Answer:
B) 0.0069
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 = 8.4, \sigma = 1.8, n = 40, s = \frac{1.8}{\sqrt{40}} = 0.2846[/tex]
Find the probability that their mean rebuild time exceeds 9.1 hours.
This is 1 subtracted by the pvalue of Z when X = 9.1. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{9.1 - 8.4}{0.2846}[/tex]
[tex]Z = 2.46[/tex]
[tex]Z = 2.46[/tex] has a pvalue of 0.9931
1 - 0.9931 = 0.0069
So the answer is B.
Evaluate Combination (6,6)
Answer:
[tex] nCx = \frac{n!}{x! (n-x)!}[/tex]
On this case n =6 and x =6 we got:
[tex] 6C6 = \frac{6!}{6! (6-6)!} = \frac{6!}{6! 0!}= \frac{6!}{6!}=1[/tex]
Step-by-step explanation:
The utility for the combination formula is in order to find the number of ways to order a set of elements
For this case we want to find the following expression:
[tex] 6C6[/tex]
And the general formula for combination is given by:
[tex] nCx = \frac{n!}{x! (n-x)!}[/tex]
On this case n =6 and x =6 we got:
[tex] 6C6 = \frac{6!}{6! (6-6)!} = \frac{6!}{6! 0!}= \frac{6!}{6!}=1[/tex]
Amy filled bags with mixed nuts. The weights of the bags are 1/8 lb, 1/4 lb, 1/8 lb, 1/2 lb, 1/8 lb, 1/4 lb, 1/8lb, 1/2 lb, 1/8 lb, 1/4 lb, 1/8 lb, 1/2 lb, 1/8 lb, 1/8 lb, 1/4 lb, and 1/2 lb.
Part A: Organize the information in a line plot. (on your own paper)
Part B: What is the average weight of the bags? ________ lb
Answer:
(a)See attached
(b)[tex]\text{Average Weight =}\dfrac{1}{4}$ lb[/tex]
Step-by-step explanation:
The weights of the bag are given below:
[tex]1/8 lb, 1/4 lb, 1/8 lb, 1/2 lb, 1/8 lb, 1/4 lb, 1/8lb, 1/2 lb \\1/8 lb, 1/4 lb, 1/8 lb, 1/2 lb, 1/8 lb, 1/8 lb, 1/4 lb, 1/2 lb.[/tex]
When sorted, we have:
[tex]1/8 lb, 1/8 lb, 1/8lb, 1/8 lb, 1/8 lb, 1/8 lb, 1/8 lb, 1/8 lb\\ 1/4 lb,1/4 lb, 1/4 lb, 1/4 lb\\ 1/2 lb, 1/2 lb, 1/2 lb,1/2 lb,[/tex]
8 bags weigh [tex]\frac{1}{8}lb[/tex]4 bags weigh [tex]\frac{1}{4}lb[/tex]4 bags weigh [tex]\frac{1}{2}lb[/tex]Part A
See attached for the Line plot
Part B
Average Weight of the bags
[tex]=\dfrac{(8X\dfrac{1}{8})+ (4X\dfrac{1}{4})+(4X\dfrac{1}{2})}{16} \\=\dfrac{1+1+2}{16}\\=\dfrac{4}{16}\\$Average Weight =\dfrac{1}{4}$ lb[/tex]
A company that produces fine crystal knows from experience that 17% of its goblets have cosmetic flaws and must be classified as "seconds." (Round your answers to four decimal places.)(a)Among seven randomly selected goblets, how likely is it that only one is a second
Answer:
0.3891 = 38.91% probability that only one is a second
Step-by-step explanation:
For each globet, there are only two possible outcoes. Either they have cosmetic flaws, or they do not. The probability of a goblet having a cosmetic flaw is independent of other globets. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
17% of its goblets have cosmetic flaws and must be classified as "seconds."
This means that [tex]p = 0.17[/tex]
Among seven randomly selected goblets, how likely is it that only one is a second
This is P(X = 1) when n = 7. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 1) = C_{7,1}.(0.17)^{1}.(0.83)^{6} = 0.3891[/tex]
0.3891 = 38.91% probability that only one is a second
The diameter of the container is 13 centimeters and
its height is 24 centimeters. Determine, in terms of
I, the volume of the ovlinder, in cubie centimeters,
In circle Qwith the measure of minor arc PR= 70°, find m/PSR.
Answer: 290 degrees
Step-by-step explanation:
subtract the minor arc's measure from 360 to get the major arc's measure
A distribution consists of three components with frequencies 200,250 and 300 having means 25,10,and 15 and standard deviations 3,4, and 5 respectively.Calculate the mean and standard deviation.
Answer:
The mean and standard deviation of the combined distribution is 16 and 7.192 respectively.
Step-by-step explanation:
We have given that a distribution consists of three components with frequencies 200, 250, and 300 having means 25, 10, and 15 and standard deviations 3, 4, and 5 respectively.
And we have to find the mean and standard deviation of the combined distribution.
Firstly let us represent some symbols;
[tex]n_1[/tex] = 200 [tex]\bar X_1[/tex] = 25 [tex]\sigma_1[/tex] = 3
[tex]n_2[/tex] = 250 [tex]\bar X_2[/tex] = 10 [tex]\sigma_2[/tex] = 4
[tex]n_3[/tex] = 300 [tex]\bar X_3[/tex] = 15 [tex]\sigma_3[/tex] = 5
Here, [tex]\bar X_1, \bar X_2 , \bar X_3[/tex] represent the means and [tex]\sigma_1,\sigma_2,\sigma_3[/tex] represent the standard deviations.
Now, as we know that Mean of the combined distribution is given by;
[tex]\bar X = \frac{n_1 \times \bar X_1+n_2 \times \bar X_2+n_3 \times \bar X_3}{n_1+n_2+n_3}[/tex]
Putting the above values in the formula we get;
[tex]\bar X = \frac{200 \times 25+250 \times 10+300 \times 15}{200+250+300}[/tex]
[tex]\bar X = \frac{5000+2500 +4500}{750}[/tex]
[tex]\bar X = \frac{12000}{750}[/tex] = 16
Similarly, the formula for combined standard deviation is given by;
[tex]\sigma = \sqrt{\frac{n_1\sigma_1^{2} + n_1(\bar X_1-\bar X)^{2}+n_2\sigma_2^{2} + n_2(\bar X_2-\bar X)^{2}+n_3\sigma_3^{2} + n_3(\bar X_3-\bar X)^{2} }{n_1+n_2+n_3} }[/tex]
[tex]\sigma = \sqrt{\frac{(200 \times 3^{2}) + 200 \times (25-16)^{2}+(250 \times 4^{2}) + 250 \times (10-16)^{2}+(300 \times 5^{2}) + 300 \times (15-16)^{2} }{200+250+300} }[/tex]
[tex]\sigma = \sqrt{\frac{1800 + (200 \times 81)+4000 + (250 \times 36)+7500 +( 300 \times 1) }{750} }[/tex]
[tex]\sigma = \sqrt{\frac{1800 + 16200+4000 + 9000+7500 +300 }{750} }[/tex]
[tex]\sigma = \sqrt{\frac{38800 }{750} }[/tex] = 7.192
Hence, the mean and standard deviation of the combined distribution is 16 and 7.192 respectively.
The baseball team ordered 140 T-shirts to sell at the school fair. Of those T-shirts, 50% are white, 20% are blue, 15% are green, 10% are red, and 5% are black. How many black T-shirts did the baseball team order? How many red T-shirts?
Answer:
The team ordered 7 black T-shirts.
The team ordered 14 red T-shirts.
Step-by-step explanation:
The team ordered 140 T-shirts.
How many black T-shirts did the baseball team order?
Of those, 5% are black.
0.05*140 = 7
The team ordered 7 black T-shirts.
How many red T-shirts?
Of those, 10% are red.
0.1*140 = 14
The team ordered 14 red T-shirts.
A student's course grade is based on one midterm that counts as 5% of his final grade, one class project that counts as 25% of his final grade, a set of homework assignments that counts as 35% of his final grade, and a final exam that counts as 35% of his final grade. His midterm score is 72, his project score is 83, his homework score is 91, and his final exam score is 74. What is his overall final score? What letter grade did he earn (A, B, C, D, or F)? Assume that a mean of 90 or above is an A, a mean of at least 80 but less than 90 is a B, and so on.His overall final score is nothing.
Answer:
His overal final score is 81.2. His letter grade is a B.
Step-by-step explanation:
Weighed average:
The sum of all values multiplied by it's weight. The weight is a proportion(a value between 0 and 1).
So.
Score of 72 on the midterm, which counts 5%.
Score of 83 on the project score, which counts 25%.
Score of 91 on homework assignments, which counts 35%.
Score of 74 on the final exam, which counts 35%.
His grade is:
G = 72*0.05 + 83*0.25 + 91*0.35 + 74*0.35 = 82.1.
His overal final score is 81.2.
At least 80 but less than 90 is a B
So his letter grade is a B.
A particular group of men have heights with a mean of 181 cm and a standard deviation of 6 cm. Earl had a height of 196 cm. a. What is the positive difference between Earl's height and the mean? b. How many standard deviations is that [the difference found in part (a)]? c. Convert Earl's height to a z score. d. If we consider "usual" heights to be those that convert to z scores between minus2 and 2, is Earl's height usual or unusual?
Answer:
a. 15
b. based on the result of part a, 15 standard deviation above the mean.
c. 2.5
d. Earl's height is unusual
Step-by-step explanation:
We have that "x" would be the height of Earl = 196, the mean m = equals 181 and the standard deviation (sd) = 6, now:
a. the positive difference between the mean and Earl's height:
D = x - m
D = 196 - 181 = 15
b. based on the result of part a, 15 standard deviation above the mean.
c. The z value is given by:
z = x - m / sd
replacing:
z = (196 - 181) / 6
z = 2.5
d. the z-score is unusual since the value of z is 2.5 which is a value greater than than 2 standard deviations above the mean, which means that Earl's height is unusual
Animal populations are not capable of unrestricted growth because of limited habitat and food supplies. Under such conditions the population follows a logistic growth model:
P(t) =
d
1 + ke−ct
where c, d, and k are positive constants. For a certain fish population in a small pond d = 1400, k = 13, c = 0.2, and t is measured in years. The fish were introduced into the pond at time t = 0.
(a) How many fish were originally put in the pond?
Correct: Your answer is correct.
fish
(b) Find the population after 10, 20, and 30 years. (Round your answers to the nearest whole number.)
10 years Fish
20 years fish
30 years fish
Answer:
a) 19,600 fishes were originally put in the pond.
b) Population of fishes after 10 years = 3,863
Population of fishes after 20 years = 1,733
Population of fishes after 30 years = 1,403
Step-by-step explanation:
The population follows a logistic model
P(t) = d (1 + ke⁻ᶜᵗ)
For a fish pond,
d = 1400, k = 13, c = 0.2
Inserting the values of these constants
P(t) = 1400 (1 + 13 e⁻⁰•²ᵗ)
a) How many fish were originally put in the pond?
At the start of the whole thing, t = 0
P(t=0) = 1400 (1 + 13 e⁰) = 1400 × 14 = 19,600
Hence, 19,600 fishes were originally put in the pond.
b) Find the population after 10, 20, and 30 years.
P(t) = 1400 (1 + 13 e⁻⁰•²ᵗ)
At t = 10, 0.2t = 0.2 × 10 = 2
P(t=10) = 1400 (1 + 13e⁻²) = 1400 (1 + 1.759) = 3,863.1 = 3,863
At t = 20, 0.2t = 0.2 × 20 = 4
P(t=20) = 1400 (1 + 13e⁻⁴) = 1400 (1 + 0.238) = 1,733.3 = 1,733
At t = 30, 0.2t = 0.2 × 30 = 6
P(t = 30) = 1400 (1 + 13e⁻⁶) = 1400 (1 + 0.00248) = 1,403.47 = 1,403
Hope this Helps!!
Which is the solution to the linear equation? 2/3 x-1/2=1/3+5/6x
Answer: X = -5
Step-by-step explanation:
1) Multiply both sides by 6, which is 4x - 3 = 2 + 5x
2) Move the terms, 4x - 5x = 2 + 3
3) Combine like terms, -x = 5
4) Multiply both sides by -1, x = -5
Michael is making a big batch of granola bars to bring to his soccer game. The oats in the granola bars contain 568.7 grams of carbohydrates.
A 2-column table with 3 rows titled Nutritional Facts Oats (1 cup). Column 1 has entries Calories, Carbohydrates, Protein. Column 2 has entries 607, 103.4 grams, 26.3 grams.
How many cups of oats did Michael use in his recipe?
0.415 cups
0.55 cups
4.15 cups
5.5 cups
Answer:
5.5
Step-by-step explanation:
From the table; one cup of oat contains 103.4 carbohydrates.
568.7/103.4 = 5.5 cups
Could someone give me the answer to this please?
Answer:
A = 55.15
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos theta = adjacent/ hypotenuse
cos A = 4/7
Take the inverse cos of each side
cos^-1 cos A = cos^-1 (4/7)
A = 55.15009542
To the nearest hundredth
A = 55.15
The domain of a function is
Answer:
The domain of a function is the complete set of possible values of the independent variable. In plain English, this definition means: The domain is the set of all possible x-values which will make the function "work", and will output real y-values.
Step-by-step explanation:
I hope this helped ;)
Defatted blackcurrant seeds (DBS) could be used as a dietary supplement in gluten-free bread but their use may affect texture. A 2011 study measured bread volume (in cm) using independent random samples of bread loaves baked with flours containing different DBS levels. The data showed no skew or outliers. Here are the summary statistics: Flour type z Mean StDev No DBS 00 552 18 5% DBS 00 525 23 15% DBS 00 485 24 We want to know if bread volume is significantly affected by the type of flour used.
Which inference procedure should be used?
1. chi-square for two-way tables
2. one sample or matched-pairs t procedure for a mean
3. z procedure for a proportion
4. two sample t procedure for two means
5. ANOVA for several means
Note: This is the correct table format.
Flour type z Mean StDev
No DBS 00 552 18
5% DBS 00 525 23
15% DBS 00 485 24
Answer:
5. ANOVA for several means
Step-by-step explanation:
In this question, three different means of the data are compared. ANOVA is used for comparing between two or more means to test for differences. It extends the z and t test that are only used for comparing two means.
Since three means are compared, the inference procedure to be used is ANOVA.
ABC
ABCD ]````````````````````` .```````````````````[
Answer:
B then C
Step-by-step explanation:
First screenshot:
Shape B because the net has a square base.
Second screenshot:
It is C
C does not make a cube
20 POINTS A number, y, is equal to twice the sum of a smaller number and 3. The larger number is also equal to 5 more than 3 times the smaller number. Which equations represent the situation?
A.2 x minus y = negative 6 and 3 x minus y = negative 5
B.2 x minus y = negative 3 and 3 x minus y = negative 5
C.2 x minus y = negative 6 and x minus 3 y = 5
D.2 x minus y = negative 3 and x minus 3 y = 5
Answer:
A.2 x minus y = negative 6 and 3 x minus y = negative 5
Step-by-step explanation:
A ) 2x-y=-6, and 3x-y=-5
Consider the provided information.
First convert the statement into mathematical representation.Consider the smaller number is x and the larger number is y.
y, is equal to twice the sum of a smaller number and 3.
This information can be written as: y=2(x+3)
The larger number is also equal to 5 more than 3 times the smaller number.
This information can be written as: y=5+3x
Answer:
A ) 2x-y=-6, and 3x-y=-5
Step-by-step explanation:
The distance traveled varies directly with the time spent in motion wh
If d represents the distance traveled and t represents time, which eq
If you travel 150 miles in 4 hours, what is the constant of variation?
If you continue traveling at a constant speed, how long will it take to
an hour.
about
hours
*
Step-by-step explanation:
The distance traveled varies directly with the time spent in motion. If d is distance and t is time taken. Then,
[tex]d\propto t[/tex]
or
[tex]d=kt[/tex]
k is the constant of variation
If d = 150 miles and t = 4 hours
[tex]k=\dfrac{d}{t}\\\\k=\dfrac{150}{4}\\\\k=37.5\ mph[/tex]
A cylinder has a diameter of 14 centimeters and a volume of 112π cubic centimeters. What is the height in centimeters of the cylinder?
Step-by-step explanation:
we have diameter and volume
and volume function is : v=(3.14)(r^2)h
so : h = 196/112
A large game cube with a three inch side length is wrapped with shrink wrap. How many square centimeters of shrink wrap will be used to wrap ten game cubes?
Answer:
see below
Step-by-step explanation:
cube has 6 square faces so 6*s*s
s =3 in =3*2.54 cm = 7.62 cm
1 in = 2.54 cm
1 cube needs 6*7.62² = 348.3864 cm²
10 cubes = 10*348.3864 =3483.864 cm²
In ΔKLM, the measure of ∠M=90°, MK = 2.7 feet, and KL = 6.6 feet. Find the measure of ∠L to the nearest degree.
Answer:
24.15° = 24° to the nearest degree
Step-by-step explanation:
If we draw the triangle we would see that the KL is the longest side and the hypothenus;
Also MK would-be the height and ML is the base of the triangle.
Since L and M are the angles at the base;
From Trigonometry Sin L = MK/ KL
= 2.7/6.6
L = Sin^{-1} (2.7/6.6)
L = Sin^{-1} (0.4091)
=24.15°
Note : sin a = height/ longest side
= Opposite/hypothenus
how much of other chemicals must be evaporated from 400grams of a hand sanitizer that is 24% alcohol to strengthen it to a hand sanitizer that is 30% alcohol? correct your answer to the nearest whole number
Answer:
llolololol
Step-by-step explanation:
Answer:80 grams
Step-by-step explanation:
Whats the answer according to the image ?
Given the functions f(x) = 7x + 13 and g(x) = x + 2, which of the following functions represents f[g(x)] correctly?
Answer:
f[g(x)]= 7x + 27
Step-by-step explanation:
g(x) = x + 2,
f(x) = 7x + 13,
f[g(x)] means you substitute the value of g(x) into the variable of f(x);
Which is 7( x+2) + 13 = 7x +14 +13
= 7x + 27
wirk out the values of 5x-2y when x=-2 and y = -2
Step-by-step explanation:
5x - 2y
5(-2) - 2(-2)
-10 + 4
= - 6
What is the conjugate
√8-√9
Answer:
[tex]\frac{-1}{(\sqrt{8}+\sqrt{9} )}[/tex]
Answer:
the water here is wet.
Step-by-step explanation:
Hannah went swimming after she woke up. It took Hannah 15 minutes to get ready to go swimming. She swam for 30 minutes and then sunbathed for 25 minutes. Then she talked on the phone with her friends for 35 minutes. She finished talking to her friends at 9:30 a.m. What time did Hannah wake up?
Find the total minutes:
15 + 30 + 25 + 35 = 105 minutes
This is equal to 1 hour and 45 minutes
Subtract 1 hour and 45 minutes from 9:30
She woke up at 7:45 am
The total surface area of a right circular cylinder is 84 pie cm square and the altitude is 11 cm .find the radius of the base
Answer:
r = 3cm
Step-by-step explanation:
Use the formula for the surface area of a cylinder and solve to obtain r=3cm
Hence radius of base is 3 cm of right circular cylinder.
What is a right circular cylinder?The cylinder is known as a right circular cylinder when the axis (one of the rectangle's sides) is perpendicular to the radius ((r)). The base and top of the right circular cylinder are both round and parallel to one another. The general formula for the total surface area of a cylinder is T. S. A. =[tex]2\pi rh+2\pi r^{2} .[/tex]
How to solve?Given total surface area of right circular cylinder =84[tex]\pi cm^{2}[/tex]
Using formula for right circular cyinder =.[tex]2\pi rh+2\pi r^{2} .[/tex]=84
and height=11 cm
[tex]2\pi r11+2\pi r^{2} =84.\pi[/tex]
⇒[tex]11r+ r^{2} =84/2[/tex]
⇒[tex]11r+ r^{2} =42[/tex]
⇒[tex]r^{2} +11r-42=0[/tex]
⇒r = [tex]\frac{-11+-\sqrt{11^{2}-4(1)42 } }{2}[/tex]
⇒r=[tex]\frac{-11+-17}{2}[/tex]
⇒r=3,-1
Hence radius of base is 3 cm as value can't be negative .
Learn more about surface area of cylinder https://brainly.com/question/12763699
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if sin B=8/17 WHAT IS TAN B?
Answer:
In first quadrant, [tex]\tan B=\frac{8}{15}[/tex]
In second quadrant, [tex]\tan B=\frac{-8}{15}[/tex]
Step-by-step explanation:
Given: [tex]\sin B=\frac{8}{17}[/tex]
To find: [tex]\tan B[/tex]
Solution:
Trigonometry explains the relationship between the sides and the angles of the triangle.
Here,
[tex]\sin B=\frac{8}{17}[/tex]
So, B can be in first or second quadrant as sine is positive both first and second quadrants.
Cosine and tangent are positive in first quadrant but negative in second quadrant.
In first quadrant:
[tex]\cos B=\sqrt{1-\sin ^2B}=\sqrt{1-\left ( \frac{8}{17} \right )^2}=\sqrt{1-\frac{64}{289}}=\sqrt{\frac{225}{289}}=\frac{15}{17}[/tex]
So, [tex]\tan B=\frac{\sin B}{\cos B}=\frac{\frac{8}{17}}{\frac{15}{17}}=\frac{8}{15}[/tex]
In second quadrant:
[tex]\cos B=-\sqrt{1-\sin ^2B}=-\sqrt{1-\left ( \frac{8}{17} \right )^2}=-\sqrt{1-\frac{64}{289}}=-\sqrt{\frac{225}{289}}=\frac{-15}{17}[/tex]
[tex]\tan B=\frac{\sin B}{\cos B}=\frac{\frac{8}{17}}{\frac{-15}{17}}=\frac{-8}{15}[/tex]
Factor 24g - 36h. Remember that your answer needs to be factored completely.
Answer:
The completed factor is [tex]=12(2g- 3h)[/tex]Step-by-step explanation:
To factor the expression we need to look for a value that is unique to both terms in the expression.
Given the expression
[tex]24g - 36h[/tex]
The available factors common to both terms are 2,3,4,6,8,12. but since we are expected to factor the expression completely we will use the greatest common factor (gcf) to find the solution
The greatest but common factor is 12, hence we have
[tex]=12(2g- 3h)[/tex]