Flaws in a carpet tend to occur randomly and independently at a rate of one every 270 square feet. What is the probability that a carpet that is 8 feet by 14 feet contains no flaws

Answer:

A. 5 < AC < 10

Step-by-step explanation:

We are given the ∆ABC

To solve for the sides of ∆ABC , we make use of Pythagoras Theorem

Pythagoras Theorem states that:

AB² = AC² + BC²

Where AB = Longest side, hence its length is always more that AC and BC.

In the above Question, we are given the values of AB and BC

AB = 10

BC = 5

Inputting these values into the Pythagoras Theorem,

10² = AC² + 5²

100 = AC² + 25

AC² = 100 - 25

AC² = 75

AC = √75

AC = 8.6602540378

According to the above calculation, we can see that the expression that is always true = Option A "5 < AC < 10"

Answer:

Diverges

Step-by-step explanation:

since the value of  P = 5/6 < 1  the p-series diverges

summation of 1/n^5/6  at n = 1 and infinity

attached below is the detailed solution using Theorem 9.11 to determine the convergence or divergence of the p-series

The value of the p in the p-series is less than one. Then the p-series is a divergence.

It is an infinite type of series.

The p-series is given below.

[tex]1 + \dfrac{1}{\sqrt[6]{32} } +\dfrac{1}{\sqrt[6]{243} }+\dfrac{1}{\sqrt[6]{1024} }+\dfrac{1}{\sqrt[6]{3125} }[/tex]

The series can be written as

[tex]\dfrac{1}{1^{5/6}}+\dfrac{1}{2^{5/6}}+\dfrac{1}{3^{5/6}}+\dfrac{1}{4^{5/6}}+\dfrac{1}{5^{5/6}}[/tex]

Then the sum will be

[tex]\rm \Rightarrow \Sigma _{n=0} ^{\infty} \dfrac{1}{n^{5/6}} \\\\\\\Rightarrow P = \dfrac{5}{6} < 1[/tex]

Since the value of the p is <1. Then the series is divergence.

More about the p-series link is given below.

https://brainly.com/question/24249275

Step-by-step explanation:

Given

[tex]\int\limits {(x+8x)} \, dx[/tex]  

to integrate we use

[tex]\frac{dy}{dx} =\int\limits {ax^n} \, dx \\[/tex]

we have

[tex]y= \frac{ax^n^+^1}{n+1}[/tex]

[tex]y= \frac{x^1^+^1}{1+1}+ \frac{8x^1^+^1}{1+1}+c\\\\y= \frac{x^2}{2}+ \frac{8x^2}{2}+c\\\\y= \frac{x^2}{2}+ 4x^2+c\\\\y= \frac{x^2+8x^2}{2}+c\\\\y= \frac{9x^2}{2}+c[/tex]

in order to verify using differentiation we use

[tex]y= ax^n\\\\ \frac{dy}{dx} = nax^n^-1[/tex]

[tex]y= \frac{9x^2}{2}+c\\\\ \frac{dy}{dx} =2* \frac{9x^2^-^1}{2}\\\\ \frac{dy}{dx} =2* \frac{9x}{2}\\\\ \frac{dy}{dx} =9x\\\\9x= x+8x\\\\ \frac{dy}{dx}= x+8x[/tex]

Answer:

2A /h = b

Step-by-step explanation:

A=1/2bh

Multiply each side by 2

2A = 2*1/2bh

2A = bh

Divide each side by h

2A/h = bh/h

2A /h = b

Step-by-step explanation: First, get rid of the fraction by

multiplying both sides of the equation by 2.

That gives us 2A = bh.

Don't be thrown off by the capital A in this problem.

Just treat it like any other variable.

To get b by itself on the right side of the equation, we now simply

divide both side of the equation by h and our answer is 2A/h = b.

Take a look back at the formula now in the original problem.

Does it look familiar?

It's the formula for the area of a triangle.

Take a look at the image I have provided below.

I have made the "b" purple so you

can see that we are solving for it.

Answer:

plz mark as BRAINLIEST....

Step-by-step explanation:

60÷3[150÷2{6+3(17-14)}]

= 60÷3[150÷2{9-3}]

=60÷3[75-6]

=20-69

=49

Answer:

width=60     length=540

Step-by-step explanation:

(w+9w)*2=1200

He starts to ride at 3:27 p.m.

85 minutes -> hours = 1 h 25 minutes (85/60 = 1 with 25 of rest)

3:27 + 1 h 25 min = h. 4:52

between 4:52 and 5:45 =>

5 hours 45 min - 4 hours 52 minutes =

4h 105 min ( 1h = 60min ) - 4h 52 min =

0h 53min

Payton has 53 minutes

Answer:

53 minutes

Step-by-step explanation:

Payton leaves at 3:27 p.m. and rides for 85 minutes.  When she has finished, the time will be 3:27 + 0:85, or

                           3:27 + 1:25, since 1 hr = 60 min

                             4:52 p.m.

Dinner will be at 5:45 p.m.  That means Payton will have (5:45 - 4:52) hours until dinner:  Borrowing 60 minutes from 5:45, we get

4:105 - 4:52 = 0:53.  That's 53 minutes to while away before dinner.

Answer:

D

Step-by-step explanation:

Let a be the number of TV sets that weight 30 kg and let b be the number of TV sets that weigh 50 kg.

So, all together, they have a total weight of 880. In other words:

[tex]30a+50b=880[/tex]

And, there are 20 TV sets all together. Thus:

[tex]a+b=20[/tex]

This is a system of equations. Solve by substitution. Subtract b from both sides in the second equation:

[tex]a+b=20\\a=20-b[/tex]

Substitute this into the first:

[tex]30a+50b=880\\30(20-b)+50b=880[/tex]

Distribute:

[tex]600-30b+50b=880[/tex]

Subtract 600 from both sides:

[tex]-30b+50b=280[/tex]

Combine like terms:

[tex]20b=280[/tex]

Divide both sides by 20:

[tex]b=14[/tex]

So, there are 14 TV sets that weight 50 kg.

Plug this in for the second equation to solve for a:

[tex]a+b=20[/tex]

Plug in 14 for b:

[tex]a+14=20[/tex]

Subtract 14 from both sides:

[tex]a=6[/tex]

Therefore, there are 6 TV sets that weigh 30 kg and 14 TV sets that weigh 50 kg.

Our answer is D :)

Step-by-step explanation:

Total number of T..V sets we have 20

Let x be the number of T.V sets that weigh 30 kg and y be the no. of sets that weigh 50 kg

When we add all we get a total of 880

[tex]\blue\star[/tex] 30a + 50b = 880

It is given to us that

[tex]\blue\star[/tex]a + b = 20. eq 1

[tex]\blue\star[/tex]a = 20-b

Put the value of a in ist equation we get,

[tex]\blue\star[/tex]30(20-b) + 50b =880

[tex]\blue\star[/tex]600 - 30b+50b = 880

[tex]\blue\star[/tex]600 + 20b = 880

[tex]\blue\star[/tex]20b = 280

[tex]\blue\star[/tex] b = 14

so there are 14 T.V sets that weigh 50 kg

put it in eq 1 we get

[tex]\blue\star[/tex] a + b =20

[tex]\blue\star[/tex]a + 14 = 20

[tex]\blue\star[/tex]a = 6

Hope it helps.

Answer:

0.072 or .072

Step-by-step explanation:

0.72 is ten times as much as 0.072.

0.072 times 10 is .72.

0.72 / 10 = 0.072 .

Answer:

0.072 or .072

Both is right

Answer: m∠ TUW =  38°

m∠WUV =  12°

m∠TUV =  103°

Step-by-step explanation:

Given: m∠ TUW = (5x + 3)°, m∠WUV=(10x-5)°, and m∠TUV=(17x-16)°

Since, m∠TUV = m∠ TUW  +  m∠WUV

So, 17X-16 = (5x + 3) + (10x-5)

⇒ 17X-16 = 5x + 3 + 10x-5   [open parenthesis]

⇒  17X-16 =5x +  10x +3 -5   [combine like trems]

⇒  17X-16 =15x -2

⇒   17X -15x = -2+16     [subtract 15x and add 16 on both sides]

⇒   2x = 14        

⇒  x= 7               [divide both sides by 2]

Now, m∠ TUW = (5(7) + 3)°=  38°

m∠WUV=(10(7)-5)° =  12°

m∠TUV=(17(7)-16)° =  103°

Hence,  m∠ TUW =  38°

m∠WUV =  12°

m∠TUV =  103°

Answer:

(x² + 4)(x - 3)

or

A

Step-by-step explanation:

Step 1: Write out expression

x³ - 3x² + 4x - 12

Step 2: Factor by grouping

x³ - 3x²

x²(x - 3)

4x - 12

4(x - 3)

Step 3: Combine

(x² + 4)(x - 3)

Answer:no its 24

Step-by-step explanation:

bc x is like 15

Answer:

k

Step-by-step explanation:

Answer:

TRUE ( A )

Step-by-step explanation:

linear regression represents/ models  the linear relationship between a dependent/scalar variable and an independent variable  or one or more independent variables

Linear regression pertains to regression models with normal equations because Linear regressions can be calculated using a linear equation/algebra

example : Y= a + bX

Answer:

6 and 7

Step-by-step explanation:

Step 1: Find 2 perfect square roots

√36 = 6

√49 = 7

√36 < √48 < √49

6 < √48 < 7

So, between 6 and 7

Answer:parameter

Step-by-step explanation:

Answer:

7*(-9)

Step-by-step explanation:

A negative multiplied by a negative causes them to cancel out and become positive and two positives being multiplied are always positive

HOPE THIS HELPS!!!!! :)

<3333333333

Answer:

7 x (-9)

Step-by-step explanation:

7 x (-9) = -63

-3 x (-5) = 15

-2 x (-1) = 2

6 x 6 = 36

Can you multiply it all out? Yes. Did you need to? No. That was just to prove that the first choice is correct.

All you have to know to answer this is that:

positive * positive = positive; + * + = +

negative * negative = negative; - * - = +

positive * negative (or negative * positive; remember that the order of the numbers you're multiplying does not matter) = negative; + * - = - or - * + = -

Or if you learn better in words:

If two factors have the same sign, the answer is positive.

If two factors have different signs, like if one is positive and the other is negative, then the answer is negative.

Please mark as Brainliest! :)

Answer:

A reflection over  x - axis

Step-by-step explanation:

If f(-x) = f (x), (ie all the signs are the same), then the function is even

also,  if f(-x) = -f (x), (ie all the signs are switched), then the function is odd.

Given;

h(x) = 12x + 49

Then test for h(-x);

h(-x) = 12(-x) + 49

h(-x) = -12x + 49,  

Thus h(-x)  ≠ h(x)  and also h(-x) ≠ -h(x)

The function is neither odd nor even.

Therefore, a reflection over  x - axis would result in a function that is neither even nor odd.

Answer:

y=2, the equation of  a line which is perpendicular to the line 3x+5=0

A(-5/3,2)  the  foot of the perpendicular from B to the line

Step-by-step explanation:

d1 : 3x+5=0, so 3x=-5, x=-5/3

y=2, the equation of  a line which is perpendicular to the line 3x+5=0

A(-5/3,2)  the  foot of the perpendicular from B to the line

Answer:

m = 48

Step-by-step explanation:

Isolate the variable, m. Note the equal sign, what you do to one side, you do to the other. Multiply 8 to both sides:

6 = m/8

(6) * 8 = (m/8) * 8

6 * 8 = m

m = 6 * 8

m = 48

48 is your answer for m.

~

Answer:

(2, 1)

Step-by-step explanation:

To solve by substitution, we solve one equation for one of its variables and then substitute the solved value for that variable into the other equation. Because this system of equations already has one solved for the variable, this makes our job much easier. We only need to implement the solved value for y into the other equation and solve for x.

y = 6x - 11

-2x - 3(6x - 11) = -7 Distribute.

-2x - 18x + 33 = -7 Combine like terms.

-20x + 33 = -7 Subtract 33 from both sides of the equation.

-20x = -40 Divide by -20 on both sides of the equation.

x = 2

Then, with this value, we will place it into the equation that was already solved for y in order to get a definite value for y.

y = 6(2) - 11

y = 12 - 11

y = 1

Using this information, the coordinate pair for this equation (the point of intersection between the two lines) is (2, 1).

Answer:

X= 60°

Y= 30°

Step-by-step explanation:

In triangle ABD, we have:

AB = BD = AD

Then triangle ABD is equilateral triangle.

Then, all its angles are equal to 60°.

=> X = 60°

____________________________________

ADC is right triangle at D.

So, X and Y are congruent angles (their sum is equal to 90°)

So, X + Y =90°

60° + Y = 90°

Y = 90 - 60

Y= 30°

[tex]hope \: this \: helps[/tex]

Answer:

(1) The point estimate for the population mean is 4.925.

(2) Therefore, a 95% confidence interval for the population mean pH of rainwater is [4.715, 5.135] .

(3) Therefore, a 99% confidence interval for the population mean pH of rainwater is [4.629, 5.221] .

(4) As the level of confidence increases, the width of the interval increases.

Step-by-step explanation:

We are given that the following data represent the pH of rain for a random sample of 12 rain dates.

X = 5.20, 5.02, 4.87, 5.72, 4.57, 4.76, 4.99, 4.74, 4.56, 4.80, 5.19, 4.68.

(1) The point estimate for the population mean is given by;

Point estimate, [tex]\bar X[/tex] = [tex]\frac{\sum X}{n}[/tex]

                            = [tex]\frac{5.20+5.02+ 4.87+5.72+ 4.57+ 4.76+4.99+ 4.74+ 4.56+ 4.80+5.19+ 4.68}{12}[/tex]

                            = [tex]\frac{59.1}{12}[/tex]  = 4.925

(2) Let [tex]\mu[/tex] = mean pH of rainwater

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

                             P.Q.  =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~  [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean = 4.925

             s = sample standard deviation = 0.33

            n = sample of rain dates = 12

            [tex]\mu[/tex] = population mean pH of rainwater

Here for constructing a 95% confidence interval we have used a One-sample t-test statistics as we don't know about population standard deviation.

So, 95% confidence interval for the population mean, [tex]\mu[/tex] is ;

P(-2.201 < [tex]t_1_1[/tex] < 2.201) = 0.95  {As the critical value of t at 11 degrees of

                                               freedom are -2.201 & 2.201 with P = 2.5%}  

P(-2.201 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 2.201) = 0.95  

P( [tex]-2.201 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]2.201 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95

P( [tex]\bar X-2.201 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+2.201 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95

95% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-2.201 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+2.201 \times {\frac{s}{\sqrt{n} } }[/tex] ]

                                      = [ [tex]4.925-2.201 \times {\frac{0.33}{\sqrt{12} } }[/tex] , [tex]4.925+2.201 \times {\frac{0.33}{\sqrt{12} } }[/tex] ]  

                                     = [4.715, 5.135]

Therefore, a 95% confidence interval for the population mean pH of rainwater is [4.715, 5.135] .

The interpretation of the above confidence interval is that we are 95% confident that the population mean pH of rainwater is between 4.715 & 5.135.

(3) Now, 99% confidence interval for the population mean, [tex]\mu[/tex] is ;

P(-3.106 < [tex]t_1_1[/tex] < 3.106) = 0.99  {As the critical value of t at 11 degrees of

                                               freedom are -3.106 & 3.106 with P = 0.5%}  

P(-3.106 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 3.106) = 0.99

P( [tex]-3.106 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]3.106 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.99

P( [tex]\bar X-3.106 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+3.106 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.99

99% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-3.106 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+3.106 \times {\frac{s}{\sqrt{n} } }[/tex] ]

                                     = [ [tex]4.925-3.106 \times {\frac{0.33}{\sqrt{12} } }[/tex] , [tex]4.925+3.106 \times {\frac{0.33}{\sqrt{12} } }[/tex] ]  

                                     = [4.629, 5.221]

Therefore, a 99% confidence interval for the population mean pH of rainwater is [4.629, 5.221] .

The interpretation of the above confidence interval is that we are 99% confident that the population mean pH of rainwater is between 4.629 & 5.221.

(4) As the level of confidence increases, the width of the interval increases as we can see above that the 99% confidence interval is wider as compared to the 95% confidence interval.

Answer:

7,257

Step-by-step explanation:

use the formula of: M = amount/discount factor

Answer:

1/10

Step-by-step explanation:

divide the numerator by the denominator. For example, 1/2 is equal to 1 divided by 2, which is equal to 0.5.

Answer:

1/10

Hoped I helped

Answer:

c=30n+20 represents the cost to rent a truck for n hours.

Step-by-step explanation:

$30 dollars an hour multiplied by n.

30n

+20 for the insurance for the truck.

Answer:

5000 pounds

Step-by-step explanation:

1 ton = 2000 pounds so 2.5 = 2000 + 2000 + 1000 = 5000

Answer:

5,000 pounds

Step-by-step explanation:

just subtract 2.5 by 1,000 5 times

Answer:

See below.

Step-by-step explanation:

So we have the expression:

[tex]4u^4+4u^3-6u^2[/tex]

First, factor out the GCF.

The GCF is 2u². Thus:

[tex]=2u^2(2u^2+2u-3)[/tex]

And this is the simplest it can get.

So we are done :)

Answer:

58

Step-by-step explanation:

We can use the Pythagorean theorem to find the area of the square for the third side.

The equation for the Pythagorean theorem is

a^2 + b^2 = c^2

where a and b are the lengths of the two legs of the triangle, and c is the length of the hypotenuse.

a^2 + b^2 = c^2

3^2+7^2=x^2

9+49=x^2

58=x^2
The area of the square for the third side of the triangle is 58 units^2 squared.