The area of a triangle is found using the formula: A=½bh
If b=3in. and h=8in., what is the area of the triangle?
Answer Choices
12 in.²

48 in²

24 in.²

5.5 in.²​

To calculate the gain on the sale of the office furniture, we need to determine the asset's book value and compare it to the sale price.

First, let's calculate the accumulated depreciation on the furniture. The furniture was purchased on January 1, 2014, and the straight-line depreciation method is used over 10 years with a salvage value of $80,200.

Depreciation per year = (Cost - Salvage Value) / Useful Life

Depreciation per year = ($746,800 - $80,200) / 10 years

Depreciation per year = $66,160

Next, we need to calculate the accumulated depreciation for the period from January 1, 2014, to May 1, 2021 (the date of the sale). This is approximately 7.33 years.

Accumulated Depreciation = Depreciation per year × Years

Accumulated Depreciation = $66,160 × 7.33 years

Accumulated Depreciation = $484,444.80

Now, we can calculate the book value of the furniture:

Book Value = Cost - Accumulated Depreciation

Book Value = $746,800 - $484,444.80

Book Value = $262,355.20

Finally, we can calculate the gain on the sale:

Gain on Sale = Sale Price - Book Value

Gain on Sale = $300,000 - $262,355.20

Gain on Sale = $37,644.80

Therefore, the gain that should be recognized on the sale of the office furniture is approximately $37,644.80.

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The gain that should be recognized on the sale of the office furniture is $84,080.

The gain is calculated by subtracting the equipment's book value from the sale price. This gain will be reported on the company's income statement. Here is how to calculate the gain:First, find the equipment's book value using the straight-line method of depreciation.

Straight-line depreciation is calculated by taking the difference between the equipment's original cost and its salvage value, and then dividing it by the number of years the equipment is used. The annual depreciation expense is then multiplied by the number of years the equipment is used to find the equipment's book value at the end of its useful life.

For this question, the book value of the equipment at the time of sale is:Cost of equipment: $746,800Salvage value: $80,200Depreciable cost: $746,800 - $80,200 = $666,600Annual depreciation: $666,600 ÷ 10 years = $66,660Book value at the end of 2020: $666,600 - ($66,660 x 7) = $156,420

Next, subtract the equipment's book value from the sale price to find the gain:Sale price: $300,000Book value: $156,420Gain: $143,580Finally, round the gain to the nearest dollar:$143,580 ≈ $143,580.00So the gain that should be recognized on the sale of the office furniture is $84,080.

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The expressions are simplified to give;

7. 4n³(3n² + 4)

8. -3x(3x² - 4)

9. 5(k² - 8k + 2)

10. -10(6 + 6n² + 5n³)

11. 3(6n³ - 4n - 7)

12. 9(7n³ + 9n + 2)

Algebraic expressions are defined as mathematical expressions that are composed of variables, coefficients, terms, factors and constants.

These algebraic expressions are also made up of arithmetic operations, such as;

To factorize the expressions, we have;

12n⁵ + 16n³

Find the common term

4n³(3n² + 4)

-9x³ - 12x

find the common term

-3x(3x² - 4)

5k² - 40k + 10

find the common terms

5(k² - 8k + 2)

-60 + 60n² + 50n³

find the common term

-10(6 + 6n² + 5n³)

18n³ -12n - 21

find the common term

3(6n³ - 4n - 7)

63n³ + 81n + 18

Find the common term

9(7n³ + 9n + 2)

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Answer:

precipitation, true

Step-by-step explanation:

the reason for this is that water such as rain, snow, hail are known as precipitation while evaporation is the act of a liquid turning into a gas while condensation is the act of a gas becoming a liquid. The water cycle makes it so that the water on Earth is constantly reused so it would be true

Capital asset pricing model (CAPM) Applications of Capital Asset Pricing Model (CAPM) are as follows;The most important application of CAPM is in the calculation of the cost of equity.

CAPM is used by financial analysts and investors to determine the appropriate rate of return for individual stocks and portfolios. CAPM is also useful in determining the required rate of return for capital projects. By calculating the cost of equity capital, companies can make better investment decisions by determining which projects will yield the greatest return on investment.

CAPM can be used in the valuation of assets, such as stocks, real estate, and other investments. Finally, CAPM is useful in evaluating risk.

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The statement that is NOT correct about hypothesis testing is: "We cannot eliminate both type l error and type II error at the same time."

In hypothesis testing, we aim to make a decision about a population parameter based on sample data. Type I error refers to rejecting a true null hypothesis, while Type II error refers to failing to reject a false null hypothesis. While it is not possible to completely eliminate both types of errors simultaneously, we can minimize the chances of committing either of them by choosing an appropriate significance level and conducting a power analysis.

Therefore, the statement that we cannot eliminate both Type I and Type II errors at the same time is incorrect.

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Answer:

Step-by-step explanation:

i think you should use the graph it will help you to get your answer and see what’s the slope

The total surface area of the pyramid is  335 square centimeters

The formula for determining the total surface area of a pyramid is expressed as;

TSI = 1/2(PI) + B

Given that;

Now, let's determine the base perimeter

Perimeter = 2( l + w)

Substitute the values

Perimeter = 2 ( 8 + 12)

Perimeter = 40 centimeters

The base area is given as;

Base area =  8(12)

Base area = 96 square centimeters

Substitute the values, we have;

Total surface area = 1/ 2 (40)(12) + 96

Total surface area = 240 + 96

Total surface area = 335 square centimeters

Hence, the value is 335 square centimeters

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Answer:

there is no equivalent ratio

Step-by-step explanation:

because 7 is a prime number

The inclination of the line with a slope of -5/2 is approximately 111.8°.

To find the inclination of the line whose slope is -5/2, follow these steps:

1. Recall the definition of the slope: the tangent of the angle of inclination (θ) is equal to the slope (m). In this case, m = -5/2. So, tan(θ) = -5/2.
2. To find the angle of inclination (θ), take the inverse tangent (arctan) of the slope. θ = arctan(-5/2).
3. Use a calculator to find the angle in degrees: θ ≈ -68.2°.

Since the inclination should be between 0° and 180°, add 180° to the negative angle: θ = -68.2° + 180° = 111.8°.

So, the inclination of the line with a slope of -5/2 is approximately 111.8°.

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The net change in the value of the function between x = 1 and x = 6 is 30.

To find the net change in the value of the function between the inputs of 1 and 6, we need to find the difference between the output values of the function at x = 1 and x = 6, and then take the absolute value of that difference.

First, we can find the output value of the function at x = 1:

f(1) = 6(1) - 5 = 1

Next, we can find the output value of the function at x = 6:

f(6) = 6(6) - 5 = 31

The net change in the value of the function between x = 1 and x = 6 is the absolute value of the difference between these two output values:

|f(6) - f(1)| = |31 - 1| = 30

Therefore, the net change in the value of the function between x = 1 and x = 6 is 30.

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The point estimate for the unknown population proportion is approximately 0.5761.

To find the point estimate for the unknown population proportion, we can use the formula:

Point Estimate = x / n

Given that x = 106 and n = 184, we can substitute these values into the formula:

Point Estimate = 106 / 184 ≈ 0.5761

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The amount you will pay back by the end of the term is; 162.18 dollar.

If n is the number of times the interested is compounded each year, and 'r' is the rate of compound interest annually, then the final amount after 't' years would be:

\(a = p(1 + r)^{t}\)

Given that you borrow $101 at 7% compounded annually for seven years, then we have;

P = 101 dollar

Rate = 7%

Times = 7 yr

Therefore,

\(a = p(1 + r)^{t}\)

\(a = 101(1 + 0.07)^{7}\\\\a = 101 (1.07)^7\\\\a = $162.18\)

Hence, The amount you will pay back by the end of the term is; 162.18 dollar.

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Answer:

A cheeseburger has 1090 calories and a taco supreme has 810 calories

To cut a 14-inch pizza into three equal area pieces using two parallel cuts placed symmetrically from the center, each piece will have an area of 150.

As we need to cut a 14-inch pizza into three pieces of equal area using two parallel cuts, we have to follow the steps given below

:Step 1: Cut the pizza with a line that goes through the center of the pizza and marks its diameter. This cut separates the pizza into two equal halves.

Step 2: The second cut needs to be made parallel to the first cut and needs to be at a distance of approximately 1/3 the diameter of the pizza from the first cut.

Step 3: Then, the pizza will be separated into three equal area pieces as required. As we have to cut the pizza into three equal area pieces, the area of each piece will be 150 square inches.

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If f(x) = √x and g(x) = 7x + b, then

f(g(x)) = f(7x + b) = √(7x + b)

If the plot of f(g(x)) passes through (4, 6), then

f(g(4)) = √(7•4 + b) = √(28 + b) = 6

Solve for b :

√(28 + b) = 6

(√(28 + b))² = 6²

28 + b = 36

b = 36 - 28

b = 8

Answer:

x = 1

Step-by-step explanation:

Both equations can be set equal to each other since they are both equal to y:

\(x-10=-4x-5\\5x-10=-5\\5x=5\\x=1\)

equate both equations !

x - 10 = -4x - 5

5x - 10 = -5

5x = 5

x = 1

therefore x = 1

The probability that Ephraim gets the same number of heads that Keiko gets is 3/8.

What is probability?

The proportion of favorable cases to all possible cases is used to determine how likely an event is to occur.

Here, we

Let K(n) be the probability that Keiko gets n heads, and let E(n) be the probability that Ephriam gets n heads.

K(0) = 1/2

K(1) =1/2

K(2) = 0 (Keiko only has one penny!)

E(0) = 1/2 ×1/2 = 1/4

E(1) =  1/2 ×1/2 +  1/2 ×1/2 = 1/2  (because Ephraim can get HT or TH)

E(2) =  1/2 ×1/2 = 1/4

The probability that Keiko gets 0 heads and Ephriam gets 0 heads is K(0)×E(0). Similarly for 1 head and 2 heads.

We get

P = K(0)× E(0) + K(1)×E(1) + K(2)× E(2)

P = 1/2 ×1/4 + 1/2 ×1/2 +0

P = 3/8

Hence, the probability that Ephraim gets the same number of heads that Keiko gets is 3/8.

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The Mean of the dispersion of z-scores will be 0, and the standard deviation will be 1. 

On the off chance that all of the scores within the populace are changed into z-scores, at that point the coming about the conveyance of z-scores will have a cruel (mean) of and a standard deviation of 1.

Usually, since the change of a crude score x to a z-score is given by:

z = (x - μ) / σ

where μ is the populace Mean.

and σ is the populace standard deviation.

When all scores within the populace are changed to z-scores, the Mean of the coming about dispersion of z-scores will be:

( Mean of z-scores)

= [(Mean  of crude scores) - μ] / σ

= (μ - μ) / σ =

So also, the standard deviation of the dissemination of z-scores will be:

(standard deviation of z-scores) = (standard deviation of crude scores) / σ = σ / σ = 1

In this manner,

The cruel of the dispersion of z-scores will be 0, and the standard deviation will be 1. 

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If all of the scores in the population are transformed into z-scores, the values for the mean and standard deviation for the complete set of z-scores will be a mean of 0 and a standard deviation of 1.

This is because the process of transforming scores into z-scores involves subtracting the mean of the population and dividing by the standard deviation, which effectively standardizes the data to have a mean of 0 and a standard deviation of 1. When all the scores in a population are transformed into z-scores, the mean of the complete set of z-scores will be 0 and the standard deviation will be 1. This is because z-scores represent the number of standard deviations a value is from the mean, and the transformation standardizes the distribution.

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Answer:

A,B,D

Step-by-step explanation:

(A) is correct because 5*900+15*300>4000

(B) is correct because 15*900+5*300>4000

(D) is correct because C+P must be less than or equal to 25

Answer:

see below

Step-by-step explanation:

¢78 per pack of 6 labels

costumer wants to buy 34 labels

= 34 labels   x   ¢ 78    

                        6 labels

= $4.42

bedroom = 14 ft. x 16 ft.

carpet cost = $2.49 per ft²

padding cost = $1.81 per ft²

find: total cost of carpet and padding

solution:

bedroom area = 14x16 = 224 ft²

carpet cost = $2.49 per ft²  x 224 ft² = $557.46

padding cost = $1.81 per ft² x 224 ft² = $405.44  

total                                                      = $ 963.2        

three makes = $9.87 per hour

two    makes = $15.35 per hour  

one   makes = $17.98 per hour

one   makes = $23.47 per hour

find: average pay for the seven workers:

solution:

add all rates divide it by number of workers

= 9.87 + 15.35 + 17.98 + 23.47

                        7

= 66.67

       7

=  $9.52

gasoline truck = 10,000 gallons full

if 4,781 gallons are delivered to gas stations

each gallon weights = 7.5 pounds apx.

find: what is the weight remaining gallons of gasoline in the 10,000 gallon tank?

solution:

a truck delivered 4,781 gallons to a 1 station

10,000 - 4,781 = 5,219 gallons

therefore, the weight of the remaining gasoline in the tank is:

= 5219 gallons  x 7.5 pounds

                                gallon

= 39,142.5 pounds

alternatively,

if a truck delivered 4,781 gallons per station:

10,000 = 2.09  (this means a gasoline truck can only deliver

 4,781                 two gas stations )

the remaining gasoline in the tank is:

= 10,000 - (2 x 4,781)

= 438 gallons of gasoline

therefore, the weight of the remaining gasoline in the tank is:

= 438 gallons  x 7.5 pounds

                                gallon

= 3,285 pounds

checking account balance = $1,266.73

write checks for $456.99, $35.00, $576.91 and $567.91

made a deposit of $892.14

find: what is your new balance?

solution:

= you write checks which is:

= $456.99, $35.00, $576.91 and $567.91

= $1,636.88 (note this is not a withdrawal)

 this means it doesn't affect the balance

= deposit of $892.14

new balance =  $1,266.73 + $892.14

                     = $2,158.87

alternatively,

if the write checks has been withdrawn, then deposited $892.14

the new balance would be = $1,266.73 - $1,636.88 + $892.14

                                             = $521.99

approximately 1250 people will be coming to get flu shot

if the shots are packed by the dozen:

find: how many dozen should be ordered to cover the estimate?

solution:

= 1250 people x      1 dozen  

                            12 flu shots

= 104.17 ⇒ 105 dozens

therefore, 105 dozens is required to cover 1250 people

wall is 81 ft wide x 52 ft tall.

paint will cover 500 ft² per gallon.

if paint cost $14.99/gallon

find: how much will it cost for enough to paint to cover the wall?

solution:

wall area = 81 x 52

               = 4,212 ft²

paint required =  4,212 ft²  x   1 gallon

                                                  500 ft²  

                        = 8.424 gallons of paint needed.

therefore, the cost of paint to cover the wall is:

= 8.424 gallons x $14.99/gallon

= $ 126.27

40 hours past. overtime pays = 1.5 times the rate

50 hours past. overtime pays = 2 times the rate

rate at less than 40 hours = $16.82

worked 56 hours in one week.

find: how much you earned?

solution:

normal  = 40 hours x $16.82          = $ 672.8

over 40 = 10 hours x 1.5 x $16.82  = $ 252.3

over 50 =  2 hours x 2 x $16.82     = $   67.2    

total                                                  = $ 992.38

therefore, the total money earned is

$ 992.38

20 ft long piece of steel weights 2.2 ton

4 ft is cut off

find: weight of the 4 foot in pounds

solution:

weight per foot = 2.2 ton

                              20 ft

                           = 0.110 ton/ft.

weight of four ft = 4 ft. x  0.110 ton

                                           1 ft.

                          = 0.440 ton x    2,240 pounds  

                                                         1 ton

                          = 985.6 pounds

odometer reads 52,513 miles

returned from trip = 84,756 miles

average gas mileage = 23.8 mpg.

find: how many gallons did you use?

solution:

mileage = 84,756 - 52,513

             = 32,243 miles

gallons used = 32,243 miles

                         23.8 mpg

                     =  1,354.7 gallons

Step-by-step explanation:

\(

\underline{\bf{Given\::}}

Given:

\underline{\bf{To\:find\::}}

Tofind:

\underline{\bf{Explanation\::}}

Explanation:

\boxed{\bf{\frac{1}{f} =\frac{1}{v} -\frac{1}{u} }}}}

\begin{gathered}\longrightarrow\sf{\dfrac{1}{-10} =\dfrac{1}{v} -\dfrac{1}{-30} }\\\\\\\longrightarrow\sf{\dfrac{1}{v} =\dfrac{1}{-10} +\dfrac{1}{30} }\\\\\\\longrightarrow\sf{\dfrac{1}{v} =\dfrac{-3+1}{30} }\\\\\\\longrightarrow\sf{\dfrac{1}{v} =\cancel{\dfrac{-2}{30} }}\\\\\\\longrightarrow\sf{\dfrac{1}{v} =\dfrac{1}{-15} }\\\\\\\longrightarrow\sf{v=-15\:cm}\end{gathered}

⟶

−10

1

=

v

1

−

−30

1

⟶

v

1

=

−10

1

+

30

1

⟶

v

1

=

30

−3+1

⟶

v

1

=

30

−2

⟶

v

1

=

−15

1

⟶v=−15cm

\boxed{\bf{M \:A \:G \:N\: I \:F \:I \:C\: A\: T \:I \:O\: N :}}

MAGNIFICATION:

\begin{gathered}\mapsto\sf{m=\dfrac{Height\:of\:image\:(I)}{Height\:of\:object\:(O)} =\dfrac{Distance\:of\:image}{Distance\:of\:object} =\dfrac{v}{u} }\\\\\\\mapsto\sf{m=\cancel{\dfrac{-30}{-15}} }\\\\\\\mapsto\bf{m=2\:cm}\end{gathered}

↦m=

Heightofobject(O)

Heightofimage(I)

=

Distanceofobject

Distanceofimage

=

u

v

↦m=

−15

−30

↦m=2cm

Thus;

The magnification will be 2 cm .

\)

An asymptote function is called such because it is a line that a curve approaches but never touches, or "asymptotically" approaches.

An asymptote is a line that a curve approaches but never actually touches. It is called an asymptote because the word comes from the Greek asymptōtos, which means "not falling together." Asymptotes are used in mathematics to describe curves that approach a particular line without ever intersecting it. For example, in a graph of a function, an asymptote is a line that the graph of the function approaches, but never intersects with, as it approaches infinity. Asymptotes are also used to describe straight lines in a plane that approach each other at a certain angle, but never meet. In both cases, the idea is that the line or curve approaches the asymptote, but never actually touches it, thus the name asymptaote.

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Answer:

Diagram 1

Step-by-step explanation:

This diagram does not represent a function because the x value 6 is outputting 2 different y values, 4 and 6. This goes directly against the rules of a function.

Answer:

112 students

Step-by-step explanation:

From this problem, we can gather that 80% of the students are not performing.

140*0.8=112

Answer:

angle 1 = 54° because this angle is a vertical angle of 54°, and vertican angles are always the same.

angle 2 = 126° because straight line = 180°, and there we have 54°, so 180-54=126°

angle 3 = 126° because this angle is vertical angle to 126°

angle 4 = 121° because this angle is alternative interior angle of the sum of the angles 12(54) and 67°

angle 5 = 59° because angle 5 and angle 4 makes a straight line, staring line = 180°, and 180°-angle 4(121°)= 59°

angle 6 = 121° because this anle is vertican angle of 121°

angle 7 = 59 because this angle is vertical angle of 59°

angle 8 = 59° because this angle is corresponding to angle 5 (59°), and corresponding angles are always the same

angle 9 = 54° because this angle is corresponding angle to 54°

angle 10 = 67 because angle 10, 9 and 8 creates straight line, straight line = 180°, angle 9(54) + angle 8(59)=113, and 180°-113°=67°, that means that angle 10 = 67°

angle 11 = 59 because this angle is corresponding to angle 7 (59°)

angle 12 = 54° because this angle is corresponding angle to angle 1 (54°)

that is it :)

We will get that the angle theta is:

θ = β/2

Remember that the sum of the interior angles of any triangle must be equal to 180°.

Now, looking at the triangle in the left, we can see that the top angle is equal to:

180 - 2α

The right angle is equal to:

180 - 2β

And the left angle is α

Then we can write:

α + (180 - 2α) + (180 - 2β) = 180

-α - 2β = -180

α = 180 - 2β

Now we can go to the other triangle, where theta is, and write:

α + β + 2θ = 180

Replacing what we found above, we get:

180 - 2β + β + 2θ = 180

-β + 2θ = 0

θ = β/2

That is the best simplification we can get with the given diagram.

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Answer:

21.4 m²

Step-by-step explanation:

To find the surface area of this whole triangular prism, we have to look at the bases (the triangles), find their surface area, then look at the sides (the rectangles) and find theirs.

Let's start with the triangles. The area of any triangle is \(\frac{bh}{2}\). The base of this triangle is 2m (because there are 2 one meters) and the height is 1.7m.

\(\frac{2\cdot1.7}{2} = \frac{3.4}{2} = 1.7\)

So the area of one of these triangles is 1.7m. Multiplying this by two, because there are two triangles in this prism:

\(1.7\cdot2=3.4\)

Now let's find the area of the sides.

The side lengths are 2 and 3, so

\(2\cdot3=6\), and there are 3 sides (including the bottom/floor) so \(6\cdot3=18\).

Now we add.

\(18+3.4=21.4\) m².

Hope this helped!

Answer: 21.4 square meters^2

Step-by-step explanation:

To find the center and radius of the sphere whose equation is given by x²+y²+z²+4x−2z−8=0, follow these steps:

Step 1: Rewrite the given equation in the standard form of a sphere.
The standard form of a sphere's equation is (x-a)²+(y-b)²+(z-c)²=r², where (a, b, c) is the center and r is the radius.

Step 2: Complete the squares for the x and z terms.
(x²+4x)+(y²)+(z²-2z)=8
(x+2)²-4+(y²)+(z-1)²-1=8

Step 3: Move the constants to the other side of the equation.
(x+2)²+(y²)+(z-1)²=13

Now the equation is in standard form. We can identify the center and radius. Step 4: Identify the center and radius.
The center (a, b, c) = (-2, 0, 1), and the radius r = √13. So, the center of the sphere is (-2, 0, 1), and the radius is √13.

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Answer:

1.) 900

2.) 300

3.) 59

4.) 48

5.) 12

Step-by-step explanation:

1.) 300 x 3 = 900

2.) 50 x 6 = 300

3.) 2,124 / 36 = 59

4.) 180 / 36 = 5 | 240 / 5 = 48

5.) 6 / 2 = 3 | 4 x 3 = 12

Hope this helps.

If there is something wrong, please let me know.

Proportional reasoning refers to the ability to compare and analyze relationships between two or more quantities that change in a consistent way. It involves understanding the concept of proportionality and applying it to solve problems.

1.) If a business jet burns 300 gallons of gasoline per hour, it burns 900 gallons of gasoline in a three-hour flight. This can be calculated by multiplying the burn rate of 300 gallons per hour by the duration of the flight, which is three hours.

2.) On average, one gallon of gasoline weighs approximately six pounds. Therefore, fifty gallons of gasoline weighs 300 pounds. This can be calculated by multiplying the weight of one gallon (six pounds) by the quantity of fifty gallons.

3.) For every one yard, there are thirty-six inches. To find the number of yards in 2,124 inches, we divide 2,124 by 36. The result is 59 yards. This can be calculated by dividing the total number of inches by the conversion factor of thirty-six inches per yard.

4.) A person who weighs 240 pounds burns 180 calories per mile of running. A person who weighs 48 pounds, burns thirty-six calories while running one mile. To find the number of pounds for which the person burns thirty-six calories while running one mile, we can set up a proportion. If we let x represent the weight in pounds, the proportion would be: 240 pounds / 180 calories = x pounds / 36 calories. Solving for x gives us x = 48 pounds.

5.) A rice casserole recipe serves four people and requires two tablespoons of butter. If a rice casserole requires six tablespoons of butter, it serves twelve people. This can be determined by setting up a proportion: 4 people / 2 tablespoons = 12 people / 6 tablespoons. Solving for the unknown number of people gives us 12 people.

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