find the slope of the line passing through the points (-2,2) and (-5,5)

Answer:

m< 2= 48°

Step-by-step explanation:

Complementary angles sum up to 90 degrees

We know that m< 1 = 42°

All we have to do is subtract 90 from 42 to find m< 2:

m< 2= 90 - 42

m< 2= 48°

Hope this answers your question :)

Answer:

100

Step-by-step explanation:

.001*100=.1

Answer:

100 thousandths

Step-by-step explanation:

The arrangement of the fraction from least to greatest is A. 5/8, 8/12, 3/4.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator, as well as the denominator, are both integers

The fraction can be changed to percentage to make it easier.

5/8 = 5/8 × 100 = 62.5%

8/12 = 8/12 × 100 = 66.7%

3/4 = 3/4 × 100 = 75%

The arrangement is 5/8, 8/12, 3/4.

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The y-intercept of the line is y = 2

What is an intercept?

A line's x-intercept and y-intercept are the points at which the x- and y-axes, respectively, are crossed.

Here,

A linear function has the following equation:

y = mx + b

Where m is the slope and b is the y-intercept, which is the value of y when x = 0.

We have given three points:

(-28, -54)

(-21, -40)

(-14, -26)

We use two of them to construct a system, to find values for m and b.

(-28, -54)

This means that when x = - 28 , y = - 54

so, y = mx + b

- 54 = - 28m + b

28m = b + 54

m = (b + 54)/28

Now, we have x = -21, y = -40

so, y = mx + b

- 40 = - 21m + b

we put the value of m here

- 40 = - 21 {(b + 54)/28} + b  we get,

7b - 1134 = - 40 × 28

b = 2

Hence, the y-intercept of the line is y = 2

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Answer:

(0,2)

Step-by-step explanation:

khan academy

If two points on the map measures 10 cm, with a scale of 1 : 1000 the actual distance is 10 000 cm

information gotten from the question

a scale of 1:1000

2 points on the map 10 cm = ?

Scale factors refer to the amount or the factor the image on a map was increased or reduced in comparison with the actual dimension of the image

A map has a scale of 1 : 1000

the scale factor is 1/1000 then 10/?

1/1000 = 10/?

cross multiplying gives

? = 10 000 cm

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The hopper will empty all of the grain in approximately 48.2 seconds .

Total amount of grain in the hopper = 2024.5 cubic feet

Rate at which the grain is emptied = 42 cubic feet /second.

Time taken to empty the grain

= 2024.5 / 42

= 48.202...

≈ 48.2 seconds

The ratio of two related quantities represented in several units is known as a rate. The numerator of something like the ratio expresses the rate of change for the other dependent variable if the denominator of both ratios is expressed as a single unit of each of these quantities and it is assumed that even this quantity can also be changed in a predictable way.

Hence the hopper will empty all the grain in about 48.2 seconds.

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The population means that the number of years worked is 14, and 73% of employees worked for the company for at least 10 years.

The mean is calculated by dividing the number of employees by the number of years of service. The total number of years of service is 417, hence the average will be

The average years worked = 417/30 = 13.9 ≈ 14 years

The % of workers who have worked there for at least ten years is calculated by calculating the number of employees who have ten or more years of service and dividing that number by the total number of employees.

The final result is presented as a percentage will be:

(10 years or more)/(total number) = 22/30 = 0.73 = 73%

Thus, the population means that the number of years worked is 14, and 73% of employees worked for the company for at least 10 years.

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The gallons of water and gallons of the premium antifreeze solution that must be mixed are 60 gallons and 120 gallons respectively.

In order to solve this word problem, we would assign a variable to the gallons of water and premium 60% antifreeze that is required, and then translate the word problem into algebraic equation as follows:

Since the premium antifreeze solution contains 60% premium antifreeze, we have the following mathematical expression:

w + p = 180      ....equation 1.

0.60p = 0.40(180)    ....equation 2.

From equation 2, we have:

0.60p = 0.40(180)

0.60p = 72

Premium antifreeze, p = 72/0.60

Premium antifreeze, p = 120 gallons.

For the gallons of water, we have:

w + p = 180

Water, w = 180 - p

Water, w = 180 - 120

Water, w = 60 gallons.

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Dwayne have to complete the race in 11.53 second or the speed of Dwayne  is 11.53 second/ 100 meter.

What is speed of an object?

Speed, expressed in terms of meters per second, is the rate at which an object's location changes. An item moves one meter in one second, for instance, if it starts at the origin and moves three meters in three seconds. The formula for speed is straightforward: time divided by distance.

Given that Chris, Kiona, Seiko, and Dwayne each run 100 meters in a relay

race. Chris runs his part of the race in 12.35 seconds, Kiona takes

13.12 seconds, and Seiko takes 11.91 seconds.

The total time that is taken by Chris, Kiona, and Seiko is (12.35 + 13.12 +  11.91) seconds = 37.38 seconds.

The team wants to break the record of 48.92 seconds.

To break the record, they should complete the race in 48.91 seconds.

Thus Dwayne have to run 100 meters in ( 48.91 - 37.38) = 11.53 seconds.

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Answer:

  21/3100000 ≈ 1/147619

Step-by-step explanation:

You want the scale of a map on which 4.2 cm corresponds to an actual distance of 6.2 km.

The scale of a drawing is the ratio of drawing distance to actual distance. It can be expressed a couple of ways. We can write the given scale as ...

  4.2 cm : 6.2 km

or, we can reduce it to ...

  2.1 cm : 3.1 km

Often, we like to have a single unit of map distance in this ratio, which would make it be approximately ...

  1 cm : 1.47619 km

Another way to write the scale of a map is as a fraction.

  (4.2 cm)/(6.2 km) = (0.042 m)/(6200 m) = 21/3100000

When this is expressed as a unit fraction, the denominator is a repeating decimal with a 6-digit repeat. We can round it to ...

  ≈ 1/147619 . . . . map scale

The scale of the map is ...

  21/3100000 ≈ 1/147619   or   2.1 cm : 3.1 km   or   ≈ 1 cm : 1.47619 km

__

Additional comment

You may need to round the answer to match one of your answer choices.

<95141404393>

The ratio of males to females in the cage is 2:3.

According to the question,

We have the following information:

For every 4 male birds in a cage there are 6 females.

The ratio of males to females = Number of males in the cage: number of females in the cage

Ratio of males to females = 4:6

We can convert this ratio into the simplest form by dividing both the numbers by 2 and this will also be the equivalent ratio of this obtained ratio.

Ratio of males to females = 2:3

Hence, the ratio of males to females in the cage is 2:3.

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The percentage of the campers prefer outdoor activities and reading is A. 24%.

From the information, the tree diagram shows campers branching off into two categories, prefer outdoor activities is labeled 80%, and those who prefer reading, which is labeled 30%.

Therefore, percentage of the campers prefer outdoor activities and reading will be:

= Percentage for outdoor × Percentage of reading

= 80% × 30%

= 24%

In conclusion, the correct option is A.

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Answer: 56% i did the test

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

Need the drawing but take the two cm measurements and multiply them together then multiply by 4   and then multiply by 4 again to get ft^2

Answer:

2 and 43.5

Step-by-step explanation:

The balance on the loan after a month is $623389.25.

The following can be deduced from the information given:

Principal = $250000

Time = 25

Rate = 6%

Interest = (Principal × Rate × Time) / 100

Interest = (250000 × 6 × 25) / 100

Interest = $375000

The total amount will be:

= Principal + Interest

= $250000 + $375000

= $625000

The balance of the loan will be:

= Amount - One month payment

= $625000 - $1,610.75

= $623389.25

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The expressions equivalent to 4^10​ are 2^20, 4^4 . 4^6, and  4^4 / 4^-6. Option B, option C, and option E are correct.

Some laws of exponents are:

We need to find all the expressions equivalent to 4^10​.

We will use laws of exponents for all the options one by one.

Option A:

2^5 . 2^2 = 2^(5 + 2) = 2^7

This is not equivalent to 4^10​.

Option B:

2^10 = 2^(2 * 10) = (2^2)^10 = 4^10

This is equivalent to 4^10​.

Option C:

4^4 . 4^6 = 4^(4 + 6) = 4^10

This is equivalent to 4^10​.

Option D:

4^7 . 4^-3 = 4^(7 + (-3)) = 4^4

This is not equivalent to 4^10​.

Option E:

4^4 / 4^-6 = 4^(4 - (-6)) = 4^10

This is equivalent to 4^10​.

So, 2^20, 4^4 . 4^6, and  4^4 / 4^-6 are equivalent to 4^10​.

So, option B, option C, and option E are correct.

Thus, the expressions equivalent to 4^10​ are 2^20, 4^4 . 4^6, and  4^4 / 4^-6. Option B, option C, and option E are correct.

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The width or short side is 12 feet

The length or long side is 18 feet

What is Area?

Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape.

On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies.

Consider your square as being composed of smaller unit squares. The number of unit squares necessary to completely cover the surface area of a specific 2-D shape is used to calculate the area of a figure. Some common units for measuring area include square cms, square feet, square inches, square meters, etc.

Let Width= x feet

so, as per question Length = x+6 feet

Area = Length x Width = x(x+6) = [tex]x^{2} +6x[/tex]

According to the question each side is increased 6 feet

New Length = x+12 feet

New Width = x+6 feet

New Area = Length x Width[tex]= 2x(x+6)[/tex] <the area is multiplied by 2>

Length x Width=[tex](x+6)(x+12) = 2x(x+6)[/tex]

x+12=2x

x=12 feet

so, original width = 12 feet

original length = 18 feet

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Answer:

[tex]16a^6x^4y^2[/tex]

Step-by-step explanation:

To simplify this expression, use the exponent rule stating that when an exponent is put to an exponent, the exponent values are multiplied (e.g., [tex](x^2)^2 = x^{2 \cdot 2} = x^4[/tex])

Using that rule, we get:

[tex](-4x^2ya^3)^2 = (-4)^2 \cdot x^{(2 \, \cdot \, 2)} \cdot y^2 \cdot a^{(3 \, \cdot \, 2)}[/tex].

This can be simplified to

[tex]16 \cdot x^4 \cdot y^2 \cdot a^6[/tex],

which can be written as:

[tex]16a^6x^4y^2[/tex]

using the commutative property of multiplication.

The correct statement regarding the critical value of the t-distribution is given as follows:

a) [tex]t_{\frac{\alpha}{2}} = 1.6753[/tex]

What defines which distribution should be used is whether the population standard deviation is known, as follows:

As stated in the problem, the population standard deviation is not known, hence the t-distribution is used, as the sample standard deviation can be calculated from the histogram.

The critical value is obtained using a t-distribution calculator, considering that:

Hence it is given as follows:

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9.5 is the largest number

Consecutive numbers are the number will follow each other in order.

The difference between every two numbers is one. if n is the number so, the consecutive number will be n+1,n+2 , . . . . . .

Let four consecutive numbers be a , a+1 , a+2 , a+3

where a+3 will be largest number

Given the sum of these is 32

a + a +1 +a + 2 + a +3 = 32

=> 4a + 6 = 32

=>4a = 26

=> a= 26/4

=> a = 6.5

putting the values,

consecutive number will be = 6.5 , 7.5 , 8.5 , and 9.5

9.5 is the largest number

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The ending inventory cost on December 31 for 21 units, under the three inventory methods, is as follows:

a) first-in, first-out (FIFO) method: $719

b) last-in, first-out (LIFO) method: $661

c) weighted average cost method: $690

The ending inventory cost is the difference between the cost of goods available for sale and the cost of goods sold determined by the various inventory methods.

Some of the inventory methods include:

Date       Activities         Units     Unit Cost   Total

Jan. 1      Inventory           16            $31       $496

Aug. 13   Purchase           14           $33         462

Nov. 30  Purchase           13           $35         455

Available for sale            43                       $1,413

Average cost = $32.86 ($1,413 ÷ 43)

Ending inventory             21

Units sold =                     22 (43 - 21)

a) FIFO:

Ending inventory = $719 (13 x $35 + 8 x $33)

Cost of goods sold = $694 ($1,413 - $719)

b) LIFO:

Ending inventory = $661 (16 x $31 + 5 x $33)

Cost of goods sold = $752 ($1,413 - $661)

c) Weighted Average:

Ending inventory = $690 (21 x $32.86)

Cost of goods sold = $723 (22 x $32.86)

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For the gross pay of $238.61 and given deduction Anita's net pay is equal to $181.59 at the rate of $9.45 per hour and she works for 25.25 hours.

When Anita works for 31 hours with the given conditions her gross pay and net pay is equal to $292.95 and $235.93 respectively.

As given in the question,

a. Anita get pay per hour = $9.45

Gross pay received by Anita = $238.61

Deductions :

Federal tax = $28.63

Society tax : $14.79

Medicare : $3.46

State tax : $10.14

Total deduction = $ ( 28.63 + 14.79 + 3.46 + 10.14 )

                          = $57.02

Net pay = Gross pay - total deduction

             = $ ( 238.61 - 57.02 )

             = $ 181.59

Let us consider Anita works for 'h' hours at the rate of $9.45,

9.45h = 238.61

⇒ h = 238.61/ 9.45

⇒ h = 25.25 hours

b. When Anita works for 31 hours

Her gross pay = 31 × 9.45

                       = $ 292.95

Deductions are same

Net pay = $ ( 292.95 - 57.02 )

            = $ 235.93

Therefore, for the gross pay of $238.61 and given deduction Anita's net pay is equal to $181.59 at the rate of $9.45 per hour and she works for 25.25 hours.

When Anita works for 31 hours with the given conditions her gross pay and net pay is equal to $292.95 and $235.93 respectively.

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x=-3.645 and x=1.645 is the solution for the given inequality.

A quadratic equation is a second-order polynomial equation in a single variable x , ax2+bx+c=0. with a ≠ 0 .

The given inequality is

y<x²+2x-6

a=1, b=2, c=-6

x=-b±√b²-4ac/2a

=-2±√2²-4(1)(-6)/2(1)

=-2±√4+24/2=

=-2±√28/2=

=-2+√28/2

=-2+5.29/2

=1.645

and -2-5.29/2

x=-3.645

Hence x=-3.645 and x=1.645 is the solution for the given inequality.

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Answer:

r = 20/7

x = 13.5

Step-by-step explanation:

Hello!

Solve for r by cross-multiplying:

The value of r is 20/7.

Solve for x by cross-multipying:

The value of x is 13.5.

Answer:

Step-by-step explanation:

7) r/2 = 10/7, value of r?

→ r/2 = 10/7

→ r = (10/7) × 2

→ r = (10 × 2)/7

→ [ r = 20/7 ]

Hence, value of r is 20/7.

8) 9/4 = x/6, value of x?

→ 9/4 = x/6

→ x/6 = 9/4

→ x = (9/4) × 6

→ x = (9 × 6)/4

→ x = 54/4

→ [ x = 27/2 ]

Hence, value of x is 27/2.

Jacob run 7/12 of the total distance around the school track.

What is distance?

Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in ordinary language.

Given: Sarah ran 7/8 of the distance around the school track.

Jacob ran 2/3 of Sarah‘s distance.

To find what fraction of the total distance around the track Jacob ran, we will find when solving 2/3 of 7/8 or symbolically

[tex](\frac{2}{3})(\frac{7}{8}) = \frac{14}{24} = \frac{7}{12}[/tex]

Hence, Jacob run 7 / 12 of the total distance around the school track.

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Answer: 22 square unit

Step-by-step explanation:

As each small square represents one square unit, we can count the squares and get the answer easily.