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-BARSIC- [3]
4 years ago
15

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
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
5 0
4 years ago
If the scale factor of figure a to figure b is 3:8,find the value of x
NeTakaya

Answer:a

Step-by-step explanation:did

3 0
3 years ago
A company is interviewing potential employees. Suppose that each candidate is either qualified, or unqualified with given probab
stira [4]

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)

P(T=1)=q\sum_{i=15}^{20}f_1(i) + (1-q)\sum_{i=15}^{20}f_0(i)\\P(T=1)=\sum_{i=15}^{20}\binom{20}{i}[qp^i(1-p)^{20-i} + (1-q)p^{20-i}(1-p)^i)]

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}

5 0
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
Morgarella [4.7K]

Answer:

-20%

My brain is weird on how i figure it out but I divided 48 by 60 and got .80 so i just got the other whole to make it 1 so it is 20%. This is not the correct way to do this but this is how i got my answer.

8 0
3 years ago
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