The equation of the parabola is y -5 = (5/6) (x - 2)^2
How do you define a parabola?a curve produced by the intersection of a cone's surface with a plane perpendicular to a straight line; a curve produced by a moving point whose distance from a fixed point is equal to its distance from a fixed line.
What is the parabola on a graph?A quadratic function's U-shaped curve is shown on a parabola graph. A right circular cone and a plane surface intersect to form one of the conic sections known as a parabola in mathematics. The plane is symmetrical. U-shaped bend
y - k = a (x - h)2
where the vertex is (h,k). Since the vertex is known to be at (7,-3), we know that h = 7 and k = -3. Consequently, the equation is
y -5 = a (x - 2)2
We utilize the fact that the parabola passes through point to determine a for (4,0). With x =- 4 and y = 0, we obtain
0 - 5 = a (-4 - 2)
-5 = a (-6)2
-5 = -6a
a = 5/6
Consequently, the parabola's equation is
y -5 = (5/6) (x - 2)^2
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Two students, Jessica and Steve, are solving the math problem below: A hiker is hiking at an elevation located 18 meters above sea level. Simultaneously a diver is diving at a location that is 12 meters below sea level. Find the distance between the two elevations. The students came up with different answers. Jessica said the answer is 6 meters. Steve said the answer is 30 meters. Who is correct?
The distance between the two elevation is 30 metres. Therefore, Steve is correct.
How to find the distance between the two elevations?A hiker is hiking at an elevation located 18 meters above sea level. Simultaneously a diver is diving at a location that is 12 meters below sea level.
The distance between the two elevation can be calculated as follows:
Jessica said the answer is 6 meters. Steve said the answer is 30 meters.
Let's find who is correct.
The hiker is 18 metres above sea level . The diver is 12 meters below sea level. For the diver to get to sea level he will travel 12 meters. For the diver to get to the hiker position he will travel extra 18 metres.
Therefore, the distance in elevation is 12 + 18 = 30 metres. Hence, Steve is correct.
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What is the area of the triangle with vertices (1, 4), (3, 1) and (11, 1)?
Answer:
Step-by-step explanation:
go to school
TRUE/FALSE. you cannot use both the current value of an explanatory variable and lags of that same explanatory variable in a regression.
It is "false" to claim that you cannot use both the present value of an explanatory variable and its delays in a regression.
Define the term regression?A statistical method called regression links a dependent variable with one or much more independently (explanatory) variables.
A regression model can demonstrate whether changes in one or more several explanatory variables are related to changes in the dependent variable.Political scientists frequently use lag- ged explanatory variables as a solution to endogeneity issues with observational data.Although some research claims that using lag dependent variables (LDVs) in regressions results in negatively biased coefficient estimates, even when the LDV is a part of the data-generating process, LDVs have been used in regression analysis provide the robust estimates of the outcomes of independent variables.Thus, it is "wrong" to claim that you cannot use both the present value of an explanatory variable and its delays in a regression.
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What is 8.123 as a decimal number
Answer: 8.123 is a decimal
Step-by-step explanation:
A decimal is a whole number and a fractional part
there is a decimal point
Quick, please! Stephanie is making a gingerbread house similar to her real-life house. She is using a scale of 1 cm equals 5 feet. If Stephanie's house is 30 feet wide, how wide will the gingerbread house be?
Answer:
6cm
Step-by-step explanation:
30 divded by 5 times 1
Answer:
Step-by-step explanation:
5cm
Use point-slope form to write the equation of a line that passes through the point
(-14, 12) with slope -7/8
Answer:
Step-by-step explanation:
find the equation of the line that is perpendicular to the line 5x-2y=12
The slope of two perpendicular lines is the negative inverse of each other thus the equation of the perpendicular line will be y = (-2/5)x + c.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant slope.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
As per the given line,
5x-2y=12
2y = 5x - 12
y = (5/2)x - 6
The slope of the above line is 5/2
Since the slope of two perpendicular lines is the negative inverse of each other.
Thus,slope of line = -1/(5/2) = -2/5
So equation will be y = (-2/5)x + c
Hence"The slope of two perpendicular lines is the negative inverse of each other thus the equation of the perpendicular line will be y = (-2/5)x + c".
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in a specific university, getting a full scholarship and getting an internship are conditionally independent given that you are a top student. it is known that 50% of top students get a full scholarship and 40% of top students get an internship. if a randomly selected student is known to be a top one, what is the probability they will get a full scholarship and an internship? assume event a: getting a full scholarship; event b: getting an internship; event c: being a top student.
The probability they will get a full scholarship and an internship Is 0.2
What is Probability?
Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can vary from 0 to 1, with 0 being an impossibility and 1 denoting a certainty, probability is a crucial subject since it teaches all the fundamental ideas of the subject. One is the probability of every event in a sample space.
However, if two coins are tossed, four outcomes might occur: (H, H), (H, T), (T, H), and (T, T).
For instance, when we flip a coin, there are just two potential results: Head OR Tail (H, T).
Given that these two events are independent. Hence,
P(Full scholarship and an internship)
= P(Full scholarship) * P(Internship)
= 0.50 * 0.40
= 0.20
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1a) as the newly hired manager of a company that provides cell phone service, you want to determine the percentage of adults in your state who live in a household with cell phones and no land-line phones. how many adults must you survey? assume that you want to be 98% confident that the sample percentage is within three percentage points of the true population percentage. use statcrunch to calculate the following sample size. assume that nothing is known about the percentage of adults who live in a household with cell phones and no land-line phones.
In this instance, a sample size of 393 adults who live in homes without landlines and use cell phones would be required.
Picking the number of observations or replicates to include in a statistical sample is known as sample size determination. Any empirical study whose objective is to draw conclusions about a population from a sample must take into account the sample size. In reality, a study's sample size is typically chosen based on the expense, convenience, or time required to collect the data as well as the requirement that the sample size have a high enough statistical power. There could be a variety of sample sizes used in complex studies; for instance, there might be different sample sizes for each stratum in a stratified survey. The intended sample size for a census is equal to the population because the entire population's data is being sought.
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Is the function even, odd, or neither?
The correct option is the third one, the function is neither odd nor even.
Is the function even, odd, or neither?
A function y = f(x) is an odd function if for all values of x in its domain:
f(x) = f(-x)
The graph of these functions have an axis of symmetry at the y-axis.
And it is an odd function is for all values of x in its domain:
f(x) = -f(x)
These functions "invert" at the y-axis,
Now let's look at the graph.
When x = 5, we can see that:
f(x) = 9
And when x = -5, the function is:
f(-5) = -0.5
Neither of the conditions is meet.
Then the function is neither odd nor even.
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Jenae noticed that many of her co-workers would opt for the coffee that appeared to be most recently brewed, regardless of the flavor of the coffee offered. This leads her to believe that what she was witnessing was not really representative of everyone's true flavor preferences. She adapted her experimental study accordingly.Select one control in Jenae's experimental study
Jane makes sure that the (B) coffee is brewed simultaneously in each pot as part of her experimental study.
What is the experimental study?Experimental investigations involve introducing an intervention and observing its results.
Typically, volunteers in experimental research are grouped randomly, or by chance.
In experimental research, the dependent and independent variables are compared to examine how they relate to one another.
A link between a certain feature of an item and the variable under investigation is either accepted or denied following the conclusion of an experimental research study.
Laboratory experiments are the most fundamental type of experimental study, albeit they can take on several forms depending on the research topic.
Laboratory experiments are the most fundamental type of experimental study, albeit they can take on several forms depending on the research topic.
So, in the given situation, Jeane makes sure that the coffee is brewed simultaneously in all of the pots.
Therefore, Jane makes sure that (B) coffee is brewed simultaneously in each pot as part of her experimental study.
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Complete question;
Jenae noticed that many of her co-workers would opt for the coffee that appeared to be most recently brewed, regardless of the flavor of the coffee offered. This leads her to believe that what she was witnessing was not really representative of everyone's true flavor preferences. She adapted her experimental study accordingly. Select one control in Jenae's experimental study:
a. Jeane places condiments at random places throughout the kitchen.
b. Jeane makes sure that the coffee in different pots is brewed at the same time.
c. Jeane uses different locations in the kitchen for the coffee pots.
d. Jeane monitors the habit of co-workers who do not drink coffee.
2. what conditions must be met if we want to perform a hypothesis test and answer the question of the management? select all that apply:
1.The following is the 90% confidence interval for the mean difference between the park's tree heights in 2009 and 2019:
(11.59, 14.21)
2. The conditions for the confidence interval are of:
A. Large samples and no extreme outliers.
D. Independently sampled pairs.
Given,
What is a confidence interval for the t-distribution?
When the population's standard deviation is unknown, the t-distribution is utilized, and the boundaries of the confidence interval are provided using the following formula:
x ± t s/√n
When the equation's variables are laid down as follows:
The sample mean = x
The critical value = t
The sample size = n
The standard deviation for the sample = s
Using a t-distribution calculator, the critical value is t = 1.6766 for a two-tailed 90% confidence interval with 50 - 1 = 49 df.
The remaining parameters are given as follows:
x = 12.9, s = 5.52, n = 50
Then the lower bound of the interval is of:
12.9 - 1.6766 x 5.52/sqrt(50) = 11.59.
The upper bound of the interval is of:
12.9 + 1.6766 x 5.52/sqrt(50) = 14.21.
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Question is incomplete. Completed question is given below;
Forest rangers wanted to better understand the rate of growth for younger trees in the park. They took measurements of a random sample of 50 young trees in 2009 and again measured those same trees in 2019. The data below summarize their measurements, where the heights are in feet.
Year Mean SD n
2009 11.4 3.6 50
2019 24.3 8.8 50
Difference 12.9 5.52 50
Round all calculated values to 4 decimal places as appropriate.
1. Construct a 90 confidence interval for the mean difference between the height of trees in the park in 2009 and in 2019.
2. What conditions must be met if we want to perform a hypothesis test and answer the question of the management? Select all that apply:
A. Large samples and no extreme outliers.
B. There must be at least 3 levels of the categorical variable.
C. np^≥10 and n(1−p^)≥10
D. Independently sampled pairs.
14 on a certain sight-seeing tour, the ratio of the number of women to the number of children was 5 to 2. what was the number of men on the sight-seeing tour?
The number of men on the sight-seeing tour was 22.
What is the proportion?
A unique class of ratio called a percentage has the numerator and denominator combined. An illustration is the ratio of deaths to men, which is calculated by dividing deaths to men by deaths to men and women (i.e. the total population).
We have,
w/c = 5/2
w/c = 5/2
w = 5x
and c=2x
for some integer x. Q : m =?
(1) on the sight-seeing tour, the ratio of the number of children to the number of men was 5 to 11
c/m = 5/11cm
c=5y and m = 11y,
for some integer y. Not sufficient to calculate m.
(2) the number of women on the sight-seeing tour was less than 30 --> w<30. Not sufficient to calculate m.
(1) + (2)
w = 5x < 30w --> x<6x.
c=2x and as c=5y,
c is a multiple of 5 --> x=5x
c = 10 = 5y --> y = 2
m = 11y = 22.
Hence, the number of men on the sight-seeing tour was 22.
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the edges of a rectangular solid have these measures: 1.5 feet by 1½ feet by 3 inches. what is its volume in cubic inches?
The volume of the rectangular solid with the given measures is equal to 972 cubic inches.
As given in the question,
Measures of edges of rectangular solid is given by :
1.5 feet by 1 1/2 feet by 3 inches
Conversion of feet to inches:
1 feet = 12 inches
Let length = 1.5 feet
= 1.5 × 12
= 18inches
Width = 1 1/2 feet
= ( 3/2 ) × 12
= 18 inches
Height = 3 inches
Volume of the rectangular solid
= length ×width ×height
= 18 × 18 × 3
= 972 cubic inches
Therefore, the volume of the rectangular solid is equal to 972cubic inches.
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There are 6 circles and 10 triangles. What is the simplest ratio of circles to total shapes?.
If there are 6 circles and 10 triangles, then the simples ratio of circles to total shapes is 3 : 8
Total number of circles = 6 circles
Total number of triangles = 10 triangles
Total number of shapes = Total number of circles + Total number of triangles
Substitute the values in the equation
Total number of shapes = 6 + 10
= 16 shapes
The ratio of circles to total shapes = Total number of circles : Total number of shapes
Substitute the values
= 6 : 16
Simplify the ratio
= 3 : 8
Therefore, the simplified ratio of circles to total shapes is 3 : 8
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which of the following is not a requirement for constructing a confidence interval for estimating the population proportion? question content area bottom part 1 choose the correct answer below. a. there are at least 5 successes and 5 failures. b. the trials are d
The option B "The trials are done without replacement" is not a requirement for constructing a confidence interval for estimating the population proportion.
In the given question we have to check which of the following is not a requirement for constructing a confidence interval for estimating the population proportion?
The given options are:
a. There are at least 5 successes and 5 failures.
b. The trials are done without replacement.
c. The sample is a simple random sample.
d. There is fixed number of trials.
As we know that, an estimate's level of uncertainty is described by a confidence interval, which is a range of numbers.
As given that we have to find which of the following is not a requirement for constructing a confidence interval for estimating the population proportion. So for constructing a confidence interval for estimating the population proportion, we can find the trials without replacement.
So the option B "The trials are done without replacement" is correct.
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hi pls help me pls
hello help me
Answer:
see pic
Step-by-step explanation:
see pic
what is the largest positive integer n for which there is a unique integer k such that 8 15 < n n k < 7 13 ?
the largest positive integer n[tex]\leq[/tex]112 for which there is a unique integer k
What is inequality?
Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare two values. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign in between. Sometimes it can be about a "not equal to" relationship, where one thing is more than the other or less than. In mathematics, an inequality is a relationship that results in a non-equal comparison between two numbers or other mathematical expressions.
Given inequality is
[tex]\frac{15}{8} < \frac{n+k}{k} < \frac{13}{7}[/tex]
[tex]\frac{8}{15} < \frac{n}{n+k} < \frac{7}{13}[/tex]
[tex]n\frac{6}{7} < k < n\frac{7}{8}[/tex]
[tex]n\frac{7}{8}-n\frac{6}{7}[/tex] > 2
n[tex]\leq[/tex]112
Hence, the largest positive integer n[tex]\leq[/tex]112 for which there is a unique integer k
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The number of sweets
s
that each friend gets is the number of sweets in a box
n
divided by the number of friends
f
the sweets are shared between. Enter a formula for the number of sweets each friend gets and enter the number of sweets each friend gets if there are 48 sweets and 8 friends.
The number of sweets each friend gets = 6
The number of sweets s that each friend gets = the number of sweets in a box n ÷ number of friends f the sweets are shared between
s = n ÷ f
s = n/ f
if there are 48 sweets and 8 friends.
That is,
n = 48 sweets
f = 8 friends
Find s,
s = n/ f
= 48 / 8
= 6
s = 6 sweets
The number of sweets each friend gets = 6
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A fence is to enclose a field and divide it into 3 equal areas. If there is 1600m of fencing available. Find the dimensions of the field that will allow for the maximum area.
The dimensions of the field that will allow for the maximum area are 200 meters by 400/3 meters
How to determine the dimensions of the field that will allow for the maximum area.From the question, we have
Fencing available, Perimeter = 1600 meters
Number of sections, n = 3
Represent the dimensions with x and y
So, we have:
Area = Number of sections* x * y = 3xy
Perimeter = (Number of sections * 2x + 2(Number of sections) * y) = 6x + 4y
Recall that
Perimeter = 1600 meters
So, we have
6x + 4y = 1600
A = 3xy
Divide 6x + 4y = 1600 by 2
3x + 2y = 800
Make y the subject
y = (800 - 3x)/2
Substitute y = (800 - 3x)/2 in A = 3xy
A = 3x(800 - 3x)/2
So, we have
A = 1200x - 4.5x²
Differentiate and set to 0
1200 - 9x = 0
So, we have
9x = 1200
Divide by 9
x = 400/3
Recall that y = (800 - 3x)/2
So, we have
y = (800 - 3 x 400/3)/2
Evaluate
y = 200
Hence, the dimensions are 200 by 400/3
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In a study to compare the perceived effects of two pain relievers, 200 randomly selected adults were given the first pain reliever, and 93% indicated appreciable pain relief. Of the 450 individuals given the other pain reliever, 96% indicated experiencing appreciable relief. A give an estimate for the difference in the proportions of all adults who would indicate perceived pain relief after taking the two pain relievers. Provide a bound on the error of estimation. B based on your answer to part (a), is there evidence that proportions experiencing relief differ for those who take the two pain relievers? why
7% people would indicate perceived pain relief after taking the two pain relievers.
What is error of estimation?
The difference between an estimated value and the true value of a parameter or, sometimes, of a value to be predicted is an error of estimation.
Evaluation :Given that,In a study comparing the perceived effects of two painkillers, 200 randomly chosen persons were given the first one, and 93% reported noticeably lessening of their pain.
96% of the 450 people who received the other painkiller reported feeling noticeably relieved.We have to estimate the percentage of adults overall who would say they felt their pain was relieved after taking each painkiller.
Give the estimate 95% confidence interval.
We know that
,p=(186+432)/(200+450)p=0.95
We getL.B= 0.93-0.96+0.96√0.95(1-0.95)(1/200+1/450)
L.B= 0.07
U.B = 0.93-0.96+0.96√0.95(1-0.95)(1/200+1/450)
U.B = 0.01
Bound of error = 096√0.95(1-0.95)(1/200+1/450) = 0.04
∴ 7% percentage of adults overall who would say they felt their pain was relieved after taking each painkiller.
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explain how the is related to the standard error of the estimated difference in average birth weight for smoking and nonsmoking mothers.
Babies born to nonsmokers typically weighed between 1,000 and 5,000 grams. Babies of smokers typically ranged in weight from 500 to 4500 grams.
Given,
What is the weight at birth?
Birth weight is the term used to describe a newborn's body weight. Typically, newborns of European heritage weigh between 2.5 and 4.5 kilos, on average 3.5 kilograms, at delivery. Babies from South Asia and China typically weigh 3.26 kg.
Here,
Babies of nonsmokers frequently ranged in weight from 1,000 to 5,000 grams. Babies born to smokers frequently weighed between 500 and 4500 grams.
The usual ranges of birth weights between the two groups do show some notable differences, though. Nearly half of neonates among nonsmokers (56 out of 115, 48.7%) have birth weights between 3,000 and 4,000 grams since there are fewer babies in the lower weight ranges. Fewer babies are in the bigger weight groups, with 40 of 74, or 54%, of the newborns delivered to smokers having birth weights between 2,000 and 3,000 grams.
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An experiment consists of 8 independent trials where the probability of success on each trial is 3 8. Find the probability of obtaining the following. Round answers to the nearest ten-thousandth. 13. Exactly 3 successes. 14. Exactly 6 successes.
As each trial has a 0.375 probability, the probability for three successes is 0.05273 and for six successes is 0.00278.
What is probability?Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, if we are unclear of how an event will turn out. Statistics is the study of occurrences subject to probability. The number of possible outcomes is divided by the total number of possible outcomes to determine probability. Odds are not the same as probability. Odds are calculated by dividing the probability of a given event by the probability that it won't. By dividing the number of preferable outcomes by the total number of potential outcomes, probability, which measures the likelihood that an event will occur, is obtained.
Here,
The probability of success in each trial=3/8
For 3 success,
P(3)=(3/8)³
=0.05273
For 6 success,
P(6)=(3/8)⁶
=0.00278
The probability for 3 success is 0.05273 and for 6 success is 0.00278 as for each trial, the probability is 0.375.
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0.5 power of 2 - 0.3 power of 2
Answer: 0.16
Step-by-step explanation:
Find the value of X
2x
3x+10
Answer:
-10 = x
Step-by-step explanation:
2x = 3x + 10 Is this what you meant to write? Subtract 2x from both sides
0 = x + 10 Subtract 10 from both sides
-10 = x
or are you combining like terms?
2x + 3x + 10
5x + 10
a pizza parlor has been experimenting with lowering the price of their large one-topping pizza to promote sales. the average revenues from the sale of large one-topping pizzas on a friday night (5 p.m. to midnight) at various prices are given below. revenue from the sale of pizzas at different prices price (dollars x) revenue (dollars r) 9.25 1202.50 10.50 1228.50 11.75 1210.25 13.00 1131.00 14.25 1054.50 (a) find the function for the quadratic model that gives the average revenue in dollars where x is the price in dollars of a large one-topping pizza, with data from 9.25 ≤ x ≤ 14.25. (round all numerical values to two decimal places.) r(x)
The function for the quadratic model that gives the average revenue in dollars where x is the price in dollars of a large one-topping pizza, with data from 9.25 ≤ x ≤ 14.25 is -105.6x² + 254.28x - 12.16.
Quadratic model
In regression, quadratic model means mathematical model represented by a quadratic equation such as Y = aX² + bX + c, or by a system of quadratic equations.
Given,
A pizza parlor has been experimenting with lowering the price of their large one-topping pizza to promote sales. the average revenues from the sale of large one-topping pizzas on a Friday night (5 p.m. to midnight) at various prices are given below.
Here we need to find the quadratic model function with data from 9.25 ≤ x ≤ 14.25.
While we plot the given table of values in the graph then we get the graph like the following.
Through the graph we have identified that the value of
mean of x 11.75
mean of y 1,165.35
correlation coefficient r 0.9924547615
A -105.6
B 254.28
C -12.16
So, through these values the quadratic model of the function is written as,
=> -105.6x² + 254.28x - 12.16.
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find the perimeter.
10ft. 13ft. 17ft.
Answer: 40
Step-by-step explanation:
P = a+b+c = 10+17+13 = 40
step 1 of 4 : state the null and alternative hypotheses in terms of the expected proportion for each day. write your answer as a fraction or a decimal rounded to six decimal places, if necessary.
By using the concept of testing of hypothesis, the null and alternative hypothesis is given by
[tex]H_0 :p_i = \frac{1}{5}[/tex]
[tex]H_a : p_i \neq \frac{1}{5}[/tex] for atleast one day
What is testing of hypothesis?
Suppose there is a hypothesis and there is a data at hand. Testing of Hypothesis determines whether a particular hypothesis is supported by the data at hand.
The null and alternative hypothesis can be written are as follows-
Null hypothesis: [tex]H_0[/tex] : There is no difference in the number of swimmers from day to day.
Alternative hypothesis: [tex]H_a[/tex] : There is a difference in the number of swimmers from day to day.
[tex]H_0 :p_i = \frac{1}{5}[/tex]
[tex]H_a : p_i \neq \frac{1}{5}[/tex] for atleast one day
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Complete Question
The manager of the city pool has scheduled extra lifeguards to be on staff for Saturdays. However, he suspects that Fridays may be more popular than the other weekdays as well. If so, he will hire extra lifeguards for Fridays, too. In order to test his theory that the daily number of swimmers varies on weekdays, he records the number of swimmers each day for the first week of summer. Test the manager’s theory at the 0.10 level of significance.
Swimmers at the City Pool
Monday Tuesday Wednesday Thursday Friday
Number 46 68 43 51 70
Step 1 of 4 :
State the null and alternative hypotheses in terms of the expected proportion for each day. Enter your answer as a fraction or a decimal rounded to six decimal places, if necessary.
H0: pi=⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
Ha: There is a difference in the number of swimmers from day to day.
a company claims that the mean weight per apple they ship is 120 grams with a standard deviation of 12 grams. data generated from a sample of 49 apples randomly selected from a shipment indicated a mean weight of 122.5 grams per apple. is there sufficient evidence to reject the company’s claim? (useα
We fail to reject H0. So there is enough evidence to state that the hypothesis H1 has the risk to make an error equal to α.
What do you mean by standard deviation?
The term "standard deviation" refers to a measurement of the data's dispersion from the mean. A lower number deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
What does it mean if standard deviation is negative?The standard deviation is positive, or greater than zero, whenever there are two uneven terms in the observations. The standard deviation is exactly zero if all of the observations are equally distributed. Thus, the standard deviation can never be negative or less than zero.
We have two hypotheses:
H0: μ= 120
H1: μ≠ 120
where μ is the mean weight and per apple the value of α is 0.05. If conditions are met we will run sample a.
random: 49 apples are randomly selected
normal: 49>=30 so CLF holds. Now,
formula of z-test for μ
Test statistic: z-test=(¯x−μ)/( σ/√n)
We are given with:
n=49
¯x=122.5
σ=12
putting values in formula:
z-test=(122.5-120)/(12/√49)
=1.458
P-value: P(z>1.458)=normal df(1.458, ∞,1)
=0.0724
And it is a two tailed test so
=2(0.0724)
=0.1448
Since P-value> α ; (0.0724>0.05)
So, we fail to reject H0. We do not have convincing evidence that there is a difference in mean weight per apple. So here we would say that there is enough evidence to state that the hypothesis H1 has the risk to make an error equal to α.
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tom went on a bike ride. after 6 miles he got a flat tire and had to jog back home. he jogs 3 mph slower than he bikes, so the jog took 1 hour longer than the bike ride. at what rate did he travel each way?
Tom Pedalled his bike at a pace of 6 km/h and ran at a speed of 3 km/h.
Given,
Tom went on a bike ride;
Distance covered = 6 miles
Speed of bike = x
Speed of jogging = x - 3
Jogging is one hour more than bike ride
That is,
(6/x - 3) - (6/x) = 1
6 (x - x + 3 / x(x - 3)) = 1
18 / x² - 3x = 1
x² - 3x = 18
x² - 3x - 18 = 0
x² - 6x + 3x - 18 = 0
x(x - 6) + 3(x - 6) = 0
(x + 3) (x - 6) = 0
x = 6
That is,
Tom travelled at a speed of 6 km/hr with bike and 3 km/hr by jogging.
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