Answer:
Using a 90% confidence level
A. A sample size of 68 should be used.
B. A sample size of 98 should be used.
Step-by-step explanation:
I think there was a small typing mistake and the confidence level was left out. I will use a 90% confidence level.
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.9}{2} = 0.05[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.05 = 0.95[/tex], so [tex]z = 1.645[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
A. If we want to estimate the population mean time for previews at movie theaters with a margin of error of 72 seconds, what sample size should be used?
We have the standard deviation in minutes, so the margin of error should be in minutes.
72 seconds is 72/60 = 1.2 minutes.
So we need a sample size of n, and n is found when M = 1.2. We have that [tex]\sigma = 6[/tex]. So
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
[tex]1.2 = 1.645*\frac{6}{\sqrt{n}}[/tex]
[tex]1.2\sqrt{n} = 6*1.645[/tex]
[tex]\sqrt{n} = \frac{6*1.645}{1.2}[/tex]
[tex](\sqrt{n})^{2} = (\frac{6*1.645}{1.2})^{2}[/tex]
[tex]n = 67.65[/tex]
Rounding up.
A sample size of 68 should be used.
B. If we want to estimate the population mean time for previews at movie theaters with a margin of error of 1 minute, what sample size should be used?
Same logic as above, just use M = 1.
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
[tex]1 = 1.645*\frac{6}{\sqrt{n}}[/tex]
[tex]\sqrt{n} = 6*1.645[/tex]
[tex](\sqrt{n})^{2} = (6*1.645)^2[/tex]
[tex]n = 97.42[/tex]
Rounding up
A sample size of 98 should be used.
the distance around the edge of a circular pond is 88m. the radius in meters is ?
(a)88π
(b)176π
(c)88/π
(d)88/2π
Answer: (d) 88/ 2π
Step-by-step explanation:
Perimeter = 88m
Perimeter of a circle = 2πr
88 = 2π x r
r = 88 / 2π
Answer:
88/2π = r
Step-by-step explanation:
The circumference is 88 m
The circumference is given by
C = 2*pi*r
88 = 2 * pi *r
Divide each side by 2 pi
88 / 2pi = 2 * pi *r / 2 * pi
88 / 2 pi = r
The probability of rolling two dice at the same time and getting a 4 with either die or the sum of the dice is 6
Answer:
Suppose that the first die we roll comes up as a 1. The other die roll could be a 1, 2, 3, 4, 5, or 6. Now suppose that the first die is a 2. The other die roll again could be a 1, 2, 3, 4, 5, or 6. We have already found 12 potential outcomes, and have yet to exhaust all of the possibilities of the first die. But with a second dice, there will be 24 different possibilities.
Step-by-step explanation:
1 2 3 4 5 6
1 (1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)
2 (2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)
3 (3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)
4 (4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)
5 (5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)
6 (6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)
The Rocky Mountain district sales manager of Rath Publishing Inc., a college textbook publishing company, claims that the sales representatives make an average of 41 sales calls per week on professors. Several reps say that this estimate is too low. To investigate, a random sample of 38 sales representatives reveals that the mean number of calls made last week was 42. The standard deviation of the sample is 3.9 calls. Using the 0.025 significance level, can we conclude that the mean number of calls per salesperson per week is more than 41?H0 : µ = 40
H1 : µ > 401. Compute the value of the test statistic. 2. What is your decision regarding H0?
Answer:
1. Test statistic t=1.581.
2. The null hypothesis H0 failed to be rejected.
There is not enough evidence to support the claim that the mean number of calls per salesperson per week is significantly more than 41.
NOTE: if the null hypothesis is µ = 40, there is enough evidence to support the claim that the mean number of calls per salesperson per week is significantly more than 40 (test statistic t=3.161).
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim is that the mean number of calls per salesperson per week is significantly more than 41.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=41\\\\H_a:\mu> 41[/tex]
The significance level is 0.025.
The sample has a size n=38.
The sample mean is M=42.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=3.9.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{3.9}{\sqrt{38}}=0.633[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{42-41}{0.633}=\dfrac{1}{0.633}=1.581[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=38-1=37[/tex]
This test is a right-tailed test, with 37 degrees of freedom and t=1.581, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t>1.581)=0.061[/tex]
As the P-value (0.061) is bigger than the significance level (0.025), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the mean number of calls per salesperson per week is significantly more than 41.
For µ = 40:
This is a hypothesis test for the population mean.
The claim is that the mean number of calls per salesperson per week is significantly more than 40.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=40\\\\H_a:\mu> 40[/tex]
The significance level is 0.025.
The sample has a size n=38.
The sample mean is M=42.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=3.9.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{3.9}{\sqrt{38}}=0.633[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{42-40}{0.633}=\dfrac{2}{0.633}=3.161[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=38-1=37[/tex]
This test is a right-tailed test, with 37 degrees of freedom and t=3.161, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t>3.161)=0.002[/tex]
As the P-value (0.002) is smaller than the significance level (0.025), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the mean number of calls per salesperson per week is significantly more than 40.
A certain group of test subjects had pulse rates with a mean of 80.9 beats per minute and a standard deviation of 10.7 beats per minute. Use the range rule of thumb to identify the limits separating values that are significantly low or significantly high. Is a pulse rate of 142.3 beats per minute significantly low or significantly high?
Answer:
We want to find the usual limits using the rule of thumb and for this case rule states that we have most of the values within 2 deviations from the mean so then we can find the usual limits like this:
[tex] \mu -2*\sigma = 80.9 -2*10.7= 59.5[/tex]
[tex] \mu +2*\sigma = 80.9 -2*10.7= 102.3[/tex]
And for this case a value of 142.3 is higher than the upper limti so then we can conclude that would be significantly high with the rule of thumb criteria
Step-by-step explanation:
For this case we have the follwing info given:
[tex] \mu = 80.9[/tex] represent the mean
[tex]\sigma = 10.7[/tex] represent the deviation
We want to find the usual limits using the rule of thumb and for this case rule states that we have most of the values within 2 deviations from the mean so then we can find the usual limits like this:
[tex] \mu -2*\sigma = 80.9 -2*10.7= 59.5[/tex]
[tex] \mu +2*\sigma = 80.9 -2*10.7= 102.3[/tex]
And for this case a value of 142.3 is higher than the upper limti so then we can conclude that would be significantly high with the rule of thumb criteria
Two spheres of the same outer diameter, one solid and the other hollow, are completely immersed in the water. We can affirm:
a) The hollow receives less push
b) The hollow receives more push
c) Both receive the same push
d) The solid receives less push
Answer:
c) Both receive the same push
Step-by-step explanation:
The buoyancy force is equal to the weight of the displaced fluid:
B = ρVg
where ρ is the density of the water, V is the volume of displaced water, and g is the acceleration due to gravity.
Since both spheres displace the same amount of water, they have equal buoyancy forces.
please assist me with the power of i(imaginary)
Let's raise i to various powers starting with 0,1,2,3...
i^0 = 1
i^1 = i
i^2 = ( sqrt(-1) )^2 = -1
i^3 = i^2*i = -1*i = -i
i^4 = (i^2)^2 = (-1)^2 = 1
i^5 = i^4*i = 1*i = i
i^6 = i^5*i = i*i = i^2 = -1
We see that the pattern repeats itself after 4 iterations. The four items to memorize are
i^0 = 1
i^1 = i
i^2 = -1
i^3 = -i
It bounces back and forth between 1 and i, alternating in sign as well. This could be one way to memorize the pattern.
To figure out something like i^25, we simply divide the exponent 25 over 4 to get the remainder. In this case, the remainder of 25/4 is 1 since 24/4 = 6, and 25 is one higher than 24.
This means i^25 = i^1 = i
Likewise,
i^5689 = i^1 = i
because 5689/4 = 1422 remainder 1. The quotient doesn't play a role at all so you can ignore it entirely
A girl walks 800 m on a bearing of 129°.
Calculate how far: a east b south she is from
her starting point.
Answer: a) 503.2m
b) 621.6m
Step-by-step explanation:
The diagram representing the scenario is shown in the attached photo.
A represents her starting point.
CD = x = how far east she is from her starting point
BC = y = how far south she is from her starting point
Angle BAC = 180 - 129 = 51°
Angle ACD = angle BAC = 51° because they are alternate angles
To determine x, we would apply the cosine trigonometric ratio
Cos 51 = x /800
x = 800Cos51 = 800 × 0.629 = 503.2m
To determine y, we would apply the sine trigonometric ratio
Sin 51 = y /800
y = 800Sin51 = 800 × 0.777 = 621.6m
Simplify.
In e =
In e 2x=
In 1 =
Answer:
ln e = 1
ln e 2x = 2x
ln 1 = 0
Step-by-step explanation:
ln e
ln(2.718282) = 1
In e 2x
ln(2.718282)(2)x = 2x
ln 1 = 0
The straight line L has equation y = 1/2x+7 The straight line M is parallel to L and passes through the point (0, 3). Write down an equation for the line M.
Answer:
y = [tex]\frac{1}{2}[/tex] x + 3
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = [tex]\frac{1}{2}[/tex] x + 7 ← is in slope- intercept form
with slope m = [tex]\frac{1}{2}[/tex]
Parallel lines have equal slopes
line M crosses the y- axis at (0, 3) ⇒ c = 3
y = [tex]\frac{1}{2}[/tex] x + 3 ← equation of line M
PLEASE QUICK!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Which number completes the system of linear inequalities represented by the graph? y > 2x – 2 and x + 4y > -12 -3 4 6
Answer:
-12
Step-by-step explanation:
Edge 2021
I want to fence in a rectangular vegetable patch. The fencing for the east and west sides costs $2 per foot, and the fencing for the north and south sides costs only $1 per foot. I have a budget of $40 for the project. What is the largest area I can enclose
Answer:
largets area is 32 feet cubed
Step-by-step explanation:
8=4 foot 2 for each side w and e and 32feet n and s 16 each side
The weights of college football players are normally distributed with a mean of 200 pounds and a standard deviation of 50 pounds. If a college football player is randomly selected, find the probability that he weighs between 170 and 220 pounds. Round to four decimal places.
Answer:
0.3811 = 38.11% probability that he weighs between 170 and 220 pounds.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 200, \sigma = 50[/tex]
Find the probability that he weighs between 170 and 220 pounds.
This is the pvalue of Z when X = 220 subtracted by the pvalue of Z when X = 170.
X = 220
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{220 - 200}{50}[/tex]
[tex]Z = 0.4[/tex]
[tex]Z = 0.4[/tex] has a pvalue of 0.6554
X = 170
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{170 - 200}{50}[/tex]
[tex]Z = -0.6[/tex]
[tex]Z = -0.6[/tex] has a pvalue of 0.2743
0.6554 - 0.2743 = 0.3811
0.3811 = 38.11% probability that he weighs between 170 and 220 pounds.
A U.S. dime has a diameter of about 18 millimeters. What is the area of one side of a dime to the nearest square millimeter? Use 3.14 as an approximation for pi. The area of one side of a U.S. dime is approximately _____ square millimeters.
Area of one side of a U.S. dime is approximately 254 square millimeters.
What is Circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
Given that U.S. dime has a diameter of about 18 millimeters.
We need to find the area of one side of a dime to the nearest square millimeter.
Diameter=18 millimeters
Diameter is two times of radius
D=2R
18=2R
Divide both sides by 2
Radius is 9 millimeters.
Area of dime=πr²
=3.14×(9)²
=3.14×81
=254 square millimeters.
Hence, area of one side of a U.S. dime is approximately 254 square millimeters.
To learn more on Circles click:
https://brainly.com/question/11833983
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The life in hours of a battery is known to be normally distributed, with a standard deviation of 1.25 hours. A random sample of 10 batteries has a mean life x = 40.5 hours.
a) Is there evidence to support the claim that battery life exceeds 40 hours? Use
α = 0.05.
b) What is the P-value for this test?
Answer:
a) Test statistic
Z = 1.265 < 1.96 at 0.05 level of significance
The battery life is not exceeds 40 hours
b)
p- value = 0.8962
Step-by-step explanation:
Step(i):-
Given sample size 'n' =10
Mean of the sample x⁻ = 40.5 hours
Mean of of the Population μ = 40 hours
Standard deviation of the Population = 1.25 hours
Step(ii):-
Null Hypothesis:H₀: μ = 40 hours
Alternative Hypothesis :H₁ : μ < 40 hours
step(ii):-
Test statistic
[tex]Z = \frac{x^{-} -mean}{\frac{S.D}{\sqrt{n} } }[/tex]
[tex]Z = \frac{40.5 -40}{\frac{1.25}{\sqrt{10} } }[/tex]
Z = 1.265
Level of significance = 0.05
Z₀.₀₅ = 1.96
Z = 1.265 < 1.96 at 0.05 level of significance
The battery life is not exceeds 40 hours
Step(iii):-
P - value
P( Z < 1.265) = 0.5 + A( 1.265)
= 0.5 + 0.3962
= 0.8962
P( Z < 1.265) = 0.8962
i ) p- value = 0.8962 > 0.05
Accept H₀
There is no significant
The battery life is not exceeds 40 hours
a. What is a residual? b. In what sense is the regression line the straight line that "best" fits the points in a scatterplot? a. What is a residual?
Answer:
a. A residual is how far off a point is from the expected value. For example, if I were to estimate the weight of my Southeastern Lubber Grasshopper, I would say it's maybe 5 ounces. But, in reality, it might be 4 ounces. So, the residual would be the reality minus the prediction, or 4 - 5, or -1 ounce.
b. The regression line is the line of predicted values for the points in the scatterplot. It tries to predict the points and make all the points be on the line.
Hope this helps!
A sample of 26 offshore oil workers took part in a simulated escape exercise, and their escape time (unit: second) were observed. The sample mean and sample standard deviation are 370.69 and 24.36, respectively. Suppose the investigators had believed a priori that true average escape time would be at most 6 minutes. Does the data contradict this prior belief? Assuming normality, test the appropriate hypotheses using the rejection region method at a significance level of 0.05.
Answer:
Yes, it contradict this prior belief as there is enough evidence to support the claim that the true average escape time is significantly higher than 6 minutes.
Test statistic t=2.238>tc=1.708.
The null hypothesis is rejected.
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim is that the true average escape time is significantly higher than 6 minutes (360 seconds).
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=360\\\\H_a:\mu> 360[/tex]
The significance level is 0.05.
The sample has a size n=26.
The sample mean is M=370.69.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=24.36.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{24.36}{\sqrt{26}}=4.777[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{370.69-360}{4.777}=\dfrac{10.69}{4.777}=2.238[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=26-1=25[/tex]
The critical value for a right-tailed test with a significance level of 0.05 and 25 degrees of freedom is tc=1.708. If the test statistic is bigger than 1.708, it falls in the rejection region and the null hypothesis is rejected.
As the test statistic t=2.238 is bigger than the critical value t=1.708, the effect is significant. The null hypothesis is rejected.
There is enough evidence to support the claim that the true average escape time is significantly higher than 6 minutes (360 seconds).
A card is drawn randomly from a standard 52-card deck. Find the probability of the given event.
(a) The card drawn is a king.
(b) The card drawn is a face card.
(c) The card drawn is not a face card.
Answer:
(a) [tex]\frac{1}{13}[/tex]
(b) [tex]\frac{3}{13}[/tex]
(c) [tex]\frac{10}{13}[/tex]
Step-by-step explanation:
The probability of an event B occurring is given by;
P(B) = [tex]\frac{n(E)}{n(S)}[/tex]
Where;
P(B) = probability of the event B
n(E) = number of favourable outcomes
n(S) = total number of events in the sampled space.
From the question, the card is drawn randomly from a standard 52-card deck. The probability of
(a) drawing a "king" card is analyzed as follows.
Let the event of drawing the "king" card be B.
In a standard 52-card deck, the number of cards that are of type king is 4. i.e 1 from the diamond pack, 1 from the spade pack, 1 from the heart pack and 1 from the club pack.
Therefore, the number of favourable outcomes is 4, while the total number of events in the sampled space is 52.
The probability of drawing a "king" card, P(B) is;
P(B) = [tex]\frac{4}{52}[/tex]
P(B) = [tex]\frac{1}{13}[/tex]
(b) drawing a "face" card is analyzed as follows.
Let the event of drawing the "face" card be B.
In a standard 52-card deck, a face card can either be a Jack, Queen or a King. There are 4 Jack cards, 4 Queen cards and 4 King cards in the deck. The number of cards that are of type face is 12.
Therefore, the number of favourable outcomes is 12, while the total number of events in the sampled space is 52.
The probability of drawing a "face" card, P(B) is;
P(B) = [tex]\frac{12}{52}[/tex]
P(B) = [tex]\frac{3}{13}[/tex]
(c) drawing a card that is not a "face" is analyzed as follows;
The sum of the probability of drawing a face card and the probability of not drawing a face card is always 1.
Let the event of drawing a "face" card be B and the event of not drawing a "face" card be C.
P(B) + P(C) = 1
P(C) = 1 - P(B)
From (b) above, the P(B) = [tex]\frac{3}{13}[/tex]
Therefore,
P(C) = 1 - [tex]\frac{3}{13}[/tex]
P(C) = [tex]\frac{10}{13}[/tex]
convert 3days to minutes
Answer:
4320 minutes
Step-by-step explanation:
Recall,
1 day ---> 24 hours
but each hour has 60 minutes, hence 1 day can also be expressed:
1 day -----> 24 x 60 = 1440 minutes
3 days -----> 1440 min/day x 3 days = 4320 minutes
Answer: 4,320 minutes
Step-by-step explanation: 1 day = 1440 days. 1440 * 3 = 4,320 minutes
What is the simplified form of the inequality below? S - 7 < 3
Answer:
s-7<3
in order to find the value adding 7 on both sides
s-7+7<3+7
s<10
Step-by-step explanation:
i hope this will help you :)
Answer:
s-7<3
in order to find the value adding 7 on both sides
s-7+7<3+7
s<10
Step-by-step explanation:
Given the equation y = 7 sec(6x– 30)
The period is:
The horizontal shift is:
Answer:
The period is of [tex]\frac{\pi}{3}[/tex] units.
The horizontal shift is of 30 units to the left.
Step-by-step explanation:
The secant function has the following general format:
[tex]y = A\sec{(Bx + C)}[/tex]
A represents the vertical shift.
C represents the horizontal shift. If C is positive, the shift is to the right. If it is negative, it is to the left.
The period is [tex]P = \frac{2\pi}{B}[/tex]
In this question:
[tex]y = 7\sec{6x - 30}[/tex]
So [tex]B = 6, C = -30[/tex]
Then [tex]P = \frac{2\pi}{6} = \frac{\pi}{3}[/tex]
The period is of [tex]\frac{\pi}{3}[/tex] units.
The horizontal shift is of 30 units to the left.
Eight times the difference between a number and six is equal to four times the number. What’s the number?
Answer:
12
Step-by-step explanation:
Given:
Let the number be x.
According to the question,
8(x-6)= 4 x
8 x-48=4 x
8 x-4 x= 48
4 x=48
x=48/4
x=12
Thank you!
what it 17.15 in 12hour clock
Answer:
Step-by-step explanation:
Hello friend
The answer is 5:15 in 12 hour clock
Answer:
5:15 PM
Step-by-step explanation:
12:00 + 5:00
17:00 in 12 hour clock is 5:00 PM.
15 minutes + 5:00 PM
⇒ 5:15 PM
What is the slope of this line?
Answer:
3/2
Step-by-step explanation:
We can find the slope of this line by using two points
(1,-3) and (3,0)
m = (y2-y1)/(x2-x1)
= (0- -3)/(3 -1)
= (0+3)/(3-1)
= 3/2
Find the coordinates of the point on a circle with radius 4 at an angle of 2pi/3
{Please help!!}
Answer:
The coordinates of the point on a circle with radius 4 at an angle of [tex]\frac{2\pi}{3}[/tex] radians are x = -2 and y = 3.464.
Step-by-step explanation:
This problem ask us to determine the rectangular coordinates from polar coordinates. The polar coordinates of the point in rectangular form is expressed by the following expression:
[tex](x,y) = (r\cdot \cos \theta, r\cdot \sin \theta)[/tex]
Where [tex]r[/tex] and [tex]\theta[/tex] are the radius of the circle and the angle of inclination of the point with respect to horizontal, measured in radians. If [tex]r = 4[/tex] and [tex]\theta = \frac{2\pi}{3}\,rad[/tex], the coordinates of the point are:
[tex](x,y) = \left(4\cdot \cos \frac{2\pi}{3},4\cdot \sin \frac{2\pi}{3} \right)[/tex]
[tex](x,y) = (-2, 3.464)[/tex]
The coordinates of the point on a circle with radius 4 at an angle of [tex]\frac{2\pi}{3}[/tex] radians are x = -2 and y = 3.464.
Which expression is the simplest form of -(x + 5) - 3(x + 2)?
Answer:
-4x -11
Step-by-step explanation:
-(x + 5) - 3(x + 2)
Distribute
-x -5 -3x -6
Combine like terms
-x-3x -5-6
-4x -11
Answer:
[tex] = - (4x + 11)[/tex]
Step-by-step explanation:
[tex]-(x + 5) - 3(x + 2) \\ -x - 5 - 3x - 6 \\ -x - 3x -5 - 6 \\ - 4x - 11 \\ = -(4x + 11)[/tex]
What is a square root
To test H0: μ=100 versus H1:≠100, a simple random sample size of nequals=24 is obtained from a population that is known to be normally distributed. Answer parts (a)-(d).(a) If x =104.2 and s=9.6, compute the test statistic.t= _ (Round to three decimal places as needed.)(b) If the researcher decides to test this hypothesis at the α=0.01 level of significance, determine the critical values.The critical values are __ .(c) Draw a t-distribution that depicts the critical region(s). Which of the following graphs shows the critical region(s) in thet-distribution?(d) Will the researcher reject the null hypothesis?
Answer:
a) Test statistic = 1.960
b) The critical values include -2.50 and 2.50.
The critical regions of rejection are thus
t < -2.50 or t > 2.50
c) The sketch of the curve is presented in the attached image to this solution. The shaded parents indicate the rejection regions.
d) The t-statistic obtained (1.96), lies within the acceptance region (-2.50 ≤ x ≤ 2.50), we fail to reject the null hypothesis.
Step-by-step explanation:
a) Test statistic is computed using the expression
t = (x - μ₀)/σₓ
x = Sample mean = 104.2
μ₀ = the standard we are comparing Against
σₓ = standard error of the mean = (σ/√n)
σ = 9.6
n = Sample size = 24
σₓ = (9.6/√24) =
t = (0.425 - 0.35) ÷ 0.07816
t = 1.9595917942 = 1.960
b) To obtain these critical values, we first find the degree of freedom
Degree of freedom = n - 1 = 24 - 1 = 23
The critical values for significance level of 0.01 and degree of freedom of 23 is given as
t(0.01, 23) = 2.50
So, since the test is two-tailled (we are testing in both directions; greater than or less than), the regions of rejection include
t < -2.50 and t > 2.50
c) since the test is two-tailled (we are testing in both directions; greater than or less than), the regions of rejection include
t < -2.50 and t > 2.50
The t-distribution curve is very similar to the normal distribution curve. The t-distribution curve is also a bell shaped curve, but it is heavier at the limits indicating that the t-distribution favours outliers more than the normal distribution.
The sketch of the curve is presented in the attached image with the shaded regions indicating the rejection region.
d) Since the t-statistic obtained (1.96), lies within the acceptance region (-2.50 ≤ x ≤ 2.50), we fail to reject the null hypothesis.
Hope this Helps!!!
Describe the possible echelon forms of a nonzero 2 x 2 matrix.
Answer:
we approach the issue by taking note of that a 2 x 2 matrix can either have 1 0r 2 pivot columns. If the matrix has no pivot columns then every entry in the matrix must be zero.
-> if our matrix has two pivot columns then : [tex]\left(\begin{array}{rr}-&*&0&-\end{array}\right)[/tex]
-> if our matrix has one pivot column then we have a choice to make. If the first column is pivot column then: [tex]\left(\begin{array}{rr}-&*&0&0\end{array}\right)[/tex]
->otherwise, if the pivot column is the second column then: [tex]\left(\begin{array}{rr}0&-&0&0\end{array}\right)[/tex]
Find all the missing side lengths for the following triangles.
Answer:
Step-by-step explanation:
A) u = 4 v = 4/(sqrt)3
B) b = 5 c = 10
C) b = 2(sqrt)2 a = 4
D) m and n are both 7(sqrt)2/2
The missing side lengths for the three triangles are 10√3, 12, and 8. The first triangle is a 30-60-90 triangle, the second triangle is a 45-45-90 triangle, and the third triangle is a right triangle. The missing side lengths were found using the properties of special triangles and the Pythagorean Theorem.
Here are the missing side lengths for the following triangles:
Triangle 1:
The missing side length is 15.
The triangle is a 30-60-90 triangle, so the ratio of the side lengths is 1:√3:2. The hypotenuse of the triangle is 20, so the shorter leg is 10 and the longer leg is 10√3. The missing side length is the longer leg, so it is 10√3.
Triangle 2:
The missing side length is 12.
The triangle is a 45-45-90 triangle, so the ratio of the side lengths is 1:1:√2. The hypotenuse of the triangle is 12√2, so each of the legs is 12. The missing side length is one of the legs, so it is 12.
Triangle 3:
The missing side length is 8.
We can use the Pythagorean Theorem to find the missing side length. The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the hypotenuse is 10 and one of the other sides is 6. Let x be the missing side length.
[tex]10^{2}[/tex] = [tex]6^{2}[/tex] + [tex]x^{2}[/tex]
100 = 36 +[tex]x^{2}[/tex]
[tex]x^{2}[/tex] = 64
x = 8
Therefore, the missing side length is 8.
Learn more about side lengths here: brainly.com/question/18725640
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researchers are interested in the average size of a certain species of mouse. They collect the length and gender of each mouse. What is the parameter likely estimated and the sample statistic
Answer:
E. The parameter is μmale - μfemale and the statistic is xmale - xfemale.
Step-by-step explanation:
The sample statistic is a piece of information about the individuals or objects that were selected from a given population. The sample is just a fraction of the total population. Since it is a herculean task studying an entire population, the sample forms a manageable size that allows us to have an insight into the entire population. The sample statistics are now the piece of information about the sample being studied such as the average, mean, median, or mode. The sample statistics have to be as specific as possible of the factors being measured. In the question, we would have to obtain the mean of both the male and female genders. This gives us an insight into the population under study.
The parameter, on the other hand, is a description of the entire population being studied. For example, we might want to determine the population mean. That is the factor we seek to measure. It is represented by the sign mu (μ).