[tex]\bar{x} = 0[/tex]
[tex]\bar{y} =\dfrac{136}{125}[/tex]
Step-by-step explanation:
Let's define our functions [tex]f(x)\:\text{and}\:g(x)[/tex] as follows:
[tex]f(x) = x^2 + 1[/tex]
[tex]g(x) = 6x^2[/tex]
The two functions intersect when [tex]f(x)=g(x)[/tex] and that occurs at [tex]x = \pm\frac{1}{5}[/tex] so they're going to be the limits of integration. To solve for the coordinates of the centroid [tex]\bar{x}\:\text{and}\:\bar{y}[/tex], we need to solve for the area A first:
[tex]\displaystyle A = \int_a^b [f(x) - g(x)]dx[/tex]
[tex]\displaystyle \:\:\:\:\:\:\:=\int_{-\frac{1}{5}}^{+\frac{1}{5}}[(x^2 + 1) - 6x^2]dx[/tex]
[tex]\displaystyle \:\:\:\:\:\:\:=\int_{-\frac{1}{5}}^{+\frac{1}{5}}(1 - 5x^2)dx[/tex]
[tex]\displaystyle \:\:\:\:\:\:\:=\left(x - \frac{5}{3}x^3 \right)_{-\frac{1}{5}}^{+\frac{1}{5}}[/tex]
[tex]\:\:\:\:\:\:\:= \dfrac{28}{75}[/tex]
The x-coordinate of the centroid [tex]\bar{x}[/tex] is given by
[tex]\displaystyle \bar{x} = \dfrac{1}{A}\int_a^b x[f(x) - g(x)]dx[/tex]
[tex]\displaystyle \:\:\:\:\:\:\:= \frac{75}{28}\int_{-\frac{1}{5}}^{+\frac{1}{5}} (x - 5x^3)dx[/tex]
[tex]\:\:\:\:\:\:\:=\dfrac{75}{28}\left(\dfrac{1}{2}x^2 -\dfrac{5}{4}x^4 \right)_{-\frac{1}{5}}^{+\frac{1}{5}}[/tex]
[tex]\:\:\:\:\:\:\:= 0[/tex]
The y-coordinate of the centroid [tex]\bar{y}[/tex] is given by
[tex]\displaystyle \bar{y} = \frac{1}{A}\int_a^b \frac{1}{2}[f^2(x) - g^2(x)]dx[/tex]
[tex]\displaystyle \:\:\:\:\:\:\:=\frac{75}{28}\int_{-\frac{1}{5}}^{+\frac{1}{5}} \frac{1}{2}(-35x^4 + 2x^2 + 1)dx[/tex]
[tex]\:\:\:\:\:\:\:=\frac{75}{56} \left[-7x^5 + \frac{2}{3}x^3 + x \right]_{-\frac{1}{5}}^{+\frac{1}{5}}[/tex]
[tex]\:\:\:\:\:\:\:=\dfrac{136}{125}[/tex]
Find the measure of of RA.
Answer:
RA = 24
Step-by-step explanation:
Since the triangle is isosceles ( 2 equal sides ) , then LU is a perpendicular bisector , so
AU = RU , that is
4r = 18 - 2r ( add 2r to both sides )
6r = 18 ( divide both sides by 6 )
r = 3
Then
RA = 18 - 2r + 4r = 18 + 2r = 18 + 2(3) = 18 + 6 = 24
I need help with this question
9514 1404 393
Answer:
x = 22, y = 123
Step-by-step explanation:
The sum of angles in a triangle is 180°.
(2x +13)° +57° +3x° = 180°
5x +70 = 180 . . . . . . . . . . . . . collect terms, divde by °
5x = 110 . . . . . . . . . . . subtract 70
x = 22 . . . . . . . . divide by 5
__
Angles in a linear pair are supplementary.
y° + 57° = 180°
y = 123 . . . . . . . . divide by °, subtract 57
write an equation in slope intercept form for the line with slope 1/4 and y-intercept -6.
Answer:
y=¼x-6
Step-by-step explanation:
y=mx+c
y=¼x+-6
y=¼x-6
What is the domain of the function f(x) =x+1/
X^2-6x+8?
Answer:
The domain of the function is all real values of x, except [tex]x = 4[/tex] and [tex]x = 2[/tex]
Step-by-step explanation:
We are given the following function:
[tex]f(x) = \frac{x+1}{x^2-6x+8}[/tex]
It's a fraction, so the domain is all the real values except those in which the denominator is 0.
Denominator:
Quadratic equation with [tex]a = 1, b = -6, c = 8[/tex]
Using bhaskara, the denominator is 0 for these following values of x:
[tex]\Delta = (-6)^2 - 4(1)(8) = 36-32 = 4[/tex]
[tex]x_{1} = \frac{-(-6) + \sqrt{4}}{2} = 4[/tex]
[tex]x_{2} = \frac{-(-6) - \sqrt{4}}{2} = 2[/tex]
The domain of the function is all real values of x, except [tex]x = 4[/tex] and [tex]x = 2[/tex]
Graph 9x + 15y = 15.
I want my answer please help
Answer:
This is pretty simple
Step-by-step explanation:
So the only thing you need to know about negatives and positives is that if your multiplying or dividing a number with 1 negative in the expreession/equation The answer will always result in a negative. If its 2 negatives its always positive. Thats all you need to know and then just solve it from there.
Answer:
See explanation and picture below.
Step-by-step explanation:
In both multiplication and division of 2 numbers, different signs give you negative and equal signs give you positive.
In other words, positive & positive or negative and negative give you a positive answer.
Negative and positive or positive and negative give you negative answer.
the cost of 7 shirts is $63. find the cost of 5 shirts
1. $35
2. $45
3. $52
4. $70
Find a power series representation for the function. (Assume a>0. Give your power series representation centered at x=0 .)
f(x)=x2a7−x7
Answer:
Step-by-step explanation:
Given that:
[tex]f_x = \dfrac{x^2}{a^7-x^7}[/tex]
[tex]= \dfrac{x^2}{a^7(1-\dfrac{x^7}{a^7})}[/tex]
[tex]= \dfrac{x^2}{a^7}\Big(1-\dfrac{x^7}{a^7} \Big)^{-1}[/tex]
since [tex]\Big((1-x)^{-1}= 1+x+x^2+x^3+...=\sum \limits ^{\infty}_{n=0}x^n\Big)[/tex]
Then, it implies that:
[tex]\implies \dfrac{x^2}{a^7} \sum \limits ^{\infty}_{n=0} \Big(\Big(\dfrac{x}{a} \Big)^{^7} \Big)^n[/tex]
[tex]= \dfrac{x^2}{a^7} \sum \limits ^{\infty}_{n=0} \Big(\dfrac{x}{a} \Big)^{^{7n}}[/tex]
[tex]= \dfrac{x^2}{a^7} \sum \limits ^{\infty}_{n=0} \Big(\dfrac{x^{7n}}{a^{7n}} \Big)}[/tex]
[tex]\mathbf{= \sum \limits ^{\infty}_{n=0} \dfrac{x^{7n+2}}{a^{7n+7}} }}[/tex]
1. Write 3.3.3.3.3 as a power.
Answer:
3^5
Step-by-step explanation:
On the iPad it looks like that but the five is on the top right smaller
Answer:
3⁵
every 3 has it own power that is 1 however that .3 confused us
show that 43\2^4×5^3 will terminate after how many places of the decimal
Answer:
4 places after the decimal.
the result is 0.0215
Step-by-step explanation:
I assume the expression is really
43 / (2⁴ × 5³)
this is the same as
(((((((43 / 2) / 2) / 2) / 2) / 5) / 5) / 5)
since the starting value is an odd number, the first division by 2 creates a first position after the decimal point, and it must be a 5, as the result is xx.5
the second division by 2 splits again the uneven end .5 in half, creating a second position after the decimal point again ending in 5, as the result is now xx.x5
the third division by 2 does the same thing with that last 5 and creates a third position after the decimal point ending again in 5, as the result is now xx.xx5
the fourth division by 2 does again the same thing, a fourth position after the decimal point is created ending in 5. now xx.xxx5
in essence, every division of the 0.5 part by 2 is the same as a multiplication by 0.5, which squares 0.5 leading to 0.5². the next division did the same thing leading to 0.5³.
and finally the fourth division to 0.5⁴.
0.5⁴ = (5/10)⁴ = 5⁴/10⁴
so, now we start to divide this result by 5. since the positions after the decimal point are divisible by 5 without remainder, as we have 5⁴ to work with.
every divisible by 5 takes one of these powers away.
so, we go from 5⁴/10⁴ to 5³/10⁴ to 5²/10⁴ to 5/10⁴.
all the time we maintain the 10⁴ in the denominator of the fraction. and that determines the positions after the decimal point.
so, after all the individual divisions we come to and end and are still limited to the 4 positions after the decimal point.
If p = 7, q = 2, r = 4; find the value of q (5p - r).
Answer: 62
Step-by-step explanation:
Given
p = 7, q = 2, r = 4
Solve
q ( 5p - r )
Substitute
(2) (5(7) - (4))
Simplify
(2) (35 - 4)
(2) (31)
62
Hope this helps!! :)
Please let me know if you have any questions
According to the graph above, College R showed
the greatest change in enrollment between which
two decades?
Given:
The graph that shows the ennoblement for college R between 1950 and 2000.
To find:
The two decades that has the greatest change in enrollment.
Solution:
From the given graph, it is clear that the change in the enrollment is:
From 1950 to 1960 is [tex]4-3.5=0.5[/tex] thousand.
From 1960 to 1970 is [tex]5-4.5=1.5[/tex] thousand.
From 1970 to 1980 is [tex]5.5-5=0.5[/tex] thousand.
From 1980 to 1990 is [tex]6.5-5.5=1[/tex] thousand.
From 1990 to 2000 is [tex]7-6.5=0.5[/tex] thousand.
The two decades 1960-1970 and 1980-1990 have the greatest change in enrollment.
Answer:1980 to 1990
Step-by-step explanation:
A trucking company buys 25,275 gallons of gasoline. The federal excise tax is $0.195 per gallon. Find the amount of excise tax due. (Round your answer to the nearest cent if necessary)
Answer: 5,055
Step-by-step explanation
multiply the amount of gallons purchased by tax and round up
$4928.625 is the answer.
An Excise tax is an indirect tax, usually paid by the manufacturer or retailer of the product. then passes along in the price of the product to the consumer.
Amount of gasoline = 25,375 gallons.
The Excise tax = $0-195/gallon.
The amount of Excise tax dece = 25.875 X $0.195
= $4928.625
Se the amount of Excise tax due for 25975 gallons of gasoline is $ 4928.625
what is Excise tax?Excise tax is generally a tax levied on the sale of a particular good or service or for a particular purpose. State excise taxes are usually levied on the sale of gasoline, air tickets, heavy trucks, road tractors, tanning beds, tires, cigarettes, and other goods and services.
Excise can be used to charge prices for externalities or to discourage the consumption of goods by others. They can also be used as royalties to generate income from people who use certain government services. Income should be used to maintain those government services.
Learn more about excise tax here:https://brainly.com/question/2871942
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What is the length of an arc with a central angle of 2/3pi radians and a radius of 24 centimeters?
Use 3.14 for pi.
Enter your answer, as a decimal, in the box.
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Answer:
50.24 cm
Step-by-step explanation:
Fill in the given numbers and do the arithmetic.
s = rθ
s = (24 cm)(2/3π) = (24 cm)(2/3)(3.14) = 50.24 cm
What are the domain and range of the function represented by the set of
ordered pairs?
{(-16, 0), (-8, -11), (0, 12), (12,4)}
Answer:
domain:-16,-8,0,12
range:0,-11,12,14
²/₃ + ¹/₃ please answer
FINAL ANSWER:
1
Step-by-step explanation:
[tex]\frac{2}{3} +\frac{1}{3}[/tex]
the denominators are the same so all we need to do is add.
[tex]\frac{2}{3} + \frac{1}{3} =\frac{3}{3}[/tex]
[tex]\frac{3}{3} =[/tex] 1 whole
final answer: 1
hope this answer helps you :)
have a great day and may God Bless You!
Which of the following is the minimum value of the equation y = 2x2 + 5?
5
0
−5
2
Test the claim that the proportion of men who own cats is significantly different than the proportion of women who own cats at the 0.2 significance level.
Answer:
Test the claim that the proportion of men who own cats is significantly different than the proportion of women who own cats at the 0.2 significance level.
The null and alternative hypothesis would be: H 0 : μ M = μ F H 1 : μ M < μ F H 0 : μ M = μ F H 1 : μ M > μ F H 0 : p M = p F H 1 : p M ≠ p F H 0 : p M = p F H 1 : p M < p F H 0 : p M = p F H 1 : p M > p F H 0 : μ M = μ F H 1 : μ M ≠ μ F
The test is:
right-tailed
left-tailed
two-tailed
Based on a sample of 40 men, 25%Based on a sample of 40 men, 25% owned cats
Based on a sample of 40 women, 40% owned cats
The test statistic is:
The p-value is:
Based on this we:
Reject the null hypothesis
Fail to reject the null hypothesis
In ABC, if CB AC≅ , m∠A = 3x + 18, m∠B = 7x – 58, and m∠C = 2x – 8, find x and the measure of each angle.
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Answer:
x = 19
A = 30°
B = C = 75°
Step-by-step explanation:
In an isosceles triangle, the angles opposite the congruent sides have the same measures.
A = B
3x +18 = 7x -58
76 = 4x . . . . . . . . add 58-4x
19 = x . . . . . . . . . divide by 4
Then the equal angles measure ...
A = B = 3(19) +18 = 75
C = 2(19) -8 = 30
Angles A, B, C measure 75°, 75°, 30°, respectively.
_____
Alternate solution
The sum of angles in a triangle is 180°, so you could write ...
(3x +18) +(7x -58) +(2x -8) = 180
12x = 228 . . . . . add 48
x = 19 . . . . . divide by 12
A researcher believes that 9% of males smoke cigarettes. If the researcher is correct, what is the probability that the proportion of smokers in a sample of 664 males would differ from the population proportion by greater than 3%
Answer:
0.0070 = 0.70% probability that the proportion of smokers in a sample of 664 males would differ from the population proportion by greater than 3%
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal 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.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
A researcher believes that 9% of males smoke cigarettes.
This means that [tex]p = 0.09[/tex]
Sample of 664
This means that [tex]n = 664[/tex]
Mean and standard deviation:
[tex]\mu = p = 0.09[/tex]
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.09*0.91}{664}} = 0.011[/tex]
What is the probability that the proportion of smokers in a sample of 664 males would differ from the population proportion by greater than 3%?
Proportion below 9 - 3 = 6% or above 9 + 3 = 12%. Since the normal distribution is symmetric, these probabilities are equal, so we find one of them and multiply by 2.
Probability the proportion is below 6%
P-value of Z when X = 0.06. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.06 - 0.09}{0.011}[/tex]
[tex]Z = -2.7[/tex]
[tex]Z = -2.7[/tex] has a p-value of 0.0035
2*0.0035 = 0.0070
0.0070 = 0.70% probability that the proportion of smokers in a sample of 664 males would differ from the population proportion by greater than 3%
Lightbulbs. A company produces lightbulbs. We know that the lifetimes (in hours) of lightbulbs follow a bell-shaped (symmetric and unimodal) distribution with a mean of 7,161 hours and a standard deviation of 564 hours. Use the Empirical Rule (68-95-99.7 rule) to answer the following question: The shortest lived 2.5% of the lightbulbs burn out before how many hours
Answer:
Please find the complete question and its solution in the attached file.
Step-by-step explanation:
Shortest had survived after 6741 hours [tex]2.5\%[/tex] of the lights burnt.
[tex]\to 0.15\% + 2.35\% = 2.50\%[/tex]
A telephone exchange operator assumes that 7% of the phone calls are wrong numbers. If the operator is accurate, what is the probability that the proportion of wrong numbers in a sample of 459 phone calls would differ from the population proportion by more than 3%
Answer:
0.0118 = 1.18% probability that the proportion of wrong numbers in a sample of 459 phone calls would differ from the population proportion by more than 3%
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal 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.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
A telephone exchange operator assumes that 7% of the phone calls are wrong numbers.
This means that [tex]p = 0.07[/tex]
Sample of 459 phone calls:
This means that [tex]n = 459[/tex]
Mean and standard deviation:
[tex]\mu = p = 0.07[/tex]
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\sqrt{\frac{0.07*0.93}{459}}} = 0.0119[/tex]
What is the probability that the proportion of wrong numbers in a sample of 459 phone calls would differ from the population proportion by more than 3%?
Proportion below 0.07 - 0.03 = 0.04 or above 0.07 + 0.03 = 0.1. Since the normal distribution is symmetric, these probabilities are the same, which means that we find one of them and multiply by 2.
Probability the proportion is below 0.04.
p-value of Z when X = 0.04. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.04 - 0.07}{0.0119}[/tex]
[tex]Z = -2.52[/tex]
[tex]Z = -2.52[/tex] has a p-value of 0.0059
2*0.0059 = 0.0118
0.0118 = 1.18% probability that the proportion of wrong numbers in a sample of 459 phone calls would differ from the population proportion by more than 3%
2(P +1) + 3(P + 2 ) > 2
Answer:
P>-6/5
Step-by-step explanation:
2(P+1)+3(P+2)>2
Use the distributive property to multiply 2 by P+1
2P+2+3(P+2)>2
Use the distributive property to multiply 3 by P+2
2P+2+3P+6>2
Combine 2P and 3P to get 5P
5P+2+6>2
Add 2 and 6 to get 8
5P+8>2
Subtract 8 from both sides
5P>2−8
Subtract 8 from 2 to get −6.
5P>−6
Divide both sides by 5. Since 5 is positive
P>−6/5
I litterally don't understand how to do this-
Answer:
Consider points (-1, 0) and (0, 1) :
[tex]{ \tt{slope = \frac{y _{2} - y _{1} }{x _{2} - x _{1} } }} \\ { \tt{slope = \frac{1 - 0}{0 - ( - 1)} }} \\ { \boxed{ \bf{slope = 1}}}[/tex]
Answer:
slope 1
Step-by-step explanation:
above ANS is correct mark it as branliest ANS
Adult men have heights with a mean of 69.0 inches and a standard deviation of 2.8 inches. Find the z-score of a man 71.2 inches tall. (to 2 decimal places)
Answer:
0.7857
Step-by-step explanation:
Given :
Mean = 69 inches
Standard deviation, = 2.8 inches
The Zscore of a man who is 71.2 inches
The ZSCORE is obtained using the relation :
Zscore = (Score, x - mean) / standard deviation
Zscore = (71.2 - 69) / 2.8
Zscore = 2.2 / 2.8
Zscore = 0.7857
Mai drives a truck for a soft drink company. Her truck is filled with 15-ounce cans and 70-ounce bottles. Let c be the number of 15-ounce cans the
truck is carrying, and let b be the number of 70-ounce bottles.
The truck must be carrying less than 4000 pounds (64,000 ounces). Using the values and variables given, write an inequality describing this.
Answer:
15c + 70b < 64,000
Step-by-step explanation:
15c will represent the amount of ounces in the truck from the 15 ounce cans.
70b will represent the amount of ounces in the truck from the 70 ounce bottles.
These need to be added together in the inequality to represent the total weight in the truck.
Then, a less than inequality sign needs to be used, since the truck has to be carrying less than 64,000 ounces.
Put this all together:
15c + 70b < 64,000
So, the inequality is 15c + 70b < 64,000
The solution set of the inequality 1 + 2y
Answer:
is it four I am not quite sure
Place the steps for finding f-1(x)
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Answer:
B, C, H, D, F, A
Step-by-step explanation:
Starting with y = f(x), swap x and y to get x = f(y), then solve for y. The solution steps "undo" what is done to y, in reverse order. Y is ...
multiplied by 721 subtracted from the productthe square root of the differenceTo "undo" these steps in reverse order, after swapping x and y, you must square both sides, add 21, then divide by 7.
If the left tiles are labeled A to H from top to bottom, the correct sequence of steps is ...
B, C, H, D, F, A
halla la suma y el producto de la PG 3,9,27,81,243
Answer:
huh ano yan huhu paki ayos ng sagot
Step-by-step explanation:
hahahhaa
Identify the domain of the function shown in the graph.