30) 3w x 36

Step-by-step explanation:

28) 20 x (6 x y)

20 x 6 = 120

y x 20 = 20 y

120 x 20y

30) (w x 12) x 3

3 x w = 3w

12 x 3 = 36

3w x 36

Answer:

120 x 20y               3w x 36

Step-by-step explanation:

Distributive Property

Answer:

The correct answer is D. 30°, 60°, 90°; 1,  √3, 2

Step-by-step explanation:

Let's find out the solution to this question:

Arc cos (β) = √3/2 = 1.732/2 = 0.866

β = 30°

Let's recall that the ratio of the sides of a triangle 90 - 60 - 30 is:

1 : 2 : √3

β = 30°, α = 60°, r = 2, h = 1, k = √3

The correct answer is D. 30°, 60°, 90°; 1,  √3, 2

Answer:

A

Step-by-step explanation:

The interval of 0-19 will increase by 20 of either Hay Bale Toss or Pie Eating Contest.

A histogram is a visual representation of statistical data that makes use of rectangles to illustrate the frequency of data items in a series of equal-sized numerical intervals. The independent variable is represented along the horizontal axis and the dependent variable is plotted along the vertical axis in the most popular type of histogram.

Given that, a class of 20 students is visiting the fair today. Each student is 16 years old or younger and will participate in either the Pie Eating Contest or the Chili Cookoff.

Number of students visiting the fair = 20

Age group = 0-16

In the histogram, this age group falls in the first interval which is 0-19.

If all 20 students joined the Hay Bale Toss then the bar of 0-19 of Hay Bale Toss will increase from 40 to 60 and the graph of Pie Eating Contest will remain the same.

If all 20 students joined the Pie Eating Contest then the bar of 0-19 of Hay Bale Toss will increase from 20 to 40 and the graph of Hay Bale Toss will remain the same.

Therefore, only one if the graph's interval of 0-19 will increase by 20 whereas the other graph would remain the same.

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Answer: try this hi i am in four

Answer:

- 6

Step-by-step explanation:

its negative so I divided —12 by 2 to get -6 also You have to get the F by itself so you have to divide the sides by 2 but bringing the negative is important

Answer:

159n - 43

Step-by-step explanation:

Write as an equation

159 * n - 43

Multiply

159n - 43

Hope this helps :)

Answer:

The graph is attached.

Step-by-step explanation:

The graph of the line with the slope [tex]m[/tex] and the y-intercept [tex]b[/tex], has the form

[tex]y=mx+b[/tex]

In our case the rate of change [tex]m[/tex] is [tex]0.4[/tex]; therefore we have the equation

[tex]y=0.4x[/tex]

The graph of which is attached.

P.S: we have set [tex]b=0[/tex]  by default, because we are not given any information for it.

The line that represents a proportional relationship between y and x where the unit rate of change (or slope) is 0.4 can be plotted on a graph. Start from the origin and for each increase of 1 in x, y increases by 0.4. Plot these points and draw a straight line which represents this proportional relationship.

To graph the line that represents a proportional relationship between y and x where the unit rate of change of y with respect to x is 0.4, you can start by creating a plot with an x- and y-axis. The y-axis represents the dependent variable and the x-axis represents the independent variable.

In this case, we're looking at a linear relationship, which means the line produced on the graph will be straight. This kind of straight-line graph typically uses the equation y = mx, where m is the slope (or unit rate of change) and x is the independent variable.

For this graph, the slope or unit rate of change is 0.4. This means that with every increase of 1 in x, y increases by 0.4. Plot some points on the graph starting from the origin (0,0). If x is 1, y will be 0.4 (1*0.4). If x is 2, y will be 0.8 (2*0.4). Keep plotting these points and connect them to draw the line. This line demonstrates the proportional relationship between x and y.

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Answer: x = 5

Step-by-step explanation:

multiply the outside number to both numbers in parenthesis

3x-15  divide

find out how many time 3 goes into 15 and divide  

three divided by fifteen equals five

Final answer:

The equivalent expression to 3(x-5) is 3x - 15, which is found by applying the distributive property of multiplication over subtraction.

Explanation:

The question asks for an expression equivalent to 3(x-5). To find an equivalent expression, we need to apply the distributive property of multiplication over subtraction. This means we will multiply the number 3 by each term inside the parentheses.

Here's the step-by-step process:

Multiply 3 by x to get 3x.

Multiply 3 by -5 to get -15.

Combine these two products to get the equivalent expression, which is 3x - 15.

Therefore, the equivalent expression to 3(x-5) is 3x - 15.

Answer:

The value of the annuity in 10 years will be US$ 15,552.90

Step-by-step explanation:

Let's use the ordinary simple annuity formula to calculate the value of the annuity in 10 years, this way:

FV = Future value of an annuity stream

PMT = Dollar amount of each annuity payment  = US% 50

r = Interest rate = 3.5% compounded biweekly = 0.035/26

n = Number of periods in which payments will be made  = 26 * 10 = 260

FV = PMT * [(1 + r)ⁿ  − 1]/r

Now, replacing with the real values, we have:

FV = 50 *  [(1 + 0.035/26)²⁶⁰  − 1]/(0.035/26)

FV = 50 *  [(1.001346154)²⁶⁰  − 1]/0.001346154

FV = 50 * 0.41873217/0.001346154

FV = 50 * 311.058148

FV = 15,552.90

We only rounded the last product to the next cent, in all the other cases we used all the decimals for the calculations.

Theorem .

Basically you already know this, and it can also be proven.

Answer:

y = -x -5

Step-by-step explanation:

The -x (i.e., multiplication of x by -1) gives the line a slope of -1. The -5 translates the line down to cross the y-axis at -5.

Answer:

Step-by-step explanation:

Horizontal

Answer:

slope = 0

Step-by-step explanation:

A horizontal line is parallel to the x- axis.

Since the x- axis has a slope of zero then the slope of a horizontal line is 0

Answer:

47 stamps

Step-by-step explanation:

You just have to subtract 15 from 62 so it looks like this: 62-15=47

Answer:

Each side of the frame is 12.35 centimeters long.

Answer:

width: 7 cm

length: 56 cm

Step-by-step explanation:

Let:

x=width

8x=length

P=2l+2w

126=2x + 2(8x)

126=2x+16x

18x=126

x=7

width: 7 cm

length: 56 cm

hope this helps!!