Answer:
Step-by-step explanation:
Given that:
[tex]\mathtt{f(x) = ax^2 + bx + c}[/tex]
The derivative of the function of x is [tex]\mathtt{f'(x) = 2ax + b}[/tex]
Thus; f(x) is increasing when f'(x) > 0
f(x) is decreasing when f'(x) < 0
i.e
f'(x) > 0 , when b > 0 and a < 0
∴
2ax + b < 0
2ax < - b
[tex]\mathtt{x < \dfrac{-b}{2a}}[/tex]
f'(x) < 0 , when b < 0 and a > 0
2ax + b > 0
2ax > - b
[tex]\mathtt{x > \dfrac{-b}{2a}}[/tex]
The circumference of a sphere was measured to be 82 cm with a possible error of 0.5 cm.
A. Use differentials to estimate the maximum error in the calculated volume.
What is the relative error?
B. Use differentials to estimate the maximum error in the calculated volume.
What is the relative error?
Answer:
A) Maximum error = 170.32 cm³
B)Relative error = 0.0575
Step-by-step explanation:
A) Formula for circumference is: C = 2πr
Differentiating with respect to r, we have;
dC/dr = 2π
r is small, so we can write;
ΔC/Δr = 2π
So, Δr = ΔC/2π
We are told that ΔC = 0.5.
Thus; Δr = 0.5/2π = 0.25/π
Now, formula for Volume of a sphere is;
V(r) = (4/3)πr³
Differentiating with respect to r, we have;
dV/dr = 4πr²
Again, r is small, so we can write;
ΔS/Δr = 4πr²
ΔV = 4πr² × Δr
Rewriting, we have;
ΔV = ((2πr)²/π) × Δr
Since C = 2πr, we now have;
ΔV = (C²/π)Δr
ΔV will be maximum when Δr is maximum
Thus, ΔV = (C²/π) × 0.25/π
C = 82 cm
Thus;
ΔV = (82²/π) × 0.25/π
ΔV = 170.32 cm³
B) Formula for relative error = ΔV/V
Relative error = 170.32/((4/3)πr³)
Relative error = 170.32/((4/3)C³/8π³)
Relative errror = 170.32/((4/3)82³/8π³)
Relative error = 170.32/2963.744
Relative error = 0.0575
A speedboat moves at a rate of 25 km/hr in still water. How long will it take
someone to ride the boat 87 km downstream if the river's current moves at a rate of
4 km/hr?
Answer:
3 hours
Step-by-step explanation:
Downstream, the speeds add up:
25 + 4 = 29 km/hIt will take:
87/29= 3 hrsTo ride 87 km.
Find the value of x to the nearest tenth. A) 5 B) 9.2 C) 3.3 D) 2.9
Answer:
B) 9.2
Step-by-step explanation:
tan(57)=x/6 multiply 6 on both sides
6.tan(57)=x use calculator to find answer
9.2 rounded
Answer:9.2 is correct
Step-by-step explanation:
in the diagram, POS,QOT and UOR are straight lines. Find the value of y.
Answer:
y = 15°
Step-by-step explanation:
Since ∠QOR and ∠UOT are vertical, they are congruent so ∠UOT = 5y. Since POS is a straight line (which has a measure of 180°) and ∠POS = ∠POU + ∠UOT + ∠TOS, we can write:
5y + 5y + 2y = 180
12y = 180
y = 15°
Find the total surface area of the farm silo in a farmer's field. Use π = 3.14. pls help asap uwu
Answer:
A) 1236 units²
Step-by-step explanation:
Cylinder = 2[tex]\pi[/tex]h+2[tex]\pi[/tex]r²
2(3.14)(7.5)(15)+2(3.14)(7.5x7.5)
706.5+353.25=1059.75
1/2 Sphere = 1/2(4)[tex]\pi[/tex]r²
2(3.14)(7.5)(7.5)
353.25
TOTAL: 1059.75+353.25=1413
HOWEVER...you need to subtract the top of the cylinder ([tex]\pi[/tex]r²) 176.625
1413-176.625=1236.375
So the answer would be A. (Silo’s do have a bottom, or else the answer would be D)
Answer:
1,236 units²
Step-by-step explanation:
I got it correct on founders edtell and screenshot below as proof
Calculate the derivative of the function. Then find the value of the derivative as specified:
f(x) = 5x + 9; f "(2)
A) f "(x) 0,f , (2)-0
B) f , (x)-9; f , (2) = 9
C)f"(x) = 5; f "(2) = 5
D) f '(x) 5x; f '(2) 10
The correct question is;
Calculate the derivative of the function. Then find the value of the derivative as specified:
f(x) = 5x + 9; f '(2)
A) f'(x) = 0; f'(2) = 0
B) f'(x) = 9; f '(2) = 9
C)f'(x) = 5; f'(2) = 5
D) f '(x) = 5x; f '(2) = 10
Answer:
Option C: f'(x) = 5 and f '(2) = 5
Step-by-step explanation:
We want to find the derivative of f(x) = 5x + 9.
Now, the derivative with respect to x will be;
f'(x) = 5
Now,we also want to find out f'(2)
This means we are to put 2 for x in the derivative function.
In the derivative function, we don't have x as we have just 5.
Thus,f'(2) = 5
A certain family has a husband, wife, son, and daughter. All together they are 68 years old. The husband is 3 years older than the wife, and the son is 3 years older than the daughter. Four years ago, all together the family was 54 years old. How old is the husband now?
Answer:
32
Step-by-step explanation:
Everyone added together = 68
Four years ago, they were 68 -16 = 52
But the question told 54 years.
So there was a girl who was 2 years.
Girl = 2
Boy = 2 +3 = 5
Husband = 3 +w
Wife =w
3 +w +w + 5 + 2 = 68
10 + 2w = 68
2w = 58
w = 29
Wife = 29
Husband = 29 +3 =32
Husband = 32 years
Answer:
[tex]\large \boxed{\sf \bf \ \ 32 \ \ }[/tex]
Step-by-step explanation:
Hello, please consider the following.
We know that "All together they are 68 years old." and "Four years ago, all together the family was 54 years old."
If all the family was alive four years ago, it means that four years ago the sum of their ages was 68 - 4 - 4 - 4 - 4 because they are four members, so it gives 68 - 16 =52 which is different from 54, right ?
It means that we have the daughter in between, 54- 52 = 2, so the daughter's age is 2, and then the son's age is 5.
The husband is 3 years older than the wife. Let's note W the wife's age, we can write W + 3 + W + 5 + 2 = 68
2 W + 10 = 68
2 W = 68 - 10 = 58 so W = 29
and then the husband's age is 29 + 3 = 32.
And we can verify that 32 + 29 + 5 + 2 = 68, and four years ago, 28 + 25 + 1 + 0 = 54.
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
PLEASE HELP ! (2/4) - 50 POINTS -
Answer:
The correct answer would be 15.5 or C.
If we were to make a poset of the form (A, |), where is the symbol for divisibility, which of the following sets A would yield a poset that is a total ordering?
I. A- (1, 4, 16, 64)
II. A- (1.2,3, 4, 6, 12)
III. A 1,2,3, 4, 6, 12, 18, 24)
IV. A+{1 , 2, 3, 6, 12)
Answer:
IV. A+{1, 2, 3, 6, 12}
Step-by-step explanation:
The set of natural numbers form a poset number under relation of > or =. The discrete variables are used to form a poset. The symbols for divisibility in poset form are when an integer is divided by the variable without integer. The correct answer is therefore 4th option.
34% of working mothers do not have enough money to cover their health insurance deductibles. You randomly select six working mothers and ask them whether they have enough money to cover their health insurance deductibles. The random variable represents the number of working mothers who do not have enough money to cover their health insurance deductibles.
Required:
Construct a binomial distribution using n= 0.6 and p=0.34
Answer:
solution below
Step-by-step explanation:
The question says 6 working mother's were selected so n = 6 not 0.6
We are expected to find
P(X = 0,1,2,3,4,4,6)
1. When x = 0
6C0*(0.34)⁰*(0.66)⁶
= 1 *1* 0.827
= 0.0827
2. When X = 1
6C1*(0.34)¹*(0.66)⁵
= 6 x 0.34 x 0.252
= 0.2555
3. When X = 2
6C2*(0.34)²*(0.66)⁴
= 15 x 0.1156 x 0.1897
= 0.3289
4. When x = 3
6C3*(0.34)³*(0.66)³
20 x 0.039304 x 0.2875
= 0.2599
5. When X = 4
6C4*(0.34)⁴*(0.66)²
= 15 x 0.01336 x 0.4356
= 0.8729
6. When x = 5
6C5*(0.34)⁵*(0.66)¹
= 6 x 0.0045 x 0.66
= 0.01782
7. When x = 6
6C6*(0.34)⁶*(0.66)⁰
1 x 0.0015 x 1
= 0.0015
In the diagram, XY bisects ZWXZ.
1
z
2
w
(5x + 3)
(7x - Y
х
mWYZ
type your answer.
In provided diagram angle WXY = angle YXZ
Angle WXY =( 7x-7)°
Angle YXZ = ( 5x +3)°
We have to find out the value of Angle WXZ
→ 7x-7 = 5x +3
→ 7x - 5x = 7+3
→ 2x = 10
→ x = 10/2
→ x = 5 .
Putting the value of x .
→ Angle WXY = 7(2)-7
→ 14-7 = 7°
→ Angle YXZ = 5(2)+3
→ 10+3 = 13°
Angle WXZ = 13° + 7 ° → 20°
So 20° is the required answer .
Answer:
SI
Step-by-step explanation:
60 is x% of 12. Find the value of x.
Answer:
20
Step-by-step explanation:
We can set up a percentage proportion to find the value of x.
[tex]\frac{12}{x} = \frac{60}{100}[/tex]
Now we cross multiply:
[tex]100\cdot12=1200\\\\1200\div60=20[/tex]
Hope this helped!
Put the following equation of a line into slope-intercept form, simplifying all
fractions.
3x + 3y = -9
Answer:
[tex]y = -x - 3[/tex]
Step-by-step explanation:
We are trying to get the equation [tex]3x + 3y = -9[/tex] into the form [tex]y = mx+b[/tex], aka slope-intercept form.
To do this we are trying to isolate y.
[tex]3x + 3y = -9[/tex]
Subtract 3x from both sides:
[tex]3y = -9 - 3x[/tex]
Rearrange the terms:
[tex]3y = -3x - 9[/tex]
Divide both sides by 3:
[tex]y = -x - 3[/tex]
Hope this helped!
woman has 7 coworkers' man. How many different possible groups of four people could do the project, if one out of three is women? g
Answer: 24ways
Step-by-step explanation:
Given data:
No of men in the workplace = 7
No of women in the workplace = 1
How many ways can a group of 4 people carry out a project if on out of the 3 must be a woman.
Solution.
A group of 4 can carry out the project with one be a woman
This means there must be 3 males and 1 female in the group
= 4p3
= 24ways
The project can be carried out by 4 groups in 24 ways
The end of a hose was resting on the ground, pointing up an angle. Sal measured the path of the water coming out of the hose and found that it could be modeled using the equation f(x) = –0.3x2 + 2x, where f(x) is the height of the path of the water above the ground, in feet, and x is the horizontal distance of the path of the water from the end of the hose, in feet. When the water was 4 feet from the end of the hose, what was its height above the ground? 3.2 feet 4.8 feet 5.6 feet 6.8 feet
Answer: 3.2 feet.
Step-by-step explanation:
Given: The end of a hose was resting on the ground, pointing up an angle. Sal measured the path of the water coming out of the hose and found that it could be modeled using the equation[tex]f(x) = -0.3x^2 + 2x[/tex], where [tex]f(x)[/tex] is the height of the path of the water above the ground, in feet, and [tex]x[/tex] is the horizontal distance of the path of the water from the end of the hose, in feet.
At x= 4 , we get
[tex]f(x) = -0.3(4)^2 + 2(4)=-0.3(16)+8 =-4.8+8=3.2[/tex]
Hence, when the water was 4 feet from the end of the hose, its height above the ground is 3.2 feet.
Answer:
3.2 feet.
Step-by-step explanation:
Identify the inverse function of f(x) = VX - 2 + 3.
Answer:
[tex]\huge\boxed{f^{-1}(x) = (x-3)^2+2}[/tex]
Step-by-step explanation:
[tex]f(x) = \sqrt{x-2} + 3[/tex]
Replace y = f(x)
[tex]y = \sqrt{x-2} + 3[/tex]
Exchange x and y
[tex]x = \sqrt{y-2}+3[/tex]
Solve for y
[tex]x = \sqrt{y-2}+3[/tex]
Subtracting both sides by 3
[tex]x - 3 = \sqrt{y-2}[/tex]
Taking square on both sides
[tex](x-3)^2 = y -2[/tex]
Adding 2 to both sides
[tex]y = (x-3)^2+2[/tex]
Substitute y = [tex]f^{-1}(x)[/tex]
[tex]f^{-1}(x) = (x-3)^2+2[/tex]
Answer:
[tex] \boxed{ {f}^{ - 1} (x) = {(x - 3)}^{2} + 2}[/tex]Option D is the correct option
Step-by-step explanation:
[tex] \mathsf{f(x) = \sqrt{x - 2} + 3}[/tex]
Replace f(x) with y
[tex] \mathsf{y = \sqrt{x - 2} + 3}[/tex]
Interchange variables
[tex] \mathsf{x = \sqrt{y - 2} + 3}[/tex]
[tex] \mathsf{{(x - 3)}^{2} = {( \sqrt{y - 2)} }^{2} }[/tex]
[tex] \mathsf{ {(x - 3)}^{2} = y - 2}[/tex]
[tex] \mathsf{ y = {(x - 3)}^{2} + 2}[/tex]
Replace y with f ⁻¹( x )
[tex] \mathsf{ {f}^{ - 1} (x) = {(x - 3)}^{2} + 2}[/tex]
Hope I helped!
Best regards!
If “n” is a positive integer divisible by 3 and n is less than or equal to 44, then what is the highest possible value of n?
Answer:
Step-by-step explanation:
positive integer divisible by 3 includes
3,6,9,12,15,18,21,24,27,30,33,36,39,42,45...
less than highest possible value is 42
pt 2 4-7 please helppp
Answer:
f = 16
Step-by-step explanation:
8
8 x 2 = _f_ x
8
f = 16
Hi there! Hopefully this helps!
-----------------------------------------------------------------------------------------------------
Answer: f = 16~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[tex]2 = \frac{f}{8}[/tex]
Multiply both sides by 8.
[tex]2 \times 8 = f[/tex]
Multiply 2 and 8 to get 16.
[tex]16 = f[/tex]
Swap sides so that all variable terms are on the left hand side.
[tex]f = 16[/tex]
Round 3.1 to the nearest whole number
Answer:
3.1 rounded off to the nearest whole number is 3.
Step-by-step explanation:
To the nearest tenth, what is the value of P(C|Y)? 0.4 0.5 0.7 0.8
Answer:
P(C|Y) = 0.5.
Step-by-step explanation:
We are given the following table below;
X Y Z Total
A 32 10 28 70
B 6 5 25 36
C 18 15 7 40
Total 56 30 60 146
Now, we have to find the probability of P(C/Y).
As we know that the conditional probability formula of P(A/B) is given by;
P(A/B) = [tex]\frac{P(A \bigcap B)}{P(B)}[/tex]
So, according to our question;
P(C/Y) = [tex]\frac{P(C \bigcap Y)}{P(Y)}[/tex]
Here, P(Y) = [tex]\frac{30}{146}[/tex] and P(C [tex]\bigcap[/tex] Y) = [tex]\frac{15}{146}[/tex] {by seeing third row and second column}
Hence, P(C/Y) = [tex]\frac{\frac{15}{146} }{\frac{30}{146} }[/tex]
= [tex]\frac{15}{30}[/tex] = 0.5.
Answer: 0.5
Step-by-step explanation:
edge
is perpendicular to . How many 90° angles are formed by the intersection?
Answer:
if a is perpendicular to b then four 90 degree angles are formed
Step-by-step explanation:
if a line is perpendicular to another that means that it forms a 90 degree angle on all of the angles
Answer:
Four
That is the right answer for Edmentum and Plato users
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The data set {3, 7, 5, 4, 1} consists of the lengths, in minutes, of a sample of speeches at an awards banquet. Use a formula to find the standard deviation of the sample, and label it with the correct variable.
Answer:
Standard deviation = 2.2360679774998
Step-by-step explanation:
We are asked to find the Standard deviation of a samples of speeches as an awards.
The formula for sample standard deviation is given as:
√[(x - μ)²/N - 1 ]
Step 1
We find the mean (μ)
The mean of the sample =>
= Sum of term/ Number of terms
= (3 + 7 + 5 + 4 + 1)/5
= 20/5
= 4
Step 2
Find the Standard deviation of the sample
√[(x - μ)²/N - 1 ]
N = number of samples or terms = 5
= √[(3 - 4) ² + (7 - 4)² + (5 - 4)² +(4 - 4)² +(1 - 4)²/ 4]
= √ (1 ² + 3² + -1² + 0² + -3²/4)
= √( 1 + 9 + 1 + 0 + 9/4)
= √20/5 - 1
= √5
= 2.2360679774998
The standard deviation of the sample = 2.2360679774998
How many solutions does the system have? x+2y=2 2x+4y=−8
Answer:
Step-by-step explanation:
x + 2y = 2
2x + 4y = -8
-2x - 4y = -4
2x + 4y = -8
0 not equal to -12
no solution
Simplify.
√20
v
Assume that the variable represents a positive real number.
Answer:
[tex]2\sqrt{5v}[/tex]
Step-by-step explanation:
We can treat 20v as a regular number and not a term.
To simplify this square root, we need to break it down into parts which can be squared.
[tex]\sqrt{20v} = \sqrt{4\cdot5v}[/tex]
Square root of 4 is 2, so that goes outside the radical.
[tex]2\sqrt{5v}[/tex].
Hope this helped!
Answer:
2 sqrt(5)
Step-by-step explanation:
sqrt(20)
sqrt(4*5)
We know that sqrt(ab) = sqrt(a) sqrt(b)
sqrt(4) sqrt(5)
2 sqrt(5)
Which quadratic equation would be used to solve for the unknown dimensions?
0 = 2w2
512 = w2
512 = 2w2
512 = 2l + 2w
Answer:
C
Step-by-step explanation:
Answer:
C: 512 = 2w2
Step-by-step explanation:
on edge
In determining your group’s estimate, what mathematical model of a tennis ball did you use? What model of the classroom did you use? Did you make other simplification or assumptions?
Answer:
bro ur question is not understandable
A rectangular city is 3 miles long and 10 miles wide. What is the distance between opposite corners of the city? The exact distance is ______ miles How far is it to the closest tenth of a mile? Answer: The distance is approximately ______ miles.
Answer:
The exact distance is [tex]\sqrt{109}[/tex] miles.
The distance is approximately 10.4 miles.
Step-by-step explanation:
It is given that a rectangular city is 3 miles long and 10 miles wide. So,
Length = 3 miles
Width = 10 miles
We need to find the distance between opposite corners of the city. It means, we need to find the length of the diagonal of the rectangle.
Using Pythagoras theorem, the length of diagonal is
[tex]d=\sqrt{l^2+w^2}[/tex]
where, l is length and w is width.
Substitute l=3 and w=10.
[tex]d=\sqrt{(3)^2+(10)^2}[/tex]
[tex]d=\sqrt{9+100}[/tex]
[tex]d=\sqrt{109}[/tex]
The exact distance is [tex]\sqrt{109}[/tex] miles.
Now,
[tex]d=\sqrt{109}[/tex]
[tex]d=10.4403065[/tex]
[tex]d\approx 10.4[/tex]
The distance is approximately 10.4 miles.
The number of chocolate chips in a bag of chocolate chip cookies is approximately normally distributed with a mean of 1262 chips and a standard deviation of 118 chips.
Required:
a. Determine the 26th percentile for the number of chocolate chips in a bag.
b. Determine the number of chocolate chps in a bag that make up the middle 96% of bags.
Answer:
(a) The 26th percentile for the number of chocolate chips in a bag is 1185
(b) The number of chocolate chips in a bag that makes up the middle 96% of the bags is between 1020 and 1504
Step-by-step explanation:
From the question, we have the following values:
μ =1262 and σ =118
(a) Let the value of x represents the 26th percentile. So the 26th percentile means 26% data is less than x. We can use the standard normal table to get the particular z-value that corresponds to this percentile.
P( Z<-0.65 )=0.2578 which is approximately 0.26
So for 26th percentile z-score will be -0.65.
Mathematically;
z-score = (x-mean)/SD
-0.65 = (x-1262)/118
-76.7 = x -1262
x = 1262-76.7 = 1185.3
This value is approximately 1,185
(b) Using a graph of standard normal distribution curve, if middle is 96% , then at both tails 2% each.
From z-table, we can find the closest probability;
P(-2.05<z<2.05) = 0.96
So we have two x values to get from the individual z-scores
-2.05 = (x-1262)/118
x = 1020(approximately)
For 2.05, we have
2.05 = (x-1262)/118
x = 1262 + 2.05(118) = 1504 (approximately)
20,000 is 10 times as much as
Answer:
2000
Step-by-step explanation:
20,000 is 2000 times the number 10.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given numbers are 20000 and 10. The number 20000 is how many times the number 10 will be calculated by dividing the number 20000 by 10.
E = 20000 / 10 = 2000
Therefore, the number 20,000 is 2000 times the number 10.
To know more about an expression follow
https://brainly.com/question/20066515
#SPJ2
Assume that random guesses are made for multiple-choice questions on a test with choices for each question, so that there are n trials, each with probability of success (correct) given by p. Find the probability of no correct answers
Complete Question
Assume that random guesses are made for 7 multiple-choice questions on a test with 5 choices for each question, so that there are n=7 trials, each with probability of success (correct) given by p=0.20. Find the probability of no correct answers.
Answer:
The probability is [tex]P(X = 0 ) = 0.210[/tex]
Step-by-step explanation:
From the question we are told that
The number of trial is n = 7
The probability of success is p = 0.20
Generally the probability of failure is
[tex]q = 1- 0.20[/tex]
[tex]q = 0.80[/tex]
Given that this choices follow a binomial distribution as there is only two probabilities i.e success or failure
Then the probability is mathematically represented as
[tex]P(X = 0 ) = \left n} \atop {}} \right. C_0 * p^{0} * q^{n- 0}[/tex]
[tex]P(X = 0 ) = \left 7} \atop {}} \right. C_0 * (0.2)^{0} * (0.8)^{7- 0}[/tex]
Here [tex]\left 7} \atop {}} \right. C_0 = 1[/tex]
=> [tex]P(X = 0 ) = 1 * 1* (0.8)^{7- 0}[/tex]
=> [tex]P(X = 0 ) = 0.210[/tex]
