Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) = 4x2 − 3x + 2, [0, 2]
Answer:
Yes , it satisfies the hypothesis and we can conclude that c = 1 is an element of [0,2]
c = 1 ∈ [0,2]
Step-by-step explanation:
Given that:
[tex]f(x) = 4x^2 -3x + 2, [0, 2][/tex]
which is read as the function of x = 4x² - 3x + 2 along the interval [0,2]
Differentiating the function with respect to x is;
f(x) = 8x - 3
Using the Mean value theorem to see if the function satisfies it, we have:
[tex]f'c = \dfrac{f(b)-f(a)}{b-a}[/tex]
[tex]8c -3 = \dfrac{f(2)-f(0)}{2-0}[/tex]
since the polynomial function is differentiated in [0,2]
[tex]8c -3 = \dfrac{(4(2)^2-3(2)+2)-(4(0)^2-3(0)+2)}{2-0}[/tex]
[tex]8c -3 = \dfrac{(4(4)-3(2)+2)-(4(0)-3(0)+2)}{2-0}[/tex]
[tex]8c -3 = \dfrac{(16-6+2)-(0-0+2)}{2-0}[/tex]
[tex]8c -3 = \dfrac{(12)-(2)}{2}[/tex]
[tex]8c -3 = \dfrac{10}{2}[/tex]
8c -3 = 5
8c = 5+3
8c = 8
c = 8/8
c = 1
Therefore, we can conclude that c = 1 is an element of [0,2]
c = 1 ∈ [0,2]
Two boys and three girls are auditioning to play the piano for a school production. Two students will be chosen, one as the pianist, the other as the alternate.
What is the probability that the pianist will be a boy and the alternate will be a girl? Express your answer as a percent.
30%
40%
50%
60%
Answer:
30% is the correct answer.
Step-by-step explanation:
Total number of boys = 2
Total number of girls = 3
Total number of students = 5
To find:
Probability that the pianist will be a boy and the alternate will be a girl?
Solution:
Here we have to make 2 choices.
1st choice has to be boy (pianist) and 2nd choice has to be girl (alternate).
[tex]\bold{\text{Required probability }= P(\text{boy as pianist first}) \times P(\text{girl as alternate})}[/tex]
Formula for probability of an event E is given as:
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]
For [tex]P(\text{boy as pianist})[/tex], number of favorable cases are 2 (total number of boys).
Total number of cases = Total number of students i.e. 5
So, [tex]P(\text{boy as pianist})[/tex] is:
[tex]P(\text{boy as pianist}) = \dfrac{2}{5}[/tex]
For [tex]P(\text{girl as alternate})[/tex], number of favorable cases are 3 (total number of girls).
Now, one boy is already chosen as pianist so Total number of cases = Total number of students left i.e. (5 - 1) = 4
[tex]P(\text{girl as alternate}) = \dfrac{3}{4}[/tex]
So, the required probability is:
[tex]\text{Required probability } = \dfrac{2}{5}\times \dfrac{3}{4} = \dfrac{3}{10} = \bold{30\%}[/tex]
Answer:
30% A
Step-by-step explanation:
I need help will rate you brainliest
Answer:
Yes you can
Step-by-step explanation:
To eliminate the denominator
Answer:
No
Step-by-step explanation:
We cannot be certain that x + 3 > 0
If it was negative then the sign of the inequality would change.
To solve find the critical values of the numerator/ denominator, that is
x = 2 and x = - 3
The domain is the split into 3 intervals
(- ∞, - 3 ), (- 3, 2), (2, + ∞ )
Use test points from each interval to determine valid solution
Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.)
an = (−3^n)/(4n!)
Answer:
[tex]a_{i} = \frac{(-3)^{i}}{4\cdot i!}[/tex] converges.
Step-by-step explanation:
The convergence analysis of this sequence is done by Ratio Test. That is to say:
[tex]r = \frac{a_{n+1}}{a_{n}}[/tex], where sequence converges if and only if [tex]|r| < 1[/tex].
Let be [tex]a_{i} = \frac{(-3)^{i}}{4\cdot i!}[/tex], the ratio for the expression is:
[tex]r =-\frac{3}{n+1}[/tex]
[tex]|r| = \frac{3}{n+1}[/tex]
Inasmuch [tex]n[/tex] becomes bigger, then [tex]r \longrightarrow 0[/tex]. Hence, [tex]a_{i} = \frac{(-3)^{i}}{4\cdot i!}[/tex] converges.
Question 18 i will maek the brainliest:)
Answer:
Median: 14.6, Q1: 6.1, Q3: 27.1, IR: 21, outliers: none
Step-by-step explanation:
Step 1: order the data from the least to the largest.
2.8, 3.9, 5.3, 6.1, 6.5, 7.1, 12.5, 14.6, 16.4, 16.4, 20.8, 27.1, 28.1, 30.9, 53.5
Step 2: find the median.
The median is the middle value, which is the 8th value in the data set.
2.8, 3.9, 5.3, 6.1, 6.5, 7.1, 12.5, [14.6,] 16.4, 16.4, 20.8, 27.1, 28.1, 30.9, 53.5
Median = 14.6
Step 2: Find Q1,
Q1 is the middle value of the lower part of the data set that is divided by the median to your left.
2.8, 3.9, 5.3, (6.1), 6.5, 7.1, 12.5, [14.6], 16.4, 16.4, 20.8, 27.1, 28.1, 30.9, 53.5
Q1 = 6.1
Step 3: find Q3.
Q3 is the middle value of the upper part of the given data set.
2.8, 3.9, 5.3, 6.1, 6.5, 7.1, 12.5, [14.6], 16.4, 16.4, 20.8, (27.1), 28.1, 30.9, 53.5
Q3 = 27.1
Step 4: find interquartile range (IR)
IR = Q3 - Q1 = [tex] 27.1 - 6.1 = 21 [/tex]
Step 5: check if there is any outlier.
Formula for checking for outlier = [tex] Q1 - 1.5*IR [/tex]
Then compare the result you get with the given values in the data set. Any value in the data set that is less than the result we get is considered an outlier.
Thus,
[tex] Q1 - 1.5*IR [/tex]
[tex]6.1 - 1.5*21 = -25.4[/tex]
There are no value in the given data set that is less than -25.4. Therefore, there is no outlier.
A test-preparation company advertises that its training program raises SAT scores by an average of at least 30 points. A random sample of test-takers who had completed the training showed a mean increase smaller than 30 points.
(a) Write the hypotheses for a left-tailed test of the mean.
(b) Explain the consequences of a Type I error in this context.
Answer:
(a) Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \geq[/tex] 30 points
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 30 points
(b) Type I error is that we conclude that test-takers who had completed the training showed a mean increase smaller than 30 points but in actual, the program raises SAT scores by an average of at least 30 points.
Step-by-step explanation:
We are given that a test-preparation company advertises that its training program raises SAT scores by an average of at least 30 points.
A random sample of test-takers who had completed the training showed a mean increase smaller than 30 points.
Let [tex]\mu[/tex] = average SAT score.
(a) So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \geq[/tex] 30 points
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 30 points
Here, the null hypothesis states that the training program raises SAT scores by an average of at least 30 points.
On the other hand, the alternate hypothesis states that test-takers who had completed the training showed a mean increase smaller than 30 points.
(b) Type I error states the probability of rejecting the null hypothesis given the fact that null hypothesis is true.
According to the question, the Type I error is that we conclude that test-takers who had completed the training showed a mean increase smaller than 30 points but in actual, the program raises SAT scores by an average of at least 30 points.
The consequence of a Type I error is that we conclude the test-takers have low SAT scores but in actual they have an SAT score of at least 30 points.
Consider the differential equation:
2y'' + ty' − 2y = 14, y(0) = y'(0) = 0.
In some instances, the Laplace transform can be used to solve linear differential equations with variable monomial coefficients.
If F(s) = ℒ{f(t)} and n = 1, 2, 3, . . . ,then
ℒ{tnf(t)} = (-1)^n d^n/ds^n F(s)
to reduce the given differential equation to a linear first-order DE in the transformed function Y(s) = ℒ{y(t)}.
Requried:
a. Sovle the first order DE for Y(s).
b. Find find y(t)= ℒ^-1 {Y(s)}
(a) Take the Laplace transform of both sides:
[tex]2y''(t)+ty'(t)-2y(t)=14[/tex]
[tex]\implies 2(s^2Y(s)-sy(0)-y'(0))-(Y(s)+sY'(s))-2Y(s)=\dfrac{14}s[/tex]
where the transform of [tex]ty'(t)[/tex] comes from
[tex]L[ty'(t)]=-(L[y'(t)])'=-(sY(s)-y(0))'=-Y(s)-sY'(s)[/tex]
This yields the linear ODE,
[tex]-sY'(s)+(2s^2-3)Y(s)=\dfrac{14}s[/tex]
Divides both sides by [tex]-s[/tex]:
[tex]Y'(s)+\dfrac{3-2s^2}sY(s)=-\dfrac{14}{s^2}[/tex]
Find the integrating factor:
[tex]\displaystyle\int\frac{3-2s^2}s\,\mathrm ds=3\ln|s|-s^2+C[/tex]
Multiply both sides of the ODE by [tex]e^{3\ln|s|-s^2}=s^3e^{-s^2}[/tex]:
[tex]s^3e^{-s^2}Y'(s)+(3s^2-2s^4)e^{-s^2}Y(s)=-14se^{-s^2}[/tex]
The left side condenses into the derivative of a product:
[tex]\left(s^3e^{-s^2}Y(s)\right)'=-14se^{-s^2}[/tex]
Integrate both sides and solve for [tex]Y(s)[/tex]:
[tex]s^3e^{-s^2}Y(s)=7e^{-s^2}+C[/tex]
[tex]Y(s)=\dfrac{7+Ce^{s^2}}{s^3}[/tex]
(b) Taking the inverse transform of both sides gives
[tex]y(t)=\dfrac{7t^2}2+C\,L^{-1}\left[\dfrac{e^{s^2}}{s^3}\right][/tex]
I don't know whether the remaining inverse transform can be resolved, but using the principle of superposition, we know that [tex]\frac{7t^2}2[/tex] is one solution to the original ODE.
[tex]y(t)=\dfrac{7t^2}2\implies y'(t)=7t\implies y''(t)=7[/tex]
Substitute these into the ODE to see everything checks out:
[tex]2\cdot7+t\cdot7t-2\cdot\dfrac{7t^2}2=14[/tex]
150,75,50 what number comes next
Answer:
35 or 25
Step-by-step explanation:
What is the equation of the following line? Be sure to scroll down first to see all answer options.
A.
y = - 1/2x
B.
y = 1/2x
C.
y = 2x
D.
y = -6x
E.
y = 6x
F.
y = 3x
Answer:
y=-6x
Step-by-step explanation:
PLS HELP !!
Define two terms, each containing the variables x and y, with exponents on each. (For Example : 10x³y–⁵)Find the quotient of the two terms. Explain step-by-step how you found the quotient
Answer:
Step-by-step explanation:
Two such terms are 7x^3*y^9 and -3x*y^5
Their quotient is
7x^3*y^9
--------------
-3x*y^5
This can be simplified as follows:
The numerical coefficients become -7/3.
x^3/x = x^3*x^1 = x^(3 - 1) = x^2 (we subtract the exponent of x in the denominator from the exponent of x in the numerator).
Next, y^9*y^5 = y^4.
The quotient in final reduced form is then (-7/3)x^2*y^4
A computer password is required to be 7 characters long. How many passwords are possible if the password requires 3 letter(s) followed by 4 digits (numbers 0-9), where no repetition of any letter or digit is allowed
Answer:
[tex]78,\!624,\!000[/tex].
Step-by-step explanation:
Note the requirements:
Repetition of letter or digit is not allowed.The order of the letters and digits matters.Because of that, permutation would be the most suitable way to count the number of possibilities.
There are [tex]\displaystyle P(26,\, 3) = \frac{26!}{(26 - 3)!} = 26 \times 25 \times 24 = 15,\!600[/tex] ways to arrange three out of [tex]26[/tex] distinct letters (without replacement.)
Similarly, there are [tex]\displaystyle P(10,\, 4) = \frac{10!}{(10 - 4)!} = 10 \times 9 \times 8 \times 7= 5,\!040[/tex] ways to arrange four out of [tex]10[/tex] distinct numbers (also without replacement.)
Therefore, there are [tex]15,\!600[/tex] possibilities for the three-letter section of this password, and [tex]5,\!040[/tex] possibilities for the four-digit section. What if these two parts are combined?
Consider: if the first three letters of the password were fixed, then there would be [tex]5,\!040[/tex] possibilities. However, if any of the first three letters was changed, the result would be another [tex]5,\!040\![/tex] possibilities, all of which are different from the previous [tex]5,\!040\!\![/tex] possibilities. These two three-letter sections along will give [tex]2 \times 5,\!400[/tex] possibilities. Since there are [tex]15,\!600[/tex] three-letter sections like that, there would be [tex]15,\!600 \times 5,\!400 = 78,\!624,\!000[/tex] possible passwords in total. That gives the number of possible passwords that satisfy these requirements.
Please help. I’ll mark you as brainliest if correct!
Answer:
(DNE,DNE)
Step-by-step explanation:
-24x-12y = -16. Equation one
6x +3y = 4. Equation two
Multiplying equation two with +4 gives
4(6x +3y = 4)
24x +12y = 16...result of equation two
-24x -12y= -16...
A careful observation to the following equation will help us notice that the both equation are same thing.
Multiplying minus to equation one gives
-(-24x-12y=-16)
24x+12y = 16.
Since the both equation are same, there is no solution to it.
Find X using the Angle Sum Theorem
Answer:
Step-by-step explanation:
x + 30 + 25 = 180
x + 55 = 180
x = 125
y + 125 = 180
y = 55
Find the value of the logarithm. log 122
Answer:
2.086
Step-by-step explanation:
Log 122 is equal to 2.086
In this diagram, bac~edf. if the area of bac= 6 in.², what is the area of edf? PLZ HELP PLZ PLZ PLZ PLZ
Answer:
Area of ΔEDF = 2.7 in²
Step-by-step explanation:
It's given in the question,
ΔBAC ~ ΔEDF
In these similar triangles,
Scale factor of the sides = [tex]\frac{\text{Measure of one side of triangle BAC}}{\text{Measure of one side of triangle EDF}}[/tex]
[tex]=\frac{\text{BC}}{\text{EF}}[/tex]
[tex]=\frac{3}{2}[/tex]
Area scale factor = (Scale factor of the sides)²
[tex]\frac{\text{Area of triangle BAC}}{\text{Area of triangle EDF}}=(\frac{3}{2})^2[/tex]
[tex]\frac{6}{\text{Area of triangle EDF}}=(\frac{9}{4})[/tex]
Area of ΔEDF = [tex]\frac{6\times 4}{9}[/tex]
= 2.67
≈ 2.7 in²
Therefore, area of the ΔEDF is 2.7 in²
What is the value of x?
Answer:
58
Step-by-step explanation:
By the property of intersecting secants outside of a circle, we have:
x° = 1/2( 141° - 25°) = 1/2 * 116° = 58°
Therefore, x = 58
What is the sum of the geometric sequence?
Answer:
B. 259
Step-by-step explanation:
6^(i - 1) for i = 1 to 4
sum = 6^(1 - 1) + 6^(2 - 1) + 6^(3 - 1) + 6^(4 - 1) =
= 6^0 + 6^1 + 6^2 + 6^3
= 1 + 6 + 36 + 216
= 259
Answer: B. 259
What is the sign of -456 +456
Answer:
0
Step-by-step explanation:
-456 +456
( - , + ) = -
so answer is 0
Answer:
0
Step-by-step explanation:
bc i know
find the area of square whose side is 2.5 cm
Answer:
6.25
Step-by-step explanation:
2.5 *2.5=6.25
Answer:
6.25cm^2.
Step-by-step explanation:
To find the area of a square, you multiply the two sides, 2.5✖️2.5.
This gives the area of 6.25cm^2.
Hope this helped!
Have a nice day:)
A box contains12 balls in which 4 are white,3 blue and 5 are red.3 balls are drawn at random from the box.Find the chance that all three balls are of sifferent color.(answer in three decimal places)
[tex]|\Omega|=_{12}C_3=\dfrac{12!}{3!9!}=\dfrac{10\cdot11\cdot12}{2\cdot3}=220\\|A|=4\cdot3\cdot5=60\\\\P(A)=\dfrac{60}{220}=\dfrac{3}{11}\approx0,273[/tex]
Answer:
0.273
Step-by-step explanation:
Total number of balls is 4+3+5 = 12
There are 6 ways to draw 3 different colors (WBR, WRB, BWR, BRW, RWB, RBW) each with a chance of 4/12 · 3/11 · 5/10 = 1/22
So the total chance is 6 · 1/22 = 6/22 = 3/11 ≈ 0.273
If a dog has 2,000,000 toys and he gives 900,000 away. Then gets 2,000 more, also looses 2,000,000. He's sad but then also got 5,000,000,000 more and gives 1,672,293 out. How much does he have now? And how much he gave away. And how much he got.
Answer:
See below.
Step-by-step explanation:
He does not have enough to loose 2,000,000 at that point, so this whole problem is nonsense.
How many times does the digit 9 appear in the list of all integers from 1 to 500? (The number $ 99 $, for example, is counted twice, because $9$ appears two times in it.)
Answer:
95 times digit 9 appears in all integers from 1 to 500.
Step-by-step explanation:
No. of 9 from
1-9: 1 time
10-19: 1 time
20-29: 1 time
30-39: 1 time
40-49: 1 time
50-59: 1 time
60-69: 1 time
70-79: 1 time
80-89 : 1 time
from 90 to 99
there will be one in 91 to 98
then two 9 in 99
thus, no of 9 from 90 to 99 is 10
Thus, total 9's from 1 to 99 is 9+10 = 19
Thus there 19 9's in 1 to 99
similarly
there will be
19 9's in 100 to 199
19 9's in 200 to 299
19 9's in 300 to 399
19 9's in 400 to 499
Thus, total 9's will be
19 + 19 + 19+ 19 + 19 + 19 = 95
Thus, 95 times digit 9 appears in all integers from 1 to 500.
Plaz guys help me on this question additional mathematics
Answer:
Step-by-step explanation:
vector OA=a
vector OB=b
vector OX= λ vector OA=λa
vector OY=μ vector OB=μb
a.
1.vector BX=(vector OX-vector OB)=λa-b
ii. vector AY=(vector OY-vector OA)=μb-a
b.
5 vector BP=2 vector BX
5(vector OP-vector OB)=2 (vector OX-vector OB)
5(vector OP-b)=2(λa-b)
5 vector OP-5b=2λa-2b
5 vector OP=2λa-2b+5b
vector OP=1/5(2λa+3b)
ii
complete it.
A cube has an edge of 2 feet. The edge is increasing at the rate of 5 feet per minute. Express the volume of the cube as a function of m, the number of minutes elapsed.
Answer:
[tex]V(m) = (2 + 5m)^3[/tex]
Step-by-step explanation:
Given
Solid Shape = Cube
Edge = 2 feet
Increment = 5 feet per minute
Required
Determine volume as a function of minute
From the question, we have that the edge of the cube increases in a minute by 5 feet
This implies that,the edge will increase by 5m feet in m minutes;
Hence,
[tex]New\ Edge = 2 + 5m[/tex]
Volume of a cube is calculated as thus;
[tex]Volume = Edge^3[/tex]
Substitute 2 + 5m for Edge
[tex]Volume = (2 + 5m)^3[/tex]
Represent Volume as a function of m
[tex]V(m) = (2 + 5m)^3[/tex]
What is the median of these figure skating ratings?
6.0 6.0 7.0 7.0 7.0 8.0 9.0
Answer:
The median would be 7.0.
Step-by-step explanation:
The median of a set of numbers means it is the middle number. since this set has 7 numbers you would need to find the number that is in the middle of the set. This would be the 4th number since it is in the middle. 7.0 is your answer.
Credit card companies lose money on cardholders who fail to pay their minimum payments. They use a variety of methods to encourage their delinquent cardholders to pay their credit card balances, such as letters, phone calls and eventually the hiring of a collection agency. To justify the cost of using the collection agency, the agency must collect an average of at least $200 per customer. After a trial period during which the agency attempted to collect from a random sample of 100 delinquent cardholders, the 90% confidence interval on the mean collected amount was reported as ($190.25, $250.75). Given this, what recommendation(s) would you make to the credit card company about using the collection agency
Answer with explanation:
A x% confidence interval interprets that a person can be x% confident thatthe true mean lies in it.
Here, Credit card companies is using the collection agency to justify the cost of , the agency must collect an average of at least $200 per customer.
i.e. [tex]H_0:\mu \geq200,\ \ \ H_a:\mu<200[/tex]
The 90% confidence interval on the mean collected amount was reported as ($190.25, $250.75) .
I recommend that we can be 90% sure that the true mean collected amount lies in ($190.25, $250.75).
Also, $200 lies in it such that it is more far from $250.75 than $190.25, that means there are large chances of having an average is at least $200 per customer.
_______% of 44 = 22
Answer:
50%
Step-by-step explanation:
22 is half of 44.
So, this means 50% of 44 is 22.
Was it evaluated correctly?
Explain your reasoning
help i need to turn it in a hour
Answer:
no
Step-by-step explanation:
2(4+10)+20
2(14)+20
28+20
48
the dot plot above identifies the number of pets living with each of 20 families in an apartment building .what fraction of families have more than two pets
Answer:
B. ⅕
Step-by-step explanation:
Fraction of families having more than 2 pets = families with pets of 3 and above ÷ total number of families in the apartment
From the dot plot above, 3 families have 3 pets, and 1 family has 4 pets.
Number of families with more than 2 pets = 3 + 1 = 4
Fraction of families with more than 3 pets = [tex] \frac{4}{20} = \frac{1}{5} [/tex]
The fraction of families that have more than two pets is B. [tex]\frac{1}{5}[/tex]
Calculations and ParametersGiven that:
Fraction of families having more than 2 pets = families with pets of 3 and above/total number of families in the apartment
From the dot plot above:
3 families have 3 pets, 1 family has 4 pets.Number of families with more than 2 pets
= 3 + 1
= 4
Fraction of families with more than 3 pets = [tex]\frac{4}{20} = \frac{1}{5}[/tex]
Read more about dot plots here:
https://brainly.com/question/25957672
#SPJ5
What is the value of b.
C=25
s=9
B=4c-s2
Answer:
82
Step-by-step explanation:
Plug in the variables into the equation and solve for B but remember your order of operations when solving multiplication/division before addition/subtraction.
B = 4*25-9*2
B = 100-18
B = 82
