Answer:
0.0174 = 1.74% probability that the sample mean hardness for a random sample of 10 pins is at least 51
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use 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 = 50, \sigma = 1.5, n = 10, s = \frac{1.5}{\sqrt{10}} = 0.4743[/tex]
What is the probability that the sample mean hardness for a random sample of 10 pins is at least 51
This is 1 subtracted by the pvalue of Z when X = 51. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{51 - 50}{0.4743}[/tex]
[tex]Z = 2.11[/tex]
[tex]Z = 2.11[/tex] has a pvalue of 0.9826
1 - 0.9826 = 0.0174
0.0174 = 1.74% probability that the sample mean hardness for a random sample of 10 pins is at least 51
Find the length of the rectangle whose area is 99 square inches and the width is 9 inches.
Answer:
the answer is 11
Step-by-step explanation:
??×9=99
9÷99=11
11×9=99
Answer: the answer is 11.
Step-by-step explanation:
because we know the width is 9, and the area is 99. but we don't know the length. so this is when you set up your equation: Lx9=99 (L= length) so the inverse operation of multiplication is division so divide 99 by 9 (99/9). and you get 11!
What's the measure of Z1 if Z CBD = 75° and ZABC = 135°?
Answer:
60°
Step-by-step explanation:
∠ABC-∠CBD=∠1
[tex]135-75[/tex]
[tex]=60[/tex]
Answer:
Brainliest goes to me!
Step-by-step explanation:
angle abc = 135 degrees
part of it is angle 1 and the other part is angle cbd
<abc (135) = cbd (75) + <1
angle 1 = 60 degrees
A random sample of college basketball players had an average height of 67.45 inches. Based on this sample, (64.9, 69.2) found to be a 95% confidence interval for the population mean height of college basketball players. Select the correct answer to interpret this interval.a. 95% of college basketball players have height between 64.9 and 69.2 inches. b. There is a 95% chance that the population mean height of college basketball players is between 64.9 and 69.2 inches. c. We are 95% confident that the population mean height of college basketball players is between 64.9 and 69.2 inches. d. We are 95% confident that the population mean height of college basketball players is 67.45 inches.
Answer:
The correct option is (C).
Step-by-step explanation:
The (1 - α)% confidence interval for population parameter implies that there is a (1 - α) probability that the true value of the parameter is included in the interval.
Or, the (1 - α)% confidence interval for the parameter implies that there is (1 - α)% confidence or certainty that the true parameter value is contained in the interval.
The 95% confidence interval for the population mean height of college basketball players is, (64.9, 69.2).
The interval (64.9, 69.2) implies that the probability that the true value of the parameter, mean height of college basketball players, is included in the interval is 0.95.
Or, there is a 95% confidence that the true mean height of college basketball players, is included in the interval (64.9, 69.2).
Thus, the correct option is (C).
If the difference between two numbers is 7 and their product is 137 what is the sum of squares if the numbers?
Answer:
323
Step-by-step explanation:
a-b= 7
ab= 137
a²+b²= ?
---------
Since (a-b)²= a²-2ab +b²
⇒ a²+b²= (a-b)² + 2ab= 7² + 2*137= 323
In the last round of a chess tournament the final match is between Alice and Diego. The winner is the first player to win three games [sometimes called "best of 5"]. Assume that they are equally matched, so that each player has an equal probability of winning each game. What is the probability that the match will be finished after the first 3 games are played?
Answer:
1/8
Step-by-step explanation:
For the match to be finished after 3 games are played, it means that 1 person my win 3 games in a row.
Since each player has a 50% chance of winning, the chances of it would be
1/2*1/2*1/2 or (1/2)^3
Therefore the answer is 1/8 chance
The probability that the match will be finished after the first 3 games are played is [tex]\frac{1}{8}[/tex]
The calculation is as follows:Since the match to be finished after 3 games are played this represent that 1 person my win 3 games in a row.
Each player has a 50% chance of winning, the chances of it should be
[tex]= (1\div 2)^3\\\\= \frac{1}{8}[/tex]
Learn more: https://brainly.com/question/864553?referrer=searchResults
Please show work for number 3 and 4!
Answer:
Three: x = 400
Four : 9
Step-by-step explanation:
Three
a = 10*√2
2a = √(2x) Square both sides.
4a^2 = 2x Divide both sides by 2
2a^2 = x Put a = 10√2 into a^2
2(10√2)^2 = x Square a
2(100*2) = x Multiply the result by 2.
2(200) = x
x = 400
Four
x^(a^2) / x ^(b^2) = x^36
Substitute a + b = 4 in for b.
x^(a^2) / x^(4 - a)^2 = x^36
Subtract powers
x^(a^2 - (4 - a)^2 = x^36
x^(a^2 - (16 - 8a + a^2) = x^36
Gather like terms
x^(8a - 16) = x^36
The powers are now equal
8a - 16 = 36
Add 16 to both sides
8a = 36 + 16
8a = 52
Divide by 8
a = 6.5
Solve for b
a + b = 4
6.5 + b = 4
b = 4 - 6.5
b = - 2.5
a - b = 6.5 - (- 2.5) = 9
Please help me....I need it
Answer:
Volume: 3x2x4=24 so the volume is 24 Meter3
Surface area:
52 Square meter
Mr. Taylor filled out a bracket for the NCAA National Tournament. Based on his knowledge of college basketball, he has a 0.54 probability of guessing any one game correctly. (a) What is the probability Mr. Taylor will pick all 32 of the first round games correctly
Answer:
The probability is [tex]2.7327 \times 10^{-9}[/tex]
Step-by-step explanation:
The probability of guessing correctly, P = 0.54
Probability of not guessing correctly, q = 1 – P
q = 1 – 0.54 = 0.46
Number of trials, n = 32
Now calculate the probability that Mr. Taylor will pick 32 correctly in first round of the game.
Below is the calculation using binomial distribution.
[tex]Probability = \left ( _{k}^{n}\textrm{} \right )P^{k}(1-P)^{(n-k)} \\= \left ( _{32}^{32}\textrm{} \right )0.54^{32}(0.46)^{(32-32)} \\= 0.54^{32} \\= 2.7327 \times 10^{-9}[/tex]
match the term with the definition
Answer:
1 - c
2 - a
3 - e
4 - d
5 - b
Answer: c, a, e, d, b
Step-by-step explanation:
1. Angle: (c) A figure consisting of two rays with the same endpoint.
2. Circle: (a) The set of all points in a plane that are a given distance from a point. That distance is called the radius.
3. Point: (e) A location, has no size.
4. Ray: (d) The portion of a line that starts at one point and goes off to infinity.
5. Vertex: (b) A point where two or more rays or "arms" of an angle meet.
Which of the following equations describes the line shown below? Check all
that apply.
(-6,4)
(3,1)
Answer:
y-4=-1/3(x+6)
y-1=1/3(x-3)
Step-by-step explanation:
4-1/-6-3
3/-9
-1/3
y-4=-1/3(x+6)
y-1=1/3(x-3)
Explain why the mass of an object remains the same both on earth and on the moon, but the same cannot be said about the weight of an object.
Answer. Mass is a measurement of how much matter is in an object; weight is a measurement of how hard gravity is pulling on that object. Your mass is the same wherever you are, on Earth; on the moon; floating in space, because the amount of stuff you're made of doesn't change. hope this help.............
In Triangle ABC, the measure of angle B is 36 degrees more than three times the measure of angle A. The measure of angle C is 54 degrees more than the measure of angle A. Find the measure of each angle.
Answer:
angle A = 18°
angle B = 36 + 3(18) = 90°
angle C = 54 + 18 = 72°
Step-by-step explanation:
A triangle is a shape with 3 sides. The total angle of a triangle is 180°. This means the sum of all the angle is 180°.
Let
angle A = a
angle B = 36 + 3a
angle C = 54 + a
The sum of angle A, B and C should be equals to 180°. Therefore,
a + 36 + 3a + 54 + a = 180°
collect like terms
5a + 90 = 180
5a = 180 - 90
5a = 90
divide both sides by 5
a = 90/5
a = 18°
angle A = 18°
angle B = 36 + 3(18) = 90°
angle C = 54 + 18 = 72°
d/3y - m/6y simplify
Answer:
(2d - m)/6y
Step-by-step explanation:
To simplify, we must first find the lowest common multiple (LCM) of the denominators which are 3y and 6y.
The LCM of 3y and 6y is 6y. We then make it the common denominator while we multiply the numerators with it.
Hence,
d/3y - m/6y
= (6y(d/3y) - 6y(m)/6y)/6y
Dividing and multiplying
= (2d - m)/6y
Answer:
(2d-m)/6y
Step-by-step explanation:
A man wants to set up a 529 college savings account for his granddaughter. How much would he need to deposit each year into the account in order to have $50,000 saved up for when she goes to college in 17 years, assuming the account earns a 5% return?
Answer:
1937.98
Step-by-step explanation:
In the given question, to find the value to be added per year we will use the formula
P= A. r/n/ (1 +r/n)ⁿ - 1
Here A = 50,000
r (rate of interest) = 5 % or 0.05.
n = 1
t = 17
P = value deposit per year
therefore, P = (50,000 X 0.05)/ (1 +0.05)¹⁷ - 1
P = 2500 / 2.29- 1
= 1937.98 $.
therefore, person has to deposit 1937.98 $ per month.
For each of the following, state whether you expect the distribution to be symmetric, right skewed, or left skewed. Also specify whether the mean or median would best represent a typical observation in the data, and whether the variability of observations would be best represented using the standard deviation or IQR. Explain your reasoning.
Housing prices in a country where 25% of the houses cost below $350,000, 50% of the houses cost below $450,000, 75% of the houses cost below $1,000,000 and there are a meaningful number of houses that cost more than $6,000,000.
The distribution is expected to be:___________.
1. symmetric
2. left skewed
3. right skewed
A typical observation is best represented by the:_______.
1. median
2. mean
The variability in the observations is best measured by the:________.
1. IQR
2. standard deviation
Answer:
Q₃ - Q₂ > Q₂ - Q₁
$550,000 > $100,000
Therefore, the distribution is expected to be right skewed.
Since the distribution is right-skewed, the median would best represent a typical observation in the data.
Since the distribution is right-skewed, The inter-quartile range (IQR) would be a better choice to represent the variability of data.
Step-by-step explanation:
Housing prices in a country where 25% of the houses cost below $350,000.
Which means that first quartile is Q₁ = $350,000
50% of the houses cost below $450,000.
Which means that second quartile is Q₂ = $450,000
75% of the houses cost below $1,000,000
Which means that third quartile is Q₃ = $1,000,000
Recall that the distribution will be symmetric if the following relation holds true
Q₃ - Q₂ = Q₂ - Q₁
Q₃ - Q₂ = $1,000,000 - $450,000 = $550,000
Q₂ - Q₁ = $450,000 - $350,000 = $100,000
Hence the distribution is not symmetric since
Q₃ - Q₂ ≠ Q₂ - Q₁
The distribution is right skewed since
Q₃ - Q₂ > Q₂ - Q₁
$550,000 > $100,000
Therefore, the distribution is expected to be right skewed.
Since the distribution is right-skewed, the median would best represent a typical observation in the data
Therefore, A typical observation is best represented by the median.
Since the distribution is right-skewed, The inter-quartile range (IQR) would be a better choice to represent the variability of data.
Therefore, the variability in the observations is best measured by the inter-quartile range (IQR).
Note:
For a symmetric distribution, the mean would best represent a typical observation in the data and the variability of observations would be best represented using the standard deviation.
Answer:
1. right skewed
2.median
3. IQR
Step-by-step explanation:
The distribution is expected to be:___________.3. right skewed
This is because most of the data lies on the right side of the observations . It has a left tail . Tail means the elongated side where the data is in lesser amount. If we analyze we see that 75% of the houses cost below $1,000,000 and a few houses are in between the cost range of $1,000,000 -$6,000,000 .
So there is lesser data on the left side meaning the distribution is right skewed.
A typical observation is best represented by the:_______.1. median
Normally when the distribution is symmetric it is best represented by the mean but since this is a right skewed the median provides the best observation.
The variability in the observations is best measured by the:________1. IQR
The interquartile range is best for skewed distributions just like the median. The standard deviation tells the percentage of observations it falls from the mean but in skewed distributions it is the interquartile range that gives the best measure of the variation from the median .The IQR ranges from the low of Q2 to the high of Q3 which is mostly the middle part .
EXREAMLY URGENT!! WILL FOREVER THANK YOU!!!! PLS JUST TAKE A LOOK!!!!! 20. What is the area of triangle XWZ?
Answer:
72√3
Step-by-step explanation:
30 60 90 triangles are what you start out with.
Step 1: 30-60-90
x = 12
WZ = 12√3
Step 2: Area formula
A = 1/2(12)(12√3)
*Since the 2 30-60-90 triangles are congruent, both segments of the base are 12
Plug it into the calc and you should get A = 72√3 as your final answer!
Alex is paid $30/hr at full rate, and $20/hr at a reduced rate. The hours of work are paid at a ratio of 2:1, full rate : reduced rate. For example, if he worked 3 hours, he would be paid 2 hours at full rate and 1 hour at reduced rate. Calculate his pay for 4 hours of work.
Answer:
$106.67
Step-by-step explanation:
Using the example, for 3 hours work, Alex would be paid ...
(2 hr)($30/hr) +(1 hr)($20/hr) = $60 +$20 = $80
At the same rate of pay, for 4 hours work, the pay would be ...
pay/(4 hr) = $80/(3 hr)
pay = $80(4/3) ≈ $106.67
Alex's pay for 4 hours of work is $106.67.
a) For what value(s) of k is the following SoLE inconsistent?
x - 2y + 4z = 3
4x + 5y + kz = 9
y + 3z = 2
Answer: z = 55.
Step-by-step explanation:
we want to find values of k that make this inconsistent.
x - 2y + 4z = 3
4x + 5y + kz = 9
y + 3z = 2
First, can you can see that k never can make some of the equations linearly dependent because of how constructed is the set. Now, let's see if there are values of k that give problems to our system.
To see it, let's solve the system.
from the third equation we can write y = 2 - 3z, and we can replace it into the first two equations:
x - 2(2 - 3z) + 4z = 3
4x + 5(2 - 3z) + kz = 9
simplify both equations and get
x + 10z = 7
4x + ( k - 15)*z = - 1
from the first equation, we have that:
x = 7 - 10z
we can replace it into the other equation:
4*(7 - 10z) + (k - 15)*z = -1
28 - 40z + (k -15)*z = -1
(k - 55)*z = -29
z = -29/(k - 55)
here you can see that the only value of z that has problems is z = 55, because we never can have a 0 in the denominator.
For each of the following, compute the present value:
Present Value Years Interest Rate Future Value
$12 4 % $18,928 4 9 43,117 16 12 806,382 21 11 663,816
Answer:
1. $11,822.61
2. $30,577.76
3. $131,546.81
4. $74,117.67
Step-by-step explanation:
The calculation of present value is shown below:-
[tex]Present\ value = \frac{Future\ value}{(1 + r)^n}[/tex]
For 1 scenario
[tex]Present\ value = \frac{\$18,928}{(1 + 0.04)^{12}}[/tex]
[tex]= \frac{\$18,928}{1.601}[/tex]
= $11,822.61
So, the present value of 1st scenario is $11,822.61
For 2nd scenario
[tex]Present\ value = \frac{\$43,117}{(1 + 0.09)^{4}}[/tex]
[tex]= \frac{43,117}{1.411}[/tex]
= $30,577.76
So, the present value of 2nd scenario is $30,577.76
For 3rd scenario
[tex]Present\ value = \frac{\$806,382}{(1 + 0.12)^{16}}[/tex]
[tex]Present\ value = \frac{\$806,382}{6.130}[/tex]
= $131,546.81
So, the present value of 3rd scenario is $131,546.81
For 4th scenario
[tex]Present\ value = \frac{\$663,816}{(1 + 0.11)^{21}}[/tex]
[tex]= \frac{\$663,816}{8.949}[/tex]
= $74,117.67
So, the present value of 4th scenario is $74,117.67
Therefore we simply applied the above formula
Jaden had 2 7/16 yards of ribbon. He used 1 3/8 yards of ribbon to make a prize ribbon. How much does he have now?
EASY!
Answer: 17/16 or 1 1/16
Step-by-step explanation:
BRO IT'S ELEMANTARY FRACTIONS!!!!
The ratio of the area of a square of side 15 cm to that of a rectangle, 24 cm long, is 5 : 4 . What is the breadth of the rectangle
Answer:
7.5cm
Step-by-step explanation:
15²=225cm²
225/5=45
45*4=180cm²
180/24=7.5
7.5cm should be your answer. If not, I am sorry.
Answer:
The breadth of the rectangle would be [tex]7.5\:cm[/tex]
Step-by-step explanation:
Write down the ratio and then solve for unknown.
[tex]\frac{5}{4}=\frac{15\cdot 15}{24\cdot w}\\\\5\cdot \:8w=4\cdot \:75\\\\w=\frac{15}{2}\\\\w=7.5\:cm[/tex]
Best Regards!
Find the value of each variable
Answer:
To find a we use sine
sin 60° = a / 4√3
a = 4√3sin60°
a = 6
To find b we use sine
sin 45° = a / b
a = 6
b = 6 / sin 45°
b = 6√2
To find c we use cosine
cos 60° = c / 4√3
c = 4√3 cos 60°
c = 2√3
To find d we use tan
tan 45° = a / d
a = 6
d = 6 / tan 45°
d = 6
Therefore a = 6 b = 6√2 c = 2√3
d = 6
That's option A.
Hope this helps
Please help! I have no clue what im doing
Answer:
y = -2x + 1
Step-by-step explanation:
So, first you can use rise over run between the two points to find the slope.
This will get you -6/3, which you can simplify to -2
Then, see where the y intercept is, which is at (0, 1)
The equation will be y = -2x + 1
Answer:
y = -2x + 1
Step-by-step explanation:
(-3 - 3) / (-2 +1) = a slope of -2
The y-intercept is 1 because that's where the line crosses the y-axis.
y = -2x + 1
X squared plus 5x plus 6 in a factor of binomials
Answer:
(x + 3)(x + 2)
Step-by-step explanation:
Given
x² + 5x + 6
Consider the factors of the constant term (+ 6) which sum to give the coefficient of the x- term (+ 5)
The factors are + 3 and + 2 , since
3 × 2 = 6 and 3 + 2 = 5 , thus
x² + 5x + 6 = (x + 3)(x + 2)
A photographer uses an online service to sell some of his work. The amount of money he will make from selling 10 copies of the same photograph is given by the expression below, where p represents the price determined for each copy: 10(0.75p - 0.5) According to this expression, which of the following most likely describes the agreement between the online service company and the photographer? A. The company keeps 25% of the amount paid for each copy and charges the photographer $0.50 for every copy purchased. B. The company keeps 25% of the amount paid for each copy and charges the photographer $0.50 for every 10 copies purchased. C. The company keeps 75% of the amount paid for each copy and charges the photographer $0.50 for every copy purchased. D. The company keeps 75% of the amount paid for each copy and charges the photographer $0.50 for every 10 copies purchased.
Answer:
Step-by-step explanation:
The expression representing the amount of money that the photographer would make from selling 10 copies is given as
10(0.75p - 0.5)
where p represents the price determined for each copy. Assuming the price charged per copy is $5, then the amount made from 10 copies is
10(0.75 × 5 - 0.5) = $32.5
It could have been
10(5 - 0.5) = $45
The price is being reduced by 25%(100 - 75)
Therefore, the option that most likely describes the agreement between the online service company and the photographer is
A. The company keeps 25% of the amount paid for each copy and charges the photographer $0.50 for every copy purchased.
Help solve attached question.
Answer:
[tex]\mathrm{12\sqrt{5} \: \: inches}[/tex]
Step-by-step explanation:
Use Pythagorean theorem, where:
[tex]a^2+b^2=c^2[/tex]
Substitute in the values.
[tex]24^2+12^2=c^2[/tex]
[tex]c^2=576+144[/tex]
[tex]c^2=720[/tex]
[tex]c=\sqrt{720}[/tex]
[tex]c=12\sqrt{5}[/tex]
[tex]c=26.83281[/tex]
2 = x-3, then x equals
Answer:
x = 5
Step-by-step explanation:
2 = x-3
Adding 3 to both sides
2+3 = x
5 = x
OR
x = 5
Answer:
[tex] \times = 2 + 3 \\ \\ x = 5[/tex]
Examine the rotation. Which best describes point D?
Answer:
Center of rotation
Step-by-step explanation:
The numbers of beans in some cocoa pods
are 30, 28, 30, 35, 40, 25, 32, 36, 38 and 40.
a Calculate the mean number of beans per
cocoa pod.
b Calculate the standard deviation of the
distribution.
Answer:
a) Mean number of beans = 33.4 per coco pad
b) Standard deviation of the beans = 5.2 per coco pad
Step-by-step explanation:
Step(i):-
a)
Given data 30, 28, 30, 35, 40, 25, 32, 36, 38 and 40.
mean of beans
x⁻ = ∑x/n
[tex]x^{-} = \frac{30+ 28+30+35+40+25+32+36+38 + 40.}{10} = 33.4[/tex]
Mean number of beans per coco pad = 33.4
step(ii):-
b)
standard deviation
∑(xi - x⁻)² = (30-33.4)²+ (28-33.4)²+(30-33.4)²+(35-33.4)²+(40-33.4)²+(25-33.4)²+(32-33.4)²+(36-33.4)²+ (38-33.4)²+(40-33.4)²
On calculation , we get
∑(xi - x⁻)² = 242.4
standard deviation
= [tex]\sqrt{\frac{sum((x-x^{-} )^{2} }{n-1} } = \sqrt{\frac{242.4}{10-1} } = 5.189[/tex]
Standard deviation of the beans (σ) = 5.2 per coco pad
UTGENT! I really need help, can anyone help me?
Answer:
x = 3.6
Step-by-step explanation:
By the Postulate of intersecting chords inside a circle.
[tex]x \times 5 = 3 \times 6 \\ 5x = 18 \\ x = \frac{18}{5} \\ x = 3.6 \\ [/tex]
