A group fitness gym classifies its fitness class attendees by class type and member status. The marketing team has gathered data from a random month, in which there were 2333 class attendees. The data is summarized in the table below. Class Type and Member Status of Class Attendees Class Type Member Non-Member Barre 157 232 Boot Camp 259 258 Boxing 282 215 Spinning 161 235 Yoga 271 263

Answer:

a: [tex]f(t)=(t+2)^2-18[/tex]

b: vertex: (-2, -18)

   minimum

c: x = -2

Step-by-step explanation:

Completing the square is difficult to explain in words. but I'll try my best. Let me know if you need any more information.

Part A ===============

Start with the given function in this form:

[tex]f(x)=ax^2+bx+c\\t^2+4t-14[/tex]

We need an additional number, d, and we'll calculate it like this:

[tex]d=(\frac{b}{2a})^2 \\\\d=(\frac{4}{2(1)} )^2\\d=2^2\\d=4[/tex]

d needs to be added and subtracted at the same time. That way we do not change the value of the expression:

[tex]ax^2+bx+d-d+c\\\\t^2+4t+4-4-14[/tex]

And you can separate them like this to make it easier to read:

[tex](t^2+4t+4) + (-4-14)\\(t^2+4t+4)-18[/tex]

Finally, we need to factor the trinomial in the parenthesis. Because we've completed the square, it's now a perfect square trinomial.  The factored form is just:

[tex](x+e)^2[/tex]

where e is half of b, or the square root of c. That looks like this in our case, and you can also expand it to make sure.

[tex](t+2)^2\\\\(t+2)(t+2)\\t^2+2t+2t+4\\t^2+4t+4[/tex]

Put that all together and you get the answer:

[tex]f(t)=(t+2)^2-18[/tex]

Part B ===============

Vertex form is this:

[tex]f(x)=a(x-h)^2+k[/tex]

where (h, k) is the vertex and a is the scale factor.

In part A, we converted the given function into vertex form. Looking at that, you can see the vertex is at (-2, -18), and the scale factor is 1. When the scale factor is positive, the parabola faces upwards. When it's negative, the parabola faces downwards.

The scale factor is a positive 1 in this case, and if you picture that in your mind, the vertex is at the very lowest point, or the minimum, of the parabola.

Part C ==============

The axis of symmetry is always on the vertex, and that is because the vertex is the exact point where the parabola changes direction from positive to negative, or negative to positive.

The vertex of this parabola is (-2, -18), so the axis of symmetry is at x = -2.

Sorry if that got too long and hard to follow, I can clarify any part of it if needed.

Answer:

I know answer. give me money I will tell everything..

An equation is a collection of variables and constants. The value of b for the given equation b + 23 = 114 will be 91.

There are many different ways to define an equation.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

More than one variable may be present inside a linear equation.

As per the given equation,

b + 23 = 114

Add -23 both sides

b + 23 - 23 = 114 - 23

b + 0 = 91

b = 91

Hence "An equation is a collection of variables and constants. The value of b for the given equation b + 23 = 114 will be 91".

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Answer:

325/12

Step-by-step explanation:

12(1/4 + 1/3)² + 23

12(7/12)² + 23

12(49/144) + 23

49/12 + 23

325/12 = 27 1/12 = 27.08333333

Answer:

700 liter

Step-by-step explanation:

because 1000 * 7/10 is 700

Answer:

1. (x - 1) × (x + 3)

2. x = 3 and y = -2

Step-by-step explanation:

rewrite the equation:

y = 3x - 11; 2x + 3y = 0

solve y = 3x - 11 for the y:

y = 3x - 11

substitute 3x - 11 for y in 2x + 3y = 0;

2x + 3y = 0;

2x + 3y = 0

2x + 3 (3x - 11) = 0

11x - 33 = 0 (simplify both sides of the equation)

11x - 33 + 33 = 0 + 33 (add 33 to both sides)

11x = 33

11x/11 = 33/11 (divide both sides by 11)

x = 3

subtitute 3 for x in y = 3x - 11

y = 3x - 11

y = (3)×(3) - 11

y = -2  

I showed one equation because the other is self explanatory, hope this helps.

Answer:

I am almost completely sure its 4.

Step-by-step explanation:

I dont mind brainiests by the way

Answer:

Circle

Step-by-step explanation:

The area of a circle is

[tex]\pi r^{2}[/tex]

A. circle

The area of a circle is 2[tex]\pi[/tex]r²

The Circle Formulas are expressed as,

The collection of all points equidistant from a fixed point in a plane is called a circle.

the circle is a closed 2-dimensional figure in which the set of all the points in the plane is equidistant from a given point called the “center”. Every line that passes through the circle forms the line of reflection symmetry.

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Answer:

3.5 cups of sugar per bag.

Step-by-step explanation:

17.5/5

3.5 cups of sugar are used to make 1 bag of cotton candy

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given:

For 5 bags of candy = 17.5 cups of sugar needed

and, For 1 bags of candy

=17.5/ 5

=3.5 cups of sugar needed

hence, 3.5 cups of sugar are used to make 1 bag of cotton candy

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The amount invested in each stock, the stock interest rate and the

duration of the investment, determines the interest.

Reasons:

Let X represent the sum of the amount Brian invested, we have;

Amount invested in stock paying 5% dividend = [tex]\dfrac{X}{2}[/tex]

Amount invested in stock paying 9% dividend = [tex]\dfrac{X}{2}[/tex]

Total annual interest = $420

Required:

The amount invested in the stocks

Solution:

The amount invested is found as follows;

[tex]\dfrac{X}{2} \times 5\% + \dfrac{X}{2} \times 9\% = 420[/tex]

0.025·X + 0.045·X = 420

0.07·X = 420

[tex]\displaystyle \mathrm{The \ amount \ invested , \, X} = \frac{420}{0.07} = \mathbf{ 6,000}[/tex]

The amount he invested = $6,000 ($3,000 in each stock)

Learn more here:

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Answer:

3.34

Step-by-step explanation:

First step: 3x44=132, 132+15=147. Then use 147 as numerator and 44 as denominator.

Second step: Divide 147/44= 3.3409090909091, round and get 3.34.

Hope this helps.

Answer:

6[tex]\frac{2}{3}[/tex] inches tall

Step-by-step explanation:

4:6 = x:10

We can set it up like this:

[tex]\frac{4}{6}=\frac{x}{10}[/tex]

And then cross multiply & solve:

40 = 6x

6[tex]\frac{2}{3}[/tex] = x

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

Answer:

30%

Step-by-step explanation:

Presuming that "survey 3,000" is the total and "900" is the factor who had problems then dividing the total amount by the amount of problems like equal the relative frequency of people that had problems

Math:

Amount of people you had problems / Amount of people who bought the new car.

900 / 3000 = 0.3

Now you need to multiply by 100% (because % in this case is a unit/measurement)

0.3 * 100% = 30%

Answer:

P = 83 in

Step-by-step explanation:

For this one, all we need to do is substitute 7 for x and 4 for y:

3x + y = ?

3(7) + 4 =?

21 +4 = ?

21 + 4 = 25 in.

Now for the next one:

4y = ?

4(4) = ?

4(4) = 16

Now we solve the final side:

6x = ?

6(7) = ?

6(7) = 42

Now to find P, we must add them all together:

25 + 16 + 42 = 83

Therefore P = 83

Answer:

A) P = 83

Step-by-step explanation:

-=======================-

3x + y

3(7) + 4 =

21 + 4 =

25

-=======================-

6x

6(7)

42

-=======================-

4y

4(4)

16

-=======================-

25 + 16 + 42 = 83

Hope this helps.

Answer:

2

Step-by-step explanation:

The graph clearly shows that when x = -1, y = 2.

Thus, the output of this function is 2.

Answer:

$15

Step-by-step explanation:

12+3+15

Answer:

Bill Amount: $12

Tip Percent: 25%

Divide By: 1  

= $15

Answer:

$76

Step-by-step explanation:

Answer:

[tex]3\dfrac{1}{4} \ \ or \ \ 3,25[/tex]

Step-by-step explanation:

[tex]\displaystyle12 \frac{3}{8} -9\frac{1}{8} =12-9+\frac{3}{8} -\frac{1}{8} =3+\frac{2}{8} =3\frac{1}{4} \ \ or \ \ 3,25[/tex]

Answer:

  x/12

Step-by-step explanation:

There are 12 inches in a foot.

  feet in x inches = x/12

_____

With units, you have ...

  (x in) × (1 ft)/(12 in) = x/12 ft

Answer:

126/1=126

Step-by-step explanation:

630:5 as a fraction would be 630/5.

630/5 simplified would be 126/1.

Hope this helps :)

Answer:

630:5 would be 126:1

Step-by-step explanation:

To solve this we would divide 630 by five giving us 126, and divide 5 by 5 giving us one

Now we have 126:1, or 126 km/hour

Answer:

the answer is 33 9/11

Step-by-step explanation:

multiply the fractions

.

.

Answer:

33 9/11

Step-by-step explanation:

22 6/11 x 1 1/2

Convert into improper fractions.

248/11 x 3/2

Reduce the numbers with the greatest common factor 2.

124/11 x 3

Calculate

372/11

=33 9/11

Hope this helps :)

Answer:

[tex]\frac{5a^2b^2}{4}[/tex]

Step-by-step explanation:

Answer:

(7) 3 2 2x 23 xy y - 10 0 Solution The equation 2x2 23xyy2-100 has A2,B 23, and (1 13) as p3 (Example 2). 13: 271279. 2 m) long and 6 ft Step-by-step explanation:

The correct answer is C. 58

Hope this helps!

Step-by-step explanation:

the answer is 58 this is the result I hope I've helped

Answer: the answer is 25

Step-by-step explanation:

First do 100/1

Then do 1 x 100/1 x 4

so then divide 100 by 4 =

25/1 =

25

Answer:

Step-by-step explanation:

just do 35-17

Answer:

Step-by-step explanation:

first find b.

To find b, subtract 17 from 35.

35 - 17 = b

35 - 17 = 18

next, add 17 and 18 to see if it equals 35.

17 + 18 = 35

so, b = 18.

Answer:

x=7/10

Step-by-step explanation:

1/5=2/10

9/10-       =2/10

Substitute the blank with X

9/10-  X  =2/10

x=7/10

Answer:

7/10

Step-by-step explanation:

9/10 - _ = 1/5

Let's represent the unknown as x

Therefore,

9/10 - x = 1/5

9/10 - 1/5 = x

x = 9/10 - 1/5 = 7/10