Model with Mathematics
The owner of a frozen yogurt stand considers different pricing options for a serving of yogurt plus toppings. For what number of toppings do the two options give the same price?
A. Define the variables.
B. Write a system of equations that models this situation.
C. Graph the system. What is the intersection point?
D. What is the solution of the problem?
E. Is the solution reasonable for this situation? Explain.

Answer:

Step-by-step explanation:

lol i poopeed

The most appropriate choice for percentage will be given by-

a)Percentage of people arrive at their office before 7 am = 10%

b)Percentage of people arrive at their office after 7:59 am = 64 %

What is percentage?

Suppose, there is ratio of two numbers and it has to be expressed as a fraction of 100, percentage is that ratio.

So percentage is the ratio of two numbers expressed as a fraction of 100.

Here,

a) Number of people arrive at their office before 7 am = 15

Total number of people = 15 + 39 + 75 + 21

                                        = 150

Percentage of people arrive at their office before 7 am = [tex]\frac{15}{150}\times 100[/tex]

                                                                                            = 10%

b)Number of people arrive at their office after 7:59 am = 75 + 21

                                                                                           = 96

Percentage of people arrive at their office after 7:59 am = [tex]\frac{96}{150}\times 100[/tex]

                                                                                              = 64 %

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The polynomial in standard form that represents the perimeter of the quadrilateral is 12x - 3

The quadrilateral is a plane that has four sides.

The sides of the quadrilateral are

3x-2, 2x+1, 5x-2 and 2x

The perimeter of the quadrilateral is the sum of all the sides of quadrilateral

The perimeter of the quadrilateral = 3x-2 + 2x+1 + 5x-2 + 2x

Rearrange the terms and add or subtract the like terms

= 3x + 2x + 5x + 2x -2 + 1 - 2

= (3+2+5+2)x - 2+1-2

= 12x - 3

Hence, the polynomial in standard form that represents the perimeter of the quadrilateral is 12x - 3

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Answer:

p=  - 50

Step-by-step explanation:

Move the p variables to one side and the constant numbers (intergers) to the other

-91=6p + 9 - 4p

-91 - 9 = 6p- 4p

-100 = 2p

[tex]\frac{-100}{2}[/tex] = [tex]\frac{2p}{2}[/tex]

-50 = p

p= -50

ANSWER: p=50

-91=6p + 9 - 4p solve for p

1. 6p - 4p = 2p

2. -91= 2p + 9

-91-9= 100

3. 100 = 2p

p= 100/2

p= 50

Answer:

9

Step-by-step explanation:

15-2*3

15-6

9

Jesus loves u hope it helps

Step-by-step explanation:

that means "calculate the result with these values".

the expression is

15 - ab

or

15 - a×b

for a = 2, b = 3 this gives us

15 - 2×3 = 15 - 6 = 9

Answer:

Kelsey ran 100 meters in 228.5 seconds.

Step-by-step explanation:

To find the answer, first find out how many seconds it takes for her to run 1 meter.

91.4/40=2.285

Now, multiply that by 100.

228.5

Kelsey ran 100 meters in 228.5 seconds.

Answer:

Isosceles

Isosceles triangles have 2 side the same length and one side different

multiplication tables from 2 to 20

table of 2

2 x 1 = 2      

2 x 2 = 4

2 x 3 = 6

2 x 4 = 8

2 x 5 = 10

2 x 6 = 12

2 x 7 = 14

2 x 8 = 16

2 x 9 = 18

2 x 10 = 20

table of 3

3 x 1 = 3

3 x 2 = 6

3 x 3 = 9

3 x 4 = 12

3 x 5 = 15

3 x 6 = 18

3 x 7 = 21

3 x 8 = 24

3 x 9 = 27

3 x 10 = 30

table of 4

4 X 1 = 4

4 X 2 = 8

4 X 3 = 12

4 X 4 = 16

4 X 5 = 20

4 X 6 = 24

4 X 7 = 28

4 X 8 = 32

4 X 9 = 36

4 X 10 = 40

table of 5

5 x 1 = 5

5 x 2 = 10

5 x 3 = 15

5 x 4 = 20

5 x 5 = 25

5 x 6 = 30

5 x 7 = 35

5 x 8 = 40

5 x 9 = 45

5 x 10 = 50

table of 6

6 x 1 = 6

6 x 2 = 12

6 x 3 = 18

6 x 4 = 24

6 x 5 = 30

6 x 6 = 36

6 x 7 = 42

6 x 8 = 48

6 x 9 = 54

6 x 10 = 60

table of 7

7 x 1 = 7

7 x 2 = 14

7 x 3 = 21

7 x 4 = 28

7 x 5 = 35

7 x 6 = 42

7 x 7 = 49

7 x 8 = 56

7 x 9 = 63

7 x 10 = 70

table of 8

8 x 1 = 8

8 x 2 = 16

8 x 3 = 24

8 x 4 = 32

8 x 5 = 40

8 x 6 = 48

8 x 7 = 56

8 x 8 = 64

8 x 9 = 72

8 x 10 = 80

table of 9

9 x 1 = 9

9 x 2 = 18

9 x 3 = 27

9 x 4 = 36

9 x 5 = 45

9 x 6 = 54

9 x 7 = 63

9 x 8 = 72

9 x 9 = 81

9 x 10 = 90

table of 10

10 x 1 = 10

10 x 2 = 20

10 x 3 = 30

10 x 4 = 40

10 x 5 = 50

10 x 6 = 60

10 x 7 = 70

10 x 8 = 80

10 x 9 = 90

10 x 10 = 100

table of 11

11 x 1 = 11

11 x 2 = 22

11 x 3 = 33

11 x 4 = 44

11 x 5 = 55

11 x 6 = 66

11 x 7 = 77

11 x 8 = 88

11 x 9 = 99

11 x 10 = 110

table of 12

12 x 1 = 12

12 x 2 = 24

12 x 3 = 36

12 x 4 = 48

12 x 5 = 60

12 x 6 = 72

12 x 7 = 84

12 x 8 = 96

12 x 9 = 108

12 x 10 = 120

table of 13

13 x 1 = 13

13 x 2 = 26

13 x 3 = 39

13 x 4 = 52

13 x 5 = 65

13 x 6 = 78

13 x 7 = 91

13 x 8 = 104

13 x 9 = 117

13 x 10 = 130

table of 14

14 x 1 = 14

14 x 2 = 28

14 x 3 = 42

14 x 4 = 56

14 x 5 = 70

14 x 6 = 84

14 x 7 = 98

14 x 8 = 112

14 x 9 = 126

14 x 10 = 140

table of 15

15 x 1 = 15

15 x 2 = 30

15 x 3 = 45

15 x 4 = 60

15 x 5 = 75

15 x 6 = 90

15 x 7 = 105

15 x 8 = 120

15 x 9 = 135

15 x 10 = 150

table of 16

16    X 1 = 16

16 X 2 = 32

16 X 3 = 48

16 X 4 = 64

16 X 5 = 80

16 X 6 = 96

16 X 7 = 112

16 X 8 = 128

16 X 9 = 144

16 X 10 = 160

table of 17

17 x 1 = 17

17 x 2 = 34

17 x 3 = 51

17 x 4 = 68

17 x 5 = 85

17 x 6 = 102

17 x 7 = 119

17 x 8 = 136

17 x 9 = 153

17 x 10 = 170

table of 18

18 x 1 = 18

18 x 2 = 36

18 x 3 = 54

18 x 4 = 72

18 x 5 = 90

18 x 6 = 108

18 x 7 = 126

18 x 8 = 144

18 x 9 = 162

18 x 10 = 180

table of 19

19 x 1 = 19

19 x 2 = 38

19 x 3 = 57

19 x 4 = 76

19 x 5 = 95

19 x 6 = 114

19 x 7 = 133

19 x 8 = 152

19 x 9 = 171

19 x 10 = 190

table of 20

20 * 1=20

20*2=40

20*3=60

20*4=80

20*5=100

20*6=120

20*7=140

20*8=160

20*9=180

20*10=200

what is the use of multiplication chart?

A grid including all the times tables is plainly displayed on a multiplication chart. It's a useful tool for remembering multiplication facts. Make a chart of the math multiplication tables and use it for calculations or daily reading. This will aid in your memorization.

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The condition is fulfilled, Law of syllogism is applied here.

What's the Law of syllogism ?

The law of syllogism, also called reasoning by transitivity, is a valid argument form of deductive reasoning that follows a set pattern. It is similar to the transitive property of equality, which reads: if a = b and b = c then, a = c

Given:

If I'm a student, then I go to school. If I go to school, then I learn

Conclusion:

If I'm a student, then I learn.

So, the Conclusion is correct and follows law of syllogism as If I'm a student then definitely i learn as i will go to school to learn according to the statement.

Therefore, the hypothesis have to be true.

Hence, the condition is fulfilled, Law of syllogism is applied here.

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The equation is x = -4.

Use slope and slope intercept form  y = mx + b,

Slope = y2 - y1/x2 - x1

Slope = 5 - (-2 )/-4 - (-4) = 7/0 = undefined

Equation of point-slope form,

(y-(-2)) = 7/0(x-(-4))

y+2 = 7/0(x+4)

7(x+4) = 0

x = -4

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Two students are selected at random from the class this can be done in 45 ways.

It is necessary for there to be one girl and one boy this is done in 24 ways.

In a given class there are six( 6 ) girls and four( 4 ) boys.

In this case, there are given two cases that two students are selected at random from the class, In how many ways can this be done

And the other case is it necessary for there to be one girl and one boy, how many ways are possible

To solve the two cases we use Combinations;

Total number of students in a class = 6 + 4 = 10

For case ( 1 ):

Two students are selected at random from the class this can be done by;

A = ¹⁰C₂

A = [tex]\frac{10!}{2!*(10-2)!}[/tex]

A = 45

For case ( 2 ):

It is necessary for there to be one girl and one boy thus is done by;

B = ⁶C₁ ˣ ⁴C₁

B = [tex]\frac{6!}{1!*(6-1)!} \\[/tex] ×[tex]\frac{4!}{1!*(4-1)!}[/tex]

B = 6 × 4

B = 24

Two students are selected at random from the class this can be done in 45 ways.

It is necessary for there to be one girl and one boy this is done in 24 ways.

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Answer:

v = -7

Step-by-step explanation:

-38 = -3 + 5v

add 3 to both sides:

-38 + 3 = -3 + 5v + 3

-35 = 5v

divide both sides by 5:

-35/5 = 5v/5

v = -7

Answer:

140,000

Step-by-step explanation:

math just times and for the 1/⁵ is 16

Using the probability concept, the proportion of times do we expect the practitioner to guess the correct hand is of 0.44.

The probability of an event in an experiment is calculated as the number of desired outcomes of the experiment divided by the number of total outcomes of the experiment.

The probability can be interpreted as the proportion of times that we expect a trial to happen.

In the context of this problem, this probability is of 44%, as stated for Emily's model, that is, out of 100 trials, the correct answer was obtained in 44 of them, hence the proportion of times do we expect the practitioner to guess the correct hand is of 0.44.

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Answer:

£20 note, £5 note, 50p,50p,50p, 5p

Step-by-step explanation:

Liam buys some fruit for £26.55 by paying 2 notes of £20 and £5 and 3 coins of 50 cent and one coin of 5 cent.

Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation.

Given:

Liam buys some fruit for £26.55.

He pays the exact amount using two notes and four coins.

So, possible notes are £1, £5, £10 and £20.

And the possible coins are 1¢, 5¢, 10¢, 25¢, 50¢, and £1.

So, through trial and error,

we get notes of £20 and £5.

And the coins are three coins of 50 cent and 1 coin of 5 cent.

The total amount = adding the amount of notes and coins.

£26.55 =  £20 + £5 + 3(50¢) + 5¢

Therefore, notes of £20 and £5 and the coins are three coins of 50 cent and 1 coin of 5 cent, Liam used.

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The percentage of students in Brookland Middle School who are attending seventh grade is 54.54%

What is percentage?

In mathematics, a percentage is a number or ratio that is expressed as a fraction of 100. Although "pct," "pct," and occasionally "pc" are also used as abbreviations, the percent symbol "%" is most usually used to denote it. A% is a number that has no dimensions and is dimensionless (pure).

We know that, to get the value of percentage we have to divide the value for which percentage needs to be calculated by total value and then multiply the resultant by 100.

So, we will divide the number of student in seventh class by the total number of student and then multiply it with 100.

(750/1375)100 = 54.54 %

Therefore, percentage of students attending Brookland Middle School are in seventh grade is 54.54%.

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Answer:

C  ( third choice )

Step-by-step explanation:

It has two equations with the operator  ' > '   ( due to the dashed lines )

  and one equation with the operator  ' ≤ '   ( due to the solid line)

So that narrows the choices to  B  or C

   C  fits the line on the Left of the graph

         when x = - 4       y = -3 (-4) - 6 = 12 -6 = 6

The least volume to greatest volume will be sphere B, sphere C, sphere A and sphere D.

The volume of the sphere is calculated as:

= 4/3 πr³

where r = radius

The volume of sphere A will be:

= 4/3 πr³

= 4/3 × π × 4³

= 85.3π

The volume for sphere B will be:

= 4/3 πr³

= 4/3 × π × (6/2)³

= 4/3 × π × 3³

= 36π

The volume for C is given as 64π.

The volume for D has a radius double that of B. This will be Radius = 3 × 2 = 6

= 4/3 πr³

= 4/3 × π × 6³

= 288π

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Answer:

David: $50.00

Pam: $47.50

Step-by-step explanation:

David:

first 10 lb $2 per lb

Additional lbs are $1

When buying 40 pounds:

first 10 lbs: $2 × 10 = $20

other 30 lbs: $1 × 30 = $30

total cost: $20 + $30 =  $50.00

_______________

Pam:

$10 entrance fee

first 10 lb $1.5 per lb

Additional lbs are $0.75

When buying 40 pounds:

Entrance: $10

first 10 lbs: $1.5 × 10 = $15

other 30 lbs: $0.75 × 30 = $22.5

total cost: $10 + $15 + $22.50 =  $47.50

Answer

(5/4) < 1.3 < 1 (8/25)

Explanation

We are told to order the given numbers from the least to the greatest number.

To do that, we will need to express the numbers in decimal form, so it is evident which one is bigger.

1 (8/25)

= 1 + (0.32)

= 1.32

1.3

= 1.30

(5/4)

= 1.25

We can easily see that

1.25 < 1.30 < 1.32

In the form of the numbers given, we have

(5/4) < 1.3 < 1 (8/25)

Hope this Helps!!!

Answer:

  (d)  y -8 = -5/8(x +8)

Step-by-step explanation:

You want the point-slope equation for the line through the points listed in the table.

The point-slope form of the equation for a line is ...

  y -k = m(x -h) . . . . . . . line with slope m through point (h, k)

The first point listed in the table is (h, k) = (-8, 8), so the equation will be of the form ...

  y -8 = m(x -(-8))

  y -8 = m(x +8)

Comparing this form to the answer choices, we see that it matches choices (b) and (d). These have m = -8/5 and m = -5/8, respectively.

The slope of the line is given by the formula ...

  m = (y2 -y1)/(x2 -x1)

  m = (4 7/8 -8)/(-3 -(-8)) = (-3 1/8)/5

Clearly the magnitude of this is less than 1, so cannot match m=-8/5, which has a magnitude greater than 1. The appropriate answer choice is (d):

  [tex]\boxed{y-8=-\dfrac{5}{8}(x +8)}[/tex]

__

Additional comments

The slope can be worked out to be ...

  (-3 1/8)/5 = (-25/8)/5 = -5/8

This confirms our answer choice.

We know the magnitude of (-3 1/8)/5 is less than 1 because 3 1/8 < 5.

The options that are clearly sources of intentional bias include:

It should be noted that bias in sampling simply gives an inaccurate information about the population.

It should be noted that using news devices for some people and using old devices is a bias that's intentional.

Also, when the test is taken using a computer, those that don't have computers will be affected. This is bias.

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Using point-slope form, the equation is [tex]y+7=-\frac{4}{3}(x-3)[/tex].

Answer:

y = - [tex]\frac{4}{3}[/tex] x - 3

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - [tex]\frac{4}{3}[/tex] , then

y = - [tex]\frac{4}{3}[/tex] x + c ← is the partial equation

to find c substitute (3, - 7 ) into the partial equation

- 7 = - 4 + c ⇒ c = - 7 + 4 = - 3

y = - [tex]\frac{4}{3}[/tex] x - 3 ← equation of line

If Megan has $50 and saves $5.50 each week. Connor has $18.50 and saves $7.75 each week. Then after 14 weeks Megan and Connor have saved the same amount.

Two or more expressions with an equal sign is called as equation.

Let  x=the number of weeks

For Megan we have:

50+5.5x

For Connor we have:

18.50+7.75x

Let us equate Megan's and Connor to have same amount.

50+5.5x=18.50+7.75x

Let us take variables on one side and numbers on other side.

50-18.50=7.75x-5.5x

31.5=2.25x

Divide both sides by 2.25

x=14

Hence after 14 weeks Megan and Connor have saved the same amount.

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The relationship between the cups of flour and the number of healthy muffins baked is C = 11M.

An equation is a representation variable and constants on both sides of the equality showing that terms of both sides of the equality sign are equal.

According to the given Fatima uses 3 cups of flour to bake 33 healthy muffins.

Assuming no. of cups to be C and no. of Muffins to be M.

If we divide M/C we get a scale factor of 11.

∴  The relationship between the cups of flour and the number of healthy muffins baked is C = 11M Or M = C/11.

We can put values of C and M to confirm that our equation is correct.

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Answer:

f(-7) = 58

Write the problem:

f(x) = -x^2 + x + 16

Plug -7 into the equation:

f(-7) = (-7)^2 + (-7) + 16

Solve:

f(-7) = 49 + (-7) + 16

f(-7) = 42 + 16

f(-7) = 58

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The inequality that represents the values of x that ensure the triangle ABC exists is 0.5 < x < 7.5

Inequality is a term used in mathematics to represent a relation that makes an unequal comparison between two functions.

As the lengths of the sides of the triangle are 6.5 units, 3.5 units, and 2.5 + x units, we can use the property which states that the sum of two sides of the triangle is always greater than the third side, therefore;

6.5 + 3.5 > 2.5 + x

10 > 2.5 + x

10 - 2.5 > x

x < 7.5

Now we use the property which states that the difference between two sides of the triangle is always less than the third side of that triangle as follows;

6.5 - 3.5 < 2.5 + x

3 < 2.5 + x

3 - 2.5 < x

0.5 < x

Now we combine both values as follows;

0.5 < x < 7.5

Therefore the inequality that represents the values of x is 0.5 < x < 7.5

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Hey there!

[tex]x+ay=b\\[/tex] for y

Add -x to both sides:

[tex]ay+x+-x=b+-x\\ay=b-x[/tex]

Now, let's divide both sides by a:

[tex]\frac{ay}{a} =\frac{b-x}{a}[/tex]

[tex]y=\frac{b-x}{a}[/tex]

Hope this helps!