Devin was born in Minnesota, but now he lives in lowa, close to where lowa, Wisconsin, and Illinois meet. He works in Wisconsin, but he buys all of his
clothes at a store in Illinois. If the sales tax rates for the four states are as
shown in the following table, which sales tax rate does Devin pay on the
clothes he buys?

State Sales tax
Illinois 6.25%
lowa 6%
Minnesota 6.875%
Wisconsin 5%

A. 5%
B. 6%
C. 6.875%
D6.25%

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Answer:

The simplified expression to the given expression is [tex]\frac{4x^6}{y^2}[/tex]

Therefore [tex]\frac{4(2x^3y^4)^4}{2(2x^2y^6)^3}=\frac{4x^6}{y^2}[/tex]

Step-by-step explanation:

Given fractional expression is [tex]\frac{4(2x^3y^4)^4}{2(2x^2y^6)^3}[/tex]

To simplify the given expression as below :

[tex]\frac{4(2x^3y^4)^4}{2(2x^2y^6)^3}[/tex]

[tex]=\frac{2(2x^3y^4)^4}{(2x^2y^6)^3}[/tex]

[tex]=\frac{2[(2)^4(x^3)^4(y^4)^4]}{(2)^3(x^2)^3(y^6)^3}[/tex]  ( using the property [tex](a^m)^n=a^{mn}[/tex])

[tex]=\frac{2[(2)^4(x^{12})(y^{16})]}{(2)^3(x^6)(y^{18})}[/tex]

[tex]=2[(2)^4(x^{12})(y^{16})](2)^{-3}(x^{-6})(y^{-18})[/tex]  (  ( using the property [tex]a^m=\frac{1}{a^{-m}}[/tex] )

[tex]=2[2^{4-3}x^{12-6}y^{16-18}][/tex]( using the property [tex]a^m.a^n=a^{m+n}[/tex] )

[tex]=2[2^1x^6y^{-2}][/tex]

[tex]=\frac{4x^6}{y^2}[/tex] ( using the property [tex]a^m=\frac{1}{a^{-m}}[/tex] )

Therefore the simplified expression is [tex]\frac{4x^6}{y^2}[/tex]

Therefore [tex]\frac{4(2x^3y^4)^4}{2(2x^2y^6)^3}=\frac{4x^6}{y^2}[/tex]

Answer:

Step-by-step explanation:

Good evening

Answer:

x = 6

y = 2

Step-by-step explanation:

Look at the photo below for the details.

:)

The domain of the given relation (-2,4), (1,3), (0,-4), (3,2) is the set of the first elements from each ordered pair, which results in the set {-2, 1, 0, 3}.

The question asks about the domain of a relation consisting of ordered pairs. A relation is a set of ordered pairs, and the domain of a relation is the set of all the first elements from each pair. In the given relation (-2,4), (1,3), (0,-4), (3,2), the domain comprises the first elements of each pair, which are -2, 1, 0, and 3. Therefore, the domain of this relation is the set {-2, 1, 0, 3}.

Answer:

216 cm^2.

Step-by-step explanation:

There are 6 faces on the prism . 3 pairs with the same area.

The surface area = 2*6*10 + 2 * 6*3 + 2*3*10

=  120 + 36 + 60

= 216 cm^2.

Answer:

d.

Step-by-step explanation:

To convert a root to a fraction in the exponent, remember this rule:

[tex]\sqrt[n]{a^{m}}=a^{\frac{m}{n}}[/tex]

The index becomes the denominator in the fraction. (The index is the little number in front of the root, "n".) The original exponent remains in the numerator.

In this question, the index is 4.

The index is applied to every base in the equation under the root. The bases are 16, 'x' and 'y'.

[tex]\sqrt[4]{16x^{15}y^{17}} = (\sqrt[4]{16})(\sqrt[4]{x^{15}})(\sqrt[4]{y^{17}}) = (2)(x^{\frac{15}{4}}})(y^{\frac{17}{4}}) = 2x^{\frac{15}{4}}}y^{\frac{17}{4}}[/tex]

To find the quad root of 16, input this into your calculator. Since 2⁴ = 16, [tex]\sqrt[4]{16}[/tex] = 2.

For the "x" and "y" bases, use the rule for converting roots to exponent fractions. The index, 4, becomes the denominator in each fraction.

[tex]2x^{\frac{15}{4}}y^{\frac{17}{4}}[/tex]

Answer:

Ella should add [tex]32\dfrac{5}{6}[/tex] lbs of water.

Total weight of syrup [tex]33\dfrac{1}{3}[/tex] lbs

Step-by-step explanation:

Weight:

Weight of sugar = 0.5 lbs.

Weight of water added = x lbs

Total weight = 0.5 + x lbs

Percentage:

0.5 + x  --  100%

0.5  --  1.5%

Write a proportion:

[tex]\dfrac{0.5+x}{0.5}=\dfrac{100}{1.5}[/tex]

Cross multiply:

[tex]1.5(0.5+x)=0.5\cdot 100\\ \\0.75+1.5x=50\\ \\1.5x=50-0.75\\ \\1.5x=49.25\\ \\x=\dfrac{49.25}{1.5}=\dfrac{4,925}{150}=\dfrac{197}{6}=32 \dfrac{5}{6}\ lbs[/tex]

Ella should add [tex]32\dfrac{5}{6}[/tex] lbs of water.

Total weight of syrup

[tex]32\dfrac{5}{6}+\dfrac{1}{2}=32\dfrac{5}{6}+\dfrac{3}{6}=33\dfrac{1}{3}\ lbs[/tex]

Answer:

Ella should add 32 5/6 lb of water, and she will have 33 1/3 lb of syrup.

Step-by-step explanation:

Answer:

[tex]21.43\%[/tex]

Step-by-step explanation:

we know that

To find out the percent of robots which are defective, divided the number of defective robots by the total number of robots and multiply the result by 100

Let

x ----> the number of defective robots

y ----> the total number of robots

p ---> percentage of robots which are defective

so

[tex]p=\frac{x}{y} (100)[/tex]

we have

[tex]x=30\\y=140[/tex]

substitute

[tex]p=\frac{30}{140}(100)[/tex]

[tex]p=21.43\%[/tex]

There are 11,375 ounces are still in the bucket ⇒ (not in the choices)

Step-by-step explanation:

An art teacher is cleaning up her room at the end of the week

We need to find how many ounces of blue paint are still in the bucket

∵ The jars have 212 ounces, 825 ounces, and 11110 ounces of blue paint

∵ She combines all of them in an empty bucket

- Add them to find the quantity of the blue paint in the bucket

∴ The bucket contains = 212 + 825 + 11110

∴ The bucket contains = 12,147 ounces

∵ This bucket is then used to fill one can with 414 ounces of

   the paint and another can with 358 ounces

- Add them to find the quantity that used from the bucket

∵ She used = 414 + 358 = 772

∴ 772 ounces is used to fill the two cans

To find how many ounces of the blue paint are still in the bucket subtract from the total amount of paint in the bucked the amount used to fill the two cans

∵ The remainder paint in the bucket = 12,147 - 772

∴ The remainder paint in the bucket = 11,375 ounces

There are 11,375 ounces are still in the bucket

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Answer:

B. {1, 2, 3, 4}.

Step-by-step explanation:

The domain is the set of x values.

The domain of the function represented by the given table, with the corresponding values of x and y being (1, 2), (2, 4), (3, 3), and (4, 2), is  Option B)  {1, 2, 3, 4}.

The domain of a function consists of all possible input values (x-values) for which there are corresponding output values (y-values). In the given table, we see the following pairs of values: (1, 2), (2, 4), (3, 3), and (4, 2).

These x-values are explicitly provided in the table, and they are 1, 2, 3, and 4. Therefore, the domain of the function, based on the data in the table, is {1, 2, 3, 4}.

This means that for this specific function, you can input any of these four values into the function, and there are corresponding y-values for each of them. Any other values not listed in the table, such as decimals or negative numbers, are not part of the domain for this function because they do not have corresponding y-values in the given data.

In summary, the domain of the function represented by the table is the Option B). set {1, 2, 3, 4}, which includes the x-values provided in the table.

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Answer:

-1/2 or/also known as. -0.5

Answer:

The answer to the given equation -g+2(3+g)=-4(g+1) is g=-2

Step-by-step explanation:

Given -g+2(3+g)=-4(g+1)

To solve the given equation :

-g+2(3+g)=-4(g+1)

Applying the distributive property we get

-g+2(3)+2(g)=-4(g)+(-4)(1)

-g+6+2g=-4g-4

g+6=-4g-4 ( adding the like terms )

g+6-(-4g-4)=-4g-4-(-4g-4)

Applying the distributive property we get

g+6-(-4g)-(-4)=-4g-4-(-4g)-(-4)

g+6+4g+4=-4g-4+4g+4

5g+10=0 ( adding the like terms )

5g+10-10=0-10

5g=-10 ( adding the like terms )

[tex]g=-\frac{10}{5}[/tex]

[tex]g=-2[/tex]

Therefore g=-2

The answer to the given equation -g+2(3+g)=-4(g+1) is g=-2

Answer:

she will be paid $480 for one week and $960 for two

Step-by-step explanation:

let P = paycheck

let d = days

let h = hours

P = d (8*h)

P = 5(8*12)

P = $480

to find two weeks multiply week one by 2

Answer:

3. times 2 divided by 36

Answer:

L=6

Step-by-step explanation:

3 x 2= 6

36 divided by 6= 6

so L= 6

The solution of the expression of 13 and three-fourths + x = 7 and one-fourth equation is x = [tex]6\frac{1}{2}[/tex]

To solve this equation, we need to find the value of x (unknown variable) in the given equation:

13 and three-fourths + x = 7 and one-fourth

First, we need to convert the mixed numbers to improper fractions.

13 and three-fourths = [tex]13 + \frac{3}{4} = 13\frac{3}{4}[/tex]

7 and one-fourth = [tex]7 + \frac{1}{4} = 7 \frac{1}{4}[/tex]

Now, the equation becomes:

[tex]13\frac{3}{4} + x =7\frac{1}{4}\\ x = 13\frac{3}{4} - 7\frac{1}{4}\\\\x = 6\frac{1}{2}[/tex]

Answer:

1/10 the value is 100% right!

Step-by-step explanation:

Answer:

Step-by-step explanation:

let

x = kg of mocha beans

y = kg of java beans

so

(1)   x + y = 50

(2)   20x + 15y = 18(50)

solve by substitution (or whatever method you prefer):

(x, y) = (30, 20)

Answer:

A. 30

Step-by-step explanation:

The answer is 30 because x= 12 so that means that x-2 is 10 because x is 12, so since its in parenthesizes that means you do that part of the problem first. So, after we have 10 we will do times 3 since the 3 is also there and it says what is the value. So, therefore the answer is A. 30.

Answer:

no solution

Step-by-step explanation:

8(2f-3)=4(4f-8)

16f-24=16f-32

16f=16f-8

0=-8

Answer:

No solution

Step-by-step explanation:

8(2f-3)=4(4f-8)

16f-24=16f-32

8=0f

Answer:

B C and E

Step-by-step explanation:

The easiest way to know if the graph was a function is the vertical line test

If you can draw a verticle line that interests the graph two or more times it is not a function and if you can't it is a function

Tree casts a shadow 30 feet long. A MHS student standing near the tree casts a shadow 9 feet long. The  student is 6 feet tall. What is the height of the tree? Show all work

Answer:

Option D

The height of tree is 20 feet tall

Solution:

From given question,

Shadow of tree = 30 feet

Height of tree = ?

Height of student = 6 feet

Shadow of student = 9 feet

We have to find the height of tree

We can solve the sum by proportion

[tex]\frac{\text{height of tree}}{\text{shadow of tree}} = \frac{\text{height of student}}{\text{shadow of tree}}[/tex]

This forms a proportion and we can solve the sum by cross multiplying

[tex]\frac{\text{height of tree}}{30} = \frac{6}{9}\\\\\text{height of tree} = 30 \times \frac{6}{9} = 30 \times \frac{2}{3}\\\\\text{ height of tree } = 10 \times 2 = 20[/tex]

Thus height of tree is 20 feet tall

Answer:

x=1.75

Step-by-step explanation:

The answer is true.

Step-by-step explanation:

To find the points all lie on the same line, we need to substitute the points in the equation of the line, to determine if the values on both sides of the equation are equal.

Substituting the point [tex](6,13)[/tex] in the equation of the line, we get,

[tex]\begin{aligned}y &=\frac{4}{3} x+5 \\13 &=\frac{4}{3}(6)+5 \\&=4(2)+5 \\&=8+5 \\13 &=13\end{aligned}[/tex]

Thus, the values on both sides are equal. The point [tex](6,13)[/tex] lie on the same line.

Substituting the point [tex](21,33)[/tex] in the equation of the line, we get,

[tex]\begin{aligned}y &=\frac{4}{3} x+5 \\33 &=\frac{4}{3}(21)+5 \\&=4(7)+5 \\&=28+5 \\33 &=33\end{aligned}[/tex]

Thus, the values on both sides are equal. The point [tex](21,33)[/tex] lie on the same line.

Substituting the point [tex](99,137)[/tex] in the equation of the line, we get,

[tex]\begin{aligned}y &=\frac{4}{3} x+5 \\137 &=\frac{4}{3}(99)+5 \\&=4(33)+5 \\&=132+5 \\137 &=137\end{aligned}[/tex]

Thus, the values on both sides are equal. The point [tex](99,137)[/tex] lie on the same line.

Thus, all the three points lie on the same plane.

Hence, the answer is true.

All three points (6 , 13), (21 , 33), and (99 , 137) lie on the line y = [tex]\frac{4}{3}[/tex]x + 5. Thus, the statement is True, all three points make the equation true. Option 3 is the correct answer.

To determine whether the points (6,13), (21,33), and (99,137) all lie on the line y = [tex]\frac{4}{3}[/tex]x + 5, we need to substitute the x-values of each point into the equation and see if the corresponding y-values match.

1. For the point (6,13):

Substitute x = 6 into the equation.

⇒ y = ([tex]\frac{4}{3}[/tex]) × 6 + 5

⇒ y = 8 + 5

⇒ y = 13

Since the y-value matches, the point (6,13) is on the line.

2. For the point (21,33):

Substitute x = 21 into the equation.

⇒ y = ([tex]\frac{4}{3}[/tex]) × 21 + 5

⇒ y = 28 + 5

⇒ y = 33

Since the y-value matches, the point (21,33) is on the line.

3. For the point (99,137):

Substitute x = 99 into the equation.

⇒ y = ([tex]\frac{4}{3}[/tex]) × 99 + 5

⇒ y = 132 + 5

⇒ y = 137

Since the y-value matches, the point (99,137) is on the line.

All three points satisfy the equation y = [tex]\frac{4}{3}[/tex]x + 5. Therefore, the statement is True: all three points make the equation true option (3).

Complete question:

True or False:

The points (6,13), (21,33) and (99,137) all lie on the same line. The equation of the line is y = [tex]\frac{4}{3}[/tex]x + 5.

Select the correct explanation.

Answer:

A parallelogram has opposite sides parallel and equal in length.

Step-by-step explanation:

Hope this helps. :)

When any given number greater than 0 is multiplied by a fraction greater than 1 Option 1  the product is always greater than the given number.

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.

In Maths, there are three major types of fractions. They are proper fractions, improper fractions and mixed fractions. Fractions are those terms which have numerator and denominator.

If any given number greater than 0 is multiplied by a fraction greater than 1 then the product is always greater than the given number.

The product is always greater than the given number because the top of the fraction i.e., the numerator is already greater than the bottom of the fraction i.e., denominator which results in a greater product than the given number.

For example, let us consider that the given number is 5 and the fraction is 6/5. So, if we multiply it together then we will get 6 as a result which is greater than the given number.

Hence, the product is always greater than the given number.

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Width = w cm

Length = 2w-7

Answer:

$812.5

Step-by-step explanation:

Given: Ethan need to save at least $500.

          He has saved so far $175

          Ethan hope to use two-fifths of his next paycheck to cover the remaining amount.

Lets assume Ethan´s paycheck amount be "x"

First finding the remaining amount to be covered.

Remaining amount= [tex]\$ 500 - \$ 175= \$ 325[/tex]

∴ The remaining amount to be covered is $325.

As given, Ethan hope to use two-fifths of his next paycheck to cover the remaining amount.

Now, using the inequality to find the amount of paycheck.

⇒ [tex]x\times \frac{2}{5} \geq \$ 325[/tex]

multiplying both side by 5

⇒ [tex]x\times 2\geq 325\times 5[/tex]

divinding both side 2

⇒ [tex]x\geq \frac{1625}{2}[/tex]

∴ [tex]x\geq \$ 812.5[/tex]

Hence, Ethan must make at least $812.5 in his paycheck to cover his remaining anount to buy dirt bike.