Solve. ⎧⎩⎨⎪⎪x+2y+z=82x−y+3z=4x+3y+2z=8 Enter your answer, in the form (x, y, z), in the boxes in simplest terms

There are 853,818,600 ways to award first, second, and third prizes in a contest with 950 contestants, assuming there are no ties.

To determine the number of ways to award first, second, and third prizes in a contest with 950 contestants, we can use the permutation formula:

P(n, r) = n! / (n - r)!

where n is the total number of contestants and r is the number of prizes to be awarded (in this case, 3).

Using this formula, we get:

P(950, 3) = 950! / (950 - 3)!

= 950! / 947!

= 950 × 949 × 948

= 853,818,600

Therefore, there are 853,818,600 ways to award first, second, and third prizes in a contest with 950 contestants, assuming there are no ties.

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Answer:

The great common factor is:

Steps:

given:

4x²yz³ = 2²x²z²yz

4x²yz³ = x(2z)²xyz

---------------------------------

12xz² = 4×3xz²

12xz² = 2²3xz²

12xz² = x(2z)²3

The great common factor is: x(2z)²

Answer:

4xz^2.

Step-by-step explanation:

GCF of 4 and 12 is 4

GCF of x^2 and x is x.

GCF of z^3 and z^2 is z^2.

The inequality that represents how many DVDs Andy can rent in one month that satisfies this condition is 10 + .75n ≤ 25

The correct answer choice is option B

Cost of rental per month = $10

Additional cost = $0.75

Number of DVD's rented = n

Total amount Andy want to spend ≤ $25

The inequality:

10 + 0.75n ≤ 25

subtract 10 from both sides

0.75n ≤ 25 - 10

0.75n ≤ 15

divide both sides by 0.75

n ≤ 15 / 0.75

n ≤ 20

Ultimately, Andy can rent no more than 20 DVD's in a month.

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42. The expression r(0.5s₀) refers to the wind speed at half the height of the maximum wind speed in the eyewall of a hurricane at landfall.

43. The equation r(s) = 0.75v₀ states that the wind speed, r(s), at any given height, s, is equal to 0.75 times the maximum wind speed, v₀, in the eyewall.

42. The expression r(0.5s₀) represents the wind speed at half the height of the maximum wind speed in the eyewall of a hurricane at landfall. In other words, it calculates the wind speed at a point that is located halfway between the ground and the height where the wind speed is greatest.

To interpret this in terms of hurricanes, imagine a hypothetical hurricane approaching land. The eyewall, which is the region of the storm with the strongest winds, has a certain height where the wind speed is at its maximum. Let's say this height is denoted as s₀.

Now, if we take half of s₀, represented as 0.5s₀, it gives us a height that is halfway between the ground and the maximum wind speed height. When we evaluate r(0.5s₀), we get the corresponding wind speed at that height.

Interpreting this in the context of hurricanes, r(0.5s₀) represents the wind speed experienced at an intermediate height within the eyewall. It provides information about the intensity of the storm at that particular height above the ground. This information can be useful in understanding the wind profile and potential impacts of the hurricane at different elevations.

43. The equation r(s) = 0.75v₀ expresses a relationship between the wind speed, r(s), at a given height, s, and the maximum wind speed, v₀, in the eyewall of a hurricane at landfall.

In this equation, r(s) represents the wind speed at height s above the ground, while v₀ represents the maximum wind speed observed in the eyewall at the height s₀. The equation states that the wind speed at any height within the eyewall is equal to 0.75 times the maximum wind speed.

Interpreting this equation in the context of hurricanes, it indicates that as we move away from the height of maximum wind speed, the wind speed progressively decreases. Specifically, for any given height within the eyewall, the wind speed is expected to be 75% (0.75) of the maximum wind speed observed at the height of maximum intensity.

This equation provides valuable insight into the wind profile of a hurricane's eyewall, highlighting how wind speeds change with increasing height. It allows researchers and meteorologists to estimate wind speeds at different elevations within the eyewall based on the maximum wind speed observed.

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Answer:

$2,009

Step-by-step explanation:

Hope this helped! <3 If correct pls mark me as brainliest! Have a great day!

Answer:

If this question is so easy then why are you asking us do it yourself

Step-by-step explanation:

The number line that represents the solution set for the inequality 3(8 – 4x) < 6(x – 5) will be D. A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the right.

It should be noted that a number line is used to illustrate the intervals between the numbers given.

Therefore, the number line that represents the solution set for the inequality 3(8 – 4x) < 6(x – 5) will be a number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the right

In conclusion, the correct option is D.

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To calculate the total distance traveled, we need to multiply the player's run time by the speed. Since speed is defined as distance divided by time, we can rearrange the formula to solve for distance.

Given that the player's run time is 41 seconds and the value of X is 69 yards, we can calculate the total distance traveled using the formula:

Distance = Speed × Time

Since the speed is constant, we can substitute the given value of X into the formula:

Distance = X × Time

Plugging in the values, we get:

Distance = 69 yards × 41 seconds

Calculating the product, we have:

Distance = 2829 yards

Therefore, the correct answer is:

d. 138.00 yd

Explanation: The total distance traveled by the player during the 41-second run is 2829 yards. This distance is obtained by multiplying the speed (given as X = 69 yards) by the time (41 seconds). The calculation is done by multiplying 69 yards by 41 seconds, resulting in 2829 yards. The correct answer choice is d. 138.00 yd, as this option represents the calculated total distance traveled. The other answer choices, a. 0.03 yd and c. 0.00 yd, are incorrect as they do not reflect the actual distance covered during the run. Answer choice b. 110.00 yd is also incorrect as it does not match the calculated result of 2829 yards.

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Answer:

\(\huge\boxed{c=17\ ft}\)

Step-by-step explanation:

Use the Pythagorean theorem:

\(leg^2+leg^2=hypotenuse^2\)

We have:

\(leg=15ft\\leg=8ft\\hypotenuse=c\)

Substitute:

\(c^2=15^2+8^2\\\\c^2=225+64\\\\c^2=289\to c=\sqrt{289}\to c=17(ft)\)

Answer:

√{26548×26548}=√26548²=±26548

Answer: 36 plums

Step-by-step explanation:

1+4+2 = 7

7 units

63 = 7 units

divide by 7 on both sides

9 = 1 unit

plums = 4 units

4*9 = 36

36 plums

The distance from the center of dilation, Q, to the image of vertex A will be 4 units.

According to the given rule of dilation, D subscript Q, two-thirds, the triangle ABC will be dilated with a scale factor of two-thirds centered at point Q.

Since point Q is the center of dilation and the distance from triangle ABC to point Q is 6 units, the image of vertex A will be 2/3 times the distance from A to Q. Therefore, the distance from A' (image of A) to Q will be (2/3) x 6 = 4 units.

By applying the scale factor to the distances, we can determine that the length of A'B' is (2/3) x  3 = 2 units, the length of B'C' is (2/3) x 7 = 14/3 units, and the length of A'C' is (2/3) x 8 = 16/3 units.

Thus, the distance from the center of dilation, Q, to the image of vertex A is 4 units.

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Using division operation, since the family buys a pool pass every two months, Renaldo's family buys a pool pass 6 times a year.

There are 12 months in a year.

The family buys the pool pass every two months.

Using division operation, which involves the dividend (12), the divisor (2), and the quotient (6), we can determine the number of times that Renaldo's family buys a pool pass for the park district swimming pools.

12 months ÷ 2 = 6 times.

Thus, based on division operation, we can conclude that the family purchases the pool pass 6 times every year.

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Answer:

6

Step-by-step explanation:

divide by 3 on both sides

The value of side length w is 13.75 .

Given right angled triangle,

Perpendicular = w

Hypotenuse = 17

Angle of triangle = 54°

So,

According to the trigonometric ratios,

tanФ = p/b

cosФ = b/h

sinФ = p/h

By using sinФ,

sinФ = p/h

sin 54° =  w/ 17

0.809 = w/17

w = 13.75 .

Thus after correction w will be 13.75

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Answer:

I.D.K! Sorry!

Step-by-step explanation:

Sorry! I Wish I New This! :)

The shape with a series of parallel cross sections that are congruent circles is a cylinder.

The cross-section that results from cutting a cylinder parallel to its base is a circle that is congruent to all other parallel cross-sections. This is true for any plane that is perpendicular to the cylinder's base. The only shape that has parallel cross-sections that are congruent circles is a cylinder, for this reason.

Two parallel, congruent circular bases that lay on the same plane make up the three-dimensional shape of a cylinder. A curved rectangle connecting the bases makes up the cylinder's lateral surface. Congruent circles are produced when a cylinder is cut in half parallel to its base.

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Why I would like to attend this Oxbridge program is simple, really however let me answer other things first. I enjoy the Workshop and stained glass classes I have been exposed too. My GPA is 3.7 in my current school. But it has been going through my family and I want to make them proud, It is something I have been interested in and enjoyed learning about. However your program is the perfect to extend my knowledge and help me expand my horizons. In my future I see myself doing this. This school hands down has one of the best programs out their.

I see that this is a competative program and that you expect the best, and I am the best. I play hard but work way harder.

The most insignificant variable to remove would be the average annual temperature.

a) At a level of significance of 0.05, the result of the F test for this model is that the null hypothesis is rejected.

This is because the Probability value associated with the F statistic (16.47955524) is less than 0.001, which is smaller than the level of significance (0.05).
b) Suppose you are going to construct a new model by removing the most insignificant variable.

We would first remove:
average annual temp.
This is because it has the highest probability value (0.5529336) among all the variables, which indicates the weakest relationship with the number of motor vehicle accidents in a city per year.

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Answer:

189

Step-by-step explanation:

You can replace the values of x with 9 and the values of y with (-3).

7(2x-3y) = 7(2 × 9 - 3 × -3)

             = 7(18 - -9)

             = 7(18+9)

             = 7 × 27

             = 189

Answer:(17/5)x−14

Step-by-step explanation:

2/5x−2+3(x−4)

2/5x−2+3x−12   [Remove the parentheses]

2/5x+3x−14         [Combine terms]

2/5x+15/5x−14    [Change 3x to (15/5)x]

(17/5)x−14               [Add (2/5)x + (15/3)x]

or (3 3/5)x - 14

Answer:

1,-5

3,1

0,0

-2,-3

Step-by-step explanation

im not sure any of this is correct but i tried my hardest

The probability that an arriving student will find at least one other student waiting in line is approximately 0.167.

To solve this problem, we'll use the M/M/1 queueing model with Poisson arrivals and exponential service times. Let's calculate the required values: (a) Percentage of time Judy is idle: The utilization of the system (ρ) is the ratio of the average service time to the average interarrival time. In this case, the average service time is 10 minutes, and the average interarrival time is 12 minutes. Utilization (ρ) = Average service time / Average interarrival time = 10 / 12 = 5/6 ≈ 0.8333

The percentage of time Judy is idle is given by (1 - ρ) multiplied by 100: Idle percentage = (1 - 0.8333) * 100 ≈ 16.67%. Therefore, Judy is idle approximately 16.67% of the time. (b) Average waiting time for a student:

The average waiting time in a queue (Wq) can be calculated using Little's Law: Wq = Lq / λ, where Lq is the average number of customers in the queue and λ is the arrival rate. In this case, λ (arrival rate) = 1 customer per 12 minutes, and Lq can be calculated using the queuing formula: Lq = ρ^2 / (1 - ρ). Plugging in the values: Lq = (5/6)^2 / (1 - 5/6) = 25/6 ≈ 4.17 customers Wq = Lq / λ = 4.17 / (1/12) = 50 minutes. Therefore, on average, a student spends approximately 50 minutes waiting in line.

(c) Average length of the line: The average number of customers in the system (L) can be calculated using Little's Law: L = λ * W, where W is the average time a customer spends in the system. In this case, λ (arrival rate) = 1 customer per 12 minutes, and W can be calculated as W = Wq + 1/μ, where μ is the service rate (1/10 customers per minute). Plugging in the values: W = 50 + 1/ (1/10) = 50 + 10 = 60 minutes. L = λ * W = (1/12) * 60 = 5 customers. Therefore, on average, the line consists of approximately 5 customers.

(d) Probability of finding at least one student waiting in line: The probability that an arriving student finds at least one other student waiting in line is equal to the probability that the system is not empty. The probability that the system is not empty (P0) can be calculated using the formula: P0 = 1 - ρ, where ρ is the utilization. Plugging in the values:

P0 = 1 - 0.8333 ≈ 0.1667. Therefore, the probability that an arriving student will find at least one other student waiting in line is approximately 0.167.

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Answer: 75

Step-by-step explanation: 7.20+7.80=15 then 15+60=75

The slope is -40, and the Y intercept is 83. The equation would be Y= -40x + 83.

1. Confidence interval =  172.16  - 187.84

2. Confidence interval = 0. 876 - 0.924

The formula for determining confidence interval is expressed as;

1. Confidence Interval = sample mean ± (Z × (population standard deviation / √sample size))

Substitute the values, we have;

Confidence Interval = 180 ± (1.96 × (48 / √144))

Find the square root and divide the values, we have;

Confidence Interval = 180 ± (1.96 × 4)

Then, we get;

Lower = 180 - (7.84) = 172.16

Upper bound = 180 + (7.84) = 187.84

2. Confidence interval = 0.9 ± 1.96 × √((0.9(1-0.9))/400)

Confidence interval = 0.9 ± 1.96 × √((0.09)/400)

Divide the values and find the square root

Confidence interval = (0.9 - 0.024) - ( 0.9 + 0. 024)

Confidence interval = 0. 876 - 0.924

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T he joint moment generating function of x and y is M(t1, t2) = (1/36)Σx=1^6Σz=1^6 e^(t1x + t2z)

Let X be the value of the first die, which takes on values {1, 2, 3, 4, 5, 6} with equal probability of 1/6 each. Let Y be the sum of the values of two dice, so Y takes on values {2, 3, ..., 12}.

The joint moment generating function of X and Y is given by:

M(t1, t2) = E[e^(t1X + t2Y)]

To compute this, we can use the law of total probability and conditioning on the value of X:

M(t1, t2) = E[e^(t1X + t2Y)]

= Σx P(X=x) E[e^(t1X + t2Y) | X=x]

= (1/6)Σx=1^6 E[e^(t1x + t2Y) | X=x]

Now we need to compute E[e^(t1x + t2Y) | X=x]. We can use the fact that the sum of two dice is the sum of two independent uniform random variables on {1, 2, 3, 4, 5, 6}:

E[e^(t1x + t2Y) | X=x] = E[e^(t1x + t2(x+Z))]

= E[e^(tx) e^(t2Z)]

= MZ(t2) e^(tx)

where Z is a uniform random variable on {1, 2, 3, 4, 5, 6} and MZ(t2) is its moment generating function, which is:

MZ(t2) = E[e^(t2Z)]

= (1/6)Σz=1^6 e^(t2z)

Substituting this back into the expression for M(t1, t2), we get:

M(t1, t2) = (1/6)Σx=1^6 E[e^(t1x + t2Y) | X=x]

= (1/6)Σx=1^6 MZ(t2) e^(tx)

= (1/6)Σx=1^6 [(1/6)Σz=1^6 e^(t2z)] e^(tx)

Simplifying the expression, we get:

M(t1, t2) = (1/36)Σx=1^6Σz=1^6 e^(t1x + t2z)

This is the joint moment generating function of X and Y.

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The factors of the equation are 4 and -1.

Given

Equation; \(\rm x^2+3x-4\)

The polynomial which has the highest degree is 2 is called the quadratic equation.

The standard form of the quadratic equation is;

\(\rm ax^2+bx+c=0\)

The factors of the given equation are;

\(\rm x^2+3x-4=0\\\\x^2-4x+x-4=0\\\\x(x-4)+1(x-4)=0\\\\ (x-4)(x+1)=0\\\\x-4=0, \ \ x=4\\\\x+1=0, \ \ x=-1\)

Hence, the factors of the equation are 4 and -1.

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Answer:

c

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

\(48 = 2 \times 2 \times 2 \times 2 \times 3 \\ \\ 30 = 2 \times 3 \times 5 \\ \\ common \: factors = 2, \: 3 \\ \\ \therefore \: GCF \: of \: 48 \: and \: 30 \: \\ = 2 \times 3 \\ = 6\)

Answer:

Step-by-step explanation:

An x- intercept would be -6 and a y-intercept would be -6 also.