Mr. Thom makes $25,900/year salary as a document processor. He has made the following chart in order to divide his weekly paycheck into his accounts: Expense type Account Weekly deposits Essential (Fixed) 1st Checking account $219 Essential (Variable) 1st Checking account $115 Non-essential 2nd Checking account $40 Other (Unexpected) Emergency savings account $20 Other (Predictable) Education investment fund $10 Other (Predictable) Retirement investment fund $40 Other (Predictable) Emergency savings account $15 Total paycheck $498 Unfortunately, he has made a mistake in adding the numbers and has not allocated all of the paycheck. If he deposits the difference into the two emergency savings accounts, how much total per week can he then put towards emergency savings?

Answer:

10 pounds

Step-by-step explanation:

We are given that Alice hall makes an apple cake (serves 6) for her family

Apples=[tex]2\frac{1}{2}=\frac{5}{2}[/tex]pounds

Flour=[tex]2\frac{1}{4}=\frac{9}{4}[/tex] cups

Margarine=[tex]\frac{1}{4}[/tex] cups

Sugar=[tex]1\frac{1}{4}=\frac{5}{4}[/tex] cups

Eggs=4

For 6 persons , apples required =[tex]\frac{5}{2}[/tex] pounds

For 24 persons=[tex]\frac{\frac{5}{2}}{6}\times 24[/tex]

For 24 persons=[tex]\frac{5}{12}\times 24=10[/tex] pounds

Hence, she should use 10 pounds of apples.

Answer:

Step-by-step explanation:The employees must sell 78 pizzas in order to get the bonus.

The percentage decrease is 0.05%

Step-by-step explanation:

Number of pizzas sold yesterday is 65 pizzas.

The owner offers the employees a bonus if the number of pizzas sold increases by 20%

So 20% of 65 pizzas is,  pizzas.

Therefore, the employees must sell 65+13=78 pizzas in order to get the bonus.

But the actual number of pizzas sold today was 60. So the number of pizza sold has decreased. Then the percent decrease is,

Therefore, the percentage decrease

We can use the formula:

F = P · ( 1 + i )^n

where: P = $125,000, i = 0.019 ( 1.9 %), n = 10

F = $125,000 · ( 1 + 0.019 )^10

F = $125,000 · 1.019^10

F = $125,000 · 1.207096

F = $150,887

And we have to add $48,3000 ( for renovations and improvements )

$150,887 + $48,300 = $199,187 ≈ $199,200

Answer: You will be sell the house for $199,200.

Answer:

$199,200

Step-by-step explanation:

Answer:

9/5×c+32 I.e.

if it is equal to 0 then

c=-32 ×5/9

c = -160/9

Step-by-step explanation:

To determine sin(5π/12) using the half-angle formula, we establish a known cos value for the double of the angle, i.e., cos(5π/6)=-√3/2. Substituting it into the half-angle sin formula: Sin(5π/12)=±√{(1+√3/2)/2}. Simplifying gives Sin(5π/12)=√{3+√3/4}.

The half angle formula for sine is given by:

Sin(x/2) = ±√{(1 - cos x) / 2}

To solve for sin(5π/12) using the half angle formula, we would look for an angle whose double is easily recognized in terms of standard angles (multiples of 30° or 45°). Luckily, the double of 5π/12 is 5π/6, a recognizable angle, and we know that cos(5π/6) = -√3/2.

Step 1: Substitute cos x value (-√3/2) into the formula:

Sin(5π/12) = √{(1 - (-√3/2 )) / 2}

Step 2: Simplify the expression inside the square root:

Sin(5π/12) = √{(1 + √3 / 2) / 2}

Step 3: Calculate the square root:

Sin(5π/12) = ± √{3 + √3 / 4}

Usually, we choose the positive root for a result in the first or second quadrant and the negative root for a result in the third or fourth quadrant. Since the angle 5π/12 is in the first quadrant, we choose the positive root:

Sin(5π/12) = √{3 + √3 / 4}

So, sin(5π/12) using the half angle formula is √{3 + √3 / 4}.

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The price of household items increases is a  result of inflation, option C is correct.

Inflation typically leads to a general rise in prices across the economy.

As the value of money decreases, it takes more money to purchase the same goods and services.

Therefore, the prices of household items, along with other consumer goods, tend to increase during periods of inflation.

However, it's important to note that inflation does not affect all goods and services uniformly.

Some prices may rise more rapidly than others, leading to changes in relative prices.

To learn more on Inflation click here:

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The correct answer is:

[tex]\[\boxed{f(x) = -3x + 60}\][/tex]

To find the linear equation representing the amount of trash removed each week, we need to determine the slope and the y-intercept.

Given:

- In week 5, there were 45 dumpster loads.

- In week 10, there were 30 dumpster loads.

Step 1: Calculate the Slope

The slope m  of a line is calculated by:

[tex]\[m = \frac{y_2 - y_1}{x_2 - x_1}\][/tex]

Here,[tex]\((x_1, y_1) = (5, 45)\) and \((x_2, y_2) = (10, 30)\).[/tex]

[tex]\[m = \frac{30 - 45}{10 - 5} = \frac{-15}{5} = -3\][/tex]

Step 2: Write the Equation in Point-Slope Form

Using the point-slope form of the equation [tex]\( y - y_1 = m(x - x_1) \):[/tex]

[tex]\[y - 45 = -3(x - 5)\][/tex]

Step 3: Convert to Slope-Intercept Form [tex]( \( y = mx + b \) )[/tex]

Simplify the equation:

[tex]\[y - 45 = -3(x - 5)\][/tex]

[tex]\[y - 45 = -3x + 15\]\[y = -3x + 15 + 45\]\[y = -3x + 60\][/tex]

Thus, the equation in function form that shows the amount of trash removed each week is:

[tex]\[f(x) = -3x + 60\][/tex]

Therefore, the correct answer is:

[tex]\[\boxed{f(x) = -3x + 60}\][/tex]

Answer:

The answer is "4x - 3(8x +9) = -22."

Step-by-step explanation:

I just finished the test and got it right.

Final answer:

To find dy/dx using implicit differentiation, differentiate both sides of the equation with respect to x. Then apply the chain rule and simplify.

Explanation:

To find dy/dx using implicit differentiation, we first differentiate both sides of the equation with respect to x. Let's go through the steps:

Answer:

(x-5y)^2 or (x-5y)(x-5y).

Step-by-step explanation:

hope this helps have a nice day! :D

Final answer:

To find the factors of x² + 25y², use the properties of complex numbers like i² = -1. The factors are (x + 5yi)(x - 5yi), representing complex conjugates.

Explanation:

The factors of x² + 25y² are (x + 5yi)(x - 5yi).

To factorize the expression, we use the fact that i² = -1, so we can rewrite 25y² as (5y)²

By factoring this expression, we can see that it represents a sum of two squares in the form of complex conjugates.

Answer:

C.3

Step-by-step explanation:

We are given that

f(w) varies inversely with w.

f(w)=0.75 when w=8

We have to find the value of f(w) when w=2

According to question

[tex]f(w)\propto\frac{1}{w}[/tex]

[tex]f(w)=\frac{k}{w}[/tex]

Where k=proportionality constant

Substitute the given values then, we get

[tex]0.75=\frac{k}{8}[/tex]

[tex]k=0.75\times 8[/tex]

[tex]k=6[/tex]

Substitute the value of k then, we get

[tex]f(w)=\frac{6}{w}[/tex]

Substitute the value of w=2

Then, we get

[tex]f(w)=\frac{6}{2}=3[/tex]

[tex]f(w)=3[/tex]

Hence, option C is true.

Answer:

Option C. $1.67

Step-by-step explanation:

The price of a bag of candy at wholesale = $1.15

The markup on candy at the discount store = 45%

The retail price for the candy = 1.15 +(45% × 1.15)

                                                = 1.15 + ([tex]\frac{45}{100}[/tex]×1.15)

                                               = 1.15 + (0.45 × 1.15)

                                               = 1.15 + 0.5175

                                               = 1.6675 ≈ $1.67

The retail price for the candy would be $1.67.

Answer: A fifth degree polynomial could have 5 linear factors. But the factors   do not have to be be distinct.

Step-by-step explanation:

Thus by corollary to fundamental theorem of algebra, a fifth degree polynomial must have 5 zeroes . But A fifth degree polynomial could have 5 linear factors if all zeroes are real numbers.

The factors could be distinct or similar.

Thus , The factors do not have to be distinct .