Answers
Answer:
4
Step-by-step explanation:
I got it right on Khan
The value of x is 4.
What is Triangle?A triangle is a polygon in two dimensional geometry. I has three sides and three angles along with three vertices.
Area of a triangle = [tex]\frac{1}{2}[/tex] × b × h
where b is the base of the triangle and h is the length of height of the triangle.
The given triangle is an obtuse triangle which has an angle equal to greater than 90 degrees. So the height of the triangle is found by drawing a perpendicular line from the base to the opposite vertex.
Here, height = x and base length = 6
Area = 12 units²
[tex]\frac{1}{2}[/tex] × 6 × h = 12
6 × h = 12 × 2
6 × h = 24
h = 24/6
h = 4 units.
Hence the length of the height which is x is 4 units.
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Related Questions
The data show the number of hours of television watched per day by a sample of 28 people. Use technology to answer parts (a) and (b) below. 1 1 2 8 8 4 8 7 8 3 1 2 8 2 4 7 4 0 5 7 7 8 9 3 6 2 2 7 a. Find the data set's first, second, and third quartiles. Upper Q 1 equals nothing Upper Q 2 equals nothing Upper Q 3 equals nothing
Answers
Answer:
Q1= 2, Q2 = 4.5, Q3 = 7.5
Step-by-step explanation:
firstly, put the data is other;
0 1 1 1 2 2 2, 2 2 3 3 4 4 4, 5 6 7 7 7 7 7, 8 8 8 8 8 8 9
the Q1 = (2+2)/2 = 2
Q2 = (4 + 5)/ 2 = 4.5
Q3 = (7 + 8)/2 = 7.5
Yelena needs to swim a total of 8 miles this
week. So far, she swam 5 miles. Use the
equation 5 + m=8 to find how many more
miles Yelena needs to swim.
Answers
Answer:
3 miles
Step-by-step explanation:
5 + m=8
Subtract 5 from each side
5-5 + m=8-5
m = 3
She needs to swim 3 more miles
Answer:
Yelena needs to swim 3 more miles
Step-by-step explanation:
You need to solve for the variable "m", which represents the miles. Based on the information, Yelena swam 5 miles and she needs to swim 8. Solve:
[tex]5+m=8[/tex]
To find the value of m, you need to isolate it on one side of the equation. To do this, you need to get the 8 and 5 on the same side of the equal operation. For this, you need to use reverse operations. This undoes the value from one side and does the same on the other, keeping the equation balanced. Since we have a "positive 5", we take the opposite, which would be a "negative 5". So subtract 5 from both sides of the equation:
[tex]5-5+m=8-5[/tex]
Simplify. The 5's cancel each other out, leaving 0. 8-5 is 3:
[tex]m=3[/tex]
The total miles left that Yelena needs to swim is 3 miles.
:Done
A human factor expert recommends that there be atleast 9 square ft of floor space in a classroom for every student in the class. Find the min space required for 49 students
Answers
All sacks of sugar have the same weight. All sacks of flour also have the same weight, but not necessarily the same as the weight of the sacks of sugar. Suppose that two sacks of sugar together with three sacks of flour weigh no more than 40 pounds and that the weight of a sack of flour is no more than 5 pounds more than the weight of two sacks of sugar. What is the largest possible weight (in pounds) of a sack of flour?
Answers
Answer:
The largest possible weight of flour is 11.25 pounds.
Step-by-step explanation:
To start with, we will assume that the weight of 1 sack of sugar = x pounds
We will also assume that the weight of 1 sack of flour = y pounds
So, the weight of 2 sacks of sugar = 2 * (x) = 2x
Same thing goes for the weight of 3 sacks of flour = 3 * (y) = 3y
Supposing that the weight of (2 sacks of sugar + 3 sacks of flour) ≤ 40 pounds
= 2x + 3y ≤ 40............ we'll call that equation 1.
Also, suppose that the weight of ( 1 sack of flour) ≤ 2 sacks of sugar + 5 pounds
= y ≤ 2x + 5........................ we'll call that equation 2
Therefore, we'll solve for the values of x and y in the two equations and we will get:
2x + 3y ≤ 40
y ≤ 2x + 5
Now, substitute the value of y into equation 1
2x + 3y ≤ 40 ⇒ 2x + 3(2x +5) =40
⇒ 2x + 6x + 15= 40
⇒ 8x + 15 = 40
⇒ 8x = 25
⇒ x = 25/8
⇒ x = 3.12
x cannot be more than 3.12 pounds, so we solve for y
Putting the value of x into equation 2, we'll get
⇒ 2y + 5 = 2(3.12) + 5
⇒ y = 11.25 pounds.
So, n cannot be more than 11.25 pounds
a lottery offers one $1000 prize one $500 and two $50 prizes. one thousand tickets are sold at $2.50. what is the expectived profit
Answers
Answer:
$900
Step-by-step explanation:
To begin with let us estimate the total cash value of the prices
$1000 x 1= 1000
$500 x 1= 500
$50 x 2= 100
Total = $1600
Now let us calculate the total cost of tickets sold at $2.50 per tickets for 1000 tickets
2.5*1000= $2,500
Assuming worse case that the lottery had winners in all three categories and i.e the total prices given out is $1600
Then the expected profit is = $2,500-$1600= $900
The volume of a rectangular prism is the products it’s dimensions. If the dimensions of a rectangle prism are approximately 1.08 feet,5.25 feet, and 3.3 feet ,what is the approximate volume of the cube?Express your answer using an approximate level of accuracy.
Answers
Answer:
To find the volume of this cube, you would have to multiply 1.08 by 5.25 by 3.3 feet. If you did this, you would get: 18.711 feet^3. This is the volume of the rectangular prism.
Hope this helped!
A parent increases a child’s monthly allowance by 20% each year. If the allowance is $8 per month now, in about how many years will it take to reach $20 per month? Use the equation 20 = 8(1.2)x to solve the problem. Round to the nearest year. 1 year 5 years 2 years 16 years
Answers
Answer:
6 years
Step-by-step explanation:
A parent increases a child’s monthly allowance by 20% each year. If the allowance is $8 per month now. This is an exponential function, An exponential function is given by:
[tex]y=ab^x[/tex]
Let x be the number of years and y be the allowance. The initial allowance is $8, this means at x = 0, y = 8
[tex]y=ab^x\\8=ab^0\\a=8[/tex]
Since it increases by 20% each year, i.e 100% + 20% = 1 + 0.2 = 1.2. This means that b = 1.2
Therefore:
[tex]y=ab^x\\y=8(1.2^x) \\[/tex]
To find the number of years will it take to reach $20 per month, we substitute y = 20 and find x
[tex]20=8(1.2)^x\\20/8=1.2^x\\1.2^x=2.5\\Taking \ natural\ log\ of \ both\ sides:\\ln(1.2^x)=ln2.5\\xln(1.2)=0.9163\\x=0.9163/ln(1.2)\\x=5.026[/tex]
x = 6 years to the nearest year
Answer:
5 years
Step-by-step explanation:444
Century Roofing is thinking of opening a new warehouse, and the key data are shown below. The company owns the building that would be used, and it could sell it for $100,000 after taxes if it decides not to open the new warehouse. The equipment for the project would be depreciated by the straight-line method over the project's 3-year life, after which it would be worth nothing and thus it would have a zero salvage value. No new working capital would be required, and revenues and other operating costs would be constant over the project's 3-year life. What is the project's NPV? (Hint: Cash flows are constant in Years 1-3.)
Answers
Question Completion:
WACC = 10.0%
Opportunity cost = $100,000
Net equipment cost (depreciable basis) = $65,000
Straight-line deprec. rate for equipment = 33.333%
Sales revenues, each year = $123,000
Operating costs (excl. deprec.), each year = $25,000
Tax rate = 35%
Answer:
Century Roofing
Project's NPV is: ($6,578)
Step-by-step explanation:
a) Data and Calculations:
WACC = 10.0%
Opportunity cost = $100,000
Net equipment cost (depreciable basis) = $65,000
Straight-line deprec. rate for equipment = 33.333%
Sales revenues, each year = $123,000
Operating costs (excl. deprec.), each year = $25,000
Tax rate = 35%
Cash outflow in year 0 = $165,000 (Opportunity and new equipment costs)
Annual Cash inflow = $123,000 - $25,000 - $34,300 = $63,700
PV of annuity for 3 years at 10% = $158,422 ($63,700 x 2.487)
NPV = Cash inflow minus Cash outflow
= $158,422 - $165,000
= ($6,578)
Negative NPV
b) Since Century Roofing could have realized $100,000 from the sale of the building if it decides not to open the new warehouse, this opportunity cost is factored into the calculation of the Net Present Value. It becomes a present cash outflow. Century Roofing's opportunity cost is defined as the loss of $100,000 being the future return from the best alternative project when it chooses to build the new warehouse instead of selling off the building.
Determine if the process appears to be within statistical control. If not, state the reason why not.
a. It does not appear to be within statistical control because there is an upward shift.
b. It appears to be within statistical control.
c. It does not appear to be within statistical control because there is an upward trend.
d. It does not appear to be within statistical control because there is increasing variation.
Answers
Answer:
c. It does not appear to be within statistical control because there is an upward trend.
Step-by-step explanation:
Statistical process control is a method for quality control which employs statistical method to monitor and control process. It ensures operation efficiency and ensuring required specification to reduce wastes in production lines. Here the process variation is out of control because the statistical control has an upward trend.
What is the constant of variation, k, of the line y=kx through (3,18) and (5,30)? 3 6
Answers
Answer:
6
Step-by-step explanation:
The constant of variation is the slope
k = (y2-y1)/(x2-x1)
= (30-18)/(5-3)
=12/2
= 6
The value of constant of variation, k, is,
⇒ k = 6
What is Equation of line?
The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Here, the constant of variation, k, of the line y = kx through (3,18) and (5,30)
Since, The constant of variation is the slope,
Hence, We get;
k = (y₂ - y₁)/(x₂ - x₁)
= (30 - 18)/(5 - 3)
= 12/2
= 6
Thus, the value of constant of variation, k, is,
⇒ k = 6
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Time spent using e-mail per session is normally distributed with a mean = to 8 minutes and standard deviation = 2minutes. If a random samples of 36 sessions were selected, the computed sample standard deviation would be
a. 0.25
b. 0.3333
c. 0.42
d. 0.48
Answers
Answer:
The correct option is (b) 0.3333.
Step-by-step explanation:
The standard deviation of the sampling distribution of sample mean [tex](\bar x)[/tex] is known as the standard error [tex](\sigma_{\bar x})[/tex].
The standard error is given as follows:
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]
The information provided is:
[tex]\mu=8\\\\\sigma=2\\\\n=36[/tex]
Compute the standard deviation of the sample mean as follows:
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]
[tex]=\frac{2}{\sqrt{36}}\\\\=\frac{2}{6}\\\\=\frac{1}{3}\\\\=0.3333[/tex]
Thus, the standard deviation of the sample mean is 0.3333.
The one-sample z test is: a. a hypothesis test b. used to test hypotheses c. concerning a single population with a known variance d. concerning at least one population e. concerning the variance in a population d. all of the above
Answers
Answer:
d. all of the above
Step-by-step explanation:
A one sample z test measures whether the mean of a population is greater, less or equal to a specific value. It is called one sampl z test since the standard normal distribution is used in calculation of critical values. It makes use of the null hypothesis and alternative hypothesis in determining if the mean is greater than or equal or less than the reference value. Variance and standard deviation is assumed to be known and at least one population is used
We have seen how to convert specified odds from a "fair bet" into the gamblerâs belief about the likelihood of an event happening. The following are related.a. Torik gives 5:3 odds that someone will walk in late for class tomorrow. What probability does lie assign for this event? b. Mikko believes there is a 60% chance that at least five students from this class will be at the next basketball game. If he were to set up odds, what would they be? c. Change the 60% to 75%. Now would would be the odds?
Answers
The present price of a bus is rs 3000000if the price of bus depreciated the first two yrs by 10% and then 15% and 20% respectively in follow yrs.what is the price of bus after 4 yrs?
Answers
Answer:
The price of bus after 4 yrs is Rs.1652400
Step-by-step explanation:
Present price of car = Rs.3000000
We are given that the price of bus depreciated the first two yrs by 10%
So, The price after first two years =[tex]3000000(1-0.1)^2=2430000[/tex]
Now the price of bus depreciated by 15%
So, The price after third year = 2430000-0.15(2430000)=2065500
Now the price of bus depreciated by 20%
The price after fourth year =2065500-0.2(2065500)=1652400
Hence the price of bus after 4 yrs is Rs.1652400
if G is the midpoint of FH, FG = 14x + 25 and GH = 73 - 2x, find FH.
Answers
Answer:
FH = 134
Step-by-step explanation:
From the question given:
G is the midpoint of FH
FG = 14x + 25
GH = 73 - 2x
FH =?
Next, we shall determine the value of x. The value of x can be obtained as follow:
Since G is the midpoint of FH, this implies that FG and GH are equal i.e
FG = GH
With the above formula, we can obtain the value of x as follow:
FG = 14x + 25
GH = 73 - 2x
x =?
FG = GH
14x + 25 = 73 - 2x
Collect like terms
14x + 2x = 73 - 25
16x = 48
Divide both side by 16
x = 48/16
x = 3
Next, we shall determine the value of FG and GH. These can be obtained as shown below:
FG = 14x + 25
x = 3
FG = 14x + 25
FG = 14(3) + 25
FG = 42 + 25
FG = 67
GH = 73 - 2x
x = 3
GH = 73 - 2x
GH = 73 - 2(3)
GH = 73 - 6
GH = 67
Finally, we shall determine FH as follow:
FH = FG + GH
FG = 67
GH = 67
FH = FG + GH
FH = 67 + 67
FH = 134
Therefore, FH is 134
opposite rays form a?
line
ray
point
plane
Answers
Answer:
ray is the answer for this
opposite rays form a line because they provide the two opposite directions in which the line extends infinitely.
Opposite rays form a what?Opposite rays are two rays that have the same endpoint but extend in opposite directions. When these opposite rays are extended infinitely in both directions, they form a straight line. A line is a set of points that extends infinitely in both directions, and opposite rays provide the two distinct directions in which the line can be extended.
The concept of opposite rays is derived from the concept of a line. A line can be defined as a straight path that extends infinitely in both directions. Opposite rays are a pair of rays that share a common endpoint and extend infinitely in opposite directions along this line.
For example, consider a line segment AB. If we extend one side of the line segment from point A and the other side from point B, we obtain two opposite rays: one from point A to infinity and the other from point B to infinity. Together, these opposite rays form the line on which the line segment AB lies.
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The following data represents the age of 30 lottery winners.
22 26 27 27 31 34
36 42 43 44 48 49
52 53 55 56 57 60
65 65 66 67 69 72
75 77 78 78 79 87
Complete the frequency distribution for the data.
Age Frequency
20-29
30-39
40-49
50-59
60-69
70-79
80-89
Answers
Answer:
Step-by-step explanation:
This is an example of a frequency distribution for a class interval. In order to complete the frequency distribution, we will count the number of data occurring in each group, and write that number as the frequency for that group. This is done as shown below:
Age Frequency ages in class
20-29 4 22, 26, 27, 27
30-39 3 31, 34, 36
40-49 5 42, 43, 44, 48, 49
50-59 5 52, 53, 55, 56, 57
60-69 6 60, 56, 65, 66, 67, 69
70-79 6 72, 75, 77, 78, 78, 79
80-89 1 87
Total 30
Translate and solve: 54 greater than x is greater than 216
Answers
Answer:
x >162
Step-by-step explanation:
x+54 > 216
Subtract 54 from each side
x+54-54 > 216 - 54
x >162
Answer:
[tex]\huge \boxed{{x>162}}[/tex]
Step-by-step explanation:
[tex]x+54 > 216[/tex]
[tex]\sf Subtract \ 54 \ from \ both \ parts.[/tex]
[tex]x+54 -54> 216-54[/tex]
[tex]x>162[/tex]
One of two small restaurants is chosen at random with equally likely probability, and then an employee is chosen at random from the chosen restaurant. Restaurant #1 has 10 full-timers and 6 part-timers. Restaurant #2 has 7 full-timers and 9 part-timers. What is the probability that Restaurant #1 was chosen at random, given that a full-time employee was chosen? Your answers should be rounded to 4 digits after the decimal.
Answers
Answer:
P(1 |F) = 10/17
Step-by-step explanation:
Let events
1 = restaurant 1
2 = restaurant 2
F = full-time worker chosen
P = part-time worken chosen
P(1 and F) = 1/2 * 10/16 = 5/16
P(2 and F) = 1/2 * 7/16 = 7/32
P( (1 or 2) and F ) = P(F) = 5/16+7/32 = 17/32
P(1 | F) Probability of choosing restaurant 1 given a full-time was chosen
= P(1 and F) / P(F)
= 5/16 / (17/32)
= 5/16 * 32/17
= 10 / 17
How many solutions does the following system have x+y=3, 2x+2y-5
Answers
Answer:
Step-by-step explanation:
x + y = 3
2x + 2y = 5
-2x - 2y = -6
2x + 2y = 5
0 not equal to -1
no solution
Which of the following is true about congruent figures?
They're the same shape and the same size.
They're the same size, but not the same shape.
They're not the same shape or size.
They're the same shape, but not the same size.
Answers
Answer:
A
Step-by-step explanation:
congruent means they have the same shape and size. hope this helps :)
5/7 minus 2/9 please
Answers
Answer:
[tex]\large \boxed{31/63}[/tex]
Step-by-step explanation:
5/7 - 2/9
Make denominators equal by LCM.
(5 × 9)/(7 × 9) - (2 × 7)/(9 × 7)
45/63 - 14/63
Subtract fractions since denominators are equal.
(45 - 14)/63
31/63
Answer:
[tex]\frac{31}{63}[/tex]
Step-by-step explanation:
Find the LCM of 7 and 9: 63Find how much we increased each number to get to 63: we increased 7 by 9, and we increased 9 by 7Multiply the numerators by the corresponding increase numbers: 5 × 9 = 45, and 2 × 7 = 14Put the new numerators over the new denominators, so it looks like this: [tex]\frac{45}{63}[/tex] and [tex]\frac{14}{63}[/tex] Finally, subtract one from the other and here's what you get: [tex]\frac{31}{63}[/tex]Therefore, the answer is [tex]\frac{31}{63}[/tex].
Please! David has several chains of length 5 and of length 7. By joining chains one after the other, David can create different lengths. Which of these lengths is impossible to make? A)10 B)12 C)13 D)14 E)15
Answers
Answer:
13
Step-by-step explanation:
A)5+5=10
B)5+7=12
C) impossible
D)7+7=14
E)5+5+5=15
For what value of x does (x + 3)^2-5=0
Answers
Answer:
x = -3±sqrt( 5)
Step-by-step explanation:
(x + 3)^2-5=0
Add 5 to each side
(x + 3)^2-5+5=0+5
(x + 3)^2 = 5
Take the square root of each side
sqrt((x + 3)^2 )=±sqrt( 5)
x+3 = ±sqrt( 5)
Subtract 3 from each side
x+3-3 = -3±sqrt( 5)
x = -3±sqrt( 5)
Solve x2 + 9x + 8 = 0 by completing the square. What are the solutions?
O (1.-8)
O (1.8)
O (-1-8)
Answers
Explanation:
x^2 + 9x + 8 = 0
x^2 + 9x = -8
Add (9/2)^2 to both sides
x^2 + 9x + (9/2)^2 = -8 + (9/2)^2
(x + 9/2)^2 = -8 + 81/4
(x + 9/2)^2 = -32/4 + 81/4
(x + 9/2)^2 = 49/4
Square root both sides
Sqrt (x + 9/2)^2 = sqrt 49/4
x + 9/2 = plus or minus 7/2
Set x + 9/2 = 7/2:
x + 9/2 = 7/2
x = 7/2 - 9/2
x = -2/2 = -1
Set x + 9/2 = -7/2:
x + 9/2 = -7/2
x = -7/2 - 9/2
x = -16/2 = -8
solve the following inequalities 7 x minus 5 / 8 x + 3 >4
Answers
Answer:
[tex]x> \frac{8}{51} [/tex]
Step-by-step explanation:
[tex]7x - \frac{5}{8} x + 3>4[/tex]
Bring constants to one side, simplify:
[tex] \frac{51}{8} x>4 - 3 \\ \frac{51}{8} x>1 \\ x>1 \div \frac{51}{8} \\ x>1 \times \frac{8}{51} \\ x> \frac{8}{51} [/tex]
*Note that the inequality sign only changes when you divide the whole inequality by a negative number.
Answer:
[tex]x>\frac{8}{51}[/tex]
Step-by-step explanation:
[tex]7x-\frac{5}{8}x+3>4\\\mathrm{Subtract\:}3\mathrm{\:from\:both\:sides}\\7x-\frac{5}{8}x+3-3>4-3\\\mathrm{Simplify}\\7x-\frac{5}{8}x>1\\\mathrm{Multiply\:both\:sides\:by\:}8\\7x\times \:8-\frac{5}{8}x\times \:8>1\times \:8\\\mathrm{Simplify}\\56x-5x>8\\51x>8\\\mathrm{Divide\:both\:sides\:by\:}51\\\frac{51x}{51}>\frac{8}{51}\\\\x>\frac{8}{51}[/tex]
I hope it helps :)
x = 4: 3x3 - 2x2 +10
Answers
Answer:
170
Step-by-step explanation:
3(4)³ - 2(4)² + 10
192 - 32 + 10 = 170
WILL GIVE BRAINLEST PLEASE!!!!!!!! Jenny has some tiles in a bag. The tiles are of three different colors: purple, pink, and orange. Jenny randomly pulls a tile out of the bag, records the color, and replaces the tile in the bag. She does this 50 times. The results are recorded in the given table: Color of Tile Purple Pink Orange Number of times the tile is drawn 6 18 26 What is the experimental probability that Jenny will pull out a purple tile? fraction 6 over 50 fraction 44 over 50 fraction 6 over 44 fraction 18 over 44
Answers
Answer:
6/50
Step-by-step explanation:
There are 50 tiles
6 purple
18 pink
26 orange
P( purple) = purple/ total
= 6/50
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:
Given the following hypotheses: H0: μ = 490 H1: μ ≠ 490 A random sample of 15 observations is selected from a normal population. The sample mean was 495 and the sample standard deviation 9. Using the 0.01 significance level:
a.) State the decision rule.
b.) Compute the value of the test statistic.
c.) What is your decision regarding the null hypothesis?
Answers
Answer:
We conclude that the population mean is equal to 490.
Step-by-step explanation:
We are given that a random sample of 15 observations is selected from a normal population. The sample mean was 495 and the sample standard deviation 9.
Let [tex]\mu[/tex] = population mean.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 490 {means that the population mean is equal to 490}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu\neq[/tex] 490 {means that the population mean is different from 490}
The test statistics that will be used here is One-sample t-test statistics because we don't know about population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_1_4[/tex]
where, [tex]\bar X[/tex] = sample mean = 495
s = sample standard deviation = 9
n = sample of observations = 15
So, the test statistics = [tex]\frac{495-490}{\frac{9}{\sqrt{15} } }[/tex] ~ [tex]t_1_4[/tex]
= 2.152
The value of t-test statistics is 2.152.
Now, at a 0.01 level of significance, the t table gives a critical value of -2.977 and 2.977 at 14 degrees of freedom for the two-tailed test.
Since the value of our test statistics lies within the range of critical values of t, so we have insufficient evidence to reject our null hypothesis as the test statistics will not fall in the rejection region.
Therefore, we conclude that the population mean is equal to 490.
