1. Kevin took $45 with him to spend on snack for himself and his friends at the movie theater. The price for each bucket of popcorn was $4. The price of each drink was half the price of a bucket of popcorn.
(a) Sketch the graph that represents the situation and label the intercepts. Use one axis to represent the number of bucket of popcorn and the other axis to represent the number of drinks.
(b) Explain your graph.

Answer: y = −6

Step-by-step explanation:

Answer:

5y−3=6y+3

Step 1: Subtract 6y from both sides.

5y−3−6y=6y+3−6y

−y−3=3

Step 2: Add 3 to both sides.

−y−3+3=3+3

−y=6

Step 3: Divide both sides by -1.

−y

−1

=

6

−1

y=−6

Step-by-step explanation:

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Answer: 60

Step-by-step explanation:6x10=60

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Answer:

16

Step-by-step explanation:

112/7=16, 16x4=64, 16x3=48, 64-48=16

By substitute values in formula for volume of cuboid we get;

x² + 12x – 220 = 0

What is mean by Volume?

Volume of cuboid is defined as the amount of space occupied by the sides of cuboid in three-dimensional space.

Given that;

A cuboid with a volume of 924 cm' has dimensions,

4 cm, (x + 1) cm and (x + 11) cm.

Since, Volume of cuboid = Length x width x height

After substitute we get;

Volume of cuboid = 4 × (x + 1) × (x + 11)

924 = 4 (x² + 11x + x + 11)

924 = 4 (x² + 12x + 11)

Divide 4 both side;

231 = x² + 12x + 11

x² + 12x + 11 - 231 = 0

x² + 12x - 220 = 0

Thus, By the formula of volume of cuboid we get;

x² + 12x - 220 = 0

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Take the prime factorization of both numbers to find the GCF. Then list the characteristics that they share. If they have more than one of the same factor (for example, two 2's), write them both down. Then multiply the factors they share.

A positive integer's prime factors are the prime numbers that divide it exactly. Finding these numbers is known as integer factorization or prime factorization. According to the fundamental theorem of arithmetic, every positive integer has a unique prime factorization.

The GCF (Greatest Common Factor) of two or more numbers is the greatest number among the given numbers' common factors. The greatest common factor (GCF) of two natural numbers x and y is the largest possible number that divides both x and y without leaving any remainder. GCF can be calculated in three ways: division, multiplication, and prime factorization.

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Given data:

The amount invested ( principal) is

The interest rate given is

The number of years is

The number of times compounded is quarterly

A quarterly event happens four times a year, at intervals of three months.

Concept:

The formula to calculate the amount compounded is given below as

By substituting the values above in the formula, we will have

By solving the equation above, we will have

Hence,

The final answer = $2,290.05

SOLUTION:

Answer:

[tex]x = \frac{196}{13} [/tex]

The length and width of the rectangular box are 13 ft and 6 ft respectively.

The length of the batter's box on a softball field is 1 ft more than twice the width.

The area of the batter's box is 78 ft².

The length and width of the rectangular batter's box can be found as follows:

Therefore,

area of a rectangle = lw

where

Therefore,

area of the rectangular box = 78 ft²

l = 1 + 2w

Hence,

78 = (1 + 2w)w

78 = w + 2w²

2w² + w - 78 = 0

Hence,

w = 6  and w =  -13  /2

we can only use positive values.

Therefore,

width = 6 ft

length  = 2(6) + 1 = 13 ft

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Answer:

Explanation:

Let x represent the number of defective cars.

Assuming that number of defective cars are uniformly distributed in the total number of cars, we can go ahead and solve for x by setting up proportion as shown below;

Given:

A passenger train traveled 35 miles in 50 minutes.

umber of miles that train can travel in one hour is 42 miles.

If Isaiah is measuring 3 1/2 inches using a ruler marked in 1/8 inch increments. The total number of eighths that Isaiah will need to count out to make his measurement is B.28.

We would be making use of the given hint to determine the total number  of eight.

The hint is to use  3 1/2 into an improper fraction with a denominator of 8.​

Hence,

Converting 3 1/2 to improper fraction

3 1/2 = 7/ 2 inches

Now let determine the total number with a denominator of 8.​

= 7 × 4 / 2 ×4

= 28 /8

Therefore the correct option is B.

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The graph of the linear equation:

y = -3x + 4

Can be seen in the image at the end.

To draw a line, we just need to find two points that belong to the line, graph them, and then connect them with a  line.

Here we know that we have the line:

y = k*x + 4

Where k = -3, then:

y = -3*x + 4

By evaluating this in a value of x, for example, x = 0, we will get:

y = -3*0 + 4 = 4

Then we also have the point (0, 4) (and the given one, (2, -2))

So we can draw these two points and then connect them with a line (just use a ruler and draw a line that passes through both points).

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1. The mathematical expression that can be used to determine the total cost of mailing a package weighing p pounds is f(Tc) = 20 + 3p.

2. Since Betty spent $56 to mail her package, the weight in pounds of the mail must be 12 pounds.

A mathematical expression is a statement containing numbers, variables, and an arithmetic operation.

Flat (fixed) rate for mailing a package = $20

Variable mailing rate per pound = $3

Expression to model the total cost:

Let Tc = total cost

p = number of pounds

Tc = 20 + 3p

If Betty spent $56 to mail her package, the number of pounds, using the mathematical expression above:

Tc = 20 + 3p

56 = 20 + 3p

56 - 20 = 3p

36 = 3p

p = 12

Check:

Tc = 20 + 3p

56 = 20 + 3 (12)

56 = 20 + 36

56 = 56

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Answer:

  (d) Domain: {x|x∈ℝ} and range: {y|y∈ℝ}

Step-by-step explanation:

You want the domain and range of the relation shown in the graph.

The graph shows a line. The arrows on the end of it mean that it extends to infinity in both directions (up and left; down and right).

The domain is the horizontal extent. It includes all real numbers (from -∞ to +∞).

The range is the vertical extent. It includes all real numbers (from -∞ to +∞).

Domain: {x|x∈ℝ} and range: {y|y∈ℝ}

6 bottles are needed.

The unitary technique involves first determining the value of a single unit,  followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

given:

2 tablets 3 times per day

so, total tablets = 6 tablets

Total days = 14

so, total tablets in 14 days = 14 x 6 = 96

and, tablets per bottle= 15

Then, the number of bottles required = 96 /15 =6.4

Hence, 6 bottles are needed.

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Answer: y= -2/5 + 36/5

Step-by-step explanation: when graphed, the slope is negative so it has to be -2/5x, and the y-intercept is positive so it has to be +36/5 (+7.2)

To know if a number is a perfect sqare of a perfect cube you:

perfect sqare

determine if its sqaure root is an integer. If is not an interger, then the number is not a perfect sqare

perfect cube

determine if its Cube root is an interger. If is not an interger then the number is not a perfect cube

Then so, 121 is a perfect cube, because is the result of (11*11)

121 is not a perfect cube

The table which represents the transformation of function f given by g(x) = 3f(x) is:

x                   - 3   - 1     1    3

f(x)                - 5   - 1     3    7

g(x) = 3f(x)    - 15  - 3    9    21

When a function is transformed, the graph's curve of the parent function either "moves to the left/right/up/down," "expands or compresses," or "reflects."

A table for every value of x and its corresponding value of f(x) is given as:

x      - 3   - 1     1    3

f(x)   - 5   - 1     3    7

Now the transformed function g is given as:

g(x) = 3f(x)

Therefore, the table that represents the transformation of f given by g will be:

x                   - 3   - 1     1    3

f(x)                - 5   - 1     3    7

g(x) = 3f(x)    - 15  - 3    9    21

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We construct  an equation and calculate that number as 7 .

The equals sign is a symbol used in mathematical formulas to denote the equality of two expressions. The word equation and its cognates can have slightly different meanings in different languages. For instance, in English, an equation is any well-formed formula that consists of two expressions linked by the equals sign, whereas in French, an equation is defined as containing one or more variables.

The equation's solutions are the values of the unknown variables that satisfy the equality, which are often referred to as the variables for which the equation must be solved.

let the number be x .

9 times the number is = 9x

5 times the number added to 3 is

(x + 3) × 5

Now let us set up an equation and find that number :

(x + 3) × 5 = 9x - 13

Simplifying the given equation we get :

5 (x + 3) = 9x - 13

5x + 15 = 9x - 13

5x - 9x = - 13 - 15

- 4x = - 28

x = - 28/-4

x = 7

Hence the required number calculated from the equation is 7 .

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Disclaimer: The complete question is :

If the sum of a number and 3 is multiplied by 5 , the result is equal to 9 times the number decreased by 13. Find the number

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(a) The area of the triangle = 6 cm squares

(b) The area of the whole shape = 76 cm squares

The shape given is formed by a triangle and a rectangle.

First we need to find the area of the triangle.

Height of the triangle = 3 cm

Base of the triangle = 4 cm

Area of the triangle = 1/2 x base x height

                                 = 1/2 x 4 x 3

                                 = 6 cm squares

Area of the whole shape = Area of the triangle + Area of the rectangle

Length of the rectangle = 10 cm

Width of the rectangle = 7 cm

Area of the rectangle = length x width

                                    = 10 x 7

                                    = 70 cm squares

Therefore, area of the whole shape = 6 + 70

                                                            = 76 cm squares

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Step-by-step explanation:

cook time = 65 min + 11 min + 60 seconds + 30 seconds

= 65 min + 11 min + 1.5 minute

cook time = 77.5 minutes or: 1 hour, 17 minutes and 30 seconds.

For food to be ready by 4PM:

4PM - 1 hour, 17 minutes and 30 seconds = when to put food in

put food in = 2:42:30 PM

Given:

Find the property.

Sol:

The additive identity property is:

So use the Additive Identity property.

The number of payments to pay off the loan of $200,000 at 6.3% interest, compounded monthly is 315 monthly payments.

Using the compounding format for determining the monthly payments, the number of periods for the periodic payments can be computed.

In this situation, we used the online finance calculator to determine the number of payments.

Compounding accumulates the interest on a loan and adds it to the principal for computing subsequent interest.

At the end of the period, the balance is made up of the principal and compounded interest.

I/Y (Interest per year) = 6.3%

PV (Present Value) = $200,000

PMT (Periodic Payment) = $-1300

FV (Future Value) = $0

Results:

N (# of periods) = 314.854

Sum of all periodic payments = $-409,309.97

Total Interest $209,309.97

Thus, you are likely to make 315 monthly payments to settle the loan.

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Use the pythagorean theorem to find side C

The right answer is 6.4

Question 14

[tex]\binom{8}{3}=\frac{8!}{5!3!}=56[/tex]

Question 15

[tex]\binom{15}{6}=\frac{15!}{9!6!}=5005[/tex]

The probability of getting someone who tested positive, given that he or she did not have the disease is 0.985

Probability is what has the potential to happen. This area of math examines how random events happen. A value between 0 and 1 is used to express it. In order to anticipate the possibility of events, probability has been introduced to mathematics. The degree of likelihood that something will happen can be used to define probability. This fundamental theory of probability, which is also applied to the probability distribution, can be used to estimate the likelihood of the results of a random experiment. We must first determine the total number of alternatives in order to determine the likelihood that a specific event will occur.

Given that : He or she did not have the disease. The individual actually had the disease No positive 9 , negative 133 Yes Positive 140 ,Negative 18 .

                      Yes              No

Positive :          140            9

negative :         18              133

P = [tex]\frac{Someone get positive }{he not had the disease}[/tex]

= [tex]\frac{140}{142}[/tex]

=0.985

The probability of getting someone who tested positive, given that he or she did not have the disease is 0.985

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The vertex form of a parabola is expressed as

y = a(x - h)^2 + k

where

a is the leading coefficient

h and k are the horizontal and vertical coordinates of the vertex.

Recall, the general expression for a quadratic equation is

y = ax^2 + bx + c

By comparing with the given equation,

a = - 2, b = 36, c = - 171

The formula for the x coordinate of the vertex is

x = - b/2a

x = - 36/(2 * - 2) = - 36/- 4 = 9

Substituting x = 9 into the equation, we have

y = - 2(9)^2 + 36(9) - 171

y =