Answer:
The p-value is 0.0012.
Step-by-step explanation:
The hypothesis is:
H₀: µ = 72 vs. Hₐ: µ > 72
The information provided is:
[tex]n =16\\\bar x=75.8\\\sigma=5[/tex]
Compute the test statistic value as follows:
[tex]z=\frac{\bar x-\mu}{\sigma/\sqrt{n}}[/tex]
[tex]=\frac{75.8-72}{5/\sqrt{16}}\\\\=3.04[/tex]
Compute the p-value as follows:
[tex]p-value=P(Z>3.04)\\\\=1-P(Z<3.04)\\\\=1-0.99882\\\\=0.00118\\\\\approx 0.0012[/tex]
*Use a z-table.
Thus, the p-value is 0.0012.
Calculus please help me
(1) f(x) = (1 - x³) / (x - 1)
(a) The domain is the set of values that this function can take on. If x = 1, the denominator becomes 0 and the function is undefined. Any other value of x is okay, though, since for x ≠ 1, we have
f(x) = (1 - x³) / (x - 1) = - (1 - x³) / (1 - x) = -(x² + x + 1)
which is defined for all x. This also tells us that the plot of f(x) is a parabola with a hole at x = 1. So, the domain is the interval (-∞, 1) ∪ (1, ∞).
(b) The range is the set of values that the function actually does take on. Taking the simplified version of f(x), we can complete the square to write
-(x² + x + 1) = -(x² + x + 1/4 - 1/4) - 1 = -(x + 1/2)² - 3/4
which is represented by a parabola that opens downward, with a maximum value of -3/4. So the range is the interval (-∞, -3/4).
(c) Judging by the plot of f, the limits at both negative and positive infinity are -∞.
(d) Same answer as part (a).
(2) f(x) = x³ - x
(a) The derivative of f at x = 3, and hence the slope of the tangent line to this point, is
[tex]f'(3)=\displaystyle\lim_{h\to0}\frac{f(3+h)-f(3)}h[/tex]
[tex]f'(3)\displaystyle=\lim_{h\to0}\frac{((3+h)^3-(3+h))-24}h[/tex]
[tex]f'(3)=\displaystyle\lim_{h\to0}\frac{(27+27h+9h^2+h^3)-(3+h)-24}h[/tex]
[tex]f'(3)=\displaystyle\lim_{h\to0}\frac{26h+9h^2+h^3}h[/tex]
[tex]f'(3)=\displaystyle\lim_{h\to0}(26+9h+h^2)=\boxed{26}[/tex]
(b) The tangent line at x = 3 has equation
y - f (3) = f ' (3) (x - 3)
y - 24 = 26 (x - 3)
y = 26 x - 54
We also want to find any other tangent lines parallel to this one, which requires finding all x for which f '(x) = 26. We could use the same limit definition as in part (a), but to save time, we exploit the power rule to get
f '(x) = 3 x² - 1
Then solve for when this is equal to 26:
3 x² - 1 = 26 ==> x² = 9 ==> x = ±3
The other tangent line occurs at x = -3, for which we have f (-3) = -24, and so the equation for the tangent is
y - f (-3) = 26 (x - (-3))
y + 24 = 26 (x + 3)
y = 26 x + 54
Plz help this is a quick question
Answer:
No it is the ticked one........
Hope it helps.......
Help I’m stuck and confused
Answer:
-8
Step-by-step explanation:
A triangle is always 180 degrees
(btw I'm not sure if this is addition or multiplication so sorry if i'm wrong!)
65 + 40 = 105
180 - 105 = 75
75 - 83 = -8
Answer:
the angle itself is 75 degrees so x=-8
Step-by-step explanation:
4. A statistician working for the National Basketball Association supplies the television announcers with interesting statistics. At a certain point in the season, he discovered that in 375 games, 300 were won by the team that was winning the game at the end of the third quarter. The margin of error in a 90% confidence interval estimate of the true proportion of games won by the team leading at the end of the third quarter with the plus-4 adjustment applied is (Show work): (5)
Answer: 0.038
Step-by-step explanation:
Given: Total games : n= 375
Number of games won by the team that was winning the game at the end of the third quarter. = 300
The proportion (p) of the team that was winning the game at the end of the third quarter: [tex]p=\dfrac{300}{375}=0.8[/tex]
Critical z-value for 90% confidence: z* = 1.645
Margin of error =[tex]z^*\sqrt{\dfrac{(1-p)p}{n}}[/tex]
The margin of error in a 90% confidence interval estimate of p [tex]=1.645\sqrt{\dfrac{0.2\times0.8}{300}}\\= 1.645\times\sqrt{0.00053333}\\\\=1.645\times0.0231\\\\=0.0379995\approx$$0.038[/tex]
Hence, the required margin of error = 0.038
Find FH. please and thank you :)
Answer:
[tex]22[/tex]
Step-by-step explanation:
If FG= 8
and GH=14
G is a midpoint
To find FH you would add 8 and 14.
[tex]8 + 14 = 22[/tex]
Answer:
add it FH +GH
=8+14
=22 ans.....
Of the people who fished at Clearwater Park today, 48 had a fishing license, 32and did not. Of the people who fished at Mountain View Park today, 72 had a license, and 18 did not. (No one fished at both parks.)Suppose that one fisher from each park is chosen at random. What is the probability that the fisher chosen from Clearwater did not have a license and the fisher chosen from Mountain View had a license?
Answer:
The probability that the fisher chosen from Clearwater did not have a license and the fisher chosen from Mountain View had a license is 0.32.
Step-by-step explanation:
Denote the events as follows:
X = a fisher at Clearwater Park had a fishing license
Y = a fisher at Mountain View Park had a fishing license
The two events are independent.
The information provided is:
n (X) = 48
n (X') = 32
n (Y) = 72
n (Y') = 18
Then,
N (X) = n (X) + n (X')
= 48 + 32
= 80
N (Y) = n (Y) + n (Y')
= 72 + 18
= 90
Compute the probability that the fisher chosen from Clearwater did not have a license and the fisher chosen from Mountain View had a license as follows:
[tex]P(X'\cap Y)=P(X')\times P(Y)[/tex]
[tex]=\frac{n(X')}{N(X)}\times \frac{n(Y)}{N(Y)} \\\\=\frac{32}{80}\times\frac{72}{90}\\\\=0.32[/tex]
Thus, the probability that the fisher chosen from Clearwater did not have a license and the fisher chosen from Mountain View had a license is 0.32.
A store sells ice cream with assorted toppings. They charge $3.00 for an ice cream, plus 50 cents per ounce of toppings. If Elena’s ice cream cost $3.50 more than jada’s ice cream, how much more did Elena’s toppings weigh?
Answer:
1 ounce
Step-by-step explanation:
so basically 1 ounce per 50 cents
Customer bill is $333.00 20% from bill is?
Answer:
$16.65
Step-by-step explanation:
333.00 divided by 0.20
the measure of an angle is 126.6 what is the measure of its supplementary angle
Answer:
The answer is 53.4°Step-by-step explanation:
Let the measure of its supplementary angle be x
Since they are supplementary , it means that the sum of their angles add up to 180°.
To find x add up subtract 126.6 from 180
We have
x = 180 - 126.6
We have the final answer as
53.4°Hope this helps you
Read the situations below and determine which relationship is not functional.
Situation 1: a cell phone bill to the amount of minutes used
Situation 2: the perimeter of a square to the length of one of the sides of a square
Situation 3: the total amount of money charged monthly on credit cards to the number of credit cards owned
Answer:
Situation 3 is not functional
Step-by-step explanation:
Here, we want to determine if there exists a functional relationship between the properties in each situation.
For there to exist a functional relationship, then one of the factors in the situation must be dependent on the other factor in the situation.
Let us consider the situations individually now;
Situation 1
There exists a functional relationship here. This is because the higher the minutes used, the higher the cell phone bill and the lower the minutes used, the lower the cell phone bill. This is because there exists a fixed rate of charge per minute
Situation 2
There exists a functional relationship here too.
This is because, the we cannot find the perimeter of the square without knowing the measure of the sides of the square. That is why there is a mathematical formula that links the perimeter of the square to the sides of the square.
In a case where we have the perimeter as P and the sides as L
Then the functional equation linking both is;
P(l ) = 4 L
Situation 3;
There is no functional relationship here. The amount owed per each credit card is tied to the credit card in question.
There is no way the total amount owed by a person is distributed across the number of credit cards the person have. Each credit card has its own money charged on it monthly due to the activities on it which is independent on the activities of the other credit cards
y = -(x + 5)2-1
Find vertex
Answer:
The vertex is (-5, -1)
Step-by-step explanation:
Standard vertex form is a(x - b)^2 + c where (b, c) is the vertex.
A small school with 606060 total students records how many of their students attend school on each of the 180180180 days in a school year. The mean number of students in attendance daily is 555555 students and the standard deviation is 444 students. Suppose that we take random samples of 555 school days and calculate the mean number of students \bar x x ˉ x, with, \bar, on top in attendance on those days in each sample.
Answer: 180,842,239
Step-by-step explanation:
Answer:
55
1.8
Step-by-step explanation:
Khanacademy
The length of a rectangle is 2 times the width. If the perimeter is to be less than 96 meters. What are the possible
values for the width? (Use w as the width)
Preview
TIP
Enter your answer using inequality notation. Example: 3 <=w<4
Use or to combine intervals. Example: w< 2 or w >= 3
Enter all real numbers for solutions of that type
Enter each value as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 243,
5+4)
Enter DNE for an empty set. Use oo to enter Infinity.
Answer:
W>16
Step-by-step explanation:
The formula for calculating the perimeter of a rectangle:
P = 2L+2W
L is the length of the rectangle
W is the width of the rectangle:
Given
P = 96m
If the length of a rectangle is 2 times the width, then L = 2W
Substitute into the formula:
Since the perimeter is less than 96m
96 < 2(2W)+2W
96 < 4W+2W
96 < 6W
Divide both sides by 6:
96/6 < 6W/6
16 < W
W>16
Hence the possible values of the width are all values greater than 16.
HELP ME PLEASE 40 POINTS!!!!!!!
Answer:
The answer is The first one -10/27
Answer:
A
Step-by-step explanation:
f(x)=1/3(4-x)^2 ................
(01.04 MC)
What is the slope of the line which passes through (2,5) and (3, 6)? (5 points)
Answer:1
Step-by-step explanation:6-5/3-2=1/1
jessie worked four more hours than Ben. They worked a total of 25 hours. How many hours did each boy workz?
Answer:
jessie: 14.5
ben: 10.5
2+2=4 because 2 fingers and then another 2 fingers
Answer:
yes
Step-by-step explanation:
Answer:
yes? That's right. ummmm lol
Complete the sentence. |-0.05| =
Answer:
|0.05|
Step-by-step explanation:
no absolute value can be negative
Answer:
0.05
Step-by-step explanation:
The lines outside the number mean absolute value. The absolute value of a number is how far it is from 0, so it's always positive. Basically, you just swap the sign of whatever number you are looking at. In this case, absolute value of -0.05 would simply be 0.05. Hope this helped!
What does a temperature of what does a temperature of 9°C mean?
Choose the best answer.
✓ Choose...
The Celsius temperature is 9 degrees above zero.
The Celsius temperature is zero.
The Celsius temperature is 9 degrees below zero.
Answer:
I think it the first answer
Step-by-step explanation:
Im not positive but hope that right
Container A and container B have leaks. Container A has 800ml of water, and is leaking 6 ml per minute. Container B has1000 ml, and is leaking 10 ml per minute. How many minutes, m, will it take for the two containers to have the same amount of water?
Answer:
50 minutes
Step-by-step explanation:
First set up an inequality to find you answer like
800 - 6x = 1000 - 10x
then subtract 800 from both sides leaving you with
-6x = 200 - 10 x
Then add 10 x to both sides giving you
4x = 200
The simplify from here by dividing 200 by 4
200/4 = 50 giving you your answer
A man bought 500 mangoes and found 1/4 of them rotten .If he sold the rest of mangoes at 3.36 each making 12% profit ,what was the cost price of each mango?
Answer:
The cost price of each mango was $3
Step-by-step explanation:
The man bought 500 mangoes, but 1/4 of them were rotten. There were 1/4*500 = 125 rotten mangoes, thus the number of mangoes he sold is
500 - 125 = 375 mangoes
Selling them at $3.36 each, he had revenue of
375*3.36=$1,260
That amount includes the 12% profit, that is, it's 112% of the cost price, thus the cost price of all mangoes is
1,260 / 112 * 100 = $1,125
The price of each mango was $1,125 / 375 = $3
The cost price of each mango was $3
fill in the two blank boxes!!! help plzzz
sorry this is not math lol its science
HELP IM GIVING BRAINLIEST
Answer:
AB, BC, AC
Step-by-step explanation:
Hopefully I helped!! :)
8 groups of ___ hundredths is 0.32
Answer:
the answer is 0.4 The reason is because 0.4 x8=0.32
Step-by-step explanation:
Slope -2/3 through (-9,10)
Answer:
y = − 2 /3 x + 4
Step-by-step explanation:
Answer: y=-2/3x + 4
Step-by-step explanation:
The Washington monument is 555 feet 5 1/8 inches tall and weighs 90,854 tons. The monument is topped by an aluminum square pyramid. The sides of the pyramid’s base measure 5.6 inches, and the pyramid is 8.9 inches tall. Estimate the slope that a face of the pyramid makes with its base.
Answer:
3.2
Step-by-step explanation:
Imagine a straight line from the top of the pyramid to the base, the point where the line will meet the base will be half the side of the pyramid. This will form a right angles triangle.
Slope is given by
[tex]\text{Slope}=\dfrac{\Delta y}{\Delta x}\\\Rightarrow \text{Slope}=\dfrac{8.9}{\dfrac{5.6}{2}}=3.17857\\\Rightarrow \text{Slope}\approx3.2[/tex]
The slope of the face of the pyramid is 3.2
Please help!!!!!! If the measure of angle 8 is 35 what is the measure of angle 4?
Answer:
35
Step-by-step explanation:
Comman knowlege. Also there is a fancy name for them because thay are the same way... Corresponding Angles
Answer:
35 degrees
Step-by-step explanation:
It is congruent to 8 and lined up so it is also 35 degrees.
A gallon of gas costs an average of two dollars is Betty spends $144 a month on gas determine how many gallons of gas she uses a month
Answer:
she uses 72 gallons
Step-by-step explanation:
just do 144/2 and the answer is 72
if you wanna check your answer just do 72x2 and it equals 144
The coordinate grid shows the graph of four equations:
Which set of equations has (1, 2) as its solution?
A and D
C and D
A and C
B and D
Answer:
its A and C
Step-by-step explanation:
hope this helps and mark me brainliest