Answer:
20.9105
Step-by-step explanation:
8.0425
2.6
80425*26=2091050
there is 5 decimals so you move the decimal over to the left 5 times
20.9105 :)
The average daily volume of a computer stock in 2011 was ų=35.1 million shares, according to a reliable source. A stock analyst believes that the stock volume in 2014 is different from the 2011 level. Based on a random sample of 30 trading days in 2014, he finds the sample mean to be 32.7 million shares, with a standard deviation of s=14.6 million shares. Test the hypothesis by constructing a 95% confidence interval. Complete a and b A. State the hypothesis B. Construct a 95% confidence interval about the sample mean of stocks traded in 2014.
Answer:
a
The null hypothesis is [tex]H_o : \mu = 35 .1 \ million \ shares[/tex]
The alternative hypothesis [tex]H_a : \mu \ne 35.1\ million \ shares[/tex]
b
The 95% confidence interval is [tex]27.475 < \mu < 37.925[/tex]
Step-by-step explanation:
From the question the we are told that
The population mean is [tex]\mu = 35.1 \ million \ shares[/tex]
The sample size is n = 30
The sample mean is [tex]\= x = 32.7 \ million\ shares[/tex]
The standard deviation is [tex]\sigma = 14.6 \ million\ shares[/tex]
Given that the confidence level is [tex]95\%[/tex] then the level of significance is mathematically represented as
[tex]\alpha = 100-95[/tex]
[tex]\alpha = 5\%[/tex]
=> [tex]\alpha = 0.05[/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} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{ \sigma }{\sqrt{n} }[/tex]
substituting values
[tex]E = 1.96 * \frac{ 14.6 }{\sqrt{30} }[/tex]
[tex]E = 5.225[/tex]
The 95% confidence interval confidence interval is mathematically represented as
[tex]\= x -E < \mu < \= x +E[/tex]
substituting values
[tex]32.7 - 5.225 < \mu < 32.7 + 5.225[/tex]
[tex]27.475 < \mu < 37.925[/tex]
Suppose that you are standing 150 feet from a building and the angle of elevation to the top of the building is 42°. What is the building's height?
Answer:
135.06 feet
Step-by-step explanation:
Since the side of the building makes a right triangle with the ground and you know one side length and the degree angle between you and the top of the building we can use trigonometric function to find the height of the building. So since we know one side other than the hypotenuse we can use tangent to solve. Tangent is the opposite side over the adjacent side of the known angle.
opposite side = x
adjacent side = 150 feet
angle = 42°
tan(42°) = x/150 feet
150 feet * tan(42°) = x
x = 135.06 feet
qaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
Answer:
32.8 miles
Step-by-step explanation:
Amy is driving to Seattle. Suppose that the remaining distance to drive (in miles) is a linear function of her driving time (in minutes). When graphed, the function gives a line with a slope of -0.95. See the figure below. Amy has 48 miles remaining after 31 minutes of driving. How many miles will be remaining after 47 minutes of driving?
Answer: The general equation of a line is given as y = mx + c, where m is the slope of the line and c is the intercept on the y axis. Given that the slope is -0.95, substituting in the general equation :
y = -0.95x + c
Amy has 48 miles remaining after 31 minutes of driving, to find c, we substitute y = 48 and x = 31. Therefore:
48 = -0.95(31) + c
c = 48 + 0.95(31)
c = 48 + 29.45
c = 77.45
The equation of the line is
y = -0.95x + 77.45
After 47 minutes of driving, the miles remaining can be gotten by substituting x = 47 and finding y.
y = -0.95(47) + 77.45
y = -44.65 + 77.45
y = 32.8 miles
A racecar is traveling at a constant speed of 150 miles per hour. How many feet does it travel in 5 seconds? Remember that 1 mile is 5280 feet.
Answer:
distance covered in 5 seconds
= 1.4283 *10^10 feet
Step-by-step explanation:
A racecar is traveling at a constant speed of 150 miles per hour.
One mile = 5280 feet
150 miles= 5290*150
150 miles= 793500 feet
A racecar is traveling at a constant speed of 793500 feet per hour.
Converting 793500 feet per hour to feet per seconds .
793500 feet per hour
= 793500*60*60 feet per seconds
=2856600000 feet per second
In 5 seconds , distance covered
= 2856600000 *5
distance covered in 5 seconds
= 1.4283 *10^10 feet
An ice cream store makes 144 quarts of ice cream in 8 hours. How many quarts could be made in 12 hours?
Hey there! I'm happy to help!
We know that the ice cream store makes 144 quarts in eight hours. What about in one hour? Let's divide this by eight to find out.
144/8=18
So, they make 18 quarts every hour. We want to figure out how many can be made in 12 hours. So, we just multiply 18 by 12!
18(12)=216
Therefore, 216 quarts of ice cream could be made in 12 hours.
Have a wonderful day! :D
The ice cream store will make 216 quarts of ice cream in 12 hours.
What is division?Division is breaking a number up into an equal number of parts.
Given that, An ice cream store makes 144 quarts of ice cream in 8 hours.
Since, they make 144 quarts of ice cream in 8 hours
Therefore, in 1 hour they will make = 144/8 = 18 quarts
So, in 12 hours = 18x12 = 216 quarts.
Hence, The ice cream store will make 216 quarts of ice cream in 12 hours.
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Let R be a system consisting of rational expressions. Which operations are closed for R?
Answer:
D
Step-by-step explanation:A set is said to be closed under an operation when the application of the operation between any two elements of the set leads to an element that belongs to the same set. If a set is closed under an operation, it is said to have the closure property of that operation. When we combine two rational expressions by adding, subtracting, multiplying, or dividing, we get a rational expression. This pattern indicates that rational expressions are closed for all four operations.
Suppose you do not know the population mean fee charged to H&R Block customers last year. Instead, suppose you take a sample of size n-8 and find a sample mean of 350. Assume that the distribution for fees is normally distributed with a sample standard deviation of $100.
i. Before conducting the survey, suppose you believed based on your previous observations, your best guess for population standard deviation of fee charged to H&R Block is $50. With this assumption in mind, What should your sample size n approximately be if you want:
Margin-of-Error of to be 2 % and confidence level to be 95 %?
Margin-of-Error of to be 4% and confidence level to be 95%?
Margin-of-Error of to be 4 % and confidence level to be 99%?
ii. 90% confidence interval for the population mean of fees H&R Block.
a. Calculate the margin of error (MOE) of x using a 10% significance level.
b. Calculate the 90 % confidence interval.
c. Suppose an analyst belief that the population mean fee is equal to $185. Using a 90% confidence level. can we conclude the analyst is right? Why or why not?
Answer:
i [tex]\to[/tex] a
[tex]n = 96040000[/tex]
i [tex]\to[/tex] b
[tex]n_1 =24010000[/tex]
i [tex]\to[/tex] c
[tex]n_2 =41602500[/tex]
ii[tex]\to[/tex]a
[tex]E = 58.16[/tex]
ii[tex]\to[/tex]b
[tex]291.84 < \mu < 408.16[/tex]\
ii[tex]\to[/tex]c
There is insufficient evidence to conclude that the analyst is right because the population mean fee by the analyst does not fall within the confidence interval
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 8[/tex]
The sample mean is [tex]\= x = \$ 350[/tex]
The sample standard deviation is [tex]\$ 100[/tex]
Considering question i
i [tex]\to[/tex] a
At [tex]E = 0.02[/tex]
given that the confidence level is 95% = 0.95
the level of significance would be [tex]\alpha =1-0.95 = 0.05[/tex]
The critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table is
[tex]Z_{\frac{ \alpha }{2} } = 1.96[/tex]
So the sample size is mathematically evaluated as
[tex]n = [ \frac{Z_{\frac{\alpha }{2} } * \sigma }{E} ]^2[/tex]
=> [tex]n =[ \frac{ 1.96 * 100}{ 0.02} ]^2[/tex]
=> [tex]n = 96040000[/tex]
i [tex]\to[/tex] b
At [tex]E_1 = 0.04[/tex] and confidence level = 95% => [tex]\alpha_1 = 0.05[/tex] => [tex]Z_{\frac{\alpha_1 }{2} } = 1.96[/tex]
[tex]n_1 = [ \frac{Z_{\frac{\alpha_2 }{2} } * \sigma }{E_1} ]^2[/tex]
=> [tex]n_1 =[ \frac{ 1.96 * 100}{ 0.04} ]^2[/tex]
=> [tex]n_1 =24010000[/tex]
i [tex]\to[/tex] c
At [tex]E_2 = 0.04[/tex] confidence level = 99% => [tex]\alpha_2 = 0.01[/tex]
The critical value of [tex]\frac{\alpha_2 }{2}[/tex] from the normal distribution table is
[tex]Z_{\frac{ \alpha_2 }{2} } = 2.58[/tex]
=> [tex]n_2 = [ \frac{Z_{\frac{\alpha_2 }{2} } * \sigma }{E_2} ]^2[/tex]
=> [tex]n_2 =[ \frac{ 2.58 * 100}{ 0.04} ]^2[/tex]
=> [tex]n_2 =41602500[/tex]
Considering ii
Given that the level of significance is [tex]\alpha = 0.10[/tex]
Then the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table is
[tex]Z_{\frac{\alpha }{2} } = 1.645[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
substituting values
[tex]E = 1.645 * \frac{100 }{\sqrt{8} }[/tex]
[tex]E = 58.16[/tex]
Generally the 90% confidence interval is mathematically evaluated as
[tex]\= x - E < \mu < \= x + E[/tex]
=> [tex]350 - 58.16 < \mu < 350 + 58.16[/tex]
=> [tex]291.84 < \mu < 408.16[/tex]
So the interpretation is that there is 90% confidence that the mean fee charged to H&R Block customers last year is in the interval .So there is insufficient evidence to conclude that the analyst is right because the population mean fee by the analyst does not fall within the confidence interval.
12) A traffic control engineer reports that 75% of the vehicles passing through a checkpoint are from within the state. What is the probability that fewer than 4 of the next 9 vehicles are from out of state
Answer:
0.8343
Step-by-step explanation:
From the question, we have the following values:
Probability of vehicles that pass within the check point that are from within the state = 75% = 0.75
Probability of vehicles that pass within the check point that are from outsode the state = 100 - 75 = 25% = 0.25
P = 0.25
n = number of random variables = 9
The probability that fewer than 4 of the next 9 vehicles are from out of state is calculated as:
P < 4 = P ≤ 3
n = 9
P(x) = n!/(n - x)! x! × p^x × q^(n - x)
x = 3
p = 0.25
q = 0.75
P(x) = 9! /(9 - 3)! × 3! × 0.25^3 × 0.75^(9 - 3)
P(x) =0.8343
The probability that fewer than 4 (x<4) of the next 9 vehicles are from out of state is 0.83427.
Given information:
75% of the vehicles passing through a checkpoint are from within the state.
So, the probability that the vehicle is from within the state is 0.75.
The probability that the vehicle is from outside the state will be 1-0.75=0.25.
Now, let x be the random variable. So, the value of n=9. and x<4
It is required to calculate the probability that fewer than 4 of the next 9 vehicles are from out of state.
So, [tex]x< 4[/tex], p=0.25 and q=0.75.
So, the required probability can be calculated as,
[tex]P(x\le3) =\sum ^nC_x\times p^x \times q^{(n - x)}\\P(x\le3)=\sum\dfrac{n!}{(n - x)! x!} \times p^x \times q^{(n - x)}\\P(x\le3)= \dfrac{9!}{(9 - 3)! 3!} \times 0.25^3 \times 0.75^{(9 - 3)}+\dfrac{9!}{(9 - 2)! 2!} \times 0.25^2 \times 0.75^{(9 - 2)}+\dfrac{9!}{(9 - 1)! 1!} \times 0.25^1 \times 0.75^{(9 - 1)}+\dfrac{9!}{(9 - 0)! 0!} \times 0.25^0 \times 0.75^{(9 - 0)}\\P(x\le3)=0.83427[/tex]
Therefore, the probability that fewer than 4 of the next 9 vehicles are from out of state is 0.83427.
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State whether the data described below are discrete or continuous, and explain why.
The widths (in centimeters) of different paintings in an art museum
nothing
Choose the correct answer below.
A. The data are continuous because the data can only take on specific values.
B. The data are discrete because the data can only take on specific values.
C. The data are discrete because the data can take on any value in an interval.
D. The data are continuous because the data can take on any value in an interval.
The length of a rectangle is twice its width. If the perimeter of the rectangle is 30m, find its area.
Answer:
If the perimeter of the rectangle is 30cm , find its area. W=5 FOR THE WIDTH. 5*10=50 FOR THE AREA.
Step-by-step explanation:
The area of the Rectangle is 50 sq.m
What is the formula of Area of Rectangle?The area of rectangle for a rectangle of length L and width W is given by
A = L* W
It is measured in square units.
Let the length of the rectangle be L
The width of the rectangle is W
The length of a rectangle is twice its width
L = 2W
Perimeter of the Rectangle is 2( Length + Width)
30 = 2 (L +W)
15 = L + W
15 = 2W +W
15 = 3W
W = 5m
L = 10m
The area of the rectangle is Length * Width
Area = 10 *5
Area = 50 sq.m
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A cubical sandbox has a volume of 91.125 cubic inches. What is the side length of the
sandbox?
Hey there! I'm happy to help!
To find the volume of a cube, you simply cube the side length (multiply it by itself three times). This is because all of the sides of a cube are the same and if you multiply the length by the width by the height it is the same number multiplied by itself three times.
We already know that the volume is 91.125 cubic inches. To find the side length, we simply do the cube root on our calculator, which tells us what number we cube to get 91.125.
∛91.125=4.5
Therefore, the side length of the sandbox is 4.5 inches.
I hope that this helps! Have a wonderful day! :D
In the diagram, ∆ABC and ∆DBE are similar. What is the scale factor of the dilation that will map the preimage ΔABC onto the image ΔDBE? A. 1.33 B. 0.75 C. 0.66 D. 0.55
Answer:
B
Step-by-step explanation:
Calculate the ratio of corresponding sides, image to preimage, that is
scale factor = [tex]\frac{DE}{AC}[/tex] = [tex]\frac{12.09}{16.12}[/tex] = 0.75 → B
The scale factor of the dilation will be 1.33. Then the correct option is A.
What is dilation?Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.
There is no effect of dilation on the angle.
In the diagram, ∆ABC and ∆DBE are similar.
Then the scale factor of the dilation that will map the preimage ΔABC onto the image ΔDBE will be
⇒ 16.12 / 12.09
⇒ 1.33
Then the correct option is A.
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Translate the statements into a confidence interval for p. Approximate the level of confidence. In a survey of 8451 U.S. adults, 31.4% said they were taking vitamin E as a supplement. The survey's margin of error is plus or minus 1%.
Answer:
The confidence interval is [tex]0.304 < p < 0.324[/tex]
Step-by-step explanation:
From the question we are told
The sample proportion [tex]\r p = 0.314[/tex]
The margin of error is [tex]E = 0.01[/tex]
The confidence interval for p is mathematically represented as
[tex]\r p - E < p < \r p + E[/tex]
=> [tex]0.314 - 0.01 < p < 0.314 + 0.01[/tex]
=> [tex]0.304 < p < 0.324[/tex]
Answer two questions about Equations A and B: A.5x=20 \ B.x=4 1) How can we get Equation B from Equation A? Choose 1 answer: (Choice A) Multiply/divide both sides by the same non-zero constant (Choice B,) Multiply/divide both sides by the same variable expression (Choice C) Add/subtract the same quantity to/from both sides (Choice D) Add/subtract a quantity to/from only one side
Answer:
Multiply/divide both sides by the same non-zero constant
Step-by-step explanation:
5x = 20
Divide each side by 5
5x/5 = 20/5
x = 4
To obtain (B) from (A) "Multiply/divide both sides by the same non-zero constant"
Given the equations :
5x = 20 ___ (A)x = 4 _____ (B)To obtain the value ; x = 4 from A
We multiply (A) by the same non-zero constantHere, the constant value which can be used is 5 in other to isolate 'x'
5x/5 = 20/5
x = 4
Therefore, to obtain (B) from (A) "Multiply/divide both sides by the same non-zero constant"
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Mathematical induction is:
Answer:
The third option.
Step-by-step explanation:
Mathematical induction is a 2 step mathematical technique which is used to prove a statement, a formula or a theorem is true for every natural number.
Step 1 (Base step) - It proves that a statement is true for the initial value.
Step 2 (Inductive step) - It proves that if the statement is true for the nth iteration (or number n), then it is also true for (n + 1)th iteration (or number n + 1)
Hope this helps.
Please mark Brainliest.
Answer:
A method of improving statments
Step-by-step explanation:
"Mathematical Induction is a mathematical technique which is used to prove a statement, a formula or a theorem is true for every natural number."
Each corner of a rectangular prism is cut off. Two (of the eight) cuts are shown. How many edges does the new figure have? Assume that the planes cutting the prism do not intersect anywhere in or on the prism. EXPLAIN PLS
Answer:
36
Step-by-step explanation:
Each cut creates a triangular face where the corner used to be. That face adds three edges to the figure. The 8 cuts add a total of 8×3 = 24 edges to the 12 edges the prism already had.
The new figure has 12+24 = 36 edges.
Oregon State University is interested in determining the average amount of paper, in sheets, that is recycled each month. In previous years, the average number of sheets recycled per bin was 59.3 sheets, but they believe this number may have increase with the greater awareness of recycling around campus. They count through 79 randomly selected bins from the many recycle paper bins that are emptied every month and find that the average number of sheets of paper in the bins is 62.4 sheets. They also find that the standard deviation of their sample is 9.86 sheets. What is the value of the test-statistic for this scenario
Answer:
The test statistic is [tex]t = 2.79[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 59.3[/tex]
The sample size is [tex]n = 79[/tex]
The sample mean is [tex]\= x = 62.4[/tex]
The standard deviation is [tex]\sigma = 9.86[/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{\= x - \mu }{ \frac{ \sigma}{ \sqrt{n} } }[/tex]
substituting values
[tex]t = \frac{ 62.2 - 59.3 }{ \frac{ 9.86}{ \sqrt{ 79} } }[/tex]
[tex]t = 2.79[/tex]
An inequality is shown: −np − 4 ≤ 2(c − 3) Which of the following solves for n?
Answer:
[tex]\huge\boxed{n\leq\dfrac{2-2c}{p}\ \text{for}\ p<0}\\\boxed{n\geq\dfrac{2-2c}{p}\ \text{for}\ p>0}[/tex]
Step-by-step explanation:
[tex]-np-4\leq2(c-3)\qquad\text{use the distributive property}\\\\-np-4\leq2c-6\qquad\text{add 4 to both sides}\\\\-np\leq2c-2\qquad\text{change the signs}\\\\np\geq2-2c\qquad\text{divide both sides by}\ p\neq0\\\\\text{If}\ p<0,\ \text{then flip the sign of inequality}\\\boxed{n\leq\dfrac{2-2c}{p}}\\\text{If}\ p>0 ,\ \text{then}\\\boxed{n\geq\dfrac{2-2c}{p}}[/tex]
Given a population with a mean of µ = 100 and a variance of σ2 = 1600, the central limit theorem applies when the sample size is n ≥ 25. A random sample of size n = 50 is obtained. • What are the mean and variance of the sampling distribution for the sample means? • What is the probability that ¯X > 110?
Answer:
The probability that the sample mean is more than 110 is 0.0384.
Step-by-step explanation:
According to the Central Limit Theorem if we have an unknown population with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from the population with replacement, then the sampling distribution of the sample mean will be approximately normally distributed.
Then, the mean of the sampling distribution of sample mean is given by:
[tex]\mu_{\bar x}=\mu[/tex]
And the variance of the sampling distribution of sample mean is given by:
[tex]\sigma^{2}_{\bar x}=\frac{\sigma^{2}}{n}[/tex]
The information provided is:
[tex]n=50\\\\\mu=100\\\\\sigma^{2}=1600[/tex]
Since n = 50 > 30, the central limit theorem can be applied to approximate the sampling distribution of sample mean by the normal distribution.
The mean variance of the sampling distribution for the sample mean are:
[tex]\mu_{\bar x}=\mu=100\\\\\sigma^{2}_{\bar x}=\frac{\sigma^{2}}{n}=\frac{1600}{50}=32[/tex]
That is, [tex]\bar X\sim N(100, 32)[/tex].
Compute the probability that the sample mean is more than 110 as follows:
[tex]P(\bar X>110)=P(\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}>\frac{110-100}{\sqrt{32}})[/tex]
[tex]=P(Z>1.77)\\=1-P(Z<1.77)\\=1-0.96164\\=0.03836\\\approx 0.0384[/tex]
*Use a z-table.
Thus, the probability that the sample mean is more than 110 is 0.0384.
Question 1 (Multiple Choice Worth 4 points)
(08.01) Looking at the spread of your data best fits which step of the statistical process?
Answer:
The answer is "Analysis the information by chart and number processes".
Step-by-step explanation:
They already have articulated a query and also gathered information unless you are searching only at the distribution of your results. Those who are ready to analyze your results for all are there.
The development of AstroWorld ("The Amusement Park of the Future") on the outskirts of a city will increase the city's population at the rate given below in people/year t yr after the start of construction. 5,700 t 11,000 The population before construction is 67,000. Determine the projected population 16 yr after construction of the park has begun. people
Complete question :
The development of AstroWorld ("The Amusement Park of the Future") on the outskirts of a city will increase the city's population at the rate given below in people/year t yr after the start of construction. 5,700√t + 11,000 The population before construction is 67,000. Determine the projected population 16 yr after the construction of the park has begun. people
Answer:
486,200
Step-by-step explanation:
Given that the rate of change in population is represented by the function:
f(t) = 5,700√t + 11,000
To get the original function, we take the integral of the rate function because the rate of change is obtained by taking the derivate of the original equation
f(t) = 5,700t^1/2 + 11,000
Taking the integral of f with respect to t:
∫(5,700t^1/2 + 11,000)
[5700t^(1/2 + 1)] / (1/2 + 1) + 11000t + C
[(5700t^3/2)/ 3/2] + 11000t + C
Where C = constant
If population before construction = 67000
Then C = 67000
t = time = 16 years
Substitute values into the original change equation:
[(5700(16)^3/2)/ 3/2] + 11000t + 67000
[(5700 * 64) / 1.5] + 11000(16) + 67000
243200 + 176000 + 67000
= 486,200
An operator wants to determine the standard deviation for a machine relative to its ability to produce windshield wipers conforming within their specifications. To do this, she wants to create a p-chart. Over a month's time, she tests 100 units every day and records the number of manufacturing defects. The average proportion of non-conforming windshield wipers is found to be 0.042. What is the standard deviation of this sample
Answer:
the standard deviation of the sample is less than 0.1
Step-by-step explanation:
Given that :
The sample size n = 100 units
The average proportion of non-conforming windshield wipers is found to be 0.042 which is the defective rate P-bar
The standard deviation of the machine([tex]S_p[/tex]) can be calculated by using the formula:
[tex]S_p =\dfrac{ \sqrt{ \overline P \times (1 - \overline P)} }{n}[/tex]
[tex]S_p =\dfrac{ \sqrt{0.042 \times (1 -0.042)} }{100}[/tex]
[tex]S_p =\dfrac{ \sqrt{0.042 \times (0.958)} }{100}[/tex]
[tex]S_p =\dfrac{ \sqrt{0.040236} }{100}[/tex]
[tex]S_p =\dfrac{ 0.2005891323 }{100}[/tex]
[tex]S_p =0.002[/tex]
Thus , the standard deviation of the sample is less than 0.1
A website developer wished to analyze the clicks per day on their newly updated website. Let the mean number of clicks per day be μ. If the website developer wants to know if the number of clicks per day is different than 200 clicks a day, on average, what are the null and alternative hypotheses?
Answer:
Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 200 clicks a day
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu\neq[/tex] 200 clicks a day
Step-by-step explanation:
We are given that a website developer wished to analyze the clicks per day on their newly updated website.
The website developer wants to know if the number of clicks per day is different than 200 clicks a day, on average.
Let [tex]\mu[/tex] = mean number of clicks per day.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 200 clicks a day
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu\neq[/tex] 200 clicks a day
Here, the null hypothesis states that the mean number of clicks per day is 200 clicks a day.
On the other hand, the alternate hypothesis states that the mean number of clicks per day is different than 200 clicks a day.
Hence, this is the correct null and alternative hypotheses.
Answer: Null Hypothesis [tex]H_0:\mu=200[/tex]
Alternate Hypothesis[tex]H_a:\mu\neq200[/tex]
Step-by-step explanation:
Let [tex]\mu[/tex] be the mean number of clicks per day.
Given, a website developer wished to analyze the clicks per day on their newly updated website.
The website developer wants to know if the number of clicks per day is different than 200 clicks a day, on average.
i.e. he wants to check either [tex]\mu=200\text{ or }\mu\neq 200[/tex]
Since a null hypothesis is a hypothesis believes that there is no difference between the two variables whereas an alternative hypothesis believes that there is a statistically significant difference between two variables.
So, Null Hypothesis [tex]H_0:\mu=200[/tex]
Alternate Hypothesis[tex]H_a:\mu\neq200[/tex]
Hence, the required null and alternative hypotheses.
Null Hypothesis [tex]H_0:\mu=200[/tex]
Alternate Hypothesis[tex]H_a:\mu\neq200[/tex]
The report "Teens and Distracted Driving: Texting, Talking and Other Uses of the Cell Phone Behind the Wheel" summarizes data from a survey of a representative sample of 800 teens between the ages of 12 and 17. The following statements were made on the basis of the resulting data.
- 75% of all American teens own a cellphone
- 66% of all American teens use a cellphone to send a receive text messages
- 26% of American teens age 16-17 have used a cellphone to text while driving
Required:
a. Is the inference made one that involves estimation or one that involved hypothesis testing?
b. What is the population of interest? American teenagers? American teenagers between ages 12-17? Americans? Teenagers?
Answer:
"Teens and Distracted Driving: Texting, Talking and Other Uses of the Cell Phone Behind the Wheel"
a. The inference made involves estimation. The question provided that the statements were made on the basis of the resulting data and not on the basis of some hypothesis testing.
This implies that some statistics were calculated from sample data to approximate the population parameter, as shown in the statements. The statements were not an attempt to establish the statistical significance of some claims.
b. The population of interest is American teenagers between 12-17.
Step-by-step explanation:
An inference from data is a statistical estimation by which some statistics are calculated based on the sample data of 800 teens between the ages of 12 and 17. The statistics serve as an approximation to the population parameter.
Inference based on hypothesis testing establishes if a claim has statistical significance by providing statistical evidence in favor of the claim or against it.
In kickboxing, it is found that the force, f, needed to break a board, varies inversely with the length, l, of the board. If it takes 7 pounds of pressure to break a board that is 3 feet long, how long is a board that requires 5 pounds of pressure to break?
Answer:
4.2
Step-by-step explanation:
f varies inversly with L can be translated matimatically as:
● f = k/L
It takes 7 pounds of pressure to break a 3 feet long board.
Replace f by 7 and L by 3.
● 7 = k/3 => k=7×3=21
■■■■■■■■■■■■■■■■■■■■■■■■■■
Let's find tge length of a board that takes 5 pounds of pressure to be broken.
● 5 = k/L
● 5 = 21/L
● L = 21/5 = 4.2
So the board is 4.2 feet long
Find the solution of the inequality 5 > r - 3.
A) r<2
B) r = 2
C) r=8
(D) r < 8
Answer:
[tex]\huge\boxed{r<8}[/tex]
Step-by-step explanation:
[tex]5 > r - 3[/tex]
Adding 3 to both sides
[tex]5 + 3 > r[/tex]
[tex]8 > r\\OR \\r < 8[/tex]
Answer: D. r<8
Step-by-step explanation:
[tex]5>r-3[/tex]
add 3 to both sides
[tex]r-3+3<5+3[/tex]
[tex]5+3=8[/tex]
simplify
[tex]r<8[/tex]
A projectile is fired vertically upward from a height of 300
300
feet above the ground, with an initial velocity of 900
900
ft/sec. Recall that projectiles are modeled by the function h(t)=−16t2+v0t+y0
h
(
t
)
=
−
16
t
2
+
v
0
t
+
y
0
. Write a quadratic equation to model the projectile's height h(t)
h
(
t
)
in feet above the ground after t seconds.
Step-by-step explanation:
It is given that, a projectile is fired vertically upward from a height of 300 feet above the ground, with an initial velocity of 900 ft/s.
The general equation with which a projectile are modled by the function is given by :
[tex]h(t)=-16t^2+v_ot+y_o[/tex]
y₀ is the initial height above the ground
v₀ = initial velocity
So,
[tex]h(t)=-16t^2+900t+300[/tex]
This is the quadratic equation that models the projectile height in feet above the ground after t seconds.
What is the solution to the system of equations? -2x-3y+z=-6, z=6, 3x-y+z=13
Answer:
B is the correct answer.
Step-by-step explanation:
-2x+3y+z=-6
z=6
-2x+3y+6=-6
-2x+3y=-12
-2(3)+3(2)
-6+6=0 A is incorrect
-2(3)+3(-2)=-12
-6-6=-12
B is the correct answer.
I am not going to show C or D, because you have the right answer. Hope this helps you. Thank you.
(II) Time intervals measured with a stopwatch typically have an uncertainty of about 0.2 s, due to human reaction time at the start and stop moments.What is the percent uncertainty of a hand-timed measurement of (a) 5.5 s, (b) 55 s, (c) 5.5 min?
Answer:
(a) 36.36%
(b) 0.36%
(c) 0.06%
Step-by-step explanation:
Given that the time intervals measured with a stopwatch have an uncertainty of about 0.2 s.
We want to know what is the percent uncertainty of a hand-timed measurement of:
(a) 5.5 s
Percentage = (0.2/5.5) × 100
≈ 36.36%
(b) 55 s
Percentage = (0.2/55)×100
≈ 0.36%
(c) 5.5 min
5.5 min = 5.5 × 60 s
= 330 s
Percentage = (0.2/330)×100
≈ 0.06%
one of these marbles is picked at random. what is the probability that a blue marble is picked?
A.1/3
B.2/5
C.1/2
D.1/4
Answer:
1/3
Step-by-step explanation:
there are twelve marbles total. there are 4 blue marbles.
4/12 = 1/3
