Two amateur marathoners were running a marathon. The first marathoner kept a steady pace and was able to finish in four hours. The second marathoner was keeping 4 the speed of the speed of the first runner. Then he was tired and his speed for the 3
second half of the distance was only 3 4 the speed of the first runner. How much did it
take the second runner to finish the distance?

The Complement of a 14° angle is 76°, while the supplement of 14° angle is 166°.

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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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:

Answer:is this an actual question

Step-by-step explanation:

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°.

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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Answer:x+2

Step-by-step explanation:

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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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.

Answer:

Step-by-step explanation:

V=15

fraction of cylinder volume is=22

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

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:

Answer:

10

Step-by-step explanation:

The value of quadratic equation with the help of  hit and trial method is 39

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.

the 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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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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The equation is given by y = 2.5x. It means that the cost of each gallon of gas is $2.5

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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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.

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).

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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The equation of the circle is (x + 1)² + (y - 1)² = 16.

option D

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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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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Jim's daily income must be less than $2 in order for him to be considered impoverished.

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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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%

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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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.

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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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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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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5.) The measure of angle D of the given triangle would be = 59.5°

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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The mean, median, mode and range are 42.2, 30, 87 and 95 respectively.

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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