Which equality represents a proportional relationship?

A) -2.8/-2 = 4.2/3
B) 2.6/1.3 = 4.2/2
C) 2/5 = 8/9
D) 3/4 = 7/12

The value of x is –3.

Solution:

Given statement:

4 and Start Fraction 3 Over 10 End Fraction minus (2 and two-fifths x + 5 and one-half) = one-half (negative 3 and three-fifths x + 1 and one-fifth)

Let's convert this into algebraic expression.

[tex]$4\frac{3}{10} -\left(2\frac{2}{5}x+5\frac{1}{2}\right)=\frac{1}{2}\left(-3\frac{3}{5}x+1\frac{1}{5}\right)[/tex]

First convert mixed fraction into improper fraction.

[tex]$\frac{43}{10} -\left(\frac{12}{5}x+\frac{11}{2}\right)=\frac{1}{2}\left(-\frac{18}{5}x+\frac{6}{5}\right)[/tex]

[tex]$\frac{43}{10} -\frac{12}{5}x-\frac{11}{2}=-\frac{18}{10}x+\frac{6}{10}[/tex]

Now, take LCM and make the denominators same.

LCM of 2, 5, 10 = 10

[tex]$\frac{43}{10} -\frac{12\times2}{5\times2}x-\frac{11\times5}{2\times5}=-\frac{18}{10}x+\frac{6}{10}[/tex]

[tex]$\frac{43}{10} -\frac{24}{10}x-\frac{55}{10}=-\frac{18}{10}x+\frac{6}{10}[/tex]

Arrange like terms one side of the equation.

[tex]$\frac{18}{10}x -\frac{24}{10}x=\frac{6}{10}-\frac{43}{10}+\frac{55}{10}[/tex]

[tex]$\frac{18x-24x}{10} =\frac{6-43+55}{10}[/tex]

[tex]$\frac{-6x}{10} =\frac{18}{10}[/tex]

[tex]$-6x=\frac{18\times10}{10}[/tex]

[tex]$-6x=18[/tex]

Divide both sides of the expression by –6, we get

⇒ x = –3

Hence the value of x is –3.

Answer:

-3

Step-by-step explanation:

Final answer:

The expression 64-16 simplifies to 48, and does not need the distributive property for simplification as it is a straightforward subtraction.

Explanation:

The question is asking to use the distributive property to simplify the expression 64-16. While this expression doesn't necessarily require the distributive property as it's a simple subtraction, sometimes in mathematics we leverage distributive properties or other algebraic rules to simplify or reorganize expressions. However, if we have a closer look at the provided reference information, none of it relates directly to the expression 64-16, which simplifies to 48. Therefore, there's no need to apply the distributive property here; the expression is already in its simplest form.

Answer:

[tex]13 \frac{1}{8} + 21 \frac{3}{4} = 13 \frac{1}{8} + 21 \frac{6}{8} = 34 \frac{7}{8} [/tex]

[tex]35 \frac{1}{2} - 34 \frac{7}{8} = 35 \frac{4}{8} - 34 \frac{7}{8} = 34 \frac{12}{8} - 34 \frac{7}{8} = \frac{5}{8} [/tex]

The correct answer is C.

To determine what percent 225 is of 150, the calculation (225 / 150) × 100% is used, resulting in 225 being 150% of 150.

To find what percent of 150 is 225, we can use the formula for calculating percents:

Percentage = (Part / Whole) × 100%

Where 'Part' is 225 and 'Whole' is 150. Now, let's calculate:

Percentage = (225 / 150) × 100%

Percentage = 1.5 × 100%

Percentage = 150%. So, 225 is 150% of 150.

Answer:

(2*7)*6 or 2*(7*6)  = $84

Step-by-step explanation:

The associative property would always give the same value as an answer no matter the way of expression, once the expressions are right. So in this case,

Since has saves $2 every day and there are 7 days in a week,

2*7

and save this continously for 6 weeks.

(2*7)*6

This equals $84

OR

7 days in a week for 6 weeks

7*6

and saved $2 per day

2*(7*6)

This equals $84

Answer:

To find the probability that both friends randomly select a romance book one after the other, we can use the concept of conditional probability.

Let's denote the events:

- Event A: First friend selects a romance book.

- Event B: Second friend selects a romance book.

Given that there are 4 romance books left and a total of 7 books left (3 mystery + 4 romance), the probability of Event A happening for the first friend is:

\[ P(A) = \frac{4}{7} \]

After the first friend selects a romance book, there are now 3 romance books left out of a total of 6 books remaining (since one book has been chosen). So, the probability of Event B happening for the second friend, given that the first friend selected a romance book, is:

\[ P(B|A) = \frac{3}{6} = \frac{1}{2} \]

Now, to find the probability of both events happening, we multiply their probabilities:

\[ P(A \text{ and } B) = P(A) \times P(B|A) \]

\[ P(A \text{ and } B) = \frac{4}{7} \times \frac{1}{2} \]

\[ P(A \text{ and } B) = \frac{4}{14} \]

\[ P(A \text{ and } B) = \frac{2}{7} \]

So, the probability that both friends randomly select a romance book one after the other is \( \frac{2}{7} \).

Answer:

13.6 years

Step-by-step explanation:

From the question;

We are needed to determine the time it took for the money to reach the given amount;

[tex]A=P(1-\frac{r}{100})^n[/tex]

Where n is the interest periods;

Therefore;

[tex]12800=7500(1-\frac{4}{100})^n[/tex]

Dividing both sides by 7500, we get;

[tex]1.7067=(1-\frac{4}{100})^n[/tex]

[tex]1.7067=(1.04)^n[/tex]

Introducing logarithms on both sides;

[tex]log1.7067=log(1.04)^n\\nlog1.04=log1.7067\\n=\frac{log1.7067}{log1.04} \\n=13.63[/tex]

Thus, n=13.6 years

Thus, it would take 13.6 years for the invested money to accumulate to 12800 dollars

Answer:

-10 + 9x - 8

Step-by-step explanation:

4x2 + 7x - 5 subtracted from

9x2 -2x + 3

8 + 7x - 5

18 - 2x + 3

(8-18) (+7x - -2x) (-5 - +3)

-10 ( +7x +2x) (-5-3)

-10 + 9x -8

The result when 4x2 + 7x − 5 is subtracted from 9x2 − 2x + 3 is found by adding the additive inverse of each term in the polynomial being subtracted. Result is: 5x2 - 9x + 8.

Subtraction of Polynomials:

To find the result when 4x2 + 7x − 5 is subtracted from 9x2 − 2x + 3, first remember that subtraction of polynomials is equivalent to adding the additive inverse of each term in the polynomial being subtracted.

So, 4x2 + 7x − 5 becomes -4x2 - 7x + 5. We then add this to 9x2 − 2x + 3 term by term.

The final result is: (9x2 + -4x2) + (-2x - 7x) + (3 + 5) = 5x2 - 9x + 8

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Final answer:

To find the number of cookies Hans baked on the second day, we solve the equation x + 2x + x/2 = 224, where x is the number of cookies baked on the first day. Solving this, we find x=64, meaning he baked 128 cookies on the second day.

Explanation:

The question involves solving a problem about Hans, who spent three days baking a total of 224 cookies. On the second day, he baked twice as many cookies as on the first day, and on the third day, he baked half as many as on the first day. To find how many cookies he baked on the second day, let's denote the number of cookies baked on the first day as x.

On the second day, he baked 2x cookies.

On the third day, he baked x/2 cookies.

Adding these together: x + 2x + x/2 = 224.

Combining like terms, we get 3.5x = 224.

Dividing both sides by 3.5 gives x = 64.

Therefore, he baked 2x = 2*64 = 128 cookies on the second day.

Will has 24 quarters from 2005, which means the total value of these quarters equals to $6.

Will has 40 state quarters in total. If 3/5 of them are from 2005, this simply means that you need to find 3/5 of 40. So, we multiply 40 by 3/5:
40 * 3/5 = 24.

So, Will has 24 quarters from the year 2005.

Next, to find the value of these quarters, remember that each quarter is worth 25 cents (or $0.25 in dollar form). Therefore, we multiply the number of quarters (24) by the value of each quarter (.25):
24 * 0.25 = $6.

So, the total value of the quarters from 2005 is $6.

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Answer:

he had 343 pieces of candy after 22 days

Step-by-step explanation:

You can find this by first divide 10/ 115 this is equal to 15.5 to find how many candies he eats per day. Then you multiply 15.5 by 22(days) to find this answer .

Andre eats 9 pieces of candy per day. After 18 days, he had 43 pieces. By calculating his daily consumption, we can deduce that after 22 days, Andre will have 7 pieces of candy left.

The question asks us to determine how many pieces of candy Andre will have after 22 days, given the information on how many he had after 10 and 18 days.

First, let's find out how much candy Andre eats each day. After 10 days, he had 115 pieces, and after 18 days, he had 43 pieces.

Therefore, Andre will have 7 pieces of candy left after 22 days.

The fraction form of the number 10.666666667 is,

⇒ 32/3

A fraction is a part of the whole number and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called a fraction.

Given that,

A number is,

⇒ 10.6666666667

For the fraction form,

Let us assume that,

⇒ x = 10.666666667 .. (i)

Multiply by 10 on both sides,

⇒ 10x = 106.666666667  .. (ii)

Subtract (ii) from (i);

⇒ 10x - x = 106.666666667 - 10.66666667

⇒ 9x = 96

Divide 9 on  both sides,

⇒ x = 96/9

Or, it can be written as,

⇒ x = 32/3

So, the fraction form is, 32/3

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Final answer:

To convert the decimal 10.6666666667 to a fraction, we write it as the sum of 10 and the repeating decimal 0.6666666667. The repeating decimal equates to 2/3 after simplification, leading to the mixed number 10 2/3 or the improper fraction 32/3.

Explanation:

To convert the decimal 10.6666666667 to a fraction, we need to express it as the sum of its whole number part and its fractional part. The whole number part is 10, and the fractional part is 0.6666666667.

First, let's focus only on the fractional part. To turn 0.6666666667 into a fraction, notice that it's a repeating decimal. If we denote the repeating part by 'x', the equation will be:

x = 0.6666666667

Multiplying by 10 gives:

10x = 6.6666666667

Subtracting the original equation from this new equation:

9x = 6

Now, we solve for 'x':

x = 6/9

However, this fraction can be simplified to:

x = 2/3

Therefore, the fraction form of 10.6666666667 is 10 2/3, which can also be written as an improper fraction:

Answer:0

Step-by-step explanation:

Because any multiples by 0 is 0

Answer:

0

Step-by-step explanation:

Since 5 x n = 0, n has to be 0 since you can’t multiply anything but 0 to get the result of 0. Hope this helped!

The cube has the dimensions of:

[tex]1.26m \ by \ 1.26m \ by \ 1.26m[/tex]

A cube is a prism whose sides all have the same length. So the dimension of this cube will be given by one of its sides. For any object that is submerged in water, the volume of the displacement liquid equals the volume of the object.

[tex]For \ any \ cube \ the \ volume \ in \ terms \ of \ one \ side \ (s) \ is: \\ \\ V=s^3[/tex]

Suppose the volume of the tank when full is [tex]16m^3[/tex], so if it is 5/8 filled with water, then:

[tex]V_{5/8}=\frac{5}{8}(16) \\ \\ V_{5/8}=10m^3[/tex]

When the metal cube is placed in the tank, it is 3/4 full:

[tex]V_{3/4}=\frac{3}{4}(16) \\ \\ V_{3/4}=12m^3[/tex]

So the difference between these two volumes is the displacement volumen that equals the volume of the cube:

[tex]V=V_{3/4}-V_{5/8} \\ \\ V=12-10 \\ \\ V=2m^3[/tex]

So, the side of the cube is:

[tex]s=\sqrt[3]{2} \\ \\ \boxed{s\approx 1.26m}[/tex]

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Answer:

10

Step-by-step explanation

6/3.6=1.6 or 1 2/3

1.6*6=10

Answer:Start by enlarging the picture 2 inches by 3 inches up to 150%. This leads to a 3 inch by 4.5 inch picture. Eduardo wants to enlarge the picture to 4 inches by 6 inches. 4/3 = 1.33 6/4.5= 1.33 Therefore, the two whole number percents are 150% and 133%.

Answer:

[tex]4a(x-9)-7(x-9)=(x-9)[4a-7][/tex]

Step-by-step explanation:

we have the expression

[tex]4a(x-9)-7(x-9)[/tex]

Factor the term (x-9)

so

[tex](x-9)[4a-7][/tex]

therefore

[tex]4a(x-9)-7(x-9)=(x-9)[4a-7][/tex]

Answer:

1. B) Figure B.

2. C) Figure C.

3. D) Figure D.

4. C) Figure C.

Step-by-step explanation:

Given: Radius of Circle A= 4

           Radius of Circle B= 5

           Radius of circle C= 6

           Radius of circle D= 7

Now, finding circumference and area of all the circle.

We know, circumference of circle= [tex]2\pi r[/tex]

Area of circle= [tex]\pi r^{2}[/tex]

Where, r= radius of circle and π = 3.14

First, solving for figure A

Circumference= [tex]2\times 3.14\times 4= 25.12\ cm[/tex]

Area= [tex]3.14\times 4^{2} = 50.24\ cm^{2}[/tex]

Solving for Figure B

Circumference= [tex]2\times 3.14\times 6= 31.4\ cm[/tex]

Area= [tex]3.14\times 5^{2} = 78.5\ cm^{2}[/tex]

Solving for Figure C

Circumference= [tex]2\times 3.14\times 6= 37.68\ cm[/tex]

Area= [tex]3.14\times 6^{2} = 113.04\ cm^{2}[/tex]

Solving for Figure D

Circumference= [tex]2\times 3.14\times 7= 43.96\ cm[/tex]

Area= [tex]3.14\times 7^{2} = 153.86\ cm^{2}[/tex]

∴ 1. Answer is Figure B.

   2. Answer is figure C.

   3. Answer is Figure D

   4. Answer is Figure C.

Answer: f(x) = |x|

Step-by-step explanation:

A function is even if for every real N, f(N) = f(-N)

As you know, the module of a function always returns the positive value of a number, so I-3I = 3 = I3I (and that for every number)

So the function f(x) = IxI is an even function.

Functions with odd powers can not be even functions, so the second and tird options are discarded.

the fourth functions seems to be:

f(x) =∛x = (x)1/3 which is not even, because if x = 1, f(1) = 1, and if x=-1, f(-1) = -1

In the given functions, an even function is [tex]f(x)=|x|[/tex]. Therefore, the correct answer is option A.

A function's even, odd, or neither properties can be expressed algebraically or graphically in a variety of ways. If a function's graph remains unchanged when reflected in the y-axis, it is said to be an even function. Consider a function f(x) that is considered an even function if f(-x) equals f(x).

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

Let [tex]x = -3[/tex], we get

[tex]f(-3)=|-3|[/tex]

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

[tex]f(-x)= f(x)[/tex]

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

Let [tex]x = -1[/tex], we get

[tex]f(-1)=(-1)^3-1[/tex]

[tex]f(-1)=-1-1[/tex]

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

[tex]f(-x)\neq f(x)[/tex]

3) [tex]f(x)=-3x[/tex]

Let [tex]x = -1[/tex], we get

[tex]f(-1)=-3(-1)[/tex]

[tex]f(-1)=3[/tex]

[tex]f(-x)\neq f(x)[/tex]

4) [tex]f(x)=\sqrt[3]{x}[/tex]

Let [tex]x = -1[/tex], we get

[tex]f(-1)=\sqrt[3]{(-1)}[/tex]

[tex]f(-x)\neq f(x)[/tex]

Therefore, the correct answer is option A.

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Answer: Reid scored 1 and Maria scored 5.

Step-by-step explanation:

5 x 2 = 10

10-4= 6

5 + 1 = 6

Answer:

$256

Step-by-step explanation:

Alright so,

There are 7 days in a week and you're only working 4 of those days. In one week you would make $32 since 4*8=32. (4 being the days you work and 8 being the amount you get a day)

There are about 4 weeks in one month and 4*2=8, therefore there are 8 weeks in 2 months.

Remember, in one week you make $32. What you can do now is multiply, it's easy work and you'll get it fast:)

32x8=$265

Hope it helps!

Answer:

256

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

2+1=3

6 divided by 3= 2

20-3-2=15

Answer:

Completely factor both the numerators and denominators of all fractions.

Step-by-step explanation:

Answer:

7/12

Step-by-step explanation:

You have to find a common denominator, so you would multiply 3 from the 1/3 by 4 which gets you twelve. And bc you multiplied the 3 you have to multiple the 1 so 1/3 would be 4/12. You would then multiply 4 by 3 and get 12. Then do the same to the one on top. So 1/4 would be 3/12. You then add 3 and 4 and get 7. That’s the numerator, the denominator stays 12. So it would be 7/12

Answer:

Enzo is not correct bc he did not multiply the length and width by the same factor

Hopes that helped:P

Answer:

the answer is d

Step-by-step explanation:

like this if you like anime

Answer:

U'(-5, -2), V'(-3, -1), W'(-3, 3), Z'(-5, 6).

Plot these points. Then connect them to form trapezoid U'V'W'Z'.

Answer:

I assume your asking who's is better and why?

Step-by-step explanation:

Ralph has stated that for 1 shirt it will cost

$7.50 + $10 shipping= $17.50

Frank says it's $10 a shirt no shipping

if you work out the cost of Ralph's up to 5 shirts using the equation

($7.50 x number of shirts ) + $10 shipping

with each equation replace number of shirts with the number 1,2,3,4 and 5

1 shirt will cost you $17.50

2 shirts will cost you $25.00

3 shirts will cost you $32.50

4 shirts will cost you $40.00

5 shirts will cost you $47.50

at Frank's shop

1 shirt will cost you $10

2 shirts will cost you $20

3 shirts will cost you $30

4 shirts will cost you $40

5 shirts will cost you $50

Frank's is better to buy no more than 4 shirts from as he's cheaper up to 4 shirts.

Ralph is cheaper for bigger orders with 5 or more shirts in them

The question deals with the comparison of the costs of buying T-shirts from Ralph’s company versus Frank’s company. The cost differs based on the number of T-shirts purchased and the associated shipping fees.

The question is asking for a comparison between the two companies selling T-shirts and the associated costs. Ralph's company sells T-shirts for $7.50 each with an additional flat rate of $10 for shipping. In contrast, Frank's company sells T-shirts at a slightly higher price of $10 each but does not charge any shipping fees.

For example: If a customer wants to buy one T-shirt from each company, from Ralph’s company it would cost $7.50 (T-shirt price) + $10 (shipping fee) = $17.50. From Frank’s, it would cost $10 (T-shirt price) since shipping is free. So the cost would be different in both cases. However, if the customer opts to buy multiple t-shirts, the total cost might change depending on the number of t-shirts they decide to buy because of the fixed shipping cost on Ralph's side.

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Answer:

option c - 12 ab

Step-by-step explanation:

Two numbers are , 24 a³b and 36 a b².

The meaning of G C F between two number is that greatest number which divide both the number.

We will factorize , 24 a³b and 36 a b² and take out the common factors to determine their G CF.

24 a³ b= 2×2×2×3×a×a×a×b  

36 a b²=2×2×3×3×a×b×b

G C F(Greatest common factor)=2×2×3×a×b

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Answer:

you take 0.002 and multiply this by 0.2, to then get your answer of 0.0004

Step-by-step explanation: