A college entrance exam company determined that a score of 2222 on the mathematics portion of the exam suggests that a student i
1 answer:
Answer:
Yes, Students are scoring above 2222 on the math portion of the exam.
Step-by-step explanation:
We are given that a college entrance exam company determined that a score of 2222 on the mathematics portion of the exam suggests that a student is ready for college-level mathematics i.e., population mean is 22.
Null Hypothesis, :
= 22 {Students are scoring equal to 2222 on the math portion of the exam}
Alternate Hypothesis, :
> 22 {Students are scoring above 2222 on the math portion of the exam}
Also, a random sample of 150 students who completed this core set of courses results in a mean math score of 22.7 on the college entrance exam with a standard deviation of 3.93 i.e.;
Sample mean, = 22.7 and Sample standard deviation, s = 3.93
The Test statistics is given by;
Z = ~
Test Statistics = ~
= 2.1815
Since, we are not given with the significance level, so we assume it to be 5%. At 5% significance level t table gives critical value of 1.6578 at 149 degree of freedom. Since our test statistics is more than the critical value so we reject null hypothesis as our test statistics fall in the rejection region.
Therefore, we conclude that Students are scoring above 2222 on the math portion of the exam.
You might be interested in
Short Answer: C
Remark
The first thing you really ought to do is get a graph from one of the graphing programs on the internet. Most of the time, I use Desmos. That will give you the answer. I will put the graph at the bottom of the page.
The second thing you could do is just set up the given points to see which one gives you the answer.
The third thing (and I'll do this one) is to actually solve the problem by completing the square.
Givens
a = -2
b = 6
c = -1
Solution
Put brackets around the first two terms.
y = (- 2x^2 + 6x ) - 1 Take out the common factor of - 2
y = -2(x^2 - 3x ) - 1 Complete the square inside the brackets.
y = -2(x^2 - 3x + (3/2)^2 ) - 1 Add what it took to complete the square after the - 1
y = -2(x^2 - 3x + (3/2)^2 ) - 1 + 2(3/2)^2 * See remark at end to see why its +
y = -2(x^2 - 3x + 9/4) - 1 + 2 * (9/4)
y = -2(x^2 - 3x + 9/4) - 1 + 18/4
y = -2(x^2 - 3x + 9/4) + 14/4 Show the brackets in square form.
y = -2(x - 3/2)^2 + 14/4 but 3/2 =1.5 and 14/4 = 3.5
y = -2(x - 1.5)^2 + 3.5
The axis of symmetry is x = 1.5 The vertex is (1.5, 3.5)
Discussion
You may wonder why you are adding 18/4 outside the brackets when you are completing the square and all you have inside the brackets is 9/4.
The reason is because first of all there is a - 2 outside the brackets. That gets you 18/4. Because you have got a minus 2, you have to compensate the result so that you get 0. The only way to do that is to add 18/4.
Remark
The first thing you really ought to do is get a graph from one of the graphing programs on the internet. Most of the time, I use Desmos. That will give you the answer. I will put the graph at the bottom of the page.
The second thing you could do is just set up the given points to see which one gives you the answer.
The third thing (and I'll do this one) is to actually solve the problem by completing the square.
Givens
a = -2
b = 6
c = -1
Solution
Put brackets around the first two terms.
y = (- 2x^2 + 6x ) - 1 Take out the common factor of - 2
y = -2(x^2 - 3x ) - 1 Complete the square inside the brackets.
y = -2(x^2 - 3x + (3/2)^2 ) - 1 Add what it took to complete the square after the - 1
y = -2(x^2 - 3x + (3/2)^2 ) - 1 + 2(3/2)^2 * See remark at end to see why its +
y = -2(x^2 - 3x + 9/4) - 1 + 2 * (9/4)
y = -2(x^2 - 3x + 9/4) - 1 + 18/4
y = -2(x^2 - 3x + 9/4) + 14/4 Show the brackets in square form.
y = -2(x - 3/2)^2 + 14/4 but 3/2 =1.5 and 14/4 = 3.5
y = -2(x - 1.5)^2 + 3.5
The axis of symmetry is x = 1.5 The vertex is (1.5, 3.5)
Discussion
You may wonder why you are adding 18/4 outside the brackets when you are completing the square and all you have inside the brackets is 9/4.
The reason is because first of all there is a - 2 outside the brackets. That gets you 18/4. Because you have got a minus 2, you have to compensate the result so that you get 0. The only way to do that is to add 18/4.
The shortest length is given by the function for the perimeter of the
rectangular table.
- The shortest length of trim he could use is <u>536.66 cm</u>
The given parameter;
Area of the rectangular table Karma is building, <em>A</em> = <u>18,000 cm²</u>
Required:
The shortest length of trim he could use which he wants to put around the four edges.
Solution:
Let <em>l</em> represent the length of the table, and let <em>w</em> represent the width, therefore;
Perimeter of the table, <em>P</em> = 2·l + 2·w
Area, <em>A</em> = l × w
Which gives;
18,000 = l × w
Which gives;
At the minimum point, we have;
Which gives;
2·w² - 36,000 = w² × 0 = 0
2·w² = 36,000
The width of the rectangular table, <em>w</em> = √(18,000)
Therefore;
The perimeter of the table, P ≈ 2 × √(18,000) + 2 × √(18,000) ≈ 536.656
The length of trim required = The perimeter of the rectangular table, <em>P</em>
Therefore;
- The shortest length of the trim he could use, given to the nearest hundredth is <u>536.66 cm</u>
Learn more about area and perimeter of a figure here: