2x + y - z = 3
-x + 2y + 4z = -3
x – 2y - 3z = 4

Answer:

1/154440

Step-by-step explanation:

To calculate the probability it would be the quotient between 1 and the number of ways to choose 5 out of 13, but in this case the order matters, so it would be the permutation 13P5, therefore:

We know that:

nPr = n! / (n-r)!

we replace and we have:

13P5 = 13! / (13-5)! = 154440

The probability  that the rack ends up in alphabetical order is 1/154440

The probability that the rack ends up in alphabetical order is 1/154440

This is a question relating to permutation and combination. In order to calculate the probability, it would be the permutation 13P5, and this will be:

nPr = n! / (n-r)!

13P5 = 13! / (13-5)!

= 13! / 8!

= 13 × 12 × 11 × 10 × 9

= 154440

Therefore, the probability that the rack ends up in alphabetical order is 1/154440.

Read related link on:

https://brainly.com/question/6034318

Answer:

Option (D)

Step-by-step explanation:

Subtraction property of equality tells that whatever subtracted from one side of the equation must be subtracted from the other side.

If x + 2 = 2,

By the property of subtraction of equality,

x + 2 - 2 = 2 - 2

x = 0

But in the given question,

[tex]\frac{x}{2}-7=-7[/tex]

[tex]\frac{x}{2}-7+7=-7+7[/tex]

shows the addition property of equality in step (2)

Therefore, subtraction property of equality was not applied.

Option (D) will be the answer.

Answer:

so x=5 1/3 and

y= -2 2/3

Step-by-step explanation:

x-3y= -2x+3y=16. First we need to move all variables to one side of the equation and whole numbers to the other side of the equation. I see

x-3y+2x-3y=16. -3y-3y equals to -6y. 2x+x=3x. so 3x-6y=16. Lets take out the -6y so our equation would be 3x=16. x would equal 5 1/3. Now lets put back -6y into our equation. Let's now substitute x as 0. 3 times 0 equals 0 so our equation would now be -6y=16 which equals to -2 2/3.

so x=5 1/3 and

y= -2 2/3

Answer: ( x = -32, y = -16 )

Step-by-step explanation:

This can be represented by the three sides of an equilateral triangle.

x - 3y = -2x + 3y , simplify

x + 2x - 3y - 3y = 0

3x - 6y =0

x - 2y = 0 ---------------------- 1

x - 3y. = 16 ---------------------2

Solve using any methods

By elimination

y. = -16.

Substitute for y in any of the equations

x - 2y = 0

x. - 2(-16) = 0

x + 32 = 0

Therefore

x. = -32

Solution is ( -32, -16 )

Answer:

16

Step-by-step explanation:

Area of circle Formula: A = πr²

d = 2r

Simply plug in what you know:

201.0624 = 3.1416r²

64 = r²

r = 8

d = 2(8)

d = 16

Third option is the correct answer.

Answer:

[tex] y = \bigg[ \frac{2b}{(2a - c)} \bigg]x - \bigg[ \frac{2bc}{(2a - c)} \bigg][/tex]

Step-by-step explanation:

[tex]y - y_1 = m(x - x_1) \\ \\ y - 0 = \bigg[ \frac{2b}{(2a - c)} \bigg] (x - c) \\ \\ y = \bigg[ \frac{2b}{(2a - c)} \bigg]x - \bigg[ \frac{2b}{(2a - c)} \bigg]c \\ \\ \purple { \boxed{ \bold{y = \bigg[ \frac{2b}{(2a - c)} \bigg]x - \bigg[ \frac{2bc}{(2a - c)} \bigg]}}} \\ [/tex]

Answer:

Step-by-step explanation:

a) AB=2AM

A__________M__________B

If M is the midpoint of AB, then AM = MB

Since AM=MB MB=2AM

Therefore AB=2AM

b)AM=1/2MB

sincs M is midpoint of AB.

then AM=BM....(1)

and also AM+BM=AB

AM+AM=AB from (1)..AM=BM

2AM=AB

AM=1/2AB

Answer:

15 km/h

Step-by-step explanation:

Leo takes 15 minutes to cycle to school at an average speed of 12 km/h. What speed will he have if he only takes 12 minutes?

15 minutes * (1 hour)/(60 minutes) = 0.25 hour

speed = distance/time

distance = speed * time

distance = 12 km/h * 0.25 hour = 3 km

He cycles a distance of 3 km.

12 minutes * (1 hour)/(60 minutes) = 0.2 hour

speed = distance/time

speed = 3 km/(0.2 hour)

speed = 15 km/h

Answer:

1. 8/4+ 3= 5

2. 5/(10/2)= 1

3. 5+10/2=10

4. 8/2+5x5= 29

5. 5+3/15+2= 10.15

6. 30+6x11-11= 25.11

7. 12 + (19+2) / 3 =19

Step-by-step explanation:

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

Student name : Aparna Guha

Class : 8th

Division : B

School : St. John's Marhauli

Suggested subject : Maths

Work given on : 08 : 07 : 2020

Completed on : 08 : 07 : 2020

Posted on : 08 : 07 : 2020

Topic : Worksheet 1

Teacher's name : Manish Goel

School name : St. John's Marhauli

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

Answer:

The answer is below

Step-by-step explanation:

Given that:

mean value (μ) = 12 cm and standard deviation (σ) = 0.04 cm

a) Since a random sample (n) of 16 rings is taken, therefore the mean (μx) ans standard deviation (σx) of the sample mean Xbar is given by:

[tex]\mu_x=\mu=12\ cm\\\sigma_x=\frac{\sigma}{\sqrt{n} }=\frac{0.04}{\sqrt{16} }=0.01[/tex]

The sampling distribution of Xbar is centered about 12 cm and the standard deviation of the Xbar distribution is 0.01 cm

b) Since a random sample (n) of 64 rings is taken, therefore the mean (μx) ans standard deviation (σx) of the sample mean Xbar is given by:

[tex]\mu_x=\mu=12\ cm\\\sigma_x=\frac{\sigma}{\sqrt{n} }=\frac{0.04}{\sqrt{64} }=0.005\ cm[/tex]

The sampling distribution of Xbar is centered about 12 cm and the standard deviation of the Xbar distribution is 0.005 cm

c) n = 16 and the raw score (x) = 11.95 cm

The z score equation is given by:

[tex]z=\frac{x-\mu_x}{\sigma_x} =\frac{x-\mu}{\sigma/\sqrt{n} } \\z=\frac{11.95-12}{0.04/\sqrt{16} }\\ z=-5[/tex]

P(x > 11.95 cm) = P(z > -5) = 1 - P(z < -5) = 1 - 0.000001 ≅ 1 ≅ 100%

d) for n = 64, the standard deviation is 0.01 cm, therefore it is more likely to be within .01cm of 12cm

Using the normal distribution and the central limit theorem, it is found that:

a) The sampling distribution is approximately normal, centered at 12 cm and with a standard deviation of 0.01 cm.

b) The sampling distribution is approximately normal, centered at 12 cm and with a standard deviation of 0.005 cm.

c) 100% probability that the average diameter of piston rings from a sample size 16 is more than 11.95 cm .

d) Due to the lower standard error, the sample of 64 is more likely to be within 0.01 cm of 12 cm.

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In this problem:

Item a:

Sample of 16, thus [tex]n = 16[/tex] and [tex]s = \frac{0.04}{\sqrt{16}} = 0.01[/tex]

The sampling distribution is approximately normal, centered at 12 cm and with a standard deviation of 0.01 cm.

Item b:

Sample of 64, thus [tex]n = 64[/tex] and [tex]s = \frac{0.04}{\sqrt{64}} = 0.005[/tex]

The sampling distribution is approximately normal, centered at 12 cm and with a standard deviation of 0.005 cm.

Item c:

This probability is 1 subtracted by the p-value of Z when X = 11.95, thus:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{11.95 - 12}{0.01}[/tex]

[tex]Z = -5[/tex]

[tex]Z = -5[/tex] has a p-value of 0.

1 - 0 = 1.

100% probability that the average diameter of piston rings from a sample size 16 is more than 11.95 cm .

Item d:

Due to the lower standard error, the sample of 64 is more likely to be within 0.01 cm of 12 cm.

A similar problem is given at https://brainly.com/question/24663213

Answer:

-1(3 - y)

Step-by-step explanation:

If you factor out a negative 1, you will get the opposite signs you already have, so -1(3 - y). To check, we can simply distribute again:

-3 + y

So our answer is 2nd Choice.

Answer:

63

Step-by-step explanation:

A composite number is an integer which can be found by mulitplying 2 smaller integers, 7 and 9 in this case

Answer:

A

Step-by-step explanation:

Because 105%*105%=1.1205

and the only number divisible by that is A

Answer:

[tex] x_1 = 5, x_2 =11, y_1 =9, y_2 = -3[/tex]

The slope can be founded with this formula:

[tex]m =\frac{y_2 -y_1}{x_2 -x_1}[/tex]

And replacing we got:

[tex] m =\frac{-3 -9}{11-5}= -2[/tex]

And the best answer for this case would be :

[tex]m=-2[/tex]

Step-by-step explanation:

For this case we have the following two points given:

[tex] x_1 = 5, x_2 =11, y_1 =9, y_2 = -3[/tex]

The slope can be founded with this formula:

[tex]m =\frac{y_2 -y_1}{x_2 -x_1}[/tex]

And replacing we got:

[tex] m =\frac{-3 -9}{11-5}= -2[/tex]

And the best answer for this case would be :

[tex]m=-2[/tex]

Answer:

see explanation

Step-by-step explanation:

According to the Fundamental theorem of Algebra.

A polynomial of degree n has n roots which may be real or complex or both.

Answer:

The Fundamental Theorem of Algebra says that a polynomial of degree n will have exactly n roots

(counting multiplicity)

Answer:

3/4

Step-by-step explanation:

r= a3/a2=3/4

or

r= a2/a1= 4÷16/3= 4×3/16= 3/4

Answer:

[tex]y(t) = 3x+8e^{-3x} -1[/tex]

Step-by-step explanation:

Recall that the following laplace transforms

[tex]L(y') = sY(s)-y(0)[/tex]

[tex]L(t) = \frac{1}{s^2}[/tex]

The laplace transform is linear, so, applying the laplace transform to the equation we get

[tex]L(y'+3y) = sY(s)-7+3Y(s) = L(9t) = \frac{9}{s^2}[/tex]

By some algebraic manipulations, we get

[tex] Y(s)(s+3) = \frac{9+7s^2}{s^2}[/tex]

which is equivalent to

[tex] Y(s) = \frac{9+7s^2}{s^2(s+3)} = \frac{9}{s^2(s+3)}+\frac{7}{s+3}[/tex]

By using the partial fraction decomposition, we get

[tex] \frac{9}{s^2(s+3)} = \frac{-1}{s} + \frac{3}{s^2} + \frac{1}{s+3}[/tex]

then

[tex]Y(s) = \frac{-1}{s} + \frac{3}{s^2} + \frac{1}{s+3} + \frac{7}{s+3} = \frac{8}{s+3} + \frac{3}{s^2}-\frac{1}{s}[/tex]

Using that

[tex] L(e^{-ax}) = \frac{1}{s+a}[/tex]

[tex]L(1) = \frac{1}{s}[/tex]

by taking the inverse on both sides we get

[tex] y(t) = L^{-1}(\frac{8}{s+3})+L^{-1}(\frac{3}{s^2})+L^{-1}(-\frac{1}{s}) = 8e^{-3x} + 3x-1[/tex]

Answer:

a) 82

b) 97

Step-by-step explanation:

a) 354 - (95+95)

354 - 190

164

164 ÷ 2 = 82

(82+82+95+95=254)

b) 8439 cm^2 = 87x

8439 cm^2 ÷ 87 = 87x ÷ 87

97 = x

The equation of the tangent line to the curve at P(7, -2) is y = 2x -16.

For each given value of x, we substitute the coordinates of P and Q into the slope formula to find the slope mPQ.

(i) For x = 6.9:

mPQ = (2/(6 - 6.9) - (-2)) / (6.9 - 7)

= 2.22

(ii) For x = 6.99:

mPQ = (2/(6 - 6.99) - (-2)) / (6.99 - 7)

= 2.020

(iii) For x = 6.999:

mPQ = (2/(6 - 6.999) - (-2)) / (6.999 - 7)

= 2.002002

(iv) For x = 6.9999:

mPQ = (2/(6 - 6.9999) - (-2)) / (6.9999 - 7)

= 2.000200

(v) For x = 7.1:

mPQ = (2/(6 - 7.1) - (-2)) / (7.1 - 7)

= 1.818182

(vi) For x = 7.01:

mPQ = (2/(6 - 7.01) - (-2)) / (7.01 - 7)

= 1.980198

(vii) For x = 7.001:

mPQ = (2/(6 - 7.001) - (-2)) / (7.001 - 7)

= 1.998002

(viii) For x = 7.0001:

mPQ = (2/(6 - 7.0001) - (-2)) / (7.0001 - 7)

= 1.999800

By observing the pattern in the calculated slopes, we can see that as x approaches 7, the slope of the secant line PQ approaches 2.

Using the point-slope form, we have:

y - y₁ = m(x - x₁)

Substituting the values of P(7, -2), we have:

y - (-2) = 2(x - 7)

y = 2x -16

Therefore, the equation of the tangent line to the curve at P(7, -2) is y = 2x -16.

Learn more about the equation of the tangent line here:

https://brainly.com/question/31583945

#SPJ12

Answer:

40%

Step-by-step explanation:

The numbers that are not even are 5 and 7.

2 numbers out of 5.

2/5 = 0.4

P(not even) = 40%

Answer:

[tex]40\%[/tex]

Step-by-step explanation:

5 and 7 are not the numbers

There are 5 numbers in the spinner

[tex]p = \frac{2}{5} \\ = \frac{2 \times 20}{5 \times 20} \\ = \frac{40}{100} \\ = 40\%[/tex]

Answer:

  0

Step-by-step explanation:

There will be no death benefit. The policy expired after 10 years.

Answer: Step 3

Step-by-step explanation:

x = -9 or 1.  She flipped the signs.

Hope it helps <3

━━━━━━━☆☆━━━━━━━

▹ Answer

Step 3

▹ Step-by-Step Explanation

Juliet flipped the signs. The final answer should be (-9, 1)

Hope this helps!

CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

Answer:

[tex](x+(3+\sqrt{11}i)) (x+(3-\sqrt{11}i))[/tex]

Step-by-step explanation:

The first step to this problem is to look at the key features of the initial expression given to us. Namely, the middle term.

Notice that it is just [tex]+6x[/tex]. This indicates that the square root terms cancel out, meaning that their signs need to be opposite, but the threes need to have the same, positive sign. This indicates that our answer is option C, but you should always double check by multiplying the expression out to confirm. Here are the steps:

[tex](x+(3+\sqrt{11}i)) (x+(3-\sqrt{11}i))[/tex]

[tex]x^{2} +(3+\sqrt{11}i)x+(3-\sqrt{11}i)x+(3+\sqrt{11}i)(3-\sqrt{11}i)[/tex][tex]x^{2}+3x+\sqrt{11}ix+3x-\sqrt{11}ix+9+3\sqrt{11}i-3\sqrt{11}i-(\sqrt{11})^{2}(i^{2})[/tex][tex]x^{2}+6x+9-(11)(-1)[/tex]

[tex]x^{2}+6x+9+11[/tex]

[tex]x^{2}+6x+20[/tex]

Therefore as we suspected, the answer is C.

Answer: L = 20.25

Step-by-step explanation:

[tex]T=2\pi \sqrt{\dfrac{L}{32}}[/tex]

Given: T = 5, π = 22/7

[tex]5=2\bigg(\dfrac{22}{7}\bigg)\sqrt{\dfrac{L}{32}}\\\\\\\dfrac{5}{2}\bigg(\dfrac{7}{22}\bigg)=\sqrt{\dfrac{L}{32}}\\\\\\\dfrac{35}{44}=\sqrt{\dfrac{L}{32}}\\\\\\\bigg(\dfrac{35}{44}\bigg)^2=\bigg(\sqrt{\dfrac{L}{32}}\bigg)^2\\\\\\\bigg(\dfrac{35}{44}\bigg)^2=\dfrac{L}{32}\\\\\\32\bigg(\dfrac{35}{44}\bigg)^2=L\\\\\\\large\boxed{20.25=L}[/tex]

Answer:

The probability that exactly 30% of these 10 telephone users do not have landlines in their homes is 0.2668.

Step-by-step explanation:

We are given that a recent survey found that 30% of telephone users have switched completely to cell phone use (i.e. they do not have landlines in their homes).

A random sample of 10 of these customers is selected.

The above situation can be represented through binomial distribution;

[tex]P(X = r) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r}; x = 0,1,2,3,......[/tex]

where, n = number of trials (samples) taken = 10 customers

            r = number of success = 30% of 10 = 3

            p = probability of success which in our question is the probability

                  that telephone users do not have landlines in their homes,

                   i.e. p = 30%

Let X = Number of telephone users who do not have landlines in their homes

So, X ~ Binom(n = 10, p = 0.30)

Now, the probability that exactly 30% of these 10 telephone users do not have landlines in their homes is given by = P(X = 3)

           P(X = 3) =  [tex]\binom{10}{3}\times 0.30^{3} \times (1-0.30)^{10-3}[/tex]

                         =  [tex]120 \times 0.30^{3} \times 0.70^{7}[/tex]

                         =  0.2668

Recall that for |x| < 1, we have

[tex]\dfrac1{1-x}=\displaystyle\sum_{n=0}^\infty x^n[/tex]

Replace x with 2x, multiply 4, and call this function f :

[tex]f(x)=\dfrac4{1-2x}=\displaystyle4\sum_{n=0}^\infty(2x)^n[/tex]

Take the derivative:

[tex]f'(x)=\dfrac8{(1-2x)^2}=\displaystyle8\sum_{n=0}^\infty n(2x)^{n-1}=\boxed{8\sum_{n=0}^\infty (n+1)(2x)^n}[/tex]

By the ratio test, the series converges for

[tex]\displaystyle\lim_{n\to\infty}\left|\frac{(n+2)(2x)^{n+1}}{(n+1)(2x)^n}\right|=|2x|\lim_{n\to\infty}\frac{n+2}{n+1}=|2x|<1[/tex]

or |x| < 1/2, so the radius of convergence is 1/2.

Answer:

-10, 3

Step-by-step explanation:

-10, 3 work since

-10 + 3 = -7

Answer: M=32°

Step-by-step explanation:

The identity sin²(x)+cos²(x)=1 can help us figure out the value of M. You can see that the problem's format fits exactly the identity. Since x is the same in the identity, we know that M=32°.

Answer:

$165.38

Step-by-step explanation:

In the question, we are asked to work with percentages. We know that the person had bought three items of a total of 250 dollars (38 + 189 + 23). We are told that the items have a 30% discount, another 10% discount on that and a 5% tax increase on all of that.

First, let's work with the 30% discount. The official way of working out the problem you would use the unitary method. The unitary method is when we divide the total cost by 100. So 250/100, is 2.5. We multiply this by the remaining percent (100%- 30%=70%) so 2.5*70 is 175.

Then, we work with ten percent. The only difference is that instead of using the original price with are using the 30% discounted price. If we use the unitary method again we find that 175/100 is 1.75 and that multiplied by 90 (because we are only subtracting the 10% not 30%) is 157.50.

Finally, we do the same for the 5% percent only difference being we add it to 157.50. 157.50/100 is 1.575 and multiplied by 105 (because we are adding 5% onto 100% so it becomes 105%).

The final answer is 165.375 and when rounded to the nearest cent it becomes $165.38.

Answer:

4/5 chance

Step-by-step explanation:

There are 4 numbers that fit the rule, 1, 3, 4, 5, since all of them are either odd or greater than 3. There will be a 4/5 chance of picking one.

Answer:

Step-by-step explanation:

This is because 5 is odd and greater than 3.

Also. 4 is greater than 3.

After that, the other odd numbers are 1 and 3

So the numbers are 1, 3, 4, and 5.

So 4 out of 5 numbers are counted in the circle.

In this way 4/5 is the answer.

Hope this helped!

Kavitha