Answer:
0.0802 = 8.02% probability that the sample mean would differ from the population mean by more than 2.2 millimeters
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 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.
Their current steel bolts have a mean diameter of 148 millimeters, and a standard deviation of 7 millimeters.
This means that [tex]\mu = 148, \sigma = 7[/tex]
Sample of 31:
This means that [tex]n = 31, s = \frac{7}{\sqrt{31}}[/tex]
What is the probability that the sample mean would differ from the population mean by more than 2.2 millimeters?
Less than 148 - 2.2 = 145.8 or more than 148+2.2 = 150.2. Due to the simmetry of the normal distribution, these probabilities are the same, which means that we find one and multiply by 2.
Probability of being less than 145.8:
The pvalue of Z when X = 145.8. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{145.8 - 148}{\frac{7}{\sqrt{31}}}[/tex]
[tex]Z = -1.75[/tex]
[tex]Z = -1.75[/tex] has a pvalue of 0.0401
2*0.0401 = 0.0802
0.0802 = 8.02% probability that the sample mean would differ from the population mean by more than 2.2 millimeters
What's the inverse of 3x+2
Answer:
The inverse is
y = 1 /3 x − 2 /3
Step-by-step explanation:
How can I solve this quadratic using the square root properly?
Answer:
x = +3
Step-by-step explanation:
4x² = 36
sqareroot both side we get,
√4x² = √36
2x = 6
x = 6/2
x = +3
Thus, The answer is +3
-TheUnknownScientist
Answer:
4x^2 = 36
________ x^2 = 9. square root of 9
4. = 4. x = 3
Step-by-step explanation:
Divide both sides by 4 to isolate the square root.
So, you will end up with x^2 = 9
then take the square root of 9,
square root of 9 is 3.
So x = 3
Find the area of the circle
Answer:
49 is the area for the circle
How do I solve this quadratic using the square root property
Answer: x=2−2√3,2+2√3
Step-by-step explanation:
I know how to solve this problem
COLLEGE MATH! HARD!
NO LINKS OR YOU WILL BE REPORTED!!!!!!!!!
Find the formula for the function of the form w(x)= Asin(Bx)+C with an (i) a maximum (3,6),(i) a minimum at (-9,6), and (iii) no critical points between these two points
Please help, brainliest for correct answer
Answer:
The volume of the cone would be 2513.27 cubic feet.
Find the third quartile Q3 of the list of 24 sorted values shown below.
30 31 31 37 38 38 39 39 42 42 43 46 47 48 50 52 54 57 61 63 68 69 76 79
The third quartile Q3 is
(Type an integer or a decimal.)
Answer:
60
Step-by-step explanation:
The computation of the third quartile is given below:
The third quartile Q3 is
= 3(n + 1)÷ 4
= 3 (24 + 1) ÷ 4
= 75 ÷ 4
= 18.75th term
Now the 18.75th term is
= 18th term + 0.75 term
= 57 + (19 term - 18term)
= 57 + 0.75 (61 - 57)
= 57 + 0.75 (4)
= 60
What is the price of a $90 mobile phone after a 30% discount?
Answer:
I believe it would be 63 because the phone costs 90 dollars originally but with the discount being 30% (90 multiply 0.3) and you get $27. However then you gotta then subtract (90-27) to get 63.
I will give Brainly plzzz ASAP
Answer:
Im pretty sure the answer would be 6
Step-by-step explanation:
Just take 42 and divide by 7 to get x
Answer:
did you finish this already
I NEED ANSWERS WITH WORKOUT PLS ANYONE HELP / WRITE ON PAPER!
-giving brainlist
Answer:
I don't know if this is all correct, but I tried
Is the graph increasing, decreasing, or constant?
O A. Constant
B. Decreasing
C. Increasing
Answer:
Decreasing because the line is going down meaning it is decreae
Abdul uses 15 1/2 cups of flour to make 3 loaves of bread. At that rate, how many cups of flour would Abdul need to make 4 loaves of bread??
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I'LL REPORT IT IF YOU DO
Answer: 10 cups of flour
Step-by-step explanation:
15 1/2 cups of flour = 7 1/2 cups
7 1/2 ÷ 3 = 2 1/2
So, it takes 2 1/2 cups of flour to make one loaf of bread
If you want to make 4 loaves of bread, you multiply 2 1/2 × 4
2 1/2 × 4 = 10
It will take 10 cups of flour to make 4 loaves of bread.
which of the following sequences of transformation maps MNO onto ABC?
Answer:
MNO no se estoy en 6th y no se pero esta es mi respuesta espero y me la saco bien
The sequence of transformations T(–2, 4) ry-axis ry-axis T(2, –4) can be used to map triangle MNO onto M"N"O".
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
The given sequence of transformations is:
T(–2, 4) - translation by (-2, 4)
ry-axis - reflection across the y-axis
ry-axis - reflection across the y-axis
T(2, –4) - translation by (2, -4)
We can check whether this sequence of transformations maps triangle MNO onto M"N"O" by applying each transformation to the coordinates of triangle MNO in order:
T(–2, 4) maps M(5,-4) to M'(3,0), N(3,-2) to N'(1,2), and O(1,-3) to O'(-1,1).
ry-axis reflects M'(-3,0) to M"(-3,0), N'(1,2) to N"(-1,2), and O'(-1,1) to O"(1,1).
ry-axis reflects M"(-3,0) back to M"(-3,0), N"(-1,2) back to N"(-1,2), and O"(1,1) back to O"(1,1).
T(2, –4) maps M"(-3,0) to M'(-1,-4), N"(-1,2) to N"(1,-2), and O"(1,1) to O"(3,-3).
The resulting coordinates M'(-1,-4), N'(1,-2), and O'(3,-3) are the coordinates of triangle M"N"O".
Therefore, the given sequence of transformations T(–2, 4) ry-axis ry-axis T(2, –4) can be used to map triangle MNO onto M"N"O".
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which statement about this triangle is true?
tan 0= 4/5
sin 0 = 3/5
cos 0 = 3/5
sin 0 = 3/4
Answer:
I'm not sure but I believe it is than 0=4/5
In ΔMNO, m = 5.6 cm, o = 4.6 cm and ∠O=39°. Find all possible values of ∠M, to the nearest 10th of a degree.
Answer:
Answer: 50∘ and 130∘
Step-by-step explanation:
deltamath:)
The measures of M are 50.0 and 130 degrees
The given parameters are:
[tex]\mathbf{m = 5.6cm}[/tex]
[tex]\mathbf{o = 4.6cm}[/tex]
[tex]\mathbf{\angle O = 39^o}[/tex]
The measure of angle M is calculated using the following sine formula
[tex]\mathbf{\frac{o}{sin\ O} = \frac{m}{sin\ M}}[/tex]
So, we have:
[tex]\mathbf{\frac{4.6}{sin\ 39} = \frac{5.6}{sin\ M}}[/tex]
Evaluate sin 39
[tex]\mathbf{\frac{4.6}{0.6293} = \frac{5.6}{sin\ M}}[/tex]
Cross multiply
[tex]\mathbf{sin\ M \times 4.6 = 5.6 \times 0.6293}[/tex]
[tex]\mathbf{sin\ M \times 4.6 = 3.5241}[/tex]
Divide both sides by 4.6
[tex]\mathbf{sin\ M = 0.7661}[/tex]
Take arc sin of both sides
[tex]\mathbf{M = sin^{-1}(0.7661)}[/tex]
[tex]\mathbf{M = 50.0}[/tex]
The other possible value of M is:
[tex]\mathbf{M = 180 -50.0}[/tex]
[tex]\mathbf{M = 130.0}[/tex]
Hence, the measures of M are 50.0 and 130 degrees
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Help please will mark brainliest!!!
Answer:
18
Step-by-step explanation:
In Middletown, Main Street and Market Street are parallel to each other. Patrick Street intersects Market Street to form a 76° angle at the northeast corner, as shown in the figure below. What is the measure of the angle formed at the southeast corner of Main Street and Patrick Street? (Note: Each street is straight and has the same uniform width.)
I WILL GIVE OUT BRAINLIEST IF CORRECT!
A. 76°
B. 90°
C. 104°
D. 142°
E. 152° (NOT E)!
Answer:
e
Step-by-step explanation:
Answer
C
Step-by-step explanation:
76+104 is 180
Tara had 1 5/8 pounds of dried nuts. She ate 1/4 pound of dried nuts each day for 6 days? How many pounds of dried nuts did Tara have left after 6 days?
Answer:
1/8
Step-by-step explanation:
its easy just count backwards by 2/8 each time
HELP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
Answer:
6/13
Step-by-step explanation:
Which of the following equations represents a linear function
Answer:
its B
Step-by-step explanation:
please like my answer . brainliest please
tonya earned $5.00 she put half of the money into savings and kept the rest to spend.she bought a toy for $2.00.how much spending money dose tonya have left?
Answer:
50 cents
Step-by-step explanation:
half of 5.00$ is 2.50$
Please help me!
1. Find the coordinates of the vertices of the feasible region. Next, Find the value for R for each vertex
2. Consider the feasible region in the xy-plane defined by the following linear equalities:
X>=0
Y>=0
X<=12
X + Y >= 4
-X + 2Y <= 14
A. Find the value of Q=70x+82y for each vertex
B. What are the minimum and maximum values of the function Q on the feasible region?
Can anyone tell me what the answer please
What you're looking at in this image are two alternate exterior angles.
Alternate exterior angles, are, essentially, exterior angles of a transversal that runs through two parallel lines. These angles are on alternating sides. These angles, assuming the lines are parallel, must be equal.
There's a proof behind why these angles are equal, but I won't bore you with the specifics as the question doesn't require it.
So - we know that these two angles must be equal to prove that the lines A and B are parallel. Knowing this, we can write an equation:
5x + 20 = 3x + 60
Subtract 20 from both sides:
5x + 20 - 20 = 3x + 60 - 20
5x = 3x + 40
Subtract 3x from both sides:
5x - 3x = 3x - 3x + 40
2x = 40
x = 20
If you have any questions on how I got to the answer, just ask!
- breezyツ
Invent measurements that would show triangle XYZ is similar to triangle NLM using the Side-Angle-Side Triangle Similarity Theorem.
Answer:
The answer is that when you put the LMN. You can rotate it. Then we know it is similar.
Using the rotation method of the triangle LMN show triangle XYZ is similar to triangle NLM using the Side-Angle-Side Triangle Similarity Theorem.
What is the similarity law for triangles?It is necessary to demonstrate compliance with the law to establish that two triangles are identical in both shape and size. The angles that correspond to those sides have the same congruence and the same ratio of sides.
It is given that the two triangles are triangle XYZ and triangle NLM.
Two triangles are said to be comparable if the ratio of one triangle's two sides to the two sides of another triangle is the same, and the angles that the two sides of both triangles inscribe are equal.
Thus, triangle XYZ is similar to triangle NLM using the Side-Angle-Side Triangle Similarity Theorem.
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Simplify
b + 4 + 4 + b=
Answer:
2b+8 is the simplify expression
Answer:
b + 4 + 4 + b=
= +b +b +4 +4
= 2b + 8
__________________________
another way
b + 4 + 4 + b=
= +b +b +4 +4
= 2b + 8
= b = [tex]\frac{8}{2} \\\\[/tex]
= b= 4
Ans: b= 4
Please help with these two problems don't rip me off I'm being generous.
Answer:
8 is $230
Step-by-step explanation:because there is a fee of $55 and $25 a week, the $55 is a one time charge and then $25 times 7 weeks is $175 then $55+$75 is $230
Is this correct? Pls help me
Answer:
I Belive so
Step-by-step explanation:
A baby fish was 1.5 centimeters in length when it first hatched . The fish grew at a rate of 0.25 centimeter per week.
Which graph best shows this relationship between the length of the fish in centimeters , y, and the time in weeks, x?
If you think about I would suggest B only because it makes more sense but I might be wrong..
Hope this helped a little!
The solution is Option A.
The equation of line is y = 0.25x + 1.5 , where the slope m = 0.25
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
The initial length of the baby fish is b = 1.5 cm
The baby fish grew at a rate of 0.25 centimeter per week
So , the slope of the line m = 0.25 cm
And , equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
Substituting the values in the equation , we get
y = 0.25x + 1.5 be equation (1)
Hence , the equation of line is y = 0.25x + 1.5
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Which choice includes all of the solutions to 2x2 + x – 3 = 0 by factoring
A. 1
B. 3, –1/2
C. –1, 3/2
D. 1, –3/2
Answer:either c or b
Step-by-step explanation: to be honest I searched up
The solution of Equation 2x² + x -3 =0 by factoring is 1 and -3/2.
What is Factorization?The breaking or decomposition of an entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, whose multiplication results in the original number, matrix, etc., is known as factorization or factoring in mathematics.
We have the equation 2x² + x -3 =0
Now, factorizing the above equation using splitting the middle term we get
2x² + x -3 =0
2x² + 3x - 2x -3 =0
x( 2x + 3) - (2x+ 3)= 0
(2x + 3)(x - 1)= 0
x = -3/2 or 1.
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4x + 7y - 3x - y show work please
Answer:
Step-by-step explanation:
4x + 7y - 3x - y
Move like terms next to each other.
4x - 3x + 7y - y
Subtract them
4x-3x= 1x or x
7y-y = 6y
So we have:
x + 6y