Greta currently works 45 hours per week and earns a weekly salary of $729. She
will soon be starting a new job where her salary will be increased by 10% and her hours reduced by 10%.

How much more will she be earning per hour at her new job?

PLEASE SHOW YOUR WORK!!

The solution is:

⇒ 6b = 95.94   (equation to determine cost of one box)

cost of one box 'b' = $`15.99

⇒ 12t = 95.94   (equation to determine cost of per tile)

cost of one tile t = $0.7995.

Given :

Jorge bought a crate of floor tiles for $95.94.

The crate had 6 boxes of floor tiles.

Each box contained 20 floor tiles .

To Find :

Write and solve equation to determine the cost per box'b'.

Write and solve a second equation to determine the cost per tile't'

Solution :

Cost of one box = b

There are 6 boxes

So, cost of 6 boxes = $  6b

Since Jorge bought 1 crate( = 6 boxes) of cost $95.94

⇒     (equation to determine cost of one box)

⇒6b = 95.94

⇒b =15.99

Thus cost of one box = $`15.99

Since 1 box 20 floor tiles

So, 6 boxes (=1 crate) contain tiles = 6*20 = 120 tiles

We are given that cost of 1 crate( = 6 boxes = 120 tiles) is $95.94

Cost of one tile = t

Cost of 120 tiles = $120t

⇒ (equation to determine cost of per tile)

⇒12t = 95.94

⇒t = 0.7995.

Thus cost of one tile t = $0.7995.

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Answer:

182 miles

Step-by-step explanation:

15 gallons -------------------------  420 miles

1 gallons --------------------------- 420/15 miles

1 gallons   ---------------------------  28 miles

6.5 gallons  -------------------------- 6.5 × 28 miles

6.5 gallons  --------------------------  182 miles

The car can go 182 miles on 6.5 gallons.

It is given that the a car can go 420 miles on a tank of gas of 15 gallons in a tank.

It is required to find the how many kilometers can this car go on 6.5 gallons.

Fraction number consists of two parts one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called denominator.

We have a car can go 420 miles on 15 gallons gas.

A car can go on 1 gallon = \(\frac{420}{15}\) = 28 miles ie.

A car can go on 1 gallon = 28 miles

On 6.5 gallons car can go = 6.5×28

= 182 miles

Thus, the car can go 182 miles on 6.5 gallons.

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Answer:

The type of error that the sociologist has made when he fails to reject the null hypothesis when it is false (and thus should have rejected it) is a:

c) Type II error.

Step-by-step explanation:

In Statistics, Type II error is made when the null hypothesis is accepted when it is not true (false).  The sociologist should have rejected the null hypothesis, but he fails to reject it.  He has, therefore, made a Type II error.  It is also called a "false negative." On the other hand, a Type I error is committed when the sociologist rejects the null hypothesis when he should have accepted it.  A Type I error is also called a "false positive."

Answer: $1.83

Step-by-step explanation:

1. Solve this problem: 1+2+4+6+8+10+12+14+16+18+20+22+24+26. There are 15 numbers for 15 days. You want to solve this because each day is doubled. For example: first day is 1 cent, second day is 2 cents, third day is 4 cents, and so on.

2. Answer is 183 cents.

3. Convert 183 cents to dollars.

4. Your answer is $1.83.

Hope it helps!

Answer:

$1.83.

You start with one cent, and add two more cents after that day.

Answer:

a) 30 people , b) C

Step-by-step explanation:

for a), 40 % answered yes. so 60% answered no.

But 20 people answered yes so 20/x = 0.4 which gives, x = 20/0.4

so x = total number of people = 50

the rest answered no so 50 - 20 = y

30 people answered no

b) C is the correct chart

Answer:

7 or 8

Step-by-step explanation:

Answer:

The answer is 6 = 3.

Step-by-step explanation:

The main address three letter sets so 1 = 3, two have three letters in order so 2 = 3, three have five letter sets so 3 = 5, four have four letters in order so 4 = 4, five have four letter sets so 4 = 5, lastly the number six have three sequential letters.

Therefore, 6 = 3 is your answer to this question.

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Answer:B

Step-by-step explanation: I did the test

The function is set of ordered pairs in which each X element has only a Y element.

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

The correct statement which does not represent a relation that is a function.

Since,

The vertical line test is used to determine the function exists or not. If the vertical line is moved across the graph one point of the graph is a function.  The line moving from point to point is a function.

Hence the option A is correct.

Thus, The function is set of ordered pairs in which each X element has only a Y element.

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Answer:

54 cm

Step-by-step explanation:

x = 11 -4 = 9

15 + 11 + 5 + 9 + 10 + 4 = 54

perimeter =54 cm

The exerxise aids as correctly identified are both hemispheres.

At the base, each of these hemispheres has a measure around it as 25 inches. This measure represnts the circumference of the circular surface at the base. We can use this bit of information to determine the radius as follows;

Where the circumference is given as 25, and the value of pi is taken as 3.14, we would now have;

We cross multiply this and we arrive at;

Rounded to two decimal places, we now have the radius as;

The formula for the surface area of a hemisphere is given as;

We now substitute for the value of the radius and we have the following;

Note however that the total surface area is an addition of the following;

The base area is

Therefore we now have the surface area as follows;

Rounded to two decimal places, this now becomes;

ANSWER:

Step-by-step explanation:

18.5-6.69

11.81

Answer:

X=3

Step-by-step explanation:

I feel like your trying to find the solution for x

the first step is to isolate the variable

3x+3-3=12-3

3x=9

now we will divide to find x

3x/3=9/3

x=3

Answer:

3x+ 3- 3= 12-3

1/3(3x + 3)= 1/3 (12)

3x +3/ 3= 12/3

Answer: .04

Step-by-step explanation:

Tara invests $555 into a savings account that has an interest rate of 12.6% and is compounded quarterly. It will take 18.6 years for the account to reach a balance of $5,600.

The amount that the lender charges the client above and beyond the initial amount is referred to as the interest rate. Given the time worth of money, a person who deposits money in a bank or other financial organisation also gets extra revenue known as interest received by the depositor.

Using the quarter compound formula given below-

\($ \rm A = P (1 + \frac{r}{4})^{4 \times t}\)

Where,

Interest in a year (r)= 12.6% = 12.6/100= 0.126

Actual amount (P)= $555

Final amount (A)= $5,600

Lets solve:

\(5,600 = 555(1+0.126/4)^{4t\)

Or, \((4.126/4)^{4t}= 5600/555\)

Or, 4t ln(4.126/4)= ln 5600/555

Or, 4t =74.532

Or, t ≈ 18.6

Hence the correct answer is 18.6 years

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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 measure of the largest angle in the kite is 26.67 (approx)°.

The given problem states that you cut out a piece of fabric in the shape of a kite so that the congruent angles of the kite are each 100°. The other two angles of the kite are not equal. If one of the angles is 4 times the size of the other, then the larger angle is 4x, and the smaller one is x.

We need to determine the measure of the largest angle in the kite. In order to find out the measure of the largest angle in the kite, we need to know the sum of all the angles in the kite. Let's recall the sum of angles in a kite. A kite is a quadrilateral whose four sides can be grouped into two pairs of adjacent sides that are equal in length. A kite has two opposite pairs of equal angles. The sum of the angles of a kite is 360°.In a kite, the angles can be represented as a, a, b, and c where a is the congruent angle and b and c are non-congruent angles.

Then, 2a + 2b = 360°2a + 2x + 4x = 360°2a + 6x = 360°2a = 360° - 6x2a = 180° - 3xa = (180° - 3x)/2

Since a = 100°, we can substitute it in the equation above, a = (180° - 3x)/2 and find the value of x.

Substituting a = 100° in the above equation, we get:

100 = (180 - 3x)/2100 × 2 = 180 - 3x200 = 180 - 3x20 = -3x/-3x = -20/(-3)x = 6.67 (approx)

Now we can substitute this value of x in the expression for the larger angle to find its measure. The larger angle is 4x, so it is equal to 4(6.67) = 26.67 (approx)°.

Therefore, the measure of the largest angle in the kite is 26.67 (approx)°.

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Answer:

P(A) = 0.3

Step-by-step explanation:

independent event:

P(A|B) = P(A) = 0.3

The value of P(A) is equal to 0.3 to the nearest tenth.

When one event's occurrence or non-occurrence doesn't affect the occurrence or non-occurrence of another event, then such events are called independent events. Comparing it with the chain rule will give

\(P(A|B) = P(A)\\P(B|A) = P(B)\)

It is showing that whether one occurred or not, the other one doesn't care about it (independence).

Given that A and B are independent events, A and C are dependent. P(A|B) = 0.3,

P(A|C) = 0.2.

We know that for the independent event:

P(A|B) = P(A)

Hence, P(A) = 0.3

The value of P(A) is equal to 0.3 to the nearest tenth.

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Solving a system of equations we can see that each pound of trail mix costs $3.50, and each pound of jelly beans costs $1.50

Let's define the variables:

Then we can write a system of equations so we will get:

5x + 3y = 22

2x + 12y = 25

To solve this, we can subtract 4 times the first equation fom the second one:

2x + 12y - 4(5x + 3y) = 25 - 4*22

2x + 12y - 20x - 12y = -63

-18x = -63

x = -63/-18

x = 3.5

That is the cost of each pound of trail mix, and replacing that in one of the equations:

2*3.5 + 12y = 25

y = (25 - 2*3.5)/12

y = 1.5

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To create an extended matrix in reduced row echelon form for a system of linear equations, you must first create the system of equations in standard form. In standard form, each equation is of the form "ax + by + cz + ... = d". where a, b, c, ... are the coefficients of the variables x, y, z, ..., d. is the constant term

For the solution (3.1+z, z), the linear system can be written as

x = 3.1 + z

y = z

To create an augmented matrix for this system, the equation can be written in the form "ax + by = d". where a, b, and d are the coefficients of variables x, y, and the constant term, respectively. The augmented matrix for this system is:

[ a b | d ]

[ 1 0 | 3.1 ]

[ 0 1 | 0 ]

To put this matrix in reduced row echelon form, we can perform the following row operations:

Subtract 3.1 times the first row from the second row, to get:

[ a b | d ]

[ 1 0 | 3.1 ]

[ 0 1 | -3.1 ]

Add 3.1 times the second row to the first row, to get:

[ a b | d ]

[ 1 0 | 0 ]

[ 0 1 | -3.1 ]

The resulting matrix is in reduced row echelon form.

For the solution (4,0,-3), we can write a system of linear equations as follows:

x = 4

y = 0

z = -3

The augmented matrix for this system is:

[ a b c | d ]

[ 1 0 0 | 4 ]

[ 0 1 0 | 0 ]

[ 0 0 1 | -3 ]

This matrix is already in reduced row echelon form, so we don't need to perform any row operations.

For the case where there is no solution set, we can write a system of linear equations such as:

x + y = 1

x + y = 2

The augmented matrix for this system is:

[ a b | d ]

[ 1 1 | 1 ]

[ 1 1 | 2 ]

This matrix is not in reduced row echelon form, but we can put it in reduced row echelon form by performing the following row operations:

Subtract the first row from the second row, to get:

[ a b | d ]

[ 1 1 | 1 ]

[ 0 0 | 1 ]

Divide the second row by 1, to get:

[ a b | d ]

[ 1 1 | 1 ]

[ 0 0 | 1 ]

The resulting matrix is in reduced row echelon form, and it represents a system of linear equations with no solution set.

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Answer:

8840

Step-by-step explanation:

Answer:

8,840

Step-by-step explanation:

The equivalent expression is 5 - 3x/2. Option D

Algebraic expressions are described as expressions that are made up of variables, their coefficients, factors and constants.

these algebraic expressions are also composed of mathematical operations. These operations includes;

From the information given, we have that;

1/ 4(8 - 6x + 12)

expand the bracket, we have;

Add the like terms

1/4(20 - 6x)

now, multiply the values, we have;

20 - 6x/4

Divide by the denominator

5 - 3x/2

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The complete question:

Simply the expression:

1/ 4(8 - 6x + 12)

Answer:

-729

Step-by-step explanation:

sequence is to multiply by -3 to get next term

Answer:

C.

Step-by-step explanation:

The GCF of 28 and 12 is 4

Soo... Distribute it to find the factors. 28/4=7 and 12/4 is 3.

4(7+3)

Answer:

I think the answer is 4 boys

Step-by-step explanation:

Let the no of boys be y.

No. of girls = 11

= 3 + 2y (equation)

3 + 2y = 11

3 - 3 + 2y = 11 - 3

2y = 8

2y/2 = 8/2

y = 4

Boys = 4

Answer:

Top-left system: (3,5)

Bottom-right

system: (-1,0)

Step-by-step explanation:

One way to solve a system of equations is to graph them. The solution is the point of intersection (where the lines cross). If you need to give the x-value and y-values separately, the first number in the pair is the x and the second number is the y.

Answer:

x=0

Step-by-step explanation:

A list of assertions and the justifications for each assertion are included in a two-column geometric proof.

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