Answer:
C
Step-by-step explanation:
We want to evaluate the definite integral:
[tex]\displaystyle \int_0^1 (x+2)(3x^2+12x+1)^{1/2}\, dx[/tex]
Again, notice that the radicand is quite similar to the outside factor. So, we can use u-substitution again. We will let:
[tex]\displaystyle u=3x^2+12x+1[/tex]
Then:
[tex]\displaystyle \frac{du}{dx}=6x+12[/tex]
Hence:
[tex]\displaystyle du=6x+12 \, dx[/tex]
And we can divide both sides by 6:
[tex]\displaystyle \frac{1}{6}\, du=x+2\, dx[/tex]
Note that the limits of integration of our original integral (from x = 0 to x = 1) is in the domain of x. Since we changed variables, we should also change the limits of integration to u. So:
[tex]u(0)=3(0)^2+12(0)+1=1[/tex]
And:
[tex]u(1)=3(1)^2+12(1)+1=16[/tex]
Hence, our new limits of integration is from u = 1 to u = 16.
Perform the substitution:
[tex]\displaystyle =\int_{1}^{16} u^{1/2}\Big(\frac{1}{6}\, du\Big)[/tex]
Simplify:
[tex]\displaystyle =\frac{1}{6}\int_1^{16}u^{1/2}\, du[/tex]
Integrate:
[tex]\displaystyle =\frac{1}{6}\Big(\frac{2}{3}u^{3/2}\Big)\Big|_{1}^{16}[/tex]
Simplify:
[tex]=\displaystyle \frac{1}{9}\Big(u^{3/2}\Big|_1^{16}\Big)[/tex]
Evaluate:
[tex]\displaystyle =\frac{1}{9}\Big(16^{3/2}-1^{3/2}\Big)=\frac{1}{9}(64-1)=7[/tex]
The answer is C.
This is really urgent!!!
Step-by-step explanation:
=4(x-1)-3(2x-5)
=4x-4-6x+16
=4x-6x-4+16
= -2x+12
hope it helps.
Answer:
2x + 11
1.) Distribute
4(x-1)-3(2x-5)
4x -4 -3 (2x-5)
2.) Connect like terms
4x -4 -6x + 15
-2x -4 +15
3.) Calculate
-2x + 11
Suppose that in the production of 60-ohm radio resistors, nondefective items are those that have a resistance between 58 and 62 ohms and the probability of a resistor’s being defective is The resistors are sold in lots of 200, with the guarantee that all resistors are nondefective. What is the probability that a given lot will violate this guarantee? (Use the Poisson distribution.)
Answer:
The probability that a given lot will violate this guarantee is [tex]1 - e^{-200x}[/tex], in which x is the probability of a resistor being defective.
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
The probability of a resistor’s being defective is x:
This means that [tex]\mu = nx[/tex], in which n is the number of resistors.
The resistors are sold in lots of 200
This means that [tex]n = 200[/tex], so [tex]\mu = 200x[/tex]
What is the probability that a given lot will violate this guarantee?
This is:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = 0) = \frac{e^{-200x}*(200x)^{0}}{(0)!} = e^{-200x}[/tex]
So
[tex]P(X \geq 1) = 1 - e^{-200x}[/tex]
The probability that a given lot will violate this guarantee is [tex]1 - e^{-200x}[/tex], in which x is the probability of a resistor being defective.
I am having a baby day so if you write something wrong I’m reporting you
Answer:
804.25 or based on the choices 803.8
Step-by-step explanation:
Answer:
804.25
Step-by-step explanation:
so the closest thing to that is 803.8
Sarah invested $2,500 in an account paying an interest rate of 2.1% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest hundred dollars, would be in the account after 14 years?
Answer:
sorry 2458946547165874%
Step-by-step explanation:
What is the mean of these numbers?4,5,5,2,3,3,2,8
Answer:
4
Step-by-step explanation:
Mean is the average of the set of the data in which two or more numbers are present. The mean is used to summarized the data set as the calculation of the mean includes all the values given in the data set. The mean value of the given data set is 4.
Given informationThe given numbers of the data set are,
4,5,5,2,3,3,2,8
Total numbers are 8.
MeanMean is the average of the set of the data in which two or more numbers are present. The mean is used to summarized the data set as the calculation of the mean includes all the values given in the data set.
Mean is the ratio of the sum of all the terms of the set to the the number of terms in the set.
The mean can be calculated with the following formula,
[tex]\overline x=\dfrac{\sum x}{N} [/tex]
Here N is the total number of the values in the set.
Put the values in the above formula,
[tex]\overline x=\dfrac{4+5+5+2+3+3+2+8}{8} \\ \overline x=\dfrac{32}{8}\\ \overline x=4[/tex]
Hence the mean value of the given data set is 4.
Learn more about the mean here;
https://brainly.com/question/12513463
Plz help quick I will give brainly points
Can somebody help me plsssss
5,0 is not a solution to the system of linear inequalities.
PLEASE HELP DEW IN 1 hour
Answer: B
Step-by-step explanation:
2(—2) + 10 = 6.
2(0) + 6 = 6.
2(2) + 2 = 6.
2(4) + (—2) = 6
What is the measure of the unknown angle?
Answer:
24
Step-by-step explanation:
x+120+36=180
x+156=180
x=180-156
x=24
13. In the given circle, AB = 13 m, BC = 6 m, and CD = 8 m. If DE = x, find the value
of x. (The figure is not drawn to scale.)
E
x
A
B
A. 13.25 m
B. 9.75 m
C. 6.25 m
D. 14.25 m
do you know what the answer was?
Is 2(6 - 3x) + x equivalent to 2(3x) + x?
Answer:
No.
Step-by-step explanation:
2(6-3x)= 12-6x and 2(3x)+x= 7x
(help?)
Look at the model.
Which of the following statements of equality is true? [png]
Answer:
H
Step-by-step explanation:
Answer:
H
Step-by-step explanation:
3 times 2 and x in each row
which equals to 6 and 3x
Roger expressed 1/5%
as 1/500. Ellen expressed 1/5% as 100/5. Who is
correct? Explain.
Answer:
Ellen is correct
Step-by-step explanation:
Roger:
The left side 20 does not equal to the right side 0.002 , which means that the given statement is false.
Ellen:
The left side 20 is equal to the right side 20, which means that the given statement is always true.
Hope I helped, Brainliest would be appreciated :)
Have a fantastic day!
-Aadi x
What is 94,353 in expanded form?
[tex] \large \color{lightblue}Answer:[/tex]
94,353 = 90,000 + 4,000 + 300 + 50 + 3Hope it helps..
Answer:
90000 + 4000 + 300 + 50 + 3 = 94353
A clothing business finds there is a linear relationship between the number of shirts, n (in thousands) it can sell and the price, P, it can charge per shirt. In particular, historical data shows that 3 thousand shirts can be sold at a price of $69 each, and that 7 thousand shirts can be sold at a price of $61 each. Find the equation of the form P(n)
Answer:
The equation of the form P(n) is:
P(n)=-0.002n+75
Step-by-step explanation:
From the information provided, you have two points: (3000, 69) and (7000, 61). With this, you can find the slope using the following formula:
m=(p1-p2)/(n1-n2)
m=slope
p1=69
p2=61
n1=3000
n2=7000
m=(69-61)/(3000-7000)
m=8/-4000
m=-0.002
Now that you have the slope, you can find the the equation of the form P(n):
P(n)=-0.002(n-3000)+69
P(n)=-0.002n+6+69
P(n)=-0.002n+75
According to this, the answer is that the equation of the form P(n) is:
P(n)=-0.002n+75
Whoever responds first will get marked Best.
The amount of wallpaper needed to cover the wall is an example of which
A: area
B: volume
C:perimeter
D:length
Answer:
A area
Step-by-step explanation:
What is 5+5+5+5+5+5+5+5+5+5+5+5+5
Answer:
65
Step-by-step explanation:
13x5 = 65
Answer:
The answer is 65 lol
Step-by-step explanation:
Hopefully this helps
there are 16 sixth graders, 11 seventh graders, and 9 eighth graders in a gym class. the gym teacher randomly selects one student to collect balls how many ways can choosing not a seventh grader occur
Answer:
34 total students.
25 are not 7th graders
27/35
sin (x-20)° =cos (5x-10)°
sin(x - 20)° = cos(5x - 10)°
Expand 5x - 10 in terms of x - 20:
5x - 10 = 5x - 100 + 90
… = 5 (x - 20) + 90
and recall that for all θ, cos(θ + 90)° = - sin(θ)°, so
sin(x - 20)° = cos(5 (x - 20) + 90)°
sin(x - 20)° = - sin(5 (x - 20))°
Replace (x - 20)° = y ° to make this a bit easier to read:
sin(y °) = - sin(5y )°
Expand the right side in terms of powers of sin:
sin(5θ) = 5 sin(θ) - 20 sin³(θ) + 16 sin⁵(θ)
so the equation becomes
sin(y °) = -5 sin(y °) + 20 sin³(y °) - 16 sin⁵(y °)
16 sin⁵(y °) - 20 sin³(y °) + 6 sin(y °) = 0
Replace z = sin(y °) to get a polynomial equation:
16z ⁵ - 20z ³ + 6z = 0
Factorize the left side:
2z (8z ⁴ - 10z ² + 3) = 0
2z (2z ² - 1) (4z ² - 3) = 0
Solve for z :
• 2z = 0 → z = 0
• 2z ² - 1 = 0 → z ² = 1/2 → z = ± 1/√2
• 4z ² - 3 = 0 → z ² = 3/4 → z = ± √3/2
Solve for y in each case above:
• z = sin(y °) = 0 → y = 0 + 360n or y = 180 + 360n
(where n is any integer)
These solutions can be combined into one family, y = 180n.
• z = sin(y °) = -1/√2 → y = 225 + 360n or y = 315 + 360n
• z = sin(y °) = 1/√2 → y = 45 + 360n or y = 135 + 360n
These solutions can also be combined, y = 45 + 90n.
• z = sin(y °) = -√3/2 → y = 240 + 360n or y = 300 + 360n
• z = sin(y °) = √3/2 → y = 60 + 360n or y = 120 + 360n
These can be combined as y = 60 + 180n or y = 120 + 180n.
Solve for x in each case:
• y = x - 20 = 180n → x = 20 + 180n
• y = x - 20 = 45 + 90n → x = 65 + 90n
• y = x - 20 = 60 + 180n → x = 80 + 180n
• y = x - 20 = 120 + 180n → x = 140 + 180n
Caleb has a board that measures 10 feet in length. How many 1/3 foot-long pieces can Caleb from the board?
please help right now
Step-by-step explanation:
[tex] \sqrt{26} is \: between 5.0and5.1[/tex]
i dont understand what im doing wrong
Answer:
8
Step-by-step explanation:
-2 x -2 = 4
4 - (-28 / 7 = -4)
4- -4 = 8
.) Suppose college students produce 650 pounds of solid waste each year, on average. Assume that the distribution of waste per college student is normal with a mean of 650 pounds and a standard deviation of 20 pounds. What is the probability that a randomly selected student produces either less than 620 or more than 700 pounds of solid waste
Answer:
0.073 = 7.3% probability that a randomly selected student produces either less than 620 or more than 700 pounds of solid waste
Step-by-step explanation:
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.
Mean of 650 pounds and a standard deviation of 20 pounds.
This means that [tex]\mu = 650, \sigma = 20[/tex]
What is the probability that a randomly selected student produces either less than 620 or more than 700 pounds of solid waste?
Less than 620:
pvalue of Z when X = 620. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{620 - 650}{20}[/tex]
[tex]Z = -1.5[/tex]
[tex]Z = -1.5[/tex] has a pvalue of 0.0668
More than 700:
1 subtracted by the pvalue of Z when X = 700. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{700 - 650}{20}[/tex]
[tex]Z = 2.5[/tex]
[tex]Z = 2.5[/tex] has a pvalue of 0.9938
1 - 0.9938 = 0.0062
Total:
0.0668 + 0.0062 = 0.073
0.073 = 7.3% probability that a randomly selected student produces either less than 620 or more than 700 pounds of solid waste
6. A hypothesis test in which rejection of the null hypothesis occurs for values of the point estimator in either tail of the sampling distribution is called _______ Group of answer choices A one-tailed test A two-tailed test The null hypothesis The alternative hypothesis g
Answer:
A two-tailed test.
Step-by-step explanation:
ANOVA is a short term or an acronym for analysis of variance which was developed by the notable statistician Ronald Fisher. The analysis of variance (ANOVA) is typically a collection of statistical models with their respective estimation procedures used for the analysis of the difference between the group of means found in a sample. Simply stated, ANOVA helps to ensure we have a balanced data by splitting the observed variability of a data set into random and systematic factors.
In Statistics, the random factors doesn't have any significant impact on the data set but the systematic factors does have an influence.
Basically, the analysis of variance (ANOVA) procedure is typically used as a statistical tool to determine whether or not the mean of two or more populations are equal through the use of null hypothesis or a F-test.
Hence, the null hypothesis for an analysis of variance (ANOVA) requires that all treatments or samples should be generated from populations having the same mean.
A hypothesis test in which rejection of the null hypothesis occurs for values of the point estimator in either tail of the sampling distribution is called a two-tailed test.
Explicit formula for
1,5,3,6,12
sorry I needed the points!
Today only a table is being sold at a 15% discount. The sale price is $629
Answer:
740
Step-by-step explanation:
Answer:
The answer is $566.73.
Step-by-step explanation:
The way that you find the answer is dividing .15 to the price
Need help on this math ASAP I will give the brainiest to the person who answers this correctly! Do the ones that are circled in red please. (67 points to the person who answers this)
The solution is, 0.39 = 39% of probability.
What is probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
here, we have,
When you need to calculate probabilities involving "or" questions, in general you should use the following formula: , where P(A) is the probability of event A and P(B) is the probability of event B.
In the problem given, P(A) = yes and P(B) = male, then:
P(yes) = 33/100
= 0.33
P(male) = 20/100
= 0.20 (all male that answered the question)
P(yes and male)
= 14/100
= 0.14 (all male that answered yes to the question)
P(yes or male) = P(yes) + P(male) - P(yes and male)
= 0.33+0.20-0.14
= 0.39
=39%
Hence, The solution is, 0.39 = 39% of probability.
To learn more on probability click:
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Complete question:
One hundred people were asked, "Do you favor the death penalty?" Of the 33 that answered "yes" to the question, 14 were male. Of the 67 that answered "no" to the question, six were male. If one person is selected at random, what is the probability that this person answered "yes" or was a male?
A gadget company randomly selects 10 toys per hour to inspect. The number of defective toys in the last six samples is shown in the table.
Based on this information, how many toys are likely to be defective in a sample of 500?
A: 1
B: 5
C: 50
D: 300
Answer:
50
Step-by-step explanation:
Using proportions, it is found that the number of toys that is likely to be defective in a sample of 500 is given by:
C: 50
What is a proportion?A proportion is a fraction of a total amount.
For the samples of 10, the mean number of errors is of:
( 0 + 2 + 1 + 1 + 2 + 0)/6 = 1
Hence, for samples of 500, the expected number of defective toys will be given by:
E = (500/10) x 1 = 50
Hence, option C is correct.
More can be learned about proportions at https://brainly.com/question/24372153
Jackie says that 200 ÷ 18 = 25. Is Jackie correct? Explain.
Answer:
Wrong
Step-by-step explanation:
200%18=11.11111111
Answer: Jackie is incorrect
Step-by-step explanation:
Because 200/18 = 11.1111111111
Is -12 greater than -5
Answer:
No. it's less than. The bigger the negative number is, the lesser it is.