The probability of a randomly selected hard drive from the company lasting between 2 years 3 months and 3 years 3 months is 32.22%
Given here,
Mean (μ) = 3 years 6 months
= (3×12)+6 = 42 months
Standard deviation (σ) = 9 months
We will find the z-score using the formula: z = (X - μ)/σ
Here X₁ = 2 years 3 months
= (2×12)+3 = 27 months
and X₂ = 3 years 3 months
= (3×12)+3 = 39 months
So, z (X₁ =27) =
and z (X₂ =39) =
According to the standard normal table,
P(z> -1.666...) = 0.0485 and P(z< -0.333...) = 0.3707
So, P(27 < X < 39)
= 0.3707 - 0.0485
= 0.3222
= 32.22 % [Multiplying by 100 for getting percentage]
So, the probability of a randomly selected hard drive from the company lasting between 2 years 3 months and 3 years 3 months is 32.22%
The probability of a randomly selected hard drive from the company lasting between 2 years 3 months and 3 years 3 months is approximately 0.279 or 27.9%.
What is a normal distribution?A normal distribution is a continuous probability distribution that describes a symmetric, bell-shaped curve of data.
It is also known as a Gaussian distribution or a bell curve.
The normal distribution is used to model many real-world phenomena, such as measurements of height, weight, blood pressure, and IQ scores, among others.
We have,
To solve this problem, we first need to standardize the values of 2 years 3 months and 3 years 3 months, using the mean and standard deviation of the distribution.
The mean of the distribution is 3 years 6 months, which is equivalent to 3.5 years, and the standard deviation is 9 months, which is equivalent to 0.75 years.
The standardized value of 2 years 3 months is:
z1 = (2 + 3/12 - 3.5) / 0.75 = -1.33
The standardized value of 3 years 3 months is:
z2 = (3 + 3/12 - 3.5) / 0.75 = -0.33
We can now use the standard normal table to find the probability of a randomly selected hard drive lasting between 2 years 3 months and 3 years 3 months.
P (-1.33 ≤ Z ≤ -0.33) = P(Z ≤ -0.33) - P(Z ≤ -1.33)
From the standard normal table, we find that:
P(Z ≤ -0.33) ≈ 0.3708
P(Z ≤ -1.33) ≈ 0.0918
Now,
P(-1.33 ≤ Z ≤ -0.33) ≈ 0.3708 - 0.0918 = 0.279
Thus,
The probability of a randomly selected hard drive from the company lasting between 2 years 3 months and 3 years 3 months is approximately 0.279 or 27.9%.
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Find all solutions of the equation below.
7^5-3=7^5x-19
Answer:
7⁵-3=7⁵x- 19
Step-by-step explanation:
16807 - 3 = 7⁵x - 19
16804 = 7⁵x - 19
16804 = 16807x - 1
adding 19 on both sides
16804 + 19 = 16807x - 19 + 19
16823 = 16807x
x = 16823 / 16807
16823 upon 16807 is the x
Find 3 ratios that are equivalent to the given ratio.
2:9
Answer:
4:18
6:27
8:36
Hope this helps! :)
on a blueprint, the area of a tennis court is 16.25cm². a) if the scale on the blueprint is 1cm: 4m, what is the actual area of the tennis court? b) if the length of the tennis court on the blue priny is 6.25 cm what it the actual length of the tennis court
Step-by-step explanation:
so,
1cm : 4m
that means the factor is 1/400 (as 1 m = 100 cm).
also to remember : 1 m² = 100cm×100cm = 10,000 cm²
the area of a rectangle is
length × width
if both dimensions are shortened by a factor (1/400) in our case :
length×1/400 × width×1/400 =
= length × width × 1/400² = length × width × 1/160,000
that means the area of the actual tennis court is
160,000 times the area of the blueprint picture :
160,000 × 16.25 = 2,600,000 cm² = 260 m²
we now know that the actual length of the tennis court is 400 times the length of the blueprint length :
400 × 6.25 = 2,500 cm = 25 m
What is the area of the triangle shown below?
m2
1/2 bxh
1/2 30 x 12
15 x12
=12
Find the length of the altitude.
[tex]135 = \frac{22 + 8}{2} \times h \\ 135 = \frac{30}{2} \times h \\ 135 = 15 \times h \\ h = \frac{135}{15} \\ h = \frac{27}{3} = 9cm[/tex]
Answer:
Area of a trapezoid :
[tex]area = \frac{a + b}{2} h[/tex]
The measures given are trapezoid
Area = 135
base 1 = 22
base 2 = 8
[tex]135 = \frac{22 + 8}{2} h \\ \\135 = \frac{30}{2} h \\ 2(135) = ( 2)\frac{30}{2} h \\ 270 = 30h \\ \frac{270}{30 } = \frac{30h}{30} \\ 9 = h[/tex]
Step-by-step explanation:
We can check if the answer is right
[tex] \frac{22 + 8}{2} \times 9 \\ \frac{30}{2} \times 9 \\ 15 \times 9 = 135[/tex]
in which quadrant is point (-4,5) located?
Find the value of X round your answer to the nearest tenths
Answer:
x = 17.9
Step-by-step explanation:
[tex]tan40^{0} =\frac{15}{x}[/tex]
[tex]x=\frac{15}{tan40^{0} } =17.88[/tex]
rounded: 17.9
Hope this helps
A board is 8 feet 10 inches long. How long is it in inches?
Answer:
106
Step-by-step explanation:
a foot is 12 inches so 8x12 would be 96 and if you add the other 10 inches that would be 106
Suppose that $x,y,z$ are positive integers satisfying $x \le y \le z$, and such that the product of all three numbers is twice their sum. What is the sum of all possible values of $z$
The possible values of z is an illustration of the sum operator
The sum of all possible values of z is 17
How to determine the possible sum of z?The conditions in the question are:
x <= y <= z
xyz = 2(x + y + z)
Using the trial by error method, the possible values of x, y and z are:
x = 1 , y = 3 , z = 8x = 1 , y = 4 , z = 5x = 2 , y = 2 , z = 4The sum of the z values are:
z = 8 + 5 + 4
Evaluate the sum
z = 17
Hence, the sum of all possible values of z is 17
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Post Falls High School in Idaho has 1160 students and is growing by 22 students per year. Richmond High School in Indiana has 1900 students and is shrinking by 15 students per year.
Brandon rolls a six sided die twenty times, and records the result in the table below. how many times did brandon roll above the average? 6 1 3 4 4 4 6 5 5 3 6 4 4 5 2 3 5 4 4 2 a. 14 b. 7 c. 5 d. 4
The average is the arithmetic mean of all the observations of a set of numbers. The number of times Brandon rolls above the average is 7.
What is average?The average is the arithmetic mean of all the observations of a set of numbers. it is found by dividing the sum of all the observations of the set by the number of observations in the set.
[tex]\rm{Average=\dfrac{Sum\ of\ observations}{Number\ of\ observations}[/tex]
In order to know the number of times Brandon rolls the dice above the average, we first need to calculate the average of the twenty rolls.
The average of the 20 times dice rolls,
[tex]\rm Average = \dfrac{6+1+3+4+4+4+6+5+5+3+6+4+4+5+2+3+5+4+4+2}{20}[/tex]
[tex]\rm Average = \dfrac{80}{20} = 4[/tex]
Thus, the average of the 20 rolls of the dice is 4.
Now, the number of times the result of the dice roll is above 4(x>4) is 7.
Hence, the number of times Brandon rolls above the average is 7.
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A week before an election 100 ople were asked who they planned to vote for or the people asked 45 said they planned to vote for
candidate and they planned to vote for candidate. The rest and they had not yet decided How many of the people that were asked
weet yetece who they plan tovorfor?
Answer:
the answer is c
Step-by-step explanation:
45% of 1500=675
38% of 1500=570
675+570=1245
1500-1245=255
Find the perimeter.
Write your answer as a fraction or as a whole or mixed number.
3
1
4
in
112 in
1
in
12
NA
1
1
in
.
inches
Answer:
7 1/3 inches
Step-by-step explanation:
2 (1 3/4 + 1 11/12)
9+11
3/4+11/12= -------------
12
20/12
=1 2/3+ 2
2(3 2/3)
= 7 1/3
How you should answer:
1. Known:
2.Unknown:
3.Rationle:
4.Equation and Solution:
Steps on how to answer:
-State the known
-State the unknown and represent it with a variable
-Provide a rationale for your approach
-Include the equation, exact answer, and decimal approximation
Question 1
Focus on the triangle on the left.
sine is the ratio of opposite over hypotenuse
sin(angle) = opposite/hypotenuse
sin(44) = w/30
w = 30*sin(44)
w = 20.839751 approximately
Now move onto the triangle on the right. We'll use cosine this time.
cos(angle) = adjacent/hypotenuse
cos(x) = w/45
cos(x) = 20.839751/45
cos(x) = 0.463106
x = arccos(0.463106) ... arccosine is the same as [tex]\cos^{-1}[/tex]
x = 62.412286
Answers:w = 20.839751 approximatelyx = 62.412286 approximately==========================================================
Question 2
Focus on the triangle on the left.
sin(angle) = opposite/hypotenuse
sin(32) = w/5
w = 5*sin(32)
w = 2.649596
Now move to the triangle on the right.
sin(angle) = opposite/hypotenuse
sin(x) = w/5
sin(x) = 2.649596/5
sin(x) = 0.5299192
x = arcsin(0.5299192) .... arcsine is the same as [tex]\sin^{-1}[/tex]
x = 31.999996
Answers:w = 2.649596 approximatelyx = 31.999996 approximately==========================================================
Question 3
This time we use the tangent ratio.
Focus on the triangle that has legs of w and 16.
tan(angle) = opposite/adjacent
tan(70) = 16/w
w*tan(70) = 16
w = 16/tan(70)
w = 5.823524
Now let y = x+w and focus on the largest triangle this time.
tan(angle) = opposite/adjacent
tan(41) = 16/y
y = 16/tan(41)
y = 18.405895
This leads to:
y = x+w
x = y-w
x = 18.405895 - 5.823524
x = 12.582371
Answers:w = 5.823524 approximatelyx = 12.582371 approximatelyWrite the vertex form of y = -x^2 + 6x + 6.
Answer:
y = - (x - 3)² + 15
Step-by-step explanation:
using the method of completing the square
y = x² + 6x + 6 ← factor out - 1 from the first 2 terms
y = - (x² - 6x) + 6
to complete the square
add/subtract ( half the coefficient of the x- term )² to x² - 6x
y = - (x² + 2(- 3)x + 9 - 9) + 6
= - (x - 3)² + 9 + 6
= - (x - 3)² + 15
PLEASE HELP
If you have a graph of two lines, explain how to find the solution to the system of equations.
Each shows two lines that make up a system of equations. If the graphs of the equations intersect, then there is one solution that is true for both equations. If the graphs of the equations do not intersect (for example, if they are parallel), then there are no solutions that are true for both equations.
Select the correct answer.
Which number is an irrational number?
A.
B.
C.
D.
Answer:
its c i just got done doing the same one
Step-by-step explanation:
got it right on my real numbers test and got 100% if you need more help comment under my answer
Use the equation, (1/27)^x=3^(-4x+6), to complete the following problems.
Rewrite the equation using the same base.
Solve for x. Write your answer as a fraction in simplest form.
Please show all work, and refrain from posting links, thank you!
Answer:
Given equation:
[tex]\left(\dfrac{1}{27}\right)^x=3^{(-4x+6)}[/tex]
27 can be written as [tex]3^3[/tex]
Also [tex]\dfrac{1}{a^b}[/tex] can be written as [tex]a^{-b}[/tex]
[tex]\implies \dfrac{1}{27}=\dfrac{1}{3^3}=3^{-3}[/tex]
Therefore, we can rewrite the given equation with base 3:
[tex]\implies (3^{-3})^x=3^{(-4x+6)}[/tex]
To solve, apply the exponent rule [tex](a^b)^c=a^{bc}[/tex]
[tex]\implies 3^{-3 \cdot x}=3^{(-4x+6)}[/tex]
[tex]\implies 3^{(-3x)}=3^{(-4x+6)}[/tex]
[tex]\textsf{If }a^{f(x)}=a^{g(x)}, \textsf{ then } f(x)=g(x)[/tex]
[tex]\implies -3x=-4x+6[/tex]
Add [tex]4x[/tex] to both sides:
[tex]\implies x=6[/tex]
sin 60 =11/x
x=11/sin (60)
Answer:
sixt
Step-by-step explanation:
thats easy the sin should be six
I need help! Giving brainiest. Please answer as many questions as you can!!!!
Answer:
2. 12
3. 1 6/8
4. 8 5/8
5. 4 4/8
6. Eli is incorrect 1 3/8 x 3 is 4 1/8 which is greater than 3 1/8
Help..............lllllllllllllllllll
Answer:
4 pepperoni pizzas
Step-by-step explanation:
3 cheese => 1 pepperoni
12cheese (3x4) => 4 (1x4) pepperoni
Plss help asap!
what fraction represents numbers between 21 - 27?
Answer:
0.7778
Step-by-step explanation:
step 1
Address the input parameters and observe what to be found:
Input values:
The fraction = 21/27
What to be found:
Find the decimal expansion of fraction 21/27.
step 2
The numerator is smaller than the denominator of the fraction 21/27, so find how many 10s should be multiplied with both numerator and denominator. Since the number of digits are equal in both numerator and denominator, multiply 10 with both numerator and denominator of 21/27.
=21
27
x10
10
step 3
Rearrange the fraction as like the below:
=10 x 21
27
x1
10
=210
27
x1
10
step 4
Simplify the above expression further:
=210
27
x1
10
=189 + 21
27
x1
10
= (189
27
+21
27
) x1
10
= (7 + 21
27
) x 1
10
step 5
Repeat the step 2 to find the decimal equivalent for the fraction 21/27 in the above expression:
= (7 + 21
27
) x 1
10
= (7 + 0.778) x1
10
step 6
Simplify the above expression further:
= (7 + 0.778) x1
10
= 7.778 x1
10
=7.778
10
21
27
= 0.7778
Hence,
21/27 as a decimal is 0.7778
A crate of pears that usually costs $50 is on sale for 10% off. What is the sale price for the crate of pears?
Sale price of the crate of pears after 10% discount on cost price $50 is equals to $45.
What is sale price?" Sale price is defined as the amount on which something is sold out."
Formula used
Sale price = Cost price - Discount amount
According to the question,
Cost price of the crate of pears = $50
Discount on sale price = 10%
Discount amount = 10% of $50
[tex]=\frac{10}{100}(50) \\\\= \$5[/tex]
Substitute the value in the formula of sale price we get,
Sale price = [tex]\$ ( 50 - 5)[/tex]
= $ 45
Hence, sale price of the crate of pears after 10% discount on cost price $50 is equals to $45.
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Find the volume of the solid. Use 3.14 for π.
Answer:
vol= 10366.3175in²Step-by-step explanation:
So this is a cylinder
formula: π r²hR= 8.75in
h=43.12in
So it will be = 3.14x8.75²x43.12
=> 3.14x76.5625x43.12
3.14x 3301.375
10366.3175in²i think it is correct
.
stay safe
.
have a nice TIME
The area of a rectangular picture frame is 93.5 square inches. The area formula for a rectangle is A = ℓw. Use the given numbers to write and solve an equation to find the width, w, of the picture frame.
Answer: w=8.5
Step-by-step explanation:
Just did it.
HELP!!!! I can’t figure this out
Answer:
[tex]A.\,\orange{ \bold{ \frac{x - 3}{3x + 1} }}[/tex]
Step-by-step explanation:
[tex] \frac{x + 2}{ {x}^{2} + 5x + 6 } \div \frac{3x + 1}{ {x}^{2} - 9} \\ \\ = \frac{x + 2}{ {x}^{2} + 3x + 2x+ 6 } \div \frac{3x + 1}{ {x}^{2} - {(3)}^{2} } \\ \\ = \frac{\cancel{x + 2}}{ \cancel{{({x}+ 3)}} \cancel{(x+ 2) }} \times \frac{\cancel{( {x} + 3)}( {x} - {3)}}{3x + 1} \\ \\ = \purple{ \bold{ \frac{x - 3}{3x + 1} }}[/tex]
The circumference of a circle is 71 π m. What is the area, in square meters? Express your answer in terms of π.
PLEASE ANSWER I NEED MY MATH GRADE UP PLEASE GUYS
The prism below is made of cubes which measure of an inch on one side. What is the volume?
Note: Figure is not drawn to scale.
A. 12 cubic in
B. 24 cubic in
C. 3 cubic in
D. 9/2 cubic in
What is the slope of the line that passes through (-1, 3) and (-1, 8)?
due today
Answer:
Slope of the line is undefined
Step-by-step explanation:
(x₁, y₁) = (-1 , 3) and (x₂, y₂) = (-1 , 8)
The line is parallel to y-axis. The slope of the line parallel to y-axis is undefined.
PLS HELP
what is the length of side s of the square shown below ?
Answer:
[tex]\sqrt{2}[/tex] A.
Step-by-step explanation:
There's a few ways you can go about solving this, but the way I would go with is using sine law.
Sine law:
[tex]\frac{sinA}{a} = \frac{sinB}{b}[/tex]
in the equation above 'A' an angle, and 'a' would be the length of the side opposite to it. Same thing for B.
You are given the angle 90 degrees, and its opposite side length is 2.
You are also given 45 degrees from one of the corners but it doesn't tell you its side length.
There is one corner where it doesn't tell you the angle but you can figure it out using the law that the angles in a triangle must add up to 180 degrees.
So you subtract the other angles to find the angle of the bottom right angle.
180-90-45 = 45
The reason we want to find that angle, is so we can use sin law to find s.
Write down what you have so far:
[tex]\frac{sin90}{2} = \frac{sin45}{s}[/tex]
Now all you need to do is solve for s.
[tex]\frac{sin90*s}{2} = \frac{sin45}{1}[/tex]
sin 90 is 1.
[tex]\frac{1*s}{2} = sin45\\ \\s = 2*sin45\\\\[/tex]
Now since the answers available are in exact values, you can't just punch this in your calculator.
[tex]sin45 = \frac{\sqrt{2} }{2}\\ \\[/tex]
so,
[tex]s = 2*\frac{\sqrt{2} }{2} = \sqrt{2}[/tex]