Answer:
Mean, median and mode are measures of central tendency. The median is a better measure of central tendency when the given data contains outliers.
Step-by-step explanation:
Mean, median and mode are all measures of central tendency. These are statistical information that gives the middle or centre of a set of data. Since the values are central, they usually represent the entire distribution.
The mean is the obtained by dividing the sum of all the scores by the number of scores. The median is the middle value when numbers are arranged in increasing or decreasing order of magnitude. The mode is the most frequently occurring score in a distribution.
Let us see an example of the median as a measure of central tendency. Given the set of values; 4, 10, 12, and 26, the median is obtained from the average of the two middle numbers in the set of values which are 10 and 12 as seen from the set of values above. Hence the median of this set of values is 11.
The median can be a very good measure of central tendency, even better than the mean mostly in situations where there are outliers, or extreme values.
Which of the following is the solution to 9|x-1|=-45
Answer:
No solutions.
Step-by-step explanation:
9|x-1|=-45
Divide 9 into both sides.
|x-1| = -45/9
|x-1| = -5
Absolute value cannot be less than 0.
Answer:
No solution
Step-by-step explanation:
=> 9|x-1| = -45
Dividing both sides by 9
=> |x-1| = -5
Since, this is less than zero, hence the equation has no solutions
Each of the following is a confidence interval for μ = true average (i.e., population mean) resonance frequency (Hz) for all tennis rackets of a certain type:(111.6, 112.4) (111.4, 112.6)(a) What is the value of the sample mean resonance frequency?
Answer:
The value of the sample mean resonance frequency is 112Hz
Step-by-step explanation:
A confidence interval has two bounds, a lower bound and an upper bound.
A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.
In this problem, we have that:
Lower bound: 111.6
Upper bound: 112.4
Sample mean: (111.6 + 112.4)/2 = 112Hz
The value of the sample mean resonance frequency is 112Hz
The value of the sample mean resonance frequency is 112 Hz.
What is the value of the sample mean resonance frequency?The value of the sample mean resonance frequency is equivalent to the average of the upper limit and the lower limit.
The sample mean resonance frequency = (lower limit + upper limit) / 2
(111.6 +112.4) / 2
= 224 / 2
= 112 Hz
To learn more about confidence interval, please check: https://brainly.com/question/15905477
If a square with a width of 30 feet a length of 72 feet, and the diagonal is 78 feet, would the square have right angles. Yes or No answer please explain
Does the graph represent a function. Explain
Answer:
Yes
Step-by-step explanation:
functions include parabolas so yes!
Can someone please help me??
Answer : The value of x is 4.1 cm.
Step-by-step explanation :
As we know that the perpendicular dropped from the center divides the chord into two equal parts.
That means,
AB = CB = [tex]\frac{15.6cm}{2}=7.8cm[/tex]
Now we have o calculate the value of x by using Pythagoras theorem.
Using Pythagoras theorem in ΔOBA :
[tex](Hypotenuse)^2=(Perpendicular)^2+(Base)^2[/tex]
[tex](OA)^2=(OB)^2+(BA)^2[/tex]
Now put all the values in the above expression, we get the value of side OB.
[tex](8.8)^2=(x)^2+(7.8)^2[/tex]
[tex]x=\sqrt{(8.8)^2-(7.8)^2}[/tex]
[tex]x=\sqrt{77.44-60.84}[/tex]
[tex]x=\sqrt{16.6}[/tex]
[tex]x=4.074\approx 4.1[/tex]
Therefore, the value of x is 4.1 cm.
The percentage of households that include at least one frequent gamer is 58%. A gaming magazine is interested in studying this further to see how it impacts their magazine advertisements. For what sample size, n, will the sampling distribution of sample proportions have a standard deviation of 0.02
Answer:
For a sample size of n = 609.
Step-by-step explanation:
Central limit theorem for proportions:
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this question:
We have that p = 0.58.
We have to find n for which s = 0.02. So
[tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
[tex]0.02 = \sqrt{\frac{0.58*0.42}{n}}[/tex]
[tex]0.02\sqrt{n} = \sqrt{0.58*0.42}[/tex]
[tex]\sqrt{n} = \frac{\sqrt{0.58*0.42}}{0.02}[/tex]
[tex](\sqrt{n})^{2} = (\frac{\sqrt{0.58*0.42}}{0.02})^{2}[/tex]
[tex]n = 609[/tex]
For a sample size of n = 609.
An experiment was conducted to record the jumping distances of paper frogs made from construction paper. Based on the sample, the corresponding 95% confidence interval for the mean jumping distance is (8.8104, 11.1248)cm. What is the corresponding 98% confidence interval for the mean jumping distance?
Answer:
[tex] 9.9676 - 2.326*0.5904 =8.594[/tex]
[tex] 9.9676 + 2.326*0.5904 =11.341[/tex]
Step-by-step explanation:
Notation
[tex]\bar X[/tex] represent the sample mean
[tex]\mu[/tex] population mean (variable of interest)
s represent the sample standard deviation
n represent the sample size
Solution to the problem
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
For this case the 9% confidence interval is given by:
[tex] 8.8104 \leq \mu \leq 11.1248[/tex]
We can calculate the mean with the following:
[tex]\bar X = \frac{8.8104 +11.1248}{2}= 9.9676[/tex]
And we can find the margin of error with:
[tex] ME= \frac{11.1248- 8.8104}{2}= 1.1572[/tex]
The margin of error for this case is given by:
[tex] ME = t_{\alpha/2}\frac{s}{\sqrt{n}} = t_{\alpha/2} SE[/tex]
And we can solve for the standard error:
[tex] SE = \frac{ME}{t_{\alpha/2}}[/tex]
The critical value for 95% confidence using the normal standard distribution is approximately 1.96 and replacing we got:
[tex] SE = \frac{1.1572}{1.96}= 0.5904[/tex]
Now for the 98% confidence interval the significance is [tex]\alpha=1-0.98= 0.02[/tex] and [tex]\alpha/2 = 0.01[/tex] the critical value would be 2.326 and then the confidence interval would be:
[tex] 9.9676 - 2.326*0.5904 =8.594[/tex]
[tex] 9.9676 + 2.326*0.5904 =11.341[/tex]
Frederick took out a 20-year loan for $70,000 at an APR of 2.2%, compounded monthly. Approximately how much would he save if he paid it off 9 years early?
Answer:
$38,645.7208
Step-by-step explanation:
Given that
Principal = $70,000
Time = 20 years
Rate = 2.2%
The calculation of the amount of saving is shown below:-
[tex]=P(1+r)^t[/tex]
A = Future amount
P = Principal amount
[tex]r = \frac{APR}{12}[/tex]
[tex]r = \frac{0.022}{12}[/tex]
0.001833333
t = 20 years which is equals to 240 months
[tex]A=\$70,000\times (1+0.001833333)^{240}[/tex]
[tex]A=\$70,000\times 1.552081726[/tex]
= $108,645.7208
And, the loan amount for 20 years is $70,000
So,
He would save by paying off 9 years early is
= $108,645.7208 - $70,000
= $38,645.7208
Its $3644.67 since everyone couldn't find it solved it myself ;)
A student carried out an experiment to determine the amount of vitamin C in a tablet sample. He performed 5 trials to produce the following results: 490 mg, 502 mg, 505 mg, 495mg, and 492 mg. The manufacturer claims that the tablet contains 500 mg of vitamin C. Do an appropriate statistical analysis to find out whether the results obtained by the student is consistent with bottle claim.
Answer:
There is not enough evidence to support the claim that the amount of vitamin C in a tablet sample is different from 500 mg.
P-value = 0.166.
Step-by-step explanation:
We start by calculating the mean and standard deviation of the sample:
[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{5}(490+502+505+495+492)\\\\\\M=\dfrac{2484}{5}\\\\\\M=496.8\\\\\\s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{4}((490-496.8)^2+(502-496.8)^2+(505-496.8)^2+(495-496.8)^2+(492-496.8)^2)}\\\\\\s=\sqrt{\dfrac{166.8}{4}}\\\\\\s=\sqrt{41.7}=6.5\\\\\\[/tex]
Then, we can perform the hypothesis t-test for the mean.
The claim is that the amount of vitamin C in a tablet sample is different from 500 mg.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=500\\\\H_a:\mu< 500[/tex]
The significance level is 0.05.
The sample has a size n=5.
The sample mean is M=496.8.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=6.5.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{6.5}{\sqrt{5}}=2.907[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{496.8-500}{2.907}=\dfrac{-3.2}{2.907}=-1.1[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=5-1=4[/tex]
This test is a left-tailed test, with 4 degrees of freedom and t=-1.1, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t<-1.1)=0.166[/tex]
As the P-value (0.166) is bigger than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the amount of vitamin C in a tablet sample is different from 500 mg.
Triangle L M N is cut by line segment O P. Line segment O P goes from side M L to side M N. The length of O L is 14, the length of O M is 28, the length of M P is y, and the length of P N is 18.
Which value of y would make O P is parallel to L N?
16
24
32
36
Answer:
The value of y that would make O P parallel to L N = 36
Step-by-step explanation:
This is a question on similar triangles. Find attached the diagram obtained from the given information.
Given:
The length of O L = 14
the length of O M = 28
the length of M P = y
the length of P N = 18
Length MN = MP + PN = y + 18
Length ML = MO + OL = 28+14 = 42
For OP to be parallel to LN,
MO/ML = MP/PN
MO/ML = 28/42
MP/PN= y/(y+18)
28/42 = y/(y+18)
42y = 28(y+18)
42y = 28y + 18(28)
42y-28y = 504
14y = 504
y = 504/14 = 36
The value of y that would make O P parallel to L N = 36
Answer:
D-36
Step-by-step explanation:
Henrique began to solve a system of linear equations using the linear combination method. His work is shown below: 3(4x – 7y = 28) → 12x – 21y = 84 –2(6x – 5y = 31) → –12x + 10y = –62 12x – 21y = 84 + –12x + 10y = –62 –11y = 22 y = –2 Complete the steps used to solve a system of linear equations by substituting the value of y into one of the original equations to find the value of x. What is the solution to the system? ( , )
Answer:
( 3.5 , -2 )
Step-by-step explanation:
Answer:
( 3.5 , -2)
Explanation:
On edge
A 2011 survey, by the Bureau of Labor Statistics, reported that 91% of Americans have paid leave. In January 2012, a random survey of 1000 workers showed that 89% had paid leave. The resulting p-value is .0271; thus, the null hypothesis is rejected. It is concluded that there has been a decrease in the proportion of people, who have paid leave from 2011 to January 2012. What type of error is possible in this situation?
Answer:
Is possible to make a Type I error, where we reject a true null hypothesis.
Step-by-step explanation:
We have a hypothesis test of a proportion. The claim is that the proportion of paid leave has significantly decrease from 2011 to january 2012. The P-value for this test is 0.0271 and the nunll hypothesis is rejected.
As the conclusion is to reject the null hypothesis, the only error that we may have comitted is rejecting a true null hypothesis.
The null hypothesis would have stated that there is no significant decrease in the proportion of paid leave.
This is a Type I error, where we reject a true null hypothesis.
from what area of the world is the earliest dated inscription with a symbol for zero?
Answer:
india
Step-by-step explanation:
what is the length of the line?
Answer:
root 61
Step-by-step explanation:
You can use the distance formula or draw a triangle with sides 5 and 6
Find the equation of the line.
Use exact numbers.
Answer:
y = 2/3x + 4
Step-by-step explanation:
Step 1: Find slope
m = (4-0)/(0+6)
m = 2/3
Step 2: Write in y-int (0, 4)
y = 2/3x + 4
Which transformations could have occurred to map AABC
to AA"B"C"?
O a rotation and a dilation
O a rotation and a reflection
O a reflection and a dilation
O a translation and a dilation
Answer:
A reflection and a dialation
Step-by-step explanation:
Reflection is when you flip a figure over a line. Rotation is when you rotate a figure a certain degree around a point. Dilation is when you enlarge or reduce a figure.In this case a rotation is not nessasary, so I would suggest a reflection in the y-axis and a dialation to shrink the triangle to A'B'C'
So for the transformations that could have occurred to map ABC to A'B'C' you should choose the answer
a reflection and a dialation
The transformations that occurred to map ABC to A'B'C are: C. a reflection and a dilation
Key Facts on TransformationsReflection is simply flipping a shape over an axis.Dilation means enlarging a figure or reducing the size of a figure.Rotation simply involves rotating a figure around a given point while maintaining same size.Translation is shifting the points of a figure to move it to another position.Thus, in the transformation shown, figure ABC was reflected over the y-axis and then dilated to give A'B'C'.
Therefore, the transformations that occurred to map ABC to A'B'C are: C. a reflection and a dilation
Learn more about transformation on:
https://brainly.com/question/1462871
A box contains 11 red chips and 4 blue chips. We perform the following two-step experiment: (1) First, a chip is selected at random from the box and is then removed from the box. (After this first step, there are 14 chips left in the box. ) (2) Then, a chip is selected at random from the box (that is, from the remaining 14 chips) . Let B 1 be the event that the chip removed from the box at the first step of the experi- ment is red. Let B 2 be the event that the chip removed from the box at the first step of the experiment is blue. Let A be the event that the chip selected from the box at the second step of the experiment is red.Find P(B1), P(B2), P(A), P(B1|A), and P(B2|A).
Answer:
P(B1) = (11/15)
P(B2) = (4/15)
P(A) = (11/15)
P(B1|A) = (5/7)
P(B2|A) = (2/7)
Step-by-step explanation:
There are 11 red chips and 4 blue chips in a box. Two chips are selected one after the other at random and without replacement from the box.
B1 is the event that the chip removed from the box at the first step of the experiment is red.
B2 is the event that the chip removed from the box at the first step of the experiment is blue. A is the event that the chip selected from the box at the second step of the experiment is red.
Note that the probability of an event is the number of elements in that event divided by the Total number of elements in the sample space.
P(E) = n(E) ÷ n(S)
P(B1) = probability that the first chip selected is a red chip = (11/15)
P(B2) = probability that the first chip selected is a blue chip = (4/15)
P(A) = probability that the second chip selected is a red chip
P(A) = P(B1 n A) + P(B2 n A) (Since events B1 and B2 are mutually exclusive)
P(B1 n A) = (11/15) × (10/14) = (11/21)
P(B2 n A) = (4/15) × (11/14) = (22/105)
P(A) = (11/21) + (22/105) = (77/105) = (11/15)
P(B1|A) = probability that the first chip selected is a red chip given that the second chip selected is a red chip
The conditional probability, P(X|Y) is given mathematically as
P(X|Y) = P(X n Y) ÷ P(Y)
So, P(B1|A) = P(B1 n A) ÷ P(A)
P(B1 n A) = (11/15) × (10/14) = (11/21)
P(A) = (11/15)
P(B1|A) = (11/21) ÷ (11/15) = (15/21) = (5/7)
P(B2|A) = probability that the first chip selected is a blue chip given that the second chip selected is a red chip
P(B2|A) = P(B2 n A) ÷ P(A)
P(B2 n A) = (4/15) × (11/14) = (22/105)
P(A) = (11/15)
P(B2|A) = (22/105) ÷ (11/15) = (2/7)
Hope this Helps!!!
24 1/2 is equal to what decimal
Answer:
24.5
Step-by-step explanation:
24 = 24
1/2 -->
convert to a decimal => 1 divided by 2
0.5
24+0.5 = 24.5
Hope this helps!
The mean annual tuition and fees for a sample of 15 private colleges was with a standard deviation of . A dotplot shows that it is reasonable to assume that the population is approximately normal. You wish to test whether the mean tuition and fees for private colleges is different from 32,500 a) state the null and alternate hypotheses b) calculate the standard error c) calculate the test statistic d) find the p - value .
Answer:
Step-by-step explanation:
The question is incomplete. The complete question is:
The mean annual tuition and fees for a sample of 15 private colleges was $35,500 with a standard deviation of $6500. A dotplot shows that it is reasonable to assume that the population is approximately normal. You wish to test whether the mean tuition and fees for private colleges is different from $32,500. State the null and alternate hypotheses. A) H0: 4 = 32,500, H:4=35,500 C) H: 4 = 35,500, H7:35,500 B) H: 4 = 32,500, H : 4 # 32,500 D) H0:41 # 32,500, H : 4 = 32,500
Solution
We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
H0: µ = 32500
For the alternative hypothesis,
Ha: µ ≠ 32500
This is a two tailed test.
Since the number of samples is small and the population standard deviation is not given, the distribution is a student's t.
Since n = 15,
Degrees of freedom, df = n - 1 = 15 - 1 = 14
t = (x - µ)/(s/√n)
Where
x = sample mean = 35500
µ = population mean = 32500
s = samples standard deviation = 6500
t = (35500 - 32500)/(6500/√15) = 1.79
We would determine the p value using the t test calculator. It becomes
p = 0.095
Assuming alpha = 0.05
Since alpha, 0.05 < than the p value, 0.095, then we would fail to reject the null hypothesis.
Please help me with this math problem
Answer:
-1/4 is the slope and the y intercept is -4
Step-by-step explanation:
Solve for y
x +4y = -16
Subtract x
4y = -x-16
Divide by 4
4y/4 = -x/4 -16/4
y = -1/4 x -4
This is in slope intercept form
y = mx+b where m is the slope and b is the y intercept
-1/4 is the slope and the y intercept is -4
Before a researcher specified the relationship among variables he must have a (an): A: Inventory of variables B: Inventory of propositions C: Arrangement of propositions D: Schematic diagram
Answer:
Option B
Step-by-step explanation:
Before a researcher specifies the relationship among variables he must have an inventory of propositions/constructs which are mostly stated in a declarative form. These are then tested by examining the relationships between measurable variables of this constructs/propositions.
Show that every triangle formed by the coordinate axes and a tangent line to y = 1/x ( for x > 0)
always has an area of 2 square units.
Hint: Find the equation of the tangent line at x = a. (It will contain a’s as well as x and y.) Then find the
x-and y-intercepts for that line to find the lengths of sides of the right triangle.
Answer:
Step-by-step explanation:
given a point [tex](x_0,y_0)[/tex] the equation of a line with slope m that passes through the given point is
[tex]y-y_0 = m(x-x_0)[/tex] or equivalently
[tex] y = mx+(y_0-mx_0)[/tex].
Recall that a line of the form [tex]y=mx+b [/tex], the y intercept is b and the x intercept is [tex]\frac{-b}{m}[/tex].
So, in our case, the y intercept is [tex](y_0-mx_0)[/tex] and the x intercept is [tex]\frac{mx_0-y_0}{m}[/tex].
In our case, we know that the line is tangent to the graph of 1/x. So consider a point over the graph [tex](x_0,\frac{1}{x_0})[/tex]. Which means that [tex]y_0=\frac{1}{x_0}[/tex]
The slope of the tangent line is given by the derivative of the function evaluated at [tex]x_0[/tex]. Using the properties of derivatives, we get
[tex]y' = \frac{-1}{x^2}[/tex]. So evaluated at [tex]x_0[/tex] we get [tex] m = \frac{-1}{x_0^2}[/tex]
Replacing the values in our previous findings we get that the y intercept is
[tex](y_0-mx_0) = (\frac{1}{x_0}-(\frac{-1}{x_0^2}x_0)) = \frac{2}{x_0}[/tex]
The x intercept is
[tex] \frac{mx_0-y_0}{m} = \frac{\frac{-1}{x_0^2}x_0-\frac{1}{x_0}}{\frac{-1}{x_0^2}} = 2x_0[/tex]
The triangle in consideration has height [tex]\frac{2}{x_0}[/tex] and base [tex]2x_0[/tex]. So the area is
[tex] \frac{1}{2}\frac{2}{x_0}\cdot 2x_0=2[/tex]
So regardless of the point we take on the graph, the area of the triangle is always 2.
A newsletter publisher believes that less than 29% of their readers own a Rolls Royce. Is there sufficient evidence at the 0.02 level to substantiate the publisher's claim? State the null and alternative hypotheses for the above scenario.
Answer:
For this case they want to proof if the proportion of readers own a Rolls royce is less than 0.29 and that wuld be the alternative hypothesis. The complement would represent the null hypothesis. Then the system of hypothesis for this case are:
Null hypothesis: [tex] p \geq 0.29[/tex]
Alternative hypothesis: [tex]p< 0.29[/tex]
Step-by-step explanation:
For this case they want to proof if the proportion of readers own a Rolls royce is less than 0.29 and that wuld be the alternative hypothesis. The complement would represent the null hypothesis. Then the system of hypothesis for this case are:
Null hypothesis: [tex] p \geq 0.29[/tex]
Alternative hypothesis: [tex]p< 0.29[/tex]
It is known that 4% of children carry a certain virus, but a leading health researcher suspects that the percentage is actually higher. Which of the following provides the most convincing evidence to support the researcher's suspicion?
A. Out of 5,000 randomly chosen children, 210 children carry the virus.
B. Out of 60 randomly chosen children, 3 children carry the virus.
C. Out of 5,000 randomly chosen children, 250 children carry the virus.
D. Out of 20 randomly chosen children, 1 child carries the virus.
Answer:
(C)Out of 5,000 randomly chosen children, 250 children carry the virus.
Step-by-step explanation:
[tex]\text{Option A}: \dfrac{210}{5000}=0.042=4.2\% \\\text{Option B}: \dfrac{3}{60}=0.05=5\% \\\text{Option C}: \dfrac{250}{5000}=0.05=5\% \\\text{Option D}: \dfrac{1}{20}=0.05=5\%[/tex]
The higher the research sample, the more credible the results. In options A and C, the research sample was 5000. However, since the relative frequency of children carrying the virus is 5% in both, we take the result with a higher number of positives.
Option C is the correct option.
5/a - 4/b as a single fraction
Answer:
I'm not completely sure what you mean by a, "single fraction," but I'm pretty sure the answer you are looking for is [tex]\frac{5-4}{a-b}[/tex]
Step-by-step explanation:
segment AB is dilated from the origin to create segment A prime B prime at A' (0, 6) and B' (6, 9). What scale factor was segment AB dilated by?
1/2
2
3
4
Answer:
the answer is 3
Step-by-step explanation:
i took the test
The sum of a number and twice the number is 24 what is the number?
Answer:
x = 8
Step-by-step explanation:
Step 1: Write out the expression
x + 2x = 24
Step 2: Combine like terms
3x = 24
Step 3: Isolate x
x = 8
And we have our final answer!
Answer:
X=8
Step-by-step explanation:
Terry has a number cube that is numbered from 1 to 6. She rolls the cube 50 times. Which equation can be used to predict the number of times that she will roll a number that is greater than 4? P (number greater than 4) = StartFraction 1 over 6 EndFraction (50) P (number greater than 4) = StartFraction 2 over 6 EndFraction (50) P (number greater than 4) = StartFraction 3 over 6 EndFraction (50) P (number greater than 4) = StartFraction 4 over 6 EndFraction (50)
Answer:
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Solve 2cos3x=0.9.
Pls help me with this trigonometric equations with multiple angles.
Answer:
[tex]x=\frac{cos^{-1}(0.45)+2n\pi}{3} ,x=\frac{2\pi- cos^{-1}(0.45)+2n\pi}{3}[/tex]
Step-by-step explanation:
Given: [tex]2 cos(3x)=0.9[/tex]
To find: solutions of the given equation
Solution:
Triangle is a polygon that has three sides, three angles and three vertices.
Trigonometry explains relationship between the sides and the angles of the triangle.
Use the fact: [tex]cos x=a[/tex]⇒[tex]x=cos^{-1}(a)+2n\pi,x=2\pi-cos^{-1}(a)+2n\pi[/tex]
[tex]2 cos(3x)=0.9[/tex]
Divide both sides by 2
[tex]cos(3x)=\frac{0.9}{2}=0.45[/tex]
[tex]3x=cos^{-1}(0.45)+2n\pi,3x=2\pi- cos^{-1}(0.45)+2n\pi[/tex]
So,
[tex]x=\frac{cos^{-1}(0.45)+2n\pi}{3} ,x=\frac{2\pi- cos^{-1}(0.45)+2n\pi}{3}[/tex]
A publisher reports that 65% of their readers own a laptop. A marketing executive wants to test the claim that the percentage is actually different from the reported percentage. A random sample of 340 found that 60% of the readers owned a laptop. State the null and alternative hypotheses. Answer
Answer:
[tex]z=\frac{0.60 -0.65}{\sqrt{\frac{0.65(1-0.65)}{340}}}=-1.933[/tex]
The p value for this case can be calculated with this probability:
[tex]p_v =2*P(z<-1.933)=0.0532[/tex]
For this case is we use a significance level of 5% we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true proportion is different from 0.65 or 65%. We need to be careful since if we use a value higher than 65 for the significance the result would change
Step-by-step explanation:
Information given
n=340 represent the random sample taken
[tex]\hat p=0.60[/tex] estimated proportion of readers owned a laptop
[tex]p_o=0.65[/tex] is the value that we want to test
z would represent the statistic
[tex]p_v{/tex} represent the p value
Hypothesis to test
We want to check if the true proportion of readers owned a laptop if different from 0.65
Null hypothesis:[tex]p=0.65[/tex]
Alternative hypothesis:[tex]p \neq 0.65[/tex]
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing we got:
[tex]z=\frac{0.60 -0.65}{\sqrt{\frac{0.65(1-0.65)}{340}}}=-1.933[/tex]
The p value for this case can be calculated with this probability:
[tex]p_v =2*P(z<-1.933)=0.0532[/tex]
For this case is we use a significance level of 5% we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true proportion is different from 0.65 or 65%. We need to be careful since if we use a value higher than 65 for the significance the result would change