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Complete Question
The mean lifetime of a tire is 42 months with a variance of 49. If 145 tires are sampled, what is the probability that the mean of the sample would be greater than 42.8 months.
Answer:
0.083793
Step-by-step explanation:
We would be using the z score formula.
z score formula = z = (x - μ)/σ/√n
where
x is the raw score = 42.8
μ is the population mean = 42
σ is the population standard deviation =
In the above question, we were given variance = 49
Standard deviation = √Variance
= √49
= 7
n = number of samples = 145
z score = z = (x - μ)/σ/√n
= (42.8 - 42)/ (7/√145)
= 0.8/ 0.581318359
= 1.37618
Approximately to 2 decimal places= 1.38
Using the z score table to find the probability.
P(x ≤ 42.8) = P(z = 1.38) = 0.91621
P(x>42.8) = 1 - P(x<42.8)
1 - 0.91621
= 0.083793
Therefore, the probability that the mean of the sample would be greater than 42.8 is 0.083793
A scientist was in a submarine, 95.7 feet below sea level, studying ocean life. Over the next ten minutes, she went down 25.3 feet. How many feet was she now below sea level?
Answer: she is now 121 feet below sea level.
Step-by-step explanation:
Given, A scientist was in a submarine, 95.7 feet below sea level, studying ocean life.
Over the next ten minutes, she went down 25.3 feet.
Then, she was (95.7+25.3) feet below sea level now. [we will add both distances ]
Then, she was 121 feet below sea level now.
Hence, she is now 121 feet below sea level.
Through a host of various investors, you have finally raised enough capital to begin producing the next summer blockbuster. You have a budget of 279 million dollars, which you must allocate between filming and editing. The general consensus among experts is that filming tends to cost twice as much as editing. How much money should you allocate to filming?
Answer:
$186 million
Step-by-step explanation:
The ratio of costs is ...
filming : editing = 2 : 1
So, the filming cost as a fraction of the total cost is ...
filming : total cost = 2 : (2+1) = 2/3
The allocation to filming is ...
(2/3)($279 million) = $186 million
what is the greatest common factor of 6d² and 18d
gcd = 6 ⋅ d
Step-by-step explanation:
We have that
6 d ^2 = 6 ⋅ d ⋅ d and 18 d = 3 ⋅ 6 ⋅ d hence the gcd = 6 ⋅ d
(Hope this helps <3)
A solid aluminum cube has sides each of length L . A second cube of the same material has sides four times the length of the first cube; i.e., 4 L . Compared to the first cube, the total surface area of the second cube is
Answer:
Compared to the first cube, the total surface are of the second cube is 16 times larger.
Step-by-step explanation:
The first cube has L*L*6=6L²
The second cube has 4L*4L*6=14L²*6=84L²
Compared to the first cube, the total surface are of the second cube is 16 times larger. (6*16=84)
1. What is the name of a number that can be written in the form a+bi where a and b are nonzero real numbers?
A. a complex number
B. a real number
C. an imaginary unit
D. a pure imaginary number
2. Which of the following statements is not true?
A. In order for a+bi to be a complex number, b must be nonzero.
B. A complex number is a number that can be written in the form a+bi where a and b are real numbers.
C. For a complex number written in the form a+bi, the value of a is called the real part of the complex number.
D. Every real number is also a complex number.
3. What is the real part of 4−5i?
4. What is the imaginary part of 7−6i?
5. Determine if the statement below is true or false. If it is false, rewrite it so it is true. Rewriting −10−−−−√ in terms of i results in −10i.
A. This statement is true.
B. This statement is false. Rewriting −10−−−−√ in terms of i results in 10i.
C. This statement is false. Rewriting −10−−−−√ in terms of i results in −10−−−−√i.
D. This statement is false. Rewriting −10−−−−√ in terms of i results in 10−−√i.
Re-writing question 5:
5. Determine if the statement below is true or false. If it is false, rewrite it so it is true. Rewriting √-10 in terms of i results in −10i.
A. This statement is true.
B. This statement is false. Rewriting √-10 in terms of i results in (√10)i.
C. This statement is false. Rewriting √-10 in terms of i results in −10√i.
D. This statement is false. Rewriting √-10 in terms of i results in 10√i.
Answer:
1) C. an imaginary number
2) A. In order for a + bi to be a complex number, b must be nonzero
3) 4
4) -6
5) B. The statement is false. Rewriting √-10 in terms of i results in (√10)i
Step-by-step explanation:
1. When a number can be expressed in the form a+bi where a and b are real numbers, then the number is said to be a complex number.
For example, the following are complex numbers where i = √-1 ;
i. 3 + 5i
ii. 4 - 7i
iii. -3 - 9i
Well, even real numbers are a subset of complex numbers. For example,
=> 5 can be written as 5 + 0i
=> -12 can be written as -12 + 0i
-- But when a and b are non-zero real numbers or at least b is a non-zero real number, then the number is said to be an imaginary number.
-- If a is zero, then the number is a purely imaginary number
-- If b is zero, then the number is a purely real number
2. For a number to be called a complex number;
i. it can be written in the form a + bi where a and b are real numbers,
ii. either a or b, or both, may be zero,
iii. a is the real part of the complex number,
iv. b is the imaginary part of the complex number.
v. it could also be a real number since every real number is also a complex number.
3. Given 4 - 5i
The real part is 4
and the imaginary part is -5
4. Given 7 - 6i
The real part is 7
and the imaginary part is -6
5. Rewrite √-10 in terms of i
Remember that i = √-1
Therefore,
√-10 = √(-1 x 10) = √-1 x √10
=> √-10 = √-1 x √10
=> √-10 = i x √10
=> √-10 = (√10)i
1.) Which of the following is the correct equation for the Pythagorean Theorem, where a and b are the side lengths and c is the length of the hypotenuse?
a.) (a+b)^2=c^2
b.) a^2+b^2=c^2
c.) a^2-b^2=c^2
d.) (a-b)^2=c^2
3.) Find the distance between the points (9, −7) and (5, −4).(1 point)
a.) 5
b.) 25
c.) √7
d.) √137
4.) To find the distance between (17, 3) and (17, −5), Marcia used the following equation. Is Marcia correct? Explain.
D = | 3 − (−5) | = 8
a.) Marcia is not correct. Since the points are in two-dimensions, the distance formula must be used to find the distance.
b.)Marcia is correct. For any pair of points, the distance between the points can be treated as if they are in one-dimension.
c.)Marcia is correct. Since the x-coordinates are the same, the distance between the points can be treated as if they are in one-dimension.
d.)Marcia is not correct. According to the distance formula, the distance should be D=√(17-17)^2+(3-(-5))^2=√8
Option d for question 4 should be:
d.)Marcia is not correct. According to the distance formula, the distance should be D=√(17-17)^2+(3-(-5))^2=8
Answer:
1. (b) a^2+b^2=c^2
3. (a) 5
4. (d) Marcia is not correct. According to the distance formula, the distance should be D=√(17-17)^2+(3-(-5))^2=8
Step-by-step explanation:
(1) From Pythagoras' theorem, the square of the hypotenuse side of a given right-angled triangle, is equal to the sum of the squares of the other two sides. Now, if the other two sides are a and b, and the hypotenuse is c, then using this theorem, the following holds:
c² = a² + b²
(2) The distance D, between two points (a, b) and (c, d) is given by;
D = √(a-c)² + (b-d)² ----------------(i)
From the question, the points given are (9, -7) and (5, -4):
This means that;
a = 9
b = -7
c = 5
d = -4
Substitute these values into equation (i) and get;
D = √(9-5)² + (-7- (-4))²
D = √(4)² + (-3)²
D = √16 + 9
D = √25
D = 5
Therefore, the distance between these points is 5 units
(4) As explained in question 3 above, Maria is not correct. To find the distance between two points, we use the relation shown in the answer to question 3 above. i.e
D = √(a-c)² + (b-d)²
Since the given points are (17, 3) and (17, -5), it implies that;
a = 17
b = 3
c = 17
d = -5
D = √(17-17)² + (3-(-5))²
D = √(0)² + (8)²
D = √8²
D = 8
A manufacturing plant has 25 fuses. 12 failures occurred within 30 days. After each failure, the molding fuse is immediately replaced. What is the MTTF for the fuses
Answer:
MTTF for the fuses = 62.5
Step-by-step explanation:
Given:
Total fuses = 25
Number of failures = 12
Number of days = 30
Find:
MTTF for the fuses.
Computation:
MTTF for the fuses = Total operation time / Number of failures
MTTF for the fuses = (25 × 30) / 12
MTTF for the fuses = 62.5
Which equation represents this sentence? SIx times the difference of a number and eight is equal to twelve. A. 6n−8=12 B. 6n+8=12 C. 6(n−8)=12 D. 6(n+8)=12
Answer:
The answer is option CStep-by-step explanation:
Let the number be n
The statement
the difference of a number and eight is written as
n - 8
It's multiplied by 6
That's
6( n - 8)
The result is 12
So we have the final answer as
6( n - 8) = 12Hope this helps you
terms and definitions of aphasia
Answer:
loss of ability to understand or express speech, caused by brain damage or loss or impairment of the power to use or comprehend words usually resulting from brain damage (as from a stroke, head injury, or infection) — see motor aphasia — compare amusia, anarthria.
Step-by-step explanation:
what is 7 over 2 as a decimal
Answer:
3.5
Step-by-step explanation:
I recommend using a calculator. Divide 7/2.
I WILL GIVE YOU LOTS OF Points
Answer:
D
Step-by-step explanation:
7^2 + 4^2 = [tex]\sqrt{65\\[/tex]
assume it is a triangle and x is the hypotenuse and use Pythagorean theorem
Answer:
D
Step-by-step explanation:
7^2 + 4^2 =
assume it is a triangle and x is the hypotenuse and use Pythagorean theorem
Find the following products: a) (−12) × (−11) × (10) b) (−25) × (−8) × (−2) WITH EXPLANATION
Step-by-step explanation:
Hey, there!!
a. (-12)×(-11)×10
Here, (-)×(-)=(+)
(-12)×(-11)=132
so,
=132×10
=1320.
For b.
(-25)×(-8)×(-2)
(-)×(-)=(+)
(-25)×(-8)=200
so,
=200×(-2) { (+)×(-)=(-)}.
= -400.
Therefore, the answer of a. no. is 1320, and no. b is (-400).
Hope it helps....
someone Help if u know the answer pls put the step by step
6 = √v-2
Answer:
64
Step-by-step explanation:
I am assuming the -2 is outside the sqrt.
8 = sqrt(v)
v = 64
1/x - 1/y = 1/4
1/x^2 - 1/y^2 = 3/16
x + y = ...
GIVEN:
1/x - 1/y = ¼.1/x² - 1/y² = 3/16.TO FIND:
The value of x + y.ANSWER:
Firstly let us assume ,
p = 1/x .q = 1/y .Now the equⁿ s becomes ,
=> p - q = 4 . ........(1)
Also , given that:
=> 1/x² - 1/y² = 3/16.
=> p² - q² = 3/16.
=> (p+q)(p-q) = 3/16.
From (1),
=> 4 (p+q) = 13/16.
=> (p+q) = 13/16 × 1/4.
=> p+ q = 13/64.
On adding (1) and (2) ,
=> 2p = 4 + 13/64.
=> 2p = 256+13/64.
=> p = 269/64 × 1/2.
=> p = 269/128.
Now lets find q ,
=> q = 13/64 - 269/128.
=> q = 26-269/128.
=> q = -243/128.
Hence
p = 269/128.q = -243/128..°. x = 128/269 , y = -128/243
On a quiz there are four multiple choice questions worth 3 points each
Answer:
12 pts total
Step-by-step explanation:
Answer:
The four multiple choice are worth 12 points total
Mountain High Ski Resort offers two “Learn to Snowboard" packages - Package A gives you 5
group snowboard lessons for $200 or Package B gives you 10 group lessons for $350. Which
package is the least expensive per lesson? How much do you save per lesson going with that
package versus the other one? (Section 17.3) (1 point)
Answer: Package B is least expensive; Will save $5
Step-by-step explanation:
Package A
$200 for 5 lesson=$40/lesson
Package B
$350 for 10 lesson=$35/lesson
35<40
Package B is least expensive
-------------------------------------------------------
40 (Package A)- 35 (Package B)
=$5
Answer:
Packages A and C.
Step-by-step explanation:
Solv for x for all of these 1. 3x+6=21 2. 33=7x-9 3. 28=7+x need to know now please help !!!!!!
Answer:
[tex] \boxed{ \sf{ \bold{1. \: \: \: x = 5}}}[/tex][tex] \boxed{ \sf{ \bold{2. \: \: x = 6}}}[/tex]
[tex] \boxed{ \bold{ \sf{3. \: \: x = 21}}}[/tex]
Step-by-step explanation:
1. [tex] \sf{3x + 6 = 21}[/tex]
Move constant to right hand side and change its sign
⇒[tex] \sf{3x = 21 - 6}[/tex]
Subtract 6 from 21
⇒[tex] \sf{3x = 15}[/tex]
Divide both sides of the equation by 3
⇒[tex] \sf{ \frac{3x}{3} = \frac{15}{3} }[/tex]
Calculate
⇒[tex] \sf{x = 5}[/tex]
--------------------------------------------------------
2. [tex] \sf{33 = 7x - 9 }[/tex]
Swap the sides of the equation
⇒[tex] \sf{7x - 9 = 33}[/tex]
Move constant to right hand side and change it's sign
⇒[tex] \sf{7x = 33 + 9}[/tex]
Add the numbers
⇒[tex] \sf{7x = 42}[/tex]
Divide both sides of the equation by 7
⇒[tex] \sf{ \frac{7x}{7} = \frac{42}{7} }[/tex]
Calculate
⇒[tex] \sf{x = 6}[/tex]
---------------------------------------------------------
3. [tex] \sf{28 = 7 + x}[/tex]
Swap the sides of the equation
⇒[tex] \sf{7 + x = 28}[/tex]
Move constant to right hand side and change it's sign
⇒[tex] \sf{x = 28 - 7}[/tex]
Subtract 7 from 28
⇒[tex] \sf{x = 21}[/tex]
Hope I helped!
Best regards!!
What is the x-intercept of the graph -4x=20
Answer:
-4x=20
x=20/-4
x=-5
maybe not sure
Hello, I need some help resolving this problem of Trigonometric Identities. Use the reciprocal identities to resolve it SinA+cosA*cotA= cscA
Answer:
Please see steps below
Step-by-step explanation:
Start by writing all trig functions in the equation in terms of their simplest forms using the two basic trig functions: [tex]sin(\alpha) \,\,and\,\,cos(\alpha)[/tex]:
[tex]sin(\alpha)+ cos(\alpha)\,\frac{cos(\alpha)}{sin(\alpha)} = \frac{1}{sin(\alpha)}[/tex]
Now work on the left side (which is the most complicated one), trying to simplify it using the properties for adding fractions with different denominators:
[tex]sin(\alpha)+ cos(\alpha)\,\frac{cos(\alpha)}{sin(\alpha)}=sin(\alpha)+\frac{cos^2(\alpha)}{sin(\alpha)} =\frac{sin^2(\alpha)}{sin(\alpha)} +\frac{cos^2(\alpha)}{sin(\alpha)}=\frac{sin^2(\alpha)+cos^2(\alpha)}{sin(\alpha)}=\frac{1}{sin(\alpha)}[/tex]
where in the last step we have used that the Pythagorean identity for:
[tex]sin^2(\alpha)+cos^2{\alpha)=1[/tex]
Notice that we arrived at the expression: [tex]\frac{1}{sin(\alpha)}[/tex], which is exactly what appears on the other side of the initial equation/identity we needed to prove, so the prove has been completed.
Determine if the following relation is a function.
Answer:
It is a function.
Step-by-step explanation:
It is proven via the vertical line test.
How much is 2/3 cups plus 1 1/4 cups
[tex]1\frac{11}{12}[/tex]
Step-by-step explanation:[tex]\frac{2}{3}+1\frac{1}{4}=\frac{2}{3}+\frac{5}{4}=\frac{8}{12}+\frac{15}{12}=\\ \\=\frac{8+15}{12}=\frac{23}{12}=1\frac{11}{12}[/tex]
use each of the digits 5 4 3 2 1 exactly once to create two different five digit numbers. Write each number on the line and compare the two numbers by using the symbols < > =
Answer:
12345 < 54321
21435 > 12534
:
Step-by-step explanation:
Given the digits:
1, 2, 3, 4 and 5
We have to use every digit only once and have to make two different five digit numbers.
Using these 5 numbers only once without repetition, we have many numbers possible.
Let us have a look at a few sets and let us compare them.
Set 1: 12345 and 54321
We can see that 12345 is lesser than 54321.
Therefore, we can write (using lesser than sign):
12345 < 54321
Set 2: 21435 and 12534
We can see that 21435 is greater than 12534.
Therefore, we can write (using greater than sign):
21435 > 12534
the distance from a boy's house to his school is 10km. he left home at 6.30am, cycling at the rate of 4km/h. if he spent 15 minutes on the way waiting for his friend, when did he get to school?
Answer:
9:15 am
Step-by-step explanation:
First you know the speed and you know the distance.
So now we have to find the time it took for him to get to school(ignore the waiting time first)
time=10/4=2.5h
now we add the waiting time,
2.5h+0.25h(15minutes is the same as 0.25h)=2.75h
convert 0.75h to minuts,
0.75*60=45minutes
6.30+2.45=9.15am
The boy arrived at school at 8:15 am after cycling for 2.5 hours and waiting for 15 minutes.
Given Distance from the boy's house to school = 10 km
Cycling speed = 4 km/h
Time spent waiting for his friend = 15 minutes
Now calculate the time it took for the boy to cycle the distance from his house to the meeting point, excluding the waiting time.
Distance = Speed × Time
10 km = 4 km/h × Time
Time = 10 km / 4 km/h
Time = 2.5 hours
Now, we need to convert the waiting time from minutes to hours, so we can add it to the cycling time.
Waiting time = 15 minutes / 60 minutes/hour
Waiting time = 0.25 hours
Add the cycling time and waiting time to determine the total time it took for the boy to reach school.
Total time = Cycling time + Waiting time
= 2.5 hours + 0.25 hours
=2.75 hours
We need to determine the arrival time by adding the total time to the departure time.
Arrival time = Departure time + Total time
Arrival time = 6.30 am + 2.75 hours
To calculate the arrival time, we need to consider the minutes and hours separately:
Minutes: 30 minutes + (0.75 hours × 60 minutes/hour)
= 30 minutes + 45 minutes
= 75 minutes
Since 75 minutes is more than an hour, we need to adjust the hours and minutes accordingly.
Adding the hours: 6 + 2 = 8
So, the boy arrived at school at 8:15 am.
Therefore, the boy arrived at school at 8:15 am.
To learn more on Distance click:
https://brainly.com/question/15172156
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A rectangular piece of metal is 20 in longer than it is wide. Squares with sides 4 in long are cut from the four corners and the flaps are folded upward to form an open box. If the volume of the box is 1200 in3,
what were the original dimensions of the piece of metal?
Answer:
width = 12.5
Step-by-step explanation:
rectangular volume = height * width * length
1200 = 4 * w * (20 + 4)
1200 = 4 * w * 24
1200 = 96w
12.5=w
Khalid wants to buy a long sandwich for a party. Store A sells a 5 foot sandwich for $42.50. Store B sells a 6 foot sandwich for $49.50. Which store has the better buy? Show your work.
Store A: 1 foot= 42.50÷5 = $8.50
Store B= 1 foot= 49.50÷6 = $8.25
Answer:
Store B has a better buy because the price for 1 foot sandwich is cheaper than Store A.
Use the compound interest formula to compute the balance in the following account after the stated period of time, assuming interest is compounded annually. $5000 invested at an APR of 4.5% for 11 years. What is the balance in account after 11 years?
Answer:
The amount $ 8114.3 is the balance in the account after eleven years
Step-by-step explanation:
From;
A= P(1+r)^n
Where;
A= amount
P= principal
r= interest rate
n= time
A= 5000(1+ 0.045)^11
A= 5000(1.045)^11
A= $ 8114.3
The amount $ 8114.3 is the balance in the account after eleven years.
Simplify 5x + 3x + 2 +4
Hi
add "x" with "x" and numbers with numbers
5x+3x+2+4 = 8x+6
Answer: [tex]8x+6[/tex]
Add
[tex]5x+3x=8x\\2+4=6\\8x+6[/tex]
simplify the answer z-4/4+8
Answer:
= z/12 - 1/3
Step-by-step explanation:
z-4/(4+8)
= z-4/12
= z/12 - 4/12
= z/12 - 1/3
Find the sum of the first 9 prime numbers.
Answer:
100
Step-by-step explanation:
The first 9 prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, and 23.
Their sum is 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 = 100
the length of tangent is 15 cm drawn from point whose distance from center of circle is 17 cm find the radius of circle
Answer:
Then what is the radius of the circle? Since, the tangent of any point of a line is perpendicular to the radius through the point of contact. Hence, radius of the circle = 8 cm.