a pizza shop delivered 8 pepperoni pizzas to a college on the first night of final exams. the total cost of the pizzas was $56. a small pizza costs $3 and contains 4 ounces of pepperoni. a medium pizza costs $5 and contains 9 ounces of pepperoni. a large pizza cost $11 and contains 12 ounces of pepperoni. the owner of the pizza shop used 4 pounds 12 ounces of pepperoni in making the pizzas. how many pizzas of each size were delivered to the college?

Answers

Answer 1

From the word problem given, the number of pizzas each that were delivered are:

1 small7 medium; and2 large.
What is the calculation justifying the above solution?

Step I

Let a = number of small pizzas delivered

Let b = number of medium pizzas delivered

Let c = number of large pizzas delivered

Step 2 - Creating relevant expressions based on number and type ordered, we have:

a + b + c = 8.............................1

3a + 5b + 11c = 56..................2
4a + 9b + 12C = 4 * 8 + 12.....3a

We can rewrite (3) as
4a + 9b + 12C = 44 ....3b

Step 3

Multiply both sides of (1) by 4

We have

4a +4b +4c = 32

If we remove (1) from (3) we have

4a + 9b + 12C = 44

-
4a +4b +4c = 32
5b +8C = 12......................(4)

Multiply both sides of (1) by 3 and subtract from (2), and we have:

3a + 3b + 3c = 24, removing this from (2) we have

3a + 5b + 11c = 56

-
3a + 3b + 3c = 24
2b + 8c = 32.....................(5)

Step 4 - Subtract (4) from (5)

2b + 8c = 32
-
5b + 8c = 12
-3b = 20

b = - 20/3

= - 6.67
Since we cannot have negative values, we work with absolute value to get:

b [tex]\approx[/tex] 7

Since b = 7

2(7) + 8c = 32
8c = 32 - 14
c = 18/8

c [tex]\approx[/tex] 2


Plug in that back into a we have

a + b + c = 8
a + 7 + 2 = 8

a = 8-9
a = -1 (recall we must have absolute values)
a therefore = 1.

Hence the number of pizzas that were ordered are:

1 small
7 medium; and

2 large.

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Related Questions

what is the common denominator of "-1/4" + "-2/3"

Answers

Answer: 12

Step-by-step explanation:

The 4 in “-1/4” can be multiplied by three.

Three 3 in “-2/3” can be multiplied by four.

These give you the common denominator of 12!

Don’t forget to multiply the numerator by the amount you multiplied the denominator by!

Calculate the value of x. Round to the nearest tenth. F 7.8 24 14.8

Answers

In this problem bout segment has the same distance so we can write an equation like:

[tex]\begin{gathered} x+7=13+8 \\ x=21-7 \\ x=14\approx14.8 \end{gathered}[/tex]

So the answer is 14.8

Represent the following fractions and decimals in a number line
a. 4/7 b. 7/11 c. 8/5 d 0 /1 e. 2/5 f. 2.5 g. 4.3 h 1.2

Answers

Answer:

d, e, a, b, h, c, f, g

Step-by-step explanation:

if you convert them all to decimals you get

a = 0.57

b = 0.64

c = 1.6

d = 0

e = 0.4

f = 2.5

g = 4.3

h = 1.2

in order it goes 0, 0.4, 0.57, 0.64, 1.2, 1.6, 2.5, 4.3

What is X in this equation

Answers

Answer:

13/4 or 3.25

Step-by-step explanation:

Since they are vertical angles, they are equal to each other. Thus, set the two equations together:

8x + 32 = 12x + 19

Isolate x

32 = 12x + 19 - 8x = 4x + 19

32 - 19 = 4x

4x = 13

4x/4 = 13/4 = 3.25

Can someone help me solve for

Answers

The answer would be 84-32=52

If you can buy one can of pineapple chunks for $2, then how many can you buy with $10?
(WITH A GRAPH PLEASE)

Answers

Answer:

you can buy 5 cans

Step-by-step explanation:

$2 per can

have $10

10 divided by 2

5

f(x)=(1/7)(7x) what is f(3)

Answers

The value obtained for f(3) after substituting x = 3 in the function f(x) is 0.0067.

What exactly is a function?

A function from a set X to a set Y assigns exactly one element of Y to each element of X. The set X is known as the function's domain, and the set Y is known as the function's codomain.

What are the Function Formulas?

The list of function formulas is divided into two categories: formulas for performing numerous arithmetic operations across functions and formulas for performing combined operations involving two or more functions.

The given function is f(x) = (1/7)/(7x)

We need to find the value of f(3) so we will substitute x = 3 in the given function as follows:

f(3) = (1/7)/(7×3)

∴ f(3) = (1/7)/21

∴ f(3) = 0.142/21

∴ f(3) = 0.0067

Therefore, after substituting x = 3 in the function f(x), the value obtained for f(3) is 0.0067.

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Do the ratios 6:1 and 18:3 form a proportion

Answers

Answer:

Yes.

Step-by-step explanation:

18/ 3 = 6

3 / 3 = 1

so,  6 : 1.

Yes divide them both by 3

a radio tower is located 350 feet from a building. from a window in the building, a person determines that the angle of elevation to the top of the tower is 42 ∘ and that the angle of depression to the bottom of the tower is 20 ∘ . how tall is the tower? round to the nearest foot.

Answers

In linear equation, $ 442.54 tall is the tower.

What are a definition and an example of a linear equation?

A linear equation with one variable is one that contains just one variable. It has the formula Ax + B = 0, with A and B being any two real numbers and x being an ambiguous variable with only one possible value. One such linear equation in one variable is 9x + 78 = 18.

Suppose A is the window, B is the top of the tower, C is the bottom of the tower, and D is the point on the tower at the same horizontal level as the window.

Find BD, DC then add these together to give this°.

For BD :  AD is 350 ft, the angle CAD is 42.  

So BD/350 = tan 42°.  

      BD =  0.9004 × 350

      BD  = 315.14

   AD/350  =  tan20°

    AD =   0.364 × 350

    AD =  127.4

AD + BD =   315.14 +   127.4  =  $ 442.54

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Solve the equation shown: 14 + 5/7x - 20 = 4/7x - 4

Answers

The value of x is determined by solving the equation  14 + 5/7x - 20 = 4/7x - 4, which is: x = 14.

How to Solve an Equation?

When given an equation, to solve the equation means to find the value of the variable in the equation.

Given the equation:

14 + 5/7x - 20 = 4/7x - 4

Combine like terms

5/7x - 6 = 4/7x - 4

Add 6 to both sides

5/7x - 6 + 6 = 4/7x - 4 + 6

5/7x = 4/7x + 2

Subtract both sides of the equation by 4/7x:

5/7x - 4/7x = 4/7x + 2 - 4/7x [subtraction property of equality]

x/7 = 2

Multiply both sides by 7

x/7(7) = 2(7) [multiplication property of equality]

x = 14

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an air conditioning and heating repair firm conducted a study to determine if the average outside temperature could be used to predict the cost of an electric bill for homes during the winter months in houston, texas. the resulting regression equation was: y

Answers

Finding the numeric value of the regression line, it is found that the electric bill in a month with temperature of 48 degrees is of $157.59.

How to find the numeric value of a function or of an expression?

To find the numeric value of a function, we replace each instance of the variable in the function by the desired value.

In the context of this problem, the function is given as follows:

y = 227.19 - 1.45x.

Which y giving the electric bill for a month of temperature x degrees.

The temperature is of 48 degrees, hence to find the electric bill, the lone instance of x in the function is replaced by 48, hence:

y = 227.19 - 1.45(48) = $157.59.

Hence the electric bill in a month with temperature of 48 degrees is of $157.59.

What is the missing information?

The regression line is missing in this problem, as is defined as follows:

y = 227.19 - 1.45x.

In which:

y is the electric bill.x is the monthly temperature.

The problem asks for the electric bill in a month with temperature of 48 degrees.

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How do you do question 7 and 8?

Answers

Answer:

7.

[tex]y = \frac{a - b \: x {}^{10} \times ln(x) }{x {}^{10} } [/tex]

8.

[tex]y = \frac{12x {}^{3} \times ln(x) - 2x {}^{4} + 1 + 4\pi {}^{2}x {}^{3} }{4x {}^{3} } [/tex]

The price of a sweater was changed from $20 to $12. This is a(n) of %?

Answers

Answer:

If the proton proton chain produces gamma ray photons, why are the majority of photons we observe from the sun at visible wavelengths?

Step-by-step explanation:

Answer:If the proton proton chain produces gamma ray photons, why are the majority of photons we observe from the sun at visible wavelengths?

Step-by-step explanation:

Step-by-step explanation:

the shapes below are mathematically similar 10,14,28,x

Answers

WE CAN USE THE SIMILARITY THEOREM WHEREIN

[tex] \frac{14}{28} = \frac{10}{x} \\ [/tex]

THE PROPORTIONS OF SIDES OF THE SIMILAR SHAPES A RE EQUAL.

NOW TO SIMPLIFY WE CAN DO CROSS MULTIPLICATION.

[tex]14(x) = 28(10) \\ 14x = 280 \\ \frac{14x}{14} = \frac{280}{14} \\ x = 20 [/tex]

x is therefore 20cm


The price of a phone was AED 1,500.
How much will you pay for this phone, after a discount of 22% and a 6% tax?

Answers

Answer:

100-22=78

78+6=84

1500 x 84/100= 1260Dhs

Plss mark as brainliest

18. Angela cleans sneakers on the weekend to make extra money. She has completed 12
pairs of shoes, which is 20% of her total orders. How many total orders does Angela have
to clean?

Answers

The total number of orders that Angela has to clean are 60.

How to calculate the Percentage of a number?A percentage is a certain number or part of every hundred. It is a fraction with the denominator 100, and the symbol for it is "%." To determine the percentage of a number use the percentage formula to transform the problem into an equation: P% * X = Y

Given:

Number of pairs of shoes cleaned by Angela = 12

Let the total number of shoes to be cleaned be x.

So,12 pairs of shoes are 20% of her total orders.

20% of x = 12

(20/100)x = 12

0.2x = 12

x = 12/ 0.2

x = 60

Therefore, Angela has to clean a total of 60 pairs of shoes.

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Write the equation of the line that passes through the points (−9,−4) and (−5,−1). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.

Answers

[tex](\stackrel{x_1}{-9}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{-5}~,~\stackrel{y_2}{-1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-1}-\stackrel{y1}{(-4)}}}{\underset{run} {\underset{x_2}{-5}-\underset{x_1}{(-9)}}} \implies \cfrac{-1 +4}{-5 +9} \implies \cfrac{ 3 }{ 4 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{ \cfrac{ 3 }{ 4 }}(x-\stackrel{x_1}{(-9)}) \implies {\large \begin{array}{llll} y +4= \cfrac{ 3 }{ 4 } (x +9) \end{array}}[/tex]

the probability of picking a blue marble out of a bag of 50 marbles is 3/25. how many marbles in the bag are not blue?

Answers

Answer:

Okay so the probability is 3 outa 25 half the amount in the bag just add 3 and 3 together (cause 25 is half of 50) you get 6 subtract that from 50 you get 44.

A bird of species A, when diving, can travel four times as fast as a bird of species B top speed. If the total speeds for these two birds is 170 miles per hour, find the fastest speed of the bird of species A and the fastest speed of the bird of species B.

Answers

The fastest speed of the bird of species A is 136 mi/hr. and the fastest speed of the bird of species B is 34 mi/hr.

What is the equation?

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

A bird of species A, when diving, can travel four times as fast as a bird of species B at top speed which is given in the question.

Let b = the speed of bird species B.

So the speed of bird species A is 4b.

If the total speed for these birds is 170, then there is an equation :

⇒ 4b + b = 170.

⇒ 5b = 170

⇒ b = 170/5 = 34 mi/hr.

So the speed of bird species A will be 4×34 ⇒ 136 mi/hr.

Therefore, the fastest speed of the bird of species A is 136 mi/hr. and the fastest speed of the bird of species B is 34 mi/hr.

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Horizontal and parallel lines e and f are intersected by diagonal and parallel lines g and h. At the intersection of lines g and e, the bottom right angle is angle 2. At the intersection of lines h and e, the bottom right angle is angle 1. At the intersection of lines f and h, the top left angle is angle 3.
Statements Reasons
1. g || h 1. given
2. ∠1 ≅ ∠2 2. corresponding angles theorm
3. ∠2 ≅ ∠3 3. given
4. ∠1 ≅ ∠3 4. transitive property
5. e || f 5. ?
What is the missing reason in the proof?

vertical angles theorem
alternate exterior angles theorem
converse corresponding angles theorem
converse alternate interior angles theorem

Answers

The line e is parallel to f by converse alternate interior angles theorem.

What is converse alternate interior angle theorem?

Converse alternate interior angle theorem states that states if two lines are cut by a transversal and the alternate interior angles are congruent, then the lines are parallel.

What is parallel lines?

Two lines are said to be parallel when they do not meet at any point in a plane. Lines which do not have a common intersection point and never cross path with each other are parallel to each other. The symbol for showing parallel lines is ‘||’.

Given,

angle 1 is congruent to angle 2 and g is parallel to h.

similarly, angle 2 is congruent to angle 3,

by transitive property angle 1 is congruent to angle 3.

By converse alternate interior angle theorem, e is parallel to f.

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how do i identify the slope and y-intercept

y=-6x-8

Answers

Answer:

the formula of a line is y=mx+c

mx is the gradient/slope and c is the y intercept

so the slope here is -6

the y intercept is -8

hope it helps, mark as brainliest if correct.

Question 3: Kylie needs to spend at least 5 hours each week practicing the piano. She has already practiced 2 and 3/4 hours this week. She wants to split the remaining practice time evenly between the last 3 days of the week. Write an inequality to determine the minimum number of hours she needs to practice on each of the 3 days.

Answers

Using proportions with mixed numbers, the inequality to determine the minimum number of hours she needs to practice on each of the 3 days is: m ≥ 3/4.

What is a proportion?

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using operations such as multiplication or division.

One example is the mean of a data-set, as the mean is given by the sum of all observations in the data-set divided by the number of values.

For this problem, we have that:

She has already practiced 2.75 hours, as the decimal part is of 3/4 = 0.75, hence 2 and 3/4 = 2 + 0.75 = 2.75.She needs to practice 5 hours.

Hence the minimum number of hours that she still needs to practice is:

5 - 2.75 = 2.25 hours.

The amount is split evenly amount the 3 days, hence the lower bound of the inequality is:

2.25/3 = 0.75 = 3/4.

Hence the amount is given by:

m ≥ 3/4.

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is (6,-2) and (8,-3); (15,9) and (13,8) parallel

Answers

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the lines above

[tex](\stackrel{x_1}{6}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{-3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{(-2)}}}{\underset{run} {\underset{x_2}{8}-\underset{x_1}{6}}} \implies \cfrac{-3 +2}{2}\implies \boxed{-\cfrac{1}{2}} \\\\[-0.35em] ~\dotfill[/tex]

[tex](\stackrel{x_1}{15}~,~\stackrel{y_1}{9})\qquad (\stackrel{x_2}{13}~,~\stackrel{y_2}{8}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{8}-\stackrel{y1}{9}}}{\underset{run} {\underset{x_2}{13}-\underset{x_1}{15}}} \implies \cfrac{-1}{-2}\implies \boxed{\cfrac{1}{2}} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \textit{different slopes, \underline{not parallel}}~\hfill[/tex]

You need a thrust block for the riser for a
fire hydrant. The pyramidal form is 1 foot
high and 18 inches by 16 inches at the
base. How many cubic inches of concrete
will you need?

Answers

The number of cubical required are [tex]3456/n[/tex] here n is the area where it is kept.

To find the the number of blocks required, first you are suppose to know the volume of each brick and the area of the place where it is suppose to be kept. The area is not mentioned in this question because it is incomplete.
So, to proceed with it the volume of this block is L×B×H.

Given; length = 18 inches

breadth= 16 inches

and height = 1 foot = 12 inches

Thus Volume of cubical is 18× 16× 12= 3456 inches.

The number of bricks required is [tex]3456/n[/tex] here n represents the area of the place where it is supposed to be kept.

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A student ran the Turkey Trot 5K (5 kilometers) race on Thanksgiving Day. Using the ratio 1 mile : 1.61 kilometers, which set-up would correctly convert 5 kilometers to miles

Answers

The conversion of 5 kiiometers to miles is 3.11 miles

How to convert the distance from kilometers to miles

The given parameters are

Distance covered by the students = 5 kilometers

The ratio of the distance is given as

1 mile : 1.61 kilometers

Multiply both sides of the ratio by 5

So, we have the following ratio expression

5 * 1 mile : 1.61 kilometers * 5

Evaluate the product in the above expression

So, we have the following ratio expression

5 miles : 8.05 kilometers

Divide both sides of the ratio by 1.61

So, we have the following ratio expression

5/1.61 miles : 8.05/1.61 kilometers

Evaluate the quotient in the above expression

So, we have the following ratio expression

3.11 miles : 5 kilometers

Rewrite as

5 kilometers : 3.11 miles

This means that

5 kilometers = 3.11 miles

Substitute 5 kilometers = 3.11 miles  in Distance covered by the students = 5 kilometers

So, we have

Distance covered by the students = 3.11 miles

Hence, the distance covered by the students is 3.11 miles

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The linear function m = 50 - 9d represents the amount m (in dollars) of money you have
left after buying d DVDs.
a. Interpret the terms and coefficient in the equation.
b. Find the domain of the function. Is the domain discrete or continuous? Explain.
c. Graph the function using its domain.

Answers

       A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

How can you tell whether a domain is continuous or discrete?

         A domain's discreteness or continuousness can be determined by examining the function's graph. The domain is continuous if the graph is a line. The domain is discrete if the graph consists of a collection of points.

What is a discrete domain example?

Private Domain

      The values that will be effective for the function are distinct from one another. The maximum number of children you can have, for instance, has a defined answer. You can have 0 children, 1, 2, 3, etc., but not 2,34.

How can you determine a discrete function's domain?

      Discrete graphs are those in which no lines connect the points. Start by locating all the x-coordinates in order to determine the domain and range of a discrete graph. The graph's entire set of x-coordinates makes up the domain. The graph's entire range of y-coordinates is considered to be the range.

What does a discrete structure's domain mean?

        The domain is the collection of all possible inputs for a function. The codomain is the collection of all permitted outputs.

What is an example of discrete structures?

     Graphs, logical assertions, and combinations are a few examples of discrete structures. Infinite or finite discrete structures are both possible. Contrary to continuous mathematics, which works with structures whose values can span the real numbers or have other non-separable qualities, discrete mathematics deals with discrete objects.

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Estimate the intercepts of the graph of the function

Answers

Answer:

x-intercept equals 5

y-intercept equals -10

Step-by-step explanation:

y-intercept: solve when x=0. y=-2|x-5|= -10

Convert 0.000 000 005 78 to scientific notation

Answers

Answer: 5.78 × 10 to the negative ninth power

Step-by-step explanation:

5.78 x 10^-9

Just move decimal point to the front

how do you do these problems

Answers

The required value of the function is 2

In the case of a function from one set to the other, each element of X receives exactly one element of Y.

The function's codomain and domain are respectively referred to as the sets Y and X as a whole.When a function is defined, the domain and codomain are not always explicitly specified, and one may just be aware that the domain is a subset of a bigger set without having to conduct any (perhaps difficult) computation. In mathematical analysis, "a function from X to Y" typically refers to a function that may have a valid subset of X as its domain.

The given function is of the form :

g(x) = - x² - 7

Now let us find the required values.

g (-3) = - (-3)² - 7 = 2

g (-2) = - (-2)² - 7 = -3

g (1 ) = - ( -1 )² - 7 = -6

Hence the required value of the function is 2 at x = -3 .

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Which of the following is most likely the next step in the series

Answers

im assuming A since it goes , 3, 4 , 5 , and A has 6
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The following question has come to the attention of the committee:"Each of the four digits 3, 4, 5, and 8 is placed in one of the boxes to form a fraction. The numerator and the denominator are two-digit whole numbers. What is the smallest value of all the common fractions that can be formed? Express your answer as a reduced fraction."There are 4 boxes arranged in a square with 2 boxes side-by-side directly on top of the other 2 boxes. There is a horizontal line representing a fraction bar separating the top 2 boxes from the bottom 2 boxes.Some committee members contend this is not a valid question.Solve the problem. (If there is no solution, enter NO SOLUTION.)Explain the solution to prove (or disprove) the question's validity.The question is valid because to make the fraction as small as possible, you make the numerator as small as possible and make the denominator as large as possible.The question is valid because to make the fraction as small as possible, you make the numerator as large as possible and make the denominator as small as possible. The question is valid because to make the fraction as small as possible, you make both the numerator and the denominator as small as possible.The question is valid because to make the fraction as small as possible, you make both the numerator and the denominator as large as possible.The question is not valid because there is no solution. in 1905 north carolinian thomas f. dixon published a novel, the clansman, which depicted the ku klux klan as heroic defenders of the south against the corruption of african american and northern "carpetbag" misrule during reconstruction Estimate the quotient of 45 1.5. 67.5 30 9 3