Andrew ate 1/3 of a pumpkin pie. sarah ate 1/6 of the pie. how much pie is left?

The cube of a positive number divided by its square simplifies to the number itself, based on the exponent subtraction rule in algebra.

The question involves a mathematical concept where the cube of a positive number is divided by the square of the same number. Mathematically, if we denote the positive number as 'x', then the expression would be x3/x2. According to the laws of exponents, when we divide two powers with the same base, we subtract the exponents. Thus, x3/x2 = x3-2 = x. This implies that the cube of 'x' divided by the square of 'x' simplifies to just 'x'. This is a fundamental mathematical operation under the topic of exponentiation and simplification of algebraic expressions.

The estimate of cutting 6 ramps from a 12 1/2 feet long board is reasonable. Each ramp will have a length of 2 1/12 feet, and no wood will be left over.

To determine if the estimate of cutting 6 ramps from a 12 1/2 feet long board is reasonable, we can calculate the length of each ramp by dividing the total length of the board by the number of ramps.

12 1/2 feet is equivalent to 12 + 1/2 feet. To divide by a fraction, we can multiply by the reciprocal. So, when we divide 12 1/2 by 6, we get (12 + 1/2) / 6 = 12/6 + 1/2 / 6 = 2 feet + 1/12 feet = 2 1/12 feet.

Therefore, each ramp will have a length of 2 1/12 feet. Since 6 ramps multiplied by 2 1/12 feet is 12 1/2 feet, the estimate is reasonable. No wood will be left over.

Final answer:

Marginal tax rate refers to the tax rate applied to each additional dollar of income. Individuals pay according to the bracket their income falls into, with higher rates applying only to income that exceeds certain thresholds. An example includes a single taxpayer earning $35,000 a year being in the 15% marginal tax rate bracket.

Explanation:

The student's question relates to understanding marginal tax rates and how they apply to an individual's income. Marginal tax rate is the tax rate incurred on each additional dollar of income, meaning as you earn more, you generally pay a higher tax rate on your incremental earnings beyond certain thresholds. However, it's important to note that lower tax rates apply to lower income brackets, meaning individuals pay progressively more only on the income that falls within higher brackets.

For instance, consider the marginal tax rate structure where the first $9,075 of income is taxed at 10%, the income from $9,075 to $36,900 at 15%, and income beyond $36,900 at 25%. If a single taxpayer earns $35,000 a year, their marginal tax rate is 15% because their last dollar earned falls into the 15% tax bracket. However, not all their income is taxed at 15%; the income up to $9,075 is taxed at 10%, and only the income over $9,075 up to $35,000 is taxed at 15%.

total of the fine = C

you would need to multiply the amount of the fine by the number of days

 so the equation would be C=Fd

by using the Pythagorean theorem

 use the height and half the base dimension for the 2 edges of a triangle and the slope ( slant height) would be the hypotenuse

 so:  SQRT(height ^2 + half of base^2) = hypotenuse ( Slant height)

The question is about continuous compound interest in finance. Given initial investment, final amount, and interest rate, we utilize the formula for continuous compound interest to calculate how many years it will take for the investment to reach a certain value.

The subject in this question is interest compounding in mathematics, specifically in the field of finance. Compounding continuously involves the application of the formula for continuous compound interest, which is A = P*e^(rt), where:

In Mazie's case, we have P=$4500, A=$7400, and r=4.3% or 0.043 in decimal form. We're solving for t, the time. Therefore, by substitution, we have 7400=4500*e^(0.043t). Solving for 't' will provide us the number of years it takes for the account to grow to $7400.

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The probability that you will roll a 5 on the red cube and a 1 or a 2 on the blue cube will be 1/18.

What is mean by Probability?

The term probability refers to the likelihood of an event occurring.

Given that;

You will roll a 5 on the red cube and a 1 or a 2 on the blue cube.

Now,

Sides of cube dice = 6

Hence, For red cube;

P (r) = 1/6

And, For blue red;

P (B₁ or B₂) = P(B₁) + P (B₂)

                = 1/6 + 1/6

                = 1/3

Thus, The probability that you will roll a 5 on the red cube and a 1 or a 2 on the blue cube = 1/6 x 1/3

                          = 1/18

Therefore, The probability that you will roll a 5 on the red cube and a 1 or a 2 on the blue cube will be 1/18.

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when x is on 2

 y is on -3

 answer is y=-3

To obtain the image of triangle ∆PQR after a 180° rotation about the origin, we applied the rotation formula to each vertex, resulting in the new coordinates P'(-1, 1), Q'(-3, 2), and R'(-3, 4). Connecting these points forms the rotated triangle ∆P'Q'R'.

To draw the image of triangle ∆PQR after a 180° rotation about the origin, we'll need to find the new coordinates of the vertices P', Q', and R'. The general formula for rotating a point (x, y) by 180° about the origin is to negate both the x and y coordinates, resulting in the point (-x, -y). Let's apply this formula to each vertex:

Vertex P(1, -1) is rotated to P'(-1, 1).

Vertex Q(3, -2) is rotated to Q'(-3, 2).

Vertex R(3, -4) is rotated to R'(-3, 4).

Now, we have the new coordinates for the vertices of the rotated triangle ∆P'Q'R'. Let's plot these points on a coordinate plane:

P'(-1, 1)

|

|

| Q'(-3, 2)

| /

|/

R'(-3, 4)

The triangle ∆P'Q'R' is formed by connecting these three points, and it is the image of ∆PQR after a 180° rotation about the origin.

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Answer:

The measure of the arc CBA is equal to 190°

Step-by-step explanation:

95 x 2 = 190

x = number of desks needed to make

equation:  150 +15.50x >= 400

solution:

150 +15.50x >=400

15.50x = 250

x = 250/15.50 = 16.129

he needs to assemble 17 desks

15.50*17 = 263.50 +150 = $413.50

Answer:

Biweekly salary is $ 720.

Step-by-step explanation:

Given,

Annual salary = 18,720,

Number of weeks in a year = 52,

Thus, the number of bi weeks in a year = [tex]\frac{52}{2}[/tex] = 26,

Hence, the biweekly salary = [tex]\frac{\text{annual salary}}{\text{Number of bi weeks in a year }}[/tex]

[tex]=\frac{18720}{26}=\$ 720[/tex]

71,000 *(1-0.15)^10 =

71,000*0.85^10 =

$13,978.08

we apply the exponential decay formula leading to an estimated worth of approximately $13,978.37 in 2013.

To calculate the value of a BMW that cost $71,000 in 2003 and depreciates at a rate of about 15% per year for 10 years, we will use the formula for exponential decay, which is:

V = [tex]P(1 - r)^t[/tex]

Where:

V is the final value after depreciation

P is the principal amount ($71,000)

r is the rate of depreciation (15%, or 0.15)

t is the time in years (2013 - 2003 = 10 years)

So, our calculation will be:

V = $71,000 *[tex](1 - 0.15)^{10}[/tex]

V = $71,000 * [tex](0.85)^{10}[/tex]

V = $71,000 * 0.19687

V ≈ $13,978.37

Therefore, the BMW would be worth approximately $13,978.37 in 2013.

Answer:

[tex]f(x)=3|x-2|-1[/tex]

Step-by-step explanation:

Identify the function that has a vertex of (2,-1) and is stretched vertically by a factor of 3.

The option are absolute function, So the parent function is y=|x|

Vertex form of absolute function is

[tex]y=|x-h|+ k[/tex] where (h,k) is the vertex

vertex of (2,-1) h=2, k =-1

the function becomes

[tex]f(x)=|x-2|-1[/tex]

function is stretched vertically by a factor of 3

when f(x) is vertically stretched by a factor of 'a'.We multiply the factor with f(x)

[tex]f(x)=3|x-2|-1[/tex]

Question:

Evaluate f(x)= 1.8 X 2^x for x=6

Answer choices:

A: 115.2

B: 2176.78

C: 21.6

Answer:

A:115.2

Step-by-step explanation:

F(x) F(6)

=1 . 8 • 2 • 1

=1 . 8 • 261

=1 . 8 • 64115.2

=115.2

Hence, your answer is A: