Answer: 0.4207
Step-by-step explanation:
Let [tex]\overline{x}[/tex] be the sample mean area.
Given: Population mean : [tex]\mu=250[/tex] sq. feet
Standard deviation: [tex]\sigma=2[/tex] sq. feet
Sample size : n= 10
The probability that the sample mean area is [tex]249.6 \text{ ft}^2[/tex] or less if the manufacturer’s claim is true.
[tex]P(\overline{x}<249.6)=P(\dfrac{\overline{x}-\mu}{\sigma}<\dfrac{249.6-250}{2})\\\\= P(z<-0.2)\ \ \ \ [z=\dfrac{\overline{x}-\mu}{\sigma}]\\\\=1-P(z<0.2)\\=1- 0.5793\\\\=0.4207[/tex]
Required probability = 0.4207
Using the normal distribution and the central limit theorem, it is found that the probability that the sample mean area is 249.6 ft^2 or less if the manufacturer’s claim is true is of 0.2636.
Normal Probability DistributionIn a normal distribution 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]
It 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, which is the percentile of X. By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].In this problem:
The mean is of 250 ft², hence [tex]\mu = 250[/tex].The standard deviation is of 2 ft², hence [tex]\sigma = 2[/tex].A sample of 10 rolls is taken, hence [tex]n = 10, s = \frac{2}{\sqrt{10}}[/tex].The probability that the sample mean area is 249.6 ft^2 or less if the manufacturer’s claim is true is the p-value of Z when X = 249.6, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{249.6 - 250}{\frac{2}{\sqrt{10}}}[/tex]
[tex]Z = -0.6325[/tex]
[tex]Z = -0.6325[/tex] has a p-value of 0.2636, which is the probability.
To learn more about the normal distribution and the central limit theorem, you can take a look at https://brainly.com/question/24663213
Are the fractions 9/6 and 6/4 equivalent?
SOLUTION:
IF YOU GIVE ME AN ANSWER GARBAGE I WILL REPORT YOU
THANK, ;)
Answer: 9/6 and 6/4 are equivalent
Step-by-step explanation:
If you simply 9/6, you get 1 3/6
Simplify 6/4, you get 1 2/4
3/6 and 2/4 both equal 1/2, so 9/6 and 6/4 both equal 1 1/2. Therefore, they are equivalent.
Hope this helped ;D
Solve the quadratic by taking square roots. Write your answer with no spaces as x=a,-a where a and -a are the values you found when solving.
3x² - 7 = 140
Answer:
x=7,−7
Step-by-step explanation:
In order to find the value of x in this quadratic equation we first need to make the equation equal 0 by getting rid of the 140. We do this by subtracting 140 on each side.
3x² - 7 = 140
3x² - 147 = 0
Now we solve as a regular quadratic formula
x= [tex]x = \frac{-(0) +- \sqrt{0^{2} - 4(3)(-147) } }{2(3)}[/tex]
[tex]x = \frac{0 +- \sqrt{1764} }{6}[/tex]
x=7,−7
find three rational numbees between -2/5 and -1/5
Answer:
-3/10, -25/100, -3/8
4x² - 12x + 8
A.Not factorable
B. factorable
Answer:
It is factorizable
Step-by-step explanation:
4(x² - 3x + 2) is the factoried version :)
twice the difference of a number and 7 is at least -21
Use the variable c for the unknown number.
Translate the sentence into an inequality
Answer:
Step-by-step explanation:
Difference of a number and 7 = c - 7
Twice the difference = 2*(c - 7) = 2*c - 7*2 = 2c - 14
2c - 14 ≥ -21
Chuck put new wallpaper in his bathroom. The pattern of the wallpaper
used 3 triangles to make a straight angle. The measures of the angles
are (9x - 72). (73x + ) and 11) What is the measure of the
obtuse angle? 7.3.5
ext
Tota
Answer:
x = 2.93
Step-by-step explanation:
The sum of angles of the triangle is 180degrees, hence;
9x - 72 + 73x + 11 = 180
82x - 61 = 180
82x = 180 + 61
82x = 241
Divide both sides by 82
82x/82 = 241/82
x = 2.93
Note that the functions might not be accurate but the same methos should be employed for any function given
1. The width of a rectangle is 6 feet and the diagonal length of the rectangle is 19 feet. Which
measurement is closest to the length of this rectangle in feet?
what is the total area of the shape below
Answer:
480 ft
Step-by-step explanation:
Given a polynomial that has zeros of −5, 4i, and −4i and has a value of 40 when x=3 write the polynomial equation
Answer:
[tex]f(x) = 0.2(x^3 + 5x^2 + 16x + 80)[/tex]
Step-by-step explanation:
Zeros of a function:
Given a polynomial f(x), this polynomial has roots [tex]x_{1}, x_{2}, x_{n}[/tex] such that it can be written as: [tex]a(x - x_{1})*(x - x_{2})*...*(x-x_n)[/tex], in which a is the leading coefficient.
Zeros of −5, 4i, and −4i
This means that [tex]x_1 = -5, x_2 = 4i, x_3 = -4i[/tex]. So
[tex]f(x) = a(x - x_{1})*(x - x_{2})*(x-x_3)[/tex]
[tex]f(x) = a(x - (-5))*(x - 4i)*(x - (-4i))[/tex]
[tex]f(x) = a(x + 5)(x - 4i)(x + 4i)[/tex]
[tex]f(x) = a(x + 5)(x^2 - 16i^2)[/tex]
Since [tex]i^2 = -1[/tex]
[tex]f(x) = a(x + 5)(x^2 + 16)[/tex]
[tex]f(x) = a(x^3 + 5x^2 + 16x + 80)[/tex]
Has a value of 40 when x=3
We use this to find a, which means that we have [tex]x = 3, f(x) = 40[/tex]. So
[tex]a(3^3 + 5*3^2 + 16*3 + 80) = 40[/tex]
[tex]200a = 40[/tex]
[tex]a = \frac{40}{200} = \frac{1}{5} = 0.2[/tex]
So
[tex]f(x) = 0.2(x^3 + 5x^2 + 16x + 80)[/tex]
(3b^3)^2 without exponents
Answer:
When (3b³)² is simplified, it equals 3b⁶
Step-by-step explanation:
3 × 2 = 6
The exponent is 6
For questions 3 that’s all i need help please !!! For a test and please put your answers below !!!
Answer:
D) 1078
Step-by-step explanation:
solve from missing angle
what fraction of an hour is 6 minutes? give answer in its simplest form
Answer:
fraction is 1hr has 60 min so 6/60 is 1/10th fraction
Step-by-step explanation:
Answer:
QUESTION: what fraction of an hour is 6 minutes? give the answer in its simplest form.
ANSWER: 0.100
Step-by-step explanation:
Hope that this helps you out! :)
If you have any questions please put them in the comment section below this answer.
Have a great rest of your day/night!
Please thank me on my profile if this answer has helped you.
The bank has 5 Vaults.Each vault contains 5 drawers 5 stacks and $25 what’s in the bank?
3. A telephone calling center performs two types of solicitations: (1) donations and (2) sales. The center wants to determine how much time on average a caller spends on each type of solicitation. The issue is complicated by the fact that some calls get busy signals, some go unanswered, and some last for less than one minute, which is interpreted to mean that the recipient is not interested or
Answer:
hang ups the receiver
Step-by-step explanation:
In this case, there is a difficulty for the call center to determine the average time that each caller spends on each type of request, since there is also the possibility that the recipient will not be interested in the call or hang up when receiving such a call. Therefore, in order to calculate this average in a more real way, the company must statistically monitor this data in relation to each hour of work and how many situations occurred in that hour, how many calls received were answered, how many received a busy signal, how many are not answered and how many calls last less than a minute if the recipient is not interested or hangs up.
Through this data, the company is able to monitor the calls and define telephone service strategies that can retain the customer more if the calls in less than a minute exceed conventional calls.
You need to make 56 servings of Caesar dressing. Each serving takes 2 teaspoons of crushed garlic. How many teaspoons of crushed garlic do you need?
Answer:
112 teaspoons just multiply 56 by 2 with a calculator
Step-by-step explanation:
Answer:
11 teaspoons
Step-by-step explanation:
I hope this helps :)
1 point
8. The dot plot below represents the number of dollars in allowance that
students receive each week in Mrs. Jimenez's class. What is the median
amount of allowance?
1...
+
2
+
4
+
12
+
14.
O
6
8
10
16
DOLLARS OF ALLOWANCE EACH WEEK
Answer:
6
Step-by-step explanation:
i am not sure but i think its right sorry if you get it wrong
plzz help me i’ll give brainlest
Answer:
An octagonal prism has 10 faces.
Step-by-step explanation:
Please mark as brainliest!
What value of x will make the equation below true?
2x=5x−6
Answer:
x=2
Step-by-step explanation:
Answer:
x = 2
Step-by-step explanation:
2x = 5x-6
Subtract 5x from each side
2x-5x = 5x-6-5x
-3x = -6
Divide by -3
-3x/-3 = -6/-3
x = 2
A quiz has 5 true-false questions and 3 multiple choice questions with 4 options each. How many possible ways are there to answer the 8 questions?
a.
48
c.
4024
b.
2024
d.
2048
Answer:
The correct answer is D
Step-by-step explanation:
the dude above me made a small typo, but they are right
The picture is my proof
have a nice day! :)
PLEASE HELP ASAP!!
Find the area of the rectangle below in terms of y. Make sure your expression is fully
simplified.
Recall, the formula for area of a rectangle is A= lw
YOU MUST SHOW ALL WORK TO RECEIVE FULL CREDIT.
Step-by-step explanation:
Area of rectangle is Length × Breadth
Where Length is 6y⁴+3y³-y²-8Width is 2y²We need to multiply these 3 terms.
[tex]\rm{2y^2 \times (6y^4 + 3y^3 - y^2 - 8)}[/tex]
Use distributive property
= 12 y⁶ + 6y⁵ - 2 y⁴ - 16 y²
Hope it helps :)
pls helppppp it's hard :(
Answer:
The answer is A .
Step-by-step explanation:
Good luck ;)
If jackeline and Raychel decide to watch only the two longest movies and take a 30 minute break in between how much of their five hours while they have left over
what's a 3 number multiplication that = 1000?
Answer:
1,1, and 1000
Step-by-step explanation:
Answer:
(10 x 10) x 10 = 1000
Step-by-step explanation:
10 x 10 = 100
100 x 10 = 1000
For thousands of years, gold has been considered one of the Earth's most precious metals. One hundred percent pure gold is 24-karat gold, which is
too soft to be made into jewelry. Most gold jewelry is 14-karat gold, approximately 58% gold. If 18-karat gold is 75% gold and 12-karat gold is 50% gold,
how much of each should be used to make a 14-karat gold bracelet weighing 300 grams?
How many grams of 18-karat gold needs to be used to make the bracelet?
Mr. Womer borrowed $1,100 to start his own business. National
Bank charged him 15% interest per year. Mr. Womer paid $330 in
interest. For what period of time did he borrow the money?
Please help will give brainlist
Answer:
Sum
Step-by-step explanation:
Remember that the plus sign (+) always means to add.
Answer:
It would be the sum of a number and eight.
Tony rolled a six-sided number cube 200 times. Her results are in the table shown. What is the experimental probability of Tony rolling a
2 ? Enter the answer as a percent.
Answer:
3
Step-by-step explanation:
3+1=5
convert 30 minutes into seconds
Answer:
1800 seconds.
Step-by-step explanation:
30 × 60 = 1800
Attendance has never been a component of the grade for this course. However, over the years I have noticed that 40% of those who attend regularly receive an above average grade (B or better), while only 10% of those who do not attend regularly receive an above average grade. About 70% of the students attend class regularly. One student is randomly selected at the end of the semester. Find the probability that the student did not attend class regularly given that (s)he did not receive an above average grade
Answer:
0.3913 = 39.13% probability that the student did not attend class regularly given that (s)he did not receive an above average grade
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Did not receive an above average grade.
Event B: Did not attend class regularly.
Probability of an student not receiving an above average grade:
100 - 40 = 60% of 70%(attend class regularly).
100 - 10 = 90% of 100 - 70 = 30%(do not attend class regularly).
So
[tex]P(A) = 0.6*0.7 + 0.9*0.3 = 0.69[/tex]
Did not receive an above average grade and did not attend class regularly:
90% of 30%. So
[tex]P(A \cap B) = 0.9*0.3 = 0.27[/tex]
Find the probability that the student did not attend class regularly given that (s)he did not receive an above average grade
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.27}{0.69} = 0.3913[/tex]
0.3913 = 39.13% probability that the student did not attend class regularly given that (s)he did not receive an above average grade