The amount of money which would guarantee a person has more money in their account than 80% of Superior, WI residents is $680 approx. The probability a random person from Superior has less than $400 or more than $1000 in their bank account is 0.9247
How to get the z scores?If we've got a normal distribution, then we can convert it to standard normal distribution and its values will give us the z score.
If we have
[tex]X \sim N(\mu, \sigma)[/tex]
(X is following normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex])
then it can be converted to standard normal distribution as
[tex]Z = \dfrac{X - \mu}{\sigma}, \\\\Z \sim N(0,1)[/tex]
(Know the fact that in continuous distribution, probability of a single point is 0, so we can write
[tex]P(Z \leq z) = P(Z < z) )[/tex]
Also, know that if we look for Z = z in z tables, the p-value we get is
[tex]P(Z \leq z) = \rm p \: value[/tex]
Let we take:
X = The balance of a person’s bank account in Superior, WI
Then, by the given data, we have:
[tex]X \sim N(\mu = 580, \sigma = 125)[/tex]
Let the amount of money which would guarantee a person has more money in their account than 80% of Superior, WI residents be X = x dollars. This is the money, below which lie 80% of Superior, WI residents, and so as their income, or values of X.
Symbolically, we have:
[tex]P(X < x) = 80\% = 0.8[/tex]
Converting X to standard normal variate Z, we have:
[tex]Z = \dfrac{X - \mu}{\sigma} = \dfrac{X - 580}{125}\\[/tex]
Thus, the probability statement can be rewritten as:
[tex]P(X < x) =0.8\\P\left( Z < z = \dfrac{x -580}{125} \right) = 0.8[/tex]
From the z-tables, the value of Z for which the p-value comes out as between 0.84 and 0.85, let it be their average 0.845.
Thus, we get:
[tex]P(Z < z = 0.845) \approx 0.8[/tex]
Thus, we get:
[tex]z = \dfrac{x - 580}{125} \approx 0.8\\\\x \approx 0.8 \times 125 + 580 = 680[/tex]
Thus, the amount of money which would guarantee a person has more money in their account than 80% of Superior, WI residents is $680 approx.
Now, for second question, we need:
The probability a random person from Superior has less than $400 or more than $1000 in their bank account.
So, income of a random person from Superior is a random value of X.
So, this probability is written as:
[tex]P(400 < X < 1000)[/tex]
Rewritting it, we get:
[tex]P(400 < X < 1000) = P(X < 1000) - P(X \leq 400)[/tex]
Converting X to Z (standard normal variate), we get:
[tex]P(400 < X < 1000) = P(X < 1000) - P(X \leq 400)\\\\P(400 < X < 1000) = P\left(Z < \dfrac{1000-580}{125} \right) - P\left(Z \leq \dfrac{400-580}{125} \right)\\\\P(400 < X < 1000) = P( Z \leq 3.36) - P(Z \leq -1.44)[/tex]
The p-value for Z = 3.36 is 0.9996
The p-value for Z = -1.44 is 0.0749
Thus, we get:
[tex]P(400 < X < 1000) = P( Z \leq 3.36) - P(Z \leq -1.44)\\\\P(400 < X < 1000) = 0.9996 - 0.0749 = 0.9247[/tex]
Thus, the probability a random person from Superior has less than $400 or more than $1000 in their bank account is 0.9247
Thus, the amount of money which would guarantee a person has more money in their account than 80% of Superior, WI residents is $680 approx. The probability a random person from Superior has less than $400 or more than $1000 in their bank account is 0.9247
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I’m confused can someone help?
Answer:
(a) check the first one, and the second one
(b) check the last one
Step-by-step explanation:
This is quite easy actually.
(A)3x+24 = 3 * x + 3 * 8
3(x+8) using distribute property.
3x + 24
You cannot simplify 3x+24 any further
And 3(8x+1) just doesn't work
since it's multiplying
The "*" is an X sign
(B)The first, second, and third are not correct
But the last one is.
A grain silo has a cylindrical shape. Its radius is 9 ft, and its height is 41 ft. What is the volume of the silo?
Use the value 3.14 for it, and round your answer to the nearest whole number.
Be sure to include the correct unit in your answer.
Answer:
As Per Provided Information
Radius of cylindrical shape silo 9 ft
Height of cylindrical shape silo 41 ft
We have been asked to determine the volume of cylindrical silo .
[tex] \boxed{\sf \: Volume_{(Cylindrical\:Silo)} = \pi {r}^{2}h}[/tex]
Substituting the given value in above formula and we obtain
[tex] \qquad\longrightarrow\sf \:Volume_{(Cylindrical\:Silo)} = 3.14 \times {9}^{2} \times 41 \\ \\ \\ \qquad\longrightarrow\sf \:Volume_{(Cylindrical\:Silo)} = 3.14 \times 81 \times 41 \\ \\ \\ \qquad\longrightarrow\sf \:Volume_{(Cylindrical\:Silo)} = 3.14 \times 3321 \\ \\ \\ \qquad\longrightarrow\sf \:Volume_{(Cylindrical\:Silo)} = 10427.94 \: {ft}^{3} \\ \\ \\ \qquad\longrightarrow\sf \:Volume_{(Cylindrical\:Silo)} = 10428 \: {ft}^{3}[/tex]
Answer:
Volume is 10428 cubic ft.
Step-by-step explanation:
Given :-
Radius of grain silo is 9ft and height is 41ftTo find:-
Volume of grain siloSolution:-
Volume of cylindrical grain silo :- πr²hPutting the known values ,
Volume:- 3.14 × 9² × 41 cubic ft.
Volume :- 10427.94 cubic ft.
rounding off to nearest whole number ,
Volume :- 10428 cubic ft.
An angle measures 26.8° less than the measure of its complementary angle. What is the measure of each angle?
Given :
An angle which measures 26.8° less than the measure of its complementary angle.⠀
To Find :
The measure of each angle.⠀
Solution :
Let's assume the one of the complementary angle as "x" and the other angle as (x – 26.8)° .⠀
Now,
⠀
According to the Question :
⠀
[tex]{\longrightarrow \qquad \sf{ x + {(x - 26.8)}^{ \circ} = {90}^{ \circ} }}[/tex]
⠀
[tex]{\longrightarrow \qquad \sf{ x + {x - 26.8}^{ \circ} = {90}^{ \circ} }}[/tex]
⠀
[tex]{\longrightarrow \qquad \sf{ 2 {x - 26.8}^{ \circ} = {90}^{ \circ} }}[/tex]
⠀
[tex]{\longrightarrow \qquad \sf{ 2 x = {90}^{ \circ} + 26.8^{ \circ}}}[/tex]
⠀
[tex]{\longrightarrow \qquad \sf{ 2 x = 116.8^{ \circ}}}[/tex]
⠀
[tex]{\longrightarrow \qquad \sf{ x = \dfrac{116.8^{ \circ}}{2}}}[/tex]
⠀
[tex]{\longrightarrow \qquad \frak{\pmb{ x =58.4^{ \circ}}}}[/tex]
⠀
Therefore,
One angle = 58.4°Other angle = 58.4° – 26.8° = 31.6°⠀
Hence,
The measure of the each angles are 58.4° and 31.6° .Answer:
The measurement of each angle is 58.4° and 31.6°
Step-by-step explanation:
Given :-
Value of an angle is 26.8° less than its complementary angleTo Find :-
Measurement of each angleSolution:-
let one angle be x and other be x - 26.8°
we know that, Sum of complementary angle is 90°
X + X - 26.8° = 90°
2x = 90° + 26.8°
x = 58.4
So , one angle is 58.4° and other one is 58.4 - 26.8 which is 31.6
From a club of 20 people, in how many ways can a group of three members be selected to attend a conference?
=============================================================
Reason:
There are 20 ways to pick the first person, 19 for the next, and 18 for the last. We count down by one each time we fill up a slot since we cannot reselect any person more than once.
If order mattered, then we'd have 20*19*18 = 6840 permutations.
However, order does not matter because no member has a special seat or role. The individual members don't matter and instead it's all about the group.
Notice that for any group of 3 people, there are 3*2*1 = 6 ways to arrange such individuals. We have to divide by 6 to go from 6840 permutations to 6840/6 = 1140 combinations.
-------------------------
Here's a more formulaic approach using the nCr combination formula.
Plug in n = 20 and r = 3
[tex]n C r = \frac{n!}{r!(n-r)!}\\\\20 C 3 = \frac{20!}{3!*(20-3)!}\\\\20 C 3 = \frac{20!}{3!*17!}\\\\20 C 3 = \frac{20*19*18*17!}{3!*17!}\\\\ 20 C 3 = \frac{20*19*18}{3!}\\\\ 20 C 3 = \frac{20*19*18}{3*2*1}\\\\ 20 C 3 = \frac{6840}{6}\\\\ 20 C 3 = 1140\\\\[/tex]
Determine the zeros of x^2 + 19x = 6x - 30
Answer:
The number of Zeros (roots) is
-3 and -10
Step-by-step explanation:
x^2 + 19x = 6x - 30
I need this done right now please i need help
Step-by-step explanation:
AB = x + 5 ...................
6. The length of Garden B is 3 more than the length of Garden A. Write, and solve the equation
you can use to find the length of Garden A.
Answer:
B = A + 3
Step-by-step explanation:
Let B be the length of Garden B and A the length of Garden A.
We are told that B = A + 3
We can use this equation to find the length of Garden B.
Please look at the attachments I posted. Anyone help me please
Answer:
This will be option D
Replace the k with -1/2 and f(x) with x^2
this will look like -1/2*x^2
plug this into a graphing website such as Desmos
A printer can print 14 pages in 28 sec.
The rate in lowest terms is____?
Answer:
1/2 or 0.5 :)
Step-by-step explanation:
We can divide to see lower forns :)
14/28 = 7/14 = 1/2
Have an amazing day!!
Please rate and mark brainliest!!
Answer:
2 pages every 7 seconds, divide by the common denominator which is 7 to get the answer
The horizontal lines (l and m) are parallel. They are crossed by two transversals (lines a and b).
Transversals a and b intersect to make a triangle. The m∠1 = 75°, and the m∠4 = 50°.
1. What is the m∠5? Explain how you know. (2 points)
2. What is the measure of the sum of the angles in a triangle? (2 points)
3. ∠3 is in a triangle with ∠4 and ∠5. Write and solve an equation to find the m∠3. (2 points)
4. What is the measure of a straight angle? (2 points)
5. ∠2 is in a straight line with ∠1 and ∠3. Write and solve an equation to find the m∠2. (2 points)
PLEASE ANSWER! WILL GIVE BRAINLIEST
1. m∠5 = 75° (corresponding angles theorem)
2. 180°
3. m∠3 = 55° (triangle sum theorem).
4. A straight angle = 180°
5. m∠2 = 50° (angles on a straight line)
What is the Triangle Sum Theorem?According to the triangle sum theorem, the sum of the angles in a triangle equals 180 degrees.
1. m∠5 = m∠1 = 75° (corresponding angles are congruent)
2. Measure of the sum of all angles in a triangle = 180°
3. To find ∠3, we would have the following equation:
m∠3 = 180 - m∠4 - m∠5 (triangle sum theorem).
Substitute and solve
m∠3 = 180 - 50 - 75
m∠3 = 55°
4. A straight angle = 180°
5. m∠2 = 180 - m∠3 - m∠1 (angles on a straight line)
Substitute and solve
m∠2 = 180 - 55 - 75
m∠2 = 50°
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This is a picture of a cube and the net for the cube.
What is the surface area of the cube?
Answer:
I don’t get it
Step-by-step explanation:
I think it is 5
its 54 also for some reason my comment keeps getting deleted for saying 54??
An electrician leans an extension ladder against the outside wall of a house so that it
reaches an electric box 31 feet up. The ladder makes an angle of 78° with the ground.
Find the length of the ladder. Round your answer to the nearest tenth of a foot if
a
necessary.
Answer:
50.41 feet
Step-by-step explanation:
Hypotenuse = length of ladder
31 = opposite side of angle
sin(angle) = (opposite)/(hypotenuse)
sin(78) = (36)/(hypotenuse)
hypotenuse = sin(78)/ (36)
hypotenuse = 50.41 feet
length of ladder = 50.41 feet
Last Friday Trevon had $29. Over the weekend he received some money for cleaning the attic. He now has $41. Write an algebraic equation to represent how much money he received
Answer:
x + 29 = 41
Step-by-step explanation:
Trevon received some money, but we don't know how much, so we will represent that with x.
The money he received will be add the amount he had last friday, $29.
The equation will equal his current amount, $41.
An inequality is shown.
Select all the values of that make the inequality true.
Answer:
2/5
1
3/2
Step-by-step explanation:
Note that:
> = Greater than
< = Less than
≤ = Less than or equal to
≥ = Greater than or equal to
Solution:
Since it given that 27/7n > 4/3
It means that
27/7n is greater than 4/3.
Now going through all answer chioces:
-----------------------------------------------------------------------------------------------------------
27/7(2/5) = 1 19/35
1 19/35 is greater than 4/3
Thus, 2/5 is true.
-----------------------------------------------------------------------------------------------------------
27/7(1/3) = 1 2/7
1 2/7 isn't greater than 4/3
Thus, 1/3 is false.
-----------------------------------------------------------------------------------------------------------
27/7(1) = 3 6/7
3 6/7 is greater than 4/3
Thus, 1 is true.
-----------------------------------------------------------------------------------------------------------
27/7(2/9) = 6/7
6/7 isn't greater than 4/3
Thus, 2/9 is false.
-----------------------------------------------------------------------------------------------------------
27/7(3/2)=5 11/14
5 11/14 is greater than 4/3
Thus, 3/2 is true.
-----------------------------------------------------------------------------------------------------------
[RevyBreeze]
(3*8-3)/3
How do you solve this?
Answer:
7
Step-by-step explanation:
Equation: (3*8-3)/3
Step 1: (24-3)/3
Step 2: 21/3
Step 3: 7
Order of operations is used in this equation. You simplify the terms in the parentheses before the other terms in the equation. According to the order of operations (parentheses, exponents, multiplication, division, addition, and subtraction, you do the multiplication before the subtraction in the parentheses. Then you subtract your three from your multiplication result (twenty-four). This leaves you with 21. Finally, you divide twenty-one by three. This gets you seven.
Which of the
following graphs
satisfies these
inequalities?
x- y< 2.
x + 2y > 8
y<4
A
B
2
f
B
is the answer. Good luck!!
Mike spins a spinner and flips a coin. What
is the probability of getting E on the spinner
and the coin landing on heads?
Answer:
3/16
Step-by-step explanation:
The probability of spining an E is 3/8 and the probability of fliping heads on a coin is 1/2 so the probablility of both those things happening is 1/2*(3/8) or 3/16
Select the correct answer.
The histogram shows the weekly attendance of participants in a school's study skills program. Student attendance numbers were the same during which two weeks of the workshop?
A.
weeks 1 and 2
B.
weeks 2 and 4
C.
weeks 5 and 6
D.
weeks 4 and 6
Answer:
That would be week 2 and 4 (B). They are both at 12 students attending
Which of the following statements is true?
The meter is a unit of volume in the U.S. customary system.
The foot is a unit of length in the metric system.
The gram is a unit of mass in the metric system.
The liter is a unit of volume in the U. S. customary system.
Answer:
Step-by-step explanation: the meter is a unit of value in the US customary system
Answer: The gram is a unit of mass in the metric system
PLEASE PLEWSE PLEASE HELP
Answer:
C) 63°
Step-by-step explanation:
Just add the numbers up together to get your solution
Solve the simultaneous equations
4x + 5y = 4
2x - y = 9
Show clear algebraic working.
Answer:
[tex]x= \dfrac 72, ~~y= -2[/tex]
Step by step explanation:
[tex]4x+5y=4~~~...(i)\\\\2x-y=9~~~...(ii)\\\\\text{Multiply eq (ii) by 2 to isolate x:}\\\\4x-2y=18~~~.....(iii)\\\\(iii)-(i):\\\\4x-2y-4x-5y=18-4\\\\\implies -7y=14\\\\\implies y = -\dfrac{14}7 = -2\\\\\text{Substitute}~ y=-2~ \text{in equation (iii):}\\\\4x-2(-2) = 18\\\\\implies 4x +4 = 18\\\\\implies 4x = 18-4\\\\\implies 4x = 14\\\\\implies x = \dfrac{14}4 = \dfrac 72\\\\\text{Hence}~ (x,y) =\left(\dfrac 72 , -2 \right)[/tex]
Step-by-step explanation:
4x+5y=4 (equation 1)
2x-y=9 (equation2)
solving equation 1 and 2 and multiplying equation 2 by 2
4x+5y=4
4x-2y=18
- + -
________
7y= -14
y= -2
putting the value of y in equation 2
2x-y=9
2x+2=9
2x=7
x=3.5
Solve each of the quadratic equations.
PT. 1
3x = 0.5x2
A. x = -6 or x = 0
B. x = -4 or x = 3
C. x = -2
D. x = 1.5 x = 0 or x = 6
PT.2
0 = 5x2 - 2x + 6
A. x= 1±3i/2
B. x=1±√11/5
C. x=1±I√29/5
Answer:
the answer to pt 1 is D. x=1.5 x=0 or x=6
and the answer to part 2 is C. x=1±I√29/5
Step-by-step explanation:
1. The solution of this equation is x = 0 or x = 6 which is option D.
2. The solution of this equation is [tex]x = \dfrac{1 \pm i\sqrt{29}}{5}[/tex] which is option C.
Use the concept of quadratic equation defined as:
The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations.
The quadratic equation has the following generic form:
ax² + bx + c = 0
1. The given quadratic equation is,
3x = 0.5x²
Rearranging it,
0.5x² - 3x = 0
Common out x,
x(0.5x - 3) = o
Then we have,
x = 0 or,
0.5x - 3 = 0
Add 3 on both sides,
0.5x = 3
Divide both sides by 0.5,
x = 3/0.5
x = 6
Hence the solution of this quadratic equation is,
x = 0 and x = 6 which is option D.
2. The given quadratic equation is:
0 = 5x² - 2x + 6
It can be written as,
5x² - 2x + 6 = 0
Since we know the quadrature formula for ax² + bx + c = 0 is,
[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
Here we have,
a = 5
b = -2
c = 6
Substitute values into the formula,
[tex]x = \dfrac{2 \pm \sqrt{4 - 120}}{10}\\\\x = \dfrac{1 \pm i\sqrt{29}}{5} \text{ }\text{ \text{ }} \text{\text{ }\ since } \sqrt{-1} = i[/tex]
Hence, option C is correct.
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The complete question is:
Solve each of the quadratic equations.
PT. 1
3x = 0.5x²
A. x = -6 or x = 0
B. x = -4 or x = 3
C. x = -2 or x = 1.5
D. x = 0 or x = 6
PT.2
0 = 5x² - 2x + 6
A. [tex]x = \dfrac{1 \pm 3i}{5}[/tex]
B. [tex]x = \dfrac{1 \pm i\sqrt{11}}{5}[/tex]
C. [tex]x = \dfrac{1 \pm i\sqrt{29}}{5}[/tex]
help me out guys thank u
Answer:
[tex] \sf \: a5 = 769[/tex]
Help picture below problem 15
Answer:
B. Pentagon
Step-by-step explanation:
A Pentagon is a polygon with 5 sides like this one.
Hope that helps!
I don’t know what is the least common factor of 18 and 12.
Answer:
the common factors for both are 1,2,3,6
2. Find the probability of throwing a 10 with a pair of dice and choosing a red from a standard deck of cards.
Answer:
Step-by-step explanation:
You can get 10 with a pair of dice with:
4 + 6, 6 + 4, 5 + 5
out of a possibile 36 results
There are 52 cards in a standard deck of cards. Reds make up half of them (hearts and diamonds) , meaning theres a 50/50 chance of pulling red
10/36 * 1/2 = 5/36 chance of throwing 10 + pulling red
A circular garden has a diameter of 10 feet. Approximately how much edging trim is needed to surround the garden by placing the trim all along the garden's circumference?
Answer:
31 feet
Step-by-step explanation:
circumference = pi × diameter
pi × diameter = 31.4 (10×3.14)
Answer: 31 ft
Step-by-step explanation:
circumference = pi × diameter
pi × diameter = 31.4 (10×3.14)
Find the perimeter of the parallelogram with these vertices.
(3.5), (-4. 2), (3.1), (-4. -2)
Give an exact answer (not a decimal approximation).
Simplify your answer as much as possible.
Check the picture below.
so we can say that two sides are "4" each in length, since opposite sides are equal, let's find how long the slanted sides are.
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-4}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{5})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[3 - (-4)]^2 + [5 - 2]^2}\implies d=\sqrt{(3+4)^2+3^2} \\\\\\ d=\sqrt{49+9}\implies d=\sqrt{58} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\Large Perimeter}}{4~~ + ~~4~~ + ~~\sqrt{58}~~ + ~~\sqrt{58}\implies 8+2\sqrt{58}}[/tex]
help i dont know how to do this and i forgot the study guide
B is the right answer
I hope it will help you
If Madeline has one week to read 1293 pages of a book and if she wants to split her reading equally each day how many pages will she need to read each day in order to finish
Answer:
184 5/7 pages
Step-by-step explanation:
There are 7 days in a week. If Madeline wants to read equal portions of the book each day, each of those portions must be 1/7 of the book, or ...
1/7 × 1293 pages = 184 5/7 pages
Madeline will need to read 184 5/7 pages each day in order to finish.
