a) The test statistic is given as t = [tex]\dfrac {14-12}{\dfrac{4.32}{\sqrt25}}}[/tex]= 2.315
b) The pa value will be P = P( t₂₄ > 2.315 ) = 0.015
c) If we compare the p-value and the significance level is given we see that so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is higher than 12 at 1% of significance
What is a null hypothesis?In null hypotheses, there is no relationship between the two phenomena under the assumption that it is not associated with the group. And in alternative hypotheses, there is a relationship between the two chosen unknowns.
X= represents the sample mean
s = represent the sample standard deviation
n = 25 sample size
[tex]\mu_o[/tex] = 12 represent the value that we want to test
[tex]\alpha[/tex] = 0.05 represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p-value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the mean is higher than 12, the system of hypothesis would be:
Null hypothesis: ≤ 12
Alternative hypothesis: > 12
If we analyze the size for the sample is > 30 but we don't know the population deviation so is better to apply a t-test to compare the actual mean to the reference value, and the statistic is given by:
[tex]t=\dfrac{X-\mu_o}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to a specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
[tex]\dfrac {14-12}{\dfrac{4.32}{\sqrt25}}}[/tex]= 2.315
P-value:-
The first step is calculate the degrees of freedom, on this case:
df = n - 1 =25 - 1 = 2
Since is a one side right tailed test the p value would be:
[tex]p_v[/tex] = P( t₂₄ > 2.315 ) = 0.015
Conclusion
If we compare the p-value and the significance level is given [tex]\alpha[/tex]= 0.05 we see that [tex]p_v < \alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is higher than 12 at 1% of significance.
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Assume the domain of the function is {1,2,3,...}. Determine the theta notation for the function f(n)=7n^2+4n+2
We have that O(n²) is the theta notation for 7n² + 4n + 2.
Let's give big-Oh a formal definition:
O(g(n)) = {the set of all f such that 0 [tex]\leq[/tex] f(n) [tex]\leq[/tex] cg(n) for any n >= n₀ fulfilling positive constants c and n₀}
To show this
We need to find c and n₀ such that:
7n² + 4n + 2 <= cn² for all n >= n₀ .
Divide both sides by n², getting:
7 + 4/n + 2/(n²) <= c for all n >= n₀ .
If we choose n₀ equal to 1, then we need a value of c such that:
7 + 4 + 2 <= c
We can set c equal to 13. Now we have:
7n² + 4n + 2 <= 13n² for all n >= 1 .
Hence, 7n² + 4n + 2=O(n²)
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Need the answer ASAP!!!
Answer:
y ≈ 15272.9(1.06306^x) . . . . from regression tool
y = 15300(1.0624^x) . . . . calculated "by hand"
Step-by-step explanation:
An exponential model is one that uses the exponential function ...
f(x) = a·b^x
to model the data. The value of 'a' is the function value when x=0, the initial value. The value of 'b' is the growth factor, the multiplier between function values for successive values of x.
__
toolAn exponential regression tool makes short work of this. Such tools are available on some calculators, apps, and spreadsheets. All that is required is entering the data into a table and invoking the tool. The one shown in the attachment tells you the model is approximately ...
y ≈ 15272.9(1.06306^x)
__
averagingWe can average the growth rate factors a couple of different ways. When we think of "averaging," we usually think of the arithmetic mean, the sum of values divided by their number. If we average the growth rates in this way, we get ...
average rate of growth =
((161/153) +(173/161) +(184/173) +(196/184) +(207/196) +(220/207))/6 ≈ 1.0624
Using the first table value as the initial value, the model formed this way is ...
y = 15300(1.0624^x)
__
For exponential growth it may make more sense to compute the geometric mean. This is the n-th root of the product of n numbers. In this case, it reduces to the 6-th root of the ratio of the last to the first:
average rate of growth = (220/153)^(1/6) ≈ 1.0624
This gives the same growth factor as above, hence the same model.
The second attachment shows the application of this model to the domain used in the table. We see there are some minor differences when rounding the function value to the nearest hundred.
The differences in our two models seem to arise from rounding the data values in the table to the nearest hundred.
__
summaryThe values given in the table can be used in different ways to arrive at two similar, but different exponential models of the table data:
y = 15272.9(1.06306^x)y = 15300(1.0624^x)Interestingly, the function calculated "by hand" has a very slightly better correlation with the table data. The difference in correlation coefficients is in the 6th decimal place.
This is part A to one of my questions to help answer the second one, the second question is posted if anyone can help
Answer:
Step-by-step explanation:
Part A: Since 400 is being multiplied 1.06^t, for it to be equal to 399 the value 1.06^t must be less than 1. The lowest value for t given the domain restriction is 0 which would only result in 1 which will given the initial amount of 400. t would need to be less than 0 for 1.06^t to start going below the value 1 but since there is a domain restriction since t represents time, that value cannot go below 400 to reach 399.
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:f(4)= -1 [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
If a point point (x , y) satifys a function, then it can be written as :
[tex]\qquad \tt \rightarrow \: f(x) = y[/tex]
Here, point (x , y) is replaced by (4 , -1)
[tex]\qquad \tt \rightarrow \: f(4) = - 1[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Determine the x and y intercepts of the equation y = -3x + 4.
Select one:
O a. y-int y = 4 and x-int x = 4/3
O b. y-int y = 4/3 and x-int x = 4
O c. y-int y = 4 and No x-int
O d. No y-int and x-int x =4/3
Answer:
O c. y-int y = 4 and No x-int
Step-by-step explanation:
In the slope-intercept equation y = -3x + 4, only slope and y-intercept are displayed as it is in slope-intercept format which is y = mx + b; m being the slope and b being the y-intercept.
There is no x-intercept present in a slope-intercept equation.
But due to the 4 being in the place of the y-intercept is the y-intercept of the graph and line depicted off this linear equation (slope-intercept equation).
Hence, the answer is C. Y-intercept = 4 and No x-intercept.
if A={4,7,10,13,17} and B={3,5,7,9}, then which of the following statements is true
A U B= {7}
B c A
B c B
Answer:
good questing it is something
Step-by-step explanation:
1-1-2- --3--1234-3
3-4
Q-
-4
-24
-4
-
q 43-
43-
3 4-3
4-
4-4
- answer is 2def not cap i need 5 poinnts i gues
The image of a point K(1,2) after translation is K¹ (-1,2). what is the coordinate of the point R whose image is R¹ (-3,3) after undergoing the same translation.
a teacher promised a movie day to the class that did better, on average, on their test. The box plot shows the results of the test
The question is incomplete. The complete question is
A teacher promised a movie day to the class that did better, on average, on their test. The box plot shown in the below-mentioned figure shows the results of the test.
Which class should get the reward, and why?
- The 2nd-period class should get the reward. They have the highest score, a perfect 100.
- The 2nd-period class should get the reward. They have a higher median.
- The 4th-period class should get the reward. Though the medians are the same, the first and third quartiles are higher, so the students did better on average than in the 2nd-period class.
- The 4th-period class should get the reward. Their lowest score is an outlier and should be thrown out.
The box plot shown in the question provides the information that
In 2nd period the minimum of the data is 77, first quartile is 78, median of the data is 89, third quartile is 92 and the maximum of the data is 100.
Hence, the mean of the results of 2nd period is
[tex]\frac{77+78+89+92+100}{5}=87.2[/tex]
In 2nd period the minimum of the data is 72, first quartile is 83, median of the data is 89, third quartile is 96 and the maximum of the data is 98.
Hence, the mean of the results of the 4th period is
[tex]\frac{72+83+89+96+98}{5}=87.6[/tex]
Hence, obviously, the 4th period is having more mean.
Moreover, we can observe that if more of the marks are on the higher side the average will automatically be more. Hence, as the first and the third quartiles are more on the 4th-period, so the average marks for the 4th period must be better.
So, just by observing the box plot, we can give the statement that "The 4th-period class should get the reward. Though the medians are the same, the first and third quartiles are higher, so the students did better on average than in the 2nd-period class. "
Therefore, the 4th-period class should get the reward. Though the medians are the same, the first and third quartiles are higher, so the students did better on average than in the 2nd-period class.
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The table shows the probabilities of certain prizes in a restaurant’s contest where the first 100 customers are winners.
A 2-column table with 6 rows. The first column is labeled prize with entries 1 dollar drink, 5 dollar meal, 5 dollar gift card, 10 dollar gift card, 20 dollar gift card, 100 dollar gift card. The second column is labeled number of prizes with entries 44, 25, 16, 10, 5, 1.
How does the $100 gift card affect the measure of center of the data?
It increases the mean value of the prizes.
It decreases the mean value of the prizes.
It increases the median value of the prizes.
It decreases the median value of the prizes.
A mean is an arithmetic average of a set of observations. The correct option is A.
What is Mean?A mean is an arithmetic average of a set of observations. it is given by the formula,
Mean = (Sum of observations)/Number of observations
Since the median is the middle value of the given data set, therefore, the median will not be changed for the given data set. But since the mean is the arithmetic average, therefore, the $100 gift will increase the mean value of the prizes.
Hence, the correct option is A.
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Answer:
this is the anwser
this
Jordan wrote the expression 850p to represent the following scenario.
The cost of renting a bowling alley for a party is $850. The price per person depends on how many people attend the party. Write an expression for the price per person if p people attend.
Explain why Jordan's expression is incorrect. Provide the correct expression that represents the scenario.
Using proportions, the expression for the price per person is:
[tex]P = \frac{850}{p}[/tex]
Jordan's expression is wrong because the price per person is inverse proportional to the number of people in the party, not direct proportional.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The cost of renting a bowling alley for a party is $850, hence the cost per person is given by:
[tex]P = \frac{850}{p}[/tex]
Jordan's expression is wrong because the price per person is inverse proportional(that is, the amount is divided by p) to the number of people in the party, not direct proportional.
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Which expression is equivalent to...
Step-by-step explanation:
hope you can understand
If the legs of a right triangle are 8 and 10, find the length of the hypotenuse.
Answer:
Given :-
Two legs of a rt. triangle : 8 and 10 respectively.
To find :-
Length of the hypotenuse
Solution :-
Using Pythagorean Theorem;
(hypotenuse)² = (8)² + (10)²
= 64 + 100
hypotenuse = √164
= 12.8 units
Answer:
12.80
Step-by-step explanation:
We have to use the Pythagoras theorem to find the value of the hypotenuse.
Let the value of the hypotenuse be c.
Let us use the below formula to find the length of the hypotenuse.
a² + b² = c²First, let us replace a and b with 8 and 10 ( the lengths of the legs of the right triangle) with a and b.
a² + b² = c²
8² + 10² = c²
64 + 100 = c²
And now let us solve the above and find the value of c.
164 = c²
√164 = c
12.80 = c
Therefore, the length of the hypotenuse is:
12.80 units
Use the parabola tool to graph the quadratic function f(x)=−(x−3)(x+1).
Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.
The parabola has roots at x=3 and x=-1, so its vertex is halfway between those points, at x=1, and so the y-coordinate of the vertex is -(1-3)(1+1)=4.
Another point that lies on the parabola is (-1, 0).
Two cars leave Chicago to go to a town in that suit up north. One car is traveling 13 mph faster in it arrived in four hours the other car took five hours to get there find the speed of each car
The speeds of the two cars will be 52 mph and 64 mph.
How to find the speed of an object?If the object is going linearly, and at constant speed, then the speed of that object is given by the distance it traveled to the time it took to travel that distance.
If the object traveled D distance in T units time, then that object's speed is S = D/T
Two cars leave Chicago to go to a town in that suit up north.
One car is traveling 13 mph faster in it arrived in four hours the other car took five hours to get there.
Let the distance traveled by both cars is x.
Speed of the first car = x/5
Speed of the second car = x/4
So, the equation form will be
x/5 + 13 = x/4
(65 + x )/ 5 = x /4
4(65 +x ) = 5x
260 + 4x =5x
x = 260
Speed of the first car = x/5 = 52mph
Speed of the second car = 52 + 13 = 65 mph
The speeds of the two cars will be 52 mph and 64 mph.
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How do you write
f(x)=-5x^2-100x+8
in vertex form?
Houses in an real estate are all identical however a person can purchase a new house with some all or none of a set of options as indicated by the set below
how many options are there for purchasing a house in this community
{ pool , alarm , lake view , balcony }
Considering the number of subsets of the set of options, it is found that there are 16 options for purchasing a house in this community.
What is the number os subsets of a set of cardinality n?The number of subsets is given by:
[tex]N_s = 2^n [/tex]
The set of options is given by:
O = { pool , alarm , lake view , balcony }
Which has cardinality n = 4.
The number of options for the purchased home is the number of subsets of set O, hence:
[tex]N_s = 2^4 = 16[/tex]
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The perimeter of a triangle is 73 inches if two sides are of equal length and the third side is 7 inches longer than the others find the length of three sides
Answer:
22,22,29 in
Step-by-step explanation:
x + x + x+7 = 73
3x = 66
x = 22 then lengths = 22, 22, 29 in
Mr Tong had some money. After giving $1300 to each 5 of his children, he had $450 left. How much money did he have at first
Answer:
Step-by-step explanation:
money given to children=1300x5
=6500
total money =6500+450
=6950
please i need this fast
Answer:
the second option
Step-by-step explanation:
UV and AB are at a right Angie to reach other.
and
UV is parallel to ZY
Ella wants to buy a home. The maximum loan she can get from the bank is $445,000
If Ella has $55,000 available to make a down payment, what is the highest valued home she can purchase?
Ella can buy a house worth $5 million
What is a Loan ?Loan is the amount of money borrowed from a bank or any other person , The amount has to be returned back with a Interest.
It is given that
The maximum loan Ella can get from the bank is $445,000
Ella has $55,000 available to make the down payment.
The highest value home that she can purchase is the sum of money she has and the maximum amount of money she can get from the bank.
It is given by
$445,000 + $55,000
$500,000
Therefore Ella can buy a house worth $5 million
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What is the equation of the line that has a slope of -4 and passes through the point (2, 3)?
If [tex]m=-4[/tex]
and a point is [tex](2,3)[/tex]
[tex]y=mx+b[/tex]
[tex]3=(-4)(2)+b[/tex] using the point and the slope
[tex]3=-8+b[/tex]
[tex]b=8+3[/tex]
[tex]b=11[/tex]
Therefore, the equation of the line will be [tex]y=-4x+11[/tex]
If f(x) = sin(x) and g(x) = sin(2x), then the derivative of f(x) + g(x) is
The derivative of f(x) + g(x) is cosx+2cos2x
Derivative : In mathematical calculus, the derivative is the rate of change of a function at a instant point.
Derivative of a function is denoted by dy/dx, where derivative of y is happening with respect to x.
We have to add f(x) and g(x), then differentiate the whole addition with respect to x.
Given that, f(x) = sin(x) & g(x) = sin(2x)
So, f(x) + g(x) = sin(x) + sin(2x)
Now, differentiating with respect to x we get,
(f(x)+g(x))' = d/dx(sinx) + d/dx(sin 2x)
= cosx+2cos2x
Derivative of f(x) + g(x) = cosx+2cos2x
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The graphs below have the same shape. The equation of the blue graph is F(x) = x^3. What is the equation of the red graph?
Answer:
g(x) = x³ - 2
(option B)
Step-by-step explanation:
because the shape of the graph has not changed, we know that there was no direct change to x
(this would have looked like 2x³ instead of x³)
and because the graph was not shifted along the x-axis (left or right), we know that the change did not happen inside the parenthesis
(this would have looked like (x³ - 3) instead of (x³) )
we know that the only change that has happened to this graph was a downward shift along the y-axis which can be expressed as
g(x) = x³ - 2
The equation of the red graph will be g(x) = x³ - 2.Option B is correct.
What is the equation?A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.
We know that there was no immediate change to x since the graph's form has not altered. Instead of x³, this would have appeared as 2x³.
Thus we can be confident that the change did not occur inside the parenthesis since the graph was not moved down the x-axis.
We may infer that this graph's sole modification was a downward shift along the y-axis, which is written as;
g(x) = x³ - 2
The graph is also attached in the attachment.
The equation of the red graph will be g(x) = x³ - 2.
Hence option B is correct.
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The following graph portrays the distribution of the number of spicy chicken sandwiches sold at a nearby Wendy's for the last 141 days.
The mean number of sandwiches sold per day is 91.9 and the standard deviation is 4.67. (Round your answers to 2 decimal places.)
If we use the Empirical Rule, on 68 percent of the days sales will be between
95 percent of the days sales will be between
68% of the day's sales will be between 87.23 and 96.57 and on 95% of the days, sales will be between 82.56 and 101.24.
What is the empirical rule?If your distribution follows a normal distribution, the standard deviation and mean can tell you where the majority of the data are.
We have:
The mean number of sandwiches sold per day is 91.9 and the standard deviation is 4.67.
As we know, from the empirical rule, 68% of the data will lie in one standard deviation of the mean, i.e., in the interval with the endpoints x±s
for samples and with endpoints u±б for the population.
x = 91.9
s = 4.67
x - s = 91.9 - 4.67 = 87.23
x + s = 91.9 + 4.67 = 96.57
68% of the day's sales will be between 87.23 and 96.57
95% of the data will lie within two standard deviations of the mean, which means in the interval with the endpoints x±2s for samples and with endpoints u±б population.
x - 2s = 82.56
x + 2s = 101.24
On 95% of the days, sales will be between 82.56 and 101.24
Thus, 68% of the day's sales will be between 87.23 and 96.57 and on 95% of the days, sales will be between 82.56 and 101.24.
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From this diagram, select the
pair of lines that must be
parallel if 24 = 23. If there
is no pair of lines, select
"none."
O is parallel to q
let's take the angle opposite to angle 4 is alpha
angle 4 = angle alpha ( vertically opposite angles)
angle alpha = angle 3 ( as angle 4 = angle 3).
hence o is parallel to q as both the angles are equal
Part B
Assume the statement is true for n=k. Prove that it must be true for n=k+1, therefore proving it true for all natural
numbers, n.
Hint: Since the total number of dots increases by n each time, prove that d (k) + (k+1)=d (k+ 1).
The inductive step is assuming that the statement is true for some n = k , where k is one of the values we want to prove the statement for, it shows that it is also true for n = k+1.
How to carry out Mathematical Induction?Suppose we have the statement 3n > 4n for all positive integers n.
Now, the statement above is false when n = 1 , since 3 is less than 4. However, it will be true for all other positive integers.
In that case, we can still prove this statement by induction for all integers n ≥ 2 .
Thus, the inductive step is assuming that the statement is true for some n = k , where k is one of the values we want to prove the statement for, it shows that it is also true for n = k+1.
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need help with this question for geometry
Answer:
[tex]31[/tex]
Step-by-step explanation:
It's 31 degrees, I hope it is the right answer
Vikram drinks 6/10 of a litter of water after gym class and 33/100 of a litter of juice with his lunch Vikram says he drank a total of 39 hundredths of a litter. use the drop-down menus to explain why Vikram is not correct?
Answer: Vikram is not incorrect because he found the sum by adding the numerators and denominators
Step-by-step explanation: The first blank doesn't have a word so I answer it
Cory drinks water from a bottle during a bike ride. The average amount of water, in
ounces, in his water bottle can be represented by the equation y = -8x+32, where y is the amount of water remaining after x hours. Based on the equation, what amount of water, in ounces, will remain in the bottle after Cory rides for 2 1/2 hours?
The amount of water will remain in the bottle after Cory rides for 2 1/2 hours will be;
⇒ y = 12 ounces
What is Equation of line?
The equation of line in point-slope form passing through the points (x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The average amount of water, in ounces, in his water bottle can be represented by the equation,
⇒ y = - 8x + 32
Where, y is the amount of water remaining after x hours.
Now,
Since, The average amount of water, in ounces, in his water bottle can be represented by the equation,
⇒ y = - 8x + 32
Hence, The amount of water will remain in the bottle after Cory rides for 2 1/2 hours is,
Substitute x = 2 1/2 in above equation,
⇒ y = - 8 × 2 1/2 + 32
⇒ y = - 8 × 5/2 + 32
⇒ y = - 20 + 32
⇒ y = 12 ounces
Thus, The amount of water will remain in the bottle after Cory rides for 2 1/2 hours is,
⇒ y = 12 ounces
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. Find the general solution to
d²y/dx²= 49y. Enter your answer as an equation y = ..
Note: d²y/dx²=k^2y
The given differential equation is linear with constant coefficients,
[tex]\dfrac{d^2y}{dx^2} - 49y = 0[/tex]
with characteristic equation
[tex]r^2 - 49 = 0[/tex]
and hence characteristic roots [tex]r=\pm7[/tex]. This means the general solution to the ODE is
[tex]y = C_1 e^{7x} + C_2 e^{-7x}[/tex]
In fact, you're given the solution already,
[tex]y = C_1 e^{kx} + C_2 e^{-kx}[/tex]
and you've determined that
[tex]\dfrac{d^2y}{dx^2} = k^2 (C_1 e^{kx} + C_2 e^{-kx}) = k^2 y[/tex]
Comparing this to the given ODE, it's obvious that [tex]k=7[/tex], so you can just replace [tex]k[/tex] with 7 in the given template solution.