It looks like you want to find
[tex]\displaystyle \int t^{11} e^{-t^6}\,\mathrm dt[/tex]
Substitute u = -t ⁶ and du = -6t ⁵ dt. Then
[tex]\displaystyle \int t^{11} e^{-t^6}\,\mathrm dt = \frac16 \int (-6t^5) \times (-t^6) e^{-t^6}\,\mathrm dt = \frac16 \int ue^u \,\mathrm du[/tex]
Integrate by parts, taking
f = u ==> df = du
dg = eᵘ du ==> g = eᵘ
Then
[tex]\displaystyle \frac16 \int ue^u \,\mathrm du = \frac16\left(fg-\int g\,\mathrm df\right) \\\\ =\frac16 ue^u - \frac16\int e^u\,\mathrm du \\\\ =\frac16 ue^u - \frac16 e^u + C \\\\ =-\frac16 t^6 e^{-t^6} - \frac16 e^{-t^6} + C \\\\ =\boxed{-\frac16 e^{-t^6} \left(t^6+1\right) + C}[/tex]
The value of square root of -9 is not -3 because
Answer:
The square root of -9 cannot be -3 because -3 squared or -3 times -3 equals 9 not -9.
Hope this helps!
Consider the probability that greater than 26 out of 124 software users will call technical support. Assume the probability that a given software user will call technical support is 97%. Specify whether the normal curve can be used as an approximation to the binomial probability by verifying the necessary conditions.
Answer:
Since [tex]n(1-p) = 3.72 < 10[/tex], the normal curve cannot be used as an approximation to the binomial probability.
100% probability that greater than 26 out of 124 software users will call technical support.
Step-by-step explanation:
Test if the normal curve can be used as an approximation to the binomial probability by verifying the necessary conditions.
It is needed that:
[tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex]
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.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
Out of 124 software users
This means that [tex]n = 124[/tex]
Assume the probability that a given software user will call technical support is 97%.
This means that [tex]p = 0.97[/tex]
Conditions:
[tex]np = 124*0.97 = 120.28 \geq 10[/tex]
[tex]n(1-p) = 124*0.03 = 3.72 < 10[/tex]
Since [tex]n(1-p) = 3.72 < 10[/tex], the normal curve cannot be used as an approximation to the binomial probability.
Consider the probability that greater than 26 out of 124 software users will call technical support.
The lowest possible probability of those is 27, so, if it is 0, since it is considerably below the mean, 100% probability of being greater. We have that:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 27) = C_{124,27}.(0.97)^{27}.(0.03)^{97} = 0[/tex]
1 - 0 = 1
100% probability that greater than 26 out of 124 software users will call technical support.
is the sequence 1/6, 1/2, 3/2,9/2 arithmetic, or geometric
Answer:
geometric
Step-by-step explanation:
write your answer as an integer or as a decimal rounded to the nearest tenth
Answer:Mark Brainliest please
Answer is 4.86 which is rounded to 5
Step-by-step explanation:
Cos 40 degree = VW/7
0.694 =VW/7
0.694 * 7 =VW
4.858 =VW
VW=4.86 is the answer
Two cards are selected with replacement from a standard deck of 52 cards. Find the probability of selecting a heart and then selecting a diamond.
Answer: 50.2 is it
Step-by-step explanation: thats easy
Probability helps us to know the chances of an event occurring. The probability of selecting a heart and then selecting a diamond is 144/2652.
What is Probability?Probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
Given that Two cards are selected with replacement from a standard deck of 52 cards. Therefore, the probability of selecting a heart and then selecting a diamond is,
Probability = (12/52) × (12/51)
Probability = 144/2652
Hence, The probability of selecting a heart and then selecting a diamond is 144/2652.
Learn more about Probability:
https://brainly.com/question/795909
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if PQR measures 75° , what is the measure of SQR
Answer:
PQR+SQR=180°(angles in a triangle)
75°+SQR=180°
SQR=180°-75°
SQR=105°
Which figure always has exactly one line of symmetry?
A. rectangle
B. trapezoid
C. isosceles right triangle
D. circle
A shape of a trapezoid has exactly one line of symmetry. The correct option is B.
What is a trapezoid?An open, flat object with four straight sides and one pair of parallel sides is referred to as a trapezoid or trapezium.
A balanced and proportionate likeness between an object's two halves is referred to as symmetry in geometry. It implies that one half is the other's mirror image.
A trapezium's non-parallel sides are referred to as the legs, while its parallel sides are referred to as the bases. The legs of a trapezium can also be parallel. The parallel sides may be vertical, horizontal, or angled.
Therefore, the shape of a trapezoid has exactly one line of symmetry. The correct option is B.
To know more about Trapezoids follow
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Find the length of x
Answer:
32
Step-by-step explanation:
Let's assume that the triangles are similar.
[tex]\frac{16}{12} = \frac{24}{18} = \frac{x}{24}[/tex]
[tex]\frac{x}{24} = \frac{4}{3} => x = \frac{24}{3} * 4= 8 * 4 = 32[/tex]
Dưới đây là bảng CĐKT gần đây nhất của VNA:
ĐVT: tỷ đồng
TÀI SẢN
NGUỒN VỐN
Tài sản lưu động
Tài sản cố định
Tổng tài sản
11.30
21.35
32.65
Nợ ngắn hạn (NH)
Nợ dài hạn
Vốn cổ phần ưu đãi
Vốn cổ phần thường
Tổng nguồn vốn
10.69
9.46
2.50
10.00
32.65
Biết: Nợ NH không chịu bất kỳ khoản phí nào, chi phí trung bình nợ NH sau thuế là 5.5%;
Chi phí nợ dài hạn trước thuế là 11.5%;
Tỷ suất sinh lời cần thiết trên vốn cổ phần ưu đãi là 13.5%; hệ số beta = 1,25
Tỷ suất lợi nhuận cho rủi ro thị trường là 8%; tỷ lệ lãi suất trái phiếu cũng 8%
Thuế TNDN là 32%.
Yêu cầu:
Tính chi phí vốn của mỗi nguồn nợ ngắn hạn, nợ dài hạn, vốn cổ phần ưu đãi, vốn cổ phần phổ thông?
Tính chi phí bình quân gia quyền vốn WACC của VNA?
equation of a line with slope -1 and y intercept 0,-2
Answer:
y = - x - 2
Step-by-step explanation:
y=mx+b
m refers to slope
b refers to y intercept
y = (-1)x + (-2)
y = - x - 2
Answer:
y=-1x-2
Step-by-step explanation:
plug in the slop and y intercept to the equation y=mx+b
Mr. Jerome has an outstanding balance of $12000 on his credit card. The interest rate on the card is 12% he intends to pay off
the card in 2 years. Find the APR on the card.
The midpoint of has coordinates of (4, -9). The endpoint A has coordinates (-3, -5). What are the coordinates of B?
9514 1404 393
Answer:
(11, -13)
Step-by-step explanation:
If midpoint M is halfway between A and B:
M = (A +B)/2
Then B is ...
B = 2M -A
B = 2(4, -9) -(-3, -5) = (8+3, -18+5)
B = (11, -13)
Answer:
Use the midpoint formula:
[tex]midpoint=(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2})[/tex]
Endpoint A = (x₁, y₁) = (-3, -5)Endpoint B = (x₂, y₂)Midpoint = (4, -9)Substitute in the values:
[tex](4, -9)=(\frac{-3+x_{2}}{2} +\frac{-5+y_{2}}{2} )[/tex]
[tex]4=\frac{-3+x_{2}}{2} \\4(2)=-3+x_{2}\\8+3=x_{2}\\x_{2}=11[/tex] [tex]-9=\frac{-5+y_{2}}{2} \\(-9)(2)=-5+y_{2}\\-18+5=y_{2}\\y_{2}=-13[/tex]
Therefore, Point B = (11, -13)
From a club of 18 people, in how many ways can a group of five members be selected to attend a conference?
1. Đường kính của một loại trục máy là một đại lượng ngẫu nhiên có phân phối chuẩn N (μ = 250mm, σ2 = 25mm2). Trục máy được gọi là hợp quy cách nếu đường kính từ 245mm đến 255mm. Cho máy sản xuất 100 trục. Tính xác suất để:
a. Có 50 trục hợp quy cách.
b. Có không quá 80 trục hợp quy cách
Answer:
cannot understand the language man
but please follow
Help with 5b please . thank you.
Answer:
See explanation
Step-by-step explanation:
We are given f(x)=ln(1+x)-x+(1/2)x^2.
We are first ask to differentiate this.
We will need chain rule for first term and power rule for all three terms.
f'(x)=(1+x)'/(1+x)-(1)+(1/2)×2x
f'(x)=(0+1)/(1+x)-(1)+x
f'(x)=1/(1+x)-(1)+x
We are then ask to prove if x is positive then f is positive.
I'm thinking they want us to use the derivative part in our answer.
Let's look at the critical numbers.
f' is undefined at x=-1 and it also makes f undefined.
Let's see if we can find when expression is 0.
1/(1+x)-(1)+x=0
Find common denominator:
1/(1+x)-(1+x)/(1+x)+x(1+x)/(1+x)=0
(1-1-x+x+x^2)/(1+x)=0
A fraction can only be zero when it's numerator is.
Simplify numerator equal 0:
x^2=0
This happens at x=0.
This means the expression,f, is increasing or decreasing after x=0. Let's found out what's happening there. f'(1)=1/(1+1)-(1)+1=1/2 which means after x=0, f is increasing since f'>0 after x=0.
So we should see increasing values of f when we up the value for x after 0.
Plugging in 0 gives: f(0)=ln(1+0)-0+(1/2)0^2=0.
So any value f, after this x=0, should be higher than 0 since f(0)=0 and f' told us f in increasing after x equals 0.
What function translates the function f(x)=|x| to the left 3 units and down 4 units?
A particle is moving with the given data. Find the position of the particle.
a(t) = [tex]t^{2}[/tex] − 4t + 5, s(0) = 0, s(1) = 20
How do I find s(t)=?
Recall that
[tex]\dfrac{dv(t)}{dt} = a(t) \Rightarrow dv(t) = a(t)dt[/tex]
Integrating this expression, we get
[tex]\displaystyle v(t) = \int a(t)dt = \int(t^2 - 4t + 5)dt[/tex]
[tex]\:\:\:\:\:\:\:= \frac{1}{3}t^3 - 2t^2 + 5t + C_1[/tex]
Also, recall that
[tex]\dfrac{ds(t)}{dt} = v(t)[/tex] or
[tex]\displaystyle s(t) = \int v(t)dt = \int (\frac{1}{3}t^3 - 2t^2 + 5t + C_1)dt[/tex]
[tex]\:\:\:\:\:\:\:= \frac{1}{12}t^4 - \frac{2}{3}t^3 + \frac{5}{2}t^2 + C_1t + C_2[/tex]
Next step is to find [tex]C_1\:\text{and}\:C_2[/tex]. We know that at t = 0, s = 0, which gives us [tex]C_2 = 0[/tex]. At t = 1, s = 20, which gives us
[tex]s(1) = \frac{1}{12}(1)^4 - \frac{2}{3}(1)^3 + \frac{5}{2}(1)^2 + C_1(1)[/tex]
[tex]= \frac{1}{12} - \frac{2}{3} + \frac{5}{2} + C_1 = \frac{23}{12} + C_1 = 20[/tex]
or
[tex]C_1 = \dfrac{217}{12}[/tex]
Therefore, s(t) can be written as
[tex]s(t) = \frac{1}{12}t^4 - \frac{2}{3}t^3 + \frac{5}{2}t^2 + \frac{217}{12}t[/tex]
write fifty and two hundreds eight thousandths as a mixed decimal
Answer:
Pretty sure it's 0.528
Express the confidence interval
2. What is the number 643,581 rounded off
to the thousands place?
(1) 640,000
(2) 643,000
(3) 643,600
(4) 644,000
(5) 644,600
Answer:
(4) 644,000
Step-by-step explanation:
643,581
The 3 is in the thousands place
We look at the hundreds place
5
It is 5 or greater so we round the thousands place up 1
644000
write your answer in simplest radical form
9514 1404 393
Answer:
4√2
Step-by-step explanation:
In a 30°-60°-90° triangle, the ratio of side lengths is ...
1 : √3 : 2
That is, the hypotenuse (c) is double the short side (2√2).
c = 4√2
Use order of operations to solve. PEMDAS
7 + 8(32-2)
Answer:
247
Step-by-step explanation:
7 + 8(32-2)
Parentheses first
7 + 8(30)
Then multiply
7+240
Then add
247
Answer:
247
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
Identify
7 + 8(32 - 2)
Step 2: Evaluate
(Parenthesis) Subtract: 7 + 8(30)Multiply: 7 + 240Add: 247There are 165 children taking swimming lessons at the pool. If 10 children will be assigned to each instructor, how many instructors are needed?
Answer:
17 instructors
Step-by-step explanation:
If each instructor will get 10 children, we have to divided the total number of children taking swimming lessons by the number of children assigned to each instructor (10):
165/10 = 16.5
Unfortunately, we can't have 16 and a half instructors. Since 5 children are remaining, we can round up 16.5 to 17 and get 17 instructors. This implies that 16 instructors will teach 10 children (160 in total) and 1 instructor will teach 5 children (5 in total). 160+5 = 165 total children.
The following three shapes are based only on squares, semi circles, and quarter circles. Find the perimeter in the area of each shaded part
Answer: 46.26
Step-by-step explanation:
Since it is a square the sides are all the same, and since it’s a half circle, the dashed line is the diameter of the circle. To find the circumference on a circle, the equation is diameter times pi. 3.14 is commonly used for pi which is what I’m using 3.14, but of you are told to use a different number use that. 9*3.14 is 28.26. Since ther are exactly two half circles in the diameter, here’s no point in dividing by 2. The rest of the perimeter are just 2 sides of the square. So 9+9+28.26 is 46.26.
properties of exponents. the answer is 1/2^12 i need help with the work
Step-by-step explanation:
Answer in attached image...
hope it helps
(2^-1 -2^-1 × 2^-4)^2
(1/2 - 1/2 × 1/2^4)^2
(1/2 - 1/2^5)^2
(1/2 - 1/32)^2
(16/32-1/32)^2
(15/32)^2
(15/2^5)^2
Must click thanks and mark brainliest
Assume that human body temperatures are normally distributed with a mean of 98.19 and a standard deviation of 0.61
Answer:
Ok I'm assuming that know what??
Step-by-step explanation:
How do you find the area of a parallelogram?
.A = lw
.A = bh
.A = 1/2 bh
.A = 1/3 bh
Answer:
1/2 bh
Step-by-step explanation:
Step-by-step explanation:
parallelogram has base and height so area of parallelogram is
A= bh
Work out the surface area of this solid quarter cylinder. give your answer in terms of pi. r:8cm h:15cm
Answer:
248 pi cm^2
Step-by-step explanation:
The surface area of a cylinder is given by
SA = 2 pi r^2 + pi rh where r is the radius and h is the height
= 2 pi( 8)^2 + pi (8)(15)
128 pi +120pi
248pi
what is the sign of x/y times 7y^3 when x<0 and y>0? A. Positive B. Negative C. Zero
X <0 means x would be negative.
For x/y, a negative divided by a positive would give a negative answer.
A negative multiplied by a positive would result in a negative.
The answer would be B. Negative
[tex] - x ^{2} + 2x - 6 = 0[/tex]
how to do,I don't know the step
answer is
[tex]x = 1 - \sqrt{5} i \: \: \: \: \: or \: \: 1 + \sqrt{5} i[/tex]
Answer:
there are several methods to "solve a quadratic"
you can look them all up...
Graphing, factoring, completing the square, taking roots, quadratic formula are the common methods....
given the way you are asking the question I think that you are supposed to use the quadratic formula ..
please look at the image of the formula and
realize that you problem has
a=-1
b=2
c=6
just plug in those numbers into the formula and you will get the results in the "answer"
NOTE [tex]\sqrt{-x}[/tex] is written as ix ( [tex]\sqrt{-25} = 5i[/tex] )
Step-by-step explanation:
x= -2+√ (2)²- (4)(-1)(-6)
(2)(-1)
and
x= -2-√ (2)²- (4)(-1)(-6)
(2)(-1)
