Gretchen and Ezia received equal scores on a test made up of multiple choice questions and an essay. Gretchen got 18 multiple choice questions correct and received 19 points for her essay. Ezia got 15 multiple choice questions correct and received 31 points for her essay.

How many points was each multiple choice question worth?

Answers

Answer 1

My solution here is as follows:

The scores were the same, so

18m+19 = 15m+31

Now solve for m, the # points for each multiple-choice question.

I hope my answer has come to your help. Have a nice day ahead and may God bless you always!

Answer 2

Answer:

Each question had 4 points.

Step-by-step explanation:

Let the questions be x points each. As both Gretchen and Ezia received equal scores, we can write the equation as:

18x+19=15x+31 (Let the questions be x points each)

Solving for x;

[tex]18x-15x=31-19[/tex]

=> [tex]3x=12[/tex]

Dividing both sides by 3;

x = 4

Hence, each question had 4 points.

Related Questions

Can someone smart help me here?

Solve the mathematical puzzle.

S is a three digit number.
Determine the digits of S from the clues.

All the digits are odd.
The last two digits add to make ten.
The first and last digits add to make eight.
The first two digits add to make twelve.

S is

Answers

The answer is 573

S is the three digit number.
h - a number of hundreds
t - a number of tens
o - a number of ones

S = 100h + 10t + o

The last two digits add to make ten: t + o = 10
The first and last digits add to make eight: h + o = 8
The first two digits add to make twelve: h + t = 12

t + o = 10 ⇒ o = 10 - t
h + o = 8 ⇒ o = 8 - h
_______
10 - t = 8 - h
h + t = 12 ⇒ h = 12 - t
_______
10 - t = 8 - (12 - t)
10 - t = 8 - 12 + t
10 - t = -4 + t
10 + 4 = t + t
2t = 14
t = 14/2 = 7
______

h = 12 - t = 12 - 7 = 5
______

o = 8 - h = 8 - 5 = 3

S = 100h + 10t + o
h = 5
t = 7
o = 3

S = 100*5 + 10*7 + 3
= 500 + 70 + 3
= 573

What is the greatest common factor of 34n and 8n^2?

Answers

The answer is: 2n .
_________________________________
The greatest common factor (GCF) of 34n and 8n² is: 2n .
__________________________________________
Explanation:
_______________
First, break down EACH term into prime factors:
__________________________________________
Start with the first term given: "34n" :
__________________________________________
34n = 17 * 2 * n
__________________________________________
Now, do so with the second term given: "8n² " :
__________________________________________
8n² = 2 * 2 * 2 * n * n
_______________________________________________
Now, look for factors that exist in EACH of the two terms:
_______________________________________________
In the term: "34n"; there is a "17", and a "2" and a "n" — and that's it!
_______________________________________________
In the term: "8n² " that is a "2" and an "n".
_______________________________________________
So: 2 * n = 2n ; which is our answer:
_______________________________________________
The greatest common factor (GCF) of 34n and 8n² is: 2n .
_________________________________________________________

The greatest common factor of 34n and 8n² is 2n, as both expressions share the variable n and the highest common numerical coefficient is 2.

The greatest common factor (GCF) of two algebraic expressions can be found by identifying the highest powers of common factors in the terms. For the expressions 34n and 8n², both terms have n as a common factor. Since we want the greatest common factor, we take the highest power of n that appears in both terms, which is n (not n² because n is the highest power in the least degree term, 34n). Next, we find the GCF of the numerical coefficients 34 and 8, which is 2. Therefore, the greatest common factor of 34n and 8n² is 2n.

What is 0.021 in fraction form?

Answers

Convert the decimal to a fraction by placing the decimal number over a power of ten. Since there are three numbers to the right of the decimal point, place the decimal number over 10^3 (1000)
= 21/1000

The population of a small town increased by 25% two years ago and then decreased by by 25% last year. The population is now 4500 persons. What was the population before the two changes?

Answers

9,000. It decreased by 50% (25%+25%) over three years, which in this case won't matter, because of the question. If 4,500 is 50% of x then just multiply 4,500 by two.

Twice a number is 36 less than -104. Find the number

Answers

Final answer:

The question 'twice a number is 36 less than -104' is an algebraic problem which can be solved by simplifying the equation '2x = -104 - 36' and dividing through by two. The solution to the equation is x = -70.

Explanation:

The problem presented is a simple algebraic equation. The question is: Twice a number is 36 less than -104. This can be expressed with the equation 2x = -104 - 36.

To solve for x, we first simplify the right side of the equation: 2x = -140. Next, we isolate x by dividing both sides of the equation by 2: x = -140 / 2. So, the number x is -70.

Learn more about Algebra here:

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What is the lcm of 21, 84, 126?

Answers

The LCM would be 252.

Their LCM would be 252. 'cause it's the smallest number by which all of them can be divide perfectly!!

So, your final answer is 252

Hope this helps!

What is the inverse of the function f(x) = 2x – 10? h(x) = 2x – 5 h(x) = 2x + 5 h(x) = x – 5 h(x) = x + 5

Answers

f(x) = 2x-10
y = 2x -10
Switch y and x,
x = 2y -10
solve for y,
x + 10 = 2y
x/2 + 10/2 = y
x/2 + 5 = y
y = x/2 + 5 or h(x) = x/2 + 5
Hence, the inverse of the function f(x) = 2x-10 is h(x) = x/2 + 5

The inverse of a function is gotten by swapping the x and y coordinates.

The inverse of function f(x) is[tex]h(x) = \frac x2 + 5[/tex]

Given

[tex]f(x) = 2x - 10[/tex]

Rewrite as:

[tex]y = 2x - 10[/tex]

Swap x and y

[tex]x = 2y - 10[/tex]

Solve for y

[tex]2y = x + 10[/tex]

Divide by 2

[tex]y = \frac x2 + 5[/tex]

So, we have:

[tex]h(x) = \frac x2 + 5[/tex]

Hence, the inverse function is[tex]h(x) = \frac x2 + 5[/tex]

Read more about inverse function at:

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Jimmy was 12 years old in 2014 and now in 2016 he is 15 how did he grow 3 years in 2 years?

A. HE WAS BORN ON MAY 1ST

B. HE WAS BORN ON DECEMBER 23RD

C. HE WAS BORN ON NOVEMBER 15TH

D. HE WAS BORN ON JANUARY 20TH

Answers

D. He was born on January 20th
If he was born on January 20th, he would be the oldest in his school classes. Right when the new year starts, his birthday comes up.

WILL UPVOTE!
Which equation is related to 89 = x + 61?

A. x = 150

B. 61 = 89 + x

C. x = 28

D. x = 18

Answers

C! x = 28. If you use simplification, and then you find the answer and use it in the equation, it would be correct.

Is x – 3 a factor of the polynomial p(x) = 2x^4– 9x^3 + 15x^2 – 22x + 12, and for what reason?
A) Yes, because p(3) is equal to 0.
B) Yes, because p(–3) is equal to 0.
C) No, because p(3) is not equal to 0.
D) No, because p(–3) is not equal to 0.

Answers

A yes because p3 is equal to 0

Which statement is modeled by the expression?

150/k

The Henderson family drove 150 miles each day of their vacation. If their vacation lasted for k days, then 150/k is the total number of miles they traveled on their vacation.

The cafeteria has a capacity of 150 seats. If k is the number of people in the cafeteria at lunch time, then 150/k is number of seats that were not used at lunch time.

A librarian had 150 books to be placed on shelves with an equal number of books on each shelf. If k is the number of shelves to be used, then 150/k is the number of books on each shelf.

Cory had 150 dollars in his savings account. He withdrew k dollars to buy a catcher's mitt. He then had 150/k dollars left in his savings account.

Answers

A librarian has 150 books to be placed on shelves with an equal number of books on each shelf. If k is the number of shelves to be used, then 150/k is the number of books on each shelf.

Example : lets say there are 10 shelves.....so k = 10
150/10 = 15 books on each shelf.

Hey

I hope you are having a great day

The answer would be A librarian had 150 books to be placed on shelves with an equal number of books on each shelf. If k is the number of shelves to be used, then 150/k is the number of books on each shelf.

Explanation: Lets see Option 1 is obviously out Option 2 does not make

sense When it comes to option 3 that makes the most sense Option 4 could be right but option 3 is the best and correct answer

So that's your answer

Hope This Helps :)

-Sprinkles

A trail mix has 4 cups of raisins, 3 cups of chocolate, 6 cups of peanuts, and 2 cups of cashews. Which ingredients are in the same ratio as cashews to raisins?

Answers

cashew: raisin 2:4 or 1:2

Chocolate: peanut 3:6 or 1:2

So it is chocolate to peanuts

What step in the construction of copying a line segment ensures that the new line segment has the same length as the original line segment?

Answers

Final answer:

To copy a line segment and ensure it has the same length as the original, use a compass to measure and create a duplicate line segment.

Explanation:

To copy a line segment and ensure that the new line segment has the same length as the original, we can use a compass. Here are the steps:

Place the compass needle on one endpoint of the original line segment.Open the compass to the length of the original line segment.Without changing the compass width, place the compass needle on the other endpoint of the original line segment and draw an arc.Use the compass to measure the same length on the arc and draw a line segment connecting the two marks.

By using this method, we can create a duplicate line segment with the same length as the original.

Learn more about Copying line segments here:

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Determine whether the dilation from A (blue figure) to B (green figure) is an enlargement or reduction, then find the scale factor of the dilation.

a. reduction; scale factor of 2/5
b. enlargement; scale factor of 5/2
c. reduction; scale factor of 2/3
d. enlargement; scale factor of 3/2

Answers

Answer:

Option B

Step-by-step explanation:

In the figure attached we have to find the scale factor of dilation of figure A to figure B.

Since figure A is smaller than figure B, it concludes figure A has been enlarged to form figure B.

Now we have to find the scale factor of enlargement.

Scale factor = [tex]\frac{\text{one side of the larger figure}}{\text{one side of the smaller figure}}[/tex]

= [tex]\frac{5}{2}[/tex]

Therefore option B is the correct answer.

What is the simplified form of the following expression? (x10)(x2)

Answers

(x^10)(x^2) Add the exponents 10+2=12 So... (x^12)

I'm pretty sure the answer would be x^12

Which of these statements about statistical models is true? I. Statistical models help better understand real-world systems. II. Statistical models represent the real world. III. Statistical models help predict future behavior.

Answers

I would think statistical models help better understand real world systems

Final answer:

Statistical models help understand real-world systems, represent simplified versions of reality, and aid in predicting future behavior. However, they are not perfect and contain uncertainties.

Explanation:

The question at hand is about statistical models and their characteristics. Statistical models do indeed serve several key functions, and among the statements listed, all are true to a certain extent:

Statistical models help better understand real-world systems by simplifying complex phenomena and making them more approachable for analysis.Statistical models represent the real world, but it is important to note that they are simplifications and may not capture all the nuances of real-world behavior.Statistical models help predict future behavior by using historical data and probabilistic methods to make informed guesses about what might happen under similar circumstances.

However, it is crucial to remember that while statistical models are powerful tools for interpretation and prediction, they are not perfect representations of reality and come with inherent uncertainties and limitations.

Will Upvote! Need help!
Find the balance in the account.
$700 principal earning 5%, compounded monthly, after 9 years
A: $79,380.00
B: $1,085.93
C: $1,096.79
D: $16,088.19

Answers

The answer would be C

I really need help solving this whole problem.

Answers

a.
No, you do not have enough information to determine the price of both gasoline and oil from the prices that "you" and "your friend" paid at the station. If you look closely, you'll notice that "your friend" bought half the amount of gas and oil that you did and paid half the price-- you won't get a satisfactory answer from just this information.
b.
Yes, with this you can use elimination to solve the systems, as you bought 2 quarts of oil and 10 gallons of gas for $45.50 and the receipt owner bought 2 quarts of oil and 8 gallons of gas for $38.40.
c.
Alright, so here is elimination, that is, eliminating a variable if you add two equations together. (This is a confusing answer so I would suggest you ask someone else for a better one).
So, first we make an equation out of the word problem in the beginning.
I'll treat 1 gallon of gas as "g", and one quart of oil as "o".
45.50 = 10g + 2o
+ 38.40 = 8g + 2o
You'll note that there are 2 "o"s in each equation. So, we'll multiply the bottom equation by -1 so the "o" cancels out and we can get the value of "g".
45.50 = 10g + 2o
+ (38.40 = 8g + 2o) * -1
This becomes:
45.50 = 10g + 2o
+ -38.40 = -8g - 2o

Subtract, and this becomes

7.1 = 2g
/2
g = 3.55
Alright, so now we know the value of a gallon of gas. Let's substitute this back into the original equation to find the price for the oil.

45.50 = 10(3.55) + 2o
45.50 = 35.5 + 2o
-35.5 -35.5
10 = 2o
/2
o = 5
So we know that 1 gallon of gas is $3.55 and one quart of oil is $5.00.

Which of the following are quadratic functions?

Check all that apply.

a. y=2(x-3x^2+1)
b. y=5+2x
c. y=1/2x^2-13x+4
d. y= x/x-1 Which of the following are quadratic functions?

Check all that apply.

a. y=2(x-3x^2+1)
b. y=5+2x
c. y=1/2x^2-13x+4
d. y= x/x-1

Answers

y=2(x-3x^2+1) and if it's a multiple choice I'd also choose y=1/2x^2-13x+4

Final answer:

The quadratic functions are: y = 2(x - 3x² + 1), y = 1/2x² - 13x + 4, and y = 1.

Explanation:

A quadratic function is a polynomial function of degree 2, which means its highest power of x is 2. The general form of a quadratic function is y = ax^2 + bx + c, where a, b, and c are constants.

Out of the given options, the quadratic functions are:

a. y = 2(x - 3x² + 1)

c. y = 1/2x² - 13x + 4

d. y = x/x - 1 (this can be simplified to y = 1)

The options b. (y = 5 + 2x) is not a quadratic function because it only has a linear term (power of x is 1).

Tina has to pay 4 percent of the purchase price toward closing costs for her mortgage. If the purchase price is $275,000, what is the closing cost amount?

Answers

x/275,000=4/100 cross multiply and you get x=11,000

Answer:

Proportion states that two fractions or ratios are equal.

Let x be the closing cost amount.

As per the statement:

Tina has to pay 4 percent of the purchase price toward closing costs for her mortgage. If the purchase price is $275,000.

Purchased Price = $275,000

then, by definition of proportion :

[tex]\frac{4}{100}=\frac{x}{275000}[/tex]

By cross multiply we have;

1,100,000 = 100x

Divide both sides by 100 we have;

11,000 = x

x = $ 11,000

Therefore, the closing cost amount is, 11,000

Is 8.92 greater or less than 8.9

Answers

8.92 is greater than 8.9

8.92 > 8.9

1)A discriminant of 0 indicates what type of roots?

A)Two Complex
B)One Rational Double
C)Two Rational
D)Two Irrational

2)The quadratic 2x2 + 6x + 3 has what type of roots?

A)Two Irrational
B)Two Complex
C)One Rational Double
D)Two Rational

3)The quadratic x2 + 20x + 100 has what type of roots?
Answer
A)Two Irrational
B)Two Rational
C)One Rational Double
D)Two Complex

4)What is the possible discriminant of the graph?(graph in the link)

A)0
B)–11
C)73
D)25

5)What is the possible discriminant of the graph?(Graph in the link)

A)0
B)17
C)25
D)–15
...?

Answers

Here are the answers to the given questions above.
1. A discriminant of 0 indicates a rational double, which will be -b/2a for a quadratic of the form ax^2 + bx + c. The answer would be C.
2. The quadratic 2x2 + 6x + 3 has two irrational roots. The answer would be option A.
3. The quadratic x2 + 20x + 100 has One Rational Double root. The answer would be C.
4. The possible discriminant of the graph given would be -11. The answer is option B.
5. The possible discriminant of the graph given would be 0. The answer is A.
Hope these answers help.

What is 0.666 in a fraction?

Answers

6/9 it is a perdiodic number with just one number on period

The khan's car averages 22 miles per gallon of gas. predict how far they can travel on 5 gallons of gas.

Answers

They can travel roughly 110 miles for 5 gallons of gas.

Answer:

110 miles

Step-by-step explanation:

If EACH GALLON of gas gives 22 miles, 5 GALLONS will give 5 times that. So,

[tex]22*5=110[/tex]

So in 5 gallons, Khan's should get around 110 miles

Determine the x values that cause the function to be (a) Zero, (b) Positive and (c) Negative, then d) sketch a graph of the function.

Answers

Factor
find roots
determine intervals between roots for which function is positive or negative
sketch

or use calculus either way

URGENT MATH HELP!

Which shows the conversion of 0.21 millimeters to inches?

There is 0.03937 inch in 1 millimeter.

A.
0.21 mm × 0.03937 in./mm = 0.0083 inches

B.
0.21 mm + 0.03937 in./mm = 0.24937 inches

C.
0.21 mm ÷ 0.03937 in./mm = 5.34 inches

D.
0.21 mm × 0.03937 in./mm = 8.3 × 10^-2 inches

Answers

The answer is: [A]:
________________________________

0.21 mm × 0.03937 in./mm = 0.0083 inches
_________________________________

Jon earns $180 per week plus $25 for each sale.write an inequality to represent how many sales he at least $500

Answers

500>180+25 does that help

What is another name for 34/8 as a mixed number??

Answers

34 ÷ 8 = 4 (remainder 2)
4 2/8 = 4 1/4
So another name for 34/8 as a mixed number is 4 1/4. I hope this helps!

A father and his daughter together weigh seven times the daughter's weight x. The father weighs 180 lbs. Which equation can be used to find the daughter's weight?

A. 180-7x = x

B. x -180 = 7x

C. 180 -x = 7x

D. 180 + x = 7x
...?

Answers

D.180+x=7x
x-7x=-180
-6x=-180
x=180/6
x=30 pounds

180+30=210

Solve the system of equations by using substitution y=x 10 and x=8-2y

Answers

you should make y feel lonely!!+

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