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1 year ago

There are 8 runners in a race. What is the probability that Abby, Becca, and Carmen place first, second, and third in any order?

2 answers:

8 0

Well there are equally 8 runners in the race , and abby and becca and carmen are three of them . now the chances of them getting first , second , and third would be 3 out of 8 or 3 over 8 .

Mkey [24]1 year ago

3 0

$|\Omega|=8!\\
|A|=3!\cdot5!\\\\
P(A)=\dfrac{3!5!}{8!}=\dfrac{2\cdot3}{6\cdot7\cdot8}=\dfrac{1}{56}\approx1,8\%$

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Suppose the Sunglasses Hut Company has a profit function given by P ( q ) = − 0.02 q 2 + 5 q − 30 , where q is the number of tho

Andrew [12]

Answer:

A) Pairs of sunglasses should be sold to maximize profits is 100 thousand.

B) The actual maximum profits that can be expected is 180 thousands dollars.

Step-by-step explanation:

Given : Suppose the Sunglasses Hut Company has a profit function given by $P(q)=-0.02q^2+4q-20$

where, q is the number of thousands of pairs of sunglasses sold and produced and P(q) is the total profit, in thousands of dollars, from selling and producing q pairs of sunglasses.

To find :

A) How many pairs of sunglasses (in thousands) should be sold to maximize profits?

Profit is $P(q)=-0.02q^2+4q-20$

Compare with general quadratic equation $ax^2+bx+c$

a=-0.02, b=4, c=-20

The maximum value of quadratic function is at $x=-\frac{b}{2a}$

So, maximum profit occur at q is given by,

$q=-\frac{4}{2(-0.02)}$

$q=\frac{4}{0.04}$

$q=100$

i.e. 100 thousand pair of sunglasses.

Pairs of sunglasses should be sold to maximize profits is 100 thousand.

B) What are the actual maximum profits (in thousands) that can be expected?

Maximum profit occurs at q=100 thousand pairs is given by,

$P(100)=-0.02(100)^2+4(100)-20$

$P(100)=-0.02\times 10000+400-20$

$P(100)=180$

The actual maximum profits that can be expected is 180 thousands dollars.

7 0

1 year ago

Classify each characteristic according to whether it is true for an amoeba, a clock, or both.

Stells [14]

Answer:

Amoeba is a single celled eukaryotic organism, found in the water body. These organisms have a false feet called as pseudopodium. It helps in the locomotion and captures food from the external environment. The organism does not exhibit a well defined shape. It has organelles like nucleus and vacuoles surrounded by cytoplasm. The food being captured by psuedopodium is engulfed inside a vacuole. It reproduces by the process of asexual reproduction called as binary fission. The genetic material replicates by the mitotic division, then the cell divides into two equal daughter cells. The amoeba obtains energy from food, and it uses this energy to move, capture food and reproduce.

A clock is a non-living thing. That displays time. It has three needles or hands, the bigger hand displays hour, the small one displays minutes and the thin needle displays seconds. These hands or needles uses energy from a cell or battery.

Characteristics features of amoeba are as follows:

Uses energy

Has internal organization

Characteristics features of clock are as follows:

Uses energy

Contains cells

Lacks genetic material reproduces

Has a defined boundary

Has internal organization

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

Which expression is equivalent to the expression below? StartFraction m + 3 Over m squared minus 16 EndFraction divided by Start

Kamila [148]

Option B: $\frac{1}{(m-4)(m-3)}$ is the correct answer.

Explanation:

The given expression is $\frac{(\frac{m+3}{m^2-16}) }{(\frac{m^2-9}{m+4} )}$

Simplifying the expression, we have,

$\frac{m+3}{m^{2}-16}\times\frac{m+4}{m^2-9}$

Factor the equations, $m^{2}-16\right$ and $m^{2}-9$ ,we get,

$m^{2}-16\right=m^{2}-4^{2}=(m+4)(m-4)$

$m^{2}-9=m^{2}-3^2=(m+3)(m-3)$

Substituting these factored expressions in the above expression, we have,

$\frac{m+3}{(m+4)(m-4)}\times\frac{m+4}{(m+3)(m-3)}$

Cancelling the common terms $m+3$ and $m+4$ , we get,

$\frac{1}{(m-4)(m-3)}$

Thus, the expression equivalent to $\frac{(\frac{m+3}{m^2-16}) }{(\frac{m^2-9}{m+4} )}$ is $\frac{1}{(m-4)(m-3)}$

Hence, Option B is the correct answer.

3 0

1 year ago

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The total cost of an item including sales tax is directly proportional to its price. If the total cost of a $32 item is $33.60 ,

pav-90 [236]

Let the total cost of the item be represented by C and the price be represented by P, then given that t<span>he total cost of an item including sales tax is directly proportional to its price, thus</span>

$C\propto P \\ \\ \Rightarrow C=kP$

where k is a constant.

Given that <span>the total cost of a $32 item is $33.60, thus

$33.60=32k \\ \\ \Rightarrow k= \frac{33.60}{32} =1.05$

Therefore, the total cost on a $55 item is given by

$C=1.05\times55=\$57.75$ </span>

3 0

2 years ago

The potential energy, P, in a spring is represented using the formula P = A equals StartFraction one-half EndFraction b h.kx2. L

Dimas [21]

Answer:

k = 2Px2

Step-by-step explanation:

4 0

2 years ago

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