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san4es73 [151]
3 years ago
12

How many pounds of candy that cells for $0.66 per Ib must be mixed with candy that sells for $1.31 per Ib to obtain 9 Ib of a mi

xture that should sell for $0.97 per Ib?
Mathematics
1 answer:
faltersainse [42]3 years ago
7 0

Answer:  \frac{306}{65} pounds

Step-by-step explanation:

Let x pounds of $ 0.66 per lb candies mixed with y pounds of $ 1.31 per lb candies to obtain 9 lb of $ 0.97 per lb candies,

Hence, we can write,

x + y = 9 ------- (1)

And, 0.66 of x + 1.31 of y = 0.97 of (x + y)

⇒ 66 x + 131 y = 97 (x+y)

⇒ 66 x +131 y - 97 x - 97 y = 0

⇒ -31 x + 34 y = 0  ------(2)

By solving equation (1) and (2)

We get,

x=\frac{306}{65} and y=\frac{279}{65}

Hence, the quantity of 0.66 per lb candies = \frac{306}{65}  pounds

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twice the number of donuts was only 6 less than 24 times the number of cream puffs. 10 times the number of cream puffs was only
Karolina [17]

donuts and cream puffs were  45 & 4 respectively !

<u>Step-by-step explanation:</u>

Here we have , twice the number of donuts was only 6 less than 24 times the number of cream puffs. 10 times the number of cream puffs was only 5 less than the number of donuts   We need to find how many donuts and cream puffs were there . Let's find out:

Let number of donuts and cream puffs are x & y respectively ! So ,

  • twice the number of donuts was only 6 less than 24 times the number of cream puffs

According to this statement equation is :

⇒ 2x=24y-6

⇒ x=12y-3            ................(1)

  • 10 times the number of cream puffs was only 5 less than the number of donuts

According to this statement equation is :

⇒ 10y= x-5

⇒ x=10y+5               ................(2)

Equation (1) & (2) :

⇒ 12y-3=10y+5

⇒ 2y=8

⇒ y=4

Putting  y=4 in  x=12y-3  :

⇒ x = 12(4)-3

⇒ x = 45

Therefore , donuts and cream puffs were  45 & 4 respectively !

7 0
3 years ago
Solve this system of linear equations. Separate
Gelneren [198K]

Answer:

x 2 y -4

Step-by-step explanation:

13x = -54 -20y give it is A

-10x = 60 + 20y give it is B

A + B the sum of the left side of equation is equal to the sum of the right side of equation

13 + (-10x) = -54 -20y + 60 + 20y

3x = 60-54

3x = 6

x=2

so put the x value in A or B equation you can receive y value (B is easier)

y = -4

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3 years ago
Find the range and interquartile range for the data represented by the box plot.
Anarel [89]

<u>Given</u>:

Given that the data are represented by the box plot.

We need to determine the range and interquartile range.

<u>Range:</u>

The range of the data is the difference between the highest and the lowest value in the given set of data.

From the box plot, the highest value is 30 and the lowest value is 15.

Thus, the range of the data is given by

Range = Highest value - Lowest value

Range = 30 - 15 = 15

Thus, the range of the data is 15.

<u>Interquartile range:</u>

The interquartile range is the difference between the ends of the box in the box plot.

Thus, the interquartile range is given by

Interquartile range = 27 - 18 = 9

Thus, the interquartile range is 9.

3 0
3 years ago
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The owner of Matt’s Gas Station wants to study gasoline purchases of customers at his station. In 2017, the mean amount of gas
gulaghasi [49]

Answer:

Step-by-step explanation:

a) We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

µ = 9

For the alternative hypothesis,

µ ≠ 9

This is a 2 tailed test

Since the population standard deviation is given, z score would be determined from the normal distribution table. The formula is

z = (x - µ)/(σ/√n)

Where

x = sample mean

µ = population mean

σ = population standard deviation

n = number of samples

From the information given,

µ = 9

x = 9.9

σ = 2.5

n = 50

z = (9.9 - 9)/(2.5/√50) = 2.55

Looking at the normal distribution table, the probability corresponding to the area above the z score is 1 - 0.99461 = 0.00539

Recall, population mean is 9

The difference between sample sample mean and population mean is 9.9 - 9 = 0.9

Since the curve is symmetrical and it is a two tailed test, the x value for the left tail is 9 - 0.9 = 8.1

the x value for the right tail is 9 + 0.9 = 9.9

These means are higher and lower than the null mean. Thus, they are evidence in favour of the alternative hypothesis. We will look at the area in both tails. Since it is showing in one tail only, we would double the area. We already got the area above the z score as z = 0.00539

We would double this area to include the area in the left tail of z = - 2.55. Thus

p = 0.00539 × 2 = 0.01078

Since alpha, 0.01 < 0.01078, we would reject the null hypothesis

But we are told to use the critical value approach, then

Since α = 0.01, the critical value is determined from the normal distribution table.

For the left, α/2 = 0.01/2 = 0.005

The z score for an area to the left of 0.005 is - 2.575

For the right, α/2 = 1 - 0.005 = 0.995

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In order to reject the null hypothesis, the test statistic must be smaller than - 2.575 or greater than 2.575

Since - 2.55 > - 2.575 and 2.55 < 2.575, we would reject the null hypothesis. This corresponds to our previous decision.

b) we would assume normal distribution because the sample size is sufficiently large and the population standard deviation is known.

c) Confidence interval is written in the form,

(Sample mean ± margin of error)

Since the sample size is large and the population standard deviation is known, we would use the following formula and determine the z score from the normal distribution table.

Margin of error = z × σ/√n

The z score for confidence level of 99% is 2.58

Margin of error = 2.58 × 2.5/√50 = 0.91

Confidence interval = 9.9 ± 0.91

The lower end of the confidence interval is

9.9 - 0.91 = 8.99

Therefore, p = 9 will be contained in the interval.

4 0
3 years ago
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Korolek [52]

Answer:

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Step-by-step explanation:

There is an easier way instead of doing 0.08 of t and then adding. You can do 108% of t which immediately gives the answer.

Hope this helps:)

3 0
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