Answer:
f(g(x)) = 9x^2 + 15x - 6
Step-by-step explanation:
We are using function g(x) = 3x - 1 as the input to function f(x) = x^2 + 7x.
Starting with f(x) = x^2 + 7x, substitute g(x) for x on the left side and likewise substitute x^2 + 7x for each x on the right side. We obtain:
f(g(x)) = (3x - 1)^2 + 7(3x - 1).
If we multiply this out, we get:
f(g(x)) = 9x^2 - 6x + 1 + 21x - 7, or
f(g(x)) = 9x^2 + 15x - 6
According to Zimmels (1983), the sizes of particles used in sedimentation experiments often have a uniform distribution. In sedimentation involving mixtures of particles of various sizes, the larger particles hinder the movements of the smaller ones. Thus, it is important to study both the mean and the variance of particle sizes. Suppose that spherical particles have diameters that are uniformly distributed between 0.02 and 0.08 centimeters. Find the mean and variance of the volumes of these particles. (Recall that the volume of a sphere is (4/3) πr3) Round your answers to four decimal places.
E(Y)= ___ x10−5 cm3
V(Y) = ___ x10−9
The expected value of a normal distribution is the mean of the distribution, while the variance measures the squared deviation of a value from the expected value. The expected value and the variance are: [tex]13.6190 \times 10^{-5}[/tex] and [tex]580.8000 \times 10^{-9}[/tex]
Given that, the diameters are:
[tex]d_1 = 0.02[/tex]
[tex]d_2 = 0.08[/tex]
The radius is:
[tex]r = \frac{d}{2}[/tex]
So, we have:
[tex]r_1 = \frac{0.02}{2} = 0.01[/tex]
[tex]r_2 = \frac{0.08}{2} = 0.04[/tex]
The volume of the sphere is:
[tex]V = \frac{4}{3} \times \pi \times r^3[/tex]
For [tex]r_1 = 0.01[/tex], the volume is:
[tex]V_1 = \frac{4}{3} \times \frac{22}{7} \times 0.01^3 = 0.419047 \times 10^{-5}[/tex]
For [tex]r_2 = 0.04[/tex], the volume is
[tex]V_2 = \frac{4}{3} \times \frac{22}{7} \times 0.04^3 = 26.819047 \times 10^{-5}[/tex]
The mean of a uniform distribution is:
[tex]E(y) = \frac{a + b}{2}[/tex]
In this case, the mean is:
[tex]E(y) = \frac{V_1 + V_2}{2}[/tex]
So, we have:
[tex]E(y) = \frac{0.419047 \times 10^{-5} + 26.819047 \times 10^{-5}}{2}[/tex]
[tex]E(y) = \frac{27.238094\times 10^{-5} }{2}[/tex]
[tex]E(y) = 13.619047 \times 10^{-5}[/tex]
Approximate
[tex]E(y) = 13.6190 \times 10^{-5}[/tex]
The variance of a uniform distribution is:
[tex]V(y) = \frac{(b-a)^2}{12}[/tex]
In this case, the volume is:
[tex]V(y) = \frac{(V_2-V_1)^2}{12}[/tex]
So, we have:
[tex]V(y) = \frac{(26.819047 \times 10^{-5}- 0.419047 \times 10^{-5})^2}{12}[/tex]
[tex]V(y) = \frac{(26.4 \times 10^{-5})^2}{12}[/tex]
[tex]V(y) = \frac{(696.96 \times 10^{-10})}{12}[/tex]
[tex]V(y) = 58.08000 \times 10^{-10}[/tex]
Rewrite as:
[tex]V(y) = 580.8000 \times 10^{-9}[/tex]
Hence, the expected value and the variance of the sphere are:[tex]13.6190 \times 10^{-5}[/tex] and [tex]580.8000 \times 10^{-9}[/tex]
Learn more about expected values and variance at:
https://brainly.com/question/4470015
One angle of a triangle is equal to the sum of the remaining angles. If the ratio of measures of the ren
is 2:1, find the measures of the three angles of the triangle.
9514 1404 393
Answer:
90°, 60°, 30°
Step-by-step explanation:
The remaining angles have a ratio of 2:1, so total 3 "ratio units". The first angle is equal to that sum: 3 ratio units, so all of the angles together total 3+2+1 = 6 ratio units. The total of angles is 180°, so each ratio unit is 180°/6 = 30°.
The first angle is 3 ratio units, or 90°.
The second angle is 2 ratio units, or 60°.
The third angle is half that, or 30°.
The three angles are 90°, 60°, 30°.
By how many minutes is 2¾h longer than 1h 55min?
What dimensions would you need to calculate the volume of a basketball?
radius and height
length, width and slant height
radius
length, width, and height
Answer:
Radius on it's own is enough
Step-by-step explanation:
you could get the radius from the other informations, but after all you will calculate the volume with it and not the otheds, so just take radius. a sphere is, in terms of information, the simplest 3D-body to describe, like with a circle in 2D
The dimensions would you need to calculate the volume of a basketball is Radius on its own is enough
We have given that,
radius and height
length, width, and slant height
radius
length, width, and height
We have to determine the dimensions would you need to calculate the volume of a basketball.
What is the dimension?
Dimensions in mathematics are the measure of the size or distance of an object or region or space in one direction.
you could get the radius from the other information, but after all, you will calculate the volume with it and not the others, so just take the radius.
A sphere is, in terms of information, the simplest 3D body to describe, like a circle in 2D.
To learn more about the dimension visit:
https://brainly.com/question/26740257
#SPJ2
A professor knows that her statistics students' final exam scores have a mean of 79 and a standard deviation of 11.3. In his class, an "A" is any exam score of 90 or higher. This quarter she has 22 students in her class. What is the probability that 6 students or more will score an "A" on the final exam?
prob =
0.1449 = 14.49% probability that 6 students or more will score an "A" on the final exam.
---------------
For each student, there are only two possible outcomes. Either they score an A, or they do not. The probability of a student scoring an A is independent of any other student, which means that the binomial probability distribution is used to solve this question.
Additionally, to find the proportion of students who scored an A, the normal distribution is used.
----------------
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 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 a success.
----------------
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation , 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.
----------------
Proportion of students that scored an A:
Scores have a mean of 79 and a standard deviation of 11.3, which means that [tex]\mu = 79, \sigma = 11.3[/tex]
Scores of 90 or higher are graded an A, which means that the proportion is 1 subtracted by the p-value of Z when X = 90, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{90 - 79}{11.3}[/tex]
[tex]Z = 0.97[/tex]
[tex]Z = 0.97[/tex] has a p-value of 0.8340.
1 - 0.8340 = 0.166
The proportion of students that scored an A is 0.166.
----------------
Probability that 6 students or more will score an "A" on the final exam:
Binomial distribution.
22 students, which means that [tex]n = 22[/tex]
The proportion of students that scored an A is 0.166, which means that [tex]p = 0.166[/tex]
The probability is:
[tex]P(X \geq 6) = 1 - P(X < 6)[/tex]
In which
[tex]P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)[/tex]
Then
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{22,0}.(0.166)^{0}.(0.834)^{22} = 0.0184[/tex]
[tex]P(X = 1) = C_{22,1}.(0.166)^{1}.(0.834)^{21} = 0.0807[/tex]
[tex]P(X = 2) = C_{22,2}.(0.166)^{2}.(0.834)^{20} = 0.1687[/tex]
[tex]P(X = 3) = C_{22,3}.(0.166)^{3}.(0.834)^{19} = 0.2239[/tex]
[tex]P(X = 4) = C_{22,4}.(0.166)^{4}.(0.834)^{18} = 0.2117[/tex]
[tex]P(X = 5) = C_{22,5}.(0.166)^{5}.(0.834)^{17} = 0.1517[/tex]
Then
[tex]P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = 0.0184 + 0.0807 + 0.1687 + 0.2239 + 0.2117 + 0.1517 = 0.8551[/tex]
[tex]P(X \geq 6) = 1 - P(X < 6) = 1 - 0.8551 = 0.1449[/tex]
Thus
0.1449 = 14.49% probability that 6 students or more will score an "A" on the final exam.
For a problem that used the normal distribution, you can check https://brainly.com/question/15181104, and for a problem that used the binomial distribution, you can check https://brainly.com/question/15557838
What is the volume of a cone with a radius of 4 inches and height of 11?
Answer:
184.22
Step-by-step explanation:
If 3(nP2 + 24)=2nP2, find the positive value of n
Answer:
[tex]n = 8[/tex]
Step-by-step explanation:
Given
[tex]3(^nP_2 + 24) = ^{2n}P_2[/tex]
Required
Find n
To do this, we simply apply permutations formula
[tex]nP_r = \frac{n!}{(n -r)!}[/tex]
So, we have:
[tex]3 * [\frac{n!}{(n -2)!} + 24] = \frac{2n!}{(2n -2)!}[/tex]
Expand
[tex]3 * [\frac{n * (n - 1) * (n - 2)!}{(n -2)!} + 24] = \frac{2n * (2n - 1) * (2n - 2)}{2n - 2}[/tex]
[tex]3 * [n * (n - 1) + 24] = 2n * (2n - 1)[/tex]
[tex]3 * [n^2 - n + 24] = 4n^2 - 2n[/tex]
Open bracket
[tex]3n^2 - 3n + 72 = 4n^2 - 2n[/tex]
Collect like terms
[tex]3n^2 - 4n^2- 3n+2n + 72 = 0[/tex]
[tex]-n^2- n + 72 = 0[/tex]
Expand
[tex]-n^2 -9n + 8n + 72 = 0[/tex]
Factorize
[tex]-n(n +9) - 8(n + 9) = 0[/tex]
Factor out n + 9
[tex](-n -8)(n + 9) = 0[/tex]
Split
[tex](-n -8)= 0 \ or\ (n + 9) = 0[/tex]
Solve for n
[tex]n =8\ or\ n = -9[/tex]
The positive value is [tex]n = 8[/tex]
6. On a number line, point A has a coordinate of -6, and point B has a coordinate of 2. Which is the coordinate of point M, the midpoint of AB ?
A) 0
B) -2
C) -3
D) 4
9514 1404 393
Answer:
B) -2
Step-by-step explanation:
The midpoint is the average of the end points.
M = (A +B)/2
M = (-6 +2)/2 = -4/2 = -2
The coordinate of M is -2.
In 2012 your car was worth $10,000. In 2014 your car was worth $8,850. Suppose the value of your car decreased at a constant rate of change. Define a function f to determine the value of your car (in dollars) in terms of the number of years t since 2012.
Answer:
The function to determine the value of your car (in dollars) in terms of the number of years t since 2012 is:
[tex]f(t) = 10000(0.9407)^t[/tex]
Step-by-step explanation:
Value of the car:
Constant rate of change, so the value of the car in t years after 2012 is given by:
[tex]f(t) = f(0)(1-r)^t[/tex]
In which f(0) is the initial value and r is the decay rate, as a decimal.
In 2012 your car was worth $10,000.
This means that [tex]f(0) = 10000[/tex], thus:
[tex]f(t) = 10000(1-r)^t[/tex]
2014 your car was worth $8,850.
2014 - 2012 = 2, so:
[tex]f(2) = 8850[/tex]
We use this to find 1 - r.
[tex]f(t) = 10000(1-r)^t[/tex]
[tex]8850 = 10000(1-r)^2[/tex]
[tex](1-r)^2 = \frac{8850}{10000}[/tex]
[tex](1-r)^2 = 0.885[/tex]
[tex]\sqrt{(1-r)^2} = \sqrt{0.885}[/tex]
[tex]1 - r = 0.9407[/tex]
Thus
[tex]f(t) = 10000(1-r)^t[/tex]
[tex]f(t) = 10000(0.9407)^t[/tex]
Which quadrilateral has equal diagonals
Select one:
a. trapezoid
b. rectangle
c. parallelogram
d. rhombus
Answer:
Option b: Rectangle
Explanation:
Give branliest pls ;)
I need help ASAP thank you
Answer:D) Under-root 25.Under-root 3
Step-by-step explanation
Under-root 25 = 5
Answer:
Answer D and B.
Step-by-step explanation:
[tex]{ \bf{5 \sqrt{3} }} \\ = { \bf{ \sqrt{ {5}^{2} } \times \sqrt{3} }} \\ = { \bf{ \sqrt{25} . \sqrt{3} }}[/tex]
Find the probability that z lies between 0 and 1.56.
Answer:
P(0 < z < 1.56)=0.4406
Step-by-step explanation:
Mr. Rowley has 16 homework papers and 14 exit tickets to return. Ms. Rivera has 64 homework papers and 60 exit tickets to retum. For each teacher, write a ratio to represent the number of homework papers to number of exit tickets they have to return. Are the ratios equivalent? Explain.
Answer:
Mr. Rowley=16:14
=8:7
Ms.Rivera= 64:60
=16:15
Which is equal to (3x + 2)(x – 3)?
Please answer asappp
(3x +2)(x -3)
FOIL method
3x^2 -9x + 2x -6
3x^2 -7x -6
Your answer: 3x^2 -7x -6
Convert 15,000 meters to centimeters.
15,000 centimeters
150,000 centimeters
15,000,000 centimeters
1,500,000 centimeters
Answer:
1500000
Step-by-step explanation:
1 metre = 100 cm
15000metre =15000*100
=1500000
Assuming that a person going to community college can't afford to go to a four-year college is an example of a) a generalization. b) discrimination. O c) a stereotype. O d) tolerance.
Answer:
a) generalization
Step-by-step explanation:
The statement is an example of a generalization. This is because the statement is assumming that all individuals who go to community college are poor. Therefore, this is why they cannot go to a four-year college, and instead go to a community college which is far cheaper. This assumption is being applied to all individuals who attend community college, without any further or more-specific information about each individual, therefore generalizing the entire situation.
Suppose a certain study reported that 27.7% of high school students smoke.
Random samples are selected from high school that has 632 students.
(i) If a random sample of 60 students is selected, what is the probability that
fewer than 19 of the students smoke?
(ii) If a random sample of 75 students is selected, what is the probability that
more than 17 of the students smoke?
The correct answer of the question is "0.7062" and "0.835". The further solution is provided below.
Given:
Probability of student smoke,
P = 27.7%
= 0.277
Number of students (n) = 632
[tex]q = 1-p[/tex]
[tex]=1-0.277[/tex]
[tex]=0.723[/tex]
(i)
Here,
Number of students (n) = 60
then,
⇒ [tex]n_P=60\times 0.277[/tex]
[tex]=16.62[/tex]
⇒ [tex]n_q=60\times 0.723[/tex]
[tex]=43.38[/tex]
We can see that [tex]n_P > 10[/tex] and [tex]n_q>10[/tex] so the normal approximation condition are met.
Now,
[tex]\mu = n_P= 16.62[/tex]
[tex]\sigma = \sqrt{n_{Pq}}[/tex]
[tex]= \sqrt{60\times 0.277\times 0.723}[/tex]
[tex]=3.9664[/tex]
Now,
⇒ [tex]P(X<19) = P(X<18.5)[/tex]
[tex]=P(Z_{18.5})[/tex]
The Z-score is:
= [tex]\frac{18.5-16.62}{3.4664}[/tex]
= [tex]0.5423[/tex]
hence,
The probability will be:
⇒ [tex]P(Z_{18.5}) = 0.7062[/tex]
or,
⇒ [tex]P(Z<19) = 0.7062[/tex]
(ii)
Here,
Number of students (n) = 75
[tex]\mu = n_P = 75\times 0.277[/tex]
[tex]=20.775[/tex]
[tex]\sigma = \sqrt{n_{Pq}}[/tex]
[tex]=\sqrt{75\times 0.277\times 0.723}[/tex]
[tex]=3.8756[/tex]
Now,
⇒ [tex]P(X>17) = P(X> 17.5)[/tex]
[tex]=1-P(X \leq 17.5)[/tex]
[tex]=1-P(Z_{17.5})[/tex]
The Z-score is:
= [tex]\frac{17.5-20.775}{3.8756}[/tex]
= [tex]-0.9740[/tex]
then, [tex]P(Z_{17.5}) = 0.165[/tex]
hence,
The probability will be:
⇒ [tex]P(X>17) = 1-0.165[/tex]
[tex]=0.835[/tex]
Learn more about Probability here:
https://brainly.com/question/9825651
f(x) = 1 + 9. Find f '(x) and its domain.
A. f-1 (z) = (x – 9)?: x2 9
B. f-1(x) = (x – 9)?; x20
c. f-1 (2) = x2 – 9;x2 9
D. f-1 (x) = x2 – 9; x2 0
Answer:
B
Step-by-step explanation:
f(x) = sqrt(x) + 9
f(x) - 9=sqrt(x)
f^(-1)(x)=(x-9)^2 and it's domain is greater than 0
A jet flew 2660 miles in 4.75 hours. What is the rate of speed in miles per hour? (The proportion would be 2660 : 4.75 ::X:1 Set the proportion in fractional form and proceed to find x.)
Answer:
X = 560
Step-by-step explanation:
Speed = distance / time
Distance = 2660 miles
Time taken = 4.75 hours
Writing the equation in terms of proportion :
Rate or speed = Distance : time
Speed = 2660 : 4.75
Reducing to lowest term ;
Divide both sides by 4.75
Hence, we have ;
Speed = 2660/4.75 : 4.75/4.75
Speed = 560 : 1
Comparing with the proportion in the question, X = 560
Instructions: State what additional information is required in order
to know that the triangles in the image below are congruent for the
reason given
Reasory. SAS Postulate
Answer:
HJ = FG
Step-by-step explanation:
SAS means side - (included) angle - side.
we have one angle confirmed (at H and at G).
we have actually one side confirmed (HG), because the graphic shows that this side is shared between the triangles. so, implicitly it is not only congruent but really identical.
so, we need the confirmation of the second side enclosing the confirmed angle.
Find the missing side lengths leave your answer as a racials simplest form
Answer:
y=3 and x=3*sqrt(3)
Step-by-step explanation:
sin(30)=y/6
1/2=y/6, y=3. As it's a right angled triangle, 6^2-3^2=x^2, x=3*sqrt(3)
Answer:
x = 3 sqrt(3)
y = 3
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp / hyp
sin 30 = y /6
6 sin 30 = y
6 (1/2) = y
3 = y
cos theta = adj / hyp
cos 30 = x /6
6 cos 30 =x
6 ( sqrt(3)/2) =x
3 sqrt(3) = x
Một tàu biển trị giá 2.500.000 USD đang chở các lô hàng A, B,C có giá trị lần lượt là 100.000 USD; 300.000USD, 500.000USD và tiền cước chưa thu thuộc chủ tàu là 60.000 USD. Trong hành trình đi từ Indonesia về cảng Sài Gòn tàu bị mắc cạn, vỏ tàu bị thủng, nước tràn vào làm hư hỏng một số hàng hóa. Để cứu tàu và hàng, thuyền trưởng quyết định bịt lỗ thủng bằng các phương tiện trên tàu và vứt một số hàng để tàu nhẹ bớt, đồng thời thuyền trưởng cũng cho máy tàu làm việc vượt công suất nhằm giúp tàu thoát cạn. Sau sự việc, các tổn thất được xác định như sau:
- Vỏ tàu thủng dự kiến phải sửa chữa hết 100.000 USD
- Máy tàu hư do hoạt động quá công suất và dự kiến phải sửa hết 250.000 USD
- Lô hàng B bị nước tràn vào giảm giá trị thương mại 100%.
- Lô Hàng A bị vứt xuống biển toàn bộ.
- Thiệt hại để cứu tàu và chi phí cho thủy thủ trong việc cứu tàu là 10.000 USD.
a. Hãy xác định các tổn thất riêng của các bên
b. Hãy xác định tổng tổn thất chung của các bên
c. Hãy xác định giá trị chịu phân bổ tổn thất chung (giá trị đóng góp của từng chủ thể trên tàu)
d. Hãy xác định các khoản đóng góp vào tổn thất chung của các bên
Answer:
ask in English then I can help
Find the degree of each polynomial and indicate whether the
polynomial is a monomial, binomial, trinomial, or none of these.
Answer:
1. Degree = 1, monomial
2. Degree = 2, monomial
3. degree = 2, trinomial
4. Degree = 2, binomial
5. Degree = 2, binomial
Step-by-step explanation:
ABC are points; (2,3), (4,7), (7,3) respectively. Find the equation of the line through the point (3,-5) which is parallel to the line with the equation 3x+2y-5=0
Answer:
y = -3x/2 - 1/2
Step-by-step explanation:
slope m = -3/2
-5 = (-3/2)×3+b
or, b = -1/2
putting it into y = mx + b
y = -3x/2 - 1/2
Answered by GAUTHMATH
what is the least common factor for 9 8 7
Answer:504
This is the answer
504
Please help me with 9 I really need it
Answer:
605 boys.
Step-by-step explanation:
5:7 means 5 parts consists of boys and 7 parts consist of girls.
Since 7 parts = 847, 1 part = 121 and 5 parts = 605
Hence there are 605 boys.
Hope you have a nice day :)
Determine the sum of the measures of the exterior angles of a convex hexagon (6-sided polygon).
A. 540
B. 720
C. 1,080
D. 360
9514 1404 393
Answer:
(d) 360°
Step-by-step explanation:
The sum of exterior angles of any convex polygon is 360°.
The question is in the screenshot
Answer:
AC is about 4.29
Step-by-step explanation:
we need to use simple trigonometry for this problem
the tangent of an angle is the ratio between the opposite side and the adjacent side
so the tangent of the angle 35º is BC / AC
tan(35) is about 0.7
this means that BC / AC = 0.7
we know BC is 3
so 3 / AC = 0.7
3 = 0.7(AC)
AC is about 4.29
Draw a frequency polygon for the following data:
Marks
0 - 10
10 - 20 20 - 30 30 - 40 40 - 5050 - 60
错误。
No. of Students
7
15
22
30
16
10
Answer:
See attachment
Step-by-step explanation:
Given
[tex]\begin{array}{ccccccc}{Marks} & {0-10} & {10-20} & {20-30} & {30-40} & {40-50} & {50-60}\ \\ {Students} & {7} & {15} & {22} & {30} & {16} & {10} \ \end{array}[/tex]
Required
The frequency polygon
We have:
[tex]\begin{array}{ccccccc}{Marks} & {0-10} & {10-20} & {20-30} & {30-40} & {40-50} & {50-60}\ \\ {Students} & {7} & {15} & {22} & {30} & {16} & {10} \ \end{array}[/tex]
First, we calculate the midpoint of each class
[tex]\begin{array}{ccccccc}{Midpoint} & {(0+10)/2} & {(10+20)/2} & {(20+30)/2} & {(30+40)/2} & {(40+50)/2} & {(50+60)/2}\ \\ {Students} & {7} & {15} & {22} & {30} & {16} & {10} \ \end{array}[/tex]
[tex]\begin{array}{ccccccc}{Midpoint} & {5} & {15} & {25} & {35} & {45} & {55}\ \\ {Students} & {7} & {15} & {22} & {30} & {16} & {10} \ \end{array}[/tex]
Lastly, we plot the midpoint against the frequency of students (see attachment)
Complete the equation describing how X and Y are related X= -2, -1, 0, 1,2,3. Y= -8, -5,-2,1,4,7
Answer:
y = 3x - 2
Happy Studying
