Answer:
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Add the first 12 terms of this sequence:
15, 45, 135, 405, 1215, ...
Answer:
Step-by-step explanation:
a₁ = 15
a₂/a₁ = 45/15 = 3
a₃/a₂ = 135/45 = 3
...
It is a geometric sequence with a common ratio r=3.
Sum of first 12 terms = a₁·(1-r¹²)/(1-r)
= 15·(1-3¹²)/(1-3)
= 15·(-531,441)/(-2)
= 3,985,800
PLEASE HELP ASAP
Solve the inequality [tex]\sqrt[3]{x+4} \ \textgreater \ \sqrt[2]{-x}[/tex]
A) x < 2
B) x > 2
C) x > –2
D) x < –2
True or False. A rational number can be expressed as the quotient a/b where b ≠ 0
Answer:
true. A rational number can be expressed as the quotient a/b where b ≠ 0
Let h(x)=20e^kx where k ɛ R (Picture attached. Thank you so much!)
Answer:
A)
[tex]k=0[/tex]
B)
[tex]\displaystyle \begin{aligned} 2k + 1& = 2\ln 20 + 1 \\ &\approx 2.3863\end{aligned}[/tex]
C)
[tex]\displaystyle \begin{aligned} k - 3&= \ln \frac{1}{2} - 3 \\ &\approx-3.6931 \end{aligned}[/tex]
Step-by-step explanation:
We are given the function:
[tex]\displaystyle h(x) = 20e^{kx} \text{ where } k \in \mathbb{R}[/tex]
A)
Given that h(1) = 20, we want to find k.
h(1) = 20 means that h(x) = 20 when x = 1. Substitute:
[tex]\displaystyle (20) = 20e^{k(1)}[/tex]
Simplify:
[tex]1= e^k[/tex]
Anything raised to zero (except for zero) is one. Therefore:
[tex]k=0[/tex]
B)
Given that h(1) = 40, we want to find 2k + 1.
Likewise, this means that h(x) = 40 when x = 1. Substitute:
[tex]\displaystyle (40) = 20e^{k(1)}[/tex]
Simplify:
[tex]\displaystyle 2 = e^{k}[/tex]
We can take the natural log of both sides:
[tex]\displaystyle \ln 2 = \underbrace{k\ln e}_{\ln a^b = b\ln a}[/tex]
By definition, ln(e) = 1. Hence:
[tex]\displaystyle k = \ln 2[/tex]
Therefore:
[tex]2k+1 = 2\ln 2+ 1 \approx 2.3863[/tex]
C)
Given that h(1) = 10, we want to find k - 3.
Again, this meas that h(x) = 10 when x = 1. Substitute:
[tex]\displaystyle (10) = 20e^{k(1)}[/tex]
Simplfy:
[tex]\displaystyle \frac{1}{2} = e^k[/tex]
Take the natural log of both sides:
[tex]\displaystyle \ln \frac{1}{2} = k\ln e[/tex]
Therefore:
[tex]\displaystyle k = \ln \frac{1}{2}[/tex]
Therefore:
[tex]\displaystyle k - 3 = \ln\frac{1}{2} - 3\approx-3.6931[/tex]
Cho hình hộp chữ nhật ABCD A B C D
Answer:
A B C D
A×B×C×D
3×3×3×6
162
A car which was advertised for sale for 95000, was ultimately sold for 83600. Find the percent reduction in the price?
Answer: 12%
Step-by-step explanation:
95,000-83,600=11,400
(11,400/95000)(100) = 12%
The percentage reduction in the price of the car is 12%
What are percentages?A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word percent means per 100. It is represented by the symbol “%”
Given here: Original price of car=95000 and Selling price=83600
Thus the reduction in price= 95000-83600
=11400
Thus percentage reduction in the price of the car is
= 11400/95000 × 100
=12%
Hence, The percentage reduction in the price of the car is 12%
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Can you please help me
Answer: 1/6
Step-by-step explanation:
Given:
4/9 and 11/18
Solve:
STEP ONE: Make the denominators equal by determining the LCM
LCM = Least Common Multiple
First Five multiples of 9 = 9, 18, 27, 36, 45
First FIve multiples of 18 = 18, 36, 54, 72, 90
As we can see from the list above, both 18 and 36 overlap, however, 18 is less than 36. Therefore, 18 is the LCM.
STEP TWO: Compare the size and determine the greater one.
4/9 = (4 × 2) / (9 × 2) = 8/18
11/18 = 11/18
Since 11 > 8, therefore, 11/18 is greater than 8/18
STEP THREE: Find the difference between the two fractions.
11/18 - 4/9
=11/18 - 8/18
=(11 - 8) / 18
= 3 / 18
= 1/6
Hope this helps!! :)
Please let me know if you have any questions
One positive number is 2 more than twice another. Their product is 180.
Step 2 of 2 : Find the numbers by solving the equation.
Answer:
9 and 20
Step-by-step explanation:
x = one number
y = 2x+2 = other number
xy = 190
x(2x+2) = 180
2x^2 +2x = 180
2x^2 +2x- 180 = 0
Factor out 2
x^2 +x -90 = 0
(x+10)(x-9) =0
Using the zero product property
x+10 = 0 x-9=0
x= -10 x=9
But they have to be positive
x = 9
y = 2x+2 = 2(9)+2 = 18+2 = 20
When f(x) =-3 what is x?
Answer:
D or -1
Step-by-step explanation:
It says that f(x) is equal to -3.
f(x) is the same as y-values, and x is the same as the x-values on a coordinate grid because x is the independent variable, meaning y is the dependent variable, where f(x) depends on the value of x to find y.
So if y is -3, it can be found on the graph on the 4th line, so x = -1 when y = -3
Aaron Lloyd what is a?
Answer:
Rugby lawyer
Step-by-step explanation:
Aaron is a partner in the firm’s dispute resolution division. He advises clients on a range of litigious and risk related matters, with particular expertise in the areas of corporate misconduct, white collar criminal and regulatory affairs, sports law and employment law. Aaron leads our sports law practice, and is a member of the firm’s health and safety, public law, and organisational integrity teams.
Well regarded by clients for his ability to analyse and strategise complex situations, Aaron is internationally recognised for his ability to implement pragmatic and commercial strategies to minimise risk and create opportunity. This ability has resulted in clients avoiding significant litigation and commercial consequences.
Aaron is an experienced advocate, having argued cases in the District Court, High Court, Employment Court, the Court of Appeal and Supreme Court of New Zealand, along with numerous tribunals.
He is recognised by international legal directories including by Chambers & Partners (Asia Pacific), Who’s Who Legal, Expert Guides, Best Lawyers and Doyles.
Before joining MinterEllisonRuddWatts Aaron practiced as a barrister with Paul Davison QC, and has lectured at the University of Auckland.
Big sleds must hold 3 children and small sleds must hold 2 children. If 17 children want to go sledding at the same time, how many of each type of sled is needed?
Answer:
5 big sleds and 1 small sled
A canoeist paddled down a river a distance of 2 miles in 45 minutes. Paddling up-stream on his return, it took him 90 minutes. Find the rate of the canoe in still water.
a2 - ab + 8b + b2 - 1
Answer:
а²-ab+8b+b²-1=a(a-b)+b(8+b)-1
Manatees can swim in water up to 20 feet deep. Write an expression that represents the depth d, that a manatee can swim
Answer:
0 ≤ d ≤ 20
Step-by-step explanation:
You mention that Manatees can swim in water up to 20 feet deep. So, this means that the largest depth that he can swim is 20 feet, not more than this. Also, keep in mind that the depth can't be negative, so ----> 0 ≤ d ≤ 20 feet
We want to write an expression (an inequality actually) that defines the depth at which a manatee can swim. The inequality is: 0ft ≤ d ≤ 20ft.
We know that the manatees can swim in water up to 20 feet deep. This represents the maximum deep at which manatees can swim, the minimum is trivial, it would be 0ft (when the manatees are on the surface of the water).
Then we can write the inequality:
0ft ≤ d ≤ 20ft.
This gives the range of possible values of d, depth at which the manatee can swim.
If you want to learn more, you can read:
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Find the lengths the missing side
Answer:
Short leg = x
Longer leg = 12
Hypotenuse = y
Short leg = 4√3
longer leg = 12
Hypotenuse = 8√3
Answered by GAUTHMATH
Hey community I thank you guys fir your help
Answer:
A, B, and E.
Step-by-step explanation:
A. 5^x * 5^x
= 5^x+x
=5^(2)(x)
=25^x
B. 5^2x
=5^(2)(x)
=25^x
C. 5*5^2x
=5^1+2x
D. 5*5^x
=5^1+x
E. (5*5)^x
=5^x*5^x
=5^(2)(x)
=25^x
F. 5^2*5^x
=5^2+x
The length of the hypotenuse of a 30 -60 -90 triangle is 32. What are the lengths of the legs?
Answer:
16, 16(sqrt3)
Step-by-step explanation:
30-60-90 triangles follow a rule where the hypotenuse is 2 times the shortest leg, and the longer leg is sqrt3 times the shorter leg.
So, the sides are x, 2x, and (sqrt3)x.
If 2x = 32, then x = 16.
Therefore the two legs are 16 and 16(sqrt3)
you can search up 30-60-90 triangle for more information
Given a sphere with radius r, the formula 4 r2 gives
O A. the volume
O B. the surface area
O c. the radius
O D. the cross-sectional area
Answer: surface area
Step-by-step explanation:
Alice wants to estimate the percentage of people who plan
on voting yes for the upcoming school levy. She surveys
380 individuals and finds that 260 plan on voting yes.
Identify the values needed to calculate a confidence interval
at the 90% confidence level. Then find the confidence interval.
zo10 z0.05 zo.025 zo01 z0.005
1.282 1.645 1.960 2.326 2.576
Use the table of common z-scores above.
Answer:
"[tex]0.6450 < p < 0.723[/tex]" is the right solution.
Step-by-step explanation:
Given:
n = 380
x = 260
Point estimate,
[tex]\hat p = \frac{x}{n}[/tex]
[tex]=\frac{260}{380}[/tex]
[tex]=0.6842[/tex]
Critical value,
[tex]Zc = 1.645[/tex]
Standard error will be:
[tex]S.E = \sqrt{\frac{0.6842(1-0.6842)}{380} }[/tex]
[tex]=0.0238[/tex]
Margin of error will be:
[tex]E = Zc\times S.E[/tex]
[tex]=1.645\times 0.0238[/tex]
[tex]=0.0392[/tex]
hence,
Confidence level will be:
= [tex]\hat p \pm E[/tex]
= [tex]0.6842 \pm 0.0392[/tex]
= [tex]0.6450 < p < 0.723[/tex]
Tính tích phân sau bằng cách dùng tọa độ cực I=∫∫ [tex]\frac{1}{\sqrt{x^{2} +y^{2} } }[/tex]dxdy R là miền nằm trọg góc phần tư thứ nhất thỏa mãn 4[tex]\leq x^{2} +y^{2} \leq 9[/tex]
It sounds like R is the region (in polar coordinates)
R = {(r, θ) : 2 ≤ r ≤ 3 and 0 ≤ θ ≤ π/2}
Then the integral is
[tex]\displaystyle \iint_R\frac{\mathrm dx\,\mathrm dy}{\sqrt{x^2+y^2}} = \int_0^{\pi/2}\int_2^3 \frac{r\,\mathrm dr\,\mathrm d\theta}{\sqrt{r^2}} \\\\ = \int_0^{\pi/2}\int_2^3 \mathrm dr\,\mathrm d\theta \\\\ = \frac\pi2\int_2^3 \mathrm dr \\\\ = \frac\pi2r\bigg|_2^3 = \frac\pi2 (3-2) = \boxed{\frac\pi2}[/tex]
Which is a perfect square?
6’1
6’2
6’3
6’5
Answer:
6'2
Step-by-step explanation:
Martina has 240 meters of fencing and wishes to form three sides of a rectangular field. The fourth side borders a river and will not need fencing.
As shown below, one of the sides has length x (in meters).
x
Side along river
(a) Find a function that gives the area Ax of the field (in square meters) in terms of x.
=Ax
(b) What side length x gives the maximum area that the field can have?
Side lengthx:meters
(c) What is the maximum area that the field can have?
Maximum area:square meters
Answer:
Step-by-step explanation:
Answering a comes from simplification, and answering b and c are done all in one step: completing the square on the quadratic that results from a.
(a) If Martina has 240 m of fencing and is only utilizing one side for the length and 2 sides for the width, the perimeter formula is
240 = x + 2w where x is a length and w is the width. Solving this for w in terms of x:
240 - x = 2w so
[tex]w=120-.5x[/tex] The area for a rectangle is L * W, so our area using the lengths we have is
A(x) = x(120 - .5x) and we simplify:
A(x) = 120x - .5x² That's the answer to a.
Now for b and c, we will complete the square on this to get the vertex.
Begin by factoring out the -.5:
[tex]A(x)=-.5(x^2-240x)[/tex] Now we take half the linear term, square it and add it both inside the parenthesis and outside the parenthesis. Our linear term is 240. Half of 240 is 120, and 120 squared is 14400:
[tex]A(x)=-.5(x^2-240x+14400)+7200[/tex] (The 7200 comes from multiplying the 14400 times the -.5; -.5 times 14400 is -7200 so to balance things out, we have to add 7200).
The perfect square binomial that results from this is
A(x) = -.5(x - 120)² + 7200. From this we determine that our vertex is
(120, 7200). The 120 is the value of x, the length we are asked to find in b; the 7200 is the max area we are asked to find in c.
The required solutions are,,
(a) area = 240x - 2x²
(b) the side adjacent to the rivers gives the maximum length of the field.
(c) the maximum area could be 6400-meter square.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
length of the field is x,
The perimeter of the field, = 240
x + x + width = 240
width = 240 - 2x
now,
(a)
area of the field,
= length * width,
= x(240-2x)
= 240x - 2x²
Similarly,
(b) the side adjacent to the rivers gives the maximum area of the field.
(c) the maximum area could be 6400-meter square.
Thus, the required solutions are mentioned above.
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A scuba diver is practicing
in a marked pool. He
begins 3 feet below the
surface of the water and
then dives down to the 9
foot marker. How far did
he dive?
Answer:
6ft
Step-by-step explanation:
Answer:
6ft
Step-by-step explanation:
help giving brainilest, heart, and 5 stars
Answer:
4 = 6
5 = -17
Step-by-step explanation:
4. a² - b / b² - c
a² = 2² = 4
b = -2
4 - (-2) = 4 + 2 = 6
6 / b² - c = 6/4 - 3 = 6/1 = 6
4 = 6
5. -3x² + 2xy + 7
-3x² = -3 * -2² = -3 * 4 = -12
2xy = 2 * -2 * 3 = -4 * 3 = -12
-12 + -12 + 7 = -24 + 7 = -17
5 = -17
If my answer is incorrect, pls correct me!
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-Chetan K
There are 768 beds in a hospital.
Each floor has 64 beds.
How many floors are there?
Answer:
12 floors
Step-by-step explanation:
768 ÷ 64 = 12.
Answer:
12
Step-by-step explanation:
768 divided by 64 =12
Louise has a hard time keeping her workspace clean at her job. She tries, but it just ends up getting messy again. Which of the following is a likely outcome of her consistent messiness? a) She will have fewer safety issues. b) She will feel more productive. c) Customers will think she is very busy. d) She will have a hard time focusing.
create a graph of 4.95 + 3.99
Answer:
????
Step-by-step explanation:
as in y = 4.95 + 3.99 or points? if so just draw a horizontal line at 8.94
Ellicott City Manufacturers, Inc., has sales of $6,344,210, and a gross profit margin of 67.3 percent. What is the firm's cost of goods sold? Round your final answer to the nearest dollar.
Answer:
$3792116
Step-by-step explanation:
that's the answer above
Mike wants to buy a scooter worth R10000 but cannot afford so he opts for the hire purchase agreement which requires a 13% deposit and a 24 equal monthly installments at a rate of 15% per annum compounded monthly
A.How much will his deposit be?
B.calculate how much does he still need to pay after the deposit
C.calculate the monthly installment
Answer: I think the answer is A
Step-by-step explanation:
Describe what is the most difficult part of solving equations, for you personally.
What do you personaly feel like is most dificult.
For me its rembering minus signs
