The numbers 82, 406 and 768 both include a 6. Which statement is true about the value represented by the 6 in 768?

$6.99 for 90 fl. oz of detergent is a better buy.

Arithmetic operations is a concept that concerns the study of mathematical operations like addition, subtraction, division, and multiplication.

The determination on the type which is a better buy can be estimated by finding the cost of each detergent in the two cases.

For the first case, we are being told that It cost $3.99 for 25 fl. oz. of detergent.

From that, the price for 1 fl. oz will be:

[tex]\mathbf{x = \dfrac{3.99 \times 1 }{25}}[/tex]

x = $0.1596

For the second case, if the price for 90 fl. oz is $6.99

For 1 fl.oz, we have:

[tex]\mathbf{x = \dfrac{6.99 \times 1 }{90}}[/tex]

x = $0.0777

Therefore, we can conclude that $6.99 for 90 fl. oz of detergent is a better buy since the amount of each detergent is lesser than that of 25 fl. oz.

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Answer: There will be 14 boys and 12 girls

Step-by-step explanation:

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The equation -9x+1=-9x+1 has infinitely many solutions.

This equation, -9x+1=-9x+1, is an example of an equation with infinitely many solutions. This means that any value of x will satisfy the equation. To see this, we can simplify the equation:

-9x + 1 = -9x + 1

By subtracting -9x from both sides, we get:

1 = 1

This is a true statement, which means that any value of x is a solution to the equation. Therefore, there are infinitely many solutions to this equation.

Abby and Lauren practiced for a total of approximately 1.58 hours on Wednesday.

The subject of this question is Mathematics and it concerns the addition of fractions. It is aimed at Middle School grade level.

Abby practiced for 11/12 of an hour and Lauren practiced for 2/3 of an hour, and to find out how long they both practiced, we need to add these two fractions together. Converting these fractions into like fractions (with same denominator), we have Abby's time as 33/36 (since 11/12 = 33/36) and Lauren's time as 24/36 (since 2/3 = 24/36).

Adding together Abby's practice time (33/36) and Lauren's practice time (24/36), gives 57/36 or 1 21/36 hours which is approximately 1.58 hours.

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The equation that represents the line y = -3x + 8

The slope intercept equation is represented as follows:

y = mx + b

where

m = slope

b = y-intercept

Therefore,

m = -3

y = -3x + b

using (5,-7)

-7 = -3(5) + b

-7 = -15 + b

b = -7 + 15

b = 8

Therefore,

y = -3x + 8

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Answer: $0.06

Step-by-step explanation:

Given : A bottle containing 64 fluid ounces of juice cost $3.84.

i.e. The cost of 64 fluid ounces of juice= $3.84

To find the unit rate , we apply unitary method.

The cost of one fluid ounces of juice = Cost of 64 fluid ounces divided by 64

= $3.84 ÷  64

= $0.06

Therefore ,  we get

The cost of one fluid ounces of juice= $0.06

Hence, the unit rate = $0.06

The quotient of 8/11 ÷ 3/5 is; 40/33

The quotient of 8/11 ÷ 3/5 can be evaluated as follows;

= 8/11 ÷ 3/5

= (8/11 ) × (5/3)

By multiplying the numerator s and denominators; we have;

= 40/33

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The mixed number equivalent to 7/12 is 0 and 7/12.

To add one-third and one-fourth, we need to find a common denominator. The least common multiple of 3 and 4 is 12.

Converting both fractions to have a denominator of 12:

1/3 = 4/12

1/4 = 3/12

Now, we can add the fractions:

4/12 + 3/12 = 7/12

The sum of one-third and one-fourth is 7/12. To express this as a mixed number, we need to divide the numerator (7) by the denominator (12):

7 ÷ 12 = 0 remainder 7

Therefore, the mixed number equivalent to 7/12 is 0 and 7/12.

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Kenny's unit rate of reading is 15/16 page per minute, which is determined by dividing the number of pages he reads by the time taken and then calculating the equivalent for one minute.

Kenny reads 3/8 page in 2/5 minute. To find Kenny's unit rate, we calculate how many pages he would read in one minute.

To find the unit rate, you divide the number of pages by the number of minutes:

(3/8) page / (2/5) minute

= (3/8) \/ (2/5)

= (3/8) \/ (5/2) [Because dividing by a fraction is the same as multiplying by its reciprocal]

= (3/8) * (5/2)

= (3*5) / (8*2)

= 15/16

So, Kenny's unit rate is 15/16 page per minute.

Answer: The given statement is FALSE.

Step-by-step explanation:  We are given to check whether the following statement is True of False :

"The expression 4x − 2(5x − 1) is equivalent to the expression 2 + 6x".

We will be using the following distributive property :

[tex]a(b+c)=ab+ac.[/tex]

We have

[tex]4x-2(5x-1)\\\\=4x-10x+2\\\\=-6x+2\\\\=2-6x\\\\\neq 2+6x.[/tex]

Therefore,  expression 4x − 2(5x − 1) is NOT equivalent to the expression 2 + 6x.

Thus, the given statement is FALSE.

The value for the expression 905 - 425 is 407.

The place value of a number is given as:

Example:

1234.567

1 = thousand place value

2 = hundred place value

3 = tens place value

4 = ones place value

5 = tenths place value

6 = hundredths place value

7 thousandths place value

We have,

905 - 435

905 = Nine hundred + zero tens + five ones

425 = Four hundreds + two tens + five ones

Now,

905 - 435

= 407

Thus,

The value is 407.

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Final answer:

To calculate how long it will take for a bank account with an initial deposit of $500 to reach $600 at a 5% simple interest rate, you first determine the total interest required ($100), then use the formula I = Prt to solve for time. The calculation shows that it will take 4 years for the account to reach $600.

Explanation:

To determine how long it will take for an account to reach $600 with an initial deposit of $500 at a simple interest rate of 5%, we can use the simple interest formula I = Prt, where I is the interest, P is the principal amount, r is the rate, and t is the time in years.

First, we calculate the total interest needed for the account to reach $600:

Next, we use the formula I = Prt to solve for time (t):

Therefore, it will take 4 years for the account to reach $600.

Answer:

[tex]y=17x-187[/tex] where x>11

Step-by-step explanation:

Niall gets $34 for 2 hours.

So, he gets [tex]34/2=17[/tex] dollars per hour.

Now, he owes $187 to his cousin.

Let the number of hours he works be = x

Let the money left with him after paying his cousin be = y

So, the equation forms:

[tex]y=17x-187[/tex]

Rather we can say it is :

[tex]y=17x-187[/tex] where x>11

If we want to know how many hours are needed to pay the debt, we can consider y = 0

[tex]17x-187=0[/tex]

[tex]17x=187[/tex]

[tex]x=187/17[/tex]

So, x = 11 hours

So, Niall needs 11 hours of work to pay back his cousin and after that all his earnings is 'y'. When x>11 then 'y' will have some money left.