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3 years ago

How many ounces of a 40%

Mathematics

1 answer:

Vinil7 [7]3 years ago

3 0

Answer:

The quantity of 40% hydrochloric acid mixed with 12 ounces of a 15% hydrochloric acid solutions is 18 ounces

Step-by-step explanation:

Given as :

Let The quantity of 40% hydrochloric acid mixed with 12 ounces of a 15%

hydrochloric acid = x ounces

So, Total quantity becomes = ( x + 12 ) ounces

Now, According to question

x × 40% + 12 × 15% = (x + 12) × 30%

Or, x × $\dfrac{40}{100}$ + 12 × $\dfrac{15}{100}$ = (x + 12) × $\dfrac{30}{100}$

Or, 40 x + 12 × 15 = (x + 12) × 30

Or, 40 x + 180 = 30 x + 360

Or, 40 x - 30 x = 360 - 180

Or, 10 x = 180

∴ x = $\dfrac{180}{10}$

i.e x = 18 ounces

So, The quantity of 40% hydrochloric acid mixed with 12 ounces of a 15% hydrochloric acid solutions = x = 18 ounces

Hence, The quantity of 40% hydrochloric acid mixed with 12 ounces of a 15% hydrochloric acid solutions is 18 ounces . Answer

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Answer:

x-intercept: (2/3, 0)

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Step-by-step explanation:

x-intercept: when y = 0

3x - y = 2

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x = 2/3

y-intercept: when x = 0

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3 years ago

A sales person in a stereo store is given a choice of two different compensation plans. One plan offers a weekly salary of $250

snow_tiger [21]

Answer:

The salesperson needs to sell 10 stereos to make the same money on both plans

Step-by-step explanation:

We'll analyze both choices for the compensation plans of a salesperson.

One plan offers a fixed weekly salary of $250 plus a $25 commission for each stereo sold. The function than models this plan is:

P1=250+25x

Where x is the number of stereos sold.

The other plan offers no fixed salary but a $50 commission on each stereo sold. The function of this plan is:

P2=50x

To find the equilibrium point for both plans, we make P1=P2:

250+25x=50x

Simplifying:

25x=250

Solving:

x = 250 / 25 = 10

The salesperson needs to sell 10 stereos to make the same money on both plans

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3 years ago

The surface area of a cube is increasing at a rate of 15 square meters per hour. At a certain instant, the surface area is 24 sq

algol13

Answer:

The volume of cube is increasing at a rate 7.5 cubic meter per hour.

Step-by-step explanation:

We are given the following in the question:

Surface area of cube = 24 square meters.

Let l be the edge of cube.

Surface area of cube =

$6l^2 = 24\\l^2 = 4\\l = 2$

Thus, at that instant the edge of cube is 2 meters.

$\dfrac{dS}{dt} = 15\text{ square meters per hour}\\\\\dfrac{d(6l^2)}{dt} = 15\\\\12l\dfrac{dl}{dt} = 15\\\\\dfrac{dl}{dt} = \dfrac{15}{12\times 2} = \dfrac{15}{24}$

We have to find the rate of change in volume.

Volume of cube =

$l^3$

Rate of change of volume =

$\dfrac{dV}{dt} = \dfrac{d(l^3)}{dt} = 3l^2\dfrac{dl}{dt}\\\\\dfrac{dV}{dt} = 3(2)^2\times \dfrac{15}{24} \\\\\dfrac{dV}{dt} = 7.5\text{ cubic meter per hour}$

Thus, the volume of cube is increasing at a rate 7.5 cubic meter per hour.

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3 years ago

What is the value for x? Enter your answer in the box. x =

BaLLatris [955]

<A = <C = 73
<B = 180 - (<A + C)
6x + 4 = 180 - 2(73)
6x + 4 = 180 - 146
6x + 4 = 34
6x = 30
x = 5

answer
x = 5

6 0

3 years ago

4. The distribution of blood cholesterol level in the population of young men aged 20 to 34 years is close to Normal, with mean

Pie

Answer:

a) 38.59% probability that a young man (aged 20 to 34) has a cholesterol level greater than 200 milligrams per deciliter.

b) By the Central Limit Theorem, the mean of the distribution of the sample mean would be 188 milligrams per deciliter

Step-by-step explanation:

Problems of normally distributed samples are 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.

In this problem, we have that:

$\mu = 188, \sigma = 41$

a. Find the probability that a young man (aged 20 to 34) has a cholesterol level greater than 200 milligrams per deciliter.

This is 1 subtracted by the pvalue of Z when X = 200. So

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

$Z = \frac{200 - 188}{41}$

$Z = 0.29$

$Z = 0.29$ has a pvalue of 0.6141

1 - 0.6141 = 0.3859

38.59% probability that a young man (aged 20 to 34) has a cholesterol level greater than 200 milligrams per deciliter.

b. Suppose you measure the cholesterol level of 100 young men chosen at random and calculate the sample mean. If you did this many times, i. what would be the mean of the distribution of the sample mean

By the Central Limit Theorem, the mean of the distribution of the sample mean would be 188 milligrams per deciliter

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3 years ago