Francois' income is $7000 a month, and he plans to budget 1/5 of his income for groceries and 1/8 of income for gas. Step 1 of 2: What fraction of his income does he plan to spend each month on these two items together? Express your answer in lowest terms.
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The statement that is equivalent to |6x-3|=3 is: 6x-3=3 or 6x-3=-3

For the equation to be true, two scenarios need to be considered:

When the expression 6x-3 is positive and equals 3:

6x-3 = 3

When the expression 6x-3 is negative and equals -3:

6x-3 = -3

By solving these two equations, we can find the equivalent statement:

Solving 6x-3 = 3:

Adding 3 to both sides gives us:

6x = 6

Dividing both sides by 6:

x = 1

Solving 6x-3 = -3:

Adding 3 to both sides gives us:

6x = 0

Dividing both sides by 6:

x = 0

Therefore, the equivalent statement to |6x-3|=3 is:

6x-3=3 or 6x-3=-3, which can be further simplified to:

6x-3=3 or 6x-3=-3

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Answer:

$1.12

Step-by-step explanation:

7% of 16 is 1.12

The compounded amount from adding the interest is $57,603.80.

Compound interest, often referred to as interest on principal and interest, is the practice of adding interest to the principal of a loan or deposit. Interest is generated on the principal amount plus any accumulated interest the following period when interest is reinvested, added to the loan's collateral rather than paid out, or forced upon the borrower. A key idea in finance and economics is compound interest.

Contrary to simple interest, which does not compound since past interest is not applied to the principle for the current period, compound interest allows interest to build up over time. The simple annual interest rate is calculated by dividing the total number of periods by the interest per period.

principal = $45000

rate = 5%

Time = 5 years

Amount = P(1+r)ⁿ

now we put the values to calculate the equation:

Amount = 45000(1+2.5)¹⁰

Amount = $57,603.80

Hence the total amount compounded is $57,603.80 .

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Answer:

P= 3200 cm

Step-by-step explanation:

Perimeter = 2(l+w)

In this case since the perimeter has to be in centimeters, we have to change the length of the rectangle to centimeter.

12 meter to centimer = 12 x 100 = 1200 cm

2( 1200 +400)

2 (1600)

=  3200 cm

The area of the shaded region = 30.903 in²

From the attached figure we can observe that the radius of the circle R is r = 6 in.

Using the forula for the area of circle, the area of circle R would be,

A₁ = πr²

A₁ = π × 6²

A₁ = 36π

A₁ = 113.097 in²

So, the diameter would be d = 6 × 2 = 12 in.

The circle R is inscribed in a square.

So, the side length of square is equal to the diameter of the circle.

This means the side length 'a' os square = 12 in.

Using the formula of the area of square,

A₂ = side²

A₂ = a²

A₂ = 12²

A₂ = 144 in²

so, the area of the shaded region would be,

A = A₂ - A₁

A = 144 -113.097

A = 30.903 in²

This is the required area.

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Answer:

the first one is 4 i think and the last one is 48 percent. im not sure if the dotted line is a underline tho

Step-by-step explanation:

:))

Multiply the numerator and the denominator by 100 to get 48/100

which is the same as 48% .

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.

Given,

Fraction = 12/25

To convert into percentage

divide the number by 100 and multiply by 100.

= ((12/25)×100)/100

= 12 × 100/25×100

= 48/100

= 48%

Hence, 48% is the expression of 12/25 as percent gotten by multiplying and dividing with 100.

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The partial fraction decomposition of the function is x⁴ + 2 / x⁵ + 4x³ = -1/8x + 1/2x³ + 9/8x(x²+4)

Partial fraction decomposition function:

In algebra, When an algebraic expression is split into a sum of two or more rational expressions, then each part is called a partial fraction.

Given,

Here we have the expression

x⁴ + 2 / x⁵ + 4x³

Here we need to find the partial fraction decomposition function.

In order to solve this, first we have to factorize the denominator, then we get,

=> x⁴ + 2 / x⁵ + 4x³ = (x⁴ + 2) / x³ (x² + 4)

Now,  Partial fraction for each factors is written as,

=> A/x + B/x² + C/x³ + (Dx + E)/ (x² + 4)

Now, we have to  Multiply through by the common denominator of x³ (x² + 4), then we get,

=>  x⁴+2=A (x²(x²+4)) + B(x(x²+4)) + C (x²+4) + (Dx + E)(x³)

When we simplify this one, then we get,

=> x⁴ + 2 =Ax⁴ + 4Ax² + Bx³ + 4Bx + Cx² + 4C + Dx⁴ + Ex³

Group the x-terms and the constant terms

=> x⁴ + 2 =(A +D)x⁴ + (4A + C) x² + (B + E)x³ + 4Bx + 4C

Coefficients of the two polynomials must be equal, so we get equations

A+D=1

B+E=0

4A+C=0

4B=0

4C=2

After solving these equations, we get

A = -1/8, B = 0, C = 1/2, D=9/8, E = 0

Then when we substitute these values in the original fraction,

=> -1/8x + 1/2x³ + 9/8x(x²+4)

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The relationship between the quantities shown in the table is +10. The values in column 2 (y) are obtained by adding 10 to the corresponding values in column 1 (x).

In the given table, the values in column 1 (labeled "x") are 1, 2, 3, and 4. The values in column 2 (labeled "y") are 11, 22, 33, and 44.

To determine the relationship between the quantities in the table, we can compare the values in column 2 (y) with the corresponding values in column 1 (x).

If we subtract each value in column 1 from the corresponding value in column 2, we find that:

11 - 1 = 10

22 - 2 = 20

33 - 3 = 30

44 - 4 = 40

By observing these results, we can see that the difference between each value in column 2 and its corresponding value in column 1 is always 10.

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Answer:

b

Step-by-step explanation:

-3x is the rate of change, so minus 3X= -17/3

The graph of the new function would be less steep than the original one but would not be shifted up or down or left or right.

Thus, the correct option is: It would be less steep.

In mathematics, a graph is a visual representation of a set of objects where some pairs of the objects are connected by links. The objects, which are usually represented by points, are called vertices or nodes, and the links, which are usually represented by lines or arcs, are called edges.

The original function y = 5x + 1 has a slope of 5, which means that for every 1 unit increase in x, y increases by 5 units.

The new function y = 2x + 1 has a slope of 2, which is less steep than the slope of the original function.

However, the y-intercept of both functions is the same, which is 1.Therefore, the graph of the new function would be less steep than the original one but would not be shifted up or down or left or right.

Thus, the correct option is: It would be less steep.

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Answer:median:249    

Step-by-step explanation:

median:198] 216} 220] 236] 246 252 [253[ 260 {290[ 369

246 +252=498

498/2=249

as for the mean  i will give you that later

Answer:

5 miles away

Step-by-step explanation:

If you walked north 8 miles, then west 4 miles, then south 5 miles, you have, in total, travelled 4 miles west and \(8-5=3\) miles north.

This creates a triangle, in which we can find the the length of the hypotenuse to find how far away you are now.

We can use the Pythagorean theorem since this is a right triangle.

\(a^2+b^2=c^2\\3^2+4^2=c^2\\9+16=c^2\\25=c^2\\c=5\)

Hope this helped!

Answer:

5 miles away

Step-by-step explanation:

Answer:

27.88 can be rounded to whatever the question wants you to, coz it needs to be a whole no.---> so I would say 28 weeks, but it depends on what the question asks

Step-by-step explanation:

18w+38= should equal to $540

rephrasing this in a mathematical way would be-

18w+38=$540

18w=$540-38

18w=502

w=502/18

w=27.88

Answer:

The answer is 27. 88 but if this is like a test and not a open end question than the answer is 27 ;)

Answer:

6

Step-by-step explanation:

Negative ×negative always gives gives a positive

Answer:

18 mugs

Step-by-step explanation:

first let's convert 6 3/4 into eights. 6 3/4 as an improper fraction is 27/4, which we multiply by 2 to get 54/8. now we do 54 divided by 3, since we can now ignore the denominator. 54 divided by 3 = 18. This is divided evenly so the "including mugs that are partially filled" is a red herring.

Answer:

-13.608

Step-by-step explanation:

-1.89 * 7.2

- (1.89 * 7.2)

- (13.608)

-13.608

Answer:

-13.608

Step-by-step explanation:

Answer: Not Perpendicular

Step-by-step explanation:

The joint density function of xy and \(z^{2}\) \(& f_T(t)=\frac{1}{2 \sqrt{t}} \quad \leqslant t \leq 1 \\&\).

From the given data

x, y, z are independent and uniformly distributed on [0,1] and also Independent.

⇒\(& f(x, y)=f_x(x) \quad f y(y) \\\)

⇒\(& \omega=x y \\\)

⇒\(& f_\omega(\omega)=P(\omega \leq \omega) \\\)

\(& =\int_A \int_1 1 d x d y \\\)

⇒\(& A \rightarrow\left\{(x, y): \quad \begin{array}{ll} & 0 \leq x \leq 1 \\0 \leq y \leq 1\end{array} \quad x y \leq \omega\right\} \\\)

⇒\(& f_\omega(w)=\omega+\int_z^1 \int_0^x(y) d y d x \\\)

\(& =\omega+\int_z^1[y]_0^{w / x} d x \\\)

\(& =\omega+y / w(\omega / x) d x \\\)

\(& =\omega+\omega[\ln x]_\omega^{\prime} \omega \\\)

\(& =\omega+\omega(0-\ln \omega) \\\)

⇒\(& f_\omega(\omega)=\omega-\omega \ln . \\\)

⇒\(& f_\omega(\omega)=\frac{\partial}{\partial \omega}(f \omega(\omega)) \\\)

\(& =1-[\omega / \omega+\ln \omega] \\\)

⇒\(& f_\omega(\omega)=-\ln \omega \quad \quad 0 \leq \omega \leq 1 \\\)

⇒\(& \text { Pdf of } z^2 \\\)

⇒\(& T=z^2 \\\)

⇒\(& f_T(t)=P(T \leq t) \\\)

\(& =p\left(z^2 \leq t\right) \\\)

\(& =p(r \leqslant \sqrt{t}) \\\)

\(& =\int_0^{\sqrt{t}} 1 d z \\\)

\(& =[z]_0^{\sqrt{t}} \\\)

\(& =\sqrt{t} \\\)

⇒\(& 0 \leq t \leq 1 \\\)

⇒\(& F_T(t)=\sqrt{t} \\\)

⇒\(& F_T(t)=F_T^{\prime}(t) \\\)

⇒\(& f_T(t)=\frac{1}{2 \sqrt{t}} \quad \leqslant t \leq 1 \\&\)

Therefore, the joint density function of xy and \(z^{2}\) \(& f_T(t)=\frac{1}{2 \sqrt{t}} \quad \leqslant t \leq 1 \\&\)

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Answer:

1) -3/4

2) (6, 0), (0, -4)

3) connect (0,-2) and (8,0) together

Step-by-step explanation:

1) (-2) - (-5) / (-1) - 3 = -3/4

2) x = 0 -3y=12 y = -4, y= 0 2x =  12 x = 6, x intercept = (6, 0) y intercept = (0, -4)

3) x - 4y = 8 this could be written as y = x/4 - 2 and y intercept is (0, -2) and x intercept is (8, 0) so connect these points together and make a line

#1

#2

Inetercept form x/a+y/b=1

x inetercept at 6 and y intercect at -4

#3

Graph attached

312/78=4

n≥4 does that make sense?

Their ages are 5 years, 25 years

Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.

Let L and Y represent the age of the older person and younger person respectively.

Using the given information, we can write:

L = 4Y + 5 --- (1)

L + Y = 30 --- (2)

From (2):

L = 30 - Y --- (3)

Put (3) in (1):

L = 4Y + 5

30 - Y = 4Y + 5

4Y + Y = 30 - 5

5Y = 25

Y = 25/5

Y = 5 years

Put Y = 5 into (3):

L = 30 - Y

L = 30 - 5

L = 25 years

Their ages are 5 years, 25 years

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Answer:

So the diameter of the pipe with the insulation around it is approximately 18.84 inches / 2 = 9.42 inches.

Step-by-step explanation:

To find the diameter of the pipe with the insulation around it, we can use the formula for the circumference of a circle:

C = 2 * π * r

Where:

· C = circumference of the pipe

· π = the mathematical constant approximately equal to 3.14

· r = the radius of the pipe

Using the given information, we know that the pipe’s diameter is 2.5 inches and that the insulation around the pipe is 0.5 inch thick. Therefore, the radius of the pipe with the insulation around it is:

r = 2.5 inches + 0.5 inch = 3 inches

Plugging in the values:

C = 2 * π * 3

C = 6.28 * 3

C = 18.84 inches

Note that this is only an approximation, as the thickness of the insulation is slightly larger than the diameter of the pipe. To obtain a more accurate result, we would need to use a geometric area formula or a numerical integration technique.

Answer:

36 po hope it helps.

Step-by-step explanation:

1728 ÷ 48 = 36.

Answer:

1/9x

Step-by-step explanation:

The parenthesis around the 9x means that the -1 exponent goes to the whole thing (the 9x) To "fix" a negative exponent push the 9x across a fraction bar to make the exponent positive. When you push the 9x down across a fraction bar that leaves a 1 on top of the fraction, that has nothing to do with the 1 exponent. Its a 1 on top because when you push the 9x down there is nothing left on top so it is a 1.

(9x)^-1

= 1/9x

To be clear, this is a 1 one top and a 9x on the bottom of a fraction.

Answer:

1/24

Step-by-step explanation:

Hope thats right

Answer:

2/8

Step-by-step explanation:

subtract 7/8 by 5/8

The probability of a prime number or a number greater than 3 coming up is given as follows:

5/6.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

When a dice is thrown, there are six possible outcomes, ranging from 1 to 6, and the desired outcomes are given as follows:

Hence the probability is given as follows:

5/6.

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Answer:

$50,861.72

Step-by-step explanation:

Answer:

it's 3a+.50b

Step-by-step explanation:

Nearest whole number will be 782318.

Nearest ones whole number is the first digit before the decimal point of a number.

For example nearest ones of 9.6 is equal to 10.

If the tenth digit (first number before decimal point) of the number is greater than or equal to 5 we round up and add 1 to ones of number, If the tenth digit of the number is less than 5 we remove the decimal part. Example:

124.6

The first number of right of decimal point is 6

6 is greater than 5, so we add 1.

Result = 125

Now given number is 782317.772

since the  first digit after decimal is 7 which is greater than 5 thus the nearest whole number will be 782318.

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