Your Student Government Association decided to do a fundraiser to raise
money for a field trip. They decide to sell t-shirts and sweatshirts. The
profit for each t-shirt is $10 and the profit for each sweatshirt is $15.
They want to sell 50 items at most. Compared to t-shirts, they want to sell
at least half as many sweatshirts, with a profit of at least $500.
after graphing What are the boundaries of the feasible region (i.e. the points that define
the region of solutions)? (Hint: There should be four points)
Are there any non-viable solutions within the feasible region
How many t-shirts and sweatshirts should they sell to maximize their profit
What is the maximum profit they can make?

Answer:

option (B) $61,422

Explanation:

Given the annual salary is $70,600

Percent of Contribution made from the income = 13%

Pretax Salary/Income is calculated by the formula, Salary – 13% of salary

Pretax income =

[tex]70600 - \frac{13}{100} \times 70600[/tex]

= 70600 – 9178 = 61422

Therefore whitney’s pretax income is $ 61422

Hence, option (B) is correct

Answer:

The correct answer is B. $61,422

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Let length of rectangle be "l"

Let width of rectangle be "w"

We know,

LENGTH is 2 MORE THAN WIDTH, we can write:

l = w + 2

Also, note the perimeter is the sum of all 4 sides of a rectangle, thus:

length + width + length + width

Now,

The perimeter is given as 72, so we can write:

l + l + w + w = 72

2l + 2w = 72

We have 2 equations that we need to solve and find the length (l).

The first equation is:

l = w + 2

Rearranging, we have:

w = l - 2

We put this into 2nd equation and find the value of l:

[tex]2l + 2w = 72\\2l + 2(l-2) = 72\\2l+2l-4=72\\4l-4=72\\4l=76\\l=\frac{76}{4}\\l=19[/tex]

The length is 19 meters, the correct answer is C

To solve the expression, rewrite each term with the same denominator and then add them together. The final answer is 2.345.

To solve the expression 1 15/100 +1/50 +1.175, we need to rewrite all the terms with the same denominator. The least common denominator (LCD) of 100 and 50 is 100. Therefore, we can rewrite the expression as follows:

1 15/100 is equivalent to 1.15

1/50 is equivalent to 0.02

Now, we can add the three terms together:
1.15 + 0.02 + 1.175 = 2.345

Therefore, the final answer is "2.345."

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Answer:

$38.00

Step-by-step explanation:

164/4=41          41-3=38

Answer: $37.45(to the nearest hundredths)

Step-by-step explanation:

% increase in last year living cost =5%

% increase in last year income =5%

This year income = $39.420

To calculate last year income implies

5% decrease of this year income; thus:

5/100 * $39.420 = $1.971

Last year income = $39.420 - $1.971 = $37.449 = $37.45 (to the nearest hundredths)

Answer:

37.4490 (rounded to the nearest hundredth) = 37.45

Step-by-step explanation:

ok so her bills or wateva went up 5% right and she gets a lil 5% raise or sumn from her job which made her money got up to $39.42. so if you think about it all you do is multiply 39.42 and (5%) which = 0.05 in decimal form and then after you multiply you should get 1.9710 and once you get that you gone take her money she getting now which is 39.42 - her 5% raise she got and once you subtract you gone get 37.4490 or 37.45 rounded

Answer:

25 tickets were purchased ahead of time

Step-by-step explanation:

25(11)=275 which is the price of the 11 bought at the door then you  take 625-275=350 which is the amount of money that was raised through purchases ahead of time so you take 350/14=25 meaning that 25 tickets were bought ahead of time.

There are 25 tickets were purchased ahead of time.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The cost of tickets to a fundraiser when purchased ahead = $14

The cost of tickets to a fundraiser when purchased at the door = $25

And, The total amount raised from all ticket sales = $625

Now,

Let number of tickets to a fundraiser when purchased ahead = x

And, The number of tickets to a fundraiser when purchased at the

door = y

We can formulate;

⇒ $14x + $25y = $625

Since, The number of tickets to a fundraiser when purchased at the

door = 11

So, y = 11

Hence, We can formulate;

⇒ $14x + $25y = $625

⇒ $14x + $25 × 11 = $625

⇒ $14x + $275 = $625

⇒ $14x = $625 - $275

⇒ $14x = $350

⇒ x = 25

Thus, There are 25 tickets were purchased ahead of time.

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Answer:

7.92

Step-by-step explanation:

0.99*8=7.92

Answer:

8a = 8(.99)

7.92

hoope it helps

Answer:

d < -28

d ∈ (-∞ , -28)

Step-by-step explanation:

[tex]\frac{d}{7}[/tex] + 4 < 0

Taking 4 on the right side of the equation,

We get,    [tex]\frac{d}{7}[/tex] < -4

Now, since 7 is positive number , we can transfer it to right side of the equation multiplying with -4,

It gives,  d < -28.

So  d belongs from -∞ to -28 excluding -28 ,

We can write, d ∈ (-∞ , -28).

Answer:

c

Step-by-step explanation:

Solve the inequality, that is

18 > 3x - 3 ( add 3 to both sides )

21 > 3x ( divide both sides by 3 )

7 > x, hence

x < 7

< is denoted by an open circle on the number line at 7, meaning that x cannot be equal to 7. Since less than 7 then the arrow head points to the left of 7

This is represented by Graph c

Answer:

(5x+10) + (x+14) =180

6x+24=180

x=26

Angles are 140 and 40

Step-by-step explanation:

Answer:

Since the multiplicative inverse of a fraction p/q is the fraction that swaps its numerator and denominator, i.e. q/p, we have that the inverse of 2/3 is 3/2.

So, if we multiply both sides of the equation by 3/2, we have

[tex]\dfrac{3}{2}\cdot\dfrac{2}{3}a=16\cdot\dfrac{3}{2}[/tex]

3/2 and 2/3 are multiplicative inverse of each other, and by definition this means that they give 1 when multiplied:

[tex]\dfrac{3}{2}\cdot\dfrac{2}{3}a=1\cdot a=a=16\cdot\dfrac{3}{2}[/tex]

On the right hand side, we have

[tex]16\cdot\dfrac{3}{2}=8\cdot 3=24[/tex]

And so the solution is [tex]a=24[/tex]

Final answer:

To find the intercepts of the given line, the equation is rearranged into the slope-intercept form, revealing the y-intercept directly and allowing for easy calculation of the x-intercept by setting y=0. Thus, the x-intercept is 4/3.

Explanation:

To determine the intercepts of the line given by the equation -3x - 4 = -5y - 8, we should find both the x-intercept and y-intercept. The general form of a line is given by y = mx + b, where m is the slope, and b is the y-intercept.

Steps to find the intercepts:

Rearrange the equation to the slope-intercept form y = mx + b by adding 3x to both sides and then adding 8, resulting in -5y = 3x - 4. By further dividing both sides by -5, we get  y = -3/5x + 4/5.

To find the y-intercept (b), set x=0 in the rearranged equation, which gives y = 4/5. Thus, the y-intercept is 4/5.

To find the x-intercept, set y=0 in the rearranged equation, resulting in 0 = -3/5x + 4/5. Multiplying both sides by 5 and then dividing by -3, we find x = 4/3. Thus, the x-intercept is 4/3.

top left i guessed and got it correct

Answer:

A is correct so technically the top left hope this helps

Step-by-step explanation:

Answer:

2x - y = 3.

Step-by-step explanation:

0.2x = 0.1y + 0.3

Multiply through by 10:

2x = y + 3

2x - y = 3.

Answer:

D)24 people

Step-by-step explanation:

Total number of people, x=300

Number of people donated blood with type A, y

[tex]=\frac{28}{100}\times x\\=\frac{28}{100} \times 300\\=84[/tex]

Number of people donated blood with type B, z

[tex]=\frac{20}{100}\times x\\=\frac{20}{100} \times 300\\=60[/tex]

⇒Number of people with Type A blood donated more than those with Type B blood= y-z=84-60= 24

Answer:

D) There are 24 more people who donated Type - A then Type -B.

Step-by-step explanation:

Total number of people who donated the blood in shelter = 300

Percentage of people who donated the type A = 28%

Percentage of people who donated the type B = 20%

Now, 28 %  of 300 = [tex]\frac{28}{100 } \times 300 = 84[/tex]

So, the total number of people who donated the Type - A  = 84 people.

Also, 20 %  of 300 = [tex]\frac{20}{100 } \times 300 = 60[/tex]

So, the total number of people who donated the Type - B  = 60 people.

So, the difference in the people who donated type A and Type B  

= Number of people who donated the {Type - A  - Type - B}

= 84 people -  60 people

= 24 people

or, the difference in the people who donated type A and Type B  = 24

Hence, there are 24 more people who donated Type - A then Type -B.

Answer:

P=0.39

Step-by-step explanation:

We use the Hypergeometric distribution to find the probability

The normal deck of cards has 52 cards, 26 red and 26 black

Taking 4 cards out of the whole deck can be done (without replacement) in

[tex]\begin{pmatrix}52\\4\end{pmatrix}[/tex]

different ways .

Taking 2 red cards can be done in

[tex]\begin{pmatrix}26\\2\end{pmatrix}[/tex]

different ways. Same applies to the black cards

So, the required probability can be computed as

[tex]P=\frac{\begin{pmatrix}26\\2\end{pmatrix}\begin{pmatrix}26\\2\end{pmatrix}}{\begin{pmatrix}52\\4\end{pmatrix}}[/tex]

[tex]{\begin{pmatrix}52\\4\end{pmatrix}}=\frac{52!}{4!48!}=270725[/tex]

[tex]{\begin{pmatrix}26\\2\end{pmatrix}}=\frac{26!}{2!24!}=325[/tex]

[tex]P=\frac{325x325}{270725}=0.39[/tex]

Answer:

4. All of the values are not proportional except 2 values

5. All of the values are non-proportional

6. All of the values are proportional

7. The two variables are proportional when, (no. of pies ordered (one of the variables)) is ≥ 12 . but the two variables are non-proportional when, 0 < (no. of pies ordered (one of the variables))  < 12.

Step-by-step explanation:

4.All of  the values in table 4. are not proportional, except 2 since,

[tex]\frac {1}{17.25} = \frac{4}{70} \neq \frac{2}{35.50}  \neq \frac{3}{50.75}[/tex]

although the units for all fractions is the same i.e.,  hour/dollar

5. All  of the  values in table 5 are non-proportional since,

[tex]\frac {1}{37} \neq \frac {2}{73} \neq \frac {3}{109} \neq  \frac{4}{145}[/tex]

although units for all the fractions are the same. i. e., hour/no. of pages

6. All  of the values of the table 6. are proportional, since,

[tex]\frac {1}{2.75} = \frac {2}{5.5} = \frac {3}{8.25} = \frac {4}{11}[/tex]

and all of the fractions  have same unit i. e.,   number of lunches/dollar

7. If no, of pies ordered is less than a dozen, then the cost is given by,

 y = 5 + 4.5x    [y in $, where x is the no. of pies ordered and 0 < x < 12]

clearly, y is not proportional to x.

The table of some values is given by,

   x          y

   1          $ 9.5

   2          $  14

   3          $ 18.5                         etc.

If no, of pies ordered ≥ 12, then the cost is given by,

   m = 4.5n [m in $, where, n is  no. of pies ordered and n ≥ 12]

clearly, m is proportional to n

The table of some values is given by,

  n               m

  12             $ 54

  13              $ 58.5            

  14              $ 63                      etc.

Answer:

6

Step-by-step explanation:

I assume you mean GCF, greatest common factor.

First, write the prime factorizations for each:

18 = 2¹ × 3²

24 = 2³ × 3¹

Next, find what they have in common.  Both have a factor of 2¹ and 3¹.

GCF = 2¹ × 3¹

GCF = 6

The greatest common factor is 6.

Answer:

6

Step-by-step explanation:

18 = 1x18 2x9 3x6

24 = 1x24 2x12 4x6 3x8

Answer:

b

Step-by-step explanation:

the only one that has a cop of 15 is b

The two ordered pairs to show that the equation y = 15x represents the data are (1, 15) and (2, 30) option (B) is correct.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

The linear equation is:

y = 15x

Plug x = 1

y = 15

Plug x = 2

y = 30

The two points are (1, 15) and (2, 30) which lie on the equation of the line y = 15x

Thus, the two ordered pairs to show that the equation y = 15x represents the data are (1, 15) and (2, 30) option (B) is correct.

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Answer:

48

Step-by-step explanation:

2x-1=6

2x=6+1

2x=7

x=7/2

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

4x^2-1

4(7/2)^2-1

4(49/4)-1

49-1

48

Answer: 48

Step-by-step explanation:

2x - 1 = 6

Add 1 to both sides of the equation , we have:

2x = 7

divide through by 2

x = 7/2

The value of [tex]4x^{2}[/tex] - 1 will be calculated by substituting in the value of x , that is

[tex]4x^{2}[/tex] - 1 = 4([tex](\frac{7}{2} )^{2}[/tex] - 1

= 4([tex]\frac{49}{4}[/tex]) - 1

= 49 - 1

= 48

Answer:

Option D =[6    18]  is the correct answer

Step-by-step explanation:

Given that:

[4  2] * [-2    5; 7    -1]

For taking product:

= [4*-2 + 2*7    4*5 + 2*-1]

=[-8 + 14        20 + (-2) ]

=[6    18]

i hope it will help you!

Answer:

x>=-12

Step-by-step explanation:

3x+7>=-29

3x>=-29-7

3x>=-36

x>=-36/3

x>=-12

Answer:

1 right angle

Step-by-step explanation:

The sides are not in common

Answer:

1 right angle

Step-by-step explanation:

They dont have the same number of sides

Answer:

The number of dimes = 32

The number of quarters  = 14

Step-by-step explanation:

Here, the total number of coins combined = 46

Let us assume the number of dimes = m

So, the Number of quarter = Total Coins - Number of dimes  = 46 - m

Now,as we know:

1 dime = $0.1

So, m dimes  = m x ($0.1) = $(0.1 m)

1 Quarter  = $0.25

So, ( 46 - m ) Quarters  = (46 - m ) x ( $ 0.25)   = 11.5 - 0.25 m

Also, given the total amount of coins = $ 6.70

⇒ Value of (Dimes + Quarters) = $ 6.70

or, (0.1 m) +  11.5 - 0.25 m  = 6.70

-0.15 m = - 4.8

or, m = 4.8/0.15  =  32

⇒ m = 32

Hence, the number of dimes = m = 32

And the number of quarters  = 46 - m= 46 -32 = 14

Answer:

The restaurant sold 175 hotdogs and 525 hamburgers.

Step-by-step explanation:

Let the restaurant sold x hotdogs and y hamburgers.

Given the restaurant sold 350 more hamburgers than hotdogs.

So, we can write x + 350 = y ....... (1)

Again given that the number of total hotdogs and hamburgers sold in the restaurant is 700.

So, x + y = 700 ........ (2)

Solving equations (1) and (2) we get  

2x + 350 =700

⇒ 2x = 350

⇒ x = 175

Then from equation (1) we get,

y = 350 + 175 = 525

Therefore, the restaurant sold 175 hotdogs and 525 hamburgers. (Answer)

Answer:

1

Step-by-step explanation:

8/2*4=8/8=1

Answer:

16990.616 $ you can expect to have in your account after five years.

Step-by-step explanation:

Given that,

Amount invested is principal amount (p) = $ 15000

Annual rate of interest (r) = 2.5% = 0.025

Compounded quarterly (n) = 4

Sum of the amount after 5 years (t)

We know that from compound interest formula,

[tex]\text { Final amount }(\mathrm{A})=P\left(1+\frac{r}{n}\right)^{n t}[/tex]

To find the final amount substitute the given values in the above formula,

[tex]\text { Final amount }(\mathrm{A})=15000\left(1+\frac{0.025}{4}\right)^{4 \times 5}[/tex]

[tex]\text { Final amount }(\mathrm{A})=15000\left(1+6.25 \times 10^{-3}\right)^{20}[/tex]

[tex]\text { Final amount }(\mathrm{A})=15000(1.00625)^{20}[/tex]

[tex]\text { Final amount }(\mathrm{A})=15000 \times 1.132707738[/tex]

Final amount (A) = 16990.62

The final amount that he can expect is $ 16990.62.