Answer:
18a^3b^2/2ab
To simplify the given expression, we apply property of exponents
18/2 = 9
x^m / x^n= x^ (m-n) In division we subtract the exponents
So given expression becomes
9a^2b
The answer has only positive exponents
i think this is what you want?
The simplified exponential notation of the given expression is [tex]9a^2b[/tex].
The given expression is: [tex]\frac{18a^3b^2}{2ab}[/tex]
What is an exponential expression?An expression in the form of [tex]a^pb^qc^r[/tex].. is called exponential expression.
We can write the above expression as:
[tex](\frac{18}{2} )(\frac{a^{3} }{a} )(\frac{b^{2} }{b} )[/tex]
We know that [tex]\frac{a^m}{a^n} =a^{m-n}[/tex]
[tex]\frac{a^{3} }{a} =a^{3-1} =a^{2} \\\frac{b^{2} }{b}=b^{2-1} =b[/tex]
So, [tex](\frac{18}{2} )(\frac{a^{3} }{a} )(\frac{b^{2} }{b} )[/tex] =[tex]9a^2b[/tex]
Hence, the simplified exponential notation of the given expression is [tex]9a^2b[/tex].
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Which of the following best classifies a quadrilateral with coordinates A(7,0), B(3, 1), C(4,7), and D(8, 6)?
A.Rectangle
B.Parallelogram
C.Trapezoid
D.Square
Answer:
B. Parallelogram
Step-by-step explanation:
The opposite sides of the quadrilateral are equal and so the quadrilateral is a rectangle, the correct option is A.
What is a Quadrilateral?A quadrilateral is a polygon with four sides.
The coordinates of a quadrilateral are:
A(7,0), B(3, 1), C(4,7), and D(8, 6)
The distance between the coordinates has to be determined to identify the type of quadrilateral
The distance formula is
[tex]\rm D = \sqrt { ( x- x_1)^2 + (y-y_1)^2}[/tex]
[tex]\rm AB = \sqrt { (3-7)^2 + (1-0)^2}\\AB = \sqrt { 17}[/tex]
[tex]\rm BC = \sqrt { ( 1)^2 + (6)^2}\\BC = \sqrt {37}[/tex]
Similarly,
[tex]\rm CD= \sqrt { 17}\\\\AD = \sqrt{37}[/tex]
The opposite sides of the quadrilateral are equal and so it is a rectangle.
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The point (-2, 4) is plotted on the coordinate plane.
The point is reflected across the y-axis. What are the coordinates of the reflected point
A (-2,-4)
B (-2,4)
C (2,-4)
D (2,4)
Answer:
I would say B
Step-by-step explanation:
Plz help me!! I’m having a bit of trouble
Answer:
x= 27
Step-by-step explanation:
solve for 26 - 4s = 9s.
26-4s=9s
⇔26=9s+4s
⇔26=13s
⇔s=2
Answer:
s = 2
Step-by-step explanation:
26 - 4s = 9s
add 4s to 4s and 9s
that equals 13
26/13 = 13s/13
s = 2
help me plz branniest to whoever is right
Answer:
x= -7, x=8
Step-by-step explanation:
factoring method..
f (x) = - x² + 12x - 20
= - x² + 10x + 2x - 20
= - x( x - 10 ) + 2( x - 10 )
= ( x - 10 ) ( -x + 2 )
=> x = 10, x = 2
What is the distance between point A and point B on the coordinate plane?
HELP PLSS
Answer:
3
Step-by-step explanation:
If you count the units its three units away from each other.
Hana is putting in a tile floor she needs to determine the angles that should be cut in the tires to fit in the corner that angle in the corner measures 90° one piece of the tire will have a measure of 38 degrees write an equation and use it to determine the measure of the unknown angle
Answer:
x = 52°
Step-by-step explanation:
I have attached an image to depict the given angles.
From the attached image, we can see that the unknown angle is x°.
Thus, since that corner is 90°, then;
x + 38 = 90
Subtract 38 from both sides to get;
x = 90 - 38
x = 52°
Many utility companies promote energy conservation by offering discount rates to consumers who keep their energy usage below certain established subsidy standards. A recent EPA report notes that 70% of the island residents of Puerto Rico hae reduced their electricity usage sufficiently to qualify for discounted rates. If five residential subscribers are randomly selected from San Juan, Puerto Rico, find the probability of each of the following events.a. All five qualify for the favorable rateb. At least four qualify for the favorable rates
Answer:
a. 0.1681 = 16.81% probability that all five qualify for the favorable rate.
b. 0.5283 = 52.83% probability that at least four qualify for the favorable rates
Step-by-step explanation:
For each Puerto Rico resident, there are only two possible outcomes. Either they qualify for discounted rates, or they do not. The probability of a person in the sample qualifying for discounted rates is independent of any other person in the sample. This means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
70% of the island residents of Puerto Rico have reduced their electricity usage sufficiently to qualify for discounted rates.
This means that [tex]p = 0.7[/tex]
Five residential subscribers are randomly selected from San Juan, Puerto Rico
This means that [tex]n = 5[/tex]
a. All five qualify for the favorable rate
This is P(X = 5). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 5) = C_{5,5}.(0.7)^{5}.(0.3)^{0} = 0.1681[/tex]
0.1681 = 16.81% probability that all five qualify for the favorable rate.
b. At least four qualify for the favorable rates
This is
[tex]P(X \geq 4) = P(X = 4) + P(X = 5)[/tex]
So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 4) = C_{5,4}.(0.7)^{4}.(0.3)^{1} = 0.3602[/tex]
[tex]P(X = 5) = C_{5,5}.(0.7)^{5}.(0.3)^{0} = 0.1681[/tex]
[tex]P(X \geq 4) = P(X = 4) + P(X = 5) = 0.3602 + 0.1681 = 0.5283[/tex]
0.5283 = 52.83% probability that at least four qualify for the favorable rates
For the following right triangle, find the side length x.
Peter Company, a produce distributer, always tries to sell its oldest produce first.
Peter company
Answer:
what is this a maths problem
7 (4 1/3) using distributive property
Answer:
so 7*4 is 28 and 7*1/3 is 2 an 1/3 so it would be 30 and 1/3
Step-by-step explanation:
find the time required for an investment of $3000 to grow to $8000 at an interest rate of 7.5% per year, compounded quarterly ( round the answer to two decimal places)
Answer:
13.20 yearsStep-by-step explanation:
Investment P = $3000Final amount F = $8000Interest rate r = 7.5% = 0.075Compound number n = 4Time t = ?Formula:
F = P(1 + r/4)^(4t)Solve for t:
8000 = 3000(1 + 0.075/4)^(4t)8/3 = 1.01875^(4t)4t log 1.01875 = log (8/3)4t = 0.42596 / 0.008067t = 1/4(52.80)t = 13.20Given that triangle ABC has angle ABC = 90 degrees, AB = 6 cm and BC = 9 cm. Calculate the length of AC in cm to 1 decimal place
Answer:
AC = 6.7
Step-by-step explanation:
If this is a 90 degree triangle which I am assuming it is you would the Pythagorean theorem c^2 = a^2 + b^2 since bc seems long I am using that as the hypotenuse.
9^2 = 6^2 + b^2
81 = 36 + b^2
81-36 = b^2
45 = b^2
6.7 = b
so AC = 6.7
If a class of 27 students had a mean of 72 on a test, interpret the mean of 72 in the sense of a fair share measure of the center of the test scores.
The fair share measure would mean that the score of 72 would be the score all 27 students got on the test if they all had the same score.
A fair share measure of the center of the test scores is 72 be the score all 27 students got on the test.
We have given that
a class of 27 students had a mean of 72 on a test,
What is the fair share?An equitable or reasonable portion or share of something
The fair share measure would mean that a score of
72 be the score all 27 students got on the test.
If they all had the same score.
Therefore 72 was the score all 27 students got on the test.
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The main office staff collected 55 cans, the counseling staff collected 89 cans, and the custodial staff collected 67 cans.
There are 120 people in a sport centre.
78 people use the gym.
46 people use the swimming pool.
45 people use the track.
21 people use the gym and the pool.
16 people use the pool and the track,
24 people use the gym and the track.
9 people use all three facilities,
Given that a randomly selected person uses at least two facilities, what is the probability they
use all the facilities?
Answer:
43/120 ≈ 0.3583
Step-by-step explanation:
Adding up the folks who use two facilities counts the folks who use all three 3 times. So, the number who use two or more facilities is ...
21 +16 +24 -2(9) = 43 . . . . people who use 2 or more facilities
The probability that a person chosen randomly from the 120 at the sports center uses at least 2 facilities is ...
43/120 ≈ 0.3583
_____
The given numbers add up as follows:
Gym only: 42
Pool only: 18
Track only: 14
Gym and Pool only: 12
Gym and Track only: 15
Pool and Track only: 7
Gym and Pool and Track: 9
No facilities: 3
Which three steps are correct when solving this quadratic equation by completing the square? X^2-10x=39
Step-by-step explanation:
Any answer that involes,
Step 1: Complete the Square
[tex] {x}^{2} - 10x = 39[/tex]
[tex]( \frac{ - 10}{2} ) {}^{2} = 25[/tex]
[tex] {x}^{2} - 10x + 25 = 64[/tex]
Step 2: Turn the left side into a binomial
[tex](x - 5) {}^{2} = 64[/tex]
Step 3: Solve for x.
[tex]x - 5 = + - 8[/tex]
[tex]x - 5 = 8[/tex]
[tex]x = 13[/tex]
OR
[tex]x - 5 = - 8[/tex]
[tex]x = - 3[/tex]
X=-3 or X=13
No links please and make sure its correct.
Answer:
it is B
Step-by-step explanation:
he is putting in by the 3/5
Answer:
C.
Step-by-step explanation:
Why its C...
You can tell that on the top it say that the total is 15 so it can not be a. So now our answer choices are B, C, ad D.
Now it says that there are 3/5 highlighted but since the rest say 3/5 we can not eliminate yet.
Next we would multiply 3 x 3 to get 9 for how many dollars there are. Cross out B.
Between C and D, C is the most reasonable answer because it says how much did he put in the bank while the other one (D) says how much did he spend?
So it would be C
Hope this helps :)
Karim began his day by drinking 1 1/8
cups of milk at breakfast. By the end of the day, he drank a total of 2 2/3
cups of milk.
Which equation and solution correctly represent the amount of milk in cups, m , Karim drank after breakfast?
Answer:
A. 1⅛ + m = 2⅔
[tex] m = 1\frac{13}{24} [/tex]
Step-by-step explanation:
Cups of milk at breakfast = 1⅛
Cups of milk after breakfast = m
Total cups of milk by the end of the day = 2⅔
Thus:
Total cups of milk by the end of the day = cups of milk at breakfast + cups of drink after breakfast
Therefore:
1⅛ + m = 2⅔ (equation)
Solve for m
Subtract 1⅛ from each side
m = 2⅔ - 1⅛
Convert to improper fraction
m = 8/3 - 9/8
m = (64 - 27)/24 = 37/24
[tex] m = 1\frac{13}{24} [/tex]
Can someone help me with this?
Find x. Round to the nearest tenth.
xº
13
15
Answer:
x= 49.1
Step-by-step explanation:
Please see the attached picture for the full solution.
A small liberal arts college in the Northeast has 350freshmen. One hundred five of the freshmen are female. Suppose sixty freshmen are randomly selected (without replacement).Step 2 of 2:Find the standard deviation of the number of females in the sample. Round your answer to two decimal places, if necessary.
Answer:
The standard deviation of the number of females in the sample is 3.21.
Step-by-step explanation:
For each freshmen, there are only two possible outcomes. Either it is a female, or it is not. Sixty freshmen are randomly selected (without replacement). This means that the hypergeometric distribution is used to solve this question.
Standard deviation of the hypergeometric distribution:
We have that:
N is the population size.
n is the sample size.
s is the number of successes in the sample.
The standard deviation is given by:
[tex]\sigma = \sqrt{n(\frac{s}{N})(1 - \frac{s}{N})(\frac{N - n}{N-1})}[/tex]
A small liberal arts college in the Northeast has 350freshmen.
This means that [tex]N = 350[/tex]
One hundred five of the freshmen are female.
This means that [tex]s = 105[/tex]
Suppose sixty freshmen are randomly selected
This means that [tex]n = 60[/tex]
Find the standard deviation of the number of females in the sample.
[tex]\sigma = \sqrt{60(\frac{105}{350})(1 - \frac{105}{350})(\frac{350 - 60}{350 -1})} = 3.21[/tex]
The standard deviation of the number of females in the sample is 3.21.
I WILL GIVE BRAINLIEST!! PLEASE HURRY
Use the excerpt below taken from the Preamble of the United States Constitution to answer the following question:
"We the People of the United States, in Order to form a more perfect Union, establish Justice, insure domestic Tranquility, provide for the common defense, promote the general Welfare, and secure the Blessings of Liberty to ourselves and our Posterity, do ordain and establish this Constitution for the United States of America."
—Public Domain
What aspect of Enlightenment influence on the early United States government does this excerpt of the U.S. Constitution illustrate? (5 points)
It gives power to the people rather than God, the Church, or the king.
It rejects the concept of social class in the American system.
It promotes the popular concept of the freedom of speech.
It encourages the development of the separation of church and state.
Answer:
B. It rejects the concept of social class in the American system.
Explanation:
The Enlightenment of the American Colonies was a period in time where the people were encouraged to become their own nation. This period was represented by many speeches and pieces of writing that boasted freedom of speech, equality, freedom of the press, and religious tolerance.
This specific piece of writing focuses on the aspect of all people in the nation of America having protected freedoms and rights to become their own people.
A spinner has 3 equal sections that are purple, green, and blue. What is the probability of not landing on blue?
Answer:
P(not landing on blue section)=2/3
Step-by-step explanation:
Not landing on blue section = landing on one of the other sections
the remaining sections are 2 each one has a P=1/3
2 × 1/3 = 2/3
Answer:
66%
Step-by-step explanation:
2 divided by 3= 0.666666666 which is then converted to percent (66%)
Find the area of of a regular octagon with side length 20 cm.
A=2(1+[tex]\sqrt{2}[/tex])a^2=2·(1+[tex]\sqrt{2}[/tex])·20^2≈1931.37085cm²
Please help! (I also put what a median is)
Answer:
Step-by-step explanation:
1. 2
2. 3
3. 6
4. 2
5. 4
Write the expanded form in the condensed form.
9z+9z
Answer:
nine z plus nine z.
lol tell me.if.its wrong
In 5 days, a scientist wrote 3 pages of a research paper, At that rate, how many days will it take the scientist to write a 30- page research paper?
A 18 days C 25 days
B 30 days D 50 days
Answer:
50 days
Step-by-step explanation:
5/3 = 50/30
pls brainliest
you can see that there is 8 cm in middle of the trapezoid. above the trapezoid, it says 6 cm, below the trapezoid, it says 11 cm. find the area of the trapezoid and answer this question in square cm.
Answer:
Step-by-step explanation:
The area of a trapezoid is the average of the parallel bases times the height or distance between the two bases
A=h(b1+b2)/2
Here we have h=8cm, b1=6cm, and b2=11cm so
A=8(6+11)/2
A=8(17)/2
A=4(17)
A=68 cm^2
can somebody help me with math TwT:
question one 1: Which number(s) are 6 units from zero on a number line?
1. 3
2. 6
3. -6
4. 12
----------------------------------------------------------------------------
Question 2 ^^: Which comparison is not correct?
1. -3 < 4
2. 3 < 6
3. 1 > -9
4. -8 > -6
tell me the answers also for question 1 its either one or more than one answer ^^ ty and please don’t steal my points :(
1. 12 (i think)
i don't know about question 2
Answer: -8 > -6
Step-by-step explanation:
Suppose that the Celsius temperature at the point (x, y) in the xy-plane is T(x, y) = x sin 2y and that distance in the xy-plane is measured in meters. A particle is moving clockwise around the circle of radius 1 m centered at the origin at the constant rate of 2 m/sec.How fast is the temperature experienced by the particle changing in degrees Celsius per meter at the point?
Missing information:
How fast is the temperature experienced by the particle changing in degrees Celsius per meter at the point
[tex]P = (\frac{1}{2}, \frac{\sqrt 3}{2})[/tex]
Answer:
[tex]Rate = 0.935042^\circ /cm[/tex]
Step-by-step explanation:
Given
[tex]P = (\frac{1}{2}, \frac{\sqrt 3}{2})[/tex]
[tex]T(x,y) =x\sin2y[/tex]
[tex]r = 1m[/tex]
[tex]v = 2m/s[/tex]
Express the given point P as a unit tangent vector:
[tex]P = (\frac{1}{2}, \frac{\sqrt 3}{2})[/tex]
[tex]u = \frac{\sqrt 3}{2}i - \frac{1}{2}j[/tex]
Next, find the gradient of P and T using: [tex]\triangle T = \nabla T * u[/tex]
Where
[tex]\nabla T|_{(\frac{1}{2}, \frac{\sqrt 3}{2})} = (sin \sqrt 3)i + (cos \sqrt 3)j[/tex]
So: the gradient becomes:
[tex]\triangle T = \nabla T * u[/tex]
[tex]\triangle T = [(sin \sqrt 3)i + (cos \sqrt 3)j] * [\frac{\sqrt 3}{2}i - \frac{1}{2}j][/tex]
By vector multiplication, we have:
[tex]\triangle T = (sin \sqrt 3)* \frac{\sqrt 3}{2} - (cos \sqrt 3) \frac{1}{2}[/tex]
[tex]\triangle T = 0.9870 * 0.8660 - (-0.1606 * 0.5)[/tex]
[tex]\triangle T = 0.9870 * 0.8660 +0.1606 * 0.5[/tex]
[tex]\triangle T = 0.935042[/tex]
Hence, the rate is:
[tex]Rate = \triangle T = 0.935042^\circ /cm[/tex]