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3 years ago

25 points

Mathematics

1 answer:

Katyanochek1 [597]3 years ago

8 0

Answer:

subtract 3.97 from 25.32 and that how much he got a profit of

Step-by-step explanation:

however much he prices it up by is the profit

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Given a+b=7 and a–b=3, find:<br> 3^a÷3^b

Talja [164]

Answer:

Step-by-step explanation:

a + b = 7 ....eq 1

a - b = 3 ....eq 2

solve simultaneously using elimination method

add eq 2 to eq 1

a + b = 7

a - b = 3

2a = 10

a = 5

substitute the value of a in eq 1

5 + b = 7

subtract 5 from both sides

5 - 5 + b = 7- 5

b = 2

Now, slot in the values of both a and b

3^a÷3^b

we will solve using PEDMAS

3^5 / 3^2

$3^{5-2}$

$3^{3}$

8 0

3 years ago

From a group of 3 men and 4 women, a delegation of 2 is selected. What is the expected number of men in the delegation?

Ostrovityanka [42]

Answer:

The expected number of men in the delegation is 0.86.

Step-by-step explanation:

Number of men = 3

Number of women = 4

A delegation of 2 is selected.

Let X be the number of men selected. So, the possible values of X are 0,1,2.

$P(X=0)=\dfrac{^3C_0\times ^4C_2}{^7C_2}=\dfrac{2}{7}$

$P(X=1)=\dfrac{^3C_1\times ^4C_1}{^7C_2}=\dfrac{4}{7}$

$P(X=2)=\dfrac{^3C_2\times ^4C_0}{^7C_2}=\dfrac{1}{7}$

The expected number of men in the delegation is

$E(x)=0\times P(X=0)+1\times P(X=1)+2\times P(X=2)$

$E(x)=0\times \dfrac{2}{7}+1\times \dfrac{4}{7}+2\times \dfrac{1}{7}$

$E(x)=\dfrac{6}{7}$

$E(x)\approx 0.86$

Therefore, the expected number of men in the delegation is 0.86.

4 0

3 years ago

A daily mail is delivered to your house between 1:00 p.m. and 5:00 p.m. Assume delivery times follow the continuous uniform dist

german

Answer:

25% of deliveries

Step-by-step explanation:

This is a uniform distribution with parameters a = 1.00 and b =5.00. With these conditions, the following probability distribution functions can be applied:

$P(X \leq x)=\frac{x-a}{b-a}=\frac{x-1.00}{5.00-1.00}\\P(X \leq x) = \frac{x-1}{4}\\P(X \geq x) = 1- P(X \leq x) \\P(X \geq x)=1- \frac{x-1}{4}$

Therefore, the probability that X ≥ 4:00 p.m. is given by

$P(X \geq 4)=1- \frac{4-1}{4}\\P(X \geq 4)=0.25=25\%$

Thus, 25% of deliveries are made after 4:00 p/m.

7 0

3 years ago

6.7.37

posledela

Answer:

a. The start-up cost for the teenagers company is $50

b. The number of mugs the teenager must sell to break even are 5 mugs or 25 mugs

c. The number of mugs that will give maximum profit is 15 mugs

d. The profit if she sells 10 mugs is $30

Step-by-step explanation:

The given profit function for selling <em>x</em> number of mugs is presented as follows;

f(x) = -0.4·x² + 12·x - 50

a. The start-up cost in dollars is given by the value of the profit function at the start, where, x = 0, as follows;

Start-up cost = f(0) = -0.4×0² + 12×0 - 50 = -50

The negative sign represents amount put in the business

The start-up cost = (The initial) $50 put into the business.

b. The break even point is the point where, the revenue and costs are equal

At break even point; Revenue = Cost

∴ Profit, at break even point, f(x) = Revenue - Cost = 0

From the profit function, we get;

At the break even point, f(x) = 0 = -0.4·x² + 12·x - 50

Dividing by -0.4 gives;

0/(-0.4) = 0 = (-0.4·x² + 12·x - 50)/(-0.4) = x² - 30 + 125

0 = x² - 30 + 125

∴ (x - 25)·(x - 5) = 0

The number of mugs the teenager must sell before she breaks even, x = 5 mugs or x = 25 mugs.

c. From the general form of a quadratic equation, which is; y = a··x² + b·x + c, the formula for the x-values at the maximum point is; x = -b/(2·a)

Comparing the profit function to the general form of the quadratic equation we have at the maximum point;

x = -12/(2×(-0.4)) = 15

Therefore, the number of mugs that will give maximum profit, x = 15 mugs.

d. The profit from selling 10 mugs, f(10) is given as follows;

f(10) = -0.4 × 10² + 12 × 10 - 50 = 30

The profit from selling 10 mugs, f(10) = $30

4 0

3 years ago

Maddox McDonald A caterpillar moves across the grass at a rate of 4 2/3 feet every 7 minutes. How fast does the caterpillar move

harina [27]

Answer: 2/3 feet per minute

Step-by-step explanation:

From the question, we are informed that a caterpillar moves across the grass at a rate of 4 2/3 feet every 7 minutes.

The rate at which the caterpillar move in feet per minute will be:

= 4 2/3 ÷ 7

= 14/3 ÷ 7

= 14/3 × 1/7

= 14/21

= 2/3 feet per minute

8 0

3 years ago