Answer:
Mean of sampling distribution = 50
Standard deviation of sampling distribution, = 0.625
Step-by-step explanation:
Given :
Mean, μ = 50
Standard deviation, σ = 5
Sample size, n = 64
The mean of sampling distribution, μxbar = population mean, μ
μxbar = μ
According to the central limit theorem, the sampling distribution converges to the population mean as the sample size increases, hence, , μxbar = μ = 50
Standard deviation of sampling distribution, σxbar = σ/√n
σxbar = 5/√64 = 5 / 8 = 0.625
Dylan has a coworker who is always showing up late and then not finishing his work on time. It's frustrating the other members of the team. What can he do that might help the situation? a) Complain about the coworker to other team members O b) Ask his coworker if he understands his job responsibilities c) Tell his boss that the coworker is slacking off O d) Complete his coworker's work for him
The function f(x) = −x2 + 18x − 72 models the daily profit, in dollars, a gym makes for selling memberships, where x is the number of memberships sold, and f(x) is the amount of profit.
Part A: Determine the vertex. What does this calculation mean in the context of the problem? (5 points)
Part B: Determine the x-intercepts. What do these values mean in the context of the problem? (5 points)
(10 points)
Answer:
Step-by-step explanation:
The way to do this so as to streamline both the vertex and finding the zeros is to complete the square. That method will provide us with the vertex, and then we can continue on to factor from that form to find the zeros. Completing the square requires us to set the quadratic equal to 0 then move over the constant, giving us
[tex]-x^2+18x=72[/tex] The leading coefficient HAS to be a positive 1; ours is negative 1 so we factor out the negative to get:
[tex]-(x^2-18x)=72[/tex] Now we're ready to complete the square.
Take half the linear term, square it, and add it to both sides. Our linear term is 18 (from -18x; don't worry about the negative because squaring it makes it positive anyway). Half of 18 is 9, and 9 squared is 81.
BUT on the left we have that -1 sitting out front that refuses to be ignored. What we actually added on to the left side, inside the parenthesis, is -1(81) which is -81. -81 is what we add to the right since that turns out to be what we added to the left:
[tex]-(x^2-18x+81)=72-81[/tex] and we clean that up.
The reason we complete the square is because when we simplify the left side, we end up with a perfect square binomial found from taking the square root of x-squared, the first sign we come to, then the square root of 81:
[tex]-(x-9)^2=-9[/tex]. Move the constant back over to get
[tex]-(x-9)^2+9=y[/tex] telling us that the vertex is (9, 9). In the context of the problem that means that the gym sells on average 9 memberships a day and the profit it makes on average per day is $9.
To factor, we will go back one step to
[tex]-(x-9)^2=-9[/tex] and begin by dividing both sides by -1 to get
[tex](x-9)^2=9[/tex] and undo the squaring by taking the square root of both sides to get
x - 9 = ±3 so
x = 9 + 3 and
x = 9 - 3 so
x = 6 and 12
Those are the zeros. This means that if they sell either 6 or 12 memberships they have a 0 profit. That may sound strange, but in business it does often work like that...selling too many of something makes your company lose money (this is often due to the cost required by you to produce or manufacture the product).
Find inverse of f(x)=(x+4)^2
Answer:
f⁻¹(x) = -4 + √x
Step-by-step explanation:
Switch the positions of x and y then solve for x.
[tex]f(x)=(x+4)^2\\x=(y+4)^2\\\sqrt{x} =y+4\\\sqrt{x} -4=y[/tex]
Question two
The lengths of the sides of a triangle are in the ratio 2:3:4. The shortest side is 14cm long.
Find the lengths of the other two sides
Answer:
14 and 21 and 28
Step-by-step explanation:
2:3:4.
The shortest side is 14
14/2 = 7
Multiply each side by 7
2*7:3*7:4*7
14 : 21 : 28
Use the image below, answer the following questions. Be sure to answer all 3 questions in order.
Answer:
a. Yes
b. VT
c. Segment RQ
Step-by-step explanation:
a. Find the slope of RS and UV
Slope = rise/run
Slope of RS = rise/run = RQ/QS
Slope of RS = 6/6
Slope of RS = 1
Slope of UV = rise/run = UT/TV
Slope of UV = 3/3
Slope of UV = 1
Thus, TS and UV have equivalent slopes
b. Slope of VT:
VT is an horizontal line.
It has no rise. But only run.
Therefore, it's rise = 0, while run = VT = 3
Slope of VT = rise/run = 0/3
Slope of VT = 0
c. Vertical lines have undefined slope.
Segment RQ is vertical line and therefore has an undefined slope.
RQ has rise but no run.
Thus:
Rise = 6
Run = 0
Slope of Segment RQ = 6/0 (this can't divide)
Therefore, slope of Segment RQ is undefined.
Complete the Similarity statement below only if the triangles are similar.
HELP ME OUT !!! im stressing out keep getting it wrong
instructions find HM = 25 and mhm = 66 , find x and y
Answer:
x=24, y = 33/360 π×24^2/(sin^2(33° (degrees)))
Step-by-step explanation:
notice that x = MK = HM = 24.
Let the center of the circle be C.
Also, notice the radius of the circle can be expressed as the hypotenuse of HMC. Using some trig, we figure out that the radius is 24/sin(33 degrees).
Using the radius of the circle, we can figure out the circumference. The circumference is pi*r^2=(24/sin(33 degrees))^2*pi=pi*24^2/(sin(33 degrees)^2)
Lastly, notice that y = 33/360*circumference = 33/360 π×24^2/(sin^2(33° (degrees)))
hopefully this helped
A few more problems and then I’m done
Answer:
((c)).g(x) = 3 × 2^x +2..
100 divided by 200-3+1000=
Answer:
997.5 is the answer to your question..
Expand and simplify the following expressions. a. (2 − 3)( − 6)
Answer:
your answer should be six I hope this help
Answer:
the should be 6
Step-by-step explanation:
(2-3)(-6)
-12+18
=6
Based on the Nielsen ratings, the local CBS affiliate claims its 11:00 PM newscast reaches 41% of the viewing audience in the area. In a survey of 100 viewers, 36% indicated that they watch the late evening news on this local CBS station.Reference: 10_02What is your decision if the calculated value of z is -1.02 and the
Answer:
at 15.39% that should not be sufficient to reject the Null
= "Fail to reject the Null hypothesis"
Step-by-step explanation:
z = -1.02 (L)0.15386 (R)0.84614
84.61% / 15.39%
Six sophomores and 14 freshmen compete
Answer:
(6C1)(5C1)/20C2
Step-by-step explanation:
Was right on egde
Pippa had 35 stickers.
She gave an equal number of stickers to 8 friends.
She gave each friend as many stickers as possible and kept the rest for herself.
How many stickers did Pippa keep for herself?
What is the misconception if a student selects D) 27?
A)3
B)4
C)11
D) 27
Answer:
A) 3
Pippa kept 3 stickers for herself
Answer to question 2:
The misconception of if a student selects D) 27 is that instead of dividing to find out how many stickers Pippa kept for herself, the student subtracted. They subtracted instead of dividing.
Step-by-step explanation:
It said that Pippa gave each of her friends an EQUAL number of stickers and AS MANY STICKERS AS POSSIBLE. This tells us that to find our answer we need to divide and what ever the remainder is, is how many stickers Pippa kept for herself.
(You will kind of need to do long division for this)
35 ÷ 8 = 4
8 x 4 = 32
35 - 32 = 3
Pippa will give each of her friends 4 stickers and will keep 3 for herself.
Step-by-step explanation for question 2:
35 stickers - 8 friends = 27
D) 27 is the wrong answer to question 1/part 1
I hope this helped! c:
Near the beginning of Lesson 5.3, a strategy for factoring trinomials of the form x^2+ bx+c was
developed by exploring the product of the binomials (x+p) and (x+q).
Explain how the development of this factoring strategy is an example of working backwards
to solve a problem.
Answer:
Step-by-step explanation:
there are function that "invert" each other..
subtraction inverts addition...
3+2 = 5 ... 5-2 = 3
division inverts multiplication
5*2 = 10 ... 10/2 = 5
Using that concept, "factoring" is basically the inverse of multiplication
3x^2 + 9x can be factored to 3x(x+3)
if you multiply that out it reverts back to the original equation
so x^2 + 5x + 6 factors to (x+3)(x+2)
if you multiply that out (foil it)
you get x^2 + 5x + 6
I WILL GIVE BRAINLEST FAST PLEASE ANSWER THE QUESTION IN THE IMAGE
Answer:
Cannot be determined
Step-by-step explanation:
We only know one angle and we could only compare one set of sides.
We do not have enough information to determine if the triangles are similar
Can some please help please thank you
Answer:
D. ( f + g)(x) = 2x^3 + 3x^2 - 5x - 3
Rewrite the polynomial in the form ax+by+c and then identify the values of a, b, and c.
x -- 1 -- 2y
Answer:
a=1, b=-2,c=-1
Step-by-step explanation:
1*(x)+(-2)*y+(-1)*1. a=1, b=-2,c=-1
Point A lies outside of plane P. How many planes can be drawn that pass through point A?
A. 0
B. an infinite number
C. 2
D. 1
Answer:
D.
Step-by-step explanation:
.
The number of planes that can be drawn that pass through point A is 1.
How to estimate the number of planes that can be drawn that pass through point A?
A perpendicular line creates an angle of 90° with a line or a plane. If a line exists to be drawn from a point to a line or a plane it can only be one. In this case, a line exists to be drawn through a point A to a plane P. If the line stands to be perpendicular, then it exists only one.
Therefore, the correct answer is option D. 1.
To learn more about points on a plane refer to:
https://brainly.com/question/10680920
#SPJ2
Bryce grew 3 1/2 inches each year for the past 4 years. How many inches total has Bryce grown in the past 4 years?
Answer:
14
Step-by-step explanation:
3 1/2 multiply by 4 equals 14
I really need the help please and thank you
Asnwer: C
-------------------------------------
Một miếng đất hình chữ nhật có chu vi 80 mét.Nếu kéo dài thêm 8 mét nữa thì diện tích tăng thêm là 72 mét vuông.Tính chiều dài và chiều rộng hình chữ nhật ban đầu ?
Answer:
Step-by-step explanation:
(D+R) = 80:2 = 40
D = 40-R
(D+8) * R = 72X
Thay D=40-R
(40-R+8)*R = 72X
R=1.55, D=38.45
Sam is five years old his brother Tom is three times as old as Sam when sam is 20 how old will Tom be?
Answer:
30
Step-by-step explanation:
5 x 3 = 15
15 - 5 = 10
20 + 10 = 30
Slope 0; through (-5, -1)
Answer:
y = -1
Step-by-step explanation:
Let f(x, y) = 2xy − 3xy + y + 1. Find the derivative of f with respect to y.
Answer:
2x-3x+1
Step-by-step explanation:
f'(x,y)=2x-3x+1
Suppose Event A is taking 15 or more minutes to get to work tomorrow and Event B is taking less than 15 minutes to get to work tomorrow. Events A and B are said to be complementary events.
a. True
b. False
Answer:
Hence the answer is TRUE.
Step-by-step explanation:
If event A is taking 15 or more minutes to urge to figure tomorrow and event B is taking but a quarter-hour to urge to figure tomorrow, then events A and B must be complimentary events. this is often because the occurring of 1 is going to be precisely the opposite of the occurring of the opposite event and that they cannot occur simultaneously. In other words, events A and B are mutually exclusive and exhaustive.
Mathematically,
P(A) + P(B) = 1.
At a restaurant, the bill comes to $55. You decide to leave a 12
%
tip. How much did you leave for the tip?
Answer:
$6.60
Step-by-step explanation:
12% = 0.12
12% of $55 = 0.12 x 55
=6.6
So, $6.60
A motorboat travels 104 kilometers in 4 hours going upstream. It travels 200 kilometers going downstream in the same amount of time. What is the rate of the boat in still water and what is the rate of the current?
[tex] \Large \mathbb{SOLUTION:} [/tex]
[tex] \begin{array}{l} \text{Let }r\text{ be the rate of the boat in still water and} \\ c\text{ be the rate of the current.} \\ \\ \text{So } \\ \begin{aligned} \quad&\bullet\:\text{Rate Upstream}= r - c \\ &\bullet\:\text{Rate Downstream}= r - c\end{aligned} \\ \\ \text{We know that }\text{Rate} = \dfrac{\text{Distance}}{\text{Time}}. \end{array} [/tex]
[tex] \begin{array}{l} \bold{Equations:} \\ \\ \begin{aligned} &\quad\quad \quad r - c = \dfrac{104}{4} = 26\quad (1) \\ \\ & \quad \quad \quad r + c = \dfrac{200}{4} = 50\quad (2)\\ \\ & \text{Adding (1) and (2), we get} \\ \\ &\quad\quad 2r = 76 \implies \boxed{r = 38\ \text{kph}} \\ \\ &\text{Using (2), it follows that} \\ \\ & \quad \quad c = 50 - r \implies \boxed{c = 12\ \text{kph}} \end{aligned} \end{array} [/tex]
What is the slope of a line that is perpendicular to the line whose equation is ax+by=c?
A. c/b
B. b/a
C. −b/a
D. a/b
Answer:
b/a
Step-by-step explanation:
ax+by=c
To find the slope solve for y
by = -ax+c
Divide by b
y = -a/b x + c/b
The slope intercept form is y = mx+b where m is the slope
The slope is -a/b
A perpendicular line has a slope that is the negative reciprocal
-1/ (-a/b)
-1 * -b/a
b/a
Solve for x the find the measure of A
Answer:
84°
Step-by-step explanation:
the total angle in a straight line sum up to 180°
Complete the table. Round your entries to the
nearest thousandth.
a
b
C
dz
ex
ASAP
a=2,5937
b=2,7048
c=2,7181
d=2,7183
e=2,7183
