The time for a professor to grade a student’s homework in statistics is normally distributed with a mean of 13.3 minutes and a standard deviation of 2.0 minutes. What is the probability that randomly selected homework will require less than 17 minutes to grade?

Answer:

Area swept by the blade = 448[tex]in^{2}[/tex]

Step-by-step explanation:

The arc the wiper wipes is for 135 degrees angle.

So, find area of sector with radius 24 inches. And the find area of arc with r=14 inches.

Then subtract the area of sector with 14 inches  from area of sector with radius as 24 inches.

So, area of sector with r=24 in =[tex]\frac{135}{360} *\pi *24^{2}[/tex]

Simplify it,

                                                  =216[tex]\pi[/tex]

Now, let's find area of sector with radius 14 inches

Area of sector with r=14 in = [tex]\frac{135}{360} *\pi *14^{2}[/tex]

Simplify it

                                          =73.5[tex]\pi[/tex]

So, area swept by the blade = 216[tex]\pi[/tex] -73.5[tex]\pi[/tex]

Simplify it and use pi as 3.14.....

Area of swept =678.584 - 230.907

                               =447.6769

Round to nearest whole number

So, area swept by the blade = 448[tex]in^{2}[/tex]

Answer:

.33x = 105.60

$371

Step-by-step explanation:

Answer:

63.44

Step-by-step explanation:

its 63.44697 but you round so its 63.44

Answer:

No unless x is being used to define only elements of an integer set.

Step-by-step explanation:

No, not in general unless x is defined as a integer or a subset of the integers like the naturals, whole numbers....

Usually 6<=x<=10 means all real numbers between 6 and 10, inclusive. This means example that 6.6 or 2pi are in this set with infinitely other numbers that I can't name.

{6,7,8,9,10} just means the set containing the numbers 6,7,8,9,10 and that's only those 5 numbers.

Answer:

0.52 = 52% probability that an email is detected as spam.

Step-by-step explanation:

Probability that an email is detected as spam:

99% of 50%(are spam).

5% of 100 - 50 = 50%(false positives, that is, e-mails that are not spam but are detected as spams).

What is the probability that an email is detected as spam?

[tex]p = 0.99*0.5 + 0.05*0.5 = 0.52[/tex]

0.52 = 52% probability that an email is detected as spam.

Answer:

8 suits

Step-by-step explanation:

Divide 30 m by 3 [tex]\frac{3}{4}[/tex] m , or 30 ÷ 3.75 , then

30 ÷ 3.75 = 8

Then 8 suits can be made from 30 m of cloth

Answer:

the answers are on the picture but the numbers may be rounded

Answer:

Step-by-step explanation:

Since you have this categorized under college math, I'm going to go out on a limb here and assume you're in calculus. We will solve using the position function and its first derivative (velocity) to solve. Remember that at an object's max height, the velocity is 0.

If the position function is

[tex]s(t)=-16t^2+24t+7[/tex] the first derivative, velocity, is

v(t) = -32t + 24. Set this equal to 0 to find the time when the object is at its max height:

0 = -32t + 24 and

-24 = -32t so

t = .75 seconds. Now we can plug that time into the position function to find where it is at that time. This "where" will be the max height:

s(.75) = [tex]-16(.75)^2+24(.75)+7[/tex] so

s(.75) = 16 feet

Answer:

 B and D are polynomial

Step-by-step explanation:

An algebraic expression with non-zero coefficients and variables having non-negative integers as exponents is called a polynomial.

A)

If it is [tex]1 -\frac{5x^{2}}{x }=1-5x[/tex]   , then it is a polynomial.

But if it is [tex]\frac{1-5x^{2}}{x}[/tex] then it is not a polynomial

Answer:

if x=0 then they have same value

1 and 2 options are out

for x=-1

g(-1)=1

h(-1)=-1

3 is true

4th

FALSE

for all values except 0, g(x)>h(x)

correct ones are

g(x) > h(x) for x = -1.

For positive values of x, g(x) > h(x).

For negative values of x, g(x) > h(x).

Step-by-step explanation:

Answer:

[tex]90[/tex] [tex]ft^3[/tex]

Step-by-step explanation:

----------------------------------------

The formula to find the volume of a rectangular prism is   [tex]V=lwh[/tex]

Let's substitute the number for the length, width, and height now.

[tex]V=(6)(5)(3)[/tex]

[tex]V=(30)(3)[/tex]

[tex]V=90[/tex]

--------------------

Hope this is helpful.

Answer:

this is the answer I got! i don't know if it helps, but I hope it does

Answer:

hey what's

Step-by-step explanation:

a question wow okay the answer is

Answer:

Step-by-step explanation:

50 X 240 = 2700. So you will need 240 packs of 50. They cost 17.95 each, so the multiply. 240 X 17.95 is 4,308. So, 4,308 is your answer.

Answer:

73.3333....

Step-by-step explanation:

please mark me brainliest

Answer:

a: t=13.6 cm

b: h=12.9 mm

Step-by-step explanation:

Hi there!

Let's start with a

in a, we are given a right triangle (notice the right angle), the length of the hypotenuse (the side OPPOSITE from the right angle) as 18 cm, one acute angle given as 41° and the length of one of the legs (the legs are the sides that make up the right angle) as t

We're asked to use the primary trigonometric ratios

Those ratios are:

Sine, which is opposite/hypotenuse

Cosine, which is adjacent/hypotenuse

Tangent, which is opposite/adjacent

We will be basing the ratio off of the 41° angle, so let's find out which sides will be which in reference to that angle

The opposite side will be the other leg, the unmarked side

The adjacent side will be t

The hypotenuse will be the side marked as 18 cm

So let's use cos(41) in this case

cos(41)=t/18

Plug cos(41) into your calculator, and remember to have the calculator in degree mode

cos(41)≈0.8 (rounded to the nearest tenth)

0.8=t/18

multiply both sides by 18

13.6 cm=t

It's already rounded to the nearest tenth :)

b.

We are given a right triangle, and the lengths of the legs as h and 9 mm, as well as one acute angle as 35°

We'll be basing our ratio off of the 35 degree angle, so let's find which sides will be which in reference to that angle

The opposite side will be the leg marked as 9 mm

The adjacent side will be the leg marked as h

The hypotenuse will be the unmarked side

Since we are given the lengths of the opposite and the adjacent, let's use tan(35)

tan(35)=9/h

Plug tan(35) into your calculator, and remember to have it in degree mode

tan(35)≈0.7

0.7=9/h

multiply both sides by h

0.7h=9

divide both sides by 0.7

h=12.9 mm (rounded to the nearest tenth)

Hope this helps!

Answer:

The answer is below

Step-by-step explanation:

The bar chart to the question is attached below.

The distance traveled by Paolo = 210 m, The distance traveled by Lucas = 150 m, The distance traveled by Jashua = 175 m, The distance traveled by Topher = 190 m

1) The farther distance walk by Paolo = The distance traveled by Paolo - The distance traveled by Topher = 210 m - 190 m = 20 m

2) The farther distance walk by Jasha = The distance traveled by Jashua - The distance traveled by Lucas = 175 m - 150 m = 25 m

3) The farther distance walk by Topher = The distance traveled by Topher - The distance traveled by Lucas = 190 m - 150 m = 40 m

4) Combined distance of Paolo's and Lucas = 210 m + 150 m = 360 m

Combined distance of Jashua and Topher = 175 m + 190 m = 365 m

Therefore the Combined distance of Jashua and Topher is more

5) Average distance = (210 + 150 + 175 + 190)/4 = 181.25 m

Answer:

[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 \sin^2y}{x^2+2y^2} = 0[/tex]

Step-by-step explanation:

Given

[tex]f(x,y) = \frac{x^2 \sin^2y}{x^2+2y^2}[/tex]

Required

[tex]\lim_{(x,y) \to (0,0)} f(x,y)[/tex]

[tex]\lim_{(x,y) \to (0,0)} f(x,y)[/tex] becomes

[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 \sin^2y}{x^2+2y^2}[/tex]

Multiply by 1

[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 \sin^2y}{x^2+2y^2}\cdot 1[/tex]

Express 1 as

[tex]\frac{y^2}{y^2} = 1[/tex]

So, the expression becomes:

[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 \sin^2y}{x^2+2y^2} \cdot \frac{y^2}{y^2}[/tex]

Rewrite as:

[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 y^2}{x^2+2y^2} \cdot \frac{\sin^2y}{y^2}[/tex]

In limits:

[tex]\lim_{(x,y) \to (0,0)} \frac{\sin^2y}{y^2} \to 1[/tex]

So, we have:

[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 y^2}{x^2+2y^2} *1[/tex]

[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 y^2}{x^2+2y^2}[/tex]

Convert to polar coordinates; such that:

[tex]x = r\cos\theta;\ \ y = r\sin\theta;[/tex]

So, we have:

[tex]\lim_{(x,y) \to (0,0)} \frac{(r\cos\theta)^2 (r\sin\theta;)^2}{(r\cos\theta)^2+2(r\sin\theta;)^2}[/tex]

Expand

[tex]\lim_{(x,y) \to (0,0)} \frac{r^4\cos^2\theta\sin^2\theta}{r^2\cos^2\theta+2r^2\sin^2\theta}[/tex]

Factor out [tex]r^2[/tex]

[tex]\lim_{(x,y) \to (0,0)} \frac{r^4\cos^2\theta\sin^2\theta}{r^2(\cos^2\theta+2\sin^2\theta)}[/tex]

Cancel out [tex]r^2[/tex]

[tex]\lim_{(x,y) \to (0,0)} \frac{r^2\cos^2\theta\sin^2\theta}{\cos^2\theta+2\sin^2\theta}[/tex]

[tex]\lim_{(x,y) \to (0,0)} \frac{r^2\cos^2\theta\sin^2\theta}{\cos^2\theta+2\sin^2\theta}[/tex]

Express [tex]2\sin^2 \theta[/tex] as [tex]\sin^2\theta+\sin^2\theta[/tex]

So:

[tex]\lim_{(x,y) \to (0,0)} \frac{r^2\cos^2\theta\sin^2\theta}{\cos^2\theta+\sin^2\theta+\sin^2\theta}[/tex]

In trigonometry:

[tex]\cos^2\theta + \sin^2\theta = 1[/tex]

So, we have:

[tex]\lim_{(x,y) \to (0,0)} \frac{r^2\cos^2\theta\sin^2\theta}{1+\sin^2\theta}[/tex]

Evaluate the limits by substituting 0 for r

[tex]\frac{0^2 \cdot \cos^2\theta\sin^2\theta}{1+\sin^2\theta}[/tex]

[tex]\frac{0 \cdot \cos^2\theta\sin^2\theta}{1+\sin^2\theta}[/tex]

[tex]\frac{0}{1+\sin^2\theta}[/tex]

Since the denominator is non-zero; Then, the expression becomes 0 i.e.

[tex]\frac{0}{1+\sin^2\theta} = 0[/tex]

So,

[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 \sin^2y}{x^2+2y^2} = 0[/tex]

Answer:

y = 2x

Step-by-step explanation:

Given that , the line passes through the point (0,0) and has a slope of 2. So here we can use the point slope form of the line as ,

[tex]\implies y- y_1 = m( x - x_1) \\\\\implies y - 0 = 2( x - 0 ) \\\\\implies y = 2(x) \\\\\implies \underline{\underline{y = 2x }}[/tex]

Answer:

[tex]option \: d \: 4.2 \times {10}^{ - 3} [/tex]

Step-by-step explanation:

Multiplication,

[tex] = 8.4 \times {10}^{ 8 } \times 5 \times {10}^{ - 11} \\ = 8.4 \times 5 \times {10}^{8 + ( - 11)} \\ = 4.2 \times {10}^{8 - 11} \\ = 4.2 \times {10}^{ - 3} [/tex]

Answer:

B."5, -3, -4, 1, -1, 6, -4"

Step-by-step explanation:

We are given that

13,5,4,9,7,14,4

We have to find the deviation.

Mean=[tex]\frac{sum\;of\;data}{total\;number\;of\;data}[/tex]

Using the formula

[tex]Mean,\mu=\frac{13+5+4+9+7+14+4}{7}[/tex]

[tex]Mean,\mu=\frac{56}{7}=8[/tex]

Deviation=[tex]x_i-\mu[/tex]

         [tex]x_i-\mu[/tex]

13          5

5           -3

4           - 4

9            1

7             -1

14            6

4            - 4

Hence, option  B is correct.

Answer:

ab=14.4

Step-by-step explanation:

This is going to be tricky to explain over text, so try to bear with me :) You have the information given above. Let's start with just ad = 11.6 for now. since these are variables, it can also be understood be understood as a times d= 11.6.  Knowing this, we can figure out that d = 11.6/a, when you divide both sides by a. You now have d, so plug (11.6/a) into cd=6.7. You have to do the same thing you did last time, except this time you are aiming to get c by itself. So, multiply both sides by a/11.6 and you get c = (6.7a)/ 11.6.  Guess what, you know c now! so you put (6.7a)/11.6 in for c in the equation given to you earlier, bc =8.3. The math gets a bit messy here, but you basically solve for b here, which, when you crunch the numbers down, ends up being ~14.3705 divided by a. You are looking for ab, so just multiply both sides by a, and round to the nearest tenth so that you have ab= 14.4  

Answer:

T = 2.215

df = 7

Critical value = 2.364

Fail to reject the null

Step-by-step explanation:

Swimmer __Spandex __Speedo Fastskin__ d

1 __________31.1 _______29.1 __ 2

2_________ 28.9 ______30.4 __ -1.5

3_________ 31.4 ______ 32.0 __ - 0.6

4_________ 34.9 ______31.7 __ 3.2

5 _________27.7 ______28.2 __ - 0.5

6_________ 36.7 _____ 32.9 ___ 3.8

7 _________ 33.3 _____28.6 ___ 4.7

8_________ 30.8 _____26.2 ___ 4.6

The mean difference = Σd / n

2, - 1.5, - 0.6, 3.2, - 0.5, 3.8, 4.7, 4.6

μd = Σd / n = 15.7 / 8 = 1.9625

Sd = standard deviation of difference = 2.5065 (using calculator)

H0 : μd = 0

H1 : μd ≠ 0

The test statistic:

T = μd / (Sd/√n)

T = 1.9625 / (2.5065/√8)

T = 2.2145574

The degree of freedom, df = n - 1 = 8 - 1 = 7

Using a Pvalue calculator :

α = 0.05

Critical value, Tcritical = 2.364 (T distribution table)

Since Test statistic < Critical value

we fail to reject H0 ;

Answer:

[tex]Sales = 86.749[/tex]

Step-by-step explanation:

Given

[tex]Sales = 0.845*(competitors) + 5.79*(population) + 13.889[/tex]

[tex]Competitors = 4[/tex]

[tex]Population = 12000[/tex]

See comment for complete question

Required

The sales

We have:

[tex]Sales = 0.845*(competitors) + 5.79*(population) + 13.889[/tex]

Substitute values for competitors and population

[tex]Sales = 0.845*4 + 5.79*12 + 13.889[/tex]

[tex]Sales = 3.38 + 69.48 + 13.889[/tex]

[tex]Sales = 86.749[/tex]

Answer:

three

P A R

A R A D

A D I S E 

P Q R

A B C D

A B C D E

There are three such pairs of letters. 

Answer:

There are 2 x intercepts

Answer:

Area: 360 cm

Perimeter: 44 cm

Step-by-step explanation:

To calculate the area, you must multiply the length x width.

If you need help calculating the perimeter too, just add all your lengths and widths together twice.