On january 1, 2020, gators corp. acquired a machine at a cost of $900,000. it is to be depreciated on the straight-line method over a five-year period with no residual value. because of a bookkeeping error, no depreciation was recognized in gators' 2020 financial statements. the oversight was discovered during the preparation of gators' 2021 financial statements. depreciation expense on this machine for 2021 should be:

Answer: 8.2

Step-by-step explanation:

As angles in a triangle add to 180 degrees,

[tex]\angle A=180^{\circ}-121^{\circ}-31^{\circ}=28^{\circ}[/tex]

So, by the Law of Sines,

[tex]\frac{a}{\sin A}=\frac{b}{\sin B}\\\\a=\frac{b \sin A}{\sin B}\\\\a=\frac{9 \sin 28^{\circ}}{\sin 31^{\circ}}\\\\a \approx \boxed{8.2}[/tex]

The value of angle x is 127 degrees.

The angle x can be found as follows:

Angle on a straight line is 180 degrees.

Therefore, the sum of 53 degrees and x degrees is 180 degrees.

Therefore,

53 + x = 180°(sum of angles on a straight line)

subtract 53 from both sides of the equation

53 - 53 + x = 180 - 53

x = 127°

Therefore, the angle of x is 127 degrees.

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Answer:

A) [tex]\frac{15}{8}[/tex]

Step-by-step explanation:

remember Soh Cah Toa!!

[tex]sin=\frac{opposite}{hypotenuse}\\ cos=\frac{adjacent}{hypotenuse} \\tan=\frac{opposite}{adjacent} \\\\cos=\frac{8}{17}\\\\a^2+b^2=c^2\\8^2+b^2=17^2\\64+b^2=289\\b^2=225\\\sqrt{b^2} =\sqrt{225}\\b=15=opposite\\\\tan=\frac{15}{8}[/tex]

The fraction of the course that are male is 1/4

The given parameter is:

Female = 3 * Male

As a fraction, we have:

Female + Male = 1

Substitute Female = 3 * Male in the above equation

3 * Male + Male = 1

This gives

4 * Male = 1

Divide by 4

Male = 1/4

Hence, the fraction of the course that are male is 1/4

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Using it's concept, the domain of the function in interval notation is given by:

(-4,2).

The domain of a function is the set that contains all possible input values for the function. In a graph, it is the set that contains the values of x.

For this function, x varies between -4 and 2, with an open circle, meaning that -4 and 2 are not part of it, hence the domain is:

(-4,2).

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Answer:

Step-by-step explanation:

Area of trapezoid = ½ (a + b) h

½ (22 + 10) 8 =

½ 32 × 8 =

16 × 8 =

128 cm²

1) ray

2) line

3) line segment

4) adjacent angles

5) vertical angles

Answer:

1) RAY

2) LINE

3) LINE SEGMENT

4) VERTICAL ANGLES

5) VERTICAL ANGLES

The sum of the vectors given is -i

Vectors consists of y and x axis. They are plotted on an xy plane known as the argand diagram.

Given the following vectors

u = 3i - 8j

v = -4i + 8j

Take the sum of the vectors

u + v = (3i - 8j) + (-4i + 8j)

Take the sum to have

u + v = (3i-4i)+(-8j+8j)

u + v = -I

Hence the sum of the vectors given is -i

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The distance between the home plate and the second base is 127.3 feet

An equation is an expression that shows the relationship between two or more variables and numbers.

Let x represent the distance between the home plate and the second base. Using Pythagoras theorem:

x² = 90² + 90²

x = 127.3 feet

The distance between the home plate and the second base is 127.3 feet

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The distance between home plate and second base is  2√4050 feet.

In a square, all sides are equal in length.

If the distance between each pair of bases is 90 feet, it means that each side of the square (representing the distance along the edge) is also 90 feet.

Since home plate and second base are opposite corners of the square, they are connected by the diagonal of the square.

In a square, the diagonal forms a right triangle with the sides of the square.

Using the Pythagorean theorem, we can find the length of the diagonal (the distance between home plate and second base):

diagonal² = side² + side²

diagonal² = 90² + 90²

diagonal²= 8100 + 8100

diagonal² = 16200

diagonal =√16200

diagonal = 2√4050 feet.

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Answer: 3 units²

Step-by-step explanation: The area of a triangle is 1/2 (Bh); 1*1= 1 (1/2)= 1/2 units². For the other shape, I cut it into a square and another triangle. The square area is length times width; 1*1= 1 units². The final triangle is 3*1= 3*1/2= 1.5 units². Lastly you add all the areas together: 1.5+0.5+1= 3 units²

Answer:

A

Step-by-step explanation:

The first picture shows the parent function,

A function assigns a x for only one y.

The inverse is opposite

The inverse assign a y for only one x.

So the answer is the table that swap x and y values.

The coordinates for the parent function are

(0,0)

(2,1)

(4,2)

So the inverse should have

(0,0)

(1,2)

(2,4)

A shows that, so a is the answer

Using the z-distribution, the sample sizes are given as follows:

a) 822.

b) 1068.

A confidence interval of proportions is given by:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which:

The margin of error is given by:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

Item a:

The estimate is of [tex]\pi = 0.26[/tex], hence we solve for n when M = 0.03.

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.03 = 1.96\sqrt{\frac{0.26(0.74)}{n}}[/tex]

[tex]0.03\sqrt{n} = 1.96\sqrt{0.26(0.74)}[/tex]

[tex]\sqrt{n} = \frac{1.96\sqrt{0.26(0.74)}}{0.03}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.26(0.74)}}{0.03}\right)^2[/tex]

n = 821.2

Rounding up, a sample of 822 is needed.

Item b:

No prior estimate, hence [tex]\pi = 0.5[/tex].

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.03 = 1.96\sqrt{\frac{0.5(0.5)}{n}}[/tex]

[tex]0.03\sqrt{n} = 1.96\sqrt{0.5(0.5)}[/tex]

[tex]\sqrt{n} = \frac{1.96\sqrt{0.5(0.5)}}{0.03}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.5(0.5)}}{0.03}\right)^2[/tex]

n = 1067.11

Rounding up, a sample of 1068 is needed.

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Answer:

about 18.3 square meters

Step-by-step explanation:

Since the circle has radius 4 meters, the area of the circle is (4^2)π, or 16π square meters, The area of the square is (4√2)^2, or 32 square meters. Subtracting, we have 16π-32, or about 18.3 square meters, for the area of the shaded region.

Answer: 11

Step-by-step explanation:

By the secant-secant theorem,

[tex]5(5+7)=(JK)(15)\\\\60=(JK)(15)\\\\JK=4\\\\\implies IJ=15-4=11[/tex]

Answer:

1

Step-by-step explanation:

1 is ans p²=h²-b²

solved

Answer:

The side of the square can be 13 or 9

Step-by-step explanation:

Let x equal the unknown side of the rectangle and y equal the side of the square. The given information is that the area of the square is 4cm^2 larger than that of the rectangle. Mathematically this can be represented as

[tex]11x+4=y^2[/tex]

The second known is that their perimeters are equal so,

[tex]22+2x=4y[/tex]

Solve the first equation in terms of x and substitute it into the second and you get the quadratic

[tex]y^2-22y+117=0[/tex]

[tex](y-13)(y-9)=0[/tex]

Therefore your side length for the square can be either of those.

Answer:

534 = R + 211

Step-by-step explanation:

So the amount of texts Riley received can be expressed as a variable, and in this case I'll use "R". So we know Bella received 534 texts. and that's 211 MORE than riley. So R+211 should be the as 534. This gives you the equation: 534 = R + 211. and if you want to solve for R, you can subtract 211 from both sides to solve for R

Answer:

Range and median

Step-by-step explanation:

Range = 9 - 3 = 6

Median = 6

Mode = 9

Answer:

Fred scored 100
Bob scored 50
Gladys scored 20

Step-by-step explanation:

Fred = 50% * 200
        = 50/100 * 200
        = 0.5 * 200
        = 100

Bob  = 25% * 200
        = 25/100 * 200
        = 0.25 * 200
        = 50

Gladys = 10% * 200
            = 10/100 * 200
            = 0.1 * 200
            = 20

1. 80 sheep when increase in the ratio 5:4 becomes 100 sheep.

2. The perimeter of the shape is : 26cm

Perimeter is the outside boundary of a shape.

It is usually calculated by summing up all the length of the sides of that shape.

Analysis:

1. if the sheep is increased in the ratio 5:4

 then new number of sheep becomes 5/4 x 80 = 400/4 = 100 sheep

2. The perimeter of the shape is the sum of all the sides of the shape = 7 + 4 + 10 +5 = 26cm

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The solution to the variables using equations 1, 2 and 3 is x = 2, y = -1 and z = 3 and the solutions in part b hold for equation 4

There are three variables in the system

To solve the three variables, there must be at least three equations in the system of equations

Hence, the variables cannot be solved because the number of equations is not enough

We have:

3x + z + y = 8

5y - x = -7

3z + 2x - 2y = 15

Make x the subject in (2)

x = 5y + 7

Substitute x = 5y + 7 in (1) and (3)

3(5y + 7) + z + y = 8

15y + 21 + z + y = 8

16y + z = -13

3z + 2(5y + 7) - 2y = 15

3z + 10y + 14 - 2y = 15

3z + 8y = 1

Multiply 16y + z = -13 by 3

48y + 3z = -39

Subtract 3z + 8y = 1 from 48y + 3z = -39

48y - 8y + 3z - 3z = -39 - 1

40y = -40

Divide by 40

y = -1

Substitute y = -1 in x = 5y + 7

x = 5(-1) + 7

x = 2

Make z the subject in 16y + z = -13

z = -13 - 16y

Substitute y = -1

z = -13 - 16(-1)

z = 3

Hence, the solution to the variables using equations 1, 2 and 3 is x = 2, y = -1 and z = 3

We have:

4x + 5y - 2z = -3

Substitute x = 2, y = -1 and z = 3

4(2) + 5(-1) - 2(3) = -3

Evaluate

-3 = -3 --- this is true

Hence, the solutions in part b hold for equation 4

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Missing part of the question

The following equations are given:

Equation #1: 3x + z + y = 8

Equation #2: 5y - x = -7

Equation #3: 3z + 2x - 2y = 15

Equation #4: 4x + 5y - 2z = -3

The error Giovanna made in her calculation is multiplying 7 by 2 and adding with 5/8(step 3)

Her calculation:

Her error was multiplying 7 by 2 and adding with 5/8(step 3)

Correct calculation:

7(2 + 5/8)

= 14 + 35/8

= (112+35) /8

= 147/8

= 18 3/8

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The radius of the sector of the circle with the given area is: B. 3.

Area of sector of a circle = ∅/360 × πr².

Given the following:

Area of sector = 9/8 π cm².

∅ = 45 degrees

Plug in the values into the formula

9/8π = 45/360 × πr²

1.125 = 0.125 × r²

1.125/0.125 = r²

9 =  r²

r = 3 cm

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By taking the quotient between the money that they make and the time spent to make that money, see can see that Amy earned more profit.

Here we can define profit as the ratio between the money that they make, and the number of hours that they worked to make that money.

Matt earned $125, and spent $50 on shoes for his work, so he earned $75.

And worked 120 hours for these $75, so his profit per hour is:

M = $75/120 = $0.625

Amy worked for 110 hours, won $230 and spent $30 on clippers, then she won a total fo $200.

Her profit per hour is:

A = $200/110h = $1.82

We can see that Amy earned more profit.

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Answer:

y=1/2x+1

Step-by-step explanation:

First use slope formula.

[tex]\frac{y2-y1}{x2-x1}[/tex]

Plug in the information needed.

[tex]\frac{1-3}{0-4}=\frac{-2}{-4}=\frac{1}{2}[/tex]

The slope is [tex]\frac{1}{2}[/tex].

Now, use point-slope formula.

y-y1=m(x-x1)

Plug in the information needed.

y-3=1/2(x-4)

y-3=1/2x-2

y=1/2x+1

The equation of the line in slope-intercept form is y=1/2x+1.

Hope this helps!

If not, I am sorry.

Answer:

[tex]3 \log 2[/tex]

Step-by-step explanation:

Given expression:

[tex]\log 2 + \log \left(\dfrac{3}{2}\right)+\log \left(\dfrac{4}{3}\right)+\log \left(\dfrac{5}{4}\right)+\log \left(\dfrac{6}{5}\right)+\log \left(\dfrac{7}{6}\right)+\log \left(\dfrac{8}{7}\right)[/tex]

[tex]\textsf{Apply the \underline{Log Product Law}}: \quad \log_ax + \log_ay=\log_axy[/tex]

[tex]\implies \log \left(2 \cdot \dfrac{3}{2} \cdot \dfrac{4}{3} \cdot \dfrac{5}{4} \cdot \dfrac{6}{5} \cdot \dfrac{7}{6} \cdot \dfrac{8}{7}\right)[/tex]

Cross out common factors:

[tex]\implies \log \left(\diagup\!\!\!\!2 \cdot \dfrac{\diagup\!\!\!\!3}{\diagup\!\!\!\!2} \cdot \dfrac{\diagup\!\!\!\!4}{\diagup\!\!\!\!3} \cdot \dfrac{\diagup\!\!\!\!5}{\diagup\!\!\!\!4} \cdot \dfrac{\diagup\!\!\!\!6}{\diagup\!\!\!\!5} \cdot \dfrac{\diagup\!\!\!\!7}{\diagup\!\!\!\!6} \cdot \dfrac{8}{\diagup\!\!\!\!7}\right)[/tex]

Therefore:

[tex]\implies \log 8[/tex]

Factor the number:  8 = 2³

[tex]\implies \log 2^3[/tex]

[tex]\textsf{Apply the \underline{Log Power Law}}: \quad \log_ax^n=n\log_ax[/tex]

[tex]\implies 3 \log 2[/tex]

Answer: f(x+3), f(x+2), f(x), f(x-1/2), f(x-4), f(x-7)

Step-by-step explanation:

For y=f(x-a), the vertex is shifted a units to the right.

So, to order from left to right, we need to order them so that the value of a increases from the least to the most.

The relationship given in the graph is not function. Option C. is True.

Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in set of y. x is independent variable while Y is dependent variable.

The relationship given in the system is not a function. because the values of y is repeating at certain values of x. And the curve has number of discontinuity.

Thus, from the options given only option c describe the relationship given in the graph is not a function because there more than one value of x corresponding yo y - 2.  

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