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2 years ago

If I mix 5 gallons of p% boric acid with 5 gallons of water, what is the concentration of the mixture?

Mathematics

1 answer:

Trava [24]2 years ago

4 0

Answer: The concentration of the mixture is 0.5 p % .

Step-by-step explanation:

Given: 5 gallons of p% boric acid is mixed with 5 gallons of water.

Amount of boric acid = p% of 5 gallons

$=\dfrac{p}{100}\times5\text{ gallons}= 0.05p\text{ gallons}$

Total solution : 5 +5 = 10 gallons

then, the concentration of the mixture = $\dfrac{\text{Amount of boric acid in solution}}{\text{Total solution}}\times100$

$=\dfrac{0.05p}{10}\times100\\\\=0.5p$

Hence, the concentration of the mixture is 0.5 p % .

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Venetta buys 2 pounds of pistachios and 3 pounds of almonds. The pistachios cost $4 more per pound than the almonds. She pays a

viktelen [127]

Answer:

A. One pound of pistachios plus 1 pound of almonds cost $20

C. Reducing the number of pounds of almonds by 1 results in a total cost of $40.

E. The cost p, in dollars, of 1 pound of pistachios is modeled by 2p + 3(p – 4) = 48.

Step-by-step explanation:

Let

x ----> the cost of one pound pistachios

y ----> the cost of one pound of almonds

we know that

x=y+4 -----> equation A

2x+3y=48 -----> equation B

substitute equation A in equation B and solve for y

2(y+4)+3y=48

2y+8+3y=48

5y=48-8

y=8

Find the value of x

x=8+4 =12

therefore

The cost of one pound pistachios is $12 and the cost of one pound of almonds is $8

Verify all statements

case A) One pound of pistachios plus 1 pound of almonds cost $20.

Is True

x+y=$12+$8=$20

case B) The pistachios cost twice as much per pound as the almonds

Is false

Because

2y=2(8)=$16

$16≠$12

case C) Reducing the number of pounds of almonds by 1 results in a total cost of $40

Is True

Because

2x+2y=2(12)+2(8)=$40

case D) The cost a, in dollars, of 1 pound of almonds is modeled by 2(a – 4) + 3a = 48.

Is false

The equation will be

2(a + 4) + 3a = 48.

case E) The cost p, in dollars, of 1 pound of pistachios is modeled by 2p + 3(p – 4) = 48

Is true

Because

p=a+4

Solve for a

a=p-4

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2 years ago

Two linear functions are shown below which function has the greater rate of change

Shtirlitz [24]

Answer:

On this case if we analyze both slopes, we see that function 2 has a greater rate of change because have a slope greater on absolute value than the slope for Function 1 (|-5|>|4|). No matter if the sign is positive or no we are analyzing the rate of change and for this case we need to use the absolute value to find the solution.

Step-by-step explanation:

Assuming the following two functions:

Function 1: y = 4x + 8

Function 2:

x y

2 20

4 10

6 0

We can find the slope for the second function like this:

$m =\frac{10-20}{4-2}=-5$

And in order to find the intercept we can use any point for example (2,20) and we got:

$20 =-5(2) +b$

And then $b=30$

So our function 2 is given by: $y =-5x +30$

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2 years ago

The vertices of ΔRST are R(–1,–1), S(–1,11) and T(4,11). Which could be the side lengths of a triangle that is similar but not c

Step2247 [10]

The side lengths could be 10, 24 and 26 units.

We must first find the side lengths. We use the distance formula to do this.

For RT:
$d=\sqrt{(11--1)^2+(-1--1)^2}
\\=\sqrt{(11+1)^2+(-1+1)^2}
\\=\sqrt{12^2+0^2}=\sqrt{144}=12$

For ST:
$d=\sqrt{(11-11)^2+(4--1)^2}
\\=\sqrt{0^2+(4+1)^2}=\sqrt{5^2}=\sqrt{25}=5$

For TR:
$d=\sqrt{(11--1)^2+(4--1)^2}
\\=\sqrt{(11+1)^2+(4+1)^2}=\sqrt{12^2+5^2}=\sqrt{144+25}=\sqrt{169}=13$

Our side lengths, from least to greatest, are 5, 12 and 13.

To be similar but not congruent, the side lengths must have the same ratio between corresponding sides but not be the same length. 10, 24 and 26 are all 2x the original side lengths, so this works.

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2 years ago

During an experiment, Juan rolled a six-sided number cube 18 times. The number two occurred four times. Juan claimed the experim

Maru [420]

Answer:

1) Juans claim is incorrect. The correct experimental probablilty is 2/9

Step-by-step explanation:

8 0

2 years ago

Read 3 more answers

Katie wants to create a rectangular frame for a picture. She has 60 inches of material. If she wants the length to be 3 more tha

Fofino [41]

Answer:

Largest possible length is 21 inches.

Step-by-step explanation:

Given:

Total material available = 60 inches

Length to be 3 more than twice of width.

To find:

Largest possible length = ?

Solution:

As it is rectangular shaped frame.

Let length = $l$ inches and

Width = $w$ inches

As per given condition:

$l = 2w+3$ ..... (1)

Total frame available = 60 inches.

i.e. it will be the perimeter of the rectangle.

Formula for perimeter of rectangle is given as:

$P = 2 \times (Width + Length)$

Putting the given values and conditions as per equation (1):

$60 = 2 \times (w+ l)\\\Rightarrow 60 = 2 \times (w+ 2w+3)\\\Rightarrow 60 = 2 \times (3w+3)\\\Rightarrow 30 = 3w+3\\\Rightarrow 3w = 27\\\Rightarrow w = 9 \ inch$

Putting in equation (1):

$l = 2\times 9+3\\\Rightarrow l = 21\ inch$

So, the answer is:

Largest possible length is 21 inches.

6 0

2 years ago