Answer:
[tex]6x^2-2x-6[/tex]
Step-by-step explanation:
[tex]f(x)=6x^2-4 \\\\g(x)=2x+2 \\\\(f-g)(x)= (6x^2-4)-(2x+2)=6x^2-2x-6[/tex]
Hope this helps!
I WILL MARK BRAINLIEST!!! I NEED HELP!! MY PARENTS ARE IN THE HOSPITAL I HAVE NO ONE TO ASK FOR HELP!!! I HAVE TWO MINUTES LEFT!!! I AM FINISHING THIS COURSE TO MAKE THEM PROUD!!! SOMEONE HELP!!!
Answer:
D
Step-by-step explanation:
Educators are testing a new program designed to help children improve their reading skills. The null hypothesis of the test is that the program does not help children improve their reading skills. For the educators, the more consequential error would be that the program does not help children improve their reading skills but the test indicated that it does help.
Which of the following should the researchers do to avoid the more consequential error?
a. Increase the significance level to increase the probability of Type I error.
b. Increase the significance level to decrease the probability of Type I error.
c. Decrease the significance level to increase the probability of Type I error.
d. Decrease the significance level to decrease the probability of Type I error.
e. Decrease the significance level to decrease the standard error.
Answer:
a
Step-by-step explanation:
increase the significance level to increase the probability of type 1 error
You can use the definition of type I and type II error to find the correct option.
To avoid the more consequential error, the researchers should do:
Option D: Decrease the significance level to decrease the probability of Type I error.
Firstly the whole story starts from hypotheses. The null hypothesis is tried to reject and we try to accept the alternate hypothesis.
The type 1 error occurs if we get false positive conclusion (false positive means we accuse null hypothesis being wrong when it was actually correct).The type 2 error occurs if we get false negative conclusion (false negative means we accept null hypothesis when it was actually false).The negative is just like the doctor's test getting negative means no disease. Similarly, if we conclude null hypothesis negative means it is accepted. If it is accepted wrongly means the negative test result was false, thus called false negative. This error is called type II error.
How are the type I error and the level of significance of the hypothesis test related?The probability of committing the type I error is called the significance level of the hypothesis test.
How to find what does researchers should do to avoid more consequential error?Since in the given context, by using the definitions of the type I error and the type II error, we have
Type I error : False positive : Accepting that the new program does help the children in improving the reading skills when it actually don't.Type II error: False negative: Failing to reject that the program doesn't help the children in improving the reading skills when it actually improves the skill.More consequential error for educators : For the educators, the more consequential error would be that the program does not help children improve their reading skills but the test indicated that it does help.
Thus, the more consequential error for the educators is committing the type I error.
To prevent committing this error, they need to decrease type I error's probability which is denoted by level of significance, need to decrease the level of significance of the hypothesis test.
Thus,
Option D: Decrease the significance level to decrease the probability of Type I error.
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Please answer this correctly without making mistakes
Answer:
56.52 mm²
Step-by-step explanation:
V= πr²h
V= 3.14*(6/2)²*2= 56.52 mm²
Explain what is meant by the equation lim x → 8 f(x) = 9. If |x1 − 8| < |x2 − 8|, then |f(x1) − 9| < |f(x2) − 9|. The values of f(x) can be made as close to 8 as we like by taking x sufficiently close to 9. f(x) = 9 for all values of x. If |x1 − 8| < |x2 − 8|, then |f(x1) − 9|≤ |f(x2) − 9|. The values of f(x) can be made as close to 9 as we like by taking x sufficiently close to 8. Is it possible for this statement to be true and yet f(8) = 6?
Explain. Yes, the graph could have a hole at (8, 9) and be defined such that f(8) = 6. Yes, the graph could have a vertical asymptote at x = 8 and be defined such that f(8) = 6. No, if f(8) = 6, then lim x→8 f(x) = 6. No, if lim x→8 f(x) = 9, then f(8) = 9.
Complete Question
1 Explain what is meant by the equation lim x → 8 f(x) = 9.
A If |x1 − 8| < |x2 − 8|, then |f(x1) − 9| < |f(x2) − 9|.
B The values of f(x) can be made as close to 8 as we like by taking x sufficiently close to 9.
C f(x) = 9 for all values of x.
D If |x1 − 8| < |x2 − 8|, then |f(x1) − 9|≤ |f(x2) − 9|.
E The values of f(x) can be made as close to 9 as we like by taking x sufficiently close to 8.
2 Is it possible for this statement to be true and yet f(8) = 6? Explain.
A Yes, the graph could have a hole at (8, 9) and be defined such that f(8) =6.
B Yes, the graph could have a vertical asymptote at x = 8 and be defined such that f(8) = 6.
C No, if f(8) = 6, then lim x→8 f(x) = 6.
D No, if lim x→8 f(x) = 9, then f(8) = 9.
Answer:
1
The correct option is D
2
The correct option is A
Step-by-step explanation:
Generally a a limit function [tex]\lim_{n \to x } f(x) = L[/tex]
Tell us that as n tends toward x the values of f(x) tends towards L hence for the first question E is the correct option
Now looking at the second question
Yes it is possible for lim x → 8 f(x) = 9. to be true and f(8) = 6 this is because the graph defined by this limit equation can have a hole the point
(8, 9) and created in such a way that f(8) = 6
Calculus's basic idea of limits in mathematics describes how a function behaves when its input approaches a specific value. No, if f(8) = 6, then lim x → 8 f(x) = 6. The correct option is C.
The statement "lim x → 8 f(x) = 9" means that as x approaches 8, the limit of f(x) is equal to 9. This implies that the function f(x) gets arbitrarily close to 9 as x gets arbitrarily close to 8.
If f(8) = 6, it means that the function f(x) has a specific value of 6 at x = 8. This contradicts the idea that f(x) gets arbitrarily close to 9 as x approaches 8.
Therefore, if f(8) = 6, it is not possible for the statement "lim x → 8 f(x) = 9" to be true.
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You take a train away from Bangkok at 1:50 a.m. on Wednesday. You ride the train for 16 hours and 40 minutes, at which point you arrive in Vladivostok at 9:30 p.m. on Wednesday, local time. How does Vladivostok’s time zone relate to Bangkok’s time zone?
a.
Vladivostok is three hours ahead of Bangkok.
b.
Vladivostok is nine hours behind Bangkok.
c.
Vladivostok is fifteen hours behind Bangkok.
d.
Vladivostok is twenty-one hours ahead of Bangkok.
Answer:
a.
Vladivostok is three hours ahead of Bangkok.
Step-by-step explanation:
Time the train left Bangkok is 1:50am
It traveled for 16 hours 40 minutes.
If the train was to be in Bangkok.
The Time Will be 1+16 hours then 50+40 minutes
Which is 17 hours + 1 hour 30 minutes
Which is 18 hours and 30 minutes
And 18 hours = 6:00 pm
So if it was in Bangkok the time with be 6:30 pm
But in Vladivostok, it was 9:30 pm
It's clear that Vladivostok time is faster by 3 hours
why should i have different units for volume and base area Ex: volume = [tex]in^{3}[/tex] Base Area = [tex]in^{2}[/tex] pyramid ^^^
Answer:
Step-by-step explanation:
Volume has three parameters and is three dimensional, thus needing a unit in the third power
In difference,
Area is two-dimensional and has only 2 parameters, thus needing a unit only in the second power
Answer:
see below
Step-by-step explanation:
Area is found by multiplying two dimensions together ( l*w)
Volume is found by multiplying three dimensions together ( l*w*n)
Academic tenure is when a teaching or research position is given to a professor indefinitely. By removing concerns about job security for scholars, offering tenure is thought to encourage freedom of thought, and leaves a tenured professor with the freedom to explore and hold a variety of views. One data set that was released by the Integrated Postsecondary Education Data System (IPEDS) in 2018 contained 1347 private schools, 743 of which had tenured faculty. Suppose that a prospective college student is considering whether to apply to private or public colleges. In addition to considerations about cost, graduation rates, etc., he wants to know about the quality of the education and decides to use tenure as a way of measuring this. He knows that the majority (more than 0.5) of public schools have avenues for professors to apply for tenure, and wants to test whether this is true for private schools as well. Which of the following is the correct null hypothesis in words?
A. The true proportion of private colleges in the U.S. that have tenure-track faculty is not equal to 0.5.
B. The true proportion of private colleges in the U.S. that have tenure-track faculty is 743/1347.
C. The proportion of private colleges in this sample that have tenure-track faculty is greater than 0.5 .
D. The long-run proportion of private colleges in the US, that have tenure-track faculty is 0.5.
Write the correct alternative hypothesis in notation.
Answer:
The correct null hypothesis in words is:
D. The long-run proportion of private colleges in the US, that have tenure-track faculty is 0.5.
[tex]H_0: \pi = 0.5[/tex]
Step-by-step explanation:
He wants to test the claim that the proportion of private schools that have avenues for professors to apply for tenure is significantly higher than 0.5, as happen with the public schools.
Then, the alternative hypothesis is:
[tex]H_a: \pi >0.5[/tex]
The null hypothesis represents the opposite claim, where the proportion is not significantly higher than 0.5. Then, the null hypothesis is expressed as:
[tex]H_0: \pi = 0.5[/tex]
The correct null hypothesis in words is:
D. The long-run proportion of private colleges in the US, that have tenure-track faculty is 0.5.
What’s the correct answer for this question?
Answer:
The answer is drawing the 6 of clubs or the 6 of spades because those are the only black 6's.
Simplify the expression to a polynomial in standard form: (x-1)(3x^2-5x-3) (x−1)(3x 2 −5x−3)
Answer: 3x^3 -8*x^2 + 8*x + 3
Step-by-step explanation:
The standard form for a plolynomial is:
a*x^n + b*x^(n-1) + c*x^(n - 2) ........
We have:
(x-1)(3x^2-5x-3)
this is equal to:
3*x^3 - 5*x^2 + 3*x - 3*x^2 +5*x + 3
where the thing that i did is distribute the multiplication
this is equal to:
3x^3 -8*x^2 + 8*x + 3
When Easton goes bowling, his scores are normally distributed with a mean of 130
and a standard deviation of 11. What percentage of the games that Easton bowls does
he score higher than 112, to the nearest tenth?
Answer:
P(X≥112) = 0.9495
The percentage of the games that Easton bowls does he score higher than 112 = 94.95%
Step-by-step explanation:
Given mean of the Population = 130
Given standard deviation of the Population = 11
Let X= 112
[tex]Z =\frac{x-mean}{S.D} =\frac{112-130}{11}=-1.636[/tex]
P(X≥112) = P(Z≥ z)
= 1-P(Z≤z)
= 1- ( P(Z≤-1.636)
= 1- (0.5-A(-1.636)
= 0.5 +A(1.636)
= 0.5 + 0.4495
P(X≥112) = 0.9495
The percentage of the games that Easton bowls does
he score higher than 112 = 94.95%
What is the simplified value of the exponential expression 16^1/4
1/2
1/4
2
4
Answer:
2
Step-by-step explanation:
16 ^ (1/4)
Rewriting 16 as 2^4
2^4 ^ 1/4
We know that a^b^c = a^(b*c)
2 ^ (4*1/4)
2 ^1
2
The right answer is 2.
please see the attached picture for full solution
Hope it helps
Good luck on your assignment
A professional writer decides to judge the value of her laptop by the number of times she presses
its keys before it breaks. The value V depends on the number of keypresses, k, according to the
formula:
V = 1200 -0.00002k
After one year, the value of her laptop is between $803.20 and $899.20.
What is the corresponding range of keypresses?.
Answer:
D.)
15040000 <= k <=19840000
Step-by-step explanation:
V = 1200 -0.00002k
Value V after one year falls in the range of $803.20 and $899.20.
Let's substract these values from 1200.
1200-803.20=396.80
1200-899.20=300.80
So it means that
0.00002k= 396.80
And
0.00002k= 300.80
So
0.00002k= 396.80
K= 396.80/0.00002
K= 19840000
And
0.00002k= 300.80
K = 300.80/0.00002
K= 15040000
So range is between
15040000 <= k <=19840000
A basketball player makes 70% of the free throws he shoots. Suppose that he tries 15 free throws.
a. What is the probability that he will make more than 7 throws?
• enter your answer as a percent (56) or as a real-value (0.05)
. you enter your answer as a percent, you must use a-sign in your answer
• your answer must be accurate to the nearest whole percent.
b. How many baskets can the player expect to make it he takes 15 shots? .
. Your answers must be accurate to the nearest hundreth.
c. What is the standard deviation of the number of successful free throws out of 15 total?
Answer:
a.) .95
b.) The expected number of baskets is 10.50.
c.) 1.7748
Step-by-step explanation:
a.) This is a binomial distribution as there are two possibilities: makes a free throw or doesn't. This means that you can use the binomial function on a calculator to figure out the answer. Use the binomial CDF function on a calculator and the number of trials=15, probability of success=.7, lower bound=0, upper bound=7. Once you have evaluated the answer, .0500, it will need to be subtracted from1, as you want everything not included in this section. The answer to part a is thus 1-.0500=.95.
b.) The expected value is calculated by taking the total number of shots and multiplying it by the probability of making the shot: 15×.7=10.5 shots.
c.) The standard deviation of a binomial distribution can be calculated by the formula [tex]\sqrt{(sample size)(probability)(1-probability)}[/tex]. Plugging in the numbers you get [tex]\sqrt{(15)(.7)(.3)}[/tex]=1.7748.
A. The probability of more than 7 throws is 0.95,
B. The player expects to make it he takes 15 shots at 10.50,
C. The standard deviation of the number of successful free throws out of 15 total of 1.775.
What is binomial probability?The probability of exactly x successes on n repeated trials in an experiment with two possible outcomes, also known as a binomial experiment, is referred to as binomial probability.
The binomial probability is ⁿCₓpₓ(1 - p)ⁿ⁻ˣ if the probability of success on an individual trial is p.
In this case, the number of distinct combinations of x objects chosen from a set of n objects is shown by ⁿCₓ. A few course readings utilize the documentation (ⁿₓ) rather than ⁿCₓ.
Keep in mind that if p is the probability of a single trial's success, then (1p) is the probability of a single trial's failure.
Given the probability of free throws at 0.7
total free throws 15
Let x be the random variable
A. the probability that he will make more than 7 throws
p(x > 7)
ⁿCₓpₓ(1 - p)ⁿ⁻ˣ
where n = 15, x = 8
¹⁵C₈(0.7)⁸(0.3)⁷
0.94998 = 0.95
B: player expect to make it he takes 15 shots
E(x) = n x p(x)
E(x) = 15 × 0.7 = 10.50
C: The standard deviation
variance = n x p x q
variance = 15 x 0.7 x 0.3 = 3.15
SD = √(variance) = √(3.15)
SD = 1.77482 ≈ 1.775
Hence the probability that he will make more than 7 throws is 0.95,
the player expects to make it if he takes 15 shots is 10.50,
The standard deviation is 1.775.
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subtract the sum of -1250 and 1138 from the sum of 1136 and 1272
Answer:
2528
Step-by-step explanation:
-1250+1130=-120
1136+1272=2408
2408-(-120)=2528
hope it helps
Find both the vector equation and the parametric equations of the line through (0 comma 0 comma negative 2 )(0,0,−2) in the direction of the vector Bold vvequals=left angle negative 2 comma negative 4 comma 0 right angle−2,−4,0, where tequals=0 corresponds to the given point.
The line (-2, -4, 0)t points in the same direction as the given vector (-2, -4, 0) and passes through the origin. To make this line pass through the point (0, 0, -2), all we need to do is translate the line by the vector (0, 0, -2). So the line has vector equation
u(t) = (-2, -4, 0)t + (0, 0, -2) = (-2t, -4t, -2)
and we see that t = 0 indeed corresponds to the given point.
In parametric form, the line is given by
x(t) = -2t
y(t) = -4t
z(t) = -2
for any real number t.
Please answer this correctly
Answer:
11 5/8
Step-by-step explanation:
Simply the 5/8 to 16th
5/8 equals to 10/16
Then add the 16ths together
The divide it by 16
Then add the whole numbers
Then add of them together to get your answer
Answer:
Exact Form:
93 /8
Decimal Form:
11.625
Mixed Number Form:
11 5 /8
Step-by-step explanation:
If you add every side together:
3 3/16 + 2 5/8 + 3 3/16 + 2 5/8 = 93/8
It's quite easy, just add everything together ;)
Can someone help Plz
Answer:
D = 67 inches
Step-by-step explanation:
The trend line is y = x+2 where x is the height
y = 65+2
y = 67
Answer: 67 inches tall
Step-by-step explanation:
y= x+2
y= 65+2
y= 67
Ashley works at an electronics store. She is paid 15% of the sales price of the items
she sells in addition to her $120 weekly salary. How can Ashley use the value of her
weekly sales total to calculate how much money she will earn that week?
Answer:
E(s) = 0.15s + 120
Step-by-step explanation:
She earns 15% of her weekly sales plus her $120 salary base.
Answer: Its the second option
Step-by-step explanation: I Promise its correct!
A rumor spreads through a small town. Let y(t) be the fraction of the population that has heard the rumor at time t and assume that the rate at which the rumor spreads is proportional to the product of the fraction y of the population that has heard the rumor and the fraction 1−y that has not yet heard the rumor.
a. Write the differential equation satisfied by y in terms of proportionality k.
b. Find k (in units of day−1, assuming that 10% of the population knows the rumor at time t=0 and 40% knows it at time t=2 days.
c. Using the assumptions in part (b), determine when 75% of the population will know the rumor.
d. Plot the direction field for the differential equation and draw the curve that fits the solution y(0)=0.1 and y(0)=0.5.
Answer:
The answer is shown below
Step-by-step explanation:
Let y(t) be the fraction of the population that has heard the rumor at time t and assume that the rate at which the rumor spreads is proportional to the product of the fraction y of the population that has heard the rumor and the fraction 1−y that has not yet heard the rumor.
a)
[tex]\frac{dy}{dt}\ \alpha\ y(1-y)[/tex]
[tex]\frac{dy}{dt}=ky(1-y)[/tex]
where k is the constant of proportionality, dy/dt = rate at which the rumor spreads
b)
[tex]\frac{dy}{dt}=ky(1-y)\\\frac{dy}{y(1-y)}=kdt\\\int\limits {\frac{dy}{y(1-y)}} \, =\int\limit {kdt}\\\int\limits {\frac{dy}{y}} +\int\limits {\frac{dy}{1-y}} =\int\limit {kdt}\\\\ln(y)-ln(1-y)=kt+c\\ln(\frac{y}{1-y}) =kt+c\\taking \ exponential \ of\ both \ sides\\\frac{y}{1-y} =e^{kt+c}\\\frac{y}{1-y} =e^{kt}e^c\\let\ A=e^c\\\frac{y}{1-y} =Ae^{kt}\\y=(1-y)Ae^{kt}\\y=\frac{Ae^{kt}}{1+Ae^{kt}} \\at \ t=0,y=10\%\\0.1=\frac{Ae^{k*0}}{1+Ae^{k*0}} \\0.1=\frac{A}{1+A} \\A=\frac{1}{9} \\[/tex]
[tex]y=\frac{\frac{1}{9} e^{kt}}{1+\frac{1}{9} e^{kt}}\\y=\frac{1}{1+9e^{-kt}}[/tex]
At t = 2, y = 40% = 0.4
c) At y = 75% = 0.75
[tex]y=\frac{1}{1+9e^{-0.8959t}}\\0.75=\frac{1}{1+9e^{-0.8959t}}\\t=3.68\ days[/tex]
Want Brainliest? Get this correct , What is the equation of this function after it is reflected over the y-axis?
Answer:
(-x+4)^3
Step-by-step explanation:
when you turn the x to negtive it filps over the y-axis and if the whole thing is negitve like -(x+4)^3 it filps over the x-axis
jus took the test. Your answer is F(x)=-(x+4)^3
n a recent awards ceremony, the age of the winner for best actor was 35 and the age of the winner for best actress was 48. For all best actors, the mean age is 48.7 years and the standard deviation is 8.9 years. For all best actresses, the mean age is 34.7 years and the standard deviation is 11.7 years. (All ages are determined at the time of the awards ceremony.) Relative to their genders, who had the more extreme age when winning the award, the actor or the actress? Explain.
Answer:
The best actor's age is farther from the mean, so he has the more extreme age when winning the award
Step-by-step explanation:
Z-score:
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:
Whichever z-score's has the highest absolute value, that is, is farther from the mean, has the most extreme age.
Best actor:
Age of 35, so [tex]X = 35[/tex].
For all best actors, the mean age is 48.7 years and the standard deviation is 8.9 years, so [tex]\mu = 48.7, \sigma = 8.9[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{35 - 48.7}{8.9}[/tex]
[tex]Z = -1.54[/tex]
Best actrees:
Age of 48, so [tex]X = 48[/tex]
For all best actresses, the mean age is 34.7 years and the standard deviation is 11.7 years, so [tex]\mu = 34.7, \sigma = 11.7[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{48 - 34.7}{11.7}[/tex]
[tex]Z = 1.14[/tex]
The best actor's age is farther from the mean, so he has the more extreme age when winning the award
-3× + 1 + 10x = x + 4
Answer:
I WANT BRAINLIESTStep-by-step explanation:
your question is
[tex]-3*1 + 10x = x+4[/tex]
-3+10x=x+4
9x=7
x = 7/9
Answer:
x=7/9
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
(−3)(1)+10x=x+4
−3+10x=x+4
10x−3=x+4
Step 2: Subtract x from both sides.
10x−3−x=x+4−x
9x−3=4
Step 3: Add 3 to both sides.
9x−3+3=4+3
9x=7
Step 4: Divide both sides by 9.
9x
9
= 7 /9
x= 7 /9
Which of the following describes the number 0.5?
The best description of the number 0.5 is a rational number and a terminating decimal.
What is a rational number?This is a number that is possible to express by using a fraction, or ration. 0.5 is a rational number because it is equivalent to the faction 1/2.
What is a terminating decimal?A decimal is terminating if it has limited or finite figures after the decimal period. This occurs with 0.5 because there is only one number after the period.
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Given P space equals space P subscript 0 space plus space rho g h, your objective is to determine the uncertainty of P by measuring P subscript 0 comma space rho comma space g space and space h , What is the expression for capital delta P subscript g , that is, the g's contributing term for the overall uncertainty of P
Answer:
the g's contributing term for the overall uncertainty of P is [tex]dP_g = [\frac{dg}{g}][/tex]
Step-by-step explanation:
From the question we are told that
The pressure is [tex]P = P_o + \rho gh[/tex]
The first step in determining the uncertainty of P in by obtaining the terms in the equation contributing to it uncertainty and to do that we take the Ln of both sides of the equation
[tex]ln P = lnP_o + ln(\rho gh )[/tex]
=> [tex]ln P = lnP_o + ln \rho + ln g + ln h[/tex]
Then the next step is to differentiate both sides of the equation
[tex]\frac{d(ln P)}{dP} = \frac{d(ln P_o)}{dP_o} + \frac{d(ln \rho)}{d\rho} +\frac{d(ln g)}{dg} + \frac{d(ln h)}{dh}[/tex]
=> [tex]\frac{dP}{P} = \frac{dP_o}{P_o} + \frac{d \rho}{\rho} +\frac{d g}{g} + \frac{d h}{h}[/tex]
We asked to obtain the contribution of the term g to the uncertainty of P
This can deduced from the above equation as
[tex]dP_g = [\frac{dg}{g}] P[/tex]
Solve the following equation algebraically:
4x2 = 100
a. +0.2
b. +5
C.
+12.5
+10
d.
Answer:
[tex]\boxed{\sf \ \ \ answer \ b. \ \ +5 \ \ \ }[/tex]
Step-by-step explanation:
Hello
let's assume that we are looking for x >=0
[tex]4x^2=100 <=> \dfrac{4x^2}{4}=x^2=\dfrac{100}{4}=25\\<=>\sqrt{x^2}=25\\<=> |x| = 5 <=> x = 5 \ or \ x=-5[/tex]
Let's assume that we are looking for x>=0
so the correct answer is 5
he mayor of a town has proposed a plan for the construction of a new community. A political study took a sample of 900 voters in the town and found that 81% of the residents favored construction. Using the data, a political strategist wants to test the claim that the percentage of residents who favor construction is more than 78%. Testing at the 0.02 level, is there enough evidence to support the strategist's claim?
Answer:
[tex]z=\frac{0.81 -0.78}{\sqrt{\frac{0.78(1-0.78)}{900}}}=2.173[/tex]
The p value for this case is given by this probability:
[tex]p_v =P(z>2.173)=0.0149[/tex]
Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true proportion of people who favored te construction is significantly higher than 0.78 or 78%
Step-by-step explanation:
Information given
n=900 represent the random sample taken
[tex]\hat p=0.81[/tex] estimated proportion of residents who favored the construction
[tex]p_o=0.78[/tex] is the value to test
[tex]\alpha=0.02[/tex] represent the significance level
z would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to test if the true proportion is more than 0.78 or not.:
Null hypothesis:[tex]p\leq 0.78[/tex]
Alternative hypothesis:[tex]p > 0.78[/tex]
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing the info we got:
[tex]z=\frac{0.81 -0.78}{\sqrt{\frac{0.78(1-0.78)}{900}}}=2.173[/tex]
The p value for this case is given by this probability:
[tex]p_v =P(z>2.173)=0.0149[/tex]
Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true proportion of people who favored te construction is significantly higher than 0.78 or 78%
A clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjects. Before treatment, 17 subjects had a mean wake time of 100.0 min. After treatment, the 17 subjects had a mean wake time of 90.3 min and a standard deviation of 21.8 min. Assume that the 17 sample values appear to be from a normally distributed population and construct a 99% confidence interval estimate of the mean wake time for a population with drug treatments. What does the result suggest about the mean wake time of 100.0 min before the treatment? Does the drug appear to be effective?
Answer:
Step-by-step explanation:
Confidence interval is written in the form,
(Sample mean - margin of error, sample mean + margin of error)
The sample mean, x is the point estimate for the population mean.
Margin of error = z × s/√n
Where
s = sample standard deviation = 21.8
n = number of samples = 17
From the information given, the population standard deviation is unknown and the sample size is small, hence, we would use the t distribution to find the z score
In order to use the t distribution, we would determine the degree of freedom, df for the sample.
df = n - 1 = 17 - 1 = 16
Since confidence level = 99% = 0.99, α = 1 - CL = 1 – 0.99 = 0.01
α/2 = 0.01/2 = 0.005
the area to the right of z0.005 is 0.005 and the area to the left of z0.005 is 1 - 0.005 = 0.995
Looking at the t distribution table,
z = 2.921
Margin of error = 2.921 × 21.8/√17
= 15.44
The confidence interval for the mean wake time for a population with drug treatments is
90.3 ± 15.44
The upper limit is 90.3 + 15.44 = 105.74 mins
The lower limit is 90.3 - 15.44 = 74.86 mins
The result suggests that the mean wake time might have really reduced since the values barely fall above 100 minutes as in before treatment with a high degree of confidence. Therefore, the drug is effective.
cones and pyramids both have only one base ?
Answer:
Yes
Step-by-step explanation:
They both have only one base. They are different from prisms and cylinders.
What errors are shown here? Check all that apply.
-the arrows should be a length of 2
-the arrows should be a length of 6
-the arrows should be pointing in the positive direction
-the arrows should start at zero
-the arrows should point in the negative direction
Answer:
-The arrows should be a length of 6
-The arrows should point in the negative direction
-The arrows should start at zero
Step-by-step explanation:
Hope this helps!
Answer:
B
D
E
Step-by-step explanation:
What is the radius of the circle whose equation is x2 + y2 = 9?
81
3
9
Answer:
3
Step-by-step explanation:
x^2 + y^2 = 9
The equation of a circle is
(x-h)^2 + (y-k)^2 = r^2
( h,k) is the center and r is the radius
x^2 + y^2 = 3^2
The radius is 3
