Answer:
Orapine: do additional processingBanango: no additional processingStep-by-step explanation:
The processing cost of split-off Orapine units is ...
GH¢20,000/(5000 units) = GH¢4/unit
The increase in revenue from the further processing is ...
GH¢25 -GH¢20 = GH¢5
The increased processing cost is less than the increased revenue, so there is additional profit from further processing 5000 units.
__
The processing cost of split-off Banango units is ...
GH¢20,000/(10000 units) = GH¢2/unit
The increase in revenue from the further processing is ...
GH¢16 -GH¢15 = GH¢1
The increased processing cost is more than the increased revenue, so the company takes a loss from further processing 10000 units. No additional processing of Banango units should be undertaken.
Can you draw the reflection Across the y-axis of the attached image.
Answer:
see graph
Step-by-step explanation:
A reflection across the y-axis means the point is equal but opposite distance from the y-axis. This has no change on the y-value of the point, because no matter the y-value, the point will still be the same distance from the y-axis. Long story short, if you're reflecting across the y-axis, change the sign of the x-coordinate. If you're reflecting across the x- axis, change the sign of the y-coordinate.
Find f. (Use C for the constant of the first antiderivative and D for the constant of the second antiderivative.)
f ''(x)= 6x +sinx
Answer:
[tex]f(x) = x^3 -sinx +Cx+D[/tex]
Step-by-step explanation:
Given that:
[tex]f ''(x)= 6x +sinx[/tex]
We are given the 2nd derivative of a function f(x) and we need to find f(x) from that.
We will have to integrate it twice to find the value of f(x).
Let us have a look at the basic formula of integration that we will use in the solution:
[tex]1.\ \int {(a\pm b)} \, dx =\int {a} \, dx + \int {b} \, dx \\2.\ \int {x^n} \, dx = \dfrac{x^{n+1}}{n+1}+C\\3.\ \int {sinx} \, dx = -cosx+C\\4.\ \int {cosx} \, dx = sinx+C[/tex]
[tex]\int\ {f''(x)} \, dx =\int\ {(6x +sinx)} \, dx \\\Rightarrow \int\ {6x} \, dx + \int\ {sinx} \, dx \\\\\Rightarrow 6\dfrac{x^2}{2} -cosx +C\\\Rightarrow 3{x^2} -cosx +C\\\Rightarrow f'(x)=3{x^2} -cosx +C\\[/tex]
Now, integrating it again to find f(x):
[tex]f(x) =\int {f'(x)} \, dx =\int{(3{x^2} -cosx +C)} \, dx \\\Rightarrow \int{3{x^2}} \, dx -\int{cosx} \, dx +\int{C} \, dx\\\Rightarrow 3\times \dfrac{x^3}{3} -sinx +Cx+D\\\Rightarrow x^3 -sinx +Cx+D\\\\\therefore f(x) = x^3 -sinx +Cx+D[/tex]
You have $50,000 in savings for retirement in an investment earning 5% annually. You aspire to have $1,000,000 in savings when you retire. Assuming you add no more to your savings, how many years will it take to reach your goal?
Answer: It will take you about 61 years for you to reach your goal.
Step-by-step explanation:
We will represent this situation by an exponential function. So if you earn 5% yearly then we could represent it by 1.05.So in exponential function we need to find the initial value and the common difference and in this case the common difference is 1.05 and the initial value or amount is 50,000 dollars.
We could represent the whole situation by the equation.
y= [tex]50,000(1.05)^{x}[/tex] where x is the number of years. so if you aspire to have 1,000,000 in some years then we will put in 1 million dollars for y and solve for x.
1,000,000 = 50,000(1.05)^x divide both sides by 50,000
20 = (1.05)^x
x= 61.40
A pyramid shaped building is 311 feet tall and has a square base with sides of 619 ft. The sides of the building are made from reflective glass. what is the surface area of the reflective glass
Answer:
Surface area of the reflective glass is 543234.4 square feet.
Step-by-step explanation:
Given that: height = 311 feet, sides of square base = 619 feet.
To determine the slant height, we have;
[tex]l^{2}[/tex] = [tex]311^{2}[/tex] + [tex]309.5^{2}[/tex]
= 96721 + 95790.25
= 192511.25
⇒ l = [tex]\sqrt{192511.25}[/tex]
= 438.761
The slant height, l is 438.8 feet.
Considering one reflecting surface of the pyramid, its area = [tex]\frac{1}{2}[/tex] × base × height
area = [tex]\frac{1}{2}[/tex] × 619 × 438.8
= 135808.6
= 135808.6 square feet
Since the pyramid has four reflective surfaces,
surface area of the reflective glass = 4 × 135808.6
= 543234.4 square feet
A psychologist is studying the effects of lack of sleep on the performance of various perceptual-motor tasks. After a given period of sleep deprivation, a measurement of reaction time to an auditory stimulus was taken for each of 36 adult male subjects.The mean and standard deviation of the reaction times (in seconds) for the fifty adult male subjects were 1.82 seconds and 0.28 seconds respectively. Previous psychological studies have shown that the true mean reaction time for non-sleep-deprived male subjects is 1.70 seconds. Does the sample evidence indicate that the mean reaction time for sleep-deprived adult males is longer than that of non-sleep-deprived adult males.
A. H0:μ=1.82;Ha:μ<1.82
B. H0:μ=1.70;Ha:μ<1.70
C. H0:μ=1.82;Ha:μ>1.82
D. H0:μ=1.70;Ha:μ>1.70
E. None of the above
Answer:
D. [tex]H_{0}[/tex] : μ = 1.70, [tex]H_{a}[/tex] : μ > 1.70
Step-by-step explanation:
The correct order of the steps of a hypothesis test is given following
1. Determine the null and alternative hypothesis.
2. Select a sample and compute the z - score for the sample mean.
3. Determine the probability at which you will conclude that the sample outcome is very unlikely.
4. Make a decision about the unknown population.
These steps are performed in the given sequence to test a hypothesis
The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted. It is not necessary that all null hypothesis will be rejected at 10% level of significance. To determine the criteria for accepting or rejecting a null hypothesis we should also consider p-value.
What is the slope of the line
described by -4X + 2Y = 16?
A. -2
B. -4
C. 4
D. 2
E. 16
Answer: THe slope is 2
SO answer d
Step-by-step explanation:
-4X + 2Y = 16 add 4x to the other side so equation is
2y=16+4x divided by 2
y=8+2x
solve the rational equation 5/x = 4x+1/x^2
Answer:
x = 1
Step-by-step explanation:
Set up the rational expression with the same denominator over the entire equation.
Since the expression on each side of the equation has the same denominator, the numerators must be equal
5x =4x+1
Move all terms containing x to the left side of the equation.
Hope this can help you
Set up a rational equation and then solve the following problems. A positive integer is twice another. The difference of the reciprocals of the two positive integers is 1/18. Find the two integers.
Answer:
9 and 18
Step-by-step explanation:
2x and x are the numbers
1/x-1/2x=1/18
2/2x-1/2x=1/18
1/2x=1/18
2x=18X=9,
2x=18
The two integers are 9 and 18
Sketch the region that corresponds to the given inequality. HINT [See Example 1.] 2x + y ≤ 10 Say whether the region is bounded or unbounded. The region is bounded. The region is unbounded. Find the coordinates of all corner points (if any). (If an answer does not exist, enter DNE.)
Answer:
See the attachment for sketch
Thr region is unbounded
DNE
Step-by-step explanation:
y≤ -2x + 10
The inequality is a straight line and region marked by the inequality. It has no boundaries. The boundaries extend to infinity. So the region is unbounded. Unbounded region has no corner points.
What is 24-(-6) because in confused
Answer:
30
Step-by-step explanation:
24 - (-6)
Apply rule : -(-a) = a
Negative (-) times a negative (-) is positive (+).
24 + 6
= 30
Answer:
-6 is in parentheses because it is a negative number. this prevents the equation from looking like a too long subtraction sign (24--6); therefore it is written as 24 - (-6).
this simplifies to 24 + 6 = 30
to negatives = a positive
The average college lecture hall (auditorium) can seat 60 students with a standard deviation of 21. Assume that a total of 60 lecture halls are selected for a sample. What is the standard deviation for the sample mean?
Answer:
The standard deviation of the sample mean is [tex]\sigma _ {\= x } = 2.711[/tex]
Step-by-step explanation:
From the question we are told that
The mean is [tex]\= x = 60[/tex]
The standard deviation is [tex]\sigma = 21[/tex]
The sample size is [tex]n = 60[/tex]
Generally the standard deviation of the sample mean is mathematically represented as
[tex]\sigma _ {\= x } = \frac{\sigma }{\sqrt{n} }[/tex]
substituting values
[tex]\sigma _ {\= x } = \frac{ 21 }{\sqrt{60} }[/tex]
[tex]\sigma _ {\= x } = 2.711[/tex]
Trade associations, such as the United Dairy Farmers Association, frequently conduct surveys to identify characteristics of their membership. If this organization conducted a survey to estimate the annual per-capita consumption of milk and wanted to be 95% confident that the estimate was no more than 0.5 gallon away from the actual average, what sample size is needed
Complete Question
Trade associations, such as the United Dairy Farmers Association, frequently conduct surveys to identify characteristics of their membership. If this organization conducted a survey to estimate the annual per-capital consumption of milk and wanted to be 95% confident that the estimate was no more than 0.5 gallon away from the actual average, what sample size is needed? Past data have indicated that the standard deviation of consumption of approximately 10 gallons.
Answer:
The sample size is [tex]n = 1537 \ gallons[/tex]
Step-by-step explanation:
From the question we are told that
The margin of error is [tex]MOE = 0.5[/tex]
The confidence level is [tex]C = 95[/tex]%
Given that the confidence level is 95% the level of significance is mathematically represented as
[tex]\alpha = 100 - 95[/tex]
[tex]\alpha = 5[/tex]%
[tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table , the values is [tex]Z_{\frac{\alpha }{2} } = 1. 96[/tex]
The reason we are obtaining critical values of
[tex]\frac{\alpha }{2}[/tex]
instead of
[tex]\alpha[/tex]
is because
[tex]\alpha[/tex]
represents the area under the normal curve where the confidence level interval (
[tex]1-\alpha[/tex]
) did not cover which include both the left and right tail while
[tex]\frac{\alpha }{2}[/tex]
is just the area of one tail which what we required to calculate the sample size
Now the sample size is mathematically represented as
[tex]n = \frac{[Z_{\frac{\alpha }{2} }] ^2 * \sigma ^2}{MOE^2}[/tex]
substituting values
[tex]n = \frac{1.96^2 * 10 ^2}{0.5^2}[/tex]
[tex]n = 1537 \ gallons[/tex]
67.805 what is the value of the 0 help please asap!
Answer:
hundreths
Step-by-step explanation:
After the decimal there is tenths, hundreths thousandnths, tens of thousands e.t.c
Answer:
Hello! The answer will be hundredths.
Step-by-step explanation:
The 5 means the thousandths.
The 0 means the hundredths.
The 8 means the tenths.
The 7 means the ones
And the 6 means the tens.
Hope this helps! :)
( below I attached a picture, which might be helpful.)
The current particulate standard for diesel car emission is .6g/mi. It is hoped that a new engine design has reduced the emissions to a level below this standard. Set up the appropriate null and alternative hypotheses for confirming that the new engine has a mean emission level below the current standard. Discuss the practical consequences of making a Type I and a Type II error. (continue #5) A sample of 64 engines tested yields a mean emission level of = .5 g/mi. Assume that σ = .4. Find the p-value of the test. Do you think that H0 should be rejected? Explain. To what type of error are you now subject?
Answer:
Step-by-step explanation:
From the summary of the given statistics;
The null and the alternative hypothesis for confirming that the new engine has a mean emission level below the current standard can be computed as follows:
Null hypothesis:
[tex]H_0: \mu = 0.60[/tex]
Alternative hypothesis:
[tex]H_a: \mu < 0.60[/tex]
Type I error: Here, the null hypothesis which is the new engine has a mean level equal to .6g/ml is rejected when it is true.
Type II error: Here, the alternative hypothesis which is the new engine has a mean level less than.6g/ml is rejected when it is true.
Similarly;
From , A sample of 64 engines tested yields a mean emission level of = .5 g/mi. Assume that σ = .4.
Sample size n = 64
sample mean [tex]\overline x[/tex] = .5 g/ml
standard deviation σ = .4
From above, the normal standard test statistics can be determined by using the formula:
[tex]z = \dfrac{\bar x- \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \dfrac{0.5- 0.6}{\dfrac{0.4}{\sqrt{64}}}[/tex]
[tex]z = \dfrac{-0.1}{\dfrac{0.4}{8}}[/tex]
z = -2.00
The p-value = P(Z ≤ -2.00)
From the normal z distribution table
P -value = 0.0228
Decision Rule: At level of significance ∝ = 0.05, If P value is less than or equal to level of significance ∝ , we reject the null hypothesis.
Conclusion: SInce the p-value is less than the level of significance , we reject the null hypothesis. Therefore, we can conclude that there is enough evidence that a new engine design has reduced the emissions to a level below this standard.
What is the next term in the sequence −10,−17,−24,−31,…?
Answer:
-38
Step-by-step explanation:
it's subtracting 7 everytime, and -31-7=-38
A car dealership earns a portion of its profit on the accessories sold with a car. The dealer sold a Toyota Camry loaded with accessories for $24,000. The total cost of the car was 8 times as much as the accessories. How much did the accessories cost? Cost of Accessories
Answer:
y = 2666.67
Step-by-step explanation:
Well to solve this we can make a system of equations.
x = cost of car alone
y = cost of accesories,
[tex]\left \{ {{x+y=24000} \atop {x=8y}} \right.[/tex]
So now we plug in 8y for x in x + y = 24000.
(8y) + y = 24000
9y = 24000
Divide both sides by 9
y = 2666.666666
or 2666.67 rounded to the nearest hundredth.
Now that we have y we can plug that in for y in x=8y.
x = 8(2.666.67)
x = 21,333.33 rounded to the nearest hundredth.
Thus,
accessories "y" cost around 2666.67.
Hope this helps :)
Select the correct answer. Sarah wants to print copies of her artwork. At the local print shop, it costs her $1 to make 5 copies and $5 to make 25 copies. How much would it cost Sarah to make 100 copies? A. $15 B. $20 C. $25 D. $30
$1 = 5copies means
$5 = 25 copies obviously
then
$x = 100 copies
100 / 5 = $x
so she needs
$20
The cost of printing 100 copies of artwork is $20.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Suppose 2 pens cost $10, So the cost of 1 pen is (10/2) = $5.
From this unitary cost of pens, we can determine the cost of any no. of pens by multiplying the unit cost by the no. of pens.
Given, The cost of printing 5 artworks is $1.
∴ The cost of printing 100 copies is $(100/5),
= $20.
learn more about the unitary method here :
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a box contains 20 blue marbes, 16 green marbles, and 14 red marbles. two marbles are selected at random. let 3 be the event that first marbke selected is green. find p(fe) g
Answer:
Let E be the event that the first marble selected is green. Let F be the event that the second marble selected is green. A box contains 20 blue marbles, 16 green marbles and 14 red marbles P(F/E)=15/49 because if the first marble selected is green there are 49 in total and 15 are green. I think this is it.
Step-by-step explanation:
URGENT!!!!!! A 5 inch × 7 inch photograph is placed inside a picture frame. Both the length and width of the frame are 2x inches larger than the width and length of the photograph. Which expression represents the perimeter of the frame? REPLY IN COMMENTS PLEASE IM GLITCHING AND CANT SEE ANSWERS
Answer:
the perimeter of the square is just "(5+2x)(2)+(7+2x)(2)
Step-by-step explanation:
Answer:
2 × 10 + 2 × 14
Step-by-step explanation:
The frame is given to have measurements 2 times that of the photograph's measurements. We also know that the photograph is given by dimensions being 5 inch by 7 inch. Therefore the measurements of the frame should be 5 [tex]*[/tex] 2, which = 10 inches, by 7 [tex]*[/tex] 2 = 14 inches.
So the dimensions of the frame are 10 inch × 14 inch. As the frame is present as a rectangle, the perimeter is given by two times both dimensions together. That would be represented by the expression " 2 × 10 inch + 2 × 14 inch. " In other words you can say that the expression is 2 × 10 + 2 × 14 - the expression that represents the perimeter of the frame.
144 + h^2 = 225 WHAT THE HECK DOES ^ MEAN!???
Answer:
h^2 means h²
(h squared)
Step-by-step explanation:
Step 1: Write equation
144 + h² = 225
Step 2: Subtract 144 on both sides
h² = 81
Step 3: Take square root
√h² = √81
h = 9
The population of Oak Forest is increasing at a rate of 4% per year. If the population is 74,145 today, what will it be in three years?
Answer:
83,403
Step-by-step explanation: Take 74,145 and multiply it by 4%. Then take that number and add it to the 74,145 and that'll give you year one. For year 2 you'll take your total from year 1 and multiply it by the 4% growth rate then you'll add the 4% to what your ending from year 1 and that'll give you your total growth after 2 years. Then you'll take your ending total from year 2 and multiply it by 4% and then you'll add that 4% to the total end from year 2 and that'll give you your total growth of 4% every year for 3 consecutive years.
Hope this helps!
Line j is a straight line. Which equation represents the relationship between the measures of Angle w and Angle z? A) Measure of angle w = measure of angle z b) Measure of angle w + measure of angle z = 90 degrees c) Measure of angle w + measure of angle z = 100 degrees d) Measure of angle w + measure of angle z = 180 degrees
Answer:
Measure of angle W + measure of angle Z = 180°
Step-by-step explanation:
The reason is that angles in a straight line add up to 180° and angles at a point add up to 360° (i.e the sum of measure of angles W, X, Y, Z is 360°)
Answer:
D is your answer
Step-by-step explanation:
I have no explanation
Write the expression as the sine, cosine, or tangent of an angle. (6 points) cos 94° cos 37° + sin 94° sin 37°
Answer:
[tex]cos57 = 0.5446[/tex]
[tex]sin57 = 0.8387[/tex]
[tex]tan57 = 1.5399[/tex]
Step-by-step explanation:
Given
[tex]cos 94\° cos 37\° + sin 94\° sin 37\°[/tex]
Required
Determine the
- sin
- cosine
- tangent
of an angle
The given expression can be represented as follows;
[tex]cosAcosB + sinAsinB[/tex]
Where A = 94 and B = 37
In trigonometry:
[tex]cosAcosB + sinAsinB = cos(A - B)[/tex]
Substitute 94 for A and 37 for B
[tex]cos(A - B) = cos(94 - 37)[/tex]
[tex]cos(A - B) = cos(57)[/tex]
Hence, the angle is 57;
Since 57 is not a special angle; I'll solve using a calculator
[tex]cos57 = 0.5446[/tex]
[tex]sin57 = 0.8387[/tex]
[tex]tan57 = 1.5399[/tex]
h(x)=-4+16 find x when h(x)=48 Plz don't say it is incomplete
Answer:
x = -8
Step-by-step explanation:
When h(x) = 48, you can simply just plug it back into the first equation. Don't let the h(x) confuse you!
Think of it like saying y = -4x + 16, y = 48.
48 = - 4x + 16
32 = - 4x
8 = -x
Divide by -1 both sides.
-8 = x
Solve the formula for the perimeter of a rectangle, with width w and length I,
for the length.
P= 2W + 2/
Answer:
( P -2w) /2 = l
Step-by-step explanation:
P= 2W + 2l
Subtract 2W from each side
P= 2W -2W + 2l
P -2W = 2l
Divide by 2
( P -2w) /2 = l
Answer:
A. [tex]\frac{P - 2w}{2} = l[/tex]
Step-by-step explanation:
Well in,
P = 2w + 2l
to solve for l we need to single it out.
P = 2w + 2l
-2w
P - 2w = 2l
divide everything by 2
[tex]\frac{P - 2w}{2} = l[/tex]
Thus,
the answer is A.
Hope this helps :)
Find the probability of each of the following, if Z~N(μ = 0,σ = 1).
(please round any numerical answers to 4 decimal places)
a) P(Z > -1.13) =
b) P(Z < 0.18) =
c) P(Z > 8) =
d) P(| Z | < 0.5) =
Answer: a) 0.8708, b) 5714, c) 0.000, d) 0.3830
Step-by-step explanation:
(a)
To find P(Z>-1.13):
Since Z is negative, it lies on left hand side of mid value.
Table of Area Under the Standard Normal Curve gives area = 0.3708
So,
P(Z>-1.13) = 0.5 + 0.3708 = 0.8708
(b)
To find P(Z<0.18):
Since Z is positive, it lies on right hand side of mid value.
Table of Area Under the Standard Normal Curve gives area = 0.0714
So,
P(Z<0.18) = 0.5 + 0.0714 = 0.5714
(c)
To find P(Z>8):
Since Z is positive, it lies on right hand side of mid value.
Table of Area Under the Standard Normal Curve gives area = 0.5 nearly
So,
P(Z>8) = 0.5 - 0.5 nearly = 0.0000
(d)
To find P(| Z | < 0.5)
that is
To find P(-0.5 < Z < 0.5):
Case 1: For Z from - 0.5 to mid value:
Table of Area Under the Standard Normal Curve gives area = 0.1915
Case 2: For Z from mid value to 0.5:
Table of Area Under the Standard Normal Curve gives area = 0.1915
So,
P(| Z | < 0.5) = 2 * 0.1915 = 0.3830
The Probability can be determine using z-Table. The z- table use to determine the area under the standard normal curve for any value between the mean (zero) and any z-score.
(a) The value of [tex]P(z>-1.13)=0.8708[/tex].
(b) The value of [tex]P(Z < 0.18) = 0.5714[/tex].
(c) The value of [tex]P(Z > 8) = 0.0000[/tex].
(d) The value of [tex]P(| Z | < 0.5) =0.3830[/tex].
Given:
The given condition is [tex]Z\sim N(\mu= 0,\sigma = 1).[/tex]
(a)
Find the value for [tex]P(Z > -1.13)[/tex].
Here Z is less than 1 that means Z is negative. So it will lies it lies on left hand side of mid value.
Refer the table of Area Under the Standard Normal Curve.
[tex]\rm Area = 0.3708[/tex].
Now,
[tex]P(Z > -1.13)=0.5 + 0.3708 = 0.8708[/tex]
Thus, the value of [tex]P(z>-1.13)=0.8708[/tex].
(b)
Find the value for [tex]P(Z < 0.18)[/tex].
Here Z is positive. So it will lies it lies on right hand side of mid value.
Refer the table of Area Under the Standard Normal Curve.
[tex]\rm Area = 0.0714[/tex].
Now,
[tex]P(Z <0.18)=0.5 + 0.0714 = 0.5714[/tex]
Thus, the value of [tex]P(Z < 0.18) = 0.5714[/tex].
(c)
Find the value for [tex]P(Z >8)[/tex].
Here Z is positive. So it will lies it lies on right hand side of mid value.
Refer the table of Area Under the Standard Normal Curve.
[tex]\rm Area \approx 0.5[/tex].
Now,
[tex]P(Z >8)\approx0.5 - 0.5 = 0.0000[/tex]
Thus, the value of [tex]P(Z > 8) = 0.0000[/tex].
(d)
Find the value for [tex]P(|Z| <0.05)[/tex].
Here Z is mod of Z, it may be positive or negative. Consider the negative value of Z.
Refer the table of Area Under the Standard Normal Curve.
[tex]\rm Area =0.1915[/tex].
Consider the positive value of Z.
Refer the table of Area Under the Standard Normal Curve.
[tex]\rm Area =0.1915[/tex].
Now,
[tex]P(|Z| <0.5)=2\times 0.1915 = 0.3830[/tex]
Thus, the value of [tex]P(| Z | < 0.5) =0.3830[/tex].
Learn more about z-table here:
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Solve the equation using the distributive property and properties of equality.
1/2(x+6) = 18
What is the value of x?
O 6
O7 1/2
O 14 1/2
0 30
Answer:
x = 30
Step-by-step explanation:
1/2(x+6) = 18
Expand brackets or use distributive law.
1/2(x) + 1/2(6) = 18
1/2x + 6/2 = 18
1/2x + 3 = 18
Subtract 3 on both sides.
1/2x + 3 - 3 = 18 - 3
1/2x = 15
Multiply both sides by 2.
(2)1/2x = (2)15
x = 30
Answer:
30
Step-by-step explanation:
A group of 59 randomly selected students have a mean score of 29.5 with a standard deviation of 5.2 on a placement test. What is the 95% confidence interval for the mean score, , of all students taking the test
Answer:
The 95% confidence interval for the mean score, , of all students taking the test is
[tex]28.37< L\ 30.63[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 59[/tex]
The mean score is [tex]\= x = 29.5[/tex]
The standard deviation [tex]\sigma = 5.2[/tex]
Generally the standard deviation of mean is mathematically represented as
[tex]\sigma _{\= x} = \frac{\sigma }{\sqrt{n} }[/tex]
substituting values
[tex]\sigma _{\= x} = \frac{5.2 }{\sqrt{59} }[/tex]
[tex]\sigma _{\= x} = 0.677[/tex]
The degree of freedom is mathematically represented as
[tex]df = n - 1[/tex]
substituting values
[tex]df = 59 -1[/tex]
[tex]df = 58[/tex]
Given that the confidence interval is 95% then the level of significance is mathematically represented as
[tex]\alpha = 100 -95[/tex]
[tex]\alpha =[/tex]5%
[tex]\alpha = 0.05[/tex]
Now the critical value at this significance level and degree of freedom is
[tex]t_{df , \alpha } = t_{58, 0.05 } = 1.672[/tex]
Obtained from the critical value table
So the the 95% confidence interval for the mean score, , of all students taking the test is mathematically represented as
[tex]\= x - t*(\sigma_{\= x}) < L\ \= x + t*(\sigma_{\= x})[/tex]
substituting value
[tex](29.5 - 1.672* 0.677) < L\ (29.5 + 1.672* 0.677)[/tex]
[tex]28.37< L\ 30.63[/tex]
if 5x - 17 = -x +7, then x =
Answer:
x=4
Step-by-step explanation:
5x - 17 = -x +7
Add x to each side
5x+x - 17 = -x+x +7
6x -17 = 7
Add 17 to each side
6x-17+17 = 7+17
6x =24
Divide each side by 6
6x/6 = 24/6
x = 4
Answer:
4
Step-by-step explanation:
5x - 17 = -x + 7
Add x on both sides.
5x - 17 + x = -x + 7 + x
6x - 17 = 7
Add 17 on both sides.
6x - 17 + 17 = 7 + 17
6x = 24
Divide both sides by 6.
(6x)/6 = 24/6
x = 4
Find the mean, median, and mode of the data, if possible. f any of these measures cannot be found or a measure does not represent the center of the data, explain why.
A sample of seven admission test scores for a professional school are listed below
11.3 10.6 11.7 9.7 11.7 9.5 11.7
What is the mean score? Select the correct choice below and fill in any answer box to complete your choice
A. The mean score is Round to one decimal place as needed.)
B. There is no mean score. Does the mean represent the center of the data?
A. The mean represents the center
B. The mean does not represent the center because it is the smallest data value.
C. The mean does not represent the center because it is not a data value.
D. The mean does not represent the center because it is the largest data value.
What is the median score? Select the correct choice below and fill in any answer box to complete your choice.
A. The median score is 0
B. There is no median score.
Does the median represent the center of the data? (Round to one decimal place as needed.)
A. The median represents the center.
B. The median does not represent the center because it is not a data value. °
C. The median does not represent the center because it is the largest data value.
D. The median does not represent the center because it is the smallest data value.
What is the mode of the scores? Select the correct choice below and fill in any answer box to complete your choice
A. The mode(s) of the scores is (are)
B. There is no mode. Does (Do) the mode(s) represent the center of the data?
(Use a comma to separate answers as needed.)
A. The mode(s) represent(s) the center
B. The mode(s) can't represent the center because it (they) is (are) not a data value.
C. The mode(s) does (do) not represent the center because it (one) is the largest data value.
D. The mode(s) does (do) not represent the center because it (one) is the smallest data value.
Answer:
Step-by-step explanation:
Given a sample of seven admission test scores for a professional school listed 11.3, 10.6, 11.7, 9.7, 11.7, 9.5 and 11.7, the mean of the numbers is the sum total of the values divided by the total number of admission test score. The mean is as calculated below.
Mean = {11.3 + 10.6 + 11.7 + 9.7 + 11.7 + 9.5 + 11.7}/7
Mean = 76.2/7
Mean = 10.9
The mean score is 10.9 to 1 decimal place.
Note that the mean does not represent the centre of the data. It represents the average value of the datas. The mean does not represent the center because it is not a data value. The mean will give a value that is different from the values given in the data.
b) The median score is the score in the centre after re-arrangement. The arrangement can either be ascending or descending order. On re-arranging in ascending order;
9.5, 9.7, 10.6, (11.3), 11.7, 11.7, 11.7
After rearranging, it can be seen that the number at the centre of the data is 11.3, hence the median score is 11.3.
The median represents the center
c) The mode is the scores that occurs most. According to the data given, the score that occur most is 11.7. The score occurs the highest number of times (3 times) compare to other scores in the data. Hence, the modal score is 11.7.
The mode(s) does (do) not represent the center because it (one) is the largest data value.