what is the range of the function on the graph? i’m

well, Mai is 21 today and when she's 25 is 4 years from now, so

\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$2000\\ r=rate\to 10\%\to \frac{10}{100}\dotfill &0.10\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &4 \end{cases} \\\\\\ A=2000\left(1+\frac{0.10}{1}\right)^{1\cdot 4}\implies A=2000(1.1)^4\implies A=2928.2\)

The number of lineups that are possible, considering only the labels S and F given that three students (S) and six faculty members (F) are on a panel discussing a new college policy is 1680.

What is permutation?

A permutation is an arrangement of items in a particular order. A permutation is an arrangement of a set of n elements in a specific order, such that the arrangement is different from the original order, and it involves all n elements.

Formula for permutation, which is:nPr = n! / (n-r)!Where n is the total number of items, and r is the number of items being chosen.

The number of lineups with three students and six faculty members is:nP9 = 9! / (9-9)!

nP9 = 9! / 0!

nP9 = 9!

nP9 = 362880

The above calculation implies that we can arrange nine people in 362880 ways if we consider the labels S and F. But in our case, only three of them are students, and the other six are faculty members. Thus, we need to exclude arrangements where the faculty members and students have been permuted within their groups.

To eliminate the effect of the arrangement within the groups, we need to divide the total number of arrangements by the number of arrangements of students and faculty members. We can arrange the students in 3! Ways, and the faculty members can be arranged in 6! ways. Thus, the number of lineups that are possible considering only the labels S and F is:9! / 3!6! = 1680

Therefore, the number of lineups that are possible, considering only the labels S and F given that three students (S) and six faculty members (F) are on a panel discussing a new college policy is 1680.

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The labels S and F is 362880.

The problem can be solved by using permutation because order is important. Permutation is a mathematical technique used for counting purposes and describes the number of possible arrangements of a set of objects (usually distinct) in a certain order.Let's count the number of ways to arrange the three students (S) and six faculty members (F) in a single row. We can use the permutation formula to count the number of possible lineups of S and F.                                      

The formula to find the number of permutations of n objects is n! (n factorial), which is the product of all positive integers less than or equal to n. We can use this formula to find the number of permutations of 3 students and 6 faculty members:9! = 362880.Therefore, the number of lineups possible, considering only the labels S and F is 362880.

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By applying algebra, it can be concluded that the number of candies remaining in the bag can be written as c = 150 - 8s, where s is the number of snacking.

Algebra is a branch of mathematics that uses symbols and mathematical operations, such as addition, subtraction, multiplication, and division to solve problems

Now we apply algebra to solve the problem:

Tyrone takes 8 pieces of candy each time snacking

After snacking 18 times, 6 pieces of candy remained in the bag

So the totals candies eaten = 8 * 18

                                              = 144 candies

Number of candies in the bag = candies eaten + remaining candies

                                                  = 144 + 6

                                                  = 150 candies

If s denotes the number of snacking, then the total number of candies eaten on s snacking = 8s

if c denotes the number of remaining candies, then:

c = total candies - candies eaten

c = 150 - 8s

Thus the number of candies remaining in the bag can be written as c = 150 - 8s, where s is the number of snacking.

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Answer:

Step-by-step explanation:

This student performed better than 68% of the other test-takers in the verbal part and better than 27% in the quantitative part.

Given,

Test-taker scored at the 68th percentile for their verbal grade and at the 27th percentile for their quantitative grade .

Now,

68% percentile : 68% scores equal or less .

27% percentile : 27^ scored equal or less .

Thus option D

This student performed better than 68% of other test taker in verbal and better than 27% in quantitative part .

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To show that the location parameter of the minimum extreme value distribution is the mode of the distribution, we set the first derivative of the density function, f(t), equal to zero and solve for t. The resulting value of t is the mode of the distribution.

The minimum extreme value distribution is characterized by its density function, which is given by:

f(t) = (1/β) * exp((t-α)/β) * exp(-exp((t-α)/β))

where α is the location parameter and β is the scale parameter. The mode of a distribution represents the value at which the density function has the highest point.

To find the mode of the minimum extreme value distribution, we differentiate the density function with respect to t and set it equal to zero:

d/dt [f(t)] = (1/β) * exp((t-α)/β) * exp(-exp((t-α)/β)) * (1/β) * (1/β) * exp((t-α)/β)

Setting the above expression equal to zero, we can simplify it to:

exp((t-α)/β) * exp(-exp((t-α)/β)) = (1/β)^2

By taking the logarithm of both sides, we have:

(t-α)/β - exp((t-α)/β) = -2 * log(β)

This equation does not have a closed-form solution. Therefore, to find the mode, we typically use numerical methods such as iterative algorithms or optimization techniques.

In conclusion, the mode of the minimum extreme value distribution can be obtained by setting the first derivative of the density function equal to zero and solving the resulting equation. However, due to the lack of a closed-form solution, numerical methods are generally used to find the mode.

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To show divergence we should show that the sequence fulfills the nullification of the meaning of convergence. A sequence of genuine numbers joins to a genuine number an if, for each certain number ϵ, there exists an N ∈ N to such an extent that for all n ≥ N, |an - a| < ϵ.

Assuming we say that a sequence joins, it implies that the constraint of the sequence exists as n→∞. Assuming the restriction of the sequence is n→∞ doesn't exist, we say that the sequence separates.

A sequence in every case either unites or veers, there could be no other choice. This doesn't mean we'll continuously have the option to tell whether the sequence combines or separates, in some cases, it tends to be undeniably challenging for us to decide convergence or divergence.

There are numerous ways of testing a sequence to see whether it unites.

Once in a while we should simply assess the constraint of the sequence at

n→∞. On the off chance that the breaking point exists, the sequence unites, and the response we found is the value of the cutoff.

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Answer:

The first equals 7/10 while the other equals 6/10

Step-by-step explanation:

That's the answer

.

.

.

.

The probability that a bridge hand will have exactly 2 queens is 0.45%.

To find the probability of getting a bridge hand with exactly 2 queens, we need to use the binomial probability formula. The formula is:

P(exactly k successes) = (n choose k) * p^k * (1-p)^(n-k)

Where:

n is the total number of trials

k is the number of successes in the trials

p is the probability of success in a single trial

In this case, the total number of trials is 13 (since a bridge hand consists of 13 cards), and the number of successes we want is 2 (since we want exactly 2 queens). The probability of success in a single trial is the probability of drawing a queen, which is 4/52 (since there are 4 queens in a deck of 52 cards).

Plugging these values into the formula, we get:

P(exactly 2 queens) = (13 choose 2) * (4/52)² * (48/52)¹¹

= (78) * (1/169) * (4/13)¹¹

= (4/169) * (4/13)¹¹

This simplifies to:

P(exactly 2 queens) = (4/169) * (4/13)¹¹

= (4/169) * (4/169)¹¹

= (4/169)¹²

The final probability is approximately 0.0045 or 0.45%. This means that the probability of getting a bridge hand with exactly 2 queens is quite low.

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To compute the integral ∫ fdx over the disk D of radius R centered at (0,0), we need to express the function f in terms of the given coordinate transformation.

In polar coordinates, a point (r, θ) in the disk D can be represented as (r cos(θ), r sin(θ)).

Now, let's substitute these polar coordinates into the integral. The differential element dx becomes r cos(θ)dr, and the integral becomes:

∫ fdx = ∫ f(r cos(θ), r sin(θ)) r cos(θ)dr dθ

We can now evaluate this integral by integrating over the range of r and θ. The range for r is from 0 to R, and the range for θ is from 0 to 2π (since we are integrating over the entire disk).

Thus, the integral becomes:

∫ fdx = ∫[0 to R] ∫[0 to 2π] f(r cos(θ), r sin(θ)) r cos(θ)dr dθ

By evaluating this double integral, we can find the value of ∫ fdx over the given disk D.

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Answer:

Step-by-step explanation:

I need the diagram

Answer:

Radius is half of diameter; the distance around a circle.

Step-by-step explanation:

Answer:

Radius is half of diameter  the distance around a circle

Brandon's total net yardage for the game is 51 yards.

To calculate Brandon's total net yardage for the game, we need to consider the yardage gained and lost on each carry.

First, let's calculate the net yardage for the first 5 carries:

Net yardage = 6 yards + 12 yards + 4 yards - 2 yards - 7 yards

= 13 yards

Next, let's calculate the net yardage for the last 3 carries:

Net yardage = 38 yards

To find the total net yardage for the game, we sum up the net yardage from the first 5 carries and the net yardage from the last 3 carries:

Total net yardage = Net yardage from first 5 carries + Net yardage from last 3 carries

= 13 yards + 38 yards

= 51 yards

Therefore, Brandon's total net yardage for the game is 51 yards.

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Answer:

A

Step-by-step explanation:

I think its a because of the way it is stated and rate it is melting at

Hello there!

-8 and -12 are constants

A constant is any real number.

Hope this helps!

~Just a determined gal

#CarryOnLearning

\(MysteriousNature\)

a. 44.4% of the time each service desk is idle.

b. The probability that both service clerks are busy is 0.22 or 22%.

c. The probability that both service clerks are idle is 11.1%.

d. On average, 0.67 customers are waiting in line in front of each service desk.

e. A customer takes, on average, 5.33 minutes to get serviced from the moment they join the queue (i.e., waiting plus service time).

a) The arrival rate is 1 customer every 6 minutes. Therefore, 10 customers arrive at each service desk every hour. The service rate is 1 customer every 4 minutes, which means that a service desk can handle 15 customers every hour.

The utilization rate of each service desk = arrival rate/service rate = (10/60) ÷ (15/60) = 2/3 Average number of customers in the system at any time (queue + service) = utilization/(1 - utilization) = (2/3)/(1 - 2/3) = 2

Therefore, the average number of customers in the queue is the average number of customers in the system minus the average number of customers in service:Average number of customers in the queue = 2 - 2 = 0

Therefore, each service desk is idle for 60% - 15.6% = 44.4% of the time.

b) The probability of a service desk being busy is equal to its utilization rate = 2/3.

Therefore, the probability of both service clerks being busy is:P(both busy) = (2/3)² = 4/9 = 0.44

c) The probability of a service desk being idle is equal to 1 - utilization rate = 1 - 2/3 = 1/3.

Therefore, the probability of both service clerks being idle is:P(both idle) = (1/3)² = 1/9 = 0.11 or 11%.

d) We can use Little's Law to calculate the average number of customers in the queue:

Average number of customers in the queue = arrival rate x average waiting time in queue Average waiting time in queue = average number of customers in queue / arrival rate = 0 / (10/60) = 0 Average number of customers in the queue = 0 Therefore, on average, 0.67 customers are waiting in line in front of each service desk.

e) The average time a customer spends in the system (waiting + service) is equal to the average number of customers in the system divided by the arrival rate:

Average time in system = average number of customers in system / arrival rate Average number of customers in system = utilization/(1 - utilization) = (2/3)/(1 - 2/3) = 2 Average time in system = 2 / (10/60) = 12/10 = 1.2 minutes = 72 seconds The service time is 4 minutes. Therefore, the average waiting time is:

Average waiting time = average time in system - service time = 1.2 - 4 = -2.8 minutes We can't have negative waiting time, so the actual waiting time is 0.

Therefore, a customer takes, on average, 5.33 minutes (4 minutes of service + 1.33 minutes of waiting) to get serviced from the moment they join the queue.

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Answer:

1. 24/40, 32/40, 24/32 (This is in order from top to bottom)

2. 21.1

3. 4.1

Step-by-step explanation:

1. Here, we only have to focus on Angle X.

Let's label in the sides:

Opposite = YZ = 24

Adjacent = XY = 32

Hypotenuse = XZ = 40

SOHCAHTOA simply means:  You can memorise this through the acrostic poem of - Slap On Head Causes A Headache Take One Aspirin, but I remember it by Suck A Toe because that's what it sounds like.

Sin(x) = Opposite/Hypotenuse

Cos(x) = Adjacent/Hypotenuse

Tan(x) = Opposite/Adjacent

Sin(X) = 24/40

Cos(X) = 32/40

Tan(X) = 24/32

The question only asks to give the ratios by using / for a fraction, so we don't simplify it.

2. We are given the angle of 64°, the opposite length 19 and we have to work out x, which is the hypotenuse. We can use the sin function as we have our opposite length and we have to work out the hypotenuse.

Sin(64) = 19/x

xSin(64) = 19

x = 19/Sin(64)

x = 21.13943687

x = 21.1

3. We are given the angle of 70°, the hypotenuse 12 and we have to work out x, which is the adjacent side. We can use the cos function as we have to work out the adjacent side and we have our hypotenuse given to us.

Cos(70) = x/12

12Cos(70) = x  All we have to do here is multiply by 12!

x = 4.10424172

x = 4.1

For the angle of elevation to the top of a building is 5 degrees from the ground, the height of building is equals to 0.1 miles.

A buliding in New York. The angle of elevation to the top of a building from ground = 5°

Distance from ground point to base of building = 1 mile

We have to determine the height of the building. Now, if we consider all scenario geometrically, then we see the right angled triangle present in above figure. The height of buliding = h

Using the Trigonometric Ratio \( tan(\theta) = \frac{height}{base} \)

Substitute all known values in above formula, \(tan(5°) = \frac{h}{1 \: miles} \)

From the trigonometric table, tan(5°) = 0.087

=> h = 1 × 0.087 miles

=> h = 0.087 miles ~ 0.1 miles

Hence, required height value is 0.1 miles

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The first tank hold 1088 - 5t gallons of water after t weeks, while the seocnd tank holds 1360 - 9t gallons after t weeks.

Both tanks hold the same amount of water when

1088 - 5t = 1360 - 9t

Solve for t :

4t = 272

t = 68

So the tanks will hold the same amount of water after 68 weeks.

Answer:

100feet

Step-by-step explanation:

-16(2)^2+72(2)+20

-16*4+144+20

-64+144+20

100feet

Answer:

The complete statement is \((R_{y-axis} \circ R_{y=x}) (2, 3) = (-3, 2)\)

Step-by-step explanation:

Given that we have a composition transformation where the operation R stands for reflection, we are to start from the right operation then we work on the left as follows

\((R_{y-axis} \circ R_{y=x}) (2, 3)\)

The reflection of a point (x, y) cross the line y = x is (y, x)

Therefore, when (2, 3) is reflected across the line y = x it becomes (3, 2)

The next operation, which is the reflection across the line y = x is then found as follows;

The reflection of a point (x, y) cross the y-axis is (-x, y)

Therefore, when (3, 2) is reflected across the y-axis it becomes (-3, 2)

Therefore, the complete statement is \((R_{y-axis} \circ R_{y=x}) (2, 3) = (-3, 2)\)

Answer:

-3,2

Step-by-step explanation:

Answer: y=mx+c

m is the gradient, and c is the y-intercept.

lmk if u want me to try to solve it::} (try)

Step-by-step explanation:

Answer:

i remember doing this but i forgot the answers

Step-by-step explanation:

sorry :(

Answer:

0,0 means the origin so put place it on the origin.

Answer:

15.5 ft

Step-by-step explanation:

C=2×pi×r

48.67=2×3.14×r

48.67÷(2×3.14)=r

r= 7.75 ft

diameter = 2× radius

diameter = 2× 7.75

d= 15.5

Hope this helps!

Answer:

4(9a - 4)

Step-by-step explanation:

Answer:

4(9a - 4)

Step-by-step explanation:

Given

36a - 16 ← factor out 4 from each term

= 4(9a - 4)

To find the maximum and minimum values of the given function f(θ), we need to find its critical points and endpoints.

First, we take the derivative of f(θ) with respect to θ:

f'(θ) = -2 sin(θ) - 2 cos(θ) sin(θ)

Setting f'(θ) = 0, we get:

-2 sin(θ) - 2 cos(θ) sin(θ) = 0

Simplifying and factoring out -2 sin(θ), we get:

-2 sin(θ) (1 + cos(θ)) = 0

This gives us two critical points: θ = 0 and θ = π.

Next, we need to evaluate the function at the endpoints of the given interval [0, 2π]:

f(0) = 2 cos(0) + cos2(0) = 3

f(2π) = 2 cos(2π) + cos2(2π) = 3

Now we compare the values of f(θ) at the critical points and endpoints to find the maximum and minimum values:

f(0) = 3 (endpoint)

f(π) = 1 (critical point)

f(2π) = 3 (endpoint)

Therefore, the maximum value of f(θ) is 3 and the minimum value is 1.

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To show that the matrix A = [XX - X'Z(ZZ)^(-1)Z'X] is positive definite, we need to demonstrate two properties: (1) A is symmetric, and (2) all eigenvalues of A are positive.

Symmetry: To show that A is symmetric, we need to prove that A' = A, where A' represents the transpose of A. Taking the transpose of A: A' = [XX - X'Z(ZZ)^(-1)Z'X]'. Using the properties of matrix transpose, we have:

A' = (XX)' - [X'Z(ZZ)^(-1)Z'X]'. The transpose of a sum of matrices is equal to the sum of their transposes, and the transpose of a product of matrices is equal to the product of their transposes in reverse order. Applying these properties, we get: A' = X'X - (X'Z(ZZ)^(-1)Z'X)'.  The transpose of a transpose is equal to the original matrix, so: A' = X'X - X'Z(ZZ)^(-1)Z'X. Comparing this with the original matrix A, we can see that A' = A, which confirms that A is symmetric.  Positive eigenvalues: To show that all eigenvalues of A are positive, we need to demonstrate that for any non-zero vector v, v'Av > 0, where v' represents the transpose of v. Considering the expression v'Av: v'Av = v'[XX - X'Z(ZZ)^(-1)Z'X]v

Expanding the expression using matrix multiplication : v'Av = v'X'Xv - v'X'Z(ZZ)^(-1)Z'Xv. Since X and Z have full column rank, X'X and ZZ' are positive definite matrices. Additionally, (ZZ)^(-1) is also positive definite. Thus, we can conclude that the second term in the expression, v'X'Z(ZZ)^(-1)Z'Xv, is positive definite.Therefore, v'Av = v'X'Xv - v'X'Z(ZZ)^(-1)Z'Xv > 0 for any non-zero vector v. Implications in econometrics: In econometrics, positive definiteness of a matrix has important implications. In particular, the positive definiteness of the matrix [XX - X'Z(ZZ)^(-1)Z'X] guarantees that it is invertible and plays a crucial role in statistical inference.

When conducting econometric analysis, this positive definiteness implies that the estimator associated with X and Z is consistent, efficient, and unbiased. It ensures that the estimated coefficients and their standard errors are well-defined and meaningful in econometric models. Furthermore, positive definiteness of the matrix helps in verifying the assumptions of econometric models, such as the assumption of non-multicollinearity among the regressors. It also ensures that the estimators are stable and robust to perturbations in the data. Overall, the positive definiteness of the matrix [XX - X'Z(ZZ)^(-1)Z'X] provides theoretical and practical foundations for reliable and valid statistical inference in econometrics.

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Using a system of equations, Phyllis invested the following at each rate:

A system of equations is two or more equations solved concurrently, simultaneously, or at the same time.

The total investment = $8,000

Investment A's simple interest rate per year = 4% = 0.04 (4/100)

Investment B's simple interest rate per year = 1% = 0.01 (1/100)

The total earnings after one year from Investments A and B = $95.00

Let the amount invested in Investment A = x

Let the amount invested in Investment B = y

x + y = 8,000 Equation 1

0.04x + 0.01y = 95 Equation 2

Multiply Equation 1 by 0.04:

0.04x + 0.04y = 320 Equation 3

Subtract Equation 2 from Equation 3:

0.04x + 0.04y = 320

-

0.04x + 0.01y = 95

0.03y = 225

y = 7,500

x = 500 (x = 8,000 - 7,500)

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Answer:

parallelogram

Step-by-step explanation:

Its a parallelogram.

Answer

parallelogram

Step-by-step explanation: