The average value of 3t^3-t^2 over the interval -1<=t<=2 is 11/4
Mean Value Theorem states if a function f(x) is continuous on the interval [a,b] and differentiable on (a,b), there is at least one value c in the interval (a<c<b) such that:
f '(c)=f(b)-f(a)/b-a
Average Value:
The average value of a function of a variable over a range represents the height of a rectangle of the same area as that defined by the function under the curve. This value can be calculated using a formula:
favg=1/b−a∫f(t)dt
consider f(x)=3t³-t² and limits are -1 to 2
Now, substitute these values in the above formula:
favg=1/2-(1)∫3t³-t²dt
favg=1/3∫(3/4t⁴-1/3t³)|₋₁²
favg=(12-8/3)-(3/4+1/3)
By solving the equation we get
favg=11/4
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Please help, ill give brainiest
A penny is dropped from the top of a new
building. Its height in feet can be modeled by
the equation y = 256 − 16x2, where x is the
time in seconds since the penny was dropped.
How long does it take for the penny to reach
the ground?
Answer:
4? I could be wrong. Sorry.
Step-by-step explanation:
A market analyst is curious what proportion Los Angeles residents have a landline telephone. A survey of 200
randomly selected Los Angeles residents shows that 96 of those selected have a landline telephone. The analyst
wants to use this data to construct a one-sample z interval for a proportion.
Based on this sample, which of the following is a 90% confidence interval for the proportion of Los Angeles
residents who have a landline telephone?
Answer:
0.48 ± 0.058
Step-by-step explanation:
Right on khan
Follow the steps to provide to answer the question
1. Find the greatest common factor of 8 and 12. 2. Use the Distributive Property and the greatest common factor to factor the expression &r-12 3.Write the equivalent expression.
Answer:
Step-by-step explanation:
1. Greatest Common Factor is the largest number that can be multiplied to get the product common to both product.
Factors of 8 Factors of 12
1 8 1 12
2 4 2 6
3 4
The GCF = 4
2. I need the expression rewritten in order to help you.
Find the Area: 12 ft 12 ft
a=12 ft
Po=(0.25×π×a²)
Pc=a²+0.5×Po
Pc=a²+0.5×(0.25×π×a²)
Pc=a²×(1+0.5×0.25×π)
Pc=a²×(1+0.5×0.25×π)
Pc=144×(1+0.5×0.25×π)
Pc≈200.55 ft²
What is the reciprocal of 1,058
Answer:
0.00094517958
Step-by-step explanation:
this is a answer I think so
3(x-4)=12x distributing or diving
Last week, the Tasha Cola company had sales of $2,346.87. This week, the company had sales of $8,867.14. Which is the best estimate of the company’s total sales for both weeks?
Answer:
$11,200 or $11,000
Step-by-step explanation:
The amounts are approximately $2,300 and $8,900 which add up to $11,200.
Answer: $11,200 or $11,000
It seems there are choices for this problem, but you did not include them, so I can't tell the exact correct answer.
13 percent of a certain company's life insurance policy holders are smokers. For each nonsmoker the probability of dying during the year is 0.002. For each smoker the probability of dying during the year is 0.02. Find the probability that a policy holder who died last year was a smoker.
Answer:
.6
Step-by-step explanation:
Using Bayes' theorem
While s = smoker
n = nonsmoker
D = died
P(s) = .13
P(n) =.87
P(D/s) =0.02
P(D/n) =0.002
P(s/D) = ??
[tex]P(s/D)=\frac{P(s)*P(D/s)}{P(s)*P(D/s)+P(n) *P(D/n)} =\frac{.13*.02}{.13*.02+.87*.002}=.6[/tex]
Simplify each expression.
ASAP PLEASE
Answer:
3
2y
Step-by-step explanation:
[tex] \bold{In \: {e}^{3} = 3In \: {e} = 3 \times 1 = 3} \\ \\ \bold{In \: {e}^{2y} = 2yIn \: {e} = 2y \times 1 = 2y}[/tex]
You may need to use the appropriate technology to answer this question. The Wall Street Journal Corporate Perceptions Study 2011 surveyed readers and asked how each rated the quality of management and the reputation of the company for over 250 worldwide corporations. Both the quality of management and the reputation of the company were rated on an excellent, good, and fair categorical scale. Assume the sample data for 200 respondents below applies to this study.
Quality of Management Reputation of Company
Excellent Good Fair
Excellent 40 25 8
Good 35 35 10
Fair 25 10 12
Use a 0.05 level of significance and test for independence of the quality of management and the reputation of the company.
a. State the null and alternative hypotheses.
b. Find the value of the test statistic. (Round your answer to three decimal places.)
c. Find the p-value. (Round your answer to four decimal places.)
Answer:
Step-by-step explanation:
The null and alternative hypothesis:
[tex]H_o \text{: Quality of management and reputation of company are independent}[/tex]
[tex]H_a \text{: Quality of management is not independent of the reputation of company }[/tex]
The observed values:
Excellent Good Fair Total
Excellent 40 25 8 73
Good 35 35 10 80
Fair 25 10 12 47
Total 100 70 30 200
The expected values = (Row total/column total)/grand total)
Excellent Good Fair
Excellent 36.5 25.55 10.95
Good 40 28 12
Fair 23.5 16.45 7.05
O E (O - E)²/E
40 36.5 0.3356
35 40 0.6250
25 23.5 0.0957
25 25.55 0.0118
35 28 1.7500
10 16.45 2.5290
8 10.95 0.7947
10 12 0.3333
12 7.05 3.4755
9.951
[tex]X^2 = \sum \dfrac{(O-E)^2}{E} \\ \\ \mathbf{X^2 = 9.951}[/tex]
Degree of freedom [tex]df = (r-1)(c-1)[/tex]
[tex]df = (3 - 1 ) (3 - 1)[/tex]
[tex]df = (2)(2)[/tex]
[tex]df = 4[/tex]
Using Excel formula =CHIDIST(x²,d.f)
The P-value = 0.0413
what is the value of X? (20 points)
Answer:
54.5
Step-by-step explanation:
[tex]x \degree = \frac{1}{2} (160 \degree - 51 \degree) \\ \\ x \degree = \frac{1}{2} \times 109 \degree \\ \\ x \degree = 54.5 \\ \\ x = 54.5 [/tex]
Use Ratio and Rate Vocabulary
RECORDING SHEET
Harper is buying fabric to make pillows. At the store, 3 yards of
flannel fabric costs $18, and 5 feet of fleece fabric costs $11. Whi
the better buy?
I know the units need to be the same to compare the prices.
First,
the length of the flannel fabric to feet.
The
of feet to yards is 3 feet: 1 yard.
How many feet are in 26 miles, 1155 feet ?
Answer:
The answer is 137,280
Step-by-step explanation:
5280 ft. = 1 mile
So....
26 x 5280 = 137,280
The larger of two numbers on three times the smaller. if the sum of the two numbers is 36 find the number?
Answer:
9 and 27
Step-by-step explanation:
Let the smaller number be x.
The larger of two numbers is three times the smaller.
Larger number = 3x
ATQ,
x+3x = 36
4x = 36
x = 9
Smaller number = 9
Larger number = 3x = 3(9) = 27
So, the numbers are 9 and 27.
pleaseee helppppppppp
Answer:
y is just being multiplyed by -4 :)
Step-by-step explanation:
in other words -4x
Answer:
y = -4x
Step-by-step explanation:
using number line what is 4-5
Answer:
-1Step-by-step explanation:
4 - 5 = -1
Count:
4, 3, 2, 1, 0, -1
Nolan is 11
4
5
years old. Jillian is 1
1
6
years older than Nolan and Jane is 1
1
3
years older than Jillian. How old is Jane?
Answer:
Jane is 13.
Step-by-step explanation:
Nolan is 11
Jillian is 12 because Jillian is 1 year older than Nolan.
Jane is one year older than Jillian. Which leads to the statement that Jane is 13 years old.
Find the area of the trapezoid
Answer:
1/2(l1+l2) is the area of trapezium
Answer:
A=a+b /2h
Step-by-step explanation:
Classify. * 6x^2 - 22x^5
a. quadratic binomial
b. quadratic polynomial
c. quintic binomial
d. not a polynomial
Answer:
Step-by-step explanation:
C
37 + 1/7 (-1/2) = ??
Answer:
517/14 good luck !!
Step-by-step explanation:
Answer: answer in photo, hope it helps.
Step-by-step explanation:
find domain (y-10)/y^2-3
Answer:
[tex] y 3 - 10 {y 2} - 3[/tex]
a total of 40 percent of the voters in a city classify themselves as independents, whereas 35 percent classify themselves as liberals, and 25 percent as conservatives. in a recent election, 40 percent of the independents, 75 percent of the liberals, and 65 percent of the conservatives voted. given that a person voted in the election, what is the probability that the person is an independent
Answer:
Probability = 0.088 ie 8.8%
Step-by-step explanation:
P (I) = 40% = 0.4
P (L) = 35% = 0.35
P (C) = 25% = 0.25
P (EV / I) = 40% = 0.4
P (EV / L) = 75% = 0.75
P (EV / C) = 65% = 0.65
P (I / EV) = [ P (EV / I) . P (I) ] / [ P ( EV) ]
[ P (EV / I) . P (I) ] / [ P (EV / I) + P (EV / L) + P (C / L)
[(0.4) (0.4)] / [ 0.4 + 0.75 + 0.65 ]
0.16 / 1.8
= 0.088 ie 8.8%
Pls help me I’ll give brainliest
Answer:
-2.7<4.5
Step-by-step explanation:
how to answer dissimilar and similar fraction using addition and subtraction?
Answer:
Make their denominators equal using the concept of least common multiple. Then subtract their numerators accordingly. Rewrite each fraction to its equivalent fraction with a denominator equal to the LCM = 30, then subtract their numerators. Make sure to reduce your answer to the lowest term.
Step-by-step explanation:
the following are scores of students:9,7,8,9,7,5,8,10,7,8 and 10. the value of the population variance is 4. true or false?
Answer:
yesStep-by-step explanation:
yyyyyyyyyyyyyyyyyyyyyy
Andrea Drew the Number line below. She said that 9/8 and 1 equal. Explain Error
Answer:
Her error was that 1 and 9/8 are not equal. 9/8 is 1/8 larger than 1 is, and therefore can not be equivalent to 1.
On the number line 9/8 and 1 are not equal, since 9/8 =1.125 which is greater than 1.
What is number line?A number line is a visual representation of numbers on a straight line. This line is used to compare numbers that are placed at equal intervals on an infinite line that extends on both sides, horizontally or vertically.
Given that, on the number line Andrea Drew marked 9/8 and 1 and she said that they are equal.
Here, 9/8 =1.125
1.125>1
Therefore, on the number line 9/8 and 1 are not equal, since 9/8 =1.125 which is greater than 1.
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the beginning is 7 ÷ 3 help
Algebra 2
How do I solve this problem
Answer:
Step-by-step explanation:
You cannot solve the problem because it doesn't have an equal sign, but I suppose you can simplify it. Look at this screenshot, it may help:
Step-by-step explanation:
-\fraction{4v^2}{m^2}
that is the answer or if u want u can search up on a calculator called symbolab or math-way
hlep plees
hi i need to do a test for mi 1 grad clas
what 2-2=
3-1=
and for my hom work
what is
56-210=
300x 285
please help
Answer:
0, 2, 154, 85,500
Step-by-step explanation:
these are the anwsers to your question
Our environment is very sensitive to the amount of ozone in the upper atmosphere. The level of ozone normally found is 6.0 parts/million (ppm). A researcher believes that the current ozone level is not at a normal level. The mean of 13 samples is 5.6 ppm with a variance of 0.49. Assume the population is normally distributed. A level of significance of 0.1 will be used. Find the value of the test statistic. Round your answer to three decimal places.
Answer:
Test statistic | t| = |-2.0607| = 2.0607
Step-by-step explanation:
Step(i):-
Given that the mean of the Population = 6.0 parts / million
The mean of sample x⁻ = 5.6ppm
The variance of the sample = 0.49
The standard deviation of the sample (s) = √0.49 = 0.7
Step(ii):-
Test statistic
[tex]t = \frac{x^{-} - mean}{\frac{S}{\sqrt{n} } }[/tex]
[tex]t = \frac{5.6 - 6.0}{\frac{0.7}{\sqrt{13} } }[/tex]
t = -2.0607
Final answer:-
Test statistic | t| = |-2.0607| = 2.0607