Answer:
The area of the region is 25,351 [tex]units^2[/tex].
Step-by-step explanation:
The Fundamental Theorem of Calculus: if [tex]f[/tex] is a continuous function on [tex][a,b][/tex], then
[tex]\int_{a}^{b} f(x)dx = F(b) - F(a) = F(x) | {_a^b}[/tex]
where [tex]F[/tex] is an antiderivative of [tex]f[/tex].
A function [tex]F[/tex] is an antiderivative of the function [tex]f[/tex] if
[tex]F^{'}(x)=f(x)[/tex]
The theorem relates differential and integral calculus, and tells us how we can find the area under a curve using antidifferentiation.
To find the area of the region between the graph of the function [tex]x^5 + 8x^4 + 2x^2 + 5x + 15[/tex] and the x-axis on the interval [-6, 6] you must:
Apply the Fundamental Theorem of Calculus
[tex]\int _{-6}^6(x^5+8x^4+2x^2+5x+15)dx[/tex]
[tex]\mathrm{Apply\:the\:Sum\:Rule}:\quad \int f\left(x\right)\pm g\left(x\right)dx=\int f\left(x\right)dx\pm \int g\left(x\right)dx\\\\\int _{-6}^6x^5dx+\int _{-6}^68x^4dx+\int _{-6}^62x^2dx+\int _{-6}^65xdx+\int _{-6}^615dx[/tex]
[tex]\int _{-6}^6x^5dx=0\\\\\int _{-6}^68x^4dx=\frac{124416}{5}\\\\\int _{-6}^62x^2dx=288\\\\\int _{-6}^65xdx=0\\\\\int _{-6}^615dx=180\\\\0+\frac{124416}{5}+288+0+18\\\\\frac{126756}{5}\approx 25351.2[/tex]
The Statue of Liberty in New York stands on top of a foundation and a pedestal. The statue, including foundation and pedestal, measures about 305 feet from the ground to the top of the statue’s torch. The statue herself stands 151 feet. What is the height of the foundation and pedestal?
Answer:
The answer is 154 ft.
Step-by-step explanation:
You would take the total height (305) and subtract is by the actual statue(151) to get your answer.
305-151=154
Answer:
154
Step-by-step explanation:
g(x) = -10x2+ 490
lesser x=
greater x =
Answer:
Greater x =+ 7
Lesser x = -7
Step-by-step explanation:
G(x) = -10x2+ 490
Let the left side = 0
So we have
0= -10x2+ 490
Solving the above now by allowing the variable with the coefficient of x cross the equal sign.
10x²= 490
Dividing by 10
X²= 490/10
X² = 49
Taking the root of both sides
X= √49
X = + 7or -7
Bigger x =+ 7
Smaller x = -7
The factory quality control department discovers that the conditional probability of making a manufacturing mistake in its precision ball bearing production is 4\%4% on Tuesday, 4\%4% on Wednesday, 4\%4% on Thursday, 8\%8% on Monday, and 12\% on Friday.The Company manufactures an equal amount of ball bearings (20\ %) on each weekday. What is the probability that a defective ball bearing was manufactured on a Friday
Answer:
The probability that a defective ball bearing was manufactured on a Friday = 0.375
Step-by-step explanation:
Let the event of making a mistake = M
The event of making a precision ball bearing production on Monday = Mo
The event of making a precision ball bearing production on Tuesday = T
The event of making a precision ball bearing production on Wednesday = W
The event of making a precision ball bearing production on Thursday = Th
The event of making a precision ball bearing production on Friday = F
the conditional probability of making a manufacturing mistake in its precision ball bearing production is 4% on Tuesday, P(M|T) = 4% = 0.04
4% on Wednesday, P(M|W) = 0.04
4% on Thursday, P(M|Th) = 0.04
8% on Monday, P(M|Mo) = 0.08
and 12% on Friday = P(M|F) = 0.12
The Company manufactures an equal amount of ball bearings (20 %) on each weekday, Hence, the probability that a random precision ball bearing was made on a particular day of the week, is mostly the same for all the five working days.
P(Mo) = 0.20
P(T) = 0.20
P(W) = 0.20
P(Th) = 0.20
P(F) 0.20
The probability that a defective ball bearing was manufactured on a Friday = P(F|M)
P(F|M) = P(F n M) ÷ P(M)
P(F n M) = P(M n F)
P(M) = P(Mo n M) + P(T n M) + P(W n M) + P(Th n M) + P(F n M)
We can obtain each of these probabilities by using the expression for conditional probability.
P(Mo n M) = P(M|Mo) × P(Mo) = 0.08 × 0.20 = 0.016
P(T n M) = P(M|T) × P(T) = 0.04 × 0.20 = 0.008
P(W n M) = P(M|W) × P(W) = 0.04 × 0.20 = 0.008
P(Th n M) = P(M|Th) × P(Th) = 0.04 × 0.20 = 0.008
P(F n M) = P(M|F) × P(F) = 0.12 × 0.20 = 0.024
P(M) = P(Mo n M) + P(T n M) + P(W n M) + P(Th n M) + P(F n M)
P(M) = 0.016 + 0.008 + 0.008 + 0 008 + 0.024 = 0.064
P(F|M) = P(F n M) ÷ P(M)
P(F n M) = P(M n F) = 0.024
P(M) = 0.064
P(F|M) = P(F n M) ÷ P(M) = (0.024/0.064) = 0.375
Hope this Helps!
The times required for a delivery firm to transport a package from one business address to another in the same metropolitan area is normally distributed with a mean of 3.8 hours and a standard deviation of 0.8 hours. Suppose the delivery firm wants to determine the time by which 55% of all deliveries would be made. Which of the following density function diagrams best depicts this problem.
What is the probability a single delivery would take more than 4 hours? What is the z value corresponding to the interval boundary?
Answer:
Step-by-step explanation:
Since; the density function diagrams were not included in the question; we will be unable to determine the best which depicts this problem.
However;
Let use X to represent the time required for the delivery.
Then X~N(3.8 ,0.8)
i.e
E(x) = 3.8
s.d(x) = 0.8
NOW; P(x>4) = P(X-3.8/0.8 > 4-3.8/0.8)
= P(Z > 0.25)
= 1-P(Z < 0.25)
=1 - Φ (0.25)
= 1 - 0.5987 ( from Normal table Φ (0.25) = 0.5987 )
= 0.4013
Thus; the probability a single delivery would take more than 4 hours is 0.4013
What is the z value corresponding to the interval boundary?
The z value is calculated as:
[tex]z = \dfrac{X- \mu}{\sigma}[/tex]
[tex]z = \dfrac{4- 3.8}{0.8}[/tex]
z = 0.25
if (x+yi)+2(3x-y)+4i-0;then the value of x and y is
Answer:
X=0 and Y= 4(2i-1)/5
Step-by-step explanation:
Here is my solution, assuming that the equation equals 0. For y, just remember the definition of complex numbers and multiply by its conjugate.
The value of x and y are -8/7 and -4 respectively if (x + yi) + 2(3x - y) + 4i = 0.
What is a complex number?It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.
We have a complex number:
(x + yi) + 2(3x - y) + 4i = 0
After arranging:
x + yi + 6x - 2y + 4i = 0
7x - 2y + yi + 4i = 0
7x - 2y + (y + 4)i = 0
7x - 2y = 0
y + 4 = 0
This is the linear equation in two variables:
Plug y = -4 in the other equation:
7x - 2(-4) = 0
7x = -8
x = -8/7
y = -4
Thus, the value of x and y are -8/7 and -4 respectively if (x + yi) + 2(3x - y) + 4i = 0.
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solve the expression x + 3 = 7
Answer:
x=4
Step-by-step explanation:
think of the equation like this: you have to do the inverse(opposite) operations so for adding you would subtract it. So for the adding 3 you would subtract it from both sides of the equation and get X=4
How do i find the measure?
Answer: angle A = 72 and angle C = 72
Step-by-step explanation:
Angle A and C are opposites so they have to equal each other so do the equation 3y+27=5y-3. y would come out to be 15 and so to find the angles you would replace y with 15.
Please select the word from the list that best fits the definition
treinta y cinco
When AE = 7, EC= 14, CB= 24, what is ED?
Answer:
ED = 8
Step-by-step explanation:
AC = 21 which means AE is 1/3 of the length of AC.
So, ED must also be 1/3 of the length of BC.
1/3 x 24 = 8
An ice-cream shop uses the following ingredients to make one sundae.
Ingredients. Amount
Ice-cream- 2 scoops
Sprinkles- 4 spoonful's
Whipped Cream- 2 tablespoons
72 sundaes are needed to meet customer demand. Calculate the ratio of ingredients needed to meet his demand.
Given points (r1, u1 ) and (r2, u2) in polar coordinates, obtain a general formula for the distance between them. Simplify it as much as possible using the identity cos2 u 1 sin2 u 5 1. Hint: Write the expressions for the two points in Cartesian coordinates and substitute into the usual distance formula.
Answer:
[tex]d=\sqrt{r_1^2+r_2^2-2r_1r_2\cos(u_2-u_1)}[/tex]
Step-by-step explanation:
The Law of Cosines gives an immediate result. No translation to Cartesian coordinates is necessary. That law makes use of the angle between the vectors, u2-u1
[tex]d^2=r_1^2+r_2^2-2r_1r_2\cos(u_2-u_1)\\\\\boxed{d=\sqrt{r_1^2+r_2^2-2r_1r_2\cos(u_2-u_1)}}[/tex]
Simplify this God please
Answer:
10
Step-by-step explanation:
[tex] \frac{ \sqrt{75a} + \sqrt{12a} + \sqrt{27a} }{ \sqrt{3a} } \\ \frac{ \sqrt{(25 \times 3)a} + \sqrt{(4 \times 3)a} + \sqrt{(9 \times 3)a} }{ \sqrt{3a} } \\ \frac{ 5\sqrt{3a} + 2 \sqrt{3a} + 3\sqrt{3a} }{ \sqrt{3a} } \\ \frac{(5 + 2 + 3) \sqrt{3a} }{ \sqrt{3a} } = 10[/tex]
Answer: See below
Step-by-step explanation:
My old math notebook had simillar question,hope that help
√75a+√12a-√27a/√3a
=√a(3*25)+√a(3*4)+√a(3*9)/√3a
=√25*√3a+√4*√3a+√9*√3a/√3a
=(5+2+3)√3a/√3a
=5+2+3=10
8. If3:8=c:56, the value of c will be
The scale for the second values is 56/8 = 7
C = 3 x 7 = 21
C= 21
Find the volume of a rectangular prism if the length is 2x, the width 4x^2, and the height is 2x^2+x+7
Answer:
V=16x^5+8x^4+56x^3.
Step-by-step explanation:
The volume of the rectangular prism is V=16x^5+8x^4+56x^3.
Formula for rectangle prism: V=whl
Formula: L*W*H
Answer: V=16x^5+8x^4+56x^3
Hope this helps.
Create an expression that fits all of the following conditions: There are exactly four terms. Exactly two of the terms are like terms. At least one term is an integer. Simplify the expression that you created.
Answer:
The expression created is: [tex]3x^2+3x+8x-7[/tex]
Simplified, we obtain : [tex]3x^2+11x-7[/tex]
Step-by-step explanation:
We are to create an expression that satisfies the following conditions
There are exactly four terms. Exactly two of the terms are like terms. At least one term is an integer.Let the two like terms be 3x and 8x
Let the integer term = -7
Let the other term [tex]=3x^2[/tex]
Our written expression is therefore:
[tex]3x^2+3x+8x-7[/tex]
We simplify the expression by solving the like terms for a single term
[tex]3x+8x=11x\\$Therefore\\3x^2+3x+8x-7=3x^2+11x-7[/tex]
simplificar A=4x2-6x2+7x2-20x2+19x2
Answer:
4x²
Step-by-step explanation:
Your equation is 4x² - 6x² + 7x² - 20x² + 19x².
Since they all have the same variable, simply combine them all to find your answer.
4x² - 6x² + 7x² - 20x² + 19x²
-2x² + 7x² - 20x² + 19x²
5x² - 20x² + 19x²
-15x² + 19x²
4x²
2 Points
This graph shows the solutions to the inequalities y> 3x+6 and y<3x - 7
Does the system of inequalities have solutions? If so, which region contains
the solutions?
A
B
С
O A. There are no solutions
B. There are solutions, and they are the points in region C.
O C. There are solutions, and they are the points in region A.
O D. There are solutions, and they are the points in region B.
Answer:
Option (A)
Step-by-step explanation:
Two inequalities have been given as,
y > 3x + 6 --------(1)
y < 3x - 7 ------(2)
Inequality (1) shows the solution area shaded in blue, means all the solutions for the inequality will lie in the blue area.
Similarly, solutions of inequality (2) will lie in red area.
No common area for the inequalities.
Therefore, system of inequalities will have no solution.
Option (A) will be the answer.
An urn contains 9 red marbles, 9 white marbles and 8 blue marbles. A child randomly selects three (without replacement).
what is the probability that all have the same color?
Answer:
8.62% probability that all have the same color
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
The order in which the marbles are selected is not important. So we use the combinations formula to solve this question.
Combinations formula:
[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]
What is the probability that all have the same color?
Desired outcomes:
Either all red(from a set of 9), all white(from a set of 9) or all blue(from a set of 8). So
[tex]D = C_{9,3} + C_{9,3} + C_{8,3} = \frac{9!}{3!6!} + \frac{9!}{3!6!} + \frac{8!}{3!5!} = 224[/tex]
Total outcomes:
3 marbles, from a set of 9 + 9 + 8 = 26. So
[tex]T = C_{26,3} = \frac{26!}{3!23!} = 2600[/tex]
Probability:
[tex]p = \frac{D}{T} = \frac{224}{2600} = 0.0862[/tex]
8.62% probability that all have the same color
Find the gradient of the line y+2x= -1
BONUS: Find the y-intercept of the line 2y=10x-10
E. coli bacteria have a doubling time of 20 minutes. Starting with 30 E. coli bacteria, how many will there be 6 hours later? Group of answer choices 7,864,410 7,864,320 7,864,452 7,864,821
Answer: 7,864,320
Step-by-step explanation:
Because the doubling time is 20 minutes, the bacteria would have gone through binary fission(cell division in bacteria) 18 times after 6hours(6*60/20)
Nt=N0 * 2^n
N0=starting population
n=number of times bacteria divide
So
30*2^18=7,864,320
A house and a lot are apprised at $212,400.If the value of the house is four times the value of the lot, how much is house worth?
Find the product of LCM and HCF of 3 and 15
Answer:
45
please see the attached picture for full solution
hope it helps
Good luck on your assignment
Choose at random a person aged 20 to 39 years. Ask their age and marital status (never married, married, or widowed/divorced/separated). Offered is the probability model for 12 possible answers. Age in years 20 – 24 25 – 29 30 – 34 35 – 39 Never married 0.227 0.156 0.089 0.054 Married 0.027 0.086 0.137 0.148 Widowed/divorced/separated 0.006 0.015 0.022 0.033 (a) Is this a legitimate finite probability model? Select the correct description. No. This is not a legitimate finite probability model because each probability is between 0 and 1 , and all sum to 1 . Yes. This is a legitimate finite probability model because each probability is between 0 and 1 , and all sum to 1 . Yes. This is a legitimate finite probability model because the probabilities are all greater than 0 and do not sum to 1 . No. This is not a legitimate finite probability model because the probabilities are all greater than 0 and do not sum to 1 . (b) What is the probability that the person chosen is a 20 ‑ to 24 ‑ year‑old who is married? (Enter your answer rounded to three decimal places.) P(20‑ to 24‑year‑old who is married)= (c) What is the probability that the person chosen is 20 – 24 years old? (Enter your answer rounded to three decimal places.) P(20–24 year old)= (d) What is the probability that the person chosen is married? (Enter your answer rounded to three decimal places.) P(married)=
Answer:
(a)(B)Yes. This is a legitimate finite probability model because each probability is between 0 and 1 , and all sum to 1 .
(b)P(20‑ to 24‑year‑old who is married)=0.027
(c)P(20–24 year old)=0.26
(d)P(married)=0.398
Step-by-step explanation:
Given the probability model below:
[tex]\left\begin{array}{|c|c|c|c|c|}$Age in years& 20 - 24& 25 - 29& 30 - 34& 35 - 39\\$Never married& 0.227& 0.156& 0.089& 0.054\\ $Married &0.027& 0.086& 0.137& 0.148\\$Widowed/divorced/separated &0.006 &0.015& 0.022& 0.033\end{array}\right\\[/tex]
(a)
Adding the probability for each row, we obtain: 0.227+0.156+0.089+0.054=0.5260.027+0.086+0.137+0.148=0.3980.006+0.015+0.022+0.033=0.0760.526+0.398+0.076=1
Therefore this is a legitimate finite probability model because each probability is between 0 and 1 , and all sum to 1 .
(b) The probability that the person chosen is a 20‑24-year‑old who is married
P(20‑ to 24‑year‑old who is married)=0.027
(c)Probability that the person chosen is 20 – 24 years old
P(20–24 year old)=0.227+0.027+0.006=0.26
(d)Probability that the person chosen is married
P(married)=0.027+0.086+0.137+0.148=0.398Which one of these statistics is unaffected by outliers?Mean Interquartile range Standard deviation Range
Answer:
Since Interquartile Range consider the middle values in the data set, i.e. 50%, it is not affected by outliers or extreme values. While other statistics mean, standard deviation and range are all affected by outliers or extreme values.
Step-by-step explanation:
hope this helps you :) can you help me please northc04 :(
Answer:
The answer is Interquartile Range. I know this is the right answer is because I got it right on a quiz.
PLEASE HELP!!! Two towns are 1100 miles apart. A group of hikers starts from each town and walks down the trail toward each other. They meet after a total hiking time of 240 hours. If one group travels one half mile per hour slower than the other group, find the rate of each group.
Answer:
2.54 miles/hr
2.04 miles/hr
Step-by-step explanation:
Given: Distance between the two towns = 1100 miles
Difference between speeds = [tex]\frac{1}{2}[/tex] miles/hr
Total time when they meet = 240 hours
To find:
Let distance traveled by first group = [tex]x[/tex] miles.
Now, the distance traveled by second group = (1100-[tex]x[/tex]) miles/hr
The relation between Speed, Time and Distance is given as:
[tex]\text{Speed =} \dfrac{\text{Distance}}{\text{Time}}[/tex]
Let speed of first group = [tex]S_1[/tex]
[tex]S_1 = \dfrac{x}{240}[/tex]
Let speed of second group = [tex]S_2[/tex]
[tex]S_2 = \dfrac{1100-x}{240}[/tex]
As per question, [tex]S_1[/tex] = [tex]S_2[/tex] + [tex]\frac{1}{2}[/tex]
[tex]\dfrac{x}{240} = \dfrac{1100-x}{240} + \dfrac{1}{2}\\\Rightarrow \dfrac{x}{240} - \dfrac{1100-x}{240} = \dfrac{1}{2}\\\Rightarrow \dfrac{x-1100+x}{240} = \dfrac{1}{2}\\\Rightarrow 2x - 1100 = 120\\\Rightarrow 2x = 1220\\\Rightarrow x = 610 ft[/tex]
Now,
[tex]S_1 = \dfrac{x}{240}[/tex]
Putting value of [tex]x[/tex]:
[tex]S_1 = \dfrac{610}{240}\\\Rightarrow S_1 = 2.54\ miles/hr[/tex]
Similarly, putting value of [tex]x[/tex] in [tex]S_2[/tex]:
[tex]S_2 = \dfrac{1100-610}{240}\\\Rightarrow S_2=\dfrac{490}{240}\\\Rightarrow S_2 = 2.04\ miles/hr[/tex]
According to the National Center for Health Statistics, in 1990, 28 % of babies in the United States were born to parents who were not married. Throughout the 1990s, this increased by approximately 0.6 % per year. If this trend continues, in which year will 76 % of babies be born out of wedlock?
Answer:
76 % of babies will be born out of wedlock in the [tex]81^{st}[/tex] year
Step-by-step explanation:
Given: In 1990, 28 % of babies in the United States were born to parents who were not married. This increased by approximately 0.6 % per year.
To find: year when 76 % of babies born out of wedlock
Solution:
A sequence is said to be in arithmetic progression if the difference between the terms is same.
For a sequence with first term as 'a' and common difference as 'd', the nth term is given by [tex]a_n=a+(n-1)d[/tex]
The given situation also forms an arithmetic progression with [tex]a=28\,,\,d=0.6[/tex]
Also, put [tex]a_n=76[/tex]
So,
[tex]a_n=a+(n-1)d\\76=28+(n-1)(0.6)\\76-28=0.6(n-1)\\48=0.6(n-1)\\\frac{48}{0.6}=n-1\\\\80=n-1\\n=80+1\\n=81[/tex]
So, 76 % of babies will be born out of wedlock in the [tex]81^{st}[/tex] year
If a rock falls from a height of 43 meters on Earth, the height H (in meters) after x seconds is approximately Upper H (x )equals 43 minus 4.9 x squared . (a) What is the height of the rock when xequals1.6 seconds? The height of the rock when xequals1.6 seconds is nothing meters.
Answer:
2.96 seconds
Step-by-step explanation:
Let H(x) = zero and solve for "x".
43 - 4.9x² = 0
4.9x²=43
x²=8.77
x=2.96
therefore, approximately when x=2.96seconds, the rock strike the ground.
Jane can paint the office by herself in 7 hours. Working with an associate, she can paint the office in 3 hours. How long would it take her associate to do it working alone?
Answer:
Step-by-step explanation:i really am lost,
The work rate for the associate is 5.3 hours.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
Given; Jane can paint the office by herself in 7 hours.
with an associate, she can paint the office in 3 hours.
The combined work rate is 3 hours per office.
WE need to find the work rate for the associate
Let the expression for the work rate be;
1/A+1/B= 1/T
1/7+1/B=1/3
1/B=1/3-1/7
1/B= 8-4/21
1/B= 4/21
B= 21/4
B=5.3 hours
Therefore, the work rate for the associate is 5.3 hours.
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Eight men and eight women have six tickets in one row to the theater. In how many ways can they sit if the first person in the row is a woman and the people alternate woman, man, woman, man and so on?
Answer:
As there are six seats in a row and the first person in the row is a woman and the people alternate woman, men, the possibility is
W
M
W
M
W
M
in that order.
Now as we four women, three seats for women can be filled in
X
4
P
3
=
24
ways
and similarly as we four men, three seats for men can be filled in
X
4
P
3
=
24
ways
Hence, total
24
×
24
=
576
permutations.
Step-by-step explanation:
A certain type of tree has seedlings randomly dispersed in a large area, with the mean density of seedlings being approximately five per square metre. If a forester randomly locates ten 1-square-metre sampling regions in the area, find the probability that none of the regions will contain seedlings.
Answer:
Step-by-step explanation:
The probability that the forester does not get the seedlings is 1/2 if the mean density of seedlings is 5 per square metre.
What is density?Density means the area within which a substance is collected or taken.
How to calculate the probability?We have been given the mean density =5 square metre.
And we have to calculate the probability that the forester will not get any seedlings.
So the probability that he will get the seedlings will be=5/10
which is 1/2
So the probability that he will not get the seedlings will be 1-1/2
that is 1/2.
Hence the probability that he will not get seedlings will be 1/2.
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