The Royal Fruit Company produces two types of fruit drinks. The first type is 40% pure fruit juice, and the second type is 65% pure fruit juice. The company is attempting to produce a fruit drink that contains 70% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 70 pints of a mixture that is 55% pure fruit juice?

The value of a that makes the solution of the equation is 1/2.

Given,

The equation: 3(2x - 4) = 4(ax - 2)

Solve,

3(2x - 4) = 4(ax - 2),

Open the bracket and multiply:

6x - 12 = 4ax - 8

Add 12 to both sides

6x -12 + 12 = 4ax + 12 - 8

We get,

6x = 4ax + 4

Add - 4ax to both sides:

6x - 4ax = 4ax - 4ax + 4

We get,

6x - 4ax = 4

Take x = 1

Then,

6 × 1 - 4a × 1 = 4

6 - 4a = 4

Now,

Add - 6 to both sides

6 - 6 - 4a = 4 - 6

We get,

-4a = -2

That is,

4a = 2

a = 2/4 = 1/2

That is,

The value of a that makes the solution of the equation is 1/2.

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Given:

The radius of the circle = 2.4 kilometers

The measure of the arc = 150°

The length of the arc is given by the formula:

Note: we will convert the angle from degrees to radian

So, the length of the arc =

So, the answer will be option D. 2π km

Recall that [tex]\phi = 1 + \frac1\phi[/tex].

In the integral, substitute [tex]y=1+x^\phi[/tex], so that [tex]x=(y-1)^{1/\phi} = (y-1)^{\phi-1}[/tex] and [tex]dx = (\phi-1) (y-1)^{\phi-2} \, dy[/tex]. We have

[tex]\displaystyle I = \int_0^\infty \frac{dx}{(1+x^\phi)^\phi} \\\\ ~~~~ = \frac1\phi \int_1^\infty \frac{(y-1)^{\phi-2}}{y^\phi} \, dy[/tex]

Substitute [tex]y=\frac1z[/tex] and [tex]dy=-\frac{dz}{z^2}[/tex] to transform [tex]I[/tex] to

[tex]\displaystyle I = \frac1\phi \int_0^1 \left(\frac1z-1\right)^{\phi-2} z^{\phi-2} \, dz \\\\ ~~~~ = \frac1\phi \int_0^1 (1-z)^{\phi-2} \, dz[/tex]

Finally, substitute [tex]u=1-z[/tex].

[tex]\displaystyle I = \frac1\phi \int_0^1 u^{\phi-2} \, du \\\\ ~~~~ = \frac1\phi \cdot \frac1{\phi-1} = \frac{\phi-1}{\phi-1} = \boxed{1}[/tex]

recall the formula for velocity, which involves distance and time:

velocity = distance / time

since the woman's velocity is: 4.5 Km/h, then in order to cover 10 km, we need to find the time in the equation:

4.5 km/h = 10 km / t

multiply both sides by the time (t)

4.5 * t = 10

divide both sides by 4.5 in order to isolate t completely

t = 10 / 4.5

then

t = 2 hours and 0.2222 hours which can be translated into minutes by multiplying this by 60: 40/3 = 13 minutes and 0.33333 minutes. which can be converted into seconds by multiplying it by 60: 20 seconds

Then she will cover that distance in 2 hours, 13 minutes and 20 seconds.

Answer:  −8x − 12y − 18q − 42p

Step-by-step explanation:

i did the exam xD

Answer:

The answer to your question is: B

Explanation:
based on the statistics given, this answer best fits the Queston.

Answer:

1.4 Relations and Functions

A relation is a correspondence between two sets. If x and y are two

elements in these sets and if a relation exists between x and y, then x

corresponds to y, or y depends on x.

DEFINITION OF A FUNCTION:

Let X and Y two nonempty sets. A function from X into Y is a relation that

associates with each element of X, exactly one element of Y.

However, an element of Y may have more than one elements of X

associated with it.

That is for each ordered pair (x,y), there is exactly one y value for each x,

but there may be multiple x values for each y. The variable x is called the

independent variable (also sometimes called the argument of the

function), and the variable y is called dependent variable (also

sometimes called the image of the function.) x = y2 is not a function from X into Y, because there

is not exactly one y value for each x.

Solving for y, you get y =

which means there are two possible values for y

Step-by-step explanation:

length of a cylinder of volume 2 litres and radius 10 cm is 0.0064cm and  the radius of a cylinder of volume 45 cm³ and length 4 cm is 1.8928cm.

PART A

Volume of Cylinder = 2 Litres

Radius of cylinder = r = 10 cm

We need to find the length of a cylinder .

We know , Volume of Cylinder = π[tex]r^{2} h\\[/tex]

On substituting the values of Volume of Cylinder and r , we get

2 = π( [tex]10^{2}[/tex])h

h = 2 / 100π = 0.0064 cm

Here h = length of a cylinder

The length of a cylinder is  0.0064cm .

PART B

radius of a cylinder = r

volume of cylinder = 45 cm³

length of cylinder = h = 4 cm

Volume of Cylinder = π[tex]r^{2} h\\[/tex]

45 = 3.14 [tex]r^{2}[/tex] (4)

[tex]r^{2}[/tex] = 3.5828

r = 1.8928

Radius of a cylinder is 1.8928cm.

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Answer:

Step-by-step explanation:

Answer:

x > 6 with an open point

Hope this helps!

Step-by-step explanation:

-2 ( x + 6 ) > -4x

-2x - 12 > -4x

-(-4x) - 2x > -(-12)

4x - 2x > 12

2x > 12

x > 6

To know how much each message sent costs, knowing that 75 messages cost $6.75, we only have to divide the cost of the total of 75 text messages by the total number of the cost of the message,

So that:

We say, that the cost of each text message is $0.09.

The representation of the expression is x/2 - 10 = -18

The mathematical statement is given as

"10 less than the quotient of a number and 2 is -18"

In expressions, quotient mean divide i.e. /

So, we have the following representation

"10 less than the quotient of a number and 2 is -18" ⇒  10 less than a number/2 is -18"

Let the number be x

So, we have

"10 less than the quotient of a number and 2 is -18" ⇒  10 less than x/2 is -18"

Less than as used here means minus

So, we have

"10 less than the quotient of a number and 2 is -18" ⇒  x/2 - 10 is -18

Rewrite as

"10 less than the quotient of a number and 2 is -18" ⇒  x/2 - 10 = -18

Hence, the expression represented by "10 less than the quotient of a number and 2 is -18" is  x/2 - 10 = -18

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Given

A right angle triangle is removed from the rectangle to create the shaded region.

That is,

To find: The area of the shaded region.

Explanation:

It is given that,

That implies,

The area of the shaded region is,

Hence, the area of the shaded region is 39ft^2.

ANSWER:

STEP-BY-STEP EXPLANATION:

We must convert the following statement "A number multiplied by -8 subtracted from the sum of 8 and two times the number" into a mathematical expression.

We know that "a number" would be x.

Therefore:

The expression y=[tex]x^{p} +2x^{q}[/tex]. [tex]\frac{dy}{dx}=11x^{10}+10x^{4}[/tex], where dy/dx is derived function. The p and q values are 11 and 5.

Given that,

The expression y=[tex]x^{p} +2x^{q}[/tex]

[tex]\frac{dy}{dx}=11x^{10}+10x^{4}[/tex], where dy/dx is derived function.

Derived function means for any value of the independent variable, the value of another function is the instantaneous rate of change of the specified function at that value of the independent variable.

We have to find the p and q values.

Take expression

y=[tex]x^{p} +2x^{q}[/tex]

[tex]\frac{dy}{dx}=px^{p-1}+2qx^{q-1}[/tex]

[tex]11x^{10}+10x^{4}=px^{p-1}+2qx^{q-1}[/tex]

Here,

we can see p=11 and

2q=10

q=5

Therefore, the p and q values are 11 and 5.

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The The set of all numbers greater than or equal to -10 and less than 9 will be -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, and 8.

It should be noted that from the information, we are to find the set of all numbers greater than or equal to -10 and less than 9.

This simply means the numbers from -10 to 8.

Therefore, the numbers will be -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, and 8.

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Applying the rules for the polar equations, the correct pairs are given in the image at the end of the answer.

The most well known polar equation rules are given as follows:

For the first pair, when x = 2, we have that:

rcos(θ) = 2.

r = 2/cos(θ)

r = 2 sec(θ), as one divided by the cosine is the secant.

For the second pair, we have that:

x² + y² = 36.

x² + y² = r², hence:

r² = 36

r = 6.

For the third pair, we have that:

x² + y² = 2y

r² = 2rsin(θ).

r²/r = 2sin(θ).

r = 2sin(θ).

For the fourth pair, we have that:

[tex]x = \sqrt{3}y[/tex]

[tex]\frac{y}{x} = \frac{1}{\sqrt{3}}[/tex]

[tex]\frac{y}{x} = \frac{\sqrt{3}}{3}[/tex]

Then the angle theta is given as follows:

θ = arctan(sqrt(3)/3) = pi/6.

For the fifth pair, we have an angle in which the sine and the cosine are equal, hence this angle is of 45º = pi/4.

The image at the end of the answer shows all the matched pairs.

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The slope of the line has increased, meaning it has become a positive number. This shift means that this year the data points were placed higher than the previous year.

Answer:

2.4m

Step-by-step explanation:

The question has already done most of the work for you. To find the initial height, simply set t = 0 and substitute it into the function.

[tex]d(0) = {0}^{2} + 2.4 + 3.2(0) \\ = 2.4m[/tex]

The largest five-digit multiple of 15 whose digits are all distinct and nonzero is 12345.

Suppose that the number is abcd.efg and belongs to the decimal numerical system. Remember one thing that the place on the left of decimal point is called ones. Move one-one places to right, and divide by 10 and 10 more and more. Move one-one places to left, and multiply (un-divide) by 10 and 10 more and more. We will call d as ones digit, c as tens digit (it get multiplied by 10), b as hundreds digit etc.

WE need to find the five-digit multiple of 15 whose digits are all distinct and nonzero.

Thus, we can see that the largest five-digit multiple of 15 could be ;

12345

Since it must be all distinct and nonzero. so the correct digit is 12345.

Hence, the largest five-digit multiple of 15 whose digits are all distinct and nonzero is 12345.

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After substituting x = -1/2 in f(x), the value of the function f(-1/2) is found to be 5.333.

A function from a set X to a set Y assigns exactly one element of Y to each element of X.

The set X is known as the function's domain, and the set Y is known as the function's codomain.

The given function is f(x) = -2/3x +5.

To obtain f(-1/2), we must substitute the value of x with -(1/2).

f(x) = -2/3x +5

f(-1/2) = -2/3×(-1/2) + 5

f(-1/2) = (2/6) + 5

f(-1/2) = 0.333 + 5

∴ f(-1/2) = 5.3333

Therefore, the value of the function f(-1/2) obtained after substituting        x = -1/2 is 5.333.

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In geometry, you can use deductive rules to prove conjectures.

Geometry is defined as a subfield of mathematics that examines the measurement and relationships of surfaces, solids, solid surfaces, angles, and points. The calculation of a triangle's angles is a geometry example.

Geometry will categorize, quantify, and lack a counterexample. Once a concept has been defined, it can be utilized in subsequent definitions; for instance, parallel lines can be used in the definition of a parallelogram once they have been defined. classification, counterexample, quantification, and parallelogram.

Given Data

In geometry, you can use deductive rules to

In geometry, you can use deductive rules to prove conjectures.

In geometry, deductive rules can be used to demonstrate whether a particular assertion or conjecture is true or untrue. We narrow down a result proving a statement must be true or untrue by using deductive principles, such as definitions, postulates, and other theorems, in a logical order.

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Using the slope formula, the value of k in the coordinates of the point given is: k = 6.

If we are given two points that lie on a line, (x1, y1) and (x2, y2), the formula that is used to find the slope (m) of the line is given as:

Slope (m) = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex] = change in y / change in x..

Given the following:

(k, -9) = (x1, y1)

(1, -6) = (x2, y2)

Slope (m) = -3/5

Plug in the values into the formula used for calculating the slope of a line:

(-6 -(-9))/(1 - k) = -3/5

3/(1 - k) = -3/5

Cross multiply and solve for the value of k

-3(1 - k) = 3(5)

-3 + 3k = 15

Add 3 to both sides

-3 + 3k + 3 = 15 + 3 [subtraction property of equality]

3k = 18

Divide both sides by 3

3k/3 = 18/3 [division property of equality]

k = 6

The value of k is: 6. Therefore, the points on the line that have a slope of -3/5 are (6, -9) and (1, -6).

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Answer:

Step-by-step explanation:

Normally we use the symbols U for set union corresponding to or and ∩ for set intersection corresponding to and.

But here i will use and and or

By the rules of probability

P(A or  B) = P(A) + P(B) - P( A and  B)  
So P(A or b ) = 0.45 + 0.65 - 0.35 = 0.75

The complement of a set A is all the elements not in A
P(A') = 1 - P(A)

If we denote the complement of a set A as A' then your second expression is asking What is the complement of A or B or P(A or B)'
P(A and  B)' = 1 - P(A or B) = 1- 0.75 = 0.25

P(A|B)  = P(A and  B)/P(B) = 0.35/0.65 = 0.54

P(B|A) = P(A and B)/P(A) = 0.35/0.45 = 0.78

Answer:

B

Step-by-step explanation:

By the triangle inequality theorem, the sum of the lengths of the two shorter sides needs to be greater than the length of the longest side.

Answer:

what

Step-by-step explanation:

i think maybe like… actually

1. The total amount that was paid for the car will be $23960.

2. The interest that Mai pay on the loan will be $1160.

1. From the information, in order to pay for a $22,800 car, Mai made a down payment of $3,800 and took out a loan for the rest and on the loan, she paid monthly payments of $420for 4 years.

The total amount that was paid for the car will be:

= $3800 + ($420 × 4 years)

= $3800 + ($420 × 48)

= $3800 + $20160

= $23960

2. The interest that Mai pay on the loan will be:

= $23960 - $22800

= $1160

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Line AB is parallel to CD, for instance, as indicated by the formula AB ll CD.

How do parallel lines work?

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The missing integer that makes the following addition statement true is -1.

The commutative law of addition is also known as the law of cumulative addition and it states that when two numbers are added together, then, the outcome is equal to the addition of their interchanged position because addition is considered as a binary operation.

Mathematically, the commutative law of addition can be represented using the following formula:

A + B = B + A.

An integer can be defined as a whole number that may either be positive, negative, or zero such as -1, 0, 1, 2, 3, etc.

Now, we would determine the missing number:

x + 3 = 2

x = 2 - 3

x = -1.

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Complete Question:

Find the missing integer that makes the following addition statement true.

+ 3 = 2