Answer:
take your time and always ask for help when needed
Step-by-step explanation:
A pizza chain monitors the total weight of pepperoni that goes on its deluxe pepperoni pizzas to make sure customers are satisfied and product isn't being wasted. Suppose that for pizzas in this population, these weights are strongly skewed to the left with a mean of 250 g and a standard deviation of 8 g. Management takes a random sample of 64 of these pizzas and calculates the mean weight of the pepperoni on the pizzas. Assume that the pizzas in the sample are independent.
What is the probability that the mean weight of the pepperoni from the sample of 64 pizzas LaTeX: \bar x is within 1 g of the true mean?
Answer:
68.26% probability that the mean weight of the pepperoni from the sample of 64 pizzas is within 1 g of the true mean.
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 normally distributed samples are solved using the z-score formula.
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.
Central Limit Theorem
The Central Limit Theorem estabilishes 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.
In this question, we have that:
[tex]\mu = 250, \sigma = 8, n = 64, s = \frac{8}{\sqrt{64}} = 1[/tex]
What is the probability that the mean weight of the pepperoni from the sample of 64 pizzas is within 1 g of the true mean?
This is the pvalue of Z when X = 64 + 1 = 65 subtracted by the pvalue of Z when X = 64 - 1 = 63. So
X = 65
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{65 - 64}{1}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a pvalue of 0.8413.
X = 63
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{63 - 64}{1}[/tex]
[tex]Z = -1[/tex]
[tex]Z = -1[/tex] has a pvalue of 0.1587
0.8413 - 0.1587 = 0.6826
68.26% probability that the mean weight of the pepperoni from the sample of 64 pizzas is within 1 g of the true mean.
(HALP PLS WILL 100% MARK BRAINLIEST!) Sage has $26 and wants to download some songs from a music
Web site. Each song costs $1.79 to download. By rounding the
cost of the songs up to the nearest whole dollar, estimate the
greatest number of songs she can download.
A) 11
B) 13
C) 15
D) 17
Answer:
≈ 13Step-by-step explanation:
First ,we round 1.79 to the nearest whole dollar:
since 7 ≥ 5 then 1.79 rounded to the nearest whole dollar is 2
now ,we can estimate the greatest number she can download:
26/2 = 13
Is the integral ſ A. dr path independent if A = (2x - y)i + (x + y)j?
Evaluate A dr around a unit circle centered at the origin. What is t
value of the integral if we take a clockwise direction?
The integral is path-independent if we can find a scalar function f such that grad(f ) = A. This requires
[tex]\dfrac{\partial f}{\partial x}=2x-y[/tex]
[tex]\dfrac{\partial f}{\partial y}=x+y[/tex]
Take the first PDE and integrate both sides with respect to x to get
[tex]f(x,y)=x^2-xy+g(y)[/tex]
where g is assumed to be a function of y alone. Differentiating this with respect to x gives
[tex]\dfrac{\partial f}{\partial y}=-x+\dfrac{\mathrm dg}{\mathrm dy}=x+y\implies\dfrac{\mathrm dg}{\mathrm dy}=2x+y[/tex]
which would mean g is *not* a function of only y, but also x, contradicting our assumption. So the integral is path-dependent.
Parameterize the unit circle (call it C) by the vector function,
[tex]\mathbf r(t)=\cos t\,\mathbf i+\sin t\,\mathbf j[/tex]
with t between 0 and 2π.
Note that this parameterization takes C to have counter-clockwise orientation; if we compute the line integral of A over C, we can multiply the result by -1 to get the value of the integral in the opposite, clockwise direction.
Then
[tex]\mathrm d\mathbf r=-\sin t\,\mathbf i+\cos t\,\mathbf j[/tex]
and the (counter-clockwise) integral over C is
[tex]\displaystyle\int_C\mathbf A\cdot\mathrm d\mathbf r[/tex]
[tex]\displaystyle=\int_0^{2\pi}((2\cos t-\sin t)\,\mathbf i+(\cos t+\sin t)\,\mathbf j)\cdot(-\sin t\,\mathbf i+\cos t\,\mathbf j)\,\mathrm dt[/tex]
[tex]\displaystyle=\int_0^{2\pi}1-\sin t\cos t\,\mathrm dt=2\pi[/tex]
and so the integral in the direction we want is -2π.
By the way, that the integral doesn't have a value of 0 is more evidence of the fact that the integral is path-dependent.
Find the value of x in the parallelogram below.
Answer:
x=106 degrees
Step-by-step explanation:
The two opposite angles in a parallelogram are always the same and we know 360 degrees in a parallelogram.
x+x+74+74=360.
2x+148=360
2x=212
x=106 degrees
which side lengths form a right triangle
Answer:
A and C
Step-by-step explanation:
A right triangle consists of two legs and a hypotenuse.To find hypotenuse, we use The Pythagorean TheoremThe Pythagorean Theorem = [tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]two legs meet at a 90° angle and the hypotenuse is the longest side3 - 4 - 5
6 - 8 - 10
7 - 24 - 25
5 - 12 - 13
are some basic right triangle
(about more, look picture)
Just use hypotenuse formula :
3 x 3 = 9
4 x 3 = 12
5 x 3 = 15
Option C is correct
[tex] {5}^{2} + { \sqrt{6} }^{2} = { \sqrt{31} }^{2} [/tex]
Option A is correct
[tex] {5}^{2} + {5}^{2} = { \sqrt{50} }^{2} [/tex]
But B isn't correct
Hope this helps ^-^
Ying Zyiyu covered the first 300 miles of a trip going at 60 mph and the last hundred going at 40 mph. What was his average speed for the entire trip?
Answer:
53.33mph
Step-by-step explanation:
Let's calculated the total time spent on the journey first;
For the first 300miles the time spent is ;
From Distance = speed× time
time = Distance/ speed
= 300/60 = 5 hours
Similarly for the last 100mile the time taken is ;
100/40 = 2.5 hours
Total time spent = 5 +2.5 = 7.5 hours
Total distance covered 400miles
Therefore average speed = 400/7.5 =53.33mph
Answer:
53.33 mph
Step-by-step explanation:
I just wanted to say that the other guy's answer is correct, I checked :)
An electronic system has each of two different types of components in joint operation. Let X and Y denote the lengths of life, in hundreds of hours, for components of type I and type II, respectively. The performance of a component is independent for each other. Let E(X) = 4, E(Y) = 2, E(X2) = 24, E(Y2) = 8.
The cost of replacing the two components depends upon their length of life at failure and it is given by C = 50 + 2X + 4Y.
(i) Compute the average cost of replacing the two components. Your final answer must be a number.
(ii) Compute the standard deviation of cost of replacing the two components. Your final answer must be a number.
Answer:
a
The average cost is [tex]E(C) = 66[/tex]
b
The standard deviation of cost is [tex]\sigma = 9.798[/tex]
Step-by-step explanation:
From the question we are told that
[tex]E(X) = 4[/tex]
[tex]E(Y) = 2[/tex]
[tex]E(X^2) = 24[/tex]
[tex]E(Y^2) = 8[/tex]
The cost of replacing the two component is C = 50 + 2 X + 4 Y
The variance of X is mathematically represented as
V(X) = [tex]E(X^2) - [E(X)]^2[/tex]
Substituting values
[tex]V[X] = 24 - 4^2[/tex]
[tex]V[X] =8[/tex]
The variance of Y is mathematically represented as
V(Y) = [tex]E(Y^2) - [E(Y)]^2[/tex]
Substituting values
[tex]V[Y] = 8 - 2^2[/tex]
[tex]V[X] =4[/tex]
The average of replacing the two component is
[tex]E(C) = 2 * E(X) + 4* E(Y)[/tex]
substituting value
[tex]E(C) = 50 + 2 * (4) + 4* (2)[/tex]
[tex]E(C) = 66[/tex]
The variance of replacing the two component is
[tex]V(C) = V(50 + 2X +4Y)[/tex] Note: The variance of constant is zero
and X and Y are independent
=> [tex]V(C) = 2^2 * V(X) + 4^2 * V(Y)[/tex]
substituting values
=> [tex]V(C) = 4 * 8 + 16 * 4[/tex]
=> [tex]V(C) = 32 + 64[/tex]
=> [tex]V(C) = 96[/tex]
The standard deviation is
[tex]\sigma = \sqrt{V(C)}[/tex]
substituting values
[tex]\sigma = \sqrt{96}[/tex]
[tex]\sigma = 9.798[/tex]
Elmo likes music. He wondered if listening to music while studying will improve scores on an exam. Fifty students who were to take the midterm in a week agreed to be part of a study. Half were randomly assigned to listen to classical music while studying for the exam. The other half were told not to listen to any music while studying for the exam. A hypothesis test is to be performed to determine if the average score of those listening to music while studying for the exam was higher than for those who did not listen to any music while studying for the exam. Let X be the midterm scores of those who listened to classical music while studying, and Y be the midterm scores of those who did not listen to any music while studying. Which of the following is the correct alternative hypothesis?
A. The average midterm score for those who listen to classical music while studying is higher than the average midterm score for those who don't listen to music while studying.
B. The midterm scores of those who listen to classical music while studying are the same as midterm scores of those who don't listen to music while studying.
C. There is a difference in the mean midterm scores between those who listen to classical music while studying and those who don't listen to music while studying
D. There is no difference in the mean midterm scores between those who listen to classical music while studying and those who don't listen to music while studying
Answer: A. The average midterm score for those who listen to classical music while studying is higher than the average midterm score for those who don't listen to music while studying.
Step-by-step explanation:
An Alternative Hypothesis is one that disproves the Null Hypothesis in that it believes that indeed there is a change in the dependent variable due to a change in the independent variable.
The Alternative Hypothesis essentially aims to prove the assertion of the Researcher that there is an effect as a result of the introduction of a variable.
Null Hypothesis on the other hand believes that no significant difference exists between a change in a dependant Variable as a result of a change in an independent one.
The correct answer above therefore is that indeed music while studying inspires people to do better in exams than those who do not listen to music while studying. This is the alternative hypothesis because it believes that there was a change in the exam results due to reading while studying.
Which expression is equivalent to -80?
-415
-415
4.V5;
45
Answer:
It would be 4.v5
An archaeologist locates a fossil of an early human skeleton. To determine the age of the fossil, the archaeologist utilizes a technique called carbon dating, where the relative amount of carbon-14 can help determine the age of the fossil. Carbon-14 has a half-life of about 5700 years. He finds that the fossil contains 15% of the amount of carbon-14 anticipated when compared to a living femur of the same size. The decay of carbon-14 can be calculated as shown below, where N0 is original amount of carbon-14, t is the time of decay, in years, r represents the rate of decay, and N(t) represents the amount of carbon-14 remaining. Rounded to the nearest year, the skeleton is approximately years old.
Answer:
The skeleton is approximately 18970 years old.
Step-by-step explanation:
The amount of Carbon-14 remaining after t years is given by the following equation:
[tex]N(t) = N(0)(1-r)^{t}[/tex]
In which N(0) is the initial amount and r is the decay rate, as a decimal.
Carbon-14 has a half-life of about 5700 years.
This means that [tex]N(5700) = 0.5N(0)[/tex]
So
[tex]N(t) = N(0)(1-r)^{t}[/tex]
[tex]0.5N(0) = N(0)(1-r)^{5700}[/tex]
[tex](1-r)^{5700} = 0.5[/tex]
[tex]\sqrt[5700]{(1-r)^{5700}} = \sqrt[5700]{0.5}[/tex]
[tex]1-r = 0.9999[/tex]
[tex]r = 1 - 0.9999[/tex]
[tex]r = 0.0001[/tex]
So
[tex]N(t) = N(0)(1-r)^{t}[/tex]
[tex]N(t) = N(0)(0.9999)^{t}[/tex]
He finds that the fossil contains 15% of the amount of carbon-14 anticipated when compared to a living femur of the same size.
The age is t for which N(t) = 0.15N(0). So
[tex]N(t) = N(0)(0.9999)^{t}[/tex]
[tex]0.15N(0) = N(0)(0.9999)^{t}[/tex]
[tex](0.9999)^{t} = 0.15[/tex]
[tex]\log{(0.9999)^{t}} = \log{0.15}[/tex]
[tex]t\log{0.9999} = \log{0.15}[/tex]
[tex]t = \frac{\log{0.15}}{\log{0.9999}}[/tex]
[tex]t = 18970.25[/tex]
Rounding to the nearest year.
The skeleton is approximately 18970 years old.
Answer:
Mark as Brainliest Please :)
Step-by-step explanation:
Find the value of x a)10 b)6 c)5
Riverside Elementary School is holding a school-wide election to choose a school color. 5/8 of the votes were for blue, 5/9 of the remaining votes were for green 48 votes were for red. How many votes were for blue? how many votes were for green? if every student got one vote, but there were 25 students absent on the day of the vote, how many students are there at Riverside Elementary School
Answer:
288 votes
Step-by-step explanation:
wright out what you know
Blue: 5/8
Green: 5/9 (of 3/8 because it is the remaining parts) so 5/24
Red: 1 - (5/8 + 5/24) = 1/6
Find the total amount of people
You know that 1/6 of the population is 48, so the total population is 288 (48×6)
Multiply the total population by the fractions to get the number of votes
QUESTION 4
What kind of passenger would be considered a false negative?
A) Someone with dangerous material that pass through security
B) Someone with dangerous material thpt is stopped by security
C) Someone without dangerous material that pass through security
D) Someone without dangerous material that is stopped by security
Please answer this correctly without making mistakes
Area = 0.785
Area=0.79
I hope it helps
Which of the following is graphed below
Answer:
The answer is C
Multiply
4.2
x0.6
Type
Type an integer or a decir
Answer:
2.52
Step-by-step explanation:
4.2 × 0.6
Multiply the terms.
= 2.52
Answer:
2.52
hope it helps
Step-by-step explanation:
4.2 x 0.6
To solve this first, you simply multiply 42*06
(Exclude the decimal point)
42 x 6
= 252
Now since there are two numbers after the point (one is 4.2 and one is 0.6)
Move 252 two decimal places to left
= 2.52
in a dog show there will be a gold and silver medal awarded. there are 3 finalists. in how many different ways can the 2 medals be awarded?
Answer: There can be 2 gold 1 silver, 2 silver one gold, 3 silver, or 3 gold.
I'm not really sure if this is correct but I hope this helps:)
Please answer this correctly
Answer:
[tex]10\dfrac{5}{8}[/tex]
Step-by-step explanation:
The perimeter of a shape is the sum of the lengths of the sides.
[tex]2\dfrac{1}{8}+3\dfrac{3}{16}+2\dfrac{1}{8}+3\dfrac{3}{16}=10\dfrac{5}{8}[/tex] yards
Hope this helps!
Answer:
10 5/8
Step-by-step explanation:
The perimeter is the sum of all sides
2 1/8 + 3 3/16 + 2 1/8 + 3 3/16
Add the whole numbers
2 + 3 + 2 + 3 = 10
Add the fractions
1/8+ 1/8 + 3 3/16 + 3 3/16
2/8 + 6/16
1/4 + 3/8
2/8+3/8 = 5/8
Put them back together
10 5/8
What is the circumference of the circle shown below (round your answer to nearest tenths)
Answer:
A. 38.3
Step-by-step explanation:
[tex]circumference \\ \: \: \: \: \: = 2 \times radius \times \pi \\ or =diameter \times \pi \\ thus \: the \: answer \: is \\ 12.2 \times 3.14 = 38.3 \\ ( \: a \: ) [/tex]
PLZ I NEED URGENT HELP
What is the mean time to get from home to school in the morning for these six students? 2. What is the mean time to get from school to home in the afternoon for these six students? 3. For which distribution does the mean give a more accurate indicator of a typical time? Explain.
Answer:
Step-by-step explanation:
morning mean: 14 mins
afternoon: 14 mins
both morning and afternoon have the same mean time
A board game has a spinner divided into sections of equal size. Each section is labeled with a number between 1 and 5. Which number is a reasonable estimate of the number of times the spinner will land on a section labeled with a 5 over the course of 300 spins?
Answer:
75
Step-by-step explanation:
first, there are three 5's on the spinner, with a total of 12 sections. 3/12 = 0.25, so you multiply 0.25 times 300 (the total spins) and get 75
If a pizza is cut into 6 slices, what is the angle measure for each slice?
Help, pls. it's due tomorrow night.
An airplane flies due north at 200 km/h, and the wind blows in a direction N30°E
at 40 km/h. Find the coordinates for the vector representing the resultant for
the airplane with the wind factored in, and the resultant airspeed. Report any
approximations to two decimal places accuracy and include a diagram.
Answer:
please please please please show please
Alicia made her aunt a garden. The width is 6 5/7 ft ft and the length is 7 3/5 ft. What is the area of the garden
Please answer!
Step-by-step explanation:
Area=Length×width
=6 5/7×7 3/5
change the improper fraction to proper
=47/7 ×38/5
=1786/35
=51.03ft²
Solve for x.
6(x - 1) = 9(x + 2)
x = -8
X = -3
X = 3
x = 8
Answer:
[tex]x=-8[/tex]
Step-by-step explanation:
[tex]6\left(x-1\right)=9\left(x+2\right)\\\mathrm{Expand\:}6\left(x-1\right):\quad 6x-6\\6\left(x-1\right)\\\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b-c\right)=ab-ac\\a=6,\:b=x,\:c=1\\=6x-6\cdot \:1\\\mathrm{Expand\:}9\left(x+2\right):\quad 9x+18\\9\left(x+2\right)\\\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b+c\right)=ab+ac\\a=9,\:b=x,\:c=2\\=9x+9\cdot \:2\\\mathrm{Multiply\:the\:numbers:}\:9\cdot \:2=18\\=9x+18\\6x-6=9x+18\\\mathrm{Add\:}6\mathrm{\:to\:both\:sides}[/tex]
[tex]6x-6+6=9x+18+6\\Simplify\\6x=9x+24\\\mathrm{Subtract\:}9x\mathrm{\:from\:both\:sides}\\6x-9x=9x+24-9x\\Simplify\\-3x=24\\\mathrm{Divide\:both\:sides\:by\:}-3\\\frac{-3x}{-3}=\frac{24}{-3}\\Simplify\\\frac{-3x}{-3}=\frac{24}{-3}\\\mathrm{Simplify\:}\frac{-3x}{-3}:\quad x\\\frac{-3x}{-3}\\\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{-b}=\frac{a}{b}\\=\frac{3x}{3}\\\mathrm{Divide\:the\:numbers:}\:\frac{3}{3}=1\\=x\\\mathrm{Simplify\:}\frac{24}{-3}:\quad -8\\\frac{24}{-3}[/tex]
[tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{-b}=-\frac{a}{b}\\=-\frac{24}{3}\\\mathrm{Divide\:the\:numbers:}\:\frac{24}{3}=8\\=-8\\[/tex]
Answer:
x=-8
Step-by-step explanation:
6(x-1)= 9(x+2)
6x-6= 9x+18
6x-9x= 18+6
-3x= 24
-3x÷-3= 24÷-3
x=-8
What is the greatest common factor of 60, 45 and 82? HALPPPPPPPPPPPPPPPPPPp
Answer:
GCF: 1
Step-by-step explanation:
Factors are numbers that can be evenly divided into another number. The greatest common factor of a set of numbers is the biggest number than can evenly divide into all the the numbers.
Let's list the factors of 60, 45 and 82
Factors of 60:
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Factors of 45:
1, 3, 5, 9, 15, 45
Factors of 82:
1, 2, 41, 82
The greatest factor that all 3 numbers share is 1.
The right answer is 1.
Please see the attached picture for full solution
Hope it helps
Good luck on your assignment..
Bartholomew went hiking over the weekend. He hiked all 4 trails in 3 hours. Which is the best estimate for the number of miles he hiked per hour
Answer:
a?
Step-by-step explanation:
Television viewing reached a new high when the global information and measurement company reported a mean daily viewing time of hours per household. Use a normal probability distribution with a standard deviation of hours to answer the following questions about daily television viewing per household.
a. what is the probability that a household views television between 6 and 8 hours a day (to 4 decimals)?
b. How many hours of television viewing must a household have in order to be in the top 5% of all television viewing households (to 2 decimals)?
c. What is the probability that a household views television more than 5 hours a day (to 4 decimals)?
Answer:
Step-by-step explanation:
The question is incomplete. The complete question is:
Television viewing reached a new high when the global information and measurement company reported a mean daily viewing time of 8.35 hours per household. Use a normal probability distribution with a standard deviation of 2.5 hours to answer the following questions about daily television viewing per household.
(a.) what is the probability that a household views television between 6 and 8 hours a day (to 4 decimals)?
(b.) How many hours of television viewing must a household have in order to be in the top 5% of all television viewing households (to 2 decimals)?
(c.) What is the probability that a household views television more than 5 hours a day (to 4 decimals)?
Solution:
Let x be the random variable representing the television viewing times per household. Since it is normally distributed and the population mean and population standard deviation are known, we would apply the formula,
z = (x - µ)/σ
Where
x = sample mean
µ = population mean
σ = standard deviation
From the information given,
µ = 8.35
σ = 2.5
a) the probability that a household views television between 6 and 8 hours a day is expressed as
P(6 ≤ x ≤ 8)
For x = 6,
z = (6 - 8.35)/2.5 = - 0.94
Looking at the normal distribution table, the probability corresponding to the z score is 0.1736
For x = 8
z = (8 - 8.35)/2.5 = - 0.14
Looking at the normal distribution table, the probability corresponding to the z score is 0.4443
Therefore,
P(6 ≤ x ≤ 8) = 0.4443 - 0.1736 = 0.2707
b) the top 5% means greater than 95%. It means that the sample mean is greater than the population mean and the z score is positive. The corresponding z score from the normal distribution table is 1.645. Therefore,
(x - 8.35)/2.5 = 1.645
Cross multiplying, it becomes
x - 8.35 = 2.5 × 1.645 = 4.11
x = 4.11 + 8.35 = 12.46
c) the probability that a household views television more than 5 hours a day is expressed as
P(x > 5) = 1 - P(x ≤ 5)
For x = 5
z = (5 - 8.35)/2.5 = - 1.34
Looking at the normal distribution table, the probability corresponding to the z score is 0.0901
Therefore,
P(x > 5) = 1 - 0.0901 = 0.9099
Help is appreciated ❤
Simplify the radical expression -2 √250
Answer:
-10 sqrt(10)
Step-by-step explanation:
-2 sqrt(250)
We know that sqrt(ab) = sqrt(a) sqrt(b)
-2 sqrt(25*10)
-2 sqrt(25)*sqrt(10)
-2 *5*sqrt(10)
-10 sqrt(10)
Answer with Explanation please! Thank you!
Answer:
D
Step-by-step explanation:
2(x+b) = ax+c
2x+2b = ax+c
c = 2b