MATHEMATICS HIGH SCHOOL

Four cups of a salad blend containing 40% spinach is mixed with an unknown amount of a salad blend containg 55% spinach. The resulting salad contains 50% spinach. How many cups of salad are in the resulting mixture?

Answers

Answer 1

Answer:

Answer: 12 cups of salad blend are in the resulting mixture

Explanation:

Since we have given that

4 cups of a salad blend contains 40% spinach

Using mixture allegation method, we get that

8 cups of a salad blend contains 55% spinach as shown in the figure below.

Now, we need to find the number of cups of salad in the resulting mixture,

$0.4* 4+0.55* 8=0.5* x\n\n1.6+4.4=0.5x\n\n6=0.5x\n\n(6)/(0.5)=x\n\n12=x$

Hence, 12 cups of salad blend are in the resulting mixture .

Answer 2

Answer:

Answer:

Option C: 12 cups of salad

Let the unknown cups of salad in the mixture be x( unknown cup in 55% mixture)

Thus, we have the following expression that shows the number of salad in the resulting mixture;

4(40%) + x(55%) = (4+x)(50%)

= 0.4(4) + x(0.55) = 0.5(4 + x)

= 1.6 + 0.55x = 0.2 + 0.5x

0.2 -1.6 = 0.55x-0.5x

0.4 = 0.05x

x = 0.4/0.05

x = 8 cups of salad

So the number of salad cups in the resulting mixture = x + 4 = 8 + 4 = 12 cups of salad

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A hot dog vendor has determined that the number of hot dogs he sells per day is inversely proportional to the price he charges. The vendor wants to decide if increasing his price by 55 cents will drive away too many customers. On average, he sells 200 hot dogs a day at a price of $3.85 per hot dog. How many hot dogs can he expect to sell if the price is increased by 55 cents? Round your answer to the nearest hot dog.

Answers

Answer:

175 hot dogs

Step-by-step explanation:

The new price will be $3.85 + 0.55 = $4.40. Since the price has increased by a factor of 4.40/3.85 = 8/7, the number of hot dogs sold, which is inversely proportional, will be ...

(7/8)·200 = 175 . . . hot dogs sold at the higher price

Final answer:

The vendor can expect to sell approximately 233 hot dogs if the price is increased by 55 cents.

Explanation:

To determine how many hot dogs the vendor can expect to sell if the price is increased by 55 cents, we can use the inverse proportionality relationship between the number of hot dogs sold and the price charged.

First, let's set up a proportion with the initial price and number of hot dogs sold:

$3.85 / 200 = (new price + $0.55) / x

Next, we can cross multiply and solve for x:

x = (200 * ($3.85 + $0.55)) / $3.85

Calculating this expression gives us a value of x ≈ 233.77.

Since the number of hot dogs sold must be a whole number, we round down to the nearest whole number, giving us an estimated value of 233 hot dogs.

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A recent study indicates that the annual cost of maintaining and repairing a car in a town in Ontario averages 200 with a variance of 260. A tax of 20% is introduced on all items associated with the maintenance and repair of cars (i.e., everything is made 20% more expensive). Calculate the variance of the annual cost of maintaining and repairing a car after the tax is introduced.

Answers

Answer:

374.4

Step-by-step explanation:

All items related to the maintenance are 20% more expensive, it means that each datum is 20% bigger including the average.

The variance its a dispersion measurof the data and its calculated of this way:

$\sigma^(2) =(1)/(n) \sum\limits^n_(i=1) (x_(i)-\var{x})^2\n$

Here n is the number of data, $\var{x}$ is the average and $x_(i)$ represent each datum. The increment in 20% in each parameter can be represented multiplying for 1.2, of this way

$\sigma_(20\%)^(2) =(1)/(n) \sum\limits^n_(i=1) (1.2x_(i)-1.2\var{x})^2\n$

Factorizing the 1.2 we have:

$\sigma_(20\%)^(2) =(1)/(n) \sum\limits^n_(i=1) (1.2(x_(i)-\var{x}))^2$

$\sigma_(20\%)^(2) =(1)/(n) \sum\limits^n_(i=1)1.2^(2) (x_(i)-\var{x})^2$

$\sigma_(20\%)^(2) =(1.2^(2))/(n) \sum\limits^n_(i=1) (x_(i)-\var{x})^2\n$

That is:

$1.2^(2)\sigma^(2)=\sigma_(20\%)^(2)$

The new variance is $1.2^(2) \sigma^(2) =1.44*260=374.4$

Final answer:

To calculate the variance of the annual cost of maintaining and repairing a car after the tax is introduced, we can use the formula var(X + c) = var(X), where X is the original cost and c is the tax rate. In this case, the tax rate is 20%, so c = 0.2. The variance of the original cost is 260, so the variance of the cost after the tax is introduced is also 260.

Explanation:

To calculate the variance of the annual cost of maintaining and repairing a car after the tax is introduced, we can use the formula var(X + c) = var(X), where X is the original cost and c is the tax rate. In this case, the tax rate is 20%, so c = 0.2. The variance of the original cost is 260, so the variance of the cost after the tax is introduced is also 260.

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Identify the property used to create the equivalent expression. (3 + 4) + 6 = 3 + (4 + 6)

Answers

Answer: associative

Step-by-step explanation:

the associative property is used to state that numbers in an addition expression can be grouped differently still giving the same sum

Help pretty please :) <3

Answers

To find the mean, add up all of the numbers, and divide by the total amount of numbers.

-5 + -7 + 0 + 8 + 9 = 5

5/5 = 1

that would be 10 and your very welcome

He daily rainfall during two April weeks was: 1, 0.5, 0.3, 0, 0 ,0, 1.2,3, 0, 1.1, 0.7, 2, 1.3, 2 inches. What was the median rainfall during
the two weeks?
(Points : 1)

Answers

0,0,0,0,0.3,0.5,0.7,1,1.1,1.2,1.3,2,2,3. So the median is 0.85

Answer:

The median is 0.93

How do you do...
cos2x-sin2x=1-2sin2x

Answers

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