Answer:
(f-g)(x) = - x² + 2 x + 8
Step-by-step explanation:
Explanation:-
Given f(x) = 2 x +1
g(x) = x² - 7
(f-g)(x) = f(x) - g(x)
= (2 x + 1) - ( x² -7)
= - x² + 2 x + 1 + 7
= - x² + 2 x + 8
(f-g)(x) = - x² + 2 x + 8
If Brooklyn College students have an IQ of 100, on average, with a standard deviation of 16 points, and I collect 48 BC Psychology students to see how Psych majors compare to all of BC, find the following:_______.
1. mu =
2. sigma =
3. mu _x bar =
4. sigma _x bar =
Answer:
1 [tex]\mu = 100[/tex]
2 [tex]\sigma = 16[/tex]
3 [tex]\mu_x = 100[/tex]
4 [tex]\sigma _{\= x } = 2.309[/tex]
Step-by-step explanation:
From the question
The population mean is [tex]\mu = 100[/tex]
The standard deviation is [tex]\sigma = 16[/tex]
The sample mean is [tex]\mu_x = 100[/tex]
The sample size is [tex]n = 48[/tex]
The mean standard deviation is [tex]\sigma _{\= x } = \frac{\sigma }{\sqrt{n} }[/tex]
substituting values
[tex]\sigma _{\= x } = \frac{16 }{\sqrt{48} }[/tex]
[tex]\sigma _{\= x } = 2.309[/tex]
An object of mass 2kg is attached to a spring. A force of 5nt is applied to move the object 0.5m from its equilibrium position. The damping force of the object sliding on the table is int when the velocity is 0.25m/second. The object is pulled to the left until the spring is stretched lm and then released with the initial velocity of 2m/second to the right.
Set up an I.V.P. to describe the motion of the object and solve it, then state the amplitude function of the motion.
Answer:
[tex]\mathbf{x(t) = \dfrac{ \sqrt 5}{2}e^{-t} }[/tex]
Step-by-step explanation:
Given that:
mass of the object = 2 kg
A force of 5nt is applied to move the object 0.5m from its equilibrium position.
i.e
Force = 5 newton
Stretchin (x) =0.5 m
Damping force = 1 newton
Velocity = 0.25 m/second
The object is pulled to the left until the spring is stretched lm and then released with the initial velocity of 2m/second to the right
SOLUTION:
If F = kx
Then :
5 N = k(0.5 m)
where ;
k = spring constant.
k = 5 N/0.5 m
k = 10 N/m
the damping force of the object sliding on the table is 1 newton when the velocity is 0.25m/second.
SO;
[tex]C \dfrac{dx}{dt}= F_d[/tex]
[tex]C* 0.25 = 1[/tex]
C = [tex]\dfrac{1 \ N }{0.25 \ m/s}[/tex]
C = 4 Ns/m
NOW;
[tex]m \dfrac{d^2x}{dt^2}+ C \dfrac{dx}{dt}+ kx = 0[/tex]
Divide through by m; we have;
[tex]\dfrac{m}{m}\dfrac{d^2x}{dt^2}+ \dfrac{C}{m} \dfrac{dx}{dt}+ \dfrac{k}{m} x= 0[/tex]
[tex]\dfrac{d^2x}{dt^2}+ \dfrac{C}{m} \dfrac{dx}{dt}+\dfrac{k}{m}x= 0[/tex]
[tex]\dfrac{d^2x}{dt^2}+ \dfrac{4}{2} \dfrac{dx}{dt}+\dfrac{10}{2}x= 0[/tex]
[tex]\dfrac{d^2x}{dt^2}+ 2 \dfrac{dx}{dt}+5x= 0[/tex]
we all know that:
[tex]x(t) = Ae^{(\alpha \ t)}[/tex] ------ (1)
SO;
[tex]\alpha ^2 + 2\alpha + 5 = 0[/tex]
[tex]\alpha = \dfrac{-2 \pm \sqrt{(4)-(4*5)}}{2}[/tex]
[tex]\alpha = -1 \pm 2i[/tex]
Thus ;
[tex]x(t) = e^{-t}[A \sin (2t)+ B cos (2t)][/tex] ------------ (1)
However;
[tex]\dfrac{dx}{dt} = e^{-t}[A \sin (2t)+ B cos (2t)]+ 2e ^{-t} [A \cos (2t)- B \ Sin (2t)][/tex] ------- (2)
From the question ; we are being told that;
The object is pulled to the left until the spring is stretched 1 m and then released with the initial velocity of 2m/second to the right.
So ;
[tex]x(0) = -1 \ m[/tex]
[tex]\dfrac{dx}{dt}|_{t=0} = 2 \ m/s[/tex]
x(0) ⇒ B = -1
[tex]\dfrac{dx}{dt}|_{t=0} =- B +2A[/tex]
[tex]=- 1 +2A[/tex]
1 = 2A
A = [tex]\dfrac{1}{2}[/tex]
From (1)
[tex]x(t) = e^{-t}[A \sin (2t)+ B cos (2t)][/tex]
[tex]x(t) = e^{-t}[\dfrac{1}{2} \sin (2t)+ (-1) cos (2t)][/tex]
[tex]x(t) = e^{-t}[\dfrac{1}{2} \sin (2t)-cos (2t)][/tex]
Assuming;
[tex]A cos \ \phi = \dfrac{1}{2}[/tex]
[tex]A sin \ \phi = 1[/tex]
Therefore:
[tex]A = \sqrt{\dfrac{1}{4}+1}[/tex]
[tex]A = \sqrt{\dfrac{1+4}{4}}[/tex]
[tex]A = \sqrt{\dfrac{5}{4}}[/tex]
[tex]A ={ \dfrac{ \sqrt5}{ \sqrt4}}[/tex]
[tex]A ={ \dfrac{ \sqrt5}{ 2}}[/tex]
where;
[tex]\phi = tan ^{-1} (2)[/tex]
Therefore;
[tex]x(t) = \dfrac{\sqrt 5}{2}e^{-t} \ sin (2 t - \phi)[/tex]
From above ; the amplitude is ;
[tex]\mathbf{x(t) = \dfrac{ \sqrt 5}{2}e^{-t} }[/tex]
g red bell pepper seeds germinates 85% of the time. planted 25 seeds. What is the probability that 20 or more germinate
Answer:
[tex] P(X\geq 20)= P(X=20)+P(X=21)+P(X=22)+P(X=23)+P(X=24)+P(X=25)[/tex]
And replacing using the mass function we got:
[tex]P(X=20)=(25C20)(0.85)^{20} (1-0.85)^{25-20}=0.156[/tex]
[tex]P(X=21)=(25C21)(0.85)^{21} (1-0.85)^{25-21}=0.211[/tex]
[tex]P(X=22)=(25C22)(0.85)^{22} (1-0.85)^{25-22}=0.217[/tex]
[tex]P(X=23)=(25C23)(0.85)^{23} (1-0.85)^{25-23}=0.161[/tex]
[tex]P(X=24)=(25C24)(0.85)^{24} (1-0.85)^{25-24}=0.0759[/tex]
[tex]P(X=25)=(25C25)(0.85)^{25} (1-0.85)^{25-25}=0.0172[/tex]
And adding the values we got:
[tex] P(X\geq 20) = 0.8381[/tex]
Step-by-step explanation:
Let X the random variable of interest, on this case we now that:
[tex]X \sim Binom(n=25, p=0.85)[/tex]
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
We want to find the following probability:
[tex] P(X\geq 20)= P(X=20)+P(X=21)+P(X=22)+P(X=23)+P(X=24)+P(X=25)[/tex]
And replacing using the mass function we got:
[tex]P(X=20)=(25C20)(0.85)^{20} (1-0.85)^{25-20}=0.156[/tex]
[tex]P(X=21)=(25C21)(0.85)^{21} (1-0.85)^{25-21}=0.211[/tex]
[tex]P(X=22)=(25C22)(0.85)^{22} (1-0.85)^{25-22}=0.217[/tex]
[tex]P(X=23)=(25C23)(0.85)^{23} (1-0.85)^{25-23}=0.161[/tex]
[tex]P(X=24)=(25C24)(0.85)^{24} (1-0.85)^{25-24}=0.0759[/tex]
[tex]P(X=25)=(25C25)(0.85)^{25} (1-0.85)^{25-25}=0.0172[/tex]
And adding the values we got:
[tex] P(X\geq 20) = 0.8381[/tex]
Suppose that a certain brand of light bulb has a mean life of 450 hours and a standard deviation of 73 hours. Assuming the data are bell-shaped: (Show work to get full credit)
a. Would it be unusual for a light bulb to have a life span of 320 hours? 615 hours? Justify each response.
b. According to the Empirical Rule, 99.7% of the light bulbs have a lifetime between what two values?
c. Determine the percentage of light bulbs that will have a life between 304 and 596 hours.
Answer:
yes it is correct
Step-by-step explanation:
plz give brainliest.
A school is 16km due west of a school q.
What is the bearing of q from p?
Answer:
16 km due west
Step-by-step explanation:
The bearing of the school p from school q is 16 km due west.
To find the bearing of school q from school p, we have to find the direction that the school q is with respect to school p.
Since p is directly west of q, then it implies that q must be directly east of p.
We now know the direction.
Since the distance from q to p is exactly the same as the distance from p to q, then, the distance from p to q is 16 km.
Hence, the bearing of q from p is 16 km due west.
Pls help me help me
Answer:
C.
Step-by-step explanation:
When two lines are parallel, their slopes are the same.
Since the slope of line l is 2/7, the slope of its parallel line m must also be 2/7.
The answer is C.
Answer:
C. 2/7
Step-by-step explanation:
Parallel lines are lines that have the same slopes.
We know that line l is parallel to line m.
Therefore, the slope of line l is equal to the slope of line m.
[tex]m_{l} =m_{m}[/tex]
We know that line l has a slope of 2/7.
[tex]\frac{2}{7} =m_{m}[/tex]
So, line m also has a slope of 2/7. The answer is C. 2/7
Assume that T is a linear transformation. Find the standard matrix of T:R2→R2T:R 2→R 2 first rotates points through −3π/4−3π/4 radian (clockwise) and then reflects points through the horizontal x1x 1-axis.
Answer:
An object balances itself when a perpendicular line drawn through its Centre of Gravity (CG), passes through its base.
See the picture of a popular toy given below. The horse, the rider and the ball are all joined together as one single unit. This entire unit is balanced on the thin black rod shown. At which of the indicated positions, could the Centre of Gravity (CG) of the horse, rider and ball unit be?
July 10 book Science up55 down8
AA BB
CC DD
Step-by-step explanation:
g Steel used for water pipelines is often coated on the inside with cement mortar to prevent corrosion. In a study of the mortar coatings of the pipeline used in a water transmission project in California, researchers noted that the mortar thickness was specified to be 7/16 inch. A very large sample of thickness measurements produced a mean equal to 0.635 inch and astandard deviation equal to 0.082 inch. If the thickness measurements were normally distributed, approximately what proportion were less than 7/16 inch?
Answer:
[tex]P(X<0.4375)=P(\frac{X-\mu}{\sigma}<\frac{0.4375-\mu}{\sigma})=P(Z<\frac{0.4375-0.635}{0.082})=P(z<-2.41)[/tex]
And we can find this probability using the z table and we got:
[tex]P(z<-2.41)=0.0080[/tex]
Step-by-step explanation:
Let X the random variable that represent the thickness of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(0.635,0.082)[/tex]
Where [tex]\mu=0.635[/tex] and [tex]\sigma=0.032[/tex]
We are interested on this probability
[tex]P(X<0.4375)[/tex]
And the best way to solve this problem is using the normal standard distribution and the z score given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
If we apply this formula to our probability we got this:
[tex]P(X<0.4375)=P(\frac{X-\mu}{\sigma}<\frac{0.4375-\mu}{\sigma})=P(Z<\frac{0.4375-0.635}{0.082})=P(z<-2.41)[/tex]
And we can find this probability using the z table and we got:
[tex]P(z<-2.41)=0.0080[/tex]
What is the measure of BAC ? Pls help
Answer: m∠BAC =36.87°
It is given, but maybe difficult to see.
Step-by-step explanation: If you had to calculate it yourself, you need a scientific calculator or a conversion chart. You could figure the sine by dividing the length of the opposite side, 6 by the length of the hypotenuse, 10. you get sine=0.6
Then use the calculator or chart to get the angle.
input sin^-1 (0.06)
the bus fare in a city is $2.00. people who use the bus have the option of purchashing a monthly coupoun book is $20.00. with the copoun bok, the fare is reduced to $1.00 Determine the number of times in a month the bus be used so that the total monthly cost without the coupon book is the same as the total monthly cost with the coupon book
Answer:
but I can do it if you want but I don't you too too y u your help and you have time can you
Step-by-step explanation:
guy who was it that you are not going to be able to make it to the meeting tonight but I can tomorrow if you have time can you come to my house
15 3/4 is what decimal
━━━━━━━☆☆━━━━━━━
▹ Answer
15.75
▹ Step-by-Step Explanation
3 ÷ 4 = .75
15 + .75 = 15.75
Hope this helps!
- CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
What is the equation of the line that is parallel to the given line and passes through the point (12, -2)? A) y = -6/5x + 10 B) y= -6/5x + 12 C) y = -5/6x -10 D) y = 5/6x - 12
Answer:
D
Step-by-step explanation:
Parallel lines are those that have the same slope, or coefficient of x.
Here, let's calculate the slope of the given line. Slope is the difference in the y-coordinates divided by the difference in the x-coordinates, so given the two coordinates (12, 6) and (0, -4):
slope = m = (-4 - 6) / (0 - 12) = -10 / (-12) = 10/12 = 5/6
So the slope is 5/6. That means the equation we want should also have a slope of 5/6. Already, we can eliminate A, B, and C, leaving D as our answer. But, let's check.
The equation of a line can be written as [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1,y_1)[/tex] is the coordinates of a given point.
Here, our slope is 5/6 and our given point is (12, -2). So plug these in:
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y-(-2)=(5/6)(x-12)[/tex]
[tex]y+2=\frac{5}{6} x-10[/tex]
[tex]y=\frac{5}{6} x-12[/tex]
This matches D, so we know that it's the correct answer.
~ an aesthetics lover
The answer is D I just took the test
A respiratory therapist predicts that the proportion of U.S. college students who smoke hookah is greater than 30%. To test this prediction, she surveys 300 random U.S. college, and it is determined that 80 of them smoke hookah. The following is the setup for this hypothesis test: H0:p=0.30 H0:p>0.30 The p-value for this hypothesis test is 0.10. At the 5% significance level, should she reject or fail to reject the null hypothesis? Select the correct answer below: Reject the null hypothesis because 0.30>0.05. Fail to reject the null hypothesis because 0.30>0.05. Reject the null hypothesis because the p-value =0.10 is less than the significance level α=0.05. Fail to reject the null hypothesis because the p-value =0.10 is more than the significance level α=0.05.
Answer:
Fail to reject the null hypothesis because the p-value =0.10 is more than the significance level α=0.05.
Step-by-step explanation:
The significant level for this case study is 5% - 0.05. If the results gotten is less than the significance level, we reject the null hypothesis, but if greater, we fail to reject the null hypothesis.
In this case study, the p-value is 0.10 which is a lot higher than 0.05, thus we will fail to reject the null hypothesis because the p-value =0.10 is more than the significance level α=0.05.
What is the value of$$\left( \sqrt{100} - \sqrt{36} \right)^2?$$
Answer:
16
Step-by-step explanation:
The square root of 100 is 10, and the square root of 36 is 6. 10-6 = 4, and 4 squared is 16.
Hope this helped!
Answer:
16
Step-by-step explanation:
[tex]\left( \sqrt{100} - \sqrt{36} \right)^2 = (10 -6)^2 = 4^2 = \boxed{16}[/tex]
anyone mind lending a helping hand (asap!?!?)
Answer:
Q9 X=42.5
Step-by-step explanation:
let unknown angle be x
cos x=45/61
X=cos^-1 45/61
X=42.463...
X=42.5 (1 decimal place)
Find the value of s(t(-2)):
s(x)= - 3x-2
t(x)=5x-4
Peter samples her class by selecting 5 girls and 7 boys. This type of sampling is called?
Answer:
Hello!
______________________
Peter samples her class by selecting 5 girls and 7 boys. This type of sampling is called?
This type of sampling is called Stratified.
Hope this helped you!
:D
Simplify the expression below.
Answer:
6x^2 +8x
Step-by-step explanation:
(12x^3 -14x^2 -40x) / (2x-5)
Factor the numerator by factoring out the greatest common factor
2x( 6x^2 -7x-20) / (2x-5)
Factor inside the parentheses
2x (3x+4)(2x-5)/ (2x-5)
Cancel like terms
2x( 3x+4)
Distribute
6x^2 +8x
A(2,9), B(4,k), and C(9, -12) are 3 collinear points.
Find the value of k.
==========================================================
Explanation:
We're going to be using the slope formula a bunch of times.
Find the slope of the line through points A and C
m = (y2 - y1)/(x2 - x1)
m = (-12-9)/(9-2)
m = -21/7
m = -3
The slope of line AC is -3. The slopes of line AB and line BC must also be the same for points A,B,C to be collinear. The term collinear means all three points fall on the same straight line.
-------
Let's find the expression for the slope of line AB in terms of k
m = (y2 - y1)/(x2 - x1)
m = (k-9)/(4-2)
m = (k-9)/2
Set this equal to the desired slope -3 and solve for k
(k-9)/2 = -3
k-9 = 2*(-3) ..... multiply both sides by 2
k-9 = -6
k = -6+9 .... add 9 to both sides
k = 3
If k = 3, then B(4,k) updates to B(4,3)
-------
Let's find the slope of the line through A(2,9) and B(4,3)
m = (y2 - y1)/(x2 - x1)
m = (3-9)/(4-2)
m = -6/2
m = -3 we get the proper slope value
Finally let's check to see if line BC also has slope -3
m = (y2 - y1)/(x2 - x1)
m = (-12-3)/(9-4)
m = -15/5
m = -3 we get the same value as well
Since we have found lines AB, BC and AC all have slope -3, we have proven that A,B,C fall on the same straight line. Therefore, this shows A,B,C are collinear.
Construct 3 linear equation starting with qiven solution z = 1/3
Answer:
(a)[tex]9z+2=5[/tex]
(b)[tex]21z-11=-4[/tex]
(c)[tex]4z=2-2z[/tex]
Step-by-step explanation:
We are required to construct 3 linear equations starting with the given solution z = 1/3.
Equation 1
[tex]z=\frac{1}{3}[/tex]
Multiply both sides by 9
[tex]9z=\frac{1}{3}\times 9\\9z=3[/tex]
Rewrite 3 as 5-2
9z=5-2
Add 2 to both sides
Our first equation is: [tex]9z+2=5[/tex]
Equation 2
[tex]z=\frac{1}{3}[/tex]
Multiply both sides by 21
[tex]21z=\frac{1}{3}\times 21\\21z=7[/tex]
Rewrite 7 as 11-4
21z=11-4
Subtract 11 from both sides
Our second equation is: [tex]21z-11=-4[/tex]
Equation 3
[tex]z=\frac{1}{3}[/tex]
Multiply both sides by 6
[tex]6z=\frac{1}{3}\times 6\\6z=2[/tex]
Rewrite 6z as 4z+2z
4z+2z=2
Subtract 2z from both sides
Our third equation is: [tex]4z=2-2z[/tex]
Vance ate a salad and Four-fifths of a turkey burger for dinner. The salad contained 80 calories and his entire meal contained 440 calories. Which equation can be used to determine x, the number of calories in the entire turkey burger?
The correct answer is A. 440 = [tex]\frac{4}{5}[/tex] x + 80
Explanation:
In mathematics, equations are often used to find an unknown value. Additionally, equations display two mathematical expressions that have an equality relation, and based on this equality the unknown value can be found. Moreover, if you need to write an equation it is important to include all the important values, and understand the relationship between them because this determines the mathematical signs that need to be used.
In the case presented, it is known the total of the calories for the burger and salad is 440. Because of this, the mathematical expression on one side should be 440. Additionally, on the other side, it is necessary to include the calories of the salad (80) plus the calories of the burger. However, because you know Vance ate only 4/5 of the burger and the value of the burger is not known the correct expression for this section is [tex]\frac{4}{5}[/tex] x as x represents the unknown value. Thus, the correct equation is "440 = [tex]\frac{4}{5}[/tex] x + 80"
Answer:
The correct answer is A. 440 = 4/5x + 80
A consultant wants to ask workers at a factory about the workers' job satisfaction. Which of the following best describes a cluster sample of workers?
a. The consultant takes a list of the workers and selects every 6" worker until 60 workers are selected.
b. The consultant forms 5 groups of workers based on the workers' shifts. Then, he selects 12 workers at random from each group.
c. The consultant forms groups of 12 workers based on the lengths of time the workers have worked at the factory. Then, he randomly chooses 5 groups and selects all of the workers in these groups
Answer:
i think option c must be correct because it has formed the grops on the basis of length of time and made the group by random selection.
Compute the critical value z Subscript alpha divided by 2 that corresponds to a 86% level of confidence.
Answer:
z = 1.476
Step-by-step explanation:
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{1-0.86}{2} = 0.07[/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]1-0.07 = 0.93[/tex], so [tex]z = 1.476[/tex]
The answer is z = 1.476
Mrs. Lang is 4 times as old as her daughter Jill. The sum of their ages is 60 years. Set up the two equations that can be used to find each of their ages. Constraint 1: The solution must satisfy the ratio of their ages. Constraint 2: The solution must satisfy the sum of their ages. Only constraint would be met if Mrs. Lang is 32 and Jill is 8. Only constraint would be met if Mrs. Lang is 45 and Jill is 15.
Answer:
The two equations that can be used to find each of their ages are [tex]x=4 \times y[/tex] and [tex]x+y=60[/tex] .
Step-by-step explanation:
We are given that Mrs. Lang is 4 times as old as her daughter Jill. The sum of their ages is 60 years.
Let the age of Mrs. Lang be 'x years' and the age of her daughter Jill be 'y years'.
Now, according to the question;
The first condition states that Mrs. Lang is 4 times as old as her daughter Jill, that means;[tex]x=4 \times y[/tex] ----------------- [equation 1]
The second condition states that the sum of their ages is 60 years, that means;[tex]x+y=60[/tex]
[tex]4y + y = 60[/tex] {using equation 1}
[tex]5y=60[/tex]
[tex]y=\frac{60}{5}[/tex]
y = 12 years
Now, putting the value of y in equation 1 we get;
[tex]x=4 \times y[/tex]
[tex]x= 4 \times 12[/tex] = 48 years
Hence, the age of Mrs. Lang is 48 years and her daughter Jill is 12 years old.
Answer:
Mrs. Lang is 48 and her daughter is 12 years old.
Step-by-step explanation:
A new fertilizer was applied to the soil of 146 bean plants. 23% showed increased growth. Find the margin of error and 95% confidence interval for the percentage of all bean plants which show increased growth after application of the fertilizer. Round all answers to 2 decimal places.
Answer:
The significance level for this case would be [tex]\alpha=1-0.95=0.05[/tex] and the critical value for this case would be:
[tex] z_{\alpha/2}=1.96[/tex]
The margin of error is given by:
[tex] ME = z_{\alpha/2} \sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]
And replacing we got:
[tex] ME = 1.96 \sqrt{\frac{0.23*(1-0.23)}{146}} =0.0683[/tex]
And the margin of error for this case would be [tex] ME = 0.07[/tex]
Step-by-step explanation:
For this case we have the following dataset given:
[tex] n= 146[/tex] represent the sample size
[tex] \hat p =0.23[/tex] represent the estimated proportion of interest
[tex] Conf=0.95[/tex] represent the confidence level
The significance level for this case would be [tex]\alpha=1-0.95=0.05[/tex] and the critical value for this case would be:
[tex] z_{\alpha/2}=1.96[/tex]
The margin of error is given by:
[tex] ME = z_{\alpha/2} \sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]
And replacing we got:
[tex] ME = 1.96 \sqrt{\frac{0.23*(1-0.23)}{146}} =0.0683[/tex]
And the margin of error for this case would be [tex] ME = 0.07[/tex]
A chemist wishes to test the effect of four chemical agents on the strength of a particular type of cloth. Because there might be variability from one bolt to another, the chemist decides to use a randomized block design, with the bolts of cloth considered as blocks. She selects five bolts and applies all four chemicals in random order to each bolt. The resulting tensile strengths follow. Analyze the data from this experiment (use α = 0.05) and draw appropriate conclusions.
Bolt
Chemical 1 2 3 4 5
1 73 68 73 71 67
2 73 67 75 72 70
3 75 68 78 73 68
4 73 71 75 75 69
Answer:
p > α
0.7038 > 0.05
Also since F < F critical
0.475 < 3.238
We failed to reject H₀
We do not have significant evidence at the given significance level to show that there is a difference among the four chemical agents on the strength of a particular type of cloth.
Step-by-step explanation:
We are given that a chemist wishes to test the effect of four chemical agents on the strength of a particular type of cloth.
Since we are given data for four independent chemical agents to determine the effect on the strength of a particular type of cloth, therefore, a one-way analysis of variance may be used for the given problem.
ANOVA:
The one-way analysis of variance (ANOVA) may be used to find out whether there is any significant difference between the means of two or more independent categories of data.
Set up hypotheses:
Null hypotheses = H₀: μ₁ = μ₂ = μ₃ = μ₄
Alternate hypotheses = H₁: μ₁ ≠ μ₂ ≠ μ₃ ≠ μ₄
Set up decision rule:
We Reject H₀ if p ≤ α
OR
We Reject H₀ if F > F critical
ANOVA in Excel:
Step 1:
In the data tab, select data analysis
Step 2:
Select "Anova single factor" from the analysis tools
Step 3:
Select the destination of input data in the "input range"
Step 4:
Select "rows" for the option "Group By"
Step 5:
Tick the option "labels in first row"
Step 6:
Set alpha = 0.05
Step 7:
Select the destination of output data in the "output options"
Conclusion:
Please refer to the attached results.
The p-value is found to be
p = 0.7038
The F value is found to be
F = 0.475
The F critical value is found to be
F critical = 3.238
Since p > α
0.7038 > 0.05
We failed to reject H₀
Also since F < F critical
0.475 < 3.238
We failed to reject H₀
We do not have significant evidence at the given significance level to show that there is a difference among the four chemical agents on the strength of a particular type of cloth.
Find the lateral (side) surface area of the cone generated by revolving the line segment y equals seven halves x , 0 less than or equals x less than or equals 5, about the x-axis. Check your answer with the following geometry formula. Lateral surface areaequalsone half times base circumference times slant height
Answer:
[tex]Area=7\,\pi\,\sqrt{\frac{53}{4}}\,\,\frac{25}{2}[/tex]
Step-by-step explanation:
Let's use the integral formula for the surface area of revolution of the function y(x) around the x-axis, which is:
[tex]Area=\int\limits^b_a {2\,\pi\,y\,\sqrt{1+(\frac{dy}{dx} )^2} } \, dx[/tex]
and which in our case, we can obtain the following:
[tex]y=\frac{7}{2} \,x\\\frac{dy}{dx} =\frac{7}{2} \\(\frac{dy}{dx})^2=\frac{49}{4} \\\sqrt{1+(\frac{dy}{dx})^2} =\sqrt{1+\frac{49}{4} } =\sqrt{\frac{53}{4} }[/tex]
Recall as well that [tex]0\leq x\leq 5[/tex], which gives us the limits of integration:
[tex]Area=\int\limits^b_a {2\,\pi\,y\,\sqrt{1+(\frac{dy}{dx} )^2} } \, dx\\Area=\int\limits^5_0 {2\,\pi\,(\frac{7}{2}\,x) \,\sqrt{\frac{53}{4} } } \, dx\\Area=7\,\pi\,\sqrt{\frac{53}{4}}\,\, \int\limits^5_0 {x} \, dx \\Area=7\,\pi\,\sqrt{\frac{53}{4}}\,\,\frac{x^2}{2} |\limits^5_0\\Area=7\,\pi\,\sqrt{\frac{53}{4}}\,\,\frac{25}{2}[/tex]
If we compare it with the geometry formula:
Lateral surface of cone = [tex]\frac{1}{2} \,\,(Base_{circ})\,\,(slant\,height)= \frac{1}{2} (2\,\pi\,\frac{7}{2} 5)\.(\sqrt{5^2+(\frac{35}{2})^2 } =\frac{7}{2} \,\pi\,25\.\,\sqrt{\frac{53}{4} }[/tex]
which is exactly the expression we calculated with the integral.
Someone pls help me
The slope greater than one would be the last image, because for every step in x, you get more than one y step.
The slope between 1 and 0 would be the second image
And the slope less than 0 would be the third image
Based only on the given information, it is guaranteed that AD = CD.
Answer:
Not really, actually it depends on the shape given whether it's a rectangle, a square etc. Because you can't conclude that the shape of a rectangle with such dimensions could be guaranteed.
An efficiency expert hired by a manufacturing firm has compiled these data relating workers output to their experience:
Experience t (months) 0 3
Output Q (units per hour) 200 190
Suppose output Q Is related to experience t by a function of the form Q (t) = 300 - A e^-kt. Find the function of this form that fits the data.
Answer:
Q(t) = 300 - 100e^0.0318tStep-by-step explanation:
Given the relationship between the output as related to the experience t to be Q (t) = 300 - A e^-kt.
From the table, at t = 0, Q(t) = 200, substituting this into he equation to get A we have:
200 = 300 - A e^-k(0).
200 = 300 - A e^-0
200 = 300 - A
A = 300-200
A = 100
Secondly we need to get the constant k by substituting the other condition into the equation. When t = 3, Q(t) = 190
190 = 300 - A e^-k(3)
190 = 300 - 100e^-3k
190-300 = -100e^-3k
-110 = -100e^-3k
e^-3k = -110/-100
e^-3k = 1.1
Taking the natural logarithm of both sides we have;
ln(e^-3k) = ln1.1
-3k = 0.09531
k = 0.09531/-3
k = -0.0318
The function of this form that fits the data can be gotten by substituting A = 100 and k = -0.0318 into the modeled equation given as shown:
Q(t) = 300 - A e^-kt
Q(t) = 300 - 100e^-(-0.0318)t
Q(t) = 300 - 100e^0.0318t