The Royal Fruit Company produces two types of fruit drinks. The first type is 55% pure fruit juice, and the second type is 80% pure fruit juice. The company is attempting to produce a fruit drink that contains 65% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 40 pints of a mixture that is 65% pure fruit juice?

Please help this is due soon

The value of ∠A in triangle ABC is 40°

A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.

The sum of the angles of a triangle is always 180°

In the given triangle ABC,

∠A=7x-16°, ∠B=81°

By alternate segment theorem,

∠C=4x+27°

The sum of all the angle of a triangle is 180°.

∠A+∠B+∠C=180°

⇒7x-16+81+4x+27=180

11x=180-92

11x=88

x=8

So the value of ∠A=7×8-16 = 40°

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Answer:

The value of ∠A in triangle ABC is 40°

Pretty much the same as the person that posted before.

Answer:

1,000 x 550.343978 = 550343.978

The value of the consecutive numbers are 7 and 8.

Consecutive integers simply means the numbers that follow each others. It should be noted that such numbers have the same difference between them.

From the information given, we want to find two consecutive positive integers such that the square of the second integer added to 6 times the first is equal to 106.

Let the numbers be x and x+1.

Therefore, 6x + (x + 1)² = 106

6x + x² + 2x + 1 = 106

Collect like terms

x² + 8x + 1 - 106

x² + 8x - 105

x² + 15x - 7x - 105

x(x + 15) - 7(x - 15) = 0

Therefore x - 7 = 0

x = 0 + 7

x = 7

Therefore x + 1

= 7 + 1

= 8

The numbers are 7 and 8.

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Answer:

All of them

Step-by-step explanation:

A rational expression is simply a quotient of two polynomials. Or in other words, it is a fraction whose numerator and denominator are polynomials.

The cost of the gas in dollars per gallon would be = $5.3 per gallon.

Liters can be converted to gallon as 1 liter = 0.264 gallon.

On the first day, the cost of gasoline = 1.28 euro per liter

On the first day, the worth of £1 = $ 1.09

Which means, if £1 = $1.09

£ 1.28 = $x

Make $x the subject of formula;

$x = 1.28 × 1.09/1

$x = $1.40

Which means that on the first day, the cost of gasoline in dollars = $1.40

To convert liters to gallon;

1 liter = 0.264 gallon

If $1.40 = 0.264 gallon

$x = 1 gallon

make $x the subject of formula;

$x = 1×$1.40/0.264

$x = 5.3

Therefore, the cost of gasoline in dollar per euro = $5.3 per gallon.

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The simplified form of the expression is -24√35

Expression

Basically, an expression is the mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given,

Here we have the expression -6√7.4√5

Now, we have to simplify the expression.

While we looking into the given expression, we have identified that the expression is in the form of multiplication,

So, the first step in solving the expression is to group the similar element,

So, the grouped form of the expression is,

=> (-6 x 4).(√7 x √5)

Now, we have to perform the multiplication on it, then we get,

=> -24√35

Therefore, the simplified form of the expression is -24√35

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The smallest distance between the origin and a point on the graph of y = 1/2(x² - 8) is √7 units.

Given, a function

y = 1/2(x² - 8)

We have to find the smallest distance between origin and a point on the graph of y = 1/2(x² - 8).

Now, the point on the graph be,

( x , 1/2(x² - 8) ) and origin be (0 , 0)

Let the function of the distance between both the points be,

D = √(x - 0)² + (1/2(x² - 8) - 0)²

D = √x² + 1/4(x² - 8)²

D² =  x² + 1/4(x² - 8)²

On differentiating, we get

2DD' = 2x + x(x² - 8)

x³ + 2x - 8x = 0

x³ - 6x = 0

x(x² - 6) = 0

So, x = 0 , √6 , -√6

and the distance is minimum for x = √6

Therefore, using distance formula, we get

Distance = √(x1 - x2)² + (y1 - y2)²

Distance = √(0 - √6)² + (0 - (-1))²

Distance = √6 + 1

So, the smallest distance between the origin and a point on the graph of y = 1/2(x² - 8) is √7 units.

Hence, the smallest distance between the origin and a point on the graph of y = 1/2(x² - 8) is √7 units.

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Answer:

[tex]x^2+2x+1[/tex]

Step-by-step explanation:

Note that [tex](a+b)^2=a^2+2ab+b^2[/tex].

Let [tex]a=x[/tex] and [tex]b=1[/tex].

[tex](x+1)^2=x^2+2(x)(1)+1^2=x^2+2x+1[/tex]

Answer: 111/250

Step-by-step explanation:

Step 1: Write down the percent divided by 100 like this:

44.4% = 44.4/100

Step 2: Multiply both top and bottom by 10 for every number after the decimal point:

As we have 1 digit after the decimal point, we multiply both numerator and denominator by 10, or, simply shift 1 decimal place to the right. So,

44.4/100 = (44.4 x 10)/(100 x 10) = 444/1000.

Step 3: Simplify (or reduce) the above fraction by dividing both numerator and denominator by the GCD (Greatest Common Divisor) between them. In this case, GCD(444,1000) = 4. So,

Answer:

[tex]-x^{3}+6x^{2} +5x-7[/tex]

Step-by-step explanation:

-x^3-x+6x^2+6x-7

Order the polynomial from exponent order to make it easier

-x^3+6x^2+6x-x-7

-x^3+6x^2+5x-7

Hopes this helps please mark brainliest

Answer:

-x^3+6x^2+5x-7

Step-by-step explanation:

open parentheses, collect like terms.

Answer: 100 is the ancer m

Step-by-step explanation: my man

Answer:

-1027.4

Step-by-step explanation:

that is the answer i got from my calculations. I hope this is right

Answer:50.8%

Step-by-step explanation:

The waterskier has a final speed of approximately 25.350 feet per second.

In this question we need to determine the final speed of the waterskier, that is, the final speed of the waterskier when she leaves the ramp. This can be done by means of the principle of energy conservation, where the total energy is the result of combining translational kinetic energy (K), in pounds-feet per second, related to the speed of the waterskier, and gravitational potential energy (U), in pounds-feet per second.

The equation that represents the situation is described below:

K = U + K'

0.5 · m · v² = m · g · h + 0.5 · m · v'²

0.5 · v² = g · h + 0.5 · v'²

v'² = v² - 2 · g · h

Where:

If we know that v = 30 ft / s, g = 32.174 ft / s² and h = 4 ft, then the final speed of the waterskier is:

v' = √[(30 ft / s)² - 2 · (32.174 ft / s²) · (4 ft)]

v' ≈ 25.350 ft / s

The final speed of the waterskier is approximately 25.350 feet per second.

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The equation to represent the relationship between h and t is

t = 30 + 19.99h.

Two or more expressions with an equal sign are defined as an equation.

Given that, the magician charges a $30 fee one time and a $19.99 fee per hour.

The total charge, t,  for the magician for h hours is,

t = 30 + 19.99h

Hence, the equation to represent the relationship between h and t is

t = 30 + 19.99h.

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A standard lot is an amount of currency which is the same as 100,000 units of a base currency .

There are three lot sizes;

In finance, a lot indicates a measure or increment of a commodity that can be transacted. Products are bought and sold using different lot sizes. Products such as spot forex are sold in lots of 100,000, 10,000, 1,000, or 100 units.

Competition and brokerage online has resulted in the introduction of various lot sizes and forms.

A change of $10 corresponds to a pip movement of a standard lot.

By buying $100,000 at ¥110.00 and the price increases to ¥110.50, which indicates a 50 pip movement and a gain of $500 and vice versa.

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Jay, because each point is fraction 1 over 8 unit from 0.

What is absolute length?

For instance, the absolute value of 12:

Absolute value is the length from which the number is from 0 in this they are adding two so it would mean that they are both 1/8 away from 0.

Hence, Jay, because each point is fraction 1 over 8 unit from 0.

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Answer:

4 4/9

is the time it will take

If the overhead was 20% of the cost of each towel. The selling price of each towel is 5.88.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

The usage of percentages is widespread and diverse. For instance, numerous data in the media, bank interest rates, retail discounts, and inflation rates are all reported as percentages. For comprehending the financial elements of daily life, percentages are crucial.

Suppose the selling price of a towel is x, according to the given condition,

5 = x - 15% of x

5=x-0.15x

5=0.85 x

x=5/0.85

x=5.88

Thus, if the overhead was 20% of the cost of each towel. The selling price of each towel is 5.88.

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Answer:

  $1544.40

Step-by-step explanation:

You want to know the amount of interest cost subsidized by the Department of Education during the 4.5-year non-payment period on an $8000 subsidized federal loan at 4.29%.

The interest accrued on the loan amount is found by the simple interest formula:

  I = Prt

The principal is $8000, the rate is 4.29%, and the time period is the non-payment period, 4.5 years. The interest is ...

  I = $8000·0.0429·4.5 = $1544.40

The DoE will subsidize $1544.40 in interest during the non-payment period.

__

Additional comment

For the purpose of this problem, the 10-year period of the loan is irrelevant, as we're only concerned with the 4.5 year period before repayment starts. Because the loan is subsidized, that interest is never "capitalized" and is not due to be repaid by the borrower.

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The simplified form of the expression 500,000 multiplied by 100 equals 50,000,000 or 5 x [tex]10^7.[/tex]

We have,

The product of 500,000 multiplied by 100.

= 500,000 x 100

= 50,000,000

This can be written as:

= 5 x [tex]10^7[/tex]

Therefore,

The simplified form of the expression 500,000 multiplied by 100 equals 50,000,000 or 5 x [tex]10^7.[/tex]

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Step-by-step explanation:

a polynomial of degree 4 must have 4 zeroes.

when we know these zeroes, we can define the polynomial by the factors defining these zeroes.

after all, a multiplication of several factors can only be zero, if at least one of the factors is zero.

we have 3 zeroes at x = -1. and 1 zero at x = 0.

so,

f(x) = (x + 1)(x + 1)(x + 1)x

you see ? this will only be zero, if x = -1 or x = 0. and -1 is built in as zero 3 times.

let's do the multiplications :

(x + 1)(x + 1) = x² + 2x + 1

(x + 1)x = x² + x

(x² + 2x + 1)(x² + x) = x⁴ + x³ + 2x³ + 2x² + x² + x =

= x⁴ + 3x³ + 3x² + x

f(x) = 1x⁴ + 3x³ + 3x² + 1x

The amount in the account after 25 years be $ 84,216.11

Given, an investment account is opened with an initial deposit of $18,500 earning 6.25% interest, compounded continuously.

We have to find the amount in the account after 25 years.

Now, on using the compound interest amount formula, we get

Amount = P(1 + r/100)^t

Amount = 18500(1 + 6.25/100)^25

Amount = 18500(1.0625)^25

Amount = 18500(4.55)

Amount = 84,216.1137

Hence, the amount in the account after 25 years be $ 84,216.11

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answer: 85+85+85+25