Answer:
Zero
Step-by-step explanation:
Given that:
the true mean is 50 and we reject the hypothesis that μ = 50
The probability of the Type II error will be zero, given that we reject the null hypothesis. This has nothing to do with if it is true or false.
Type II error is occurs when you accept a false null hypothesis. The probability of this error is denoted by beta which relies on sample size and population variance.
The probability of rejecting is equal to one minu beta. i.e it is the researchers goal to reject a false null hypothesis.
what are the comparison symbols for 5/6 and 2/5, 4/10 and 7/8, and 3/12 and 1/4
Answer like this: Example
=
<
>
Answer:
5/6 > 2/44/10 < 7/83/12 = 1/4Step-by-step explanation:
The comparison will be the same if you subtract the right side and compare to zero:
a/b ?? c/d . . . . . . . using ?? for the unknown comparison symbol
a/b - c/d ?? 0 . . . . subtract the fraction on the right
(ad -bc)/bd ?? 0 . . . combine the two fractions
ad - bc ?? 0 . . . . . . multiply by bd to make the job easier
__
5/6 and 2/5
5(5) -6(2) = 25 -12 > 0 ⇒ 5/6 > 2/5
4/10 and 7/8
4(8) -10(7) = 48 - 70 < 0 ⇒ 4/10 < 7/8
3/12 and 1/4
3(4) -12(1) = 0 ⇒ 3/12 = 1/4
_____
Of course, you can use your calculator (or your memory) to change each of these to a decimal equivalent. The comparison should be easy at that point.
0.833 > 0.400
0.400 < 0.875
0.250 = 0.250
Lila is camping with her family. She wants to hike to the lake, go fishing, and hike back before 6:05 P.M. It will take 1 hour and 10 minutes to hike to the lake and 1 hour and 50 minutes to hike back. Lila wants to fish for 3 hours and 10 minutes. What is the latest time Lila can start the hike to the lake?
Lila will need to start the hike at 11: 55 a.m. to be back at exactly 6: 05 p.m. or at 11: 54 a.m. to be before 6: 05 p.m (6: 04 p.m.)
Explanation:
To solve this question, the first step is to calculate how much time does hiking to the lake, go fishing, and go back takes in total. This can be calculated by adding the time of the three activities. This means 1 hour 10 minutes + 3 hours 10 minutes + 1 hour 50 minutes which is equal to 6 hours 10 minutes. The detailed process is shown below.
Add the hours: 1 + 3 + 1 = 5
Add the minutes: 10+50 +10 = 70
Also, because the total of minutes is above 60 (each hour has 60 minutes) it is necessary to subtract 60 minutes and add 1 hour.
5 hours + 1 hour and 70 minutes - 60 minutes = 6 hours and 10 minutes
Now, to solve the question subtract the time of the activities to the time Lila needs to complete all the activities.
6: 05 p.m. - 6 hours and 10 minutes = 11: 55 a.m
You can get this result by substracting first the hours and then the minutes
6: 05 p.m. - 6 hours = 12: 05 p.m.
12: 05 - 10 minutes = 11: 55 a.m.
According to this, Lila will need to start the hike at 11: 55 a.m. to be back at exactly 6: 05 p.m. or at 11: 54 a.m. to be before 6: 05 a.m because if she starts at 11: 54 a.m. she will be back at 6:04, which is a minute before 6:05 p.m.
Write all the factors of 32
Matj
Answer
Answer: 1, 2, 4, 8, 16, and 32.
Step-by-step explanation:
Factors are what we can multiply to get the number.
Factors of 32:
1 x 32=32
2 x 16=32
4 x 8=32
Therefore, the factors of 32 are 1, 2, 4, 8, 16, and 32.
Consider the function f(x) = x2. Which of the following functions shifts f(x)
downward 5 units and to the right 3 units?
A)f(x) = (x + 3)2 - 5
B) f(x) = (x - 3)2 - 5
C) f(x) = (x - 5)2 - 3
D) f(x) = (x - 5)2 + 3
Answer:
f(x) = (x - 3)² - 5
Step-by-step explanation:
equate equation to 0
(x - 3)² = 0
take the square root on both sides
x - 3 = 0
add 3
x = 3
If x = 3 then you are moving to 3 units to the right.
- 5 means you are going downward 5 units.
NEED HELP ASAP PLEASE!! The graph of F(x), shown below, resembles the graph of G(x) = x2, but it has
been stretched and shifted. Which of the following could be the equation of
Fx)?
10
G(X) = x2
10
Fx) = ?
Answer:
D. F(x) = ( (1/5)x)^2 - 4
Step-by-step explanation:
The standard transformation with a stretch and a shift is
F(x) = f(x/b) + k
The red curve has a vertex at (0,-4), and cuts the x-axis at (10,0)
That means that before the vertical shift (of k=-4), the vertex was at (0,0), and the curves passes through (10,4).
Substituting in the equation
F(10) = (10/b)^2 -4 = 0
solve for b
(10/b)^2-4 = 0
(10/b)= sqrt(4) = 2
b = 10/2 = 5
Therefore the transformation equation is
F(x) = (x/5)^2-4
The answer is
F(x) = ( (1/5)x)^2 - 4
sasha has some pennies nickels and dimes in her pocket. the number of coins is 18 the expression is 0.01p+0.05n+0.10d represents the value of the coins which is 1.08 she has twice as many dimes as pennies. How many of each coin does Sasha have
Answer:
3 pennies, 9 nickels, and 6 dimes
Step-by-step explanation:
We have three conditions:
(1) p + n + d = 18
(2) 0.01p + 0.05n + 0.10d = 1.08
(3) d = 2p
Multiply (2) by 100 and rearrange (3) to get a standard array.
(4) p + n + d = 18
(5) p + 5n + 10d = 108
(6) -2p + d = 0
Subtract (4) from (5). This gives
(4) p + n + d = 18
(7) 4n + 9d = 90
(6) -2p + d = 0
Multiply (4) by 2 and add to (6). This gives
(4) p + n + d = 18
(7) 4n + 9d = 90
(8) 2n + 3d = 36
Double (8) and subtract from (7). This gives
(4) p + n + d = 18
(7) 4n + 9d = 90
(9) 3d = 18
Divide (9) by 3. This gives
(10) d = 6
Substitute (10) into (7). This gives
4n + 9(6) = 90
4n + 54 = 90
4n = 36
(11) n = 9
Substitute (10) and (11) into (4). This gives
p + 9 + 6 = 18
p + 15 = 18
p = 3
Sasha has 3 pennies, 9 nickels, and 6 dimes.
Find the measure of the remote exterior angle. mZx = (4n – 18)º
m2y = (n+9)°
m2z = (151 – 5n)º
y
Х
Z
Answer:
71°
Step-by-step explanation:
The sum of two interior angles in a triangle is equal to an exterior angle
m<x + m<y = m<z
4n - 18 + n + 9 = 151 - 5n
5n - 9 = 151 - 5n add like terms
10n = 160
n = 16
Since m<z = 151 - 5n we replace n with 16 and 151 - 5×16 = 71
Answer:
A. 71
Step-by-step explanation:
x + y = z
4n - 18 + n + 9 = 151 - 5n
5n - 9 = 151 - 5n
10n = 160
n = 16
Z = 151 - 5(16) = 71
A video rental store keeps a list of their top 15 movie rentals each week. This week the list includes 6 action, 4 comedies, 3 dramas, and 2 mysteries. The store manager removes a copy of each of the 15 movies from the shelf, then randomly selects 3 of the 15 to show on the display monitors in the store. What is the probability that she selected 2 comedies and 1 action movie?
Answer:
32/1125Step-by-step explanation:
Probability is the likelihood or chance that an event will occur.
Probability = Expected outcome of event/Total outcome.
If a video rental store keeps a list of their top 15 movie rentals each week, the total outcome is 15.
If the list for the week includes 6 action, 4 comedies, 3 dramas, and 2 mysteries and the store manager removes a copy of each of the 15 movies from the shelf, then randomly selects 3 of the 15 to show on the display monitors in the store, the probability that she selected 2 comedies and 1 action movie will be calculated as shown;
Probability of selecting 2 comedies = 4/15*4/15 = 16/225 (Note that the expected outcome in this case is 4).
Probability of selecting 1 action movie = 6/15 = 2/5
Hence, the probability that she selected 2 comedies and 1 action movie will be equivalent to 16/225*2/5 = 32/1125
Note that the rented movies will have to be returned hence reason for the replacement.
Which option is correct and how would one solve for it?
Answer:
28
Step-by-step explanation:
We need to find the value of [tex]\Sigma_{x=0}^3\ 2x^2[/tex]
We know that,
[tex]\Sigma n^2=\dfrac{n(n+1)(2n+1)}{6}[/tex]
Here, n = 3
So,
[tex]\Sigma n^2=\dfrac{3(3+1)(2(3)+1)}{6}\\\\\Sigma n^2=14[/tex]
So,
[tex]\Sigma_{x=0}^3\ 2x^2=2\times 14\\\\=28[/tex]
So, the value of [tex]\Sigma_{x=0}^3\ 2x^2[/tex] is 28. Hence, the correct option is (d).
My town has two cell phone providers. The provider Don’tTalkMuch charge is $80 per month plus 1 dollar per hour the provider TalkLots charges $20 per month plus 4 dollars per hour how much do you have to use your phone in a month in order for Don’tTalkMuch’s much is a deal to be better for you?
Answer:
The author have to use his/her phone less than 20 hours in a month in order for Don’tTalkMuch's is a deal to be better than TalkLots's is.
Step-by-step explanation:
Call X is the number of hours that the author uses on monthly basis.
Total bill value if the author uses Don’tTalkMuch service is $80 + $1 X.
Total bill value if the author uses TalkLots service is $20 + $4X
The total fees between 2 providers equal as:
$80 + $1 X = $20 + $4X => 3X = $60 => X = 20
Hence: The author have to use his/her phone less than 20 hours in a month in order for Don’tTalkMuch's is a deal to be better than TalkLots's is.
If there are 25 students in a class - 11 are guys and 14 are girls what is the probability that one of the students on the class is a guy?
Answer:
0.44
Step-by-step explanation:
11/25 = 0.44 = 44%
Answer:
11/25
Step-by-step explanation:
since there are 25 students, there will be 25 choices, and the 25 will be the denominator
and there are 11 guys so there will be 11 choices of guys and the 11 will go on top
find the value of each variable and the measure of each angle
Answer:
Left angle = 60°
Top angle = 120°
Right angle = 60°
Step-by-step explanation:
Use what you know about angle relationships to set up equations you can solve for each variable.
The top top angle, for example, added to one of the other angles must equal 180° because they are supplementary.
You have two variables, so you need at least two equations (I made three but only used two).
The work is in my attachment, comment of you have questions.
Policeman A and Policeman B hand out 70 speeding tickets in a month.
Policeman A hands out 4 times as many speeding tickets as Policeman B.
Policeman A handed out ? Speeding tickets.
Answer:
Policeman A = 56 tickets
Step-by-step explanation:
Policemen A + B = 70
If Policeman B hands out x no of tickets...
Then Policeman A hands out 4x no of tickets
meaning...
x + 4x = 70
5x = 70
x = 70/5
x = 14
Therefore Policeman A hands out..
4x = 4 × 14 = 56 tickets
A European study of thousands of men found that the PSA screening for prostate cancer reduced the risk of a man’s dying from prostate cancer from 3.0 percent to 2.4 percent. "But it’s already a small risk. I don’t think a difference of less than 1 percent would be of practical importance," said Ed. Do you agree with Ed’s conclusion?
Answer:
Following are the answer to this question:
Step-by-step explanation:
In the given statement, we don't agree with Ed’s conclusion, because it is not relevant simply since it is not statistically significant. The reduction of prostate cancer is the death risk, which is highly significant even if it decreases significantly. It can also be something statistically important without becoming important.
helpppppppppppppppppppppppppppp give bralienst
Answer:
Brainliest! Hope I helped!
Step-by-step explanation:
you know its greater than 1cm and less than 2cm,
1 and 7hundreths cm is = 1.07 cm
thats not right because you know it is greater than that for sure!
so the only answer left is 1.7 cm
You answer is 1.7 cm
another way...
read the ruler and see the answer
Answer:
1.7 cm.
Step-by-step explanation:
The midpoint of 1 - 2 is 5 so count the lines after 5 and you get .7 to add to one cm.
Hope this helps, have a good day :)
A random sample of 10 single mothers was drawn from a Obstetrics Clinic. Their ages are as follows: 22 17 27 20 23 19 24 18 19 24 We want to determine at the 5% significance level that the population mean is not equal to 20. What is the rejection region?
Answer:
0.09
Step-by-step explanation:
Let x = ages of mother
x : 22 17 27 20 23 19 24 18 19 24
N = 10
Mean = ∑x/N = 218/10 = 21.8
Difference in mean = 21.8 - 20 = 1.8
If significance level = 5% or 0.05
∴ Rejection region = 1.8 X 0.05 = 0.09
please solution this question now .thank you very much
Answer:
5/2
Step-by-step explanation:
Let u = sin(t). Then this is the integral ...
[tex]\displaystyle\int_0^{\frac{\pi}{2}}{5u}\,du=\left.\dfrac{5u^2}{2}\right|_0^{\frac{\pi}{2}}=\dfrac{5}{2}(\sin(\frac{\pi}{2})^2-\sin(0)^2)=\dfrac{5}{2}(1-0)=\boxed{\dfrac{5}{2}}[/tex]
What is the rise over run for the slope -11/9
Answer: 11 down and 9 right
Step-by-step explanation:
Slope IS rise over run where the top number of the fraction (numerator) determines the vertical distance --> positive is up, negative is down
and the bottom number of the fraction (denominator) determines the horizontal distance --> positive is right, negative is left.
Given slope = -11/9
the numerator is -11 so the "rise" is DOWN 11 units
the denominator is 9 so the "run" is RIGHT 9 units
Kristin is building a pattern using triangles. The table shows the number of triangles in the first 4 terms of the pattern.
Term Number (7)
1 2 3 4
Number of Triangles (t) 1 3 5 7
Which formula describes the number of triangles in the nth term of the pattern?
O A n=1+2
O B. n=1+3
Oc. n = 21-1
OD n = 2t + 3
Answer:
[tex]\bold{n =2t-1}[/tex]
Step-by-step explanation:
Given table is:
[tex]\begin{center}\begin{tabular}{ c c}Term Number (t) & Number of triangles (n) \\ 1 & 1 \\ 2 & 3 \\ 3 & 5 \\ 4 & 7 \\\end{tabular}\end{center}[/tex]
i.e. when term number, t = 1, number of triangles (n) = 1
when term number, t = 2, number of triangles (n) = 3
when term number, t = 3, number of triangles (n) = 5
when term number, t = 4, number of triangles (n) = 7
If we closely look at the pattern, number of triangles (n) in each row are 1 lesser than twice of term number (t).
i.e. for [tex]t=1, n = 2\times 1 -1=1[/tex]
[tex]t=2, n = 2\times 2 -1=3[/tex]
[tex]t=3, n = 2\times 3 -1=5[/tex]
[tex]t=4, n = 2\times 4 -1=7[/tex]
Therefore, the number of triangles in the nth term will be given as:
[tex]\bold{n =2t-1}[/tex]
Answer:
an = 2t -1
Step-by-step explanation:
We are adding 2 each time
1+2 =3
3+2 = 5
5+2 = 7
an is the nth term in the sequence and t is the number of triangle
an =1+ 2(t-1)
Distribute
an = 1 +2t -2
an = 2t -1
A box is filled with 8 blue cards, 6 red cards, and 6 yellow cards. A card is chosen at a random from the box. What is the probability that the card is not red ? Write your answer as a fraction.
Answer:
14/20 or .7 or 70%
Step-by-step explanation:
Total Number of cards: 20
Number of Red cards: 6
The leftover cards: 20 -6 = 14
The probability of not getting a red = 14/20
14/20 as a decimal = 14/20 = 70/100 = .7
14/20 as a percent = 14/20 = 70/100 = 70%
Among cases of heart pacemaker malfunctions, were found to be caused by firmware, which is software programmed into the device. If the firmware is tested in different pacemakers randomly selected from this batch of and the entire batch is accepted if there are no failures, what is the probability that the firmware in the entire batch will be accepted? Is this procedure likely to result in the entire batch being accepted?
Complete question is;
Among 8834 cases of heart pacemaker malfunctions, 504 were found to be caused by firmware, which is software programmed into the device. If the firmware is tested in three different pacemakers randomly selected from this batch of 8834 and the entire batch is accepted if there are no failures, what is the probability that the firmware in the entire batch will be accepted? Is this procedure likely to result in the entire batch being accepted?
Answer:
P(All three are not caused by firmware) = 83.84%
Probability that the entire batch will be accepted = 0.8384
Step-by-step explanation:
We are told that out of the 8834 cases of heart pacemaker malfunctions, 504 were found to be caused by firmware.
Thus,
Cases not caused by firmware = 8834 - 504 = 8330
So, probability of the first case not being affected by firmware is;
P(first case not caused by firmware) = 8330/8834
Also,
Probability of second case not being affected by firmware is given as;
P(second case not caused by firmware|first case not affected by firmware) = 8329/8833
Similarly,
Probability of third case not being affected by firmware is given as;
P(third case not caused by firmware|first and second not caused by firmware) = 8328/8832
Now, looking at the 3 Probabilities gotten, it is obvious that the events are not independent because the probability of occurence of one event depends on the probability of occurence of the other event.
Thus, we will make use of the general multiplication rule which is;
P(A & B) = P(B) × P(A|B)
Thus;
P(All three not caused by firmware) = P(first case not caused by firmware) × P(second case not caused by firmware|first case not affected by firmware) × P(third case not caused by firmware|first and second not caused by firmware)
Plugging in the relevant values, we have;
P(All three not caused by firmware) = (8330/8834) × (8329/8833) × (8328/8832)
P(All three are not caused by firmware) = 0.83840506679 ≈ 83.84%
George's height is 1.75 meters and Martha's height is 160 centimeters. How much taller is George than Martha in millimeters?
George should be 150 mm taller than Martha.
Calculation of the height in millimeters:
Since George's height is 1.75 meters and Martha's height is 160 centimeters.
So here we convert the meters to mm
So,
[tex]= 1.75\times 100\\\[/tex]
= 1750 mm
Now 160 cm to mm
So,
[tex]= 160\times 10[/tex]
= 1,600 mm
So, the difference should be
= 1,750 - 1,600
= 150 mm
Therefore, George should be 150 mm taller than Martha.
Learn more about height here: https://brainly.com/question/15810288
An honest die is rolled. If the roll comes out even (2, 4, or 6), you will win $1; if the roll comes out odd (1,3, or 5), you will lose $1, Suppose that in one evening you play this game n=2500 times in a row.
(a) Estimate the probability that by the end of the evening you will not have lost any money.
(b) Estimate the probability that the number of "even rolls" (roll a 2, 4, or 6) will fall between 1250 and 1300.
(c) Estimate the probability that you will win $100 or more.
Answer:
(a) 50%
(b) 47.5%
(c) 2.5%
Step-by-step explanation:
According to the honest coin principle, if the random variable X denotes the number of heads in n tosses of an honest coin (n ≥ 30), then X has an approximately normal distribution with mean, [tex]\mu=\frac{n}{2}[/tex] and standard deviation, [tex]\sigma=\frac{\sqrt{n}}{2}[/tex].
Here the number of tosses is, n = 2500.
Since n is too large, i.e. n = 2500 > 30, the random variable X follows a normal distribution.
The mean and standard deviation are:
[tex]\mu=\frac{n}{2}=\frac{2500}{2}=1250\\\\\sigma=\frac{\sqrt{n}}{2}=\frac{\sqrt{2500}}{2}=25[/tex]
(a)
To not lose any money the even rolls has to be 1250 or more.
Since, μ = 1250 it implies that the 50th percentile is also 1250.
Thus, the probability that by the end of the evening you will not have lost any money is 50%.
(b)
If the number of "even rolls" is 1250, it implies that the percentile of 1250 is 50th.
Then for number of "even rolls" as 1300,
1300 = 1250 + 2 × 25
= μ + 2σ
Then P (μ + 2σ) for a normally distributed data is 0.975.
⇒ 1300 is at the 97.5th percentile.
Then the area between 1250 and 1300 is:
Area = 97.5% - 50%
= 47.5%
Thus, the probability that the number of "even rolls" will fall between 1250 and 1300 is 47.5%.
(c)
To win $100 or more the number of even rolls has to at least 1300.
From part (b) we now 1300 is the 97.5th percentile.
Then the probability that you will win $100 or more is:
P (Win $100 or more) = 100% - 97.5%
= 2.5%.
Thus, the probability that you will win $100 or more is 2.5%.
Given the following computer printout for a set of sample data, which one of the following represents the value of the Interquartile Range?
Descriptive Statistics: Cycle Time
Variable N Mean StDev Variance Minimum Q1 Median Q3 Maximum
Cycle Time 52 31.808 5.333 28.436 21.700 27.825 31.000 36.075 44.000
A. 22.3
B. 3.175
C. 5.075
D. 8.25
Answer: D. 8.25
Step-by-step explanation: A data set can be divided into 4 equal parts, called Quartile. A quartile divides the data into three points:
Lower quartile: Q1;Median: Q2;Upper quartile: Q3;Interquartile Range (IQR) is a measure of variability based on data divided into quartiles or the measure of where the bulk of the values are.
To calculate interquartile range:
IQR = Q3 - Q1
The table shows Q1 = 27.825 and Q3 = 36.075, then
IQR = 36.075 - 27.825
IQR = 8.25
The value of interquartile range is 8.25.
What does it mean when the resulting temperature is above 0 on the number line? What does it mean when a temperature is below 0?
Answer:
It means that above 0 degrees Celsius the water does not freeze, whereas 0 degrees are freezing teperatures of water.
Step-by-step explanation:
Water freezes at 0 degrees Celsius, but the freezing temperature can be lowered by adding salt to the water. A student discovered that adding half a cup of salt to a gallon of water lowers its freezing temperature by 7 degrees Celsius. What is the freezing temperature of the gallon of salt water?
0° - 7° = -7°
Can someone please help me ASAP:(
Answer:
3 =x
Step-by-step explanation:
(segment piece) x (segment piece) = (segment piece) x (segment piece)
3x(x+1) = 4x*x
Divide each side by x
3(x+1) = 4x
Distribute
3x+3 = 4x
Subtract 3x from each side
3x-3x +3 = 4x-3x
3 =x
In this diagram, bac~edf. if the area of bac= 6 in.², what is the area of edf? PLZ HELP PLZ PLZ PLZ
Answer:
2.7 in²
Step-by-step explanation:
Given:
∆BAC ~ ∆EDF
Area of BAC = 6 in²
EF = 2 in
BC = 3 in
Required:
Area of ∆EDF
SOLUTION:
Let x = area of ∆EDF
[tex] \frac{6 in^2}{x} = (\frac{3 in}{2 in})^2 [/tex] (theorem of area of similar triangles)
[tex] \frac{6 in^2}{x} = (\frac{3 in}{2 in})^2 [/tex]
[tex] \frac{6}{x} = \frac{9}{4} [/tex]
Cross multiply:
[tex] 6*4 = 9*x [/tex]
[tex] 24 = 9x [/tex]
Divide both sides by 9
[tex] \frac{24}{9} = x [/tex]
[tex] 2.67 = x [/tex]
Area of ∆EDF = 2.7 in²
If x =y, then x-a=y-a represents the blank property of equality. A-addition B-symmetric C-subtraction D.transitive
Answer:
Subtraction property
Step-by-step explanation:
Answer:
Subtraction
Step-by-step explanation:I took the test
n a genetics experiment on peas, one sample of offspring contained 372 green peas and 35 yellow peas. Based on those results, estimate the probability of getting an offspring pea that is green. Is the result reasonably close to the value of 3 4 that was expected?
Complete Question
In a genetics experiment on peas, one sample of offspring contained 372 green peas and 35 yellow peas. Based on those results, estimate the probability of getting an offspring pea that is green. Is the result reasonably close to the value of 3/4 that was expected?
Answer:
The probability is [tex]P(g) = 0.9140[/tex]
No it is not close to the probability expected
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 372 + 35= 407[/tex]
The number of green peas is [tex]n_g = 372[/tex]
The number of yellow peas is [tex]n_y = 35[/tex]
The probability of getting an offspring pea that is green is mathematically represented as
[tex]P(g) = \frac{n_g}{n}[/tex]
substituting values
[tex]P(g) = \frac{372}{ 407}[/tex]
[tex]P(g) = 0.9140[/tex]
The expected probability is [tex]\frac{3}{4} = 0.75[/tex]
But what we got is [tex]P(g) = 0.9140[/tex]
So we can say that the value obtained is not equal to the expected value
What is the simplified form of the following expression? 2 StartRoot 18 EndRoot + 3 StartRoot 2 EndRoot + StartRoot 162 EndRoot 6 StartRoot 2 EndRoot 18 StartRoot 2 EndRoot 30 StartRoot 2 EndRoot 36 StartRoot 2 EndRoot
Answer:
[tex]18\sqrt2[/tex]
Step-by-step explanation:
To simplify:
[tex]2 \sqrt{18}+ 3 \sqrt2+ \sqrt{162 }[/tex]
First of all, let us write 18 and 162 as product of prime factors:
[tex]18 = 2 \times \underline{3 \times 3}\\162 = 2 \times \underline{3 \times 3} \times \underline{3 \times 3}[/tex]
The pairs are underlined as above.
While taking roots, only one of the numbers from the pairs will be chosen.
Now, taking square roots.
[tex]\sqrt{18} =3 \sqrt2[/tex]
[tex]162 = 3 \times 3 \times \sqrt 2 = 9 \sqrt2[/tex]
So, the given expression becomes:
[tex]2 \sqrt{18}+ 3 \sqrt2+ \sqrt{162 } = 2 \times 3\sqrt2 + 3\sqrt2 +9\sqrt2\\\Rightarrow 6\sqrt2 + 3\sqrt2 +9\sqrt2\\\Rightarrow \sqrt2(6+3+9)\\\Rightarrow \bold{18\sqrt2}[/tex]
So, the answer is:
[tex]18\sqrt2[/tex] or 18 StartRoot 2 EndRoot
Answer:
its B. 18 sqrt(2)
Step-by-step explanation:
just took test
