Qualification exams for becoming a state-certified welding inspector are based on multiple-choice tests. As in any multiple-choice test, there is a possibility that someone who is simply guessing the answers to each question might pass the test. Let x denote the number of correct answers given by a person who is guessing each answer on a 25-question exam, with each question having five possible answers (for each question, assume only one of the five choices is correct).(a) What type of probability distribution does x have?(b) For the 25-question test, what are the mean and standard deviation of x?(c) The exam administrators want to make sure that there is a very small chance, say, 1%, that a person who is guessing will pass the test. What minimum passing score should they allow on the exam to meet this requirement?
Answers
Answer:
(a) The probability distribution of the random variable X is Binomial.
(b) The mean and standard deviation of the 25-question test are 5 and 2 respectively.
(c) The value of x is 0.34.
Step-by-step explanation:
The random variable X is defined as the number of correct answers given by a person who is guessing each answer on a 25-question exam.
There are five possible answer for every question.
This implies that the probability of getting a correct answer is:
P (X) = 0.20.
There are a total of n = 25 questions.
Every answer is independent of the others.
(a)
The random variable X has finite number of independent trials (i.e. 25 questions). There are only two outcomes for each trial, i.e. Success = correct answer and Failure = wrong answer. Each trial has the same probability of success (, i.e. P (X) = 0.25).
Thus, the probability distribution of the random variable X is Binomial with parameters n = 25 and p = 0.20.
(b)
Compute the mean of the random variable X as follows:
\(E(X)=np\\=25\times 0.20\\=5\)
Compute the standard deviation of the random variable X as follows:
\(SD(X)=\sqrt{np(1-p)}\\=\sqrt{25\times 0.20\times (1-0.20)}\\=2\)
Thus, the mean and standard deviation of the 25-question test are 5 and 2 respectively.
(c)
The sample is large and the probability of success is close to 0.50.
So a Normal approximation to binomial can be applied to approximate the distribution of X if the following conditions are satisfied:
1. np ≥ 5
2. n(1 - p) ≥ 5
Check the conditions as follows:
\(np=25\times 0.20=5=5\\\\n(1-p)=25\times (1-0.20)=20>5\)
Thus, a Normal approximation to binomial can be applied.
So, \(X\sim N(5, 2^{2})\)
It is provided that the minimum passing score foe the test is such that only 1% of students who are guessing will pass the test.
That is P (X < x) = 0.01.
⇒ P (Z < z) = 0.01
The value of z is -2.33.
Compute the value of x as follows:
\(z=\frac{x-\mu}{\sigma}\\\\-2.33=\frac{x-5}{2}\\\\x=5-(2.33\times 2)\\\\x=0.34\)
Thus, the value of x is 0.34.
Related Questions
. If two of the angles in a scalene triangle are 54° and 87°, what is the other angle?
Answers
The answer is:
⇨ x = 39°Work/explanation:
Bear in mind that the sum of all the angles in a triangle is 180°.
Given two angles, we can easily find the third one.
Let's call it x.
Next, we set up an equation:
\(\sf{54+87+x=180}\)
\(\sf{141+x=180}\)
Subtract 141 on each side.
\(\sf{x=180-141}\)
\(\sf{x=39}\)
Hence, the other angle is 39°.A polygon with an area of 10 square inches is dilated by a scale factor of 4, what is the new area?
Answers
The new area would be 40 square inches. When a scale factor dilates a polygon, the area is multiplied by the square of the scale factor. If the original area is 10 square inches and the scale factor is 4, the new area would be 10 x 4^2 = 10 x 16 = 40 square inches.
The ratio of flour to sugar in a recipe is 3 cups to 2 cups. If this amount makes 3 dozen
cookies, how many cups of sugar are required in order to make 24 cookies?
Answers
Answer:
10 cups
Step-by-step explanation:
The ratio of flour to sugar to make 3 dozen cookies is 3/2 then a total of 1.33 cups of sugar is required to make 24 cookies.
What is an arithmetic operation?Addition, subtraction, multiplication, and division of two or even more integers are the four basic mathematical operations. Included among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.
As per the given data provided in the question,
3 dozen = 12 × 3 = 36 cookies.
2 cups of sugar are required to make 36 cookies
Let x cup of sugar is required to make 24 cookies.
36 cookies = 2 cups
24 cookies = x cups
Cross-multiply both the equations above
x = (24 × 2)/36
x = 1.33 cups.
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Triangle ABC has the vertices A(2, 0), B(4, 2), and C(3, 4).
Name the ordered pair of C' after a reflection across the
x-axis.
Answers
Answer: C’(3,-4)
Step-by-step explanation: All you have to do is count how many blocks away is the point from the x axis and then count down the x axis where you stop counting and that is how you get your point.
What is the exact distance from (−1, 4) to (6, −2)? square root of 80. units square root of 82. units square root of 85. units square root of 89. units
Answers
Answer:
\(\sqrt{85}\).
Step-by-step explanation:
\(x\)-coordinates:
First point: \(-1\).Second point: \(6\).Difference: \(|-1 - 6| = |-7| = 7\).\(y\)-coordinates:
First point: \(4\).Second point: \(-2\).Difference: \(|4 - (-2)| = |6| = 6\).Refer to the diagram attached. Consider these two points as the two end points of the hypotenuse of a right triangle. The lengths of the two legs are equal to:
the difference between the two \(x\)-coordinates, \(7\), and the difference between the two \(y\)-coordinates, \(6\).Apply Pythagorean Theorem to find the length of the hypotenuse (which is equal to the distance between the two points in question.)
\(\begin{aligned}\text{Hypotenuse} &= \sqrt{(\text{First Leg})^2 + (\text{Second Leg})^2} \\ &= \sqrt{7^2 + 6^2} \\ &= \sqrt{85}\end{aligned}\).
Answer:
C
Step-by-step explanation:
Select all lengths that are equal to 3 yards 16 inches.
Answers
The lengths equal to 3 yards 16 inches are 3 yards, 108 inches, 3.44 yards (approximately), and 108.44 inches (approximately).
To determine the lengths that are equal to 3 yards 16 inches, we need to convert the measurements into a consistent unit. Since both yards and inches are units of length, we can convert the inches into yards or the yards into inches to find the equivalent lengths.
1 yard is equal to 36 inches (since 1 yard = 3 feet and 1 foot = 12 inches).
Therefore, 3 yards is equal to 3 * 36 = 108 inches.
Now, we can compare 108 inches to 3 yards 16 inches.
108 inches is equal to 3 yards, so it matches the given length.
To convert 16 inches into yards, we divide it by 36 since 1 yard = 36 inches. 16 inches / 36 = 0.44 yards.
Therefore, 3 yards 16 inches is equivalent to:
3 yards
108 inches
3 yards 0.44 yards (or approximately 3.44 yards)
108 inches 0.44 yards (or approximately 108.44 inches)
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Describe the transformation that maps the pre-image A to the image A.
A)
translated 8 units up and then reflected across the y-axis
B)
translated 8 units down and then reflected across the y-axis
C)
translated 1 unit to left and then rotated 180° counterclockwise about the
origin
D)
translated 1 unit to right and then rotated 180° counterclockwise about the
origin
Answers
Answer:
C) translated 1 unit to the left and then rotated 180° counterclockwise about the origin
Step-by-step explanation:
by inspection, shape A has been translated 1 unit to the left and then rotated 180° counterclockwise about the origin
3.) Given the graph of the line represented by the equation f(x) = -3x + b,
if b is decreased by 5 units, the graph of the new line would be shifted 5 units
1) right
2) up
3) left
4)down
Answers
Answer: (4)
Step-by-step explanation:
Rose wants to get 90% on a 40 question quiz. How many questions must she get correct?
Answers
Answer:
36 questions
Step-by-step explanation:
Find 90% of 40 by turning 90 to a decimal and multiplying 0.9 x 40
Answer:
36!!! (I answered on other question too)
Step-by-step explanation:
Nathan has a bicycle where the wheels are have a 13 inch radius. He makes two revolutions. How far did he
travel?
Answers
Answer:
163.28 inches
Step-by-step explanation:
Find the circumference:
2π r
2 X 3.14 X 13
6.28 X 13
=81.64 inches.
81.64 X 2 =163.28 inches
What is the solution to Three-fourths a greater-than negative 16?
a greater-than negative 21 and one-third
a less-than negative 21 and one-third
a greater-than 21 and one-third
a less-than 21 and one-third
will give brainliest
Answers
Answer:
a greater-than negative 21 and one-third
Step-by-step explanation:
3/4a>-16
divide both sides by 3/4
a>-16*4/3
a>-64/3
a>-21 1/3
so then
a greater-than negative 21 and one-third
Good luck on the test.
Haryati had 1250 oranges.She gave away 242 oranges.
Answers
Answer:
She has 1008 oranges left.
Step-by-step explanation:
Haryati has 1250 oranges.
She gives 242 away.
1250-242 = 1008
Therefore, she has 1008 oranges left.
Answer:
Hope my answer helps mark me brainliestStep-by-step explanation:
total number of oranges= 1250total given away oranges=242oranges left with haryati=1250-242 =1008an airplane flies 390 miles in 3/4 hour. what is its average speed in miles per hour
Answers
Answer:
1,560mi/h
Step-by-step explanation:
390 miles in 15 minutes
X miles in 60 minutes
(Cross multiplication)
(390*60)/15 = 1560
Use the Rational Zeros Theorem to write a list of all possible rational zeros of the function. f(x) = -2x4 + 4x3 + 3x2 + 18
Answers
Step-by-step explanation:
USING RATIONAL ROOT THEOREM:
a = ±2
Factors of a are ±1 ,±2
For the constant term
c= ±18
The factors of c are ±1,±2,±3,±6,±9 and ±18
THE POSSIBLE ZEROES ARE GIVEN BY
c/a=(±1,±2,±3,±6,±9,±18)/(±1 ,±2)
Therefore, the possible zeroes are
±1,±2,±3,±6,±9,±18,±1/2,±3/2,±9/2
For the function f(x) = 5x^2 + 3x - 8. What is the value of the function when x=3 ?
Answers
Answer:
46Step-by-step explanation:
\(f(x) = 5x^2 + 3x - 8\\x =3\\\\= 5(3)^2+3(3)-8\\\mathrm{Follow\:the\:PEMDAS\:order\:of\:operations}\\\\\mathrm{Calculate\:exponents}\:\left(3\right)^2\::\quad 9\\=5\cdot \:9+3\left(3\right)-8\\\\\mathrm{Multiply\:and\:divide\:\left(left\:to\:right\right)}\:5\cdot \:9\::\quad 45\\=45+3\left(3\right)-8\\\\\mathrm{Multiply\:and\:divide\:\left(left\:to\:right\right)}\:3\left(3\right)\::\quad 9\\=45+9-8\\\\\mathrm{Add\:and\:subtract\:\left(left\:to\:right\right)}\:45+9-8\:\\:\quad 46\)
Hope this helps :)
PLEASE I NEED HELP ITS DUE SOON
Answers
Answer:
Third choice from top to bottom.
Step-by-step explanation:
The total amount of students would be exactly - 220 students. So that means reading would be exactly 20% of the students, as of 40/220 = 0.2 = 20%. That means automaticially the third choice would be correct, but let's do more calculations to make sure- 55/220 = 25%, 66/220 = 30%. That means that our answer is in fact correct.
A dot plot is shown.
Answers
Answer:
C i think but I could be wrong
Step-by-step explanation:
Determine which of the following transformations are linear transformations
A. The transformation T1
defined by T1(x1,x2,x3)=(x1,0,x3)
B. The transformation T2
defined by T2(x1,x2)=(2x1−3x2,x1+4,5x2)
.
C. The transformation T3
defined by T3(x1,x2,x3)=(x1,x2,−x3)
D. The transformation T4
defined by T4(x1,x2,x3)=(1,x2,x3)
E. The transformation T5
defined by T5(x1,x2)=(4x1−2x2,3|x2|)
.
Answers
The transformation T1 defined by T1(x1,x2,x3)=(x1,0,x3) is linear transformation among the five given questions.
A linear transformation satisfies two properties: additivity and homogeneity. That is, for any vectors u and v, and any scalars a and b:
T(u + v) = T(u) + T(v)
T(au) = aT(u)
Using these properties, we can determine which of the given transformations are linear transformations:
A. The transformation T1 defined by T1(x1,x2,x3)=(x1,0,x3)
T1(u+v) = (u1+v1, 0, u3+v3) = (u1, 0, u3) + (v1, 0, v3) = T1(u) + T1(v)
T1(au) = (au1, 0, au3) = a(u1, 0, u3) = a*T1(u)
Therefore, T1 is a linear transformation.
The transformation T2 defined by T2(x1,x2)=(2x1−3x2,x1+4,5x2)
T2(u+v) = (2(u1+v1)−3(u2+v2), u1+v1+4, 5(u2+v2))
= (2u1−3u2, u1+4, 5u2) + (2v1−3v2, v1+4, 5v2) = T2(u) + T2(v)
However, T2 does not satisfy homogeneity property. Consider a = -1 and u = (1, 1):
T2(-u) = (-2, 5, -5)
-1*T2(u) = (-2, -5, -5)
Therefore, T2 is not a linear transformation.
The transformation T3 defined by T3(x1,x2,x3)=(x1,x2,−x3)
T3(u+v) = (u1+v1, u2+v2, -(u3+v3)) = (u1, u2, -u3) + (v1, v2, -v3) = T3(u) + T3(v)
T3(au) = (au1, au2, -au3) = a*(u1, u2, -u3) = a*T3(u)
Therefore, T3 is a linear transformation.
The transformation T4 defined by T4(x1,x2,x3)=(1,x2,x3)
T4(u+v) = (1, u2+v2, u3+v3) ≠ (1, u2, u3) + (1, v2, v3) = T4(u) + T4(v)
T4(au) = (1, au2, au3) ≠ a(1, u2, u3) = a*T4(u)
Therefore, T4 is not a linear transformation.
The transformation T5 defined by T5(x1,x2)=(4x1−2x2,3|x2|)
T5(u+v) = (4(u1+v1)−2(u2+v2), 3|u2+v2|)
= (4u1−2u2, 3|u2|) + (4v1−2v2, 3|v2|) ≠ T5(u) + T5(v)
T5(au) = (4au1−2au2, 3|au2|) ≠ a*T5(u)
Therefore, T5 is not a linear transformation.
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how do I solve the equation x/5 + 13 = 25
Answers
Answer:
\( \frac{60}{5} + 13 = 25 \\ 12 + 13 = 25\)
Step-by-step explanation:
\(25 = \frac{x}{5} + 13 \\ 25 - 13 = \frac{x}{5} \\ 12 = \frac{x}{5 } \\ 12 \times 5 = x \\ 60 = x\)
Answer:
x=60
Step-by-step explanation:
Move all terms not containing x to the right side of the equation.
Subtract 13 from both sides of the equation.
x/5=25-13
Subtract 13 from 25 .
x/5=12
Multiply both sides of the equation by 5 .
5*x/5=5*12
Simplify both sides of the equation.
Cancel the common factor of 5 .
x=5*12
Multiply 5 by 12 .
x=60
Hope this helped!!
Have a great day!!
Of the respondents, 514 replied that America is doing about the right amount. What is the 95 % confidence interval for the proportion of all American adults who feel that America is doing about the right amount to protect the environment. g
Answers
Complete Question
In 2015 as part of the General Social Survey, 1127 randomly selected American adults responded to this question: “Some countries are doing more to protect the environment than other countries. In general, do you think that America is doing more than enough, about the right amount, or too little?” Of the respondents, 514 replied that America is doing about the right amount. What is the 95 % confidence interval for the proportion of all American adults who feel that America is doing about the right amount to protect the environment.
Answer:
The 95% confidence interval is \( 0.427 < p < 0.4852 \)
Step-by-step explanation:
From the question we are told that
The sample size is n = 1127
The number that America is doing the about the right amount is k = 514
Generally the sample proportion of the number that say america is doing about the right amount is mathematically represented as
\(\^ p = \frac{k}{n}\)
=> \(\^ p = \frac{514 }{ 1127}\)
=> \(\^ p = 0.4561\)
From the question we are told the confidence level is 95% , hence the level of significance is
\(\alpha = (100 - 95 ) \%\)
=> \(\alpha = 0.05\)
Generally from the normal distribution table the critical value of \(\frac{\alpha }{2}\) is
\(Z_{\frac{\alpha }{2} } = 1.96\)
Generally the margin of error is mathematically represented as
\(E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\^ p (1- \^ p)}{n} } \)
=> \(E = 1.96 * \sqrt{\frac{ 0.4561 (1- 0.4561)}{1127} } \)
=> \(E = 0.0291 \)
Generally 95% confidence interval is mathematically represented as
\(\^ p -E < p < \^ p +E\)
=> \( 0.4561 -0.0291 < p < 0.4561 +0.0291 \)
=> \( 0.427 < p < 0.4852 \)
given a matrix of non-negative reals, show it is a non-negative linearr combination of permutation matrices
Answers
Q is a non-negative linear combination of permutation matrices.
A non-negative linear combination of permutation matrices is a matrix P that can be expressed as a linear combination of permutation matrices P1, P2, ..., Pn such that each coefficient in the linear combination is non-negative. This can be expressed as:
\(P = c1P1 + c2P2 + ... + cnPn\)
where c1, c2, ..., cn are all non-negative real numbers. For example, consider the following matrix Q:
\(Q = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0 \end{bmatrix}\)
We can express Q as a non-negative linear combination of permutation matrices P1, P2, P3 as follows:
\(Q = \frac{1}{3}\begin{bmatrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0 \end{bmatrix} + \frac{1}{3}\begin{bmatrix} 0 & 0 & 1 \\ 1 & 0 & 0 \\ 0 & 1 & 0 \end{bmatrix} + \frac{1}{3}\begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}\)
Therefore, Q is a non-negative linear combination of permutation matrices.
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Estimate 147+14+85 by first rounding each number to the nearest ten.
Answers
Answer:
250
Step-by-step explanation:
because 147 rounded is 150 14 is 10 and 85 is 90 these added together are 250
Help! I’m confused and need help finding the answer!
Answers
Answer:
y=11x
Step-by-step explanation:
we use formula y2-y1/x2-x1 with 2 of the order pairs
22-11/2-1
11/1
11 is the slope
We find y intercept by finding when x is equal to zero and we subtract 11 until we find the 0 x unit since it goes down 11 every time
When x is zero y is zero so we write it like this
Y=11x
Hopes this helps please mark brainliest
HOME ASSIGNMENTS ASSIGNMENT
1/5/22 -DUPLICATE
1 2 3 4 5 6 7
On the number line, between which two rational numbers is V52 located?
es
A)
between 8 an 9
Eliminate
B)
between 7 and 8
between 6 and 7
D)
between 5 and 6
Answers
ILL GIVE YOU BRAINLEST IF RIGHT!!
Answers
Answer:
6
Step-by-step explanation:
Which of the following represents the solution to the inequality 4x - 2 ≤ 10?
Answers
Answer:
Step-by-step explanation:
Okay so solving an inequality is essentially the same as solving an expression, just with a different symbol.
We can first separate the x to the left and whole numbers to the right side.
TIP INPORTANT: Put your variable numbers on the left side and your whole numbers which are the numbers without variables on the right side
so,
4x ≤ 10 + 2
which is,
4x ≤ 12, therefore,
x ≤ 3.
Hope this helps!
The solution is x ≤ 3
What is an Inequality Equation?
Equations and inequalities are both mathematical sentences formed by relating two expressions to each other. Where as in an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
4 x - 2 ≤ 10
Adding 2 on both sides , we get
4 x ≤ 12
Divide by 4 on both sides , we get
x ≤ 3
Hence , the solution is x ≤ 3
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A video game system and several games are sold for 504$ . The cost of the game is 3 times as much as the cost of the system . Find the cost of the system and the cost of the games
Answers
We get the cost of the system and cost of the games as $126 and $378 respectively.
Given, the price of the video game and several games are sold for $504.
The cost of the game is 3 times as much as the cost of the system.
we need to determine the cost of the system and the cost of the game = ?
Let x = the cost of the games.
Let y = the cost of the system.
therefore, x+y=504
and y = 3x
substitute the value of y.
⇒ x + y = 504
⇒ x + 3x = 504
combine like terms.
⇒ 4x = 504
Divide both sides by 4.
⇒ x = 504/4
⇒ x = 126
The cost of the system is $126.
Use y = 3x substituting 126 for x.
g = 3(126)
g = 378
The cost of the games is $378.
Hence we get the cost of the system and cost of the games as $126 and $378 respectively.
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Jorge swam a total of 173 minutes during 3 days. He swam the same number of
minutes each day, Which of the following is the best estimate of the number of
minutes Jorge swam each day?
o
60
40
20
30
Answers
Answer:
60
Step-by-step explanation:
Answer:
60
Step-by-step explanation:
173 divided by 3 =57.6666667. So i estimated it to 60
Someone help me please!!!Divide 100 in the ratio 2:3.
Answers
Answer:
pirwvjihpwrugh
Step-by-step explanation:
wrhfuwhfuhugfrifhi
Answer:
not possible
Step-by-step explanation:
It can't be possible because the ratio would be 50:1 is possible
Which of the four is it?
Answers
Answer:
option 1 i believe
Step-by-step explanation:
just worked it out
i hope this is right and helps <3
