The sum of two numbers is 72. If twice the smaller number is subtracted from the larger number, the result is 9. Find the two numbers.
The larger number is
The smaller number is

Answers

Answer 1

Answer:

51

21

Step-by-step explanation:

Let x be larger number

Let y be smaller number

x - 2y = 9

==>

x = 9 + 2y

AND

x + y = 72

SO

(9 + 2y) + y = 72

==>

3y = 72 - 9 = 63

==>

y = 21

SINCE

x = 9 + 2y = 9 + (2×21)

==>

x = 51


Related Questions

15 points work out ratio for x

Answers

Answer:

x = 25

Step-by-step explanation:

x : (x+10) = 5:7

Fractional form

x / x+10 = 5/7

Cross multiply:

x * 7 = (x+10) * 5

7x = 5x + 50

7x - 5x = 5x + 50 - 5x

2x = 50

x = 25

Check:

25 : 25 + 10

25 : 35

25/35 = 5/7

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

The equation of a line is (3)/(5)x+(1)/(3)y=(1)/(15) . The x-intercept of the line is , and its y-intercept is .

Answers

bxf-mgii-whr

Step-by-step explanation:

come I will teach

(4x - 3) × (x + 2)=0

Answers

Hi,

AxB = 0 means A=0. or B=0

so 2 solutions :

4x-3= 0

4x=3

x = 3/4

and x+2 = 0.

x= -2

solutions are : -2 +and 3/4

2 answers

1) -2

2) -3/4

If 10 wholes are divided into pieces that are one half of a whole each how many pieces are there?

Answers

9514 1404 393

Answer:

  20

Step-by-step explanation:

A whole can be divided into two pieces that are each 1/2 of the whole.

 (10 wholes) × (2 pieces per whole) = 20 pieces

If car eyelashes sold for $13.99. If you bud double that, how much would you have paid for them? (Hint if needed: if they had been exactly $14, how different would your answer be?)

Answers

Answer:

13.99 x 2 = 27.98 dollars

now if they were 14 dollars exactly and you doubled that it would be 28 dollars so the difference would be 0.02 cents

Step-by-step explanation:

Full-time Ph.D. students receive an average of $12,837 per year. If the average salaries are normally distributed with a standard deviation of $1500, find these probabilities. a. The student makes more than $15,000. b. The student makes between $13,000 and $14,000.

Answers

Answer:

a) 0.0749 = 7.49% probability that the student makes more than $15,000.

b) 0.227 = 22.7% probability that the student makes between $13,000 and $14,000.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Full-time Ph.D. students receive an average of $12,837 per year.

This means that [tex]\mu = 12837[/tex]

Standard deviation of $1500

This means that [tex]\sigma = 1500[/tex]

a. The student makes more than $15,000.

This is 1 subtracted by the p-value of Z when X = 15000.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{15000 - 12837}{1500}[/tex]

[tex]Z = 1.44[/tex]

[tex]Z = 1.44[/tex] has a p-value of 0.9251.

1 - 0.9251 = 0.0749

0.0749 = 7.49% probability that the student makes more than $15,000.

b. The student makes between $13,000 and $14,000.

This is the p-value of Z when X = 14000 subtracted by the p-value of Z when X = 13000.

X = 14000

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{14000 - 12837}{1500}[/tex]

[tex]Z = 0.775[/tex]

[tex]Z = 0.775[/tex] has a p-value of 0.7708.

X = 13000

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{13000 - 12837}{1500}[/tex]

[tex]Z = 0.11[/tex]

[tex]Z = 0.11[/tex] has a p-value of 0.5438.

0.7708 - 0.5438 = 0.227

0.227 = 22.7% probability that the student makes between $13,000 and $14,000.

7.49% of the student makes more than $15,000, while 23.85% of the student makes between $13,000 and $14,000

What is z score?

Z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:

z = (raw score - mean) / standard deviation

Given that:

Mean = $12837, standard deviation = $1500

a) For >15000:

z = (15000 - 12837)/1500 = 1.44

P(z > 1.44) = 1 - P(z < 1.44) = 1 - 0.9251 = 0.0749

b) For >13000:

z = (13000 - 12837)/1500 = 0.11

For <14000:

z = (14000 - 12837)/1500 = 0.78

P(0.11 < z < 0.78) = P(z < 0.78) - P(z < 0.11) = 0.7823 - 0.5438 = 0.2385

7.49% of the student makes more than $15,000, while 23.85% of the student makes between $13,000 and $14,000

Find out more on z score at: https://brainly.com/question/25638875

What type of line is PQ?
A. side bisector
B. angle bisector
C. median
D. altitude

Answers

Answer:

B: I think

Step-by-step explanation:

correct me if im wrong

The line PQ is an angle bisector because it divides the angle P into two equal half option (B) angle bisector is correct.

What is an angle?

When two lines or rays converge at the same point, the measurement between them is called a "Angle."

We have a triangle shown in the picture.

As we know,  

in terms of geometry, the triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.

From the figure the segment PQ divides the angle into two equal half.

From the definition of the angle bisector, the angle bisector can be defined as a line segment that divides the angle into two half.

Angle P = 40 + 40 = 80 degrees

Thus, the line PQ is an angle bisector because it divides the angle P into two equal half option (B) angle bisector is correct.

Learn more about the angle here:

brainly.com/question/7116550

#SPJ5

Solve each system by graphing.

Answers

Answer:

it is 2 te he

Step-by-step explanation:

ONCE THE 5 6 = 7 10 .. ?% =1 x 7 =2 te he

(02.02 MC) Use the graph to fill in the blank with the correct number.
Numerical Answers Expected!
Answer for Blank 1:​

Answers

Answer:

The answer is "2"

Step-by-step explanation:

When we check the points where the x is -2

by calculating the "y-value":

It is 2, right?  

it implies that [tex]f(-2)=2[/tex]

that's why the final answer is "2"

Nadia is ordering cheesecake at a restaurant, and the server tells her that she can have up to five toppings: caramel, whipped cream, butterscotch sauce, strawberries, and hot fudge. Since she cannot decide how many of the toppings she wants, she tells the server to surprise her. If the server randomly chooses which toppings to add, what is the probability that Nadia gets just caramel, butterscotch sauce, strawberries, and hot fudge

Answers

Answer:

The probability that Nadia gets just caramel, butterscotch sauce, strawberries, and hot fudge is P =  1/32 = 0.03125

Step-by-step explanation:

There are up to 5 toppings, such that the toppings are:

caramel

whipped cream

butterscotch sauce

strawberries

hot fudge

We want to find the probability that,  If the server randomly chooses which toppings to add, she gets just caramel, butterscotch sauce, strawberries, and hot fudge.

First, we need to find the total number of possible combinations.

let's separate them in number of toppings.

0 toppins:

Here is one combination.

1 topping:

here we have one topping and 5 options, so there are 5 different combinations of 1 topping.

2 toppings.

Assuming that each topping can be used only once, for the first topping we have 5 options.

And for the second topping we have 4 options (because one is already used)

The total number of combinations is equal to the product between the number of options for each topping, so here we have:

c = 4*5 = 20 combinations.

But we are counting the permutations, which is equal to n! (where n is the number of toppings, in this case is n = 2), this means that we are differentiating in the case where the first topping is caramel and the second is whipped cream, and the case where the first topping is whipped cream and the second is caramel, to avoid this, we should divide by the number of permutations.

Then the number of different combinations is:

c' = 20/2! = 10

3 toppings.

similarly to the previous case.

for the first topping there are 5 options

for the second there are 4 options

for the third there are 3 options

the total number of different combinations is:

c' = (5*4*3)/(3!) = (5*4*3)/(3*2) = 10

4 toppings:

We can think of this as "the topping that we do not use", so there are only 5 possible toppings to not use, then there are 5 different combinations with 4 toppings.

5 toppings:

Similar to the first case, here is only one combination with 5 toppings.

So the total number of different combinations is:

C = 1 + 5 + 10 + 10 + 5 + 1 = 32

There are 32 different combinations.

And we want to find the probability of getting one particular combination (all of them have the same probability)

Then the probability is the quotient between one and the total number of different combinations.

p = 1/32

The probability that Nadia gets just caramel, butterscotch sauce, strawberries, and hot fudge is P =  1/32 = 0.03125

Max has 3 fiction books and 6 nonfiction books to donate to the community center. He wants to package them so that there is an equal number of fiction and nonfiction books in each group. He also wants to have as many packages as possible. How many books are in each group?

Answers

Answer:

Each group has 1 fiction book and 2 nonfiction book(s).

15. On Sports Day, Mike runs 100 metres in 13.89 seconds and Neal runs the same distance in 13.01 seconds. Who is the FASTER runner?​

Answers

Answer:

Neal

Step-by-step explanation:

13.01 < 13.89

Damaris will be working at the local pool over his ten-week summer break. His net pay will be $167.30 each week. He hopes to have enough money to purchase a new pair of shoes that cost $175 by the end of his break. What percent of his net pay does Damaris need to save each week to reach his goal? Round to the nearest hundredth. (2 points)
1.05%
10.46%
11.37%

Answers

Damaris needs to save 10.46% of his net pay each week to purchase the new pair of shoes by the end of his break.

Given:

Net pay per week is $167.30Cost of new pair of shoes is $175Summer break is for 10 weeks

To find: The percentage of his net pay that Damaris needs to save each week to purchase the shoes by the end of his break

Let us assume that Damaris needs to save x% of his net pay each week to buy the shoes by the end of his break.

Then, savings per week is x% of $167.30, that is,

[tex]\frac{x}{100}\times 167.30[/tex]

Then, his savings for 10 weeks is,

[tex]10 \times \frac{x}{100}\times 167.30[/tex]

Since the summer break is for 10 weeks, Damaris' savings for the entire summer break is,

[tex]10 \times \frac{x}{100}\times 167.30[/tex]

Damaris wants to buy the new pair of shoes by then end of the break. Then, his savings for the entire summer break should equal the cost of the new pair of shoes.

It is given that the cost of the new pair of shoes is $175.

Then, according to the problem,

[tex]10 \times \frac{x}{100}\times 167.30 =175[/tex]

[tex]x=\frac{175\times 100}{10\times167.30}[/tex]

[tex]x=10.460251[/tex]

Rounding to the nearest hundredth, we have,

[tex]x=10.46[/tex]

Thus, Damaris needs to save [tex]10.46[/tex]% of his net pay each week to buy the shoes by the end of his break.

Learn more about percentage here:

https://brainly.com/question/22400644

Ahmed bought a TV for his room in 2016 for AED 1,500. he decided to sell it in 2020 for AED 900. what is the rate of depreciation when he bought the TV and when he sold it

Answers

Answer:

40% depreciation over the 4 years

10% depreciation per year

Step-by-step explanation:

The number of years between buying and selling is:

2020 - 2016 = 4

4 years

The amount of depreciation in the 4 years is:

AED 1,500 - AED 900 = AED 600

The percent depreciation for the 4 years is:

(1500 - 900)/1500 * 100% = 40%

The percent depreciation per year is:

40%/4 = 10%

The average weight of a professional football player in 2009 was pounds. Assume the population standard deviation is pounds. A random sample of professional football players was selected.

Required:
a. Calculate the standard error of the mean.
b. What is the probability that the sample mean will be less than 230 pounds?
c. What is the probability that the sample mean will be more than 231 pounds?
d. What is the probability that the sample mean will be between 248 pounds and 255 pounds?

Answers

Answer:

6.286;

0.0165

0.976

0.1995

Step-by-step explanation:

Given that :

Mean, μ = 243. 4

Standard deviation, σ = 35

Sample size, n = 31

1.)

Standard Error

S. E = σ / √n = 35/√31 = 6.286

2.)

P(x < 230) ;

Z = (x - μ) / S.E

P(Z < (230 - 243.4) / 6.286))

P(Z < - 2.132) = 0.0165

3.)

P(x > 231)

P(Z > (231 - 243.4) / 6.286))

P(Z > - 1.973) = 0.976 (area to the right)

4)

P(x < 248)

P(Z < (248 - 243.4) / 6.286))

P(Z < 0.732) = 0.7679

P(x < 255)

P(Z < (255 - 243.4) / 6.286))

P(Z < 1.845) = 0.9674

0.9674 - 0.7679 = 0.1995

For each of the following numbers, find the smallest whole number by which it should be multiplied so as to get a perfect square number. Also find the square root of the square number so obtained.
(i) 242
(ii) 1280
(iii) 245
(iv)968
(v) 1728
(vi) 4851​

Answers

Answer:

BELOW

Step-by-step explanation:

242: multiply it by 2 to get 484 and its square root is 22

1280: multiply it by 5  to get 6400 and its square root is 80.

245: multiply it by 5 to get 1225  and its square root is 35.

968: multiply it by 2 to get 1936 and its square root is 44.

1728: multiply it by 3 to get 5184 and its square root is 72

4851: multiply it by 11 to get 53361 and its square root is 231.

HOPE THIS HELPED

Solve the following equation for the given variable.
4x + 19 + 3x = -5
Round your answers to the nearest tenths place.

Answers

Step-by-step explanation:

4x + 19 + 3x = - 5

4x + 3x + 19 = - 5 collect the like terms

7x + 19 = - 5

7x = - 5 - 19 bring 19 to the right

7x/ 7x = - 24/ 7

x = - 3.4

I hope this answers your question

here's a graph of a linear function write the equation that describes the function express it in slope-intercept form

Answers

Answer:

y = 3/4 x - 3

Step-by-step explanation:

the slope of a line is the factor of x in the equation and is expressed as ratio of y/x : defining how many units y changes, when x changes a certain number of units.

in our graph here we can see that when increasing x from e.g. 0 to 4 (the x-axis intercept point, a change of +4), y changes from -3 to 0 (a change of +3).

so, the slope and factor of x is y/x = 3/4

and for x=0 we get y=-3 as y-axis intercept point.

so, the line equation is

y = 3/4 x - 3

Is this a function help

Answers

Yes because it create lines that won’t hit two points (probably doesn’t make sense)

A random sample of 25 graduates of four-year business colleges by the American Bankers Association revealed a mean amount owed in student loans was $14,381 with a standard deviation of $1,892. Assuming the pop is normally distributed:
a) Compute a 90% confidence interval, as well as the margin of error.
b) Interpret the confidence interval you have computed.

Answers

Answer:

a) The 90% confidence interval for the mean amount owed in student loans of graduates of four-year business colleges is ($13,600, $15,162), having a margin of error of $781.

b) We are 90% sure that the mean amount owed in student loans of graduates of  all four-year business colleges is between $13,600 and $15,162.

Step-by-step explanation:

Question a:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom,which is the sample size subtracted by 1. So

df = 25 - 1 = 24

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 24 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 2.0639

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 2.0639\frac{1892}{\sqrt{25}} = 781[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 14381 - 781 = $13,600

The upper end of the interval is the sample mean added to M. So it is 14381 + 781 = $15,162

The 90% confidence interval for the mean amount owed in student loans of graduates of four-year business colleges is ($13,600, $15,162), having a margin of error of $781.

b) Interpret the confidence interval you have computed.

We are 90% sure that the mean amount owed in student loans of graduates of  all four-year business colleges is between $13,600 and $15,162.

7. 20x + 10 = 110
a. X= 1
b. X= 5
c. x= 12

Answers

Answer:

b x=5

Step-by-step explanation:

20x+10=110

20x+10-10=110-10

20x/20=100/20

x=5

Answer:

x=5

Step-by-step explanation:

20x + 10 = 110

Subtract 10 from each side

20x +10-10 = 110-10

20x = 100

divide by 20

20x/20 =100/20

x= 5

Instructions: Find the missing length indicated.

Answers

Answer:

x = 65

Step-by-step explanation:

x = √(25×(25+144))

x = √(25×169)

x = 5×13

x = 65

Answered by GAUTHMATH

Simplify your answer as much as possible.

Answers

Answer:

x = -4

Step-by-step explanation:

2 = 3x + 22/5

Numerator = denominator x quotient

Numerator = 5 x 2

Numerator = 10

3x + 22 = 10

Subtract 22 from both sides

3x = -12

x = -12/3

x = -4
•••••••••••••••••••••••••••
Hope this helps!

Bye love you.

- doomdabomb

The lengths of two sides of the right triangle ABC shown in the illustration given

a= 7cm and b= 24cm

Answers

Answer:

25 cm.

Step-by-step explaination:

Given,

Two sides of a triangle:

a = 7cm

b = 24 cm

To find,

Third side:

c = ?

By Pythagorean Theorem;

a² + b² = c²

[where c is the longest side,hypotenuse]

Putting the value of a and b;

we get,

7² + 24² = c²

49 + 576 = c²

625 = c²

25² = c² (square root)

25 = c

c = 25

Therefore, the length of the third side will be equal to 25 cm.

Question:-

The lengths of two sides of the right triangle ABC shown in the illustration given

a= 7cm and b= 24cm

Given,

> a= 7cm

> b= 24cm

To find?

Side c (third side)

Solution:-

Using Pythagoras theorem,

▶️ a² + b² = c

▶️ 7cm ² + 24cm² = c²

▶️ 49cm + 576cm = c²

▶️ 625cm = c²

▶️ 25² = c² (25×25 = 625)

▶️ c = 25

The value of c is 25 cm.

Ell takes the 17 apples home, and the bakes as many apple pies
as he can. He uses 7 apples in each ple. How many apple pies does
El bake? How many apples are left?
Counters
17:7
10
10
c
Boles
pies
apples are en

Answers

Answer:

Tedyxhcj eydyfhxrstetdhsawe

Find the midpoint of the segment with the given endpoints.
(7,10) and (-1,- 8)

Answers

Answer:

(3,1) is the midpoint

Step-by-step explanation:

To find the x coordinate of the midpoint, average the x coordinates of the endpoints

(7+-1)/2 = 6/2 =3

To find the y coordinate of the midpoint, average the y coordinates of the endpoints

(10+-8)/2 = 2/2 = 1

(3,1) is the midpoint

Answer:

(3, 1)

Step-by-step explanation:

We can use the formula [ (x1+x2)/2, (y1+y2/2) ] to solve for the midpoint.

7+(-1)/2, 10+(-8)/2

6/2, 2/2

3, 1

Best of Luck!

write your answer in simplest radical form​

Answers

Answer:

z = √3

Step-by-step explanation:

sin (30°) = z / 2√3

z = sin (30°) 2√3

z = √3

Need help answer plz help

Answers

Answer:

BONANA MY NANA

Step-by-step explanation:

How many permutations of letter of the word APPLE are there?​

Answers

Answer:

There are 60 permutations.

Step-by-step explanation:

Arrangements formula:

The number of possible arrangements of n elements is given by:

[tex]A_n = n![/tex]

With repetition:

For each element that repeats, with [tex]n_1, n_2, ..., n_n[/tex] times, the formula is:

[tex]A_n^{n_1,n_2,...,n_n} = \frac{n!}{n_1!n_2!...n_n}[/tex]

In this question:

Apple has 5 letters.

P appears two times. So

[tex]A _5^{2} = \frac{5!}{2!} = 60[/tex]

There are 60 permutations.

Suppose h(x)=3x-2 and j(x) = ax +b. Find a relationship between a and b such that h(j(x)) = j(h(x))

Probably a simple answer, but I'm completely lost at what I'm being asked here.

Answers

Answer:

[tex]\displaystyle a = \frac{1}{3} \text{ and } b = \frac{2}{3}[/tex]

Step-by-step explanation:

We can use the definition of inverse functions. Recall that if two functions, f and g are inverses, then:

[tex]\displaystyle f(g(x)) = g(f(x)) = x[/tex]

So, we can let j be the inverse function of h.

Function h is given by:

[tex]\displaystyle h(x) = y = 3x-2[/tex]

Find its inverse. Flip variables:

[tex]x = 3y - 2[/tex]

Solve for y. Add:

[tex]\displaystyle x + 2 = 3y[/tex]

Hence:

[tex]\displaystyle h^{-1}(x) = j(x) = \frac{x+2}{3} = \frac{1}{3} x + \frac{2}{3}[/tex]

Therefore, a = 1/3 and b = 2/3.

We can verify our solution:

[tex]\displaystyle \begin{aligned} h(j(x)) &= h\left( \frac{1}{3} x + \frac{2}{3}\right) \\ \\ &= 3\left(\frac{1}{3}x + \frac{2}{3}\right) -2 \\ \\ &= (x + 2) -2 \\ \\ &= x \end{aligned}[/tex]

And:

[tex]\displaystyle \begin{aligned} j(h(x)) &= j\left(3x-2\right) \\ \\ &= \frac{1}{3}\left( 3x-2\right)+\frac{2}{3} \\ \\ &=\left( x- \frac{2}{3}\right) + \frac{2}{3} \\ \\ &= x \stackrel{\checkmark}{=} x\end{aligned}[/tex]

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