Answer:
0.2358 = 23.58% probability that at least 18 of the 75 sampled employees would like to move into management.
Step-by-step explanation:
Binomial probability distribution
Probability of exactly x successes on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed distributions can be 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.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
20% of employees would like to move into management and be the boss.
This means that [tex]p = 0.2[/tex]
Sample of 75:
This means that [tex]n = 75[/tex]
Mean and standard deviation:
[tex]\mu = E(X) = np = 75(0.2) = 15[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{75*0.2*0.8} = 3.4641[/tex]
Find the probability that at least 18 of the 75 sampled employees would like to move into management.
Using continuity correction, this is [tex]P(X \geq 18 - 0.5) = P(X \geq 17.5)[/tex], which is 1 subtracted by the p-value of X = 17.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{17.5 - 15}{3.4641}[/tex]
[tex]Z = 0.72[/tex]
[tex]Z = 0.72[/tex] has a p-value of 0.7642.
1 - 0.7642 = 0.2358
0.2358 = 23.58% probability that at least 18 of the 75 sampled employees would like to move into management.
Find an equation of the plane orthogonal to the line
(x,y,z)=(0,9,6)+t(7,−7,−6)
which passes through the point (9, 6, 0).
Give your answer in the form ax+by+cz=d (with a=7).
The given line is orthogonal to the plane you want to find, so the tangent vector of this line can be used as the normal vector for the plane.
The tangent vector for the line is
d/dt (⟨0, 9, 6⟩ + ⟨7, -7, -6⟩t ) = ⟨7, -7, -6⟩
Then the plane that passes through the origin with this as its normal vector has equation
⟨x, y, z⟩ • ⟨7, -7, -6⟩ = 0
We want the plane to pass through the point (9, 6, 0), so we just translate every vector pointing to the plane itself by adding ⟨9, 6, 0⟩,
(⟨x, y, z⟩ - ⟨9, 6, 0⟩) • ⟨7, -7, -6⟩ = 0
Simplifying this expression and writing it standard form gives
⟨x - 9, y - 6, z⟩ • ⟨7, -7, -6⟩ = 0
7 (x - 9) - 7 (y - 6) - 6z = 0
7x - 63 - 7y + 42 - 6z = 0
7x - 7y - 6z = 21
so that
a = 7, b = -7, c = -6, and d = 21
An equation of the plane orthogonal to the line 7x - 7y - 6z = 21.
The given line is orthogonal to the plane you want to find,
So the tangent vector of this line can be used as
The normal vector for the plane.
The tangent vector for the line is,
What is the tangent vector?A tangent vector is a vector that is tangent to a curve or surface at a given point.
d/dt (⟨0, 9, 6⟩ + ⟨7, -7, -6⟩t ) = ⟨7, -7, -6⟩
Then the plane that passes through the origin with this as its normal vector has the equation
⟨x, y, z⟩ • ⟨7, -7, -6⟩ = 0
We want the plane to pass through the point (9, 6, 0), so we just
translate every vector pointing to the plane itself by adding ⟨9, 6, 0⟩,
(⟨x, y, z⟩ - ⟨9, 6, 0⟩) • ⟨7, -7, -6⟩ = 0
Simplifying this expression and writing it in standard form gives
⟨x - 9, y - 6, z⟩ • ⟨7, -7, -6⟩ = 0
7 (x - 9) - 7 (y - 6) - 6z = 0
7x - 63 - 7y + 42 - 6z = 0
7x - 7y - 6z = 21
So that, a = 7, b = -7, c = -6, and d = 21.
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How many edges are there?
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Answer:
24
Step-by-step explanation:
The front face is an 8-sided star, so has 8 edges. We presume the back face is the same, so it also has 8 edges. Each of the front vertices is connected by an edge to each of the corresponding back vertices, so there are 8 more edges connecting front and back.
The total number of edges is 8 + 8 + 8 = 24.
State if the scenario involves a permutation or a combination. Then find the number of possibilities.
A team of 15 basketball players needs to choose two players to refill the water cooler.
Permutation/Combination:
Answer:
Answer:
Permutation ; 210 ways
Step-by-step explanation:
Permutation and combination methods refers to mathematical solution to finding the number of ways of making selection for a group of objects.
Usually, selection process whereby the order of selection does not matter are being treated using permutation, while those which takes the order of selection into cognizance are calculated using combination.
Here, selecting 2 players from 15 ; since order does not matter, we use permutation ;
Recall :
nPr = n! ÷ (n - r)!
Hence,
15P2 = 15! ÷ (15 - 2)!
15P2 = 15! ÷ 13!
15P2 = (15 * 14) = 210 ways
which of the following illustrates commutative property of addition? 17+4=4+17
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Answer:
17 +4 = 4 +17
Step-by-step explanation:
The only expression shown here illustrates that property.
Reason Can you subtract a positive integer from a positive integer
and get a negive result? Explain your answer.
Answer:
No
Step-by-step explanation:
No matter the situation, when you multiply a negative by a negativeyou get a positive and a positive by a positive you get a positive. but if its two different like a negative and a positive then its NEGITIVE.
let's say you have 23 and you're multiplying by 2.
It's always increasing so it doesnt ever reach the negitive numbers.
Find the length of the arc.
A. 539π/12 km
B. 9π/3 km
C. 9π/2 km
D. 18π km
Answer:
b because it is I found out cus I took test
The length of the arc 9π/2 km.
The answer is option C.9π/2 km.
What is the arc of the circle?
The arc period of a circle can be calculated with the radius and relevant perspective using the arc period method.
⇒angle= arc/radius
⇒ 135°=arc/6km
⇒ arc =135°*6km
⇒arc=135°*π/180° * 6km
⇒arc = 9π/2 km
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Find the slope of the line that goes through the
(2,6) and (-1, -6)
Write the standard form of the equation of the circle with center (8,−1) that passes through the point (6,7)
Answer:
(x - 8)^2 + (y + 1)^2 = 68
Step-by-step explanation:
The standard form of the equation of the circle with center (8,−1) is :
(x - 8)^2 + (y + 1)^2 = R^2
If the circle passes through the point (6,7) that means that the point (6,7) is a solution of the equation and we can replace (x,y) with (6,7) to find R.
If the mean of a given dataset is
42 and the standard deviation is
4, where will a majority of the
data lie?
Answer:
A majority of the data will lie between 38 and 46.
Step-by-step explanation:
It can be said that a majority of the data of a distribution lies within 1 standard deviation of the mean.
In this question:
Mean of 42, standard deviation of 4.
42 - 4 = 38
42 + 4 = 46
A majority of the data will lie between 38 and 46.
please solve the question
Answer:
[tex]g(-1) = -1[/tex]
[tex]g(0.75) = 0[/tex]
[tex]g(1)= 1[/tex]
Step-by-step explanation:
Given
See attachment
Solving (a): g(-1)
We make use of:
[tex]g(x) = -1[/tex]
Because: [tex]-1 \le x < 0[/tex] is true for x =-1
Hence:
[tex]g(-1) = -1[/tex]
Solving (b): g(0.75)
We make use of:
[tex]g(x) = 0[/tex]
Because: [tex]0 \le x < 1[/tex] is true for x =0.75
Hence:
[tex]g(0.75) = 0[/tex]
Solving (b): g(1)
We make use of:
[tex]g(x) = 1[/tex]
Because: [tex]1 \le x < 2[/tex] is true for x =1
Hence:
[tex]g(1)= 1[/tex]
Solve for x: 10/3 = x/(−5/2)
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Answer:
x = -25/3
Step-by-step explanation:
Multiply by the inverse of the coefficient of x. Reduce the fraction.
(-5/2)(10/3) = (-5/2)(x/(-5/2))
-50/6 = x = -25/3
Answer:
-25/3
Step-by-step explanation:
the other person is also correct. khan said so
Select all sets in which the number - 15 is an element.
A. natural numbers
B. real numbers
C. irrational numbers
D. rational numbers
E. whole numbers
F. integers
-15 is an element of-
B. real numbers
D. rational numbers
F. integers
What is a number?A number is a mathematical object used to count, measure, and label. The original examples are natural number 1,2,3,4 and so forth.
Given number is 15.
A. natural numbers
The natural numbers are the set of all the whole numbers excluding zero. They are positive whole number.
Here, -15 is a negative number,
Hence, -15 is an not element of natural number.
B. real numbers
Real numbers are those numbers that has no imaginary part. It also include both rational and irrational number.
Since -15 has no imaginary part
Hence, -15 is an element of real number.
C. irrational numbers
An irrational number is real number that cannot be expressed as a ratio of two integers.
Here -15 can be expressed as ratio of two integers,
Hence,-15 is not an element of irrational number.
D. rational numbers
A rational number is real number that can be expressed as a ratio of two integers.
Here -15 can be expressed as ratio of two integers,
Hence, -15 is an element of rational number.
E. whole numbers
Whole numbers are positive numbers, including zero, without any decimal or fractional parts. Negative numbers are not considered "whole numbers."
Since,Negative numbers are not considered whole numbers
Hence, -15 is not an element of whole number.
F. integers
An integer is a whole number (not a fractional number) that can be positive, negative, or zero. Examples of integers are: -5, 1, 5, 8, 97, and 3,043
Hence, -15 is an element of integers.
Hence, we conclude that,
-15 is an element of-
B. real numbers
D. rational numbers
F. integers
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Which ratio is equal to 27 : 81?
Answer:
1:3
Step-by-step explanation:
27 : 81
Divide each side by 27
27/27 : 81/27
1:3
11 divided by 9876
Thank youuuu
Answer:
770,7272727272727
Step-by-step explanation:
Answer:
8478 divided by 11= 770.7272727
Identify the transformed function that represents f(x) = ln x stretched vertically by a factor of 17, reflected across the x-axis, and shifted by 19 units left.
A. g(x) = −17ln (x + 19)
B. g(x) = 17ln (x − 19)
C. g(x) = 17ln (x + 19)
D. g(x) = −17ln (x − 19)
Answer:
b
Step-by-step explanation:
ANSWER. EXPLANATION. The given logarithmic function is. The transformation,. stretches the graph of y=f(x) vertically by a factor of c units ...
4 votes
ANSWER[tex]y = - 3 ln(x - 7) [/tex]EXPLANATIONThe given logarithmic function is [tex]f(x) = ln(x) [/tex]The transformation, [tex]y = - cf(x - k)[/tex]stretches
The length of a rectangle is twice its width. If the area of the rectangle is 72in², find its perimeter
Let breadth be x
Length=2x[tex]\\ \sf\longmapsto Area=Length\times Breadth[/tex]
[tex]\\ \sf\longmapsto 72=2x(x)[/tex]
[tex]\\ \sf\longmapsto 2x^2=72[/tex]
[tex]\\ \sf\longmapsto x^2=\dfrac{72}{2}[/tex]
[tex]\\ \sf\longmapsto x^2=36[/tex]
[tex]\\ \sf\longmapsto x=\sqrt{36}[/tex]
[tex]\\ \sf\longmapsto x=6[/tex]
Length=6×2=12inBreadth=6in[tex]\\ \sf\longmapsto Perimeter=2(L+B)[/tex]
[tex]\\ \sf\longmapsto Perimeter=2(12+6)[/tex]
[tex]\\ \sf\longmapsto Perimeter=2(18)[/tex]
[tex]\\ \sf\longmapsto Perimeter=36in[/tex]
Graph y=|x|+5, how does it compare to parent graph y=|x|
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Answer:
it is shifted 5 units upward
Step-by-step explanation:
The y-coordinate is a measure of the distance above the x-axis. When 5 is added to a y-coordinate, the point is shifted 5 units upward.
The function y = |x| +5 adds 5 units to the y-value of every point of the graph of y = |x|. The graph of y=|x|+5 is shifted 5 units upward from the parent graph.
In a class of 70 pupils, 36 like tasty time , 34 like ice-
cream, 6 like both tasty time }
draw a Venn diagram to show the data.
find how
many
like neither tasty time nor ice-cream
Step-by-step explanation:
I think this might be the correct answer
The number of pupils that like neither tasty-time nor ice cream is 6 if in a class of 70 pupils, 36 like tasty time, 34 like ice cream, 6 like both tasty times.
What is the Venn diagram?It is defined as the diagram that shows a logical relation between sets.
The Venn diagram consists of circles to show the logical relation.
We have:
In a class of 70 pupils, 36 like tasty time, 34 like ice cream, 6 like both tasty time.
Total = 70 pupils
Number of like tasty time = 36
Number of like ice cream = 34
Number of like both = 6
Let x be the total number of pupils that like neither tasty-time nor ice cream
The number of pupils that like ice cream only = 34 - 6 = 28
The number of pupils that like tasty-time only = 36 - 6 = 30
From the Venn diagram:
28 + 30 + 6 + x = 70
x = 70 - 64
x = 6
Thus, the number of pupils that like neither tasty-time nor ice cream is 6 if in a class of 70 pupils, 36 like tasty time, 34 like ice cream, 6 like both tasty times.
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2. About how much is 123.1 do you weigh in pounds? Estimate if you don't know☺ Find an online converter and find out how many kilograms that is.
Answer:
123.1 pounds is vary long, and I don't want to repeat, so 55.8372207 repeat.
Step-by-step explanation:
If you have any questions regarding my answer, tell me them in the comments, and I will come answer them for you. Have a good day.
if 25 liters of milk can make 8 tin of cheese how many liters of milk would b needed to make 11 tin of cheese?
Answer:
Step-by-step explanation:
34.375 Liters of milk make 11 tins of cheese. Assuming that milk is available in whole liters only, 35 Liters of milk are needed.
Find the sum of ∑4/k=1 (-4k)
Answer:
Hello,
Answer C: -40
Step-by-step explanation:
[tex]\displaystyle \sum_{k=1}^4\ (-4k)\\\\=-4*\sum_{k=1}^4\ k\\\\=-4*4*\dfrac{1+4}{2} \\\\=-4*5*2\\\\=-40\\[/tex]
1.) Three numbers form a geometric sequence whose common ratio is 0.5. If the first is reduced to 10 more than one quarter its value, the second decreased by 10, and the third increased by 10 more than twice its value, the resulting three numbers form an arithmetic sequence. Determine the original three numbers.
Let x be the first number in the sequence, so the first three numbers are
{x, 0.5x, 0.5²x}
Then
{x/4 + 10, 0.5x - 10, 2(0.5²x) + 10}
is arithmetic, so there is some constant c such that
0.5x - 10 = x/4 + 10 + c ==> x/2 - 10 = x/4 + 10 + c
2(0.5²x) + 10 = 0.5x - 10 + c ==> x/2 + 10 = x/2 - 10 + c
Solve the second equation for c :
x/2 + 10 = x/2 - 10 + c
c = 20
Substitute this into the first equation and solve for x :
x/2 - 10 = x/4 + 10 + 20
x/4 = 40
x = 160
Then the terms are
{160, 80, 40}
Find the length represented by x for each pair of similar triangles.
18cm, 9cm, and x
30cm, 15cm, and 25cm
Answer:
15 cm
Step-by-step explanation:
Since the traingles are similar, we can find the ratio between the side lengths, and it will be the same for each side.
We can use the side length 9 and 15 to find this ratio. 15/9=5/3. So, the ratio of a side length of the larger triangle to the smaller one is 5/3, so our equation becomes 5/3 = 25/x. Use any method you like to find that x=15.
Hope this helped,
~cloud
Ron has 22 coins with a total value of $ 1.85. The coins are nickels (5 cents) and dimes (10 cents). How many of each coin does he have?
Please help asap and thank you in advance!!
Answer:
18 dimes and 1 nickle
Step-by-step explanation:
This is because 18 time 10 is 180 and one of 5 add it and this is $1.85
Remeber a dollar is 100 cents
A bookkeeper needs to post the cost of the desk and the chair into his records. The cost of the desk is fives times the cost if the chair. The total cost of the desk and the chair is $720, what is the cost of the chair?
Answer:
120
Step-by-step explanation:
720÷6
why?
becoz 6= 1+5
1 is the cosy of the chair
5 is the cost of the desk
An article is marked to sell at a gain of 10%. If it be sold for Rs. 7.50 less there would be loss of 5%, find the cost price.
Answer:
750,. is answer
I hope it helps
"What mathematical ideas are you curious to know more about as a result of takingthis class? Give one example of a question about the material that you'd like to explorefurther, and describe why this is an interesting question to you."
One mathematical idea I've always been curious about is "integration and derivation".
Integration is about assimilating different variables. Derivation is a mathematical process whereby a result is gotten from some initial assumptions.
Integration is used everyday in different aspects of our lives. For example, if a person is travelling from let's say point A to point B, the speed used by the person might vary but through integration, one can easily get the accurate speed.
Through the division of equations into smaller bits, once can use integration to get the answer that one seeks. Architect can use integration in building the right structures at the exact places where the structures fits.
Likewise derivatives can be used by businesses in assessing whether a profit or loss will be made for a particular transaction or sale of product.
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You are dealt one card from a 52-card deck. Find the probability that you are not dealt a heart.
The probability is ___.
(Type an integer or a fraction. Simplify your answer.)
Answer:
3/4
Step-by-step explanation:
There are 13 hearts in a 52 deck.
52-13=39
39/52=3/4
The probability that you are not dealt a heart from the deck of cards is 3/4.
What is the probability that you are not dealth with a heart?Probability determines the chances that an event would occur. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability that you are not dealth with a heart = 1 - (number of hearts / total number of cards)
1 - 13/52 = 39/52 = 3/4
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Find the missing length. The triangles are similar.
Answer:
Missing length = 12
Step-by-step explanation:
Let x represent the missing length.
Since the triangles are similar, ∆KLM ~ ∆KRS, therefore, the ratio of their corresponding side lengths would be the same. This implies that:
KL/KR = KM/KS
KL = 65
KR = 65 - 52
KR = 13
KM = 60
KS = x
Plug in the values
65/13 = 60/x
Cross multiply
65*x = 60*13
65x = 780
Divide both sides by 65
65x/65 = 780/65
x = 12
Let two events A and B be independent. Knowing P(A)=0.8 and P(A+B)=0.93. Calculate the probability P(B).
Answer:
Hello,
P(B)=0.65
Step-by-step explanation:
If P(A+B) means P(A∪B)=0.93 then you may read below.
Let's say x=P(B)
A and B being independent, P(A∩B)=P(A)*P(B)=0.8*x
Since P(A∪B)=P(A)+P(x)-P(A∩B) ,
0.93=0.8+x-0.8*x
0.2*x=0.13
x=0.65
