Which expression is equivalent to 2.8

A hair care company makes three batches of scented shampoo using the recipe shown. Each batch contains a different total amount

mr_godi [17]

Answer:

Batch 1: Pineapple = 3 1/2; Banana = 1 2/5

Batch 2: Pineapple = 8; Coconut = 4 4/5

Batch 3: Banana = 1; Coconut = 1 1/2

Step-by-step explanation:

For Batch 1:

We know that coconut is 3/10 of the mixture, and we have 2 1/10 coconut:

3/10x = 2 1/10

Converting 2 1/10 to an improper fraction, we have

3/10x = 21/10

Divide both sides by 3/10:

3/10x ÷ 3/10 = 21/10 ÷ 3/10

To divide fractions, flip the second one and multiply:

x = 21/10 × 10/3 = 210/30 = 7

This means we have 7 total of the mixture.

1/2 of this is pineapple: 1/2(7) = 7/2 = 3 1/2

1/5 is banana: 1/5(7) = 7/5 = 1 2/5

For Batch 2:

1/5 of the total is banana; we have 3 1/5 banana:

1/5x = 3 1/5

Convert the second fraction to an improper fraction:

1/5x = 16/5

Divide both sides by 1/5:

1/5x÷1/5 = 16/5÷1/5

Flip the second fraction and multiply:

x = 16/5×5/1 = 80/5 = 16

We have 16 of the total shampoo.

Pineapple is 1/2 of this:

1/2(16) = 8

Coconut is 3/10 of the total:

3/10(16) = 48/10 = 4 8/10 = 4 4/5

For Batch 3:

Pineapple is 1/2 of the total. We have 2 1/2 pineapple:

1/2x = 2 1/2

Convert the fraction on the right to improper:

1/2x = 5/2

Divide both sides by 1/2:

1/2x÷1/2 = 5/2÷1/2

Flip the second fraction and multiply:

x = 5/2×2/1 = 10/2 = 5

We have 5 total shampoo.

Banana is 1/5 of this:

1/5(5) = 1

Coconut is 3/10 of this:

3/10(5) = 15/10 = 1 5/10 = 1 1/2

4 0

3 years ago

Read 2 more answers

How do I solve this ? (5+i)(4-2i)

denpristay [2]

(5 + i)(4 - 2i)
20 - 10i + 4i - 2i²
20 - 6i - 2(-1)
20 - 6i + 2
20 + 2 - 6i
22 - 6i

3 0

3 years ago

Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.

Kisachek [45]

Answer:

https://newsela.com/read/lib-ushistory-roman-republic/id/27389/

Step-by-step explanation:

8 0

3 years ago

Find the missing factor 6s^2-7s-5=(3s-5)()

victus00 [196]

Answer: 2s + 1

Explanation:

1) Given expression: 6s² - 7s- 5 = (3s - 5) ( )

2) The missing factor ( ) is such that when it is multiplied by (3s - 5) the product is 6s² - 7s- 5.

3) Since the first term of the first factor starts with 3s, the first term of the second factor shall be 2s (since they have to yield 6s²). Then, you can write:

6s² - 7s- 5 = (3s - 5) (2s + )

4) The second term of the missing factor is positive because the product (+)(-) = (-) which is the sign of the third term of the polynomial.

5) The second term is such that when multiplied by - 5 is equal to the last term of the polynomial (also - 5), so this second terms is +1.

And you get: 6s² - 7s- 5 = (3s - 5) (2s + 1)

6) You can expand, using distributive property to confirm the result:

(3s - 5) (2s + 1 ) = (3s)(2s) + (3s)(1) - (5)(2s) -(5)(1) = 6s² - 7s- 5, which confirms the result.

3 0

3 years ago

A furniture shop refinishes chairs. Employees use two methods to refinish chairs. Method I takes 0.5 hours and the material cost

sveta [45]

Answer:

With Method I, they should plan to refinish 92 chairs and with Method II they should plan to refinish 70 chairs.

Step-by-step explanation:

This problem can be solved by means of a system of equations, that is to say a system that in this case will contain 2 linear equations with two variables: "x" and "y".

First you must define what your variables x and y are:

x: Chairs refinished by method I.
y: Chairs refinished by method II.

On the one hand, you know that between method I and method II they plan to work 151 hours. In method I, each chair takes 0.5 hours of work, this means that to obtain the total amount of time it takes to work in the "x" chairs by this method, 0.5 must be multiplied by the number of chairs. You can apply the same reasoning to calculate the total amount of time it takes to work on the "y" chairs by method II knowing that each chair takes 1.5 hours. Everything said above is represented by the equation:

 $\frac{1}{2} *x+\frac{3}{2} *y=151$ Equation (A)

In the equation the values 0.5 and 1.5 are represented in the form of a fraction (1/2 and 3/2 respectively) to be able to solve more in a way how the system of equations.

On the other hand, to state the other equation of the system, it must be taken into account that by method I the material costs $ 9 for each chair and by method II the material costs $ 7 for each chair. To determine the value of the material in each method, multiply the value of each chair by the amount of chairs refinished in each case. And the sum of the value of the materials of both methods must be $ 1318. This is represented by the equation:

9*x+7*y=1318 Equation (B)

Having both equations, you can solve the system. There are several methods to solve it, but one of the easiest and most widely used methods is substitution. This consists of isolating one of the variables from one of the equations and replacing it in the other equation.

In this case you can choose to isolate the variable x from equation B, resulting in:

$x=\frac{1318}{9} -\frac{7}{9} *y$ Equation (C)

It is always preferable to work in fractions for convenience to solve the calculations.

Now you replace the expression obtained from x in equation A, obtaining:

$\frac{1}{2} *(\frac{1318}{9} -\frac{7}{9} *y)+\frac{3}{2} =151$

Now you have an equation with a variable, "y", which can be solved, that is, you can get the value of "y". So "y"=70

Remembering that the variable "y" is the number of chairs refinished by method II, the value of "y" means that 70 chairs by that method were refinished.

To calculate the value of "x", you simply replace the value of "y" in either of the two equations (A) or (B) of the system and solve the equation. Or you can replace the value of "y" in equation (C): Either way the result must be the same: "x"=92

Remembering that the variable "x" is the number of chairs refinished by method I, the value of "x" means that 92 chairs by that method were refinished.

6 0

3 years ago

Which expression is equivalent to 2.8 – 8.2?