f(x)=-3x+8, find f^-1(x) then state whether f^-1(x) is a function

Answer:

y = -1/4x +4

Step-by-step explanation:

Slope intercept form is

y = mx+b where m is the slope and b is the y intercept

-2x-8y = -32

Add 2x to each side

-2x+2x-8y =2x -32

-8y = 2x-32

Divide each side by -8

-8y/-8 = 2x/-8 -32/-8

y = -1/4x +4

Answer:

68% of buyers paid between $147,700 and $152,300.

Step-by-step explanation:

We are given that prices of a certain model of a new home are normally distributed with a mean of $150,000.

Use the 68-95-99.7 rule to find the percentage of buyers who paid between $147,700 and $152,300 if the standard deviation is $2300.

Let X = prices of a certain model of a new home

SO, X ~ Normal([tex]\mu=150,000 ,\sigma=2,300[/tex])

The z score probability distribution for normal distribution is given by;

                             Z  =  [tex]\frac{X-\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = population mean price = $150,000

            [tex]\sigma[/tex] = standard deviation = $2,300

Now, according to 68-95-99.7 rule;

Around 68% of the values in a normal distribution lies between [tex]\mu-\sigma[/tex] and [tex]\mu-\sigma[/tex].

Around 95% of the values occur between [tex]\mu-2\sigma[/tex] and [tex]\mu+2\sigma[/tex] .

Around 99.7% of the values occur between [tex]\mu-3\sigma[/tex] and [tex]\mu+3\sigma[/tex].

So, firstly we will find the z scores for both the values given;

         Z  =  [tex]\frac{X-\mu}{\sigma}[/tex]  =  [tex]\frac{147,700-150,000}{2,300}[/tex]  = -1

         Z  =  [tex]\frac{X-\mu}{\sigma}[/tex]  =  [tex]\frac{152,300-150,000}{2,300}[/tex]  = 1

This indicates that we are in the category of between [tex]\mu-\sigma[/tex] and [tex]\mu-\sigma[/tex].

SO, this represents that percentage of buyers who paid between $147,700 and $152,300 is 68%.

Approximately 95% of the buyers paid between $147,700 and $152,300.

To find the percentage of buyers who paid between $147,700 and $152,300, we can use the 68-95-99.7 rule for normal distributions. According to this rule, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.

The mean of the prices is $150,000 and the standard deviation is $2,300. The difference between $147,700 and $152,300 is $4,600, which is 2 standard deviations away from the mean. Therefore, we can expect approximately 95% of buyers to have paid between $147,700 and $152,300.

So, approximately 95% of the buyers paid between $147,700 and $152,300.

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Answer:

The mean is the average of the numbers. It is easy to calculate: add up all the numbers, then divide by how many numbers there are. In other words it is the sum divided by the count.

The median is also the number that is halfway into the set. To find the median, the data should be arranged in order from least to greatest. If there is an even number of items in the data set, then the median is found by taking the mean (average) of the two middlemost numbers.

The range of a set of data is the difference between the highest and lowest values in the set. To find the range, first order the data from least to greatest. Then subtract the smallest value from the largest value in the set.

i hope i helped a bit

Step-by-step explanation:

Answer:

22

Step-by-step explanation:

It can be strung 22 ways!!

Answer:

22!

Step-by-step explanation:

The circular permutation formula requires n-1. So the answer is 22!

The length of the 'top' vector is sqrt(3^2 + 3^2) = 3sqrt2

The length of the 'bottom' vector is sqrt(4^2 + 1^2) = sqrt17

Answer:

Quiana has 8 text messages from Pierre.

Step-by-step explanation:

This question can be solved using a rule of three.

Quiana has 7 times more text messages from Yolanda than from Pierre.

This means that for each message that she receives from Pierre, she receives 7 from Yolanda.

She received 56 from Yolanda.

So

7 messages from Yolanda - 1 messages from Pierre

56 messages from Yolanda - x messages from Pierre

[tex]7x = 56[/tex]

[tex]x = \frac{56}{7}[/tex]

[tex]x = 8[/tex]

Quiana has 8 text messages from Pierre.

Quiana has 8 text messages from Pierre.

To find how many text messages Quiana has from Pierre, represented as p, given that Quiana has 7 times more text messages from Yolanda than from Pierre, and she received 56 text messages from Yolanda, we can set up the following equation:

p × 7 = 56

To solve for p, we divide both sides of the equation by 7:

p = 56 ÷ 7

p = 8

So, Quiana has 8 text messages from Pierre.

The correct student is Dean.

To determine which student is correct, let's analyze the information given in the box plots for both classes:

For Mr. Yan's class, the box plot shows:

- Minimum value (lower whisker): 1

- Maximum value (upper whisker): 9

- Lower quartile (Q1): 2

- Median (Q2): 4

- Upper quartile (Q3): 7

- Interquartile range (IQR): Q3 - Q1 = 7 - 2 = 5

For Mrs. Gonzalez's class, the box plot shows:

- Minimum value (lower whisker): 1

- Maximum value (upper whisker): 9

- Lower quartile (Q1): 4

- Median (Q2): 5.5

- Upper quartile (Q3): 7

- Interquartile range (IQR): Q3 - Q1 = 7 - 4 = 3

Now let's evaluate each student's statement:

- Nadine: The medians are the same because both sets of data have the same minimum and maximum values. This statement is incorrect because the medians are different. Mr. Yan's class has a median of 4, while Mrs. Gonzalez's class has a median of 5.5.

- Kendrick: Mr. Yana's class has a greater median because the box in that box plot is larger. This statement is incorrect because the size of the box does not determine the median. The median is the value that divides the data into two equal halves, and it is indicated by the line inside the box.

- Tahara: Mrs. Gonzalez's class has a greater median because the line inside that box is located at a greater value. This statement is correct. The median for Mrs. Gonzalez's class is 5.5, which is greater than the median for Mr. Yan's class, which is 4.

- Dean: The medians are both 7 because the upper quartile for the sets of data is 7. This statement is incorrect because the median is not determined by the upper quartile but by the value that separates the higher half from the lower half of a data sample.

Therefore, the only correct statement is made by Tahara, who correctly identifies that Mrs. Gonzalez's class has a greater median because the line inside the box is located at a greater value (5.5) compared to Mr. Yan's class (4).

Answer:

4x-5y =5

Step-by-step explanation:

First we need to find the slope of the line

m = (y2-y1)/(x2-x1)

   = (0-10)/(0- -8)

   = -10/(0+8)

   -10/8  

   -5/4

We want a line with a perpendicular slope

That line will have a negative reciprocal slope

-1 (-5/4)

4/5

We have the slope and a point

y= mx+b is the slope intercept form of a line

y = 4/5x+b

Substitute the point into the equation

3 = 4/5(5)+b

3 =4+b

b = -1

The equation of the line is y = 4/5x-1

Multiply each  side by 5 to get rid of the fractions

5y = 4x -5

Subtract 4x from each side

-4x+5y = -5

Multiply each side by -1

4x-5y =5

Answer:

4x - 5y = 5

Step-by-step explanation:

Slope of the given line:

(-10-0)/(8-0)

-10/8

-5/4

Slope of the Perpendicular line

4/5

y = ⅘x + c

3 = (4/5)(5) + c

3 = 4 + c

c = -1

y = (4/5)x - 1

5y = 4x - 5

4x - 5y = 5

Answer:180

Step-by-step explanation:

100 - 10 is 90

90 x 2 is 180

I did a reverse calculation you can also check this is correct by knowing that half of 180 is 90 and 100 dollars is 10 more than 90 dollars.

Answer:

  c.  x>1/2

Step-by-step explanation:

Distribute the -2 to eliminate parentheses:

  6x -2x -2 > 0

  4x -2 > 0 . . . . . . combine terms

Now, you can divide by 4:

  x -2/4 > 0

and add 1/2

  x > 1/2 . . . . . matches choice C

Answer:

[tex]x > \frac{1}{2} [/tex]

Answer:

0.5

Step-by-step explanation:

The sample space of a fair six-sided die and a fair four-sided die rolled simultaneously is given below:

[tex](1,1),(1,2),(1,3),(1,4),(1,5),(1,6)\\(2,1),(2,2),(2,3),(2,4),(2,5),(2,6)\\(3,1),(3,2),(3,3),(3,4),(3,5),(3,6)\\(4,1),(4,2),(4,3),(4,4),(4,5),(4,6)\\[/tex]

where in each pair (x,y), x represents the four-sided die and y represents the six sided die.

Total Number of Possible Outcomes =24

Event A is the event that the six-sided die is an even number.

n(A)=12

Therefore, the probability that the six-sided die is an even number:

P(A)=12/24=0.5

Answer: (7,3)

Step-by-step explanation:

The coordinates of point B(7, 3).

The formula below gives the coordinates of the point A(x, y), which internally splits the line segment between the points P([tex]x_1[/tex],  [tex]y_1[/tex]) and Q([tex]x_2[/tex], [tex]y_2[/tex]) in the ratio [tex]m_1[/tex]: [tex]m_2[/tex],

A (x, y) = [tex]((m_1 x_2 + m_2 x_1) / ( m_1 + m_2), \;\; (m_1 y_2 + m_2 y_1) / ( m_1 + m_2)[/tex]

Given:

Point A is (-7, 5) and point M is at (0, 4).

and, Point M is the midpoint of point A and Point B.

A (x, y) = [tex](m_1 x_2 + m_2 x_1) / ( m_1 + m_2)[/tex]

So, x= [tex](m_1 x_2 + m_2 x_1) / ( m_1 + m_2)[/tex]

0 = ( 1 x [tex]x_2[/tex] + 1 x (-7)) / (1 + 1)

0 = [tex]x_2[/tex] - 7

[tex]x_2[/tex] =7

and, y= [tex](m_1 y_2 + m_2 y_1) / ( m_1 + m_2)[/tex]

4= ( 1 x [tex]y_2[/tex] + 1 x 5)/ 2

8 = [tex]y_2[/tex] + 5

[tex]y_2[/tex] = 3

Hence, the coordinates of B(7, 3).

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Answer:

Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \leq[/tex] 250 W  

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 250 W    

Step-by-step explanation:

We are given that an appliance manufacturer claims to have developed a compact microwave oven that consumes a mean of no more than 250 W.

They take a sample of 20 microwave ovens and find that they consume a mean of 257.3 W.

Let [tex]\mu[/tex] = mean power consumption of microwave ovens.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \leq[/tex] 250 W  

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 250 W    

Here, null hypothesis states that the mean power consumption of microwave ovens is no more than 250 W.

On the other hand, alternate hypothesis sates that the mean power consumption of microwave ovens is more than 250 W.

The test statistics that would be used here is One-sample z test statistics as we know about the population standard deviation;

                       T.S. =  [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]  ~ N(0,1)

Hence, this would be the appropriate hypotheses to determine if the manufacturer's claim appears reasonable.

Answer:

D.) 108 in.2

Step-by-step explanation:

Use the equations you know to help you figure this out. It may not be easy, but for you to understand, you need to learn how to do it. If you want work, try it out.. Not to be rude...

Answer:

D) 108 inches squared.

Step-by-step explanation:

When you have the height of a pyramid, you must find the area of the base. Then multiply the base and height. When you find the product, divide this by three. There's your answer.

Answer:

1) b1=5.831

2) b0=12.510

3) y(34)=210.764

4) y(0)=12.510

5) y=12.510+5.831x

6) R^2=0.85

Step-by-step explanation:

We have the linear regression model [tex]y=b_0+b_1 x[/tex].

We start by calculating the all the parameters needed to define the model:

- Mean of x:

[tex]\bar x=\dfrac{1}{5}\sum_{i=1}^{5}(2+3+4+5+7)=\dfrac{21}{5}=4.2[/tex]

- Uncorrected standard deviation of x:

[tex]s_x=\sqrt{\dfrac{1}{n}\sum_{i=1}^{5}(x_i-\bar x)^2}\\\\\\s_x=\sqrt{\dfrac{1}{5}\cdot [(2-4.2)^2+(3-4.2)^2+(4-4.2)^2+(5-4.2)^2+(7-4.2)^2]}\\\\\\ s_x=\sqrt{\dfrac{1}{5}\cdot [(4.84)+(1.44)+(0.04)+(0.64)+(7.84)]}\\\\\\ s_x=\sqrt{\dfrac{14.8}{5}}=\sqrt{2.96}\\\\\\s_x=1.72[/tex]

- Mean of y:

[tex]\bar y=\dfrac{1}{5}\sum_{i=1}^{5}(25+33+34+45+48)=\dfrac{185}{5}=37[/tex]

- Standard deviation of y:

[tex]s_y=\sqrt{\dfrac{1}{n}\sum_{i=1}^{5}(y_i-\bar y)^2}\\\\\\s_y=\sqrt{\dfrac{1}{5}\cdot [(25-37)^2+(33-37)^2+(34-37)^2+(45-37)^2+(48-37)^2]}\\\\\\ s_y=\sqrt{\dfrac{1}{5}\cdot [(144)+(16)+(9)+(64)+(121)]}\\\\\\ s_y=\sqrt{\dfrac{354}{5}}=\sqrt{70.8}\\\\\\s_y=8.414[/tex]

- Sample correlation coefficient

[tex]r_{xy}=\sum_{i=1}^5\dfrac{(x_i-\bar x)(y_i-\bar y)}{(n-1)s_xs_y}\\\\\\r_{xy}=\dfrac{(2-4.2)(25-37)+(3-4.2)(33-37)+...+(7-4.2)(48-37)}{4\cdot 1.72\cdot 8.414}\\\\\\r_{xy}=\dfrac{69}{57.888}=1.192[/tex]

Step 1

The slope b1 can be calculated as:

[tex]b_1=r_{xy}\dfrac{s_y}{s_x}=1.192\cdot\dfrac{8.414}{1.72}=5.831[/tex]

Step 2

The y-intercept b0 can now be calculated as:

[tex]b_o=\bar y-b_1\bar x=37-5.831\cdot 4.2=37-24.490=12.510[/tex]

Step 3

The estimated value of y when x=34 is:

[tex]y(34)=12.510+5.831\cdot(34)=12.510+198.254=210.764[/tex]

Step 4

At x=0, the estimated y takes the value of the y-intercept, by definition.

[tex]y(0)=12.510+5.831\cdot(0)=12.510+0=12.510[/tex]

Step 5

The linear model becomes

[tex]y=12.510+5.831x[/tex]

Step 6

The coefficient of determination can be calculated as:

[tex]R^2=1-\dfrac{SS_{res}}{SS_{tot}}=1-\dfrac{\sum(y_i-f_i)}{ns_y^2}\\\\\\\sum(y_i-f_i)=(25-24.17)^2+(33-30)^2+(34-35.83)^2+(45-41.67)^2+(48-53.33)^2\\\\\sum(y_i-f_i)=0.69+ 8.98+ 3.36+ 11.12+ 28.38=52.53\\\\\\ ns_y^2=5\cdot 8.414^2=353.98\\\\\\R^2=1-\dfrac{52.53}{353.98}=1-0.15=0.85[/tex]

Answer:

a. $ 285,349,947

b.  $ 34,055,227

c. $ 283,294,720 and $ 32,000,000

Step-by-step explanation:

We have the following data as of Jan. 1, 2013:

Cash 283,294,720

Discount on Bonds Payable 36,705,280

Bonds Payable 320,000,000

Now for the date of June 30, 2013, we do the following calculations:

320,000,000 x 10% x 2 = $ 16,000,000 cash payment

interest expense:

283,294,720 carrying value x 6% market rate = 16,997,683

to calculate depreciation:

16,997,683 - 16,000,000 = $ 997,683 discount amortization

Now for the new carrying value of bonds, we do the following:

283,294,720 + 997,683 = 284,292,403

As of Dec. 31, 2013, we have to:

320,000,000 x 10% x 2 = $ 16,000,000 cash payment

interest expense:

284,292,403 carrying value x 6% market rate = 17,057,544

to calculate depreciation:

17,057,544 - 16,000,000 = $ 1,057,544 discount amortization

Now for the new carrying value of bonds, we do the following:

284,292,403 + 1,057,544 = 285,349,947

Answering the questions:

a. The bonds would be listed at their current carrying value, $ 285,349,947

b. Interest Expense : 16,997,683 + 17,057,544 = $ 34,055,227

c. The $ 283,294,720 cash received from the sale of bonds would be added to cash flows under financing activities. The $ 32,000,000 in interest payments would be subtracted from cash flows under operating activities.

The net amount of liability, amount in income statement, and cash outflows related to Myriad Solutions, Inc.’s bonds are all calculated based on semiannual interest payments and the amortization of the discount over the life of the bonds. The carrying value of the bonds increases each year, and the interest expense and cash payments are reported in the financial statements.

To determine the net amount of the liability Myriad Solutions, Inc. would report in its balance sheet at December 31, 2018, we need to calculate the carrying value of the bonds five years after issuance. Assuming the bonds were issued at a discount because the market rate of 12% was higher than the coupon rate of 10%, the discount is being amortized over the life of the bonds. This means the liability in the balance sheet is increasing every year until it reaches the face value at maturity.

The amount related to the bonds that Myriad would report in its income statement for the year ended December 31, 2018, includes the interest expense. Since the interest is paid semiannually, there would be two interest payments in 2018. Each payment would be a portion of the annual 10% coupon rate on the face value of $320 million, adjusted for any amortization of the bond discount over the reporting period.

For the statement of cash flows for the year ended December 31, 2018, Myriad would report the actual cash paid out as interest payments on the bonds. This would total the semiannual payments made on June 30 and December 31, which would be 10% of the $320 million face value divided by two, reflecting that interest is paid semiannually.

Answer:

The answers are in the explanation.

Step-by-step explanation:

a)

X1 -Absolute frecuency -cumulative absolute frequency -Relative frecuency

44                 1                                      1                                              0.021

48                 1                                     2                                              0.021

52                 1                                     3                                              0.021

54                 1                                     4                                              0.021

58                 1                                     5                                              0.021

60                 1                                     6                                              0.021

62                 2                                    7                                              0.042

64                 1                                     8                                              0.021

66                 3                                    12                                              0.063

68                 2                                    14                                             0.042

70                 2                                    16                                             0.042

72                 6                                    22                                              0.126

74                 2                                    24                                             0.042

76                 2                                    26                                             0.042

78                 2                                    28                                             0.042

80                 1                                     29                                             0.021

82                 3                                    32                                              0.063

84                 4                                    36                                             0.084

86                 2                                    38                                             0.042

88                 2                                    40                                             0.042

90                 3                                    43                                              0.063

92                 1                                     44                                             0.021

96                 1                                     45                                             0.021

100                 1                                     46                                             0.021

102                 1                                     47                                             0.021

104                 2                                    49                                             0.042

108                 1                                     50                                             0.021

Total:             50                                   50                                                1

Answer:

33 yd

Step-by-step explanation:

To find the area of a triangle, you can follow the formula:

(base x height) / 2

By putting this formula into context, you can substitute the values of the terms with the information provided in the problem:

(base x height) / 2

(11 yd x 6 yd) / 2

66 yd / 2

33 yd

Answer:

(i) The student who weighed the rock 20 times.

Step-by-step explanation:

The margin of error of a confidence interval is:

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which z is related to the confidence level, [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

From the equation above, the larger the size of the sample, the lower the margin is, that is, the narrower the interval is.

In this question:

A student weighed the rock 20 times and other the 5. From above, the one who weighed the rock 20 times will have the more precise interval.

So the correct answer is:

(i) The student who weighed the rock 20 times.

Answer:

Pi (π) is one of the most important and fascinating numbers in mathematics. Roughly 3.14, it is a constant that is used to calculate the circumference of a circle from that circle's radius or diameter.[1] It is also an irrational number, which means that it can be calculated to an infinite number of decimal places without ever slipping into a repeating pattern.[2] This makes it difficult, but not impossible, to calculate precisely.

Step-by-step explanation:

Pi (π) is one of the most important and fascinating numbers in mathematics. Roughly 3.14, it is a constant that is used to calculate the circumference of a circle from that circle's radius or diameter.[1] It is also an irrational number, which means that it can be calculated to an infinite number of decimal places without ever slipping into a repeating pattern.[2] This makes it difficult, but not impossible, to calculate precisely.

Answer:

a.) 26.2

Step-by-step explanation:

b.)13.8

hope this helps

Answer:

A) 26.2

B)  13.8

Step-by-step explanation:

Perimeter is just adding

Answer:

4/5 and 1

Step-by-step explanation:

4/5 is greater then 3/5 and 5/5=1 whole which is greater than 3/5, 4/5 and 1 is greater than 3/5 and 1 1/5, 1 2/5 so on and so on it could go forever but 4/5, and 1 is the only ones that our after 3/5 so those are the two greatest ones in this quistion.

Hope this helps.

The  two values are 4 by 5 and 1

The following information should be considered:

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Answer:

f(x) = x^2

g(x) = 4*x^2​

=> For a value of x, the g(x) is 4 times larger than f(x).

=> g(x) is the stretched version of f(x) with stretched ratio = 4).

=> Option D is correct

Hope this helps!

:)

Answer:

D

Step-by-step explanation:

The multiple "4" is the stretch factor. The stretch is parallel to y-axis, which is a vertical stretch

Answer:

The sample consisting of 64 data values would give a greater precision.

Step-by-step explanation:

The width of a (1 - α)% confidence interval for population mean μ is:

[tex]\text{Width}=2\cdot z_{\alpha/2}\cdot \frac{\sigma}{\sqrt{n}}[/tex]

So, from the formula of the width of the interval it is clear that the width is inversely proportion to the sample size (n).

That is, as the sample size increases the interval width would decrease and as the sample size decreases the interval width would increase.

Here it is provided that two different samples will be taken from the same population of test scores and a 95% confidence interval will be constructed for each sample to estimate the population mean.

The two sample sizes are:

n₁ = 25

n₂ = 64

The 95% confidence interval constructed using the sample of 64 values will have a smaller width than the the one constructed using the sample of 25 values.

Width for n = 25:

[tex]\text{Width}=2\cdot z_{\alpha/2}\cdot \frac{\sigma}{\sqrt{25}}=\frac{1}{5}\cdot [2\cdot z_{\alpha/2}\cdot \sigma][/tex]        

Width for n = 64:

[tex]\text{Width}=2\cdot z_{\alpha/2}\cdot \frac{\sigma}{\sqrt{64}}=\frac{1}{8}\cdot [2\cdot z_{\alpha/2}\cdot \sigma][/tex]

Thus, the sample consisting of 64 data values would give a greater precision

Answer:

Confidence Interval with sample size 25 = Broader, less precision; Confidence Interval with sample size 64 = Narrower, more precision

Step-by-step explanation:

Confidence Interval is the range around sample statistic, which contains the actual population parameter. Confidence level is the percentage probability, with which the population parameter is expected to be in confidence interval.

When sample size increases : the margin of error, ie sampling error between population parameter & sample statistic decreases. The reduced margin of error increases the level of confidence & precision in confidence interval range. So, the confidence interval range becomes narrower.  

Hence, confidence interval becomes narrower & has more precision, when sample size increases from sample number = 25 to sample number = 64.

2 mile per hour

Step-by-step explanation:

I use the equation :

[tex] \frac{ \frac{1}{2} }{ \frac{1}{4} } = \frac{x}{1} \\ x = \frac{ \frac{1}{2} \times 1}{ \frac{1}{4} } \\ x = \frac{ \frac{1}{2} }{ \frac{1}{4} } \\ x = \frac{1}{2} \times \frac{4}{2} \\ x = \frac{4}{2} \\ x = 2 \: mile[/tex]

So, she walked 2 mile per hour

Hope it helpful and useful :)

Answer:

a 0.5

b 0.4831

c 0.4354 < P < 0.53008

Step-by-step explanation:

Given that :

Probability (P) of a head or a tail when a coin is being tossed or flipped = 1/2 = 0.5

Sample size (n) = 296

Selected sample (X) = 143

a) Given that Emily used a coin toss to select either her right hand or her left hand, what proportion of correct responses would be expected if the touch therapists made random guesses?

The  proportion of correct responses that would be expected if the touch therapists made random guesses is 0.5

b) Using Emily's sample results, what is the best point estimate of the therapists' success rate?

Point estimate [tex](p') = \frac{X}{n}[/tex]

= [tex](p') = \frac{143}{296}[/tex]

= 0.4831

c) Using Emily's sample results, construct a 90% confidence interval estimate of the proportion of correct responses made by touch therapists.

The [tex]Z_c[/tex] for 90% is 1.645

Using the formula P" -E < P < P" + E

where E = margin of error :  [tex]Z_c * \sqrt{\frac{P(1-P)}{n} }[/tex]

[tex]=1.645 * \sqrt{\frac{0.4831(0.5169)}{296} }[/tex]

[tex]=1.645 * \sqrt{\frac{0.2497}{296} }[/tex]

[tex]=1.645*0.029[/tex]

= 0.0477

∴ P" -E < P < P" + E

= 0.4831 - 0.0477 < P < 0.4831 + 0.0477

= 0.4354 < P < 0.53008

Answer:

The proportion of correct responses would be in between [tex](0.4345)<P<(0.53008)[/tex]

Step-by-step explanation:

Given information:

Sample size [tex](n)=296[/tex]

Selected sample [tex](x) =143[/tex]

Probability of head or tail will be 0.5 because a coin is tossed.

So the proportion of correct responses if the therapist made random decision will be 0.5.

Now with the help of sample result:

Point estimate:

[tex](p)'=x/n\\(p')=143/296\\(p')=0.4831[/tex]

Now, if we take confidence level of 90%

Then, [tex]Z=1.645[/tex]

As,

[tex](P"-E)<(P)<(P"+E)[/tex]

Where , E is the margin of error.

[tex]E=Z \times \sqrt \frac{P(1-P)}{n} \\E=1.654 \times \sqrt \frac{(0.4831 \times0.5169}{296} \\E=1.645\times 0.029\\E=0.0477[/tex]

Therefore:

[tex](P"-E)<(P)<(P"+E)[/tex]

[tex](0.4831-0.0477)<P<(0.4831+0.0477)\\(0.4345)<P<(0.53008)[/tex]

Hence, the proportion of correct responses would be in between [tex](0.4345)<P<(0.53008)[/tex].

For more information visit:

https://brainly.com/question/14677517?referrer=searchResults

Answer: 947

Step-by-step explanation:

71 x 8 = 568

568 + 379 = 947

Answer = 947

Answer:

947

Step-by-step explanation

multiply 71 and 8 then add 379

Answer: P= 0.174

Step-by-step explanation:

Using the principle of probability, the probability of obtaining a green and round block from the toy box would be 0.174

P(green and round) can be interpreted as P(GREEN n ROUND)

From the table given :

Recall :

Hence, P(green and round) = 4/23 = 0.1739 = 0.174

Learn more : https://brainly.com/question/14375199

Answer:

Step-by-step explanation:

Let x represent the quantity (in liters) of the higher percentage solution, the 0.23% solution. Then 1-x will be the quantity of 0.03% solution. The amount of salt in the mix is ...

  0.23%·x +0.03%·(1 -x) = 0.18%·1

Multiply by 100% and subtract 3:

  20x = 15

  x = 15/20 = 0.75 . . . . liters of 0.23% solution

  1-x = 1-0.75 = 0.25 . . liters of 0.03% solution

The lab tech needs 750 mL of 0.23% solution and 250 mL of 0.03% solution.

Answer:

25.1

Step-by-step explanation:

area = pi x r x r

r x r = 50.3 / pi = 16.0109

r = 4.00137

circumference = pi x 2 x r = pi x 2 x 4.00137 = 25.141