Duke wants to hire someone to re-tile his bathroom. The research he found for three local tilers is presented in the table below. He was able to find the average area of their tiling jobs and the time it took the tilers to complete the job.

Tiler Area Tiled
(square feet) Time
(hours:minutes)
Toni's Tiles 803 2:12
Bob's Bathrooms 1,460 4:00
Rhonda's Restroom Redos 753 1:30
Calculate the unit rate for each tiler above to determine if proportional relationships exist.

The rates at which Toni's Tiles and Bob's Bathrooms tile are ?
to one another.

The rates at which Toni's Tiles and Rhonda's Restroom Redos tile are ?
to one another.

The rates at which Bob's Bathrooms and Rhonda's Restroom Redos tile are ?
to one another.

Two items are in a proportional relationship if they ?
the same unit rate.

Answers

Answer 1

Answer:

Toni's Tiles and Bob's Bathrooms are in a proportional relationship as they have the same unit rate

Step-by-step explanation:

The given parameters are;

,                                           Area Tiled (ft²)                                    Time (Hr:min)

,                                            

Toni's Tiles,                                   803                               2:12

Bob's Bathrooms,                         1,460                             4:00

Rhonda's Restroom Redos          753                                1:30

The unit rate for each tiler

Toni's Tiles = 803/2:12 = 803/(2×60 + 12) =  6.083 ft²/min

Bob's Bathrooms = 1460/(4×60) =  6.083 ft²/min

Rhonda's Restroom Redos  = 753/(60 + 30) = 8.37 ft²/min

Therefore we have;

The rates at which Toni's Tiles and Bob's Bathrooms tile are to one another = 6.083 to 6.083  = 1:1

The rates at which Toni's Tiles and Rhonda's Restroom Redos tile are to one another = 73/12×30/251 = 365:502

The rate at which Bob's Bathrooms  and Rhonda's Restroom Redos tile are to one another = 73/12×30/251 = 365:502

Therefore, Toni's Tiles and Bob's Bathrooms are in a proportional relationship as they have the same unit rate.


Related Questions

A box contain 12 balls in which 4 are white 3blue and 5 are red.3 balls are drawn at random from the box. Find the chance that all three balls are of different colour

Answers

Answer:

white: 1/3, blue: 1/4, red: 5/12

Step-by-step explanation:

Take the amount of balls each color has and divide by 12.

White:

4/12 = 1/3

Blue:

3/12 = 1/4

Red:

5/12 (can't simplify)

Answer:

3/44 or 0.068

Step-by-step explanation:

(3/12 × 2/11 × 1/10)+(5/12 × 4/11 × 3/10)+(4/12 × 3/11 × 2/10)

=3/44

Factor completely 2c5 + 44c4 + 242c3. 2c3(c + 11)2 2(c + 11)2 2c3(c + 11)(c − 11) 2c3(c2 + 22c + 121)

Answers

Answer:

2c^3(c+11)^2

Step-by-step explanation:

2c^5 + 44c^4 + 242c^3

Factor out the greatest common factor

2c^3(c^2+22c+121)

Recognizing inside the parentheses is (a+b) ^2 where a =c and b = 11

2c^3(c+11)^2

How many liters of a 35% salt solution must be mixed with 20 liters of 70% salt solution to obtain a solution that is 45% salt? What is the equation?

Answers

Answer:

.35 x + .70 (20) = .45(x+20)

50=x

Step-by-step explanation:

Let x = liters of 35% salt solution

We have 20 liters of 70%

We have a total of 20+x liters of 45%

.35 x + .70 (20) = .45(x+20)

Distribute

.35x + 14 = .45x +9

Subtract .35x from each side

14 = .10x +9

Subtract 9 from each side

5 = .10x

Divide each side by .1

5/.1 = x

50=x

What are the factors of the quadratic function represented by this graph?


A. 

(x − 1) and (x − 5)

B. 

(x + 1) and (x + 5)

C. 

(x − 1) and (x + 5)

D. 

(x + 1) and (x − 5)

Answers

The factors of the quadratic equations are (x + 1) and (x + 5) which is represented on the graph.

What is quadratic equation?

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is [tex]ax^2 + bx + c = 0,[/tex]

Here in the graph we can see that the x coordinate cut by the curve of the quadratic equation is in the negative side of x at -1 and -5.

So the factors of the quadratic equations are (x + 1) and (x + 5) which is represented on the graph.

To know more about quadratic equation follow

https://brainly.com/question/1214333

#SPJ2

Answer:

Check Screenshot

Step-by-step explanation:

Factor 2x2 − 4x − 30 completely. (5 points) 2(x − 5)(x + 3) 2(x − 3)(x + 5) (2x + 3)(x − 5) (2x − 5)(x + 3)

Answers

Answer:

The answer is

2( x + 3)(x - 5)

Step-by-step explanation:

To factor the expression

2x² - 4x - 30

First factor 2 out of the expression

That's

2( x² - 2x - 15)

Next write - 2x as a difference

2( x² + 3x - 5x - 15)

Factor out x from the expression

That's

2 [ x( x + 3) - 5x - 15 ]

Factor out -5 from the expression

2 [ x ( x + 3) - 5( x + 3) ]

Factor out x+3 from the expression

We have the final answer as

2( x + 3)(x - 5)

Hope this helps you

Answer:

C. 2(x - 5) (x + 3)

Step-by-step explanation:

I took the test

State if the triangles are similar. If so, how do you know they are similar and complete the similarity statement. Triangle LKJ≈____

Answers

Answer: C) similar, SAS similarity, triangle LQR

==============================================

Explanation:

The vertical angles KLJ and QLR are congruent. This forms the "A" in "SAS". The angles in question are between the marked sides.

KL = 18 is twice that of QL = 9, or put another way, KL/QL = 18/9 = 2. The ratio of the sides is 2. Also, JL/RL = 16/8 = 2 is the same ratio. Because both pairs of sides have the same ratio, the sides are in proportion. This helps form the two "S" letters of "SAS".

The original triangle has LKJ mentioned at the top. Note the order as its important. We start with L and move to K, so LK is the first segment mentioned. LK = 18 pairs up with LQ = 9, meaning that LQ must be the first segment mentioned of the answer triangle. Therefore LQR is the correct letter sequence if we start with point L. Writing QLR is not correct because Q is the first letter here but Q does not pair up with L.

What is the maximum number of pages the report can have so that it can be completely stored on a USB drive that holds 4 \cdot 10^6 \text{ KB}4⋅10 6 KB4, dot, 10, start superscript, 6, end superscript, start text, space, K, B, end text?

Answers

Answer:

2,300,000pages  report.

Step-by-step explanation:

Given a USB drive with memory of 4.6*10⁶KB, in order to know the maximum number of pages a report can have so that it can be completely stored on the drive, the conversion factor must be used.

We must first understand that 1 page of a document uses up approximately 2kB of the storage.

Since 2kB = 1page

4.6*10⁶KB = x page

Cross multiply

2kB * x = 4.6*10⁶KB * 1

2x =  4.6*10⁶

x =  4.6*10⁶/2

x =  2.3*10⁶

x = 2,300,000

Hence the maximum number of pages that the report can have so that it can be completely stored on a USB drive that holds 4.6*10⁶KB is approximately 2,300,000pages  report.

The line plot below displays the fraction of incoming calls answered before the second ring by a group of employees. What fraction of employees answered less than of their incoming calls before the second ring?

Answers

Answer:

1/6

Step-by-step explanation:

People who answered less than 1/2 were:  2 +  1 + 3 = 6 people.

There are a total of 36 people.

People who answered their calls before the second ring were only 6/36.

When we simplify the fraction, we get 1/6.

So, the answer is 1/6.

HELPP PLEASE I’ll give a brainlist

Answers

The lowest you can go without adding fractions is four to three, but you can do two to a half too.

A 3 L bottle of oil costs $36 and contains 12 cups. Dinesh puts 1 cup of oil, 10 garlic gloves and 1 cup of
lemon juice in each batch of hummus recipe that he makes. Dinesh makes 5 batches of hummus.
What is the total cost of oil that he uses in the 5 batches of his recipe?

Answers

The correct answer is $15

Explanation:

The first step is to determine the total of oil that was used for the 5 batches. To find this, you just need to multiply the amount of oil used for one batch by the total batches.

1 cup of oil per batch x 5 batches = 5 cups of oil

This means, in the 5 batches the oil Dinesh used was 5 cups of oil. Additionally, you know the total of cups in the bottle of oil is 12 cups, and these 12 cups or total costs $36. Now to find what is the cost of the 5 cups use the rule of three and cross multiplication.

12 cups of oil = $36   1. Write the values

5 cups of oil  = x      

12 x = 180           2.  Cross multiply this means 36x 5 and 12 multipy by x

x = 180 ÷ 12        3. Solve the equation

x=  15 - Cost for 5 cups used in the batches

You know that the average college student eats 0.75 pounds of food at lunch. If the standard deviation is 0.2 pounds of food, then what is the total amount of food that a cafeteria should have on hand to be 90 percent confident that it will not run out of food when feeding 50 college students?

Answers

Answer: $53.95

Step-by-step explanation:

Given: [tex]\mu=0.75[/tex] pounds

[tex]\sigma= 0.2[/tex] pounds

n= 50

Two tailed critical z-value for 90% confidence level = 1.645

Let x be the total amount of food that a cafeteria should have on hand to be 90 percent confident that it will not run out of food .

z-score = [tex]\dfrac{x-\mu}{\sigma}[/tex] [tex]=\dfrac{x-0.75}{0.2}[/tex]

Then, [tex]\dfrac{x-0.75}{0.2}=1.645[/tex]

[tex]x-0.75=1.645\times0.2\\\\\Riightarrow\ x-0.75=0.329\\\\\Rightarrow\ x= 0.329+0.75\\\\\Rightarrow\ x= 1.079[/tex]

Foe 50 students, total amount of food = 1.079 x 50 = $53.95

hence, the cafeteria should have food of amount $53.95 so that it is be 90 percent confident that it will not run out of food.

If x =2.3,5x.3= DONT MAKE ANSWERS THAT DONT MAKE ANY SENSE OR YOU WILL GET REPORTED

Answers

Answer:

34.5

Step-by-step explanation:

5 times x(2.3) = 11.5.

11.5 times 3 is 34.5

you put 2.3 in place of x because x was the unknown value, but now that we know it is 2.33 we plug it in.

A baking scale measures mass to the tenth of a gram up to 650 grams .Which of the following measurements is possible

Answers

Answer:

A. 3.8 grams

Step-by-step explanation:

A baking scale measures mass to the tenth of a gram, up to 650 grams. Which of the following measurements is possible using this scale?

a.3.8 grams

b.120.01 grams

c.800.0 grams

d.54 milligrams

Solution

The scale measures mass to the tenth of a gram

The scale measures up to 650 grams

a.3.8 grams

This measures to the tenth of a gram (to one decimal place) and it is not up to 650 grams

b.120.01 grams

This measures to hundredth of a gram ( 2 decimal places) and it is not up 650 grams.

c.800.0 grams

This measures to the tenth of a gram but exceeds the 650 grams limit

d.54 milligrams

This is in milligram, so it is wrong

Option a.3.8 grams is the only possible scale measurement among the options.

When you roll two number cubes, what are the odds, in simplest form, in favor of getting two numbers less than 3? A. 1:8 B. 8:1 C. 1:9 D. 9:1

Answers

Answer:

1:9 is my best guess because 9 is a factor of 3 and 1 would be the lowest ratio for a number less than 3 :)

Step-by-step explanation:

Hope this helps, have a good day :)

6x + 11 + 3x .........................................

Answers

Answer: I'm assuming you want this problem simplified.

6x + 11 + 3x

Combine like terms: 9x + 11

Your expression now looks like: 9x + 11

There is nothing left to simplify, so you're done!

Hope this helps!

Answer:

9x+11

Step-by-step explanation:

6x + 11 + 3x

Combine like terms

9x+11

help! ill give brainliest

Answers

Answer:

84 square inches is the correct answer.

Step-by-step explanation:

I am 100% sure of that.

Hope this helps....

Have a nice day!!!!

Find the graph of the inequality y<-1/5X+1.

Answers

Answer:

Please refer to attached image for the graph of inequality.

Step-by-step explanation:

Given the inequality:

[tex]y<-\dfrac{1}{5}x+1[/tex]

To graph this, first let us convert it to corresponding equality.

[tex]y=-\dfrac{1}{5}x+1[/tex]

As we can see that the above equation is a linear equation in two variables so it will be a straight line.

Now, let us find at least two points on the above equation so that we can plot them and then extend it to get the complete graph.

Two points that can be easily found, are:

1st put [tex]x = 0[/tex] , [tex]y=-\frac{1}{5}\times 0+1 =1[/tex]

So one point is (0, 1 )

Now, put y = 0,  

[tex]0=-\frac{1}{5}\times x+1\\\Rightarrow 1=\frac{1}{5}\times x\\\Rightarrow x = 5[/tex]

Second point is (5, 0)

Let us plot the points on the graph and extend the straight line.

Now, we know that it is an inequality, the are will be shaded.

As there is no equal to sign in the inequality, so the line will be dashed.

Let us consider one point and check whether that satisfies the inequality or not.

If the point is satisfied in the inequality, we will shade that area towards the point.

Let us consider the point (0, 0).

0 < 0 +1

Point is satisfied.

Please refer to the attached image for the graph of given inequality.

How many unit cubes would it take to completely fill the prism with no gaps between unit cubes?

Answers

Answer:

72 cubes

Step-by-step explanation:

Top view of the rectangular prism shows the unit cubes arranged in two rows along the length.

In each row number of unit cubes arranged = 9

Right view side of the prism shows the unit cubes arranged in two columns.

Number of unit cubes in each column = 4

Total number of cubes arranged in the prism = (Number of cubes in each row × Number of cubes arranged in two columns) × Number of columns

= (9 × 4) × 2

= 72

Therefore, number of cubes filled completely in the prism with no gaps = 72

Just need the final answer

Answers

Answer:

[tex]\boxed{\sf a) \ 15.9}[/tex]

Step-by-step explanation:

The triangle is a right triangle.

We can use trig functions to solve for x.

cos θ = adj/hyp

cos(51) = 10/x

x = 10/cos(51)

x = 15.89015729

A certain pole has a cylinder-like shape, where the base's radius is 10 centimeters and the height is 2 meters. What calculation will give us the estimated surface area of the pole in square centimeters?

Answers

Answer:

2 pi •10•210

Step-by-step explanation:

Khan academy

A man traveled 1/3 of the distance between
two cities in 3/4 of an hour. At this rate, how
many hours will it take him to travel the
entire distance between the two cities?

Answers

Answer: 2 hours 15 minutes

Step-by-step explanation:

3/4 of an hour times 3 will be 9/4; each fourth is 15 minutes. 9 times 15 is 135 minutes, which is 2 hours and 15 minutes

Answer:

2.25 hours

Step-by-step explanation:

The man traveled 1/3 of the distance in 3/4 of an hour.

This means that he needs to travel for 3 times as long to travel the entire distance.

3 * 3/4 = 9/4 = 2.25

2.25 hours.

Or, 2 hours and 15 minutes (as 0.25 = 1/4).

The shape on the left is translated to the shape on the right.

Which statement about the transformation is true?

A.The name of the shape on the right is MNOPQRS' because it is the image of the shape on the left.

B.The name of the shape on the right is MNOPORS' because it is the pre-image of the shape on the left.

C.The name of the shape on the right is M’N’O’P’Q’R’S because it is the pre-image of the shape on the left.

D. The name of the shape on the right M’N’O’P’Q’R’S
Because it is the pre-image if the shape in the left.

Answers

Answer:

sorry i am late but the answer is The name of the shape on the right is M prime N prime O prime P prime Q prime R prime S prime because it is the image of the shape on the left. and if you dont  want to read that  its D

hope it helped anyone :)

The name of the shape on the right is M’N’O’P’Q’R’S' because it is the pre-image of the shape on the left

Transformation

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.

Translation is the movement of a point up, down, left or right.

The name of the shape on the right is M’N’O’P’Q’R’S' because it is the pre-image of the shape on the left

find out more on Transformation at: https://brainly.com/question/1462871

16. Expand (2x - 1)(x - 3).
A. 2x2 - 7X+3 B. 2x2 +7x+3
C. 2x2-7X-3 D. 2x2+7X-3 E. x2+7X-3​

Answers

Answer:

Hey there!

[tex](2x-1)(x-3)[/tex]

[tex]2x^2-1x-6x+3[/tex]

[tex]2x^2-7x+3[/tex]

Hope this helps :)

Answer:

see below

Step-by-step explanation:

the simple answer is a if you need an explanation just comment

(01.02 HC)Morris is showing his work in simplifying (−6.7 + 4.3) − 1.2. Step 1: (4.3 − 6.7) − 1.2 Step 2: 4.3 − (6.7 + 1.2) Step 3: 4.3 − (7.9) Step 4: −3.6

Answers

Answer:

Option (C)

Step-by-step explanation:

This question is incomplete; here is the complete question.

Morris is showing his work in simplifying,

(-6.7 + 4.3) - 1.2

Step 1: (4.3 - 6.7) - 1.2

Step 2: 4.3 - (6.7 + 1.2)

Step 3: 4.3 - 7.9

Step 4: -3.6

Which statement is true ?

A). Step 1, Morris used the commutative property.

B). Step 2, Morris used the distributive property.

C). Step 3, Morris used the associative property.

D). Step 4, Morris's answer is incorrect.

In associative property,

a + (b + c) = (a + b) + c

By this property,

(-6.7 + 4.3) - 1.2

Step 1, (-6.7 + 4.3) - 1.2 = (4.3 - 6.7) - 1.2

Step 2, (4.3 - 6.7) - 1.2 = 4.3 - (6.7 + 1.2) [Use of associative property]

Step 3, 4.3 - 7.9

Step 4, -3.6

Which expression is equivalent to 125x6, 1533?

Answers

Answer:

511 x 3 = 1533

Step-by-step explanation:

here's another:

219 x 7

hope this helpes

Sandy's older sister was given $2,400 and was told to keep the balance of the money after sharing with her siblings. Give Sandy exactly $350. Write Sandy's portion

Answers

Answer:

Sandy's portion = [tex]\mathsf{\dfrac{7}{48}}[/tex]

Step-by-step explanation:

Sandy's older sister was given $2,400

She was told to keep the balance of the money after sharing with her siblings.

She gave  Sandy exactly $350

The objective is to write Sandy's portion.

Sandy's portion will be the ratio of the amount given to Sandy divided by the total amount at her sister disposal.

Let Sandy's older sister be y,

So, y = 2400

Sandy's portion = [tex]\dfrac{350}{2400}[/tex]

Sandy's portion = [tex]\dfrac{35}{240}[/tex]

Sandy's portion = [tex]\mathsf{\dfrac{7}{48}}[/tex]

Hunter is copying an angle. His work so far follows. Explain the importance of his next step, which is drawing a line through A and Y using a straightedge.

This is to check to make sure that A is in the right place, since it was drawn using the arcs.

Using a straightedge ensures that there is a line passes through A and Y.

Because a line was drawn through point L, a similar line should be drawn through the corresponding point on ∠AYZ.

This is the other ray that will make up the angle ∠AYZ and will complete the construction.

Answers

Answer:

  This is the other ray that will make up the angle ∠AYZ and will complete the construction.

Step-by-step explanation:

The point of the construction is to copy the angle. That is, the end result must be an angle with identical measure to the original. The construction so far has no angle at Y. Drawing ray YA will complete the construction and create the desired angle. That is, YA ...

  This is the other ray that will make up the angle ∠AYZ and will complete the construction.

what is the answer to 4x^2+2x-10

Answers

Answer:

2 (2x^2 + x - 5)

Step-by-step explanation:

Factor  2  out of  4 x^ 2

Factor  2  out of  2 x

Factor  2  out of  − 10

Factor  2  out of 2 (2x^2) + 2x

Factor  2  out of  2  ( 2 x^ 2 + x )  +  2  ⋅  − 5

Hope this can help you

make u the subject of the formula
u-x/v-x=u/v²​

Answers

Answer:

See below.

Step-by-step explanation:

[tex]\frac{u-x}{v-x}=\frac{u}{v^2} \\[/tex]

Cross multiply and distribute.

[tex]u(v-x)=v^2(u-x)\\uv-ux=uv^2-xv^2[/tex]

Move all the u to the left side:

[tex]uv-ux-uv^2=-xv^2[/tex]

Factor out a u:

[tex]u(v-x-v^2)=-xv^2[/tex]

Divide:

[tex]u=\frac{-xv^2}{v-x-v^2}=\frac{xv^2}{x+v^2-v}[/tex]

(I factored out a negative in the second term.)

13) The diameter of a plant cell is 1.26 m and the length of a bacterium is 5.1 m. Compare their diameters.

Answers

Answer:

The diameter of the bacterium is 4.05 times the diameter of the plant cell

Step-by-step explanation:

Given

The given parameters both represent diameters

Plant Cell; P = 1.26m

Bacterium; B = 5.1m

Required

Compare both diameters;

Write out both expressions

[tex]P = 1.26[/tex]

[tex]B = 5.1[/tex]

Divide B by P

[tex]\frac{B}{P} = \frac{5.1}{1.26}[/tex]

[tex]\frac{B}{P} = 4.04761904762[/tex]

Approximate

[tex]\frac{B}{P} = 4.05[/tex]

Multiply both sides by P

[tex]P * \frac{B}{P} = 4.05 * P[/tex]

[tex]B = 4.05 * P[/tex]

[tex]B = 4.05P[/tex]

This implies that;

The diameter of the bacterium is 4.05 times the diameter of the plant cell

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