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KonstantinChe [14]

2 years ago

10

A new mixture of self-tanning & moisturizing lotions for everyday use is being developed. This mixture is made by mixing 90

0 ounces of everyday moisturizing lotion for $0.90 per ounce with self-tanning lotion worth $33 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?

1 answer:

butalik [34]2 years ago

7 0

I don't know but i need points so thanks

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Suppose that 20% of the adult women in the United States dye or highlight their hair. We would like to know the probability that

Rasek [7]

Answer:

71.08% probability that pˆ takes a value between 0.17 and 0.23.

Step-by-step explanation:

We use the binomial approxiation to the normal to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

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.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

$p = 0.2, n = 200$ . So

$\mu = E(X) = np = 200*0.2 = 40$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{200*0.2*0.8} = 5.66$

In other words, find probability that pˆ takes a value between 0.17 and 0.23.

This probability is the pvalue of Z when X = 200*0.23 = 46 subtracted by the pvalue of Z when X = 200*0.17 = 34. So

X = 46

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{46 - 40}{5.66}$

$Z = 1.06$

$Z = 1.06$ has a pvalue of 0.8554

X = 34

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{34 - 40}{5.66}$

$Z = -1.06$

$Z = -1.06$ has a pvalue of 0.1446

0.8554 - 0.1446 = 0.7108

71.08% probability that pˆ takes a value between 0.17 and 0.23.

6 0

2 years ago

A large ice chest holds 62 liters of water. A smaller chest holds 4/5 as much water

dedylja [7]

Answer:

Step-by-step explanation:

Since a large ice chest holds the water = 62 liters

And smaller chest holds the water = $\frac{4}{5}$ of the larger ice chest

= $\frac{4}{5}\times 62$

= $\frac{248}{5}$ liters

Therefore, fraction that represents the amount of ice water in the smaller ice chest will have 0 in the first box, 248 in the numerator and 5 in the denominator.

$0\frac{248}{5}$

6 0

2 years ago

A furniture company is introducing a new line of lounge chairs next quarter. These are the cost and revenue functions, where x r

QveST [7]

Answer:

No lower than $208, and no higher than $956.8

Step-by-step explanation:

Notice that the revenue (income) function is represented by a quadratic expression (a parabola with branches pointing down), and the cost function is linear with negative slope.

When we plot them, we obtain the graphs shown in the attached image. Notice as well that there are two points of intersection for these two functions. The revenue exceeds (lays above) the cost in between the two points of intersection (marked in red and green).

For the company to make a profit, the revenue has to be larger than the cost, so we study the limiting values for that to happen, which is the points of intersection of these two curves.

The first one (pictured in red) is associated with coordinates (35, 33488) which tells us that is the production of 35 chairs with a revenue of $33,488. That is a cost per chair of $33,488 / 35 = $956.8

The second intersection (pictured in green) is associated with coordinates (125, 26000), which tells us that is the production of 125 chairs with a revenue of $26,000. That is a cost per chair of $26000 / 125 = $ 208

So these values give us the minimum and maximum that the company can charge to make a profit.

6 0

2 years ago

Read 2 more answers

Mackin Investing charges its customers a 1% commission. The Ross Group, a discount broker, charges $25 per trade. For what amoun

olchik [2.2K]

Answer:

The amount of stock for which both brokers would charge the same commission is $2500.

Step-by-step explanation:

i) Let the amount of stock to be traded be worth $x

ii) therefore for both the brokers to charge the same commission we can write

1% of x = $25 $\RIghtarrow$ $\Rightarrow$ 0.01 $\times$ x = 25 $\therefore$ x = $\frac{25}{0.01} = 2500$

The amount of stock for which both brokers would charge the same commission is $2500.

5 0

1 year ago

Determine whether or not the vector field is conservative. if it is conservative, find a function f such that f = ∇f. (if the ve

sweet [91]

A conservative vector field $\mathbf f$ has curl $\nabla\times\mathbf f=\mathbf0$ . In this case,

$\nabla\times\mathbf f=12xy^2z(1-z)\,\mathbf j+4yz^2(2z-3x)\,\mathbf k\neq\mathbf 0$

so the vector field is not conservative.

3 0

2 years ago