a food server examines the amount of money earned in tips after working an 8-hour shift. the server has a total of $95 in denominations of $1, $5, $10, and $20 bills. the total number of paper bills is 26. the number of $5 bills is 4 times the number of $10 bills, and the number of $1 bills is 1 less than twice the number of $5 bills. write a system of linear equations to represent the situation. (assume x

Answers

Answer 1

The solution to the system equation  is (x, y, z, w) = (23, 12, 3, 1).

What is equation?

An equation could be a formula that expresses the equality of 2 expressions, by connecting them with the sign =

Main body:

Here is a system of linear equations that represents the situation.

x +5y +10z +20w = 133 . . . total amount earned

x +y +z +w = 39 . . . . . . . . . total number of bills

y = 4z . . . . . . . . . . . . . . . . . . the number of 5s is 4 times the number of 10s

x = 2y -1 . . . . . . . . . . . . . . . . the number of 1s is 1 less than twice the number of 5s

_____

We can substitute for x and z in the first two equations:

... (2y-1) +5y +10(y/4) +20w = 133

... (2y-1) +y +(y/4) +w = 39

These simplify to

... 9.5y +20w = 134

... 3.25y +w = 40

Solving by your favorite method, you get

... y = 12

... w = 1

So the other values can be found to be

... x = 2·12 -1 = 23

... z = 12/4 = 3

hence ,The solution to the system is (x, y, z, w) = (23, 12, 3, 1).

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Related Questions

Find the digits in the ones,tens,and thousandth place

603.2798

Answers

Answer:

3 is in the ones place

0 is in the tens place

9 is in the thousandths place

Step-by-step explanation:

thousands, hundreds, tens, ones (DECIMAL) tenths, hundredths, thousandths

One year, the population of a city was 117,000. Several years later it was 136,890. Find the percent increase.

Answers

The percentage of increase in the population is  17 %

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the percentage increase in the population be = A

Now , the equation will be

The initial population of the city = 117,000

The increase in population of the city = 136,890

Now , the percentage increase in population is given by the formula

initial population of the city + ( A / 100 ) x  initial population of the city = increase in population of the city

So , on substituting the values in the equation , we get

Percentage increase in population = 117000 + ( A/100 ) x 117000 = 136890

117000 + ( A/100 ) x 117000 = 136890

Subtracting 117000 on both sides of the equation , we get

( A/100 ) x 117000 = 19890

Divide by 117000 on both sides of the equation , we get

A / 100 = 0.17

Multiply by 100 on both sides of the equation , we get

A = 17 %

Therefore , the value of A is 17 %

Hence , The percentage of increase in the population is 17 %

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(-11)-2= I need to know the answer to this question

Answers

Answer: I = -13

Step-by-step explanation:

We just need to take the -11 -2 = -13.  A negative -11 subtracts negative 2 = -13

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Answer: -13

Step-by-step explanation:

The answer is negative 13 because a negative added by a negative equals a negative

Aaden took a taxi from his house to the airport. The taxi company charged a pick-up fee of $3. 10 plus $2. 75 per mile. The total fare was $27. 85, not including the tip. Write and solve an equation which can be used to determine xx, the number of miles in the taxi ride.

Answers

The equation that will be used to solve the given question is [2.75x+3.10=27.85] and with the help of this equation we know that Aaden took a ride of 9 miles.

What is an equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

So, we know that:
The pick-up fee that the company charges is: #3.10

Ride charges per mile: $2.75

Total fare price: $27.85

So, let x be the number of miles ridden, the equation that will be used to solve the given question will be:

2.75x + 3.10 = 27.85

Now, solve as follows:

2.75x + 3.10 = 27.85

2.75x = 27.85 - 3.10

2.75x = 24.75

x = 24.75/2.75

x = 9

Therefore, the equation that will be used to solve the given question is [2.75x+3.10=27.85] and with the help of this equation we know that Aaden took a ride of 9 miles.

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the surface area of a rectangular box is given by the polynomial 2hl 2lw 2hw and is measured in square units. a rectangular box is to be constructed for shipping materials. the box is to have dimensions of 5 inches by 3 inches by 7 inches. find the surface area of the box.

Answers

Surface area of the box measuring 5 inches by 3 inches by 7 inches is 142 square inches.

What is surface area ?

The surface area of the object that refers to the overall space that is filled by its surfaces. Different 3D shapes in the geometry have various surface areas, which can be quickly estimated using the formulas. Two categories are used to classify the surface area:

Curved surface area or Lateral surface area

Surface area in total

Surface area of rectangle = 2 ( lb + bh + hl )

Dimensions of box = 5 inches by 3 inches by 7 inches

Hence,

Length = 5 inches

Breadth = 3 inches

Height = 7 inches

By putting it in formula of surface area of rectangle

= 2 ( lb + bh + hl )

= 2 ( 5*3 + 3*7 + 7*5 )

= 2 ( 15 + 21 + 35 )

= 2 * 71

 = 142 square inches

Hence, the total surface area of the box is 142 square inches.

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american express executives hypothesize that 40% of college students own an american express credit card. testing this hypothesis is an example of

Answers

Testing the hypothesis "Americans express executives hypothesize that 40% of college students own an Americans express credit card." is an example of generalizing.

What is hypothesis?

A hypothesis is a theory put up to explain a phenomenon. A hypothesis must be testable according to the scientific method for it to be considered a scientific hypothesis. Scientific hypotheses are typically based on prior observations that cannot be adequately explained by the current body of knowledge. A straightforward hypothesis only hypothesizes the relationship between two independent and dependent variables.

An example of testing a generalization is "American Express executives' hypothesis that 40% of college students own an American Express credit card."

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Evaluate:
please help fast

Answers

Answer: 256

Step-by-step explanation:

8^8/3 is the same as an 8 square root! We have to factor out and I get 2^8 after finish factor the smallest number and get 256!

Problem 9. Find the perimeter of quadrilateral PORS with the vertices P(-2-2), Q(-1,3), R(5,3), and S(4,-2)​

Answers

Answer:

Perimeter is 12+2√26

Step-by-step explanation:

Question:

The perimeter of quadrilateral PQRS with the vertices

P(-2, -2), Q(-1, 3), R(5, 3), and S(4, -2)​

Find distances PS and QR:

Notice the y-coordinates are the same for 2 pairs of points

P(-2, -2), S(4, -2)​ and Q(-1, 3), R(5, 3)

So the distance PS = |-2|+4= 6 and QR = |-1|+5 = 6

Find the distances PQ and SR:

Use the distance formula:

[tex]d= \sqrt{(x_{2}-x_{1} ) ^{2} + (y_{2}-y_{1} ) ^{2} }[/tex]

P([tex]x_{1}[/tex] = -2, [tex]y_{1}[/tex] = -2), Q( [tex]x_{2}[/tex] = -1, [tex]y_{2}[/tex] = 3)

PQ = [tex]\sqrt{(-1--2)^{2} +(3- -2)^{2} } = \sqrt{1^{2} +5^{2} } = \sqrt{26}[/tex]

SR = [tex]\sqrt{26}[/tex], because of PQ and SR are equal.

Find the perimeter of quadrilateral PQRS:

The perimeter is equal to the sum of all sides of the quadrilateral.

P= PS + QR + PQ + SR = 6+6+ √26 +√26 = 12+2√26

A product sells at a regular price of $150 which is on sale for 60% off the regular price. Find the sale price.

Answers

The new sale price of the product after the deduction of discount is $60

What is the sale price?

In order to solve the given task, use the concept of percentage.

Regular price of the product = $150Percentage discount = 60%

New price of the product = Regular price of the product - (Percentage discount × Regular price of the product)

= 150 - (60% × 150)

= 150 - (0.6 × 150)

= 150 - 90

= $60

Consequently, the new selling price of the product is $60

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Adrian took out a students' loan that charges 10% annual simple interest. If Adrian paid back a total of $1200 in interest alone during the first four years , how much was Adrian's original loan, in dollars?
$1,000
$3,000
$4,000
$ 6,000
$12,000

Answers

The required simple interest of 10% of four year on principle amount is $857.

What is simple interest?

Simple interest depends on the chief measure of a credit or the first store in quite a while account. Straightforward interest doesn't build, and that implies a loan boss will just compensation interest on the chief sum and a borrower couldn't have ever to pay more interest on the recently gathered interest.

According to question:

We have,

Amount of four year = $1200

simple interest = 10%

Let loaned amount is x

Then,

interest of four year =×4 x×10/100 = 4x/10

According,

x + 4x/10 = $1200

14x/10 = $1200

x = $12000/14

X = $857 (appox)

Thus, the required loaned amount is $857.

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PLS HELP Me out!!! 30pts

Answers

Answer: D is correct

Step-by-step explanation: Another angle is needed to prove the triangles are congruent by the ASA theorem. The angle that needs to be added has to have segment QS in between it and angleQSR. The only angle that does that is angleRQS. For the 2nd triangle, do the same thing. The angle that needs to be added has to have segment ST in between it and angleUST. The only angle that does that is angleSTU.

in the xy-plane, the line x y k   , where k is a constant, is tangent to the graph of 2 y x x    3 1. what is the value of k?

Answers

The value of k is -3.

What is a tangent line?

The straight line that "just touches" the curve at a given location is referred to as the tangent line to a plane curve in geometry. It was described by Leibniz as the path connecting two points on a curve that are endlessly close to one another.

Here, we have

Given

x + y = k

y = x² + 3x

slope of tangent line = dy/dx = 2x+3

k is y-intercept of the tangent line

2x+3 = -1

x = -2

y = (-2)^2+3(-2)+1 = -1

The tangent line passes through the point (-2,-1)

k = x+y

k = -2 -1

k = -3

Hence, the value of k is -3.

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Which one blue, light blue , yellow or red

Answers

answer:

f(g(x))=4x^2-2

step-by-step explanation:

plug g(x) into f(x) to get f(g(x))=2(x^2-1). when this is simplified, you get the answer presented above. the correct answer would be the green option. hope that helps!

The radius of a circle is 10 feet. What is the area of a sector bounded by a 180° arc?

Answers

Answer:

50π feet^2

Step-by-step explanation:

area of the circle = 10^2 π = 100π feet^2

A of the sector = 100π/2 = 50π feet^2

Chris earns $7.00 per hour working on the weekends
He needs at least 210.00 for a new cell phone
Just look at the picture and help please

Answers

it’s d the last one. this is because of the greater than and equal sign

4 a. Graph the following system of equations.
y = -3x
y = x + 4
b. what does the graph show to be the solution of the system?

5 DeAndre and Leah are making origami cranes. their goal is to complete 1,000 cranes by the end of the summer.
- DeAndre already has 30 cranes and makes 5 more each day.
- Leah already has 10 cranes and makes 15 more each day.
The graph shows how many cranes, c, each person has made after d days.
a. what does the graph show to be the solution of the system?
b. what does the solution mean in this context?

Answers

4. a. The graph of the system is attached below.

b. The solution is: (-1, 3).

5. a. (2, 40) is the solution as shown by the graph.

b. (2, 40) means that both will complete 40 cranes after 2 days

How to Graph a System of Equation?

On a graph, when two lines are plotted for different equations, the solution is the coordinates of the point where both lines intersect.

4. a. The graph of y = -3x is the red line in the image attached below, while that of y = x + 4 is the blue line. They both intersect each other at (-1. 3).

b. The solution of the system is therefore, (-1, 3).

5. a. Using the graph given that shows the lines of the equations of DeAndre and Leah, both lines intersect at (2, 40).

We can therefore state that the solution to the system as shown in the graph is: (2, 40).

b. In the context of the scenario given, the solution (2, 40) means that both will have completed equal amounts of 40 cranes after 2 days.

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the actual answer pleaseee hellpp asapp

Answers

Answer:

∠BEC is supplementary to ∠AEB

∠AED and ∠BEC are a pair of vertical angles

which expression is equivalent to (1 tanθ)tan(2θ) for all values of θ for which (1 tanθ)tan(2θ) is defined?

Answers

The given expression of trigonometry is equivalent to cos(2θ).

What is trigonometric function ?

trigonometry capability, in math, one of six capabilities (sine [sin], cosine [cos], digression [tan], cotangent [cot], secant [sec], and co-secant [csc]) that address proportions of sides of right triangles. These six geometrical capabilities comparable to a right triangle.

According to question:

We have,

1 - tan^2(θ)/1 +  tan^2(θ)

Use 1 + tan^2(θ) = sec^2(θ)

1 - tan^2(θ)/ sec^2(θ)

1/ sec^2(θ) - tan^2(θ)/sec^2(θ)

Use tan(θ) = sin(θ)/cos(θ)

cos^2(θ) - sin^2(θ)×cos^2(θ)/cos^2(θ)

cos^2(θ) - sin^2(θ)

Using sin^(θ) + cos^2(θ) = 1

cos^2(θ) - (1 - cos^2(θ))

2cos^2(θ) - 1

Here we have 2cos^2(θ) - 1 = cos(2θ)

Then, simplification of given expression is cos(2θ).

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Correct question:

which expression is equivalent to 1 - tan^2(θ)/1 +  tan^2(θ) for all values of θ for which 1 - tan^2(θ)/1 +  tan^2(θ) is defined?

Plot the points (0, 6) and (3, 0). What is the slope?
6/-3
O 1/2
-1/2
6/3

Answers

Slope is "change in y over change in x".

    [tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Using those two points, you'd have

    [tex]m=\dfrac{y_2-y_1}{x_2-x_1} = \dfrac{0-6}{3-0}=\dfrac{-6}{3}=-2[/tex]

Notice that doesn't match any of the listed answers.  The reason is that two of those answers aren't reduced.

If you reduce the first answer of [tex]\dfrac{6}{-3}[/tex], you have  [tex]\dfrac{6}{-3}=-2[/tex].  So that first answer is equivalent to the calculation above.

The answer from your list is the first one.

7x4+10÷5 can someone pls help i have been on this question for 2 1/2 hours periodtttt

Answers

Answer:

30.

Step-by-step explanation:

First, we have to split up the equation:

(7 x 4) + (10 ÷ 5)

Now, we simplify:

(7 x 4) + (10 ÷ 5)

28 + 2

28 + 2 = 30.

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a cowboy agreed to work for one year for $\$19{,}200$ plus a horse. he quit after 7 months and was paid $\$10{,}450$ plus a horse. how many dollars was the horse worth, if the paid salary reflects the fair proportion of his yearly salary?

Answers

The horse was worth it for $1800.

What is proportion?

A mathematical comparison of two numbers is called a proportion. Ratios and fractions are the main bases on which proportion is explained. Two ratios are equal when they are expressed as a fraction in the form of a/b, ratio a:b, and then a proportion. In this case, a and b can be any two integers.

Based on the given question condition, where, 'h' denotes the amount for the horse in dollars,  the proportion can be defined as:

or,  [tex]\frac{19200 + h}{12} = \frac{10450+h}{7}[/tex]

or, (19200 + h)7 = (10450 + h)12

or, 134400 + 7h = 125400 + 12h

or, 12h - 7h = 134400 - 125400

or, 5h = 9000

or, h = 9000/5 = 1800

Hence, the horse was worth $1800.

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Jose spent 7 days at soccer camp. Each day he spent 4.5 hours training in the midfield. Each hour of training, he ran 1.5 miles. How many miles did he run while at soccer camp?

Answers

7x4.5= 31.50x 1.5 =47.25

An elevator i on the twentieth floor. It goe to 22 floor. What floor i the elevator on now?

Answers

The elevator is on the 42th floor on moving 22 floor up to the present location of 20th floor.

Define the term addition of the numbers?Combining objects and counting them as one big group is done through addition. In math, addition is the process of adding two or more integers together. Addends are also the numbers that are added, while the total refers to the outcome of the operation.

Regarding the posed query:

Initial position of the elevator = 20th floor.Number of floor travelled by elevator = 22.

Thus,

Current position = 20 + 22

Current position = 42

Thus, the present location of the elevator is on 42th floor.

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The price of Stock A at 9 A.M. was $12.71. Since​ then, the price has been increasing at the rate of $0.08 each hour. At noon the price of Stock B was $13.21. It begins to decrease at the rate of $0.11 each hour. If the two rates​ continue, in how many hours will the prices of the two stocks be the​ same?

Answers

In 2.63  hours the prices of the two stocks be the​ same

What is Equation?

Two or more expressions with an Equal sign is called as Equation.

Given,

The price of Stock A at 9 A.M. was $12.71.

Price has been increasing at the rate of $0.08 each hour

Price of Stock B was $13.21

The price has been decrease at the rate of $0.11 each hour.

We can write in the form of equation , to find how many hours will the prices of the two stocks be the​ same

12.71+0.08h=13.21-0.11h

0.11h+0.08h=13.21-12.71

0.19h=0.5

Divide both sides by 0.19

h=0.5/0.19

h=2.63

Hence, in 2.63  hours the prices of the two stocks be the​ same

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Suppose are running a study/poll about the probability of catching the flu this year. You randomly sample 142 people and find that 69 of them match the condition you are testing. Suppose you have the following null and alternative hypotheses for a test you are running: H 0 : p = 0.54 H a : p < 0.54 Calculate the test statistic, rounded to 3 decimal places

Answers

The test statistic of null and alternative hypotheses for a test is 0.811.

69 of the 142 persons that were randomly chosen from a sample are found to meet the condition we are testing.

The sample proportion phat = 69 ÷ 142 = 0.489

n = 69

p = 0.54

the following are your test's null and alternate hypotheses:

[tex]H_0[/tex] : p = 0.54

[tex]H_a[/tex] : p < 0.54,

test statistic,

z = (phat - p) ÷ √(p × (1 - p) ÷ n)

z = (0.489 - 0.54) ÷ √((0.79 × 0.21) ÷ 42) = 0.811

A test statistic is a figure obtained from a statistical analysis. It explains how distant the observational values seem to be from the null hypothesis, which states that there is no correlation between the variables or distinction between the sample groups.

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in one of the properties of logarithms, the division becomes subtraction. explain what it means. provide an example where this property may be applied. include reference(s) in your post.

Answers

Explained the quotient property "one of the properties of logarithms, the division becomes subtraction" has been explained with an example

In one of the properties of logarithms, the division becomes subtraction. That is the quotient property of the logarithm

Consider the two positive numbers x and y and a ≠ 0

Then,

[tex]log_a[/tex] (m /n) = [tex]log_a[/tex] m -  [tex]log_a[/tex] n

Here division became the subtraction

For example

To find the value of  [tex]log_2[/tex] (15/ 7) we will use the quotient property of logarithm, here the division of the numbers will be subtraction

[tex]log_2[/tex] (15 / 7) =  [tex]log_2[/tex] 15 -  [tex]log_2[/tex] 7

Therefore, the quotient property of the logarithm has been explained with example

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Which figure is
misleading?
1) Figure A
2) Figure B

Answers

Answer:

Figure B.

Step-by-step explanation:

Figure A uses what is visually similar in size cylinders to give a detailed image of the amount of money (assumingly as profit). Each given cylinder that is in similar size represents $200, and so it is easy to figure out how the amount of money per store.

In the case of Figure A,

Save Store = $400

Leff's Store = $800

Low Pricer = $1200

In the case of Figure B, however, while it gives a legend for price per cylinder of that proportion, it does not make use of the legend, and does not give a adequate legend to decipher the Figure. In essence, the data given in Figure B is useless as it makes no use of its legend.

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Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator.
42:48

Answers

Answer:

7/8

Step-by-step explanation:42/48 divide both by 6 since that's the greatest common number that divides both

g what is the probability of flipping at least 3 heads in 4 flips of 2 fair coin given that the first flip is heads?

Answers

The probability is 0.25.

What is probability?

Probability is the ability to happen. The subject of this area of mathematics is the occurrence of random events. From 0 to 1 is used to express the value. To determine how likely an event is to occur, mathematics has created the concept of probability.

Given there are 2 coins flipped 4 times, we get the following sample space

S = {HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, TTTT}

Now, A = event of having at least 3 heads.

A= {HHHH, HHHT, HHTH, HTHH, THHH}

The number of events having the first flip heads is 4.

Therefore, the probability is:

P(A) =

[tex]=\frac{successful \space\ events}{total\space\ sample\space\ events}\\=\frac{4}{16}\\=0.25[/tex]

Therefore, the probability of flipping at least 3 heads in 4 flips of 2 fair coins given that the first flip is heads is 0.25.

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(71+9+3)-(9-11+2) I really need help

Answers

Answer:  The correct answer is 83

Step-by-step explanation:

Complete the equations within each set of brackets

(71+9+3)-(9-11+2)

71+9+3 = 83

9-11+2 = 0

Subtract the results

83 - 0 = 83

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