A series of books has 30 volumes, each with 700 pages. What is the total number of pages in the series?

Answer: radius=8, circumference=16π

Step-by-step explanation:

diameter is 16 centimeters

the radius of a circle is half its diameter

so, radius = 16/2 = 8

circumference of a circle = 2πr

so, circumference = 2π(8cm) = (16π) cm

Answer:

The two numbers are 12 , 10

Step-by-step explanation:

Given as :

The least common multiple of two numbers = LCM = 60

The ratio of the greater number to lesser number = 6 : 5

let the greater number = 6 x

And The smaller number = 5 x

∵ The LCM of numbers = 60

So, 6 × 5 × x = 60

Or,  30 × x = 60

∴  x = [tex]\frac{60}{30}[/tex]

I.e x = 2

So The greater number = 6 x = 6 × 2 = 12

And  The smaller number = 5 x = 5 × 2 = 10

Hence The two numbers are 12 , 10 Answer

Final answer:

To find the alcohol percentage in the 4:1 ratio, we use the information from the 3:2 ratio. For every 3 parts alcohol, there are 2 parts water. When mixed at a ratio of 4:1, the alcohol percentage is 24%.

Explanation:

To determine the alcohol percentage of the solution when mixed at a ratio of 4:1, we can use the information given in the question. When mixed at a ratio of 3:2, the solution contains 18% alcohol. This means that for every 3 parts alcohol, there are 2 parts water. We can use this information to find the alcohol percentage for the 4:1 ratio.

Let's say we have 4 mL of alcohol and 1 mL of water. The total volume is 4+1 = 5 mL. In the 3:2 ratio, the alcohol percentage is 18%. So, for 3 mL of alcohol, the total volume is 3+2 = 5 mL. Therefore, the alcohol percentage for the 4:1 ratio is (18/3) * 4 = 24%.

Answer:

Annual rate of interest is 8%.

Answer:

5/2 is the scale factor.

Step-by-step explanation:

To calculate scale factor, divide the similar sides.

According to the problem, EFGH is the drawing, or the "result".

Divide a side of the result by the original.

EFGH / ABCD = scale factor

We can use the widths.

Width of EFGH / Width of ABCD

= 10 / 4

= 5/2

Check using the lengths:

Length of EFGH / Length of ABCD

= 20 / 8

= 5/2

The scale factor is 5/2.

Answer:

Step-by-step explanation:

Answer:

500 miles per hour

Step-by-step explanation:

6000 miles/12 hours = 500 miles per hour

Answer:

1.25 miles/hr

Step-by-step explanation:

5miles in 4 hours, this means  5miles/ 4hrs

To find the rate per hour:

5/4 = 1.25 miles/hr

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Answer:

5/4

Step-by-step explanation:

Divide the miles by the hours. It gives you the ratio.

Answer:

$75.26

Step-by-step explanation:

base cost = $49.95

total mile cost = 1.19*18 =$21.42

gas cost = $3.89

total cost =$(49.95 +21.42+3.89)=$75.26

The expression to represent total cost of the trip is $49.95 + $1.19m + (m/18)($3.89).

Given that, the rental has a base cost of 49.95, plus an additional cost of 1.19 per mile driven.

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

If we let m = total distance, then we can set up an equation to find the total cost.

The additional cost for distance would be $1.19m

The cost for gas would be (m/18)($3.89)

So the total cost of the trip could be represented by $49.95 + $1.19m + (m/18)($3.89).

Therefore, the expression to represent total cost of the trip is $49.95 + $1.19m + (m/18)($3.89).

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Answer:

c = 36

Step-by-step explanation:

Given

a² + 12a + c

To complete the square

add ( half the coefficient of the a- term )² to a² + 12a

a² + 2(6)a + 6²

= (a + 6)² + 36

Hence the value of c = 36

Answer:

$87.76

Step-by-step explanation:

108.25/100 = 95/x

95×100=9500

9500÷108.25=87.76

To find the total price including tax after a meal at a restaurant, convert the tax rate to a decimal, then multiply it by the total cost and add the result to the original total cost.

First, find the amount of sales tax. To do this, convert the percent to a decimal by dividing by 100: 8.25% = 0.0825.

Then multiply the total cost by the decimal tax rate to get the tax amount. In this case, $95 * 0.0825 = $7.8375.

Next, add the tax amount to the original total cost to find the total price: $95 (original cost) + $7.8375 (tax) = $102.8375.

Therefore, the total price, including tax, for Shirley and her family's meal last night was $102.84.

Each increase of 1 in x decreases y by 7, i.e. increases y by -7.  That's a slope of

Answer: -7

Answer:

[tex] -7[/tex]

Step-by-step explanation:

Use the rise over run equation

[tex] \frac{y2 - y1}{x2 - x1} [/tex]

Answer: 7

Step-by-step explanation:

3(n+3) = - (1 - 5n) – 4

3n+9=-1+5n-4

n=7

Answer:

n=7

Step-by-step explanation:

3(n+3)=-(1-5n)-4

3n+9=-1+5n-4

3n+9=-5+5n

3n+14=5n

14=2n

7=n

I used PEMDAS and moving numbers and combing like terms

Answer:

Each box has 800 spoons.

Step-by-step explanation:

4800/6=800

Final answer:

Three half squared is (3/2)², which equals 9/4 when you square the numerator (3² = 9) and the denominator (2² = 4) separately.

Explanation:

The expression 'three half squared' refers to the quantity (3/2) squared. To square a fraction, you square the numerator and the denominator separately. Therefore, (3/2) squared is (3 squared) over (2 squared), which is 9 over 4. Since there are no further simplifications to make, 9/4 is the final answer as a fraction.

To understand this conceptually, think about the process of squaring as finding the area of a square with side lengths of the original number. So, if the side length of a square is 3/2, the area (which represents the square of the number) will be 9/4 square units.

Final answer:

To determine what three-half squared is as a fraction, you simply square the numerator and denominator separately, arriving at the fraction 9/4.

Explanation:

Calculating Three-Half Squared as a Fraction

To find what three half squared is as a fraction, you square both the numerator and the denominator of the fraction 3/2. When you square the numerator (3), you get 9, and when you square the denominator (2), you get 4. Therefore, the answer to three half squared is 9/4, as we have calculated (3/2)² = (3²)/(2²) = 9/4.

This calculation is similar to understanding that if you start with half of a pie and you multiply this amount by itself, you are essentially getting a fraction of the original whole. In our example, by squaring half, we get a quarter, thereby following the intuitive sense of fractions.

Answer:

-12x^3+17x^2+x+2

Step-by-step explanation:

3x^2+x+2-4x^2(3x-4)

3x^2+x+2-12x^3+14x^2

3x^2+14x^2-12x^3+x+2

17x^2-12x^3+x+2

-12x^3+17x^2+x+2

The answer is -.75 because y=mx+b, and the slope is m.

Answer:

$0.10x + $0.25y = $0.80

The equation in standard form that represents the situation is 10x + 25y = 80.

To represent the situation in terms of the number of dimes and quarters, we can use the equation 0.10x + 0.25y = 0.80. This equation states that the value of the dimes (0.10x) plus the value of the quarters (0.25y) equals $0.80. Rearranging the equation to standard form, we have:

0.10x + 0.25y = 0.80

10x + 25y = 80

So, the equation in standard form that represents the situation is 10x + 25y = 80.

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Answer:

2.5%

Step-by-step explanation:

The price increased from 2 to 2.05. So the increase was:

2.05 - 2 = 0.05 dollars

Now, to find percentage increase, we use the formula below:

[tex]\frac{New-Old}{Old}*100[/tex]

Where

New is the latest price (here it is the increased price of 2.05)

Old is the previous price (here it is the less price of 2.00)

Now, we substitute and find:

[tex]\frac{2.05-2.00}{2.00}*100=2.5[/tex]

So the price increase was 2.5%

Answer:

Length = 25 inches and width = 15 inches.

Step-by-step explanation:

Let us assume that the length of the rectangle is L inches and the width of the rectangle is W inches.

Now, the area of the rectangle is A = LW = 375 sq. inches ........... (1)

Now, given that the length to width ratio of the rectangle is 5 : 3.

Let L = 5x and W = 3x, then from equation (1) we get,

(5x)(3x) = 375

⇒ 15x² = 375

⇒ x² = 25

⇒ x = 5 {Neglecting the negative root, as length can not be negative}

Now, Length = L = 5x = 25 inches and Width = W = 3x = 15 inches. (Answer)

The complete question is:

In order to prepare for your summer bash, you go to the supermarket to buy hamburgers and chicken. Hamburgers cost $2 per pound and chicken costs $3 per pound. You have no more than $30 to spend.  You expect to purchase at least 3 pounds of hamburgers.  

Justify your answers

Answer:

A) System of inequalities:

B) Graph: see the picture attached

C) Three possible combinations:

Explanation:

A) Write the system of inequalities to represent this situaction.

1. Variables:

2. Costs:

3. First constraint:

4. Second constraint:

5. Additional constraints:

6. System of equations:

B) Graph

You have to graph all the constraints in a x-y coordinate system.

1. To graph 2x + 3y ≤ 30 graph the line 2x + 3y = 30

2. To graph x ≥ 3 just draw the vertical line x = 3 and shade the region to the right of it. The points of the line are included (solid line).

3. The constraints x ≥ 0 and y ≥ 0 mean that the region is restricted to the first quadrant (including the positive axis).

4. The feasible solutions are the set of points inside the common regions (intersection).

With all that information the graph is the one attached. The feasible solutions is the region defined by the triangle with vertices (3,8), (3,0), and (15,0).

C) Give 3 possible combinations.

You can pick any three points inside the region, as long as the coordinates are integer numbers. For instance the 3 vertices are solutions:

You could also prove that (5,4), 5 pounds of hamburgers and 4 pounds of chicken meet, the inequalities.

This is how you prove it:

And you can do the same for any pairs to verify whether they are solution or not.

Answer:

Part 1) [tex]x=\frac{g}{c}[/tex]

Part 2) [tex]a=\frac{1}{3b}[/tex]

Part 3) [tex]a=\frac{n+p}{m}[/tex]

Part 4) [tex]x=g-y+c[/tex]

Part 5) [tex]x=\frac{z}{m-1}[/tex]

Part 6) [tex]a=\frac{g+b}{c}[/tex]

Part 7) [tex]b=\frac{A}{h}[/tex]

Part 8) [tex]W=\frac{P}{2}-L[/tex]

Part 9) [tex]d=2Q-c[/tex]

Part 10) [tex]a=\frac{Q}{3+5c}[/tex]

Part 11) [tex]N=\frac{A)}{P-IR}[/tex]

Part 12) [tex]b=P-a-c[/tex]

Step-by-step explanation:      

Part 1) we have

[tex]g=xc[/tex]

solve for x

That means---> Isolate the variable x

Divide by c both sides

[tex]\frac{g}{c}=\frac{xc}{c}[/tex]

simplify

[tex]x=\frac{g}{c}[/tex]

Part 2) we have

[tex]12ab=4[/tex]

solve for a

That means---> Isolate the variable a

Divide by 12b both sides

[tex]\frac{12ab}{12b}=\frac{4}{12b}[/tex]

simplify

[tex]a=\frac{1}{3b}[/tex]

Part 3) we have

[tex]am=n+p[/tex]

solve for a

That means---> Isolate the variable a

Divide by m both sides

[tex]\frac{am}{m}=\frac{n+p}{m}[/tex]

simplify

[tex]a=\frac{n+p}{m}[/tex]

Part 4) we have

[tex]g=x-c+y[/tex]

solve for x

That means---> Isolate the variable x

Subtract y both sides

[tex]g-y=x-c+y-y[/tex]

[tex]g-y=x-c[/tex]

Adds c both sides

[tex]g-y+c=x-c+c[/tex]

[tex]g-y+c=x[/tex]

rewrite

[tex]x=g-y+c[/tex]

Part 5) we have

[tex]xm=x+z[/tex]

solve for x

That means---> Isolate the variable x

Subtract x both sides

[tex]xm-x=x+z-x[/tex]

[tex]xm-x=z[/tex]

Factor x left side

[tex]x(m-1)=z[/tex]

Divide by (m-1) both sides

[tex]\frac{x(m-1)}{m-1}=\frac{z}{m-1}[/tex]

[tex]x=\frac{z}{m-1}[/tex]

Part 6) we have

[tex]g=ca-b[/tex]

solve for a

That means---> Isolate the variable a

Adds b both sides

[tex]g+b=ca-b+b[/tex]

[tex]g+b=ca[/tex]

Divide by c both sides

[tex]\frac{g+b}{c}=\frac{ca}{c}[/tex]

[tex]a=\frac{g+b}{c}[/tex]

Part 7) we have

[tex]A=bh[/tex]

solve for b

That means---> Isolate the variable b

Divide by h both sides

[tex]\frac{A}{h}=\frac{bh}{h}[/tex]

simplify

[tex]b=\frac{A}{h}[/tex]

Part 8) we have

[tex]P=2L+2W[/tex]

solve for W

That means---> Isolate the variable W

Subtract 2L both sides

[tex]P-2L=2L+2W-2L[/tex]

simplify

[tex]P-2L=2W[/tex]

Divide by 2 both sides

[tex]\frac{P-2L}{2}=\frac{2W}{2}[/tex]

simplify

[tex]W=\frac{P-2L}{2}[/tex]

[tex]W=\frac{P}{2}-L[/tex]

Part 9) we have

[tex]Q=\frac{c+d}{2}[/tex]

solve for d

That means---> Isolate the variable d

Multiply by 2  both sides

[tex]2Q=(2)\frac{c+d}{2}[/tex]

simplify

[tex]2Q=c+d[/tex]

subtract c both sides

[tex]2Q-c=c+d-c[/tex]

[tex]2Q-c=d[/tex]

rewrite

[tex]d=2Q-c[/tex]

Part 10) we have

[tex]Q=3a+5ac[/tex]

solve for a

That means---> Isolate the variable a

Factor the variable a in the right side

[tex]Q=a(3+5c)[/tex]

Divide by (3+5c) both sides

[tex]\frac{Q}{3+5c}=\frac{a(3+5c)}{3+5c}[/tex]

simplify

[tex]a=\frac{Q}{3+5c}[/tex]

Part 11) we have

[tex]I=\frac{PN}{RN+A}[/tex]

solve for N

That means---> Isolate the variable N

Multiply in cross

[tex]I(RN+A)=PN[/tex]

Apply distributive property left side

[tex]IRN+AI=PN[/tex]

subtract PN both sides

[tex]IRN+AI-PN=PN-PN[/tex]

[tex]IRN+AI-PN=0[/tex]

subtract AI both sides

[tex]IRN+AI-PN-AI=-AI[/tex]

[tex]IRN-PN=-AI[/tex]

Factor N left side

[tex]N(IR-P)=-AI[/tex]

Divide by (IR-P) both sides

[tex]\frac{N(IR-P)}{IR-P}=-\frac{A}{IR-P}[/tex]

simplify

[tex]N=-\frac{A}{IR-P}[/tex]

[tex]N=\frac{A}{P-IR}[/tex]

Part 12) we have

[tex]P=a+b+c[/tex]

solve for b

That means---> Isolate the variable b

subtract (a+c) both sides

[tex]P-(a+c)=a+b+c-(a+c)[/tex]

simplify

[tex]P-(a+c)=b[/tex]

rewrite

[tex]b=P-a-c[/tex]

Answer:

m = 0 or 5

Step-by-step explanation:

m² − 5m = 0

Factor out m:

m (m − 5) = 0

Set each term to 0:

m = 0

m − 5 = 0

Solve for m:

m = 0

m = 5

Answer:

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36.

Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42.

Step-by-step explanation:

Answer:

6,3,2,1

Step-by-step explanation:

the factors of 36 are 36, 18, 12, 9, 6, 4, 3, 2, 1

The factors of 42 are 42, 21, 14, 7, 6, 3, 2, 1

The factors that they have in common are therefore 6,3,2, and 1 when compared

Answer:

She did not drive consistently because if 65 = 1 hour, the two-hour mark would be 130, not 120 and the second-hour mark would be 185, not 195. You have to have the same mileage added to each hour to make it consistent.

Answer:

The answer would be 3; 1.3

Answer:

30 yellow straws and 45 red straws

30:45

Step-by-step explanation:

Make a ratio:

2:3, 2 being the yellow straw and 3 being the red straws

They are now asking how many red if there are 30 yellow straws

2:3 = 30:x

You could either cross multiply or simply do 30 ÷ 2 = 15 then 15 × 3 = 45. Your answer is 45

Cross multiplying

2x = 90

90 ÷ 2 = 45

Final answer:

The point estimate for the proportion of homeowners in the given sample is 75%, calculated by dividing the number of homeowners (24) by the total number surveyed (32).

Explanation:

To obtain a point estimate of the proportion of homeowners from the given sample, we would calculate the proportion of those who did not rent, since owning and renting are the only two options provided. Out of 32 people, 8 said they rented, which means 32 - 8 = 24 owned their home. The point estimate for the proportion of homeowners is then given by the number of homeowners divided by the total number of people surveyed:

Point estimate for homeowners = (Number of homeowners) / (Total number surveyed) = 24 / 32 = 0.75 or 75%

This mean 75% of the surveyed individuals are estimated to be homeowners.

Answer:

3

Step-by-step explanation:

11-8=3

3 saves were left out of the 11 for the second game

Answer:

He has made 3 saves in the second game

Step-by-step explanation: