MATHEMATICS COLLEGE

A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 70% salt and Solution B is 95% salt. She wants to obtain 150 ounces of a mixture that is 75% salt. How many ounces of each solution should she use?

Answers

Answer 1

Answer:

Answer:

Solution A: 120 ounces

Solution B: 30 ounces

Step-by-step explanation:

Let's call A the amount of Solution A. Solution A is 70% salt

Let's call B the amount of Solution B. Solution A is 95% salt

The resulting mixture should have 75% salt and 150 ounces .

Then we know that the total amount of mixture will be:

$A + B = 150$

Then the total amount of salt in the mixture will be:

$0.7A + 0.95B = 0.75 * 150$

$0.7A + 0.95B = 112.5$

Then we have two equations and two unknowns so we solve the system of equations. Multiply the first equation by -0.95 and add it to the second equation:

$-0.95A -0.95B = 150 * (-0.95)$

$-0.95A -0.95B =-142.5$

$0.7A + 0.95B = 112.5$

--------------------------------------

$-0.25A = -30$

$A = (-30)/(-0.25)$

$A = 120\ ounces$

We substitute the value of A into one of the two equations and solve for B.

$120 + B = 150$

$B = 30\ ounces$

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Find the discount on a leather recliner with a regular price of $260 if the recliner is 30% off. What is the sale price of the recliner?The discount on the leather recliner is

Answers

260x 30% = 78
260-78=$182
The sale price of the recliner is $182
The discount on the leather recliner is $78

It is 182, hope this helps!

A quality-control manager for a company that produces a certain soft drink wants to determine if a 12-ounce can of a certain brand of soft drink contains 120 calories as the labeling indicates. Using a random sample of 10 cans, the manager determined that the average calories per can is 124 with a standard deviation of 6 calories. At the .05 level of significance, is there sufficient evidence that the average calorie content of a 12-ounce can is greater than 120 calories? Assume that the number of calories per can is normally distributed.

Answers

Answer:

We conclude that the average calorie content of a 12-ounce can is greater than 120 calories.

Step-by-step explanation:

We are given that a quality-control manager for a company that produces a certain soft drink wants to determine if a 12-ounce can of a certain brand of soft drink contains 120 calories as the labeling indicates.

Using a random sample of 10 cans, the manager determined that the average calories per can is 124 with a standard deviation of 6 calories.

Let $\mu$ = average calorie content of a 12-ounce can.

So, Null Hypothesis, $H_0$ : $\mu \leq$ 120 calories {means that the average calorie content of a 12-ounce can is less than or equal to 120 calories}

Alternate Hypothesis, $H_A$ : $\mu$ > 120 calories {means that the average calorie content of a 12-ounce can is greater than 120 calories}

The test statistics that would be used here One-sample t test statistics as we don't know about the population standard deviation;

T.S. = $(\bar X-\mu)/((s)/(√(n) ) )$ ~ $t_n_-_1$

where, $\bar X$ = sample average calories per can = 124 calories

s = sample standard deviation = 6 calories

n = sample of cans = 10

So, test statistics = $(124-120)/((6)/(√(10) ) )$ ~ $t_9$

= 2.108

The value of t test statistics is 2.108.

Now, at 0.05 significance level the t table gives critical value of 1.833 at 9 degree of freedom for right-tailed test. Since our test statistics is more than the critical values of t as 2.108 > 1.833, so we have sufficient evidence to reject our null hypothesis as it will in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the average calorie content of a 12-ounce can is greater than 120 calories.

Brainliest if you provide a valid explanation!*IF YOU STEAL POINTS YOU WILL BE REPORTED*

Q: The table shows the weights of apples at a grocery store. If this represents a proportional relationship, what is the weight of 12 apples? Remember to explain your answer :)

Answers

Step 1: So to start us off, because every 5 apples weighs 0.60 kilograms, we're going to divide 0.60 by 5 to get the weight of ONE apple.

0.60 divided by 5= 0.12

Now we know how much a single apple weighs in kilograms and we can move onto the next step.

Step 2: The next step is to times the weight of one apple by 12 because that would give us our answer for the weight in kilograms of 12 apples.

0.12 times 12=1.44

Hopefully, this is correct and helps you! Sorry if I made any errors, it would be best to go back and do the steps yourself just to make sure if that makes you feel any better. Good luck! xxoo

-Sav

Answer:

1.44kg

Step-by-step explanation:

If they are proportional then you can use the unitary method:

If 5 apples=0.6kg then 1 apple=0.12kg as this is 0.6/5 (because you divided the apples by 5 so you have to do the same to the kg)

then you can work out that 12 apples=1.44kg because 0.12*12 is 1.44 and you multiply by 12 as this is what you multiplied the apples by so (becasue they are proportional then you have to do the same to the kg)

hope this helps :)

(Based on Q1 ~ Q3) According to the Bureau of the Census, 18.1% of the U.S. population lives in the Northeast, 21.9% inn the Midwest, 36.7% in the South, and 23.3% in the West.. In a random sample of 200 recent calls to a national 800-member hotline, 39 of the calls were from the Northeast, 55 from the Midwest, 60 from the South, and 46 from the West. At the 0.05 level, can we conclude that the geographical distribution of hotline callers could be the same as the U.S. population distribution?

Answers

Answer:

We can therefore conclude that the geographical distribution of hotline callers could be the same as the U.S population distribution.

Step-by-step explanation:

The null Hypothesis: Geographical distribution of hotline callers could be the same as the U.S. population distribution

Alternative hypothesis: Geographical distribution of hotline callers could not be the same as the U.S. population distribution

The populations considered are the Midwest, South, Northeast, and west.

The number of categories, k = 4

Number of recent calls = 200

Let the number of estimated parameters that must be estimated, m = 0

The degree of freedom is given by the formula:

df = k - 1-m

df = 4 -1 - 0 = 3

Let the significance level be, α = 5% = 0.05

For α = 0.05, and df = 3,

from the chi square distribution table, the critical value = 7.815

Observed and expected frequencies of calls for each of the region:

Northeast

Observed frequency = 39

It contains 18.1% of the US Population

The probability = 0.181

Expected frequency of call = 0.181 * 200 = 36.2

Midwest

Observed frequency = 55

It contains 21.9% of the US Population

The probability = 0.219

Expected frequency of call = 0.219 * 200 =43.8

South

Observed frequency = 60

It contains 36.7% of the US Population

The probability = 0.367

Expected frequency of call = 0.367 * 200 = 73.4

West

Observed frequency = 46

It contains 23.3% of the US Population

The probability = 0.233

Expected frequency of call = 0.233 * 200 = 46

$x^(2) = \sum ((O_(i) - E_(i)) ^(2) )/(E_(i) ) , i = 1, 2,.........k$

Where $O_(i) =$ observed frequency

$E_(i) =$ Expected frequency

Calculate the test statistic value, x²

$x^(2) = ((39 - 36.2)^(2) )/(36.2) + ((55 - 43.8)^(2) )/(43.8) + ((60 - 73.4)^(2) )/(73.4) + ((46 - 46.6)^(2) )/(46.6)$

$x^(2) = 5.535$

Since the test statistic value, x²= 5.535 is less than the critical value = 7.815, the null hypothesis will not be rejected, i.e. it will be accepted. We can therefore conclude that the geographical distribution of hotline callers could be the same as the U.S population distribution.

MP of an article is $1400. Find the SP of that article in cents if the shopkeeper adds 13% VAT after allowing 45% discount. (100 cents =$1)

Answers

Answer:

87,010 cents is the SP.

Step-by-step explanation:

MP = $1400

VAT = 13%

Discount = 45%

so,

discount amount = 45% of MP

= 45% of $1400

= 45/100 * $1400

= 9/20 * $1400

= 9* $70

= $630

so,

MP - discount amount

= $1400 - $630

= $770(SP)

so,

VAT amount = 13% of SP

= 13% of $770

= 13/100 * $770

= $100.1

so,

SP + VAT

= $770 + $100.1

= $870.1

so,

$1 = 100 cents

$870.1 = 100*870.1

= 87,010 cents

At the "cloth for you" shop, you can buy a top for £10.00 and a Bermuda trouser for £12.00. Due to a sensational sell, there is a 20% discount on all tops. If you buy one top and two Bermuda trousers, how much money do you spend in total?