how many liters each of a 50% acid solution and a 65% acid solution must be used to produce 60 liters of a 55% acid solution?

Answer: 20,-13

Step-by-step explanation:

We can rewrite the problem as an equation. This equation is x(x-7)=260 (x being the mystery number). We can simply this into x^2 -7x=260. We can then rewrite this as x^2 -7x -260=0. We need to find the roots of this quadratic, which are -13 and 20. You can find this by factoring the quadratic.

A mean is an arithmetic average of a set of observations. The score of the student is equal to 63.4.

A mean is an arithmetic average of a set of observations. it is given by the formula,

Mean = (Sum of observations)/Number of observations

Given the mean score was 75, while the standard deviation was 8. Therefore, the score of the student is,

Scre of the student = μ - 1.45σ = 75 - 1.45(8) = 63.4

Hence, the score of the student is equal to 63.4.

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The result of expanding the trigonometry expression [tex]\sin^2(\theta) * (1 + \cos(\theta))[/tex] is [tex]cos^0(\theta) + \cos(\theta) - \cos^2(\theta) - \cos^3(\theta)[/tex]

The expression is given as:

[tex]\sin^2(\theta) * (1 + \cos(\theta))[/tex]

Express [tex]\sin^2(\theta)[/tex] as [tex]1 - \cos^2(\theta)[/tex].

So, we have:

[tex]\sin^2(\theta) * (1 + \cos(\theta)) = (1- \cos^2(\theta)) * (1 + \cos(\theta))[/tex]

Open the bracket

[tex]\sin^2(\theta) * (1 + \cos(\theta)) = 1 + \cos(\theta) - \cos^2(\theta) - \cos^3(\theta)[/tex]

Express 1 as cos°(Ф)

[tex]\sin^2(\theta) * (1 + \cos(\theta)) = cos^0(\theta) + \cos(\theta) - \cos^2(\theta) - \cos^3(\theta)[/tex]

Hence, the result of expanding the trigonometry expression [tex]\sin^2(\theta) * (1 + \cos(\theta))[/tex] is [tex]cos^0(\theta) + \cos(\theta) - \cos^2(\theta) - \cos^3(\theta)[/tex]

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Answer:

Equation = [tex]\frac{3}{4}[/tex] x - 2 = [tex]\frac{5}{12}[/tex]

First: [tex]\frac{3}{4}[/tex] x = [tex]\frac{5}{12}[/tex] + 2

Then: [tex]\frac{3}{4}[/tex] x = [tex]\frac{29}{12}[/tex]

Answer: x = [tex]\frac{29}{9}[/tex] —> 9x = 29

—-

Have a nice day!!

Answer:

Step-by-step explanation:

The solution to a one-variable inequality can be graphed on a number line. The number line is shaded where the values satisfy the inequality. Boundaries of shaded regions are marked by points that are either a solid dot, or an open circle, depending on whether the point is included in the solution or not.

__

Here, the inequality tells us any value of x that is less than or equal to -1 will satisfy the inequality. Since -1 is part of the solution set, that boundary point will be marked with a solid dot. Values less than -1 are shown on a number line to the left of the point marked -1.

The graph will be a solid dot at x=-1, and shading to its left.

__

Possible solutions are any values less than or equal to -1. Some are ...

  -1

  -1.073

  -429

Answer:

x = 10

Step-by-step explanation:

I assume you mean

sqrt(x + 6) = x - 6

let's square the whole equation :

x + 6 = (x - 6)² = x² - 12x + 36

x² - 13x + 30 = 0

the general solution to a quadratic equation is

x = (-b ±sqrt(b² - 4ac))/(2a)

in our case

a = 1

b = -13

c = 30

x = (13 ±sqrt(13² - 4×1×30))/(2×1) =

= (13 ±sqrt(169 - 120))/2 = (13 ±sqrt(49))/2 =

= (13 ± 7)/2

x1 = (13 + 7)/2 = 20/2 = 10

x2 = (13 - 7)/2 = 6/2 = 3

for x = 10 we get for the original equation

sqrt(10+6) = 10-6 = 4

sqrt(16) = 4

4 = 4

so, x = 10 is a valid solution.

for x = 3 we get

sqrt(3 + 6) = 3 - 6 = -3

sqrt(9) = -3

3 = -3

so, this (x = 3) counts as an invalid solution, because most teachers nowadays expect the square root symbol operation to deliver only the positive solution.

although a square root is actually representing both : the positive AND the negative solution, because the negative number multiplied by itself is the same result as the positive number multiplied by itself.

so, actually

sqrt(9) = -3

± 3 = -3

is still correct and valid. but not what your teacher expects most likely.

in my younger days only the square root of a negative number counted as invalid operation (in the space of Real numbers, of course), and therefore only a solution leading to a square root of a negative number was an invalid solution.

Volume of a Rectangular Prism = length x width x height

Volume = 20

Length = 2

Width = 2

Height = d

20 = 2 x 2 x d

20 = 4 x d

d = 5

Answer: d = 5 centimeters

Hope this helps!

Answer:

d = 5 cm

Step-by-step explanation:

Volume of a rectangular prism: L*W*H

Substitute the values above into the formula:

V = L*W*H

20 = 2*2*d

20 = 4d

/4    /4

5 = d

Therefore, the value of d is 5 cm.

Hope this helps!

Answer: [tex]b^{2}(1-21a^{3})[/tex]

Step-by-step explanation:

[tex]b^{2} - 21a^{3} b^{2} \\b^{2}(1-21a^{3})[/tex]

Answer:

80 feet

Step-by-step explanation:

Area = length x width

We need to find length

[tex]2280 = 28.5l[/tex]

divide both sides by 28.5

[tex]l = 80[/tex]

22.5 = 1.5x

x = 22.5/1.5

x = 15

hope it helps...!!!

Answer:

x = 15

Step-by-step explanation:

1.5x = 22.5

x = 22.5/1.5

assuming your finding x

Answer:

£225

Step-by-step explanation:

[For percentage increase, add the percentage with 100, for percentage decreases substract the percentage from 100.]

100 + 25 = 125%

[tex]\frac{125}{100}[/tex] × 180 = £225

Answer:

165 divided by 11 = 15

154 divided by 14 = 11

306 divided by 17 = 18

322 divided by 14 = 23

Answer:A

Step-by-step explanation:

the correct choice is: B. The numbers in the pattern are odd.

To determine if the numbers in the pattern are even, odd, or alternate between even and odd, let's examine the first few numbers in the pattern:

First number: 41

Second number: 41 - 4 = 37

Third number: 37 - 4 = 33

Fourth number: 33 - 4 = 29

As we can see, the numbers in the pattern are decreasing by 4 in each step. The first number (41) is odd, and subsequently, each number is decreasing by an even value (4). Therefore, all the numbers in the pattern will be odd.

So, the correct choice is:

B. The numbers in the pattern are odd.

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Answer:

1.45

Step-by-step explanation:

weight of all books= 14×1.1= 15.4

weight of all duster=7×0.2= 1.4

weight of books and duster= 15.4+1.4=16.8

weight of the empty box = 18.25-16.8=1.45

A population about which we want to get some information is called the sample.

This is a portion of a population that is known to contain several parts of the population. The information that is gotten from the sample would be used to draw conclusion about the entire information.

Therefore from the definition above the answer to the question is the population sample.

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Answer:

0.0109056604

that is the answer, I used a calculator

The tangent is the ratio of the perpendicular and the base of the right triangle. Then tan A will be x/y.

The connection between the lengths and angles of a triangular shape is the subject of trigonometry.

The right-angle triangle ΔABC is given.

The angle ∠C is 90°.

And the perpendicular is x, the base is y, and the hypotenuse is z.

Then the value of the tangent of angle ∠A will be

The tangent is the ratio of the perpendicular and the base of the right triangle.

tan A = x/y

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Answer:

so the next 2 sequences would be 60 and 62

Step-by-step explanation:

The next two terms in the given arithmetic sequence are 60 and 62.

The arithmetic sequence is given as follows:

20, 32, 42, 50, 56, ?

To find the next two terms in the sequence, let's analyze the pattern:

The sequence increases by the following increments:

12, 10, 8, 6

We can observe that the increments are decreasing by 2 each time.

To find the next two terms, we can continue this pattern:

Increment: 4 (6 - 2)

Increment: 2 (4 - 2)

Adding the increments to the previous terms:

56 + 4 = 60

60 + 2 = 62

Therefore, the next two terms in the arithmetic sequence are 60 and 62.

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Answer:

4.03 < 16.5

Step-by-step explanation:

Four and three hundreths = 4.03

sixteen and five-tenths = 16.5

4.03 < 16.5

Answer:

C.

Step-by-step explanation:

7 7/8 rounds up to 8

2 1/10 rounds down to 2

8-3(2)=2

8 - 6 = 2

he would have about 2 pounds left

so the three pounds left is not reasonable

Answer:

Acount is a great place to work for a loved ones like you a few months

Answer:

The rule a+b=b+a, for all real numbers a,b, is the commutative law for addition. The fact that we can have g∘h≠h∘g, for some functions g,h, says that composition of functions is not commutative. Composition of functions is not the same as multiplication of functions: f=h∘gmeansf(x)=h(g(x))j=h⋅gmeansj(x)=h(x)g(x).

Answer:

answer = 12

Step-by-step explanation:

Let the smallest number be x

So

X+(x+2)+(x+4)+(x+6)=60

4x+12=60

4x=48

X=12

Answer:

Step-by-step explanation:

National car rental equation is

C = 14d + 0.20m  

- where C= total cost, d = the number of days and m = the total number of miles driven.

The list of the set of dimension for fencing the building around a rectangular plot of land is 10.5 meters and 21 meters.

area of rectangle = lw

where

Therefore,

perimeter = 2w+ l

42 = 2w + l

l = 42  - 2w

Hence,

area = w(42 - 2w)

180 = 42w - 2w²

-2w² + 42w - 180 = 0

-w² + 21w - 90 = 0

The dimension w can be found as follows;

w = - b / 2a

where

w = - 21 / 2 ×  -1

w = 10.5 meters

Then,

l = 42  - 2w

l = 42 - 2(10.5)

l = 21 meters

Therefore, the dimensions are 10.5 meters and 21 meters.

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Answer:

10.672hrs ( maybe)

Step-by-step explanation:

A can complete the work in 20 hrs then 1/3 part can be completed in 20*1/3=6.67hrs

B can complete the 1/4 part of the work in same time then B can complete hole work in 6.67*4=26.68 hrs

B can complete the 1/5 part of work in 26.67/5=5.336hrs

according to question C can complete 1/2part of work in same time then the whole work can complete in

2*5.336=10.672hrs

a) Triangle A is rotated 90 degrees anticlockwise about (-1,0) to give triangle A'.

Triangle A' is then reflected in the line y=0 to give triangle A''.

b) Rotation

a) Triangle A is rotated 90 degrees anticlockwise about (-1,0) to give triangle A'. Triangle A' is then reflected in the line y=0 to give triangle A''.

b) Rotation

Given,

Triangles A , A' , A'' .

Here,

The triangles are rotated and reflected to get different triangles .

Firstly ,

Triangle A is made to be rotated by 90° in anticlockwise direction at point (-1 , 0) .

To get A'' triangle A' is reflected from horizontal axis.

Triangle A maps into triangle A'' by rotation .

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