How many gallons of a 80% antifreeze solution must be mixed with 60 gallons of 30% antifreeze to get a mixture that is 70% antifreeze?

Answers

Answer 1

Let x be the number of gallons.

(x)(80%) + (60)(30%) = (x+60)((70%)

0.8x + 18 = 0.7x +42

0.8x - 0.7x = 42-18

0.1x = 24

and x = 240 Gal.

Related Questions

What side lengths should be used to model a rectangle with an area of x2 + 3x – 10 square units?
x – 5 and x + 2
x – 2 and x + 5
x and x + 3
x + 3 and x – 10

Answers

The side lengths of the rectangle are (x - 2) and (x + 5)

What are areas?

The area of a shape is the amount of space on the shape

The area of the rectangle is given as;

[tex]Area = x^2 + 3x - 10[/tex]

Expand the expression

[tex]Area = x^2 + 5x - 2x - 10[/tex]

Factorize the expression

[tex]Area = x(x + 5) - 2(x + 5)[/tex]

Factor out x + 5

[tex]Area = (x - 2)(x + 5)[/tex]

Hence, the side lengths of the rectangle are (x - 2) and (x + 5)

Answers

Answer:

850,000

Step-by-step explanation:Meow

Alex is saving money because she would like to purchase the new video gaming system that everyone has been talking about. After two weeks of saving, she had $47. After 24 weeks of saving, she had $430. Approximately how many dollars per week did Alex save on average between weeks 2 and 24?

Answers

About $7 a day because nothing multiplied by two gives you $47.

First we take out the first two weeks

24-2 = 22
430-47 = 383

Now we are just left with after the two first weeks

383/22= 17.41 dollars

Find the cost of laminating decolam to a circular table of radius 1.4 m if the rate of decolam is rupees 50 per square metre

Answers

[tex]\bf \textit{area of a circle}\\\\ A=\pi r^2\quad \begin{cases} r=radius\\ -----\\ r=1.4 \end{cases}\implies A=\pi 1.4^2\implies A=\stackrel{m^2}{1.96\pi} \\\\\\ \textit{now, decolam is }\stackrel{rupees}{50}~per~m^2\implies \stackrel{\textit{total cost}}{50\cdot 1.96\pi }[/tex]

He total cost (in dollars) of producing xx coffee machines is c(x)=2300+40x−0.9x2. c(x)=2300+40x−0.9x2. (a) find the exact cost of producing the 21st machine.

Answers

$2743.1 .

Cost of producing 21st machine = $2743.1 .

What is function?A function is defined as a relationship between a set of inputs that each have one output. A function is a relationship between inputs in which each input is related to exactly one output. Every function has a domain and a codomain, as well as a range. In general, a function is denoted by f(x), where x is the input.When f and its derivatives are substituted into the equation, a solution is a function y=f(x) that satisfies the differential equation.The highest order of any derivative of the unknown function that appears in the equation is the order of a differential equation.

Given function,

c(x)=2300+40x−0.9x².

To find the cost of producing the 21st machine,

We have to find c(21).

c(21) = 2300+40(21)−0.9(21)²

= 2300 + 840 - 0.9 x 441

= 2300 + 840 - 396.9

= $2743.1

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Final answer:

To find the exact cost of producing the 21st coffee machine, substitute x = 21 into the given cost function, resulting in a cost of $2743.1.

Explanation:

The question asks for the exact cost of producing the 21st coffee machine given the cost function c(x) = 2300 + 40x - 0.9x². To find this, we substitute x = 21 into the cost function.

First, let's plug in x = 21 into the cost function:

c(21) = 2300 + 40(21) - 0.9(21²)c(21) = 2300 + 840 - 0.9(441)c(21) = 3140 - 396.9c(21) = 2743.1

Therefore, the exact cost of producing the 21st machine is $2743.1.

help me with this I don't get it help4help?

Answers

1) Divide 3/4 by 1/2. Remember how to divide fractions. Switch the problem into a multiplication problem.
3/4 x 2/1 = 3/2 (so you could only have 1 and 1/2 servings with 1/2 pound of chicken in each serving.

2) Set up a little algebra problem. Let x = the multiplier of the original 3/4 pounds of chicken needed to make two full servings with 1/2 pound of chicken in each.
(3/4)x = 2(1/2) (Found this online V(0-0)v)

Nancy purchased bed sheets for 36.00. They were on sale for 25% off. What was the original price

Answers

36.00 ÷ (1 - 0.25)
36.00 ÷ 0.75
$48

Hope this helps!

it is $144 because $36 is just 25% so you would multiply
$36 x 4 =144 hopes this helps you.

Which number when multiplied by 3/4 gives a product between 3/4 and 1?

A: 0
B: 1/4
C: 3/4
D: 1 1/4

Answers

1 1/4 = 5/4

5/4 * 3/4 = 15/16

Answer is D 1 1/4

D is the answer
3/4*1 1/4

the length of a banquet table is 3 feet longer than 5 times it's width. if the perimeter is 54 feet. What are the dimensions of the table?

Answers

First set up the equations for the length:

5x + 3

Now, lets find the perimeter:

5x + 3 +5x + 3 + x + x = 54
12x + 6 = 54
12x = 48
x = 4

Hope this helps!

solve the system of equations by graphing 4x-5y=20

Answers

Here is your graph of the system. Where they cross is the answer, which is -4. Pretty much you have to graph each equation and where they meet is the answer.

and doing some vandalizing to the posted image by MathJot, check the picture below.

[tex]\bf \begin{cases} 4x-5y=20\\ 3x+y=-4 \end{cases}\\\\ -------------------------------\\\\ 4x-5y=20\implies 4x-20=5y\implies \cfrac{4x-20}{5}=y\\\\\\ \boxed{\cfrac{4x}{5}-4=y} \\\\\\ 3x+y=-4\implies \boxed{y=-4-3x}[/tex]

the sum of 5 times a number and 2 is equal to 4 times the number

Answers

5x +2 =4x

subtract 2 from each side

5x= 4x-2

subtract 4x from each side

x = -2

Alan bought 3 pencils and a notebook. The notebook cost $6, and he spent a total of $12. How much did each pencil cost? Use p to represent the cost of each pencil. A. ; each pencil cost $2.50. B. ; each pencil cost $1.50. C. ; each pencil cost $2. D. ; each pencil cost $2.

Answers

So the pencils all together would be $6 so divide that by 3 and you get D as your answer each pencil costs $2

Cost of each pencil will be $2

What is Linear Equation ?

A linear equation is an equation in which the highest power of the variable is always 1 .

Number of pencil bought = 3

Number of notebook bought = 1

Cost of each notebook = $6

Cost of each pencil = ? let say its = x

Total money spent = $12

according to question , linear equation will be :

3* (x) + 1 * (6) = 12

3x = 6

x = 2

cost of each pencil will be $2

answer is d) $2

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write an equation of the circle that is tangent to both axes with radius sqrt5 and center in quadrant 3

Answers

check the picture below.

[tex]\bf \textit{equation of a circle}\\\\ (x-{{ h}})^2+(y-{{ k}})^2={{ r}}^2 ~~ \begin{array}{lllll} center~(&\quad {{ h}},&\quad {{ k}}\quad )\qquad radius=&{{ r}}\\ &-\sqrt{5}&-\sqrt{5}&\sqrt{5} \end{array} \\\\\\\ [x-(-\sqrt{5})]^2+[y-(-\sqrt{5})]^2=(\sqrt{5})^2 \\\\\\ (x+\sqrt{5})^2+(y+\sqrt{5})^2=5[/tex]

365 x 11? please answer!!!

Answers

365 x 11 = 4015

hope this helps

The expression 365 multiplied by 11 is equal to 4,015.

We have,

Calculating 365 multiplied by 11 is the basic multiplication algorithm.

This algorithm involves multiplying each digit of the multiplier (11) by each digit of the multiplicand (365), starting from the rightmost digit and moving toward the left

365 multiplied by 11 equals 4,015.

To explain the calculation:

We can perform long multiplication to find the product of 365 and 11:

365

x 11

------

365 (multiply 365 by 1)

+3650 (multiply 365 by 10)

------

4015 (sum the two products)

Therefore,

365 multiplied by 11 is equal to 4,015.

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An arithmetic sequence has this recursive formula

Answers

Answer: B
This is because 7 is standing in place for a1 and -4 is standing in place for d in the explicit equation: an=a1+(n-1)d

Answer:

[tex]\text{The explicit formula is }a_n=7+(n-1)(-4)[/tex]

Option B is correct.

Step-by-step explanation:

Given the recursive formula of arithmetic sequence

[tex]a_1=7[/tex]

[tex]a_{n}=a_{n-1}-4[/tex]

we have to find the explicit formula for the above sequence.

[tex]a_{n}=a_{n-1}-4[/tex]

[tex]a_{n}-a_{n-1}=-4[/tex]

which is the common difference, d=-4

The explicit formula for A.P is

[tex]a_n=a_1+(n-1)d[/tex]

[tex]a_n=7+(n-1)(-4)[/tex]

Option B is correct.

Using simple linear regression, calculate the trend line for the historical data. say the x axis is april = 1, may = 2, and so on, while the y axis is demand. (round your intercept value to the nearest whole number and slope value to 2 decimal places.

Answers

Given a table of historical demand for a product as follows:

[tex]\begin{tabular} {|c|c|} &Demand\\[1ex] April&60\\ May&55\\ June&75\\July&60\\August&80\\September&75\\ \end{tabular}[/tex]

The linear regression equation is given by

[tex]\hat{Y}=bx+a[/tex]

where:

[tex]b= \frac{n\Sigma xy-\Sigma x\Sigma y}{n\Sigma x^2-(\Sigma x)^2} [/tex]
and
[tex]a= \frac{1}{n} (\Sigma y-b\Sigma x)[/tex]

We calculate the required values using the following table, where
April = 1, May = 2, and so on.

[tex]\begin{tabular} {|c|c|c|c|} X &Y&X^2&XY\\[1ex] 1&60&1&60\\ 2&55&4&110\\ 3&75&9&225\\ 4&60&16&240\\ 5&80&25&400\\ 6&75&36&450\\[1ex] \Sigma X=21&\Sigma Y=405&\Sigma X^2=91&\Sigma XY=1,485 \end{tabular}[/tex]

Thus,

[tex]b= \frac{6(1,485)-21(405)}{6(91)-(21)^2} \\ \\ = \frac{8,910-8,505}{546-441} = \frac{405}{105} \\ \\ \approx3.86[/tex]

and

[tex]a= \frac{1}{6} (405-(3.86)(21)) \\ \\ = \frac{1}{6} (405-81)= \frac{1}{6} (324) \\ \\ =54[/tex]

Therefore, the trend line for the historical data is given by [tex]\hat{Y}=3.86x+54[/tex]

How to divide 546 divided 78

Answers

7 is the answer to this question

You can either do long division or list out 78's multiples.

007
1. 78√546

2. 78, 156, 234, 312, 390, 468, 546

What is 5x923 in expanded
form

Answers

4,615

Hope this helped!

5 x 900+20+3
There you go

What is the least number of line segments that make exactly 100 squares?

Answers

the answer for this question is 10

Answer with explanation:

First Possibility

→→100 Squares in a Row Requires 101 smaller line segments of equal length ,and 2 line segments of Larger Length having length equal to 100 times the length of one of the Smaller segments.

→→100 Squares in a Column Requires 101 smaller line segments of equal length ,and 2 line segments of Larger Length having length equal to 100 times the length of one of the Smaller segments.

So, total number of line segments =101 +2=103

Second Possibility

If you draw 11 line segments of equal length in a column and 11 line segments in a row, you can draw 100 square of equal size.

So, total number of line segments =11+11=22

A superhero recently asked his nemesis how many cats she has. She answered with a riddle: "Seven-eighths of my cats plus five." How many cats does the nemesis have?

Answers

Final answer:

The question presents a riddle that can be solved by setting up and solving an algebra equation. Based on the provided information, the solution to the problem is that the nemesis has 40 cats.

Explanation:

The problem describes a riddle: "Seven-eighths of my cats plus five." This scenario is a typical mathematical representation of an algebra problem where you need to find the total number of cats.

Let us denote the total number of cats as 'C'. According to the riddle, 7/8 of the cats plus 5 equals the total cats. As per this, the equation can be written as 7/8*C + 5 = C. Solving this will lead us to find the number of cats.

Subtract 7/8*C from both sides of the equation: 5 = C - 7/8*C, which simplifies into: 5 = 1/8*C. To solve for 'C', we then multiply both sides of the equation by 8: 5*8 = C. Hence, the nemesis has 40 cats.

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which rate converts to a unit rate of 65 miles per hour

Answers

(lol were both doing unit rate rn im just pausing to do some brainly questions)

We know that Unit Rate can be found by dividing.
i think you want the answer right now so if you need an explanation then tell me in the comments
Its number A. Hope this helped!

Felicia has 34 quarters,25 dimes and 36 pennies,how many coins does Felicia have?

Answers

Your math problem would be 36+34+25 which equals 95

In order to find the total number of coins, we need to add all the coins that she has:

34 coins + 25 coins + 36 coins = 95 coins

Felicia has a total of 95 coins.

The correct answer is C

A construction firm is trying to decide which of two models of a crane to purchase. Model A costs $100,000 and requires $4,000 per year to maintain. Model B has an initial cost of $78,000 and a maintenance cost of $13,000 per year. For how many years must model A be used before it becomes more economical than B? (Round your answer to one decimal place.)

Answers

Let A and B be the functions which calculate the cost of purchase and maintenance of the models for x years.

The functions are as follows:

A(x)=100,000+4,000x (dollars)

B(x)=78,000+13,000x (dollars)

Model A becomes more economical than Model B when A(x)<B(x),

so we solve:

100,000+4,000x<78,000+13,000x

100,000-78,000<13,000x-4,000x

22,000< 9000x

22<9x

x>22/9=2.444

Model A becomes more economical in the third year, that is after the first 2 years.

Which function below has the largest slope? f(x) x f(x) −3 −10 −1 −7 1 −4 g(x) equals one half x plus 3 h(x) Lance gains 1 level each time he plays his favorite video game. He started at level 10.

Answers

f(x) and h(x) both have a slope of 1 and g(x) has a slope of 0.5 from the info you gave. check for typos

Answer:

f(x)

Step-by-step explanation:

The expression -3m - [2m + (5 - m)] + 7 was simplified as 2 - 4m.

Answers

Question: The expression -3m - [2m + (5 - m)] +7 was simplified as 2 - 4m. Without simplifying, explain how you can show that it has been simplified correctly.

Answer may include:

If the expression has been simplified correctly, then the expressions will be equivalent.

The expressions will have the same value when numbers are substituted in for the variable m.

Choose a value for m and substitute in to both expressions.

Simplify each expression using the order of operations and show they are the same value.

The given expression is simplified correctly.

What is an expression?

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

The given expression is -3m-[2m+(5-m)]+7

= -3m-2m-5+m+7

= (-3m-2m+m)-5+7

= -4m+2

= 2-4m

Hence, the given expression is simplified correctly.

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"Your question is incomplete, probably the complete question/missing part is:"

The expression -3m-[2m+(5-m)]+7 was simplified as 2 - 4m. Without simplifying, explain how you can show that it has been simplified correctly.

please help!!ASAP!!!!!!!

Answers

y + 7 = 5x is a linear function ... y = 5x - 7 (equation of a LINE which is LINE A R)

I put these all in my calculator and the linear equation is B. Y+7=5X

This is a standard deviation contest. you must choose four numbers from the whole numbers 22 to 9595, with repeats allowed. choose four numbers that have the largest possible standard deviation. (give your answer in the form of comma separated list of numbers in ascending order.)

Answers

Given a set numbers, to get the largest possible standard deviation, we use the numbers at the extreme.

Therefore, if we are to choose 4 numbers from 22 to 9,595 such that we have the largest possible standard deviation, the four numbers are 22, 22, 9,595 and 9,595.

Gordon Rosel went to his bank to find out how long it will take for $2,500 to amount to $3,090 at 6% simple interest. Calculate the number of years. (Round time in years to the nearest tenth.)

Answers

It will take 4 years

A(t) = P(1+rt)
2310 = 1800(1+0.0775*t)
1.2833 = 1+0.0775t
0.0775t = 0.2833

Find the area of a triangle with vertices at D(2,0), B(-1,0), and R(2,-7)

Answers

check the picture below.

you can pretty much get the lengths right off of the grid.

What is 265888 rounded to nearest ten thousands

Answers

It would be 270,000. The 6 is higher then 5 so you round up

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