The parallelogram with the parametric equations 1 + 2u + v is the surface integral.
What is the explanation?The surface element is
dS is equal to || r/u x r/dv || du dv.
where
r (u, v) is equal to x (u, v) I plus y (u, v) j plus z (u, v) k
r (u, v) = (u + v) I plus (u -v) j plus (1 + 2u + v) k
is the surface S's vector parameterization.
The surface's normal vector is
R / u x R / d
= I + j + k + 2) x I - j + k)
= 3 I + j - 2 k
as well as norm
|| r/dv x u r/u || = √(3² + 1² + (-2)²) = √(14) (14)
Calculate the integral now:
∫∫ (x + y + z) dS = √(14) ∫₀¹ ∫₀² (1 + 2u + v) = ((u + v) + (u - v)) du dv
= (14)... 01... 02 (3u + v + 1) du dv
= (14), 01 (3/2 u2, uv, and u), |02 dv
= √(14) ∫₀¹ (8 + 2v) dv
= √(14) (8v + 2v²) |₀¹
= 10 √(14) (14).
The parallelogram with the parametric equations x = u + v, y = u â' v, and z = 1 + 2u + v is the surface integral.
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below are representations of three different linear functions. write an equation for each representation table: x -3, -2, -1, 0. y 9,8,7,6
The representation table given indicates that the function is linear, as the difference between consecutive y-values (9-8, 8-7, and 7-6) is constant. Therefore, we can represent the function with a linear equation of the form y = mx + b, where m is the slope and b is the y-intercept.
To find the equation of the function, we can use the x- and y-values given in the table to solve for m and b. For example, using the x- and y-values (-3,9) and (-2,8), we can solve the equation 9 = m(-3) + b for m and b:
9 = -3m + b
8 = -2m + b
Subtracting the second equation from the first equation gives us:
1 = -m
So the slope of the function is -1. Substituting this value back into either equation gives us:
9 = -3(-1) + b
9 = 3 + b
6 = b
So the y-intercept of the function is 6. Therefore, the equation of the function is y = -1x + 6.
The other two representations can be solved in the same way to find the equations of those functions.
Ashley 1/2 package of raisins for a fruit cake. she then uses 1/9 of the remainder for muffins. what fraction of the package of raisins does she have left?..
The fraction of the package of raisins Ashley left with will be equal to 7/18.
What are arithmetic operations?The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.
They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.
As per the given information in the question,
Amount of raisins used for fruit cake = 1/2
Amount of raisins used for muffins = 1/9
Then, the amount of raisins left will be,
1 - (1/2 + 1/9)
= [18 - (9 + 2)]/18
= (18 - 11)/18
= 7/18
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The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures the motivation, attitudes, and study habits of college students. Scores range from 0 to 200 and follow (approximately) a Normal distribution, with mean of 115 and standard deviation 25. A researcher suspects that incoming freshmen have a mean ?, which is different from 115, because they are often excited yet anxious about entering college. To verify her suspicion, she tests the hypotheses H0: ? = 115 Ha: ? ? 115. The researcher gives the SSHA to 100 incoming freshmen and observes a mean score of 119. Assume that the scores of all incoming freshmen are approximately Normal with the same standard deviation as the scores of all college students. Based on the P-value computed choose the correct choice. Group of answer choices the data are statistically significant at level ? = .05 and at level ? = .01. the data are not statistically significant at level ? = .05 and not statistically significantat level ? = .01. the data are statistically significant at level ? = .05, but not at level ? = .01 the data are statistically significant at level ? = .01, but not at level ? = .05
The data are statistically significant at level = 0.05, but not at level = 0.01.
Given-
H0: μ = 115
HA: μ ≠ 115
The sample mean = 120
The standard deviation = 25
Standard error of mean 2.5
Solution-
If z = (xbar- μ ) / SE
Then the solution would be
z = (120-115) / 2.5
z = 2
P of the value = 2 P( z > 2) = 2(0.0228) = 0.0456 is the statistically significant level.
Therefore the answer is technically at .05 level of significance.
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Find the answers to the following multiplication problems without using a calculator. Reduce the product to their lowest terms and change improper fractions to mixed numbers.
2 / 8 x 15
After reducing the product in the lowest form and changing to mixed fraction , the answer is [tex]3\frac{3}{4}[/tex] .
In the question ,
it is given that ,
the two numbers are 2/8 and 15 ,
we have to find the product without using the calculator and express it in lowest form and then convert the improper fraction in to mixed fraction .
So , the product of 2/8 × 15 = 30/8
in lowest form it is 15/4 .
after converting the improper fraction 15/4 in mixed form ,
we get ,
15/4 = [tex]3\frac{3}{4}[/tex].
Therefore , the product of 2/8 × 15 is [tex]3\frac{3}{4}[/tex] .
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find the 25th, 50th, and 75th percentile from the following list of 32 data. please enter exact answers.
the 25th, 50th, and 75th percentile from the following list of 32 data are 25th percentile: 13 , 50th percentile: 21 , 75th percentile: 29.
To find the 25th percentile:
25th percentile: 25% of 32 = 8th number = 13
Count the total number of values in the data set, which is 32
Calculate 25% of 32, which is 8
Count 8 numbers from the beginning of the list and the 25th percentile is the 8th number, which is 13
To find the 50th percentile:
50th percentile: 50% of 32 = 16th number = 21
Count the total number of values in the data set, which is 32
Calculate 50% of 32, which is 16
Count 16 numbers from the beginning of the list and the 50th percentile is the 16th number, which is 21
To find the 75th percentile:
75th percentile: 75% of 32 = 24th number = 29
Count the total number of values in the data set, which is 32
Calculate 75% of 32, which is 24
Count 24 numbers from the beginning of the list and the 75th percentile is the 24th number, which is 29
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A chocolate chip cookie recipe calls for 2 3/4 cups of flour. You only have a 1/4 - cup measuring cup and a 3/4 - cup that you can use.
a. What are different combinations of the measuring cups that you can use to get a total of 2 3/4 cups of flour?
Answer:
Step-by-step explanation:
You could use 1 3/4's of a cup and 8 1/4's of a cup.
1 of the 3/4 cups is 3/4 so that covers the 3/4 of the cups of how much flour is needed.
8 of the 1/4 cups is 8/4 which is equal to 2 so that covers the rest of the flour needed.
And 2 + 3/4 is 2 3/4 which is the amount of flour that is needed.
OR
You could use 3 3/4's of a cup and 2 1/4's of a cup.
3/4 + 1/4=4/4
3/4+1/4=4/4
4/4 + 4/4 is the same thing as 1+1 which is 2, so that covers the 2 cups of the flour that is needed, and then you add another 3/4, now you have
2 3/4, which is the amount of flour needed.
(I think that there might be other ways/combinations but I only included 2..)
Which number completes the
sequence? Type in your answer.
1, 2, 4, 7, 12, 19, 30, ?
The required next term at the end of the sequence is 43.
What is arithmetic progression?Arithmetic progression is the series of numbers that have common differences between adjacent values are equal.
here,
1, 2, 4, 7, 12, 19, 30,
As
the sequence is the prime addition of the number, as.
1,
1 + 1 = 2
2 + 2 = 4,
4 + 3 = 7
7 + 5 = 12
12 + 7 = 19
19 + 11 = 30
30 + 13 = 43
Thus, At the end of the sequence, the required next term is 43.
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I need the statement and reason. It's difficult for me.
Answer:
DF is congruent to FG
Step-by-step explanation:
segment subractive property means to subract a part of a segment from another if they are equal. If we do this in this situation, we will see that DF is congruent to FG
Statement Reason
CF = EG GivenCD = EF GivenCF = CD + DF Segment additionEG = EF + FG Segment additionEG = CD + FG Substitution propertyCD + DF = CD + FG Substitution propertyDF = FG Subtraction propertyProvedA population has a mean of 200 and a standard deviation of 50. Supposed a sample of size 100 is selected and x is used to estimate μ.
What is the probability that the sample mean will be within ±5 of the population mean?
The probability that the sample mean will be within ±5 of the population mean is 0.6826
What is the probability of the sample mean?If the population is normally distributed, the sample means will be normally distributed even with smaller samples. [This is known as the Central Limit Theorem, which states that when a large number of random samples are drawn from a population, the means of these samples will be normally distributed.]
Z=X-μ/σ
Given here, σ = 50 , μ =200 , σₓ = 5 , n = 100 ,
z = 205-200/5 z = 195-200/5
we get z= ±1
From the z table, we get P( z= -1) = 0.1587
From the z table we get P( z= 1) = 0.8413
Thus the final answer is = 0.8413- 0.1587
= 0.6826
Hence, the probability that the sample mean will be within ±5 of the population mean is 0.6826
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Show that the function is increasing and decreasing on the given open intervals. (Enter your answers as a comma-separated list if necessary.)
y = x4 + 7; decreasing on (−[infinity], 0); increasing on (0, [infinity]).
The function y = x⁴ + 7 is decreasing on (-∞ , 0) and increasing on (0 , ∞) .
In the question ,
it is given that ,
the function is y = x⁴ + 7 ,
we have to show that function y is decreasing on (-∞ , 0) and increasing on (0 , ∞) .
differentiating the function y = x⁴ + 7 , with respect to x ,
we get ,
y'(x) = d/dx(x⁴ + 7) = 4x³
putting y'(x) = 0 , then 4x³ = 0 ;
x³ = 0 that means , x = 0 .
thus , the critical number is ⇒ x = 0 .
y'(-1) = 4(-1)³ = -4 So , it is decreasing
y'(1) = 4(1)³ = 4 So , it is increasing .
Therefore , the function y is decreasing in (-∞ , 0) and increasing in (0 , ∞) .
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Select the choice that shows the first step in finding 3,584÷7 using the standard algorithm.
Answer:
You did not provide the choices, but the first step to find the result of the operation using standard algorithm is to set up a long division
Use the determinant function det(A) and rank function rank(A) to determine whether or not the following vectors are linearly dependent.
(a) (2, 4, 5, -3), (-3, 2, 7, 0), (9, 2, 4, 6), (3, 2, -6, 5)
(b) (1, -1, 3, 2), (-1, 2, 4, -5), (3, -4, 2, 9), (7, 2, 1, 3)
(a) Determinant: det(A) = -18; Rank: rank(A) = 4. The determinant and rank are non-zero, so the vectors are linearly independent.(b) Determinant: det(A) = 0; Rank: rank(A) = 3. The determinant is zero and the rank is less than 4, so the vectors are linearly dependent.
(a)
2 4 5 -3
-3 2 7 0
9 2 4 6
3 2 -6 5
Det = -18
(b)
1 -1 3 2
-1 2 4 -5
3 -4 2 9
7 2 1 3
Det = 0
The determinant and rank of the vectors can be used to determine whether or not they are linearly dependent. If the determinant is non-zero and the rank is equal to the number of vectors, then the vectors are linearly independent. If the determinant is zero and the rank is less than the number of vectors, then the vectors are linearly dependent.
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if a rectangle and a square have the same perimeter then which one will have a larger area
Answer:
The area of the square is larger than the area of the rectangular field.
Find f(-2) f(x)= -1/6 (1/4)^x
Answer: 8/3
Step-by-step explanation:
In this equation, x=-2
so
f(-2)=-1/6 (1/4)^(-2)
(1/4)^(-2)=4^2=16
f(-2)=-1/6 16
I am going to assume that it's (1/6)*(1/4)^x meaning:
f(-2)=16/6
=8/3
I hope I assumed correctly.
Answer:
f(-2) = - 8/3---------------------------
Given function:
f(x) = - 1/6 (1/4)ˣFind f(-2), by plugging in the value of x:
f(-2) = - 1/6 (1/4)⁻² = - 1/6 (4²) = - 16/6 = - 8/3let c and d be disjoint compact subspaces of the hausdorff space x. then there exist disjoint open sets u and v containing c and d, respectively.
The statement "let c and d be disjoint compact subspaces of the Hausdorff space x and then there exist disjoint open sets u and v containing c and d, respectively." is proved.
Here we have given the let A and B be disjoint compact subspaces of the Hausdorff space X.
And we have to prove the statement.
According to the given question, let us consider that x be an arbitrary coordinate of A and here the points of x isn't in Y because A and B are disjoint.
Then according to Lemma 26.4 disjoint open sets Ux and Vx such that x Î Ux and Ux contain B.
Here the collection {Ux} is a covering of A by sets open in X.
And the finite collection of them {U1, ..,Un} covers A because A is compact.
Here the open set U = U1 U....U Un contains A and it is disjoint from
V = V1 I.....I Vn that contains B because it's the finite intersection of the corresponding open sets containing.
Therefore, here there exists disjoint open sets U and V containing A and B, respectively.
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Someone please help me! What’s the answer??
Answer:
Step-by-step explanation:
its 2
find the magnitude and direction angle of the following vector. Write your angle in degrees rounded to four decimal places. u = 2i + 8j nswer 4 Points ecall that answers entered in degrees will require a degree symbol, which is located in the keypad. ||u|| = 0 =
The magnitude of vector is 8.24 and angle is 75.9638.
What is vector?
A vector could be a amount that not solely describes the magnitude however additionally describes the movement of an object or the position of an object with reference to another purpose or object.
Main body:
we know that the magnitude of vector is found out by,
| u | = [tex]\sqrt{i^{2}+j^{2} }[/tex]
so here , u = 2i + 8j
|u| = [tex]\sqrt{2^{2} +8^{2} }[/tex]
|u| = [tex]\sqrt{68}[/tex]
|u| = 8.24
now to find the direction , angle
tan∅ = j/k
tan∅ = 8/2
∅ = tan⁻¹ (4)
∅ = 75.9638°
Hence , direction angle of the following vector is ∅ = 75.9638°
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Identify the slope of the line and the slopes of any parallel and perpendicular lines y=-1/2x+2
Answer:
Slope of the line, [tex]m_{1} = -\frac{1}{2}[/tex]
Slope of parallel line, same as the slope above
Slope of perpendicular line, [tex]m_{2} = 2[/tex]
Step-by-step explanation:
Parallel line: [tex]m_{1} = m_{2}[/tex]
Perpendicular line: [tex]m_{1} * m_{2} = -1[/tex]
[tex]y = mx +b[/tex]
Where, m = slope
Thus, in the equation provided, the slope is [tex]-\frac{1}{2}[/tex]
Finding the slope of perpendicular line:
[tex]m_{1} * m_{2} = -1\\m_{2} = \frac{-1}{m_{1}}\\m_{2} = -1 * -2\\m_{2} = 2[/tex]
Describe and correct the error.
By midpoint segment theorem DE=1/2BC for AD≅BD and AE≅EC of the triangle ABC.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
A line segment that connects two midpoints of the sides of a triangle is called a midsegment.
DE is the midsegment of AB and AC.
AD≅BD and AE≅EC.
The Midsegment Theorem states that the midsegment connecting the midpoints of two sides of a triangle is parallel to the third side of the triangle, and the length of this midsegment is half the length of the third side.
DE=1/2BC
5=1/2(10)
5=5
Hence, DE=1/2BC for AD≅BD and AE≅EC of the triangle ABC.
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Given BC over AC congruent to EF over EG
Prove FG=10
Proof:
Let's start of by solving for the length of AC, which is just the sum of lengths AB and BC, which is 10 + 3 = 13 units.
Because of our second given, AC ≅ EG, we know that EG is also 13 units in length. Also, from our first given, BC ≅ EF, we know that EF is 3 units.
We also know that the length of EG is the sum of lengths EF and FG so we can write the equation
EG = EF + FG
13 = 3 + FG
FG = 10 meaning FG is 10 units
Write the following inequality in slope-intercept form.
13x - y < 15
Answer:
y < 13x – 15
Step-by-step explanation:
13x – y < 15
–y < –13x +15
divide both sides by (–)
–(–y) < –(–13)x –(15)
y < 13x – 15
The quotient of a number and 5 plus 25 is no more than 45. What are the possible values for the number?
All the possible values for the number 'x' will be less than or equal to 1,350.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The remainder of a number and 5 in addition to 25 is something like 45.
Let the number be 'x'. Then the inequality is given as,
x / (5 + 25) ≤ 45
x / 30 ≤ 45
x ≤ 1,350
All the possible values for the number 'x' will be less than or equal to 1,350.
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4. Kaya ran 1 2/5miles on Monday and 2 1/3 miles on
Tuesday. What was the total distance, in miles, Kaya
ran during those 2 days?
Answer: 3 11/15 please mark brainliest If I helped you.
the question is kayar and 12 by 5 miles on Monday and 21 by three miles on Tuesday what is the total distance in miles kayuren during those two days first phone on Monday how much run that was 12 by 5 miles on Tuesday Shirin to 1 by 3 minus now this whole part and fractional part are written separately so this can be converted into a mixed fraction like when a number is of the form of p by see that is one whole number and fraction then it is written as a + b by c so we can write Monday that was 12 by 5 miles that is
12 by 1 + 2 by 5 that will be 5 will be LCM of 5 + 2 will be 7 by 5 MI and Tuesday it will be 21 by 3 that is 2 + 1 by 3 3 will be the LCM of 3 and 22 will be 6 plus one that is 7 by 3 minus in question is asked that what was the total distance kayar and thus during today's so Monday plus Tuesday will be the total total 27 by 5 + 7 by 3 that will be equal to LCM will be 15 this will be X 307 into 3 + 7 and 25 that
is 21 + 45 upon 15 that will be equal to 56 upon 15 Now since we have to give answer in mixed fraction in whole number and fraction this a bi bi can be divided into a whole number and fraction part when divided by be the remainder is remainder is written here b is written here and question is written here so 56 by 15 can be written as 15 and 23 is 45 three years question remainder will be 11:00 that is 56 - 45 and below will be the denominator will be 15 so this is our answer and the correct
what is a 500 doller diposet for 20 years witha intrest rate of 2%
The value of the amount will be $721.40.
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
Given that;
500 dollar deposit for 20 years with a interest rate of 2%.
Now,
We know that;
The formula for amount is,
⇒ [tex]A = P (1 + r)^n^t[/tex]
Where, A is total amount, P is principle amount, r is interest rate.
Here, We have;
P = $500
t = 20 years
r = 2%
Substitute all the values, we get;
⇒ [tex]A = P (1 + r)^n^t[/tex]
⇒ [tex]A = 500 (1 + 0.02)^2^0[/tex]
⇒ A = 500 × 1.02²⁰
⇒ A = 500 × 1.44
⇒ A = $721.40
Thus, The value of the amount = $721.40
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00/1
Vanessa went to the store to pick up some groceries for her family. She brought $20 to the
store. Vanessa's family needed a carton of eggs, which costs $3 and oranges that cost $0.50
each. Let x represent the amount of oranges that she buys. Write an inequality that can be
used to determine the amount of oranges she can buy at the store.
Vanessa can buy a maximum of x oranges, where x is the number of oranges she can buy at the store. We can represent this mathematically as an inequality by letting x represent the number of oranges she can buy and setting it equal to the total amount of money she has minus the cost of the eggs divided by the cost of each orange:
x ≤ ($20 - $3) / $0.50
This inequality tells us that Vanessa can buy at most x oranges as long as the total cost of the oranges (x * $0.50) is less than or equal to the amount of money she has remaining after buying the eggs ($20 - $3).
In other words, Vanessa can buy at most x oranges as long as the total cost of the oranges is less than or equal to $17.50. This means she can buy at most 35 oranges, since 35 * $0.50 = $17.50. Therefore, the inequality that represents the maximum number of oranges Vanessa can buy is:
x ≤ 35.
A drug-testing laboratory produces false negative results 2% of the time and false positive results 5% of the time. Suppose that the laboratory has been hired by a company in which 10% of the employees use drugs.
a) If an employee tests positive for drug use, what is the probability that they actually use drugs?
b) What is the probability that a nondrug user will test positive for drug use twice in a row?
c) What is the probability that someone who tests positive twice in a row is not a drug user?
a) The probability that they actually use drugs, if an employee tests positive for drug use is 69%
b) The probability that a nondrug user will test positive for drug use twice in a row is 0.25%
c) The probability that someone who tests positive twice in a row is not a drug user is 23%
What is Bayes' theorem in probability?Based on past knowledge of circumstances that might be relevant to the event, Bayes' theorem estimates the likelihood of an event.
The theorem explains how a degree of belief, stated as a probability, should logically alter to account for the presence of relevant data using Bayesian probability interpretation.
The question state that
Pr(D) = 0.10
Pr(D') = 0.90
Pr (P/D) = 0.98 ( (2% False negatives means for drug users, 2% will get a negative result, so 98% will get positive result)
Pr(P/D') = 0.05
a) The probability that they actually use drugs, if an employee tests positive for drug use Pr(D/P) = Pr(D)*Pr (P/D) / Pr(D)*Pr (P/D)+Pr(D')*Pr(P/D')
⇒ Pr(D/P) = (0.10*0.98)/(0.10*0.98 + 0.90*0.05)
⇒ Pr(D/P) = 0.098/(0.098+0.045)
⇒ Pr(D/P) = 0.098/0.143
⇒ Pr(D/P) ≈ 0.6853
⇒ Pr(D/P) ≈ 69%
b) The probability that a nondrug user will test positive for drug use twice in a row Pr (P*2/D') = Pr(P/D')*Pr(P/D')
⇒ Pr (P*2/D') = 0.05*0.05
⇒ Pr (P*2/D') = 0.0025
⇒ Pr (P*2/D') = 0.25%
c) The probability that someone who tests positive twice in a row is not a drug user Pr (D'/P*2) = Pr(D')*Pr (P*2/D') / Pr(D')*Pr (P*2/D')+Pr(D)*Pr (P*2/D)
⇒ Pr (D'/P*2) = (0.90*.0.05²)/(0.90*0.05²+0.10*0.98²)
⇒ Pr (D'/P*2) = 0.00225/ 0.00225+0.09604
⇒ Pr (D'/P*2) = 0.00225/0.09829
⇒ Pr (D'/P*2) ≈ 0.2289
⇒ Pr (D'/P*2) ≈ 23%
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Hi, Can anyone help me solve this please?
Ma'am there is nothing to solve...
Emoji::<
Answer:
Step-by-step explanation:
Yes there is literally nothing to solve:(
a local eat- in pizza restaurant wants to investigate the possibility of starting to deliver pizzas. the owner of the store has determined that home delivery will be successful if the average time spent on the deliveries does not exceed 36 minutes. the owner has randomly selected 21 customers and has delivered pizzas to their homes in order to test if the mean delivery time actually exceeds 36 minutes. suppose the p-value for the test was found to be .0277.
By using p-value hypothesis test,we find that the mean delivery time actually exceeds 34 minutes.
what is p-value hypothesis test?It is a number calculated from a statistical test that describes how you are found a particular set of observation ,if the null hypothesis were true.P-values are used in hypothesis testing to help to decide whether to reject the null hypothesis .The lower the p-value the greater the statistical significance of observation differences.
what is null and alternate hypothesis?The null hypothesis states that as the assumption that there is no change , no difference and no relationship between two variables.The alternate hypothesis stated that there is a change, difference and relationship between two variables or group.
let we use p-value test
Let u=average time spend on deliveries
so,null hypothesis H0;u[tex]\leq[/tex]34 minutes
alternate hypothesis HA; u >34
Now the decision rule based on the p-value to whether null hypothesis should be accepted or rejected is given by;
.If hypothesis p-value of test statistical is less than the level of significance,then we will our null hypothesis.
.If the p-value of test statistical is more than the level of significance.then we will not reject our null hypothesis.
Here, we assume that the level of significance is 5%.
Since the p-value test statistics is less than the level of significance as 0.029<0.05.
so,we have evidence to reject our null hypothesis.
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3.) What is the slope intercept form of the line graphed below?
Superman pro
Step-by-step explanation:
Superman pro
A trough is 12 feet long and 3 feet across the top (see figure). Its ends are isosceles triangles with altitudes of 3 feet. 12f 3 ft 31 (a) if water is being pumped into the trough at 2 cubic feet per minute, how fast is the water level rising when h is 1.2 feet deep? X ft/min (b) if the water is rising at a rate of 3/8 inch per minute when h - 2.3, determine the rate at which water is being pumped into the trough fo/min
Therefore ,the water level is rising by 0.1388 ft/min when h is 1.2 feet deep and the water is being pumped at rate of 0.8625 cubic feet per min when water is rising at 3/8 inch/min
What is volume?A three-dimensional space's occupied volume is measured. It is typically quantified using a variety of imperial or US-standard units as well as SI-derived units. The concept of length and volume are related.
Here,
Given: A trough has a 12 foot length and a 3 foot top width. Three-foot-high isosceles triangles make up its ends. 12f 3 ft 31
So the first case:
using this we find the rate of Volume,
So,
=> dV/dt = length * height *dh/dt
=> dV/dt = 12 * 1.2 *dh/dt
=> 2 = 12*1.2* dh/dt
=> 2 = 14.4 * dh/dt
=>dh/dt = 2/14.4
=>dh/dt = 0.1388 ft/min
Therefore ,the water level is rising by 0.1388 ft/min when h is 1.2 feet deep .
Second case:
Since water level is rising by 3/8 inch per min =0.03125 feet/min
=> dV/dt = length * height *dh/dt
=> dV/dt = 12 * 2.3 *0.03125
=>dV/dt = 0.8625 cubic feet per min
Therefore , the water is being pumped at rate of 0.8625 cubic feet per min.
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