In a study commuting patterns of people in a large metropolitan area, respondents were asked to report the time they took to travel to their work on a specific day of the week. What is the individual?a. travel timeb. a personc. day of the weekd. city in which they lived

Answer: 17.3

Step-by-step explanation:

Since it is a right angled triangle , we will use the application of SOHCAHTOA in solving it  ,which means

sine Ф = opposite / hypotenuse

cosine Ф = adjacent / hypotenuse

Tangent Ф = opposite / adjacent

Ф stands for the given angle.

From the diagram , the given angle is 25 ,this means that

opposite = x

hypotenuse = 41

This means that we will use sine Ф = opposite / hypotenuse to find the value of x.

Therefore:

sin 25 = x/41

x = 41 sin 25

x = 41 x 0.4226

x = 17.3273

x ≈ 17.3

Answer: Mary need to make at-least 95 on her fourth test to earn an A in her algebra course.

Step-by-step explanation:

Let x be the grades scored by Mary in the fourth algebra test.

Mary has grades of 95, 82, 88 on her first three algebra tests.

Then, the combined scores in four test will become = 95+82+88+x =  265+x

Average score = (Sum of all scores) ÷ (Number of tests)

[tex]=\dfrac{265+x}{4}[/tex]

As per given ,

To earn an A in an algebra course, a student must have a test average of at least 90.

i.e. Average score ≥ 90

[tex]\Rightarrow\ \dfrac{265+x}{4}\geq90\\\\\Rightarrow\ 265+x\geq 90\times4=360\\\\\Rightarrow\ x\geq360-265 =95\\\\\Rightarrow\ x\geq90[/tex]

Hence, Mary need to make at-least 95 on her fourth test to earn an A in her algebra course.

The histogram depicts the year-by-year damage in millions of dollars caused by tornadoes from 1950 to 1999. It uses class intervals to display the frequency of damage costs, where each bar represents a specific cost range.

In the given question, we discuss a histogram that represents the commutative property damage caused by tornadoes from 1950 to 1999 across the 50 US states and Puerto Rico. The histogram's class intervals are set from 0 to < 10, 10 to < 20, and so forth, and the data are in millions of dollars. A histogram is a type of graphical representation used in statistics to display the distribution of data. Each bar in a histogram represents the tabulated frequency at each interval. In this case, the frequency is the year count in which the commutative property damage caused by tornadoes falls within a specific monetary range.

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Answer:

0.4

Step-by-step explanation:

Equation is

x-(-3.8)=2(x-1.7)

solving for x,

x+3.8=2x-3.4

x=0.4

Final answer:

The value of x is found by setting up an equation based on the distances provided and considering two separate cases for the absolute value. After solving the equation, the positive value of x is determined to be 7.2.

Explanation:

To solve for the value of x in this problem, we need to set up an equation based on the information given about the distances on a number line. The distance between x and -3.8 is twice the distance between x and 1.7. This translates to the following equation:

|x - (-3.8)| = 2|x - 1.7|

We then solve this equation step-by-step:

Therefore, the value of x to the nearest tenth is 7.2.

Answer:

[tex]x + y = 650[/tex]              

Step-by-step explanation:

We are given the following in the question:

Total calories in a bag of carrot and a container of hummus dip = 650

Rosarita's snack:

Some of the bag of carrots and some of the container of hummus.

Total calories in Rosarita's snack = 260

Let x represents the total number of calories in the bag of carrots and y represents the total number of calories in the container of hummus.

Then, we can write the following equation to represent total number of calories in both a bag of carrot and a container of hummus dip:

[tex]x + y = 650[/tex]

Since Rosarita did not eat the whole bag of carrot and the whole container of hummus and also x and y are the total calories in whole bag of carrot and container of hummus respectively.

Answer:

x+y=650

Step-by-step explanation:

its right on edge 8th grade math

Answer:

Cost per Electricity Unit= $0.61

Cost per Gas Unit= $0.22

Step-by-step explanation:

Suppose,

Cost per Electricity Unit: e

Cost per Gas Unit: g

for the first month condition, equation would be

[tex]600*e+100*g=388...........................................(i)[/tex]

and for the next month condition, equation would be like

[tex]400*e+150*g=277...........................................(ii)[/tex]

By solving both linear equations simultaneously, we get

e=0.61    and     g=0.22

Answer:

In step 2, the LCD was not used correctly to make equivalent fractions.

Step-by-step explanation:

Answer:

In step 2, the LCD was not used correctly to make equivalent fractions.

Step-by-step explanation:

Answer:

Cost of steak-in-a-bun burger is $1.95 and cost of queen-size burger is $1.05.

Step-by-step explanation:

Let the cost of queen-size burger be 'q'.

Let the cost of steak-in-a-bun be 's'.

Given:

a steak-in-a-bun cost $0.90 more than a queen-size burger.

So we can say that;

[tex]s=0.9+q \ \ \ \ equation\ 1[/tex]

Given:

the coach took ten students to burger box.

Hence Number of person at burger box = 11

The coach and three students ordered steak-on-a-bun while the other students ordered queen-size burgers.

So we can say that;

Number of queen sized burger = 11 - 4 =7

Number of steak on a bun burger = 4

Also Given:

Total bill = $15.11

Now we can say that;

Total bill is equal to sum of Number of queen sized burger multiplied by Cost of queen sized burger and Number of steak on a bun burger multiplied by cost of steak on a bun burger.

framing in equation form we get;

[tex]4s+7q =15.15\ \ \ \ equation\ 2[/tex]

Substituting equation 1 in equation 2 we get;

[tex]4(0.9+q)+7q=15.15[/tex]

Applying distributive property we get;

[tex]3.6+4q+7q=15.15\\\\3.6+11q=15.15[/tex]

Subtracting both side by 3.6 we get;

[tex]3.6+11q-3.6 =15.15-3.6\\\\11q=11.55[/tex]

Dividing both side by 11 we get;

[tex]\frac{11q}{11}=\frac{11.55}{11}\\\\q=\$1.05[/tex]

Substituting the value of q in equation 1 we get;

[tex]s=0.9+q=0.9+1.05=\$1.95[/tex]

Hence Cost of steak-in-a-bun burger is $1.95 and cost of queen-size burger is $1.05.

Final answer:

The cost of one steak-on-a-bun is $2.055, and the cost of one queen-size burger is $1.155.

Explanation:

The student's question involves finding the cost of one steak-on-a-bun and one queen-size burger given that the total bill for a group order at a restaurant was $15.15 and that a steak-on-a-bun costs $0.90 more than a queen-size burger.

Let's define Q as the price of a queen-size burger.

Therefore, the price of a steak-on-a-bun would be Q + $0.90. According to the problem, four people (the coach and three students) ordered steak-on-a-bun, and six students ordered queen-size burgers.

The equation representing the total cost is:

4(Q + $0.90) + 6Q = $15.15

Solving for Q, we first expand the equation:

4Q + $3.60 + 6Q = $15.15

Combining like terms, we get 10Q + $3.60 = $15.15.

Subtracting $3.60 from both sides, we get 10Q = $11.55.

Dividing both sides by 10, we find that Q = $1.155, which is the cost of a queen-size burger.

Finally, the cost of a steak-on-a-bun is Q + $0.90 = $1.155 + $0.90 = $2.055.

The cost of one steak-on-a-bun is $2.055, and the cost of one queen-size burger is $1.155.

Answer:

The area is 54

Step-by-step explanation:

6x18 = 108

108 x 1/2 = 54

Answer:

area 51

Step-by-stareaep explanation:

Answer:

Step-by-step explanation:

The cost of the three books that James bought from the bookstore.

He has a coupon for 25% off the original price. This means that the amount by which the original price was reduced would be

25/100 × 39.99 = 0.25 × 39.99 = $9.8325

The cost of the books would be

39.99 - 9.8325 = $30.1575

He is charged 8.5% sales tax. This means that the amount paid for tax would be

8.5/100 × 30.1575 = 0.085 × 30.1575 = $2.56

the total cost of his purchase would be

2.56 + 30.1575 = $32.7175

Answer:

$32.7175

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

x             frequency

4.8        1

4.83       1

4.85     2

4.89     1

4.91     1

4.94    2

4.96   1

4.99   1

5.04    3

5.05    1

5.12    3

5.14   1

5.15   1

5.17   1

5.19   2

5.24    1

5.26     1

5.27     1

5.28     1

find the dot plot as attached below

Step-by-step explanation:

Construct a dotplot for the following data. 4.85 4.94 5.12 5.14 4.80 4.99 5.19 4.94 4.85 5.12 5.04 4.96 5.28 5.05 4.83 5.27 5.12 5.19 4.89 5.15 5.04 5.17 5.24 5.04 4.91 5.26

Rearranging the data into frequency table

x             frequency

4.8        1

4.83       1

4.85     2

4.89     1

4.91     1

4.94    2

4.96   1

4.99   1

5.04    3

5.05    1

5.12    3

5.14   1

5.15   1

5.17   1

5.19   2

5.24    1

5.26     1

5.27     1

5.28     1

Answer:

The number of fiction books is 500 and non fiction books is 1500.

Step-by-step explanation:

Given:

Total book library contains = 2000.

There are 3 times as many non fiction books as fiction books.

Now, to determine the number of non fiction books and fiction books.

Let the fiction books be [tex]x.[/tex]

And the non fiction books be [tex]3x.[/tex]

Total books = 2000.

Now, to get the number of non fiction books and fiction books we put an equation:

[tex]3x+x=2000.[/tex]

[tex]4x=2000.[/tex]

Dividing both sides by 4 we get:

[tex]x=500.[/tex]

Fiction books = 500.

Non fiction books = [tex]3x=3\times 500=1500.[/tex]

Therefore, the number of fiction books is 500 and non fiction books is 1500.

To solve for the number of nonfiction and fiction books in the library, set up a system of equations and solve them to find there are 500 fiction books and 1500 nonfiction books.

To determine the number of nonfiction and fiction books in the library, we can use a system of equations. Let's denote the number of fiction books as F and the number of nonfiction books as NF. According to the problem, the total number of books in the library is 2000, and there are 3 times as many nonfiction books as there are fiction books.

Our two equations will be:

F + NF = 2000 (Total number of books)

NF = 3F (3 times as many nonfiction books)

To solve these equations:

Substitute the second equation into the first one:

F + 3F = 2000

4F = 2000

Divide both sides by 4 to find F:

F = 2000 / 4

F = 500

There are 500 fiction books. Now we can find the number of nonfiction books by multiplying 500 by 3:

NF = 3 * 500 = 1500

So, the library has 500 fiction books and 1500 nonfiction books.

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Answer:

[tex]g(x)=|x+4|-2[/tex]

Step-by-step explanation:

All the absolute value functions given in the option are of the form:

[tex]g(x)=|x-h|+k[/tex], where (h,k) is the vertex

From your description the absolute value graph has vertex at (-4,-2)

Hence h=-4 and k=-2.

We substitute to get:

[tex]g(x)=|x--4|+-2[/tex]

We simplify to get:

[tex]g(x)=|x+4|-2[/tex]

Answer:

a) 1805.55$

b) 2.14$

c)0.005$

d)0.064$

e)1805.55$

Step-by-step explanation:

Density of mercury is 844.9 lb/ft3.

a) 76 pound flask of mercury is 76/844.9=0.09 ft^3. 0.09 ft^3 mercury cost 162.5$, then 1 ft^3 mercury is

[tex]p=(162.5/0.09)=1805.55[/tex]

1805.55$

b) One pound of mercury is 2.14$

[tex]p=162.5/76=2.14[/tex]

c)76 pound equals 34473 grams. It makes:

[tex]p=162.5/34473=0.005[/tex]

0.005$ is the price of one gram mercury.

d)Total amount of mercury is 34473 grams. Then total volume of mercury is:

[tex]V=34473/13.534=2547.14[/tex]

2547.14 cm3. And the unit price is:

[tex]p=162.5/2547.14=0.064[/tex]

e) 1805.55$. It is found already.

Question is Incomplete;Complete question is given below;

Caleb made $105 mowing lawns and walking dogs, charging the rates shown. If he mowed half as many lawns as dogs walked, how many lawns did he mow and how many dogs did he walk? $7.50 for walking dogs and $20 for mowing lawns

Answer:

Caleb mowed 3 lawns and walked 10 dogs.

Step-by-step explanation:

Let the number of dogs he walked be 'd'.

Let number of lawn he mowed be 'l'.

Given:

If he mowed half as many lawns as dogs walked

So we can say that;

[tex]l=\frac{1}{2}d=0.5d \ \ \ \ equation\ 1[/tex]

Now given:

Cost for mowing each lawn = $20

Cost for walking each dog = $7.50

Total amount made = $105

Now we can say that;

Total amount made is equal to Cost for mowing each lawn multiplied by number of lawn he mowed and Cost walking each dog multiplied by number of lawn he mowed.

framing in equation form we get;

[tex]20l+7.5d=105 \ \ \ \ \ equation \ 2[/tex]

Substituting equation 1 in equation 2 we get;

[tex]20(0.5d)+7.5d=105[/tex]

Applying distributive property we get;

[tex]10d+7.5d=105\\\\17.5d=105[/tex]

Dividing both side by 17.5 we get;

[tex]\frac{17.5d}{17.5}=\frac{105}{17.5}\\\\d= 6[/tex]

Substituting the value of 'd' in equation 1 we get;

[tex]l=0.5d=0.5\times6=3[/tex]

Hence Caleb mowed 3 lawns and walked 10 dogs.

Answer D.It will increase 8 times.

Step-by-step explanation:

Answer: It will increase 8 times

Step-by-step explanation:

Range simply means the smallest number subtracted from the biggest number. Initially, the scores were 70, 72 and 68 then making the range 68-72 = 4. Now a new score is added which is 100 and it is obviously the biggest number now. So we subtract 68 from 100 that is ; 100-68= 32. This new range is 8 times more than the former. That is, 32/4 = 8.

Answer:445 student tickets were sold.

75 adult tickets were sold.

Step-by-step explanation:

Let x represent the number of student tickets that were sold in the talent show.

Let y represent the number of adult tickets that were sold in the talent show.

The talent show committee sold a total of 530 tickets in advance. This means that

x + y = 530

Student tickets cost $3 each and the adult tickets cost $5 each. The total receipts were $1740. This means that

3x + 5y = 1740 - - - - - - - - - - - - 1

Substituting x = 530 - y into equation 1, it becomes

3(530 - y) + 5y = 1740

1590 - 3y + 5y = 1740

- 3y + 5y = 1740 - 1590

2y = 150

y = 150/2 = 75

x = 530 - y = 530 - 75

x = 455

.

Answer:

Continuous observation

Step-by-step explanation:

Generally, the weight of any person is displaced in whole numbers without the inclusion of decimal numbers. The decimal numbers are mostly rounded up to the whole number. Based on the argument made in the given problem, the type of weight variable for this type of analysis is known as continuous observation.

Answer:the total cost of the collar is $5.11

Step-by-step explanation:

To make a collar for her dog, she needs to buy some chain,a clasp, and a name tag.

The length of the chain that she wants to buy is 40 centimeters.

1000 centimeters = 1 meter

40 centimeters = 40/1000 = 0.04 meters.

One meter of chain costs $9.75. Therefore, 0.04 meters of chain would cost

0.04 × 9.75 = $0.39

The clasp is $1.29 and the name tag is $3.43. Therefore, the total cost of the collar would be

0.39 + 1.29 + 3.43 = $5.11

Answer:

y = (7/8)x

Step-by-step explanation:

Exponential decay is represented when the number used is less than 1. 7/8 is the only choice that is less than 1.

y = (7/8)ˣ is an exponential decay because b = 7/8 < 1.

An exponential decay is in the form:

y = abˣ

where y, x are variables, a is the initial value of y and b is the multiplier which is less than 1.

From the question y = (7/8)ˣ is an exponential decay because b = 7/8 < 1.

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Answer:

2,400cm^2

Step-by-step explanation:

This is quite an interesting question.

Now, we know the frame measures 60 by 80. We also know that the thickness of the frame is 10cm in length. Hence from the side of the mirror to the other side of the frame is 10cm.

We have the 10cm on each side of the frame. Making a total of 40cm and 20cm each allowance on the length and breadth of the mirror. The length and breadth of the mirror is thus 40cm by 60cm.

The area of a rectangle is L * B

The area of the mirror is 40 * 60 = 2,400cm^2

The fact that the width of each side of the frame is 10 cm means that each side of the mirror is 20 cm smaller than the corresponding side of the frame. Therefore, the mirror measures 40 cm by 60 cm, with an area of 2400.

Answer:

Below.

Step-by-step explanation:

a  = tangential velocity

b  = tangential acceleration

c  = Angular acceleration

d  = angular displacement

e  =  Angular velocity

f   =   radius.

Attached is a graph of the function [tex]f(x)=\sqrt{9}[/tex]

Answer:

a) Matrix B = [tex]\left[\begin{array}{c}5\\7\\9\end{array}\right][/tex]

b) Matrix AB = [tex]\left[\begin{array}{c}2525\\3620\\2845\\3705\end{array}\right][/tex]

c) $12,695

Step-by-step explanation:

Matrix A = [tex]\left[\begin{array}{ccc}225&110&70\\95&160&225\\280&65&110\\0&240&225\end{array}\right][/tex]

a) Matrix B = [tex]\left[\begin{array}{c}5\\7\\9\end{array}\right][/tex]

Gross Receipt = AB

[tex]\left[\begin{array}{ccc}225&110&70\\95&160&225\\280&65&110\\0&240&225\end{array}\right][/tex] . [tex]\left[\begin{array}{c}5\\7\\9\end{array}\right][/tex] = [tex]\left[\begin{array}{c}2525\\3620\\2845\\3705\end{array}\right][/tex]

c) Total revenue is the sum of receipts from 4 cinemas given in part b

Hence,

Total revenue = $2525 + $3620 + $2845 + $3705 = $12,695

The student is given two functions, d(x) = 500-2x and p(x) = x+5, which represent the demand and price, respectively, of a company's product. To find the relationship between price and quantity, we can substitute the demand function into the price function.

The subject of this question is Mathematics. The student is given two functions, d(x) = 500-2x and p(x) = x+5, which represent the demand and price, respectively, of a company's product. To find the relationship between price and quantity, we can substitute the demand function into the price function:

p(x) = x + 5 = d(x) + 5 = (500 - 2x) + 5 = 505 - 2x

So the price can be represented by the equation p(x) = 505 - 2x.

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Answer:

The answer to your question is height = 12 mm

Step-by-step explanation:

Data

l = w = 9 mm

V = 324 mm³

h = ?

Formula

V = [tex]\frac{Ab x h}{3}[/tex]

Solve for h

                       3V = Ab h

                       3V / Ab = h    or     h = 3V / Ab

Find the area of the base

Ab = l x w

     = 9 x 9

     = 81 mm²

Substitution

                       h = [tex]\frac{3(324)}{81}[/tex]

Simplification

                       h = [tex]\frac{972}{81}[/tex]

Result

                       h = 12 mm                    

Answer: c. 72% is a statistic and 56% is a parameter.

Step-by-step explanation:

Given : A study of voting chose 663 registered voters at random shortly after an election.

Population of interest : "registered voters"

Sample : " 663 registered voters "

72%  of 663 registered voters said they had voted in the election.

⇒ Statistic = sample proportion registered voters voted in the election.= 72%

Election records show that only 56% of registered voters voted in the election.

⇒ Parameter = Population proportion of registered voters voted in the election =  56%

Hence, the correct answer is "c. 72% is a statistic and 56% is a parameter."

Answer:

Step-by-step explanation:

The figure has 4 sides, so is a quadrilateral. Opposite sides are parallel, so the figure is a parallelogram.

Angles are not 90°, so the figure is not a rectangle. Sides are not all the same length, so the figure is not a rhombus. Because the figure has two pairs of parallel sides (not just one pair), it is not a trapezoid.

Answer:

a and b on edge

Step-by-step explanation:

The bonds are being sold at 110.611% of their face value, so each bond costs roughly $1,106.11. Therefore, to purchase three bonds, Sean would need to pay roughly $3,318.33.

When the question states that the bonds are 'selling at 110.611', it means that each bond is sold at 110.611% of its face value, which is $1,000. So to find the price of one bond you would multiply $1,000 by 1.10611 (110.611%), which equals roughly $1,106.11. Thus, if Sean wishes to purchase three bonds, you would simply multiply the price of one bond by three: $1,106.11 times 3 equals $3,318.33. So, Sean should expect to pay approximately $3,318.33 if he wants to purchase three bonds from the city of Tavel Gorge.

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Answer:

The bonds are being sold at 110.611% of their face value, so each bond costs roughly $1,106.11. Therefore, to purchase three bonds, Sean would need to pay roughly $3,318.33.

Step-by-step explanation: