Using the normal distribution and the central limit theorem, it is found that there is a 0.9878 = 98.78% probability that the mean lifetime of components in this sample will be longer than 99 months.
In 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 9 years, hence, in months, [tex]\mu = 9(12) = 108[/tex]The standard deviation is of 1 year, hence, in months, [tex]\sigma = 12[/tex].Sample of 9 pacemakers, hence [tex]n = 9, s = \frac{12}{\sqrt{9}} = 4[/tex].The probability is 1 subtracted by the p-value of Z when X = 99, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{99 - 108}{4}[/tex]
[tex]Z = -2.25[/tex]
[tex]Z = -2.25[/tex] has a p-value of 0.0122.
1 - 0.0122 = 0.9878.
0.9878 = 98.78% probability that the mean lifetime of components in this sample will be longer than 99 months.
A similar problem is given at https://brainly.com/question/24663213
what is half of 56 ft or 56 mm
Do you want the half of 56 ft or 56 mm? In both the case, you'll get the same value...you just need to change the unit.
Half of 56 ft
= ½ × 56
= 56/2
= 28 ft
Half of 56 mm
= ½ × 56
= 56/2
= 28 mm
_______
Hope it helps ⚜:))
On the accompanying grid, draw and label quadrilateral ABCD with points A(1,2), B(6,1), C(7,6), and D(3,7). On the same set of axes, plot and label quadrilateral A′B′C ′D′, the reflection of quadrilateral ABCD in the y-axis. Determine the area, in square units, of quadrilateral A′B′C′D′.
Answer: Refer to figure 1 for the diagram needed.
A ' = (-1, 2)
B ' = (-6, 1)
C ' = (-7, 6)
D ' = (-3, 7)
Area = 24 square units
============================================================
Explanation:
Start by drawing an xy axis. Plot the given points A,B,C,D on this grid.
To reflect any given point over the y axis, we apply this rule
[tex](x,y) \to (-x,y)[/tex]
which means we change the sign of the x coordinate, but keep the y coordinate the same. For example, a point like A(1,2) moves to A ' (-1,2). The other points are handled in a similar fashion.
After all of the points have been reflected, you'll get what is shown in figure 1.
------------------
To find the area of quadrilateral ABCD, we can form a bounding box as small as possible around the quadrilateral. Refer to figure 2.
The area of rectangle FEHG is 6*6 = 36 square units
Then we subtract off the areas of these four outer triangles
Triangle AED = 5*2/2 = 5Triangle AFB = 1*5/2 = 2.5Triangle BCG = 1*5/2 = 2.5Triangle CDH = 1*4/2 = 2Meaning we'll end up with 36-5-2.5-2.5-2 = 24 as the area of quadrilateral ABCD. Because a reflection is a mirror copy, quadrilateral A'B'C'D' will have the same area as ABCD.
The median of the observations, 8,11,15, x +1, X +3, 30, 35, 40, 43, Arranged in ascending Order in 22 Find the value of x
Middle terms are x+1 and x+3
(X+1+x+3)/2= 22
2x+4 = 44
2x = 40
X = 20
Given that p varies directly as q and
[tex] \sqrt{q} [/tex]
varies inversely with t², show how p varies with t.
Answer:
p varies inversely with t⁴Step-by-step explanation:
Direct variation:
y = kx, where k is constantInverse variation:
y = k/x, where k is constantGiven:
p = kq (1)and
√q = k/t² (2)From the first equation we can see:
kq = p ⇒ q = (1/k)p ⇒ q = np, where n is a constantIt means if p varies directly as q, then q directly varies as p.
Square the second equation:
q = k²/t⁴ = m / t⁴, where m is constantSince p varies directly as q and q varies inversely with t⁴, we can state p varies inversely with t⁴.
The grocery store carries diapers for children. Each diaper container has 48 diapers. Two dozen babies each need a container of diapers. How many diapers are needed?
Answer:
A 1152 diapers
Step-by-step explanation:
2dozen is 24, so 24×48=1152
each container= 48 diapers
2 dozen babies
to find:the amount of diapers needed
solution:[tex]12 \times 2[/tex]
[tex] = 24[/tex]
[tex]24 \times 48[/tex]
[tex] = 1152[/tex]
hence, 1152 diapers are needed for 2 dozen of babies.
answer= option A
-8,-8,-6,-2,4,12,22
What. Is the answer
Answer:
-8-8-6-2= -24, -24+4+12+22=14
Please help me pretty please
Answer:
805, 835, 865, 885
Step-by-step explanation:
divided into 20 parts
900-800=100
100/20=5
each part is 5
first one is 1 part away from 800
800+5=805
second one is 7 away from 800
800+7*5=835
third one is 7 away from 900
900-7*5=865
fourth one is 3 away from 900
900-3*5=885
Answer:
Solution :Here we can see that horizontal line divided into 20 vertical lines between the horizontal line. Then,
= 900 - 800
= 100
Finding the value of 1 vertical line.
➝ 1 line = 100
➝ 1 line = 100/20
➝ 1 line = 5
Hence, 1 line = 5
Finding part 1 :
➝ 800 + (1 × 5)
➝ 800 + 5
➝ 805
Finding part 7 :
➝ 800 + (7 × 5)
➝ 800 + 35
➝ 835
Finding part 13 :
➝ 800 + (13 × 5)
➝ 800 + 65
➝ 865
Finding part 17 :
➝ 800 + (17 × 5)
➝ 800 + 85
➝ 885
Hence, the answer is 805, 835, 865, 885.
please someone help. I really need help with this question. I will give brainliest
Answer:
3/200
Step-by-step explanation:
total medicine = 9/50 liter
evenly divided into 12
so 1 prescription = 9/50 / 12
= 9/50*12
=3/50*4
=3/200
Find the solution of the system of equations.
−
10
x
−
9
y
=
−10x−9y=
10
10
8
x
+
9
y
=
8x+9y=
10
10
Answer:
sitting ai week few ai is
please help me with this question!!
Answer:
Step-by-step explanation:
9/50 // 12 / 1 You have a 4 tier fraction here. You must invert the denominator (12/1) and multiply
9/50 * 1/12 Cancel 3 in the 9 and 3 in the 12
3/50 * 1 / 4 Multiply the numerators together and the denominators together.
3 / 200 each bottle with have 3/200 L or 1.5 / 100 L syrup in it.
1.5 / 100 L = 1.5 * 10 / 100 * 10 = 15 mL of medication in each bottle.
(ASAP) I HAVE C- IN MATH RIGHT NOW AND I NEED TO GET UP MY GRADE PLSSS HELP
Answer:
Step-by-step explanation:
The product of a number, n, and 0.4 is 8:
(n)(0.4) = 8
n = (8/0.4)
n = 20
help me pleaseeeeee!!!!!!
Answer:
A' (1, -1) B' (4, -5) C' (6, -2)
Step-by-step explanation:
Since you're reflecting over the x (horizontal) axis, the y value has to change to show the height is increasing or decreasing (Decreasing in this case).
A (1, 1) --> A' (1, -1) So (x,y) becomes (x,-y)
Hope this helps!
David was thinking of a number. David doubles it, then adds 3 to get an answer of 81. 6. What was the original number?.
Answer:
The answer is 39.3
Step-by-step explanation:
81.6 - 3 = 78.6
78.6 ÷ 2 = 39.3
help plssss PLSS I BEG YOu
Answer: Just Try to Do somthing because i cant tell you the Answer
Step-by-step explanation:
What is the value of x in the equation ?
Answer:
[tex]x=2[/tex]
Step-by-step explanation:
This is our equation
[tex]2.5\left(6x-4\right)=10+4\left(1.5+0.5x\right)[/tex]
First off we can distribute the 2.5 and the 4
Now our equation is [tex]15x-10=10+6+2x[/tex]
subtract [tex]2x[/tex] from both sides
[tex]13x-10=16[/tex]
add [tex]10[/tex] to both sides
[tex]13x=26[/tex]
Divide both sides by [tex]13[/tex]
[tex]x=2[/tex]
Nicole makes $26,400 per year. Her monthly rent is 25% of her monthly income. (find the monthly income to find the monthly rent) What is her monthly rent? I assume $26,375?
Samir's sister goes for kathak dance lessons on Tuesday ,Thursday and Saturday every week .If each lesson lasts 50 minutes ,how much time did he practice dance at her class in 3 weeks?
Answer:
450 minutes or 7.5hours
Step-by-step explanation:
for 1 week = 50 *3 (min)
=150 minutes
for 3 weeks = 150* 3(min )
=450 minutes
solve the proportion (someone pls help)
Answer:
y = 16
Step-by-step explanation:
11y = 2(24 + 4y)
11y = 48 + 8y
3y = 48
y = 16
Pls solve this I don't get it
Which expressions are equivalent to 35x + 3. Select the TWO that apply.
25x + 315x
45x - 15x + 3
25x + 335x - 1
1 + 35x + 2
1 + x5+ 2
1 + 25x + 3
Consider the number 9,953. Is this number divisible by 2, 3, 4, 5, 9, or 10? Provide justification for each number without using a calculator. Hint: If a number is not divisible by 2, then what other numbers is it also not divisible by?
Answer:
Divisible by none
Step-by-step explanation:
9,953 is odd
9+9+5+3 = 2 + 6 = 8 (not divisible)
53/4 is not a whole number
9,953 doesn't end with 5 or 0.
9 + 9 + 5 + 3 = 26 (not divisible by 9)
9,953 has no 0 at end.
You are welcome!
Kayden Kohl
8th Grade Student
The number 9,953 is divisible by neither of the digits 2, 3, 4, 5, 9, 10.
What is the importance of knowing divisibility rules?The importance of knowing divisibility rules is that we can determine whether a number is divisible by certain numbers generally from 1 to 20 or not without actually dividing.
Given, 9,953. Is this number divisible by 2, 3, 4, 5, 9, 10 or not.
A number is divisible by 2 if it's unit digit is divisible by 2.
A number is divisible by 3 if the sum of the digits is divisible by 3.
A number is divisible by 4 if the last two digits is divisible by 4.
A number is divisible by 5 if its unit digit is 5 or 0.
A number is divisible by 9 if the sum of the digits is divisible by 9.
A number is divisible by 10 if its unit digit is 0.
learn more about divisibility rules here :
https://brainly.com/question/10703980
#SPJ2
100 POINTS ANSWER QUICK
A sphere has a diameter of 9 inches.
What is the volume of the sphere rounded to the nearest tenth?
Use 3.14 for pi.
95.4 in³
381.5 in³
763.0 in²
3052.1 in³
Now
Volume=
4/3πr³4/3π(4.5)³121.5π381.5in³Option B
15 divided by 1/5 as quotient
Answer:
15/1/5=15*5=75.
Step-by-step explanation:
What is the length of segment AB?
A-5
B-6
C-8
D-10
I need help please each number has its own equation number it off please
Your visually impaired friend asked you to enlarge your notes from class so he can study. You took notes on 8.5-inch by 11-inch paper. The enlarged copy has a smaller side with a length of 10 inches. What is the scale factor of this dilation?
Find the scale factor.
Answer:FINDING A SCALE FACTOR Your visually impaired friend asked you to enlarge your notes from class so be can study. You took notes on 8.5-inch by 11-inch.
Step-by-step explanation:thank you
The scale factor is 20/17.
According to the question, you took notes on a paper with dimensions 8.5 inches × 11 inches.
the breadth of the paper is 8.5 inches
the length of the paper is 11 inches
Now, to make an enlarged copy, you used a paper that has its smaller side dimension of 10 inches.
Which means the breadth of the new paper is 10 inches.
So, if we calculate the ratio of the breadths we get the scale factor.
k = 10 / 8.5
k = 20/17 is the scale factor of dilation.
Learn more about scale factor:
https://brainly.com/question/20341092
What is dehydrogenation ?
Answer:
Dehydrogenation is the a chemical reaction that involves the removal of hydrogen, usually from an organic molecule. It is the reverse of hydrogenation. Dehydrogenation is important, both as a useful reaction and a serious problem.
Find the GCF of the set of numbers.
8 and 12
Enter the correct answer in the box.
Answer:
4
Step-by-step explanation:
prime factorization of 8 is 2x2x2
prime factorization of 12 is 2x2x3
2x2 are the only common factors, therefore GCF is 4
Answer:
4 is the GCF
Step-by-step explanation:
12/4 = 3
8/4 = 2
GIVING BRAINLIEST PLEASE HELP! :D
Answer:
x+20=41
Step-by-step explanation:
You already have some number of seashells, x, and add 20. Then you have 41, so:
x + 20 = 41
Hope that helps! :)
a line passes through the point (10,-5) and a slope of -3/2
Write an equation in slope-intercept form for this line.
Answer:
y = -3/2x + 10
Step-by-step explanation:
The slope = -3/2
Using the slope = -3/2 and the point (10, -5) substitute into y = mx + b and solve for "b"
y = mx + b
-5 = -3/2(10) + b -3/2 · 10 = -30/2 = -15
-5 = -15 + b
-5 + 15 = b
10 = b
The equation of the line is y = -3/2x + 10