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zimovet [89]
3 years ago
6

A new mixture of​ self-tanning & moisturizing lotions for everyday use is being developed. This mixture is made by mixing 70

0 ounces of everyday moisturizing lotion for ​$0.70 per ounce with​ self-tanning lotion worth ​$3 per ounce. If the new​ self-tanning & moisturizing lotion mixture is to cost $ 1.60 per​ ounce, how many ounces of the​ self-tanning lotion should be in the​ mixture?
Mathematics
1 answer:
777dan777 [17]3 years ago
7 0

Answer:

450 ounces

Step-by-step explanation:

We know that the cost of the mixture C_m must be the cost of the everyday moisturizing lotion C_e plus the cost of the self-tanning lotion C_s, which means C_m=C_e+C_s.

The cost of any substance will be the cost per ounce of the substance (c), multiplied by the number of ounces (n), which means C=nc, so we have from the previous formula that we have:

n_m c_m=n_e c_e + n_s c_s

But we also know that the number of ounces of the mixture must be the sum of the number of ounces of the everyday moisturizing lotion with the number of ounces of the self-tanning lotion, so we have

n_e c_e + n_s c_s=n_m c_m=(n_e+n_s) c_m=n_e c_m+n_s c_m

We want to calculate the number of ounces of the​ self-tanning lotion (n_s), so we solve for that variable:

n_e c_e + n_s c_s=n_e c_m+n_s c_m

n_s c_s-n_s c_m=n_e c_m-n_e c_e

n_s (c_s-c_m)=n_e(c_m-c_e)

n_s=\frac{n_e (c_m-c_e)}{(c_s-c_m)}

And substitute our values in this formula, to get:

n_s=\frac{(700\ ounces) (\$1.6-\$0.7)}{(\$3-\$1.6)}=450\ ounces

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AlladinOne [14]

L=2W-4

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58=2(2W-4)+2W

58=4W-8+2W

58=6W-8

6W=58+8

6W=66

W=66/6

W=11 ANS. FOR THE WIDTH.

L=2*11-4

L=22-4

L=18 ANS. FOR THE LENGTH.

PROOF:

58=2*18=2*11

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5 0
3 years ago
Need help with this math.
madreJ [45]

The end behavior of the function y = x² is given as follows:

f(x) -> ∞ as x -> - ∞; f(x) -> ∞ as x -> - ∞.

<h3>How to identify the end behavior of a function?</h3>

The end behavior of a function is given by the limit of f(x) when x goes to both negative and positive infinity.

In this problem, the function is:

y = x².

When x goes to negative infinity, the limit is:

lim x -> - ∞ f(x) = (-∞)² = ∞.

Meaning that the function is increasing at the left corner of it's graph.

When x goes to positive infinity, the limit is:

lim x -> ∞ f(x) = (∞)² = ∞.

Meaning that the function is also increasing at the right corner of it's graph.

Thus the last option is the correct option regarding the end behavior of the function.

<h3>Missing information</h3>

We suppose that the function is y = x².

More can be learned about the end behavior of a function at brainly.com/question/24248193

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3 0
1 year ago
What is the value of the hundreds digit in the number 943? (For example, in 280, the value of the hundreds digit is 200.) What i
Eddi Din [679]

Answer:

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Step-by-step explanation:

I hope this helps :)

8 0
2 years ago
Helppppppppp plzzzzz
Shkiper50 [21]

Answer: 4

Step-by-step explanation:

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11+(-7)

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8 0
3 years ago
In 2012 your car was worth $10,000. In 2014 your car was worth $8,850. Suppose the value of your car decreased at a constant rat
monitta

Answer:

The function to determine the value of your car (in dollars) in terms of the number of years t since 2012 is:

f(t) = 10000(0.9407)^t

Step-by-step explanation:

Value of the car:

Constant rate of change, so the value of the car in t years after 2012 is given by:

f(t) = f(0)(1-r)^t

In which f(0) is the initial value and r is the decay rate, as a decimal.

In 2012 your car was worth $10,000.

This means that f(0) = 10000, thus:

f(t) = 10000(1-r)^t

2014 your car was worth $8,850.

2014 - 2012 = 2, so:

f(2) = 8850

We use this to find 1 - r.

f(t) = 10000(1-r)^t

8850 = 10000(1-r)^2

(1-r)^2 = \frac{8850}{10000}

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\sqrt{(1-r)^2} = \sqrt{0.885}

1 - r = 0.9407

Thus

f(t) = 10000(1-r)^t

f(t) = 10000(0.9407)^t

7 0
3 years ago
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