A carpenter has a 6-foot long board. He wants to cut the board into pieces that are 4/5 foot long. How many pieces of length 4/5 foot can the carpenter cut from the board? What length of the original board will be left after the carpenter has cut all the pieces that are 4/5 foot long?

Answers

Answer 1

Ok so take 6 divided by 4/5 or 6 x 5/4 = 7.5 but you don't want .5 of a board so you will have 7 boards and 0.4 feet of board left over because half of 4/5 is 0.4

Answer 2

Answer:

Number of pieces=7

Length of board remaining=[tex]\frac{2}{5}[/tex]

Step-by-step explanation:

We are given that a carpenter has board of length=6 foot

Length of each piece of board=[tex]\frac{4}{5}[/tex] foot

We have to find the number pieces of given length of piece can be made from given board.

In order to find the number of pieces we will divide the total length of board by the length of each piece.

Therefore, number of pieces =[tex]\frac{6}{\frac{4}{5}}[/tex]

Number of pieces=[tex]7\frac{1}{2}[/tex]

Length of each piece =[tex]\frac{4}{5}[/tex]

Therefore, number of pieces=7

Length used in 7 pieces =[tex]7\times\frac{4}{5}=\frac{28}{5}[/tex]

Length of board remaining=[tex]6-\frac{28}{5}=\frac{2}{5}[/tex]

Related Questions

How are the variables on the graph related?

Answer choices:

A. As speed decreases, height stays constant.

B. As speed decreases, height increases.

C. As speed increases, height decreases.

D. As speed increases, height increases.

Answers

Having a look at the graph, we will find that:
For speed: it is increasing along the x-axis
For height: it is increasing along the y-axis

This means that the function is linearly increasing.

Based on this, the correct choice would be:
D. As speed increases, height increases

The answer because I don’t know it

Answers

What's the highest term that goes into 12x³, 8x², and 12x evenly? If it helps, you can break it up into two questions: what's the greatest common factor between 12 and 8, and what's the greatest common factor between x³, x², and x? Once you have those, multiply the two together, and you'll have the greatest common factor for all three monomials.

Also important to keep in mind: when we say we want to "factor" an expression with more than one term added together, what we really want to do is reverse the distributive property. In case you've forgotten, the distributive property is a property of multiplication that states that if you have three numbers a, b, and c, a(b+c) = ab + ac. You distribute the a to each of the terms in the parentheses. Here, you're given the ab + ac part, and you have to work your way back. To give an example, if we had the expression:

[tex]24x+36[/tex]

We can use the fact that 12 is the greatest common factor of 24x and 36 to rewrite it:

[tex]12(2x)+12(3)[/tex]

And, realizing that 12 has been distributed to the 2x and the 3, reverse the distributive property to get:

[tex]12(2x)+12(3)=12(2x+3)[/tex]

which of the following shows a strategy to use to find 4x275 (4x300)+(4x25)
(4x300)-(4x25) (4x275)-100 (4x200)+75

Answers

[tex]4*275 (4x^3^0^0)+(4x^2^5) (4x^3^0^0)-(4x^2^5) (4x^2^7^5)-100 (4x^2^0^0)+75[/tex]

The correct strategy is (4x275) - 100. So option (3) is correct.

To find 4 multiplied by 275 using the given strategies, let's go through each one:

1. (4x300) + (4x25):

First, calculate (4x300) = 1200. Then, calculate (4x25) = 100. Finally, add these results together: 1200 + 100 = 1300.

2. (4x300) - (4x25):

Calculate (4x300) = 1200. Then, calculate (4x25) = 100. Now, subtract the second result from the first: 1200 - 100 = 1100.

3. (4x275) - 100:

Simply multiply 4 by 275 to get 1100. Then, subtract 100: 1100 - 100 = 1000.

4. (4x200) + 75:

Calculate (4x200) = 800. Then, add 75: 800 + 75 = 875.

The correct strategy is the third one: (4x275) - 100.

Detailed Calculation:

1. [tex]$4 \times 275 = 1100$[/tex]

2. [tex]$1100 - 100 = 1000$[/tex]

So, using the strategy of (4x275) - 100, the result is 1000.

Write ratio in simplest form

6:3/5

Answers

you cdan simplify the ratio 6:3 by dividing both terms GCF ( greatest common factor) divide both terms by three 6 divided by 3 is 2 . 3 divided by 3 is 1. so 6:3 is 2:1

The value V of a square glass varies directly as the square of its length X cm. If the value of a square glass with length 3 cm is $243, find the value of a glass with length 5 cm

Answers

Given that the value V of a square glass varies directly as the square of its length X cm.

Then, the variation equation is given by

[tex]V\propto X^2 \\ \\ \Rightarrow V=kX^2[/tex]

Given that value of a square glass with length 3 cm is $243, we have:

[tex]243=k(3)^2=9k \\ \\ \Rightarrow k= \frac{243}{9} =27 \\ \\ \Rightarrow V=27X^2[/tex]

Thus, the value of a glass with length 5 cm is

[tex]V=27(5)^2=27\times25=\bold{\$675} [/tex]

The value V of a square glass varies directly as the square of its length X cm. This means that V is proportional to [tex]X^2[/tex], which can be expressed as:

[tex]\[ V = kX^2 \][/tex]

where k is the constant of proportionality.

Given that the value of a square glass with length 3 cm is $243, we can use this information to find the constant k:

[tex]\[ 243 = k(3)^2 \][/tex]

[tex]\[ 243 = 9k \][/tex]

[tex]\[ k = \frac{243}{9} \][/tex]

[tex]\[ k = 27 \][/tex]

Now that we have the value of k, we can find the value of a glass with length 5 cm by substituting X = 5 into the original equation:

[tex]\[ V = 27(5)^2 \][/tex]

[tex]\[ V = 27 \times 25 \][/tex]

[tex]\[ V = 675 \][/tex]

Therefore, the value of a glass with length 5 cm is $675.

The answer is: 675.

A total of 29,183 votes were casted I’m an election. The winning candidate in the election received 61.3% of the votes. Which of the following is closest to the number of votes received by the winning candidate

Answers

61.3/100 × 29183
the Winning candidate had an approx of 17889 votes or 17890

Multiply 29183 votes by 0.613 and then round off to the nearest integer number of votes:

0.613(29183) = 17889.179, which must be rounded off to 17,889 votes.

a cereal box contains 15 3/4 ounces of cereal. If a bowl holds 2 2/5 ounces of cereal how many bowls are in 1 box

Answers

Hello! So to solve this problem, we need to divide fractions. Convert the mixed numbers into improper fractions by multiplying the denominator by whole number and adding the numerator. The rule for dividing fractions is keep, change, flip. In other words, keep the first fraction the same, change division into multiplication, and flip the second fraction over. The problem will now look like this: 63/4 * 5/12. Multiply straight across. n * n / d * d. When you do that, you get 315/48 or 6 9/16 in mixed number form. There are 6 9/16 servings, which is enough to serve approx. 7 bowls if you don't mind having a partial servings. Otherwise, only 6 bowls will get all of the 2 2/5 ounces of cereal.

Find the tangent plane to z 2 = x 3 + 2xy + y 3 at x, y = 1, 1.

Answers

z=mx+b is the formula

What is the unit rate 3 for $5 4 for$6

Answers

The unit rate for 3 for $5 is around $1.70 or $1.60

The unit rate for 4 for $6 is $1.50

You have two separate problems here.

a) 3 for $5 needs to be expressed as cost per unit. Write $5/(3 units), and then simplify. Here the unit rate is ($5/3) / unit, or $1.67 per unit.

b) 4 for $6: Write $6/(4 units), and then reduce to lowest terms:
(6/4) dollars per unit, or $1.50/unit

Find the largest odd number that divides the product of 16*24*60 evenly

Answers

odd = odd × odd

Prime factor
16*24*60
(4*4)(3*8)(6*10)
(2*2*2*2)(3*2*2*2)(3*2*5*2)

multiple all the odd prime factors together
3*3*5 = 45

A 1950 kg car moves with a velocity of 11 m/s. What is its kinetic energy? Joules

Answers

The formula for Kinetic Energy is given by

KE = 0.5 × mv²

We have:
m, the mass = 1950 kg
v, the velocity = 11 m/s

KE = 0.5 × 1950 × 11²
KE = 117975 joules

clay is reading a map to decide his vacation route. The map has a scale of 1cm equals 18miles. If he estimates the length of his vacation route on a map is 14 centimeters what is the length in miles

Answers

The scale is 1 cm equals 18 miles.
If a distance on the map is 14 cm, it is 14 times larger than 1 cm.
That means the real distance is 14 times larger than 18 miles.
What is 14 * 18 miles?

Using the map scale of 1cm equals 18 miles, the actual length of Clay's vacation route is calculated as 252 miles by multiplying 14 centimeters (the length on the map) by 18 miles (the scale conversion factor).

Clay is using a map scale to plan his vacation route. The scale of the map is given as 1cm equals 18 miles. To calculate the actual length of Clay's vacation route in miles, we can set up a simple proportion. Since 1cm on the map represents 18 miles in reality, we multiply the length on the map, which is 14 centimeters, by 18 to find out how many miles this length represents:

Length in miles = 14 cm * 18 miles/cm

After performing the multiplication, we get:

Length in miles = 252 miles

Therefore, Clay’s vacation route is 252 miles long according to the map's scale.

Given the equation D =m/v if D=2/3 and v=m+1., then m=
-3
2
1

Answers

D = m/v D = 2/3 v = m + 1

2/3 = m/m + 1

2/3(m + 1) = m

2(m + 1)/ 3 = m

2(m + 1) = 3m

2m + 2 = 3m

2 = 3m - 2m

2 = m

m = 2

hope that helps, God bless!

Which equation represents a linear function? A) y – 2 = –5(x – 2) B) x + 7 = –4(x + 8) C) y – 3 = y(x + 4) D) y + 9 = x(x – 1)

Answers

it's (A) y-2=-5(x-2)

i believe its the option A

A single 6-sided die is rolled twice. find the probability of getting a 55 the first time and a 11 the second time. express the probability as a simplified fraction.

Answers

They are independent events therefore they will not affect each other so rolling a certain number will always be 1/6.

1/6 x 1/6 x 1/6 x 1/6 = 1/1296

Tom received a coupon in the mail for 30%off one regular priced item for a local sporting goods store He wishes tp purchase a soccer ball for 22.50 and shin guards for 17.00 which item would he use his coupon justify your answer by comparing the discount taken for each item

Answers

it should be used on the higher priced item to get a bigger discount.

So it should be used on the soccer ball

soccer ball: 22.50 * 0.30 = 6.75 discount

shin guards: 17.00 * 0.30 = 5.10 discount

6.75 is greater than 5.10

rewrite 8/9 with a denominator of 63

Answers

To write 9 as 63, you need to multiply it by a number. 63/9 = 7.
So you need to multiply 9 by 7 to get 63.

But since it's a fraction, you can't multiply the denominator without multiply the numerator. So you need to multiply the denominator, 9, by 7 and the numerator, 8, by 7.

8/9 = (8*7) / (9*7) = 56/63

So 8/9 = 56/63

Hope this helps! :)

Final answer:

To rewrite the fraction 8/9 with a denominator of 63, multiply both the numerator and denominator by 7 to get 56/63.

Explanation:

To rewrite 8/9 with a denominator of 63, you need to find a number that you can multiply both the numerator (8) and the denominator (9) of the original fraction by, so that the denominator becomes 63. To do this, divide 63 by the original denominator, 9, which gives you 7. Thus, the number you need to multiply by is 7.

Multiply both the numerator and the denominator by 7:

Numerator: 8 times 7 = 56

Denominator: 9 times 7 = 63

Therefore, the fraction 8/9 with a denominator of 63 is 56/63.

Evaluate 4x-3 when x=_3

Answers

Final answer:

To evaluate the expression 4x-3 for x = -3, we substitute -3 into the expression and follow the order of operations, resulting in a value of -15.

Explanation:

To evaluate the expression 4x-3 when x is -3, we simply substitute -3 in place of x and calculate the result as follows:

Replace x with -3: 4(-3) - 3.Multiply 4 by -3: -12 - 3.Finally, subtract 3 from -12 to get: -15.

Therefore, evaluating 4x-3 when x is -3 gives us -15.

3. Find the scale factor using the given scale drawings and measurement below

Answers

Final answer:

The question asks to find the scale factor for given scale drawings and measurements. A scale factor is computed by creating a ratio comparing the measurement of the scale drawing to the actual measurement, simplifying that ratio to find the scale factor.

Explanation:

The subject of the question is concerned with finding the scale factor from a given scale drawing and measurements. In mathematics, particularly in geometry, a scale factor is used to transform the size of a figure without altering its shape.

Step-by-Step Explanation

To find the scale factor for each given scale drawing, you will need to create a ratio or a fraction that compares the scale measurement to the actual measurement. Here’s how you might solve one of the problems:

Example: What is the scale factor if 3 inches is equal to 12 feet?

Solution:

Convert all measurements to the same unit, for instance, turn feet into inches (1 foot = 12 inches).Write the ratio of the scale drawing to the actual measurement.Reduce the ratio to its simplest form to find the scale factor.

The sum of the square of two consecutive whole number is 25. Find the numbers

Answers

Don't you mean "the sum of the squares ..."?
The sum of the squares of two consecutive whole numbers is 25. Find the numbers. Let the first be represented by x and the second by x+1.
Then x^2+(x+1)^2=25. Expanding, x^2+x^2+2x+1=25.
Rewriting this as a quadratic equation in standard form,

2x^2+2x+1=25, or 2x^2+2x-24=0. Simplifying, x^2+x-12=0.
Factoring, (x-3)(x+4)=0. Solving for x: x-3=0, so x=3; x+4=0, so x=-4.
Choose the positive x value: x=3. Then the next consecutive number is 2+1=3+1=4.

Check: Does 3^2 + 4^2 = 5^2 = 25? Yes.
The numbers are 3 and 4.

24 loaves of bread cost 48 dollars how much does 10 loaves cost?

Answers

$20
One loaf costs 2 dollars- Multiply both sides of the ratio by 10 and you get 20 as ur answer.

24 is double 48 so 10 loves coast 20 dollars

Interest of $1,632 with principal of $16,000 for 306 days(ordinary interest) results in a rate of

Answers

$21,341.67 is the answer

Given the functions f(x) = −2x − 1 and g(x) = −3x + 4, which operation results in the smallest coefficient on the x term?

Answers

There are 3 different operations we can perform. Addition, Subtractions and Multiplication.

Subtraction
(−2x − 1) - (−3x + 4)
x - 5
x coefficient = 1

Addition:
(−2x − 1) + (−3x + 4)
3 - 5x
x coefficient = -5

Multiplication:
x(6x - 5) -4
x coefficient = 6

-5 is the least so addition is the answer

It’s -3x because it’s the furthest away from zero on the number line.

Assume that the distance from Earth to the moon is exactly 238,855 miles and that it took astronauts 75 hours to reach the moon in 1969. How far did the astronauts travel each hour, on average, during their trip to the moon? 3,004.73 miles mc026-1.jpg miles 3,317.4305 miles mc026-2.jpg miles

Answers

you would do 238855 divided by 75 ===3184.73333 mph

On average during their trip, their speed was 3184.8 miles/hr.

What is a unitary method?

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

We know Distance = Speed×Time.

∴ Speed = Distance/Time.

Given, The distance from Earth to the moon is exactly 238,855 miles and it took astronauts 75 hours.

So, the average speed is (238855/75) miles/hr.

= 3184.8 miles/hr.

learn more about unitary method here :

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If a project is handed in late you receive 8/9 of your earned points. You received 72 points on your late project. How many points did you lose

Answers

Final answer:

In this situation, because the project was handed in late, you lost a total of 9 points. The full score was 81, and you got 72 after a deduction.

Explanation:

The principal in this problem is understanding proportion. Given that handing in a project late results in receiving 8/9, or approximately 88.88%, of the total points, we'll figure out the total possible score by dividing the received points (72) by the portion of the full score you got for handing in the project late, which is 8/9. So, 72 ÷ 8/9 = 81. This would be the original points you could have received. You can then subtract the received points (72) from the original points (81) to ascertain the number of points lost. Therefore, 81 - 72 = 9. Consequently, you lost 9 points because the project was handed in late.

Learn more about Proportion here:

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Write the equation of a vertical line containing (5,-8)

Answers

check the picture below.

Brooke bought all seven members of her family a chocolate bar at the chocolate factory in Hershey, Pennsylvania. Each chocolate bar was .8 ounces. How many ounces of chocolate did Brooke buy?

Answers

seven times 0.8 equals 5.6, so Brooke bought 5.6 ounces of chocolate

She bought 0.56 ounces of chocolate, or 3.5 pounds. I hope this helps! :)

The Red Sox have won 3 World Series titles in the last 11 years. At this rate, how long will it take them to win 20 World Series?

Answers

The answer is 74 years. do 11/3=3.67. Then 3.67x20 =73.4 and since that .4 is not a full year you would have to round up to 74

73 1/3 years
What I did was use a proportion:

11/3 and x/20
Then you cross multiply:

3x=220
Then solve.

Ella has 50 stacks of ten pennies in each stack. Describe how to find how many pennies ella has in all

Answers

To find how many pennies Ella has in all, just do 50 * 10. Cross the two zeros out and drop them as part of the answer. Then do 5 * 1 to get 5. When you do this, your answer is 500. Ella has 500 pennies in all.

Find the volume of the solid whose base is the circle x^2+y^2=81 and the cross sections perpendicular to the x-axis are triangles whose height and base are equal.

Find the area of the vertical cross section A at the level x=6.

Answers

Sent a picture of the solution to the problem (s). Just rotate pic.

The volume of the cone will be 1526.8 cubic units. The area of the vertical cross-section A at level x = 6 will be 72 square units.

What is Geometry?

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

The equation of the base circle is given below.

x² + y² = 81

x² + y² = 9²

Then the radius of the circle is 9 units. Then the height of the cone is the same as the diameter of the circle.

h = 2r

h = 2 x 9 = 18

The volume of the cone will be

V = (1/3)πr²h

V = (1/3) × π × 9² × 18

V = 1526.8 cubic units

The area of the vertical cross-section A at the level x = 6 will be

A = (1/2) x (18 - 6) x (18 - 6)

A = (1/2) x 12²

A = (1/2) x 144

A = 72 square units

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