In the first week students at RSM solved 25 percent of their monthly quota of problems. In the second week, they solved 110 percent of the number of problems solved in the first week. In the third week they solved 60 percent of the number of problems they had solved in the first two weeks and, in the fourth week, they solved the remaining 320 problems. How many problems did students solve in the four-week month?

Answers

Answer 1

Answer:

The number of problems solved = 2000

Step-by-step explanation:

Let us assume the monthly quota of problems be x

number of problem solved in first week = 25 % of x =[tex]0.25x[/tex]

number of problems solved in 2nd week = 110% of (problems solved in 1st       week)

                                                         = [tex]1.10 (0.25x)[/tex]

                                                         =[tex]0.275x[/tex]

number of problem solved 3rd week= 60% of ( problems solved in 1st and 2nd week)

                                                            = [tex]0.60(0.25x+0.275x)[/tex]

                                                            =[tex]0.60(0.525x)[/tex]

                                                            =[tex]0.315x[/tex]

number of problem solved in 4th week = [tex]320[/tex]

now we have

number of problems solved in ll 4 weeks = x

[tex]0.25x +0.275x+0.315x+320=x[/tex]

[tex]0.84x+320=x[/tex]

[tex]320=x-0.84x[/tex]

[tex]320=0.16 x[/tex]

[tex]x=\frac{320}{0.16}[/tex]

[tex]x=2000[/tex]

Hence the number of problems solved = 2000



Answer 2

Final answer:

In the third week they solved 60% of the number of problems they had solved in the first two weeks and, in the fourth week, they solved the remaining 320 problems. The total number of problems solved in the four-week month is 492.

Explanation:

To solve this problem, we need to find the number of problems solved in each week and then add them together to get the total number of problems solved in the four-week month.

In the first week, the students solved 25% of their monthly quota of problems. Let's say their monthly quota is 'x'. So, they solved 0.25x problems in the first week.

In the second week, they solved 110% of the number of problems solved in the first week. That means they solved 1.1 * 0.25x = 0.275x problems in the second week.

In the third week, they solved 60% of the number of problems they had solved in the first two weeks. So, they solved 0.6 * (0.25x + 0.275x) = 0.345x problems in the third week.

In the fourth week, they solved the remaining 320 problems. This means the total number of problems solved in the first three weeks is 0.345x, and we can set up the following equation to find x: 0.345x + 320 = x.

Solving this equation, we get x = 491.429. Since we can't have a fractional number of problems, we can round x up to 492. Therefore, the students solved a total of 492 problems in the four-week month.


Related Questions

Which of the following is not part of the protein synthesis?

replication

transcription

respiration

translation

Answers

Answer: The correct answer is respiration.

Respiration can be defined as the biochemical process, by which cells obtain energy as ATP from oxygen and glucose, with release of carbon dioxide, water. This process is not at all involved in the synthesis of protein, as it produces energy for the cells of the body.




Please factorise these

Answers

Hope you are having a good day.
1) 4x(2x-3y)
2)5a(2x-3y)
3)a^2-b^2(a-b)

Which pairs of variables have a linear relationship check all that apply

Answers

Answer:

Can I have the options? I cant check all that apply if i don't have options.

Step-by-step explanation:


A conical storage building stores landscaping stone. The diameter of the base of the building is 36 feet, the height is 57.2 feet, and the slant height of the building is 60 feet. How many square feet does the base of the building measure? Use 3.14 for pi and round to the nearest hundredth. A. 1,017.36 ft2 B.2,568.39 ft2 C.3,391.20ft2 D.4,096.44 ft2

Answers

Answer:

Option A is correct.

1,017.36 square feet does the base of the building measure.

Step-by-step explanation:

Given: Diameter of the base (d) = 36 feet , Height of the building (h) = 57.2 feet and slant height of the building(l) = 60 feet.

We have to find the area of the base of the building.

Since, the building is in the form cone.

Area of the base(A) of the cone is given by:

[tex]A= \pi r^2[/tex] ......[1]; where r is the radius of the cone

Diameter(d) = 2r

36 = 2r

Divide both sides by 2 we get;

r = 18 feet.

Substitute the value of r = 18 feet and [tex]\pi = 3.14[/tex] in [1] we get;

Area of the base of the building = [tex]3.14 \times (18)^2 = 3.14 \times 324 = 1017.36[/tex] square feet.

Therefore, 1,017.36 square feet does the base of the building measure.



Answer:

A

Step-by-step explanation:

16 adults and 40 students attended a charity event. The adults and students sat at 8 tables.

Question 1: Each table had the same number of adults how many adults are there?

Question 2: Each table had the same number of students. How many students sat at each table?

Question 3: How many people in all sat at each table?

Please answer all these questions and tell me that answer as soon as possible please and thank you!

Answers

Answer:

1) 16 adults

2) 2 adults at each table

3) 7

Step-by-step explanation:


Which statement describes data that is negatively skewed?

A- The majority of the data is to the left of the mean

B- The majority of the data is to the right of the mean

C- The majority of the data is in the center with the mean

D- The majority of the data is split to the right and left of the mean

Answers

B is the correct answer
ANSWER

B- The majority of the data is to the right of the mean

EXPLANATION

The data that is negatively skewed has its mean less than the median and the mode.


The arrangement for the measures of central tendency for a data set that is negatively skewed is

[tex]mean \: < \: median \: < mode[/tex]


Since the mode is to the right, it means majority of the the data is to the left of the mean.

The correct answer is B

Heidi takes 45 minutes to cover a distance of 5.4 miles on a treadmill. Find the average distance covered by Heidi in one minute.

Answers

Answer:


Step-by-step explanation:

answer:heidi goes 0.12 miles a minute .

steps

average distance=time/miles

45/5.4

0.12

mark me as brainlest


Answer:

0.12 mile/minute

Step-by-step explanation:

Here you're being asked to find a unit rate.

Compute:

5.4 miles

--------------- = 0.12 mile/minute

45 min

This is the average distance covered in one minute.

Please help!!!! Last question i have left to do!!!! thanks


5.8=z/2.2
A) 127.6
B) 0.37
C) 3.7
D) 12.76

please help fast this is the only question I have left to do and cant figure it out

Answers

1. simplify 11/5
- 58/10 - 11/5 =0

2. Divide z by 11/5
- 58/10 - 5z/11 =0

3. simplify 29/5
29/5 - 5z/11 =0

4. calculating the least common multiple
4.1 find the least common multiple
the left denominator is: 5
the right deniminator is: 11

least common multiple:55
....
solution z=319/25 = 12.760

write some numbers that are equal to 15÷12

Answers

Answer

14 / 13 hope this helps


Step-by-step explanation:


5 / 4 = 1.25
2.5 / 2 = 1.25

Which polygon has interior angles whose sum is 1440°? octagon nonagon decagon 11-gon

Answers

Answer:

Decagon

Step-by-step explanation:

We can use the general equation to determine the sum of interior angles:

[tex]I.A. = 180 \times (n-2)[/tex]

Since we know the sum of interior angles (I.A.) is 1440°, we must figure out n - the number of sides and so:

[tex]1440=180(n-2)\\\\\frac{1440}{180}=n-2\\\\8=n-2\\\\n=10[/tex]

Since n=10 this means that it is a 10 sided shape meaning it's a decagon.

Answer:

decagon

Step-by-step explanation:

1440=180(n-2)

8=n-n

n=10  

this means that your answer is going to is decagon.

Which coefficient before hydrogen (H2) balances this chemical equation? N2 + __H2 2NH3 A. 2 B. 3 C. 4 D. 5

Answers

Answer:


Step-by-step explanation:

The answer to this question is 3

Hope this helps

Final answer:

To balance the chemical equation N2 + __H2 -> 2NH3, we need to have the same number of each type of atom on both sides. We have 2 Nitrogen atoms on each side of the equation, but the Hydrogen atoms are unbalanced. By placing a coefficient of 3 before H2, we get a balanced chemical equation; N2 + 3H2 -> 2NH3. Hence, the correct answer is option B, 3.

Explanation:

In order to balance a chemical equation, the same number of each type of atom must be present on both sides of the equation. In the initial chemical equation given, N2 + __H2 -> 2NH3, we have 2 Nitrogen atoms on both sides which is balanced. However, for Hydrogen we have 2 Hydrogen atoms on the left side (from H2) but 6 on the right side (as each NH3 molecule has 3 Hydrogen atoms). Therefore, we need to balance the Hydrogen atoms.

Putting a coefficient of 3 before H2 on the left side of the equation, we will have 3 * 2 = 6 Hydrogen atoms. This balances the Hydrogen atoms on both sides of the equation. Hence, the balanced chemical equation becomes N2 + 3H2 -> 2NH3. Therefore, the correct answer is B. 3.

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what is the image of (-9,3) when it is reflected across the line y = x?

Answers

Answer:

(3, -9)

Step-by-step explanation:

To reflect an image across the line y = x, (x, y) → (y, x).

(-9, 3) → (3, -9)

(3, -9) the x and y coordinates change places

Mariana tried to drink a slushy as fast as she could. She drank the slushy at a rate of 4.5 milliliters per second. After 17 seconds, 148.5 milliliters of slushy remained. How long did it take for her to finish the slushy if she originally started with 225 milliliters? Who finished first?

Answers

This is what i did to get the answer.

225/ 4.5 = 50 seconds to finish the slushy.

How to simplify fractions

Answers

Step-by-step explanation:

[tex]\frac{2}{3} + \frac{2}{9} \\\\\frac{6+2}{9}\\\\\frac{8}{9}[/tex]

The length of a diagonal of a quadrilateral shaped field Is 48 m And the length of perpendicular dropped on it from the remaining apposite vertices are 16 m and 26 m find the area of the field

Answers

Answer:

[tex]1008\text{ m}^2[/tex]

Step by step explanation:

Please find the attachment.    

We have been given that the length of a diagonal of a quadrilateral shaped field Is 48 m. The length of perpendicular dropped on it from the remaining apposite vertices are 16 m and 26 m.

We can see from our attachment that diagonal AC divides our quadrilateral field into two triangular fields and AC will be the base of both triangles.

To find the area of our given quadrilateral we will find the areas of both triangles and add the areas.

Let us find area of triangle ABC with base 48 m and height 26 m.

[tex]\text{Area of triangle}=\frac{1}{2}(\text{ Base}\times\text{ Height})[/tex]

[tex]\text{Area of triangle ABC}=\frac{1}{2}\times 48\times 26[/tex]  

[tex]\text{Area of triangle ABC}=24\times 26[/tex]  

[tex]\text{Area of triangle ABC}=624[/tex]

Therefore, the area of triangle ABC will be 624 square meters.

Now let us find area of triangle ADC with base 48 m and height 16 m.

[tex]\text{Area of triangle ADC}=\frac{1}{2}\times 48\times 16[/tex]  

[tex]\text{Area of triangle ADC}=24\times 16[/tex]  

[tex]\text{Area of triangle ADC}=384[/tex]    

Therefore, the area of triangle ADC will be 384 square meters.

Now let us add areas of triangles ABC and ADC to get the area of our quadrilateral ABCD.

[tex]\text{Area of quadrilateral ABCD}=384+624[/tex]  

[tex]\text{Area of quadrilateral ABCD}=1008[/tex]  

Therefore, the area of quadrilateral shaped field will be 1008 square meters.



what is the importance of the quadratic formula?

Answers

obviously, it is used to solve quadratic equations. but it’s also used in forming/determining a parabola in that they can predict patterns on graphs. they are useful in real life situations.

Find the value of m in this equation below

Answers

Answer:

m=0

Step-by-step explanation:

Zero power rule: a^0 = 1,   Anything raised to the zero power is 1  (a≠ 0).

So if m=0, as long as x does not equal zero   (x^8/yz^5)^m will equal one.


Rewrite the function by completing the square F(x)=2x^2+13x+20

Answers

Answer:

[tex]F(x)=2\left(x+\dfrac{13}{4}\right)^2-\dfrac{9}{8}.[/tex]

Step-by-step explanation:

Consider the function [tex]F(x)=2x^2+13x+20.[/tex]

Rewrite it as follows:

[tex]F(x)=(2x^2+13x)+20=2\left(x^2+\dfrac{13}{2}x\right)+20=2\left(x^2+\dfrac{13}{2}x+\left(\dfrac{13}{4}\right)^2-\left(\dfrac{13}{4}\right)^2\right)+20=2\left(x^2+\dfrac{13}{2}x+\dfrac{169}{16}\right)-2\cdot \dfrac{169}{16}+20.[/tex]

Since

[tex]x^2+\dfrac{13}{2}x+\dfrac{169}{16}=\left(x+\dfrac{13}{4}\right)^2,[/tex]

you get

[tex]F(x)=2\left(x+\dfrac{13}{4}\right)^2+20-\dfrac{169}{8}=2\left(x+\dfrac{13}{4}\right)^2-\dfrac{9}{8}.[/tex]

Answer:

the correct answer is: f(x)=2(x+13/4)²+-9/8. i hope it help

Christian is reading 1/4 books every 2/3 week. How many books does christian read per week
A) 1/6
B) 3/8
C) 2 2/3
D) 6

Answers

Answer:

(1/4) / (2/3) = x / 1...1/4 book to 2/3 week = x books to 1 week

cross multiply because this is a proportion

2/3x = 1/4

x = 1/4 * 3/2

x = 3/8 per week

MARK ME BRAINLIEST
This answer is B) 3/8 per week <3

Donata bought 4 lemons and 4 plums at the local supermarket for a total of $ 21.60. Dan bought 11 lemons and 6 plums at the same store for a total of $40.90 how much does one lemon cost. .... helppppp. How Much does 1 plum cost?

Answers

the answer to the question

Mrs Li is x years old Mr Li is 6 years older than Mrs Li. David is one third of Mr Li.
Write an expression in terms of x for Davids age and the Sum of their 3 ages giving your answer in simplest form.

Answers

Mrs. Li: x
Mr. Li: 6+x
David: the word "of" means multiplication so
1/3 * (6+x)
Sum: x+6+x+1/3*(6+x)
Multiplication first, so = x+6+x+2+x/3
Combine like terms: (x+x+x/3) + (6+2)
Find common denominator : (3x+3x+x)/3 + 8
Simplify : 7x/3 + 8

Find the missing term (need help)

Answers

Answer:

x² - 10x + 34

Step-by-step explanation:

given the roots are x = 5 ± 3i then the factors are

(x - (5 + 3i))(x - (5 - 3i))

= (x - 5)² - 9i² ← expand (x - 5)²

= x² - 10 x + 25 + 9 → [ i² = - 1 ]

= x² - 10x + 34

the missing term is 10x



The freshman class at Central High totals 522 students, with 100 more girls than boys. Which equation can be used to find the number of boys?

Answers

Answer:

The required equation is (1) and the number of boys is 211.

Step-by-step explanation:

Let the number of boys be x.

It is given that there are 100 more girls than boys. It means the number of girls is x+100.

The total number of students is 522.

Number of boys + Number of girls = 522

[tex]x+(x+100)=522[/tex]          ... (1)

Combine like terms.

[tex]2x+100=522[/tex]

Subtract 100 from both the sides.

[tex]2x+100-100=522-100[/tex]

[tex]2x=422[/tex]

Divide both sides by 2.

[tex]x=211[/tex]

Therefore the required equation is (1) and the number of boys is 211.

Answer:

[tex]2x+100=522[/tex]

Step-by-step explanation:

Let the no. of boys be x

We are given that there are 100 more girls than boys.

So, No. of girls = x+100

Total number students = [tex]x+x+100[/tex]

                                      = [tex]2x+100[/tex]

We are given that The freshman class at Central High totals 522 students

So, equation becomes : [tex]2x+100=522[/tex]

Hence an equation can be used to find the number of boys is  [tex]2x+100=522[/tex]

What is the unit price if a dozen rolls cost 3.99?

Answers

Answer:

$.33 cents per roll

Step-by-step explanation:

a dozen rolls are 12 rolls

To find the unit prices, take the price and divide by the number of rolls.

$3.99/12

$.3325

But this is money so we round to the nearest cent

$.33 cents per roll

(hope this helps)

ANSWER :

.33 for 1 roll

STEP BY STEP :

We know that the price of 12 rolls is $3.99. To solve this we have to find the unit rate, or the price of each roll. Divide each number by 12. ⇩

$3.99 price / 12 rolls

Divided by 12⇩

~ .33 cents / 1 roll


What is the quotient 240,000 divided 100

Answers

240,000/100=2,400.

-TheOneandOnly003

Have a blessed day.


the answer of 240,000 ÷ 100 is 2.4

Who can help me answer this question ASAP please and thank you please show work

Answers

I'll do the first one to get you started

So we have g(f(x)) which means that we start with g(x) and replace the 'x' with 'f(x)' to get g(f(x))

g(x) = ( x - 4 )/2

g(f(x)) = ( f(x) - 4)/2 .... replace every x with f(x)

g(f(x)) = (2x+4-4)/2 .... replace f(x) on the right side with 2x+4

g(f(x)) = (2x+0)/2

g(f(x)) = (2x)/2

g(f(x)) = 1x/1

g(f(x)) = 1x

g(f(x)) = x

Let me know if you need help with the other one.

12,192÷48 long divison

Answers

the answer is 254, but here is the walkthrough: First, I recommend trying to remember the steps of long division by using Daddy, mommy, sister, brother. Daddy for divide, mommy for multiply, sister for subtract, and brother for bring down. Then, simply follow the steps:
The answer is 254. Hope this helps

A cyclist can travel 29.6 miles in 2 hours. At this rate, how far can the same cyclist travel in 45 minutes?

Answers

Answer:

x=11.1mi

Step-by-step explanation:

29.6mi          x    

120 min       45 min


cross multiply and divide

120x = 45*29.6

x = 45*29.6/120

x = 11.1 mi

There is your answer!

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Solve the following proportion: x-5:4 = 8:10. I NEED THIS DONE ASAP IM IN CLASS

Answers

I’m not 100% sure if this is right but I think it is x=13:14

The equation y = 11x describes the amount of money Louis earns, where x is the number of hours he works and y is the amount of money he earns. The table shows the amount of money Carl earns for different numbers of hours worked. Carl’s Earnings
Time (h) 3 5 8 10
Money earned ($) 42 70 112 140
(a) How much money does Carl earn per hour? Show your work.
(b) Who earns more per hour? Justify your answer.
(c) Draw a graph that represents Carl’s earnings over time in hours.
Label the axes

Answers

Answer:


Step-by-step explanation:

(a) Carl earns $42 per 3 hours as given. To find the amount he earns per hourdivide:


$42/3 hours = $14/hour


(b) To see how much Louis makes per hour, simply plug in 1 for the hours value x:


y = $11(1 hours)


y = $11/hour


Thus Carl makes more than Louis.


(c) The equation of Carl's dollars per hour is similar to Louis' = 14x 


where x is the number of hours he works and y is the number of dollars he earns. Plug in whole number values of hours for x and plot the points (x, y) on a graph




Is him in your bias?

Carl earns $14 per hour, which is more than Louis' hourly wage of $11. A graph that represents Carl's earnings should have time in hours on the x-axis and money earned on the y-axis.

The question relates to comparing Hourly Earnings of Louis and Carl, and analyzing earnings overtime through graphs.

(a) To determine Carl's hourly earnings, we divide the amount of money earned by the hours worked.

For example, when he works 3 hours, he earns $42.

Therefore, the hourly rate is $42/3 = $14 per hour.

(b) By comparing Carl's hourly earning which is $14/hour to Louis' earning which is $11/hour according to the equation y = 11x, it is clear that Carl earns more per hour.

(c) To plot the graph for Carl's earnings, you need to put the time in hours on the x-axis and the money earned on the y-axis.

Each point on the graph represents the amount Carl earns after a certain number of hours.

For example the point (3,42) represents that Carl earns $42 after 3 hours of work.

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