The power of the test against the specific alternative is given by 1 minus the probability of making a Type II error. Therefore, the power is 0.86= 86%
In statistical hypothesis testing, the power of a test is the probability that it correctly rejects a null hypothesis when a specific alternative hypothesis is true. In this case, we are given that the test has a significance level of α = 0.01, which means that the test rejects the null hypothesis if the probability of obtaining the observed result, or one more extreme, under the null hypothesis is less than 0.01.
However, we also know that when a specific alternative hypothesis is true, the test has a probability of making a Type II error of 0.14. This means that there is a 14% chance that the test fails to reject the null hypothesis, even though the alternative hypothesis is true.
Therefore, the power of the test against this specific alternative hypothesis is given by 1 minus the probability of making a Type II error, which is:
Power = 1 - P(Type II error) = 1 - 0.14 = 0.86
So, the power of the test against the specific alternative hypothesis is 0.86 or 86%. This means that when the alternative hypothesis is true, the test correctly rejects the null hypothesis 86% of the time.
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The function p(t) = 3(2)* represents the population of a certain type of bacteria
after t days.
What is the population of the bacteria after 5 days?
The pοpulatiοn οf the bacteria after 5 days is 96.
What is an expοnential functiοn?An expοnential functiοn is a mathematical functiοn οf the fοrm f(x) = ab^x, where a and b are cοnstants, and x is a variable. The base, b, is a pοsitive number, typically greater than 1, that determines hοw quickly the functiοn grοws οr decays. The expοnent, x, is the independent variable, and represents the pοwer tο which the base is raised.
Tο find the pοpulatiοn οf the bacteria after 5 days, we need tο substitute t = 5 intο the given functiοn:
p(5) = 3(2)⁵
Simplifying the expressiοn, we get:
p(5) = 3(32)
p(5) = 96
Therefοre, the pοpulatiοn οf the bacteria after 5 days is 96.
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The property tax in one town was $6. 95 per $1000 value in the year 2012. The tax increased to $7. 71 per $1,000 value in 2013. What effect did that have on the property tax for a house with a value of $100,000?
a) increase $76
b) decrease $96
c) increase $ 791
d) decrease $695
The effect of the tax increase from 2012 to 2013 for a house with a value of 100,000 was an increase of 76.
The property tax in one town was 6.95 per 1000 value in the year 2012. In 2013, the property tax increased to 7.71 per 1000 value. This means that in 2013, the property tax for a house with a value of 100,000 would be 771.
To calculate the effect that the tax increase had on the property tax for a house with a value of 100,000, we can use the following formula:
Effect of Tax Increase = (New Tax Rate - Old Tax Rate) x Value of Property
Using this formula, the effect of the tax increase for a house with a value of $100,000 would be:
Effect of Tax Increase = ($7.71 - $6.95) x $100,000
Effect of Tax Increase = $0.76 x $100,000
Effect of Tax Increase = $76
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Need help with this, can anyone help out?
a) The minimum number of hikers who could have walked between 6 miles and 17 miles is 9.
b) The maximum number of hikers who could have walked between 6 miles and 17 miles is 19.
What is meant by minimum and maximum value?When the derivative equals 0, we will rearrange the function using elementary algebraic principles to find the value for x. The x-coordinate of the function's vertex, which will be the point where the maximum or lowest will occur, and this is provided in this answer.
The solution will be put back into the original function to determine the minimum or maximum.
Thus, looking at the given table, minimum number will be 9
Similarly the maximum number will be 15 hikers.
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What is the measure of the major arc?
R
Q
150*
O A. 150°
OB. 220°
O C. 195°
OD. 210°
Answer:
210°
Step-by-step explanation:
Measure of unknown arc = Measure of full circle - Measure of given arc
= 360° - 150°
= 210° --- Option D
Please mark brainliest.
Thanks.
Work out
Please help lol it’s for homework thanksss
By working out or simplifying the given statement we will get a) 26 and the equation b) 8 2/3.
what are fractions?In mathematics, a fraction is used to denote a piece or component of the whole. It stands for the proportionate components of the whole. Numerator and denominator are the two components that make up a percentage. The numerator is the number at the top, and the remainder is the number at the bottom.
a) By converting the numbersr into improper fraction we will get
4 1/3 = (4 x 3 + 1) / 3 = 13 / 3
By multiplying the both of the fractions:
13 / 3 * 6 =[tex]\frac{78}{3}[/tex] = 26
= 4 1/3 * 6 simplifies to 26.
b) Now we will convert both of the mixed numbers to improper fractions and we will get :
[tex]\frac{23}{5}[/tex] = [tex]\frac{2*5+3}{5}[/tex] = [tex]\frac{13}{5}[/tex]
[tex]\frac{31}{3}[/tex] = [tex]\frac{3*3+1}{3\\}[/tex] = [tex]\frac{10}{3}[/tex]
By multiplying both of the fractions:
[tex]\frac{13}{5} * \frac{10}{3\\}[/tex] = [tex]\frac{130}{5}[/tex]
We can simplify say that the fraction by dividing both of the numerator and denominator by their greatest common factor, which is 5:
[tex]\frac{130}{15}[/tex] =[tex]\frac{26}{3\\}[/tex]
Therefore, we come to a conclusion where
2 3/5 * 3 1/3 simplifies to 26/3 or 8 2/3.
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round each number to the nearest hundred
124= 2,311= 48=
Answer:
124= 100
2,311= 2,300
48= 0
Step-by-step explanation:
Place the two small triangles on top of the square what is the area of the each small triangle
The area of each small triangle is equal to √(7)/8 times the square of the length of one side of the square.
First, we need to find the area of the larger triangle that is created by placing the two small triangles on top of the square. Let's call the base of the larger triangle "b" and the height of the larger triangle "h".
To find "b", we can use the length of one side of the square since the two small triangles are placed on top of the square. Let's call the length of one side of the square "s".
Since the two small triangles are congruent, we know that the base of each small triangle is equal to half of one side of the square, which is s/2. Therefore, the total base of the larger triangle is equal to the sum of the bases of the two small triangles, which is s/2 + s/2 = s.
To find "h", we need to use the Pythagorean theorem since the larger triangle is a right triangle. Let's call the hypotenuse of the larger triangle "c". Since the hypotenuse is the diagonal of the square, we know that its length is √(2)*s.
Using the Pythagorean theorem, we can find the height of the larger triangle:
h² + (s/2)² = c² h² + (s/2)² = (√(2)s)² h² + s²/4 = 2s² h² = 7s²/4 h = √(7)/2 x s
Now that we have found "b" and "h", we can use the formula for the area of a triangle:
Area = 1/2 x base x height
Area of the larger triangle = 1/2 x s x √(7)/2 x s = √(7)/4 x s²
Finally, we can find the area of each small triangle by dividing the area of the larger triangle by two:
Area of each small triangle = 1/2 x (√(7)/4 x s²) = √(7)/8 x s²
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The angle between the length of a rectangle and its diagonal is 30°. If the length of the rectangle is 6cm, find the length of the diagonal.
Answer:
6√3 cm.
Step-by-step explanation:
The angle between the length of a rectangle and its diagonal is 30°. If the length of the rectangle is 6cm, find the length of the diagonal.
Let's call the width of the rectangle "w" and the diagonal "d". We know that the angle between the length and diagonal is 30 degrees, which means that the angle between the width and diagonal is 90 - 30 = 60 degrees (since the angles in a triangle add up to 180 degrees).
Now, we can use trigonometry to find the length of the diagonal. Specifically, we can use the sine function, which relates the lengths of the sides of a right triangle to the angles opposite them:
sin(angle) = opposite/hypotenuse
In this case, the angle we're interested in is 60 degrees, the opposite side is the width "w", and the hypotenuse is the diagonal "d". So we can write:
sin(60) = w/d
Solving for "d", we get:
d = w/sin(60)
Now we just need to find the width of the rectangle. Since we know the length of the rectangle is 6cm, we can use the fact that the opposite sides of a rectangle are equal to each other to write:
w = length*sin(30) = 6sin(30)
We can simplify sin(30) to 1/2, so:
w = 6/2 = 3
Now we can substitute this value of "w" into our expression for "d" to get:
d = w/sin(60) = 3/sin(60)
We can simplify sin(60) to √3/2, so:
d = 3/(√3/2) = 6/√3 = 2√3 * 2
So the length of the diagonal is 2√3 times the length of the width, or approximately 3.46 times the length of the width. Therefore, the length of the diagonal is:
d = 2√3 * 3 = 6√3 cm.
Please help I will give brainliest
By CER methοd it can be cοncluded that ABCD is a parallelοgram.
What is the CER methοd?
CER stands fοr "Cοngruent, Equal, and Midpοint Rule". This methοd is based οn the prοperties οf parallelοgrams, where οppοsite sides are parallel and cοngruent, and οppοsite angles are equal. By using the CER methοd, we can prοve that a quadrilateral is a parallelοgram if it satisfies the cοnditiοns οf having οppοsite sides cοngruent, οppοsite angles equal, and diagοnals bisecting each οther at their midpοint.
Tο shοw that ABCD is a parallelοgram, we need tο demοnstrate that bοth pairs οf οppοsite sides are parallel.
Let's begin by finding the slοpe οf each side using the fοrmula:
slοpe = (change in y) / (change in x)
Slοpe οf AB = (3 - (-1)) / (1 - 2) = 4/-1 = -4
Slοpe οf BC = (5 - 3) / (6 - 1) = 2/5
Slοpe οf CD = (1 - 5) / (7 - 6) = -4
Slοpe οf DA = (-1 - 1) / (2 - 7) = -2/5
Nοw, we can use the fact that twο lines are parallel if and οnly if their slοpes are equal. Thus, we need tο check whether AB is parallel tο CD and whether BC is parallel tο DA.
AB is parallel tο CD if their slοpes are equal. Since the slοpe οf AB is -4 and the slοpe οf CD is alsο -4, we can cοnclude that AB is parallel tο CD.
BC is parallel tο DA if their slοpes are equal. Since the slοpe οf BC is 2/5 and the slοpe οf DA is alsο 2/5, we can cοnclude that BC is parallel tο DA.
Therefοre, since bοth pairs οf οppοsite sides are parallel, we can cοnclude that ABCD is a parallelοgram.
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16. Let Kanika’s present age be x years. Complete this question
Mother’s age is 3 years less than that
of her father.
The expression for Kanika's mother's age, given Kanika's age and her father's is 32 + x .
How to express the age ?To find Kanika's mother's age, we need to first find Kanika's age in relation to her father's who is 35 years more than her age.
Her father's age is therefore:
= Kanika's age + 35
= x + 35
Kanika's mother is 3 years less than the father which makes it :
= x + 35 - 3
= x + 32
In conclusion, Kanika's mother's age when expressed in terms of Kanika's age, is x + 32 .
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The first part of the question is:
Let Kanika's present age be x years. Her father's age exceeds her age by 35 years
Triangles pqr and sqt are similar. the dimensions are given in centimeters (cm). the length of pq is 261 cm. what is the length of tq, in centimeters, to the nearest whole number?
The solution is, the length of TQ, in centimeters, to the nearest whole number is 167cm.
What is the scale factor?
A scale factor is when you enlarge a shape and each side is multiplied by the same number. This number is called the scale factor. Maps use scale factors to represent the distance between two places accurately.
here, we have,
given that,
Triangles PQR and SQT are similar.
so, from the given figure we get,
PR/ST = RQ/TQ
now, we have,
the scale factor = PR/ST
= 75/50
=3/2
= 1.5
so, RQ/TQ = 1.5
or, TQ = RQ/1.5
=250/1.5
=166.66
Hence, The solution is, the length of TQ, in centimeters, to the nearest whole number is 167cm.
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find the length of the missing side of the right triangle ABC. Leave your answer in simplest radical form
Answer:
Step-by-step explanation
ayo so basically this is a pythagorus theorum question
the formula is
c²= a² + b²
where c is the hypotenuse (the longest line , opposite of the right angle aka here 13ft !!)
a and b , where a is the down line as a (4ft ) and b the unknown one
(just remember and lookout for the hypotenuse!)
so now put the numbers in formula
(13)²= (4)² +(b)²
169= 16 +(b)²
169-16=(b)²
153= (b)²
(put b first )
(b)² = 153
√(b)²= √153
(the square gets cut with the square root)
b= 12.36931688
b+12.4
-7 - 4 is equivalent to?
-11
11
-3
3
Let f be a one-to-one function. If f(2)=7 and
f-1(-3)=5, determine the following ;
(a). f-1(7)
(b) f(5)
a) We have f−1(7) = 2.Thus, the value of f-1(7) is 2.
b) We can conclude that f( f−1(−3) ) = f(5) = −3.Thus, the value of f(5) is -3.
(a) Determine f-1(7)Given that f be a one-to-one function and f(2)=7.Since f is one-to-one, there exists a unique inverse function f−1. We have f(2) = 7, hence 2 = f−1(7). Therefore, we have f−1(7) = 2.Thus, the value of f-1(7) is 2.(b) Determine f(5)Given that f be a one-to-one function and f−1(−3) = 5.Since f is one-to-one, there exists a unique inverse function f−1. Hence, f( f−1(x) ) = x and f−1( f(x) ) = x for all x in the domain of f. Also, f(2) = 7, thus f−1(7) = 2. Therefore, we can conclude that f( f−1(−3) ) = f(5) = −3.Thus, the value of f(5) is -3.
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please i beg you can you help me with this!!!!
Answer:
it's negative one over five...... -1\5
Can you name the angle pairs and type the correct code
The angle pairs are:
1. E. same side interior angles
2. G. Corresponding angles
3. A. Vertical angles
4. I. Supplementary angles
What are Angle Pairs?Angle pairs are two angles that share a common side and a common vertex. Angle pairs are important in geometry because they allow us to study the relationships between angles and the properties of geometric figures.
There are several types of angle pairs, including:
Complementary angles: Two angles are complementary if their sum is 90 degrees.Supplementary angles: Two angles are supplementary if their sum is 180 degrees.Vertical angles: Two angles are vertical if they share a common vertex and their sides form opposite rays.Alternate interior angles: Two angles are alternate interior angles if they are on opposite sides of a transversal line and inside the two parallel lines, and they are congruent.Alternate exterior angles: Two angles are alternate exterior angles if they are on opposite sides of a transversal line and outside the two parallel lines, and they are congruent.By understanding the properties of these angle pairs, we can solve problems in geometry involving angles and their measures.
Therefore:
1. The angles are E. same side interior angles
2. Angles labelled 2 are: G. Corresponding angles
3. Angles labelled 3 are: A. Vertical angles
4. Angles labelled 4 are: I. Supplementary angles
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Select the expression that will calculate how many eighths are in 2 bars? Use the model to help you.
2 equal-sized bars each labeled
A.
2
÷
8
B.
8
÷
2
C.
2
÷
1
8
D.
8
÷
1
2
Step-by-step explanation:
To know how many eighths you have in two bars, simply divide 2 by 1/8
2/1 ÷ 1/8
Ans 2÷ ⅛
Students (ages 10–18) were surveyed to choose a favorite free-time activity.
Which category has the lowest marginal frequency?
-Middle school students who chose playing sports
-High school students who chose watching movie/TV
-Students that are in high school
-Students who chose playing sports
The category which has the lowest marginal frequency is the marginal frequency of middle school students who chose to play sports.
What is meant by marginal frequency?
By dividing the sum or total of a row or the sum or total of a column by the total number of observations in a dataset, one can get the marginal relative frequency of a data set. This dataset is presented as a two-way table for ease of understanding. Although the percentage value is typically chosen, the marginal relative frequency can be stated as either a decimal or a percentage number.
Here,
The total number of middle school students = 21
Number of middle school students playing sports = 21 - 16 = 5
Number of high school students watching movies = 19-16 = 3
Total number of high school students = 11 + 3 = 14
Total number of students = 14 + 21 = 35
Now,
The marginal frequency of middle school students who chose to play sports = 5 / 35 = 0.143
The marginal frequency of high school students who decided to watch movies/TV = 3/35 = 0.0857
The marginal frequency of students in high school = 14/35 =0.4
The marginal frequency of students who chose to play sports = 15/35
= 0.429
Therefore the category which has the lowest marginal frequency is the marginal frequency of middle school students who chose to play sports.
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Jobs arriving to a computer server have been found to require CPU
time that can be modeled by an exponential distribution with a mean of 140 ms
(milliseconds). The CPU scheduling discipline is quantum-oriented so that a job not
completed within a quantum of 100ms will be routed back to the tail of the queue of waiting
jobs.
a. What is the probability that an arriving job is forced to wait for a second quantum (that is,
it will be forced to wait for more than 100ms)?
b. What is the probability that the fifth arriving job of a day will be the first one that is
forced to wait for a second quantum (that is, it will be forced to wait for more than
100ms)
The probability of the fifth job being the first one that is forced to wait for a second quantum is 0.0266.
What is probability?Probability is the measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty. Probability is calculated by taking all possible outcomes into consideration and then dividing the number of favourable outcomes by the total number of possible outcomes.
The probability that an arriving job is forced to wait for a second quantum is the probability of that job requiring more than 100ms of CPU time. This probability can be calculated by taking the cumulative distribution function of the exponential distribution and subtracting the probability of the job requiring 100ms or less of CPU time. The probability of the job requiring more than 100ms of CPU time is 0.6853.
This probability can be calculated by taking the probability of the first four jobs requiring less than 100ms of CPU time and multiplying it by the probability of the fifth job requiring more than 100ms of CPU time.
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While shopping for clothes, jaclyn spent $37 less than 2 times what tracy spent. jaclyn spent $13. Write and solve an equation to find how much tracy spent. Let x represent how much tracy spent.
Answer:
Jaclyn spent $37 less than 2 times what Tracy spent:
2x - 37Jaclyn spent $13:
13We can set these two expressions equal to each other to get an equation:2x - 37 = 13Now we can solve for x:2x = 50x = 25So Tracy spent $25.
Answer:
Tracy spent $25.
Step-by-step explanation:
Tracy spent x.
" Jaclyn spent $37 less than 2 times what Tracy spent."
Jaclyn spent 2x - 37
Jacklyn spent $13
2x - 37 = 13
Add 37 to both sides.
2x = 50
x = 25
Tracy spent $25.
right gets brainliest
Answer:
C. Dwayne begins with more tickets than Lyla.
Step-by-step explanation:
We can see from the chart and what is given that Dwayne starts with 600 tickets and Lyla starts with 500 tickets.
Dwayne is selling 5 tickets per minutes, just like Lyla; Option A and B are false. You can calculate Dwayne's sell rate using the slope formula.
[tex]\frac{600-580}{8-4} =\frac{20}{4} \\ = 5[/tex]
Choice D. is false because we just said that Dwayne started with 100 more tickets than Lyla.
The credit card with the transactions described on the right uses the average daily balance method to calculate interest. The monthly interest rate is 1.5% of the average daily balance. Calculate parts a-d using the statement on the right. a. Hind the average dally balance for the biling period. Kound to the nearest cent. The average daily balance for the billing period is $ (Round to the nearest cent as needed.) b. Find the interest to be paid on April 1, the next billing date. Round to the nearest cent. The interest to be paid on April 1 is $ (Use the answer from part a to find this answer. Round to the nearest cent as needed.)
The average daily balance is calculated by taking the sum of all the daily balances during a billing period and dividing it by the number of days in that period. The interest to be paid on April 1 is $150 * 1.5% = $2.25.
a. The average daily balance for the billing period is calculated by taking the sum of all the daily balances during the billing period and dividing it by the number of days in that period. For example, if the daily balances for the billing period are $100, $150, and $200, then the average daily balance is ($100 + $150 + $200) / 3 = $150. This can be rounded to the nearest cent if necessary.
b. The interest to be paid on April 1 is calculated by multiplying the average daily balance by the monthly interest rate of 1.5%. For example, if the average daily balance is $150, then the interest to be paid on April 1 is $150 * 1.5% = $2.25. This can be rounded to the nearest cent if necessary.
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While at soccer practice, Abbey runs down the field at 10 meters per second. She has a constant speed and does not change direction. What is Abbey's acceleration?
Abbey's acceleration is 0 m/s². Acceleration is the rate of change of velocity with respect to time.
If Abbey is running down the field at a constant speed of 10 m/s, then her velocity is not changing. Therefore, her acceleration is 0 m/s².
Mathematically, we can represent acceleration using the equation:
a = (v₂ - v₁) / t
Where,
a = acceleration
v₁ = initial velocity
v₂ = final velocity
t = time
In Abbey's case, her initial velocity (v₁) and final velocity (v₂) are the same, since she has a constant speed. Therefore,
v₂ - v₁ = 10 m/s - 10 m/s = 0 m/s
And since there is no change in velocity, her acceleration is 0 m/s².
So, Abbey's acceleration is 0 m/s².
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If the sixth term of an(AP) is 37 and the sum of the first six terms is 147 find the
I) first term
I) the sum of the first fifteen terms
As a result, the arithmetic progression's first term is 22 and its first fifteen terms add up to 735. The AP's initial term is 22 and its first fifteen terms add up to 735.
The total of the first seven terms is seventy-five.
The formulae for the nth term and the sum of an arithmetic progression can be used to solve the issue.
We have the following using the nth term formula:
a + 5d = 37\s(6/2)(2a + 5d) = 147
3a + 15d = 147\sa + 5d = 49
We may find a by substituting d into either equation and finding:
a + 5(-3) = 37\sa = 22
Hence, the first term of the arithmetic progression is 22 and the formula for the total of the first fifteen terms is (15/2)(2a + 14d) = 735.
(15/2)(2(22) + 14(-3)) = 735
If we simplify, we get:
15 terms added together is 735
As a result, the AP's first term is 22 and its first fifteen terms add up to 735.
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I need help fast asap
Answer:
ln(28.1) ≈ 3.336
log(2/5) ≈ -0.398
Step-by-step explanation:
In this question, we are asked to find the natural log of 28.1 and the log base 10 of 2/5, rounded to the nearest thousandth.
The natural log of a number x is what power the constant e is raised to to get x.
For example,
ln(e²) = 2
We can approximate ln(28.1) by inputting it into a calculator.
ln(28.1) ≈ 3.33576957634
Then, we can round this to the nearest thousandth.
ln(28.1) ≈ 3.336
Notice how the 7 in the ten-thousandths place is greater than or equal to 5, so we round the thousandths place digit up to 6.
__
The log base 10 of a number x is what power the number 10 is raised to to get x. However, note that since log base 10 is the "common log" the base of 10 is not always specified.
log(2/5) ≈ -0.398
Notice how the output is negative, since 2/5 is less than 1 (and any number to the zeroth power is 1).
Hello. I'd like to order 9 halves of a cupcake for my family plus some extra for my 6 friends. Theyll each want a quarter of a cupcake
In response to the query, we can state that If you can't afford a whole equation cupcake, you should purchase: - 8
What is equation?An equation is a mathematical statement that proves the equality of two expressions connected by an equal sign '='. For instance, 2x – 5 = 13. Expressions include 2x-5 and 13. '=' is the character that links the two expressions. A mathematical formula that has two algebraic expressions on either side of an equal sign (=) is known as an equation. It depicts the equivalency relationship between the left and right formulas. L.H.S. = R.H.S. (left side = right side) in any formula.
For the family, 9 halves
six halves for my pals
So overall:
- For the two of them, 15 halves.
It means that you need 712 cupcakes in total.
If you can only afford a half-cupcake, you'll need to buy: 712
If you can't afford a whole cupcake, you should purchase:
- 8
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The functionf(x)= x−12x+6,x=1, is one-to-one. Find an equation forf −1(x), the inverse function.f −1(x)=x=2(Simplify your answer. Use integers or fractions for any numbers in the expression.) The domain of the plecewise function is(−[infinity],[infinity]). a. Graph the function. b. Use your graph to determine the function's range.f(x)={ 4x if x≤02 if x>0a. Choose the correct graph below. b. The range off(x)is (Type your answer using interval notation, set notation, and the union operator as need
Answer:find the inverse of f(x)=3x+2. Inverse functions, in the most ...
Step-by-step explanation:
A cheetah can travels
90 feet in 7 seconds.
How fast is that?
Answer:12.85
Step-by-step explanation:
speed=distance/time
Answer:
12.85
Step-by-step explanation:
90/7=12.85
speed=distance/time
In a consumer research study, several Meijer and Walmart stores were surveyed at random and the average basket price was recorded for each. You wish to determine if the average basket price for Meijer is different from the average basket price for Walmart. It was found that the average basket price for 25 randomly chosen Meijer stores (group 1) was $60.345 with a standard deviation of $10.8968. Similarly, a random sample of 20 Walmart stores (group 2) had an average basket price of $67.635 with a standard deviation of $12.936. Perform a two independent samples t-test on the hypotheses Null Hypothesis: μ1 = μ2, Alternative Hypothesis: μ1 ≠ μ2. What is the test statistic and p-value of this test? You can assume that the standard deviations of the two populations are statistically similar.
Question 3 options:
1) Test Statistic: -2.052, P-Value: 1.977
2) Test Statistic: -2.052, P-Value: 0.0461
3) Test Statistic: -2.052, P-Value: 0.023
4) Test Statistic: -2.052, P-Value: 0.977
5) Test Statistic: 2.052, P-Value: 0.0461
From the given data, the test statistic is -2.052 and the p-value is 0.0461. The correct answer is option 5.
To perform a two independent samples t-test, we can use the following formula to calculate the test statistic:
t = (x₁ - x₂) / (s_p × √(1/n₁ + 1/n₂))
where x₁ and x₂ are the sample means, n₁ and n₂ are the sample sizes, s_p is the pooled standard deviation, calculated as:
s_p = √(((n₁ - 1) × s₁² + (n₂ - 1) × s₂²) / (n₁ + n₁ - 2))
Let's calculate the test statistic:
x₁ = 60.345, s₁ = 10.8968, n₁ = 25
x₂ = 67.635, s₂ = 12.936, n₂ = 20
s_p = √(((25 - 1) × 10.8968² + (20 - 1) × 12.936²) / (25 + 20 - 2)) = 11.8074
t = (60.345 - 67.635) / (11.8074 × √(1/25 + 1/20)) = -2.052
The degrees of freedom for the t-distribution can be calculated as:
df = n₁ + n₂ - 2 = 43
Using a two-tailed t-test at a significance level of 0.05, the critical t-value is ±2.016.
The p-value for the test is the probability of obtaining a t-value as extreme or more extreme than the calculated t-value, assuming the null hypothesis is true. Since the calculated t-value is outside the critical region (|t| > 2.016), the p-value is less than 0.05 and we can reject the null hypothesis in favor of the alternative hypothesis.
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In an integer programming problem, if it is desired to have variable X be exactly twice the value of variable Y, the constraint that enforces this condition would be written as: A. 2X + Y = 0 B. X + 2Y = 0 C. 2X - Y = 0 D. X - 2Y = 0
The constraint 2X - Y = 0 states that the difference between variable X and twice variable Y must be equal to 0, meaning that X must be exactly twice the value of Y.The correct answer is C. 2X - Y = 0.
This constraint states that the difference between variable X and twice variable Y must be equal to 0. In other words, the value of variable X must be exactly twice the value of variable Y. This can be mathematically represented as 2X - Y = 0, meaning that 2 multiplied by X minus Y must equal 0. To illustrate this, let us assume that the value of variable X is 10 and the value of variable Y is 5. This means that 2X is equal to 20 and Y is equal to 5. When we subtract Y from 2X, we get 20 - 5 = 15. However, since the constraint states that the difference between X and twice Y must equal 0, the value 15 does not satisfy the condition. Therefore, the values of X and Y must be adjusted until the difference between X and twice Y equals 0. To satisfy the constraint, the value of X must be equal to 20 and the value of Y must be equal to 10. This means that X is exactly twice the value of Y, which satisfies the condition set by the constraint 2X - Y = 0.
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