Answer:
B) b=13
Step-by-step explanation:
13-4x is the same as -4x+13
Find the domain of the following functions?
Answer:
d. D: (-∞ , ∞) , R: (-10 , ∞)
Step-by-step explanation:
The Lazy River has a current of 5 miles per hour. A motorboat can travel 20 miles
down the river in and back in 3 hours. What is the speed of the boat in still water?
Please show your work and use table to relate time, speed, distance.
Answer:
5 mph
Step-by-step explanation:
Answer:
15 mph = rate of boat in still water
Step-by-step explanation:
D = RT
Let R = rate of boat in still water
Rate down stream = R + 5
Time down stream = 20/(R + 5)
Rate upstream = R - 5
Time upstream = 20/(R - 5)
Total time = 20/(R + 5) + 20/(R - 5) = 3
20(R - 5) + 20(R + 5) = 3(R + 5)(R - 5)
20R - 100 + 20R + 100 = 3R^2 - 75
3R^2 + 40R - 75 = 0
(3R + 5)(R - 15) = 0
R = -5/3 or 15
Rate cannot be negative, so R = 15 mph = rate of boat in still water
Individual gas mileages (in miles per gallon) of Model Extra SS (Extra Super-Sporty) sedans are normally distributed with a population mean of 20 and a population standard deviation of 2. Based on these information, if you bought a Model Extra SS sedan, what is the probability that the gas mileage (in miles per gallon) of your single, individual sedan is between 19.5 and 20.5
Answer: 0.1974
Step-by-step explanation:
Let X be a random variable that denotes the gas mileage (in miles per gallon) of the individual sedan.
Given: Population mean: [tex]\mu=20[/tex]
Standard deviation: [tex]\sigma=2[/tex]
The probability that the gas mileage (in miles per gallon) of your single, individual sedan is between 19.5 and 20.5:
[tex]P(19.5<x<20.5)=P(\dfrac{19.5-20}{2}<\dfrac{x-\mu}{\sigma}<\dfrac{20.5-20}{2})\\\\=P(-0.25<z<0.25)=2P(0.25)-1 [P(-z<Z<z)=2P(Z<z)-1]\\\\=2(0.5987)-1=0.1974[/tex]
The required probability=0.1974
9. A juice glass holds 180mL. If a client drinks 7/2 glasses , how many milliliters did
the client consume? (5 points)
Answer:
630 ml
Step-by-step explanation:
1 glass contains 180 ml juice
7/2 glasses contains = 180 × 7/2 = 630 ml
Power +, Inc. produces AA batteries used in remote-controlled toy cars. The mean life of these batteries follows the normal probability distribution with a mean of 36 hours. hours and a standard deviation of 5.5 hours. As a part of its quality assurance program, Power +, Inc. tests samples of 9 batteries.
a. What can you say about the shape of the distribution of the sample mean?
b. What is the standard error of the distribution of the sample mean? (Round your answer to 4 decimal places.)
c. What proportion of the samples will have a mean useful life of more than 38 hours? (Round z value to 2 decimal places and final answer to 4 decimal places.)
d. What proportion of the sample will have a mean useful life greater than 34.5 hours? (Round z value to 2 decimal places and final answer to 4 decimal places.)
e. What proportion of the sample will have a mean useful life between 34.5 and 38 hours? (Round z value to 2 decimal places and final answer to 4 decimal places.)
Answer:
a) By the Central Limit Theorem, it is approximately normal.
b) The standard error of the distribution of the sample mean is 1.8333.
c) 0.1379 = 13.79% of the samples will have a mean useful life of more than 38 hours.
d) 0.7939 = 79.39% of the samples will have a mean useful life greater than 34.5 hours
e) 0.656 = 65.6% of the samples will have a mean useful life between 34.5 and 38 hours
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 z-score 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 p-value, 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.
Mean of 36 hours and a standard deviation of 5.5 hours.
This means that [tex]\mu = 36, \sigma = 5.5[/tex]
a. What can you say about the shape of the distribution of the sample mean?
By the Central Limit Theorem, it is approximately normal.
b. What is the standard error of the distribution of the sample mean? (Round your answer to 4 decimal places.)
Sample of 9 means that [tex]n = 9[/tex]. So
[tex]s = \frac{\sigma}{\sqrt{n}} = \frac{5.5}{\sqrt{9}} = 1.8333[/tex]
The standard error of the distribution of the sample mean is 1.8333.
c. What proportion of the samples will have a mean useful life of more than 38 hours?
This is 1 subtracted by the pvalue of Z when X = 38. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{38 - 36}{1.8333}[/tex]
[tex]Z = 1.09[/tex]
[tex]Z = 1.09[/tex] has a pvalue of 0.8621
1 - 0.8621 = 0.1379
0.1379 = 13.79% of the samples will have a mean useful life of more than 38 hours.
d. What proportion of the sample will have a mean useful life greater than 34.5 hours?
This is 1 subtracted by the pvalue of Z when X = 34.5. So
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{34.5 - 36}{1.8333}[/tex]
[tex]Z = -0.82[/tex]
[tex]Z = -0.82[/tex] has a pvalue of 0.2061.
1 - 0.2061 = 0.7939
0.7939 = 79.39% of the samples will have a mean useful life greater than 34.5 hours.
e. What proportion of the sample will have a mean useful life between 34.5 and 38 hours?
pvalue of Z when X = 38 subtracted by the pvalue of Z when X = 34.5. So
0.8621 - 0.2061 = 0.656
0.656 = 65.6% of the samples will have a mean useful life between 34.5 and 38 hours
A tennis ball was thrown from the top of a tall building. The height of the tennis ball above the ground can be found using the function y = -12.5x + 50, where x is the time in seconds the tennis ball has been in the air.
how many seconds did it take the tennis ball to reach the ground?
Answer:
t = 4 seconds
Step-by-step explanation:
Given that,
The height of the tennis ball above the ground can be found using the function y = -12.5x + 50
where x is the time in seconds the tennis ball has been in the air.
We need to find how many seconds did it take the tennis ball to reach the ground.
When it reaches the ground, y = 0
So,
-12.5x + 50 = 0
12.5x = 50
x = 4 seconds
So, it will take 4 seconds for the ball to reach the ground.
help plssssssssssssssssss
Help answer this question please
Answer:
no and no
Step-by-step explanation:
1. 9+6 = 15 not 17
2. 9 - 3 = 6 not 5
please leave a like if this answers your question
5
Find the value of x. Show work to prove your answer.
(3x +
18)
93°
Answer:
x=34.5
Step-by-step explanation:
(3x+18)° and 93° lie along a straight line. The angles in a straight line add up to 180. So:
3x+18+93=`80
2x=180-111
x=69/2
x=34.5
You select a marble without looking and then put it back. If you do this 6 times, what is the
best prediction possible for the number of times you will pick a purple marble?
Answer:
One time
Step-by-step explanation:
The probability of picking a purple marble once is 1/6, so if I pick a marble 6 times, then (1/6)*6=1
Four people recorded the number of minutes they exercised today. Mackenzie exercised for 3 as many minutes as Brinley. Brinley exercised for 17 fewer minutes than Ariana. Ariana exercised for 3 times as many minutes as Seth Together, Ariana and Mackenzie exercised for 20 more minutes than Brinley and Seth. Let z represent the number of minutes Seth exercised.
Answer:
False
True
True
False
Yw hope this helped yall
Step-by-step explanation:
The equation represents this situation is
3x + 1/2 x (3x + - 17) = x + (3x - 17 ) + 20 — False
x = 40 — True
Brinley and Seth exercised for a combined 95 minutes —-True
Mackenzie exercised for 26 minutes. — False
Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined that the population of potential clientele have head breadths that are Normally distributed with a mean of 5.9 inches and a standard deviation of 0.8 inches.
According to the 68-95-99.7 rule, we expect 95% of head breadths to be
between blank and blank inches.
Answer:
We expect 95% of head breadths to be between 4.3 inches and 7.5 inches.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 5.9 inches, standard deviation = 0.8 inches.
We expect 95% of head breadths to be between
Within 2 standard deviations of the mean, so:
5.9 - 2*0.8 = 5.9 - 1.6 = 4.3 inches
5.9 + 2*0.8 = 5.9 + 1.6 = 7.5 inches
We expect 95% of head breadths to be between 4.3 inches and 7.5 inches.
Two planes, which are 2920 miles apart, fly toward each other. Their speeds differ by 80mph. If they pass each other in 4 hours, what is the speed of each?
9514 1404 393
Answer:
405 mph; 325 mph
Step-by-step explanation:
The total of their speeds is ...
2920 mi/(4 h) = 730 mi/h
If s represents the speed of the slower plane, then we have ...
s + (s+80) = 730
2s = 650 . . . . . . . subtract 80
s = 325 . . . . . . . divide by 2
s+80 = 405 . . . find the faster speed
The speeds of the planes are 405 mi/h and 325 mi/h.
1/7+7/12+something =1
13. Which fraction is halfway between 3/5 and
5/7?
Answer:
18/35....
....
YESTERDAY
which of the following is written as a rational function
Answer:
f(x)=x-5/3x
Step-by-step explanation:
Which expression is equivalent to
y
2
Answer:
Hello!
Distributive property: a(b+c)=ab+ac
Minus and plus sign.
Then multiply by the numbers.
Hope this helps!
Thanks!
Have a great day!
Step-by-step explanation:
so, this is in math and, I NEED HELP!!!!!. could you first multiply the width by the height? Explain.
Answer:
Explain what?? May I ask
Please answer the question in the picture
Answer:
Step-by-step explanation:
use the distance formula
dist = sqrt[ (x2-x1)^2 + (y2-y1)^2 ]
where point one ,P1, is A and point 2, P2, is C, so
P1 = (x1,y1) = (-7,3)
P2 =(x2,y2) = (0,6)
then
dist = sqrt[ (0 - (-7))^2 + (6-3)^2 ]
dist = sqrt [ 7^2 + 3^2 ]
dist = sqrt [49 +9 ]
dist = sqrt [58]
dist = 7.6157....
AC = 7.6 ( rounded to nearest tenth)
Each day, the number of births in the world is 92 thousand less than three times the number of deaths. If the
population increase in a single day is 214 thousand, determine the number deaths per day.
Answer:
two points in the xy plane has cartesian coordinate (2,-4) and (-3,3) where the units are in m determine.
a) the distance between these points and
b) their polar coordinates.
simplify
[tex] {a}^{3} - {b}^{3} [/tex]
Answer:
[tex] {a}^{3} - {b}^{3} [/tex]
[tex] = (a - b)( {a}^{2} + ab + {b}^{2} )[/tex]
Hence, simplified.
Photo Attached
Please Help ASAP
Answer:
C
Step-by-step explanation:
A is just the opposite value of the second integral.
B is just 3 times the first.
D-you can write a sum of integrals over the same intervals as one integral of the sum of the integrands of those integrals over that same interval. The answer would be 3(8)+-2.
For choice C, we would need more information.
Quadrilateral PQRS is parallelogram.What is the length of the diagonal SQ?
ST=x^2-8
TQ=3x+2
Answer:
3x+x^2-6
Step-by-step explanation:
Have a great rest of your day.
Bye
Mathematical logic for this game to make the best
Answer:
Ok tell me which mathematic game
Need help with this if possible
Answer:
hope it helps...
Step-by-step explanation:
If f(x)=3x^2+2x=1 find f(x+2)
Answer:
f(x+2) = 3(x+2)^2 + 2(x+2) + 1
Step-by-step explanation:
Replace x with x+2 and you get the solution above. Hope this helps!
Help ASAP!!!!!! Plzzzzzz
Answer:
2nd option
Step-by-step explanation:
CAN SOMEONE PLEASE ANSWER THIS QUICKLY I DONT GOT TIME
Answer:
5/20 x 4/15 =1/15
6/7 x 7/6 =1
2 x 7/10 =7/5
Hope this helps!
Again I don’t know this . Plz help me
Answer:
y-2=0(x-3)
Step-by-step explanation:
What is the intermediate step in the form (x+a)^2 = b as a result of x^2-16x= -68
Answer:
The intermediate step is determining what a is, knowing also that (x+a)²=x²+(2a)x+a².
Also, x²-16x= -68 (in the form (x+a)²=b) is (x-8)²=-4
Step-by-step explanation:
x²-16x=-68
x²-16x+68=0
I suppose the intermediate step is finding (x+a)².
Remember that (x+a)²=x²+(2a)x+a², so 'a' will be half the coefficient of x (number beside x, not x²). The coefficient of x here is -16, so a is -8.
(x-8)²=x²-16x+64
So, if we can create 'x²-16x+64' out of 'x²-16x+68', we'll be on our way:
x²-16x+68=0
(x²-16x+64)+4=0
(x-8)²+4=0
(x-8)²=-4
