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professor190 [17]

1 year ago

5

A building engineer analyzes a concrete column with a circular cross section. The circumference of the column is 18pi meters. Wh

at is the area A of the cross section of the column?

2 answers:

ella [17]1 year ago

3 0

Answer

Circumference(C) of a circle is given by:

$C = 2\pi r$

where r is the radius and value of $\pi = 3.14$

As per the given statement:

A building engineer analyzes a concrete column with a circular cross section.

The circumference of the column is $18 \pi$ meters.

then;

$18 \pi= 2\pi r$

Divide both sides by $2 \pi$ we have;

9 = r

or

r = 9 meters

We have to find the area of the cross section of the column

Area of a circle is given by:

$A = \pi r^2$

then;

$A = \pi \cdot 9^2 = 81 \pi$ meter square.

therefore, the area A of the cross section of the column is $81 \pi$ meter square.

iren [92.7K]1 year ago

3 0

Check the picture below

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A construction company is considering submitting bids for contracts of three different projects. The company estimates that it h

julsineya [31]

Answer:

a. $P(x)=\frac{n!}{x!(n-x)!}*p^{x}*(1-p)^{n-x}\\$

b. $E(x) = 0.3$

c. $S(x)=0.5196$

d. $E=5,000$

Step-by-step explanation:

The probability that the company won x bids follows a binomial distribution because we have n identical and independent experiments with a probability p of success and (1-p) of fail.

So, the PMF of X is equal to:

$P(x)=\frac{n!}{x!(n-x)!}*p^{x}*(1-p)^{n-x}\\$

Where p is 0.1 and it is the chance of winning. Additionally, n is 3 and it is the number of bids. So the PMF of X is:

$P(x)=\frac{3!}{x!(3-x)!}*0.1^{x}*(1-0.1)^{n-x}\\$

For binomial distribution:

$E(x)=np\\S(x)=\sqrt{np(1-p)}$

Therefore, the company can expect to win 0.3 bids and it is calculated as:

$E(x) = np = 3*0.1 = 0.3$

Additionally, the standard deviation of the number of bids won is:

$S(x)=\sqrt{np(1-p)}=\sqrt{3(0.1)(1-0.1)}=0.5196$

Finally, the probability to won 1, 2 or 3 bids is equal to:

$P(1)=\frac{3!}{1!(3-1)!}*0.1^{1}*(1-0.1)^{3-1}=0.243\\P(2)=\frac{3!}{2!(3-2)!}*0.1^{2}*(1-0.1)^{3-2}=0.027\\P(3)=\frac{3!}{3!(3-3)!}*0.1^{3}*(1-0.1)^{3-3}=0.001$

So, the expected profit for the company is equal to:

$E=-10,000+50,000(0.243)+100,000(0.027)+150,000(0.001)\\E=5,000$

Because there is a probability of 0.243 to win one bid and it will produce 50,000 of income, there is a probability of 0.027 to win 2 bids and it will produce 100,000 of income and there is a probability of 0.001 to win 3 bids and it will produce 150,000 of income.

5 0

2 years ago

A country's population in 1993 was 94 million. in 1999 in was 99 million. estimate the population in 2005 using the exponential

Jet001 [13]

The initial population is
P₀ = 94 million in 1993

The growth formula is
$P(t) = P_{0}e^{kt}$
where P(t) is the population (in millions) after t years, measured from 1993.
k = constant.

Because P(5) = 99 million (in 1999),
$94e^{5k} = 99 \\e^{5k}=1.0532 \\ 5k = ln(1.0532) \\ k = 0.010367$

In the year 2005, t = 12 years, and
$P(12)=94e^{0.010367*12} = 106.45$

Answer: 106 million (nearest million)

7 0

1 year ago

a lunch stand makes a $.75 profit on each chef's salad and $1.20 profit on each caesar salad. On a typical weekday, it sells bet

tangare [24]

Answer:

<em>50 Chef's salads and 50 Caesar salads should be prepared in order to maximize profit.</em>

Step-by-step explanation:

Suppose, the number of Chef's salad is $x$ and the number of Caesar salad is $y$

On a typical weekday, it sells between 40 and 60 Chefs salads and between 35 and 50 Caesar salads.

So, the two constraints are: $40\leq x\leq 60$ and $35\leq y\leq 50$

The total number sold has never exceed 100 salads. So, another constraint will be: $x+y\leq 100$

According to the graph of the constraints, the vertices of the common shaded region are: $(40,35), (60,35), (60,40), (50,50)$ and $(40,50)$ <em>(Refer to the attached image for the graph)</em>

The lunch stand makes a $.75 profit on each Chef's salad and $1.20 profit on each Caesar salad. So, the profit function will be: $P=0.75x+1.20y$

For (40, 35) , $P=0.75(40)+1.20(35)=72$

For (60, 35) , $P=0.75(60)+1.20(35)=87$

For (60, 40) , $P=0.75(60)+1.20(40)=93$

For (50, 50) , $P=0.75(50)+1.20(50)=97.5$ <u><em>(Maximum)</em></u>

For (40, 50) , $P=0.75(40)+1.20(50)=90$

Profit will be maximum when $x=50$ and $y=50$

Thus, 50 Chef's salads and 50 Caesar salads should be prepared in order to maximize profit.

6 0

2 years ago

Each month for 5 months, sophie makes 2 quilts. how many more quilts does she need to make before she has made 16 quilts?

Zigmanuir [339]

6 quilts are needed

5 0

2 years ago

Read 2 more answers

Given: circle O with tangent AB mBC= 2x -16; mCD = x+40; mDE = x; mEB = 60 <br><br>find the x

murzikaleks [220]

Answer:

69

Step-by-step explanation:

All the given arcs cover the entire circle circumference, so their measures add up to a full 360.

(2x - 16) + (x + 40) + x + 60 = 360

4x + 84 = 360

4x = 276

x = 69

6 0

1 year ago