Carolyn Was asked to solve the following system of equations, her work is shown.

Answer:

2 outcomes

Step-by-step explanation

The Roslin has 32 students in her class, of these students, 14 are girlsl number of outcomes are 252.

It is a branch of mathematics that deals with the occurrence of a random event.

The total number of outcomes can be found by multiplying the number of options for choosing a boy by the number of options for choosing a girl:

Number of outcomes = number of options for choosing a boy x number of options for choosing a girl

Since Mrs. Roslin has 32 students in her class, there are 32 - 14 = 18 boys in her class.

So the number of options for choosing a boy is 18, and the number of options for choosing a girl is 14.

Therefore, the total number of outcomes is:

18 x 14 = 252

Hence, the total number of outcomes is 252.

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A- they are parallel because they have equal slopes.

Given:

Admission to the local movie theater is $3 for each child and $7 for each adult.

A group of 12 people pay $64 admission.

To find:

The number of children in a group.

Solution:

Let the number of children be x and number of adults be y.

According to the question,

Total persons : [tex]x+y=12[/tex]          ...(i)

Total cost : [tex]3x+7y=64[/tex]     ...(ii)

Multiply equation (i) by 7 and subtract the result from (ii).

[tex]3x+7y-7(x+y)=64-7(12)[/tex]

[tex]3x+7y-7x-7y=64-84[/tex]

[tex]-4x=-20[/tex]

Divide both sides by -4.

[tex]x=5[/tex]

Therefore, the number of children is 5.

Answer:

Option (A)

Step-by-step explanation:

From the graph attached,

Right and left ends of the graph are moving downwards.

Ends moving upwards or downwards (In the same side of x-axis) tells the graph to be an even function.

There are two maximum points (points having maximum y-values)represent the two relative extrema of the function.

Therefore, Option (A) will be the correct option.

Answer:

19.67

Step-by-step explanation:

divide 177 by 9. the answer is 19.66666667, but you might have to round ;)

this is the answer for this question

Answer:

a.  The car sweeps out 0.799 radians per second.

b. f(t) = 8 cos (0.799t)

Step-by-step explanation:

Given that:

The radius r = 8 feet

a.

The time t it takes to complete one full lap = 7.854 seconds

Recall that:

Angular velocity ω = 2π / t

So if in 7.854 seconds, the car sweeps = 2π radian

∴

per second, the car will sweep ω  = 2π/ 7.854

ω = 0.799 rad/sec

Thus, the car sweeps out 0.799 radians per second.

b.

Since, r = 8 feet.

Suppose the car travels an angle θ in time (t),

Then the general equation for the horizontal component is:

f(t) = rcos( ωt)

f(t) = 8 cos (0.799t)

The true statements are:

The given parameters are:

To do this, we simply calculate the angular velocity as follows:

[tex]\omega = \frac{2\pi}{T}[/tex]

Substitute 7.854 for T

[tex]\omega = \frac{2\pi}{7.854}[/tex]

Simplify

[tex]\omega = 0.255 \pi[/tex]

Hence, the car swept out [tex]0.255 \pi[/tex] radians per seconds

To do this, we simply make use of the general equation for the horizontal component as follows:

[tex]f(t) = r\cos( \omega t)[/tex]

Substitute 8 for r

[tex]f(t) = 8\cos( \omega t)[/tex]

Substitute [tex]\omega = 0.255 \pi[/tex]

[tex]f(t) = 8\cos( 0.255\pi t)[/tex]

Hence, the function f that determines the car's distance at time t is: [tex]f(t) = 8\cos( 0.255\pi t)[/tex]

Read more about angular velocity at:

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Answer:

Triangles 3 and 4 are both isosceles. They each have a 60 degree angle.

This is a similar triangle.

Step-by-step explanation:

Isosceles triangle is one in which two sides are equal.

Similar triangles are triangles which have all corresponding angles equal and which have corresponding sides with the same ratio.

Now the given isosceles triangle both have all three angles equal to 60 degrees which makes them similar triangles.

The other choices given are not similar triangles because

1) they do not have all corresponding angles equal

2) their lengths are unknown and cannot be assumed to be in ratio.

Answer:

5:9

Step-by-step explanation:

There are 5 blue shapes out of 9 total shapes.

Answer: 3x + 14

Step-by-step explanation: you have to combine the terms 11 + 3 = 14  5x - 2x = 3x

Answer:

$2662.5 is the answer in my opinion

Answer:

negative

Step-by-step explanation:

Positive numbers do not change the polarity of a number in multiplication, only negative numbers.

Answer:

Well, you look at each individual place value.

1.679 and 1.697

Compare 1 to 1. They are the same. Move on.

Compare 0.6 to 0.6. They are the same. Move on

Compare 0.07 and 0.09. They are not the same. 0.07 is less than 0.09

Therefore 1.679 < 1.697

Hope this helps :)

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Answer:

-5x-4y

Step-by-step explanation:

Combine like terms:

-4x-x+5y-9y rearrange

-5x-4y.

Hope this helps :D

Given:

Total number of tickets = 600

Cost of adult ticket = $6.00

Cost of student ticket = $4.00

Total sales = $2900.00

To find:

The number of tickets of each type.

Solution:

Let the number of adult tickets be x and number of student tickets be y.

According to the question,

[tex]x+y=600[/tex]        ...(i)

[tex]6x+4y=2900[/tex]      ...(ii)

Multiply equation (i) by 4 and subtract the result from (ii),

[tex]6x+4y-4(x+y)=2900-4\times 600[/tex]

[tex]6x+4y-4x-4y=2900-2400[/tex]

[tex]2x=500[/tex]

Divide both sides of 2.

[tex]x=250[/tex]

Put x=250 in (i).

[tex]250+y=600[/tex]

[tex]y=600-250[/tex]

[tex]y=350[/tex]

Therefore, number of adult tickets is 250 and number of student tickets is 350.

Answer: it’s D

Step-by-step explanation:

Answer:

8 floor tickets and 7 balcony tickets.

Step-by-step explanation:

f+b=15

25f+17.50b=322.50

Answer:

8 floor tickets, 7 balcony tickets

Step-by-step explanation:

F + B = 15

25F + 17.50B = 322.50

Answer:

One pair of gloves costs $3.75.

Step-by-step explanation:

Systems of equations

x=hats y=gloves

2x+3y=28.25  

x+y=12.25

2(12.25-y)+3y=28.25

24.5+y=28.25

y=3.75

Answer:

y = [tex]\frac{3}{2}[/tex] x - 8

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{3}{2}[/tex] , thus

y = [tex]\frac{3}{2}[/tex] x + c ← is the partial equation

To find c substitute (8, 4) into the partial equation

4 = 12 + c ⇒ c = 4 - 12 = - 8

y = [tex]\frac{3}{2}[/tex] x - 8 ← equation of line

The equation of a line that has a slope of 3/2 and passes through (8, 4) can be written as:

[tex]y - 4 = \frac{3}{2} (x - 8)[/tex] (point-slope form) or

[tex]y = \frac{3}{2}x - 8[/tex] (slope-intercept form).

Given:

a point on a line: (8, 4)

slope of the line: 3/2

The equation of the line can be written in either point-slope form or slope-intercept form.

First, let's write the equation in point-slope form since we know one of the points and the slope.

Where,

[tex]y - 4 = \frac{3}{2} (x - 8)[/tex] =>> point-slope form.

[tex]y - 4 = \frac{3}{2} (x - 8)[/tex]

[tex]y - 4 = \frac{3}{2}x - 12[/tex]

[tex]y - 4 + 4 = \frac{3}{2}x - 12 + 4\\\\y = \frac{3}{2}x - 8[/tex](slope-intercept form)

Therefore, the equation of a line that has a slope of 3/2 and passes through (8, 4) can be written as:

[tex]y - 4 = \frac{3}{2} (x - 8)[/tex] (point-slope form) or

[tex]y = \frac{3}{2}x - 8[/tex] (slope-intercept form).

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Answer:

[tex] \frac{3x}{5} - \frac{1}{10} = \frac{x + 2}{10} - 2 \\ \frac{6x - 1 = x + 2 - 20}{10} \\ 6x - x = - 18 + 1 \\ 5x = - 17 \\ x = - \frac{17}{5} [/tex]

Answer:

x= -17/5 or x=-3.4

Step-by-step explanation:

1. multiply both sides of equation by 10 (6x-1 = x+2-20)

2, calculate the difference (6x -1=x-18)

3. move the terms ( 6x-x-1=-18)

4. collect like terms ( 5x=-18+1)

5. divide both sides (x=-17/5)

Answer:

282

Step-by-step explanation:

47*6=282

Forty seven six times.

B.

you can eliminate A and D because grades are distributed by 100. and c only has 4.85 when the question says she made a 48.5

Complete Question

The complete question is shown on the first uploaded image

Answer:

The correct option is  C

Step-by-step explanation:

The  sample  

                                                                                          Household Income

                                                                                     < $60,000    > $60,000

I would never purchase a newspaper subscription.          40                63

I might or might not purchase a newspaper subscription. 53                70

I would probably purchase a newspaper subscription.     65                 32

I already purchase a newspaper subscription.                   73                 16

Generally the sample size is mathematically represented as

       [tex]n = 40 + 53 + 65+ 73 + 63 + 70 + 32+ 16[/tex]

=>    [tex]n = 412[/tex]

Generally the number of the sample with an income greater $60,000 is mathematically represented as

        [tex]N = 63 + 70 + 32 + 16[/tex]

=>     [tex]N = 181[/tex]

Generally the number of  families with an income more than $60,000 who might or might not purchase a newspaper subscription is

      [tex]X = 70[/tex]

Generally the percentage of families with an income more than $60,000 who might or might not purchase a newspaper subscription is

           [tex]P(X) = \frac{70}{181} * 100[/tex]

=>        [tex]P(X) = 39\%[/tex]

Answer:

1.)  1,380

2.) 138

Step-by-step explanation:

I know i'm 5 days late but why let the question go to waste

If  He earns 10 percent of the total amount he sells, He would Get-

The total amount of Rashad’s sales- 1,380

How much does Rashad earn from his sales- 138

Have a Nice day!

Answer:

1380

138

Step-by-step explanation:

Answer:

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

Step-by-step explanation:

Equation of a Line

The equation of a line passing through points (x1,y1) and (x2,y2) can be found as follows:

[tex]\displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

The table shows the relation between x and y. It contains the following points

(-3,1), (6,4), (12,6), (30,12).

Taking the two first points, we find the equation of the line:

[tex]\displaystyle y-1=\frac{4-1}{6+3}(x+3)[/tex]

[tex]\displaystyle y-1=\frac{3}{9}(x+3)[/tex]

Simplifying:

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

To ensure the rest of the points belong to the line, we test them:

For the point (12,6):

[tex]\displaystyle 6-1=\frac{1}{3}(12+3)[/tex]

[tex]\displaystyle 5=\frac{1}{3}(15)[/tex]

5=5

Since equality is true, the point belongs to the line.

For the point (30,12):

[tex]\displaystyle 12-1=\frac{1}{3}(30+3)[/tex]

[tex]\displaystyle 11=\frac{1}{3}(33)[/tex]

11=11

Since equality is true, the point belongs to the line.

Thus, the equation of the line is:

[tex]\mathbf{\displaystyle y-1=\frac{1}{3}(x+3)}[/tex]

Answer:

17 / 8

Step-by-step explanation:

sec A = [tex]\frac{1}{cos A}[/tex]

cos A = [tex]\frac{40}{85}[/tex] = [tex]\frac{8}{17}[/tex] ⇒ sec A = [tex]\frac{17}{8}[/tex]

Answer:

30

Step-by-step explanation:

(3x12)-(4+2)

36-6

30

Answer:

9

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

AnswerX=9

Step-by-step explanation:

6x-42=39-3x