Notice that
6 + 7 = 13
13 + 7 = 20
so if the pattern continues, the underlying sequence in this series is arithmetic with first term a = 6 and difference d = 7. This means the k-th term in the sequence is
a + (k - 1) d = 6 + 7 (k - 1) = 7k - 1
The last term in the series is 111, which means the series consists of 16 terms, since
7k - 1 = 111 ==> 7k = 112 ==> k = 16
Then in summation notation, we have
[tex]\displaystyle 6+13+20+\cdots+111 = \boxed{\sum_{k=1}^{16}(7k-1)}[/tex]
b) Use Greens theorem to find∫x^2 ydx-xy^2 dy where ‘C’ is the circle x2 + y2 = 4 going counter clock wise.
It looks like the integral you want to find is
[tex]\displaystyle \int_C x^2y\,\mathrm dx - xy^2\,\mathrm dy[/tex]
where C is the circle x ² + y ² = 4. By Green's theorem, the line integral is equivalent to a double integral over the disk x ² + y ² ≤ 4, namely
[tex]\displaystyle \iint\limits_{x^2+y^2\le4}\frac{\partial(-xy^2)}{\partial x}-\frac{\partial(x^2y)}{\partial y}\,\mathrm dx\,\mathrm dy = -\iint\limits_{x^2+y^2\le4}(x^2+y^2)\,\mathrm dx\,\mathrm dy[/tex]
To compute the remaining integral, convert to polar coordinates. We take
x = r cos(t )
y = r sin(t )
x ² + y ² = r ²
dx dy = r dr dt
Then
[tex]\displaystyle \int_C x^2y\,\mathrm dx - xy^2\,\mathrm dy = -\int_0^{2\pi}\int_0^2 r^3\,\mathrm dr\,\mathrm dt \\\\ = -2\pi\int_0^2 r^3\,\mathrm dr \\\\ = -\frac\pi2 r^4\bigg|_{r=0}^{r=2} \\\\ = \boxed{-8\pi}[/tex]
Which equation can be used to find the length of Line segment A C?
Answer:
I don't see the problem.
Step-by-step explanation:
Assume that the matrices below are partitioned conformably for block multiplication. Compute the product.
[I 0] [W X]
[K I] [Y Z]
Multiplying block matrices works just like multiplication between regular matrices, provided that component matrices have the right sizes.
[tex]\begin{bmatrix}\mathbf I&\mathbf 0\\\mathbf K&\mathbf I\end{bmatrix}\begin{bmatrix}\mathbf W&\mathbf X\\\mathbf Y&\mathbf Z\end{bmatrix} = \begin{bmatrix}\mathbf{IW}+\mathbf{0Y}&\mathbf{IX}+\mathbf{0Z}\\\mathbf{KW}+\mathbf{IY}&\mathbf{KX}+\mathbf{IZ}\end{bmatrix}[/tex]
[tex]\begin{bmatrix}\mathbf I&\mathbf 0\\\mathbf K&\mathbf I\end{bmatrix}\begin{bmatrix}\mathbf W&\mathbf X\\\mathbf Y&\mathbf Z\end{bmatrix} = \begin{bmatrix}\mathbf W+\mathbf 0&\mathbf X+\mathbf 0\\\mathbf{KW}+\mathbf Y&\mathbf{KX}+\mathbf Z\end{bmatrix}[/tex]
[tex]\begin{bmatrix}\mathbf I&\mathbf 0\\\mathbf K&\mathbf I\end{bmatrix}\begin{bmatrix}\mathbf W&\mathbf X\\\mathbf Y&\mathbf Z\end{bmatrix} = \begin{bmatrix}\mathbf W&\mathbf X\\\mathbf{KW}+\mathbf Y&\mathbf{KX}+\mathbf Z\end{bmatrix}[/tex]
(I assume I is the identity matrix and 0 is the zero matrix.)
A history teacher gives a 17 question True or false exam. In how many different ways can the test be answered if the possible answers are true or false or possibly to leave the answer blank?
Answer:
Step-by-step explanation:
if it's only true or false there are 2¹⁷=131072 outcomes
if it's true, false, or blank there are 3¹⁷=129140163 outcomes
Suppose Event A is taking 15 or more minutes to get to work tomorrow and Event B is taking less than 15 minutes to get to work tomorrow. Events A and B are said to be complementary events.
a. True
b. False
Answer:
Hence the answer is TRUE.
Step-by-step explanation:
If event A is taking 15 or more minutes to urge to figure tomorrow and event B is taking but a quarter-hour to urge to figure tomorrow, then events A and B must be complimentary events. this is often because the occurring of 1 is going to be precisely the opposite of the occurring of the opposite event and that they cannot occur simultaneously. In other words, events A and B are mutually exclusive and exhaustive.
Mathematically,
P(A) + P(B) = 1.
what is the least common multiple between 25 and 8
Answer:
200
Step-by-step explanation:
Break down 25 = 5*5
Break down 8 = 2*2*2
They have no common factors
The least common multiple is
5*5*2*2*2 = 25*8 = 200
Answer:
200
Step-by-step explanation:
list the factors of 25: 5,5
factors of 8:2,2,2,
If a seed is planted, it has a 90% chance of growing into a healthy plant.
If 6 seeds are planted, what is the probability that exactly 2 don't grow?
Answer:
[tex]\displaystyle\frac{19,683}{200,000}\text{ or }\approx 9.84\%[/tex]
Step-by-step explanation:
For each planted seed, there is a 90% chance that it grows into a healthy plant, which means that there is a [tex]100\%-90\%=10\%[/tex] chance it does not grow into a healthy plant.
Since we are planting 6 seeds, we want to choose 2 that do not grow and 4 that do grow:
[tex]\displaystyle \frac{1}{10}\cdot \frac{1}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}[/tex]
However, this is only one case that meets the conditions. We can choose any 2 out of the 6 seeds to be the ones that don't grow into a healthy plant, not just the first and second ones. Therefore, we need to multiply this by number of ways we can choose 2 things from 6 (6 choose 2):
[tex]\displaystyle \binom{6}{2}=\frac{6\cdot 5}{2!}=\frac{30}{2}=15[/tex]
Therefore, we have:
[tex]\displaystyle\\P(\text{exactly 2 don't grow})=\frac{1}{10}\cdot \frac{1}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \binom{6}{2},\\\\P(\text{exactly 2 don't grow})=\frac{1}{10}\cdot \frac{1}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot 15,\\\\P(\text{exactly 2 don't grow})=\boxed{\frac{19,683}{200,000}}\approx 9.84\%[/tex]
Answer:
[tex] {?}^{?} However, this is only one case that meets the conditions. We can choose any 2 out of the 6 seeds to be the ones that don't grow into a healthy plant, not just the first and second ones. Therefore, we need to multiply this by number of ways we can choose 2 things from 6 (6 choose 2):
\displaystyle \binom{6}{2}=\frac{6\cdot 5}{2!}=\frac{30}{2}=15(26)=2!6⋅5=230=15
Therefore, we have:
\begin{gathered}\displaystyle\\P(\text{exactly 2 don't grow})=\frac{1}{10}\cdot \frac{1}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \binom{6}{2},\\\\P(\text{exactly 2 don't grow})=\frac{1}{10}\cdot \frac{1}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot 15,\\\\P(\text{exactly 2 don't grow})=\boxed{\frac{19,683}{200,000}}\approx 9.84\%\end{gathered}P(exactly 2 don’t grow)=101⋅101⋅109⋅109⋅109⋅109⋅(26),P(exactly 2 don’t grow)=101⋅101⋅109⋅109⋅109⋅109⋅15,P(exactly 2 don’t grow)=200,00019,683≈9.84%
[/tex]
find the missing length indicated
explainion:
[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]
Use The (Pythagorean Theorem) to find the length of any side of a right triangle. Form it like its shown in picture above. Follow the instructions that also shown in the picture above.
Question with last attempt is displayed for your review only
Amanda rented a bike from Ted's Bikes.
It costs $9 for the helmet plus $5.25 per hour.
If Amanda paid about $43.13, how many hours did she rent the bike?
Let h = the number of hours she rented the bike. Write the equation you would use to solve this problem.
Answer:
[tex]43.13 = 5.25h + 9[/tex]
Step-by-step explanation:
Let's solve this by making an equation.
$9 for the helmet, and $5.25 per hour.
h will stand for hours, C will stand for Amanda's cost.
[tex]C = 5.25h + 9[/tex]
Now, substitute in what we learned from the problem.
[tex]43.13 = 5.25h + 9[/tex]
This is an equation you can use to solve for the hours.
While walking in the country, you count 39 heads and 116 feet in a field of cows and chickens. How many of each animal are there?
Answer: 58
Step-by-step explanation:
its 58 because chickens have two feet each so divide 2 % 166 and its 58
because each chicken has 2 legs count the 2 legs up to 116 then u get ur answer
Can someone help me out plz
Volume = πr²h
Radius = 3yd
Height = 12yd
Take π = 22/7
Volume = 22/7×3×3×12
= 2376/7
= 339.4285714yd³
Rounding off to nearest tenth
= 339.43yd³
Answered by Gauthmath must click thanks and mark brainliest
The population standard deviation for the heights of dogs, in inches, in a city is 3.7 inches. If we want to be 95% confident that the sample mean is within 2 inches of the true population mean, what is the minimum sample size that can be taken?
z0.101.282z0.051.645z0.0251.960z0.012.326z0.0052.576
Use the table above for the z-score, and be sure to round up to the nearest integer.
========================================================
Explanation:
At 95% confidence, the z critical value is roughly z = 1.960
The population standard deviation is given to be sigma = 3.7
The error is E = 2 since we want to be within 2 inches of the population mean mu
The min sample size needed is:
n = (z*sigma/E)^2
n = (1.960*3.7/2)^2
n = 13.147876
n = 14
We always round up to the nearest whole number to ensure that we clear the hurdle (otherwise, the sample is too small). It doesn't matter that we're closer to 13 than to 14.
May I get some help with this question?
Karissa purchased a set of LED lights online that normally sells for $72.00 but was marked down to $48.96. What is the discount rate Karissa received? (2 points)
32%
47%
68%
please help this is due right now
Answer:
108.82
Step-by-step explanation:
Help please ….. help
Answer:
Step-by-step explanation:
a) categorical
b) add all of the numbers and divide by how many numbers there were.
c) outliers means any that were far away from the rest of the data
d) not entirely, you can make an estimate based on it, but nat an exact answer.
in how many ways 6 gentleman and 4 ladies can be choosen out of 10 gentleman and 8 ladies?
Answer:
5880 ways
Step-by-step explanation:
For selections like this, we solve using the combination theory. Recall that
nCr = n!/(n-r)!r!
Hence given to find the number of ways 6 gentleman and 4 ladies can be choosen out of 10 gentleman and 8 ladies,
= 10C6 * 8C4
= 10!/(10-6)!6! * 8!/(8-6)!6!
= 10 * 9 * 8 * 7 * 6!/4 *3 *2 * 6! * 8 * 7 * 6!/2 * 6!
= 210 * 28
= 5880 ways
The arrangement can be done in 5880 ways
A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment.
n=12, p=0.35, x=2
Answer:
0.1088 or 10.88%
Step-by-step explanation:
q = 1 - 0.35 = 0.65
P(X=2) = 12C2 × (0.35)² × (0.65)¹⁰
= 0.1088
Shaun is planting trees along his driveway, and he has 66 redwoods and 66 pine trees to plant in one row. What is the probability that he randomly plants the trees so that all 66 redwoods are next to each other and all 66 pine trees are next to each other
Answer:
0.0022 = 0.22% probability that he randomly plants the trees so that all 6 redwoods are next to each other and all 6 pine trees are next to each other.
Step-by-step explanation:
The trees are arranged, so the arrangements formula is used to solve this question. Also, a probability is the number of desired outcomes divided by the number of total outcomes.
Arrangements formula:
The number of possible arrangements of n elements is given by:
[tex]A_n = n![/tex]
Desired outcomes:
Two cases:
6 redwoods(6! ways) then the 6 pine trees(6! ways)
6 pine trees(6! ways) then the 6 redwoods(6! ways)
So
[tex]D = 2*6!*6![/tex]
Total outcomes:
12 trees, so:
[tex]D = 12![/tex]
What is the probability that he randomly plants the trees so that all 6 redwoods are next to each other and all 6 pine trees are next to each other?
[tex]p = \frac{D}{T} = \frac{2*6!*6!}{12!} = 0.0022[/tex]
0.0022 = 0.22% probability that he randomly plants the trees so that all 6 redwoods are next to each other and all 6 pine trees are next to each other.
A student majoring in accounting is trying to decide on the number of firms to which he should apply. Given his work experience and grades, he can expect to receive a job offer from 70% of the firms to which he applies. The student decides to apply to only four firms.
(a) What is the probability that he receives no job offer?
(b) How many job offers he expects to get?
(c) What is the probability that more than half of the firms he applied do not make him any offer?
(d) What assumptions do you need to make to find the probabilities? To increase the chance of securing more job offers, the student decides to apply to as many companies as possible, he sent out 60 applications to all different accounting firms.
(e) What is the probability of him securing more than 3 offers?
Answer:
a) 0.0081 = 0.81% probability that he receives no job offer
b) He expects to get 2.8 job offers.
c) 0.0837 = 8.37% probability that more than half of the firms he applied do not make him any offer.
d) Each job must be independent of other jobs. Additionaly, if [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex], the normal approximation to the binomial distribution can be used.
e) 0.2401 = 24.01% probability of him securing more than 3 offers.
Step-by-step explanation:
For each application, there are only two possible outcomes. Either he gets an offer, or he does not. The probability of getting an offer for a job is independent of any other job, which 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.
He can expect to receive a job offer from 70% of the firms to which he applies.
This means that [tex]p = 0.7[/tex]
The student decides to apply to only four firms.
This means that [tex]n = 4[/tex]
(a) What is the probability that he receives no job offer?
This is [tex]P(X = 0)[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{4,0}.(0.7)^{0}.(0.3)^{4} = 0.0081[/tex]
0.0081 = 0.81% probability that he receives no job offer.
(b) How many job offers he expects to get?
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
In this question:
[tex]E(X) = 4(0.7) = 2.8[/tex]
He expects to get 2.8 job offers.
(c) What is the probability that more than half of the firms he applied do not make him any offer?
Less than 2 offers, which is:
[tex]P(X < 2) = P(X = 0) + P(X = 1)[/tex]
So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{4,0}.(0.7)^{0}.(0.3)^{4} = 0.0081[/tex]
[tex]P(X = 1) = C_{4,1}.(0.7)^{1}.(0.3)^{3} = 0.0756[/tex]
Then
[tex]P(X < 2) = P(X = 0) + P(X = 1) = 0.0081 + 0.0756 = 0.0837[/tex]
0.0837 = 8.37% probability that more than half of the firms he applied do not make him any offer.
(d) What assumptions do you need to make to find the probabilities? To increase the chance of securing more job offers, the student decides to apply to as many companies as possible, he sent out 60 applications to all different accounting firms.
Each job must be independent of other jobs. Additionaly, if [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex], the normal approximation to the binomial distribution can be used.
(e) What is the probability of him securing more than 3 offers?
Between 4 and n, since n is 4, 4 offers, so:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 4) = C_{4,4}.(0.7)^{4}.(0.3)^{0} = 0.2401[/tex]
0.2401 = 24.01% probability of him securing more than 3 offers.
Find the length of the missing side
Answer:
Step-by-step explanation:
Side=AC=9[tex]\sqrt{2}[/tex]
Side AB= x
Hypotenuse =CB= y
Side AB = 9[tex]\sqrt{2}[/tex]
Hypotenuse CB = 36
Enter a formula in cell B10 to return the value of 35000 if the net profit after tax cell B9 is greater than or equal to 470000 or 100 if it is not
Answer:
I hope it help and I guess it is correct
help fast please
how far does light travel per second?
9514 1404 393
Answer:
3×10^8 m/s
Step-by-step explanation:
The desired speed is ...
[tex]\dfrac{\dfrac{9.45\times10^{15}\text{ m}}{\text{yr}}}{\dfrac{3.15\times10^7\text{ s}}{\text{yr}}}=\dfrac{9.45}{3.15}\times10^{15-7}\text{ m/s}=\boxed{3.00\times10^8\text{ m/s}}[/tex]
__
Your calculator can help you figure this out.
what percent of 70 is 35
Answer:
50%
Step-by-step explanation:
35 is halve of 70 therefore it is 50%
hope it helps u...........
Find m
a 24.7
b 79.2
c 68.3
d 57.4
e 46.5
f 80.1
g 35.6
Answer:
68.3 degrees
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan I = opp side / adj side
tan I = sqrt(82) / sqrt(13)
tan I = sqrt(82/13)
Taking the inverse tan of each side
tan ^-1 ( tan I) = tan ^-1( sqrt(82/13))
I = 68.2892
Rounding to the nearest tenth
I = 68.3 degrees
A.) Evaluate f(1)
B.) given: f(x) =1, find x
Answer:
f(1) = -2
f(x) =1 when x=0 or x=-2
Step-by-step explanation:
f(1) is the y value when x=1
f(1) = -2
f(x) = 1 means find the x value when y=1
when y =1, x =0 and -2
An expression is shown below:
6x2y − 3xy − 24xy2 + 12y2
Part A: Rewrite the expression by factoring out the greatest common factor. (4 points)
Part B: Factor the entire expression completely. Show the steps of your work. (6 points)
Given:
The given expression is:
[tex]6x^2y-3xy-24xy^2+12y^2[/tex]
To find:
Part A: The expression by factoring out the greatest common factor.
Part B: Factor the entire expression completely.
Solution:
Part A:
We have,
[tex]6x^2y-3xy-24xy^2+12y^2[/tex]
Taking out the highest common factor 3y, we get
[tex]=3y(2x^2-x-8xy+4y)[/tex]
Therefore, the required expression is [tex]3y(2x^2-x-8xy+4y)[/tex].
Part B:
From part A, we have,
[tex]3y(2x^2-x-8xy+4y)[/tex]
By grouping method, we get
[tex]=3y(x(2x-1)-4y(2x-1))[/tex]
[tex]=3y(x-4y)(2x-1)[/tex]
Therefore, the required factored form of the given expression is [tex]3y(x-4y)(2x-1)[/tex].
Customers receive rewards pints based on the purchase type:
Select the statement that best justifies the conclusion based on the given information.
If a(b + c) = d, then ab + ac = d.
associative
commutative
distributive
closure
Answer:
distributive
Step-by-step explanation:
a(b + c)=ab + ac
it's distributive one
Charity is planting trees along her driveway, and she has 6 pine trees and 6 willows to plant in one row. What is the probability that she randomly plants the trees so that all 6 pine trees are next to each other and all 6 willows are next to each other
Answer:
0.0022 = 0.22% probability that she randomly plants the trees so that all 6 pine trees are next to each other and all 6 willows are next to each other.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this question, the elements are arranged, so we have to use the arrangements formula.
Arrangements formula:
The number of possible arrangements of n elements is:
[tex]A_{n} = n![/tex]
Desired outcomes:
Pine trees(6!) then the willows(6!) or
Willows(6!) then the pine trees(6!). So
[tex]D = 2*6!*6! = 1036800 [/tex]
Total outcomes:
12 trees, so:
[tex]T = 12! = 479001600 [/tex]
What is the probability that she randomly plants the trees so that all 6 pine trees are next to each other and all 6 willows are next to each other?
[tex]p = \frac{D}{T} = \frac{1036800 }{479001600 } = 0.0022[/tex]
0.0022 = 0.22% probability that she randomly plants the trees so that all 6 pine trees are next to each other and all 6 willows are next to each other.
