22. The table shows the number of students
going on a field trip. One chaperone is
needed for every 12 students.


Fifth grade students 310


Sixth grade students 305

Seventh grade students 225


Write two equations with variables that you can use to find a number of chaperones needed


How many chaperones are needed?

In order to get the value of n, which is what we are trying to find, it is important to know how to isolate the variable.

When something is added to n, you subtract to isolate n. Going with this logic, you would multiply by a number if you wanted to isolate n with a fraction.

[tex]\frac{n}{5}+4=-4[/tex]

The first step would be to get rid of the 4 on the left side so we can work on the variable. We can do this by subtracting both sides by 4, so the left side cancels out to 0.

[tex]\frac{n}{5}+4-4=-4-4[/tex]

[tex]\frac{n}{5} =-8[/tex]

Next, we can multiply both sides by 5, so we can isolate the variable, because it is being divided by 5.

[tex]\frac{n}{5} *5=-8*5[/tex]

n=-40

Answer:

165 students or the sophomore class of 220 are not athletic.

Step-by-step explanation:

60/240 = .25 This means that 25% of the class is athletic.  That would mean and .75 or 75% are not athletic.

220 x .75 = 165

A linear system has one solution if the slopes of the equation of lines are different.

The 3  possible solutions of a linear system are:

- Unique or one solution

- Infinite solutions

- No solution

A linear equation is equal to the equation of a line, which has the form:

y = mx +b

where m = slope

If the slopes are different, then their graphs will intercept in one point. Hence, the system of linear equation will have one solution.

Example:

2x + 5y = 34  .. .. (equation 1)

x + 5y = 32  .........(equation 2)

Change the equation 1 and equation 2 into slope-intercept form:

y = (-2/5) x + 34/5   ..... (equation 1a)

y =  (-1/5) x + 32/5   ..... (equation 2a)

The slope of equation is (-2/5) while equation 2 is (-1/5), which is different from equation 1.  Hence, the system of linear equation has one solution.

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By translating, stretching and contracting, or reflecting, two functions from the same function family can become one another. Any function from a function family can be obtained by applying one or more transformations to a parent function.

By altering the graph of the parent absolute value function, many other absolute value functions can be created. The resulting absolute value functions take the following form:

[tex]y = |x-h| + k[/tex], where h and k are real numbers.

Absolute value functions can be created using the same kinds of operations that produce new linear functions. They also have a similar impact on absolute value functions. The transformations may, however, appear differently graphically due to some important discrepancies between linear functions and absolute value functions.

Here are some of the transformations:

Vertical Transformations

Horizontal Transformations

This is how we graph the transformation of an absolute value function.

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Answer:

37/56

Step-by-step explanation:

Answer: 3/5 = 0.6

Step-by-step explanation:

1. 2 2/5 x 1/4 = 12/20

2. 2 times 5 over 5 + 2/5 = 10 + 2 over 5 = 12/5

3. 12/5 times 1/4 = 12/20

4. 12/20=3/5

Three possible solutions when solving a system of equation are: one solution, no solution, and infinite solutions.

The 3  possible solutions of a system of equations are:

- Unique or one solution

- Infinite solutions

- No solution

In case of   a system of linear equations, we can determine the type of its solution as follows:

- If the slopes are different, then their graphs will intercept in one point. Hence, the system of linear equation will have one solution.

-  If the slopes are the same but the equation of the lines are different, the lines are parallel, hence they will not intercept. Therefore, there is no solution.

- If the linear equations are exactly (or can be transformed to exactly) the same equations, the solution is infinite.

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A and E are the vowels that theoretical probability was closet to the experimental probability.

The probability is 0.1685%

Probability:

Probability defines the probability of an event occurring. There are many real world situations where we need to predict the outcome of an event. We may or may not be certain about the outcome of an event. In such cases, I say that this event may or may not occur. Probability in general has excellent applications for making probability-based predictions in games and economics, and it also has widespread applications in this emerging field of artificial intelligence. The probability of an event can be calculated by simply dividing the number of favorable outcomes by the total number of possible outcomes using the probability formula. The value of the probability that an event will occur can range from 0 to 1. This is because the preferred number of outcomes can never exceed the total number of outcomes. Also, the resulting favorable number can never be negative. The formula for calculating the probability of a

event is:

probability (event) = favorable outcome/total outcome

Now,

According to the Question:

N vowels = N(A) + N(E) + N(I) + N(O) + N(U)

                =9 + 12 + 9 + 8 + 4

                =42

The total number of letters is:

1×5+2×10+3×1+4×4+6×3+8×1+9×2+12×1=100

This is because dragging the tile reduces the number of vowels and the total number of letters.

p =42×41×...×36100×99×...×94

= 5916335104300

≈ 0.1685%

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If triple of a number added to its half part its equal to the difference between four times the number and 12 then the number is 24.

Two or more expressions with an Equal sign is called as Equation.

Let us consider the number be x

tripple of a number added to its half part

3x+x/2

Difference between four times the number and 12

4x-12

So tripple of a number added to its half part its equal to the difference between four times the number and 12

3x+x/2=4x-12

6x+x=2(4x-12)

Apply distributive property on RHS

7x=8x-24

Subtract 7x on both sides and add 24

24=x

Hence, if triple of a number added to its half part its equal to the difference between four times the number and 12 then the number is 24.

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Answer:

3

Step-by-step explanation:

Given,

v = 54

l = 6

w = 3

To find : Value of h = ?

Formula : -

v = lwh

h = v/lw

h = 54/( 6 × 3 )

= 54/18

h = 3

Hence, the value of h is 3.

a) The probability that a student will study and will pass is 0.765.

b) The probability that a student will pass is 0.715.

What is probability?

Simply put, probability is the likelihood that something will occur. When how an event will turn out is not known, one can discuss the likelihood of several outcomes.

Define some events -

A: A  student studies.

B: A student will pass.

Given that P(A)=0.85 and

P(B|A)=1-P([tex]\bar{B}[/tex]|A)

=1-0.10

=0.90

a) P(a student will study and will Pass)= P(A∩B)

= P(A)·P(B|A)

= 0.85×0.90

= 0.765

b) Given that P( student will either study or pass), the probability is -

=P(A∪B)= 0.8 then P(a student will pass)

=P(B)

It is known that P(A∪B)= P(A)+P(B)-P(A∩B)

Then P(B)=P(A∪B) -P(A) +P(A∩B)

=0.8-0.85 + 0.765

=0.715

Therefore, the probabilities are 0.765 and 0.715.

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The original price of the pair of shoes is $62.5.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Original price = 100%

Offer price = $50

Offer = 20%

Now,

80% = 50

Multiply 100/80 on both sides.

100% = 100/80 x 50

100% = $62.5

Thus,

The original price is $62.5.

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Answer:

8 + v

Step-by-step explanation:

assuming Lamar didn't buy any other cupcakes outside of the chocolate and vanilla ones mentioned, the expression that gives you the total amount of cupcakes bought for the party is 8 + v. since you don't know the number of vanilla cupcakes Lamar bought, it is represented as the variable v in this problem. Then just add 8 and the variable v together. hope this helped :]

Answer: 1st, 4th, and 5th choices

The coordinates of the reflected points are R' (1, -6), S' (5, -3), T' (3, 2) and the graph is attached.

Given are the coordinates of the vertices of ΔRST are R(1, 6), S(5, 3), and T(3,-2).

The rule for a reflection over the x -axis is (x, y) →(x, −y). Now we can write the coordinates of the reflection as -

R' (1, -6)

S' (5, -3)

T' (3, 2)

The graph is attached.

Therefore, the coordinates of the reflected points are R' (1, -6), S' (5, -3), T' (3, 2) and the graph is attached.

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The equation 2x² + 3x - 2 = 0 has the solutions or roots 1 and -2. The quadratic equation is 2x² + 3x - 2 = 0

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to express the connection between two phrases on either side of a letter.

given

Below is the quadratic equation.

2x² + 3x - 2 = 0

When you factor the equation, you get

2x² + 3x - 2 = 0

2x² + 4x - x - 2 = 0

2x(x + 2) - 1(x + 2) = 0

(x - 1)(x + 2)

x = 1, -2

The equation 2x2 + 3x - 2 = 0 has the solutions or roots 1 and -2

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Answer:

d

Step-by-step explanation:

The diameter of a given circle, measured in inches, is 26.8 inches, according to the solution.

The correct option  is A.

A circle is a circular shape that can be created by tracing a moving point in a plane so that its distance from thea specified point remains constant. From the Greek word kirks, which means hoop or ring, comes the term circle.

Circular shapes give us a feeling of completion, assurance, and harmony from a psychological perspective. They stand for the concepts of oneness, integration, and wholeness. In addition to lacking angles, they also lack a beginning and an end. Because of this, a circle is a strong, yet secure, kind, and benign element.

Given,

Radius of circle= 34cm=13.36 inches

Diameter= 2x radius

Diameter = 26.8 inches

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The equation of the line is 3x + y - 11 = 0.

The slope-intercept formula y = mx + b is used when you know the slope of the line to be examined and the point given is also the y intercept (0, b). In the formula, b represents the y value of the y intercept point.

First we find the slope of the line y=-3x+10 by placing it into slope-intercept form:

y = -3 x + 10

Therefore, the slope of the line is m= -3

Now since the equation of the line with slope m passing through a point

(x₁ ,y₁) is y-y₁ = m(x-x₁)

Here the point is (1,8) and slope is m= -3, therefore, the equation of the line is:

y - 8 = -3(x - 1)

y - 8 = -3x +3

3x + y - 11 = 0

Hence, the equation of the line is 3x + y - 11 = 0.

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Step-by-step explanation:

1:13

2:26

3:39

4:52

5:65

6:78

Rule - ×13

The system y = 3x + 4 and 6x - 2y = 8 has no solutions.

A system of equations is a set of equations with multiple variables. To determine the number of solutions for a system of equations, one can use the following methods: graphing, substitution, or elimination. In this case, we can use the elimination method by adding or subtracting the equations to eliminate one of the variables.

If we add the two equations, we get y = 3x + 4 + 6x - 2y = 8, which results in 3x + 4 = 8. This is an inconsistent equation and does not have any solutions. Therefore, the system y = 3x + 4 and 6x - 2y = 8 has no solutions.

This shows that the system is inconsistent, which means that there's no solution that satisfies both equations.

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Answer:

16.74

Step-by-step explanation:

-1.8 times -9.3 will have a positive answer because 2 negative numbers will have a positive sum

  -1.8

x -9.3

---------

    5 4

1 6 2 0

---------

1 6 7 4 ||| add two decimal spaces

16.74

Answer:

Step-by-step explanation:

a. we konw triangle have 180°

b. A straight line have 180°， so

∠abc=180-5x-12=168-5x,

∠bca=180-10x+37=217-10x

∠cab=180-9x-1=179-9x

then  add them all 564 - 24x = 180

c.384=24x, x=16

d.so ∠bca=217-10·16=57.

Answer:

-------------------------------------------

Sum of exterior angles is 360°:

The exterior angle at vertex C is:

The ∠BCA is the linear pair with 123°:

At the rate of 126cm/s is the area of the square increasing when the area of the square is 81cm2.

If each side of a square is increasing at a rate of 7 cm/s.

The area of the square increasing rate,

Area, A = s2

each side of the square is increasing at the rate of 7cm / s (= dx / dt).

s is the side length

=> dA/dt = 2s. ds/ dt

ds/dt = 7cm/s

Area of the square = 81 cm2

81 cm2 = s2

s = 9 cm

so, dA /dt = 2. 9. 7

               = 126 cm2/s

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Thus, complete scale is: 1 inch = 57.7 miles

This can be solved by the concept of cross-multiplication method.

A centimeter is smaller than an inch. On the other side of the centimeter ruler, inches are denoted by the large, continuous hash marks that are inscribed above the digits. On a ruler, the inch is the largest unit and is denoted by the longest line. There is a number next to each 1-inch line on the ruler that designates.

Since the international yard was adopted in the 1950s and 1960s, standards for the precise length of an inch have fluctuated, but the inch is now based on the metric system and is defined as precisely 25.4 mm.

Correct order is:

d. 27 / 1557 = 1/d

e. 27 . d = 1 . 1557

a. 27d = 1557

f. 27d / 27 = 1557 / 27

b. d = 57.7

c. scale: 1 inch = 57.7 miles

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Answer:

y = -3x -27

Step-by-step explanation:

Parallel lines have the same slope.  So the slope will be -3

We need to solve for the y-intercept.  Us the x and y values from the point (-6,-9) to find the y-intercept

m = -3 given

y = -9  from the point( -6,-9)

x = -6  from the point (-6,-9)

y = mx + b  substitute in what you know and solve for b

-9 = (-3) (-6) + b

-9 = 18 + b  Subtract 18 from both sides

-9 -18 = 18 - 18 +b

-27 = b

The equation of the line is y = -3x -27

Answer:

0.25 in/h

Step-by-step explanation:

1. change 2 3/4 t0 2.75

2. 2.75/11= 0.25

The number of hats that Leah had on Monday, given that half the hats were destroyed and four hats were bought, was, A. 22 hats.

If half the hats that Leah owns were destroyed on Wednesday such that only 13 hats were left, then it means that the total hats before the destruction, was :

= 13 hats x 2

= 26 hats

Seeing as Leah bought four hats on Tuesday, this means that the hats she had on Monday were :

= Total hats - Hats purchased on Tuesday

= 26 - 4

= 22 hats

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Therefore , the solution to this problem of unitary method comes out to be he should use 4 teaspoons of chocolate syrup instead of 5.

A single or distinct variable is referred to by the word unitary. Therefore, the goal of this strategy is to establish values in reference to a single unit. The unitary technique, for instance, can be used to calculate how many kilometers a car will go on one litre of gas if it travels 44 km on two litres of fuel.

Here,

Given :This recipe was doubled by Kiran. He used 4 cups of crushed ice, 6 tablespoons of chocolate syrup, 6 tablespoons of peanut butter, and 2 cups of yogurt.

1. Kiran's smoothie would be more chocolatey than Clare's. All ingredients are doubled, but there is an extra teaspoon of chocolate syrup in his smoothie.

2. Answers vary. Sample response: he should use 4 teaspoons of chocolate syrup instead of 5.

Therefore , the solution to this problem of unitary method comes out to be  he should use 4 teaspoons of chocolate syrup instead of 5.

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