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4 years ago

How many gallons of a 20% salt solution must be mixed with 4 gallons of a 30% salt solution to make a 25% salt solution?

Mathematics

1 answer:

denis-greek [22]4 years ago

6 0

Answer:

4 gallons

Step-by-step explanation:

Say that g = the number of gallons of a 20% salt solution,

The first thing we want to do here is to convert each " percentage " into decimal form, to make things a bit simpler here.

( $20(percent) = 0.20$

( $30( percent ) = 0.30$

( $25( percent ) = 0.25$

Before this mixture takes place, the 20% salt solution is associated with g, the number of gallons of a 20% salt solution. Respectively the 30% salt solution is associated with 4 gallons. After mixing the two ( g and 4 ) the 25% salt solution should be associated with g + 4. We can therefore conclude the following equation -

0.20( g )+0.30( 4 ) = 0.25( g + 4 )

And now, let us solve for " g, "

0.2g + 1.2 = 0.25g + 1

- 0.2g = - 0.2g

_________________

1.2 = 0.05g + 1

- 1 = - 1

_________________

0.2 = 0.05g,

g = <u><em>4 gallons of a 20% salt solution</em></u>

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It is possible to score higher than 1600 on the combined mathematics and reading portions of the SAT, but scores 1600 and above

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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

If the scale factor of figure a to figure b is 3:8,find the value of x

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Answer:a

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3 years ago

A company is interviewing potential employees. Suppose that each candidate is either qualified, or unqualified with given probab

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Answer:

$P(C=1|T=1)=q(\sum_{i=15}^{20}\binom{20}{i} p^i(1-p)^{20-i})( \sum_{i=15}^{20}\binom{20}{i}[qp^i(1-p)^{20-i} + (1-q)p^{20-i}(1-p)^i])^{-1}$

Step-by-step explanation:

Hi!

Lets define:

C = 1 if candidate is qualified

C = 0 if candidate is not qualified

A = 1 correct answer

A = 0 wrong answer

T = 1 test passed

T = 0 test failed

We know that:

$P(C=1)=q\\P(A=1 | C=1) = p\\P(A=0 | C=0) = p$

The test consist of 20 questions. The answers are indpendent, then the number of correct answers X has a binomial distribution (conditional on the candidate qualification):

$P(X=x | C=1)=f_1(x)=\binom{20}{x}p^x(1-p)^{20-x}\\P(X=x | C=0)=f_0(x)=\binom{20}{x}(1-p)^xp^{20-x}$

The probability of at least 15 (P(T=1))correct answers is:

$P(X\geq 15|C=1)=\sum_{i=15}^{20}f_1(i)\\P(X\geq 15|C=0)=\sum_{i=15}^{20}f_0(i)\\$

We need to calculate the conditional probabiliy P(C=1 |T=1). We use Bayes theorem:

$P(C=1|T=1)=\frac{P(T=1|C=1)P(C=1)}{P(T=1)}\\P(T=1) = qP(T=1|C=1) + (1-q)P(T=1|C=0)$

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$P(C=1|T=1)=q(\sum_{i=15}^{20}\binom{20}{i} p^i(1-p)^{20-i})( \sum_{i=15}^{20}\binom{20}{i}[qp^i(1-p)^{20-i} + (1-q)p^{20-i}(1-p)^i])^{-1}$

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3 years ago

Write a function that models the distance D from a point on the line y = 9 x - 8 to the point (0,0) (as a function of x).

lakkis [162]

The function that models the distance D from a point on the line y = 9 x - 8 to the point (0,0) (as a function of x) is y = 9x

Given the equation of a line in standard form as y = 9x - 8

Get the slope of the line

mx = 9x

m = 9

Since the line passes through the origin (0, 0), substitute the slope and the point in the point-slope form of the equation as shown below:

$y-y_0=m(x-x_0)$

$y-0=9(x-0)\\y =9x$

Hence the function that models the distance D from a point on the line y = 9 x - 8 to the point (0,0) (as a function of x) is y = 9x

Learn more here: brainly.com/question/15816805

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3 years ago

Sally’s dance school had 60 students last year. This year there are only 48 students enrolled. By what percent did the enrollmen

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Answer:

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3 years ago