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?

There are 5/9 groups in 1

6 divided by 9/5 is 3 1/3.

An improper fraction is a non integer where the numerator is greater than the denominator. An example is 9/5.

In order to determine the the number of groups of 9/5 that are in 1, divide 1 by 9/5

1 ÷ 9/5

1 × 5/9

9/9 × 5/9 = 5/9

6 ÷ 9/5

6 × 5/9 = 10 / 3 = 3 1/3

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Answer:

1/4

Step-by-step explanation:

Convert fractions to decimals

[tex]1-0.25-1/2\\1-0.25-0.5\\[/tex]

Add/Subtract

[tex]1-0.25-0.5\\= 0.75-0.5\\= 0.25\\= \frac{1}{4}[/tex]

-3/8 - 7/12 =

First we need to get the denominators same.

(-3 x 3/8 x3) - (7 x 2/12 x 2) =

-9/24 - 14/24 =

-9 - 14/24 =

-23/24

Answer = -23/24

Answer:

5/24

Step-by-step explanation:

y-x y is 7/12 so its positive x is -3/8 so its negative the answer is 5/24

The proposed skyscraper is 172.8 m tall

From the question, we are to determine the how tall the proposed skyscraper is in meters

From the given information,

The scale of the model is

1 in : 7.2 m

and

The model is 2 ft tall

First, convert 2 ft to inches

NOTE: 1 foot = 12 inches

∴ 2 feet = 2 × 12 inches

= 24 inches

Now,

If 1 inch represents 7.2 m

Then,

24 inches will represent 24 × 7.2 m

24 × 7.2 m = 172.8 m

Hence, the proposed skyscraper is 172.8 m tall

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The weight of both books when put on the scale together is [tex]\frac{37}{24}=1\frac{13}{24}[/tex].

The smallest positive integer that is divisible by both a and b is known as the least common multiple (lcm), lowest common multiple (lcm), or smallest common multiple of two numbers a and b in mathematics and number theory.

Let the weight of the two books Paulette had be x and y.

The weight of one of the books is x = 7/8 pounds.

The weight of the other book is y = 2/3 pound.

If the books are put on the scale then the total weight of the books will be:

[tex]x+y=\frac{7}{8}+\frac{2}{3}[/tex]

The least common multiple or LCM of 8 and 3 is 24.

[tex]x+y=\frac{21+16}{24}[/tex]

[tex]x+y=\frac{37}{24}[/tex]

The correct option is (B) [tex]\frac{37}{24}=1\frac{13}{24}[/tex].

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Answer:

The third option.

The others are being multiplied by a negative, which a negative times a negative is a positive, but the third is 3 negatives and 1 positive so it is positive.

Step-by-step explanation:

Hope it helps! =D

Answer:

2

Step-by-step explanation:

PRT = I = 2700

P = 27,000

R = 0.05

Find T

2700 = 27000 x 0.05 x T

T = 2700/ ( 27000 × 0.05 ) = 2 years

The vertex of the function is a = 1 , b = -8 and c = 15

The intercept of the function is 15

The equation is given as

                               g(t) = t² - 8t + 15

which gives us the parabolic graph and lets us keep the domain as

-6 ≤ t ≤ 6

The graph of this equation is attached.

The vertex of the function can be found by comparing it with the parabolic equation.

                      at² + bt + c = 0

                        t² -  8t + 15 = g(t)

Therefore, the vertex of the function is

           a = 1 , b = -8 and c = 15

The intercept can be found by taking t=0 , we get

   g(0) = 0² - 8(0) + 15

Therefore, the intercept of the function is 15

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Answer:

C

Step-by-step explanation:

at starting time x = 0    the fish is at   -3 meters

 for each second the fish goes another -7 meters

If there are 7 red balls and 10 black balls in a bag, then we can say that  red and black balls are present in the bag in ratio 7: 10

Ratio is a relationship between two or more values. a  units per b units.

a/b or a:b .

A part to part ratio of 7:10 can be written in the form of example given below:

If there are 7 red balls  and 10 black balls in a bag, then we can say that red and black balls are present in the bag in ratio 7:10

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The correct statement for y = x - 13 is C. It is the graph of y = x translated 13 units to the right to the parent function y = x.

A function can be thought of as output for the given or specified set of inputs.

Given a parent function y = x and it is a linear function and also reflexive.

The function y = x - 13 implies

x - 13 = 0 or x = 13.

∴ The graph of the function y = x - 13 will shift to the right along the x-axis by 13 units to the right. This is also known as translation.

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Answer:The correct statement for y = x - 13 is C. It is the graph of y = x translated 13 units to the right to the parent function y = x.

Step-by-step explanation:

What is a function?

A function can be thought of as output for the given or specified set of inputs.

Given a parent function y = x and it is a linear function and also reflexive.

The function y = x - 13 implies

x - 13 = 0 or x = 13.

∴ The graph of the function y = x - 13 will shift to the right along the x-axis by 13 units to the right. This is also known as translation.

Answer:

The answer is 5x+17

Answer:

X = 7

Step-by-step explanation:

2(x+7) +3(x+7)

2x + 14 + 3x + 21

2x +3x +14 +21

5x ÷5 + 35 ÷5

x. = 7

Answer:

10 masks

Step-by-step explanation:

divide 6 1/4 yards by 5/8 yards

change 6 1/4 to an improper fraction - 25/4

25/4 ÷ 5/8

to divide fractions, find reciprocal of divisor

25/4 * 8/5

=10

so 10 masks

Answer:

[tex]7x + 6[/tex]

Step-by-step explanation:

We can combine all terms that share the same variable.

For example, we can combine [tex]3x + 5x[/tex], which is 8x, however, we cannot combine [tex]3x + 4t[/tex], as 3x and 4t are terms with different variables. The latter applies to combining terms that include variables and terms that do not - You cannot combine them.

The trick to combining terms with common variables is to combine them like you'd combine any pair of regular numbers.

Just like [tex]6 + 3 = 9[/tex], then [tex]6x + 3x = 9x[/tex].

Just like [tex]6 - 3 = 3[/tex], then [tex]6x - 3x = 3x[/tex].

This is done through a process known as factorizing, however, I believe you will learn this later if you are just now studying combining terms with variables.

Onto your question, we can combine 10x and -3x together, however, we cannot combine either of those terms with 6.

[tex]10x - 3x + 6 \to 7x + 6[/tex]

Answer: q I made 2 quarts of lemonade using 1/4 quarts is x = 1/8 lemonade

q I made 8 quarts of lemonade using 1/4 quarts is x = 1/32 lemonade

q I made 12 quarts of lemonade using 1/4 quarts is x = 1/48 lemonade

q I made 18 quarts of lemonade using 1/4 quarts is x = 1/72 lemonade

Step-by-step explanation:

Given data,

If q I s the number of quarts of lemonade, then 1/4 quarts can be used the number of cups of lemonade mix.

we know that, first we can use 2 quarts,

Then,

q I made 2 quarts of lemonade using 1/4 quarts

so,

using proportion

Find out the amount of sugar needed to make 1 quart of lemonade

Let,

x ----> the amount of lemonade

[2/(1/4)]  lemonade/quarts of lemonade = (1/x)(quarts lemonade/quarts of lemonade)

                   [2/(1/4)] = 1/x

                    8/1 = 1/x

                    x = 1/8 lemonade

q I made 8 quarts of lemonade using 1/4 quarts

so, we can write,

                   [8/(1/4)] = 1/x

                   32/1 = 1/x

                   x = 1/32

q I made 12 quarts of lemonade using 1/4 quarts

so, we can write,

                   [12/(1/4)] = 1/x

                   48/1 = 1/x

                   x = 1/48

q I made 18 quarts of lemonade using 1/4 quarts

so, we can write,

                   [18/(1/4)] = 1/x

                  72 /1 = 1/x

                  x = 1/72

q I made 2 quarts of lemonade using 1/4 quarts is x = 1/8 lemonade

q I made 8 quarts of lemonade using 1/4 quarts is x = 1/32 lemonade

q I made 12 quarts of lemonade using 1/4 quarts is x = 1/48 lemonade

q I made 18 quarts of lemonade using 1/4 quarts is x = 1/72 lemonade

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The value of (f + g)(x) can be find out by adding both given functions f(x) and g(x) and its value will be x² - x + 6.

What is function ?

A function is a relationship between inputs and outputs where each input has precisely one output and the output can be linked to its input.

The given functions are :

f(x) = x² + 1

g(x) = 5 - x

We now have to find the value of (f + g)(x).

We know that the value of (f + g)(x) can be calculated by simply adding the values of both given functions which are f(x) and g(x).

So ,

(f + g)(x) = f(x) + g(x)

Now , let's substitute the values of both functions f(x) and g(x) into the above equation , so we will get :

(f + g)(x) = (x² + 1 ) + (5 - x)

Rearranging and solving the terms we get the value of (f + g)(x) as :

(f + g)(x) = x² - x + 6

Therefore , the value of (f + g)(x) can be find out by adding both given functions f(x) and g(x) and its value will be x² - x + 6.

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Answer:

I think (2x−3)(3x+5)

The answer is C.....................

Answer:

A) 0.

Step-by-step explanation:

There is no yellow on the plane, therefore, the probability that the spinner would land on a nonexistent part of the plane is 0.

Answer:

[tex]\frac{5}{4}[/tex]

Step-by-step explanation:

To find the slope on a graph, the easiest way is to use the "rise-over-run method."

First, from the leftmost point, count how many points it takes to get to the same y-coordinate as the point.(only count UP and DOWN. If you have to go up to reach the point, the numerator is positive. Otherwise it is negative) Next, figure out how many points it takes to get to the same x-coordinate starting from where you counted up from, therefore landing on the rightmost point. (only count LEFT and RIGHT. If you have to go right to reach the point, the denominator is positive. Otherwise it is negative)

In this graph, we go up 5 and right 4. Therefore the answer is [tex]\frac{5}{4}[/tex].

(I like starting on the leftmost point first and then doing rise-over-run. You don't necessarily have to but remember, if both the numerator and denominator are negative, then the fraction is positive)

Answer:

slope: [tex]\frac{5}{4}[/tex]

Step-by-step explanation:

Slope Formula:  [tex]\frac{rise}{run}[/tex]

tip:

EASIER WAY to find the slope: From the bottom dot (-1,-1) count up until you reach the line where the other dot (3,4) so this would be 5 (the RISE)

then count ACROSS (run) it until you reach the dot. This would be 4.

Answer: 5/4 is the slope of the line.

video explanation: https://youtu.be/sOnIGoPC4y4

Answer:

  1

-------

  2

Step-by-step explanation:

    2                1

- ------- ×  - 1 -------

   5                 4

    2                5

- ------- ×  -   -------

   5                 4

   2(4)          5(5)

- ------- ×  -   -------

   5(4)          4(5)

   8               25

- ------- ×  -   -------

   20             20

--------------------------------------------------------------

(-8) × (-25) = 200

20 × 20 = 400

---------------------------------------------------------------

200 ÷ 200

-------

400 ÷ 200

  1

-------

  2

I hope this helps!

3 times 15 will get us close to 45 tenths without going over

x=3

This is further explained below.

Generally, In the field of mathematics, a formula is referred to as an equation when it is used to represent the equivalence of two expressions by connecting them with the equals sign (=). In other terms, an equation is an expression that is used in mathematics.

In conclusion, The equation for the word problem is given as

x*15 ≡45

Therefore

x ≡45/15

x=3

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Using translation concepts, the rule for each vertex of the triangle after the translation 9 units right and 9 units down is given by:

(x,y) -> (x + 9, y - 9).

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

For this problem, the transformations on the triangle are given as follows:

Thus the rule for each vertex of the triangle after the translation 9 units right and 9 units down is given by:

(x,y) -> (x + 9, y - 9).

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[tex] \large \bf \implies \: \boxed{ \tt{y = {4x}^{2} + 24x + 38}}[/tex]

[tex] \bf \longrightarrow \: x = - \frac{24}{2 \times 4} = - 3 \\ \\ \bf \longrightarrow \: y = \frac{4 \times 4 \times 38 - {24}^{2} }{4 \times 4} = 2 \\ \\ \\ \bf \longrightarrow \: y = {4x}^{2} + 24x + 38[/tex]

11/4 or 2.75 part is remaining out of 13 ¼

Total sheet of steel will be 13 ¼

So dividing the whole sheet into 3 parts : let one piece be x and other be y and the remaining be z

as per the question x=2 3/4 and y amounts to = 31/4

so we need to find z

x + y + z= 13 1/4 (equation 1)

substituting the value of x= 2 3/4 and y = 31/4 in equation 1

2 3/4 + 31/4 + z= 13 1/4

converting mixed fraction into improper fraction

11/4 + 31/4 + z =53/4

z =53/4 -(11/4 + 31/4)

z = 11/4

hence z= 11/4

Therefore, out of 13 ¼, 11/4 or 2.75 part remains

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The equation  4x + 12 = -2x + 16 is one solution.

A statement of equality between two expressions consisting of variables and/or numbers.

Given:

4x + 12 = -2x + 16

Now solving for x

4x + 2x = 16 - 12

6x = 4

x= 4/6

x=2/3

Hence, the equation  4x + 12 = -2x + 16 has one solution.

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The expressions matched with their corresponding simplified expressions are

(5⁻⁹)⁴         →   1/5³⁶

5⁹/5⁴         →   5⁵

5⁴ × 5⁹      →   5¹³

(5⁴)⁹          →   5³⁶

5⁻⁹/5⁴       →   5⁻¹³

From the question, we are to match each of the given expressions on the left with the terms of the right

First, we will simplify each of the expressions

Multiplying the exponents

5⁻⁹ˣ⁴

= 5⁻³⁶

= 1/5³⁶

Applying the division law of indices

5⁹/5⁴ = 5⁹⁻⁴

= 5⁵

Applying the multiplication law of exponents

5⁴ × 5⁹ = 5⁴⁺⁹

= 5¹³

Multiplying the exponents

5⁴ˣ⁹

= 5³⁶

Applying the division law of indices,

5⁻⁹⁻⁴

= 5⁻¹³

Hence, the expressions matched with their corresponding simplified expressions is

(5⁻⁹)⁴         →   1/5³⁶

5⁹/5⁴         →   5⁵

5⁴ × 5⁹      →   5¹³

(5⁴)⁹          →   5³⁶

5⁻⁹/5⁴       →   5⁻¹³

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The area of the circle, in terms of pi is calculated as: 72.25π in.²

The circumference/perimeter of a circle = 2πr

The area of a circle = πr², where the radius of the circle is represented as "r".

Given the following:

The circumference of the circle = 17π inches.

Therefore:

17π = 2πr [circumference formula]

Divide both sides by 2π to find r (radius of the circle)

17π/2π = 2πr/2π

17/2 = r

r = 17/2 or 8.5 inches

Area of the circle = πr² = π(17/2)²

Area of the circle = πr² = π(8.5)²

Area of the circle = πr² = 72.25π square inches.

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Answer:

i) -2.5

ii) 3/4 - 0.250

iii) 0.282

iv) 85% - 0.850

v) [tex]\sqrt{3\\[/tex] - 1.7320