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viktelen [127]
3 years ago
12

How many gallons of a 70% antifreeze solution must be mixed with 90 gallons of 20% antifreeze to get a mixture that is 60% antif

reeze?
gallons
The number of gallons that must be mixed is
(Round to the nearest whole number.)
Mathematics
1 answer:
Oliga [24]3 years ago
8 0

Answer:

360

Step-by-step explanation:

If x is gallons of 70% antifreeze solution, then:

0.70x + 0.20(90) = 0.60(x + 90)

0.70x + 18 = 0.60x + 54

0.10x = 36

x = 360

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Vera_Pavlovna [14]

Answer:

A. (x-5)(x-7)

B. It means the zeroes of the graph are at (5,0) and (7,0)

Step-by-step explanation:

A

find what + what equals -12, and multiples to 35.

List all multiples of 35.

1 35

<em>5 7</em>

- 12 is negative so that means it is -5 and -7

(x-5)(x-7)

B

The factor numbers are where the zeroes on a graph are, <u>but</u> whatever is in parenthesis, the number is opposite on a graph (e.g. if it was (x-3), the zero would be (3,0)

4 0
4 years ago
An office and apartment building is made up of modules. Each module is a rectangular prism. The building has 150 modules, and is
Elis [28]

Answer:

Part 1) 10 modules per floor

Part 2) Two different rectangular prism

Step-by-step explanation:

Part 1)

Let

x ----> the number of modules

y ---> the number of stories

we have

x=150\ modules\\y=15\ stories

Divide the number of modules by the number of stories

so

\frac{x}{y}=\frac{150}{15}=10\ \frac{modules}{floor}

Part 2) How many different rectangular prisms could be made from that number?

The number is 10

Look at the factors of  10

They are  1,2 ,4,5 and 10

Pick any two of these factors and determine if there is a third value from this list so that the product of the three factors is 10

There are 2 combinations that will work :

1 0×1×1

2 ×5×1

4 0
3 years ago
Kala, Deandre, and Eric have a total of $119 in their wallets, Kala has $6 more than Deandre. Eric has 3 times what kala has. Ho
Tomtit [17]
Deandre = x
Kala = x + 6
Eric = 3(x+6)
x + x + 6 + 3(x+6) = 119
2x + 6 + 3x + 18 = 119
5x + 24 = 119
5x = 95, x = 19
Deandre has $19
Kala has 19 + 6 = $25
Eric has 3(25) = $75
4 0
3 years ago
A rectangle has a length of x inches and a width of y inches
NNADVOKAT [17]
Jdhshdhshdhhdhdidhhsbsshhs 80
3 0
3 years ago
20% of US High School teens vape. A local High School has implemented campaigns to reduce vaping among students and believes tha
zaharov [31]

Answer:

10.93% probability of observing 51 or fewer vapers in a random sample of 300

Step-by-step explanation:

I am going to use the normal approximation to the binomial to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

\sqrt{V(X)} = \sqrt{np(1-p)}

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that \mu = E(X), \sigma = \sqrt{V(X)}.

In this problem, we have that:

n = 300, p = 0.2

So

\mu = E(X) = np = 300*0.2 = 60

\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{300*0.2*0.8} = 6.9282

What is the approximate probability of observing 51 or fewer vapers in a random sample of 300?

Using continuity corrections, this is P(X \leq 51 + 0.5) = P(X \leq 51.5), which is the pvalue of Z when X = 51.5 So

Z = \frac{X - \mu}{\sigma}

Z = \frac{51.5 - 60}{6.9282}

Z = -1.23

Z = -1.23 has a pvalue of 0.1093.

10.93% probability of observing 51 or fewer vapers in a random sample of 300

4 0
3 years ago
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