The temperature in Fairbanks, Alaska, fell 10 degrees in 2 hours.

Explain why the average temperature change was –5ºF per hour.

Answer:

Danny should have sold 124 refreshments every hour for the 3 hours that he helped sell.

Step-by-step explanation:

Answer:  One

Why?  In math a function is something that works and is paired with exactly one input value and one output value.

Final answer:

To find the length of the shadow cast by a 35-foot building with a 60° angle of elevation to the sun, we can use trigonometry. The shadow is approximately 60.6 feet long.

Explanation:

To find the length of the shadow, we can use the concept of trigonometry. In a right triangle, the opposite side is proportional to the shadow length and the adjacent side is proportional to the height of the building. Using the angle of elevation of 60° and the height of the building as 35 feet, we can set up the trigonometric equation as follows:

tan(60°) = x/35

Solving for x, we get x = 35 * tan(60°) = 60.6 feet. Therefore, the shadow is approximately 60.6 feet long to the nearest tenth of a foot.

a. m<5=40° (Given)

b. m<2=140° (Given)

c. <5 and <2 are supplementary angles

Because they add 180°: <5+<2=40°+140°=180°

d. <5 and <2 are same-side interior angles

You can see it in the graph

e. a // b

Because they are same-side interior angles and they are supplementary angles, the lines a and b must me parallels.

28° and 152°

let the angle be x then supplementary angle = 3x + 68

Supplementary angles sum to 180° , hence

x + 3x + 68 = 180

4x + 68 = 180 ( subtract 68 from both sides )

4x = 112 ( divide both sides by 4 )

x = [tex]\frac{112}{4}[/tex] = 28

the angles are 28° and ( 3 × 28) + 68 = 84 + 68 = 152°

There are 8 sitcoms that can be recorded on the remaining tape.

To find out how many 30-minute sitcoms can be recorded on the remaining tape, we need to subtract the duration of the existing movie from the maximum capacity of the VHS tape. So, 360 minutes - 120 minutes = 240 minutes remaining. Since each sitcom is 30 minutes long, we can divide the remaining time by 30 to find out the number of sitcoms: 240 minutes ÷ 30 minutes = 8 sitcoms can be recorded on the remaining tape.

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It's a linear function. We need only two points to draw a graph.

We choose any values of x and calculate the value of y.

[tex]6x-2y=2\qquad|-6x\\\\-2y=-6x+2\qquad|:(-2)\\\\y=3x-1[/tex]

for x= 0 → y = 3(0) - 1 = 0 - 1 = -1 → (0, -1)

for x = 2 → y = 3(2) - 1 = 6 - 1 = 5 → (2, 5)

[tex]9x-3y=1\qquad|-9x\\\\-3y=-9x+1\qquad|:(-3)\\\\t=3x-\dfrac{1}{3}[/tex]

for x = 0 → y = 3(0) - 1/3 = 0 - 1/3 = -1/3 → (0, -1/3)

for x = 2 → y = 3(2) - 1/3 = 6 - 1/3 = 5 2/3 → (2, 5 2/3)

-140

Max has -140 points

118 book on each shelf 9440 divided by 80=118

Answer: There are 118 books on each shelf.

Step-by-step explanation:

Since we have given that

Number of non fiction books a library has = 9440

Number of shelves = 80

So, Number of books on each shelf would be

[tex]\dfrac{\text{Number of non fiction books}}{\text{Number of books on each shelf}}[/tex]

[tex]\dfrac{9440}{80}\\\\=118[/tex]

Hence, there are 118 books on each shelf.

3x9-10/2

First take mind of PEMDAS

First multiply 3x9

27-10/2

now divide 10 by 2

27-5

22

so 3x9-10/2=22

Set up  a proportion:

$288/$48000 = x/$59000

Cross multiply

16992000 = 48000x

x = 354

The tax on the $59000 house was $354

To find the tax on a house assessed at $59,000 using the same tax rate, we can set up a proportion and solve for the unknown tax value.

To find the tax on a house assessed at $59,000 using the same tax rate, we can set up a proportion. The tax paid by Serena is $288 and the house assessed value is $48,000. Let's call the tax on the house assessed at $59,000 as 'x'. The proportion will be:

$$\frac{288}{48000} = \frac{x}{59000}$$

Cross multiplying, we get:

$$288 \times 59000 = 48000 \times x$$

Simplifying, we find:

$$x = \frac{288 \times 59000}{48000}$$

Using a calculator, we can evaluate this to find the tax on a house assessed at $59,000.

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The mean of a set of numbers is the average.  In this problem, add all of the numbers together ( negative numbers for the losses) and then divide by the amount of games total.

Here are the numbers we have to use:

+7

-3

-2

+4

+9

the problem would be 7-3-2+4+9=15

Now divide 15 by your total amount of games which would be 5.

15/5=3

The average difference would be 3.  Now a rule in math is to answer a word problem with a sentence.  

The mean difference in scores over the five games played would be 3.

Hope this helps!

Answer:

3

Step-by-step explanation:

Given:

A volleyball team played five games, the team won by 7 points, lost by 3, lost by 2 , won by 4 and won by 9

To find :  the mean difference in scores over the five games

Solution:

Mean basically refers to sum of all observations divided by number of observations.

The mean of scores over the five games refers to sum of all scores divided by 5.

Scores :

won by 7 points means + 7

lost by 3 means - 3

lost by 2 means - 2

won by 4 means + 4

won by 9 means + 9

Therefore,

sum of all scores = 7 - 3 - 2 + 4 + 9 = 15

Also, total number of games played by the team  = 5

So, mean difference in scores over the five games = sum of all scores /  total number of games played by the team = 15 / 5 = 3

In 4 days it will be 10 and 2/3

To find out how many inches elephant grass will grow in 4 days, multiply the daily growth rate by the number of days. The elephant grass will grow approximately 10 2/3 inches in 4 days.

To find out how many inches of elephant grass will grow in 4 days, we need to multiply the daily growth rate by the number of days. The daily growth rate is 2 2/3 inches. To convert this mixed number to an improper fraction, we multiply the whole number (2) by the denominator (3), which gives us 6. Adding the result to the numerator (2), we get 8. So the daily growth rate is 8/3 inches.

Next, we multiply the daily growth rate by the number of days: 8/3 * 4 = 32/3 inches. To simplify this fraction, we divide the numerator (32) by the denominator (3), which equals 10 with a remainder of 2. So the elephant grass will grow approximately 10 2/3 inches in 4 days.

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1 inch = 400 miles The scale gives the relationship between the measurements of the model and the measurements of the real object. Hope this helps.

Hi,

Here is the solution...

We convert this fraction into percentage.

To convert the fraction into percentage, we need to multiply the fraction by 100.

Math test score = [tex]\frac{21}{23} *100 = \frac{2100}{23} = 91.30[/tex]%

Science test score = [tex]\frac{29}{32} *100 = \frac{2900}{32} = 90.63[/tex]%

Now you can compare the percentage.

Julie scored higher in Math test.

Hope you will understand the steps.

Thank you. :)

To find the answer you divide the whole amount of 1456 by 7 since there is the 1 regular priced group and the remaining 6  discounted priced ticked. When you divide the 1456 by 7 it comes out to be 208 and to find the amount of the group of 6 you would multiply the 208 times the 6 and that will give you the amount of the dicount tickets sold. which is 1248.

Answer:

Option A is correct.

Change in the y-values is 40 and the change in x-values is 1.

Step-by-step explanation:

Let x represents the time in minutes and y represents the temperature(in Fahrenheit).

Given two points on the line graph i.e,

[tex]A(x_1, y_1)= (2 , 150)[/tex]  and  [tex]B (x_2, y_2)= (3, 190)[/tex]

we have to find the change in the y-value and x-value on the graph:

Change in the x-values for the given points is;

[tex](x_2 - x_1)[/tex] = 3 - 2 = 1

Similarly,

Change in the y-values for the given points is;

[tex](y_2 - y_1)[/tex] = 190-150 =40.

Since, the slope or the rate of change of the given line graph is the ratio of the change in the y-value over the change in the x-value i.e, slope = 40.

Therefore, change in the y-values is 40 and the change in x-values is 1.

Answer:

Option A

Step-by-step explanation:

edge 2021

1 hour = 3600 seconds

Calculate feet per hour first:

3600 seconds / 3 = 1200

1200 x 20 feet = 24,000 feet in 1 hour

1 mile = 5280 feet

Calculate miles per hour:

24,000 / 5280 = 4.54 miles per hour.

Round the answer as needed.

Answer:

Answer 4

Step-by-step explanation:

[tex]180:2=90\\90:2=45\\45:3=15\\15:3=5\\5:5=1\\\\180=\boxed{2}\cdot2\cdot\boxed{3}\cdot\boxed{3}\cdot5\\\\594:2=297\\297:3=99\\99:3=3\\33:3=11\\11:11=1\\\\594=\boxed{2}\cdot\boxed{3}\cdot\boxed{3}\cdot3\cdot11[/tex]

[tex]LCM(180,\ 594)=\boxed{2}\cdot\boxed{3}\cdot\boxed{3}\cdot2\cdot3\cdot5\cdot11=5940\\\\GCF(180,\ 594)=\boxed{2}\cdot\boxed{3}\cdot\boxed{3}=18[/tex]

So, the ratio between the LCM of 180 and 594 and the GCF of 180 and 594 is [tex]\(990:1\)[/tex].

To find the ratio between the least common multiple (LCM) and the greatest common factor (GCF) of two numbers, we need to calculate both the LCM and the GCF first.

1. Calculate the LCM of 180 and 594:

  The prime factorization of 180 is [tex]\(2^2 \times 3^2 \times 5\)[/tex].

  The prime factorization of 594 is [tex]\(2 \times 3^3 \times 11\)[/tex].

  The LCM is the product of the highest power of each prime factor:

  LCM [tex]\(= 2^2 \times 3^3 \times 5 \times 11 = 5940\)[/tex].

2. Calculate the GCF of 180 and 594:

  The common factors of 180 and 594 are [tex]\(2 \times 3 = 6\)[/tex]  

  So, GCF [tex]\(= 6\)[/tex].

Now, let's find the ratio between the LCM and the GCF:

[tex]\[ \text{Ratio} = \frac{\text{LCM}}{\text{GCF}} = \frac{5940}{6} = 990 \][/tex]

Answer:

A total of 72 passenger planes came in yesterday.

Explanation:

  Blue Sky International Airport handles passenger to cargo traffic in a ratio of 8 to 5.

  Number of cargo planes landed yesterday = 45

  Number of passenger planes landed = [tex]\frac{8}{5}[/tex] x  Number of cargo planes landed.

 Number of passenger planes landed yesterday = [tex]\frac{8}{5}[/tex] x 45

                                                                               = 8 x 9

                                                                               = 72 passenger planes.

 So a total of 72 passenger planes came in yesterday.

The number 6.62 x 10 in standard form can be written as 66.2.

It is required to write 6.62 x 10 in standard form.

Standard form directly represents the number and scientific notation represents the number in the form of a number multiplied by the power of tens.

So, the given number can be written as,

[tex]6.62 \times 10=\dfrac{662}{100}\times 10\\=\dfrac{662}{10}\\=66.2[/tex]

Therefore, the number 6.62 x 10 in standard form can be written as 66.2.

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Multiply 36.50 by 8 and then multiply that answer by 5 to get your answer

$1,460 a week

36.50 by 8 multiply the answer by 5 to get your answer $1,460 a week

12 of each color will be used.

                                                   hope it helps

Answer: There are 12 greatest number of arrangements that she can make and every balloon is used.

Step-by-step explanation:

Since we have given that

Number of white balloons = 24

Number of blue balloons = 60

We need to find the greatest number of arrangements that she can make and every balloon is used.

So, For greatest number of arrangements we will find H.C.F.

So, H.C.F. of 24 and 60 = 12.

Hence, there are 12 greatest number of arrangements that she can make and every balloon is used.

The number that, when raised to the 10th power and divided by the same number to the 7th power equals 27, is 3. This is resolved by simplifying the initial equation to realize that we are looking for the cube root of 27.

The question is asking for a number which, when raised to the 10th power and divided by the same number raised to the 7th power, equals 27. Let's denote the number as 'x'. The mathematical representation of this would be x10 / x7 = 27. Since x10 / x7 simplifies to x3, our equation becomes x3 = 27. Now if we solve this, the number 'x' equals the cube root of 27, which is 3.

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13.

y - the amount from the sale

x - a number of tickets

y = 5x + 40

Domain: x ∈ {0, 1, 2, 3, 4, 5}

Range = {40, 45, 50, 55, 60, 65}

15.

y - the cost of renting a law firm

x - a number of hour

y = 100x + 300

Domain: x ∈ {1, 2, 3}

Range = {400, 500, 600}

Y intercept means the y-coordinate of the point where the graph crosses the y-axis.

Given equation is:

[tex]-2x+6y=5[/tex]

Let x be 0, as at the y-intercept point, the x-coordinate of that point is always 0.

[tex]-2(0)+6y=5[/tex]

[tex]6y=5[/tex]

y=[tex]\frac{5}{6}[/tex]

Slope-intercept form is y = mx + b

where m is the slope of the line and b is the y-intercept of the line {the number without a variable}

-2x+6y = 5

6y = 2x+5

y= [tex]\frac{2x}{6}+\frac{5}{6}[/tex]

Hence, slope is [tex]\frac{2}{6}or\frac{1}{3}[/tex]