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3 years ago

Find the constant of variation for the relationship f(x)= 40x.

2 answers:

8 0

We are given the expression f(x) = 40x where f(x) is the dependent variable and x is the independent variable. In this case, we can see that f(x) is directly proportional to x and that the constant of propotionality is 40. Answer then to this problem is D. 40

Vadim26 [7]3 years ago

4 0

Constant of variation is 40

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The skittles jar has a radius of 3.5 cm and a height of 11.5 cm. using the two given boxes for reference what would be a good es

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C) 1059 skittles

Step-by-step explanation:

We know that the first container held 192 skittles. Knowing the dimension of the container we can calculate the volume of 192 skittles:

Volume of 192 skittles = 5 × 4 × 4 = 80 cm³

Volume of 1 skittle = 80 / 192 = 0.42 cm³

We also know that the second container held 258 skittles. Knowing the dimension of the container we can calculate the volume of 258 skittles:

Volume of 258 skittles = 12 × 3 × 3 = 108 cm³

Volume of 1 skittle = 108 / 258 = 0.42 cm³

We found that the volume of 1 skittle is equal to 0.42 cm³. Now we calculate the volume of the skittles jar:

volume of cylinder = π × radius² × height

volume of skittles jar = 3.14 × 3.5² × 11.5 = 442 cm³

Now we can calculate the number of skittles in the jar:

number of skittles in the jar = volume of the jar / skittle volume

number of skittles in the jar = 442 / 0.42 = 1052 which is close the C) 1059

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volume of cylinder

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3 years ago

If Gabe's Soccer Ball Company is able, due to competitive pressure, to charge $60 for a new soccer ball, while one soccer ball c

Brums [2.3K]

Answer:

Results are below.

Step-by-step explanation:

Giving the following information:

Selling price= $60

Unitary variable cost= $28

Fixed costs= $15,000

First, we need to calculate the average total cost:

Average cost= total cost / number of units

For example, for 1 unit and 10,000 units:

1 unit:

Average cost= 15,028/1 = 15,028

10,000 units:

Average cost= (15,000 + 28*10,000) / 10,000

Average cost= $29.5

Now, we can calculate the break-even point in units:

0= (60*x) - (28*x) - 15,000

x= number of units to break-even

0= 32x - 15,000

15,000/32= x

468.75=x

break-even point in units= 469

For the desired profit of $10,000:

10,000 = (60*x) - (28*x) - 15,000

25,000= 32x

781.25= x

Break-even point= 782 units

Finally, fixed costs dropped by $8,000:

0= 32x - 7,000

x= 7,000/32

x= 218.75

Break-even point= 219

Difference= 250 units

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3 years ago

A group of high school athletes has an average GPA of 2.7 with a standard deviation of 0.9. a)Find the percentage of athletes wh

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Answer:

a) The percentage of athletes whose GPA more than 1.665 is 87.49%.

b) John's GPA is 3.645.

Step-by-step explanation:

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:

$\mu = 2.7, \sigma = 0.9$