(05.06A LC)

Line segment AB has a length of 4 units. It is translated 1 unit to the right on a coordinate plane to obtain line segment A'B'. What is the length

of A'B'?

1 unit

4 units

5 units

6 units

Answers

Answer 1

Answer:

4 units

Step-by-step explanation:

A transformation is the movement of a point from one position to another position. If a shape is transformed all its points are also transformed. Types of transformations are translation, rotation, reflection and dilation.

If a shape is transformed, the length of its sides and shape remains the same, only the position changes.

If Line segment AB has a length of 4 units. It is translated 1 unit to the right on a coordinate plane to obtain line segment A'B, the length of A'B' remains the same which is 4 unit. To prove this:

Let A be at ([tex]x_1,y_1[/tex]) and B be at ([tex]x_2,y_2[/tex]). The length of AB is:

[tex]AB=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]

If AB is translated to the right by 1 unit the new points are A' at ([tex]x_1+1,y_1[/tex]) and B' at ([tex]x_2+1,y_2[/tex]). The length of A'B' is:

[tex]A'B'=\sqrt{(y_2-y_1)^2+(x_2+1-(x_1+1))^2}=\sqrt{(y_2-y_1)^2+(x_2+1-x_1-1)^2}\\\\A'B'=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]

AB = A'B' = 4 units


Related Questions

I need some help pls! I'm getting stuck!

Answers

Answer: 3 pounds.

Step-by-step explanation:

We have two metals:

One that contains 20% nickel, let's call it metal A.

One that contains 80% nickel, let's call it metal B.

We have 6 pounds of metal B, in those 6 punds we have:

0.80*6lb = 4.8lb of nickel.

Now, if we add X pounds of metal A, then we will have:

X + 6lb in total weight.

4.8lb + 0.2*X of nickel.

And we want to have exactly 60% of nickel, so we must have that the quotient between the amount of nickel and the total weight is equal to 0.6

(4.8lb + 0.2*X)/(6lb + X) = 0.6

now we solve it for X:

(4.8lb + 0.2*X) = 0.6*(6lb + X) = 3.6lb + 0.6*X

4.8lb - 3.6lb = 0.6*X - 0.2*X

1.2lb = 0.4*X

1.2lb/0.4 = 3lb = X

We should use 3 pounds of the metal with 20% of nickel.

Why is f (x) = (3x + 1/3)^2 + 8/9 not the vertex form of f (x)
not the vertex form of f (x) = 9x^2 +2x +1?
O The expression has a constant outside of the squared term.
O Some of the terms are fractions instead of integers.
O The expression is not the product of two binomials.
O The variable x has a coefficient.

Answers

Answer:

The Variable has a coefficient.

Step-by-step explanation:

There were 18,652 geese on a lake. What is this number rounded to the ten
thousands place?​

Answers

Answer:

20,000

Step-by-step explanation:

To round a number to the nearest ten thousands place, we have to look at the thousand place and see whether it crosses the "hill" of 5 as it's digit.

The thousand digit is 8, so it will round UP, making 18,652 become 20,000.

Hope this helped!

Answer:

[tex]\boxed{20,000}[/tex]

Step-by-step explanation:

Hey there!

Well the ten thousands number is 1 and the 1rst thousands place number is 8 so since 8 is more than 5 we have to round 1 UP to 2,

so the answer is 20,000.

Hope this helps :)

Actual time in seconds recorded when statistics students participated in an experiment t test their ability to determine when one minute 60 seconds has passed are shown below.Find the mean median mode of the listed numbers. 55 51 70 64 68 60 49?49

Answers

Step-by-step explanation:

mean add upp all the numbers and divide by how many they are

Find the measure of a.
A. 60
B. 57
C. 40
D. 80

Answers

Answer:

Option (C)

Step-by-step explanation:

Since angle 'a' is the inscribed angle of the given triangle

Therefore, angle measure of the intercepted arc will be equal to the double of the inscribed angle.

x = 2a ⇒ a = [tex]\frac{x}{2}[/tex]

By the tangent-chord theorem,

"Angle between a chord and tangent measure the half of the angle measure of intercepted minor arc"

[tex]\frac{x}{2}[/tex] = 40°

Therefore, a = [tex]\frac{x}{2}[/tex] = 40°

Option (C) will be the answer.

PLEASE HELP!!! The question is.. [tex]163-y=-5[/tex] ANSWER GETS BRAINLIEST

Answers

Answer:

y = 168Step-by-step explanation:

[tex]163 -y =-5\\Collect\:Like\:terms\\163+5 = y\\Simplify\\168 =y\\\\y = 168[/tex]

Hello There!

Answer: [tex]163-168=-5[/tex]Explanation:

[tex]163-y=-5[/tex]

To solve your equation, you can just change the -5 to 5 and move it to where y is. After that, change the minus sign to addition.

[tex]163+5=y[/tex]

Now all you have to do is sum it up.

[tex]163+5=168[/tex]

So y = to 168

So your answer is

[tex]163-168=-5[/tex]

Hope this Helps!

Jan. 2 Purchased merchandise on account from Nunez Company, $20,000, terms 3/10, n/30. (Lily uses the perpetual inventory system.)

Feb. 1 Issued a 9%, 2-month, $20,000 note to Nunez in payment of account.

Mar. 31 Accrued interest for 2 months on Nunez note.

Apr. 1 Paid face value and interest on Nunez note.

July 1 Purchased equipment from Marson Equipment paying $10,000 in cash and signing a 10%, 3-month, $63,600 note.

Sept. 30 Accrued interest for 3 months on Marson note.

Oct. 1 Paid face value and interest on Marson note.

Dec. 1 Borrowed $22,800 from the Paola Bank by issuing a 3-month, 8% note with a face value of $22,800.

Dec. 31 Recognized interest expense for 1 month on Paola Bank note.

Answers

Hug hbhbu n b n j j n. N n. Non notable n n

Evaluate 1 + (-2/3) - (-m) where m = 9.2.

Answers

Answer:

9.533

Step-by-step explanation:

1+(-2/3)-(-9.2)

1-2/3--9.2

1-2/3+9.2=9.533

Answer: See below

Explanation:

1 + (-2/3) - (-m)
m = 9.2

1 - 2/3 + m
= 1 - 2/3 + 9.2
= 3/3 - 2/3 + 9.2
= 1/3 + 9.2
= 1/3 + 27.6/3
= 28.6/3

Megan has 12 pounds of cheesecake. On Monday, she and her friends eat 4 pounds. On Tuesday, she and her friends eat another 3 pounds. On Wednesday, her friend Mark gives her some more cheesecake so that she has 3 times as much as she had at the end of Tuesday. On Thursday, some of her cheesecake goes bad, so she has the amount that she had at the end of Wednesday, but divided by 5. On Friday, she gives 3 pounds to her dog. On Saturday, her mom gives her one more pound. On Sunday, how many pounds of cheesecake does Megan have left?

Answers

Answer:

Step-by-step explanation:

First we start with 12 pounds

On Monday, she and her friends eat 4 pounds. So we have 8 now.

On Tuesday, she and her friends eat another 3 pounds. So we gave 5 now.

On Wednesday, her friend Mark gives her some more cheesecake so that she has 3 times as much as she had at the end of Tuesday. 5 * 3 = 15

On Thursday, some of her cheesecake goes bad, so she has the amount that she had at the end of Wednesday, but divided by 5. She had 15 at the end of Wednesday. 15/5 = 3.

On Friday, she gives 3 pounds to her dog. 5 - 3 = 2.

On Saturday, her mom gives her one more pound. 2 + 1 = 3.

On Sunday, she finally has 3 pounds.

Answer:

nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn

Step-by-step explanation:

Please answer this correctly without making mistakes

Answers

Answer:

1/8

Step-by-step explanation:

3/8-1/8-1/8=1/8

Kim is earning money for a trip. She has saved and she earns per hour babysitting. The total amount of money earned (y) after (x) number of hours worked is given by the equation . How many hours will she need to work in order to earn for her trip?

Answers

Answer:

what is the amount of money Kim earn per hour of babysitting? Also I need to know how much trip cost to find out how many hours she need to work.

Step-by-step explanation:

Identifying the Property of Equality

Quick

Check

Identify the correct property of equality to solve each equation.

3+x= 27

X/6 = 5

Answers

Answer:

a) Compatibility of Equality with Addition, b) Compatibility of Equality with Multiplication

Step-by-step explanation:

a) This expression can be solved by using the Compatibility of Equality with Addition, that is:

1) [tex]3+x = 27[/tex] Given

2) [tex]x+3 = 27[/tex] Commutative property

3) [tex](x + 3)+(-3) = 27 +(-3)[/tex] Compatibility of Equality with Addition

4) [tex]x + [3+(-3)] = 27+(-3)[/tex] Associative property

5) [tex]x + 0 = 27-3[/tex] Existence of Additive Inverse/Definition of subtraction

6) [tex]x=24[/tex] Modulative property/Subtraction/Result.

b) This expression can be solved by using the Compatibility of Equality with Multiplication, that is:

1) [tex]\frac{x}{6} = 5[/tex] Given

2) [tex](6)^{-1}\cdot x = 5[/tex] Definition of division

3) [tex]6\cdot [(6)^{-1}\cdot x] = 5 \cdot 6[/tex] Compatibility of Equality with Multiplication

4) [tex][6\cdot (6)^{-1}]\cdot x = 30[/tex] Associative property

5) [tex]1\cdot x = 30[/tex] Existence of multiplicative inverse

6) [tex]x = 30[/tex] Modulative property/Result

Answer:

3 + x = 27

✔ subtraction property of equality with 3

x over 6  = 5

✔ multiplication property of equality with 6

An economist is interested in studying the spending habits of consumers in a particular region. The population standard deviation is known to be $1,000. A random sample of 50 individuals resulted in an average expense of $15,000. What is the width of the 99% confidence interval for the mean of expense? a. 364.28 b. 728.55 c. 329.00 d. 657.99

Answers

Answer:

The  width is  [tex]w = \$ 729.7[/tex]

Step-by-step explanation:

From the question we are told that

   The population standard deviation is  [tex]\sigma = \% 1,000[/tex]

    The  sample size is  [tex]n = 50[/tex]

    The sample mean  is  [tex]\= x = \$ 15,000[/tex]

Given that the confidence level is  99% then the level of significance is mathematically represented as  

               [tex]\alpha = 100 - 99[/tex]

=>            [tex]\alpha = 1\%[/tex]

=>             [tex]\alpha = 0.01[/tex]

Next we obtain the critical value of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table, the value is

             [tex]Z_{\frac{\alpha }{2} } = Z_{\frac{0.01 }{2} } = 2.58[/tex]

Generally margin of error is mathematically represented as

             [tex]E = Z_{\frac{\alpha }{2} * \frac{\sigma }{\sqrt{n} }[/tex]

substituting values

              [tex]E = 2.58 * \frac{1000 }{\sqrt{50} }[/tex]

              [tex]E = 2.58 * \frac{1000 }{\sqrt{50} }[/tex]

               [tex]E = 364.9[/tex]

The width of the 99% confidence interval is mathematically evaluated as

         [tex]w = 2 * E[/tex]

substituting values

          [tex]w = 2 * 364.9[/tex]

          [tex]w = \$ 729.7[/tex]

Question:
If V7 - y = 6, then y =
A. -29
B. -5
C. 1
D. 29
[tex] \sqrt{7 - y = 6} [/tex]

Answers

Answer:

-29

Step-by-step explanation:

[tex] {\sqrt{7 - y }}^{2} = {6}^{2} [/tex]

[tex]7 - y = {6}^{2} [/tex]

y = 7-36

y = -29

Timothy invested $2,000 in an account earning 3.5% annual interest that is compounded continuously. How long will it take the investment to grow to $3,500?

Answers

Answer: 16 years

Step-by-step explanation:

The exponential function for continuous growth is given by :-

[tex]P=Ae^{rt}[/tex]

, where A = initial amount, r= rate of growth and t = time.

As per given , we have

A= $2,000, =r 3.5%=0.035 and P= $3500

put these vales in equation , we get

[tex]3500=2000e^{0.035t}\\\\\Rightarrow\ \dfrac{3500}{2000}=e^{0.035t}\\\\\Rightarrow\ 1.75=e^{0.035t}[/tex]

Taking log on both sides , we get

[tex]\ln 1.75=0.035t\\\\\Rightarrow\ t=\dfrac{\ln1.75}{0.035}=\dfrac{0.560}{0.035}=16[/tex]

Hence, it will take 16 years to grow to $3,500.

One more than the quotient of a number x and 4. Write an expression to represent:

Answers

Answer:

x/4 +1

Step-by-step explanation:

A 14 sided die is rolled find the probability of rolling an odd number the set of equally likely outcomes is shown below

Answers

Answer:

Probability= 0.5

Step-by-step explanation:

A 14 sided die is rolled

Total number of occurrence= 14 numbers

Total odd numbers present

= 1,3,5,7,9,11,13

Total number of odd numvers present

= 7

Probability= number of required outcome/total possible outcome

Probability= 7/14

Probability= 0.5

Find the equation of the para bola that has zeros of x = -2 and x = 3 and a y-intercept of (0,-30)

Answers

Answer:

y = 5x^2-5x-30

Step-by-step explanation:

A parabola with x-intercepts at (-2,0) and (3,0) has the equation

y = a(x+2)(x-3)

where a is to be determined.

We know that it passes through the point (0,-30), so

-30 = a(0+2)(0-3) = -6a

Therefore solve for a to get

a = 5

y = 5(x+2)(x-3)

y = 5(x^2-x+6)

y = 5x^2-5x-30

A market researcher believes that brand perception of one of the company's products may vary between different groups. After interviewing 307 persons, the following data was compiled. Can we conclude that brand perception is dependent on age?
Age Favorable Unfavorable Neutral Total
18-30 67 24 20 111
30-45 50 14 16 80
Over 45 69 41 26 116
Total 186 59 62 307
Find the value of the test statistic.

Answers

Answer:

The value for the Chi -square  test statistics = 1.149

Step-by-step explanation:

The observed value Table can be shown better as:

Observed Value

Age            Favorable          Unfavorable            Neutral              Total

18-30             67                            24                       20                   111

30-45            50                            14                        16                    80

Over 45         69                           21                        26                   116

Total              186                         59                        62                   307

NOTE: when computing the question, in the third row and the second column, there is a mistake , the value is supposed to be 21 and not  41 because :

69 +21+ 26 will eventually give = 116

69 + 41 + 26 = 136  

With that error being fix , let's get started.

Expected Value

The expected value can be determined by using the formula:

[tex]Expected \ Value = \dfrac{ row \ total \times column \ total }{grand \ total }[/tex]

For 67; (111 * 186)/307 = 67.251

For 24 : (111 * 59)/307 = 21.332

For 20 : (111 * 62)/307 = 22.417

For 50 :(80*186)/307 = 48.469

For 14 : (80* 59)/307 = 15.375

For 16 : ( 0 * 62)/307 = 16.156

For 69 : (116 * 186)/307 = 70.280

For 21 : (116* 59)/307 = 22.293

For 26 : (116*62)/307 = 23.427

Expected Value :

Age            Favorable          Unfavorable            Neutral              Total

18-30         67.251                 21.332                     22.417                  111

30-45        48.469                15.375                     16.156                  80

Over 45    70.280                22.293                     23.427               116

Total              186                         59                        62                   307

The Chi - square test statistics = [tex]\dfrac{(observed \ value - Expected \ value)^2}{Expected \ value}[/tex]

For 67.251 : ( 67 - 67.251)²/67.251 = 0.0009

For 21.332 : ( 24 - 21.332)²/21.332 = 0.3337

For 22.417 : ( 20 - 22.417)²/ 22.417 = 0.2606

For 48.469 : ( 50 - 48.469)²/ 48.469 = 0.0484

For 15.375 : ( 14 - 15.375)²/ 15.375 = 0.1230

For 16.156 : ( 16 - 16.156)²/ 16.156 = 0.0015

For 70.280 : ( 69 - 70.280)²/ 70.280 = 0.0233

For 22.293 : ( 21 - 22.293)²/ 22.293 = 0.0750

For 23.427 : ( 26 - 23.427)²/ 23.427 = 0.2826

The chi square table is as follows:

Age            Favorable          Unfavorable            Neutral          Total

18-30          0.0009              0.3337                   0.2606           0.5952

30-45         0.0484               0.1230                   0.0015            0.1729

Over 45     0.0233               0.0750                  0.2826            0.3809

Total          0.0726                0.5317                   0.5447              1.149

The value for the Chi -square  test statistics = 1.149

i need help will rate you branliest

Answers

Answer D. the bottom one is the answer, because hyperbola is two curves that curve infinitely

Hope

Answer:

D. the bottom one is the answer, because hyperbola is two curves that curve infinitely

Find the volume of the cylinder. Round your answer to the nearest tenth.

Answers

Answer:

716.75 m^3

Step-by-step explanation:

Volume of a cylinder:

=> PI x R^2 x H

H = Height

R = Radius

=> PI x 3.9^2 x 15

=> PI x 15.21 x 15

=> PI x 228.15

=> 228.15 PI

           or

=> 228.15 x 3.14159

=> 716.75 m^3

Find the distance between (-8, 4) and (-8, -2).
10 units
2 units
6 units
8 units​

Answers

Answer:

10

Step-by-step explanation:

A father is three times as old as his son. After fifteen years the father will be twice as old as his son's age at that time. Hence the father's present age is

Answers

Answer:

Step-by-step explanation:

let present age of father=y

present age of son=x

then y=3x

after 15 years age of father=y+15

and age of son=x+15

∴y+15=2(x+15)

y+15=2x+30

y-2x=30-15

y-2x=15

∴3x-2x=15

x=15

y=3x=15×3=45

father's present age=45 years

Identify the decimals labeled with the letters A, B, and C on the scale below. Letter A represents the decimal Letter B represents the decimal Letter C represents the decimal

Answers

There are [tex]10[/tex] divisions between $3.2$ and $3.3$

so that means each division is $\frac{3.3-3.2}{10}=0.01$

A is the 3rd division after $3.2$, So A is $3.2+3\times0.01=3.23$

similarly, C is 3 division behind $3.2$ so it will be $3.17$

and B is $3.34$

A represents the decimal 3.23

B represents the decimal 3.34

C represents the decimal 3.17

Calculating the decimal values:

We can see that there are 10 divisions between 3.2 and 3.3.

The difference between the two points for 10 divisions is 3.3 -3.2 = 0.1 unit.

Therefore, one division will be equal to 0.1/10 = 0.01 unit

So, point A is 3 divisions after 3.2, thus

A = 3.2 + 0.01×3

A = 3.23

Similarly,

B = 3.3 + 0.01×4

B = 3.34

And,

C = 3.2 - 0.01×3

C = 3.17

Learn more about decimals:

https://brainly.com/question/548650?referrer=searchResults

henry incorrectly said the rate 1/5 pound/ 1/20 quart can be written as the unit rate 1/100 pound per quart. What is the correct unit rate? What error did Henry likely make?

Answers

Answer:

4 pounds per quart

Step-by-step explanation:

Henry divided by 20 instead of multiplying by 20.

1/5 pound is the numerator and 1/20 quart is the denominator. To make the denominator equal to 1 quart, you need to multiply by 20.

So 1/5 x 20 = 4 pounds.

Literally, a unit rate means a rate for one.

The unit rate is 4 pounds per quartHenry used the wrong arithmetic operator

The rate is given as:

[tex]\mathbf{Rate = \frac{1}{5}\ pound\ per\ \frac{1}{20}\ quart}[/tex]

Per means divide.

So, the expression becomes

[tex]\mathbf{Rate = \frac{1}{5}\ pound\ \div \frac{1}{20}\ quart}[/tex]

Express as products

[tex]\mathbf{Rate = \frac{1}{5}\ pound\ \times \frac{20}{1\ quart}}[/tex]

Simplify

[tex]\mathbf{Rate = \frac{1}{1}\ pound\ \times \frac{4}{1\ quart}}[/tex]

Rewrite as:

[tex]\mathbf{Rate = \frac{4\ pound}{1\ quart}}[/tex]

So, the unit rate is 4 pounds per quart

Henry's error is that: He multiplied 1/5 by 1/20, instead of dividing 1/5 by 1/20

Read more about unit rates at:

https://brainly.com/question/18065083

Help with this please

Answers

[tex](f+g)(x)=\sqrt{4x+6}+\sqrt{4x-6}[/tex]

Answer:

[tex]\huge\boxed{Option \ 4: (f+g)(x) = \sqrt{4x+6} + \sqrt{4x-6}}[/tex]

Step-by-step explanation:

[tex]f(x) = \sqrt{4x+6}\\ g(x) = \sqrt{4x-6}[/tex]

Adding both

[tex](f+g)(x) = \sqrt{4x+6} + \sqrt{4x-6}[/tex]

What is the true solution to the equation below? 2 in e in2×-in e in 10×= in 30 A x=30 B x=75 C x=150 D x=300

Answers

Answer:

Option B.

Step-by-step explanation:

Let as consider the given equation:

[tex]2\ln e^{\ln 2x}-\ln e^{\ln 10x}=\ln 30[/tex]

It can be written as

[tex]2(\ln 2x)-(\ln 10x)=\ln 30[/tex]         [tex][\because \ln e^a=a][/tex]

[tex]\ln (2x)^2-(\ln 10x)=\ln 30[/tex]        [tex][\because \ln a^b=b\ln a][/tex]

[tex]\ln \dfrac{4x^2}{10x}=\ln 30[/tex]        [tex][\because \ln \dfrac{a}{b}=\ln a-\ln b][/tex]

[tex]\ln \dfrac{2x}{5}=\ln 30[/tex]

On comparing both sides, we get

[tex]\dfrac{2x}{5}=30[/tex]

Multiply both sides by 5.

[tex]2x=150[/tex]

Divide both sides by 2.

[tex]x=75[/tex]

Therefore, the correct option is B.

Answer:

b x=75

Step-by-step explanation:

A bag contains two six-sided dice: one red, one green. The red die has faces numbered 1, 2, 3, 4, 5, and 6. The green die has faces numbered 1, 2, 3, 4, 4, and 4. A die is selected at random and rolled four times. You are told that two rolls were 1's and two were 4's. Find the probability the die chosen was green.

Answers

Answer:

the probability the die chosen was green is 0.9

Step-by-step explanation:

Given that:

A bag contains two six-sided dice: one red, one green.

The red die has faces numbered 1, 2, 3, 4, 5, and 6.

The green die has faces numbered 1, 2, 3, 4, 4, and 4.

From above, the probability of obtaining 4 in a single throw of a fair die is:

P (4  | red dice) = [tex]\dfrac{1}{6}[/tex]

P (4 | green dice) = [tex]\dfrac{3}{6}[/tex] =[tex]\dfrac{1}{2}[/tex]

A die is selected at random and rolled four times.

As the die is selected randomly; the probability of the first die must be equal to the probability of the second die = [tex]\dfrac{1}{2}[/tex]

The probability of two 1's and two 4's in the first dice can be calculated as:

= [tex]\begin {pmatrix} \left \begin{array}{c}4\\2\\ \end{array} \right \end {pmatrix} \times \begin {pmatrix} \dfrac{1}{6} \end {pmatrix} ^4[/tex]

= [tex]\dfrac{4!}{2!(4-2)!} ( \dfrac{1}{6})^4[/tex]

= [tex]\dfrac{4!}{2!(2)!} \times ( \dfrac{1}{6})^4[/tex]

= [tex]6 \times ( \dfrac{1}{6})^4[/tex]

= [tex](\dfrac{1}{6})^3[/tex]

= [tex]\dfrac{1}{216}[/tex]

The probability of two 1's and two 4's in the second  dice can be calculated as:

= [tex]\begin {pmatrix} \left \begin{array}{c}4\\2\\ \end{array} \right \end {pmatrix} \times \begin {pmatrix} \dfrac{1}{6} \end {pmatrix} ^2 \times \begin {pmatrix} \dfrac{3}{6} \end {pmatrix} ^2[/tex]

= [tex]\dfrac{4!}{2!(2)!} \times ( \dfrac{1}{6})^2 \times ( \dfrac{3}{6})^2[/tex]

= [tex]6 \times ( \dfrac{1}{6})^2 \times ( \dfrac{3}{6})^2[/tex]

= [tex]( \dfrac{1}{6}) \times ( \dfrac{3}{6})^2[/tex]

= [tex]\dfrac{9}{216}[/tex]

The probability of two 1's and two 4's in both dies = P( two 1s and two 4s | first dice ) P( first dice ) + P( two 1s and two 4s | second dice ) P( second dice )

The probability of two 1's and two 4's in both die = [tex]\dfrac{1}{216} \times \dfrac{1}{2} + \dfrac{9}{216} \times \dfrac{1}{2}[/tex]

The probability of two 1's and two 4's in both die = [tex]\dfrac{1}{432} + \dfrac{1}{48}[/tex]

The probability of two 1's and two 4's in both die = [tex]\dfrac{5}{216}[/tex]

By applying  Bayes Theorem; the probability that the die was green can be calculated as:

P(second die (green) | two 1's and two 4's )  = The probability of two 1's and two 4's | second dice)P (second die) ÷ P(two 1's and two 4's in both die)

P(second die (green) | two 1's and two 4's )  = [tex]\dfrac{\dfrac{1}{2} \times \dfrac{9}{216}}{\dfrac{5}{216}}[/tex]

P(second die (green) | two 1's and two 4's )  = [tex]\dfrac{0.5 \times 0.04166666667}{0.02314814815}[/tex]

P(second die (green) | two 1's and two 4's )  = 0.9

Thus; the probability the die chosen was green is 0.9

What are the roots for x?

Answers

Answer:

B

Step-by-step explanation:

Use the quadractic equation, x=-b+or-sqrtb^2-4ac/2a, then simplify.

I'm really sorry that it looks messy, I don't know how to make my text look better :(

The mean salary of federal government employees on the General Schedule is $59,593. The average salary of 30 state employees who do similar work is $58,800 with \sigmaσσ= $1500. At the 0.01 level of significance, can it be concluded that state employees earn on average less than federal employees? What is the critical value? Round your answer to the nearest hundredths.

Answers

Answer:

Yes it can be concluded that state employees earn on average less than federal employees

  The critical value is  [tex]Z_{\alpha } = - 2.33[/tex]

Step-by-step explanation:

From the question we are told that

   The  population mean is  [tex]\mu = \$ 59593[/tex]

   The sample size is  n =  30

    The  sample mean is [tex]\= x = \$ 58800[/tex]

     The  standard deviation is  [tex]\sigma = \$ 1500[/tex]

     The significance level is  [tex]\alpha = 0.01[/tex]

   

The null hypothesis is  [tex]H_o : \mu = \$ 59593[/tex]

 The  alternative hypothesis is  [tex]H_a : \mu < \$ 59593[/tex]

The critical value of [tex]\alpha[/tex] from the normal distribution table is  [tex]Z_{\alpha } = - 2.33[/tex]

 Generally the test statistics is  mathematically evaluated as

            [tex]t = \frac{\= x - \mu}{ \frac{ \sigma }{ \sqrt{n} } }[/tex]

=>         [tex]t = \frac{ 58800 - 59593 }{ \frac{ 1500 }{ \sqrt{30} } }[/tex]  

=>          [tex]t = -2.896[/tex]

The  p-value is obtained from the z-table

   [tex]p-value = P(t < -2.896) = 0.0018898[/tex]

Since [tex]p-value < \alpha[/tex] , we reject the null hypothesis, hence it can be concluded that state employees earn on average less than federal employees  

   

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