It takes the second marathoner 4 hours and 40 minutes to complete the marathon.
Let's assume the distance of the marathon is "d" miles.
The first marathoner runs at a constant speed for 4 hours, so we can find their speed as:
speed = distance / time = d / 4
The second marathoner starts by running at 4 times the speed of the first marathoner, so their speed is:
speed = 4(d / 4) = d
For the second half of the race, the second marathoner's speed drops to 3/4 of the first marathoner's speed. Let's assume it takes "t" hours for the second marathoner to complete the second half of the race. Then, we can write:
d / 2 = (3/4)(d / 4)(t)
Simplifying this equation, we get:
t = (2/3) hours
So the total time it takes the second marathoner to finish the race is:
4 + (2/3) = 4 2/3 hours = 4 hours and 40 minutes.
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Salary Raise: Men According to the same survey quoted in Problem 13, of the men interviewed, 20% had asked for a raise and 59% of the men who had asked for a raise received the raise. If a man is selected at random from the survey population of men, find the following probabilities: P(man asked for a raise); P(man received raise, given he asked for one); P(man asked for raise and received raise).
The evaluated probabilities for the given question are 0.20 for the men who asked for promotion, 0.59 for the men who received the promotion when asked, and 0.118 for men who asked for promotion and received.under the condition that from the men interviewed 20% had asked for a promotion and 59% of the men who had asked for a promotion and received.
Then,
P(man asked for a promotion)
= 20/100
= 0.20
P(man received promotion, given he asked for one)
= 59/100
= 0.59
P(man asked for promotion and received )
= P(man asked for a promotion) x P(man received promotion, given he asked for one)
= 0.20 x 0.59
= 0.118
Probability is considered as the percentage of an event taking place in a specific time frame, in a given place. It is said to be a great aid in the horizons of science and mathematics.
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find the median mode and range for each set of data 23,87,19,34,37,87,5,14,100,26
The mean, median, mode and range are 42.2, 30, 87 and 95 respectively.
What is mean, mode median and range?The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set.
Therefore mean = (23+87+19+34+37+37+5+14+100+26)/10
= 422/10 = 43.2
The median is the middle value when a data set is ordered from least to greatest. The mode is the number that occurs most often in a data set.
median = 26+34/2 = 60/2 = 30
Mode is the number with the highest frequency
Therefore, the mode is 87
Range Is the difference between the highest and the lowest
= 100-5 = 95
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Answer one of the questions & show work if you’re team Selena
5.) The measure of angle D of the given triangle would be = 59.5°
How to calculate the missing angles using sine rules?To calculate the missing angles, sine rule is used which is ;
Sine rule = a/sin A = b/sin B
Where a = 23
A = 56°
b = 24
B = X
That is;
23/sin56° = 24/sinx
Make sin X the subject formula;
Sin X = sin56×24/23
= 0.829037572×24/23
= 19.89690174/23
= 0.865082684
X = Sin-1 (0.865082684)
= 59.89214806
= 59.9° (approximately)
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Object 1: Cereal Box
3D shape: Rectangular Prism
Dimensions:
length = 12 inches
width = 8 inches
height = 1.75 inches
find the volume formula and the volume
The volume of the rectangular prism for the given dimensions length , width , and the height is equal to 168 cubic inches.
Dimensions of the rectangular prism is equal to,
length of the rectangular prism = 12 inches
width of the rectangular prism = 8 inches
height of the rectangular prism = 1.75 inches
The formula for the volume of a rectangular prism is equal to,
Volume of the rectangular prism = length x width x height
Plugging in the given values of the dimensions , we have,
⇒ Volume of the rectangular prism = 12 inches x 8 inches x 1.75 inches
Simplifying this expression to get the volume of rectangular prism, we get,
⇒ Volume of the rectangular prism = 168 cubic inches
Therefore, the volume of the rectangular prism is 168 cubic inches.
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3/8x - 6 = 1/2(4 - x)
Answer:
x= 64/ 7
Step-by-step explanation:
3/8x - 6 = 1/2(4 - x)
3/8x - 6 = 2- 1/2 x
3/8x - 8 = - 4/8 x
so 7/8 x = 8
x = 64/7
Which polynomial represents the difference below?
(7x² + 8) - (4x²+x+6)
A. 3x²+x+14
OB. 3x²-x+2
OC. 11x²-x+ 2
OD. 11x²+x+14
SUBMIT
Quiz Active
Does anyone know the answer
The equation of the circle is (x + 1)² + (y - 1)² = 16.
option D
What is the equation of the circle?
The radius of the circle is 4, and the center of the circle is (-1, 1).
The equation of a circle with center (a,b) and radius r is given by:
(x - a)² + (y - b)^2 = r²
In this case, the center of the circle is (-1, 1) and the radius is 4. Plugging these values into the equation, we get:
(x - (-1))² + (y - 1)² = 4²
Simplifying the equation, we get:
(x + 1)² + (y - 1)² = 16
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What is the value of the quadratic equation: y=4x^2+8x+7
The value of quadratic equation with the help of hit and trial method is 39
what is quadratic equation ?A quadratic equation is a polynomial equation of degree 2, which means that the highest power of the variable (usually x) in the equation is 2. It is in the form:
ax^2 + bx + c = 0
where a, b, and c are constants and a is not equal to zero.
According to given informationthe value of given quadratic equation is
given
y=4x²+8x+7
using hit and trial method:
The value of the quadratic equation y = 4x² + 8x + 7 depends on the value of x.
To find the value of y for a specific value of x, simply substitute that value of x into the equation and solve for y.
For example, if x = 2, then:
y = 4(2)² + 8(2) + 7
y = 16 + 16 + 7
y = 39
So the value of the quadratic equation y = 4x^2 + 8x + 7 when x = 2 is 39.
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Which is the simplified form of m^8p^0
Assume that A and B are independent events.
a. Explain why P(B) = P(B|A) and P(A) = P(A|B).
b. Can P(A and B) also be defined as P(B) • P(A|B)?
Justify your reasoning.
Assume that A and B are independent events. it means that the occurrence of event A does not affect the probability of event B and vice versa.
b. Assume that A and B are independent events. My response is Yes, P(A and B) can be defined as P(B) • P(A|B).
Why the reasoning above?In the event that A and B are independent events, at that point the probability of A happening is one that is influenced by the event of B and vice versa. Hence, P(B) is comparable to P(B|A), showing that the probability of occasion B happening remains unaltered in any case of event A's event. Within the same vein, the likelihood of event A happening remains consistent whether event B has stay put or not, indicated as P(A) = P(A|B).
Therefore in response to question 2, The reason why independent events are not affected by one another is that the likelihood of one event happening has no effect on the probability of the other event occurring.
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Subtract. Write your answer in simplest form.
6 3/4-2 3/20
The graph shows the number of handbags that Mandy made in one day. What are the variables? Describe how the variables are related.
PLEASE HELP!
Question 1: y is directly proportional to x. If y=5 when x is 25:
a) Find an equation for y in terms of x.
b) Use your equation from part a) to find y when x is 100.
Question 2:
y ∝ x and y=132 when x=10
a) Find the value of y when x=14.
b) Sketch the graph of this proportion for x>0 and mark two points on the line.
1) The value of an equation for y in terms of x is, y = 1/5x
And, y = 20 at x = 100
2) y = 184.8 , at x = 14
The value of an equation for y in terms of x is, y = 13.2x
Given that;
1) y is directly proportional to x.
2) y ∝ x and y=132 when x=10
Now, For 1;
1) Since, y is directly proportional to x.
Hence, We get;
y = kx
Plug y = 5 and x = 25
5 = 25k
k = 1/5
Hence, The value of an equation for y in terms of x is,
y = 1/5x
And, Plug x = 100,
y = 1/5 x 100
y = 20
2) Since, y ∝ x and y=132 when x=10
y = kx
132 = 10k
k = 13.2
Hence, At x = 14;
y = 13.2 x 14
y = 184.8
Thus, The correct equation is,
y = 13.2x
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I need help pretty please
Answer:x+2
Step-by-step explanation:
Listen to the following recommendations and answer the question.
What is the first recommendation?
O Buy more than one ticket at a time.
O Buy tickets in a travel agency.
O Buy a round-trip ticket.
O Buy plane tickets way in advance
The first recommendation among the given options is "Buy more than one ticket at a time".
This recommendation suggests that purchasing multiple tickets in a single transaction can result in cost savings. Many airlines offer discounted fares for group bookings, which means buying multiple tickets at once can save money compared to buying them individually.
Buying tickets in bulk not only saves money, but it also provides a level of flexibility in terms of travel plans. For instance, if a group of travelers plan to visit a particular destination together, they can book their tickets together and have a better chance of securing seats on the same flight. Additionally, in case there are changes in the travel plans, such as the need to reschedule or cancel, group bookings provide more flexibility in terms of making changes or requesting refunds.
Overall, buying more than one ticket at a time can be a wise decision, especially if one is traveling with a group or planning multiple trips in the near future. By doing so, one can save money and have more flexibility in terms of travel plans, making the overall travel experience smoother and more enjoyable.
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The probabilities by subject of on-time assignment submission and on-time arrival in class are given in the table.
Subject On-time Assigment
Submission On-time Arrival
in Class
Physics 89. 7% 82. 3%
Math 88. 2% 88. 7%
Chemistry 89. 4% 83. 1%
Biology 90. 1% 82. 4%
Total 88. 5% 84. 7%
Identify the probability of on-time arrival in class given that the subject is biology.
Given that biology is the subject, the Probability of being on time is 32.8%.
In this case:
P(on-time arrival in class | biology) = P(on-time arrival in class and biology) / P(biology) is the result of applying the conditional probability formula.
According to the table, 82.4% of students will be on time for biology class. Since there are four topics listed, each with an equal weight, the likelihood of biology is 25%. Therefore, we have:
P(on-time arrival in class | biology) = 82.4% / 25% = 0.328 = 32.8%
Therefore it can be concluded that the probability of on-time arrival in class given that the subject is biology is 32.8%.
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(a) How many strings of seven hexadecimal digits do not have any repeated digits? 43680 x (b) How many strings of seven hexadecimal digits have at least one repeated digit? 21856 X (c) What is the probability that a randomly chosen string of seven hexadecimal digits has at least one repeated digit? (Round your answer to the nearest tenth of a percent. ) 33. 4 X % Need Help? Read It Talk to a Tutor
a) the total number of strings of seven hexadecimal digits that do not have any repeated digits is 450,450
b) The number of strings of seven hexadecimal digits have at least one repeated digit is 267,985,006
c) the probability that a randomly chosen string of seven hexadecimal digits has at least one repeated digit is 99.8%
How is this so?The total number of strings of seven hexadecimal digits is 16⁷.
For a string to not have any repeated digits, the first digit can be chosen in 16 ways, the second in 15 ways (since one digit has already been used),
the third in 14 ways, and so on, giving a total of 16 * 15 * 14 * 13 * 12 * 11 * 10 = 13,608,960 strings.
So
(16 * 15 * 14 * 13 * 12 * 11 * 10)/ (2 * 2 *2* 2* 2 *2* 2)
= 450,450
b) the number of strings with no repeated strings is 450450, so the nubmer of strings with at least one rpeated digit is
16⁷ - 450450 = 267,985,006
c) the probability that a a randomly chosen string of seven hexadecimal digits has at least one repeated digit
= 267,985,006/ 16⁷
= 0.99832194298
= 99.8%
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a cycloid is the plane curve traced out by a point on the circumference of a circle as it rolls without slipping along a straight line. (a) assume that the line is the x-axis, and the circle has radius 1. find a parametriza- tion of the cycloid. (b) what is the arclength of one period of the cycloid?
Answer: (a) Let the circle roll along the x-axis with the center at the origin. Then, the parametric equations of the cycloid are given by:
x = t - sin(t)
y = 1 - cos(t)
where t is the angle in radians that the circle has rotated from its initial position.
(b) The arclength of one period of the cycloid is given by the integral:
L = ∫(0,2π) √[dx/dt]^2 + [dy/dt]^2 dt
Substituting the parametric equations from part (a), we get:
dx/dt = 1 - cos(t)
dy/dt = sin(t)
Therefore,
[dx/dt]^2 + [dy/dt]^2 = 2 - 2cos(t)
Substituting back into the arclength integral, we get:
L = ∫(0,2π) √(2 - 2cos(t)) dt
This integral can be evaluated using the half-angle formula:
cos(t) = 1 - 2sin^2(t/2)
Substituting this into the integral and simplifying, we get:
L = 8∫(0,π/2) √(sin^3(t/2)) dt
This integral can be evaluated using a substitution u = cos(t/2), du = -sin(t/2)dt:
L = 16∫(0,1) √[(1-u^2)^3] du
This integral can be further simplified by making the substitution u = sin(θ):
L = 16∫(0,π/2) cos^4(θ) dθ
This integral can be evaluated using integration by parts and trigonometric identities. After some algebraic manipulations, we get:
L = 8π
Step-by-step explanation:
Find the are length of An Leave your answer in terms of it and round to the nearest hundredths
The exact length of arc AB is π feet. To round to the nearest hundredths, we get:
AB ≈ 3.14 feet
What is a circle?
It is the center of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.
we can use the central angle and the fact that a full circle has a central angle of 360° to calculate the fraction of the circumference that AB represents.
Since the central angle, APB is 45°, we can calculate the fraction of the circumference that AB represents as:
45°/360° = 1/8
Therefore, AB represents 1/8 of the circumference of the circle.
If we let C be the circumference of the circle, then the length of AB can be calculated as:
AB = (1/8) * C
Since we do not know the value of C, we cannot calculate the exact length of AB. However, we can leave our answer in terms of π as:
AB = (1/8) * π * d
where d is the diameter of the circle.
If the diameter of the circle is 8ft, then the radius (r) is half of that, or 4ft. We can now use this value to find the exact length of AB.
The circumference (C) of the circle can be found using the formula:
C = 2πr
where π is the constant pi.
Plugging in the given value of the radius, we get:
C = 2π(4ft) = 8πft
Therefore, the exact length of AB is:
AB = (1/8) * C = (1/8) * 8π ft = π ft
Hence, the exact length of arc AB is π feet. To round to the nearest hundredths, we get:
AB ≈ 3.14 feet
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Define:
Permutation
Factorial
Series
Circular permutation
Answer: Permutation: A permutation is an course of action of a set of objects in a particular arrange. The number of conceivable changes of a set of n objects is n factorial (n!), which is the item of all positive integrability up to n.
Factorial: The factorial of a non-negative numbers n is signified by n! and is characterized as the item of all positive integrability less than or rise to to n. For case, 5! = 5 x 4 x 3 x 2 x 1 = 120.
Series: A arrangement may be a entirety of terms organized in a particular arrange. The entirety of the terms in a arrangement is called its add up to.
Circular permutation: A circular stage may be a stage of a set of objects in a circular course of action, where the arrange of objects things, but the beginning point is subjective. For case, orchestrating the letters A, B, and C in a circle would result in 3 circular stages: ABC, BCA, and CAB. The number of conceivable circular stages of a set of n objects is (n-1)!.
Step-by-step explanation:
Solve the equation. Round to the nearest tenth if necessary. 196=n^2
Answer:
10
Step-by-step explanation:
Marcus fills his tank with premium gasoline. The graph shows the relationship between the number of gallons he puts in the tank and the total cost for the gas.
The equation is given by y = 2.5x. It means that the cost of each gallon of gas is $2.5
What is an equation?An exponential equation is an expression that shows how numbers and variables using mathematical operators.
Let y represent the cost in dollars for x gallons of gas she puts in the tank
The graph passes through point (0, 0) and (3, 7.5), hence:
y - 0 = [(7.5 - 0) / (3 - 0)](x - 0)
y = 2.5x
The equation is given by y = 2.5x
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A composite figure is formed with two cones and a cylinder.
What is the surface area of the composite figure?
32 cm
26 cm
12 cm
15 cm
A 5127.56 cm²
B
C
D
3317.52 cm²
1056 cm²
4222.30 cm²
Answer:is this an actual question
Step-by-step explanation:
Find the measure
Find the measure
of the complement of a 14° angle.
of the supplement of a 14° angle.
The Complement of a 14° angle is 76°, while the supplement of 14° angle is 166°.
What is the Complement of an Angle?Recall that two angles that have a sum of 90 degrees are referred to as complementary angles. This implies that, if x is an angle, its complement is (90 - x).
Also, the supplement of an angle is the angle measure that is added to it to make it 180 degrees. This implies that if x is an angle, its supplement would be (180 - x).
Therefore, we have:
Complement of a 14° angle = 90 - 14 = 76°.
Supplement of 14° angle = 180 - 14 = 166°.
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DUE FRIDAY PLEASE HELP WELL WRITTEN ANSWERS ONLY!!!! 20 POINTS
Students in a high school mathematics class decided that their term project would be a study of the strictness of the parents or guardians of students in the school. Their goal was to estimate the proportion of students in the school who thought of their parents or guardians as “strict”. They do not have time to interview all 1000 students in the school, so they plan to obtain data from a sample of students.
1. Describe the parameter of interest and a statistic the students could use to estimate the parameter.
2. Is the best design for this study a sample survey, an experiment, or an observational study? Explain your reasoning.
3. The students quickly realized that, as there is no definition of “strict”, they could not simply ask a student, “Are your parents or guardians strict?” Write three questions that could provide objective data related to strictness.
4. Describe an appropriate method for obtaining a sample of 100 students, based on your answer in question 1.
The percentage of students at the school who describe their parents or guardians as "strict" is the key statistic. 2. A sample survey is the ideal research design for this project.
What is Proportion?Since it would be impractical to poll all 1000 kids at the school, the students intend to collect data from a sample of students in order to concentrate on the strict guardians, which is a population parameter.
The sample proportion could be used by the students as a statistic to determine this population proportion. They can ask a sample of pupils drawn at random from the school whether they think their parents or guardians are "strict". The percentage of sample kids who respond "yes" can be used to approximate the percentage of school-wide students who view their parents or guardians as "strict". A statistic that offers an estimate of the population parameter of interest is the sample proportion.
Random sampling would be a suitable technique for generating a sample of 100 pupils. Each kid in the school might be given a number, and the pupils could then use a random number generator to choose 100 numbers from the list. The chosen students might then be contacted and asked to take part in the study. This technique lessens the possibility of bias in the sample selection process and aids in ensuring that the sample is representative of the population.
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Find the compound interest and the total amount after one year if the
interest is compounded quarterly.
Principal
3256
Rate of interest = 100% per annum
=
Total amount = {
Compound interest=
Answer: The compound interest is $409.49, and the total amount after one year is $3,665.49.
Step-by-step explanation:
We can use the formula for compound interest to solve this problem:
A = P(1 + r/n)^(nt)
where:
P = the principal (in this case, $3,256)
r = the annual interest rate (100%, or 1 as a decimal)
n = the number of times the interest is compounded per year (4, since it's compounded quarterly)
t = the number of years (1)
Plugging in the values we know, we get:
A = $3,256(1 + 1/4)^(4*1)
A = $3,256(1.25)^4
A = $3,665.49 (rounded to the nearest cent)
To find the compound interest, we can subtract the principal from the total amount:
Compound interest = $3,665.49 - $3,256 = $409.49
Therefore, the compound interest is $409.49, and the total amount after one year is $3,665.49.
(4x+11°) = (5x-10)
Please answer this
Help me
Answer:
x = 21
Step-by-step explanation:
(4x+11°) = (5x-10)
4x + 11 = 5x - 10
-x + 11 = -10
-x = -21
x = 21
Answer:
Step-by-step explanation:
1)Move all x terms to one side
11° = x - 10°
2)Move all constant terms to the other side
11° + 10° = x - 10° + 10°
21° = x
So the solution to the equation is x = 21°.
(I NEED THIS ASAP)
5. A cylinder has radius 3 inches and height 5 inches. A cone has the same radius and height. (Lesson 5-13)
b. Find the volume of the cone.
c. What fraction of the cylinder's volume is the cone's volume?
Answer:
Step-by-step explanation:
V=15
fraction of cylinder volume is=22
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. Jim is categorized as poor. Thus Jim’s daily income must be less than how much dollars? Jim must be earning less than dollars per day.
Jim's daily income must be less than $2 in order for him to be considered impoverished.
What is Income?Income is an entity's ability to save and spend money during a given period of time, and it usually appears in terms of money. In principle, income can be hard to establish, and there may be variations depending on the field.
According to the World Bank's definition, there are two categories for impoverished people's salaries:
a) Moderate Poverty - A person is deemed to be in moderate poverty if their daily income is less than $2.
b) Extreme Poverty - While a person is deemed to be living in extreme poverty if they make less than 1.2 dollars per day.
Jim's daily wage must be less than $2 in order for him to be classified as impoverished.
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An amount of R6000 is made up of R100 and R50 notes. There are 4 times as many R50 notes as there are R100 notes. how many notes are there?
Answer:
There are 20 R100 notes and 80 R50 notes.
Step-by-step explanation:
Let's call the number of R100 notes "x" and the number of R50 notes "4x" (since there are 4 times as many R50 notes as R100 notes).
We can set up an equation to represent the total value of the notes:
100x + 50(4x) = 6000
Simplifying:
100x + 200x = 6000
300x = 6000
x = 20
So there are 20 R100 notes and 4 times as many R50 notes:
4x = 4(20) = 80
Therefore, there are 20 R100 notes and 80 R50 notes.