In geometry, a hypotenuse is the longest side of a right-angled triangle, the side opposite the right angle. The length of the hypotenuse can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides.
It is useful in different situations involving the need to find distance or the measure of an angle.
Use the Pythagorean theorem to calculate the hypotenuse from right triangle sides. Take a square root of sum of squares: c = √(a² + b²)
A certain type of automobile battery is known to last an average of 1,150 days with a standard deviation of 40 days. If 100 of these batteries are selected, find the following probabilities for the average length of life of the selected batteries. (Round your answers to four decimal places.) A button hyperlink to the SALT program that reads: Use SALT. (a) The average is between 1,142 and 1,150. (b) The average is greater than 1,158. (c) The average is less than 950.
Answer:
a) 0.4772 = 47.72% probability that the average is between 1,142 and 1,150.
b) 0.0228 = 2.28% probability that the average is greater than 1,158.
c) 0 = 0% probability that the average is less than 950.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set 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]
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 p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
A certain type of automobile battery is known to last an average of 1,150 days with a standard deviation of 40 days.
This means that [tex]\mu = 1150, \sigma = 40[/tex]
Sample of 100:
This means that [tex]n = 100, s = \frac{40}{\sqrt{100}} = 4[/tex]
(a) The average is between 1,142 and 1,150.
This is the pvalue of Z when X = 1150 subtracted by the pvalue of Z when X = 1142. So
X = 1150
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{1150 - 1150}{4}[/tex]
[tex]Z = 0[/tex]
[tex]Z = 0[/tex] has a pvalue of 0.5
X = 1142
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{1142 - 1150}{4}[/tex]
[tex]Z = -2[/tex]
[tex]Z = -2[/tex] has a pvalue of 0.0228
0.5 - 0.0228 = 0.4772
0.4772 = 47.72% probability that the average is between 1,142 and 1,150.
(b) The average is greater than 1,158.
This is 1 subtracted by the pvalue of Z when X = 1158. So
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{1158 - 1150}{4}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a pvalue of 0.9772
1 - 0.9772 = 0.0228
0.0228 = 2.28% probability that the average is greater than 1,158.
(c) The average is less than 950.
This is the pvalue of Z when X = 950. So
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{950 - 1150}{4}[/tex]
[tex]Z = -50[/tex]
[tex]Z = -50[/tex] has a pvalue of 0
0 = 0% probability that the average is less than 950.
Bonus Is the point (-3, -5) inside, outside, or on the circle whose equation is (x + 7)² + (y − 2)² = 62? (SOMEONE PLEASE EXPLAIN!!)
Answer:
Outside, as the distance between the point and the center of the circle is more than the radius.
Step-by-step explanation:
Equation of a circle:
The equation of a circle has the following format:
[tex](x-x_0)^2 + (y-y_0)^2 = r^2[/tex]
In which [tex](x_0,y_0)[/tex] is the center and r is the radius.
Testing if a point is inside the circle:
Point (x,y), we replace in the equation. If it is less than the radius squared(in this case, 62), it is in.
In this question:
Point (-3,-5). So
[tex](-3+7)^2 + (-5-2)^2 = 4^2 + (-7)^2 = 16 + 49 = 65[/tex]
The square distance of the point to the center is of 65, which is more than the square of the radius, meaning that the point is outside the circle.
Answer:
Outside
Step-by-step explanation:
pls help quick it is in the picture
Answer:
90 degrees it looks like
Step-by-step explanation:
What is the volume, in cubic meters, of a cylinder with a height of 3 meters and a base
radius of 4 meters, to the nearest tenths place?
Answer:
answer is 150
Step-by-step explanation:
hope it helps
In a popular online role playing game, players can create detailed designs for their character's "costumes," or appearance. Aaron sets up a website where players can buy and sell these costumes online. Information about the number of people who visited the website and the number of costumes purchased in a single day is listed below.
41 visitors purchased no costume.
78 visitors purchased exactly one costume.
10 visitors purchased more than one costume.
If next week, he is expecting 2000 visitors, about how many would you expect to buy more than one costume? Round your answer to the nearest whole number.
Answer:
115
Step-by-step explanation:
41 no costume, 78 exactly one costume, 10 more than one costume.
41+78+\color{steelblue}{10}=
41+78+10=
\,\,\color{indianred}{129}
129
There were a toal of 129 visitors. 10 purchased more than one costume.
Probability the next customer will purchase more than one costume:
\frac{\color{steelblue}{10}}{\color{indianred}{129}}\phantom{=}
129
10
=
\,\,
Out of 2000 new trials, we would expect more than one costume to be selected:
\color{purple}{2000}\times\frac{\color{steelblue}{\color{steelblue}{10}}}{\color{indianred}{\color{indianred}{129}}}=
2000×
129
10
=
\,\,155.038759...
155.038759...
\approx
≈
\,\,155
155
The number of visitors that expect to buy more than one costume will be 155.
What is the expected value?The expected value is given below.
E(x) = np
Where n is the number of samples and p is the probability.
Aaron creates a website where players may trade and purchase these costumes. The numbers below show how many people visited the website and how many costumes were bought in a single day.
The probability of visitors purchasing more than one costume is calculated as,
p = 10 / (41 + 78 + 10)
p = 10 / 129
If next week, he is expecting 2000 visitors. Then the expected value is given as,
E = 2000 x (10 / 129)
E = 155.038
E ≈ 155
The number of visitors that expect to buy more than one costume will be 155.
More about the expected value link is given below.
https://brainly.com/question/13945225
#SPJ2
Right Triangles
Solve the right triangle shown in the figure
∠C = 90°, BC = 7.50mi, AC = 11.43mi
a. AB = 19.5mi, ∠A = 31.2°, ∠B = 58.8°
b. AB = 16.mi, ∠A = 35.2°, ∠B = 54.8°
c. AB = 13.7mi, ∠A = 33.3°, ∠B = 56.7°
d. No triangle satisfies the given conditions.
Please select the best answer from the choices provided
Answer:
C. AB = 13.7mi, ∠A = 33.3°, ∠B = 56.7°
Step-by-step explanation:
I calculated it logically
6 members of the Benton family are going to their school's Community Day. They have a coupon for $4.50 off their total. If they pay $40.50 for all their tickets, how much does one ticket cost without the coupon?
Answer:
$7.50
Step-by-step explanation:
you add 40.50 + 4.50 which then equals 45 and you divide that by 6 and you get 7.50
One ticket costs $7.50 without the coupon this we obtained by dividing total cost before discount by Number of tickets
Let us find the total cost of the tickets before the coupon is applied. We can do this by adding the discount amount ($4.50) to the final cost ($40.50):
Total cost before discount = Final cost + Discount amount
Total cost before discount = $40.50 + $4.50
Total cost before discount = $45.00
Now we can divide the total cost before discount by the number of tickets
(6) to find the cost of one ticket:
Cost of one ticket = Total cost before discount / Number of tickets
Cost of one ticket = $45.00 / 6
Cost of one ticket = $7.50
Therefore, one ticket costs $7.50 without the coupon.
To learn more on Discount click:
https://brainly.com/question/3541148
#SPJ2
simplify 1/3 : 2.5 : 3 3/4
Answer:
1/3x3 3/4 /2.5 = 0.3
will give 50 point privetely if correct and show work
Ms. White invests $ 2000 in a savings plan. The savings account pays an annual interest rate of 5.75 % on the amount she puts in at the end of each year. How much will be in her savings plan at the end of 10 years?
Answer:
The solution is 2000 + 0.0575*2000*10 = 3150 dollars at the end of 10 years.
Step-by-step explanation:
HELP ME PLZZZZZZ AND THANK YA ILL GIVE BRAINILIEST THINGY-MA-GIGGY
a cone has a volume of 24 cubic feet. a cylinder has a congruent base to the cone. the cylinder is the same height as the cone. how many cubic feet will the cylinder hold?
A) 8 B)58 C)72
Answer:
hewo Asuna here
your answer is C
Step-by-step explanation:
hope this helps^^
The following is a geometric series.
6+8+11+15+20+26+...
O True
False
EXPLAIN ANSWER FOR BRAINLIEST
9514 1404 393
Answer:
False
Step-by-step explanation:
The terms of a geometric series would have a common ratio. The terms of this series do not. (The differences increase by 1 each time, so it is a quadratic series.)
False, the series is not geometric.
Answer:
Solution :-We are given with the series
6 + 8 + 11 + 15 + 20 + 26
Since
the series is increasing by +1. So, it will be not a geometric series
[tex] \\ [/tex]
Can someone help me with this?
Answer:
I can help you via Watsapp
Find the measure of the angle(s)
Help
Answer:
759
Step-by-step explanation:
You are walking along a path y= 2x + 12 and your
best friend is walking along 4x + y = 6. At what point will
you cross paths?
Answer:
(-1,10)
Step-by-step explanation:
At the point when the paths cross, the respective x and y values of each equation will be equal.
Your path is y=2x+12, and your friends path is 4x+y=6. Sub 2x+12 in for y (from your path's equation) into your friends equation to find the value of x:
4x+2x+12=6
6x=-6
x=-1
y=2x+12
y=2(-1)+12=10
So you will cross paths at (-1,10)
Approximate the value of 5(pi)
A)Slightly more than 20
B)Slightly less than 15
C)Slightly more than 15
D)Slightly less than 20
Answer: C
Step-by-step explanation: 5pi converts to 15.70796
Answer:
slightly less than 15 of b.
Given
f(x) = 2x - 1 and g(x) = 4x + 6,
which operation completes the statement?
f(x) ___ g(x) = 8x^2 + 8x - 6
i need to determine what math sign i have to use on the ____ the options are *,+,-, and the divide symbol
this is operations on functions!!!
f(x) times g(x) = 8x^2+8x-6
(2x-1) times (4x+6) = 8x^2+8x-6
====================================================
Explanation:
The functions f(x) and g(x) are linear functions. The result of f(x) ___ g(x) is some quadratic function.
It's very likely that the answer is a multiplication sign because of the general template of
(linear)*(linear) = (quadratic)
For example, x*3x = 3x^2.
Let's see if the two functions multiply out to 8x^2+8x-6 or not.
-----------------------
f(x) * g(x) = ( f(x) ) * ( g(x) )
f(x) * g(x) = ( 2x-1 ) * ( 4x+6 )
f(x) * g(x) = y * ( 4x+6 ) ......... let y = 2x-1
f(x) * g(x) = 4xy + 6y ......... distribute
f(x) * g(x) = 4x( y ) + 6( y )
f(x) * g(x) = 4x( 2x-1 ) + 6( 2x-1 ) .... replace y with 2x-1
f(x) * g(x) = 8x^2-4x + 12x-6 .... distribute twice more
f(x) * g(x) = 8x^2+8x-6
We end up getting the correct result. So this confirms that a multiplication sign is needed to fill in the blank.
The total number of running yards in a football game was less than 100. The inequality x <100 represents the
situation. Which graph represents the inequality?
95 96 97 98 99 100101102103104105
95 96 97 98 99 100 101 102103104105
95 96 97 98 99 100 101 102103104105
95 96 97 98 99 100101102103104105
Answer:
answer is B
Step-by-step explanation:
got it right on edge :)
Pls help me with math
Answer:
true
Step-by-step explanation:
They are dependent because the outcome of the event affects them
What is the measure of X , in degrees? HELPP!
Answer:
86°
Step-by-step explanation:
How many outcomes are possible if you chose one letter from the word FUN and another letter from the word NOT.
Answer:
9
Step-by-step explanation:
The first question is how many ways can I get one letter from the word FUN?
That is 3.
Similarly, how many ways can I get one letter from the word NOT?
That is also 3.
Then one letter from FUN and one letter from NOT gives= 3 * 3 = 9
The knockoff Jersey store sold 6 more Leafs jerseys than Senators. Four times the number of Senators Jersey sold plus three times the number of Leafs jerseys sold is 102. How many Leaf Jerseys were sold?
Answer:
72
Step-by-step explanation:
6x4=24x3=72
What is the area of the isosceles triangle shown?
Answer:
672 meters squared
Step-by-step explanation:
Area of Triangle: b*h*1/2
The isosceles triangle's height, splits the base in half.
Answer:
672
Step-by-step explanation:
Area of a triangle = [tex]\frac{bh}{2}[/tex]
where b = base length and h = height
In the triangle shown, we are only given the base length
This means that we must find the height in order to find the area.
We can do this by using the Pythagorean theorem
[tex]a^2+b^2=c^2[/tex]
where a and b = legs and c = hypotenuse
Two right triangles are formed within the isosceles triangle.
Each has a hypotenuse of 50 m, a base length of 28/2=14m ( because they are sharing the base length ) and they are both sharing the height.
So we are given the hypotenuse and a leg and we need to find the other leg
So we plug in what we are given and solve for the missing side length
[tex]50^2=a^2+14^2\\50^2=2500\\14^2=196\\2500=a^2+196[/tex]
step 1 subtract 196 from each side
2500 - 196 = 2304
196 - 196 cancels out
we now have 2304 = a²
step 2 take the square root of each side
[tex]\sqrt{a^2} =a\\\sqrt{2304} =48[/tex]
we're left with a = 48
This means that the height of the isosceles triangle is 48m
Now we can find the area.
Using the formula stated previous....
[tex]A=\frac{28*48}{2} \\28*48=1344\\\frac{1344}{2} =672[/tex]
Hence, the area is 672m²
3X + 2 = 17 how do i show my work for this help
Martha Stewart needs a total of 520 napkins for her restaurant. She currently has 234 napkins. If each package of napkins has 20 napkins, what is the minimum number of packets of napkins she should buy? Write an algebraic equation, solve, and conclude.
Answer:
520=20x+234
15 packages
Step-by-step explanation:
520-234
286
286/20
14.3, so she needs 15 packages
Ebony discovered she had $8 in quarters how many quarters are there in $8 choose the division expression you would use to find the number of quarters and $8
1. $8 ÷4
2. $8 ÷ 1/4
3. $8 ÷ 1/2
im trying to test u to see if u know it. :D
28 ÷ 13
Answer:
[tex]\huge \fbox \pink {A}\huge \fbox \green {n}\huge \fbox \blue {s}\huge \fbox \red {w}\huge \fbox \purple {e}\huge \fbox \orange {r}[/tex]
[tex] \frac{28}{13} \\ = 2.15[/tex]
Answer:
28/13 or 2.15384615
Step-by-step explanation:
28/13 is the most simplified form of the fraction. If you were to calculate it out it would be 2.15384615.
Can someone help me find the measure of each angle indicated please
Answer:
Option B, 105 would be correct
Step-by-step explanation:
The Vertical Angles Theorem states that angles that are opposite diagonally are congruent, therefore; ? = 105°
Hope this helps!
solve for x 9.2, 16.5, x
Answer:
152
Step-by-step explanation:
100 pts and brainiest for the right answer
A skateboard halfpipe is being designed for a competition. The halfpipe will be in the shape of a parabola and will be positioned above the ground such that its focus is 20 ft above the ground. Using the ground as the x-axis, where should the base of the halfpipe be positioned? Which equation best describes the equation of the halfpipe?
(0, 20); y equals one over eighty times x squared plus 20
(0, 20); y equals one over eighty times x squared minus 20
(0, 10); y equals one over forty times x squared plus 10
(0, 10); y equals one over forty times x squared minus 10
Answer:
Option A , (0, 20); y equals one over eighty times x squared plus 20
Step-by-step explanation:
The equation of parabola is given by
(X-h)^2 = 4p(Y-k)^2
In this case h = 0
So we get
Y = X^2/4P +k
Focus point is (h, p+k) , p+k = 40
Hence h, k = (0,20)
P = 40-k = 20
Equation Y = X^2/80 +20
Hence, option A is correct
plz mark brainliest
Answer: A
Step-by-step explanation:
1 mark question please answer me
Given:
The polynomial is:
[tex]P(x)=ax+b[/tex]
To find:
Whether [tex]x=-\dfrac{b}{a}[/tex] is a zero of the given polynomial or not.
Solution:
We have,
[tex]P(x)=ax+b[/tex]
Putting [tex]x=-\dfrac{b}{a}[/tex], we get
[tex]P(-\dfrac{b}{a})=a(-\dfrac{b}{a})+b[/tex]
[tex]P(-\dfrac{b}{a})=-b+b[/tex]
[tex]P(-\dfrac{b}{a})=0[/tex]
Since the value of the given polynomial is 0 at [tex]x=-\dfrac{b}{a}[/tex], therefore [tex]x=-\dfrac{b}{a}[/tex] is a zero of the given polynomial.