Eddie Fantin is paid every two weeks. For the first week of his pay period he worked 42 hours, 4 of which were overtime hours. In the second week he worked 40 regular hours and 7 overtime hours. His regular pay rate is $14.40 an hour with time-and-a-half for overtime. What are his regular, , overtime, and total wages for the two weeks?

Using compound interest, the amount in the account at the end of the day on her 11th birthday is $240,019.25.

To solve this problem, we can use the formula for compound interest:

A = \(P(1 + r/n)^{(nt)}\)

where A is the amount of money in the account at the end of the 11th year, P is the principal amount (initial deposit), r is the annual interest rate (9%), n is the number of times interest is compounded per year (once annually), and t is the number of years (11).

First, we need to calculate the total amount of money that Gilberto deposited into the account over the 11 years:

1500 + 1500 × 10 = $16,500

Next, we can plug the values into the formula and solve for A:

A = 1500\((1 + 0.09/1)^{(1 * 11)}\) + 1500\((1 + 0.09/1)^{(2 * 11)}\) + ... + 1500\((1 + 0.09/1)^{(11 * 11)}\)

A = 1500 × [\((1.09)^{11}\) + \((1.09)^{22}\) + ... + \((1.09)^{121}\)]

A = 1500 × [\((1.09^{11}\) - 1)/(1.09 - 1)]

A = 1500 × [(1.315 - 1)/(0.09)]

A = $240,019.25

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The option that specifies the graph that matches the graph of the system of equations: 7·x + 2·y = -6, 6·x - 7·y = 21 is option a.

a. A line includes points negative 2 comma 4 and 0 comma negative 3. A line includes points 6 comma 2 and 0 comma negative 3

A system of equations consists of two or more equations that have common variables and operate simultaneously.

The system of linear equations is presented as follows;

7·x + 2·y = -6...(1)

6·x - 7·y = 21..(2)

The above system of equation can be presented in slope-intercept form as follows;

The equation (1) can be evaluated as follows;

7·x + 2·y = -6

2·y = -6 - 7·x

y = -3.5·x - 3

The slope of the above equation is -3.5, the y-intercept is the point (0, -3)

When x = -2, y = -3.5 × (-2) - 3 = 4. A point on the graph is therefore, the point (-2, 4)

The equation (2) can be evaluated as follows;

6·x - 7·y = 21

6·x = 21 + 7·y

6·x - 21 = 7·y

7·y = 6·x - 21

y = 6·x/7 - 21/7 = 6·x/7 - 3

y = 6·x/7 - 3

The slope of the graph of the equation (2) is therefore (6/7)

The coordinates of the y-intercept of the graph is; (0, -3)

When x = 6, y = 6 × 6/7 - 3 ≈ 2.14

A point on the graph is the point (6, 2.14)

The graph that most closely matches the system of inequalities is option a.

a. A line includes points -2, 4) and (0, -3). A line includes points (6, 2) and (0, -3)

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Answer:

\(x = -\frac{12}{5}\)

Step-by-step explanation:

To solve the equation, isolate x. Whatever you do to isolate x one on side, you must do to the other.  

1) Multiply both sides by 9 to get rid of the fractions.  

\(\frac{21-4x}{9} +\frac{8x+15}{3} = 2 \\21-4x + 3(8x + 15) =18 \\\)

2) Distribute the 3 to 8x and 15. Then, combine like terms.

\(21-4x + 24x + 45 = 18 \\66 + 20x = 18\)

3) Move the 66 to the other side, subtracting 18 by 66, then divide each side by 20 to finally isolate x.

\(20x = -48\\x = -\frac{48}{20} \\x =- \frac{12}{5}\)

Thus, \(x = -\frac{12}{5}\).

A. a^1/12

When dividing two exponents with the same base, subtract the denominator exponent from the numerator's exponent.

the difference is the value of the new exponent with the same base.

Answer:

5 1/2 + 3/4

11/2 + 3/4

22+3/4

25/4

=6 1/4

Answer: 28.25%

Step-by-step explanation:

113/400=0.2825=28.25%

Answer:

Step-by-step explanation:

360

Answer:

3.012  

Step-by-step explanation:

Let use x to represent the length of time  some computer part may work

where ; we have a sample of  size n = 80

Say \(X_1, X_2, ... X_{80\)

\(X_i\)  \(\approx\) \(exp (\lambda)\)   where ( λ =26 days)

\(E( \bar X) = \frac{1}{n} \sum \limits^n_{i=1} E( {x_i})= 26\)

\(V(\bar X) = \frac{1}{n^2} \sum \limits ^n_{i=1} U(X_i) = \frac{(26)^L}{n}\)

So find \(\bar X 's\) distribution using the Normal approximation.

\(\bar X \approx N (26, \frac{(26)}{n}^L)\)

\(Z = \dfrac{\bar {X} - 26}{\frac{26}{\sqrt n}} \approx N (0,1)\)

However, let's determine c such that:

\(P (-c \leq \bar x \leq c) = 0.8 \\ \\ P ( \dfrac{-c-26}{\frac{26}{\sqrt n}} \leq \dfrac{\bar x -26 }{\frac{26}{n} } \leq \dfrac{c-26}{\frac{26}{\sqrt n}}) =0.8\)

\(P ( \dfrac{-c-26}{\frac{26}{\sqrt n}} \leq Z \leq \dfrac{c-26}{\frac{26}{\sqrt n}}) =0.8\)

where; \(Z \approx N (0,1)\)

\(P ( Z > \dfrac{c-26}{\frac{26}{\sqrt n}}) =0.15 = P ( Z < \dfrac{-c-26}{\frac{26}{\sqrt n}})\)

\(\dfrac{c-26}{\frac{26}{\sqrt n}}= 1.036\)

\(c= 26+\frac{26}{\sqrt 80}}* 1.036\)

c = 29.0115

Given that :

The 80% percentile of the distribution of the average is of the form

E(X) + c

Then;

29.0115-26 = 3.0115

≅ 3.012    (to 3 decimal place)

Answer:

Step-by-step explanation:

y= 53/3 prob wrong but idek

Answer:

if c = 6, the d= 8c = 8(6) = 48.

Step-by-step explanation:

Let c = weight of cat.

Let d = weight of dog.

     d = 8c                  (the dog weights 8 times as much as the cat)

d + c = 54                  (together, they weigh 54 pounds)

Substitute  8c  for  d  from the first equation into the second equation:

8c + c = 54

     9c = 54

       c = 6

if c = 6, the d= 8c = 8(6) = 48.

Calculator Use

Calculate the sale price you will pay for an item based on the type of discount in the sale promotion:

Percent off list price

Fraction off list price

Multi-item discount

You can also compare discounts to find the lowest price for an item. Enter a percentage off price, fraction off price, multiple items for the price of one or other "two-for" type discounts. Compare the final discounted price for each in the answer table.

Delete any pricing inputs you don't need for your calculations.

Sale Price Formulas and Calculations

Percent Off Price Formula

Discounted price = List price - (List price x (percentage / 100))

Example: Sale price is 25% off list price of $130

Convert 25% to a decimal by dividing by 100: 25/100 = 0.25

Multiply list price by decimal percent: 130*0.25 = 32.50

Subtract discount amount from list price: 130 - 32.50 = 97.50

With the formula:

130 - (130*(25/100)) =

130 - (130*0.25) =

130 - 32.50 = 97.50

25% off $130 is $97.50

Answer:

103.96

Step-by-step explanation:

100% (full price)                                                             --> 129.95

80% (retail price = 100%(full price) - 20% (discount)) --> x

x = 80*129.95/100 = 103.96

Answer:

number of non students=140, students=280

Step-by-step explanation:

let non students be x.

so according to condition, non students=x*9

students=2x*7

now,

2x*7+x*9=3220

so, x=140

Answer:

A

Step-by-step explanation:

Here, we want to find the value farthest to the right here.

What this means is that we want the value that is most positive. The values farthest to the right side are the most positive;

A is 10-(-7) = 17

B is 3

C is -17

D is -3

The value farthest to the right is 17 which is A and it is the most positive value

The number she'd have is:

Explanation:

First, let's see which number is in the tens place and which number is in the ones place (the units place).

In the number 548, the place value of 5 is hundreds, the place value of 4 is tens, and the place value of 8 is ones (or units).

So if Sera adds two to the units, she'll have 10. But, since we can't write the number as 5410 (that would be a totally different number), we just write 0 in the units place, and shift 1 to the tens place, which gives us :

550

That's not all, since we also add 1 to the tens:

560

The cost of making 35 items is 1100 and the domain is (-∞,∞)

The cost of making 35 items :

plug the value into the cost equation

C(35) = 10(35) + 800

C(35) = 350 + 800

C(35) = 1100

Hence, cost of making 35 items is 1100

Since the value of X can be any real number, we can plug in any real number for x and get a real number output.

Hence, the domain = (-∞,∞)

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Answer: The expression 2√2 + √50 is equivalent to 7√2.

Step-by-step explanation: When 2√2 + √50 is added together, the result if 7√2.

Answer:

translation 2 units down and 90

rotation about the origin

Step-by-step explanation:

Answer:

the value of r that makes the slope of the line passing through (3, 5) and (-3, r) equal to 3/4 is r = 1/2

Step-by-step explanation:

We can use the formula for the slope of a line passing through two points, which is:

m = (y2 - y1)/(x2 - x1)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

In this case, we have two points (3, 5) and (-3, r), and we know that the slope m is 3/4. So we can write:

3/4 = (r - 5)/(-3 - 3)

Simplifying this equation, we get:

3/4 = (r - 5)/(-6)

Multiplying both sides by -6, we get:

-9/2 = r - 5

Adding 5 to both sides, we get:

r = -9/2 + 5

Simplifying, we get:

r = 1/2

Answer: 3/4 is greater than 1/2  

                                   >

Step-by-step explanation:

We know that,

each digit in a number has a place value. The place a number occupies in a number tells us its importance. The product of a number and the digit value it occupies gives the digit value.

What are some example location values?

Product Importance Image Results

A digit value can be defined as a value represented by a digit within a number given its position within the number. For example, the sevens digit value of 3,743 is 7000 or 700. However, the 7th digit value of 7,432 is 7,000 or 7,000.

tens

According to the question,

We find the value of tens

1. 4 tens ×8 =320

2.5×6 tens=30 tens =300

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Answer:

Small bag: £7.20 for 3 kg

Medium bag: £7.80 for 3 kg

Best value: small bag

Step-by-step explanation:

3 kg = 3000 g

Small bag: 60p/250 g = 0.24p/g

For 3000 g: 0.24p/g * 3000 g = £7.20

Medium bag: £1.30/500 g = 0.0026 £/g

For 3000 g: 0.0026 £/g * 3000 g = £7.80

Large bag:

For 3000 g: £7.50

Best value: small bag

We have to find the equation of the line, in point-slope form, that is perpendicular to y - 25 = 2(x - 10) and passes through (-3,7).

The line y - 25 = 2(x - 10) has a slope m = 2.

Perpendicular lines have slopes that are negative reciprocals, so our line will have a slope that is:

Then, we have the slope m = -1/2 and the point (-3,7), so we can write the point-slope form of the equation as:

Answer: y - 7 = -1/2 * (x + 3) [Option C]

The true statements are;

1) AB + BC = AC

Length of BC = |6 - 1|

2) ∠JMK = 50°

∠KML = 35°

1) From the given number line interval, we can deduce the interpretation as follows;

AB + BC = AC

Length of BC = 5 units or |6 - 1|

Length of B = 3 Units

2) We can see that ∠JML is an angle triangle. Thus, ∠JML = 85°. Thus;

6x + 2 + 4x + 3 = 85

10x + 5 = 85

10x = 85 - 5

10x = 80

x = 80/10

x = 8°

Thus;

∠JMK = 6(8) + 2

∠JMK = 50°

∠KML = 85° - 50°

∠KML = 35°

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Answer:

Step-by-step explanation:

The Conjugate Roots Theorem states that imaginary roots come in pairs. If -8i is a root of the polynomial, then so is +8i.

If both -8i and +8i are factors, we rewrite them as (x + 8i) and (x - 8i) in factored form. Since imaginary terms aren't accepted, you can FOIL these to get a quadratic with no imaginary terms.

x2 - 8ix + 8ix - 64i2

Simplify. Replace i2 with -1 because √-1 = i

x2 - 64(-1)

x2 + 64

The quadratic x2 + 64 has roots -8i and 8i. You can use the quadratic formula to verify this.

Now, let's tackle the rest of the polynomial. If x2 + 64 is a factor of the polynomial

x4 + 10x3 + 85x2 + 640x + 1344, divide it out to see what is left. I will use long division of polynomials. Note, I am using the square root symbol as a division symbol.

x2 + 10x + 21

x2 + 64 √ (x4 + 10x3 + 85x2 + 640x + 1344)

x4 + 64x2

_____________

10x3 + 21x2

10x3 + 640x

__________

21x2 +1344

21x2 + 1344

___________

0

There is no remainder, meaning x2 + 64 went in evenly. The quotient left when we divide out x2 + 64 from

x4 + 10x3 + 85x2 + 640x + 1344 is x2 + 10x + 21. Factor the quotient to get (x + 7)(x + 3).

x4 + 10x3 + 85x2 + 640x + 1344 = (x2 + 64)(x + 7)(x + 3)

You can check this factored form by FOILing out, and you should get the original polynomial.

Answer:

The answer is 52.6038

Step-by-step explanation:

Answer:

Step-by-step explanation:

52.6038