The chart below shows the number of students in each grade who are members of the spirit club at Lone Star Middle School.

If 10 more 8th graders join the club, how many 6th graders will need to join the club so that the ratio of 8th graders to 6th graders remains the same?

Answer:

The percentage increase in [tex]T[/tex] is 20 %.

Step-by-step explanation:

Let be [tex]T = \frac{k\cdot x}{y}[/tex], whose initial parameters are [tex]k = k_{o}[/tex], [tex]x = x_{o}[/tex] and [tex]y = y_{o}[/tex]. If these three parameters are increased by 20 %, then initial and final values of [tex]T[/tex] are, respectively:

Initial value

[tex]T_{i} = \frac{k_{o}\cdot x_{o}}{y_{o}}[/tex] (1)

Final value

[tex]T_{ii} = \frac{(1.2\cdot k_{o})\cdot (1.2\cdot x_{o})}{1.2\cdot y_{o}}[/tex]

[tex]T_{ii} = \frac{1.2\cdot k_{o}\cdot x_{o}}{y_{o}}[/tex] (2)

(1) in (2):

[tex]T_{ii} = 1.2\cdot T_{i}[/tex]

And the percentage increase in T is:

[tex]\%T = \frac{T_{ii}-T_{i}}{T_{i}}\times 100\,\%[/tex] (3)

[tex]\%T = \frac{1.2\cdot T_{i}-T_{i}}{T_{i}}\times 100\,\%[/tex]

[tex]\%T = 20\,\%[/tex]

The percentage increase in [tex]T[/tex] is 20 %.

Answer:

Step-by-step explanation:

Lets subsitute k, x and y as  100 to make it easier for us

So k = 100, x = 100, y = 100

Step 1 :-   T = kx/y

- T = 100 * 100 / 100 = 100

Step 2 :- Increase by 20% = 100 * 20% = 20,    100 + 20 = 120

Step 3 :- Percentage Increase = Increased value OVER original calue          MULTIPLIED by 100%

SO = ( 120 - 100 ) ,,,,   20/100 * 100% = 0.2* 100 = 20%

Answer:

86

Step-by-step explanation:

Answer:

183/25 is an equivalent fraction form for decimal 7.32

Step-by-step explanation:

Answer:

7 8/25

Step-by-step explanation: 183/25 = 7 8/25 = 7.32

Answer:

x = 58°

Step-by-step explanation:

cos x = 9/17 = 0.5294

x = 58.03°

Answer:

2(1.75+3.00) and 3.50x+6.00

Step-by-step explanation:

have a great day :D

Step-by-step explanation:

D

Answer:

Radius of convergence is 1/10

Step-by-step explanation:

Answer: 6

Step-by-step explanation:

9514 1404 393

Answer:

  A, D

Step-by-step explanation:

Assuming that Mr. Layte must pay for his mortgage from his (otherwise) disposable income, that disposable income will decrease. As in choice A, there will likely be additional ownership expenses besides the mortgage. Under our assumption, Mr. Layte's disposable income does not remain the same or increase.

The appropriate choices are A and D: the amount of money he has to spend on things will decrease ...

Answer:

if we are doing the same thing it should be D-Andy’s study shows neither correlation nor causation.

Step-by-step explanation:

The average energy of the class after a different number of hours is given below.

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

From the graph,

We can make two ordered pairs (x, y).

Where y = average energy level and x = the number of hours.

Now,

From the graph, we see that,

The average energy after 1 hour = 7

The average energy after 2 hours = 8

The average energy after 3 hours = 5

The average energy after 4 hours = 5

The average energy after 5 hours = 4

The average energy after 6 hours = 5

The average energy after 7 hours = 3

Thus,

The average energy of the class after a different number of hours is given above.

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Answer:

4/7

Step-by-step explanation:

numbers between 8 to 15 is 7

so d even numbers are 4

that is d answer is 4/7

The probability that the number is an even number is 1/2.

The probability is defined as the ratio of number of favourable outcomes and the the total number of possible outcome.

A number from 8 to 15 is drawn at random.

The number between 8 to 15 are 8, 9, 10, 11, 12, 13, 14, 15 = 8

Total even number = 8, 10, 12, 14 = 4

The probability that the number is an even number is;

[tex]\rm Probability =\dfrac{Total \ even \ number }{Total \ numbers}\\\\ Probability =\dfrac{4}{8}\\\\ Probability =\dfrac{1}{2}[/tex]

Hence, the probability that the number is an even number is 1/2.

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Answer:

17. The puppy will grow 16 in - ( 1 foot = 12in and 28-12=16)

Step-by-step explanation:

18 .

21; 17.5; 14; 10.5; and 7

3 x 7 = 21

2.5 x 7 = 17.5

2 x 7 = 14

1.5 x 7 = 10.5

1 x 7 = 7

The inequalities s ≥ 12 - t, s ≤ 22 - t, 0.25t + s ≤ 15, s ≥ 0; t ≥ 0 represent the scenario provided option (A) is correct.

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

It is given that:

Greg sells the T-shirts for $7 each and the shorts for $14.

Greg can work 15 hours a day, at most it takes him 15 minutes to design a T-shirt and an hour to design a pair of shorts

Let s is the number of shorts

Let t is the number of t-shirts

We can formulate the inequality based on the data provided:

s ≥ 12 - t

s ≤ 22 - t

0.25t + s ≤ 15

s ≥ 0; t ≥ 0

Thus, the inequalities s ≥ 12 - t, s ≤ 22 - t, 0.25t + s ≤ 15, s ≥ 0; t ≥ 0 representing the scenario provided option (A) is correct.

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Answer:

A 12 x 6

Step-by-step explanation:

Answer:

hi

Step-by-step explanation:

Answer:

The side lengths of a right triangle is 11cm, 60cm and 61cm, that could be selected from the given measurements.

Step-by-step explanation:

The measurements are,

                  7cm, 11cm, 54cm, 60cm, 61cm, 65cm

Step:1

                 To check the right angle triangle, Pythagorean theorem can be used.

                For a Pythagorean theorem,

                                     ..........................(1)

               The side values are lower than the hypotenuse,

                                                        ...................................(2)

               Where,

                         a,b - side values

                            c - Hypotenuse

               For right angle triangle,  c > a, b

               Alternative : 1

               Take, a = 7cm, b = 11cm

               From eqn (2),

                                                   =  = 13.04

              The above value is not equal to the any one of the values of ( 54cm. 60cm, 61cm, 65cm ), So its not an sides of right triangle.

               Alternative : 2

               Take, a = 7cm, b = 54cm

               From eqn (2),

                                                   =  = 54.45

              The above value is not equal to the any one of the values of (60cm, 61cm, 65cm ), So its not an sides of right triangle.

               Alternative : 3

               Take, a = 7cm, b = 60cm

               From eqn (2),

                                                   =  = 60.406

              The above value is not equal to the any one of the values of (61cm, 65cm ), So its not an sides of right triangle.

               Alternative : 4

               Take, a = 7cm, b = 61cm

               From eqn (2),

                                                   =  = 61.40

              The above value is not equal to the values of (65cm ), So its not an sides of right triangle.

                 Alternative : 5

               Take, a = 11cm, b = 54cm

               From eqn (2),

                                                   =  = 55.1089

              The above value is not equal to the any one of the values of (60cm, 61cm, 65cm ), So its not an sides of right triangle.      

                Alternative : 6

               Take, a = 11cm, b = 60cm

               From eqn (2),

                                                  =  = 61

              The above value is equal to the values of (61cm ), So its an sides of right triangle. The three sides are 11, 60 and 61.

Step:2

            Check for solution,

Result:

            The side lengths of a right triangle is 11cm, 60cm and 61cm, that could be selected from the given measurements.                

Step-by-step explanation: The side lengths of a right triangle is 11cm, 60cm and 61cm.

Answer:

the maximum number would be 243 cookies

Step-by-step explanation:

Answer:

7.5 bags of snack mix, 3.5 bottles of water.

Step-by-step explanation:

This can be found by looking at a system of equations. Setting up our system, we know that they bought 11 items, and that there was a total of $20. Our system would be this:

[tex]x+y=11\\2.5x+1.25y=20[/tex]

We can then solve for a variable in any equation. Let's solve for x in the second equation.

[tex]2.5x+1.25y=20\\2.5x=20-1.25y\\x=8-0.5\\x=7.5[/tex]

Now, we substitute into the other equation.

[tex]x+y=11\\7.5+y=11\\y=11-7.5\\y=3.5[/tex]

We now know both amounts; they bought 7.5 bags of snack mix and 3.5 bottles of water.

Answer: 125

Step-by-step explanation

Answer:

25.12

Step-by-step explanation:

That is the correct answer. Thank you! :)

Answer:

Its B. x = -5y2

Step-by-step explanation:

The equation for the parabola is x = -5y² option (B) x = -5y² is correct.

It is defined as the graph of a quadratic function that has something bowl-shaped.

We have a graph of a parabola.

As we can, in the graph of a parabola:

The equation for the left side opening:

x = -ay²

Here a = 5

x = -5y²

Thus, the equation for the parabola is x = -5y² option (B) x = -5y² is correct.

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Answer:

112

Step-by-step explanation:

x - 90 = 22

add (solve for x)

x = 112

Answer:

your answer will be 6cm^2

Step-by-step explanation:

hope it helps you

have a great day

Answer:

c = 10

Step-by-step explanation:

9 + 10 +6c = -1 +8c

19 +6c = -1 + 8c

19 + 1+ 6c  = -1 +1 + 8c

20 +6c -6c = 8c - 6c

20/2 = 2c/2

10 =c

Answer:

The anwser i think it's D

Step-by-step explanation:

Answer: B

Step-by-step explanation:

Answer:

The Answer is option 2

Step-by-step explanation:

Answer:

70 degrees

Step-by-step explanation:

The measure of the central angle equal the measure of the arc it intercepts.

So arc BC is 70 degrees.

Answer: The inequality required to express the above condition is   x     ≥    18.75

Step-by-step explanation:Renata and her family go through an average of more than 15 cans of sparkling water each day.

The number of cases of 24 cans of sparkling water.

We can take the number of cases to be x.

Each case is said to cost $3.50.

An inequality for the number of cases that Renata's family go through in 24 days can be written as

      x ≥            ⇒     x    ≥            ⇒   x ≥     18.75

Therefore the inequality required to express the above condition is

x     ≥    18.75

Answer:

your answer will be

2 and 1/12

Step-by-step explanation:

hope it helps you

have a great day!!

8.3 (repeating) percent or 2 out 24 children

Answer:

3

Step-by-step explanation:

I did the math

Answer:

3

Step-by-step explanation:

Answer:

1a. 3/8

1b. 4/12-1/3

Step-by-step explanation:

to get the answers you have to find a common denominator and then add them

Answer:

The answer would be

a) 3/8

b) 1/3