four times the sum of a number and 2/3 is 16/3. find the number. express your answer as a fraction in simplest form

Answers

Answer 1

times= multiply
sum= addition
is= equal sign

x= a number

4 times x plus 2/3 equals 16/3.

4x + 2/3= 16/3
subtract 2/3 from both sides

4x= 14/3
divide both sides by 4

x= 14/3 ÷ 4
to divide fractions, multiply by reciprocal/inverse of 4

x= 14/3 * 1/4
multiply numerators (top); multiply denominators (bottom)

x= (14*1)/(3*4)
x= 14/12
simplify by 2

x= 7/6

ANSWER: The number in simplest form is 7/6.

Hope this helps! :)

Related Questions

Cheryl used 40% of her money to buy a dress and 1/5 of the remainder to buy a pair of shoes. She then donated $60 to charity and had $132 left How much money did Cheryl have at first?

Answers

Let the amount be a
Amount used for dress= 40% of a
amount left =60% of a
amount used for shoe= 1/5*60a/100=3a/25
left=60a/100-12a/100=48a/100
=>48a/100-60=132
=>a=192*100/49=400
She had $400 at first.
Hope I helped, good luck.

Let the amount of money she has at first be x.

Dress = 40% x = 0.4x

Amount left = x - 0.4x = 0.6x

Shoes = 1/5 x 0.6x = 0.12x

Amount left = 0.6x - 0.12x = 0.48x

Donated $60 and had $132 left:
⇒ 0.48x - 60 = 132

Solve x:

0.48x - 60 = 132

0.48x = 192

x = $400

Answer: $400

A crane is rented at $1000 per day plus a charge per hour of use. The crane was used for 7 hours on a day, and the total charge was $3450. Which equation can be used to find the charge x, in dollars, per hour of use?

Answers

The equation can be (3450-1000)÷7=350.

370x1/10 = please help

Answers

37,
It is thirty seven, use a calculator

Answer: 37
This is because 370 times 1/10 is the same as 370 times 0.1 which would be equal to 37

what does x equal
5x+2y=3
1x+2y=6

Answers

[tex]\underline{-\left\{\begin{array}{ccc}5x+2y=3\\x+2y=6\end{array}\right }\ \ \ \ |subtract\ both\ sides\\\\4x=-3\ \ \ |:4\\\\x=-\dfrac{3}{4}\to x=-0.75[/tex]

Find the future value of $1800 deposited at 8% for 5 years if the account pays simple interest, and the account pays interest compounded annually.

Answers

For one year:
0.08(1800) + 1800
But because it is 5 years:
5(0.08(1800)) + 1800
0.4(1800) + 1800
We can make it simpler:
1.4(1800)
Multiply:
2520
YOU NOW HAVE $2520

Answer:

The answer is 2,644.79.

You would have to calculate the three variables to get and complete your answer.

Step-by-step explanation:

The big bend national park covers 800,000 acres. Brazos Bend state park covers about 5,000 acres. About how many more acres does Big Bend National Park cover then Brazos Bend state park?

Answers

795,000 I dont totally understand why you asked
this but okay....

Final answer:

Big Bend National Park is larger by approximately 795,000 acres than Brazos Bend State Park. This figure was obtained by subtracting the area of the Brazos Bend State Park from the area of the Big Bend National Park.

Explanation:

The Big Bend National Park and the Brazos Bend State Park have a substantial difference in size. You can calculate this size difference by performing a simple subtraction operation. In this case, the size of the Big Bend National Park is 800,000 acres, whereas Brazos Bend State Park covers about 5,000 acres. By subtracting the size of Brazos Bend State Park from the size of the Big Bend National Park, we will get about 795,000 acres, which represents the size difference.

So, the formula would appear as follows:
800,000 acres (Big Bend National Park) - 5,000 acres (Brazos Bend State Park) = 795,000 acres difference.

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Find the area of the trapezoid to the nearest tenth.

Answers

The area of the trapezoid would be 153. What I’d did was 1.3 added to 1.5 added to 0.6, multiplied by 45, and I got the answer of 153.

A patrolman spends 25% every day completing paperwork. The patrolman’s shift each day is 8 hours. How much of his time does he spend doing paperwork each day?

Answers

[tex]8 \times 25\% \\ = 8 \times \dfrac{25}{100} \\ = 2[/tex]

Answer : He spends 2 hours doing paperwork each day.

Hope this helps. - M

mary draws the number line below to repersent the solution set of the inequality 50-8t<90
what mistake did Mary make?

Answers

50-8t<90
50-90<8t
-40<8t
8t>-40
t>-5
Solutions should go to the right.
Mary probably was solving it as following
50-8t<90
-8t<90-50
-8t<40 (here, when she divided both sides by -8, she had to change sign < to the sign >)
But she did not change the sign, and got
t<-5

What is the range of the following graph?

Answers

Range is the set of possible y values. If you look at the end behavior of the function, as x approaches both infinity and negative infinity, y continues to increase in magnitude, meaning that the range is from negative infinity to infinity. the correct answer is B.

Robin’s scores: 99, 108, 102, 107, 119 Evelyn’s scores: 125, 137, 138, 145, 145 Find and compare the medians of the data sets. Do the medians support your conclusion that Robin is winning the game?

Answers

To find the median, just sort the numbers from least to greatest and find the number in the center.

Robin's scores: 99, 102, 107, 108, 119. Median is 107.

Evelyn's scores: 125, 137, 138, 145, 145. Median is 138.

The median from Evelyn's scores is greater than the median from Robin's. Therefore, the medians do NOT support the conclusion that Robin is winning the game.

Answer:

The median score for Robin is 107. The Median Score of Evelyn is 138. The medians are the same as the means, so the same conclusion that Robin is winning will be drawn.

Step-by-step explanation:

Add the two expressions. 4.6x−3 and −5.3x+9 Enter your answer, in simplified form, in the box. PLEASE ANSWER FAST THIS IS A BIG DEAL!!!

Answers

So you have 4.6x − 3 and −5.3x + 9. You can only add like terms, which are terms where their variables (and the exponents on the variable) are the same. That means you can add 4.6x and −5.3x, and you can also add −3 and 9:
[tex]4.6x - 3 + - 5.3x + 9\\ = (4.6x - 5.3x) + (-3 + 9)\\ = -0.7x + 6[/tex]

-----

Answer: -0.7x + 6

An expression is defined as a set of numbers, variables, and mathematical operations. The addition of the two given expressions (4.6x-3) and (-5.3x+9) is (-0.7x+6).

What is an Expression?

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The addition of the two given expressions (4.6x-3) and (-5.3x+9) is,

(4.6x-3) + (-5.3x+9)

= 4.6x - 3 - 5.3x + 9

= -0.7x + 6

Hence, The addition of the two given expressions (4.6x-3) and (-5.3x+9) is (-0.7x+6).

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Determine whether quantities vary directly or inversely and find the constant of variation. It takes three identical water pumps 8 hours to fill a pool. How long would it take four of these same pumps to fill the pool, assuming they all pump at the same rate?
PLEASE HELP!!

Answers

8 * 3 = 24
24/4 = 6 HOURS

Find the area of a parallelogram....

Answers

The area of a parallelogram is ...
A = bh
Substituting the given values, you have
A = (3x +5)(7x -1)
We presume you want the product multiplied out. Use the distributive property for that.
A = 3x(7x -1) +5(7x -1)
A = 21x² -3x +35x -5
A = 21x² +32x -5

The area of the parallelogram is 21x² +32x -5.

What is the formula for the perimeter of a rectangle?

Answers

A= L x W / 2 length times width divided by 2

Please help me answer this question. Explain if possible.

Answers

The functions have the same initial value is correct

"The functions have the same rate of change" is wrong because as we can see, the table goes up by 10, however, the graph goes up by 15

"Both functions are the same" is also wrong, we already proved they have a different slope, how could they possibly be the same?

"The rate of change for Tour 1 is greater" is also wrong because tour 2 goes by 15, which is greater than 10.

"The functions have the same initial value is correct because as we can see on the graph(tour 2), the y-intercept is 35, using the slope on the tab;e(tour 1) we can calculate that when x is 0, the y-value is 35, which means both of the tours has a y-intercept of 35, therefore, this is the correct choice

It's possibly "The functions have the same rate of change."

Explanation: Alright let's do answer of elimination. It cannot be "Both functions are the same" Due to the fact that for one person in Tour 1 is 45 dollars while for Tour 2 is 50. It cannot be "The functions have the same initial value. Since for initial value it's kind of like a constant. For example for 1 person it would be 20 dollars for 2 it would be 40 and so on. It cannot be the last one since rate of change is obviously different. I don't think I have to go into that.

Also I see your doing an IReady Lesson

vector works the same number of hours every week he worked a total of 532.5 and hours in the last 15 weeks. how many hrs did he work in one week

Answers

532.5/15
this will give you the hours in one week
= 35.5

Divide 532.5 hours by 15 weeks.
532.5/15 = 35.5

Vector worked 35.5 hours in one week.

The equation below shows The area of a trapezoid, a, with a height of 9 cm, and one base 35 cm. A=9/2(b+35)
Which formula correctly solves for the other base, b?

Answers

For this case we have the following equation:
A = 9/2 (b + 35)
We must clear b from the equation, to obtain the value of the other base.
Clearing b we have:
(b + 35) = (2/9) A
b = (2/9) A - 35
Answer:
A formula that correctly solves for the other base, b is:
b = (2/9) A - 35

Find f(x) if it is known that f(3k)=3k+7.

Answers

f(3k)=3k +7 Equals 9k+7. So 9k+7 would be the Answer.

Since f(3k) = 3k+7 (Equation 1)

We have to determine the value of f(x).

That is we have to replace 3k by x,

3k = x

Substituting the value of 3k in equation 1.

So, f(x) = x + 7

Therefore, f(x)=x+7 is the required function.

Can someone please help me with number 25

Answers

Answer:

x² + 10x + 24 = (x + 4)(x + 6)

b = 4 or 6

if i started a business making braclets for $2 and necklaces for $3 with a budget >200 what would be the inequality equation?
How would I graph

Answers

If i started a business making braclets for $2 and necklaces for $3 with a budget >200 what would be the inequality equation?
How would I graph

Solution:
let x= number of bracelets
y= number of necklaces

Thus, the equation would be:
$2x+$3y>200

In graphing this equation, you just have to substitute any number for the values of x and y as long as when substituted, their sum is greater than 200

Triangle BCD is similar to triangle ACE. If the triangles are isosceles, what is the length of AB?
F.) 16cm
G.) 11cm
H.) 40cm
J.) 35cm

Answers

[tex] \frac{2.75}{22} = \frac{5}{ac} \\ ac = 5 \div ( \frac{2.75}{22} ) = 40 \\ ab = 40 - 5 = 35[/tex]
Correspondind sides, similar triangles

Can I have some help with this question?

Answers

-10(1-9x) +6(x-10)
-10+90x+6x-60

96x-70

so d is the answer

This question asks for distribution, which can be done by multiplying; then adding to the total.
-10(1-9x)=90x-10
6(x-10)=6x-60
(90x-10)+(6x-60)=96x-70 (same thing as -70+96x)
So, the answer is D. -70+96x
Have a nice day! ♪

A researcher randomly surveyed a sample of high school students in a town to find out which career area they were most interested in pursuing. This table shows the results of the sample. The town has a total of 1000 high school students.

Art Science Finance Health Law Education
26 24 16 21 18 20
Based on this sample, how many high school students in the school are predicted to be most interested in pursuing a career in health?

Enter your answer in the box.

Answers

total of students sampled:
26 + 24 + 16 + 21 + 18 + 20 = 125 total
21 picked health so 21 / 125 = 0.168 of the students picked health
multiply that by total students:
1000 * 0.168 = 168 total students will pick health

The total number of students who will pick health is 168 if a researcher randomly surveyed a sample of high school students in a town.

What is a survey?

A survey is a means of gathering information from a sample of people using pertinent questions with the goal of understanding populations as a whole.

We have:

A researcher randomly surveyed a sample of high school students in a town to find out which career area they were most interested in pursuing.

The town has a total of 1000 high school students.

Total of students sampled = 26 + 24 + 16 + 21 + 18 + 20

= 125 total

21 picked health:

= 21 / 125

= 0.168 of the students picked health

Total students will pick health:

= 1000×0.168

= 168

Thus, the total number of students will pick health is 168 if a researcher randomly surveyed a sample of high school students in a town.

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ANSWER ASAP PLEASE!!!
Johnny wants to know how many students in his school enjoy watching science programs on TV. He poses this question to all 26 students in his science class and finds that 75% of his classmates enjoy watching science programs on TV. He claims that 75% of the school's student population would be expected to enjoy watching science programs on TV. Is Johnny making a valid inference about this population?
A. Yes, it is a valid inference because his classmates make up a random sample of the students in the school
B. Yes, it is a valid inference because he asked all 26 students in his science class
C. No, it is not a valid inference because he asked all 26 students in his science class instead of taking a sample from his math class
D. No, it is not a valid inference because his classmates do not make up a random sample of the students in the school

Answers

The answer is D. No, it is not a valid inference because his classmates do not make up a random sample of the students in the school.

Answer:D

Step-by-step explanation:

i got it right onn a test

Sudhanshu is solving a system representing a race between two remote control cars. The variable x is defined as time in seconds, and y is the distance in meters from the starting line. How many solutions should Sudhanshu find?

Answers

It all depends on the speeds of the cars. If they are going the same speed, the lines could never cross. Or they could could cross once, if one car passes the other.
However, if the speeds are changing, then there could be multiple solutions.

Answer:

The lines would only cross ONCE. So the answer is ONE.

Step-by-step explanation:

If using a graphing calculator you will see that the lines are at different slopes and will soon cross at (5,20) on a graph. Which means that the second cars is also faster even though the first car had a head start.

Solve the equation (x-5)1/2+5=2

Answers

The first thing we are going to do for this case is to rewrite the equation correctly:
((x-5) ^ (1/2)) + 5 = 2
Clearing x we have:
(x-5) ^ (1/2) = 2-5
(x-5) ^ (1/2) = -3
x-5 = root (-3)
x-5 = i * root (3)
x = 5 + i * root (3)
Answer:
The value of x is given by:
x = 5 + i * root (3)

(x - 5)1/2 + 5 = 2
(x - 5)1/2 + 5 - 5 = 2 - 5
(x - 5)1/2 = -3
1/2x - 2.5 = -3
1/2x - 2.5 + 2.5 = -3 + 2.5
1/2x = -1/2
(1/2x)/(1/2) = (-1/2)/(1/2)
x = -1 <-------------answer :)

Originally priced at $15.99 was marked down 15% and then it was moved to a clearance rack marked take an additional 50% off the lowest marked price what is the final price of the PlayStation game

Answers

First, the mark down 15% would make the value 85% of the original, so doing 15.99*0.85 gives you 13.59. Then take that and multiply that by 0.5, because of the half price, to get a final price of $6.79

what does a highter and lower standard deviation tell you!!!!?
what does a higher and lower z-score tell you ?
what does the varience tell you?

Answers

The larger the standard deviation, the more spread out the data values will be. A smaller standard deviation, and the values are more closely grouped together. The variance is equal to the standard deviation squared. In terms of symbols
V = s^2
where V = variance and s = standard deviation
So the variance can also be used to determine how grouped or spread out the data values are

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

The z score tells us where this score is located in terms of the group. If the z score is positive, then it is above the mean. If the z score is negative, then it is below the mean. The further the z score is from zero, the further the raw score is from the mean. A score of z = 0 is right at the mean.

Enter the value of 5 times (13.5-4.5)

Answers

The answer is 45 because you do parenthesis first which is 13.5-4.5=9 then you multiply 9×5=45 therefore the answer is 45.

Expansion is a means by which complex function are simplified. The value of the expression 5 times (13.5-4.5) is 45

Factorization and expansion

Expansion is a means by which complex function are simplified by multiplying the expression with one another.

Given the expression:

5(13. 5 - 4.5)

According to the distributive property:

= 5(13. 5 - 4.5)

= 5(13.5) - 5(4.5)

= 67.5 - 22.5

= 45.0

Hence the value of the expression 5 times (13.5-4.5) is 45

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