Mathematics College

A rectangular floor is 21 ft long and 12ft wide. Reuben wants to carpet the floor with carpet tiles sold by the square yard. Use the facts to find the area in square yards.

Conversion facts for length:
1 foot (ft) = 12 inches
1 yard (yd) =3 feet
1 yard (yd) = 36 inches

Answers

Answer 1

1 yard = 3 feet:

21 feet / 3 ft = 7 yards

12 feet  / 3 feet = 4 yards

7 x 4 = 28 square yards

he will need 28 tiles

Answer 2

The area of the rectangular floor will be 28 square yards.

What is the area of the rectangle?

Let L be the length and W be the width of the rectangle.

Then the area of the rectangle will be

Area of the rectangle = L × W square units

A rectangular floor is 21 ft long and 12 ft wide.

We know that 1 foot = 1/3 yards.

Then the dimension of the rectangle in yards will be

L = 21 x 1/3 = 7 yards

W = 12 x 1/3 = 4 yards

Then the area of the rectangle will be

A = 7 x 4

A = 28 square yards

The area of the rectangular floor will be 28 square yards.

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Related Questions

The ordered pair (a, b) gives the location of point P on the coordinate plane. The value of a is zero and the value of b is not zero. Where could point P be located on the coordinate plane?





Select one or more:
x-axis
Quadrant IV
y-axis
Quadrant I
Quadrant II
Quadrant III

Answers

Answer:

y axis and

Step-by-step explanation:

The point P(a, b) where the value of a is 0, hence point P is located on the y axis.

Coordinate plane

The coordinate plane is a two-dimensional surface formed by two lines known as the horizontal axis (x axis) and the vertical axis (y axis). The origin is the point of intersection of both axis and it serves as a reference point.

A point on the coordinate plane is located using the x and y coordinates.

Given the point P(a, b) where the value of a is 0, hence point P is located on the y axis.

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What percentage of muscle weight would you have if 60 pounds out of 140 pounds is muscle weight?

Answers

What percentage of muscle weight would you have if 60 pounds out of 140 pounds is muscle weight?
all you have to do is divide the muscle weight by the total weight which is...60/140=
ANSWER: about 42.86%
Percent literally means per one hundred...

p/100=60/140  multiply both sides by 100

p=6000/140  

p=300/7 %

p≈42.86%  (to nearest hundredth of a percent)

The perimeter of a triangle is 240. Its sides are proportional to 3:4:5. The largest side of the triangle is ?

Answers

If the sides are proportional you can use the formula:

3x + 4x + 5x = 240 and solve for x.

which is:  12x = 240
x = 20

The longest side is 5x, so the longest side is 100.

Marty has saved $72. He spent $8 on a video rental. Write a ratio as a fraction in simplest form to represent what portion of his savings he has left.

Answers

It would be 8/72, which equals 1/9

A circular pond is to be surrounded by a gravel path. Use the diagram to find the square feet of gravel needed if we know the pond has a radius of 200 ft and the radius of the whole space is 250 ft?

Answers

check the picture below.

HELP!! PLEASE A carpenter is framing a window with wood trim where the length of the window is 9 and 1/3 feet. If the width of the window is 6 and 3/ 4 feet, how many feet of the wood is needed to frame the window? Write your answer as a proper or improper fraction

Answers

We need the perimeter of the window for framing

The window is in the shape of a rectangle with the height of [tex]9 \frac{1}{3} [/tex] feet and width of [tex]6 \frac{3}{4} [/tex]. The diagram of the shape is shown below

The perimeter of a shape is obtained by adding up the length of all the sides that form the shape.

The perimeter of the window is [tex]9 \frac{1}{3}+9 \frac{1}{3}+6 \frac{3}{4}+6 \frac{3}{4} [/tex] = [tex]18 \frac{2}{3}+12 \frac{6}{4} [/tex] 

We have two whole numbers 18 and 12 and two fractions [tex] \frac{2}{3} [/tex] and [tex] \frac{6}{4} [/tex]

Adding the two fractions that have different denominator 
[tex] \frac{2}{3}+ \frac{6}{4} = \frac{8}{12}+ \frac{18}{12}= \frac{26}{12} [/tex], which is an improper fraction which we can change into a mixed number [tex]2 \frac{1}{6} [/tex]

So the perimeter of the window is 
[tex]18+12+2 \frac{1}{6} =32 \frac{1}{6} [/tex] 

and the length of wood needed for the frame is [tex]32 \frac{1}{6} [/tex] feet


Claire has received scores of 85,88,87,and 85 on her algebra tests. What is the minimum score she must receive on the fifth test to have an overall test score average of at least 88?

Answers

88*5 = 440

 so all 5 tests need to equal at least 440

85 +88 +87 +85 = 345

440-345 = 95

 she needs at least a 95 to have an 88 average

95 is the minimum score she must receive on the fifth test to have an overall test score average of at least 88.

88*5 = 440

All 5 tests need to equal at least 440.

85 +88 +87 +85 = 345

440-345 = 95.

What is average in maths?

In Maths, an average of a list of records is the expression of the primary price of a set of statistics. Mathematically, it's far described as the ratio of summation of all the facts to the range of units present inside the listing. In phrases of records, the common of a given set of numerical records is also called the mean.

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martin brought 30 shares of microsoft at the close price of $24.53. In a few years, Martin sells all of his shares at $33.71. How much money did martin make?

Answers

Difference: 33.71 - 24.53 = 9.18

9.18*30 = 275.4

Of course, we can't take into account inflation, because nothing is said, I mean that the $24 a few years ago are not the same as today ...

Answer:

Money did martin make = 275.4 $

Step-by-step explanation:

Martin brought 30 shares of Microsoft at the close price of $24.53.

Number of shares = 30

Cost per share = 24.53 $

Total cost = 30 x 24.53 = 735.9 $

Martin sells all of his shares at $33.71

Selling price per share = 33.71 $

Total selling price = 30 x 33.71 = 1011.3 $

Gain for Martin = 1011.3 - 735.9 = 275.4 $

Money did martin make = 275.4 $

An experiment consist of drawing 1 card from a standard 52 -card deck. Let E be the event that card drawn is a 2. Find P(E').

Answers

The sum of the probabilities of an event E and its complement E' is  1, 

that is P(E)+P(E')=1, where E' is "not E".

The event E can happen in 4 ways, because there are four 2's that can be drawn.

P(E)=n(E)/52=4/52=0.08

P(E')=1-P(E)=1-0.08=0.92


Answer: 0.92

Rita borrowed 8000 at a rate of 10.5% compounded monthly assuming she makes no payments how much willshe owe after8 years

Answers

[tex]\bf \qquad \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to &\$8000\\ r=rate\to 10.5\%\to \frac{10.5}{100}\to &0.105\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve times} \end{array}\to &12\\ t=years\to &8 \end{cases} \\\\\\ A=8000\left(1+\frac{0.105}{12}\right)^{12\cdot 8}[/tex]

A company has a sales revenue of $10,000, cost of goods sold of $4500, and other operating expenses of $1500. what is this company's pre-tax income?

Answers

$10,000-$1500= $8,500- $4500=$4,000

Choose the point-slope form of the equation below that represents the line that passes through the points (−3, 2) and (2, 1).
A. y + 3 = −5(x − 2)
B. y − 2 = −5(x + 3)
C. y + 3 = −one fifth(x − 2)
D. y − 2 = −one fifth(x + 3)

Answers

[tex]\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ -3}}\quad ,&{{ 2}})\quad % (c,d) &({{ 2}}\quad ,&{{ 1}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{1-2}{2-(-3)}\implies \cfrac{1-2}{2+3}[/tex]

[tex]\bf y-{{ y_1}}={{ m}}(x-{{ x_1}})\qquad \begin{array}{llll} \textit{plug in the values for } \begin{cases} y_1=2\\ x_1=-3\\ m=\boxed{?} \end{cases} \end{array}\\ \left. \qquad \right. \uparrow\\ \textit{point-slope form}[/tex]
the answer is C or y-2=-1/5(x+3)

x+3menor que 8 qual o resultado

Answers

x+3<8

8-3 =5

 X<5

 any number less than 5 will work

How do i simplify this?

Answers

[tex]\bf \left.\qquad \qquad \right.\textit{negative exponents}\\\\ a^{-{ n}} \implies \cfrac{1}{a^{ n}} \qquad \qquad \cfrac{1}{a^{ n}}\implies a^{-{ n}} \qquad \qquad a^{{{ n}}}\implies \cfrac{1}{a^{-{{ n}}}}\\\\ -------------------------------\\\\[/tex]

[tex]\bf \cfrac{(xy^{-3})^{-5}}{(x^{-3}y)^{-6}}\impliedby \textit{first off, distribute the exponent} \\\\\\ \cfrac{x^{1\cdot -5}y^{-3\cdot -5}}{x^{-3\cdot -6}y^{1\cdot -6}}\implies \cfrac{x^{-5}y^{15}}{x^{18}y^{-6}}\implies \cfrac{y^{15}\cdot y^6}{x^{18}\cdot x^5}\implies \cfrac{y^{15+6}}{x^{18+5}}\implies \cfrac{y^{21}}{x^{23}}[/tex]

Match each word from Column A with the correct definition from Column B. Column A Column B 1. impulse 2. muster 3. naught 4. renown 5. vacancy 6. thrifty A. the state of being empty or not filled B. nothing, nonexistence C. to stir up or bring to action D. a sudden stirring to do something E. fame F. careful with money

Answers

1. D
2. C
3. B
4. E
5. A
6. F

Answer:

The correct matches are:

1. impulse - a sudden stirring to do something

2. muster - to stir up or bring to action. Like to muster up the courage to speak against the wrong doer.

3. naught - nothing, nonexistence

4. renown - fame ; the condition when you are known or talked about by many people.

5. vacancy - the state of being empty or not filled. Like vacancy for new candidates for a job.

6. thrifty - careful with money . Like a person is thrifty about his own time.

Outside diameter of a pipe is five and 7/32 inches the wall of the pipe or 5/32 inches thick find the inside diameter

Answers

5  7/32 = 167/32

5/32 + 5/32 (2 wall thicknesses of the pipe) =10/32

167/32 - 10/32 = 157/32

= 4 29/32

determine the heat energy received per kilogram of steam produced

Answers

According to steam tables, steam produced from liquid water at 100 deg. C and standard atmospheric pressure (101.3 kPa) is 2257.0 kJ/kg.K.

Note : this value varies greatly with pressure and temperature.

A recipe calls for 1/2 cup of ingredient A for every 1 2/5 cups of ingredient B. You use 4 cups of ingredient A. How many cups of ingredient B do you need?

Answers

Let x = number of cups of ingredient B if 2 cups of ingredient A are used. Set up a proportion:  (1/2)/(1 2/5) = (2)/x. Cross multiplying we get (1/2)x = (1 2/5)(2) 
 (1/2)x = 14/5, so x = 28/5 = 5 3/5 cups.
you use 1 2/5 of B for every 1/2 A and they use 4 of A so times 1 2/5 by 8 and you get 11.2 cups of B

Salun is assembling floor lamps. After 3 hours, there are 75 lamps available for shipment. After 5 hours, there are 97 lamps available for shipment. How many lamps are available at the end of an 8-hour shift?

Answers

the correct answer is 163

Answer:

130 lamps are available at the end of an 8-hour shift

Step-by-step explanation:

Salun is assembling floor lamps. After 3 hours, there are 75 lamps available for shipment. After 5 hours, there are 97 lamps available for shipment

LEt x be the number of hours and y be the lamps available

(3,75)   (5,97)

Make the equation y=mx+b

m is the slope and b is the y intercept

[tex]m=\frac{y_2-y_1}{x_2-x_1} =\frac{97-75}{5-3} =\frac{22}{2} =11[/tex]

y=11x+b

Now solve for b using (3,75)

75 = 11(3) +b

75 = 33 + b

Subtract 33 from both sides

42= b

So equation becomes y= 11x + 42

To find available lamps at the end of 8 hours, plug in 8 for x

y= 11(8) + 42= 130

Find the linear approximation of the function f(x, y, z) = x2 + y2 + z2 at (6, 6, 3) and use it to approximate the number 6.022 + 5.972 + 2.992 .

Answers

Near the point (6, 6, 3), we have the approximation

[tex]f(x,y,z)\approx f(6,6,3)+f_x(6,6,3)(x-6)+f_y(6,6,3)(y-6)+f_z(6,6,3)(z-3)[/tex]

where the subscripted [tex]f[/tex]'s refer to the corresponding partial derivatives.

[tex]f(x,y,z)=x^2+y^2+z^2[/tex]
[tex]\implies\begin{cases}f_x(x,y,z)=2x\\f_y(x,y,z)=2y\\f_z(x,y,z)=2z\end{cases}[/tex]

So

[tex]f(6.02,5.97,2.99)\approx80.8288[/tex]

Compare to more precise value,

[tex]f(6.02,5.97,2.99)\approx80.8214[/tex]

Which polygon has an interior angle sum of 1080°?

Answers

The polygon which has an interior angle sum of 1080° is an Octagon

Interior angles of a Polygon

From the question, we are to determine which polygon has an interior angle sum of 1080°

To find that, we will determine the number of sides the polygon has.

From the formula for sum of the interior angles in a polygon

Sum of interior angles = (n-2)180°

Where n is the number of sides

Then,

1080° = (n-2) 180°

1080° ÷ 180° = n-2

6 = n-2

n = 6 + 2

n = 8

A polygon with 8 sides is called an Octagon

Hence, the polygon which has an interior angle sum of 1080° is an Octagon

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Leon watched a beetle and a spider on the sidewalk the beetle crawled 2 yards and the spider crawled 1/6 of the yard how much further did the beetle crawled in the spider

Answers

The spider crawled 1/6 of a yard and the beetle crawled 2 yards. To find how much further the beetle crawled, you need to find the difference between these two numbers.

2yards - 1/6 yards = 1 5/6 yards

This means that the beetle crawled 1 whole yard and 5/6 of another yard further than the spider.

The beetle crawled 11/6 yards, or 1 and 5/6 yards, further than the spider.

The question asks how much further the beetle crawled compared to the spider. The beetle crawled 2 yards, and the spider crawled 1/6 of a yard. To find out how much further the beetle crawled, we subtract the distance the spider crawled from the distance the beetle crawled.

Step 1: Convert the distances to the same unit, if necessary. Here, both distances are already in yards, so no conversion is needed.

Step 2: Subtract the spider's distance from the beetle's distance: 2 yards - 1/6 yard.

Step 3: Calculate the difference: 2 yards - 1/6 yard = 12/6 yards - 1/6 yard = 11/6 yards.

Therefore, the beetle crawled 11/6 yards, or 1 and 5/6 yards, further than the spider.

Megumi earned a salary of $39,312 last year. How much did she earn per month

Answers

2 months in a year

39312/12 = 3276 per month

Answer:

She earned $ 3,276 per month.

Step-by-step explanation:

We know that,

1 year = 12 months,

Given,

Megumi earned a salary of $39,312 last year

⇒ His salary of one year = $ 39,312

⇒ Salary of 12 months = $ 39,312

[tex]\implies \text{salary of 1 month} = \frac{39312}{12}=\$ 3276[/tex]

Hence, she earned $ 3,276 per month.

Tim count his friends fingers by fives. he counts the fingers on six hands. what number does he say?

Answers

6*5= 30 fingers, so tim would say there are 30 fingers.

11.   Edgar Anderson earns $200 a week plus a 15% commission on all sales over $1,000. If Mr. Anderson's sales for one week are $2,500, what is his gross pay for that week?

Answers

well, for that one week, he made his salary, 200 bucks, plus 15% of his sales, because his sales were over $1000, to be exact, they were $2500, so he made 15% of 2500 extra on top of his salary.

so, what's 15% of 2500? well, is just (15/100) * 2500.

so, add that to his $200 salary, and that's his gross pay.

9 x 3? Help me please lol I don't have a clue.

Answers

9 x 3 =

9 + 9 +9

9+9 = 18, 18+9 = 27

so 9x3 = 27

For randomly selected adults, IQ scores are normally distributed with a standard deviation of 15. The scores of 14 randomly selected college students are listed below. Use a 0.10 significance level to test the claim that the standard deviation of IQ scores of college students is less than 15. Round the sample standard deviation to three decimal places. 115 128 107 109 116 124 135 127 115 104 118 126 129 133

Answers

We would need the sample standard deviation for our hypothesis test.

STEP 1: Work out the mean of data set
μ = Sum of values in the set ÷ Number of values in the set
μ = 1686 ÷ 14
μ = 120.4 (rounded to one decimal place)

STEP 2: Subtract the mean from each value in the data set, and then square each answer. The table attached below shows the details of the calculation

STEP 3: Add the answers in STEP 2, then divide by 13.
Note: we divide by 13 instead of 14 because our data set is a sample set.

(∑x₁-μ)/13 = 1253.44÷13 = 96.42

The value obtained in STEP 3 is the variance. To obtain the standard deviation, we square root the variance
s = √96.42 = 9.819 (rounded to three decimal places)
----------------------------------------------------------------------------------------------------------------

We want to test the claim that the standard deviation of IQ scores of college students is less than 15. Putting this in the form of hypotheses we get:

H₀: σ=15
H₁: σ<15

The significance level, α, is 0.10

The degrees of freedom, v, is 14 - 1 = 13
Reading from the  Chi² table for α = 0.1 and degree of freedom = 13, we have the critical value ≥19.812 

The value of the test statistic is given as [(n-1)²s²] ÷ σ²
We have n = 14, s = 9.819, and σ = 15
test statistic = [(13)²(9.819)²] ÷ 15² = 72.417

72.417 is in the critical region (which is values ≥ 19.812) so the result is significant and H₀ is rejected. The standard deviation of IQ scores of college students is less than 15.

Final answer:

To test if the standard deviation of college students' IQ scores is less than 15, we must calculate the sample standard deviation and then perform a chi-square test for variance. Comparing the test statistic to the chi-square distribution at a 0.10 significance level allows us to accept or reject the null hypothesis.

Explanation:

To test the claim that the standard deviation of IQ scores of college students is less than 15, we first need to calculate the sample standard deviation. The scores provided are 115, 128, 107, 109, 116, 124, 135, 127, 115, 104, 118, 126, 129, 133. We find the mean of these scores and then use the formula for sample standard deviation.

Step 1: Calculate the mean of the IQ scores.

Step 2: Find the sum of the squared deviations of each score from the mean.

Step 3: Divide by the number of scores minus one (n-1) to get the variance.

Step 4: Take the square root of the variance to find the sample standard deviation.

Once we have the sample standard deviation, we use the chi-square test for variance since we are testing about the population variance. Under the null hypothesis, we assume that the population standard deviation is 15. At a significance level of 0.10, we compare the test statistic to the corresponding chi-square distribution to determine if we can reject the null hypothesis.

If a person is randomly selected, find the probability that his or her birthday is in May. ignore leap years

Answers

May has 31 days

 there are 365 days in a year

31/365 probability someone has a birthday in May

The probability of the event A that represents that the man's birthday is in May is 0.084.

What is probability?

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur. Mathematically -

P(A) = n(A)/n(S)

Given is a person who is randomely selected.

Assume that the Event A represents that the man's birthday is in may.

Total number of days in the month of may = n(A) = 31

Total number of days in a year = n(S) = 365

Therefore, the probability that the man's birthday is in may will be -

P(A) = n(A)/n(S)

P(A) = 31/365

P(A) = 0.084

Therefore, the probability of the event A that represents that the man's birthday is in May is 0.084.

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A total of 

644

 tickets were sold for the school play. They were either adult tickets or student tickets. There were 

56

 fewer student tickets sold than adult tickets. How many adult tickets were sold?

Answers

a + s = 644
s = a - 56

a + (a - 56) = 644
2a - 56 = 644
2a = 644 + 56
2a = 700
a = 700/2
a = 350 <=== adult tickets

s = a - 56
s = 350 - 56
s = 294 ...student tickets

A rectangular container 20 cm long and 15 cm wide contains sone water. When an iron ball was put in the water level rose by 3cm, find the the volume of the iron ball

Answers

Given that an object will always displace the same amount of water that its mass is, the ball has a volume of 900cm^3. The displacement method. You get this by multiplying 20 x 15 (the lengths and widths) and multiply it by 3 (the height the water rose) to find the volume.

The volume of the iron ball in the rectangular container that is 20 cm long and 15 cm wide is 900cm³.

How to calculate volume?

The volume of a rectangular cuboid can be calculated by multiplying the length, breadth and the height of the shape.

According to this question, a rectangular container 20 cm long and 15 cm wide contains sone water. When an iron ball was put in the water level rose by 3cm.

Volume of the iron ball = 20cm × 15cm × 3cm

Volume of the iron ball = 900cm³

Therefore, the volume of the iron ball in the rectangular container that is 20 cm long and 15 cm wide is 900cm³.

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