Graph the line with the given point and slope.
The line through (-1,-2) with slope
6/5

a) Probability of receiving no e-mails during an hour = 0.0067

b) Probability of receiving at least three e-mails during an hour = 0.8754

c) Expected number of e-mails received during 15 minutes = 1.25

d) Probability that no e-mails are received during 15 minutes = 0.2865

Given that five emails are typically received every hour. If X represents the number of emails received in an hour, then X is poisoned with the given parameter, λ = 5.

⇒ P (X = x) = [tex]\frac{e^{ -x} X^{x}}{x!} = \frac{e^{-5} 5^{x}}{x!}[/tex]

(a) Likelihood of not receiving any emails for an hour = p (x = 0)

= (e⁻⁵5⁰) / 0! = (e⁻⁵ * 1) / 1 = e⁻⁵ = 0.00674 ≈ 0.0067

(b) Likelihood of receiving three or more emails in a single hour P(x ≥ 3)

= 1 - [P (x < 3) = 1 - [P(x = 0) + P(x = 1) + P(x = 2)]

= 1 - [(e⁻⁵5⁰) / 0! + (e⁻⁵5¹) / 1! + (e⁻⁵5²) / 2!]

= 1 - [0.00674 + 0.03369 + 0.08422]

= 1 - 0.12465

= 0.87535 ≈ 0.8754

(c) The number of emails that should be received in the next 60 minutes = an hour's worth of emails on average = 5

As a result, the anticipated quantity of emails received in 15 minutes = 5 / 4 = 1.25

(d) Number of emails received on average every 15 minutes = Number of emails that should be received in the next 15 minutes = 1.25

Let X represent how many emails were received in 15 minutes. X then proceeds with a parameterized Poisson distribution, λ = 1.25

⇒ P (x = X) = [tex]\frac{e^{-x} X^{x} }{x!} = \frac{e^{-1.25}1.25^{x} }{x!}[/tex]

The likelihood that no emails will be received during the next 15 minutes = [tex]\frac{e^{-1.25}* (1.25)^{0} }{0!} = \frac{e^{-1.25}*1 }{1} = e^{-1.25} = 0.2865[/tex]

COMPLETE QUESTION: According to a 2017 survey conducted by the technology market research firm The Radicati Group, U.S. office workers receive an average of 121 e-mails per day (Entrepreneur magazine website). Assume the number of e-mails received per hour follows a Poisson distribution and that the average number of e-mails received per hour is five.

a. What is the probability of receiving no e-mails during an hour (to 4 decimals)?

b. What is the probability of receiving at least three e-mails during an hour (to 4 decimals)? For this question, if calculating the probability manually make sure to carry at least 4 decimal digits in your calculations.

c. What is the expected number of e-mails received during 15 minutes (to 2 decimals)?

d. What is the probability that no e-mails are received during 15 minutes (to 4 decimals)?

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The simplified expression of (x¹² ÷  x⁴). x³ is x¹¹

The expression can be solved as follows:

(x¹² ÷  x⁴). x³

The law of indices can be used to solve the expression.

Therefore,

[tex]\frac{x^{a} }{x^{b} } = x^{a - b}[/tex]  and [tex](x^{a} )^{b} = x^{ab}[/tex] and [tex]x^{a} .x^{b} = x^{a+b}[/tex]

Hence,

(x¹² ÷  x⁴) = x¹² / x⁴ = x¹²⁻⁴ = x⁸

Therefore,

(x⁸). x³ = x⁸⁺³

Finally,

x⁸⁺³ = x¹¹

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2x² - x²

Factor:

x²(2 - 1)

x²(1)

x²

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

(3x² + x + 8) + (x² - 9)

Add like terms:

(3x² + x²) + x +(8 - 9)

4x² + x - 1

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

-3x² - 7x + 9 - 5x² + 6x - 4

Add like terms:

(-3x² - 5x²) + (-7x + 6x) + (9 - 4)

-8x² - x + 5

Answer:

Hope it helps you

Step-by-step explanation:

(a) medical treatment that reduces time off of work due to illness or injury.

Answer:

15 I did 15+15+15 or 15x3 and it equals 45

Step-by-step explanation:

Brainliest?

15

Divide 45 by 3 because newton has 15 base ball cards and each card has fifteen card in each pack

Answer:

Polynomials with a negative constant term are not perfect squares, hence polynomial 4, with constant term of -121, is not a perfect square.

What are perfect square expressions?

Perfect square expressions are formed in two ways, either with the square of the sum or the square of the subtraction, as follows:

Square of the sum: (a + b)² = a² + 2ab + b².

Square of the subtraction: (a - b)² = a² - 2ab + b².

The constant term is the final term. Since this term is squared, it will always be positive for perfect squares, hence if the constant term is negative, it will guarantee that the polynomial is not a perfect square.

For the expressions in this problem, we have that:

The expression with a constant term of 36 can be a perfect square, as 36 is a positive number.

The expression with a constant term of -121 cannot be a perfect square, as -121 is a negative number.

Hope this helps :)

Step-by-step explanation:

Number of weeks required before Jacob and Diego will be tied in the race to complete community service hours for scouting is equal to 50 weeks.

As given in the question,

Let number of weeks be represented by a variable x.

Jacob plans to devote 5 hours per week from now onwards. Hence his volunteer hours will cumulate to 5x+50 as he has already completed 50 weeks.

Diego plans to devote 6 hours per week from now onwards. Hence his volunteer hours will cumulate to 6x.

For Jacob and Diego to tie in the race, their volunteer hours should be equal. Translating this into a linear algebraic equation,

6x = 5x+50

=> 6x-5x = 50

=> x = 50

Therefore, number of weeks required before Jacob and Diego will be tied in the race to complete community service hours for scouting is equal to 50 weeks.

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The answer is a) 27/6 b) 1/2 c) 0.6 = 6/10 = 3/5 and their sum is 5.6

The four basic arithmetic operations in Maths, for all real numbers, are:

→ Addition (Finding the Sum; ‘+’)

→ Subtraction (Finding the difference;  ‘-’)

→ Multiplication (Finding the product; ‘×’ )

→ Division (Finding the quotient; ‘÷’)

In this given question ;

a) [tex]\frac{3}{4}[/tex] + 6

first take LCM so we will get : [tex]\frac{3+24}{6}[/tex] = [tex]\frac{27}{6}[/tex]

b) [tex]\frac{2}{4}[/tex]÷ 1

this implies [tex]\frac{1}{2}[/tex] ÷ 1 = [tex]\frac{1}{2}[/tex]× 1 = [tex]\frac{1}{2}[/tex]

c) [tex]\frac{3}{5}[/tex] = 0.6

If we were to solve a + b + c we get : 27/6 = 4.5

b= 1/2 = 0.5

so 4.5+ 0.5 + 0.6 = 5.6

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Based on the taxes in the first city and the tax in the second city as well as the total hotel tax paid in the two cities, the hotel charge for each city before taxes was:

The hotel charge before taxes was $500 higher in the second city than in the first. Assuming the charge in the first city was x, the charge in the second city was:

= x + 500

The total charge in the first city would be:

0.065x + 0.06(x + 500) = 748.75

0.065x + 0.06x + 30 = 748.75

0.125x + 30 = 748.75

0.125x = 748.75 - 30

0.125x = 718.75

x = 718.75/0.125

x = $5,750

The total charge in the second city would be:

= 5,750 + 500

= $6,250

In conclusion, the charges in the first and second cities are $5,750 in the first city and $6,250 in the second city.

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When the population has a mean of 30, if 3 points are added to each score, the mean for the new distribution is 33.

It should be noted that mean simply means the average of a given set of numbers that are given. The entire group about whom you want to make conclusions is referred to as a population. The particular group from which you will gather data is known as a sample. The sample size is always smaller than the population as a whole. A population in research doesn't usually refer to humans.

In this case, the population has a mean of 30 a and 3 points are added to each score.

In this case, the new mean will be the addition of the numbers. This will be illustrated as:

= 30 + 3

= 33

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Answer:

he must make sure he gets up to 49 and higher to obtain an average of 76 or greater

Step-by-step explanation:

logically from 49 - 100 :)

Slope is [tex]\frac{-2}{3}[/tex] of coordinates (6,5) and (9,-7).

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. [1] The letter m is frequently used to represent slope; however, there is no obvious reason for this. The slope of a curve at a point in differential calculus is defined as the slope of the tangent line at that point as a generalization of this practical definition. The slope can be determined between any two locations when the curve is represented by a series of points in a diagram or list of point coordinates. Maybe when the curve is represented as a continuous function.

Given Data

coordinates - (6,-5) and (9,-7)

slope of the line denoted as m

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

m = [tex]\frac{-7-(-5)}{9-6}[/tex]

m = [tex]\frac{-2}{3}[/tex]

Slope is [tex]\frac{-2}{3}[/tex]

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olution:

iven;

Applyin the power property of logarithm given as;

Thus;

Simplify further, we have;

ivide both sides by 2;

NSWER:

Answer:

Formula for slope is given as (y2-y1) ÷ (x2-x1) or (y1-y2) ÷ (x1-x2), where x and y are the coordinates of the points.

Slope = (6 - 3)÷(- 1 - 4)

= -3/5

An infinite set is infinite from start to end, but both sides can have continuity, unlike a finite set, which has both start and end elements. The finite() function in R Language is used to determine whether or not the elements of a vector are Finite values. It returns a Boolean value for each vector element.

Hence, The finite() function in R Language is used to determine whether or not the elements of a vector are Finite values.

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The weekly deduction, including FICA is a $60

Define percentage.

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%"

Given,

Jessica makes in a year = $24000

She receives weekly pay checks is = 12%

We know, in 1 month there are 4 weeks and for 12 months there are 48 weeks.

so, Jessica makes per week = $24000 / 48

                                                = $500

And, we know Jessica receives 12% paychecks then,

find, 12% of weekly payment

⇒12% of 500

⇒ (12 * 500) / 100

⇒$60

Hence, The weekly deduction, including FICA is a $60

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Using the hypergeometric distribution, the probabilities are given as follows:

a) All 13 hearts: [tex]1.57 \times 10^{-12}[/tex]

b) 13 cards of the same suit: [tex]6.30 \times 10^{-12}[/tex]

c) Seven spades and six clubs: [tex]5.4 \times 10^{-9}[/tex]

The formula is:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

The general parameters in this problem are given as follows:

In item i, there are 13 hearts in a standard deck, hence k = 13 and the probability is P(X = 13), hence:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 13) = h(13,52,13,13) = \frac{C_{13,13}C_{39,0}}{C_{52,13}} = 1.57 \times 10^{-12}[/tex]

For item ii, we consider the same context of item i, just now we can consider any of the four types of cards, hence:

[tex]p = 4 \times 1.57 \times 10^{-12} = 6.30 \times 10^{-12}[/tex]

For item iii, we want:

Hence the probability is given as follows:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 7) = h(7,52,13,13) = \frac{C_{13,7}C_{13,6}}{C_{52,13}} = 5.4 \times 10^{-9}[/tex]

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1/[tex]a^{2}[/tex] is the answer.

Given,

a^-2

Solution:

a^-2

Expand it

a^-2 = 1/a^2

= 1/[tex]a^{2}[/tex]

Therefore,

a^-2 = 1/[tex]a^{2}[/tex]

1/[tex]a^{2}[/tex] is the answer.

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The probability is that the mean of their test scores is less than 70.

What is probability?

A probability is a number that reflects tha chance of particular event will occur.

Sol-

As per the question given-

Mean = 73

Standard daviation=7.2

Number of students randomly selected =22

Let's take n number for experiment of outcomes.

The number of favorable outcomes can be denoted by x.

The formula to calculate the probability is -

probability = favorable

Outcomes/total outcomes =x/n

The number of standard daviation form the mean is called z.

Z = (x-¥)/€

Z=(75-73)(7.2/√22)

Z= -37.0582965

P(z<-37.05)

= 37.05

There for the probability is 37.05.

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the answer is definitely 9

Answer:

$50

Step-by-step explanation:

We will call x the original price of the sunglasses.

We can create the equation below using the information given.

[tex]x*\frac{30}{100} =15[/tex]

Now solve for x.

[tex]x = 15*\frac{100}{30}[/tex]

[tex]x = \frac{100}{2}[/tex]

[tex]x=50[/tex]

Given the exression:

Let's solve the expression and identify the error.

Since both expressions have the same denominator, let's combine the numerators:

Apply distributive property:

Combine like terms in the numerator:

The error in the problem was that distributive property was not applied when the numerators were combined.

ANSWER:

Answer:

Each bag of lemons cost $3.30

Step-by-step explanation:

The equation will be

6x = 26.10 - 6.306x=26.10−6.30

Solve for x to get,

6x = 19.86x=19.8

x = 3.3x=3.3

Answer:

$3.30 for each bag of lemons

Step-by-step explanation:

We know that Omar only bought both lemons and eggs. We also know that the total amount of money he spent on groceries is $26.30 and that the eggs are worth $6.30 out of the total.

So, if we can subtract the cost of the eggs from his total cost of groceries to find how much the lemons cost. After that we can divide the cost of all the lemons, which is $19.80, by the number of bags, which is 6, to find how much each bag costs.

(26.10 - 6.30) / 6 = ?

19.8/6 = 3.30

Using the PEMDAS ( In order to know the order of the operations)

P = Parentheses

E = Exponents

M = Multiplication

D = Division

A = Addition

S = Subtraction

Accordint to this, we need to divide first, and then we need to add the resultant number, so:

Answer:

10

The place value of the underlined digit (6) is tens of thousands and should be rounded to 70,000.

A place value simply refers to a numerical value (number) which denotes a digit based on its position in a given number and it includes the following:

In this scenario, the place value of the underlined digit (6) is tens of thousands and 9 is the next digit to six (6). Therefore, we would add one (1) to the underlined digit (6) and then change all of the other digits to zero (0) as follows:

69,807 = 70,000

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Answer:

7.36 g/cm3

Step-by-step explanation:

Density = mass ÷ volume

Mass in grams = 9200g

Volume in cm3 = 1250cm3

9200 ÷ 7850 = 7.36

7.36 is already in 2 d.p.

Given:

The given expression is,

Required:

To select the equivalent expression.

Explanation: