Maureen's job is to provide technical support to computer users. Suppose the arrival of calls can be modeled by a Poisson distribution with a mean of 5.4 calls per hour. What's the probability that in the next 20 minutes there will be 2 or more calls

Answer:

I = $360

Step-by-step explanation:

Calculate the interest I using

I = PRN

with P = 1500, R = 3% = \(\frac{3}{100}\) = 0.03 , N = 8 , then

I = $1500 × 0.03 × 8 = $360

This question is about to determine the conditional statement,  proposition and either that is true or false.

The explanation of each part in this question is given below:

a) The given proposition can be written as the conjunction of two conditional statements as follows:

If a = 2 (mod 8), then \((a^2 + 4a) = 4 (mod 8)\).

If \((a^2 + 4a) = 4 (mod 8)\), then a = 2 (mod 8).

b) To prove the first conditional statement, assume a = 2 (mod 8). Then, there exists an integer k such that a = 8k + 2. Substituting this value of a into \((a^2 + 4a)\), we get:

\(a^2 + 4a = (8k + 2)^2 + 4(8k + 2) = 64k^2 + 36k + 8\)

Reducing this expression modulo 8, we get:

a^2 + 4a ≡ 64k^2 + 36k + 8 ≡ 0 + 4k + 0 ≡ 4 (mod 8)

Therefore, we have shown that if a = 2 (mod 8), then (a^2 + 4a) = 4 (mod 8).

To prove the second conditional statement, assume (a^2 + 4a) = 4 (mod 8). Then, there exists an integer k such that (a^2 + 4a) = 8k + 4. Substituting this value of (a^2 + 4a) into the equation a^2 + 4a - 8k = 0, we can use the quadratic formula to solve for a:

a = (-4 ± √(16 + 32k))/2 = -2 ± √(4 + 8k)

Since a is an integer, it follows that √(4 + 8k) must be an integer as well. This implies that 4 + 8k is a perfect square. The only perfect squares that are congruent to 4 (mod 8) are those of the form 8m + 4 for some integer m. Therefore, we have:

4 + 8k = 8m + 4

k = m

Substituting k = m back into the expression for a, we get:

a = -2 + √(4 + 8k) = -2 + √(8m + 4) = -2 + 2√(2m + 1)

Since a is an integer, it follows that √(2m + 1) must be an integer as well. This implies that 2m + 1 is a perfect square. The only perfect squares that are congruent to 1 (mod 8) are those of the form 8n + 1 for some integer n. Therefore, we have:

2m + 1 = 8n + 1

m = 4n

Substituting m = 4n back into the expression for a, we get:

a = -2 + 2√(2m + 1) = -2 + 2√(8n + 1) = 2(√(2n + 1) - 1)

Therefore, we have shown that if (a^2 + 4a) = 4 (mod 8), then a = 2 (mod 8).

Since both conditional statements have been proven, the given proposition is true.

(c) The given proposition is true, as shown in the proofs of the two conditional statements in part (b).

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The vertex of the graphed function f(x) = [x - 4] + 3 is (4, 3).

The function f(x) = [x - 4] + 3 is in the form of an absolute value function, where the expression inside the absolute value brackets represents the input value shifted horizontally by 4 units to the right.

The constant term of 3 represents a vertical shift upwards by 3 units.

To find the vertex of this function, we need to determine the x-coordinate that corresponds to the minimum value of the absolute value function.

In this case, since the absolute value function is within brackets and not being multiplied or divided by a coefficient, the minimum value occurs at the point where the expression inside the brackets equals zero.

Therefore, setting x - 4 = 0, we find x = 4.

Substituting this x-value into the function, we find f(4) = [4 - 4] + 3 = 3. So the vertex of the graphed function is located at the point (4, 3), where x = 4 and y = 3. This means that the graph is shifted 4 units to the right and 3 units upward from the origin.

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If outcome O₁ has a frequency 4/a, outcome O₂ has a frequency 12/a, and outcome O₃ has frequency 3/a, then the value of a is 19

Frequency of outcome O₁ = 4/a

Frequency of outcome O₂ = 12/a

Frequency of outcome O₃ = 3/a

Let's say 1/a = x

Now, the Frequency of outcome O₁ = 4x

Frequency of outcome O₂ = 12x

Frequency of outcome O₃ = 3x

The sum of the respective frequencies must equal 1.

So, 4x + 12x + 3x = 1

                      19x = 1

x = 1/19

That means that the “a” in the problem is 19.

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Answer:

2pi(5) - 2pi(3)

Step-by-step explanation:

hopefully that helped. just use formula and plug in the radius (:

Answer:

28.26 cm ^2

Step-by-step explanation:

A= \(\pi\) r ^2

A= 3.14 x 3 x 3

A = 28.26 cm ^2

The Vales of x in the equations are : 1) 3 (2) 1  (3) 5  (4) 14  (5) 10 respectively

A linear equation in one variable is that in which the highest power of its variable is 1

The given equations and their solutions are

2x +1 = 7

By collecting like terms we have

2x = 3

x = 3

2) The given equation is 4x +7 = 11

By collecting like terms we have

4x = 4

Making x the subject we have

x = 1

3) 2x -3 = 7

By collecting like terms we have

2x = 10

Making x the subject we have

x = 5

4) 1/2 x - 3 = 7

By collecting like terms we have

1/2x = 7

x= 14

5) The given equation is 3x - 11 = 19

By collecting like terms we have

3x= 30

Therefore x= 10

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Answer:

The zeroes are -1, 2, and 4. Factored: (x+1)(x-4)(x-2)=0

Step-by-step explanation:

The answer is ...

Parallel

Answer:

Parallel

Step-by-step explanation:

Sana makatulong yung sagot ko# carry on your learning dipo ako masyadong matalino pero kaya ko po kayung tulungan sa lahat nang question

Yes, 7/56 and 6/48 are proportional because 7×48 = 56×6. Therefore, the correct answer is option B.

Given that, a truck needs 7 gallons of fuel to travel 56 miles.

The truck travel 48 miles with 6 gallons of fuel.

Here, the proportion is

7:56::6:48

We know that, the proportion is product of extremes = product of means

7×48 = 56×6

336 = 336

Therefore, the correct answer is option B.

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Answer:

Rounds down to 7000.

Step-by-step explanation:

Answer:

x = - 1

Step-by-step explanation:

P = \(\frac{x-2}{x+1}\)

the denominator of the rational function cannot be zero as this would make it undefined. Equating the denominator to zero and solving gives the value that x cannot be.

x + 1 = 0 ( subtract 1 from both sides )

x = - 1

P is undefined when x = - 1

Answer: B

Step-by-step explanation:

I did this before and got a 100%.

Answer:

The question isn't clear. Can you provide more information or context? What is A? Is it a set or a number? Without this information, I can't provide a meaningful answer.

Answer: Yes. For example: (27)^2/3 would be 3^2 which = 9.

Step-by-step explanation: Hopefully this help :D ask for more help if you need!

Answer:

Runner A is running at 9 mph while runner B is running at 4 mph

Step-by-step explanation:

From online values, 4 laps make 1 mile.

We are told Runner A has made 18 laps in the time it took Runner B to make 8 laps.

This means that runner A has run in mile; 18/4 = 4.5 miles

While runner B has run in miles; 8/4 = 2 miles

Runner A is running 5 mph faster than Runner B, thus speed of runner A is;

V_b + 5 while speed of runner B is V_b.

We know that; time = distance/speed

Thus;

t_a = 4.5/(V_b + 5)

t_b = 2/V_b

Since the times are equal from the question, then;

4.5/(V_b + 5) = 2/V_b

Cross multiply to get;

4.5V_b = 2(V_b + 5)

4.5V_b = 2V_b + 10

4.5V_b - 2V_b = 10

2.5V_b = 10

V_b = 10/2.5

V_b = 4 mph

Since V_a = V_b + 5

Thus, V_a = 4 + 5 = 9 mph

Runner A is running at 9 mph while runner B is running at 4 mph

Answer:

∠3

∠4

∠KVM

∠KVL

∠LVM

Step-by-step explanation:

The vertex of an angle are the corners of the angle that form a "V". Given that information, we know that angles 3 and 4 have the vertex of V, while the others have v as a vertex [of their own] in that scenario.

Answer:

189 gumdrops

Step-by-step explanation:

Answer:

The probability that none of the households are tuned to 50 Minutes is 0.04398.

Step-by-step explanation:

We are given that the television show 50 Minutes has been successful for many years. That show recently had a share of 20, meaning that among the TV sets in use, 20% were tuned to 50 Minutes.

A pilot survey begins with 14 households have TV sets in use at the time of a 50 Minutes broadcast.

The above situation can be represented through binomial distribution;

\(P(X = r)= \binom{n}{r} \times p^{r} \times (1-p)^{n-r} ;x = 0,1,2,3,.........\)

where, n = number of samples (trials) taken = 14 households

r = number of success = none of the households are tuned to 50 min

p = probability of success which in our question is probability that households were tuned to 50 Minutes, i.e. p = 20%

Let X = Number of households that are tuned to 50 Minutes

So, X ~ Binom(n = 14, p = 0.20)

Now, the probability that none of the households are tuned to 50 Minutes is given by = P(X = 0)

               P(X = 0)  =  \(\binom{14}{0} \times 0.20^{0} \times (1-0.20)^{14-0}\)

                              =  \(1 \times 1 \times 0.80^{14}\)

                              =  0.04398

The scale factor that was used to convert triangle ABC into the image in A ' B ' C ' is 1 / 2.

To find the scale factor, you need to find the length of a side of triangle ABC and then the length of the corresponding side in A ' B ' C '.

The side length we will pick is AB which is:

= 6 - 2

= 4 units

The side length of the other triangle is A' B' :

= 3 - 1

= 2 units

The scale factor is:

= 2 / 4

= 1 / 2

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Answer:

Both drop-down answers are 0

Step-by-step explanation:

You are just replacing the x with a 0.

ALSO: The question at the top: Yes 2x + 6x is equivalent to 9x in this equation, because multiplying anything times 0 equals 0, so it doesn't matter what number comes before the x, it will always equal 0.

So when x = 0: 2x + 6x = 0, and 9x = 0, they are equivelant.

The solution is:

If my parents are going to pay the 5%, then, they will pay: $2979.

I will need to save $62.06 each month to accomplish my goal.

Here,

I'm going to a 4-year college that will cost $14895/year.

It means that I will need to pay: 14895*4 = $59.580

If my parents are going to pay the 5%, then, they will pay: $2979.

Now, if I want to save my total contribution for all four years, and I have four years to accomplish  the goal, then:

Then, if I have 4 years to pay it. It means I have 4*12 = 48 months.

Then I will need to save $2979./48 = $62.06 each month to accomplish my goal.

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complete question:

You are going to a 4-year college in 4 years that will cost $14,895.00/yr. Your parents expect you to pay 5% of the total cost.

How much do you need to pay for each year of attending?

If you want to save your total contribution for all four years before you start attending college, how much do you need to save each month if you have four years to accomplish your goal?

Answer:

The solution to a system of linear equation on a graph is the point where the two lines intersect.

Step-by-step explanation:

Step-by-step explanation:

step 1. 0.12 = 12/100 (by definition)

step 2. 12/100 = 6/50 =3/25.

Answer:

9.80 / 20 = 0.49.  Justin payed $0.49 per pound.

Step-by-step explanation:

Bob can deduct a total of $2,210 on his Schedule C related to these expenses.

To determine the total amount Bob can deduct on his Schedule C related to these expenses, consider the specific categories that can be deducted. Based on the information provided, categorize the expenses as follows:

Course fees for continuing legal education: $1,400

Airfare and hotel room: $500

Meals provided by the hotel's restaurant: $300

Snacks from the newsstand: $10

To calculate the total amount that Bob can deduct, add up these expenses:

$1,400 + $500 + $300 + $10 = $2,210

Therefore, Bob can deduct a total of $2,210 on his Schedule C related to these expenses.

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Answer:

3/15 < 1/3

Step-by-step explanation:

We have two fractions, 3/15 and 1/3. The question is asking us to compare them using the less than sign <, greater than sign >, or equal sign =.

To solve this question, what we must do is try to get both fractions the same denominators, which will be done through multiplying 3 by a certain number to get to 15, then doing the same for the numerator.

So what multiplied by 3 gets us 15?

5.

Multiply both the numerator and denominator by 5.

\(\frac{1*5}{3*5}\)

\(\frac{5}{15}\)

Now that they both have the same denominator, we can compare and see which is bigger.

5/15 (1/3) and 3/15.

By this we can see that 3/15 is less than 5/15.

Therefore 3/15 < 1/3

$2.568, cents:5058

Step-by-step explanation:

maybe...

Answer:

B

Step-by-step explanation:

It is given that the correlation coefficient is 0.52.

From the correlation coefficient table, it follows;

Coefficient 0.9 to 1.00 is very high positive.

Coefficient 0.7 to 0.9 is strong positive.

Coefficient 0.5 to 0.7 is moderately positive.

Hence the value 0.52 lies between 0.5 to 0.7.

So it is moderate positive correlation.

Fourth option is correct.