Standard Form: 589,203
Expanded forms can be written like a sentence or stacked for readability as they are here.
Expanded Notation Form: 589,203
= 500,000 + 80,000 + 9,000 + 200 + 0 + 3
Expanded Factors Form: 589,203
= 5 × 100,000 + 8 × 10,000 + 9 × 1,000 + 2 × 100 + 0 × 10 + 3 × 1
Expanded Exponential Form: 589,203
5 × 105 + 8 × 104 + 9 × 103 + 2 × 102 + 0 × 101 + 3 × 100
Sorry if i was not helpful hope this helps !
Lim x-> vô cùng ((căn bậc ba 3 (3x^3+3x^2+x-1)) -(căn bậc 3 (3x^3-x^2+1)))
I believe the given limit is
[tex]\displaystyle \lim_{x\to\infty} \bigg(\sqrt[3]{3x^3+3x^2+x-1} - \sqrt[3]{3x^3-x^2+1}\bigg)[/tex]
Let
[tex]a = 3x^3+3x^2+x-1 \text{ and }b = 3x^3-x^2+1[/tex]
Now rewrite the expression as a difference of cubes:
[tex]a^{1/3}-b^{1/3} = \dfrac{\left(a^{1/3}-b^{1/3}\right)\left(a^{2/3}+a^{1/3}b^{1/3}+b^{2/3}\right)}{\left(a^{2/3}+a^{1/3}b^{1/3}+b^{2/3}\right)} \\\\ = \dfrac{a-b}{a^{2/3}+a^{1/3}b^{1/3}+b^{2/3}}[/tex]
Then
[tex]a-b = (3x^3+3x^2+x-1) - (3x^3-x^2+1) \\\\ = 4x^2+x-2[/tex]
The limit is then equivalent to
[tex]\displaystyle \lim_{x\to\infty} \frac{4x^2+x-2}{a^{2/3}+(ab)^{1/3}+b^{2/3}}[/tex]
From each remaining cube root expression, remove the cubic terms:
[tex]a^{2/3} = \left(3x^3+3x^2+x-1\right)^{2/3} \\\\ = \left(x^3\right)^{2/3} \left(3+\dfrac3x+\dfrac1{x^2}-\dfrac1{x^3}\right)^{2/3} \\\\ = x^2 \left(3+\dfrac3x+\dfrac1{x^2}-\dfrac1{x^3}\right)^{2/3}[/tex]
[tex](ab)^{1/3} = \left((3x^3+3x^2+x-1)(3x^3-x^2+1)\right)^{1/3} \\\\ = \left(\left(x^3\right)^{1/3}\right)^2 \left(\left(3+\dfrac3x+\dfrac1{x^2}-\dfrac1x\right)\left(3-\dfrac1x+\dfrac1{x^3}\right)\right)^{1/3} \\\\ = x^2 \left(9+\dfrac6x-\dfrac1{x^3}+\dfrac4{x^4}+\dfrac1{x^5}-\dfrac1{x^6}\right)^{1/3}[/tex]
[tex]b^{2/3} = \left(3x^3-x^2+1\right)^{2/3} \\\\ = \left(x^3\right)^{2/3} \left(3-\dfrac1x+\dfrac1{x^3}\right)^{2/3} \\\\ = x^2 \left(3-\dfrac1x+\dfrac1{x^3}\right)^{2/3}[/tex]
Now that we see each term in the denominator has a factor of x ², we can eliminate it :
[tex]\displaystyle \lim_{x\to\infty} \frac{4x^2+x-2}{a^{2/3}+(ab)^{1/3}+b^{2/3}} \\\\ = \lim_{x\to\infty} \frac{4x^2+x-2}{x^2 \left(\left(3+\dfrac3x+\dfrac1{x^2}-\dfrac1{x^3}\right)^{2/3} + \left(9+\dfrac6x-\dfrac1{x^3}+\dfrac4{x^4}+\dfrac1{x^5}-\dfrac1{x^6}\right)^{1/3} + \left(3-\dfrac1x+\dfrac1{x^3}\right)^{2/3}\right)}[/tex]
[tex]=\displaystyle \lim_{x\to\infty} \frac{4+\dfrac1x-\dfrac2{x^2}}{\left(3+\dfrac3x+\dfrac1{x^2}-\dfrac1{x^3}\right)^{2/3} + \left(9+\dfrac6x-\dfrac1{x^3}+\dfrac4{x^4}+\dfrac1{x^5}-\dfrac1{x^6}\right)^{1/3} + \left(3-\dfrac1x+\dfrac1{x^3}\right)^{2/3}}[/tex]
As x goes to infinity, each of the 1/x ⁿ terms converge to 0, leaving us with the overall limit,
[tex]\displaystyle \frac{4+0-0}{(3+0+0-0)^{2/3} + (9+0-0+0+0-0)^{1/3} + (3-0+0)^{2/3}} \\\\ = \frac{4}{3^{2/3}+(3^2)^{1/3}+3^{2/3}} \\\\ = \frac{4}{3\cdot 3^{2/3}} = \boxed{\frac{4}{3^{5/3}}}[/tex]
Clarinex-D is a medication whose purpose is to reduce the symptoms associated with a variety of allergies. In clinical trials of Clarinex-D, 5% of patients in the study experienced insomnia as a side effect of taking the medication. Suppose a random sample of 20 patients who took Clarinex-D is obtained and the number of patients who experienced insomnia, X, is recorded. For parts (b)-(d), write a probability statement, such as P(X>3), and calculate the probability (either by hand or using software). Be careful of the wording. Know the difference between less than, at most, etc.
Required:
a. What are the possible values of X?
b. Find the probability that exactly 3 experience insomnia as a side effect?
c. Find the probability 3 or fewer experience insomnia?
d. Between 1 and 4 experience insomnia.
e. Would it be unusual to find 4 or more patients experience insomnia as a side effect?
Using the binomial distribution, it is found that:
a) The possible values of X are between 0 and 20.
b) 0.0596 = 5.96% probability that exactly 3 experience insomnia as a side effect.
c) 0.9842 = 98.42% probability 3 or fewer experience insomnia.
d) 0.639 = 63.9% probability that between 1 and 4 experience insomnia.
e) Since [tex]4 > E(X) + 2.5\sqrt{V(X)}[/tex], it would be unusual to find 4 or more patients experience insomnia as a side effect.
For each patient, there are only two possible outcomes, either they experience insomnia, or they did not. The probability of a patient having experienced insomnia is independent of any other patient, which means that the binomial distribution is used to solve this question.
Binomial probability distribution
Probability of exactly x successes on n trials, with p probability.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The expected value is:
[tex]E(X) = np[/tex]
The standard deviation is:
[tex]\sqrt{V(X)} = \sqrt{np(1 - p)}[/tex]
If a measure is more than 2.5 standard deviations above the mean, it is considered unusual.
In this problem:
20 trials, thus [tex]n = 20[/tex]5% experience insomnia, thus [tex]p = 0.05[/tex]Item a:
The possible values of X are always between 0 and n, thus in this case, it is between 0 and 20.
Item b:
This probability is P(X = 3), thus:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{20,3}.(0.05)^{3}.(0.95)^{17} = 0.0596[/tex]
0.0596 = 5.96% probability that exactly 3 experience insomnia as a side effect.
Item c:
This probability is [tex]P(X \leq 3)[/tex], given by:
[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]
Then:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{20,0}.(0.05)^{0}.(0.95)^{20} = 0.3585[/tex]
[tex]P(X = 1) = C_{20,1}.(0.05)^{1}.(0.95)^{19} = 0.3774[/tex]
[tex]P(X = 2) = C_{20,2}.(0.05)^{2}.(0.95)^{18} = 0.1887[/tex]
[tex]P(X = 3) = C_{20,3}.(0.05)^{3}.(0.95)^{17} = 0.0596[/tex]
[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.3585 + 0.3774 + 0.1887 + 0.0596 = 0.9842[/tex]
0.9842 = 98.42% probability 3 or fewer experience insomnia.
Item d:
This probability is:
[tex]P(1 \leq X \leq 4) = P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)[/tex]
Then
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 1) = C_{20,1}.(0.05)^{1}.(0.95)^{19} = 0.3774[/tex]
[tex]P(X = 2) = C_{20,2}.(0.05)^{2}.(0.95)^{18} = 0.1887[/tex]
[tex]P(X = 3) = C_{20,3}.(0.05)^{3}.(0.95)^{17} = 0.0596[/tex]
[tex]P(X = 4) = C_{20,4}.(0.05)^{4}.(0.95)^{16} = 0.0133[/tex]
[tex]P(1 \leq X \leq 4) = P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.3774 + 0.1887 + 0.0596 + 0.0133 = 0.639[/tex]
0.639 = 63.9% probability that between 1 and 4 experience insomnia.
Item e:
[tex]E(X) = np = 20(0.05) = 1[/tex]
[tex]\sqrt{V(X)} = \sqrt{np(1 - p)} = \sqrt{20(0.5)(0.95)} = 0.975[/tex]
[tex]E(X) + 2.5\sqrt{V(X)} = 1 + 2.5(0.975) = 3.44[/tex]
Since [tex]4 > E(X) + 2.5\sqrt{V(X)}[/tex], it would be unusual to find 4 or more patients experience insomnia as a side effect.
A similar problem is given at https://brainly.com/question/24863377
Need helppppppppppppppp
Answer:22% or A!
Step-by-step explanation: 400 x 9 = 3600 he has ran 792 so far so its about 22.%
The cost of a cantaloupe at the supermarket is represented by the equation c = 1.19p. What does the equation mean? If the cantaloupe weighs 3.5 pounds, what will be the price of the cantaloupe?
Let's say c is the cost of the cantaloupe, and that p is how many pounds the cantaloupe weights.
In that case, $1.19 is the amount of money it will cost per pound of cantaloupe.
If the cantaloupe you buy is 3.5 pounds, it will cost you $4.165, but since money is only two decimal places, and since you can only round up when it's a 5 at the end, it becomes $4.17.
In other words, each pound of cantaluope you buy will cost you $1.19, and a cantaloupe that weighs 3.5 pounds will cost you $4.17.
One of the legs of a right triangle measures 12 cm and the other leg measures 9 cm.
Find the measure of the hypotenuse. If necessary, round to the nearest tenth.
Answer:
cm
Submit Answer
attempt 1 out of 2
שת
Answer:
15
Step-by-step explanation:
Ok, first the formula for this is a^2+b^2=c^2
or leg^2+ leg^2= hypotenuse^2
so (12)^2+(9)^2=hy^2
144+81, 225=hy^2
hy=square root of 225: 15
Sophie invested $170 in an account paying an interest rate of 2\tfrac{3}{4}2 4 3 % compounded continuously. Wyatt invested $170 in an account paying an interest rate of 3\tfrac{1}{8}3 8 1 % compounded monthly. After 9 years, how much more money would Wyatt have in his account than Sophie, to the nearest dollar?
Answer:
$7
Step-by-step explanation:
Wyatt will have $7 more in his account than Sophie.
What is compound interest?Compound interest is the interest you earn on interest.
Given that, Sophie invested $170 in an account paying an interest rate of [tex]2\tfrac{3}{4}[/tex]% compounded continuously.
Wyatt invested $170 in an account paying an interest rate of [tex]3\tfrac{1}{8}[/tex]% compounded monthly.
We need to find how much more money would Wyatt have in his account than Sophie after 9 years,
For compounded continuously = [tex]Amount = Principal \times e^{rt[/tex]
Sophie =
[tex]Amount = 170 \times e^{0.0275 \times 9[/tex]
A = $217.74
Therefore, Sophie will have $217.74 in her account after 9 years.
For Wyatt,
So, using the formula of CI,
[tex]Amount = Principal(1+r/n)^{nt[/tex]
So,
[tex]= 170(1.0026)^{108[/tex]
A = $225
Therefore, Wyatt will have $225 in his account after 9 years.
The amount Wyatt have more than Sophie = 225-217.74 = $7.26 ≈ $7.
Hence Wyatt will have $7 more in his account than Sophie.
Learn more about compound interest click;
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For the points (3.1, -13.4) and (0.1, -9.4), (a) Find the exact distance between the points. (b) Find the midpoint of the line segment whose endpoints are the given points. Darts
i can't type because im slow
Given that sin 2x = cos(2x - 30). Find the value of tan x.
Answer:
x=30o+n90on∈Z
Step-by-step explanation:
cos2x=sin(90o−2x)=sin(2x−30o)
Which mean 90o−2x=2x−30o+n360o
or 90o−2x+2x−30o=(2n+1)180o
The later cannot be true.
so x=30o+n90on∈Z
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The value of tan x is :
[tex]\boxed{ \boxed{ \frac{1}{ \sqrt{3} } }}[/tex]solution is in attachment !
Hello, hope you had a good day, I need help on this pls (:
Answer:
The decimal point should be moved 4 places to the right
Step-by-step explanation:
38.75x10000= 387500
Cecelia is paid $120 for 6 hours of work. At this rate, how much money will she make if she works for 2.5 hours? Show your work or explain your reasoning.
I REALLY NEED IT ITS FOR A SUMMITIVE
Determine the relationship between the two triangles and whether or not they can be proven to be congruent.
Answer:
- ASA stands for "angle, side, angle" and means that we have two triangles where we know two angles and the included side are equal.
- If two angles and the included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.
Step-by-step explanation:
Simplify 6 - (-2) - 3(-5).
6- (-2) - 3(-5)
= 6- (-2) +15
= 6+ 2 +15
= 8+ 15
=23.
Thus, your answer is 23
Answer:
look at the photo..............
How to solve 3,14 x 0,8 =
Answer:
Q1. 3.14 × 0.8 = 2.512
Q2. 6.28 × 6.8 = 42.704
Q3. 25.5 × 9.3 = 237.15
Q4. 1.3 × 5.7 = 7.41
Q5. 7.41 × 3.7 = 27.417
Solve and give answer
Answer:
X=6 Because if you multiply 16×3= 48
and If you do it with 2 it is 2×3= 6
Step-by-step explanation:
16×3= 48
2×3=6
The price of 1kg of potato is ₹ 8 1/2
What will be the price of 2 1/4
kg of potato.
Answer:
₹ 19 1/8.
Step-by-step explanation:
That is 8 1/2 * 2 1/4
= 17/2 * 9/4
= 153/8
= 19 1/8.
Answer:
₹ 19.125 or ₹ 19 1/8
Step-by-step explanation:
1 kg = ₹ 8 1/2
2 1/4 kg = x
8 1/2 can be written as 8.25
2 1/4 can be written as 2.25
To find x:
1. Multiply both sides by 2.25:
1kg × 2.25 = 2.25kg
₹ 8.5 × 2.25 = ₹ 19.125
Answer = ₹ 19.125 or ₹ 19 1/8
Given the functions: f(x)=4x^2-2x+5 and g(x)=x^2+7x=8
1. Find f(x)+g(x)
2. Find g(x)-f(x)
3. Find 5f(x)+g(x)
4. Find g(x)-4f(x)
5. Find f(-2)-g(3)
6. Find g(-2)-f(3)
Answer:
1. f(x)+g(x)=3x−7+x2+5x
2. 5x+x2-7+3x
Step-by-step explanation:
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answer:
The domain is the set of x-values:
{-4, -2, 1, 2, 4}The range is the set of y-values:
{-4, -2, -1, 1, 4}This can be a function as each x- value has exactly one corresponding y- value.
Points are
(-4,-1)(-2,1)(1,-2)(4,-4)(2,4)All x values has a unique image in y so it's a function
[tex]\\ \sf\longmapsto D_f=\{-4,-2,1,4,2\}[/tex]
[tex]\\ \sf\longmapsto R_f=\{-1,1,-2,-4,4\}[/tex]
Find the measures of the labeled angles.
Answer:
x + 93 = 124
Step-by-step explanation:
4x = x + 93 {Vertically opposite angles are equal}
Subtract 'x' from both sides
4x - x = 93
3x = 93
Divide both sides by 3
x = 93/3
x = 31
x + 93 = 31+ 93 = 124
A football team gained 9 yards on one play and then lost 22 yards on the
next. Write a sum of integers to find the overall change in field position
Answer:
9-22=c
-13=c
The football team lost 13 yards in overall change in field position. Meaning, the team didn't gain any yards, they lost 13.
What's the simplified expression of –2a^–3 b^0?
9514 1404 393
Answer:
-2/a^3
Step-by-step explanation:
Anything (except 0) to the 0 power is 1, so b^0 = 1. This immediately simplifies the expression to -2a^-3. If you also want it with positive exponents, this will be ...
-2/a^3
SOMEONE PLEASE HELP ME I HAVE EXACTLY 5 MINUTES LEFT
Answer:
I would estimate 923
Step-by-step explanation:
In the figure below lines m and n are parallel. in the diagram shown, Angle 7 measures 92 degrees. What is the measure of Angle 8?
A. 8 degrees
B. 88 degrees
C. 92 degrees
D. 180 degrees
Answer:
b
Step-by-step explanation:
The sum of angles 7 and 8 is 180, so to find angle 8 you would subtract angle 7 from 180. So:
180 - 92 = 88
The answer is B, 88 degrees.
Answer:
88° is your answer......
Use substitution to solve each system of equations.
y = 5x -2
3 x- 5y =4
Step-by-step explanation:
y = 5x - 2…Equation 1
3x - 5y = 4…Equation 2
Subtitute value of y to Equation 2 :
3x - 5(5x - 2) = 4
3x - 25x + 10 = 4
-22x + 10 = 4
10 - 4 = 22x
6 = 22x
6/22 = x
3/11 = x
Subtitute value of x to one of Equation :
for example Equation 2…
3x - 5y = 4
3(3/11) - 5y = 4
9/11 - 5y = 4
9/11 - 4 = 5y
(9 - 44)/11 = 5y
(-35)/11 = 5y
(-35)/11 × 1/5 = y
-7/11 = y
PLEASE ANSWER THESE QUICK I NEED HELP PLEASE ITS ALGEBRA
1. Describe the graph of y = -|x + 4| - 5.
2. Describe how to use the Vertical Line Test and what it can tell us.
Step-by-step explanation:
1.) y = - |x - 4| - 5 is an absolute value graph, where its vertex occurs at point (4, -5). The general form of the absolute value function is y = a |x – h| + k, where where:
a ≠ 0, and the value of a determines whether the graph opens up or down. If a is between 0 and 1, the graph is wider than the parent function.(h, k ) represents the vertex.The given absolute value function, y = - |x - 4| - 5 is a downward-facing graph, where it is translated 4 units to the right (as given by the value of h = 4), and 5 units downward (as given by the value of k = 5).
2.) The Vertical Line Test allows us to know whether or not a graph is actually a function. If a vertical line intersects the graph in all places at exactly one point, then the relation is a function. To use the vertical-line test, imagine dragging a ruler held vertically across the graph from left to right. If the graph is that of a function, the edge of the ruler would hit the graph only once for every x -value. If you do this for the given graph, every vertical line intersects the graph in at most one point.
Attached is the graph of the given function, where I performed the Vertical Line Test. As evidenced in the graph, every green vertical line intersects the graph at exactly one point (red dots on the graph). Thus, the graph passed the Vertical Line Test, thereby qualifying as a function.
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solve pls brainliest
The sum of 15 and twice Carlos' age.
The sum would be addition. So;
[tex]15\: +[/tex]
Twice means 2 times Carlos' age. And [tex]c[/tex] is the variable, so;
[tex]15+2c[/tex]
Note that 2 and c together like that is multiplication.
Graph the line with y-intercept 1 and slope 3.
Shaundra bought a pipe that was 4 m long. She cut it into equal size pieces. 1 point
Each piece was 2/5 m long. How many pieces were there?
6
10
12
O 100
2 points
There were 400 people at a music festival. 2/5 of them were adults and
9288*300/136=20 488 ,2353
кАК ЗАПИСАТЬ???
Answer:
Step-by-step explanation:
???what
What is the next term of the arithmetic sequence? -7 -7 1 5 9
Answer:
No solution, this is not an arithmetic sequence
Step-by-step explanation:
An arithmetic sequence is the same number being added over and over. This is not the case.
Which decimal number is equal to 49? 0.4 0.44 0.444 0.4⎯⎯
Answer:
0.4⎯⎯
Step-by-step explanation:
BRAINLIEST?