Answer:
To get least possible number of cubes, first find the HCF of 6, 12 and 15
HCF of 6, 12 and 15 = 3
Least possible number of cubes = (6/3)×(12/3)×(15/3)
=2 × 4 ×5
= 40
The hourly median power (in decibels) of received radio signals transmitted between two cities
follows a lognormal distribution with parameter values u = 3.5 and o2 = 1.22.
(5 points) What is the 90th percentile of this distribution?
(5 points) What is the probability that received power for one of these radio signals is
less than 150 decibels?
(5 point) Consider a random sample of 10 radio signals. What is the probability that for
6 of these signals, the received power is less than 150 decibels?
Using the lognormal and the binomial distributions, it is found that:
The 90th percentile of this distribution is of 136 dB.There is a 0.9147 = 91.47% probability that received power for one of these radio signals is less than 150 decibels.There is a 0.0065 = 0.65% probability that for 6 of these signals, the received power is less than 150 decibels.In a lognormal 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{\ln{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.In this problem:
The mean is of [tex]\mu = 3.5[/tex].The standard deviation is of [tex]\sigma = \sqrt{1.22}[/tex]Question 1:
The 90th percentile is X when Z has a p-value of 0.9, hence X when Z = 1.28.
[tex]Z = \frac{\ln{X} - \mu}{\sigma}[/tex]
[tex]1.28 = \frac{\ln{X} - 3.5}{\sqrt{1.22}}[/tex]
[tex]\ln{X} - 3.5 = 1.28\sqrt{1.22}[/tex]
[tex]\ln{X} = 1.28\sqrt{1.22} + 3.5[/tex]
[tex]e^{\ln{X}} = e^{1.28\sqrt{1.22} + 3.5}[/tex]
[tex]X = 136[/tex]
The 90th percentile of this distribution is of 136 dB.
Question 2:
The probability is the p-value of Z when X = 150, hence:
[tex]Z = \frac{\ln{X} - \mu}{\sigma}[/tex]
[tex]Z = \frac{\ln{150} - 3.5}{\sqrt{1.22}}[/tex]
[tex]Z = 1.37[/tex]
[tex]Z = 1.37[/tex] has a p-value of 0.9147.
There is a 0.9147 = 91.47% probability that received power for one of these radio signals is less than 150 decibels.
Question 3:
10 signals, hence, the binomial distribution is used.
Binomial probability distribution
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes. n is the number of trials. p is the probability of a success on a single trial.For this problem, we have that [tex]p = 0.9147, n = 10[/tex], and we want to find P(X = 6), then:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 6) = C_{10,6}.(0.9147)^{6}.(0.0853)^{4} = 0.0065[/tex]
There is a 0.0065 = 0.65% probability that for 6 of these signals, the received power is less than 150 decibels.
You can learn more about the binomial distribution at https://brainly.com/question/24863377
An object is launched directly in the air at a speed of 8 feet per second from a platform located 4 feet above the ground. The position of the object can be modeled using the function f(t)=−16t2+8t+4, where t is the time in seconds and f(t) is the height, in feet, of the object. What is the maximum height, in feet, that the object will reach?
Write the value of the underlined digit in words 5.3479? 7 being the underlined number.
The place value of 7 in words in 5.3479 is seven thousandths
The given number is 5.3479
The underlined digit has been identified as 7
The place values of each of the digits in 5.3479 are:
5 = 5 units
3 = 3 tens
4 = 5 hundredths
7 = 7 thousandths
9 = 9 ten thousandths
Therefore, the place value of 7 in words in 5.3479 is seven thousandths
Learn more here: https://brainly.com/question/25750254
resolve this equation
The expression above can be resolved to become; (5a + b)³
According to the question:
We are required to determine resolve the expression as given in the question.To resolve the expression given;
We are required to multiply the polynomials as follows;(5a + b) (25a² + 10ab² + b²)= 125a³ + 50a²b² + 5ab² + 25a²b + 10ab³ + b³However; the expression above can be factorised to become;
(5a + b)³Upon expansion; (5a + b)³ yields the expression gotten earlier;
125a³ + 50a²b² + 5ab² + 25a²b + 10ab³ + b³Learn more about equation:
https://brainly.com/question/21879915
I went to many other places, I saw their answers and turns out the only answer I searched up was wrong!
Answer:
I understand how that feels
Step-by-step explanation:
which is the correct word form of 8.16
a . eight and sixteen tenths
b. eight and sixteen hundredths
c. eight hundred sixteen hundredths
d. eight hundred sixteen thousandths
The correct word form of 8.16 is b. eight and sixteen hundredths
Since the number is 8.16, we have 8.16 = 8 + 0.16 = 8 + 16/100
Since we have 8 in the units place, it is pronounced eight.
Also, we have our decimal part 0.16 = 16/100 which is pronounced as sixteen hundredths.
So, combining both we have eight and sixteen hundredths.
So, the correct word form of 8.16 is b. eight and sixteen hundredths
Learn more about decimals here:
https://brainly.com/question/8829988
What is the equation of the line that passes through the point (2, -6) and
has a slope of – 3/2
-
-
y= -3/2x - 3
putting them firstly in the point slope formula and then distributing ...... I can't really explain what I did so here is the picture
solve the literal equation for x ax=bx-c
Answer:
Collect terms in x on the left side
subtract
b
x
from both sides
a
x
−
b
x
=
−
c
take out a
common factor
x
x
(
a
−
b
)
=
−
c
divide both sides by
a
−
b
x
=
−
c
a
−
b
Step-by-step explanation:
im sorry if its not cleear to explain
At gym A is 76.50 for 8.5 hours. At gym B cost is 10.50 for 3/4 hours which plan of offers the best deal
Matrix fractions 1/2+2/6. I don't understand the steps in this.
Answer: 5/6
Step-by-step explanation:
You have to multiply the denominator and numerator by 3 to get the same denominato. Then you ONLY add the numerator. 3/6 + 2/6 = 5/6.
Order the numbers –0.5, 1.25, 0.75, and –1.08 from least to greatest.
Answer:
Least to greatest
0.75 , 1.25 , -1. 08 , -0. 5
Step-by-step explanation:
Hope my answer helps you
ends of diameter: (9, 15) and (15, 7)
(
x
−
12
)
2
+
(
y
−
11
)
2
=
25
Solve the compound inequality.
3x + 1 <4 or 9x > 31
Answer:
Step-by-step explanation:
3x < 4 - 1 or x > 31/9
3x < 3 or x > 31/9
x < 1 or x > 31/9
The graph shows the distribution of the amount of time (in minutes) people spend watching TV shows on a popular streaming service. The distribution is approximately Normal, with a mean of 71 minutes and a standard deviation of 15 minutes.
A graph titled Streaming T V has time (minutes) on the x-axis, going from 11 to 131 in increments of 15. The highest point of the curve is at 71.
What percentage of people spend between 41 and 56 minutes watching TV shows on this streaming service?
a- 13.5%
b- 34%
c- 47.5%
d- 95%
answer:a 13.5
Using the normal distribution, it is found that the percentage of people spend between 41 and 56 minutes watching TV shows on this streaming service is:
a) 13.5%
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.In this problem:
The mean is of 71, hence [tex]\mu = 71[/tex]The standard deviation is of 15, hence [tex]\sigma = 15[/tex]The proportion between 41 and 56 minutes is the p-value of Z when X = 56 subtracted by the p-value of Z when X = 41, hence:
X = 56:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{56 - 71}{15}[/tex]
[tex]Z = -1[/tex]
[tex]Z = -1[/tex] has a p-value of 0.16
X = 41:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{41 - 71}{15}[/tex]
[tex]Z = -2[/tex]
[tex]Z = -2[/tex] has a p-value of 0.025
0.16 - 0.025 = 0.135
0.135 x 100% = 13.5%
Hence option a is correct.
A similar problem is given at https://brainly.com/question/25769446
Solve for z.
57 = –10z +7
Answer:
z = -5
Step-by-step explanation:
Hi there!
We are given the equation 57 = -10z + 7, and we want to solve for z
In order to solve an equation for a variable, we want to isolate that variable on one side; in other words, we want just z on one side of the equation.
So that means that we'll need to get rid of everything else that's also on the right side. That starts with subtracting 7 from both sides:
57 = -10z + 7
-7 -7
_____________
50 = -10z
Now on the right side, there aren't any other extra terms, but remember: we want just z (also written as 1z, with the coefficient of 1), not z written with a coefficient of -10
If you divide a number by itself, the result is 1. For example. [tex]\frac{3}{3}[/tex]= 1. So in order to get a coefficient of 1, let's divide both sides by -10
[tex]\frac{50}{-10} = \frac{-10z}{-10}[/tex]
Divide, and cancel:
The zeros cancel out, leaving the equation as:
[tex]\frac{5}{-1} = \frac{-1z}{-1}[/tex]
Dividing a number by -1 is pretty much the same as multiplying a number by -1; it simply changes the sign of the number
So 5/-1 will become -5, while -1z/-1 will become 1z, or z
Hence:
-5 = z, or written the other way: z = -5
We found z.
Hope this helps!
PLEASE ASAP HELPPPP PICK THEM ALL!!
Answer:
B
Step-by-step explanation:
In which quadrant does the point (13 , -6) lie?
A.
Quadrant III
B.
Quadrant I
C.
Quadrant IV
D.
Quadrant II
Answer:
C
Step-by-step explanation:
i hope you'll find these useful......
Answer:
C, quadrant IV
Step-by-step explanation:
The X (13) is positive meaning the point is on the right side of the graph, and Y (-6) is negative so it's below the x axis
someone help me i really need it!
NO BOTS
Answer:
11
Step-by-step explanation:
the first 2 before it splits to 30mins is 9 and 2 so the answer by addition is 11 hope this helps
What is the equation of the line in slop-intercept form?
Enter your answer in the blank spots
y= __x + __
Answer:
y = 2 1/2 x + 5
Step-by-step explanation:
We were recently going over this. Slope formula: y2 - y1 / x2 - x1. In our case the slope is 2 1/2, and the y-intercept is 5.
Tell me if I'm wrong :)
Can someone help me please
Answer:
answer for question 7. 0.17×70 = $11.9
Answer:
Question 1:
bill = $70
tip percentage = 17%
so tip = 70x(17/100)
= 11.9$
Question 2:
total voters = 20500
supported voters percentage = 49%
so supported voters = 20500x(49/100)
= 10045
Question 3:
price = 154$
vat percentage =5%
so vat = 154x(5/100)
= 7.7$
pleaseeeeeeeeeeeeeeeeeeeeeeeeeeee answer
Answer:
no its not a function
Step-by-step explanation:
i hope i help ;)
Rewrite each equation in standard form.
4 and 5 only
Answer:
4) 2=4x-3y
5) 51=21x-3y
Step-by-step explanation:
I gave it my best shot, I used fraction busters to cancel out the fractions and then I used simple math and distributive property. Hope it helps.
I'll mark brainiest.. no links
Answer:
20.5
Step-by-step explanation:
Use Pythagorean theorem,
[tex]x^2 = 14^2 +15^2 \\\\\implies x^2 =421\\\\\implies x =\sqrt{421}\\\\\implies x =20.5[/tex]
sarah had $40 at the beginning of the week. She babysat 3 days and by Saturday had $110. what is the percent increase
Answer:
175% increase
Step-by-step explanation:
Suppose a principal amount of $7500 was invested at an interest rate of 6%. How long did it take to reach $10650?
Based on the information how long did it take to reach $10650 is 7years.
Given:
Principal=$7,500
Rate=6%
Amount=$10650
Time=?
Simple Interest(SI)=A-P
=$10650-$7500
=$3150
Time=(100×SI)/(p×r)
T=(100×3150)/(7500×6)
T=315,000/45,000
T=7 years
Inconclusion how long did it take to reach $10650 is 7years.
Learn more here:
https://brainly.com/question/15610358
The period it took the $7,500 investment to reach a future value of $10,650 at a compounding interest rate of 6% is 6 years.
What is the future value?The future value refers to the compounded value of present cash flows in the future, using an interest rate.
The future value can be determined using the future value table or formula.
We can also determine the future value using an online finance calculator, which also enables us to determine the period required to get a stated future value.
Data and Calculations:PV (Present Value) = $7,500
I/Y (Interest per year) = 6%
PMT (Periodic Payment) = $0
FV (Future Value) = $10,650
Results:
N (# of periods) = 6 years
Total Interest = $3,142.17
Thus, the period it took the $7,500 investment to reach a future value of $10,650 at a compounding interest rate of 6% is 6 years.
Learn more about future values and periods at https://brainly.com/question/12890404 and https://brainly.com/question/20392017
helppppppppp
what is -12x<60
Answer:
x > -5
Step-by-step explanation:
-12x < 60
To solve the equation for x, we want x to be by itself on one side. Let's start by dividing both sides by -12:
-12x/-12 < 60/-12
When dividing or multiplying by a negative number, we have to turn around the inequality sign, so now we have:
x > 60/-12
And 60/-12 = -5, so:
x > -5
Which statement best explains the relationship between
lines AB and CD?
-They are parallel because their slopes are equal.
-They are parallel because their slopes are negative
reciprocals.
-They are not parallel because their slopes are not
equal.
-They are not parallel because their slopes are
negative reciprocals.
Answer:
they are parallel because their slopes are equal
Answer:
They are parallel because their slopes are equal.
Step-by-step explanation:
Find the slope using the points indicated on each line
The slope of AB
m = rise/run = 6/8 = 3/4
The slope of CD
m = rise/run = 3/4
They are parallel because their slopes are equal.
The expression on the left side of an equation is shown below. -6x+6=0 If the equation has an infinite number of solutions, which expression can be written in the box on the other side of the equation? 06 0 1 O 6x 6x6l
Answer:
I think 0
Step-by-step explanation:
Write 640 : 30 in the lowest form.
Answer:
should be 64:3
Step-by-step explanation:
divide by 10
round of the underlined digit in each day decimal number
Answer:
6) 25.57
7) .9
8) don't see a number underlined
Step-by-step explanation:
