Find the value of X and Y

Answer:

Well it could be a number of fractions. It could be 1/8 and 4/8, or 2/8 and 3/8.

Answer:

1a

  [tex]P(39 < X < 48 ) = 0.8767[/tex]

1b

    95% of all sample means will fall between [tex] 40.1  <  \mu < 49.9 [/tex]

1c

    [tex]\= x = 41. 795[/tex]

2

   [tex]n = 25[/tex]

Step-by-step explanation:

From the question we are told that

   The mean is [tex]n = 45[/tex]

   The population standard deviation is  [tex]\sigma = 10[/tex]

   The sample size is n  =  16

Generally the standard error of the mean is mathematically represented as

       [tex]\sigma_{x} = \frac{ \sigma}{\sqrt{n} }[/tex]

=>    [tex]\sigma_{x} = \frac{ 10 }{\sqrt{16 } }[/tex]

=>    [tex]\sigma_{x} = 2.5[/tex]

Generally the probability that the sample mean will be between 39 and 48 minutes is

    [tex]P(39 < X < 48 ) = P( \frac{ 39 - 45}{ 2.5} < \frac{X - \mu }{\sigma } < \frac{ 48 - 45}{ 2.5} )[/tex]

=> [tex]P(39 < X < 48 ) = P(-2.4 < Z< 1.2 )[/tex]

=> [tex]P(39 < X < 48 ) = P( Z< 1.2 ) - P(Z < -2.4)[/tex]

From the z table  the area under the normal curve to the left corresponding to  1.2  and  -2.4  is

=> [tex]P( Z< 1.2 ) = 0.88493[/tex]

and  

    [tex]P( Z< - 2.4 ) = 0.0081975[/tex]

So

   [tex]P(39 < X < 48 ) = 0.88493 -0.0081975[/tex]

=> [tex]P(39 < X < 48 ) = 0.8767[/tex]

From the question we are told the confidence level is  95% , hence the level of significance is    

      [tex]\alpha = (100 - 95 ) \%[/tex]

=>   [tex]\alpha = 0.05[/tex]

Generally from the normal distribution table the critical value  of   is  

   [tex]Z_{\frac{\alpha }{2} } =  1.96[/tex]

Generally the margin of error is mathematically represented as  

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

=>   [tex]E = 1.96 * 2.5 [/tex]  

=>   [tex]E =4.9 [/tex]  

Generally the  95% of all sample means will fall between

      [tex]\mu -E <  and  \mu  +E[/tex]

=>   [tex]45  -4.9\  and \ 45  + 4.9[/tex]

Generally the value which  90% of sample means is  greater than is mathematically represented

      [tex]P( \= X > \= x ) = 0.90[/tex]

=>   [tex]P( \= X > \= x ) = P( \frac{\= X - \mu }{ \sigma_x} > \frac{\= x -45 }{ 2.5} ) = 0.90[/tex]

=>  [tex]P( \= X > \= x ) = P( Z > z ) = 0.90[/tex]

Generally from the z-table  the critical  value  of  0.90  is  

      [tex]z = -1.282[/tex]

      [tex]\frac{\= x -45 }{ 2.5} = -1.282[/tex]

=>   [tex]\= x = 41. 795[/tex]

Considering question 2

 Generally we are told that the standard deviation of the mean to be one fifth of the population standard deviation, this is mathematically represented as

         [tex]s = \frac{1}{5} \sigma[/tex]

  Generally the standard deviation of the sample mean is mathematically  represented as

          [tex]s = \frac{\sigma }{ \sqrt{n} }[/tex]

=>       [tex]\frac{1}{5} \sigma = \frac{\sigma }{ \sqrt{n} }[/tex]

=>       [tex]n = 5^2[/tex]

=>       [tex]n = 25[/tex]

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

1)

a) 0.8767 = 87.67% probability that the sample mean will be between 39 and 48 minutes.

b) 95% of all sample means will fall between 40.1 and 49.9 minutes.

c) 90% of the sample means will be greater than 41.8 minutes.

2) A sample size of 25 is needed.

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 1, question a:

The probability is the p-value of Z when X = 48 subtracted by the p-value of Z when X = 39, hence:

X = 48:

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

By the Central Limit Theorem

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

[tex]Z = \frac{48 - 45}{2.5}[/tex]

[tex]Z = 1.2[/tex]

[tex]Z = 1.2[/tex] has a p-value of 0.8849.

X = 39:

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

[tex]Z = \frac{39 - 45}{2.5}[/tex]

[tex]Z = -2.4[/tex]

[tex]Z = -2.4[/tex] has a p-value of 0.0082.

0.8849 - 0.0082 = 0.8767

0.8767 = 87.67% probability that the sample mean will be between 39 and 48 minutes.

Item b:

The critical value for a 95% confidence interval is |z| = 1.96, hence:

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

[tex]-1.96 = \frac{X - 45}{2.5}[/tex]

[tex]X - 45 = -1.96(2.5)[/tex]

[tex]X = 40.1[/tex]

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

[tex]1.96 = \frac{X - 45}{2.5}[/tex]

[tex]X - 45 = 1.96(2.5)[/tex]

[tex]X = 49.9[/tex]

95% of all sample means will fall between 40.1 and 49.9 minutes.

Item c:

Greater than the 10th percentile, which is X when Z has a p-value of 0.1, so X when Z = -1.28.

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

[tex]-1.28 = \frac{X - 45}{2.5}[/tex]

[tex]X - 45 = -1.28(2.5)[/tex]

[tex]X = 41.8[/tex]

90% of the sample means will be greater than 41.8 minutes.

Item 2:

This is n for which [tex]s = \frac{10}{5} = 2[/tex], hence:

[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]

[tex]2 = \frac{10}{\sqrt{n}}[/tex]

[tex]2\sqrt{n} = 10[/tex]

Simplifying both sides by 2:

[tex]\sqrt{n} = 5[/tex]

[tex](\sqrt{n})^2 = 5^2[/tex]

[tex]n = 25[/tex]

A sample size of 25 is needed.

A similar problem is given at https://brainly.com/question/14789302

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what do u need help with

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229.9

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Answer:

229.9

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Answer:

44

Step-by-step explanation:

The answer is B because it has to have a right angle in it

Answer:

Standard Form: 2x - y = -2

Answer:

2. x = 3

3. x = 5

Answer:

Below.

Step-by-step explanation:

(2).   6x + 51 + 111 = 180

        6x = 180 - 162 = 18

         x = 3.

(3).   6x = 30

        x = 5.

Answer: -8

Step-by-step explanation: because the formula is mx+b=y and the -8 is the b

Answer:

32 miles

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32 miles is equal to 51.499008 Kilometers

12.7 kilometers is equal to 7.891414 miles

Answer:

Simplify the solution: 13^1d^3

Step-by-step explanation:

Any expression raised to the power of one equal itself.

Answer:

123.6cm^2

Step-by-step explanation:

24^2=576

area of all four quarter circles combined: 144pi

576-122pi

Answer:

16.1

Step-by-step explanation:

Answer:

The answer for the question is 11 and 12 I just got a test back and it was correct

Step-by-step explanation:

Answer:

32 and 146

Step-by-step explanation:

Answer:

[tex]P = (-5,5)[/tex]

Step-by-step explanation:

Let the segments be A and B

[tex]A = (-9,3)[/tex]

[tex]B = (1,8)[/tex]

[tex]m:n = 2:3[/tex]

Required

Determine the endpoints after it is divided into ratios.

Let the point be represented with P

The formula to use is:

[tex]P = (\frac{mx_2 + nx_1}{m + n},\frac{my_2 + ny_1}{m + n})[/tex]

Where

[tex]A = (-9,3)[/tex]  ----- [tex](x_1,y_1)[/tex]

[tex]B = (1,8)[/tex] ------ [tex](x_2,y_2)[/tex]

So:

[tex]P = (\frac{mx_2 + nx_1}{m + n},\frac{my_2 + ny_1}{m + n})[/tex]

[tex]P = (\frac{2 * 1 + 3 * -9}{2 + 3},\frac{2 * 8 + 3 * 3}{2 + 3})[/tex]

[tex]P = (\frac{-25}{5},\frac{25}{5})[/tex]

[tex]P = (-5,5)[/tex]

Answer:

x=19

Step-by-step explanation:

x+8=2x-11

-11+11=0

8+11=19

x-x=0

2x-x=x

x=19

Answer:

3.72

Step-by-step explanation

2x3.42=6.82

6.82-3.1=3.72

Answer:

First, substitute y by the value

2(3.41)-3.1

Multiply the bracket by 2

It will be 0.58651026393, so you’ll round it up to make it shorter to make it easy for calculation

0.59-3.1=-2.51

-2.51 is the answer to your question

Step-by-step explanation:

I hope this helped, please give me brainliest

Answer: b

Step-by-step explanation:Step 1: Simplify both sides of the equation.

6x=x2+9

Step 2: Subtract x^2+9 from both sides.

6x−(x2+9)=x2+9−(x2+9)

−x2+6x−9=0

Step 3: Factor left side of equation.

(−x+3)(x−3)=0

Step 4: Set factors equal to 0.

−x+3=0 or x−3=0

Answer:

m=2

Step-by-step explanation:

if that's not how you write it then try y=2x

Answer:

THEY ARE EQUAL =

Step-by-step explanation:

Answer:

AAS (Angle-Angle-Side)

Step-by-step explanation:

Topic: congruence and similarity

If you like to venture further, feel free to check out my insta (learntionary). I'll be constantly posting math tips and notes! Thanks!

Answer:

Angle Angle Side

Step-by-step explanation:

You can see you have two angles next to each other and one side next to that so just see which proof it fits

Hope This Helps

Answer: it would be g because if you distribute 9, you end up with x+72 and the bottom one is 9•8 (also 72)+x

Answer:

increases

Step-by-step explanation:

on on the side, it looks like you need to enter stuff into the table. All you need to do is copy the numbers from the table and transfer them to the empty one.

also this answer just makes sense. If you look at the table, you can see for the x values, they are always increasing. For The y values they are also increasing. Therefore, is the number of hours studying increases the corresponding test scores also increase

Answer:

hey so the answer is m=-4

hope this helps!!~~

Answer:

1 cup of hot chocolate is $2.5

1 slice of pumpkin pie is $2.5

Step-by-step explanation:

Represent Pumpkin Pie with P and Hot Chocolate with C:

Marty:

[tex]2P + 2H = 10[/tex]

Patty:

[tex]4P + 5H = 22.5[/tex]

So, we have the following set of equation:

[tex]2P + 2H = 10[/tex] -------- (1)

[tex]4P + 5H = 22.5[/tex] -------- (2)

Multiply the first equation by 2

[tex]2(2P + 2H = 10)[/tex]

[tex]4P + 4H = 20[/tex] -------- (3)

Subtract (3) from (2)

[tex]4P + 5H = 22.5[/tex]

[tex]4P + 4H = 20[/tex]

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

[tex]5H - 4H = 22.5 - 20[/tex]

[tex]H = 2.5[/tex]

Substitute 2.5 for H in [tex]2P + 2H = 10[/tex]

[tex]2P + 2 * 2.5 = 10[/tex]

[tex]2P + 5 = 10[/tex]

[tex]2P = 10 - 5[/tex]

[tex]2P = 5[/tex]

Divide through by 2

[tex]P = \frac{5}{2}[/tex]

[tex]P=2.5[/tex]

Hence, 1 cup of hot chocolate is $2.5 and 1 slice of pumpkin pie is $2.5