there are 45 runners in a race. how many ways can the runners finish first, second, and third?

In a case whereby sheri’s cab fare was $32, with a 20% gratuity and no taxes. sheri's write a check to the cab driver for $40, this can be considered as being reasonable amount because it is  $1.60 more to the cab driver.

A gratuity is a sum of money that customers typically give to specific service sector employees, including those in the hotel industry, in addition to the service's base charge for the work they have completed.

Given ; Sheri’s cab fare was $32 and the percentage of gratuity is 20%

amount of gratuity = 20% 0f 32 = 6.40

The fare of the cab  + gratuity = 32 + 6.40 = 38.40

Check to the cab driver for $40 ,  implies ($40 - $38.40)= $1.60 more to the cab driver.

Hence, it is reasonable.

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Answer: 2,3,4

Step-by-step explanation:

Apple’s is represented by 8 and oranges is represented by 5. So the ratio 8:5 means every 8 apples their are 5 oranges

Answer:

Step-by-step explanation:

15,13,11,9,1,3,5,7

Answer:

13

Step-by-step explanation:

Supplementary angles add up to 180 and angles on a straight line add up to 180 so 13

Answer:

give me poi tasjnsaklaalwkdbfbdjwo

Answer:

(4x - 3)(4x + 3)

Step-by-step explanation:

16x² - 9 ← is a difference of squares and factors in general as

a² - b² = (a - b)(a + b) , then

16x² - 9

= (4x)² - 3²

= (4x - 3)(4x + 3)

Answer:

ayla had 45 cupcakes for the class jayla gave a number out to the cladd Jayla took 15 cupcakes back home what is the does n equal to

Answer:

Any x-value other than 4, 8, or 9 would make this set of points a function.

The sum from i = 1 to n of 2^i is 2(2^n - 1), the sum from i = 1 to n of 1/(i(i+1)) is n/(n+1), n! > 2^n for n ≥ 4, and therefore, sqrt(2) is irrational. The intersection of sets A and B has |A ∩ B| elements, the union of sets A and B has |A ∪ B| elements, and the number of students on the CS team is 6.

Let's break down the questions and provide the proofs and solutions step by step:

Sum of powers of 2: We want to find the sum from i = 1 to n of 2^i for each n ≥ 1. We can use the formula for the sum of a geometric series to simplify the expression:

The sum of a geometric series is given by the formula Sn = a(r^n - 1)/(r - 1), where a is the first term, r is the common ratio, and n is the number of terms. In this case, a = 2, r = 2, and we need to find Sn.

Plugging in the values, we get Sn = 2(2^n - 1)/(2 - 1) = 2(2^n - 1).

Therefore, the sum from i = 1 to n of 2^i is 2(2^n - 1).

Sum of fractions: We want to find the sum from i = 1 to n of 1/(i(i+1)) for each n ≥ 1. We can rewrite the expression as follows:

1/(i(i+1)) = 1/i - 1/(i+1).

Now, we can observe that the terms cancel out in pairs when we sum them. The first term 1/1 remains, and the last term 1/(n+1) remains as well.

Therefore, the sum from i = 1 to n of 1/(i(i+1)) is 1 - 1/(n+1) = n/(n+1).

Proof of n! > 2^n: We will prove this by induction. The base case is n = 4: 4! = 24 > 2^4 = 16.

Now, assume the inequality holds for some k ≥ 4, i.e., k! > 2^k.

We need to prove it for k + 1: (k + 1)! = (k + 1) * k! > (k + 1) * 2^k (since k! > 2^k by the induction hypothesis).

It suffices to show that (k + 1) * 2^k > 2^(k + 1), which simplifies to k + 1 > 2.

Since k ≥ 4, the inequality holds.

Therefore, by induction, we can conclude that n! > 2^n for each n ≥ 4.

Proof that sqrt(2) is irrational: We will prove this by contradiction. Assume that sqrt(2) is rational, i.e., sqrt(2) can be expressed as a ratio of two integers p and q in its simplest form, where q ≠ 0.

sqrt(2) = p/q.

Squaring both sides, we get 2 = p^2/q^2.

Rearranging, we have p^2 = 2q^2.

This implies that p^2 is even, and thus p must be even.

Let p = 2k, where k is an integer.

Substituting back, we have (2k)^2 = 2q^2, which simplifies to 4k^2 = 2q^2.

Dividing by 2, we get 2k^2 = q^2.

This implies that q^2 is even, and thus q must be even.

However, if both p and q are even, then p/q is not in its simplest form, contradicting our initial assumption.

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Answer:

The equations are

X + Y = 48 ----Eq (1)

Y = 2 X -----Eq (2)

Solution of the equations and the two number are

X = 16, Y = 32

Step-by-step explanation:

Let the two numbers be X and Y

Given -

The sum of two numbers is 48.

Thus, X + Y = 48 ----Eq (1)

The second number is twice the first

Thus, Y = 2 X -----Eq (2)

Substituting the value of Y in equation (1), we get -

X + 2X = 48

3 X = 48

X = 16

Y = 2 X = 32

Answer:

Step-by-step explanation:

Answer:

x=41

Step-by-step explanation:

x/50=82/100

cross multiply

100x= 82×50

100x= 4100

x= 4100/100

x= 41

check our work

41/50 × 100= 82 percent

Answer:

Keep adding 8 56 times subtract three which is 472

Step-by-step explanation:

mulitiply 59 times 8

Answer:

FV= $3,726.93

Step-by-step explanation:

Giving the following information:

Initial investment (PV)= $2,500

Interest rate (i)= 0.04/12= 0.003333 monthly

Number of periods (n)= x months

To calculate the future value giving any number of months, we need to use the following formula:

FV= PV*(1 + i)^n

For 10 years:

n=10*12= 120 months

FV= 2,500*(1.003333^120)

FV= $3,726.93

Answer:

m∡ADE = 80°

Step-by-step explanation:

m∡ADE = m∡ABC

m∡B = 180-(30+70) = 80°

therefore, m∡ABC = 80° and so does m∡ADE because they are congruent

The statement that is true is (LS – ES) >= 0. Option C

The latest possible time to begin an activity is denoted as LS in project management, while the earliest possible time is indicated by ES.

The distinction between LS and ES signifies the flexibility an activity possesses, allowing it to be postponed without affecting the ultimate timeframe of the project.

The calculation for Slack involves subtracting the earliest possible finish time (LS) from the latest possible finish time (LF). One must note that (LS - ES) will never be negative as the earliest start time (ES) can never be greater than the latest start time (LS).

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Answer:

6 for $1.1

Step-by-step explanation:

The sample size required to estimate the proportion of inedible fish in the lake with a margin of error of at most 0.053 and a 97.5% confidence level is 491.

To determine the sample size needed for the estimation, we can use the formula:

Plugging in these values, we get:

Therefore, a sample size of 491 will ensure a margin of error of at most 0.053 for a 97.5% confidence interval when estimating the proportion of inedible fish in the lake.

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To evaluate the line integral ∫c xy⁴ ds, we need to parameterize the curve c, then substitute into the integrand, and integrate with respect to the parameter.

The right half of the circle x² + y² = 9 can be parameterized as x(t) = 3cos(t), y(t) = 3sin(t) for t in [0, pi]. Note that this parameterization traces out the right half of the circle oriented counterclockwise.

Now, we can express ds as ds = sqrt(dx/dt² + dy/dt²) dt. Using the parameterization x(t) = 3cos(t), y(t) = 3sin(t), we get dx/dt = -3sin(t) and dy/dt = 3cos(t). Thus, ds = sqrt((-3sin(t))² + (3cos(t))²) dt = 3dt.

Substituting x(t) = 3cos(t), y(t) = 3sin(t), and ds = 3dt into the integrand xy⁴, we get xy⁴ = (3cos(t))(3sin(t))⁴ = 81/4 sin⁴(t) cos(t).

So, the line integral becomes:

∫c xy⁴ ds = ∫₀ᴨ (81/4 sin⁴(t) cos(t))(3 dt)

Using trigonometric identities, we can simplify the integrand to:

(81/4)(1/5)(sin⁵(t))' = 81/20 sin⁵(t)

Evaluating the integral from t = 0 to t = pi, we get:

∫c xy⁴ ds = ∫₀ᴨ 81/20 sin⁵(t) dt = 81/16π

Therefore, the value of the line integral is 81/16π.

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Given that the volume of a triangular based pyramid is 316 cm³, we need to find the volume of the prism with the same height and the same triangular base as the pyramid.

Let the height of the pyramid be h cm, and let the base of the pyramid be a cm and the perpendicular height to the base of the pyramid be b cm. '

1. Volume of the pyramid: The volume of a triangular-based pyramid is given by the formula V = 1/3abhGiven V = 316 cm³, a = 7 cm and b = 12 cm, we have; 316 = 1/3 × 7 × 12 × h => h = (316 × 3) / (7 × 12) => h = 9 cm

2. Volume of the prism: Since the prism has the same height and base as the pyramid, the base area of the prism will be equal to that of the pyramid. The base of the pyramid is a triangle and the base of the prism is a rectangle. Let the length of the rectangular base be L cm.

Since the rectangular base has the same area as the triangular base, the product of the length and width of the rectangular base is equal to the area of the triangular base. Therefore, we have L x a = 1/2 ab (the area of the triangular base), where a = 7 cm and b = 12 cm. L = 1/2 b = 1/2 × 12 = 6 cm

The volume of the prism is given by the formula V = La h = 6 × 9 = 54 cm³

Therefore, the volume of the prism is 54 cm³.

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The  direction of the magnetic field at P is perpendicular to both the current direction and the direction of the curl of our fingers.

The direction of the magnetic field at point P due to the current-carrying wire can be determined using the right-hand rule. If we point our right thumb in the direction of the current (which is along the positive x-axis), and curl our fingers toward the point P, then the direction of the magnetic field at P is perpendicular to both the current direction and the direction of the curl of our fingers.

In this case, since the wire is straight and lies in the x-y plane, the direction of the magnetic field at point P will be perpendicular to the plane of the page, and will either be pointing into or out of the page. To determine which direction, we need to know the orientation of point P relative to the wire. If point P is above the wire, then the magnetic field will be pointing into the page, and if it is below the wire, then the magnetic field will be pointing out of the page.

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To apply Rouché's Theorem, we consider two functions: f(z) = 2z⁸ + 3z⁵ - 9z³ + 2 and g(z) = 2z⁸. We want to analyze the number of roots of f(z) = 0 inside the region 1 < |z| < 2.

First, let's examine the behavior of f(z) and g(z) on the boundary of the region. When |z| = 1, the term 2z⁸ dominates over the other terms in f(z), so |f(z)| < |g(z)|. On the other hand, when |z| = 2, the term 2z⁸ is still dominant, and again |f(z)| < |g(z)|.

Since |f(z)| < |g(z)| on the boundary of the region, Rouché's Theorem guarantees that f(z) and g(z) have the same number of roots inside the region, counting multiplicities. In this case, g(z) = 2z⁸ has exactly eight roots, counting multiplicities.

Therefore, by Rouché's Theorem, we can conclude that the equation 2z⁸ + 3z⁵ - 9z³ + 2 = 0 has eight roots, counting multiplicities, inside the region 1 < |z| < 2.

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After considering the given data we conclude that the generated two year discount factor is 0.9132, under the condition that three year annuity factor is 2.6065.

Applying the formula for the annuity factor, we can find the two year discount factor:
[tex]annuity factor = (1 - discount factor^n) / r[/tex]
Here,
n = number of years
r = annual interest rate.
We are given that the three year discount factor is 0.7773 and the one year discount factor is 0.9434. We are also given that the three year annuity factor is 2.6065.
Applying the formula for the annuity factor, we can evaluate the annual interest rate:
[tex]2.6065 = (1 - 0.7773^3) / r[/tex]
r = 0.1
Now, we can evaluate the two year discount factor:
[tex]annuity factor = (1 - discount factor^2) / 0.1[/tex]
[tex]2.6065 = (1 - discount factor^2) / 0.1[/tex]
[tex]discount factor^2 = 0.89335[/tex]
discount factor = [tex]\sqrt(0.89335)[/tex]
discount factor = 0.9132
Therefore, the two year discount factor is 0.9132.
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Answer:

1/10

Step-by-step explanation:

1) find a common factor between the two denominators.

2 and 5 have a common factor of 10. you can find this by multiplying the denominators.

2) now that you have a common denominator of 10, you'll need to change the numerators too. you do this by finding out how many times the denominator goes into your common factor. 5 goes into 10 two times so you would multiply 2 x 2. two goes into 10 five times so multiply 5 x 1.

3) you now have both fractions that share a common factor. now you have to subtract them.

5/10 - 4/10 = 1/10

Answer:

230.98 meters

Step-by-step explanation:

Answer:

126m

Step-by-step explanation:

Use sine because we want to find the opposite length but only know the hypotenuse.