The lengths of a professor's classes has a continuous uniform distribution between 50.0 min and 52.0 min. If one such class is randomly selected, find the probability that the class length is between 51.5 and 51.7 min. P(51.5 < X < 51.7)

Answer:

He can be 99% confident that the mean number of calls per day is between 266.5 and 292.3.

Step-by-step explanation:

Confidence interval:

A confidence interval is symmetric, which means that the difference between the sample mean and the lower bound is the same as the difference between the upper bound and the sample mean.

In this question:

Sample mean: 279.4 calls

Lower bound: 266.5 calls

Upper bound: x calls

Due to the symmetry of the confidence interval:

[tex]x - 279.4 = 279.4 - 266.5[/tex]

[tex]x = 12.9 + 279.4[/tex]

[tex]x = 292.3[/tex]

So

He can be 99% confident that the mean number of calls per day is between 266.5 and 292.3.

Answer:

5 Probability

5.1 Probabilities

Probabilities are used to describe how likely or unlikely it is that something will happen.

Weather forecasters often talk about how likely it is to rain, or perhaps snow, in particular

parts of the country.

Worked Example 1

(a) When you roll a dice, which number are you most likely to get?

(b) If you rolled a dice 600 times how my sixes would you expect to get?

(c) Would you expect to get the same number of ones?

Solution

(a) You are equally likely to get any of the six numbers.

(b) You would expect to get a six in about 1

6

of the throws, so 100 sixes.

(c) Yes, in fact you would expect to get about 100 of each number.

Worked Example 2

Use one of the following to describe each one of the statements (a) to (d).

Certain

Very likely

Likely

Unlikely

Very unlikely

Impossible

(a) It will snow tomorrow.

(b) It will rain tomorrow.

(c) You win a car in a competition tomorrow.

(d) You are late for school tomorrow.

Solution

(a) Very unlikely for most places in Britain, especially in summer.

(b) Likely or Very likely in Britain in winter.

(c) Very unlikely if you have entered the competition. Impossible if you have not

entered the competition.

(d) Very unlikely, unless the school bus breaks down.

Answer:

798

Step-by-step explanation:

first you do 40x20=800 then 800-6=794 then 794+4=798

Answer:

sin b

Step-by-step explanation:

Answer:

cos A

Step-by-step explanation:

sine = [tex]\frac{opposite}{hypotenuse}[/tex]

sine B = [tex]\frac{3}{5}[/tex]

cos = [tex]\frac{adjacent}{hypotenuse}[/tex]

cos A = [tex]\frac{3}{5}[/tex]

Answer:

Perimeter = 12.246 units

Area = 11.314 units²

Step-by-step explanation:

A=2√2r²=11.314

P=2(8)(√2-√2)=12.246

Answer:

Angle 3 is = to angle 2 because:

Angle 3 & angle 7 are corresponding angles, meaning they have the same measure.

Angle 7 & angle 2 are vertical angles, meaning they also have the same measure.

Therefore, if angle 7 is equal to angle 3, then angle 2 must also be equal to angle 3.

Hope this helps! Have a great day!

Answer:

The slope is POSITIVE.  

The line has a slope of positive 4/3

Step-by-step explanation:

It rises 4 then runs 3.

Answer: Just look it up on goo gle

Step-by-step explanation:

The rate per annum compound interest is approximately 11.5%.

To find the rate per annum compound interest, we can use the formula for compound interest:

[tex]A = P(1 + r/n)^{nt}[/tex]

Where:

A = the final amount (N5353 in this case)

P = the principal amount (N4000 in this case)

r = the annual interest rate (what we want to find)

n = the number of times interest is compounded per year (assuming once per year)

t = the number of years (5 years in this case)

Now, we can plug in the values:

[tex]N5353 = N4000(1 + r/1)^{1*5}[/tex]

Divide both sides by N4000:

[tex]1.33825 = (1 + r)^5[/tex]

Now, isolate (1 + r) by taking the fifth root of both sides:

[tex]1 + r = (1.33825)^{1/3}\\1 + r \approx 1.115[/tex]

Now, subtract 1 from both sides to find the interest rate (r):

r ≈ 1.115 - 1

r ≈ 0.115

Finally, convert the interest rate to a percentage:

r ≈ 0.115 * 100

r ≈ 11.5%

To know more about rate:

https://brainly.com/question/32398403

#SPJ2

Answer:

[tex]3x^5+6x^4+12x^3[/tex]

Step-by-step explanation:

Given that,

[tex]f(x) = 3x^3+ 6x^2+ 12x[/tex]

and

[tex]g(x)=x^2[/tex]

We need to find the product of f(x) and g(x). SO,

[tex]f(x)\times g(x)=(3x^3+ 6x^2+ 12x)\times (x^2)\\\\=3x^3\times x^2+6x^2\times x^2+12x\times x^2\\\\=3x^5+6x^4+12x^3[/tex]

Hence, the correct option is (d).

Answer:

x-6=6

Step-by-step explanation:

6+6=12

Answer:

c

Step-by-step explanation:

because 6+6=12 and the missing number would be 12 because 12-6=6

Answer:

it needs time wait for 10 min.

Answer:

4

Step-by-step explanation:

1) Simplify 2⁴ to 16.

[tex]20 - 16[/tex]

2) Simplify.

[tex]4[/tex]

Therefor, the answer is 4.

Answer:

20 - 2^4 =4

Step-by-step explanation:

Answer:

trust your instincts

Step-by-step explanation:

I can not interfere with your destiny you will need to decide your destiny

Answer:

-3

Step-by-step explanation:

-11(-3)+7=40

33+7=40

Answer:

C. 280 ft cubed

Step-by-step explanation:

1/2x7x5x16=280

Answer:

B

Step-by-step explanation:

Answer:

Its E

Step-by-step explanation:

Answer:

The developer bought 4.9 acres of land, increasing its property to 29.4 acres.

Step-by-step explanation:

Given that a developer has 24.5 acres of land, and she buys an adjacent plot of land and increases the total acreage she owns by 20%, to determine the amount of acres she bought and the total acres she now owns, the following calculations must be done:

24.5 x 1.2 = 29.4

24.5 x 0.2 = 4.9

Thus, the developer bought 4.9 acres of land, increasing its property to 29.4 acres.

Answer:

No DB is not a perpendicular bisector of AC

Step-by-step explanation:

This is because as AC is a straight line it's angle degree is 180 which when bisected by DB becomes,

180 ÷ 2 = 90

On both the angles i.e <BDC = <NDA = 90°

To make it a perpendicular bisector but

<BDC is not equal to <NDA is not equal to 90°.

Hence, DB is not a perpendicular bisector of line AC.

Answer:

10/1

Step-by-step explanation:

Answer: 5850 milliliters

Step-by-step explanation:

First, you have to do 0.65L x 9 days = 5.85L

And then you have to convert it to milliliters so:

5.85L= 5850 milliliters

Answer:

What do you want us to find?

Step-by-step explanation:

Answer:I don’t understand

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

and the answer is c

Answer:

6

Step-by-step explanation:

2 ft = 24in so 4 to 24 is times 6

3ft=36 in and 6 to 46 is times 6

Answer:

6/1

Step-by-step explanation:

2ft=24 inches

3ft=36 inches

poster/original photo

24in/4in=6/1

36in/6in=6/1

6/1

If the 0's are indeed zeroes, then it would appear that you're using degrees, so that the equation

r(θ) = 2 sin(0°) + 3 sin(90°)

describes a circle r = 3 (since sin(0°) = 0 and sin(90°) = 1). In this case, the area would simply be π r ² = 9π.

But I suspect you meant to use θ, so the curve has the far more interesting equation,

r(θ) = 2 sin(θ) + 3 sin(9θ)

Since sin(9θ) has a period of 2π/9 and sin(θ) has a period of 2π, their sum has a period of 2π. (That is, 2π times the LCM of 1 and 1/9, which is 1.) But we observe r(θ) is odd, since

r(-θ) = 2 sin(-θ) + 3 sin(-9θ)

… = -2 sin(θ) - 3 sin(9θ)

… = - r(θ)

which tells us that the curve closes itself over a half-period. So the area bounded by the curve is given by the integral,

[tex]\displaystyle\int_0^\pi\int_0^{r(\theta)}r\,\mathrm dr\,\mathrm d\theta[/tex]

If you're not familiar with double integrals yet, all you need to know is that this reduces to the area formula you may/should be familiar with,

[tex]\displaystyle\frac12\int_0^\pi r(\theta)^2\,\mathrm d\theta[/tex]

Compute the integral:

[tex]=\displaystyle\frac12\int_0^\pi(2\sin(\theta)+3\sin(9\theta))^2\,\mathrm d\theta[/tex]

[tex]=\displaystyle\frac12\int_0^\pi(4\sin^2(\theta)+12\sin(\theta)\sin(9\theta)+9\sin^2(9\theta))\,\mathrm d\theta[/tex]

Apply some identities:

sin²(θ) = (1 - cos(2θ)) / 2

sin(θ) sin(9θ) = (cos(9θ - θ) - cos(9θ + θ)) / 2 = (cos(8θ) - cos(10θ)) / 2

sin²(9θ) = (1 - cos(18θ)) / 2

[tex]=\displaystyle\frac14\int_0^\pi(4(1-\cos(2\theta))+12(\cos(8\theta)-\cos(10\theta))+9(1-\cos(18\theta))\,\mathrm d\theta[/tex]

[tex]=\displaystyle\frac14\int_0^\pi(13 - 4\cos(2\theta) + 12\cos(8\theta) - 12\cos(10\theta) - 9\cos(18\theta))\,\mathrm d\theta[/tex]

[tex]=\dfrac14 \left(13\theta-2\sin(2\theta)+\dfrac32\sin(8\theta)-\dfrac65\sin(10\theta)-\dfrac12\sin(18\theta)\right)\bigg|_0^\pi[/tex]

[tex]=\dfrac1{40} \left(130\theta-20\sin(2\theta)+15\sin(8\theta)-12\sin(10\theta)-5\sin(18\theta)\right)\bigg|_0^\pi[/tex]

[tex]=\dfrac{130\pi-20\sin(2\pi)+15\sin(8\pi)-12\sin(10\pi)-5\sin(18\pi)}{40}[/tex]

= 13π/4

Answer: 8x - 6

Step-by-step explanation:

Perimeter is found by doing 2l + 2w

The length is 3x - 7 and width is x + 4

2(3x - 7) + 2(x + 4) =

6x - 14 + 2x + 8 =

8x - 6