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Mnenie [13.5K]
3 years ago
7

The Royal Fruit Company produces two types of fruit drinks. The first type is 60% pure fruit juice, and the second type is 85% p

ure 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 120 pints of a mixture that is 65% pure fruit juice?
Mathematics
1 answer:
elena-s [515]3 years ago
5 0
Make 2 equations from the question first
x is the number of pints for type 1
y is the number of pints for type 2

The equation
x + y = 120
60% x + 85% y = 65% (x + y)

Solve the equation
From the 2nd equation
0.6x + 0.85y = 0.65(x + y)
0.6x + 0.85y = 0.65x + 0.65y
0.85y - 0.65y = 0.65x - 0.6x
0.2y = 0.05x
y = 4x

From the 1st equation
x + y = 120
x + 4x = 120
5x = 120
x = 24

y = 4x
y = 96

The first type should be 24 pints, the second type should be 96 pints
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3 years ago
It is possible to score higher than 1600 on the combined mathematics and reading portions of the SAT, but scores 1600 and above
Citrus2011 [14]

Answer:

The proportion of scores reported as 1600 is 0.0032

Step-by-step explanation:

Let X be the score for 1 random person in SAT combining maths and reading. X has distribution approximately N(μ = 1011,σ = 216).

In order to make computations, we standarize X to obtain a random variable W with distribution approximately N(0,1)

W = \frac{X-\mu}{\sigma} = \frac{X-1011}{216} \simeq N(0,1)

The values of the cummulative distribution function of the standard Normal random variable, lets denote it \phi are tabulated, you can find those values in the attached file. Now, we are ready to compute the probability of X being bigger than 1600

P(1600< X) = P(\frac{1600-1011}{216} < \frac{X-1011}{216}) = P(2.7269 < W) = 1- \phi(2.7269)\\= 1- 0.9968 = 0.0032

Hence, the proportion of scores reported as 1600 is 0.0032.

Download pdf
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4 years ago
What are the vertices of triangle PQR?
Sergeeva-Olga [200]

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Step-by-step explanation:

<em>The vertices of the triangle PQR - it is P, Q and R.</em>

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3 years ago
If f(x) = kx^3+ x^2 − kx + 2, find a number k such that the graph of f contains the point (k, -10)
Elina [12.6K]

If we write k where we see x in the equation and set the result equal to -10, we get the result.

  • f(k)=k(k)^3+k^2-k(k)+2
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  • k_{1}=\sqrt[4]{3}(-1-i)
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Answer:

y = - \frac{2}{3} x - 8

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - \frac{2}{3} and c = - 8, hence

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