The manager of a movie theater found that Saturdays sales were $3675. He knew that a total of 650 tickets were sold on saturday. Adult tickets cost $7.50, and children tickets cost $4.50. How many of each kind of ticket were sold?

Answer:

1. 5417.412

2. 401.13

Step-by-step explanation:

1. First, rewrite

[tex]5\times 10^3+4\times 10^2+1\times 10^1+7\times 10^0+4\times \dfrac{1}{10^1}+1\times \dfrac{1}{10^2}+2\times \dfrac{1}{10^3}[/tex]

as

[tex]5\times 1000+4\times 100+1\times 10+7\times 1+4\times 0.1+1\times 0.01+2\times 0.001[/tex]

So, this is

[tex]5000+400+10+7+0.4+0.01+0.002\\ \\=5417.412[/tex]

2. First, rewrite

[tex]4\times 10^2+1\times 1 \dfrac{1}{10^1}+3\times \dfrac{1}{10^2}[/tex]

as

[tex]4\times 10^2+1\times 1 +1\times \dfrac{1}{10^1}+3\times \dfrac{1}{10^2}[/tex]

This is

[tex]4\times 100+1\times 1+1\times 0.1+3\times 0.01[/tex]

So, this is

[tex]400+1+0.1+0.03\\ \\=401.13[/tex]

Answer: 593/500

Step-by-step explanation: To write a percent as a fraction in lowest terms, first remember that a percent is a ratio that compares a number to 100.

So here, 118.6% can be written as the ratio 118.6 to 100 or 118.6/100.

To write 118.6/100 in lowest terms, we first will need to multiply the numerator and the denominator by 10 to remove the decimal point. When we do this, we get the equivalent fraction 1186/1000.

Now, we can divide the numerator and the denominator by the greatest common factor of 1186 and 100 which is 2 and we get the equivalent fraction 593/500.

Therefore, 118.6% can be written as the improper fraction 593/500.

Answer:

(C) Stock Variable

Step-by-step explanation:

With the $50,000 in the bank, it is assumed the value is earnings from stock. $3,000 worth of goods in the warehouse also make up the stocks hence the $50000 plus $3000 to make up $53,000 stock variable

Answer:

no

Step-by-step explanation:

1 foot is 30.48 cm

So 1 yard is 3(30.48 cm) = 91.44 cm (less than 100 cm = 1 meter)

So 2 yards is about 183 cm, less than 200 cm

Answer:

c

Step-by-step explanation:

Answer:

101.8 meters in 1 minute

Step-by-step explanation:

509/5=101.8

Answer:

After Albert  builds the frame, 1.174 meters  of wood will be left.

Step-by-step explanation:

Here, the total length of wood required to build wooden frame  = 30 meters

The length of the wooden pieces collected  are:

First piece = 12.5  m

Second Piece  = 11.43  m

and Third Piece  =  7.244 m

Now, the total length of wood all pieces combined

= Length of (First + second + third ) Piece

= 12.5 m +  11.43 m +  7.244 m  = 31.174 m

So, the combined length of all wooden pieces  = 31.174 m

Now, the left over length = Total wood collected - The length required

                                              = 31.174 m = 30 m  =  1. 174 m

Hence, after he builds the frame, 1.174 meters  wood will be left.

Answer:

y = 10*x

Step-by-step explanation:

y = kr --> 400

r = 4k

400 = k (4k) = 4k^2

k^2 = 400/4 = 100

k = sqrt(100) = 10  

k = 10

Answer:

For the first question [tex]x = 4\\ y = -1[/tex] and

For the second question [tex]x = 0.5\\ y = -1[/tex]

Step-by-step explanation:

Given:

1.

x - 3y = 7

3x + 3y = 9

2.

8x+ 3y = 1

4x + 2y = 0

Elimination method :

In the elimination method we need to make the coefficient of x or the coefficient of y same in both the equation so by adding or subtracting we can eliminate the x term or the y term.

Then substitute that values which you will get on eliminating in any equation you will get the corresponding value.

For the first question, the y coefficient is same hence by adding both the equation we can eliminate 3y term. so on solving we get

[tex](x - 3y) + (3x + 3y) = 7 + 9\\4x = 16\\x = \frac{16}{4}\\x = 4[/tex]

Now substitute X equal to 4 in equation x -3y = 7 we get

[tex]4 - 3y = 7\\-3y = 7 - 4\\-3y = 3\\y = \frac{3}{-3}\\ y = -1\\[/tex]

This way we have x is equal to 4 and y is equal to -1  for question number 1.

For the second question, we will make X coefficient same in the second equation that is multiplying by 2 to the equation 4x + 2y = 0 then we get

[tex]8x + 4y = 0\\[/tex]

Now the coefficient of x term become same now we will subtract the two equations that is 8x + 3y = 1 and 8x + 4y =0 we get

[tex](8x + 3y) - (8x + 4y) = 1 - 0\\3y - 4y = 1\\ -y = 1\\y = -1[/tex]

Now substitute y equal to -1 in equation 8x +3y = 1 we get

[tex]8x + 3\times -1 = 1\\8x - 3 = 1\\8x = 1 + 3\\8x = 4\\x = \frac{4}{8}\\ x = 0.5\\[/tex]

This way we have x is equal to 0.5 and y is equal to -1  for question number 2.

Answer:

- 4 h ≥ - 80

Step-by-step explanation:

The temperature of the metal is 0°C and the gets to no colder than - 80°C.

If the temperature is decreasing at the rate of - 4°C per hour, then the temperature after h hours will be t = 0 + (- 4) h which will not be less than - 80°C.

So the inequality that models the situation is 0 + (- 4) h ≥ - 80

⇒ - 4 h ≥ - 80 (Answer)

Final answer:

The inequality to ensure that the temperature of the metal does not fall below -80°C as it drops steadily at -4°C/hour is 0 - 4h ">= -80. This represents the highest number of hours (h) the physicist can allow before the temperature reaches the limit.

Explanation:

The student has asked to write an inequality based on a physicist's experiment where a metal's temperature decreases at a steady rate of -4°C per hour and should not get colder than -80°C. Starting at 0°C, the relationship between time (in hours) and temperature can be represented mathematically.

To express this as an inequality, we can set up a relationship where the temperature (t) after a certain number of hours (h) is no less than -80°C. Since the temperature is decreasing at -4°C per hour, we can write the inequality as:

t ≥ -80

Where t = 0 + (-4 × h), and h represents the number of hours passed.

Substituting the expression for t into the inequality:

0 - 4h ≥ -80

This inequality tells us that regardless of how many hours go by at this rate, the temperature of the metal should remain higher than -80°C.

75% of the teachers were first-year teachers

Step-by-step explanation:

the formula for percentage will be used for the problem

The percentage is given by:

[tex]Percentage=\frac{Quantity}{Total}*100\\[/tex]

Here

Total teachers = 57+19 = 76

First-year teachers = 57

So,

[tex]Percentage\ of\ first\ year\ teacher = \frac{57}{76}*100\\=0.75*100\\=75\%[/tex]

Hence, 75% of the teachers were first-year teachers

Keywords: Percentage, Percent

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Answer:

7x-8y+11z

Step-by-step explanation:

Because this is the only one that doesn't have an equal sign. Therefore, this is an example of an expression, not a equation. All of the other answer choices have an equal sign, they're equations.

Answer:

{12, 4, -6}

Step-by-step explanation:

The relation is given by the equation as 12x + 6y = 24 ........... (1)

Now, the domain of this function is {-4, 0, 5}

We have to find the range of this function corresponding to the given domain.

Now, for x = - 4,  

12(-4) + 6y = 24 {From equation (1)}

⇒ 6y = 72

⇒ y = 12

Now, for x = 0,  

12(0) + 6y = 24 {From equation (1)}

⇒ 6y = 24

⇒ y = 4  

Now, for x = 5,  

12(5) + 6y = 24 {From equation (1)}

⇒ 6y = -36

⇒ y = -6

Hence, the range for the relation is {12, 4, -6} (Answer)

The value of [tex]2 \times(7 \times 1)[/tex] is -80

Given that x y is a real number

Also given that [tex]x \times y = x(x - y)[/tex]

We are asked to find the value of [tex]2 \times (7 \times 1)[/tex]

To solve it we have to first solve terms in brackets.

[tex]\begin{array}{l}{\text {So, } 7 \times 1=7(7-1) \quad[\text {from given rule }]} \\\\ {\rightarrow 7 \times 1=7 \times 6} \\\\ {\rightarrow 7 \times 1=42} \\\\ {\text {Now, the required expression is modified as } 2 \times 42} \\\\ {\text {Then, } 2 \times 42=2(2-42)=2(-40)=-80} \\\\ {\text {Hence, the value of } 2 \times(7 \times 1)=-80}\end{array}[/tex]

Answer:

A. [tex]\frac{4^{8} }{4^3}[/tex]

D. [tex]4^{5}[/tex]

Step-by-step explanation:

We have to calculate to find the result -

The expression is = 4^(-3)/4^(-8)

According to the indices rule, the power will be deducted if it is a division.

Therefore, [tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{m-n}[/tex]

Using that formula,

= [tex]4^{-3-(-8)}[/tex]

= [tex]4^{-3+8}[/tex]

= [tex]4^{5}[/tex]

Therefore, the answer choice D is the option, and the answer is 4^5.

Option A is also correct. Because we can find 4^5 with the help of that option.

[tex]\frac{4^8}{4^3}[/tex]

= [tex]4^{5}[/tex]

Alternative way,

4^(-3)/4^(-8)

= 4^(-3+8)

= 4^(8-3)

= 4^8/4^3

In the is way, we can also find option A is correct.

Answer:

A&D

1 & 4

[tex]\frac{4^8}{4^3}[/tex] and [tex]4^{5}[/tex]

Step-by-step explanation:

edge 2021

Answer:

7 months

Step-by-step explanation:

260=134+18m

126=18m

7=m

Answer: 7 months.

$18 × 7 months = $126

$134 + $126 = $260

Answer:

Yes.

Step-by-step explanation:

21/25=84/100=84%

Answer:

Yes

Step-by-step explanation:

If you got all off it that means you have 100 and to make it more simpler you are removing 4 points for every question that you failed so if you got 21 questions right then you have 84%

How many vases are there?

The number of flowers in each vase is 31 and the number of flowers left over is 3.

Given that, Alexandra has 127 flowers and 4 vases.

The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.

Here,

The same number of flowers in each of her vases =Total number of flower/Number of vases

= 127/4

Now, 4|127|31

            124
         _______
               3

Number of flowers left over =3

Therefore, the number of flowers in each vase is 31 and the number of flowers left over is 3.

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"Your question is incomplete, probably the complete question/missing part is:"

Alexandra has 127 flowers and 4 vases. She puts the same number of flowers in each of her vases. How many flowers will be left over?

Answer:

The number of pine tress more than the number of ash trees is 8 .

Step-by-step explanation:

Given as

The number of pine trees = 10

The number of ash trees = 2

Let The number of pine tree more than that of ash tress = x

So, The number of ash trees + x = 10

Or, 2 + x = 10

I.e x = 10 - 2

∴  x = 8

So, The pine trees is 8 more than the ash trees

Hence The number of pine tress more than the number of ash trees is 8 . Answer

Answer:

92%

Step-by-step explanation:

there are 4 cards of "7"

52-4=48

48÷52×100=92.307...%

Answer:

The width of rectangle is 1 unit.

Step-by-step explanation:

Given:

The area of rectangle is 6 units and its width is 5 units less than the length.

So, to find the width of rectangle.

Let the length be [tex]x[/tex] and the width be [tex]x-5[/tex].

Now, to find the width we put the formula of area of rectangle:

Area = length × width

[tex]6= x\times (x-5)[/tex]

[tex]6=x^{2}-5x[/tex]

[tex]0=x^{2}-5x-6[/tex]

[tex]0=x^{2}-6x+x-6[/tex]

[tex]0=x(x-6)+1(x-6)[/tex]

[tex]0=(x-6)(x+1)[/tex]

On solving equation we get:

[tex]x-6=0, x+1=0[/tex]

Therefore, we take the value x=6 as it is positive value:

[tex]x-6=0[/tex]

[tex]x=6[/tex]

So, the width of rectangle:

Width = [tex]x-5[/tex]

          = [tex]6-5[/tex]

          = [tex]1[/tex]

Therefore, the width of rectangle is 1 unit.

Answer:

the year 2010

Step-by-step explanation:

since the end of high school is 12th grade, you have to numbers. 12, and 5.

subtract 5 from 12 and you get seven. subtract seven from 2017, and you get 2010

You were in 5th grade in the year 2010.

To determine what year you were in 5th grade, you can subtract 7 from the year you graduated high school. In this case, if you graduated in 2017, you subtract 7to get 2010. Therefore, you were in 5th grade in the year 2010.

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Answer:

x=-50

Step-by-step explanation:

31/25x=-62

x=-62/(31/25)

x=(-62/1)(25/31)

x=--1550/31

x=-50

Answer:

X = 50

Step-by-step explanation:

31/25 x = 62

25 times 31/25 x = 62 times 25

31x = 1550

31/31 = 1550/31

x = 50

Answer:

[tex]135\pi\ ft^3[/tex]

Step-by-step explanation:

we know that

The volume of a cylinder (concrete column) is equal to

[tex]V=\pi r^{2}h[/tex]

we have

[tex]r=3\ ft\\h=15\ ft[/tex]

substitute

[tex]V=\pi (3)^{2}(15)[/tex]

[tex]V=135\pi\ ft^3[/tex]

Answer:

-225/8

Step-by-step explanation:

-3/2(24-5 1/4)

5 1/4=21/4

-3/2(24-21/4)

-3/2(96/4-21/4)

-3/2(75/4)

-225/8

Answer:

The equation needed is [tex]\textrm{Cost of 1 ream of paper}  =  \frac{20}{5} [/tex]

The cost per ream of paper  = $4

Step-by-step explanation:

Here, the cost of 5 reams of paper  = $ 21

The tax on her purchase  = $1

So, the actual cost of 5 reams of paper  = Total Cost paid  - Tax amount

= $ 21 -  $ 1  = $20

So, the actual cost of 5 reams of the paper is $20.

Now, to find out the cost of 1 ream of paper:

[tex]\textrm{Cost of 1 ream of paper}  = \frac{\textrm{Total amount paid for 5 reams}}{\textrm{ 5}}  \\= \frac{20}{5}  = 4[/tex]

=  $4

Hence, the cost of each ream of paper  = $ 4.

Answer:7 months

Step-by-step explanation:

$35 x 5 months = $175

175 / 25 = 7

Answer:

7 months

Step-by-step explanation:

Answer:

x = 9.6

Step-by-step explanation:

Given that x varies directly as y then the equation relating them is

x = ky ← k is the constant of variation

To find k use the condition x = 4 when y = 15

k = [tex]\frac{x}{y}[/tex] = [tex]\frac{4}{15}[/tex]

x = [tex]\frac{4}{15}[/tex] y ← equation of variation

When y = 36, then

x = [tex]\frac{4}{15}[/tex] × 36 = [tex]\frac{144}{15}[/tex] = 9.6

The problem is related to direct variation and can be solved using the formula x=ky which expresses the direct proportionality of x and y. The constant of variation k is found using the values of x and y given and is applied to find the new x value when y=36.

The problem discussed here is related to the concept of direct variation or direct proportionality. When we say that 'x varies directly as y', it means that x is proportionally related to y, and that relationship can be expressed by the equation x = ky, where k is the constant of variation.

In this case, you are given that x = 4 when y = 15. So, you can find the constant of variation 'k' by dividing x by y. Hence, k = x/y = 4/15.

Now, you are asked to find the value of x when y = 36. Given that x = ky, simply substitute k = 4/15 and y=36 into this equation. Therefore, x = (4/15)*36 which will yield the value of x.

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Answer:

The graph in the attached figure

Step-by-step explanation:

Let

x ----> the number of horses

y ---> the number of sheep

In this problem the relationship between the variables, x, and y, represent a proportional variation.

Remember that, if the linear equation represent a proportional variation then it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]

we have

For x=1, y=3

Find the value of the constant of proportionality k

[tex]k=\frac{3}{1}=3\ \frac{sheeps}{horse}[/tex]

substitute

[tex]y=3x[/tex]

using a graph tool

The graph in the attached figure

Answer:

A. About half of the animals at the zoo weigh less than 106 pounds

B. The average weight of al animals at the zoo is about 145.50

Step-by-step explanation:

The median weight is 106 pounds and the average weight of the animals at the zoo are 145.40