Answer:
n(A∪B)=n(A)+n(B)−n(A∩B)−−−−−−−(1)
Given n(A)=7
n(B)=9
n(A∪B)=14
Substituting in 1
14=7+9−n(A∩B)
⇒n(A∩B)=16−14=2
Step-by-step explanation:
ok
Answer:
The question is incomplete.
It should be:
If n(A)=36, n(B)=10, n(A∪B)=40, and n(A')=27. Find n(∪) and n(A∩B)Find n(U)
n(A') = n(∪) - n(A)27 = n(∪) - 36n(∪) = 27 + 36n(∪) = 63Find n(A∩B):
n(A∪B) = n(A) + n(B) - n(A∩B)40 = 36 + 10 - n(A∩B)n(A∩B) = 46 - 40n(A∩B) = 6if cos7x-cos8x/1+2cos5x=cos(ax)-cos(bx),where a,b are positive integers, then a²+b²=??
pls help! :(
Step-by-step explanation:
[tex]hope \: its \: helful[/tex]
if cos7x - cos8x/1 + 2cos5x = cos(ax) - cos(bx), where a, b are positive integers, then a²+b²= 100.
The given equation is:
cos7x - cos8x/1 + 2cos5x = cos(ax) - cos(bx)
The LHS can be expanded as follows:
cos7x - cos8x/1 + 2cos5x = (2*cos4x*sin3x)/(2*cos2x) = sin3x
The RHS can be expanded as follows:
cos(ax) - cos(bx) = -2sin((a + b)/2)*sin((a - b)/2)
For the given equation to be true, the following must be true:
sin3x = -2sin((a + b)/2)*sin((a - b)/2)
3x = 180(a + b)/2
3x = 180(a - b)/2
Solving for a and b, we get a=6 and b=3.
Therefore, a² + b² = 6² + 3²=100.
To learn more about positive integers, here
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find the missing side lengths answers are in simplest radical form with the denominator rationalized
Explanation:
For any 30-60-90 triangle, the short leg is half of the hypotenuse. The short leg is opposite the smallest angle 30 degrees.
So this means n = 10/2 = 5
Because n = 5, there's only one answer choice that fits and it's choice C.
asap help -------------------
Answer:
C. Complex
Step-by-step explanation:
A complex number consists of a real part (-4.8) and an imaginary part (56i)
How do I solve this
Step-by-step explanation:
subtracting equation i from it got cropped
so the answer for x is 7 and y is -17
hope this helps. :)
someone help me with this please!!!!
Answer:
0*i+5j
Step-by-step explanation:
The vector is given by 0*i+5j
Explain why cos(-3π/4)=cos(5π/4).
Answer:
Step-by-step explanation:
Because the cosine is a positive function from which we can deduce [tex]\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\la\la\la\la\ddddddddddddddddddddddddddddddddcleverdddddd\ffffffffffffffffffffffffffffffffffffffff\pppppppppppppppppppppppppppppppppppp\dddddd \displaystyle \Large \boldsymbol{Rule : cos(-\alpha)=cos\alpha } \\\\\\ \cos\bigg(\frac{-3\pi }{4} \bigg)=cos135=-sin45=-\frac{\sqrt{2} }{2} \\\\\\cos\bigg(\frac{5\pi }{4} \bigg)=cos225=-sin45=-\frac{\sqrt{2} }{2}[/tex] Therefore, they are equal
Joshua buys a $6000 car on the following terms:
30% deposit
• monthly repayments of $210 for 2 years.
Find:
a) the deposit paid.
How can you use what you know about 5(2) to find 5(-2)?
Please help
Answer:
-10
Step-by-step explanation:
5(2) or fives times two is positive ten. The rule about multiplying with negatives is a negative times a positive is a negative. We take the multiplication answer from 5(2)=10 and apple the nagative from 5(-2). Hope this helps:)
Solve the equation using the zero-product property.
(2x − 8)(7x + 5) = 0
Answer:
x=4and -5/7
Step-by-step explanation:
i hope it will be easy
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\text{Equation}\downarrow[/tex]
[tex]\large\textsf{(2x - 8)(7x + 5) = 0}[/tex]
[tex]\large\text{Step-by-Step}\downarrow[/tex]
[tex]\large\text{SIMPLIFY EACH SIDES OF THE EQUATION}[/tex]
[tex]\large\textsf{14x}\mathsf{^2} \large\textsf{ - 14x - 40 = 0}[/tex]
[tex]\large\text{FACTOR the LEFT SIDE of the EQUATION}[/tex]
[tex]\large\textsf{2 (7x + 5) (x - 4) = 0}[/tex]
[tex]\large\text{SET the FACTORS to EQUAL 0}[/tex]
[tex]\large\textsf{7x + 5 = 0 OR x - 4 = 0}[/tex]
[tex]\large\text{SIMPLIFY BOTH OF YOUR EQUATIONS \& YOU HAVE YOUR ANSWER}[/tex]
[tex]\boxed{\boxed{\large\textsf{Therefore, your ANSWER is: \bf x = }\mathsf{\bf - \dfrac{5}{7}\large\textsf{ \bf or x = 4}}}} \huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
82,92,76,72,92,74,80 and 78
What is the median
Answer:
Step-by-step explanation:
we have 8 choises 8 its even number so
we can write 8= 2*4
X=4 ss the answear between the fiveth and sixeth choise 72+92/2 AND YOU WILL FIND THE ANSWEAR
(a) Write
[tex] {2}^{5} \div {2}^{5} [/tex]
as a single power if 2.
Answer:
2^0
Step-by-step explanation:
When you are dividing 2 exponents with the same base (in this case, 2) you subtract them. 2^5 ➗ 2^5 => 2^(5-5) = 2^0 => which is equal to 1, but the answer here would be 2^0.
There are two ways to go about this problem.
The first way, the generic way, is to know that,
[tex]\frac{a^n}{a^m}=a^{n-m},a\neq0[/tex].
So,
[tex]\frac{2^5}{2^5}=2^{5-5}=\boxed{2^0}[/tex].
The second way is to realise that both numerator and denominator are equal and when diving two equal numbers you obtain 1. (except when diving zeros) aka,
[tex]\frac{a}{a}=1, a\neq0[/tex]
And 1 equals to any number raised to the power of zero,
[tex]a^0=1,a\neq0[/tex]
So we just have to say that the 1 we got is rewritten as some base to the power of zero.
Since our base needs to be 2, we just simply say,
[tex]2^0[/tex].
Et Viola.
Hope this helps.
everything I do is not right help please
49 - 2/3 x = 32 - 1/6 x
Move the constant terms to one side and the terms containing x to the other:
49 - 32 = 2/3 x - 1/6 x
Simplify the left side, and pull out the common factor of x on the right side:
17 = (2/3 - 1/6) x
Write the fractions in terms of a common denominator. In this case, you would take
2/3 = 4/6
so that
(2/3 - 1/6) x = (4/6 - 1/6) x = 3/6 x = 1/2 x
Then the equation is
17 = 1/2 x
Multiply both sides by 2:
2 × 17 = 2 × 1/2 x
34 = x
Find the amount and the compound interest on rupees 5000 for 2 years at 6% per annum, Interest payable yearly. Answer with full steps and formula NO BAD ANSWERS REQUIRED :D
Answer:
I. Amount = 5618 Rupees
II. Compound interest = 618 Rupees
Step-by-step explanation:
Given the following data;Principal = 5000 RupeesTime = 2 yearsInterest rate = 6%To find the compound interest;
Mathematically, compound interest is calculated using the formula;
A = P(1 + r)^t
Where;
A is the future value.P is the principal or starting amount.r is annual interest rate.t is the number of years for the compound interest.Substituting into the formula, we have;
A = 5000(1 + 0.06)^2
A = 5000(1.06)^2
A = 5000 * 1.1236
A = 5618 Rupees
Next, we would determine the compound interest using the formula;
C.I = A - P
C.I = 5618 - 5000
Compound interest (C.I) = 618 Rupees
If a cylindrical vessel is 12 cm long and its surface area is 540 cm2, set up an
equation to find its radius.
Answer:
Option (1)
Step-by-step explanation:
Surface area of a cylindrical vessel is given by the expression,
Surface area = [tex]2\pi r^{2}+2\pi rh[/tex]
= [tex]2\pi r(r+h)[/tex]
Here, r = Radius of the vessel
h = Length of the vessel
By substituting the values of 'h' and surface area in the expression,
2πr(12 + h) = 540
Therefore, Option (1) will be the correct option.
A hot air balloon is flying at an altitude of 2926 feet. If the angle of depression from the pilot in the balloon to a house on the ground below is 25°
25
°
, how far is the house from the pilot? Round to the nearest tenth.(1 point)
Choices:
The house is 1236.6 feet from the pilot.
The house is 6274.8 feet from the pilot.
The house is 3228.5 feet from the pilot.
The house is 6923.5 feet from the pilot.
Answer:
The house is 6274.8 feet from the pilot.
Step-by-step explanation:
need help with this!!
Answer:
The answer is B..... The corresponding is the identical number between all
The is 7 in each...
Rose has $83. She is saving up for a new bike. If she saves $15 per week, how much money will she have after 8 weeks?
How much money does Rose have after 8 weeks? Solve on paper, then enter your answer on Zearn.
Rose has $
after 8 weeks.
Answer:
$203
Step-by-step explanation:
15x8=$120
120+83=$203
Mary wants to buy a mobile phone; the least expensive one she's spotted so far is $15. Mary has $4.25 saved for a mobile phone. If Mary works at a rate of $2.15 per hour, how many hours (H) will she have to work in order to afford a mobile phone?
Answer:
Mary would have to work 5 hours to afford a mobile phone.
Step-by-step explanation:
$15-$4.25= $10.75 that Mary would need to save.
2.15 x 5= 10.75
tìm 2 phân số có tử số bằng 1 mẫu số là 2 số tự nhiên liên tiếp sao cho 7/59 ở giữa 2 phân số
Answer:
Bajaj Pulsar of a great time in the 7th century there where you will have the gall the subcontinent the
In the diagram, what is the measure of angle 1 to the nearest degree?
33 degrees
55 degrees
75 degrees
105 degrees
Answer:
75 degrees
Step-by-step explanation:
From the first part of the diagram,
vertically opposite angles are equal,
hence we have
125° + (4x-5)° + 125° + (4x-5)° = 360°
(Angles about a point equals 360°)
4x – 5 + 4x – 5 + 125 + 125 = 360
8x + 250 – 10 = 360
8x = 360–250 + 10
8x = 120
x = 15°
Now we have (5x)° in the second part.
5x = 5 × 15 = 75°
1 is vertically opposite to angle 75°
hence it is equal to 75 degrees.
Answer:75
Step-by-step explanation:
can someone pls help me
On the last option, since you can substitute y=3x+1 into the other equations to solve for x.
solve for x *show work*
Answer:
x = 14
Step-by-step explanation:
The sum of the interior angles of a six sided figure is 720
10x + 8x-16+12x-8 +7x+2 +9x+4 +6x+10 = 720
Combine like terms
52x-8=720
Add 8 to each side
52x-8+8 = 720+8
52x = 728
Divide by 52
52x/52 = 728/52
x = 14
Step-by-step explanation:
here's the answer for thy question
A basketball team won 8 games and lost 7 games. Based on these results what is the probability of winning a game
the probability is made of the desired outcome divided by the total outcome.
desired = wins = 8
total = wins and losses = 15
8/15 is the probability (approx. 53%)
hope it helps :)
*(30 points)* One pump can fill a tank of water in 2 hours. A second tank can fill the same tank in 3 hours. If both pumps are used together, how long will it take to fill the tank?
The first pump fills one tank in 2 hours, so it works at a unit rate of (1 tank)/(2 hours) = 0.5 tanks/hour.
The second pump takes 3 hours to fill the same tank, so it works at a rate of (1 tank)/(3 hours) ≈ 0.33 tanks/hour.
Working together, the pumps can fill one tank at a rate of
(1/2 + 1/3) tanks/hour = (3/6 + 2/6) tanks/hour = 5/6 tanks/hour ≈ 0.83 tanks/hour
Then the time it takes both pumps to fill one tank is
(1 tank) / (5/6 tanks/hour) = 6/5 hours = 1.2 hours = 72 minutes
What is the simplified form of ((15xy^2)/(x^2+5x+6))/((5x^2y)/2x^2+7x+3))
Answer:
(27xy +3)/5x^2 +6x
Step-by-step explanation:
((15xy^2 )/ x^2 + 5x + 6 ) × ((2x^2 + 7x + 3) / 5x^2y)
(3y ×(2x+ 7x + 3)) / 5x^2 +6x)
wo large tanks A and B are each partially filled with 100 gallons of salt water. Initially,80 pounds of salt is dissolved in the solution in tank A, and 30pounds of salt is dissolvedin the solution in tank B. The system is closed so that the wellstirred saline solution ispumped only between tanks A and B. The saline solution in tankA travels to tank Balong a pipe at the rate of 3 gallons per minute, and the salinesolution in B travels totank A at the rate of 2 gallons per minute. Write a system of IVPs that will describe theamount of salt,x1, in tank A at timetand the amount of salt,x2in tank B at timet.
At the start, it's given that x₁ (0) = 80 lb and x₂ (0) = 30 lb.
The amounts of salt in either tank change according to
dx₁/dt = (2 gal/min) (x₂/(100 - t ) lb/gal) - (3 gal/min) (x₁/(100 + t ) lb/gal)
dx₂/dt = (3 gal/min) (x₁/(100 + t ) lb/gal) - (2 gal/min) (x₂/(100 - t ) lb/gal)
To break this down a bit, consider tank A, for instance:
• solution flows in from B at a rate of 2 gal/min
• the volume of liquid in tank B after t minutes is
100 gal + (2 gal/min - 3 gal/min) (t min) = (100 - t ) gal
because the tank starts with 100 gallons of liquid, and 2 gallons are pumped in while 3 gal are pumped out each minute
• at any time t, the solution in B contains x₂ pounds of salt
• the concentration of the solution in A is then x₂/(100 - t ) lb/gal
• multiplying this by the inflow rate tells you how much salt is moving around each minute
find the mean of the following, 1.5 m,1.7 m,1.6 m,1.5m,1.5m.
Solve for a.
a
2
8
a =
✓ [?]
Pythagorean Theorem: a2 + b2 = c2
Enter
Answer: [tex]a=\sqrt{60}[/tex]
Step-by-step explanation:
To solve for a, we want to use Pythagorean Theorem as provided int eh problem. a and 2 are the legs while 8 is the hypotenuse.
[tex]a^2+2^2=8^2[/tex] [exponent]
[tex]a^2+4=64[/tex] [subtract both sides by 4]
[tex]a^2=60[/tex] [square root both sides]
[tex]a=\sqrt{60}[/tex]
Now we know that [tex]a=\sqrt{60}[/tex].
Three dressers are placed side by side. One dresser is 5 feet 5 inches wide, another is 5 feet 10 inches wide, and the third is 3 feet 11 inches wide. How wide are they combined?
Answer:
15 feets 2 inches
Step-by-step explanation:
Given the widths :
1st dresser = 5 feets 5 inches
2nd dresser = 5 feets 10 inches
3rd dresser = 3 feets 11 inches
Their combined width is :
5ft + 5ft + 3 ft + 5in + 10in + 11in
13 feets 26 inches
Recall :
1 foot = 12 inches
26 inches = 26/12 feets = 2 feets 2 inches
Hence,
13 feets + 2feets 2 inches
Combined width = 15 feets 2 inches
Need help on this activity!!
In this activity, you will rearrange and solve a rational equation and find and use the inverse of a rational equation.
As we’ve seen, for a circuit with two resistors arranged in parallel, we can calculate the total resistance in the circuit, , in ohms, with this equation.
Question 1
Part A
Question
Rewrite the equation to represent the resistance of resistor 2, , in terms of and .
Answer:
My best guess rn is the first option
Step-by-step explanation:
the last dude had it close but it was basically flipped as you can tell.
The answer is (C) [tex]R_2=\frac{R_TR_1}{(R_1-R_T)}[/tex]
We need to make [tex]R_2[/tex] the subject of the formula [tex]R_T=\frac{R_1R_2}{R_1+R_2}[/tex]
First remove the denominator by multiplying both sides by the binomial [tex](R_1+R_2)[/tex]
[tex]R_T\times (R_1+R_2)=\frac{R_1R_2}{R_1+R_2}\times(R_1+R_2)\\\\R_TR_1+R_TR_2=R_1R_2[/tex]
Arrange all terms containing [tex]R_2[/tex] on one side
[tex]R_1R_2-R_TR_2=R_TR_1[/tex]
Factor out [tex]R_2[/tex] from the LHS
[tex]R_2(R_1-R_T)=R_TR_1[/tex]
Finally, divide both sides by the binomial [tex](R_1-R_T)[/tex] to leave [tex]R_2[/tex]
[tex]R_2(R_1-R_T)\times\frac{1}{(R_1-R_T)}=R_TR_1\times\frac{1}{(R_1-R_T)}\\\\R_2=\frac{R_TR_1}{(R_1-R_T)}[/tex]
Learn more about change of subject of formula here: https://brainly.com/question/343660
