Given:
27y and 54y³
To find:
The highest common factor (HCF) using prime factorization.
Solution:
We have,
27y and 54y³
Using the prime factorization, we get
[tex]27y=3\cdot 3\cdot 3\cdot y[/tex]
[tex]54y^3=2\cdot 3\cdot 3\cdot 3\cdot y\cdot y\cdot y[/tex]
Now, the common prime factors are 3, 3, 3 and y. So,
[tex]HCF=3\cdot 3\cdot 3\cdot y[/tex]
[tex]HCF=27y[/tex]
Therefore, the highest common factor of the given terms is 27y.
the sum of 2 integers are -396, if one is 64, find the other
Find the missing length. If needed, round to the nearest tenth.
B
6
7
5
Х
A
The value of x is
Answer:
x=5.8
Step-by-step explanation:
5/6=x/7
cross multiply
6x=35
x=35/6
x=5.8
Three oil companies, A, B and C, are exploring for oil in an area. The probabilities that they will discover oil are, respectively, 0.40, 0.60 and 0.20. If B discovers oil, the probability that A will also discover oil is increased by 20%. Assume that the chance of C discovering oil is independent of A and B.
i) What is the probability that oil will be discovered in the area by one or more of the three companies?
ii) If oil is discovered in the area, what is the probability that it will be discovered by company C?
Answer:
Step-by-step explanation:
i )
the probability that oil will be discovered in the area by one or more of the three companies = probability of oil to be discovered by one company + probability that oil will be discovered by two companies + probability that oil will be discovered by three companies.
probability of oil to be discovered by one company = .40 x .40 x .80 + .60 x .60 x .80 + .60 x .40 x .20 = .128 + .288 + .048 = .464
probability that oil will be discovered by two companies = probability to be discovered by A and B and not discovered by C + probability to be discovered by A and C and not discovered by B + probability to be discovered by B and C and not discovered by A
= .40 x .80 x .80 + .40 x .20 x .40 + .60 x .20 x .60
= .256 + .032 + .072
= .36
probability that oil will be discovered by three companies.
= .40 x .60 x .20 = .048
Total probability = .464 + .36 + .048 = .872
ii )
Probability of discovery by C = Probability by C and not by A and B + Probability by C and A and not by B + Probability by C and B and not by A
+ Probability by A , B and C .
= .20 x .6 x .4 + .20 x .40 x .40 + .20 x .60 x .60 + .40 x .60 x .20
= .048 + .032 + .072 + .048
= .20
If oil is discovered in the area, what is the probability that it will be discovered by company C = .20 / .872
= .23
The probability that oil will be discovered in the area by one or more of the three companies is 86.24%, and if oil is discovered in the area, the probability that it will be discovered by company C is 16.66%.
Given that three oil companies, A, B and C, are exploring for oil in an area, and the probabilities that they will discover oil are, respectively, 0.40, 0.60 and 0.20, and if B discovers oil, the probability that A will also discover oil is increased by 20%, assuming that the chance of C discovering oil is independent of A and B, to determine 1) what is the probability that oil will be discovered in the area by one or more of the three companies, and 2 ) if oil is discovered in the area, what is the probability that it will be discovered by company C, the following calculations must be made:
1)
The discovery probabilities of 1, 2 or 3 companies must be added. (0.40 x 0.40 x 0.80 + 0.60 x 0.60 x 0.80 + 0.60 x 0.40 x 0.20) + (0.48 x 0.60 x 0.80 + 0.40 x 0.60 x 0.20 + 0.60 x 0.60 x 0.20) + (0.40 x 0.60 x 0.20) + (0.40 x 0.60 x 0.20) (0.128 + 0.288 + 0.048) + (0.2304 + 0.048 + 0.072) + 0.048 = X 0.464 + 0.3504 + 0.048 = X 0.8624 = X
2)
1.20 = 100 0.20 = X 0.20 x 100 / 1.20 = X 20 / 1.20 = X 16.66 = X
Therefore, the probability that oil will be discovered in the area by one or more of the three companies is 86.24%, and if oil is discovered in the area, the probability that it will be discovered by company C is 16.66%.
Learn more about maths in https://brainly.com/question/26138968
Allentown, Bakersfield, and Cowville are not in a line. If it is 57 miles in aline from Allentown to Bakersfield and 35 miles from Bakersfield to Cowville , how far is it from Allentown to Cowville?
Answer:
27
Step-by-step explanation:
322415154551
Answer:
92Step-by-step explanation:
Just simply add 57 to 35.
57+35=92
14x² - 21x³ + 49x⁴
ayudenme porfavor
no se
sólo lo hago esto para poder preguntar
4 friends share 3 pounds of grapes equally.how much pounds of grapes does each friend get?
Answer:
0.75 lb
Step-by-step explanation:
3 divided by 4 is 0.75
Help
Please ..................
Answer:
-86
Step-by-step explanation:
Substitute -11 for x in the equation:
8(-11)+2
=-88+2
=-86
Elena finds that the length of a house on a scale drawing is 5 inches. The actual length of the house is 45 feet. What is the scale of the drawing?
Answer:
81 is the scale of the drawing.
Step-by-step explanation:
Andrew wants to buy new shirts for his job.
Andrew wants to buy at least 5 new shirts to wear to his new job.
Short sleeve shirts cost $14 each and long sleeve shirts cost $18 each.
Andrew wants to spend no more than $100.
Which system of inequalities can be used to find how many short sleeve shirts, x, and how many long sleeve shirts, y, he can buy?
Answer:
my anm,e is andrew and i dont have a job :/
Step-by-step explanation:
Answer:
x + y ≤ 5
14x + 18y ≥ 100
Step-by-step explanation:
just trust me
never trust strangers
PLEASE HELP I WILL GIVE BRAINLIEST
Is RST = XYZ? If so, name the postulate that applies.
A. Might not be congruent
B. Congruent - SSS
C. Congruent - ASA
D. Congruent - SAS
Answer:
D
Step-by-step explanation:
two sides are congruent and in between is an angle
Draw a model to show 3/4 of 16.
Answer:
Draw a box and split it into four pieces. Write 4 in each of those pieces. Put a "{" or "}" around 3 of them. Next to it write. 4 x 3 OR 4 + 4 + 4 = 12
Step-by-step explanation:
Draw a box and split it into four pieces. Write 4 in each of those pieces. Put a "{" or "}" around 3 of them. Next to it write. 4 x 3 OR 4 + 4 + 4 = 12
Hope that helps!
Please help me there is a picture right there
Answer:
90 mm^2
Step-by-step explanation:
split into two rectangles.
First rectangle: 5 x 6 = 30 mm^2
Second rectangle: 10 x 6 = 60 mm^2
30 + 60 = 90 mm^2
Answer:
90 [tex]mm^{2}[/tex]
Step-by-step explanation:
Hi!
What we have over here is a composite figure.
Basically, it's made up of different shapes
We can either make a rectangle by making a horizontal line from the point in between 6 mm and 5 mm
Or we can make a rectangle by going verticle from the point in between 6 mm and 5 mm
Either way, we have two rectangles now, and we can use our formula [tex]l*w[/tex] to find the area.
For the first example, we would do:
[tex]6*5[/tex] [tex]=30[/tex]
[tex]6*10=60[/tex]
Then we add the two areas of the two rectangles:
[tex]60+30=90[/tex] [tex]mm^{2}[/tex]
For the second example, we would do:
[tex]5*6=30[/tex]
[tex]5*12=60[/tex]
[tex]60+30=90[/tex] [tex]mm^{2}[/tex]
Just cut the figure into shapes you can calculate the area of and you should be good to go!
Let me know if you have any questions
PLEASE HELP WITH THIS I WILL MARK YOU AS BRAINLIEST PLS AND TY
Answer:
it would be multiplying by 2 Soo 2•2= 4
and 4•2= 8. and 6•2 = 12. and 8•2=16 and 10•2=20
Using the Distributive Property, rewrite 2x + 16 as a product of two factors. *
1. 2x + 8
2. 2(16x)
3. 2(x + 8)
4. 2(x + 16)
3(6+b)-(2b +1)
Simplify the expression
Step-by-step explanation:
3(6+b)-(2b+1)
=18+3b-2b+1
=18+1+3b-2b
=19+b
Andrea collected this data: 5, 8, 9, 12 What is one value that she could add to the data so that the median would be 11?
Answer:
19
Step-by-step explanation:
Median= Middle number
12-5= 7
12+7=19
YALL PLEASE HELP I WILL MARK YOU AS BRAINLEST
Step-by-step explanation:
But you can search on other applications
Can U tell me U are in which std
Select all the expressions equivalent to 2.8⁴.
A. 6.8
B. 2.8 + 2.8 + 2.8 + 2.8
C. 11.2
D 2.8 + 4
E. 2.8 × 2.8 × 2.8 × 2.8
F. 61.4656
G. 2.8 × 4
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\text{Select all the expressions equivalent to }\mathsf{2.8^4}[/tex]
[tex]\large\text{Exponents is a number that is being said how many times to use}\\\large\text{when you are multiplying}[/tex]
[tex]\large\text{Now lets try to solve for your answer(s)}[/tex]
[tex]\bold{2.8^4 = 2.8\times2.8\times2.8\times2.8}\\\bold{2.8\times2.8\times2.8\times2.8}\\\bold{2.8\times 2.8 = 7.84}\\\bold{7.84\times7.84= answer}\\\uparrow\large\text{Solve above and you should have one of your answers!}\\\bold{\rightarrow 7.84\times7.84= 61.4656}[/tex]
[tex]\bold{2.8^4\ is\ EXPRESSED\ approximately\ 4\ times}\\\\\bold{\rightarrow 2.8^4= 2.8\times2.8\times 2.8\times2.8}[/tex]
[tex]\boxed{\boxed{\large\text{Answer: \underline{\bf{Option E.) 2.8 * 2.8 * 2.8 * 2.8 \& Option F. 61.4646}}}}}\huge\checkmark[/tex]
[tex]\textsf{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Find the missing numbers:
1) 1 + 4.000 + 900 +
= 4,911
which of the following is not a composite number a6 b7 c8 d9
Answer:
7 isn't a composite number
Step-by-step explanation:
Answer:
7, it's a prime number
Step-by-step explanation:
Imagine you are a financial analyst at an investment bank. According to your research of publicly-traded companies, 60% of the companies that increased their share price by more than 5% in the last three years replaced their CEOs during the period. At the same time, only 35% of the companies that did not increase their share price by more than 5% in the same period replaced their CEOs. Knowing that the probability that the stock prices grow by more than 5% is 4%, find the probability that the shares of a company that fires its CEO will increase by more than 5%.
Answer:
0.0667 = 6.67% probability that the shares of a company that fires its CEO will increase by more than 5%.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this problem:
Event A: Company fires the CEO
Event B: Shares increase by more than 5%.
Probability of a company firing it's CEO:
35% of 100 - 4 = 96%(shares did not increase by more than 5%).
60% of 4%(shared did increase by more than 5%).
So
[tex]P(A) = 0.35*0.96 + 0.6*0.04 = 0.36[/tex]
Intersection of events A and B:
Fires the CEO and shared increased by more than 5%, is 60% of 4%. So
[tex]P(A \cap B) = 0.6*0.04 = 0.024[/tex]
Probability that the shares of a company that fires its CEO will increase by more than 5%.
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.024}{0.36} = 0.0667[/tex]
0.0667 = 6.67% probability that the shares of a company that fires its CEO will increase by more than 5%.
15. 12 kg çilekten 6 kg reçel
yapılıyor.
22 kg reçel yapmak
için kaç kg çileğe ihti-
yaç olur?
Answer:
12kg
Step-by-step explanation:
because 2×2×2+4=12
jskgx
Please tell me the answer to this. Very easy points if you ask me.
x + 8x = ?
x + 8x = 9x
(like 1 + 8 but with x's)
Which algebic expression is “ten less than a number divided by twelve”?
StartFraction n Over 12 EndFraction minus 10
StartFraction 12 over n EndFraction minus 10
10 minus StartFraction n Over 12 EndFraction
10 minus StartFraction 12 Over n EndFraction
Answer:
It is n/12-10
Step-by-step explanation:
Which is A
The algebraic expression that represents "ten less than a number divided by twelve" is Start Fraction n - 10 Over 12 End Fraction.
To properly calculate the algebraic expression for "ten less than a number divided by twelve," we can break it down step by step.
The expression "ten less than a number" can be written as "n - 10," where n represents the unknown number.
Next, we divide the expression "n - 10" by twelve:
Start Fraction n - 10 Over 12 End Fraction
Therefore, the correct algebraic expression for "ten less than a number divided by twelve" is Start Fraction n - 10 Over 12 End Fraction.
Among the given choices, the correct expression is Start Fraction n - 10 Over 12 End Fraction.
To know more about algebraic:
https://brainly.com/question/29131718
#SPJ6
Zoey surveyed 580 of the students in her school about their favorite color. 35% said their favorite color was purple. How many students' favorite color was purple?
Answer:
203 students surveryed purple as their favorite color
Step-by-step explanation:
Let's set this up like a fraction
Percentages are always out of 100 so the denoninator will be 100
Since the number of students who's favorite color is equal to 35%, we will equal both fractions together
Variable x = number of students for purple
x/580 = 35/100
Cross multiply
x × 100 = 580 × 35
100x = 20,300
Isolate the variable by dividing both sides by 100
x = 203
203 students surveryed purple as their favorite color
Geometry problem above ^ ABC is similar to...
Answer:
B. 20 units
Step-by-step explanation:
You can see that the each of the sides of triangle XYZ are half the length of each the sides of triangle ABC.
So 40 / 2 = 20 units
Hope that helps!
Rectangle A is a scaled version of rectangle B. The dimensions of rectangle A are four times the dimensions of rectangle B. The
area of rectangle A is 288 sq cm.
What is the area of rectangle B?
Answer:
1152
Step-by-step explanation:
288 x 4=1152
A utility company charges $0.12 per kilowatt-hour for energy a customer uses.They give a credit of $0.0025 for every kilowatt-hour of electricity a customer with a solar panel generates that they don't use themselves.A customer has a charge of $82.04 and a credit of -$4.10 on this mouth bill. How many kilowatt-hours did they use (Nearest-whole number?
Answer:
2,324.
Step-by-step explanation:
Given that a utility company charges $ 0.12 per kilowatt-hour for energy a customer uses, and they give a credit of $ 0.0025 for every kilowatt-hour of electricity a customer with a solar panel generates that they don't use themselves, if a customer has a charge of $ 82.04 and a credit of - $ 4.10 on this mouth bill, to determine how many kilowatt-hours did they use the following calculation must be performed:
(82.04 / 0.12) + (-4.10 / - 0.0025) = X
683,666 + 1,640 = X
2,323.66 = X
Thus, rounded to the nearest whole number, users used 2,324 kilowatts per hour.
The function f is defined by f(x) = x + 3 / 4x - 5 . Find f(x+3).
Answer:
x+6 / 4x-5
Step-by-step explanation:
What is 2 7/9 + 8/9 ?
Answer:
11/6
Step-by-step explanation:
2 7/9 + 8/9
2 7/9 into a mixed fraction which is 25/9
now 25/9 + 8/9 = 33/18 then simplify which is 11/6
