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3 years ago

What is the equation of the line that passes through the point (3,-7) and has a slope of -4/3?

Mathematics

1 answer:

Gemiola [76]3 years ago

3 0

Answer:

4x + 3y + 9 = 0

Step-by-step explanation:

When a slope of a line and a point passing through it is given then we use slope - one point form to determine the equation of the line.

It is given by:

$(y - y_1) = m (x - x_1)$

where $m$ is the slope of the line and

$(x_1, y_1)$ is the point passing through it.

Here, $m = \frac{-4}{3}$ and $(x_1 , y_1) = (3 , -7)$ .

Substituting in the formula $y + 7 = \frac{-4}{3} (x - 3)$

$\implies 3y + 21 = -4x + 12$

$4x + 3y + 9 = 0$

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Ghost, Inc., has no debt outstanding and a total market value of $369,600. Earnings before interest and taxes, EBIT, are project

arlik [135]

Answer:

Ghost Inc.

A1.

Earnings Per share (EPS)

EPS in normal projection is $4.61 per share

EPS in an expansion is $5.31 Per share

EPS in a recession is $3.51 Per share

A2.

Changes to EPS in an expansion is +15.18%

Changes to EPS in a recession is -23.86%

B1.

Earnings Per share (EPS)

EPS in normal projection is $7.23 per share

EPS in an expansion is $8.62 Per share

EPS in a recession is $5.01 Per share

B2.

Changes to EPS in an expansion is +19.23%

Changes to EPS in a recession is -30.71%

Step-by-step explanation:

Underlying Information:

Earnings before interest and taxes, EBIT projections = $51,000

Expansionary EBIT projections = $51,000 x (100% + 15%) = $58,650

Recessionary EBIT projections = $51,000 x (100% -24%) = $38,760

Tax Rate = 24%

Market to Book Ratio = 1.0

Stock Price is constant.

Solution to A1.

Scenario 1 (Projected Earnings)

Earnings Per Share (EPS) = Net Income (Earnings after Tax) divided by Outstanding Shares in Issue

Net Income = EBIT minus tax = $51,000 - ($51,000 x 24%)

= $51,000 - $12240

= $38,760

Outstanding shares in issue = 8,400 ordinary Shares

EPS = $38,760 divided by 8,400 shares = $4.61 Per share

Scenario 2 (Projected Earnings in a strong expansion)

Earnings Per Share (EPS) = Net Income (Earnings after Tax) divided by Outstanding Shares in Issue

Net Income = EBIT minus tax = $58,650 - ($58,650 x 24%)

= $58,650 - $14,076

= $44,574

Outstanding shares in issue = 8,400 ordinary Shares

EPS = $44,574 divided by 8,400 shares = $5.31 Per share

Scenario 3 (Projected Earnings in a Recession)

Earnings Per Share (EPS) = Net Income (Earnings after Tax) divided by Outstanding Shares in Issue

Net Income = EBIT minus tax = $38,760 - ($38,760 x 24%)

= $38,760 - $9,302.4

= $29,457.6

Outstanding shares in issue = 8,400 ordinary Shares

EPS = $44,574 divided by 8,400 shares = $3.51 Per share

Solution to A2.

1.Changes to EPS in an expansion = EPS (Expansion) minus EPS (normal projection), all divided by EPS (normal projection)

= (5.31 - 4.61) / 4.61

= +15.18% change during an expansion

2.Changes to EPS in a recession = EPS (Recession) minus EPS (normal projection), all divided by EPS (normal projection)

= (3.51 - 4.61) / 4.61

= -23.86% change during a recession

Underlying Information:

Debt issue = $185,000

Interest on debt issued = 6% = $11,100

Market to Book Ratio = 1.0

Stock Price is constant.

Therefore Share Price = Market Value divided by Outstanding shares in issue = 369,600 / 8400 = $44

This implies our proceeds of $185,000 from debt issue would have repurchased $185,000 divided by $44 = 4,205 ordinary shares

This decision to repurchase its shares indicates the shares outstanding will reduce by 4,205. New outstanding shares will now be 4,195 shares

*Earnings before interest and taxes, EBIT normal projections = $51,000 & Earnings Before Tax (EBT) = $51,000 minus $11,100 (debt interest) = $39,900

*Expansionary EBIT projections = $51,000 x (100% + 15%) = $58,650 & Earnings Before Tax = $58,650 minus $11,100 (debt interest) = $47,550

*Recessionary EBIT projections = $51,000 x (100% -24%) = $38,760 & Earnings Before Tax = $38,760 minus $11,100 (debt interest) = $27,660

Tax Rate = 24%

Solution to B1.

Scenario 1 (Projected Earnings)

Earnings Per Share (EPS) = Net Income (Earnings after Tax) divided by Outstanding Shares in Issue

Net Income = EBT minus tax = $39,900 - ($39,900 x 24%)

= $39,900 - $9,576

= $30,324

Outstanding shares in issue = 4,195 ordinary Shares

EPS = $30,324 divided by 4,195 shares = $7.23 Per share

Scenario 2 (Projected Earnings in a strong expansion)

Earnings Per Share (EPS) = Net Income (Earnings after Tax) divided by Outstanding Shares in Issue

Net Income = EBT minus tax = $47,550 - ($47,550 x 24%)

= $47,550 - $11,412

= $36,138

Outstanding shares in issue = 4,195 ordinary Shares

EPS = $36,138 divided by 4,195 shares = $8.62 Per share

Scenario 3 (Projected Earnings in a Recession)

Earnings Per Share (EPS) = Net Income (Earnings after Tax) divided by Outstanding Shares in Issue

Net Income = EBT minus tax = $27,660 - ($27,660 x 24%)

= $27,660 - $6,638.40

= $21,021.60

Outstanding shares in issue = 4,195 ordinary Shares

EPS = $21,021.60 divided by 4,195 shares = $5.01 Per share

Solution to B2.

1.Changes to EPS in an expansion = EPS (Expansion) minus EPS (normal projection), all divided by EPS (normal projection)

= (8.62 - 7.23) / 7.23

= +19.23% change during an expansion

2.Changes to EPS in a recession = EPS (Recession) minus EPS (normal projection), all divided by EPS (normal projection)

= (5.01 - 7.23) / 7.23

= -30.71% change during a recession

6 0

3 years ago

Find the area of the figure. Round to the nearest tenth if necessary.

baherus [9]

Hello!

First of all, let's find the triangle. As we can see, it is eight units long and four units tall. We can use the triangle formula and half the product.

4(8)=32

32/2=16

Now we need to find the area of the semicircle. We can use circle formulas and half our final answer. We will find the area using A= $\pi$ r².

We know that the diameter of this circle is eight. Therefore our radius is 4.

A= $4\pi$ ²

A= $16\pi$

Now we multiply.

16 $\pi$ ≈50.27

Now we add our triangle.

50.27+16=66.27

The nearest answer to this is B)66.2. It may have been a bit over as we used $\pi$ , not 3.14.

I hope this helps!

3 0

3 years ago

Find the median of the data.

kipiarov [429]

Answer:

92.5

Step-by-step explanation:

The data given:

93, 81, 94, 71, 89, 92, 94, 99

Put the data in the ascending order:

71, 81, 89, 92, 93, 94, 94, 99

Since the data size is even, the median is the average of middle two:

median = (92 + 93)/2 = 92.5

4 0

2 years ago