What is the exact distance from (−1, 4) to (6, −2)? square root of 80. units square root of 82. units square root of 85. units square root of 89. units
Answers
Answer:
[tex]\sqrt{85}[/tex].
Step-by-step explanation:
[tex]x[/tex]-coordinates:
First point: [tex]-1[/tex].Second point: [tex]6[/tex].Difference: [tex]|-1 - 6| = |-7| = 7[/tex].[tex]y[/tex]-coordinates:
First point: [tex]4[/tex].Second point: [tex]-2[/tex].Difference: [tex]|4 - (-2)| = |6| = 6[/tex].Refer to the diagram attached. Consider these two points as the two end points of the hypotenuse of a right triangle. The lengths of the two legs are equal to:
the difference between the two [tex]x[/tex]-coordinates, [tex]7[/tex], and the difference between the two [tex]y[/tex]-coordinates, [tex]6[/tex].Apply Pythagorean Theorem to find the length of the hypotenuse (which is equal to the distance between the two points in question.)
[tex]\begin{aligned}\text{Hypotenuse} &= \sqrt{(\text{First Leg})^2 + (\text{Second Leg})^2} \\ &= \sqrt{7^2 + 6^2} \\ &= \sqrt{85}\end{aligned}[/tex].
Answer:
C
Step-by-step explanation:
Related Questions
Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x, y) = 8 sin(xy), (0, 9)
Answers
Answer:
The maximum rate of change of f at (0, 9) is 72 and the direction of the vector is [tex]\mathbf{\hat i}[/tex]
Step-by-step explanation:
Given that:
F(x,y) = 8 sin (xy) at (0,9)
The maximum rate of change f(x,y) occurs in the direction of gradient of f which can be estimated as follows;
[tex]\overline V f (x,y) = \begin {bmatrix} \dfrac{\partial }{\partial x } (x,y) \hat i \ + \ \dfrac{\partial }{\partial y } (x,y) \hat j \end {bmatrix}[/tex]
[tex]\overline V f (x,y) = \begin {bmatrix} \dfrac{\partial }{\partial x } (8 \ sin (xy) \hat i \ + \ \dfrac{\partial }{\partial y } (8 \ sin (xy) \hat j \end {bmatrix}[/tex]
[tex]\overline V f (x,y) = \begin {bmatrix} (8y \ cos (xy) \hat i \ + \ (8x \ cos (xy) \hat j \end {bmatrix}[/tex]
[tex]| \overline V f (0,9) |= \begin {vmatrix} 72 \hat i + 0 \end {vmatrix}[/tex]
[tex]\mathbf{| \overline V f (0,9) |= 72}[/tex]
We can conclude that the maximum rate of change of f at (0, 9) is 72 and the direction of the vector is [tex]\mathbf{\hat i}[/tex]
Fertilizing bromeliads. Bromeliads are tropical flowering plants. Many are epiphytes that attach to trees and obtain moisture and nutrients from air and rain. Their leaf bases form cups that collect water and are home to the larvae of many insects. As a preliminary to a study of changes in the nutrient cycle, Jacqueline Ngai and Diane Srivastava examined the effects of adding nitrogen, phosphorus, or both to the cups. They randomly assigned 8 bromeliads growing in Costa Rica to each of 4 treatment groups, including an unfertilized control group. A monkey destroyed one of the plants in the control group, leaving 7 bromeliads in that group. Here are the numbers of new leaves on each plant over the seven months following fertilization:
Nitrogen Phosphorus Both Neither
15 15 14 14
14 17 18 19
18 13 14 11
16 13 15 16
14 14 15 13
11 17 14 15
13 12 15 15
(a) Give the degrees of freedom for the F statistic. numerator degrees of freedom denominator degrees of freedom
(b) Find the F-statistic. (Round your answer to two decimal places.)
(c) Find the associated P-value. (Round your answer to four decimal places.)
Answers
Answer:
Calculated value of F = 0.0535
The critical region is F >F ₀.₀₅ (6,21) = 2.575
Reject H0
Step-by-step explanation:
1. Null hypothesis
H0: µ Nitrogen = µ Phosphorus = µ Both = µ Neither
2. Alternative hypothesis
H1: Not all means are equal.
3. The degrees of freedom for the numerator of the F-ratio = k- 1= 7-1=6
4.The degrees of freedom for the denominator of the F-ratio = n-k= 28-7
= 21
5. The significance level is set at α-0.05
The critical region is F >F ₀.₀₅ (6,21) = 2.575
The test statistic to use is
F = sb²/ sw²
Which if H0 is true has an F distribution with v₁=k-1 and v₂= n-k degrees of freedom
Correction Factor = CF = Tj²/n = (410)²/28= 6003.57
Total SS ∑∑X²- C. F = 6108- 6003.57= 104.43
Between SS ∑T²j/r - C.F = 42036/ 7 - 6003.57 = 1.57286
Within SS = Total SS - Between SS= 104.43- 1.573= 102.86
The Analysis of Variance Table is
Source Of Sum of Mean Computed
Variation d.f Squares Squares F
Between
Samples 6 1.57286 0.2621 0.0535
Within
Samples 21 102.86 4.898
Calculated value of F = 0.0535
Pvalue = 2.575
Since it is smaller than 5 % reject H0.
Evaluate C 3y − esin(x) dx + 7x + y4 + 1 dy, where C is the circle x2 + y2 = 16. SOLUTION The region D bounded by C is the disk x2 + y2 ≤ 16, so let's change to polar coordinates after applying Green's Theorem: C 3y − esin(x) dx + 7x + y4 + 1 dy
Answers
By Green's theorem,
[tex]\displaystyle\int_{x^2+y^2=16}(3y-e^{\sin x})\,\mathrm dx+(7x+y^4+1)\,\mathrm dy[/tex]
[tex]=\displaystyle\iint_{x^2+y^2\le16}\frac{\partial(7x+y^4+1)}{\partial x}-\frac{\partial(3y-e^{\sin x})}{\partial y}\,\mathrm dx\,\mathrm dy[/tex]
[tex]=\displaystyle4\iint_{x^2+y^2\le16}\mathrm dx\,\mathrm dy[/tex]
The remaining integral is just the area of the circle; its radius is 4, so it has an area of 16π, and the value of the integral is 64π.
We'll verify this by actually computing the integral. Convert to polar coordinates, setting
[tex]\begin{cases}x=r\cos\theta\\y=r\sin\theta\end{cases}\implies\mathrm dx\,\mathrm dy=r\,\mathrm dr\,\mathrm d\theta[/tex]
The interior of the circle is the set
[tex]\{(r,\theta)\mid0\le r\le4\land0\le\theta\le2\pi\}[/tex]
So we have
[tex]\displaystyle4\iint_{x^2+y^2\le16}\mathrm dx\,\mathrm dy=4\int_0^{2\pi}\int_0^4r\,\mathrm dr\,\mathrm d\theta=8\pi\int_0^4r\,\mathrm dr=64\pi[/tex]
as expected.
A wheel on a race car has 21-inch diameter. To qualify for an upcoming race, cars must be able to travel a minimum of 130 miles per hour. The wheel on this car can turn at the rate of 36 revolutions per second. Determine the linear speed of a point on the rim of this wheel (nearest inch per second) and determine if this car with this wheel would qualify for the upcoming race. 5 To convert inches per second to miles per hour, multiply by 5/88.
A) The linear speed is 756 inches per second, so this car would not quality
B) The linear speed is 4750 inches per second, so this car would quality
C) The linear speed is 2375 inches per second, so this car would quality
D) The linear speed is 378 inches per second, so this car would not qualify.
Answers
Answer: B) The linear speed is 4750 inches per second, so this car would qualify.
Step-by-step explanation: To determine linear speed using revolutions per second, i.e., angular speed (ω):
v = ω.r
where r is radius.
As ω is in revolutions per second, transform into rad/s:
ω = 36 revolutions/s
1 revolution = 2π rad
ω = 36.2π rad/s
ω = 72π rad/s
Radius is 21 inches, which can be written as
r = 21 inches/rad
Linear speed is
v = [tex]\frac{72.\pi rad}{s} .\frac{21 in}{rad}[/tex]
v ≈ 4750 inches per seconds
Converting to miles per hour:
v = [tex]4750.\frac{5}{88}[/tex]
v = 270mph
At linear speed of 4750 inches per second, a car with wheel of radius 21-inch can qualify.
Answer:
Above is correct
Step-by-step explanation:
9. There are 50 pupils in a class. Out of this
number, 1/10 speak French only and 4/5 of the remainder speak both French and
English. If the rest speak English only,
i) find the number of students who speak
Answers
Answer:
Step-by-step explanation:
50 : 10 = 5 speaks French only
50 -5= 45 the remainder
4/5 * 45= 36 speaks French and English
45 - 36= 9 speaks English only
The number of students who speak:
i) French only = 5 students,
ii) both French and English = 36 students,
iii) English only = 9 students.
Step 1: Find the number of students who speak French only.
Step 2: Find the remainder (students who speak both French and English) after subtracting the French-only speakers.
Step 3: Find the number of students who speak both French and English.
Step 4: Find the number of students who speak English only.
Let's calculate it step by step:
Step 1: Find the number of students who speak French only.
1/10 of 50 pupils speak French only:
French-only speakers = (1/10) * 50 = 5 students.
Step 2: Find the remainder (students who speak both French and English) after subtracting the French-only speakers.
Remaining students = Total students - French-only speakers
Remaining students = 50 - 5 = 45 students.
Step 3: Find the number of students who speak both French and English.
4/5 of the remaining students speak both French and English:
Both French and English speakers = (4/5) * 45 = 36 students.
Step 4: Find the number of students who speak English only.
To find the English-only speakers, subtract the total number of French-only speakers and both French and English speakers from the total number of students:
English-only speakers = Total students - (French-only speakers + Both French and English speakers)
English-only speakers = 50 - (5 + 36) = 50 - 41 = 9 students.
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Complete question is:
There are 50 pupils in a class. Out of this number, 1/10 speak French only and 4/5 of the remainder speak both French and English. If the rest speak English only, find the number of students who speak
i) French only,
ii) both French and English,
iii) English only,
Solve the system 2x + 3y = 3 and 3x − 2y = 11 by using graph paper or graphing technology. What is the solution to the system? (2 points) (−3, 3) (−1, −7) (1, −4) (3, −1)
Answers
Answer:
(3,-1)
Step-by-step explanation:
Graph boths functions (picture below)
Find an equation of the tangent plane to the given surface at the specified point. z = ln(x − 8y), (9, 1, 0)
Answers
Answer:
x - 8y - z = 1
Step-by-step explanation:
Data provided according to the question is as follows
f(x,y) = z = ln(x - 8y)
Now the equation for the tangent plane to the surface
For z = f (x,y) at the point P [tex](x_0,y_0,z_0)[/tex] is
[tex]z - z_0 = f_x(x_0,y_0)(x-x_0) + f_y(x_0,y_0)(y-y_0)\\[/tex]
Now the partial derivatives of f are
[tex]f_x(x,y) = \frac{1}{x-8y} \\\\f_y(x,y) = \frac{8}{x-8y} \\\\P(x_0,y_0,z_0) = (9,1,0)\\\\f_z(9,1,0) = (\frac{1}{x-8y})_^{(9,1,0)}[/tex]
[tex]\\\\=\frac{1}{9-8}[/tex]
= 1
Now
[tex]f_y(9,1,0)=(\frac{8}{x-8y})_{(9,1,0)}\\\\ = -\frac{8}{9 - 8}[/tex]
= -8
So, the tangent equation is
[tex]z - 0 = 1\times (x - 9) -8\times (y - 1)[/tex]
Now after solving this, the following equation arise
z = x - 9 - 8y + 8
z = x - 8y - 1
Therefore
x - 8y - z = 1
The equation of the tangent plane is [tex]x-8y-z=1[/tex]
Tangent Plane:An equation of the tangent plane to the given surface at the point [tex]P(x_0,y_0,z_0)[/tex] is,
[tex]z-z_0=f_x(x_0,y_0)(x-x_0)+f_y(x_0,y_0)(y-y_0)[/tex]
The function is,
[tex]z = ln(x-8y)[/tex]
And the point is (9,1,0)
Now, calculating [tex]f_x,f_y[/tex]
[tex]f_x(x,y)=\frac{1}{x-8y}\\ f_y(x,y)=\frac{x-8}{x-8y}[/tex]
Now, substituting the given points into the above functions we get,
[tex]f_x(9,1)=\frac{1}{9-8(1)}=1\\ f_y(x,y)=\frac{-8}{9-8(1)}=-8[/tex]
So, the equation of the tangent plane is,
[tex]z-0=1(x-9)-8(y-1)\\z=x-8y-1\\x-8y-z=1[/tex]
Learn more about the topic tangent plane:
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What does the tape measure say Measurement # 4 is?
Answers
Answer:
It looks like 6 and one eighth of an inch.
In 2014, the population of India1 was 1.236 billion people and increasing at a rate proportional to its population. If the population is measured in billions of people and time is measured in years, the constant of proportionality is 0.0125. Define P to be the population of India, in billions of people, in the year t, where t represents the number of years since 2014. (a) Write a differential equation to describe the relationship.\
Answers
Answer: i don’t kno I’m 6 years old
Step-by-step explanation:
Choose the best answer
Question
Cube A has volume V The edges of cube Bare 3 times as long as the edges of cube A. What is the
volume of cube B, in terms of V?
1.3V
2.9V
3.18V
4.27V
Answers
Answer:
4). 27V
Step-by-step explanation:
Let the edge of the cube A be x
Volume of Cube A= V
Volume= x*x*x= x³
so V = x³
Edge of cube B = 3 times edge of cube A
Edge of cube B = 3x
Volume of cube B =( 3x)³
volume of cube B = 27x³
But x³= V
So volume of cube B = 27v
how many feet are in 53 yards, 2 feet? enter only the number. Do not include units
Answers
There are 161 feet are in 53 yards, 2 feet.
What is unit conversion?
Unit conversion is the process of changing a quantity's measurement between various units, frequently using multiplicative conversion factors.
As we know that;
1 yard = 3 feet
53 yards = 3 ×53 feet
53 yards = 159 feet
53 yards, 2 feet = 159 feet + 2 feet
53 yards, 2 feet = 161 feet
Hence, there are 161 feet in 53 yards, 2 feet.
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State whether the data described below are discrete or continuous, and explain why.
The widths (in centimeters) of different paintings in an art museum
nothing
Choose the correct answer below.
A. The data are continuous because the data can only take on specific values.
B. The data are discrete because the data can only take on specific values.
C. The data are discrete because the data can take on any value in an interval.
D. The data are continuous because the data can take on any value in an interval.
Answers
Let s1 = k and define sn+1 = √4sn − 1 for n ≥ 1. Determine for what values of k the sequence (sn) will be monotone increasing and for what values of k it will be monotone decreasing.
Answers
Answer:
The answer is "[tex]\bold{\frac{1}{4}<k\leq 2+\sqrt{3}}[/tex]"
Step-by-step explanation:
Given:
[tex]\ S_1 = k \\\\ S_{n+1} = \sqrt{4S_n -1}[/tex] [tex]_{where} \ \ n \geq 1[/tex]
In the above-given value, [tex]S_n[/tex] is required for the monotone decreasing so, [tex]S_2 :[/tex]
[tex]\to \sqrt{4k-1} \leq \ k=S_1\\\\[/tex]
square the above value:
[tex]\to k^2-4k+1 \leq 0\\\\\to k \leq 2+\sqrt{3} \ \ \ \ \ and \ \ 4k+1 >0\\\\[/tex]
[tex]\bold{\boxed{\frac{1}{4}<k\leq 2+\sqrt{3}}}[/tex]
x − 6 ≤ 3 solve for x please
Answers
Answer:
x ≤ 9
Step-by-step explanation:
x − 6 ≤ 3
Add 6 to each side
x − 6+6 ≤ 3+6
x ≤ 9
Answer:
x ≤ 9
I hope this helps!
Each power smoothie that Theo makes has 3 scoops of mango, 1 scoop of strawberries, and 1 scoop of spinach. If Theo makes 7 power smoothies, how many scoops will he use in all?
Answers
Answer: 35 scoops total!
Step-by-step explanation: FIrst, you would add the number of scoops in total which is 3+1+1=5 scoops.
Now you would do 7*5=35
Therefore, Theo uses 35 scoops in all. I hope this helps you!
How to simplify this expression??
Answers
Answer :
1
Step-by-step-explanation :
[tex] {x}^{2} + 4x + 5 - {(x + 2)}^{2} \\ {x}^{2} + 4x + 5 - ( {x}^{2} + 4x + 4) \\ [/tex]
[tex]{x}^{2} + 4x + 5 - {x}^{2} - 4x - 4 = {x}^{2} - {x}^{2} + 4x - 4x + 5 - 4 = 5 - 4 = 1[/tex]
Answer:
(x+1) • (x-5)
Step-by-step explanation:
The first term is, x2 its coefficient is 1 .
The middle term is, -4x its coefficient is -4 .
The last term, "the constant", is -5
Step-1 : Multiply the coefficient of the first term by the constant 1 • -5 = -5
Step-2 : Find two factors of -5 whose sum equals the coefficient of the middle term, which is -4 .
-5 + 1 = -4 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -5 and 1
x2 - 5x + 1x - 5
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-5)
Add up the last 2 terms, pulling out common factors :
1 • (x-5)
Step-5 : Add up the four terms of step 4 :
(x+1) • (x-5)
PLEASE HELP ! (4/4) - 50 POINTS -
Answers
Answer:
The correct answer, again, is A; Z = -0.6
Answer:
im pretty sure its A; Z = -0.6 sorry if im wrong
Step-by-step explanation:
#1: Simplify the expression below. Type your answer as an integer.
7 + 1 - 18 : 6
Answers
Answer:
5
Step-by-step explanation:
Steps of calculation:
7 + 1 - 18 : 6 = 7 + 1 - 3 = 8 - 3 =5Answer is 5
this person made an error. what is it, and what is the right answer?
Answers
Answer:
Base area (B) should not be added.
Step-by-step explanation:
Base area should not be added as cone is not solid. Only Lateral surface area is sufficient in order to find the required paper.
Find the surface area of the triangular prism.
Answers
Answer:
169 [tex]cm^{2}[/tex]
Step-by-step explanation:
Surface area (SA) = 2B + PH
SA = 2 ([tex]\frac{1}{2}[/tex] x 9 x 6) + (7+7+9) 5
= 2 (27) + (23) 5
= 54 + 115
SA = 169 [tex]cm^{2}[/tex]
Find
two consecutive numbers
odd numbers such that the
sum of the
greater number
and 5 times the smaller
number is 92. Please give detailed step by step answer
Answers
Answer:
The two odd numbers are 15 and 17
Step-by-step explanation:
Given
Let the odd numbers be represented with x and y
Let x be the greater number
[tex]x + 5y = 92[/tex]
Required
Find x and y
Since x and y are consecutive odd numbers and x is greater, then
[tex]x = y + 2[/tex]
Substitute y + 2 for x in [tex]x + 5y = 92[/tex]
[tex]y + 2 + 5y = 92[/tex]
Collect Like Terms
[tex]y + 5y = 92 - 2[/tex]
[tex]6y = 90[/tex]
Divide both sides by 6
[tex]\frac{6y}{6} = \frac{90}{6}[/tex]
[tex]y = \frac{90}{6}[/tex]
[tex]y = 15[/tex]
Substitute 15 for y in [tex]x = y + 2[/tex]
[tex]x = 15 + 2[/tex]
[tex]x = 17[/tex]
Hence; the two odd numbers are 15 and 17
Answer:
Maths
Step-by-step explanation:
Answer:
The two odd numbers are 15 and 17
Step-by-step explanation:
Given
Let the odd numbers be represented with x and y
Let x be the greater number
Required
Find x and y
Since x and y are consecutive odd numbers and x is greater, then
Substitute y + 2 for x in
Collect Like Terms
Divide both sides by 6
Substitute 15 for y in
Hence; the two odd numbers are 15 and 17
What is the value of x?
Answers
Answer:
7
Step-by-step explanation:
The two angles created by the angle bisector are the same measure, so we have ...
2x +y = 14 +y
2x = 14 . . . . . . . subtract y
x = 7 . . . . . . . . . divide by 2
someone please help me
Answers
32 to 34 Directions: Given the following set of
numbers find the mean, median, and mode.
12, 13, 15, 15, 16, 19, 19, 19, 20, 21, 25
39.
32. Mean =
a. 17.64
b. 19
c. 15
40. 1
33. Median
a. 17.64
b. 19
c. 15
Answers
Answer:
32. A
33. B
Step-by-step explanation:
32. Mean: In order to find the mean, add all of the #up which is 194 then divide by how many # there is
33. Start by crossing out the beginning # and the end # all the way till you get the # without another pair in the end
Please help helppp :((((
Answers
Answer:
m∠Q = 61°
m∠S = 61°
m∠R = 58°
Step-by-step explanation:
Since we have an isosceles triangle, we know that ∠Q and ∠S are congruent.
Step 1: Definition of isosceles triangle
2x + 41 = 3x + 31
41 = x + 31
x = 10
Step 2: Find m∠Q
m∠Q = 2(10) + 41
m∠Q = 20 + 41
m∠Q = 61°
Step 3: Find m∠S
Since m∠Q = m∠S,
m∠S = 61°
Step 4: Find m∠R (Definition of a triangle)
Sum of angles in a triangle adds up to 180°
m∠R = 180 - (61 + 61)
m∠R = 180 - 122
m∠R = 58°
1. Solve the system of equations. y = –3x + 4 x + 4y = –6 A. x = –2,y = –1 B. x = –2,y = 10 C. x = 2,y = –2 D. x = 3,y = –5 E. x = 4,y = –8
Answers
Answer:
C. x = 2, y = -2
Step-by-step explanation:
y = -3x + 4
x + 4y = -6
x + 4(-3x + 4) = -6
x - 12x + 16 = -6
-11x = -22
x = 2
y = -3(2) + 4 = -2
Daniella accidentally left the drain partially open as she began filling the bathtub. The amount of water, in gallons, pouring into the tub after x minutes is given by the function f. f( x )=12x The amount of water, in gallons, draining from the tub after x minutes is given by the function g. g( x )=6x What is the equation of a function k that gives the amount of water in the tub in this situation after x minutes?
Answers
Answer:
k(x) = 6x
Step-by-step explanation:
A function shows the relationship between two or more variables. It shows the relationship between an independent and a dependent variable.
Given that the amount of water being poured into the tube is given by f(x) = 12x, where x is in minutes and the amount of water draining out of the tub is given by the function g( x )=6x. The amount of water remaining in the tube after x minutes is gotten by finding the difference between the amount of water entering the tube and the amount leaving the tube after x minutes. If k is the function representing the amount of water in the tube after x minutes, it is given by:
k(x) = f(x) - g(x)
k(x) = 12x - 6x
k(x) = 6x
Which formula used in probability to find Independence question
Answers
Answer:
Events A and B are independent if the equation P(A∩B) = P(A) · P(B) holds true. You can use the equation to check if events are independent; multiply the probabilities of the two events together to see if they equal the probability of them both happening together.
Answer:
Events are independent if the outcome of one effect does not effect the outcome
Step-by-step explanation:
The graph of the function f(x) = (x − 3)(x + 1) is shown.
On a coordinate plane, a parabola opens up. It goes through (negative 1, 0), has a vertex at (1, negative 4), and goes through (3, 0).
Which describes all of the values for which the graph is positive and decreasing?
all real values of x where x < −1
all real values of x where x < 1
all real values of x where 1 < x < 3
all real values of x where x > 3
Answers
Answer:
x < -1
Step-by-step explanation:
Since the parabola opens upward, it is positive and decreasing where the left branch is above the x-axis: all points to the left of x=-1.
all real values of x where x < -1
The Eastern and Western Major League Soccer conferences have a new Reserve Division that allows new players to develop their skills. Data for a randomly picked date showed the following annual goals for six different teams in each division.
Eastern Western
9 9
3 8
4 7
3 6
4 5
4 3
Does the data show there is a difference in the annual goals for the eastern and western divisions? Test the claim at the 0.05 significance level.
A) The null and alternative hypothesis would be:
1. H0: PE = Pw
H1: PE > PW
2. H0: PE - Pw
H1: PE Pw
3. H0: Ps Pw
H1: PE Pw
4. H0: ME MW
H1: MMW
5. H0: HEW
H1: TME > HW
6.H0: ME Hw
H1: EMW
B) Determine the test statistic.
Answers
Answer:
A)
2. H0: Pe = Pw
H1: Pe [tex]\neq[/tex] Pw
B) Test statistics 1.96
Step-by-step explanation:
Null hypothesis is a statement that is to be tested against the alternative hypothesis and then decision is taken whether to accept or reject the null hypothesis. In the given scenario the test is to identify whether there is any difference in annual goals between western division and eastern division. The null hypothesis will be the Goals of western are equal to eastern division and alternative hypothesis will be Goals of western are not equal to eastern division.
