4. A scientist needs 10 liters of a 20% acid solution for an experiment, but she has
only a 5% solution and a 40% solution. To the nearest tenth of a liter, about how
many liters of the 5% and the 40% solutions should she mix to get the solution
she needs? Write and solve an equation to match the situation.
Equation:

Answer:

I think its 315

Step-by-step explanation:

because I think I have to multiply if u do I think it's 21x2.50x6 and it's equal to 315

The dimensions of the original shapes are 15 and 25 inches respectively

The formula for volume of a rectangle is expressed as;

Volume = length × width × height

From the information given, we have;

Substitute the values

1875 = 5 × y × y + 10

Divide both sides 5

1875 / 5 = y(y + 10)

expand the bracket

375 = y² + 10y

y² +10y - 375 = 0

y² + 25y - 15y - 375 = 0

y(y + 25) - 15( y + 25) = 0

y= 15 or y = -25

If y = 15 Inches

Width = 15 + 10 = 25 Inches

Thus, the dimensions of the original shapes are 15 and 25 inches respectively

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Answer:

50.2655

Step-by-step explanation:

Answer:

$166.75

Step-by-step explanation:

look at the photo.

Hope this helps. Please mark me brainliest!

The mathematical term that describes 2.12 in the expression 9.2y - 7.5y + 2.12 is a constant

Expressions are mathematical statements that are represented by constants, variables, coefficients and operators

The expression is given as

9.2y - 7.5y + 2.12

In the above expression, we can see that the variable is y

However, the number 2.12 has no variable attached to it

This means that the number is a constant

Hence, the mathematical term that describes 2.12 in the expression 9.2y - 7.5y + 2.12 is a constant

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Answer:

1/2

Step-by-step explanation:

When x = 20, y = 0

When x = 40, y = 10

When x = 60, y = 20

When x = 80, y = 30

When x = 100, y = 40

The slope is the change in y divided by the change in x.

First, find the change in x and y between any two points. We will use the first two points, (20, 0) and (40,10)

The change in x is 40 - 20 = 20

The change in y is 10 - 0 = 10

Divide the change in y by the change in x.

10 / 20 = 1/2

The slope is 1/2

Answer:

13

Step-by-step explanation:

9 - 3 = 6

5 - 12 = -7

6 - ( -7 ) = 13

Answer:

-1

Step-by-step explanation:

Absolute value means distance from zero.

9-3 is 6 so nothing special there. 5-12, though is negative 7, but since we need the absolute value of that it is just 7.  So our math problem becomes 6 - 7, which is -1.

The equation that shows the amount Christa and Megan each had in sales in July is 630 + 0.03x = 609 + 0.035x

An equation is used to show the relationship between numbers and variables. An equation can be linear, quadratic depending on the degree.

Let x represent the amount Christa and Megan each had in sales in July. Hence:

For Christa = 18(35) + 0.03x

For Megan = 21(29) + 0.035x

630 + 0.03x = 609 + 0.035x

The equation that shows the amount Christa and Megan each had in sales in July is 630 + 0.03x = 609 + 0.035x

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when testing for ODD or EVEN behaviour in a function, let's recall that we check what would the original function be if we were to use the argument -x in it?  well, hell let's do that and check what's cooking.

keeping in mind that if EVEN, we'll get back the original function, if ODD well get back a negative version of the original function.

[tex]\stackrel{original}{f(x)=7x^3-5x} \\\\[-0.35em] ~\dotfill\\\\ f(~-x~)=7(-x)^3-5(-x)\implies f(~-x~)=7(-x)(-x)(-x)-5(-x) \\\\\\ f(~-x~)=7(-1)(x)(x)(x)+5x\implies f(~-x~)=-7x^3+5x \\\\\\ f(~-x~)~~ = ~~-\underset{f(x)}{(7x^3-5x)}\qquad \leftarrow \qquad \stackrel{\textit{\LARGE odd}}{\textit{negative version of the original}}[/tex]

Answer: 4.5 x 10^-11

Step-by-step explanation:

4.5E-11 = 4.5 x 10^-11      ==> 4.5e-11 is basically 10^-11 multiplied by 4.5

The number of years it would take to double at 6% compounded annually is 11.55 years

The number of years it would take to double at 10.2% compounded annually is 6.8 years

When an amount earns at a compound interest, it means that the investment increases at an exponential rate. This means that the rate of growth in a new compounding period would be greater than the rate of growth at the previous compounding period.

When an amount is compounded monthly, it means that both the amount invested and the interest that has already been earned increases in value once a month, twelves times a year.

The formula that can be used to determine the number of years it would take the investment to double is:

Number of years it would take to double = In (FV / PV) / r

Where:

r = 6/12 = 0.5%

r = 10.2 /12 = 0.85%

Number of years it would take to double = In2 / 0.005 = 138.629 months

138.629 months / 12 = 11.55 years

Number of years it would take to double = In2 / 0.0085 = 81.547 months

81.547 months / 12 = 6.8 years

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Answer:

In plane Euclidean geometry, a rhombus is a quadrilateral whose four sides all have the same length. Another name is equilateral quadrilateral, since equilateral means that all of its sides are equal

Step-by-step explanation:

Answer:

mr walker sorted the dataset and got

Step-by-step explanation:

Answer:

x = -13

Step-by-step explanation:

-2 (x + 4) = 18

distributive property  -2x + (-8) = 18

simplify   -2x - 8 = 18

cancel out 8 by addition  -2x = 26

cancel out -2 by division  x = -13

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:105 R 0

945 divided by 9 equals

105 with a remainder of 0

Step-by-step explanation:

Answer:

112.5 días

Step-by-step explanation:

450 vacas (45 días/220 vacas) = 112.5 días

The parent function behind f(x) = 1 / (x - 4) - 3 is g(x) = 1 / x, which is modified by horizontal and vertical translations.

In this problem we find an expression that is shown as the image of a previous one, whose procedure of transformation must be inferred and explained. A direct inspection let us suppose that parent function might be g(x) = 1 / x and that the resulting expression is the result of a sequence of rigid transformations.

Let suppose that g(x) = 1 / x, then we apply the following two rigid transformations:

Horizontal translation

g'(x) = 1 / (x - 4)

Vertical translation

f(x) = 1 / (x - 4) - 3

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If the loan offers no payments for the first 5 months, the amount owed by Dillion when he begins making the payments is $2,441.03

What is the effective monthly interest rate on the loan?

The effective monthly interest rate on the loan is determined as the annual percentage rate(APR) of 6.6% divided by 12 months since there are 12 months in a year

effective monthly interest=6.6%/12

effective monthly interest=0.0055

FV=PV*(1+r)^N

FV=the balance owed after 5 months=unknown

PV=the loan amount=$2375

r=effectively monthly interest rate=0.0055

N=number of months that have passed since the loan was taken=5

FV=$2375*(1+0.0055)^5

FV=$2,441.03

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After solving the set of linear equation so formed, we conclude that value  of "S" and "J" is 4 and 5 respectively.

As per the question statement, A woman bought "S" shirts at $20 each and "J" jerseys at $ 15 each at a total Cost of $ 155. However, the total cost would have been $190 if she had purchased half as many shirts and twice as many jerseys. We are supposed to find the value of "S" and "J"

Let us first form the set of linear equation so formed.

Cost of one shirt = $20

Cost of "S" shirts = $20 x S = 20S

Cost of one jersey = $15

Cost of "J" jerseys = $15 x J = 15J

Total cost = $155

20S + 15J = 155 is our first linear equation obtained.

Now if however she bought half as many Shirts, and twice as many jerseys, then the total Cost would have been $190 and the equation formed will be :

20(S/2) + 15(2*J) = 190

or 10S + 30J = 190, is our second equation

This question is a classic example of forming a set of linear equation in two variable out of any given statement.

Solving the two sets of equation we get, S = 4 and J = 5

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The ages of Alan, Nate and Kai is 26, 24 and 13 years respectively

63 = x + (x - 2) + 1/2x

63 = x + x - 2 + 1/2x

63 = 2 1/2x - 2

63 + 2 = 2 1/2x

65 = 5/2x

x = 65 ÷ 5/2

x = 65 × 2/5

= 130/5

x = 26

Recall,

Alan's age = x years

= 26 years

Nate's age = (x - 2) years

= (26 - 2)

= 24 years

Kai's age = 1/2x

= 1/2(26)

= 13 years

Therefore, the ages of Alan, Nate and Kai is 26, 24 and 13 years respectively

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The figure with these coordinates are G'(3, -5), H'(2, 0), I'(0, -1) and J'(-1, -4)  given below. Therefore, option C is the correct answer.

Given that the shape is reflected across the y-axis.

The reflection of point (x, y) across the x-axis is (x, -y). When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).

The coordinates of the given figure are G(-3, -5), H(-2, 0), I(0, -1) and J(1, -4)

When the coordinates of the figure GHIJ are reflected across the y-axis we get G(-(-3), -5), H(-(-2), 0), I(0, -1) and J(-(1), -4)

So, the coordinates are G'(3, -5), H'(2, 0), I'(0, -1) and J'(-1, -4)

The figure with these coordinates are G'(3, -5), H'(2, 0), I'(0, -1) and J'(-1, -4)  given below. Therefore, option C is the correct answer.

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the probability that the sample contains two white balls and one green ball is 21/40.

In probability and statistics, an urn problem is an idealized mental exercise in which some objects of real interest (such as atoms, people, cars, etc.) are represented as colored balls in an urn or other container. One pretends to remove one or more balls from the urn; the goal is to determine the probability of drawing one color or another, or some other properties.

Total number of balls: 7 White and 3 Green = 10 balls

Cases for three balls are drawn at random:

Selection of 3 balls from 10 balls = [tex]^1^0C_3[/tex]

Case A: 1 White and 2 Green = [tex]\frac{^7C_1 * ^3C_2}{^1^0C_3} = \frac{7*3}{120} = \frac{21}{120} \\[/tex]

Case B: 2 White and 1 Green = [tex]\frac{^7C_2 * ^3C_1}{^1^0C_3} = \frac{21*3}{120} = \frac{63}{120}[/tex]

Case C: 3 White and 0 Green = [tex]\frac{^7C_3 * ^3C_0}{^1^0C_3} = \frac{28*1}{120} = \frac{28}{120}[/tex]

Case D : 0 White and 3 Green = [tex]\frac{^7C_0 * ^3C_3}{^1^0C_3} = \frac{1*1}{120} = \frac{1}{120}[/tex]

The probability that the sample contains two white balls and one green ball = Case B

So, the probability that the sample contains two white balls and one green ball = 63/120 = 21/40

Therefore, the probability that the sample contains two white balls and one green ball is 21/40.

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the probability that the sample contains two white balls and one green ball is 21/40.

In probability and statistics, an urn problem is an idealized mental exercise in which some objects of real interest (such as atoms, people, cars, etc.) are represented as colored balls in an urn or other container. One pretends to remove one or more balls from the urn; the goal is to determine the probability of drawing one color or another, or some other properties.

Total number of balls: 7 White and 3 Green = 10 balls

Cases for three balls are drawn at random:

Selection of 3 balls from 10 balls = [tex]^1^0C_3[/tex]

Case A: 1 White and 2 Green = [tex]\frac{^7C_1*^3C_2}{^1^0C_3} =\frac{7*3}{120}= \frac{21}{120}[/tex]

Case B: 2 White and 1 Green = [tex]\frac{^7C_2*^3C_1}{^1^0C_3} =\frac{21*3}{120}= \frac{63}{120}[/tex]

Case C: 3 White and 0 Green = [tex]\frac{^7C_3*^3C_0}{^1^0C_3} =\frac{35*1}{120}= \frac{35}{120}[/tex]

Case D : 0 White and 3 Green = [tex]\frac{^7C_0*^3C_3}{^1^0C_3} =\frac{1*1}{120}= \frac{1}{120}[/tex]

The probability that the sample contains two white balls and one green ball = Case B

So, the probability that the sample contains two white balls and one green ball = 63/120 = 21/40

Therefore, the probability that the sample contains two white balls and one green ball is 21/40.

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The written form of number/expression given; 2-⁴ such that the number is written as a fraction or whole number without exponents is; 1/16

It follows from the task content that 2-⁴ is to be written as a fraction without exponents.

On this note, it follows from the laws of indices that the expression can be evaluated as follows;

2-⁴

= 1/2⁴

= 1/(2×2×2×2)

= 1/16.

Ultimately, the written form of number/expression given; 2-⁴ such that the number is written as a fraction or whole number without exponents is; 1/16.

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The Function that has a range of {y|y ≤ 5} is  mathematically given as

f(x) = –(x – 4)2 + 5

This is further explained below.

Generally, the equation for the function is  mathematically given as

f(x)=-(x-4)^2+5

Where

f(x)=-(x-4)^2+5 is a quadratic function. Its graph looks like a parabola. One of the vertices in the graph is (4,5) and opens in a downward direction.

Proving that f(x)=-(x-4)^2+5≤  5 for all x

[tex]x^2 \geq 0 \Rightarrow(x-4)^2 \geq 0 \\\\-(x-4)^2 \leq 0 \\\\-(x-4)^2+5 \leq 5 \text {. }[/tex]

In conclusion, The Function that has a range of {y|y ≤ 5} is  mathematically given as

f(x) = –(x – 4)2 + 5

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Answer: (3+3*5):6

Step-by-step explanation:

[tex](3+3*5):6=\\(3+15):6=\\18:6=\\3[/tex]

Answer:

12

Step-by-step explanation:

1. \: 3 + 15 - 6 \\ 2. \: 18 - 6 \\ 3. \: 12

The fraction of the fabric is 7 3/24m.

It should be noted that from the information, Flor bought different fractions of fabric and we want to calculate the total.

Therefore the total fractions will be:

= 2 5/8 + 1 1/3 + 3 1/6

= 2 15/24 + 1 8/24 + 3 4 / 24

= 6 27 / 24.

= 7 3/24

The total fraction is 7 3/24 m.

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The percentage is 50%

From the question we are told that  

The  mean is μ= 14 hours

The  standard deviation is σ=1 hour

Generally on the normal distribution curve the mean divides the curve into  two. with the half to the left of the mean (50% to the left )representing the percentage of the batteries that will last less than 14 hours and  the area under the curve to the right (50% to the right)representing the percentage of batteries that will last longer than mean (14 hours )

Hence the percentage of the cell phone batteries that will be expected to last longer than 14 hours is 50%

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All steps to prove for the value of x are given below.

What is meant by Angle bisector?

Angle bisector is refer to a line that split an angle into two equal angles.

Given that;

Measure of ∠DEH = (10x - 2)°

Measure of ∠HEF = (6x + 10)°

Ray EH is angle bisector of ∠DEF.

Now, Ray EH is angle bisector of ∠DEF.

Hence,

1. Measure of ∠DEH = Measure of ∠HEF

Reason = Ray EH is angle bisector of ∠DEF.

2. (10x - 2)° =  (6x + 10)°

Reason = Measure of ∠DEH = (10x - 2)° and Measure of ∠HEF = (6x + 10)°

3. 10x - 2 - 6x = 6x + 10 - 6x

Reason = Subtract 6 both side.

4. 4x - 2 = 10

Reason = Apply sum or difference rule.

5. 4x - 2 + 2 = 10 + 2

Reason = Add 2 both side.

6. 4x = 12

Reason = Apply sum or difference rule.

7. x = 3

Reason = Divide 4 both side.

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[tex]\bf \longrightarrow{f(x) = \frac{1}{x - 7} \: \: \: \: , \: \: \: g(x) = \frac{1}{x - 5} }[/tex]

[tex]\bf \longrightarrow{f \circ g = \frac{1}{ \frac{1}{x - 5} - 7} }[/tex]

[tex] \bf \longrightarrow{so \: \: x - 5 \neq0 \: \: , \: \: \frac{1}{x - 5} \neq7} \\ \\ \bf \longrightarrow{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x \neq0 \: \: , \: \: \frac{1}{x - 5} \neq0 }\\ \\\bf \longrightarrow{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x = 5 \frac{1}{7} } \\ \\ \bf \longrightarrow{and \: a < b }\\ \bf \longrightarrow{so \: a = 5 \: , \: b = 5\frac{1}{7} }[/tex]