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KengaRu [80]
3 years ago
6

In melanie's styling salon, the time to complete a simple haircut is normally distributed with a mean of 25 minutes and a standa

rd deviation of 4 minutes. for a simple haircut, the middle 90 percent of the customers will require:
Mathematics
1 answer:
vovikov84 [41]3 years ago
6 0
They will require between 18.42 and 31.58 minutes.

We want the middle 90%.  The two probability values associated with this would be 0.95 and 0.05; this would leave 5% below and 5% above, giving us the middle 90%.

Using a z-table (http://www.z-table.com) we see that the z-score associated with an area to the left of 0.05 is between -1.64 and -1.65; since it is equally distant from both we will use -1.645.

The z-score associated with an area of the left of 0.95 is between 1.64 and 1.65; since it is equally distant from both we will use 1.645.

The formula for a z-score is

z = (X-μ)/σ
-1.645 = (X-25)/4

Multiplying by 4 on both sides,
-1.645(4) = X-25
-6.58 = X-25

Adding 25 to both sides,
-6.58+25 = X
18.42 = X

For the upper bound,
1.645 = (X-25)/4

Multiplying both sides by 4,
1.645(4) = X-25
6.58 = X-25

Adding 25 to both sides,
6.58+25 = X
31.58 = X

The times are between 18.42 and 31.58 minutes.
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your friend claims that two isosceles triangles ABC and DEF are congruent if two corresponding sides are congruent. he explains
Svetach [21]
Think about the fact that you can have two types of isosceles triangle: one of them that is a right triangle (isosceles right triangle) such as a 45-45-90 triangle and the other type can be just a regular triangle that has two sides that are congruent but it isn't a right triangle. 

Thus, you would need more info about the triangles in order to conclude that the two isosceles triangles are congruent to each other. 
7 0
3 years ago
A bag of chips is 24 ounces. A serving size is 3/4 ounce. How many servings are in the bag of chips?
marysya [2.9K]

Answer:

The correct answer to the following question will be "32 servings".

Step-by-step explanation:

The given values are,

A bag of chips = 24 ounces

Serving size = 3/4 ounces

Servings = ?

Now,

On dividing "24 ounces" by "3/4 ounce", we get

⇒  \frac{24}{\frac{3}{4}}

⇒  24\times \frac{4}{3}

⇒  8\times 4

⇒  32

Thus, the bag of chips contains "32" servings.

4 0
3 years ago
Can you find the marginal profit of a,b and c?
MakcuM [25]
Keeping in mind that for a cost C(x) and profit P(x) and revenue R(x), the marginal cost, marginal profit and marginal revenue are respectively dC/dx, dP/dx and dR/dx, then

\bf P(x)=0.03x^2-3x+3x^{0.8}-4400
\\\\\\
\stackrel{marginal~profit}{\cfrac{dP}{dx}}=0.06x-3+2.4x^{-0.2}
\\\\\\
\cfrac{dP}{dx}=0.06x-3+2.4\cdot \cfrac{1}{x^{0.2}}\implies \cfrac{dP}{dx}=0.06x-3+2.4\cdot \cfrac{1}{x^{\frac{1}{5}}}
\\\\\\
\cfrac{dP}{dx}=0.06x-3+\cfrac{2.4}{\sqrt[5]{x}}

\bf a)\qquad 
\cfrac{dP}{dx}=0.06(200)-3+ \cfrac{2.4}{\sqrt[5]{200}}
\\\\\\
b)\qquad \cfrac{dP}{dx}=0.06(2000)-3+\cfrac{2.4}{\sqrt[5]{2000}}
\\\\\\
c)\qquad \cfrac{dP}{dx}=0.06(5000)-3+\cfrac{2.4}{\sqrt[5]{5000}}
\\\\\\
d)\qquad \cfrac{dP}{dx}=0.06(10000)-3+\cfrac{2.4}{\sqrt[5]{10000}}
3 0
3 years ago
A 30% solution of fertilizer is to be mixed with a 70% solution of fertilizer in order to get 40 gallons of a 60% solution. How
Murrr4er [49]

Answer:10 gallons of 30% solution and 30 gallons of 70% solution should be mixed.

Step-by-step explanation:

Let x represent the number of gallons of the 30% solution that should be mixed.

Let y represent the number of gallons of the 70% solution that should be mixed.

The total number of gallons of the mixture to be made is 40. This means that

x + y = 40

The 30% solution of fertilizer is to be mixed with a 70% solution of fertilizer in order to get 40 gallons of a 60% solution. This means that

0.3x + 0.7y = 0.6 × 40

0.3x + 0.7y = 24- - - - - - - - - - - - - -1

Substituting x = 40 - y into equation 1, it becomes

0.3(40 - y) + 0.7y = 24

12 - 0.3y + 0.7y = 24

- 0.3y + 0.7y = 24 - 12

0.4y = 12

y = 12/0.4

y = 30

x = 40 - y = 40 - 30

x = 10

5 0
3 years ago
Suppose that the probability of a baseball player getting a hit in an at-bat is 0.3089. If the player has 25 at-bats during a we
klio [65]

Answer:

P(X>9) = 0.3593

Step-by-step explanation:

Previous concepts  

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".  

Solution to the problem

Let X the random variable of interest, on this case we now that:

X \sim Binom(n=25, p=0.3089)  

The probability mass function for the Binomial distribution is given as:  

P(X)=(nCx)(p)^x (1-p)^{n-x}  

For this case we want this probability:

P(X >9)

And we can use the complement rule like this:

P(X>9) = 1-P(X \leq 8)= 1-[P(X=0) + P(X=1) +....+P(X=8)]And we can find the individual probabilities like this:

P(X=0) =(25C0)(0.3089)^0 (1-0.3089)^{25-0} =0.0000974  

P(X=1) =(25C1)(0.3089)^1 (1-0.3089)^{25-1} =0.0011  

P(X=2) =(25C2)(0.3089)^2 (1-0.3089)^{25-2}=0.00584  

P(X=3) =(25C3)(0.3089)^3 (1-0.3089)^{25-3}= 0.02  

P(X=4) =(25C4)(0.3089)^4 (1-0.3089)^{25-4}=0.049  

P(X=5) =(25C5)(0.3089)^5 (1-0.3089)^{25-5}=0.092  

P(X=6)=(25C6) (0.3089)^6 (1-0.3089)^{25-6} = 0.138

P(X=7) =(25C7)(0.3089)^7 (1-0.3089)^{25-7}=0.167

P(X=8) =(25C8)(0.3089)^8 (1-0.3089)^{25-8}=0.168

And in order to do the operations we can use the following excel code:

"=1-BINOM.DIST(8,25,0.3089,TRUE)"  

And we got:

P(X>9) = 0.3593

4 0
3 years ago
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