Answer:
a) 0.5714 = 57.14% probability that it is overloaded because they have a mean weight greater than 158 lb
b) No, because the probability of being overloaded is considerably high(57.14%). Ideally, it should be under 5%, which would be considered an unusual event.
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 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.
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.
Assume that weights of males are normally distributed with a mean of 160 lb and a standard deviation of 35 lb.
This means that [tex]\mu = 160, \sigma = 35[/tex]
Sample of 10:
This means that [tex]n = 10, s = \frac{35}{\sqrt{10}} = 11.07[/tex]
a) Find the probability that it is overloaded because they have a mean weight greater than 158 lb.
This is 1 subtracted by the pvalue of Z when X = 158. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{158 - 160}{11.07}[/tex]
[tex]Z = -0.18[/tex]
[tex]Z = -0.18[/tex] has a pvalue of 0.4286
1 - 0.4286 = 0.5714
0.5714 = 57.14% probability that it is overloaded because they have a mean weight greater than 158 lb.
b.) Does this elevator appear to be safe?
No, because the probability of being overloaded is considerably high(57.14%). Ideally, it should be under 5%, which would be considered an unusual event.
what is the value of k if - 2/3(k - 6) = 3/2(k+6)
*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆
Answer: -30/13
I hope this helped!
<!> Brainliest is appreciated! <!>
- Zack Slocum
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PLEASE HELP!!! DUE IN 10 MIN!!!
Answer:
Option B
Step-by-step explanation:
Surface area of a triangular prism = Area of the triangular sides + Area of the rectangular sides
Area of the triangular sides = 2(Area of the triangular base)
= [tex]2[\frac{1}{2}(\text{Base})(\text{Height})][/tex]
= 10 × 12
= 120 ft²
Area of the rectangular sides = (Perimeter of the triangular side)(Height of the prism)
= (10 + 13 + 13)(15)
= 36 × 15
= 540 ft²
Surface area of the prism = 120 + 540
= 660 square feet
Option B will be the answer.
Find the length of the third side. If necessary,
round
to
the nearest tenth.
4
7
Answer:
The answer would be 8.1
Step-by-step explanation:
Acellus
A
-3
-2.
-1
B
The distance AB rounded to the
nearest tenth = [?].
Hint: d= V(x2 – x1)2 + (y2 - y1)2
Enter
haha help plz
Answer:
[tex]AB = 3.6[/tex]
Step-by-step explanation:
Given
The attached graph
Required
Distance AB
From the graph:
[tex]A = (-2,1)[/tex]
[tex]B = (1,-1)[/tex]
The distance is:
[tex]AB = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
[tex]AB = \sqrt{(-2 -1)^2 + (1- -1)^2}[/tex]
[tex]AB = \sqrt{(-2 -1)^2 + (1+1)^2}[/tex]
[tex]AB = \sqrt{13}[/tex]
[tex]AB = 3.6[/tex]
m∠Q =
m∠R =
m∠S =
40 POINTS!!!!!!!
9514 1404 393
Answer:
∠Q = 89°
∠R = 123°
∠S = 91°
Step-by-step explanation:
It seems easiest to start by finding the measures of each of the arcs. The measure of an arc is double the measure of the inscribed angle it subtends.
arc QRS = 2·∠P = 114°
So, ...
arc QR = arc QRS - arc RS = 114° -41° = 73°
The total of the arcs around the circle is 360°, so ...
arc PQ = 360° -arc PS -arc QRS
arc PQ = 360° -137° -114° = 109°
__
∠Q = (1/2)(arc RS + arc PS) = (1/2)(41° +137°)
∠Q = 89°
__
∠R = (1/2)(arc PS +arc PQ) = (1/2)(137° +109°)
∠R = 123°
__
∠S = (1/2)(arc PQ +arc QR) = (1/2)(109° +73°)
∠S = 91°
HELP PLS WUICK! GIVING OUT BRAINLIST
A rectangle has a base of 4 feet and a height of 30 inches.
What is the area of the rectangle? Choose the correct answer below.
A
4.5 square feet
B
10 square feet
C
46 square inches
D
120 square inches
A triangle has sides 12cm, 9cm and 15cm. Is the triangle right-angled? Justify your answer
Answer:
yes
Step-by-step explanation:
Yes this triangle is right angled and can be justified using the Pythagorean theorem. The theorem states that: [tex]a^{2} +b^{2} = c^{2}[/tex]. Substitute using the given values:
(9^2)+(12^2)=15^2
81 + 144 = 255
255 = 255.
It satisfies the theorem therefore it is a right angle triangle.
11/60 as a mixed number
Answer:
5 /11 is the Mixed Number.
Have a good day! :D
Step-by-step explanation:
Sarah invested $2,500 in an account paying an interest rate of 2.1% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest hundred dollars, would be in the account after 14 years?
Answer:
sorry 2458946547165874%
Step-by-step explanation:
how to write two pounds and four pence
Krish and Aanya gor to a restaurant for dinner. Their meals total $13.75. The tax is 5%
a. How much tax is added to the bill?
b. Aanya and Krish want to leave a 15% tip based on their bill and tax combined. How much should they leave?
Answer:
A) $6.87
B) $3.09
Step-by-step explanation:
8 + 6 − (8 ÷ 4) x 2 i need help
Answer:
10
Step-by-step explanation:
8 + 6 - (8 ÷ 4) × 2
8 + 6 - 2 × 2
8 + 6 - 4
14 - 4
10
HELP ME PLEASE
Part 2: What is the quotient of
5
3
?
4
12
Answer:
addition=24
subtraction=6
multiplication=720
division=1.8
Which expression is equivalent to 4(-2c) - c
-6c
8c - 1
-9c
7c + 1
I'm not good at this stuff -_-
Answer:
none of those?
Step-by-step explanation:
4(-2c) = -8c
Answer: -9c
Step-by-step explanation:
4(-2c) - c
= -8c - c
= -9c
-9c is the answer
Please help I will give brainliest
Answer:
c.42
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
10+4= 14 so that is one side
14x3=42
So the answer is 42 so C
Missy has a box that is 5 in. high, 20 in. long, and 5 in. wide. Use a formula to find the volume of the box.
Which of the following is the volume?
OA. 50 cubic inches
OB. 100 cubic inches
C. 250 cubic inches
O D. 500 cubic inches
Answer:
Its D
Step-by-step explanation:
I just submited that same exact test from connexus
Answer: D 500 cubic centimeters
Step-by-step explanation:
The formula of a volume is Volume = Length x Width x Height. In this case, it already gave us all of the sides that we need! So all we need to do is multiply 5 x 5 x 20 which gives us 500 cubic centimeters!
Hope this helped! ^^
How many 6 digit combinations are there using only numbers 1-9?
Answer:
With no digits repeated that would be 60,480
Step-by-step explanation:
9×8×7×6×5×4 = 60,480
Find tan x in the triangle pictured above
Answer:
Hi Marie, use the reminder
Step-by-step explanation:
Use SOH CAH TOA to recall how the trig functions fit on a triangle
SOH: Sin(Ф)= Opp / Hyp
CAH: Cos(Ф)= Adj / Hyp
TOA: Tan(Ф) = Opp / Adj
Tan(x) = Opp / Adj
Tan(x) =32 / 24
X = arcTan(32/24)
X = 53.13°
Last year, Jason's average in math was a 72. This year, his average is a 90. What is the percent increase in Jason's grade?
Answer:
20% increase
Step-by-step explanation:
All you have to do is divide 72 by 90n and it will give you .8, move the decimal two places to the right to give you 80 and subtract 80 from 100 to get 20
The remaining questions refer to the following situation: Suppose a certain farmer wants to find out if the average length of the green beans in her field is 4 inches. She collects a random sample of 100 beans and get a sample mean of 3.75 inches. (Suppose she knows that the population standard deviation of bean length is 0.5.) What is the population in this situation
Answer:
The population in this situation is all green beans in her field.
Step-by-step explanation:
Informally, if you take a sample of an object, the population in all of these objects.
In this question:
Sample of 100 green beans in her field. This means that the population in this situation is all green beans in her field.
Write the explicit formula for the
sequence below. Then, find the number
term in the sequence as listed.
140,130,120,110...
Answer:
[tex]a_n=-10n+150[/tex]
Step-by-step explanation:
This is consider a linear pattern (arithmetic pattern).
We know this because it is either going up or down by the same number each time. It's going down by 10 in this case.
So -10 is the slope of this linear pattern.
The equation for a linear pattern is:
y=mx+b
where x represents the position the term is in
and
where y represents the actual term
and
where m is the slope
So we have y=-10x+b.
(x,y)
(term position in sequence, actual term)
(1,140)
(2,130)
(3,120)
(4,110)
We can find b by using a number with it's position in the sequence (that is plug in one of your points above).
y=-10x+b
140=-10(1)+b
140=-10+b
150=b (after adding 10 on both sides)
The explicit equation for the sequence is y=-10x+150.
They probably prefer you to write: [tex]a_n=-10n+150[/tex] instead.
HELP PLS!!
Write the inequality shown by the graph
Answer: y>-2/6+2
Step-by-step explanation:
We know it's greater then so we just need to find the line. Let's look at the Slope, since 0,2 is greater than -6,4 we start there. The y of 0,2 is 2 so we subtract 4 from 2 which is -2 and now we subtract -6 from 0 which is 6 so now we have -2/6 and the intercept is 2 so we now have y=mx+b which is the line in black: y=-2/6+2. But it is greater than so its y>-2/6+2
Moriah studied for 3 hours to prepare for her history exam. How many minutes did she study?
Answer:
180
Step-by-step explanation:
Every hour is 60 minutes. To find the total number of minutes she studied, you would have to multiply 3 x 60.
3 x 60 = 180
Answer: 180 minutes.
Step-by-step explanation: 3 hours is equal to 60+60+60 because there is 60 minutes in 1 hour so 60+60 is 120+60=180 therefore, she studied for 180 minutes.
Solve for the two variables in the following system of equations. 7x-8y=-12
--4x+2y=3
Answer:
x=0, y=3/2. (0, 3/2).
Step-by-step explanation:
7x-8y=-12
-4x+2y=3
----------------
7x-8y=-12
4(-4x+2y)=4(3)
-----------------------
7x-8y=-12
-16x+8y=12
----------------
-9x=0
x=0/-9
x=0
7(0)-8y=-12
0-8y=-12
8y=0-(-12)
8y=0+12
8y=12
y=12/8
simplify
y=3/2
evimi
Simplify 6(3+4) - 5(1 + 2).
Step-by-step explanation:
6(3+4) - 5(1+2)
= 6 x 7 - 5 x 3
= 42 - 15
= 27
Step-by-step explanation:
6(3+4) - 5(1+2)
6×7 - 5×3
42 - 15 = 27
Solve the following values for x and y 1) (8x + 7) 5y (7y - 34) (9x - 4)
9514 1404 393
Answer:
x = 11y = 17Step-by-step explanation:
Vertical angles have the same measure, so we can equate expressions for each vertical angle pair:
top and bottom
8x +7 = 9x -4
11 = x . . . . . . . . . . add 4-8x to both sides
left and right
7y -34 = 5y
2y = 34 . . . . . . . . add 34-5y to both sides
y = 17 . . . . . . . divide by 2
_____
Additional comment
As a check on the integrity of the problem, we can see if these angles form linear pairs.
8x+7 = 8·11+7 = 95
5y = 5·17 = 85
95 +85 = 180 . . . . . . angle values have the expected relationship
what is the surface area of the jewlery box below ?
( click on the image for the full box )
A. 146 cm
B. 292 cm
C. 336 cm
D. 672 cm
Answer:
B 292
Step-by-step explanation:
Hello There!
The first thing we want to do is find the formula for surface area of a rectangle
[tex]SA=2(wl+hl+hw)[/tex]
where w = width h = height and l = length
we are given the dimension:
h = 7
w = 8
l = 6
all we have to do is plug in
[tex]SA=2(8*7+6*7+6*8)\\8*7=56\\6*7=42\\6*8=48\\48+42+56=146\\146*2=292\\SA=292[/tex]
so we can conclude that the surface area is 292
Which single function can be used to determine the length of BC? :v
Answer:
Step-by-step explanation:
Can anyone help me with this question?
Answer:
A = 78.5
Step-by-step explanation:
to find the area of a quarter of a circle, find the area of the whole circle and divide it by 4:
A = (π[tex]r^{2}[/tex]) ÷ 4
A = (3.14 x [tex]10^{2}[/tex]) ÷ 4
A = (3.14 x 100) ÷ 4
A = 314 ÷ 4
A = 78.5