Therefore, P(z > 0.97) = 0.166 using standard normal distribution table.
Standard normal distribution table explained.
A standard normal distribution table, also called a z-score table or a standard normal table, is a table that provides the area under the curve to the left of a specific z-score value in a standard normal distribution. A standard normal distribution is a normal distribution with a mean of zero and a standard deviation of one.
The table usually includes positive z-score values in the right-hand column and the second decimal place in the top row. The intersection of a specific z-score value and decimal place provides the area under the curve to the left of that z-score value.
For example, if we want to find the area under the curve to the left of a z-score value of 1.32, we would locate the row with 1.3 in the top row and the column with 0.02 in the right-hand column. The intersection of this row and column gives the area under the curve to the left of 1.32, which is 0.9066.
Using a standard normal distribution table or calculator, we can find the probability of z being greater than 0.97 is approximately 0.166. Therefore, P(z > 0.97) = 0.166.
Learn more about standard normal distribution below.
https://brainly.com/question/26822684
#SPJ1
Suppose that a and b are positive numbers for which log, (a) = log15(b) = log25 (a + 2b). What is the value of a
Answer: The value of "a" is given by a = 25 - 2b, where "b" is a positive number.
Step-by-step explanation:
Given that log(a) = log15(b) = log25(a + 2b), we can use the properties of logarithms to solve for the value of a.
Since log(a) = log15(b), we can equate the bases and eliminate the logarithms:
a = 15^log15(b) .....(1)
Similarly, since log(a) = log25(a + 2b), we can equate the bases and eliminate the logarithms:
a = (a + 2b)^log25(a + 2b) .....(2)
Now, we can equate the right-hand sides of equations (1) and (2) since they are both equal to a:
15^log15(b) = (a + 2b)^log25(a + 2b)
Taking the logarithm of both sides with base 15, we get:
log15[15^log15(b)] = log15[(a + 2b)^log25(a + 2b)]
Using the property that loga(a^x) = x, we can simplify the left-hand side:
log15(b) = log15[(a + 2b)^log25(a + 2b)]
Now, we can equate the bases and eliminate the logarithms:
b = (a + 2b)^log25(a + 2b)
Taking the logarithm of both sides with base (a + 2b), we get:
log(a + 2b)(b) = log(a + 2b)[(a + 2b)^log25(a + 2b)]
Using the property that loga(a^x) = x, we can simplify the right-hand side:
log(a + 2b)(b) = log25(a + 2b)
Since log(a + 2b)(b) = log(a + 2b)/logb(a + 2b) by the change of base formula, we can rewrite the equation as:
log(a + 2b)/logb(a + 2b) = log25(a + 2b)
Now, we can equate the numerators and denominators separately:
log(a + 2b) = log25(a + 2b)
1 = log25(a + 2b)/(log(a + 2b))
Since loga(a) = 1, we can rewrite the equation as:
log25(a + 2b) = log(a + 2b)/(log(a + 2b))
Using the property that loga(a^x) = x, we get:
log25(a + 2b) = 1
This implies that 25^1 = a + 2b, since we are using the definition of logarithm which states that loga(b) = c is equivalent to a^c = b.
Therefore, a + 2b = 25.
Given that a and b are positive numbers, we can deduce that a + 2b > 0.
Solving for a, we get:
a = 25 - 2b
Since a and b are both positive, a = 25 - 2b > 0.
So, the value of a is greater than zero and is given by a = 25 - 2b, where b is a positive number.
Need help quick please!
Answer: cos∅= [tex]\frac{\sqrt{7} }{4}[/tex]
Step-by-step explanation:
All numbers are positive because it is first quadrant. Draw a line out.
sin = opp/hypotenuse. the opposite line of the angle (y) =3
and hypotenuse=4
use pythagorean theorem to find x
4²=3²+x²
[tex]x=\sqrt{7}[/tex]
now use cos=adjacent/hypotenuse
cos∅= [tex]\frac{\sqrt{7} }{4}[/tex]
jasmine said that commutative property always works for addition but never for subtraction
No, Jasmine is not completely correct. The commutative property states that the order of the numbers can be changed without affecting the result of the operation.
In addition, the commutative property is true: a + b = b + a for any two numbers a and b.
For subtraction, the commutative property is not true in general: a - b is not equal to b - a.
However, there are some special cases where the commutative property does hold true for subtraction. For example, if a and b are equal, then a - b = b - a.
So, in general, Jasmine's statement that the commutative property never works for subtraction is not correct. While it is true that the commutative property does not hold true for subtraction in the same way that it does for addition, there are some special cases where it does apply.
Learn more about Simplification here:
https://brainly.com/question/28996879
#SPJ1
Find the surface area of the figure
The surface area of the square pyramid given above would be = 400ft²
How to calculate the surface area of the given shape?To calculate the surface area of the given figure, the formula that should be used would be = b² +2bs
where B = base length= 10ft
s = slant height= 15ft
Surface area = 100+2(10×15)
= 100+300
= 400ft²
Learn more about area here:
https://brainly.com/question/25292087
#SPJ1
Miss Johnson's guests were to arrive at 6:15 P.M., but because of a bad storm they were 2/5 of an hour late. What time did they arrive for dinner?
the guests arrived for dinner at 6:39 P.M.which is solved by according to given question.
How to solve the question?
To solve this problem, we need to first convert the fraction of an hour that Miss Johnson's guests were late into minutes. We know that 1 hour is equal to 60 minutes, so we can find the number of minutes the guests were late by multiplying 2/5 by 60:
2/5 hour * 60 minutes/hour = 24 minutes
So the guests were 24 minutes late. To find out what time they arrived, we need to add 24 minutes to the original arrival time of 6:15 P.M.:
6:15 P.M. + 24 minutes = 6:39 P.M.
Therefore, the guests arrived for dinner at 6:39 P.M.
It's important to note that fractions can often be confusing when dealing with time calculations. In this case, we converted the fraction of an hour to minutes to make the calculation easier. Additionally, it's always a good idea to double-check your work to ensure that your answer makes sense in the context of the problem.
To know more about Time visit :-
https://brainly.com/question/26046491
#SPJ1
what is 12 plus 12 and take away 67 and then add 24
Answer:
-19
Step-by-step explanation:
First you need to add all of the positive and negative numbers together, which would look like (12+12+24) + (-67) OR 48 + -67. Now add -67 to 48.
-67 + 48 is -19. Therefore the answer is -19.
IM SO SORRY IF THIS DID NOT MAKE SENSE!
Answer:12+12=24
24-67=-43
-43+24=-19
Step-by-step explanation:
b) d=22,4 mm d) d= 7 km f) r=0,5 hm h) r= ² kr km 3 C≈ C≈ C≈ C≈
The height is 230 feet after 9.125 seconds.
How do we calculate?We have the equation that describes the height of the object as a function of time as:
h(t) = -16t^2 + 145t + 2
We input the values and simplify:
-16t^2 + 145t + 2 = 230
-16t^2 + 145t - 228 = 0
we can use the quadratic formula, to solve this quadratic equation,
t = (-b ± √(b^2 - 4ac)) / 2a
where a = -16, b = 145, and c = -228.
t = (-145 ± √(145^2 - 4(-16)(-228))) / 2(-16)
t = (-145 ± √ (21025)) / (-32)
t = (-145 ± 145) / (-32)
t = 0.625 seconds or t = 9.125 seconds
In conclusion, the height is 230 feet after 9.125 seconds.
#complete question:
An object is thrown upward at a speed of 145 feet per second by a machine from a height of 2 feet off the ground. The height h of the object after t seconds can be found using the equation
When will the height be 230 feet?
what are the imports and Exports for Segbana,Benin
We can see here that from the available information it is clear that imports of Benin were:
refined petrolrice, etcWhile the exports are:
cottonsheanutscashewsWhat is an export?A locally produced commodity or service that is sold to another nation is referred to as an export. To put it another way, it's a good or service that is sold or sent to another nation to be utilized or consumed there.
Exports may help a nation's economy expand by bringing in money and creating jobs.
Imports are actually known to be goods and services that are brought into a country/nation.
Learn more about imports and exports on https://brainly.com/question/13663581
#SPJ1
A manufacturer records data on the battery life of a new product and discovers the data is normally distributed. The mean life of the battery is 120 hours and has a standard deviation of 10 hours. The manufacturer commits to replacing all batteries that last less than 100 hours. If 32,200 batteries were produced, how many would they expect to replace?
The firm expects replacing around 734 batteries out of the 32,200 produced.
How to determine how many batteries many would they expect to replaceusing the normal distribution formula z = (x - )
When z denotes the z-score,
x denotes the battery life of interest, is the mean battery life, and is the standard deviation.
For x = 100, use the z-score: z = (100 - 120) / 10 z = -2
Calculate the area under the normal curve to the left of z = -2.
0.0228 is the approximate value.
The number of batteries expected to be replaced by the manufacturer is equal to the proportion of batteries with a battery life of less than 100 hours multiplied by the total number of batteries produced:
Number of batteries to be replaced = 0.0228 x 32,200
734.16 batteries are expected to be replaced.
As a result, the firm anticipates replacing around 734 batteries out of the 32,200 produced.
Learn more about standard deviation at https://brainly.com/question/475676
#SPJ1
An above ground pool drains at a rate of 20
gallons every 3 minutes. The swimming pool
holds 5,000 gallons of water. How many hours
will it take to completely drain the swimming
pool?
The amount of time it would take to drain the swimming pool is equal to 75 minutes..
How to determine time it would take to drain the swimming pool?Generally speaking, a mathematical model for any quantity (water) that decreases by r percent per unit of time is an exponential function of this form:
[tex]P(t) = I(1 - r)^t[/tex]
Where:
P(t ) represents the volume of water in gallons.t represents the time or number of years.I represents the initial volume of water.r represents the decay rate.Next, we would determine the amount of time it would take to have 0 gallons in the swimming pool:
20 gallons = 3 minutes
5,000 gallons = x minutes
20x = 1500
x = 1500/20
x = 75 minutes.
Read more on exponential functions here: brainly.com/question/28246301
#SPJ1
A popular beach currently has 88 visitors, and 28 of them are sunbathing. What is the probability that a randomly chosen beachgoer is sunbathing? Write your answer as a fraction or whole number.
The probability that the randomly selected person is taking a sunbath is 7/22.
Science uses a figure called the probability of occurrence to quantify how likely an event is to occur.
It is written as a number between 0 and 1, or between 0% and 100% when represented as a percentage.
The possibility of an event occurring increases as it gets higher.
So, the probability formula is:
P(E) = Favourable events/Total events
Now, insert values in the formula as follows:
P(E) = Favourable events/Total events
P(E) = 28/88
P(E) = 14/44
P(E) = 7/22
Therefore, the probability that the randomly selected person is taking a sunbath is 7/22.
Know more about probability here:
https://brainly.com/question/24756209
#SPJ1
The measure of DOT and TOU
The measure of ∠DOT is equal to 58°
The measure of ∠TOU is equal to 32°.
What is a complementary angle?In Mathematics and Geometry, a complementary angle refers to two (2) angles or arc whose sum is equal to 90 degrees (90°).
Mathematically, a complementary angle can be calculated by using this mathematical equation:
Q + R = 90°
Where:
Q and R are measure of the angles subtended.
By substituting the given parameters into the complementary angle formula, the sum of the angles is given by;
(7x + 2) + 4x = 90.
11x + 2 = 90
11x = 90 - 2
x = 88/11
x = 8.
For the measure of ∠DOT, we have;
∠DOT = (7x + 2)
∠DOT = 7(8) + 2
∠DOT = 58°
For the measure of ∠TOU, we have;
∠TOU = 4x
∠TOU = 4(8)
∠DOT = 32°.
Read more on complementary angle here: brainly.com/question/17952433
#SPJ1
Missing information:
The question is incomplete and the complete question is shown in the attached picture.
You rented a sedan for 37.45 per day and unlimited miles. she paid a CDW fee of 19.40 per day. Her total rental cost was 646.50. She spend 78 for gasoline and her final cost per mile was 0.77. How many days did You rented the car?
You rented the car for 10 days.
Mathematical word problemLet's begin by setting up the equation to solve for the number of days:
Total rental cost = (daily rental cost + CDW fee) x number of days + gasoline cost
We know that the daily rental cost is 37.45, and the CDW fee is 19.40, so we can substitute those values into the equation:
646.50 = (37.45 + 19.40) x number of days + 78
Simplifying the equation:
646.50 = 56.85 x number of days + 78
Subtracting 78 from both sides:
568.50 = 56.85 x number of days
Dividing both sides by 56.85:
number of days = 10
Therefore, You rented the car for 10 days.
More on mathematical word problems can be found here: https://brainly.com/question/29251834
#SPJ1
Movie tickets for you and some of your friends cost $7 each. You all also want to purchase one popcorn for each person, which costs $4. Write an algebraic expression to represent the total cost of tickets and popcorn for any number of people.
The lengths of the sides of a right triangle are three consecutive integers, right, and solve an equation to find the three integers
The only possible solution is x = 2. Therefore, the three consecutive integers that form the sides of the right triangle are 2, 3, and 4.
How to find side of triangle?Since they are consecutive integers, let's assume that the hypotenuse, which is the longest side of the right triangle, is x+2, as it is three units longer than the shortest side.
In a right triangle, the hypotenuse's square is equal to the sum of the squares of the other two sides, according to the Pythagorean theorem. We can thus write:
[tex](x+2)^2 = x^2 + (x+1)^2[/tex]
Expanding the squares, we get:
[tex]x^2 + 4x + 4 = x^2 + x^2 + 2x + 1[/tex]
Simplifying and rearranging terms, we get:
[tex]2x^2 - 2x - 3 = 0[/tex]
We can solve this quadratic equation by using the quadratic formula:
x = (-b ± [tex]\sqrt{b^2 - 4ac}[/tex]) / 2a
where a = 2, b = -2, and c = -3.
Plugging in these values, we get:
x = (-(-2) ± [tex]\sqrt{((-2)^2 - 4(2)(-3)))[/tex] / 2(2)
x = (2 ± [tex]\sqrt{(4 + 24))[/tex] / 4
x = (2 ± [tex]\sqrt28}[/tex] / 4
x = (2 ± [tex]2\sqrt{7}[/tex]) / 4
x = 1/2 ± [tex]\sqrt{7}[/tex]/2
The only option is x = 2, since x must be an integer. As a result, the numbers 2, 3, and 4 are the three consecutive integers that make up the sides of the right triangle.
know more about triangle visit :
https://brainly.com/question/2773823
#SPJ1
using formula : if a block of wood has dimensions of 4.55cm x 9.1cm x 2.54cm
a) the volume of the block of wood (V = I x w x h)
b) the total surface area of the block of wood (SA = 2lh + 2wh + 2lw)
show work please
The volume of the block of wood is 104.7634 cm³ and the total surface area is 186.4502 cm².
Volume is the measure of the amount of space occupied by a three-dimensional object. It is typically measured in cubic units such as cubic meters (m³), cubic centimeters (cm³), or cubic inches (in³).
The volume of the block of wood will be;
V = l x w x h = 4.55 cm x 9.1 cm x 2.54 cm
= 104.7634 cm³
Therefore, the volume of the block of wood is 104.7634 cm³.
The total surface area of the block of wood will be;
SA = 2lh + 2wh + 2lw
= 2(4.55 cm x 2.54 cm) + 2(9.1 cm x 2.54 cm) + 2(4.55 cm x 9.1 cm)
= 58.0094 cm² + 46.4314 cm² + 82.0094 cm²
= 186.4502 cm²
Therefore, the total surface area is 186.4502 cm².
To know more about total surface area here
https://brainly.com/question/30991207
#SPJ1
NO LINKS!! URGENT HELP PLEASE!!
If the given angle is in standard position, find two positive coterminal angles and two negatives coterminal angles.
a. 110° positive angles:
negative angles:
b. 165° positive angles:
negative angles:
c. -10° positive angles:
negative angles:
Answer:
a. 110°
Positive coterminal angles: 110° + 360° = 470°, 110° + 2(360°) = 830°
Negative coterminal angles: 110° - 360° = -250°, 110° - 2(360°) = -610°
b. 165°
Positive coterminal angles: 165° + 360° = 525°, 165° + 2(360°) = 885°
Negative coterminal angles: 165° - 360° = -195°, 165° - 2(360°) = -555°
c. -10°
Positive coterminal angles: -10° + 360° = 350°, -10° + 2(360°) = 710°
Negative coterminal angles: -10° - 360° = -370°, -10° - 2(360°) = -730°
Step-by-step explanation:
When an angle is in the standard position, it means that the initial side of the angle is the positive x-axis, and the terminal side of the angle is located in one of the four quadrants of the coordinate plane.
To find coterminal angles, we need to add or subtract multiples of 360 degrees to the given angle while keeping the terminal side in the same position. This is because a full rotation around the origin in the coordinate plane is 360 degrees.
For positive coterminal angles, we add multiples of 360 degrees to the given angle. In the case of 110 degrees, we can add 360 degrees once or twice to get 470 degrees or 830 degrees, respectively.
For negative coterminal angles, we subtract multiples of 360 degrees from the given angle. In the case of -10 degrees, we can subtract 360 degrees once or twice to get -370 degrees or -730 degrees, respectively.
It's important to note that there are infinitely many coterminal angles for any given angle, but we usually restrict our answers to the smallest positive and negative angles that differ from the given angle by a multiple of 360 degrees.
How many times smaller is 1.2 × 106 than 1.47 × 107?
Answer: It is 1.24x smaller.
Step-by-step explanation:
1.2(106)= 127.2
1.47(107)= 157.3
157.3/127.2 = 1.24x smaller
I need help solving this question
Answer:
C. y = 3/2x + 4
Step-by-step explanation:
C. y = 3/2x + 4
Find the surface area of the figure ( on photo)
The surface area of the figure is 344 m².
What is area?Area is the region bounded by a plane shape.
To calculate the surface area of the figure, we use the formula below.
Formula:
A = bh+L(a+b+c)..................... Equation 1Where:
A = Surface areab = Base of the triangleh = Height of the triangleL = Length of the prisma, c = Other two sides of the triangular baseFrom the diagram,
Given:
b = 6 mh = 4 ma = 5 mc = 5 mL = 20 mSubstitute these values into equation 2
A = (6×4)+20(5+5+6)A = 24+320A = 344 m²Hence, the area is 344 m².
Learn more about area here: https://brainly.com/question/28470545
#SPJ1
12,110 members is what percent of 21,625 members? Please show work
Answer:
56
Step-by-step explanation:
12110 × 100
21625
=1211000
21625
=56
Select all functions that have a y-intercept of 0,5. I need help (posts test!!!)
Use the power-reducing formulas to rewrite the expression in terms of first powers of the cosines of multiple angles.
5 cos4(x)
Using the power reducing formulas the expression [tex]5cos^4(x) = 5(1 + cos(2x))^{2/4}[/tex].
What are power-reducing formula?We can define higher powers of a trigonometric function in terms of lower powers of the same function using the power-reducing formulas, which are trigonometric identities. Higher powers of cosine can be expressed using this formula in terms of sine and cosine's initial powers. For the other trigonometric functions, such as sine and tangent, there are equivalent formulas. These formulas can be used to solve trigonometric equations and to simplify trigonometric expressions.
The given function is 5cos^4(x).
Now, the power reducing formulas are given by:
[tex]cos(2x) = cos^2(x) - sin^2(x) = 2cos^2(x) - 1\\cos^2(x) = (1 + cos(2x))/2[/tex]
Substituting the value of second equation in 1 we have:
cos(2x) = 2(1 + cos(2x))/4 - 1
[tex]cos(2x) = (2cos^2(x) - 1) = cos^2(x) - sin^2(x)[/tex]
Now we have:
[tex]cos^2(x) = (1 + cos(2x))/2[/tex]
Thus,
[tex]cos^4(x) = (1 + cos(2x))/2)^2[/tex]
Now multiplying by 5:
[tex]5cos^4(x) = 5(1 + cos(2x))^{2/4}[/tex]
Learn more about trigonometric functions here:
https://brainly.com/question/14746686
#SPJ1
PLEASE HELP QUICK How many clubs have at least 30 members?
A.5 clubs
B.6 clubs
C.8 clubs
D.9 clubs
Answer:
D. 9 clubs
Step-by-step explanation:
Given a stem-and-leaf plot of the number of members in clubs, you want to know the number of clubs with 30 or more members.
Stem and Leaf PlotThe plot shows the club membership to be ...
{10, 13, 15, 24, 26, 30, 36, 39, 50, 55, 59, 61, 66, 78}
The 9 clubs whose member numbers are in bold have at least 30 members.
The number of clubs with at least 30 members is ...
D. 9 clubs
<95141404393>
A. Using the given variables, translate the following to mathematical
expressions.
1. the sum of n and 8
2. M reduced by x
3. 12 subtracted from z
4. cincreased by d
5. 20 more than twice f
6. the square of the sum of x and y
7. twice the product of m and n
8. six less than twice b
9. the sum of the squares of u and v
10.the product of x and y divided by 2
Answer:
n + 8
M - x
z - 12
c + d
2f + 20 or 20 + 2f
(x + y)^2 or (x + y) × (x + y)
2mn or 2 × m × n
2b - 6 or 6 - 2b
u^2 + v^2 or v^2 + u^2
(xy)/2 or xy/2
Amelia bought a t-shirt for 15$ and 3 pairs of pants. She spent a total of 117$ wich equation matches this problem
The equation that matches this problem is 15 + 3p = 117
Which equation matches this problemLet the cost of one pair of pants be represented by the variable p.
Then, the cost of three pairs of pants is 3p.
We are also given that the cost of a t-shirt is $15.
The total cost of Amelia's purchase is $117.
Therefore, the equation that matches this problem is:
15 + 3p = 117
This equation represents the total cost of Amelia's purchase, which includes the cost of one t-shirt and three pairs of pants.
Read more about equation at
https://brainly.com/question/148035
#SPJ1
In a poll of 510 human resource professionals, %45.9% said that body piercings and tattoos were big personal grooming red flags. Complete parts (a) through (d) below.
By sample distribution, (0.431,0.487) is Complete parts (a) through (d) below.
What does a statistical sample distribution mean?
An accurate probability distribution of a statistic is known as a sampling distribution, and it is created by repeatedly sampling a certain population. It depicts a spectrum of potential results for a statistic, such as the mean or mode of a variable, for a population.
Given
Favourable cases (X)=?
Sample size(n)=510
Sample proportion (p_hat)=X/n=0.459
X=np_hat=510*0.459=234.09=234
Confidence level(1-α)=99%=0.99
α=0.0
The critical value for α=0.01 is Zc=2.576
The margin of error is E=Zc* √((p_hat(1-p_hat)/n))
E=2.576* √((0.459(1-0.459)/510))=0.0568
The 99% confidence interval for p
CI=(p_hat-E,p_hat+E)
CI=(0.459-0.0568,0.458+0.0568)
CI=(0.402,0.516)
Confidence level(1-α)=80%=0.80
α=0.20
The critical value for α=0.2 is Zc=1.282
The margin of error is E=Zc* √((p_hat(1-p_hat)/n))
E=1.282* √((0.459(1-0.459)/510))=0.0283
The 80 % confidence interval for p
CI=(p_hat-E,p_hat+E)
CI=(0.459-0.0283,0.458+0.0283)
CI=(0.431,0.487)
Learn more about sample distribution
brainly.com/question/13501743
#SPJ1
if n = 4 then σ(4)=1+2+4=7 and H4 = 1+1/2+1/3+1/4. Solve this equation to either prove or disprove the following inequality n≥1? Does it hold for all n≥1?
Using the method of mathematical induction, we show that the inequality σ(n) > H(n) holds for all n≥1. Thus, the inequality n≥1 is true for all n≥1.
What is mathematical induction?It is a a technique used in mathematics to prove that a statement is true for every positive integer or natural number. It consists of two steps:
Base case: Prove that the statement is true for the first positive integer (usually 1).Inductive step: Assume that the statement is true for some arbitrary positive integer k, and then prove that it must also be true for the next positive integer (k+1).We can calculate like this:
Base case: Show that the inequality holds for n=1.
When n=1, we have σ(1) = 1 and H1 = 1, so the inequality 1 ≤ 2^(σ(1)/H1) becomes 1 ≤ 2^(1/1), which is true.Inductive hypothesis: Assume that the inequality holds for some arbitrary positive integer k, i.e., k ≤ 2^(σ(k)/Hk).
Inductive step: Show that the inequality also holds for k+1. Consider σ(k+1) and H(k+1). We can express them as σ(k+1) = σ(k) + k+1 and H(k+1) = H(k) + 1/(k+1).
Using the inductive hypothesis, we have:
k ≤ 2^(σ(k)/Hk),So, we can raise both sides to the power of (k+1)/(kH(k+1)) to get:
k^(1/(kH(k+1))) ≤ 2^((k+1)/(kH(k+1)) * σ(k)/Hk).By the AM-GM inequality, we know that σ(k+1)/k+1 ≥ H(k+1), so we can replace the denominator (kH(k+1)) with H(k+1) and simplify to get
k^(1/H(k+1)) ≤ 2^(σ(k+1)/H(k+1)).Therefore, we have shown that k+1 ≤ 2^(σ(k+1)/H(k+1)), which means the inequality holds for all positive integers n by mathematical induction.
Find out more about inequality at:
https://brainly.com/question/24372553
#SPJ1
5. Patty starts at the bottom of a Ferris wheel with a radius of 8 m. The Ferris wheel rotates so Patty is now at the top. Arlene is on a merry-go-round with a radius of 6 m. The merry-go-round moves two- thirds of the way around its axle. Who travels farther? How much farther to the nearest tenth of a metre ?
Answer is down below!
Step-by-step explanation:
This is of the form h = a + b cos ct, where: a = 40 m. This is the height of the axle of the Ferris wheel. b = -30 m. The magnitude of this number is the radius of the wheel.
Y=2x to the power of 2 plus 4x minus one