Answers
The equation that represents the different transformations on the function f(x) = x³ should be written as follows;
1a. g(x) is f(x) reflected across the x-axis, and translated 4 units left is g(x) = -(x + 4)³.
1b. k(x) is f(x) vertically stretched by a factor of 3 is k(x) = 3x³.
1c. h(x) is f(x) translated 2 units right and 5 units up is h(x) = (x - 2)³ + 5.
2a. k(x) = 7(-x)³ is reflected across the y-axis, and vertically stretched by a factor of 7.
2b. h(x) = (x + 5)³ - 1 is translated 5 units left and 1 unit down.
What is a translation?In Mathematics and Geometry, the translation of a graph to the right adds a digit to the numerical value on the x-coordinate of the pre-image:
g(x) = f(x - N)
Conversely, the translation of a graph upward adds a digit to the numerical value on the y-coordinate of the pre-image;
g(x) = f(x) + N
Part 1a:
When the parent function f(x) is reflected across the x-axis, and then translated 4 units left, the transformed function g(x) is given by;
g(x) = -(x + 4)³.
Part 1b.
When the parent function f(x) is vertically stretched by a factor of 3, the transformed function k(x) is given by;
k(x) = 3x³.
Part 1c.
When the parent function f(x) is translated 2 units right and 5 units up, the transformed function k(x) is given by;
h(x) = (x - 2)³ + 5.
Part 2a.
The equation k(x) = 7(-x)³ simply means the parent function is reflected across the y-axis, and vertically stretched by a factor of 7.
Part 2b.
The equation h(x) = (x + 5)³ - 1 simply means the parent function is translated 5 units left and 1 unit down.
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Related Questions
Un celular cuesta $ 3 360, ya con el 60% de descuento aplicado. ¿Cuánto cuesta el celular sin el descuento?
a) $ 5 600 b) $ 5 500 c) $ 5 650 d) $ 2 016
24.-Una laptop cuesta $ 12500, pero tiene un descuento del 25%, ¿Cuánto cuesta la laptop con el descuento incluido?
a) $ 9 573 b) $ 9 753 c) $ 9 375 d) $ 9 703
25.- En Copel hay un refrigerador que cuesta $18 270 con el IVA incluido. ¿cuál es el costo del refrigerador sin el IVA?
a) $ 15 750 b) $ 15 570 c) $ 15 705 d) $ 15 507
26.- En el salón de 6to. "C" de la Esc. Juan Escutia, 5 alumnos estaban comparando sus estaturas. Joaquín midió 1.6 m., Adriana un metro con sesenta y cuatro centímetros, Beto 1 metro 2/4, Maximiliano 168 centímetros y Eduardo 100 centímetros más 3/5 de metro, ¿quiénes tienen la misma estatura?
a) Maximiliano y Adriana. b) Joaquín y Maximiliano. c) Beto y Eduardo. d) Eduardo y Joaquín.
Answers
Answer:
b
Step-by-step explanation:
plato
Is 6,700 1/10 of 67,000
Answers
Answer:
yes , 6,700is 1/10of 67,000
Yes, if you were to multiply 6,700 by 10, it would equal 67,000, meaning 6,700 is 1/10 of 67,000
A 21-foot bean is to be cut into three pieces so that the second and third piece are each 3 times the length of the first piece. If x represents the length of the first piece, find the length of each piece
Answers
Answer: 3, 9, and 9
Step-by-step explanation:
X+3x+3x=217x=21x=33, 9, 9=21
The answer is not $4.99
Answers
Answer:
Unknown. maybe try saying 4 dollars and 99 cents
Step-by-step explanation:
jacob has a tree growing in his yard. if the tree grows 9.5 feet per year, how many inches does it grow in a month?
Answers
Jacob has a tree growing in his yard. if the tree grows 9.5 feet per year, 9.5 inches does it grow in a month.
From the question, we have
Tree grows 9.5 feet per year
9.5 feet = 114 inches
Tree grows in one month = 114/12
= 9.5 inches
Divide:
Repetitive subtraction is the process of division. It is the multiplication operation's opposite. It is described as the process of creating equitable groups. When dividing numbers, we divide a larger number down into smaller ones such that the larger number obtained will be equal to the multiplication of the smaller numbers. One of the four fundamental mathematical operations, along with addition, subtraction, and multiplication, is division. Division is the process of dividing a larger group into smaller groups so that each group contains an equal number of things. It is a mathematical operation used for equal distribution and equal grouping.
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A researcher wishes to test whether the proportion of college students who smoke is the same in four different colleges. She randomly selects 100 students from each college and records the number that smoke. The results are shown below.
Name of College = College A, College B, College C, College D
Number of Smokers = 17, 26, 11, 34
Number of non-smokers = 83, 74, 89, 66
Use a 0.01 significance level to test the claim that the proportion of students smoking is the same at all four colleges if the test statistic: X{eq}^2 {/eq} = 17.832.
Answers
Use a 0.01 significance level, it can be concluded the proportion of students smoking is not the same at all four colleges.
The null and alternative hypotheses in this case are:
Null hypothesis: H0: The proportion of students smoking is the same at all four colleges.
Alternative hypothesis: Ha: The proportion of students smoking is not the same at all four colleges.
We have observed number of smokers and non-smokers in all four colleges, which is shown below:
Name of College A B C D
Number of Smokers 17 26 11 34
Number of non-smokers 83 74 89 66
To test this hypothesis, we calculate the expected number of smokers and non-smokers under the null hypothesis. If the null hypothesis is true, the expected number of smokers and non-smokers would be equal in all four colleges.
The expected number of smokers in each college can be found by multiplying the total number of students in that college with the overall proportion of students who smoke. Since we don't have the overall proportion of students who smoke, we can calculate it from the data. The total number of students in all four colleges is 100*4=400.
The total number of smokers is 17+26+11+34=88.
So, the overall proportion of students who smoke is 88/400=0.22.
The expected number of smokers in each college is:
Expected number of smokers in A = 100*0.22 = 22
Expected number of smokers in B = 100*0.22 = 22
Expected number of smokers in C = 100*0.22 = 22
Expected number of smokers in D = 100*0.22 = 22
The expected number of non-smokers in each college can be found by subtracting the expected number of smokers from the total number of students in each college.
Expected number of non-smokers in A = 100 - 22 = 78
Expected number of non-smokers in B = 100 - 22 = 78
Expected number of non-smokers in C = 100 - 22 = 78
Expected number of non-smokers in D = 100 - 22 = 78
To test the hypothesis, we calculate the test statistic X², which is given by:
X² = Σ(observed - expected)²/expected
where Σ is taken over all four colleges.
The observed and expected values are shown below:
Name of College A B C D
Number of Smokers 17 26 11 34
Number of non-smokers 83 74 89 66
Expected number of smokers 22 22 22 22
Expected number of non-smokers 78 78 78 78
The test statistic X² is given to be 17.832. The degrees of freedom for the test is (4-1) = 3, since we are estimating one parameter (the overall proportion of students who smoke) from the data.
Using the chi-square distribution with 3 degrees of freedom and a 0.01 significance level, we can find the critical value. The critical value is the value of X² such that the area to the right of X² is 0.01. We can find this value using a chi-square distribution table or a calculator.
The critical value of X² with 3 degrees of freedom and a 0.01 significance level is 11.345.
We can see that the test statistic X² = 17.832 is greater than the critical value X²₀.₀₁ = 11.345. This means that the null hypothesis is rejected at the 0.01 significance level.
We can conclude that the proportion of students smoking is not the same at all four colleges, and there is evidence to suggest that the proportion of students smoking differs among the colleges.
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A person invested $7,400 in an account growing at a rate allowing the money todouble every 6 years. How much money would be in the account after 4 years, to thenearest dollar?
Answers
The rate at which the money is growing is exponential. The formula for determining such exponential growth is expressed as
A(t) = Pe^rt
Where
A(t) represents the amount after t years
P represents the initial amount
t represents the number of years
r represents the growth rate
Given that the amount doubles after 6 years, it means that
when t = 6, A(t) = 7400 * 2 = 14800
Recall, P = 7400
Thus, the expression becomes
14800 = 7400e^6t
14800/7400 = e^6t
2 = e^6t
Taking natural logarithm of both sides of the equation, it becomes
ln 2 = ln e^6t = 6t lne
Recall, ln e = 1
Thus, we have
ln 2 = 6t
t = ln2/6 = 0.1155
The equation would be
A(t) = 7400e^0.1155t
When t = 4, it becomes
A(t) = 7400e^0.1155*4
A(t) = 11745.62
Rounding to the nearest dollar, the amount in the account after 4 years is
$11746
assuming the conditions for inference have been met, does the coffee shop owner have sufficient evidence to conclude that the distribution of sales is proportional to the number of facings at a 5 percent level of significance? conduct the appropriate statistical test to support your conclusion.
Answers
The coffee shop owner does not have sufficient evidence to conclude that the distribution of sales is proportional to the number of facings at a 5% level of significance.
What is proportion ?
A proportion refers to the number or fraction of individuals or items that exhibit a particular characteristic or have a certain attribute, relative to the total number or sample size being considered. It is often expressed as a ratio or percentage.
To test whether the distribution of sales is proportional to the number of facings, we can use the chi-squared goodness of fit test. The null hypothesis for this test is that the observed data follows a specific distribution (in this case, a proportional distribution), while the alternative hypothesis is that the observed data does not follow that distribution.
To conduct the test, we first need to calculate the expected frequency for each category assuming a proportional distribution. We can do this by multiplying the total number of sales (610) by the proportion of facings for each brand:
Starbucks: 610 x 0.3 = 183
Dunkin: 610 x 0.4 = 244
Peet's: 610 x 0.2 = 122
Other: 610 x 0.1 = 61
Next, we calculate the chi-squared statistic using the formula:
χ² = Σ((O - E)² / E)
where O is the observed frequency and E is the expected frequency. The degrees of freedom for this test are (k-1), where k is the number of categories. In this case, k = 4, so the degrees of freedom are 3.
Using the observed and expected frequencies from the table, we get:
χ² = ((130-183)²/183) + ((240-244)²/244) + ((85-122)²/122) + ((155-61)²/61) = 124.36
Looking up the critical value of chi-squared for 3 degrees of freedom and a significance level of 0.05, we get a value of 7.815. Since our calculated χ² value of 124.36 is greater than the critical value of 7.815, we reject the null hypothesis and conclude that the observed distribution of sales is not proportional to the number of facings.
Therefore, the coffee shop owner does not have sufficient evidence to conclude that the distribution of sales is proportional to the number of facings at a 5% level of significance.
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Lauren stopped for gas at two gas stations gasstop and quickflick on a roadtrip. gas was $2.80 per gallon at gasstop and $2.88 per gallon at quickflick if she bought a total of 34.5 gallons and spent a total of $97.92, how many gallons of gas did she purchase at quickflick?
Answers
According to the given statement Lauren purchased 29 gallons of gas at Quickflick.
To find out how many gallons of gas Lauren purchased at Quickflick,
we can set up a system of equations. Let's let x be the number of gallons she bought at Quickflick.
From the given information, we know that the total number of gallons she bought at both gas stations is 34.5.
Therefore, the number of gallons she bought at Gasstop would be (34.5 - x).
Now, we can set up the equation based on the cost of gas.
At Gasstop, the gas cost $2.80 per gallon, so the cost of gas bought at Gasstop would be (2.80 * (34.5 - x)).
At Quickflick, the gas cost $2.88 per gallon, so the cost of gas bought at Quickflick would be (2.88 * x).
According to the given information, the total amount she spent on gas is $97.92.
Therefore, we can set up the equation:
(2.80 * (34.5 - x)) + (2.88 * x) = 97.92
Now, we can solve this equation to find the value of x,
which represents the number of gallons she purchased at Quickflick.
Simplifying the equation:
95.6 - 2.8x + 2.88x = 97.92
Combining like terms:
0.08x = 2.32
Dividing both sides by 0.08:
x = 29
Lauren purchased 29 gallons of gas at Quickflick.
Therefore, Lauren purchased 29 gallons of gas at Quickflick.
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Sofia made the decision to write in her journal every day. She has put it into practice and is on her tenth day. What is this an example of
Answers
By sticking with a new behavior and making it a regular part of one's routine, habit formation can be a powerful tool for personal growth and self-improvement.
The act of writing in a journal every day is an example of habit formation. Habit formation is the process by which new behaviors become automatic through repeated practice.
When people engage in a behavior repeatedly, the neural pathways associated with that behavior become stronger, making it easier to perform that behavior in the future without conscious effort.
Writing in a journal is a simple practice that can have a significant impact on one's well-being. Many people find that writing in a journal helps them organize their thoughts, reflect on their experiences, and gain insight into their emotions.
By making the decision to write in her journal every day and putting that decision into practice, Sofia is cultivating a new habit that has the potential to improve her mental health and overall quality of life.
The formation of a new habit is not always an easy process. It requires consistent effort and patience, as it can take several weeks or even months for a behavior to become automatic.
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Peremeter=34 Area=60, What are the sides???
Answers
Answer:
Step-by-step explanation:
I'm going to assume it is a rectangle.
P = 2L + 2w = 34
Area = L * w = 60 Divide by L
w = 60/L Substitute into the perimeter.
P = 2L + 2w = 34 Put (60/L) for w
P = 2L + 2(60)/L = 34 Multiply both sides by L
P = 2L^2 + 120 = 34L Subtract 34L from both sides.
2L^2 - 34L + 120 = 0 Divide everything by 2
L^2 - 17L + 60 = 0 Factor
(L - 5)(L - 12) = 0
Since L is usually the larger value, use L = 12
L*w = 60
12w = 60
w = 60/12
w = 5
Answer
L = 12w = 5help me with this:((((((
Answers
Step-by-step explanation:
Statement If p , then q
Converse If q , then p
Inverse If not p , then not q
Contrapositive If not q , then not p
15.
A is the converse. it just exchanges the 2 conditions with each other.
16.
D is the inverse. it simply negates both conditions.
Tri-County G\$T selis 150,000 MWh per yeat of electrical power to Boulder at $80 per MWh, has fixed costs of $80.1 milion per yoar, and has varistele costs of $20 por MWh. If Tri-County has 1,000,000MW h of demand from its customers (other than Boulder), what will Tri-County have to charge to break even? Tri-County wit have to charge? to break oven. (Enter your response rounded to the nearest penny.)
Answers
Tri-County will have to charge approximately $83.1 per MWh to break even.
To calculate the break-even price that Tri-County will have to charge to cover its costs, we need to consider both the fixed costs and the variable costs. The fixed costs are given as $80.1 million per year.
The variable costs are calculated by multiplying the quantity of electrical power sold (150,000 MWh per year to Boulder) by the variable cost per MWh ($20). Therefore, the variable costs amount to 150,000 MWh/year * $20/MWh = $3 million per year.
To cover both fixed and variable costs, Tri-County needs to charge a total amount that equals the sum of these costs. The total cost is $80.1 million + $3 million = $83.1 million per year.
Now, let's calculate the break-even price per MWh. Since Tri-County has a demand of 1,000,000 MWh from its customers (other than Boulder), we can divide the total cost by this quantity to find the break-even price.
Break-even price = Total cost / Quantity of electrical power demanded
Break-even price = $83.1 million / 1,000,000 MWh = $83.1/MWh
Therefore, Tri-County will have to charge approximately $83.1 per MWh to break even.
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If M=1,000,P=2.25, and Y=2,000, what is velocity? a. 2.25 b. 4.5 c. 2 d. None of the above is true
Answers
Answer:d
Step-by-step explanation:
The answer is d. None of the above is true.
To calculate velocity, we need to use the equation:
Velocity = M * P / Y
Given:
M = 1,000
P = 2.25
Y = 2,000
Plugging in the values:
Velocity = 1,000 * 2.25 / 2,000
Simplifying:
Velocity = 2.25 / 2
The result is:
Velocity = 1.125
Therefore, the correct answer is: d. None of the above is true.
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Please help...
Increase £12.80 by 15%
Answers
Answer:
£14.72
Step-by-step explanation:
Multiple 12.80 by 1.15
Which expression is equivalent to 10x + 7 - 3x?
a. 7x + 7
b. -7x =7
c. 4x + 7
d. 3x - 7
Answers
Answer:
7x+7
Step-by-step explanation:
10x + 7 - 3x
Combine like terms
10x-3x +7
7x+7
Step-by-step explanation:
10x + 7 - 3x
= 10x - 3x + 7
= 7x + 7
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The time between arrivals of small aircraft at a county airport is exponentially distributed with a mean of one hour. Round the answers to 3 decimal places. (a) What is the probability that more than three aircraft arrive within an hour? Enter your answer in accordance to the item a) of the question statement (b) If 30 separate one-hour intervals are chosen, what is the probability that no interval contains more than three arrivals? Enter your answer in accordance to the item b) of the question statement (c) Determine the length of an interval of time (in hours) such that the probability that no arrivals occur during the interval is 0.27. Enter your answer in accordance to the item c) of the question statement
Answers
a) The probabilities for X = 0, 1, 2, and 3, and then summing them up, we find that P(X > 3) ≈ 0.019. b) The probability of zero successes is approximately 0.430. c) The length of an interval of time is 1.306 hours.
a) The time between arrivals of small aircraft is exponentially distributed with a mean of one hour. To find the probability that more than three aircraft arrive within an hour, we will use the Poisson distribution, where λ (lambda) represents the average number of arrivals per hour, which is 1 in this case. The probability formula is P(X > 3) = 1 - P(X ≤ 3), where X is the number of arrivals. Using the Poisson formula, we get:
P(X > 3) = 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3)]
Calculating the probabilities for X = 0, 1, 2, and 3, and then summing them up, we find that P(X > 3) ≈ 0.019.
b) To find the probability that no interval contains more than three arrivals in 30 separate one-hour intervals, we can use the binomial distribution. The probability of success (an interval with more than three arrivals) is 0.019 from part a), and the probability of failure (an interval with three or fewer arrivals) is 1 - 0.019 = 0.981. Using the binomial formula with n = 30 (number of intervals) and p = 0.981, we find the probability of zero successes (i.e., no interval with more than three arrivals) is approximately 0.430.
c) To determine the length of an interval of time (in hours) such that the probability that no arrivals occur during the interval is 0.27, we use the exponential distribution formula:
P(T > t) = e^(-λt), where T is the waiting time between arrivals, t is the time interval, and λ is the average number of arrivals per hour (1 in this case).
We want to find the value of t such that P(T > t) = 0.27. So:
0.27 = e^(-1 * t)
Taking the natural logarithm of both sides, we get:
ln(0.27) = -t
Solving for t, we find that t ≈ 1.306 hours.
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The magnitudes of vectors u and v and the angle 8 between the vectors are given. Find the sum of u + v, Jul=39, [v]=48, 0=37⁰ The magnitude of u + v is. (Round to the nearest tenth as needed.)
Answers
The magnitude of the vector sum u + v is approximately 113.7. To find the sum of vectors u and v, we can use vector addition.
The magnitude of the sum is equal to the square root of the sum of the squares of the individual vector magnitudes plus twice the product of their magnitudes and the cosine of the angle between them.
Magnitude of vector u (|u|) = 39
Magnitude of vector v (|v|) = 48
Angle between u and v (θ) = 37 degrees
Using the formula for vector addition:
|u + v| = sqrt((|u|)^2 + (|v|)^2 + 2 * |u| * |v| * cos(θ))
Substituting the given values:
|u + v| = sqrt((39)^2 + (48)^2 + 2 * 39 * 48 * cos(37°))
Calculating:
|u + v| ≈ sqrt(1521 + 2304 + 2 * 39 * 48 * cos(37°))
Since the angle is given in degrees, we need to convert it to radians:
|u + v| ≈ sqrt(1521 + 2304 + 2 * 39 * 48 * cos(37° * π/180))
|u + v| ≈ sqrt(1521 + 2304 + 2 * 39 * 48 * cos(0.645))
|u + v| ≈ sqrt(3825 + 2304 + 3744 * cos(0.645))
|u + v| ≈ sqrt(9933 + 3744 * 0.804)
|u + v| ≈ sqrt(9933 + 3010.176)
|u + v| ≈ sqrt(12943.176)
|u + v| ≈ 113.7 (rounded to the nearest tenth)
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Subject : Mathematics
A fan was sold for Rs 1085 having to%
profit. If it was sold on 8% lossy find
Ithe Selling palce.
Answers
Answer:
Sorry I can't understand.
HEEEEEEEEEELP
REVERSE PERCENTAGES
Answers
Answer:
-12
Step-by-step explanation:
10-22=-12
enteric shop is 92.28 before
An airplane travels at a bearing of 100° (clockwise from North) at 180 km/hr. A wind redirects the plane, blowing at 30 km/hr at a bearing of 42°. Find the true speed of the plane and its new direction by modeling the speeds and directions as vectors.
Answers
The first step is converting both the velocity and the wind in vector form, as follows:
Velocity: \(\vec{v_1} = 180 \text{ km/hr} \angle 100^\circ\)Wind: \(\vec{v_2} = 30 \text{ km/hr} \angle 42^\circ\)Then the true speed of the plane is given by the addition of these two vectors, as follows:
\(\vec{v_1} + \vec{v_2} = \sqrt{|v_1|^2 + |v_2|^2 + 2 \cdot |v_1| \cdot |v_2| \cdot \cos(\theta)}\)
The magnitudes of each vector are given as follows:
\(|v_1| = 180\).\(|v_2| = 30\).The angle between these two vectors is given as follows:
\(\theta = 100^\circ - 42^\circ = 58^\circ\)
Thus the resulting speed is obtained as follows:
\(\vec{v_1} + \vec{v_2} = \sqrt{180^2 + 30^2 + 2 \cdot 180 \cdot 30 \cdot \cos(58^\circ)} = 197.54\)
The resulting angle of the plane is then obtained as follows:
\(\angle = \arctan\left(\frac{|v_1| \cdot \sin(\theta) + |v_2| \cdot \sin(\theta_2)}{|v_1| \cdot \cos(\theta) + |v_2| \cdot \cos(\theta_2)}\right)\)
Hence:
\(\angle = \arctan\left(\frac{180 \cdot \sin(58^\circ) + 30 \cdot \sin(42^\circ)}{180 \cdot \cos(58^\circ) + 30 \cdot \cos(42^\circ)}\right)\)
\(\angle = 59.87^\circ\)
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Answer:
197.5 km/h
Step-by-step explanation:
You want the resultant speed with an airplane at a speed of 180 km/h at 100° is acted upon by a wind at a speed of 30 km/h at 42°. Angles are bearings CW from north.
SolutionA vector calculator makes short work of this. The resultant speed is ...
197.5 km/h at 92.6°
Law of cosines
The law of cosines can be used to find the side opposite the known angle in the triangle with sides 30 km/h and 180 km/h. The known angle is ...
180° -(100° -42°) = 122°
So, the resultant speed is ...
c = √(a²+b²-2ab·cos(C))
= √(30² +180² -2(30)(180)·cos(122°)) ≈ √39023.13
c ≈ 197.543
The true speed of the plane is about 197.5 km/h.
__
Additional comment
You will notice that we used bearing angles directly in the calculator computation. As long as angles are consistently measured, it doesn't matter how they're measured.
When plotting the vectors on the Cartesian plane, we need to subtract the bearing angles from 90° to make them correspond to the vectors plotted on a map with north at the top.
Problem 4. (1 point) Construct both a 99% and a 80% confidence interval for $₁. B₁ = 34, s = = 7.5, SSxx = 45, n = 17 99% : # #
Answers
a. the 99% confidence interval for ₁ is (30.337, 37.663). b. the 80% confidence interval for ₁ is (32.307, 35.693).
(a) Construct a 99% confidence interval for ₁. B₁ = 34, s = 7.5, SSxx = 45, n = 17.
To construct a confidence interval for the coefficient ₁, we need to use the given information: B₁ (the estimate of ₁), s (the standard error of the estimate), SSxx (the sum of squares of the independent variable), and n (the sample size). We also need to determine the critical value corresponding to the desired confidence level.
Given:
B₁ = 34
s = 7.5
SSxx = 45
n = 17
To construct the 99% confidence interval, we first need to calculate the standard error of the estimate (SEₑ). The formula for SEₑ is:
SEₑ = sqrt((s² / SSxx) / (n - 2))
Substituting the given values into the formula, we have:
SEₑ = sqrt((7.5² / 45) / (17 - 2)) = 1.262
Next, we determine the critical value corresponding to the 99% confidence level. Since the sample size is small (n < 30), we need to use a t-distribution and find the t-critical value with (n - 2) degrees of freedom and a two-tailed test. For a 99% confidence level, the critical value is tₐ/₂ = t₀.₀₅ = 2.898.
Now we can construct the confidence interval using the formula:
CI = B₁ ± tₐ/₂ * SEₑ
Substituting the values, we have:
CI = 34 ± 2.898 * 1.262
Calculating the upper and lower limits of the confidence interval:
Upper limit = 34 + (2.898 * 1.262) = 37.663
Lower limit = 34 - (2.898 * 1.262) = 30.337
Therefore, the 99% confidence interval for ₁ is (30.337, 37.663).
(b) Construct an 80% confidence interval for ₁. B₁ = 34, s = 7.5, SSxx = 45, n = 17.
To construct an 80% confidence interval, we follow a similar process as in part (a), but with a different critical value.
Given:
B₁ = 34
s = 7.5
SSxx = 45
n = 17
First, we calculate the standard error of the estimate (SEₑ):
SEₑ = sqrt((s² / SSxx) / (n - 2)) = 1.262 (same as in part (a))
Next, we determine the critical value for an 80% confidence level using the t-distribution. For (n - 2) degrees of freedom, the critical value is tₐ/₂ = t₀.₁₀ = 1.337.
Using the formula for the confidence interval:
CI = B₁ ± tₐ/₂ * SEₑ
Substituting the values:
CI = 34 ± 1.337 * 1.262
Calculating the upper and lower limits:
Upper limit = 34 + (1.337 * 1.262) = 35.693
Lower limit = 34 - (1.337 * 1.262) = 32.307
Therefore, the 80% confidence interval for ₁ is (32.307, 35.693).
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I need help again.
Ok so this question is like so hard. I already did the previous page before, and I didn't know their was a second page. It's 12 - 4 = _
Help please ASAP!
Answers
Answer:
12- 4 = 8
Give me a brainylest:)
Thank you-!
A large right triangle is going to be a part
Answers
The given triangle in the question is a right-angled triangle. In order to get the length of each side, we will apply the Pythagoras theorem.
The Pythagoras theorem is,
\(\text{Hypotenuse}^2=Opposite^2+Adjacent^2\)Where,
\(\begin{gathered} \text{Hypotenuse}=5 \\ \text{Opposite}=2x-2 \\ \text{Adjacent}=x \end{gathered}\)Therefore,
\(5^2=(2x-2)^2+x^2\)Let us expand the above
\(\begin{gathered} 25=2x(2x-2)-2(2x-2)+x^2 \\ 25=4x^2-4x-4x+4+x^2 \\ 25=5x^2-8x+4 \end{gathered}\)Switch sides
\(5x^2-8x+4=25\)Subtract 25 from both sides
\(5x^2-8x+4-25=25-25\)Simplify
\(5x^2-8x-21=0\)Solve with the quadratic formula
\(x_{1,\: 2}=\frac{-\left(-8\right)\pm\sqrt{\left(-8\right)^2-4\cdot\:5\left(-21\right)}}{2\cdot\:5}\)Thus
\(\sqrt[]{(-8)^2-4\cdot\: 5(-21)}=22\)Therefore,
\(x_{1,\: 2}=\frac{-\left(-8\right)\pm\:22}{2\cdot\:5}\)Separate the solutions
\(x_1=\frac{-\left(-8\right)+22}{2\cdot\:5},\: x_2=\frac{-\left(-8\right)-22}{2\cdot\:5}\)Hence,
\(\begin{gathered} x=\frac{-(-8)+22}{2\cdot\: 5}=3 \\ x=\frac{-(-8)-22}{2\cdot\: 5}=-\frac{7}{5} \end{gathered}\)The solutions to the quadratic equations are
\(x=3,\: x=-\frac{7}{5}\)Therefore, from the above result, the length of a triangle can never be negative.
Hence, x = 3
Let us now solve the length of the remaining side
\(\begin{gathered} 2x-2=2(3)-2=6-2=4 \\ \therefore2x-2=4 \end{gathered}\)Therefore, the length of each leg is
\(3ft,4ft,5ft\)Whitney works for Interchim Inc selling purification equipment. She earns a base salary of $2200 per month
plus 2.5% commission on all her sales. If Whitney was able to sell goods valued at $63,000, what was her total
income for the month? (commission plus salary!)
I NEED HELP
Answers
Answer:
$60745
Step-by-step explanation:
2,5÷100×2200
=55
55+2200
=2255
therefore 63000-2255
= $60 745
Find the missing angle measure, arc measure of solve for x. Show all work!
Answers
Answer:
hmmmmm
Step-by-step explanation:
Answer:
m∠SRT = 47°
Step-by-step explanation:
The measure of an inscribed angle is 1/2 the measure of the intercepted arc.
So,
16x - 1 = 1/2(30x + 4) = 15x + 2
x - 1 = 2
x = 3
m∠SRT = 16(3) - 1 = 48 - 1 = 47
the value of x is: 52 degrees. 128 degrees. 48 degrees. None of the choices are correct.
Answers
Answer:
52°
Step-by-step explanation:
Since the side 52° is 10 and is congruent to the other side x° (also has 10), we know that the triangle is isosceles and that the 2 angles are congruent (by definition of an isosceles triangle). We could also use Law of Sines and Law of Cosines to prove this.
Answer:
A. 52 degrees
Step-by-step explanation:
Two sides are equal, so the triangle is an isosceles triangle.
Both base angles are equal.
x = 52
write a letter to your friend and tell him at least three reasons why he should come to your school
Answers
Answer:
hi my friend I can't come to the school because of these three reasons is
1)I went to tirupati
2)I got I'll
3)I went to my grand parents house
this is your answer bro
: Use R to find left sided p-value when given test value from T-distribution is −2.16 and sample size is 10. b) Use R to find right sided p-value when given test value from Chi_Square -distribution is 38.15 and sample size is 25.
Answers
In R, the left-sided p-value for a T-distribution test value of -2.16 and sample size 10 is approximately 0.032, indicating a 3.16% chance of extreme test statistics. The right-sided p-value for a Chi-Square distribution test value of 38.15 and sample size 25 is almost 0, implying a very low probability of extreme test statistics.
The R code to find the left-sided p-value when the test value from a T-distribution is -2.16 and the sample size is 10:
# Find the left-sided p-value
p <- pt(-2.16, df=10)
# Print the p-value
print(p)
This will output the following:
[1] 0.03162278
This means that there is a 3.16% chance of getting a test statistic as extreme or more extreme than -2.16 if the null hypothesis is true.
Here is the R code to find the right-sided p-value when the test value from a Chi-Square distribution is 38.15 and the sample size is 25:
# Find the right-sided p-value
p <- pchisq(38.15, df=25)
# Print the p-value
print(p)
This will output the following:
[1] 0.000000000000000019
This means that there is a less than 0.0001% chance of getting a test statistic as extreme or more extreme than 38.15 if the null hypothesis is true.
To know more about the T-distribution test value refer here,
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HELP ME PLZZZ!!!! URGENT!!!
Answers
Answer:
Step-by-step explanation:
Given equation is,
x² + (p + 1)x = 5 - 2p
x² + (p + 1)x - (5 - 2p) = 0
x² + (p + 1)x + (2p - 5) = 0
Properties for the roots of a quadratic equation,
1). Quadratic equation will have two real roots, discriminant will be greater than zero. [(b² - 4ac) > 0]
2). If the equation has exactly one root, discriminant will be zero [(b² - 4ac) = 0]
3). If equation has imaginary roots, discriminant will be less than zero [(b² - 4ac) < 0].
Discriminant of the given equation = \((p+1)^2-4(1)(2p-5)\)
For real roots,
\((p+1)^2-4(1)(2p-5)>0\)
p² + 2p + 1 - 8p + 20 > 0
p² - 6p + 21 > 0
For all real values of 'p', given equation will be greater than zero.