Answer:
- 6 + 24 i
Step-by-step explanation:
Use distributive property to remove parentheses and then combine like terms:
6 + 9i - 12 + 15 i = - 6 + 24 i
Test the series for convergence or divergence (using ratio test)
Answer:
[tex]\lim_{n \to \infty} U_n =0[/tex]
Given series is convergence by using Leibnitz's rule
Step-by-step explanation:
Step(i):-
Given series is an alternating series
∑[tex](-1)^{n} \frac{n^{2} }{n^{3}+3 }[/tex]
Let [tex]U_{n} = (-1)^{n} \frac{n^{2} }{n^{3}+3 }[/tex]
By using Leibnitz's rule
[tex]U_{n} - U_{n-1} = \frac{n^{2} }{n^{3} +3} - \frac{(n-1)^{2} }{(n-1)^{3}+3 }[/tex]
[tex]U_{n} - U_{n-1} = \frac{n^{2}(n-1)^{3} +3)-(n-1)^{2} (n^{3} +3) }{(n^{3} +3)(n-1)^{3} +3)}[/tex]
Uₙ-Uₙ₋₁ <0
Step(ii):-
[tex]\lim_{n \to \infty} U_n = \lim_{n \to \infty}\frac{n^{2} }{n^{3}+3 }[/tex]
[tex]= \lim_{n \to \infty}\frac{n^{2} }{n^{3}(1+\frac{3}{n^{3} } ) }[/tex]
= [tex]= \lim_{n \to \infty}\frac{1 }{n(1+\frac{3}{n^{3} } ) }[/tex]
[tex]=\frac{1}{infinite }[/tex]
=0
[tex]\lim_{n \to \infty} U_n =0[/tex]
∴ Given series is converges
A contractor needs to buy nails to build a house. The nails come in small boxes and large boxes. Each small box has 100 nails and each large box has 350 nails. The contractor bought a total of 9 boxes that have 2400 nails altogether. Write a system of equations that could be used to determine the number of small boxes purchased and the number of large boxes purchased. Define the variables that you use to write the system.
Answer:
3 small boxes and 6 large ones
Step-by-step explanation:
3 times 100 equals 300 and 6 times 350 is 2100 and 2100 plus 300 is 2400.
A plane traveled 1232 miles each way to New York City and back. The trip there was with the wind. It took 11 hours.
The trip back was into the wind. The trip back took 22 hours. Find the speed of the plane in still air and the speed of the wind.
The bus fare in a city is $2.00 . People who use the bus have the option of purchasing a monthly coupon book for $28.00. With the coupon book, the fare is reduced to $1.00. Determine the number of times in a month the bus must be used so that the total monthly cost without the coupon book is the same as the total monthly cost with the coupon book
I have an answer but I’m not sure if it’s correct can someone pls correct me or confirm pls
Answer:
looks good to me
Step-by-step explanation:
Lily and William are both driving along the same highway in two different cars to a stadium in a distant city. At noon, Lily is 313 miles away from the stadium and
William is 334 miles away from the stadium. Lily is driving along the highway at a
speed of 44 miles per hour and William is driving at speed of 51 miles per hour. Let L
represent Lily's distance, in miles, away from the stadium t hours after noon. Let W
represent William's distance, in miles, away from the stadium t hours after noon.
Write an equation for each situation, in terms oft, and determine the interval of
hours, t, for which Lily is closer to the stadium than William.
Answer:
L= -44t +313 W=-51t+334
Lily is closer to the stadium than William when t < 3 hours
Step-by-step explanation:
Determine if the sequence is arithmetle or geometne, and find the common difference or ratio
(1,81), (2,72),(3,63),(4,54)
I’m desperate ✨
y= x - 5
y= -3x + 3
graph please ASAP FOR EXAMS
Answer:
(2,-3)
Step-by-step explanation:
The intersection point of y=x-5 and y=-3x+3 is (2,-3) on a graph.
Which sequence of transformations performed on triangle J could result in similar triangle J'?
Answer:
B
Step-by-step explanation:
Answer:
Its b
Step-by-step explanation:
JUst got right
A certain drug dosage calls for 17 mg per kg per day and is divided into two doses (1 every 12 hours). If a person weighs 255 pounds, how many milligrams of the drug should he receive every 12 hours? Round your dosage to the tenth of a milligram.
Answer:
985.15mg
Step-by-step explanation:
Calculation for how many milligrams of the drug should he receive every 12 hours
First step is to calculate the weight in kg
255 lbs = 255/2.2 = 115.9 kg
Second step is multiply mg/kg in order to get total medicine per day
Dose per day=115.9kg × 17 mg
Dose per day= 1,970.3
Third step is to calculate how many milligrams of the drug should he receive by dividing the day dose by 2
Dose milligrams=1,970.3/2
Dose milligrams=985.15mg
Therefore how many milligrams of the drug should he receive every 12 hours will be 985.15mg
According to the 68-95-99.7% rule, what percentage of the data from a bell-shaped distribution will be within one standard deviation of the mean
Answer:
68% of the distribution will be within one standard deviation of the mean
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
Bell-shaped = Normally distributed.
This means that 68% of the distribution will be within one standard deviation of the mean
Answer:
c 95%
Step-by-step explanation:
If figure 1 needs 3 toothpicks, figure 2 needs 6 toothpicks and figure 3 needs 9 toothpicks then how many toothpicks will be needed in figure 4?
Answer:
Figure 4 will need 12 toothpicks.
Can someone tell me how to do this?
Answer:
6w+32
Step-by-step explanation:
Calculate the time it would take to infuse 1550ml of medication being infused at 100ml/h
Answer:
15.5hr
Step-by-step explanation:
Speed = Distance/Time
Given
Distance = 1550ml
Speed = 100ml/hr
Required
Time
From the formula;
Time = Distance/Speed
Time = 1550/100
Time = 15.5hr
Hence it will take 15.5hr
what the sqare units of a 3 bye 7
There is 21 square units by 3 and 7. 3 as the column and 7 as a row. You can solve it by multiplying 3 with 7 which gives you 21 or adding 7+7+7 or 3+3+3+3+3+3+3 and all three gives you 21 as the answer. So the square unit of 3 and 7 is 21.
Brandon buys a radio for $45.29 in a state where the sales tax is 7%.What is the total Brandon pays for the radio?
Answer:
Net Amount (excluding tax)$45.29
Tax (7.0%)$3.17
Gross Amount (including tax)$48.46
Step-by-step explanation:
Please don't hate me if i'm wrong.
Answer:
48.46
Step-by-step explanation:
To find the sales tax of this you would have to multiply
$45.29*1.07=48.46
which would get you your answer
Example
You can plug it in with other things like sales tax of 9% for any number like 67.98 so you can just do
$67.98*1.09=74.10
plzzzz help asaaaap look at the filllle plzzzzz
Answer:
29) x=8
30) x=18
Step-by-step explanation:
The picture tells you that ∠AOB and ∠COD are equal. So,
29: m∠AOB = m∠COD
Substitute.
4x - 2 = 2x + 14
Solve.
2x = 16
x = 8°
30. again, m∠AOB = m∠COD = 28
m∠AOD = m∠AOB + m∠BOC + m∠COD
Substitute.
6x = 28 + 3x -2
Simplify.
6x = 3x + 54
Solve.
3x = 54
x = 18
Is 5/11 equivalent to -5
Answer:
false, no
Step-by-step explanation:
Answer:
no
Step-by-step explanation:
Solve for X
Answers:
3
5
-8
11
Please Help
The diagram below represents a generic right triangle.
Which statement BEST explains why the sine of an acute angle is equal to the cosine of the angle's complement?
A
Both sin A and cos B are equal to
B
Both sin A and cos B are equal to
ОО O
С
For sin A to equal cos B. a and c must be equal.
D
For sin A to equal cos B a and b must be equal
Dan is serving his child french fries and chicken wings for lunch today. Let f be the number of french fries in the lunch, and let c be the number of chicken wings. Each french fry has 25 calories, and each chicken wing has 100 calories. Dan wants the total calorie count from the french fries and chicken wings to be less than 500 calories. Using the values and variables given, write an inequality describing this.
Answer:
25f + 100c < 500
Step-by-step explanation:
I hope it helps.
The third set in a tennis match went for
71.28
minutes, which was
8%
longer than the second set. The second set was
10%
longer than the first set.
Answer:
First set = 60 minutes
Second set = 66 minutes
Step-by-step explanation:
Given that:
Length of third set = 71.28 minutes ;
Third set was 8% longer than second set ;
Length of second set = x
Third set = (100% + 8%) = 108% of second set
71.28 = 1.08 * x
71.28 = 1.08x
x = 71.28 / 1.08
x = 66
Hence, second set = 66 minutes
Second set was 10% longer than the first
(100 + 10)% of first set = second set
110% of first set = second set
Let first set = y
1.1 * y = 66
1.1y = 66
y = 66 / 1.1
y = 60
Hence, first set = 60 minutes
First set = 60 minutes
Second set = 66 minutes
SOLVE FOR X AND Y !! WILL GIVE BRAINLIEST
Answer:
x=21, y=17
Step-by-step explanation:
180-42= 138
2x+138=180
2x= 42
x= 21
8y+2+2x=180
8y+2 + 42=180
8y= 136
y= 17
Answer:
x=21, y=68
Step-by-step explanation:
We're given that the quadrilateral on the left is a parallelogram as indicated by the arrow markings on the sides. We're also told that the angle on the right is 42 degrees. So, we can find the bottom right angle in the parallelogram by subtracting 42 from 180, because it forms a straight angle. 180-42 is 138. By the alternate interior angles theorem, 8y+2=138, because 138 is also the angle measure of the opposite corner. we also know that the bottom left angle in the parallelogram is the same as 2x. by the alternate interior angles theorem. Notice how the sides of the parallelogram with two arrow markings are parallel, which means that the bottom left angle and the 42 degree angle are congruent, or have the same measure, because of the parallel lines. This means that 2x=42, and the bottom left angle is 42. We can solve for x and y with simple algebra now. 8y+2=138, 8y=138-2, 8y=136, y=68. 2x=42, x=42/2, x=21. So, x is 21 and y is 68.
1) Define the three trigonometric ratios (sine, cosine, and tangent) using opposite side, adjacent side, and hypotenuse)
Answers:
sin(angle) = opposite/hypotenusecos(angle) = adjacent/hypotenusetan(angle) = opposite/adjacentThese three ratios are often expected to be memorized or written on a flashcard, or reference sheet. I recommend memorizing them as they will come up quite often in trigonometry.
One way to remember is to use phrase "SOH CAH TOA" which could sound like "soak a toe-a" when you pronounce it out.
SOH = sine opposite hypotenuse
CAH = cosine adjacent hypotenuse
TOA = tangent opposite adjacent
Dan buys a car for £2100.
It depreciates at a rate of 2.2% per year.
How much will it be worth in 6 years?
Give your answer to the nearest penny where appropriate.
Answer:£472.92
Step-by-step explanation:
£2100(0.78)^6
How much money will Tracy repay to the bank for a loan of $1000 that she borrows for 2 years 8 months at a 12% simple interest rate?
Ned took a test with 20 questions. He lost 3 points for each of the 5 questions he got wrong and earned an additional 12 points for answering a bonus question correctly. How many points did Ned receive or lose overall?
Answer:
He lost 15 points and recieved 12 points back now he missing 3 points
Each day martin lifts weights for 10 minutes and runs on the treadmill
Answer:
I can see ur question but I'm not getting it is there any answers I can chose from to work it out
what is 48 as a product of its prime factors... SHOW ALL WORKING
Answer: 48 as a product of its prime factors is 48 or 2*2*2*2*3
Step-by-step explanation:
First find the prime factors of 48
48
∧
2 24
∧
2 12
∧
3 4
∧
2 2
The prime factors are 2 * 2 * 2 * 2 * 3 or [tex]2^{4} * 3[/tex]
Find the coordinates for point R that proves figure TRAP is an isosceles trapezoid.
Answer:b
Step-by-step explanation: I got it right on my test
The coordinates for point R that proves figure TRAP is an isosceles trapezoid is (c - a, b)
From the diagram, we have the following highlights
There are two parallel sides in the trapezoidThe parallel sides of the trapezoid are horizontal linesThis means that the y-coordinate of point R is the same as the y-coordinate of point T.
Given that the y-coordinate of point T is b, the y-coordinate of point R can be represented as:
[tex]R =(x,b)[/tex]
For the shape to be an isosceles trapezoid, then the following must be true
[tex]x = c - a[/tex]
So, we have:
[tex]R =(c - a,b)[/tex]
Hence, the coordinates of R is (c - a, b)
Read more about trapezoid at:
https://brainly.com/question/2141851
