Evaluate the expression: log base3 81

The probability that the single server queuing system will contain 6 or more customers is 0.9779 (option d). This means that there is a high likelihood that the system will have at least 6 customers at any given time.

To calculate this probability, we can use the formula for the steady-state probability of the system being in state n or more, which is given by:
P(n or more) = (1 - ρ) * ρ^n / (1 - ρ^(N+1))
where ρ is the traffic intensity (arrival rate / service rate) and N is the number of servers. In this case, we have a single server, so N = 1.
First, we need to calculate the traffic intensity ρ. The arrival rate is 7 customers per hour, and the service rate is 15 customers per hour.
ρ = 7 / 15 = 0.4667
Next, we substitute the values into the formula:
P(6 or more) = (1 - 0.4667) * (0.4667^6) / (1 - 0.4667^(1+1))
P(6 or more) ≈ 0.9779
Therefore, the probability that the system will contain 6 or more customers is approximately 0.9779, or option d.

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Answer:lol

Step-by-step explanation: supercalifragelesticexpialidocious

If the ratio of students who prefer muffins to bagels is 4 to 5. if the number of students surveyed who prefer muffins is 420 then the number of students who prefer bagels is 21

Ratio: In mathematics the quantitative relation between two amounts showing the number of times one value contains or is contained within the other is known as ratio.

Given that,

The ratio of the students who prefer muffins to bagels is 4:5 means 4/5.

Number of students who prefer muffins is 420

Let, the number of students who prefer bagels is x

According to the question,

4a:5a = 420:x

⇒4a/5a = 420/x

⇒4/5 = 420/x

⇒x(4/5) = 420

⇒4x = 420×5

⇒4x = 84

⇒x = 21

Therefore the number of students who prefer bagels is 21

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Answer:

360 feet

Step-by-step explanation:

We need to multiply the number of hours, 6, with 60 feet: 6*60 = 360 feet The submarines depth after 6 hours will be 360 feet.

Answer:

8 and 4

Step-by-step explanation:

that's just the answer

Hello!

surface area

= 2(6*2) + 2(4*2) + 4*6

= 2*12 + 2*8 + 24

= 24 + 16 + 24

= 64 square inches

Answer:

19. B

20. C

Step-by-step explanation:

Answer:

The width equals 2x+3

Step-by-step explanation:

Area of a Rectangle = Length x Width

(2x² + 5x + 3) / (x + 1) = 2x + 3

(x + 1) × (2x + 3) = 2x² + 5x + 3

So the width is 2x + 3

Let the first number be x.

The second number is 5 times less than x => x - 5

Therefore, we can write the statement as

Solving the quadratic equation:

Let us replace -5x in the equation with -4x and -x to be able to factorize.

Hence,

Hence,

Therefore, the number can be 1 or 4.

The second number can be

Therefore, the pair of numbers can be

The location of the transformed point will be at the coordinate (0,4).

In mathematics, a translation moves a shape left, right, up, or down but does not turn it. The translated (or picture) shapes appear to be the same size as the original shape, showing that they are congruent. They've just moved in one or more directions.

Given that a point at (−3,−2) is transformed in two steps. It is reflected in y = x. It is translated as 3 units right and 2 units up.

The translated point will be,

(−3,−2) ⇒ (-3,2)

Translation of the point,

(-3,2) ⇒ (-3+3, 2+2) ⇒(0,4)

Therefore, the location of the transformed point will be at the coordinate (0,4).

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The order for 50 chain saws will be shipped at the start of week 8.As the manager, I will ensure that the assembly of the 50 chain saws begins at the start of week 6 to meet the shipping deadline at the start of week 8.

To determine the shipping date, we need to consider the production time for assembling the chain saws. Assuming a standard production time of 2 weeks, we can calculate the start date for production.

Start date for production = Shipping date - Production time = Week 8 - 2 weeks = Week 6

Therefore, the assembly of the chain saws should start at the beginning of week 6 in order to meet the shipping deadline at the start of week 8.

As the manager, I will ensure that the assembly of the 50 chain saws begins at the start of week 6 to meet the shipping deadline at the start of week 8. This will ensure that the order is fulfilled on time and the customer's expectations are met.

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The area of the sheet of paper in correct metric units is 602.6c\(m^{2}\).

A region's size on a plane or curved surface is expressed by the term "area," which is a mathematical concept. As opposed to surface area, which refers to the area of an open surface or the boundary of a three-dimensional object, plane region or plane area refers to the area of a form or planar lamina. Area can be thought of as the volume of material, at a particular thickness, required to create a model of the shape, or as the volume of paint required to paint the surface in a single coat. It is equivalent to the volume of a solid or the length of a curve in two dimensions (a three-dimensional concept).

Calculations:

The length of a 8 X 11 paper in metric unit is 27.9 cm and width of 8 X 11 paper in metric unit is 21.6 cm.

Area of sheet of paper=length*width

               =27.9*21.6

               =602.6 c\(m^{2}\)

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​

Answer:

I'll help. First of all, you aren't stupid, second of all believe in yourself and you can do anything.

:)

P.S

Sorry if I sound like a school counselor.

lol :)

The two polygons are similar if the corresponding angles are congruent and the corresponding sides are proportional,the value of x is 8.

The two polygons are similar if the corresponding angles are congruent and the corresponding sides are proportional. Therefore, the ratio of the lengths of the sides of the two polygons is equal to the ratio of the measures of the corresponding angles.

In this case, the ratio of the corresponding side lengths of the two polygons is equal to the ratio of the measures of the corresponding angles. The ratio of the lengths of the two sides of the larger polygon (x-3 , 8 and 16) is (x-3)/8 : 8/16. This ratio is equal to the ratio of the measures of the corresponding angles of the two polygons, which is 2.5/2 : 2/4.

Equating these two ratios, we get (x-3)/8 = 2.5/2 and 8/16 = 2/4. Solving these two equations, we get x-3 = 5 and 8 = 4. Adding 3 to both sides, we get x = 8. Hence, the value of x is 8.Therefore, the value of x is 8.

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The probability that the sample mean would differ from the true mean by more than $2.5 is 0.0062

Mean cost of the five pound shrimp bag = $40

Variance of the five pound shrimp bag = $36

The number of the shrimp bag = 43

The given mean value = $2.5

The z-score = $2.5

The probability of the sample mean differ by $2.5 from the true mean can be calculated by

  P(z > 2.5) = 1 - P(z < 2.5)

From the z table , we can get the value of  z < 2.5 which is 0.9938

    P(z > 2.5) = 1 - 0.9938

   P(z > 2.5) = 0.0062

Therefore , the probability of sample mean from the true mean by 2.5 is 0.0062

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Answer:

The error is at (-4, 0) where 0 should be changed to 1

Step-by-step explanation:

The error was made at (-4, 0). The point should be (-4, 1) instead, because the y values should be increasing by 3 each time.

Answer: A

Step-by-step explanation:

\(\pi > 3 \implies 5\pi > 15\)

The bags of candy that was sold is 6

The bags of cookies that was sold is 10.

$8.50c + $4.50o = 79 equation 1

o - c = 6

o = 6 + c  equation 2

Where:

Substitute for o in equation 1 using equation 2

$8.50c + $4.50(6 + c) = 79

$8.50c + 27 + 4.50c = 79

$8.50c + 4.50c = 79 - 27

$13c = 52

c = 52 / 13

c = 4

Substitute for c in equation 2

0 = 6 + 4 = 10

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Answer:

w ≈ 68,3

Step-by-step explanation:

Use trigonometry:

\( \sin(42) = \frac{w}{102} \)

Cross-multiply to find w:

\(w = 102 \times \sin(42°) ≈68.3\)

why is 20/2 bigger than 25/15​?

because 20/10 = 2

and 25/15 = 5/3 or 1.66

2 is bigger than 1.66

Answer:

1 is your answer if not idk

Step-by-step explanation:

because if there is 4 and its 3 then its 1

Answer:

27.7 days

Step-by-step explanation:

volume of a cylinder = nr^2h

n = 22/7

r = radius

the diameter is the straight line that passes through the centre of a circle and touches the two edges of the circle.

A radius is half of the diameter

radius = 8/2

(22/7) x (4^2) x 11 == 553.14 in^3

if it rains 20 cm^3 per day, the can would fill in : volume of can / amount of rain = 553.14/20 = 27.7 days

Answer:

assuming <3 is supplementary to <7 then <7 is 57

Step-by-step explanation:

180-123=57

Answer:

-3p

Step-by-step explanation:

Answer:

-3p

Step-by-step explanation:

5p - 4p = 1p - 4p = -3p

Part i) Simple interest = $600,000.00.

Part ii) Selling price = $2,900,000.00.

Part i) The formula for simple interest is;

SI = PRT/ 100

P = principal amount = $2,000,000.00.

R = rate of interest  = 15%

T = time in years = 2 years.

Put the value in the formula;

SI = ( $2,000,000 × 2 × 15)/100

On simplification;

SI = 600,000

Thus, the simple interest at the end of 2 years is $600,000.oo

Part ii) the selling price

Selling price = cost price + profit

Selling price = cost price + 45%of cost price

Cost price = $2,000,000.00

45%of cost price = 45× $2,000,000.00/100

45%of cost price = 900,000.00

Selling price = $2,000,000.00 + 900,000.00

Selling price = $2,900,000.00.

The the selling price of the fridge is found as $2,900,000.00.

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Therefore, the probability that in a random sample of size 9, a total of more than 108 pizzas are consumed is approximately 0.9332, or 93.32%.

To find the probability that in a random sample of size 9, a total of more than 108 pizzas are consumed, we need to calculate the cumulative probability of the sample total being greater than 108.

Given that the number of pizzas consumed per month by university students is normally distributed with a mean of 14 and a standard deviation of 4, we can use the properties of the normal distribution to solve this problem.

Calculate the mean and standard deviation of the sample total:

Mean of the sample total = sample size * population mean = 9 * 14 = 126

Standard deviation of the sample total = square root(sample size) * population standard deviation = √9 * 4 = 12

Standardize the value 108 using the formula:

z = (x - mean) / standard deviation

For 108:

z = (108 - 126) / 12 = -1.5

Calculate the cumulative probability using the standard normal distribution table or a calculator:

P(Z > -1.5)

Looking up the value in the standard normal distribution table or using a calculator, we find that P(Z > -1.5) is approximately 0.9332.

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Answer:

A. 4 m

Step-by-step explanation:

The formula for the volume of a cylinder is πr^2 x h

r = radius    h = height

So, with this you can reverse it to find the radius since you know the height.

96π/6 = 16π

√16π = 4π

radius = 4 m

Answer:

A. 4m

Step-by-step explanation:

your welcome

Answer:

x ≈ 20.31

Step-by-step explanation:

By applying tangent rule in the given right triangle,

tan(55°) = \(\frac{\text{Opposite side}}{\text{Adjacent side}}\)

Measure of the opposite side = 29 units

Measure of the adjacent side = x

Substitute these values in the expression,

tan(55) = \(\frac{29}{x}\)

x = \(\frac{29}{tan(55)}\)

x = 20.306

x ≈ 20.31

Answer:

15 miles per hour

Step-by-step explanation:

unit rate is when you how much it is for 1 like 3 dollars for 1 pound or 15 miles per hour

Hopes this helps please mark brainliest

Answer:

15 miles per hour

Step-by-step explanation:

Let's remember what exactly unit rate is:

Unit rate means a rate for one of something. We write this as a ratio with a denominator of one. For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second. Both of the ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but the 7 yards in 1 second is a unit rate. Or, it takes one second to run the 7 yards.

For this question, I first notice that we have 2 answers that pertain to the same thing:

15 miles per hour and 30 miles in two hours

We have 1 cake / 3 hours, but the 1 is not in the denominator so it is not a unit rate.

And we have $5.50 per 1.5 pounds. Again, the one is not in the denominator so it is not a unit rate.

Going back to the other two (15 miles per hour and 30 miles in two hours)

We can write these in fraction form

\(\frac{15 miles}{1hour}\) and \(\frac{30miles}{2hours}\)

The 15 miles per hour has the one in it's denominator, so it is the unit rate.