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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Factor the polynomial.
2x^3 + 4x^2 + 8x
A) 2x^3 + 4x^2 + 8x
B) 2x^2(x + 2x + 4)
C) x(2x^2 + 4x + 8)
D) 2x(x^2 + 2x + 4)
[tex] {2x}^{3} + 4 {x}^{2} + 8x \\ \\ 2x( {x}^{2} + 2x + 4)[/tex]
Hope it helpsWhat is the best way to describe the center of the data represented in this line plot?
Select from the drop-down menus to correctly complete the statement.
The Choose is Choose. your options are for the first one is Mean or Median then for the second one is 2 inches, 2.5 inches, 3 inches, or 3.2 inches
.
The best way to describe the center of the data represented in this line plot include the following: the median is 2.5 inches.
What is a median?In Mathematics, a median refers to the middle number (center) of a sorted data set, which is when the data set is either arranged in a descending order from the greatest to least or an ascending order the least to greatest.
Since the data set representing the amount of rainfall has an outlier, the median would be best way to describe the center of the data represented in this line plot.
First of all, we would sort the 10 observations from the least to greatest as follows:
1, 1, 2, 2, 2, 3, 3, 5, 6, 7
Median = (2 + 3)/2
Median = 5/2
Median = 2.5 inches.
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Which function is the inverse of f(x) = -5x -4?
Answer:
f−1(x)=x5+45
Step-by-step explanation:
Ama and Kwame shared an amount of money.
If Ama received one third of the money. Which
fraction is for Ama's share?
Find the distance between the two points in simplest radical form.
(9,-1,) and (3,3)
x1 = 9, x2 = 3
y1 = -1, y2 = 3
By using Distance formula[tex] \sqrt{ {(x2 - x1) + (y2 - y1)}^{2} } \\ \\ \sqrt{ {(3 - 9)^{2} + (3 - ( - 1))}^{2} } \\ \\ \sqrt{ {( - 6)}^{2} + {(4)}^{2} } \\ \\ \sqrt{ 36 + 16 } \\ \\ \sqrt{52} \\ \\ 7.21 \: units[/tex]
Hope it helpsQuestion 1
1 pts
A private parking lot in downtown Philadelphia is being built. It's 120' long by 75' wide. To put a
fence around it, the construction company will need at least 390' of fencing material. True or false?
We will see that the perimeter of the rectangle is exactly 390 ft, so the statement is true.
Is the fence enough?
For a rectangle of length L and width W, the perimeter is given by:
P = 2*(L + W).
In this case, we know that:
L = 120 ft
W = 75 ft
Replacing that on the perimeter equation we get:
P = 2*(120 ft + 75 ft) = 390 ft
So the perimeter is exactly 390 ft, meaning that to put a fence around the parking lot the company will need at least 390 ft of fence.
So the statement is correct.
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HELP PLEASE!!
Discuss the steps that you used
to create your tangent line.
What was the most important
step?
Give an example of tangents in
the real world that have not
been presented in this lesson.
Explain how you know the
tangent and the radius are
perpendicular.
Answer:
You need to have both the opposite and adjacent side of the right angled triangle. Tan = Opp/Adj
Step-by-step explanation:
Tangents are pretty much everywhere. A good example is maybe a slide at the playground. You’d need the tangent to figure out the angle of the slide and how it is.
The radius from the center of a circle to the point of tangency point shows that it would be perpendicular to the tangent line considering that anything with a radius is circular and the tangent line is… a line, making it impossible to be parallel.
Instructions: Drag the correct term for
this definition.
The perpendicular bisectors of the
sides of a triangle intersect in a
point that is equidistant from the
vertices.
Answer:
The three perpendicular bisectors of the sides of a triangle meet in a single point, called the circumcenter . A point where three or more lines intersect is called a point of concurrency. So, the circumcenter is the point of concurrency of perpendicular bisectors of a triangle.
If you can please give brainliest thank you <3
Step-by-step explanation:
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answer:
y = 8 , x = 15
Step-by-step explanation:
[tex]\frac{24}{51}= \frac{y}{17} \\[/tex]
Cross Multiply.
51 * y = 24 * 17
Then solve for y.
[tex]y=\frac{24*17}{51}[/tex]
y = 8
Same thing for the x.
[tex]\frac{45}{51}=\frac{x}{17}[/tex]
Cross Multiply.
51 * x = 45 * 17
Solve for x.
[tex]x=\frac{45*17}{51}[/tex]
x = 15
How many different ways can the letters of grade be arranged?
( I have to use permutation to solve please and thank you )
Explanation:
Assuming you want to arrange the letters of "grade", then we have 5 unique letters. That gives 5! = 5*4*3*2*1 = 120 different permutations. Order matters. The exclamation mark means factorial. It means we start at 5 and count our way down to 1, multiplying along the way.
In other words, we have 5 choices for the first slot, then 4 choices for the next slot, and so on. We count down because we cannot reuse any previously selected letter.
Alternatively, you can use the nPr permutation formula
[tex]_nP_r = \frac{n!}{(n-r)!}[/tex]
where n = 5 and r = 5 since we have 5 letters to pick from and 5 slots to fill.
Answer:
120 ways
Step-by-step explanation:
The given word is :
GRADEIt has five letters⇒ Any of the 5 letters can be in each place
⇒ 5! ways is the number
⇒ 5 x 4 x 3 x 2 x 1
⇒ 20 x 6
⇒ 120 ways
HELP!! What is the surface area of this figure?
Answer:
448 is the answer
Step-by-step explanation:
If u need complete solution do let me know
Answer:
448 yd^2.
Step-by-step explanation:
The surface area consists of 3 rectangles and 2 congruent triangles
= 12*11 + 2 * 10*11 + 2 * 1/2 * 12*8
= 132 + 220 + 96
= 448 yd^2.
ANSWER QUICK WITH THE ANSWER FOR EXTRA POINTS ⭐️⭐️⭐️⭐️!
Ruby is painting her house. She uses 2 2/7 gallons of paint in the living room. To paint the kitchen, Ruby uses 5/8 of the amount of paint she uses in the living room. Which expression can be used to find the number of gallons of paint Ruby uses to paint the kitchen?
Answer:
ur momma
Step-by-step explanation:
yea so you take the 5/8 and the 2 and the 2/7 and you dd then subtract then divide
I need help finding the surface area of this shape
Answer:
1030 [tex]yd^{2}[/tex]
Step-by-step explanation:
split it into 2 different rectangular prisms
first one is 27 yd by 8 yd by 9 yd
second is 10yd by 8 yd by 12 yd
Answer:
1494 [yd²].
Step-by-step explanation:
1) the required area can be calculated as (see the attached picture):
A=A1+A2+A3+A4+A5+A6+2*A7;
2) finally,
A=9*8+17*8+8*12+10*8+(12+9)*8+27*8+2*(27*9+12*10);
A=1494 [yd²].
Note, the suggested solution is not the shortest one.
Calculate the perimeter of the following figure.
11 inches
4 inches
3 inches
4 inches
7 inches
Answer:
29 inches
Step-by-step explanation:
add all the sides
11+4+3+4+7=29
Answer:
29 inches
Step-by-step explanation:
⇒ Perimeter = Sum of the lengths of the sides
⇒ P = 11 + 4 + 3 + 4 + 7
⇒ P = 18 + 11
⇒ P = 29 inches
Brenda walked a distance represented by the expression 5(2y + 4). It is 5 times the
distance John walked. Interpret the expression 2y + 4 and identify the correct choice.
Answer:
Option DStep-by-step explanation:
Let the distance Brenda walked is B and distance John walked is J.
We have
B = 5Jand
B = 5(2y + 4)Comparing the two equations we see
J = 2y + 4It means 2y + 4 is the distance walked by John
Correct answer choice is D
I NEED HELP ASAP NO LINKS PLEASE I WILL MARK YOU BRAINLIEST
IF YOU DO NOT KNOW THE ANSWER PLEASE DO NOT EVEN TYPE A SENTENCE UDEE THIS THREAD
Answer:
354.5
Step-by-step explanation:
The area of a circle is calculated as A = πr².
Answer:
358.36(rounded to nearest hundredth)
Step-by-step explanation:
area of sector =
[tex] \frac{120}{360} \times area \: of \: circle \\ = \frac{120}{360} \times (3.14 \times {18.4}^{2} ) \\ = 354.3594667 \\ = 354.36(nearest \: hundredth)[/tex]
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Mark Wolfman is the director of safety at Waterworld. He needs to order a new wire for the tallest tower in the park. One end of the wire is attached to the top of the tower and the other end is attached to stake in the ground that is 44 feet away from the base of the tower. The wire makes a 78 degree angle with the flat ground. How much wire will he need?
Answer: Approximately 211.628311 feet of wire is needed
==========================================================
Explanation:
Draw out a right triangle with 44 as the horizontal component. The angle 78 is the angle of elevation right next to the horizontal side.
Let x be the length of the wire needed. This is the hypotenuse of the triangle.
Use the cosine ratio to say the following:
cos(angle) = adjacent/hypotenuse
cos(78) = 44/x
x*cos(78) = 44
x = 44/cos(78)
x = 211.628311 feet approximately
Round this value however you need to.
Answer:
211.63 ft (nearest hundredth)
Step-by-step explanation:
**Refer to the attached diagram**
We need to find the hypotenuse of the right triangle.
To do this, we should use the cos trig ratio:
[tex]\sf cos(\theta)=\dfrac{A}{H}[/tex]
where:
[tex]\theta[/tex] is the angleA is the side adjacent to the angleH is the hypotenuseGiven:
[tex]\theta[/tex] = 78°A = 44 ftH = wSubstitute given values into the equation and solve for w:
[tex]\sf \implies cos(78)=\dfrac{44}{w}[/tex]
[tex]\sf \implies w=\dfrac{44}{cos(78)}[/tex]
[tex]\sf \implies w=211.6283112[/tex]
Therefore, the length of wire needed is 211.63 ft (nearest hundredth)
Use the order of operations to find the value of the expression.
2
+
3
×
16
−
2
×
21
−
3
A.
5
B.
14
C.
35
D.
44
Using the order of operations to find the value of the expression, we have; A. 5
How to carry out order of operations?We want to use order of operations to solve the problem;
2 + 3 × 16 − 2 × 21 − 3
Now, the order is called BODMAS which means;
Bracket, Of, Division, Multiplication, Addition, Subtraction.
From the order above and looking at our question, we will first carry out multiplication to get;
2 + 48 - 42 - 3
Next is addition to get;
50 - 42 - 3 = 5
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Prove: AB/CD =AC/CD
Check out the other post with this question to understand it fully.
Answer:
Step-by-step explanation:
Please please help me !
Thank you for the help.
Point and brainliest
1. no
2. no
3. strong
4. positive
this is what i think is right. lmk which is wrong :)
After a successful fishing trip, Leo weighed his catch. He determined he caught a total 6.5 kilograms of fish. The recipe Leo wants to use to make fish stew lists their measurements in grams. Help Leo convert the weight of his fish from kilograms to grams.
Answer:
6 1/2 Grams
Step-by-step explanation:
Hope this helped!!
The weight of Leo's fish from kilograms to grams is 6500 grams
What is kilograms?Kilograms is the "SI unit of mass (equivalent to approximately 2.205 lb), first introduced as a unit of mass for the metric system".
According to the question,
Leo catch a total 6.5 kilograms of fish. He wants to convert kilograms into grams.
Formula to convert kilograms into grams 1 kilograms = 1000 grams
In order to find kilograms into grams only if multiply given kilogram into 1000.
6.5 × 1000 = 6500 grams
Hence, the weight of Leo's fish from kilograms into grams is 6500 grams.
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What is the range of the function graphed below?
Please help I'll mark brainliest
Answer:
32
Step-by-step explanation:
Add up all the numbers and then divide by how many numbers there are.
39 28. If y = (1 - 3x), find the value of dy! dx at x = -1.
Answer:
the answer to this question is 52.18
I’m really confused… feedback would be appreciated!
Answer: 13/34
Step-by-step explanation: In total there are 34 people
There are 13 professors and instructors.
That means that there is a 13/34 chance.
I NEED HELP ASAP!!!!!!!!!!!
Answer: Below
Step-by-step explanation:
Let's start with 12. Going off of basic quadrilateral rules, adjacent angles will be equal to 180. So we make the equation:
8x - 12 + 3x + 5 = 180
Simply.
11x - 7 = 180
11x = 187
x = 17
Since R = P, R = 3(17) + 5 = 56
Now with 14.
We know ABC is both 115 and 4x+6, so:
115 = 4x + 6
109 = 4x
x = 27.25
ADB is 6x - 11, so 6(27.5) - 11 = 152.5
12) 56
14) 152.5
If (x, 42) is a solution to the equation y = -6 (x – 15) – 3, find x
Put y and find x
y=-6(x-15)-342=-6(x-15)42+3=-6(x-15)45=-6x+90-6x=-45x=45/6x=15/2The expression below is a sum of cubes.
125x^3 + 144
A. True
B. False
Answer:
False
Step-by-step explanation:
Hey there!
If this is a sum of cubes, this means that both numbers have whole numbers as the cube root of that number
The cube root of 125 is 5
But the cube root for 144 is a decimal meaning this is not a sum of cubes
if x+y = -10 and x-y = 2 what is the value of x
Answer:
x= -4
Step-by-step explanation:
adding the two equations,
x+x+y-y=-10+2
2x= -8
x=-4