Using the normal probability distribution and the central limit theorem, it is found that the probabilities are given by:
a) 0.0119 = 1.19%.
b) 0.121 = 12.1%.
c) 0.9257 = 92.57%.
Normal Probability DistributionIn a normal distribution 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]
It 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, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].In this problem:
The mean is of [tex]\mu = 45000[/tex].The standard deviation is of [tex]\sigma = 12720[/tex].A sample of 144 is taken, hence [tex]n = 144, s = \frac{12720}{\sqrt{144}} = 1060[/tex].Item a:
The probability is the p-value of Z when X = 42600, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{42600 - 45000}{1060}[/tex]
[tex]Z = -2.26[/tex]
[tex]Z = -2.26[/tex] has a p-value of 0.0119.
The probability is of 0.0119 = 1.19%.
Item b:
The probability is the 1 subtracted by the p-value of Z when X = 46240, hence:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{46240 - 45000}{1060}[/tex]
[tex]Z = 1.17[/tex]
[tex]Z = 1.17[/tex] has a p-value of 0.879.
1 - 0.879 = 0.121.
The probability is of 0.121 = 12.1%.
Item c:
The probability is the p-value of Z when X = 46980 subtracted by the p-value of Z when X = 43190, hence:
X = 46980:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{46980 - 45000}{1060}[/tex]
[tex]Z = 1.87[/tex]
[tex]Z = 1.87[/tex] has a p-value of 0.9693.
X = 43190:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{43190 - 45000}{1060}[/tex]
[tex]Z = -1.71[/tex]
[tex]Z = -1.71[/tex] has a p-value of 0.0436.
0.9693 - 0.0436 = 0.9257.
The probability is of 0.9257 = 92.57%.
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If x = 15 cm, y = 36 cm, and z = 39 cm, what is the surface area of the geometric shape formed by this net? A. 1,890 cm2 B. 2,880 cm2 C. 2,430 cm2 D. 738 cm2
Answer:
I belive it’s C
Step-by-step explanation:
I don’t know if it’s correct tell me if I’m wrong
Answer Pls I need this question
Answer:
T = 1.5
Step-by-step explanation:
If you count all the boxes with T in them there is 6 and if you divide 6 by 9 you get 1.5, 9 divided by 6 = 1.5
Hope this helps!
Which interval notation represents the set of all numbers less than or equal to -6 or greater than or equal to -2
Answer: 1≤x<12
Step-by-step explanation:
The values that are greater than or equal 1 but less than 12 are values ranging from 1 to 11 i.e {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}. Note that 1 is included because the number is greater than or equal to 1 (1 included) and less than 12(12 not included).
x≥1 and x< 12
if x≥1, it means 1≤x
combining both inequality
1≤x and x<12
1≤x<12
The interval notation that represent the set S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} will be given as S = {x: 1≤x<12}
i once met six siblings whose ages are 6 consecutive whole numbers. i asked each of them the question how old is your oldest sibling. which of the following could not be the sum of their answers.
A. 95
B. 125
C. 167
D. 205
E. 233
The consecutive ages of the siblings mean that each sibling is a year older than the younger sibling
All the options cannot be the sum of their ages
How to determine the sum of their ages
Represent the age of the smallest sibling with x.
So, the sum of their ages is:
[tex]Sum =x + x + 1 + x + 2 + x + 3 + x + 4 + x + 5[/tex]
Evaluate the like terms
[tex]Sum =6x + 15[/tex]
When the sum is 95 (from the options), we have:
[tex]6x + 15 = 95[/tex]
Subtract 15 from both sides
[tex]6x = 80[/tex]
Divide by 6
[tex]x = 13.3[/tex] -- this is not an integer
When the sum is 95 (from the options), we have:
[tex]6x + 15 = 125[/tex]
Subtract 15 from both sides
[tex]6x = 110[/tex]
Divide by 6
[tex]x = 6.875[/tex] -- this is not an integer
When the sum is 167 (from the options), we have:
[tex]6x + 15 = 167[/tex]
Subtract 15 from both sides
[tex]6x = 152[/tex]
Divide by 6
[tex]x = 25.33[/tex] -- this is not an integer
When the sum is 205 (from the options), we have:
[tex]6x + 15 = 205[/tex]
Subtract 15 from both sides
[tex]6x = 190[/tex]
Divide by 6
[tex]x = 31.67[/tex] -- this is not an integer
When the sum is 233 (from the options), we have:
[tex]6x + 15 = 233[/tex]
Subtract 15 from both sides
[tex]6x = 218[/tex]
Divide by 6
[tex]x = 36.33[/tex] -- this is not an integer
Hence, all the options cannot be the sum of their ages
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Answer:
Step-by-step explanation:
An ordinary (falr) dle is a cube with the numbers 1 through 6 on the sides (represented by painted spots). Imagine that such a dle is rolled twice in succession
and that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of a random experiment.
Compute the probability of each of the following events.
Event A: The sum is greater than 8.
Event B: The sum is divisible by 5.
Write your answers as fractions.
(a) P(X) =
(b) P(B) =
By finding the number of outcomes that meet each criteria, we will see that the probabilities are:
A) P = 0.25B) P = 7/36 = 0.194How to find the probability?
We know that the fair die has 6 outcomes, so if we roll it twice, there are a total of:
6*6 = 36 outcomes.
To find the probability of getting a given event, we need to find the number of outcomes that make the event true.
A) The sum is greater than 8.
The outcomes that make this true are:
first roll second roll sum
4 5 9
4 6 10
5 5 10
5 6 11
6 3 9
6 4 10
6 5 11
6 6 12
3 6 9
So there are 9 outcomes whose sum is greater than 8, so the probability to getting this event is:
P = 9/36 = 0.25
B) The sum is divisible by 5.
The sum must be 5 or 10, the outcomes that give that are:
first roll second roll sum
1 4 5
2 3 5
3 2 5
1 4 5
4 6 10
5 5 10
6 4 10
There are 7 outcomes, so the probability is:
P = 7/36 = 0.194
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Help with number 17 please
Answer:
B is the answer
Step-by-step explanation:
it goes downward if viewed left-right
PLEASE HELP!!
WILL GIVE BRAINLIEST FOR CORRECT ANSWER!!
Graph the line with slope 1/3 passing through the point (-4,-5).
Answer:
graphing done below.
Step-by-step explanation:
using the formula: y - y₁ = m(x - x₁)
equation:
[tex]\sf y - -5 = \frac{1}{3} (x - - 5)[/tex]
[tex]\sf y +5 = \frac{1}{3} x + \frac{5}{3}[/tex]
[tex]\sf y = \frac{1}{3} x + \frac{5}{3}-5[/tex]
[tex]\sf y = \frac{1}{3} x - \frac{10}{3}[/tex]
Find the value of x, y, and z in the rhombus below
Answer:
Step-by-step explanation:
Opposite angles of a rhombus are congruent, so [tex]6x+8=86 \longrightarrow x=13[/tex]
Also, adjacent angles of a rhombus are supplementary, so [tex]86+5z+4=86+7y+3=180 \longrightarrow y=13, z=18[/tex]
What is the slope of the line passing through the points (-1, – 7) and (-9, - 2)?
» What is the slope of the line passing through the points (-1, – 7) and (-9, - 2)?
[tex]\color{brown} \mathbb{ANSWER:}[/tex][tex] \color{hotpink} \bold{(Slope) \: m = - \frac{5}{8} }[/tex][tex] \sf \:As \: a \: decimal: \color{hotpink} \bold{ \: m = - 0.625 }[/tex]— — — — — — — — — —
[tex] \color{darkblue} \mathbb{FORMULA:}[/tex][tex] \tt \: \underline{ \boxed{ \tt m = \frac{ y_{2} - y_{1}}{x_{2} - x_{1}}}} \\ [/tex][tex] \color{darkblue}\mathbb{GIVEN:}[/tex][tex] x_{ 1} = - 1\: \: \: \: \: \: \: y_{1} = - 7 \\ x_{2} = - 9 \: \: \: \: \: \: \: y_{2} = - 2[/tex][tex] \color{darkblue} \mathbb{SOLUTION:}[/tex][tex] \tt m = \frac{ y_{2} - y_{1}}{x_{2} - x_{1}} \\ [/tex][tex] \tt m = \frac{ ( - 2) - ( - 7)}{( - 9) - ( - 1)} \\ [/tex][tex] \tt m = \frac{ \: 5}{ - 8 \: } \\ [/tex][tex] \tt m = \underline{ \boxed{ \bold{ - \frac{ 5}{ 8 } }}} \\ [/tex][tex] \tt m = \underline{ \boxed{\bold{ - 0.625}}}[/tex]_______________❦︎_______________
34
Which expression represents the phrase below?
3 fewer than a number, P
3-p
В
p=3
C
3 +p
D
P-3
Answer:
D) P - 3
Step-by-step explanation:
"fewer than" a number means "less than" a number. So "3 fewer than" means "subtract 3" from the number.
⇒ P - 3
17. Observe the figure and name the following
a) Vertices of the polygon
b) Two pairs of adjacent sides
c) Two diagonals
d) Sides of the polygon
By using the image of the polygon and the definition for the parts, we can see that:
a) A, B, C, D, and E.b) DC and CB, AE and ED.c) AD, BEd) AB, BC, CD, DE, and EA.How to identify the parts of the figure?a) The vertices are the points where two sides connect, in this case, each letter represents a different vertex, so the vertices of the polygon are A, B, C, D, and E.
b) Adjacent sides are any pair of sides that are connected by a vertex.
For example, DC and CB are connected through vertex C, so these are adjacent sides.
Another pair can be BA and AE.
c) Diagonals are the segments between two non-consecutive vertices.
For example, E and D are consecutive vertices (because there are next to each other). And A and D are non-consecutive vertices.
Then AD is a diagonal. Another example can be EB.
d) The sides of the polygon are the segments between consecutive vertices, in this case, the sides are:
AB, BC, CD, DE, EA.
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y-3=4(x+2) solution for x and y please
Answer:
Solutions: (0,11) ; (1,15) ; (2, 19)
Step-by-step explanation:
y - 3 = 4(x +2)
y - 3 = 4x + 8
y = 4x + 8 + 3
y = 4x + 11
When x = 0 , y = 11 (0,11)
When x = 1 ; y = 4 +11 = 15 (1, 15)
When x = 2 ; y = 8 + 11 = 19 (2 , 19
There are 20 members of taekwondo club, 40 math club members, 60 drama
theatre members, and 30 members of science club. The researchers want to get 20
respondents out of these organizations. Identify the samples to be taken in each
organization.
⚘Refer to the attachment for solution!!~
The sample to be taken in each organization such as 2.6 in the taekwondo club, 5.3 in the math club, 8 in the drama club, and 4 in the science club.
Total members of taekwondo club = 20
Total members of math club = 40
Total members of drama club = 60
Total members of science club = 30
The researchers want to get 20 respondents out of these organizations.
What is the stratified sampling method?The stratified sampling method is the process of dividing members of data into homogenous subgroups before sampling.
The total number of members = 150
For taekwondo club
= Total members of taekwondo club /total number of members × 20
= 20/150 × 20
= 2.6
For math club
= Total members of math club/total number of members×20
= 40/150 × 20
= 5.3
For drama club
= Total members of drama club/total number of members × 20
= 60/150 × 20
= 8
For science club
= Total members of the science club/total number of members × 20
= 30/150 × 20
= 4
Therefore, The sample to be taken in each organization such as 2.6 in the taekwondo club, 5.3 in the math club, 8 in the drama club, and 4 in the science club.
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calculate the area of the rigt triangle
Answer:
Area = 1/2 × base × height
A = 1/2 × 5 × 3,3/5
= 9
Bethany bought 42 liters of water for the running team. There are 16 members on the team. If each member gets an equal amount of water, how many liters does each memberget?
3. Barb wants to get 8 out of every 10 questions right on her test. If there are 35 questions on the
test, how many will Barb want to get right?
Hcf of 32 and 48 pls
HCF/GCF 32 and 48
listing factor
32: 1, 2, 4, 8, 16, 32
48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
HCF: 16
prime factorization
32: 2 x 2⁴
48: 3 x 2⁴
HCF: 2⁴ = 16
find the slope of the line through the given points (-6,17),(-6,13)
Answer:
As Per Provided Information
Given points are (-6,17) & (-6,13).
here
x₁ = -6
x₂ = -6
y₁ = 17
y₂ = 13
We have been asked to find the slope of the line.
Using Formula
[tex] \bf \: m \: = \dfrac{y_{2} - y_{1}}{x_{2} - x_{1}} [/tex]
m is the slope of line
Put the given value we get
[tex] \qquad \sf \longrightarrow \: m = \ \dfrac{ - 6 - ( - 6)}{13 - 17} \\ \\ \\ \qquad \sf \longrightarrow \: m = \ \dfrac{ - 6 + 6}{13 - 17} \\ \\ \\ \qquad \sf \longrightarrow \: m = \dfrac{0}{ - 4} \\ \\ \\ \qquad \sf \longrightarrow \: m = 0[/tex]
Therefore,
Slope of the line is 0 .Which function is the inverse of f(x) = (x − 3)3 + 2?
Answer: f = 3x -7 / x
Step-by-step explanation:
fx=(x−3)(3)+2
Step 1: Divide both sides by x.
fx/x = 3x -7 / x
f = 3x -7 / x
Answer: f = 3x -7 / x
Jane has already run 6 miles this month. She plans to run an additional 2.5 miles per day.
At this rate, how long will it take Jane to run 41 miles?
You spent $24 on baking ingredients, and you sell your cupcakes at a bake sale for $4 each. You sold 25 cupcakes. Did you make enough money to buy a $60 video game?
Solve the equation by using the quadratic formula.
3x² - 1 = 7x
Answer:
Solutions: [tex]\displaystyle\mathsf{x\:=\:\frac{7+ \sqrt{61}}{6}}[/tex] , [tex]\displaystyle\mathsf{x\:=\:\frac{7 - \sqrt{61}}{6}}[/tex]Step-by-step explanation:
We are given the following quadratic equation, 3x² - 1 = 7x, which requires us to find its possible solutions using the quadratic formula.
Definitions:In a quadratic equation, the leading term has a second-degree (or squared) variable. The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are real numbers, and that a ≠ 0. Quadratic Formula:The quadratic formula is given by:
[tex]\displaystyle\mathsf{x\:=\:\frac{-b\pm\sqrt{b^2-4ac}}{2a}}[/tex]
We will use this formula to solve for the roots or the solution of the given quadratic equation.
Solution:Step 1: transform the given equaton into standard form.
First, we must subtract "7x" from both sides of the equation:
3x² - 7x - 1 = 7x - 7x
3x² - 7x - 1 = 0 ⇒ This is the standard form of the given quadratic equation where a = 3, b = -7, and c = - 1.
Step 2: Plug in the values for a, b, & c into the quadratic formula.
The derived values for a, b, & c from the previous step are: a = 3, b = -7, and c = - 1. Substitute these values into the following quadratic formula:
[tex]\displaystyle\mathsf{x\:=\:\frac{-b\pm\sqrt{b^2-4ac}}{2a}}[/tex]
[tex]\displaystyle\mathsf{x\:=\:\frac{-(-7)\pm\sqrt{(-7)^2-4(3)(-1)}}{2(3)}}[/tex]
Step 3: Following the PEMDAS Order of Operations, start by applying the Power rule of Exponents [tex]\displaystyle\mathsf{(a^m)^n = (a^{m*n})}[/tex] (under the radical) :
[tex]\displaystyle\mathsf{x\:=\:\frac{-(-7)\pm\sqrt{49-4(3)(-1)}}{2(3)}}[/tex]
Step 4: Next, multiply the integers under the radical, PEMDAS Order of Operations.
[tex]\displaystyle\mathsf{x\:=\:\frac{-(-7)\pm\sqrt{61}}{2(3)}}[/tex]
Step 5: Multiply the integers in the denominator, and apply the multiplication integer rule, -(-a) = a.
[tex]\displaystyle\mathsf{x\:=\:\frac{7\pm\sqrt{61}}{6}}[/tex]
Since [tex]\displaystyle\mathsf{\sqrt{61}}[/tex] is not a perfect square, it can remain the same.Step 6: Separate the solutions.
[tex]\displaystyle\mathsf{x\:=\:\frac{7+ \sqrt{61}}{6}}[/tex] , and [tex]\displaystyle\mathsf{x\:=\:\frac{7 - \sqrt{61}}{6}}[/tex]
Final Answer:Therefore, the solution to 3x² - 1 = 7x are: [tex]\displaystyle\mathsf{x\:=\:\frac{7+ \sqrt{61}}{6}}[/tex], [tex]\displaystyle\mathsf{x\:=\:\frac{7 - \sqrt{61}}{6}}[/tex].
_____________________Keywords:Quadratic equation
Quadratic function
Standard form
Parabola
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6. Rhombus (3 points)
A
N
I
a. If AN = 12, what is the measure of NT?
b. Diagonal AT intersects diagonal ZN at point M. If the mZZMT = 4x, what is the value of x?
c. Diagonal AT intersects diagonal Z N at point M. If the mZZAM = 3x + 2 and the
MZNTM = 8x - 90, what is the mZN?
Square (2 points)
Answer:
44 is my answer thank you please ask me questions a little bit easier and not reach the level I am still in jss2 class
Find the LCM and the GCF of 100 and 120.
Answer:
Step-by-step explanation:
LCM is least common multiple. It means the least multiple that both 100 and 120 have in common. 600 is the LCM. 20 is the GCF.
.The world's tallest mammal is a giraffe at a height of 19 feet. What is the height of the giraffe in inches?????
Answer:
228 inches
Step-by-step explanation:
There are 12 inches in a foot.
19 × 12 = 228
Jo and Val are a couple. Jo's monthly net earnings are $4000, and Val's are $6000. Following the 80/20 rule, how much should the couple save every month?
Answer:
about 400
Step-by-step explanation:
What is the area of the triangle?
(-5,6)
(1,3)
(-5,-3)
Answer:
27
Step-by-step explanation:
Base is 6 - (-3) = 9
height is 1 - (-5) = 6
so Area = 9 * 6/2 = 27
Question 1 of 5
Jenn's carpool ride has been late 6 days out of the past 20 days. What is the
estimated probability, based on relative frequency, that her ride will be late
tomorrow?
A. 70%
B. 40%
C. 60%
O D. 30%
SUBMIT
what is the solution for 11 = y-6
Answer:
y = 17
Step-by-step explanation:
11 = y - 6
11 + 6 = y17 = yprove that the value of y is 17
11 = y - 6
11 = 17 - 611 = 11proven
Hello.
Let's solve this equation for y.
First, subtract 11 from both sides:
[tex]\mathrm{11-11=y-6-11}[/tex]
[tex]\mathrm{0=y-6-11}[/tex]
[tex]\mathrm{0=y-17}[/tex]
Subtract y from both sides:
[tex]\mathrm{-y=-17}[/tex]
[tex]\Large\boxed{\sf{y=17}}[/tex]
I hope it helps.
Have a nice day.
[tex]\boxed{imperturbability}[/tex]
Which statement does not describe a normal distribution?
A. The distribution can have two modes.
B. Most of the observations are near the mean.
C. The number of observations trails off as you move away from the
mean.
D. The median and mean are equal.
A .the distribution observation can have two modes