an elementary school is offering 3 language classes: one in spanish, one in french, and one in german. the classes are open to any of the 100 students in the school. there are 28 students in the spanish class, 26 in the french class, and 16 in the german class. there are 12 students that are in both spanish and french, 4 that are in both spanish and german, and 6 that are in both french and german. in addition, there are 2 students taking all 3 classes.

We typically write linear equations in slope-intercept form:

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

We're given:

1) Determine the slope (m)

To find the slope, we can use the slope equation:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex] where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are two points through which the line passes

⇒ Plug in the given points:

[tex]m=\dfrac{-1-(-4)}{0-(-13)}\\\\m=\dfrac{-1+4}{0+13}\\\\m=\dfrac{3}{13}[/tex]

Therefore, the slope of the line is [tex]\dfrac{3}{13}[/tex]. Plug this into [tex]y=mx+b[/tex]:

[tex]y=\dfrac{3}{13}x+b[/tex]

1) Determine the y-intercept (b)

In this case, the y-intercept is already given to us.

The y-intercept is the value of y when x=0. Given that the line passes through (0,-1), we know that this is -1.

Plug this into [tex]y=\dfrac{3}{13}x+b[/tex]:

[tex]y=\dfrac{3}{13}x+(-1)\\\\y=\dfrac{3}{13}x-1[/tex]

[tex]y=\dfrac{3}{13}x-1[/tex]

Answer:

4.25c + 3.5p = 36.50

c + 6 = p

c = candies and p = pretzels

Step-by-step explanation:

So for the first equation, the prices will be the coefficients of each variable, since for each candy/pretzel it will be that price. We also know that both of these prices together equal 36.50, so that will be on the other side of the equal sign. So the equation representing this info is 4.25c + 3.5p = 36.50

And for the second equation I saw that Mason bought 6 more pretzels than candies. So no matter what number the candies is, the pretzels should always be 6 more than the candies. So the equation representing this information is c + 6 = p

Lastly I just defined the variables that I used to right the system. That is all! Hope this helps you this should be correct :)

Function transformation: Function transformation is the process of changing one function into another.

The f(x) graph will be shifted 1 unit down in the vertical direction.

Function transformation: Function transformation is the process of changing one function into another.

changing a function's form from one to another

Transformational rule

The function will move 'a' units higher when f(x)->f(x)+a is used.

f(x)-> f(x)-a The action is going to be 'a' units down.

The function will be relocated 'a' units left if f(x)->f(x+a).

The function will be relocated 'a' units right if f(x)->f(x-a).

The fundamental job is [tex]f(x)=\frac{1}{x}[/tex]

F(x)-1 is used in place of f(x).

It indicates that the graph of f(x) will shift down by one unit.

A unit down will be added to the vertical translation of the f(x) graph.

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Based on the amount earned by Justin per hour, and the overtime work rate, Justin's gross pay for the week is $764.50

First, find the amount that Justin earns from Rite Aid Pharmacy for his regular work:

= Number of hours in regular week x Pay per week

= 40 x 13.9

= $556

The overtime hours was:

= 50 - 40

= 10 hours

The overtime pay is:

= 10 x 13.9 x 1.5

= $208.50

The total gross pay for the week is:
= 556 + 208.50

= $764.50

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The probability that it is a female with long hair is 0.75 .

Potential is described by probability. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability generally refers to the degree to which something is likely to occur. Gonna determine how likely something is to occur, use probability. Many things are hard to predict with 100% certainty. We can only anticipate the possibility of an event occurring using it, or how likely it is. In the probability scale, 0 indicates an impossibility and 1 indicates a certainty. Every event's probability in a sample space is one.

the likelihood of an occurrence, E is

P(E) = The proportion of positive outcomes to all outcomes.

In probability, an event is said to be independent if it is completely unaffected by the occurrence of any other event, and it is considered to be dependent if it is affected by other occurrences.

Using the literature and formulas mentioned above, we have:

Let F stand for the circumstance that the student is a female and L for the circumstance that the student has long hair.

In this illustration, the probability are as follows:

P(F) = 0.60; P(L) = 0.50

P(F AND L) = 0.45 and P(L|F) = 0.75 as a result.

As a result, there is a 0.75 percent chance that a randomly chosen student has long hair.

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The way she can use the number line to model the division is; Maria should start at 0 and then make “bounces” of 4 to the right until landing at 12. She will make 3 bounces of 4 because 12 divided by 4 is 3.

She is using a number line to model division, 12 ÷ 4  =  3

To carry out a division operation using a number line, follow the steps below:

For the division operation 12 ÷ 4, Maria should:

Therefore, the points on the number line will be 0, 4, 8, and 12

Count the number of gaps between these points

That is, 0 to 4, 4 to 8, and 8 to 12.

Since there are three gaps between 0 and 12 on the number line, using a gap difference of 4, then 12 ÷ 4  =  3

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Answer:

Property of Equality

Step-by-step explanation:

B=D and D=B so they are the same value so its a property of equality

Answer:

each point needs to be transformed using (-y,x) for the new coordinate

Answer:

D.   [tex]x^4-x^3+x^2-x+1-\frac{6}{5x+5}[/tex]

Step-by-step explanation:

Volume of a rectangular box = Base Area x Height

V = Ah

Here we are give V and h and asked to compute A

From the equation for V, dividing both sides by h gives
V/h = A

A = V/h

V = 5x⁵ - 1
h = 5x + 5

[tex]V = \dfrac{5x^5-1}{5x + 5}[/tex]

The simplified result is [tex]x^4-x^3+x^2-x+1-\frac{6}{5x+5}[/tex]

I solved this using synthetic division and can provide the steps if you want

Answer: 4AB

Step-by-step explanation:

[tex](A+B)^2-(A-B)^2=\\((A+B)+(A-B))((A+B)-(A-B))=\\(A+B+A-B)(A+B-A+B)=\\(2A)(2B)=\\4AB[/tex]

Answer:

add a picture

Step-by-step explanation:

Answer:

x = 15

z = 64

Step-by-step explanation:

Lets make an equation -

(14x - 94) + z = 8x - 4 +z

Both sides are parallel to each other, and therefore the sum is also 180.

Then we solve it -

14x - 8x - 94 + z = -4 + z

Bring the z on the other side to eliminate it.

6x - 94 = - 4

Add 94 on both sides

6x = 90

Divide 6 on both sides and you get x = 15

Substitute x into 8x -4 + z = 180

8*15 - 4 + z = 180

120 - 4 + z = 180

116 + z = 180

Subtract 116 on both sides.

z = 64.

HOPE THIS HELPS!!

CAN U PLSSS HELP ME! I have been stuck on this problem for hours! Pls try to see if u can solve it. This is the problem -

Sean and Emily love making origami. Sean can make a paper crane in 6 minutes, and

Emily can make a paper crane in 8 minutes. One day, they decided to make some paper

cranes together. They started making cranes at the same time, and after a while, they

have 112 total paper cranes. How many of those paper cranes did Sean make?

THANKS A LOT!!

Answer:

Step-by-step explanation:

1. To find the value of x, you'll need to set 14x-94 equal to 8x-4. We do this since the two angels are congruent, and congruent angles are equal to each other:

[tex]14x-94=8x-4[/tex]

You'll then solve for x by isolating the x value.

[tex]14x-8x=94-4[/tex]

[tex]6x=90[/tex]

[tex]x=\frac{90}{6}[/tex]

[tex]x=15[/tex]

2. To find z I would plug in the x value to one of the equations, such as 8x-4, in order to find the measure of that angle:

[tex]8(15)-4\\=116[/tex]

We now know that 14x-94 and 8x-4 are equal to 116. To find z you'll add the angle opposite to it, the blank angle since they are congruent. Now you'll add all the angles together and set the equation equal to 360:

[tex]z+z+116+116=360\\2z+232=360\\2z=(360-232)\\2z=128\\\frac{2z}{2} =\frac{128}{2} \\z=64[/tex]

Your final answers are x=15 and z=64, hope this helps!

The weight of a person in Venus who weighs 210 pounds on Earth is 185.5 pounds.

It is given in the question that weight of a person on Venus varies directly with his or her weight on Earth. Also, a person weighing 120 pounds on Earth weighs 106 pounds on Venus.

We have to find the weight of the person in Venus who weighs 210 pounds on Earth.

Let weight on Earth be e and,

weight on Venus be v.

From the data given in the question, we can write,

e ∝ v

e = kv

Where k is the constant of proportionality

120 = k*106

k = 120/106 = 60/53

Hence, we can write,

210 = (60/53)*v

(210*53)/60 = v

v = 185.5 pounds

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Answer:

-15by

Step-by-step explanation:

distribute

rearrange terms

The number which is at a distance of 23 unit from 12 on a number line is 11.

A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numbers (numerical values) that are placed at equal intervals along its length.

This ultimately implies that, a number line can be used to determine the difference between two numbers such as 23 and 12. Also, a number line typically increases in numerical value towards the right and decreases in numerical value towards the left.

Now, we can determine the distance as follows:

Distance = 23 - 12

Distance = 11.

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0.030844 is the probability that the test results are correct, and that this student is not overstressed.

What is a probability math example?

Given that a particular  students test negative for stress negative for stress then probability  that the test result are correct and this student is not over stressed.

  = 0.5% × 95% / ( 99.5% × 15% ) + ( 0.5% × 95% )

 = 0.030844

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The complete question is -

A new test has been developed to determine whether a given student is overstressed. This test is 95% accurate if the student is not overstressed, but only 85% accurate if the student is in fact overstressed. It is known that 99.5% of all students are overstressed. Given that a particular student tests negative for stress, what is the probability that the test results are correct, and that this student is not overstressed?

Step-by-step explanation:

I hope this will be helpful for you.

The answer is :   X = 9

Answer:

9

Step-by-step explanation:

75 + 25x = 300

subtract 75 from both sides:

75 + 25x - 75 = 300 - 75

25x = 225

divide both sides by 25:

25x/25 = 225/25

x = 9

Answer:

6.25

Step-by-step explanation:

a quarter=1/4 which is 0.25; 0.25 for each person is 0.25(25)=6.25

Answer:

Answer: The line does not represent a direct variation because it does not go through the origin.

The the coordinates of endpoint J on line segment JL with a midpoint of (-2, 6) is ( -3,15 ).

A midpoint is simply a point that divides a line segment into two equal halves.

The midpoint formula is expressed as;

M = ( (x₁+x₂)/2, (y₁+y₂)/2

Given the data in the question;

Midpoint K(-2, 6)

Point L(-1, -3).

Point J

To determine the coordinate of point J, plug the given points into the midpoint formula above and simplify.

First, we get the x-coordinate of point J

x = (x₁+x₂)/2

2x = x₁ + x₂

2( -2 ) = x₁ + ( -1 )

-4 = x₁ - 1

x₁ = -4 + 1

x₁ = -3

Next, we get the y-coordinate of point J

y = (y₁+y₂)/2

2y = y₁ + y₂

2(6) = y₁ + (-3)

12 = y₁ - 3

y₁ = 12 + 3

y₁ = 15

Therefore, the coordinates (x₁,y₁) of the endpoint point J is ( -3,15).

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Answer:

[tex] = 8^{2} \\ = 8 \times 8 \\ = 64[/tex]

ATTACHED IS THE SOLUTION

Answer: [tex]y=-\frac{7}{2}x+7[/tex]

Step-by-step explanation:

The slope of the line is [tex]\frac{7-0}{0-2}=-\frac{7}{2}[/tex].

So, since the y-intercept is 7, the equation is [tex]y=-\frac{7}{2}x+7[/tex].

Time is considered to be the dimension on which any system evolves.

9.2 seconds will take for him to strike the ground.

Time can be thought of as the dimension in which the evolution of every system occurs.

It can be calculated using the following units: seconds, minutes, hours, days, weeks, months, and years.

Given,

h = 45m

g = -9.8m/s

Solution:

Vi = 0

h = Vi t + 1/2gt^2

Since Vi is 0

2h = gt^2

t^2 = 2h/g

t = [tex]\sqrt{2h/g}[/tex]

[tex]t =\sqrt{2 * -45/-9.8}[/tex]

t = 9.183s

9.2 seconds will take for him to strike the ground.

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[tex]7a = b[/tex]

THIS SIMPLY MEANS THAT TO ATTAIN b we have to multiply a by 7.

Answer:

Tile a rectangle with unit squares. It is 8 unit squares long and 7 unit squares wide. Each unit square represents one square inch.

Step-by-step explanation:

The time taken to create a 2-foot by 4-foot pattern drive is 38.4 minutes.

A unit rate means a rate for one of something.

It is written as a ratio with a denominator of one.

We have,

A rectangle tile area = 3-inch by 5-inch

Area = 15 inches

Time taken to position 15 inches tile = 6 minutes.

We can write as,

15 inches = 6 minutes _____(1)

We have a 2-foot by 4-foot pattern drive.

Area = 8 feet

We know that,

1 foot = 12 inches

Multiply both sides by 8.

8 feet = 8 x 12 inches

8 feet = 96 inches _______(2)

Now,

From (1) and (2) we get,

15 inches = 6 minutes

Multiply 96/15 on both sides we get,

96/15 x 15 inches = 96/15 x 6 minutes

96 inches = 38.4 minutes

Thus the time taken to create a 2-foot by 4-foot pattern drive is 38.4 minutes.

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The absolute function f(x) = 4x+5 as a piecewise-defined function is:

f(x) = { -4x-5   ,   x<-5/4

           4x+5   ,   x ≥-5/4 }

Given, the absolute function  f(x) = 4x+5

The fundamental tenet of piecewise linear regression is that we should construct the regression function in "pieces" if the data exhibit various linear trends over various parts of the data. The components may or may not be joined.

when  4x+5 < 0

4x < -5

x < -5/4

f(x) = -(4x+5) = -4x-5

when 4x+5 ≥ 0

4x ≥ -5

x ≥ -5/4

f(x) = 4x+5

so f(x) =  { -4x-5   ,   x<-5/4

                4x+5   ,   x ≥-5/4 }

since, I x I =  { -x   ,   x<0

                        x    ,   x ≥0}

Therefore, we get the required piecewise-defined function with linear parts.

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Answer:The mean is commonly referred to as average, but it is not the only kind of average. The mean is often used in research, academics and in sports.

Step-by-step explanation:

There are diffrerent ways to use the word

The average in general is the same as the term average in mathematics.

Arithmetic mean or average can be obtained by adding all the given values and then dividing the total sum by the number of values.

The meaning of average, in general, is quite similar to average in maths.

Suppose If we say the average income of a population is five thousand.

This implies that some portion of the population earns more than five thousand and some portion of the population earns below five thousand.

We can also say that the average rate growth of height of a person per year is 5cm this also means that some years the growth is more than 5cm and some years it is less than 5 cm.

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