A chef that manages two restaurants buys seven bags of rice and six bags of flour.
Restaurant A receives four bags of rice and two bags of flour for a total cost of
$78. Restaurant B receives three bags of rice and four bags of flour for a total
cost of $71.50. What is the cost of each bag of rice and each bag of flour?

Answers

Answer 1

Answer:

   - A bag of rice is $16.9

   - A bag of flour is $5.20

Step-by-step explanation:

Let R and F stand for the price of a bag of Rice and Flour, respectively.

We can use the information provided to set an equation that will predict the total cost for that restaurant, given the quantities of rice and flour received (Restaurants A and B)

A) 4R + 2F = 78   [4 bags of rice and 2 bags of flour, when multiplied by the prices per bag, R and F, will result in a total cost of $78.

B)  3R + 4F = 71.5  [Now it is 3 bags of rice and 4 of flour, for a total cost of $71.50

We have 2 equations and 2 unknowns.  We can use substitution to find the answers.  Take one of the equations and reorganize it to isolate one of the variables (R or F).  We'll take the equation for A and isolate F

---

A) 4R + 2F = 78

     2F = 78-4R      [subtract 4R from both sides]

       F = 39-2R      [divide both sides by 2]

We've isolated F, and we can use this definition of F in the second equation:

===

B)  3R + 4F = 71.5

3R + 4(39 - 2R) = 71.5  [Use the definition of F derived above.  In this manner, we have legally eliminated one of the two variables.  (Sneaky, effective, and fun)]

3R + 156 - 8R = 71.5   [Multiply, combine like terms, and simplify]

-5R = -84.5                  [Isolate R]

R = $16.9                      A bag of rice costs $16.9

Now use the price of rice (R=$16.9) in one of the equations.  Since the rearranged equation we used above is already conveniently written for F, we'll use it:

F = 39 - 2R

F = 39 - 2(16.9)

F = 39 - 33.8

F = $5.20                     A bag of flour costs $5.20

===

CHECK:

Do these two prices satisfy both equations we first formulated?

Restaurant A:  4R + 2F = 78?

                        4(16.9) + 2(5.20) = 78  YES

Restaurant B:  3R + 4F = 71.5?

                        3(16.9) + 4(5.20) = 71.5  YES

These are the correct answers.


Related Questions

Herald cut 18 1/2 Inches of a rope that was 60 inches long. How is the length of the remaining rope In inches Written in decimal form?

Answers

Answer:

41.5 inches

Step-by-step explanation:

You subtract 18.5 from 60.

find the value of x. round your answer to the nearest tenth.

Answers

Answer:

x = 56.7

Step-by-step explanation:

cos theta = adjacent/hypotenuse

cos x = 17/31

x = arccos(17/31)

x = 56.7

express -3/5 as the rational number with denominator 20​

Answers

Answer:

-12/20

hope this helps

have a good day :)

Step-by-step explanation:

Step-by-step explanation:

-3/5*4= -12/20

pls gimme brainliest I need it

Consider your construction of pentagon ABCED. What segments, if any, are perpendicular? Explain how you made your determination

Answers

Answer:

Sine                                                                                                                                                                                                                                         AB is perpendicular to sides AE and BC/                                                                                                                                                  

Step-by-step explanation:

The slope is the change in y over the change in x.

Line segment AE has a slope of 3/4

(0,4)(4,7)

The y values are 7 and 4.

The x values are 4 and 0.  

You find the change by subtracting

[tex]\frac{7-4}{4-0}[/tex] = [tex]\frac{3}{4}[/tex]

Line segment BC has the same slope

((3,0)(7,3)

The y values are 3 and 0.

The x values are 7 a d 3.  

You find the change by subtracting

[tex]\frac{3-0}{7-3}[/tex] = [tex]\frac{3}{4}[/tex]

Since line segments Ae and BC has the same slope.  They are parallel.

Line segments that are perpendicular will have opposite reciprocals slopes.  In this case the slope should be  - [tex]\frac{4}{3}[/tex].

Let's look at line segment AB

(0,4)(3,0)

The y values are 0 and 4.

The x values are 3 and 0.

You find the change by subtracting  

[tex]\frac{0-4}{3-0}[/tex] = [tex]\frac{-4}{3}[/tex]

Since the slopes are opposite reciprocals, side AB is perpendicular to sides AE and BC                                                                                                                                        

Jessica planted a rosebush in her garden. The rosebush has a height of 30 cm. Each month the rosebush increases by cm. Which equation can be used to determine the height of the plant in centimetres, y, after x months?
A) y = 30 - 6x
B) y = 6x - 30
C) y = 6x + 30
D) y = 6(x - 30)

Answers

Answer:

c

Step-by-step explanation:

Jessica planted a rosebush in her garden. The rosebush has a height of 30 cm. Each month the rosebush increases by 6 cm. Which equation can be used to determine the height of the plant in centimetres, y, after x months?

the rate of increase of the bush every month is 6 cm

Rate of increase of the bush in x months = 6x

because the bush increases every month, 6x would be added to 30cm

y = 6x + 30

If the bush decreased at a rate of 6cm every month, the equation would be y = 30 - 6x

Im taking an algebra exit exam that I need for high school, tips on what to study or do?

Answers

i took this kinda test and what i did was search up subjects for algebra 1 and practice each one or look at videos

consider the relation below
1.Is the relation A function
2. Is the relation a one to one function
3. Is the inverse of the relation below itself a function

Answers

Answers:

Yes it's a function.No, the function is not one-to-one.No, the inverse isn't a function.

=============================================

Explanation:

We have a function since the curve passes the vertical line test. Recall that this test is where we try to draw a single vertical line through more than on point on the curve. Such a task isn't possible in this case.

-----------

On the other hand, the curve does not pass the horizontal line test. It is possible to draw a single horizontal line through more than one point on the curve.

This function is not one-to-one since it does not pass the horizontal line test.

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

Because the graph isn't one-to-one, the inverse won't be a function. The process of finding the inverse involves swapping x and y; which means we swap from "horizontal line test" to "vertical line test".

The original function failing the horizontal line test would mean the inverse fails the vertical line test.

Which pairs of events are independent? Select all that apply.

Answers

Answer:the last one is right, because you cannot control when rain happens, or where at that matter.

the researcher administers a survery to 15 students who are seated at the front of the laboratory. how could this study be improved

Answers

Pick a random selection of students who attend the work lab.

What is meant by random selection?

Picking a random sample of students is the most effective strategy to ensure accurate results. The findings of a survey that the student conducts among those sat in the lab's front rows might be skewed.

The students seated in front of the lab could exhibit a certain trait (e.g., they might be particularly diligent students), which would undoubtedly yield a different outcome.  The survey is in good shape. No special equipment is required to evaluate our comprehension of statistical analysis.

Additionally, there won't be much of a difference if more students are included in the sample that are sat in front of the lab. Finally, it makes no sense to administer instruments to a group that does not visit the work laboratory. Effectiveness cannot be evaluated based on students who do not participate in class.

Therefore the correct option is B)  Select a random sample of students who go to the work laboratory

The complete question is:

A student researcher wishes to examine the effectiveness of a statistical work laboratory on graduate students' overall understanding of application of statistical analyses. The researcher administers a survey to 15 students who are seated at the front of the laboratory. How could this study be improved? Select all that apply.

A. Use an instrument to test statistical analysis understanding.

B. Select a random sample of students who go to the work laboratory

C. Use a larger sample size.

D. Administer instruments to a group who does not go to the work laboratory, as well.

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s = 40, u
12, mZS = 37

Answers

What do you need help with?

A ratio is a comparison of two quantities. For example, the ratio of cows to pigs on a farm could be 1 to 3. For every 1 cow, there are 3 pigs. The ratio of chocolate chips to raisins in a cookie could be 5 to 9. For every 5 chocolate chips in the cookie, there are 9 raisins. Do you notice a repeating phrase in these examples? “For every” is key ratio language. It tells you how much of one quantity exists in comparison to the other quantity. A ratio consists of just the numbers, not the units. If someone asked the ratio of chocolate chips to raisins in the cookie example, you’d say 5 to 9.

Which of these could you represent with a ratio?

Answers

The solution is given by the equation A = how many diet sodas there are in the fridge compared to how many regular sodas

What is Proportion?

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

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

Given data ,

Let the proportion be represented as A

Now , the equation will be

The ratio of cows to pigs on a farm could be 1 to 3

So , the proportion is 1 : 3

Now , The ratio of chocolate chips to raisins in a cookie could be 5 to 9

So , the proportion is 5 : 9

Now , the number of diet sodas there are in the fridge compared to number of regular sodas is also a proportion

Hence , the proportion is number of diet sodas to number of regular sodas

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helppp please last question !!!

Answers

Answer:

Step-by-step explanation:

y = 1/4x +10

and why do you use your phone, it makes it sooo much tuffer to read the question.   just "prt screen"   and paste into paint.. and save as a jpg,  and then post that pic..  don't use your phone.  :/

The mean height of 15-year-old boys is 175 cm and the variance is 64. For girls, the mean is 165 and the variance is 64. If 8 boys and 8 girls were sampled, what is the probability that the mean height of the sample of boys would be at least 6 cm higher than the mean height of the sample of girls

Answers

The probability of the mean height of the sample of boys being at least 6 cm higher than the mean height of the sample of girls can be calculated using a two-sample t-test. The t-test compares the means of two samples and determines whether they are different from one another. The t-test requires the assumption of equal variances and normal distribution of the data.

What does the math term "probability" mean?

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

Given that the variances are equal, the t-test statistic can be calculated as:

t = (mean_boys - mean_girls - 6) / (sqrt(variance/n))

where n is the sample size of each group (8 in this case).

The probability of observing a t-value as extreme or more extreme than this value can be calculated using the cumulative distribution function (CDF) of a t-distribution with n1 + n2 - 2 degrees of freedom.

Because you are looking for the probability that the mean height of the sample of boys is at least 6cm higher than the mean height of the sample of girls, this is a one-tailed test. The probability of a one-tailed test can be calculated by subtracting the probability of a two-tailed test from 1.

The probability can be calculated using a t-distribution table with 14 d.f. or using software such as R or excel.

It is important to note that the sample size is very small, with 8 boys and 8 girls, which may not be representative of the population. As sample size increases the probability of getting a significant difference increases.

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A rock is dropped from a height of 88.6 m and falls toward Earth in a straight line. In t seconds the rock falls 4.9t2 meters.

Answers

Answer:

The average speed is 9.8 meter per second in the first two seconds

Step-by-step explanation:

Complete Question

What is the average velocity of the rock in first 2 secs?

Solution

Distance travelled in first two seconds  

[tex]4.9 t^2 = 4.9*2*2 = 19.6[/tex] m

Average speed = [tex]S2-S1/2 = 19.6-0/2 = 9.8[/tex] meter per second  

can someone please help me ( check the link for the question

Answers

The equation of the line that passes through the point (3, 2) and is perpendicular to 3x + 5y = 15 is y = (5/3)x - 3

What is an equation of a line?

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

The equation of the line is y = m(1)x + c

The line passes through (3, 2) and is perpendicular to 3x + 5y = 15.

This means,

3x + 5y = 15

5y = -3x + 15

y = (-3/5)x + 3

m(2) = (-3/5)

Now,

m(1) x m(2) = -1

m(1) = -1 / ((-3/5)

m(1) = 5/3

Now,

(3, 2) = (x, y)

y = m(1)x + c

2 = (5/3) x 3 + c

2 = 5 + c
c = 2 - 5

c = -3

Thus,

The equation of the line is y = (5/3)x - 3.

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EMERGENCY NEED HELP PLEASE HELP THE QUESTION IS ATTACHED TO THE QUESTION THING PLEASE HELP!!!

Answers

Graph of given system of equations is shown in figure with intersection point (2, 4).

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.

We have to given that;

The system of equation is,

⇒ 2x + y = 8

⇒ - x + 2y = 6

By solving both equation , we get;

⇒ (x, y) = (2, 4)

Thus, The graph of system of equation intersect on point (2, 4).

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Simplify the expression below:
20-10y-7y + 9
A) Зу — 29
B) 3y + 11
C) 3y + 29
D) -17y + 11
E) -17y + 29

Answers

To simplify the expression 20-10y-7y + 9, we can combine like terms.

Like terms are terms that have the same variables raised to the same exponents. For example, 10y and -7y are like terms because they both have the variable y raised to the exponent 1.

We can start by combining the like terms:

20 - 10y - 7y + 9

= 20 + (-10y - 7y) + 9

= 20 + (-17y) + 9

Next, we can combine the constants:

20 + (-17y) + 9

= (20 + 9) + (-17y)

= 29 + (-17y)

The simplified expression is: 29 + (-17y)

[tex]20-10y-7y + 9[/tex]

Combine Like Terms:

[tex](-10y+-7y)+(20+9)[/tex]

[tex]-17y+29[/tex]

[tex]\fbox{Option E}[/tex]

plz help filipino words and 3-5 sentences

Answers

Step-by-step explanation:

Bagong balita tungkol sa corona virus 19 sa Pilipinas, Ayon sa WHO at DOH mayroong 2.5M na vaccine na ang pinangangasiwaan ang Pilipinas at naitala ring mayroon ng 2.02M ang na bakunahan na indibiduwal.

A pair of shoes that normally costs $75 is on sale for $55. What is the percent decrease in the price, to the nearest whole percent?​

Answers

Answer:

100% -> 75

1% -> 0.75

75-55=20

20 ÷ 0.75 =26.666666.........

               ≈ 27%

What is the solution to this system of linear equations x − 3y − 2x 3y 16?

Answers

solution of the linear equation is x = (2a - 16)/ 3 and y = - (a+16)/ 9

What is linear equation?

An algebraic expression that shows a relationship between two variables   that have only first order term. One of the main criteria for linear equation is that we get a straight line when plot this equation in a coordinate system.

.

What is the solution of the system of linear equation?

we are given, two linear equations x - a -3y = 0

and a - 2x -3y - 16 =0

from the first equation, x = a + 3y

we put the value of x in the second equation, a - 2(a +3y) - 3y -16= 0

                                                                     a - 2a - 6y - 3y -16 = 0

                                                          - a - 9y -16 =0

                                                   - (a + 16) = 9y

                                              y = - (a+16) / 9

now we put the value of y in the equation, x = a + 3y

                                    get, x = a+ 3 [ - (a+16)] / 9

                                      x = a + [ - (a+16)] / 3

                                          x = (3a - a -16) / 3

                              x = (2a - 16)/ 3

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Choose three true statements about the angles of the figure

1: Z1 and the 55* angle are adjacent

2: mZ1=55* because Z1 and the 55* angle are vertical angles

3: mZ2=125* because Z2 and the 55* angle are supplementary

4: mZ2 cannot be determined from the information

5: mZ1=180*-55*

6: mZ2=180*-55*-45*

Answers

Answer:

2,5,6

Step-by-step explanation:

-Z1 and 55*are vertical angles

-Z1 and 55*are angles on a straight line=180*

this means 180*=55*+Z1

make Z1 subject of the formula- Z1=180*-55*

- mZ2,55*,45* are all angles in the given triangle

since the sum of angles in a triangLe =180*

therefore-180*=Z2+55*+45*

make Z2 the subject of the formulary

Z2=180*-55*-45*

How many times smaller is 1.2 × 106 than 1.38 × 107?

Answers

The number 1.2 × 10⁶ is 11.5 times smaller in comparison to the number 1.38 × 10⁷.

The two given numbers here have been written using the method of powers of 10. In this method, very large or very small numbers are easily simplified and written by denoting the powers of 10. These power are integral in nature. Very large numbers are of the form y × 10ⁿ and very small numbers can be expressed in the form z × 10⁻ⁿ.

In the given problem, we have the numbers 1.2 × 10⁶ and 1.38 × 10⁷ and we have to tell how much the former number is from the latter. For this, we divide the two and easily find our solution. Before this, we have to make the powers of 10 in both numbers the same. We can rewrite the  1.38 × 10⁷ as 13.8 × 10⁶. Now, we divide the two and get-

⇒ 11.5

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Answer: B. 11.5

Step-by-step explanation: I took the test

I need the answer fast please

Answers

I think it’s c since like most of them make yellow, while one makes brown, even if it’s just one different colour added

GAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA

Answers

Answer:

Step-by-step explanation:

GAAAAAAAAAAAAAAAAAAAAAAAAAA

(0,4) (2,-6) find the slope

Answers

Answer:

Slope = -5

Step-by-step explanation:

Slope Formula:

y2-y1/x2-x1


So


-6-4/2-0=

-10/2


Therefore -5 is the Answer


Hope this helps

help with this question

Answers

The answer is D
x+y=-1
x-2y=14
(use desmos graphing calculator)

559
8
X
о
10.5
O
55
O
8
O
11.4

Answers

Answer:

what is the question?????

Adina read 60 out of 100 pages in a comic book.Write the fraction of the pages she read in simplest form

Answers

Answer:

3/5 is 60/100 in it's simplest form.

Step-by-step explanation:

60 divided by 20 is 3 and 100 divided by 20 is 5.

So 3/5

explain how you would use algebra tiles to solve x - 3 = 7

Answers

Answer:

Start by laying out 7 tiles, and then adding 3. Whatever that number of tiles is equals x.

x = 10

10 - 3 = 7

answer: x=10
explanation: switch subtraction to addition to both sides and add 3 to both sides making it 7 + 3 witch equals 10

pleaseee helpppp:)))

Answers

Answer:

Option B:112 families

Step-by-step explanation:

Given,

No. of families = 75

Out of 75 no. of families had cars = 42

Out of 1, no. of families can have cars

[tex] = \frac{42}{75} [/tex]

Therefore,

Out of 200 families, no. of families had cars

[tex] = 200 \times \frac{42}{75} [/tex]

[tex] =200 \times \frac{14}{25} [/tex]

= 8 × 14

= 112

Hence,

option B is correct as 112 families have cars out of 200 families (Ans)

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