Given the vertex (2, -1 )and the point(0,7), write the vertex form equation of the
quadratic function
Pls help!!!

The partial sum of the given sequence, 1 + 10 + 19 + ... + 199, can be found by identifying the pattern and using the formula for the sum of an arithmetic series.  Hence, the partial sum of the sequence 1 + 10 + 19 + ... + 199 equals 4497.

To find the partial sum of the given sequence, we can observe the pattern in the terms. Each term is obtained by adding 9 to the previous term. This indicates that the common difference between consecutive terms is 9.

The formula for the sum of an arithmetic series is Sₙ = (n/2)(a + l), where Sₙ is the sum of the first n terms, a is the first term, and l is the last term.

In this case, the first term a is 1, and we need to find the value of l. Since each term is obtained by adding 9 to the previous term, we can determine l by solving the equation 1 + (n-1) * 9 = 199.

By solving this equation, we find that n = 23, and the last term l = 199.

Substituting the values into the formula for the partial sum, we have:

S₂₃ = (23/2)(1 + 199),

= 23 * 200,

= 4600.

However, this sum includes the terms beyond 199. Since we are interested in the partial sum up to 199, we need to subtract the excess terms.

The excess terms can be calculated by finding the sum of the terms beyond 199, which is (23/2)(9) = 103.5.

Therefore, the partial sum of the given sequence is 4600 - 103.5 = 4496.5, or approximately 4497 when rounded.

Hence, the partial sum of the sequence 1 + 10 + 19 + ... + 199 equals 4497.

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A. The arrival rate per hour must increase to at least 10 customers per hour to justify a second telephone boothe.

B. The arrival rate per hour must increase by at least 1.6 customers per hour to justify a second telephone booth under the new criterion.

To get the how much arrival rate must increase, we must get the expected waiting time for a customer.

Assuming;

X is the number of customers who arrive per hour

Y is the length of a phone call in minutes.

Then, X follows a Poisson distribution with λ = 4 (since 4 customers per hour use the phone on average)

Y follows a negative exponential distribution with mean μ = 5 (since the mean length of a phone call is 5 minutes).

Total time is given as sum of waiting time and length of call;

T = W + Y

The waiting time W is the difference between the time a customer arrives and the time that the phone becomes available. waiting time follows a uniform distribution where mean= 1/λ (since the arrivals follow a Poisson process);

Then we have;

E(W) = 1/(2λ) = 1/8 hours

The expected total time T that a customer spends at the phone booth is:

E(T) = E(W) + E(Y) = 1/8 + 5/60 = 11/48 hours

For a second telephone booth to be justifiable, new customer that arrives must wait 3 minutes or longer for the phone.

E(W) ≥ 1/20

To get λ,

1/(2λ) ≥ 1/20

λ ≤ 10

This means that, the arrival rate per hour must increase to at least 10 customers per hour to justify a second telephone booth.

b. Getting how much the arrival rate per hour must increase to justify a second telephone booth under the new criterion,

we need to find the probability that a customer has to wait at all.

Let P(W > 0) be the probability that a customer has to wait.

P(W > 0) = 1 - P(W = 0)

The waiting time W follows a uniform distribution with mean 1/λ, so we have:

P(W = 0) = 1 - λ/4

The length of a phone call Y follows a negative exponential distribution with mean 5 minutes = 1/12 hours, so we have:

P(Y > t) = e^(-μt) = e^(-t/12)

The probability that a customer has to wait is given as;

P(W > 0) = 1 - P(W = 0) = λ/4

To justify a second telephone booth, the probability of having to wait at all must exceed 0.6. so we have;

P(W > 0) > 0.6

λ > 2.4

The arrival rate per hour must increase by at least 2.4 - 4 = 1.6 customers per hour to justify a second telephone booth under the new criterion.

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Answer:

Step-by-step explanation:

we have to know what the numbers are

Answer:

27

Step-by-step explanation:

0.45 divide by 60 and you get 27

Answer:

27

Step-by-step explanation:

x/60 = 45/100

if you write it out, cross multiply then solve for x

Answer:

The expression 3r - 6 can be written as 3(r - 2)

Step-by-step explanation:

We know that 3r-6=3(r-2) because 3*r is the same as 3r and we know that 3*-2 is -6 hence making them equal. And to check it we know that 3r-6 is equal to 3r-6.

Answer:2 beacuse if u divide 4 by 2 and 6 by 2 u get 2/3

Step-by-step explanation:

Answer: nearest tenth is 49.0

Step-by-step explanation:

Hope this helps!

Answer:

8 The victim wasn't mauled by a cougar - Clue 1

20 Dr. Alpha was in the kitchen cooking - Clue 2

-12 The victim had no venomous bites - Clue 3

72 Miss Beta was at the movie theater - Clue 4

14 The victim wasn't electrocuted - Clue 5

14 Coach Omega was sleeping at the atrium - Clue 6

-8 The murder did not include a firearm - Clue 7

-12 Mrs.Gamma was doing yoga at the gym - Clue 8

169 The murder wasn't drowning - Clue 9

-274 Mr.Epsilon was swimming laps at a pool - Clue 10

is what i know, i will figure out in a bit! :D

Step-by-step explanation:

The solution to the system of linear equations y=x-1 and 2x-3y=-1 is (4, 3)

Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient

A system of linear equations is a collection of at least two linear equations.

In this case, the system of equations is given as

y=x-1 and 2x-3y=-1

Rewrite the system of equations as

y = x - 1

2x - 3y = -1

Next, we plot the graph of the equations

From the graph of the equations, we have the point of intersection to be

(x, y) = (4, 3)

This point represents the solution

Hence, the solution to the system of linear equations y=x-1 and 2x-3y=-1 is (4, 3)

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Answer:

4 = 151.70

5a=75.85

Step-by-step explanation:

Answer:

There are 72 candles in each box

Step-by-step explanation:

Key skills needed for this problem: Division

1) The problem says there are 1728 candles in 24 boxes. We need to find the number of candles in one box.

2) To solve this equation, we need to divide 1728 by 24. 1728 divided by 24 is 72.

This means there are 72 candles in each box.

Hope you understood and have a nice day!! :D

Answer:

three of them contain exactly two presidents, thus the probability of flipping exactly three heads is 3/8.

Step-by-step explanation:

Answer: As for the inequality question you asked,

-2/3, -11/3, and 2.5 are decimal numbers.

-11/3 is smaller than -2/3 because -3.67 is smaller than -0.67

-2/3 is smaller than 2.5 because -0.67 is smaller than 2.5

So the inequality that correctly orders the numbers -2/3, -11/3, and 2.5 is -11/3 < -2/3 < 2.5

It's worth noting that this inequality uses the less than (<) symbol to show the order of the numbers from the smallest to the largest, and it's also worth to remember that this inequality is true only for these specific values, if any of the values were changed it would've resulted in a different inequality.

Step-by-step explanation:

If M is the midpoint of CD, then the  is cos ABM = 8 / (235) sqrt

The Platonic solid known as the regular tetrahedron has four polyhedron vertices, six polyhedron edges, and four equal equilateral triangular faces. It is frequently referred to as "the" tetrahedron. Also included are the Wenninger model and uniform polyhedron.

1: According to a rule of trigonometry, the square of a side in a plane triangle is equal to the sum of the squares of the other sides minus twice that much of the product of those sides and the cosine of the angle between them.

To make things easier, set the tetrahedron's side equal to 1.

A  = ( -1/2 , 0 , 0)

B  = ( 1/2, 0, 0  )

C =  (0, sqrt (3)/2, 0)

D =  (0, sqrt (3)/4 , 6/sqrt (3) )

M =  (0 , (3/8) sqrt (3) , 3/sqrt (3) )  =  (0, (3/8)sqrt (3) , sqrt (3) )

AB  = 1

AM = BM   =  sqrt   [ (-1/2)^2  + (3sqrt (3) / 8)^2  + (sqrt 3)^2   =  sqrt [ 1/4 + 27/64 + 3 ]   = sqrt (235) / 8

By the Law of Cosines

AM^2  =  AB^2 + BM^2 - 2 (AB) (BM)cos (ABM)

0 = 1 - 2 (1) (235 squared / 8) cos ABM

0 = 1 - [sqrt ( 235) / 8] since ABM

cos ABM = -1 / - [ sqrt (235) / 8]

8 / (235) sqrt = cos ABM

If M is the midpoint of CD, then the  is cos ABM = 8 / (235) sqrt

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Angle 1 - 72 degrees

Angle 2 - 36 degrees

Angle 3 - 18 degrees

Angle 4 - 144 degrees

Hope this helped!

Answer:  

10

Step-by-step explanation:

6 x 10(x) = 60

60+12=72

hope this helps!

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Answer:

5x^2 + 4x - 7 = 0

<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3

Answer:

(-3)^5 = 1/x

x = 1 ÷ (-3)^5

x = 1/ -243

x = -1/243

Step-by-step explanation:

hi thaks

Answer:

72

Step-by-step explanation:

you multiply 36 *2 therefore giving you 72centimeters squared

Answer: D:144

Step-by-step explanation:

Answer:

if  youre factoring, there is no possible factors

if youre solving for x, it is

x =−1.5+0.87i

x =−1.5-0.87i

i believe

Step-by-step explanation:

quadratic equation

Answer:

48.0 m

Step-by-step explanation:

12.0*4 = 48.0m

There's some unknown (but derivable) system of equations being modeled by the two lines in the given graph. (But we don't care what equations make up these lines.)

There's no solution to this particular system because the two lines are parallel.

How do we know they're parallel? Parallel lines have the same slope, and we can easily calculate the slope of these lines.

The line on the left passes through the points (-1, 0) and (0, -2), so it has slope

(-2 - 0)/(0 - (-1)) = -2/1 = -2

The line on the right passes through (0, 2) and (1, 0), so its slope is

(0 - 2)/(1 - 0) = -2/1 = -2

The slopes are equal, so the lines are parallel.

Why does this mean there is no solution? Graphically, a solution to the system is represented by an intersection of the lines. Parallel lines never intersect, so there is no solution.

Answer:

2115

Explanation:

To evaluate the expression (60−6)×(13)3+27÷3 we use BODMAS

BODMAS is an acronym/rule in mathematics that dictates the order we should solve mathematical operations such as the above.

BODMAS stands for bracket first, order or of, division, multiplication, addition and then lastly subtraction

To solve the expression using BODMAS, we solve the brackets first

(60−6)×(13)3+27÷3 =54×39+27/3

Then division

=54×39+9

=2106+9

Then addition

=2106+9=2115

Answer=2115

Answer: 0.01090566037

Answer: The short answer to this is 0.0109

Answer:

? = 5

Step-by-step explanation:

You use cross-multiplying. Let's say ? is x.

First step:  \(\frac{30}{x}=\frac{48}{8}\)

Second step: You cross them so 30(8)= 280. 48(x)= 48x.

Third step: \(\frac{280}{48x}\)= 5

To double check this:

30/5= 6

48/8= 6

42/7= 6

I hope this helps.

I did this while struggling with my homework too lol.

Contribution margin is the excess of sales revenue over total variable costs. This means that all of the answer choices are correct.

Contribution margin is an important financial metric used in managerial accounting to assess the profitability of a company's products or services. It represents the amount of revenue available to cover fixed costs and contribute to the company's operating income. The contribution margin is calculated by subtracting the total variable costs from the sales revenue. Variable costs are expenses that vary directly with the level of production or sales, such as direct materials, direct labor, and variable overhead. Fixed costs, on the other hand, remain constant regardless of the level of production or sales. By analyzing the contribution margin, managers can make informed decisions regarding pricing strategies, product mix, and cost control measures. A higher contribution margin indicates that a greater portion of each sales dollar is available to cover fixed costs and generate profits. It is important for companies to maintain a healthy contribution margin to ensure their long-term financial viability.

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The compound interest formula is:

Where

P is principal

r is rate of interest

n is number of compounding

t is number of years

Putting the given information, we have:

Interest amount is:

15,439.60 - 13,500 = $1939.60 (in a year/12 months)

In 10 months:

Justin would owe $1616.33 after 10 months.

The population mean of the ba column is calculated using the equation μ = Σ(x) / N, while the population standard deviation is found using the equation σ = √[Σ((x-μ)^2) / N].

To find the population mean of the batting average (ba) column, we can use the following equation:

μ = Σ(x) / N

where:

- μ represents the population mean,

- Σ(x) denotes the sum of all values in the ba column, and

- N represents the total number of data points in the ba column.

The population mean of the ba column is μ = Σ(x) / N.

To calculate the population standard deviation of the batting average (ba) column, we can utilize the following equation:

σ = √[Σ((x-μ)^2) / N]

where:

- σ represents the population standard deviation,

- Σ((x-μ)^2) denotes the sum of the squared differences between each data point and the population mean (μ), and

- N represents the total number of data points in the ba column.

The population standard deviation of the ba column is σ = √[Σ((x-μ)^2) / N].

In summary, the population mean of the ba column is calculated using the equation μ = Σ(x) / N, while the population standard deviation is found using the equation σ = √[Σ((x-μ)^2) / N].

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Answer:

5.81$

Step-by-step explanation: