The graph below shows a company's profit f(x), in dollars, depending on the price of pencils x, in dollars, sold by the company.
Part A: What do the x-intercepts and maximum value of the graph represent? What are the intervals where the function is increasing and decreasing, and what do they represent about the sale and profit? (4 points)
Part B: What is an approximate average rate of change of the graph from x = 2 to x = 5, and what does this rate represent? (3 points)
Part C: Describe the constraints of the domain. (3 points)
Answer:
Step-by-step explanation:
Part A
The x-intercept are the values of the variable "x" for which the value of the function, f(x) is zero (f(x) = 0)
The given parameters are;
The values of the function, f(x) = The company's profit
The values of the independent variable, "x" = The price of erasers
Therefore, at the x-intercept, where the values of the variable "x" are 0 and 8, the profit of the company, (f(x)) is 0 (the company does not make any profit)
2) The maximum value, which is the highest point of the graph with coordinate (4, 270), gives the company's maximum profit, f(x) = $270, and the price of the eraser, x-value, at which the company makes maximum profit which is at the price of an eraser, x = $4
3) The intervals where the function is increasing is 0 ≤ x ≤ 4
At the interval where the function is increasing, the sale price is increasing and the profits are increasing
The intervals where the function is decreasing is 4 ≤ x ≤ 8
At the interval where the function is decreasing, the sale price is increasing and the profits are decreasing
Part B
The appropriate average rate of change of the graph from x = 1 to x = 4 where f(x) = 120 and 270 respectively is given as follows
Rate of change of the graph from x = 1 to x = 4 is (270 -120)/(4 - 1) = 50
The average rate of change of the graph represents that the as the price of the eraser increases by $1.00 the profits increases by $50.00
THIS WAS NOT MY OWN ANSWER, PLEASE LET oeerivona TAKE THE POINTS!!
Can someone please do these three and number them? -Numbers: 10,11,12-
Answer:
10. Option: c11. Option: a12. Option: a4, 1 and 0, -4 on a graph
Answer:
Hope this will help.
Engineers are designing a large elevator that will accommodate 44 people. The maximum weight the elevator can hold safely is 8228 pounds. According to the National Health Statistics Reports, the weights of adult U.S. men have mean 186 pounds and standard deviation 60 pounds, and the weights of adult U.S. women have mean 157 pounds and standard deviation 69 pounds.
a. If 44 people are on the elevator, and their total weight is 8228 pounds, what is their average weight?
b. If a random sample of 44 adult men ride the elevator, what is the probability that the maximum safe weight will be exceeded?
c. If a random sample of 44 adult women ride the elevator, what is the probability that the maximum safe weight will be exceeded?
Answer:
a) Their average weight is of 187 pounds.
b) 0.4562 = 45.62% probability that the maximum safe weight will be exceeded.
c) 0.002 = 0.2% probability that the maximum safe weight will be exceeded
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
a. If 44 people are on the elevator, and their total weight is 8228 pounds, what is their average weight?
8228/44 = 187
Their average weight is of 187 pounds.
b. If a random sample of 44 adult men ride the elevator, what is the probability that the maximum safe weight will be exceeded?
For men, we have that [tex]\mu = 186, \sigma = 60[/tex]
Sample of 44 means that [tex]n = 44, s = \frac{60}{\sqrt{44}}[/tex]
This probability is 1 subtracted by the p-value of Z when X = 187. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{187 - 186}{\frac{60}{\sqrt{44}}}[/tex]
[tex]Z = 0.11[/tex]
[tex]Z = 0.11[/tex] has a p-value of 0.5438.
1 - 0.5438 = 0.4562
0.4562 = 45.62% probability that the maximum safe weight will be exceeded.
c. If a random sample of 44 adult women ride the elevator, what is the probability that the maximum safe weight will be exceeded?
For women, we have that [tex]\mu = 157, \sigma = 69[/tex]
Sample of 44 means that [tex]n = 44, s = \frac{69}{\sqrt{44}}[/tex]
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{187 - 157}{\frac{69}{\sqrt{44}}}[/tex]
[tex]Z = 2.88[/tex]
[tex]Z = 2.88[/tex] has a p-value of 0.998.
1 - 0.998 = 0.002.
0.002 = 0.2% probability that the maximum safe weight will be exceeded
Someone help please
66 because you have to solve the problem next time
Under which transformation can the image be a different size than the original
figure?
A. translation
B. rotation
C. dilation
D. reflection
C. Dilation.
Dilation can resize the image.
Translation will shift the imagine's position but won't change its actual size.
Rotation will mangle with image's orientation but also won't change its size.
Reflection is just a type of rotation which as established, also won't change its size.
Hope this helps.
A television stand at Wiles' Discount Mart is $187, and the sales tax is 6%. What is the amount of tax to be paid for the TV?
Answer:
$11.22
Step-by-step explanation:
100% = 187
1% = 187/100 = $1.87
6% = 1%×6 = 1.87×6 = $11.22
Answer:
In this case, you need to calculate the 6% of the price, which is 187 $.
We only need to multiply the price (187) by the percentage (6%):
187 * 0.06 = 11.22
So the tax would be $11.22
In a recent health survey, 333 adult respondents reported a history of diabetes out of 3573 respondents. What is the critical value for a 90% confidence interval of the proportion of respondents who reported a history of diabetes
Answer:
The critical value for the 90% confidence interval is [tex]Z_c = 1.645[/tex].
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
The critical value for the 90% confidence interval is [tex]Z_c = 1.645[/tex].
I need help.
You are interested in finding a 95% confidence interval for the average commute that non-residential students have to their college. The data below show the number of commute miles for 12 randomly selected non-residential college students. Round answers to 3 decimal places where possible.
Answer:
(11.847 ; 15.813)
Step-by-step explanation:
We are given 12 samples which are :
8, 20, 20, 11, 18, 12, 6, 5, 7, 22, 12, 25
We use a T-distribution to find the confidence interval since the sample size. is small, n < 30
Using a calculator :
The sample mean, xbar = 13.83
Sample standard deviation, s = 6.87
The confidence interval, C.I
C.I = xbar ± Tcritical * s/√n)
Tcritical at 95%, df = n - 1, 12 - 1 = 11
Tcritical(0.05, 11) = 2.20
Hence,
C.I = 13.83 ± 2.20(6.87/√12)
C.I = 13.83 ± 1.9831981
C. I = (13.83 - 1.983 ; 13.83 + 1.983)
C. I = (11.847 ; 15.813)
Which ratio expresses the scale used to create this drawing?
1 square=10 yards
Answer:
option B
Step-by-step explanation:
option B
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Let sin A = -5/13 with 270 degrees < A < 360 degrees and cos B = -15/17 with 90 degrees < B < 180 degrees find sin (A+B)
Answer:
Step-by-step explanation:
Sudhanshu is solving a system representing a race between two remote control cars. The variable x is defined as time in seconds, and y is the distance in meters from the starting line.
Red car: y = 3 x + 5. Blue car: y = 4 x.
How many solutions should Sudhanshu find?
zero
one
two
infinite
Answer:
One
General Formulas and Concepts:
Algebra I
Slope-Intercept Form: y = mx + b
m - slope b - y-interceptSolving systems of equations
Step-by-step explanation:
Step 1: Define
Identify systems
y = 3x + 5
y = 4x
Step 2: Solve
If we compare the 2 lines, we can see that they both have a different slope. If they had the same slope but different y-intercepts, then they would be parallel and have no solution. We can also see that the 2 lines aren't the same. If they were, then they would have infinite solutions.
∴ the systems should have only one solution.
Answer:
B
Step-by-step explanation:
Find the length of the missing side. triangle with an 8 inch side and 12 inch side with a right angle 8.9 in. 104 in. 4 in 14.4 in
Given:
In a triangle, length of one side is 8 inches and length of another side is 12 inches, and an angle is a right angle.
To find:
The length of the missing side.
Solution:
In a right angle triangle,
[tex]Hypotenuse^2=Perpendicular^2+Base^2[/tex]
Suppose the measures of sides adjacent to the right angle are 8 inches and 12 inches.
Substituting Perpendicular = 8 inches and Base = 12 inches, we get
[tex]Hypotenuse^2=8^2+12^2[/tex]
[tex]Hypotenuse^2=64+144[/tex]
[tex]Hypotenuse^2=208[/tex]
Taking square root on both sides, we get
[tex]Hypotenuse=\sqrt{208}[/tex]
[tex]Hypotenuse=14.422205[/tex]
[tex]Hypotenuse\approx 14.4[/tex]
The length of the missing side is 14.4 inches. Therefore, the correct option is D.
F(x) = 4x^3 + 7x^2-2x-1
G(x) = 4x-2
Find (f-g)(x)
Halp me please. This questions is killing me. I need the answer. Solve $3a + 4b = a - 8b + 24$ for $a$ in terms of $b$.
Answer:
a=12-6b
Step-by-step explanation:
move b and a to their respective sides, getting a = -6b+12
tada :)
As per linear equation, the value of 'a' in terms of 'b' will be
a = 12 - 6b.
What is a linear equation?A linear equation is an equation that has one or multiple variables with the highest power of the variable is 1.
Given, (3a + 4b) = (a - 8b + 24)
⇒ 3a - a = - 8b + 24 - 4b
⇒ 2a = - 12b + 24
⇒ a = (- 12b + 24)/2
⇒ a = - 6b + 12
⇒ a = 12 - 6b
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A new restaurant sells cheeseburgers for 6$, french fries for 3$, and salads for 8$ On opening night, the restaurant sold items and made 1070$. They sold 4 times as many fries as salads. How many cheeseburgers were sold?
Answer:
25 cheeseburger
Step-by-step explanation:
I checked and get that 4 times fries as many as salad means that fries = 4 times Salad.
Brainliest please~
25 cheeseburgers were sold.
What is algebraic expression?In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions.
Let cheeseburger be x
Price of x = 6
Let French Fries be y
Price of y = 3
Let salads be z
Price of z=8
x+ y+ z =220
6x + 3y + 8z = 1070
4 y = z 4 times as many as
= 4 times - Fries is more than Salad
Substitute 3 in 1
x + 4 z + z =220
x+5z =220
Substitute 3 in 2
6x + 12z +8z = 1070
6x + 20z = 1070
3x + 10z - 535
From 4: x=220-5z
Substitute into 3 (220-5z) +10z = 535
660 - 15z+10z=535
- 5z = - 125
z = 25
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I need to know the answer and the work it asks for
Answer:
b 25x6 = 150
25 decreases every month so
150 decreses every 6 month
800-150
650 are the bees remaining after 6 month
21. Gabe Amodeo, a nuclear physicist, needs 80 liters of a 30% acid solution. He currently has a 20% solution and a 60%
solution. How many liters of each does he need make the needed 80 liters of 30% acid solution?
Gabe needs
liters of the 20% solution.
He also needs
liters of the 60% solution.
Let x be the amount (in liters) of 20% solution that Gabe uses, and y the amount (also in L) of the 60% solution.
He needs 80 L of 30% solution, so that
x + y = 80
0.20x + 0.60y = 0.30 (80) = 24
Solve for y in terms of x :
y = 80 - x
Substitute this into the second equation and solve for x :
0.20x + 0.60 (80 - x) = 24
0.20x + 48 - 0.60x = 24
24 = 0.40x
x = 60
Solve for y :
y = 80 - 60
y = 20
Please Help! What's the rule that represents the sequence 13, 27, 41, 55, ...?
Answer:
B
Step-by-step explanation:
an = a+(n-1)d
an=13+(n-1)14
d=14
Find X?
please help?
Look at one side of the triangle. It forms a right triangle with 45 degree angles.
A 45 degree triangle the base and height are the same, so the height would also be 26.
The hypotenuse(x) of a 45 degree right triangle is the side length time the sqrt(2)
The answer is: 26 sqrt(2)
The length of a rectangle is 7cm less than 3 times it's width. It's area is 20 square cm. Find the dimensions of the rectangle
Answer:
4 cm by 5 cm (4 x 5)
Step-by-step explanation:
The area of a rectangle with length [tex]l[/tex] and width [tex]w[/tex] is given by [tex]A=lw[/tex]. Since the length of the rectangle is 7 less than 3 times its width, we can write the length as [tex]3w-7[/tex]. Therefore, substitute [tex]l=3w-7[/tex] into [tex]A=lw[/tex]:
[tex]A=lw,\\20=(3w-7)w[/tex]
Distribute:
[tex]20=3w^2-7w[/tex]
Subtract 20 from both sides:
[tex]3w^2-7w-20=0[/tex]
Factor:
[tex](w-4)(3w+5)=0,\\\begin{cases}w-4=0, w=\boxed{4},\\3w+5=0, 3w=-5, w=\boxed{-\frac{5}{3}}\end{cases}[/tex]
Since [tex]w=-\frac{5}{3}[/tex] is extraneous (our dimensions cannot be negative), our answer is [tex]w=4[/tex]. Thus, the length must be [tex]20=4l, l=\frac{20}{4}=\boxed{5}[/tex] and the dimension of the rectangle are 4 cm by 5 cm (4 x 5).
Anthony steps on a bathroom scale that records his weight at 195 pounds. He immediately steps back onto the same scale, which records his weight at 205 pounds. It is MOST accurate to describe these scales as:
Answer:
Moving upwards with an acceleration.
Step-by-step explanation:
weight of the person = 195 pounds
Apparent weight = 205 pounds
As the weight increases so the scale is moving upwards with some acceleration.
The scale is in elevator which is moving upwards.
James, Aimee and Zack have
weighed their suitcases. Each
weighs a prime number of
kilograms and the total weight
is 40kg.
an
What's the difference between
the lightest and heaviest
suitcase?
Answer:
29Kg
Step-by-step explanation:
P1=2Kg
P2=7Kg
P3=31Kg
P3-P1=29Kg
To find P1, P2 and P3 I started assigning the first prime number, 2, to P1 and tried to assign prime numbers to P2 and P3 so that the sum was 40, increasing them at each step.
I was lucky and I got the result after few steps :-)
Matthew Travels 42/50 Meters In 26/30 Minutes. Find The Speed of Mathew In Meters Per Second.
Answer:
Matthew travels 0.0161 meters per second.
Step-by-step explanation:
Given that Matthew travels 42/50 meters In 26/30 minutes, to find the speed of Mathew in meters per second the following calculation must be performed:
42/50 = 0.84
26/30 = 0.86
0.86 x 60 = 52
0.84 meters in 52 seconds
0.84 / 52 = 0.01615
Therefore, Matthew travels 0.0161 meters per second.
(c³d)a(cd⁷)a
Simplify
Answer:
= c^4 d^8 a^2
Step-by-step explanation:
Apply exponent rule: aa= a^2
= c^3 da^2 cd^7
= c^4 da^2 d^7
= c^4 d^8 a^2
SAT scores are normally distributed with a mean of 1,500 and a standard deviation of 300. An administrator at a college is interested in estimating the average SAT score of first-year students. If the administrator would like to limit the margin of error of the 82% confidence interval to 25 points, how many students should the administrator sample
Answer:
The appropriate solution is "259".
Step-by-step explanation:
According to the question,
[tex]\sigma = 300[/tex]
[tex]M.E=25[/tex]
At 82% CI,
[tex]\alpha = 0.18[/tex]
Critical value,
[tex]Z_c=1.341[/tex]
Now,
The sample size will be:
⇒ [tex]n=(Z_c\times \frac{\sigma}{E} )^2[/tex]
By substituting the values, we get
[tex]=(1.341\times \frac{300}{25} )^2[/tex]
[tex]=(1.341\times 12)^2[/tex]
[tex]=259[/tex]
PLEASE i need the answers!!!!!!!!!
I have no time please if you know the answer please tell MEEE!!!!!!!!!!!
Answer:
5x^2(2-3x)
(n+4)(x+y)
Step-by-step explanation:
...............................................................
5. A Ferris wheel at an amusement park measures 16m in diameter. It makes 3 rotations
every minute. The bottom of the Ferris wheel is 1m above the ground. Riders board the
Ferris wheel at the minimum point.
a) Determine the equation that models Emily's height (m) with respect to time (in seconds)
above ground. [3A]
b) A 12m tree stands near the Ferris wheel. For how long (in seconds) is Emily higher than
the tree during the first rotation? Round to 2 decimal places. [4A]
Following are the responses to the given points:
For point a:
[tex]Diameter\ (d)= 16\ m\\\\[/tex]
Calculating the 3 rotations for every minute:
Calculating time for completing 1 rotation:
[tex]1\ rotation=\frac{60}{3}= 20\ second\\\\period=20 \ second\\\\[/tex]
The standard form of the equation of the sine and cosine function is:
[tex]y=A \sin \{ B(x-c)\} +D\\\\y=A \cos \{ B(x-c)\} +D\\\\[/tex]
Calculating the Amplitue:
[tex]A=\frac{max-min}{2}=\frac{17-1}{2}=\frac{16}{2}=8\\\\Period=\frac{2\pi}{B}\\\\20=\frac{2\pi}{B}\\\\B=\frac{2\pi}{20}\\\\B=\frac{\pi}{10}\\\\[/tex]
Calculating the phase shift:
for [tex]\sin[/tex] function: [tex]c=5[/tex]
for [tex]\cos[/tex] function: [tex]c=10[/tex]
Calculating the vertical shift:
[tex]\to D=\frac{max+ min }{2}=\frac{17+ 1}{2}=\frac{18}{2}=9\\\\y=8 \sin \{ \frac{\pi}{10}(t-5)\} +9\\\\y=8 \cos \{ \frac{\pi}{10}(t-10)\} +9\\\\[/tex]
For point b:
[tex]y> 12\ m\\\\12=8 \sin \{ \frac{\pi}{10}(t-5)\} +9\\\\12-9=8 \sin \{ \frac{\pi}{10}(t-5)\} \\\\3=8 \sin \{ \frac{\pi}{10}(t-5)\} \\\\\frac{3}{8}=\sin \{ \frac{\pi}{10}(t-5)\} \\\\\sin^{-1}\frac{3}{8}=\frac{\pi}{10}(t-5) \\\\\frac{\pi}{10} (0.38439677)=(t-5) \\\\1.22357+5=t \\\\t=6.22357\ second\\\\t=6.22\ second\\\\\sin^{-1}\frac{3}{8}=\frac{\pi}{10}(t-5) \\\\\frac{\pi}{10} (2.7571961)=(t-5) \\\\t=8.7764+5\\\\t=13.78\ second\\\\t_2-t_1=13.7764-6.22357= 7.55283\approx 7.55\ second \\\\[/tex]
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Refer to the values described below, then identify which of the following is most appropriate: discrete random variable, a. Responses to the survey question "How many pets do you have?" b. Exact heights of the next 100 babies born in a region c. Responses to the survey question "What is your eye color?" d. Exact foot length of humans e. Number of people in families a. Since the outcomes are b. Since the outcomes are countable, this is this is a discrete random variable. random variable.
Answer:
Exact heights of the next 100 babies born in a region.
Step-by-step explanation:
A discrete random variable involves two key factors ; discrete and randomness ; Hence, a discrete random variable should have a finite or countable Number of outputs or values. It should also stem from a random procedure. Here, the height of the next hundred babies is a random procedure as the next 100 babies in the region are unknown until Given birth too and as such all pregnant women have the chance of having their babies among. Since, we are dealing with exact height values which are countable (100), then we this is a discrete random variable.
