|x – 4| > –3 will have what type of solution set

Answer:

10

i hope it will help you

Answer:

Step-by-step explanation:

No, For 69 to be a prime number, it would have been required that 69 has only two divisors, itself and 1. It has more than just itself and one there are four divisors including 1, 3, 23, and 69.

Answer: 350

Step-by-step explanation:

times 10 by 7 so do 7 times 10 then u get 70 then do 70 times 5 and youll get 350

Answer:

Part A:

1. Computation of Basic EPS

Basic EPS = (Net Income - Preferred Dividends) / Weighted Average Shares Outstanding²

Net Income = $120,000

Preferred Dividends = 4% x $50,000 = $2,000

Weighted Average Shares Outstanding = 100,000 (assuming no change in common stock during the year)

Basic EPS = ($120,000 - $2,000) / 100,000

Basic EPS = $1.18

2. Individual dilution/anti-dilution with decision making

We need to check if any of the convertible securities or stock options are dilutive or anti-dilutive by comparing their impact on EPS with the basic EPS.

Convertible Preferred: Each preferred share can be converted into 1.9 common shares (1,900 / 1,000). The conversion would increase the common shares outstanding by 1,900 and decrease the preferred dividends by $2,000.

EPS after conversion = ($120,000 - $0) / (100,000 + 1,900)

EPS after conversion = $1.16

Since this is lower than the basic EPS of $1.18, the convertible preferred is dilutive and should be included in the diluted EPS calculation.

Stock Options - A: Each option can be exercised at $12 to buy one common share when the average market price is $11. This means that the options are out of the money and would not be exercised by the holders. Therefore, they have no impact on EPS and are anti-dilutive.

Stock Options - B: Each option can be exercised at $7 to buy one common share when the average market price is $8. This means that the options are in the money and would be exercised by the holders. The exercise would increase the common shares outstanding by 4,000 and generate cash proceeds of $28,000 ($7 x 4,000). The cash proceeds can be used to buy back some common shares at the market price of $8. The number of shares bought back is 3,500 ($28,000 / $8). The net increase in common shares outstanding is 500 (4,000 - 3,500).

EPS after exercise = ($120,000 - $2,000) / (100,000 + 500)

EPS after exercise = $1.17

Since this is lower than the basic EPS of $1.18, the stock options - B are dilutive and should be included in the diluted EPS calculation.

Convertible Bonds: Each bond can be converted into 40 common shares (40,000 / 1,000). The conversion would increase the common shares outstanding by 40,000 and decrease the interest expense by $50,000 ($1,000,000 x 5%). The interest expense is net of tax, so we need to multiply it by (1 - tax rate) to get the after-tax amount. The tax rate is 30%.

EPS after conversion = ($120,000 - $2,000 + $50,000 x (1 - 0.3)) / (100,000 + 40,000)

EPS after conversion = $1.19

Since this is higher than the basic EPS of $1.18, the convertible bonds are anti-dilutive and should be excluded from the diluted EPS calculation.

3. Ranking of potential dilutors

We need to rank the potential dilutors from the most dilutive to the least dilutive based on their impact on EPS.

The most dilutive security is the convertible preferred with an EPS of $1.16.

The second most dilutive security is the stock options - B with an EPS of $1.17.

The least dilutive security is the convertible bonds with an EPS of $1.19.

4. Step-by-step inclusion of individual dilutors to arrive at reportable EPS with decision making.

We need to include the potential dilutors in order of their dilution until we reach a point where the next security would be anti-dilutive.

The first security to include is the convertible preferred.

EPS with convertible preferred = ($120,000 - $0) / (100,000 + 1,900)

EPS with convertible preferred = $1.16

The next security to include is the stock options - B.

EPS with stock options - B = ($120,000 - $0) / (100,000 + 1,900 + 500)

EPS with stock options

the answer to the equation is x=15

Approximately 17.65% of Ana's salary is withheld for taxes.

To calculate the percentage of Ana's salary that is withheld for taxes, we need to determine the amount of tax withheld and then express it as a percentage of her net salary.

Number of hours worked per week (H) = 25 hours

Hourly wage (W) = $10

Net salary (S) = $212.50

Calculate the total earnings before taxes:

Total earnings = Hours worked * Hourly wage

Total earnings = 25 hours * $10/hour

Total earnings = $250

Determine the amount of tax withheld:

Tax withheld = Total earnings - Net salary

Tax withheld = $250 - $212.50

Tax withheld = $37.50

Calculate the percentage of salary withheld for taxes:

Percentage withheld = (Tax withheld / Net salary) * 100

Percentage withheld = ($37.50 / $212.50) * 100

Percentage withheld ≈ 17.65%

Therefore, approximately 17.65% of Ana's salary is withheld for taxes.

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Answer:

  GHc 208.33 per day

Step-by-step explanation:

Gloria's pay is the product of her daily rate and the number of days she works. This relation can be used to find her daily rate.

__

  (pay for 12 days) = (daily rate) × (12 days)

  GHc 2500 = (daily rate) × (12 days)

Dividing both sides of the equation by (12 days), we find the daily rate to be ...

  (GHc 2500)/(12 days) = (daily rate)

  GHc 208.33/day = daily rate

Gloria's daily rate of payment is GHc 208.33 per day.

Answer:

9460

Step-by-step explanation:

Answer:

x^2+9x+20

Step-by-step explanation:

(x + 4) × (x + 5)

x^2+9x+20

Answer:

A

Step-by-step explanation:

It is option A: -2, -1, 0, 1

Number of seats in each row is 51 given that a rectangular auditorium seats 2244 people and number of seats in each row exceeds the number of rows by 7. This can be obtained by assuming the value of number of seats in each row, forming quadratic equation and using quadratic formula to find root.

Here in the question it is given that,

We have to find the number of seats in each row.

Let us assume that the number of seats in each row be x.

From the given statement, number of seats in each row exceeds the number of rows by 7, we can write that,

Number of seats in one row = Number of rows + 7

x = Number of rows + 7

⇒ Number of rows = x - 7

Total number of seats in the auditorium can be written as,

⇒ (Number of seats in one row)(Number of rows) = Total number of seats

(x)(x - 7) = 2244

x² - 7x = 2244

⇒ x² - 7x - 2244 = 0

By using quadratic formula we can find the root,

x = (-b ± √b² - 4ac)/2a

here in the question, a = 1, b = -7, c = -2244

√b² - 4ac = √(-7)² - 4(1)(-2244)

√b² - 4ac = √49 + 8976

√b² - 4ac = √9025

√b² - 4ac = 95

x = (-b ± √b² - 4ac)/2a

x = (7 ± 95)/2

x = 102/2 or x = -88/2

⇒ x  = 51 or x = -44

Hence number of seats in each row is 51 given that a rectangular auditorium seats 2244 people and number of seats in each row exceeds the number of rows by 7.

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Answer:

312.3

Step-by-step explanation:

Answer:

it increased by 15%

Step-by-step explanation:

im just omega smart

Answer: 53.1

Step-by-step explanation: Divide 35.40 by 2 to get 17.7. now add 35.40 with 17.7 and you get 53.1

The absolute value of the Rational number -474/513 is 474/513.

To find the sum of the rational numbers -8/9 and -2/57, you need to have a common denominator. The least common multiple (LCM) of 9 and 57 is 513. So, you can rewrite the fractions with a common denominator:

-8/9 = (-8/9) * (57/57) = -456/513

-2/57 = (-2/57) * (9/9) = -18/513

Now, you can add the fractions:

-456/513 + (-18/513) = (-456 - 18)/513 = -474/513

To find the absolute value of the rational number -474/513, you simply ignore the negative sign and take the value as positive:

| -474/513 | = 474/513

Therefore, the absolute value of the rational number -474/513 is 474/513.

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Answer:

4 packets

Step-by-step explanation:

A=L x W              8 2/3= 26/3

78/12  =3/4 x 26/3  

78/12= 6 1/2

6 1/2 divided by 2 is 3 1/4

Hope this helps let me know if you need more explaining

Solution

AB and A' B' are on distinct parallel lines. TRUE

Since when we apply the scale factor the new A'B' is on a different line but parallel

AD and A'D' are on the same line. FALSE

The new triangle with the scale factor produce an A'D' line different

Answer:

BC = 88.88

Step-by-step explanation:

Comment.

This looks like an example of the cos law.

Givens

AB = 100 m

<A = 60 degrees

AC = 70 m

Cos(60) = 1/2

BC = ?

Formula

BC^2  = AB^2 + AC^2 - 2*AB*AC * Cos(60)

Solution

BC^2 = 100^2 + 70^2 - 2*100*70 * 1/2     1/2 and 2 cancel out

BC^2 = 10000 + 4900 - 7000      

BC^2 = 7900                                             Take the sqr root of both sides

√BC^2 = √7900

BC = 88.88

Answer:

-35/-7=5

Step-by-step explanation:

Diviser par de nombre négatif alors sa devient positif pareil pour la multiplication

Answer:

\(z=\frac{0.45 -0.47}{\sqrt{\frac{0.47(1-0.47)}{631}}}=-1.007\)  

Now we can find the p value with the alternative hypothesis and using this probability:

\(p_v =P(z<-1.007)=0.157\)  

Since the p value is higher than the significance level given of 0.05 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true proportion of interest is not significantly lower than 0.47

Step-by-step explanation:

Information given

n=631 represent the random sample selected

X=284 represent the people who said that they thought unemployment would increase

\(\hat p=\frac{284}{631}=0.45\) estimated proportion of people who said that they thought unemployment would increase

\(p_o=0.47\) is the value that we want to test

\(\alpha=0.05\) represent the significance level

z would represent the statistic

\(p_v{/tex} represent the p value

System of hypothesis

We want to verify if the proportion of Australians in November 1997 who believe unemployment would increase is less than the proportion who felt it would increase in July 1997 (0.47), then the system of hypothesis are:  

Null hypothesis:\(p\geq 0.47\)  

Alternative hypothesis:\(p < 0.47\)  

The statistic would be given by:

\(z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}\) (1)  

Replacing the info given we got:

\(z=\frac{0.45 -0.47}{\sqrt{\frac{0.47(1-0.47)}{631}}}=-1.007\)  

Now we can find the p value with the alternative hypothesis and using this probability:

\(p_v =P(z<-1.007)=0.157\)  

Since the p value is higher than the significance level given of 0.05 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true proportion of interest is not significantly lower than 0.47

Answer:

The best test to see if more mosquitoes are attracted to people after drinking beer is the z-test for the difference in proportion of two populations

Step-by-step explanation:

The study tested if drinking bear increases the attractiveness to mosquitoes

The number of people the taking part in the study, n = 30 people

The total number of mosquitoes in the study = 50 mosquitoes

The proportion of mosquitoes flying to each volunteer is measured before and one hour after consuming bear

The mean number of mosquito flying towards a volunteer can be found by summing the other proportions that fly towards the 30 volunteers and dividing by n₁ = 30, before and n₂ = 30 after the respondents had bear to obtain \(\hat{p}_{1}\) and \(\hat{p}_{2}\)

Given that the variances are equal and the sum of the sample for the two tests, n₁ + n₂ = 60 > 30, it is, best to use the the z-test for the difference in proportion as follows;

\(Z=\dfrac{\hat{p}_1-\hat{p}_2}{\sqrt{\hat{p} \cdot (1-\hat{p}) \cdot \left (\dfrac{1}{n_{1}}+\dfrac{1}{n_{2}} \right )}}\)

Where the pooled mean, \(\hat p\), is given as follows;

\(\hat p = \dfrac{n_1 \cdot \hat p_1 + n_2 \cdot \hat p_2}{n_1 + n_2}\)

Answer:

A: 9:5  B: 5:14

Step-by-step explanation:

Answer:

green line or "b"

Step-by-step explanation:

we can set this up into the slope intercept form

y=mx+b

where m is the slope and b is y intercept

12=3x+4y

-3x -3x

-3x+12=4y

/4.  /4.  /4

-3/4x+3=y

we can see the only line with a negative slope and a y intercept at 3 is the green line or "b"

hopes this helps please mark rainliest

Answer:

84 cookies

Step-by-step explanation:

First, find the amount she bakes per minute. It is given that Marissa bakes 30 cookies every 15 minutes, or:

30 cookies/15 minutes = 2 cookies/minute.

Marissa bakes 2 cookies per minute. Multiply 2 with 42 minutes to find the total cookies baked in 42 minutes:

42 x 2 = 84

84 cookies is your answer.

~

Answer: 84 cookies

Step-by-step explanation:

30 cookies = 15 minutes

? cookies = 1 minute

30 ÷ 15 = 2

2 cookies = 1 minute

? cookies = 42 minutes

2 x 42 = 84

84 cookies = 42 minutes

--> if this is right can u plz mark me brainliest.

The x-intercept is (3.2, 0), and the y-intercept is (0, -32) if the equation of the line is y = 10x - 32.

Answer:  x= 3.2

Step-by-step explanation:

by graphing we can see where the line crosses the x axis at 3.2

I attached a graph to show you this method

to solve algebraically, y = 10x - 32 is your equation

put this in standard form ax + by = c

-10x + y = -32

to solve for x, substitute 0 for y and solve

-10x + 0 = -32

divide both sides by -10

-10/-10 x = -32/ -10

x = 3.2

Answer:

the correct answer is 193

Step-by-step explanation:

25×1-0=25

25×2-1=49

49×2-1=97

97×2-1=193

Answer:

The solutions are

x = -1, 1, -2√2, and 2√2.

Step-by-step explanation:

Given the equation

x^4 - 9x² + 8 = 0

Let u = x², then the equation becomes

u² - 9u + 8 = 0

u² - u - 8u + 8 = 0

(u² - u) - (8u - 8u) = 0

u(u - 1) - 8(u - 1) = 0

(u - 8)(u - 1) = 0

u - 8 = 0

=> u = 8

Or

u - 1 = 0

=> u = 1

For u = 8

=> x² = 8

=> x = ±√8 = ±2√2

For u = 1

=> x² = 1

=> x = ±√1 = ± 1

Answer:

B

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

2+2=4

Answer:

Step-by-step explanation:

4