Answer: c = 4.97 and c = -1.97
Step-by-step explanation: Mean Value Theorem states if a function f(x) is continuous on interval [a,b] and differentiable on (a,b), there is at least one value c in the interval (a<c<b) such that:
[tex]f'(c) = \frac{f(b)-f(a)}{b-a}[/tex]
So, for the function f(x) = [tex]2x^{3}-9x^{2}-60x+1[/tex] on interval [-4,9]
[tex]f'(x) = 6x^{2}-18x-60[/tex]
f(-4) = [tex]2.(-4)^{3}-9.(-4)^{2}-60.(-4)+1[/tex]
f(-4) = 113
f(9) = [tex]2.(9)^{3}-9.(9)^{2}-60.(9)+1[/tex]
f(9) = 100
Calculating average:
[tex]6c^{2}-18c-60 = \frac{100-113}{9-(-4)}[/tex]
[tex]6c^{2}-18c-60 = -1[/tex]
[tex]6c^{2}-18c-59 = 0[/tex]
Resolving through Bhaskara:
c = [tex]\frac{18+\sqrt{1740} }{12}[/tex]
c = [tex]\frac{18+41.71 }{12}[/tex] = 4.97
c = [tex]\frac{18-41.71 }{12}[/tex] = -1.97
Both values of c exist inside the interval [-4,9], so both values are mean slope: c = 4.97 and c = -1.97
Consider the surface f(x,y) = 21 - 4x² - 16y² (a plane) and the point P(1,1,1) on the surface.
Required:
a. Find the gradient of f.
b. Let C' be the path of steepest descent on the surface beginning at P, and let C be the projection of C' on the xy-plane. Find an equation of C in the xy-plane.
c. Find parametric equations for the path C' on the surface.
Answer:
A) ( -8, -32 )
Step-by-step explanation:
Given function : f (x,y) = 21 - 4x^2 - 16y^2
point p( 1,1,1 ) on surface
Gradient of F
attached below is the detailed solution
The length of a rectangle is three times its width. If the perimeter of the rectangle is 160 cm, what are the dimensions of this rectangle?
Answer:
The dimensions or Area of the rectangle is 1200cm².
How many numbers from 10 to 99 have a tens place exactly 3 times greater than their ones place? PLZZZ answer this question . I will be very happy whoever answers this I will give u brainliest too.
Answer:
45
Step-by-step explanation:
2 digit number starts from 10 ends at 99
between 10 and 19 there is only one number whose tens digit is more than ones digit.
that is 10
between 20 and 29 there are two numbers
20 and 21
like the same
between 30 and 39 there are 3 numbers
10–19. 1
20–29. 2
30–39. 3
40–49. 4
50–59. 5
60–69. 6
70–79. 7
80–89. 8
99–99. 9
sum of first n natural numbers is n(n+1)/2
9(9+1)/2=45
Three numbers between 10 and 99 have tens places that are precisely three times larger than their one's places.
What is Place value?The foundation of our whole number system is place value. In this approach, the value of a digit in a number is determined by where it appears in the number.
The tens digit must be three times larger than the units digit in order to meet the requirement. The units digit can have one of the following values: 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9.
Since we are seeking two-digit integers, it is not possible if the unit digit is zero for the tens digit also be zero.
In the case when the unit digit is 1, the tens digit must be 3, resulting in the number 31. Similar to the previous example, if the unit digit is 2, the tens digit must be 6, resulting in the number 62.
As we proceed, we discover the following integers meet the condition:
31, 62, 93
Therefore, there are three numbers from 10 to 99 that have a tens place exactly 3 times greater than their one's place.
Learn more about place values here:
https://brainly.com/question/27734142
#SPJ3
Among a simple random sample of 331 American adults who do not have a four-year college degree and are not currently enrolled in school, 48% said they decided not to go to college because they could not afford school.
Part II: Exercise 6.16 presents the results of a poll where 48% of 331 Americans who decide to not go to college do so because they cannot afford it.
#1: Calculate a 90% confidence interval for the proportion of Americans who decide to not go to college because they cannot afford it, and interpret the interval in context.
(a) lower bound: ______ (please round to four decimal places)
(b) upper bound: _____ (please round to four decimal places)
#2: Interpret the confidence interval in context:
(A) We can be 90% confident that our confidence interval contains the sample proportion of Americans who choose not to go to college because they cannot afford it
(B) 90% of Americans choose not to go to college because they cannot afford it
(C) We can be 90% confident that the proportion of Americans who choose not to go to college because they cannot afford it is contained within our confidence interval
#3: Suppose we wanted the margin of error for the 90% confidence level to be about 1.5%. How large of a survey would you recommend?
(a) A survey should include at least ________ people.
Answer:
(1) Therefore, a 90% confidence interval for the proportion of Americans who decide to not go to college because they cannot afford it is [0.4348, 0.5252].
(2) We can be 90% confident that the proportion of Americans who choose not to go to college because they cannot afford it is contained within our confidence interval
(3) A survey should include at least 3002 people if we wanted the margin of error for the 90% confidence level to be about 1.5%.
Step-by-step explanation:
We are given that a simple random sample of 331 American adults who do not have a four-year college degree and are not currently enrolled in school, 48% said they decided not to go to college because they could not afford school.
Firstly, the pivotal quantity for finding the confidence interval for the population proportion is given by;
P.Q. = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of Americans who decide to not go to college = 48%
n = sample of American adults = 331
p = population proportion of Americans who decide to not go to
college because they cannot afford it
Here for constructing a 90% confidence interval we have used a One-sample z-test for proportions.
So, 90% confidence interval for the population proportion, p is ;
P(-1.645 < N(0,1) < 1.645) = 0.90 {As the critical value of z at 5% level
of significance are -1.645 & 1.645}
P(-1.645 < [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < 1.645) = 0.90
P( [tex]-1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < [tex]\hat p-p[/tex] < [tex]1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.90
P( [tex]\hat p-1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < p < [tex]\hat p+1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.90
90% confidence interval for p = [ [tex]\hat p-1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] , [tex]\hat p+1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ]
= [ [tex]0.48 -1.96 \times {\sqrt{\frac{0.48(1-0.48)}{331} } }[/tex] , [tex]0.48 +1.96 \times {\sqrt{\frac{0.48(1-0.48)}{331} } }[/tex] ]
= [0.4348, 0.5252]
(1) Therefore, a 90% confidence interval for the proportion of Americans who decide to not go to college because they cannot afford it is [0.4348, 0.5252].
(2) The interpretation of the above confidence interval is that we can be 90% confident that the proportion of Americans who choose not to go to college because they cannot afford it is contained within our confidence interval.
3) Now, it is given that we wanted the margin of error for the 90% confidence level to be about 1.5%.
So, the margin of error = [tex]Z_(_\frac{\alpha}{2}_) \times \sqrt{\frac{\hat p(1-\hat p)}{n} }[/tex]
[tex]0.015 = 1.645 \times \sqrt{\frac{0.48(1-0.48)}{n} }[/tex]
[tex]\sqrt{n} = \frac{1.645 \times \sqrt{0.48 \times 0.52} }{0.015}[/tex]
[tex]\sqrt{n}[/tex] = 54.79
n = [tex]54.79^{2}[/tex]
n = 3001.88 ≈ 3002
Hence, a survey should include at least 3002 people if we wanted the margin of error for the 90% confidence level to be about 1.5%.
Ellen baked 115 cookies and shared them equally with her 23 classmates. How many whole cookies each can Ellen and her classmates have?
Step-by-step explanation:
Ellen - 115/23
Classmates and Ellen got = 5 each
Log 1/10 how do you convert this without a calculator
Answer:
log(1/10) = -1
Step-by-step explanation:
Use the law of exponents and the meaning of logarithm.
1/10 = 10^-1
log(10^x) = x
So, you have ...
log(1/10) = log(10^-1)
log(1/10) = -1
1) Given P(A) = 0.3 and P(B) = 0.5, do the following.
(a) If A and B are mutually exclusive events, compute P(A or B).
(b) If P(A and B) = 0.2, compute P(A or B).
2) Given P(A) = 0.4 and P(B) = 0.2, do the following.
(a) If A and B are independent events, compute P(A and B).
(b) If P(A | B) = 0.7, compute P(A and B).
Answer:
1) a) 0.8
b) 0.6
2) a) 0.08
b) 0.14
Step-by-step explanation:
1) Given
[tex]P(A) = 0.3[/tex] and [tex]P(B) = 0.5[/tex]
Let us learn about a formula:
[tex]P(A\ or\ B) = P(A) +P(B) -P(A\ and\ B)\\OR\\P(A\cup B) = P(A) +P(B) -P(A\cap B)[/tex]
(a) If A and B are mutually exclusive i.e. no common thing in the two events.
In other words:
[tex]P(A\ and\ B)[/tex] = [tex]P(A \cap B)[/tex] = 0
Using above formula:
[tex]P(A\ or\ B) = P(A) +P(B) -P(A\ and\ B)\\\Rightarrow P(A\ or\ B) = 0.3 + 0.5 -0 = \bold{0.8}[/tex]
(b) P(A and B) = 0.2
Using above formula:
[tex]P(A\ or\ B) = P(A) +P(B) -P(A\ and\ B)\\\Rightarrow P(A\ or\ B) = 0.3 + 0.5 -0.2 = \bold{0.6}[/tex]
*************************************
1) Given
[tex]P(A) = 0.4[/tex] and [tex]P(B) = 0.2[/tex]
Let us learn about a formula:
[tex]P(A\ and\ B) = P(B) \times P(A/B)[/tex] for dependent events
[tex]P(A\ and\ B) = P(A) \times P(B)[/tex] for independent events.
(a) If A and B are independent events :
Using the above formula for independent events:
[tex]P(A\ and\ B) = 0.4 \times 0.2 = \bold{0.08}[/tex]
(b) [tex]P(A / B) = 0.7[/tex]
Using above formula:
[tex]P(A\ and\ B) = P(B) \times P(A/B) = 0.2 \times 0.7 = \bold{0.14}[/tex]
Simple math! What is the issue with my work? I got it wrong.
Answer:
x = 6
Step-by-step explanation:
In the third line of the solution on right side of the equal sign, middle term should be 8x instead of 4x.
The final value of x will be 6.
[tex] PQ^2 + QO^2 = PO^2 \\
x^2 + 8^2 = (4+x)^2 \\
x^2 + 64 = 16 + 8x + x^2 \\
64 = 16 + 8x \\
64 - 16 = 8x \\
48 = 8x \\
6 = x\\[/tex]
Plzz help i really need help..
Answer:
D. neither.
Step-by-step explanation:
A function is when one x-value only has one corrisponding y-value.
The answer it's D. Neither
29. Identify the end behavior of the function f(x) = 3x^4 + x^3 − 7x^2 + 12.
options:
A. As x → –∞, y → +∞, and as x → +∞, y → –∞
B. As x → –∞, y → –∞, and as x → +∞, y → –∞
C. As x → –∞, y → +∞, and as x → +∞, y → +∞
D. As x → –∞, y → –∞, and as x → +∞, y → +∞
Answer:
C. As x → –∞, y → +∞, and as x → +∞, y → +∞
Step-by-step explanation:
The leading coefficient of this even-degree function is positive, so y goes to +∞ when the magnitude of x gets large.
_____
When the function is even degree, its value for large magnitude x heads toward the infinity with the same sign as the leading coefficient.
When the function is odd degree, its value for large magnitude x will head toward the infinity with the sign that matches the product of the sign of x and the sign of the leading coefficient.
My town has two cell phone providers. The provider Don’tTalkMuch charge is $80 per month plus 1 dollar per hour the provider TalkLots charges $20 per month plus 4 dollars per hour how much do you have to use your phone in a month in order for Don’tTalkMuch’s much is a deal to be better for you?
Answer:
The author have to use his/her phone less than 20 hours in a month in order for Don’tTalkMuch's is a deal to be better than TalkLots's is.
Step-by-step explanation:
Call X is the number of hours that the author uses on monthly basis.
Total bill value if the author uses Don’tTalkMuch service is $80 + $1 X.
Total bill value if the author uses TalkLots service is $20 + $4X
The total fees between 2 providers equal as:
$80 + $1 X = $20 + $4X => 3X = $60 => X = 20
Hence: The author have to use his/her phone less than 20 hours in a month in order for Don’tTalkMuch's is a deal to be better than TalkLots's is.
In a large on-the-job training program, half of the participants are female and half are male. In a random sample of six participants, what is the probability that an investigator will draw at least one male?† (Round your answer to four decimal places.) P(X ≥ 1) =
Answer: 0.9844
Step-by-step explanation:
given data:
sample size n = 6
It’s assumed that half the population are male and the remaining half are females
F = 1/2
M = 1/2
the probability that the investigator would draw altleats one male
P ( x ≥ 1 ) =
= 1 - ( 0.5 ) ^ 6
= ( 0.5 )^6
= 0.9844
Two friends are standing at opposite corners of a rectangular courtyard. The dimensions of the courtyard are 12 ft. by 25 ft. How far apart are the friends?
Answer:
27.73 feet
Step-by-step explanation:
Use the Pythagorean theorem. It easiest to think of the distance between the two friends as a triangle in the rectangle. One side is 12ft and the other is 25ft.
12^2+25ft^2=769
The square root of 769 is 27.73
Answer:
27.73 Ft
Step-by-step explanation:I took the test
The scores for all the Algebra 1 students at Miller High on a test are normally distributed with a mean of 82 and a standard deviation of 7. What percent of students made scores above 89?
Answer:
15.7% of students made above an 89.
Step-by-step explanation:
If the data is normally distributed, the standard deviation is 7, and the mean is 82, then about 68.2% of students made between 75 and 89. 13.6% made between 90 and 96, and 2.1% made over 96. 13.6+2.1=15.7%
A bike wheel. A bike wheel is 26 inches in diameter. What is the bike wheel's diameter in millimeters (1 inch = 25.4 millimeters)?
Answer:
its multiple choice
A. 26inches (1inch/25.4mm)
B. 26inches (25.4mm/1inch)
C. 25.4inches (1mm/26inch)
D. 26inches (1mm/25.4inch)
and its b
please help! algebra 2 work
I need help pls. Algebra
Answer:
The answer is option AStep-by-step explanation:
f(x) = (x+1)³ + 4
To find f-¹(x) equate f(x) to y
That's
y = (x+1)³ + 4
Next interchange the terms x becomes y and y becomes x
That's
x = ( y+1)³ + 4
Make y the subject
(y+1)³ = x - 4
Find the cube root of both sides
That's
[tex]y + 1 = \sqrt[3]{x - 4} [/tex]
Send 1 to the right side of the equation
That's
[tex]y = \sqrt[3]{x - 4} - 1[/tex]
So we have the final answer as
[tex]f ^{ - 1} (x) = \sqrt[3]{x - 4} - 1[/tex]
Hope this helps you
Answer:
option 1
Step-by-step explanation:
f(x)=(x+1)³+4
to find the inverse interchange the variable and solve for y
inverse f(x)=(y+1)³+4
x=(y+1)³+4
x-4=(y+1)³
y+1=∛x-4
y=∛x-4 -1
A pharmacist needs 16 liters of a 4% saline solution. He has a 1% solution and a 5% solution available. How many liters of the 1% solution and how many liters of the 5% solution should he mix to make the 4% solution?
x = liters of 1% solution
y = liters of 5% solution
x + y = 16
0.01x + 0.05y = 0.04*16 = 0.64
y = 16 - x
0.01x + 0.05(16 - x) = 0.64
0.01x + 0.8 - 0.05x = 0.64
0.16 = 0.04x
x = 4
y = 12
If the sum of the daily unpaid balances is $7,812 over a 31-day billing cycle, what is the average daily balance?
Answer:
252
Step-by-step explanation:
Divide 7812 by 31 and we get the average daily answer... Hope this helps!!
Isreal spends the most time on social media with a total of 11.1.peru has a total of 8.3 how much more time does israel spend on social media
Answer:
2.8
Step-by-step explanation:
11.1-8.3=2.8
HOPE I HELPED
PLS MARK BRAINLIEST
DESPERATELY TRYING TO LEVEL UP
✌ -ZYLYNN JADE ARDENNE
JUST A RANDOM GIRL WANTING TO HELP PEOPLE!
PEACE!
A population has a mean and a standard deviation . Find the mean and standard deviation of a sampling distribution of sample means with sample size n. nothing (Simplify your answer.) nothing (Type an integer or decimal rounded to three decimal places as needed.)
Complete Question
A population has a mean mu μ equals = 77 and a standard deviation σ = 14. Find the mean and standard deviation of a sampling distribution of sample means with sample size n equals = 26
Answer:
The mean of sampling distribution of the sample mean ( [tex]\= x[/tex]) is [tex]\mu_{\= x } = 77[/tex]
The standard deviation of sampling distribution of the sample mean ( [tex]\= x[/tex]) is
[tex]\sigma _{\= x} = 2.746[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 77[/tex]
The standard deviation is [tex]\sigma = 14[/tex]
The sample size is [tex]n = 26[/tex]
Generally the standard deviation of sampling distribution of the sample mean ( [tex]\= x[/tex]) is mathematically represented as
[tex]\sigma _{\= x} = \frac{ \sigma }{ \sqrt{n} }[/tex]
substituting values
[tex]\sigma _{\= x} = \frac{ 14}{ \sqrt{26} }[/tex]
[tex]\sigma _{\= x} = 2.746[/tex]
Generally the mean of sampling distribution of the sample mean ( [tex]\= x[/tex]) is equivalent to the population mean i.e
[tex]\mu_{\= x } = \mu[/tex]
[tex]\mu_{\= x } = 77[/tex]
I am performing a before and after evaluation on 30 students who have taken a keyboarding class. I want to see if the course improved their words per minute keyed.
Required:
a. State the Null and Alternate Hypothesis.
b. The statistic that I would use is:_________
c. What would my t critical be for this calculation at a 0.10 level of significance?
d. If my t calculated = 1.62, would I reject or fail to reject the null hypothesis?
Answer:
a)
H₀ : µd = 0
H₁ : µd < 0
b)
The test statistic is
tₙ₋₁ = α / s√n
c)
at 0.10 level of significance,
tₙ₋₁ , ₐ
t₃₀₋₁ , ₀.₁₀ = t₂₉, ₀.₁₀ = 1.311
d)
given that T(critical) = 1.62
∴ T(critical) = 1.62 > t₂₉, ₀.₁₀ = 1.311
at 10% level of significance,
REJECT H₀
Since 1.62 > 1.311, we can reject the null hypothesis.
Laura is bowling 5 games. Her first 4 scores were 135, 144, 116, and 132.
To end up with an average score of at least 136.8, what is the lowest score Laura will need in the fifth game?
Answer:
157
Step-by-step explanation:
135+144+116+132=527
527+136.8=762.8
762.8÷5= 157
How many petals are on the graph? Find the trigonometric form of a given function.
Answer:
Attachment 1 : Option A,
Attachment 2 : Option C
Step-by-step explanation:
( 1 ) Here we know that " n " is 6. Now remember if n is odd, the number of petals on the graph will be n. However if n is even, the number of petals on the graph will be 2n.
6 is even, and hence the number of petals will be 2(6) = 12 petals. Solution : 12 petals
( 2 ) To solve such problems we tend to use the equation [tex]z = x + y * i = r(cos\theta +isin\theta)[/tex] where [tex]r = \sqrt{x^2+y^2}[/tex] etc. Here I find it simpler to see each option, and convert each into it's standard complex form. It might seem hard, but it is easy if you know the value of (cos(5π / 3)) etc...
The answer here will be option c, but let's prove it,
cos(5π / 3) = 1 / 2,
sin(5π / 3) = [tex]-\frac{\sqrt{3}}{2}[/tex]
Plugging those values in for " [tex]8\left(\cos \left(\frac{5\pi }{3}\right)+i\sin \left(\frac{5\pi }{3}\right)\right)[/tex] "
[tex]8\left(-\frac{\sqrt{3}i}{2}+\frac{1}{2}\right)[/tex]
= [tex]8\cdot \frac{1}{2}-8\cdot \frac{\sqrt{3}i}{2}[/tex] = [tex]4-4\sqrt{3}i[/tex]
Hence proved that your solution is option c.
22)
Subtract (4 - 21) - (3 - 51)
A)
1+3i
B)
1-71
7+3i
D)
7-7i
Answer:
1 +3i
Step-by-step explanation:
(4 - 2i) - (3 - 5i)
Subtract the reals
4 - 3 =1
Subtract the imaginary
-2i - -5i
-2i + 5i = 3i
1 +3i
Answer:
A
Step-by-step explanation:
Subtract all real numbers
4 - 3 = 1
Subtract all imaginary numbers
-2i - (-5i) = 3i
Put back together
1 + 3i
Best of Luck!
A household survey of 10 families was conducted by students of 4th year MBBS. In the collected data, the ages of heads of families were: 32, 34, 35, 36, 36, 42, 44, 46, 48, and 52. The mean age of heads of families is
a. 36
b. 38.5
c. 40
d. 40.5
e. 42
Answer:
Which polynomial is prime?
7x2 – 35x + 2x – 10
9x3 + 11x2 + 3x – 33
10x3 – 15x2 + 8x – 12
12x4 + 42x2 + 4x2 + 14
Step-by-step explanation:
Which polynomial is prime?
7x2 – 35x + 2x – 10
9x3 + 11x2 + 3x – 33
10x3 – 15x2 + 8x – 12
12x4 + 42x2 + 4x2 + 14 SO IT IS RIGHT
According to psychologists, IQs are normally distributed, with a mean of 100 and a standard deviation of 15 . a. What percentage of the population has IQs between 85 and 100 ?
Simplify to create an equivalent expression.
-k-(-8k+7)
a=7k−7
b=-7k-7
c=7k+7
d=-7k+7
choose one
Answer:
a. 7k - 7
Step-by-step explanation:
Step 1: Write out expression
-k - (-8k + 7)
Step 2: Distribute negative
-k + 8k - 7
Step 3: Combine like terms
7k - 7
And we have our answer!
Which rule describes this transformation? (Zoom in to see it clearly)
Answer:
(x,y) -> (x+6, y-3)
Step-by-step explanation:
I followed c and it translated like the last ans choice.
Find the area of the shape shown below.
2
2
nd
2
Need help Plz hurry and answer!!!
Answer:
=6 units squared
Step-by-step explanation:
area=1/2h(a+b)
=1/2×2(4+2)
=6
