How much of a(n) 70% orange juice drink must be mixed with 18 gallons of a 30% orange juice drink to obtain a mixture
that is 50% orange juice?

After simplifying the expression, - ( 7 x - 3 y ) + 2 ( 3/4 x + 1/2 y), we get the result as - 11 / 2 x + 4 y.

- ( 7 x - 3 y ) + 2 ( 3/4 x + 1/2 y)

First we will multiply 2 and open the brackets.

So, we get that:

- 7 x + 3 y + 3/2 x + y

Combining the like terms, we get that:

= ( - 14 + 3 ) x / 2 + 3 y + y

Simplifying and solving the expression to obtain the result, we get that:

= - 11 / 2 x + 4 y.

Therefore, after simplifying the expression, - ( 7 x - 3 y ) + 2 ( 3/4 x + 1/2 y), we get the result as - 11 / 2 x + 4 y.

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The height of the cylinder is 20 meters.

The density of a cylinder is determined by its volume, which represents how much material may be immersed in it or carried inside of it. The formula r2h, where r is the radius of the circular base and h is the height of the cylinder, determines the volume of a cylinder. Any substance that can fill the cylinder consistently with liquid or another material may be used as the material. Check the shape's volume here.

Formula= V = π r² h

According to the given value,

The formula for the volume of a cylinder is V=πr²h.

The cylinder to the right has an exact value of 500π cubic meters.

Its radius is given as 5 meters in the figure.

volume of the cylinder.

V = π r² h

We have,

V = 500π cubic meters

500π cubic meters = πr²h

Find the height of the cylinder.

We have,

500π cubic meters = πr²h

Divide both sides by π

500cubic meters = r²h

We have,

r = 5

500 cubic meters = 5² square meters x h

500cubic meters =  25 square meters x h

Divide both sides by 25

20 meter = h

h = 20 meters

Thus the height of the cylinder is 20 meters.

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Step-by-step explanation:

f(x) = 2x² - 5x

= f(x-4) + f(x)

= [2.(x-4)² - 5.(x-4)] + [2x² - 5x]

= [2.(x² - 8x + 16) - 5x + 20] + [2x² - 5x]

= [2x² - 16x + 32 - 5x + 20] + [2x² - 5x]

= [2x² - 21x + 52] + [2x² - 5x]

= 4x² - 26x + 52

Answer:

2,957,468

Step-by-step explanation:

Each digit to the left is worth 10 times more than the same digit one place to the right.

If 2,957,648 becomes 2,957,468, the 4 moves from the tens place to the hundreds place, and now its value is 400 instead of 40, so it's 10 times greater.

=========================================================

Explanation:

The output of an absolute value is never negative.

The result of |2x+2| can never be negative, so we will have no solutions for the portion |2x+2| < 0

There will be one solution for |2x+2| = 0 as shown in the steps below

|2x+2| = 0

2x+2 = 0

2x = -2

x = -2/2

x = -1

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

Check:

|2x+2|  ≤ 0

|2(-1)+2| ≤ 0

|-2+2| ≤ 0

|0| ≤ 0

0 ≤ 0

We get a true statement at the end to fully confirm the single solution of x = -1

Answer:

0

Step-by-step explanation:

The area of the circular plate is 9234 inches²

The plate is circular and have a circumference of 34.54 inches.

Hence, let's find the radius of the circular plate using the circumference of the circular plate.

circumference of the circular plate = 2πr

where

Therefore,

34.54 = 2π × r

r = 34.54  / 2π

r = 17.27π

Therefore,

area of the circular plate = πr²

area of the circular plate = π × ( 17.27π)²

area of the circular plate = π³ × 298.2529

area of the circular plate = 3.14³ × 298.2529

area of the circular plate = 9233.65447952

area of the circular plate = 9234 inches²

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Answer: The equations are:

X+3=Y;

45X + 75Y  = 1455 ;

The variables used are X and Y specifying number of small and large boxes

Step-by-step explanation:

Let X be  the number of small boxes

Let Y be  the number of big boxes

The first equation is:  X+3=Y;  (  Since there were 3 more small boxes shipped than large boxes )

The second equation is:    45X + 75Y  = 1455   ( this is because the small box weighs 45 pounds and big box weighs 75 pounds.  The total weight of the small boxes is 45 times the weight of each individual box. And the total weight of the second boxes is equal to 75Y.)

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Answer:

Step-by-step explanation:

The variables used are A and B specifying number of small and large boxes

Let the number of small box is A

Let the number of large box is B

The first equation is:  A+3=B;

(  Since there were 3 more small boxes shipped than large boxes )

The second equation is:    45A + 75B  = 1455   ( this is because the small box weighs 45 pounds and large box weighs 75 pounds.  The total weight of the small boxes is 45 times the weight of each  box. And the total weight of the second boxes is equal to 75B.)

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64.71% percent of the data values are greater than 80.

What is the percentage?

Min. value = 30

Max. value  = 85

Percentage (%) of data values greater than 30(thirty) = [tex]\frac{55}{85} X 100[/tex]

                                              = 64.71%

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Answer:

Step-by-step explanation:

      Atsu  :  Sabu

         3     :     7

         x     :    x + 20

x is equal to the number of cedis

cross multiply the ratio above

3(x+20) = 7x

3x + (20×3) = 7x

3x + 60 = 7x

3x - 3x + 60 = 7x - 3x                  (put - 3x on both sides of the equation)

60 = 4x

60/4 = 4x/4                                (divide both sides by 4)

15 = x

Answer:

-16=0.2b

-16/0.2=b

b= -80 answer

Answer:

In the equation "-16 = 0.2b", b is equal to -80.

Step-by-step explanation:

-16 = 0.2b

Turn the decimal into a fraction. This will make solving simpler.

-16 = [tex]\frac{1}{5}b[/tex]

Multiply both sides by 5.

-80 = 1b

Simplify.

b = -80

The  number corrected to 1 decimal place is 78.5

The number corrected to the nearest hundredth is 78.47

From the question, we are to estimate the given number to the nearest 1 decimal place

The given number is

78.4695

Correcting to 1 decimal place

In the given number, we can observe that the hundredth digit is greater than 5, thus we will add 1 to the tenth digit

Thus,

78.4695 corrected to 1 decimal place is 78.5

Correcting to the nearest hundredth

The thousand digit is greater than 5, thus we will add 1 to the hundredth  digit

Thus,

78.4695 corrected to the nearest hundredth is 78.47

Hence,

The  number corrected to 1 decimal place is 78.5

The number corrected to the nearest hundredth is 78.47

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Expressing x in terms of 0 and y gives x = 0 + (32/23)y

Given the expression 23x-32y = 0 with number bases x and y.

This equation actually expresses 0 in terms of x and y as 0 is isolated to one side of the equality.

We have to express x in the same equation in terms of 0 and y.

So we need to isolate x to one side of the equality.

23x-32y = 0

⇒23x = 0 +32y

Dividing throughout by 23 gives,

⇒ x = 0 + (32/23)y

This is x expressed in terms of 0 and y

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X = 0.6444

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions.

There are numerous distinctive trigonometric identities that relate a triangle's side length and angle. Only the right-angle triangle is consistent with the trigonometric identities.

The six trigonometric ratios serve as the foundation for all trigonometric identities. Sine, cosine, tangent, cosecant, secant, and cotangent are some of their names. The adjacent side, opposite side, and hypotenuse side of the right triangle are used to define each of these trigonometric ratios. The six trigonometric ratios are the source of all fundamental trigonometric identities.

tan x +sec x =2

⇒sin x /cosx + 1/ cos x = 2

⇒1+sin x / cos x  =2

⇒ (sin² x/2 +cos ² x/2 +2 sin x/2 cos x/2 )/( cos ² x/2 - sin²x/2 ) = 2

⇒(cos x/2 +sin x/2)² / ( cos ² x/2 - sin²x/2 ) = 2

⇒( cos x/2+sin x/2)² / (cos x/2 + sin x/2)(cos x/2-sinx/2) = 2

⇒(cos x/2 +sin x/2)/ (cos x/2-sin x/2) = 2

Dividing by cos x/2 in both numerator and denominator,

⇒(1+tan x/2)/(1-tan x/2) =2

⇒ 1 + tan x/2 = 2 - 2tanx/2

⇒ tan x/2 = 1/3

⇒ x= 0.6444

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Using linear functions, we have that:

a. For 6 or more games, the cost a bowling alley A is less, and for 4 or less games, the cost at bowling alley B is less.

b. For any number of games, the cost at alley B will be less.

A linear function is modeled by:

y = mx + b

In which:

For the functions in this problem, we have that:

Hence they are given as follows:

The cost for A will be less when:

A(x) < B(x).

Hence:

4x + 7.5 < 4.5x + 5

-0.5x < -2.5

0.5x > 2.5

x > 2.5/0.5

x > 5.

Hence for 6 or more games, the cost a bowling alley A is less, and for 4 or less games, the cost at bowling alley B is less.

For item b, with the increase of $0.5 per game, we have that:

A(x) = 4.5x + 7.5.

Then the costs per game will be the same, while alley B has the lower intercept, meaning that for any number of games, the cost at alley B will be less.

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Answer:

66

Step-by-step explanation:

Step-by-step explanation:

x1=2 , y1= -8

x2=5 , y2=-6.

distance= rootunder x2-x1 whole square + y2-y1 whole square

=(5-2)whole square + (-6-(-8)) whole square

= root under 9+4

=rootunder 13 units

Answer:

C

Step-by-step explanation:

(2x - 12)(2x + 12)

4x² + 24x - 24x - 144

4x² - 144

Answer:

it is 3

Step-by-step explanation:

beacuse i did it

Mean and standard deviation is more affected by extreme observations.

Mean is the summation of all the values divided by the total number of values. It is also called as average. Median is the middle value.Standard deviation is the dispersion of a dataset relative to its mean. In case of extreme items arithmetic mean is affected very much. For this reason, it no longer remains representative of the distribution. As standard deviation is the positive square root of the arithmetic mean of the square of deviations of all given values, it is also affected by extreme items. As median is a partition value, it is not affected by extreme items.

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Inferential statistic is concerned with making prediction about a population from analyzing a sample or through observation.

Here,

We have to find the concerned with making prediction about a population from analyzing a sample or through observation.

What is Inferential statistic?

Inferential statistics is used in measurements from the sample of subjects in the experiment to compare treatment groups and to make generalizations about the larger population of subjects.

Now,

Inferential statistic is concerned with making prediction about a population from analyzing a sample or through observation.

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The ratio of circumference/diameter for all circles is π. And the ratio of force/mass for all freely-falling bodies will be g.

Let d be the diameter of the circle. The circumference of the circle will be

C = πd units

The ratio of circumference to diameter for all circles is pie.

C/D = πd / d

C/D = π

Then the ratio of force to mass for all freely-falling bodies will be

The force acting on a free-falling body of mass (m) is mg. Then we have

Force/Mass = mg / m

Force/Mass = g

Where g is the acceleration due to gravity.

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Answer:

a) P(X < 24) = 0.1151

b) P(24 < X < 36) = 0.7698

c) X value for P(x < X) = 0.95 is X = 38.225

Step-by-step explanation:

a) P(X < 24)

Since μ = 30  and   σ = 5 we have:

[tex]\text {z value = } \dfrac{24-30}{5}} = -1.2[/tex]

P(X < 24) =  P(Z < -1.2) = 0.1151
You can use a calculator or the standard normal tables to determine P(Z < -1.2)

b) P(24 < X < 36)

First find P(X < 36) using the technique detailed in part a)

For 36, the Z value is  
[tex]\dfrac{36-30}{5} = 1.2[/tex]

P(X < 36) = P(z < 1.2) = 0.8849

P(24 < X < 36) = P(X < 36) - P(X < 24) = 0.8849 - 0.1151 = 0.7698

c) X value below which 95% of the area is covered

Using a calculator (or tables) the z value corresponding to P(z < Z) = 0.95 is Z = 1.65(approx)

[tex]\text{We have } \dfrac{X - \mu}{\sigma} = z\\\\\dfrac{X - 30}{5} = 1.645\\\\\text{Multiplying both sides by 5: }\\\\X - 30 = 1.645 \times 5 = 8.225\\\\X = 30 + 8.225 = 38.225[/tex]

So X value is 38.225-

Answer:

Step-by-step explanation:

One

23 + 52 = 75    This can be done using columns

2  3

5  2      No carries Add.

7   5

Two

72 - 33 = 39

7    2

3    3     You have to borrow a ten from the 7 to make this work

3   9

Three

82 + sqrt(100)

sqrt(100) = 10

82 + 10 = 92

Answer:

Q=-8

Step-by-step explanation:

Q-2-6

Antawan's solution is the absolute value of Maggie's solution is the solution related to Antawan's and Maggie's solution.

Given

Antawan determines the distance between two points as 9.

Maggie finds the difference between two numbers ₋ 7 ₋ 2 = ₋9

Hence we notice that Antawan's solution is the absolute value to the Maggie's solution.

The non-negative value of x, regardless of its sign, is the absolute value (or modulus) | x | of a real number x. For instance, 5 has an absolute value of 5 and so does 5, which likewise has an absolute value of 5. One way to conceptualize a number's absolute value is as its separation from zero on the real number line.

hence option 2 is right.

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Let the middle integer be x.

We're given:

[tex](x-1) + x + (x+1) = -27[/tex]

Open up the brackets:

[tex]x-1 + x + x+1 = -27[/tex]

Combine like terms:

[tex]3x = -27[/tex]

Divide both sides by 3:

[tex]\dfrac{3x}{3} = \dfrac{-27}{3}[/tex]

[tex]x=-9[/tex]

The value of the middle integer is -9.