If P(A|B) = 35%, and P(B) = 70%. Find P(A) given that A and B are independent.

olution:

iven;

Applyin the power property of logarithm given as;

Thus;

Simplify further, we have;

ivide both sides by 2;

NSWER:

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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If the width of a rectangle is 15 cm less than the length and the perimeter of the rectangle is 150 cm, then the length is 45 cm and width is 30 cm

The width of a rectangle is 15 cm less than the length

Consider the length of the rectangle as x

The the width of the rectangle = x-15

The perimeter of the rectangle = 150 cm

The perimeter of the rectangle = 2(l+w)

Where l is the length and w is the width

Substitute the values in the equation

2(x+(x-15))=150

2(2x-15)=150

4x-30 = 150

4x = 180

x = 45 cm

The width of the rectangle = x-15

= 45-15

= 30 cm

Hence, If the width of a rectangle is 15 cm less than the length and the perimeter of the rectangle is 150 cm, then the length is 45 cm and width is 30 cm

The complete question is

The width of a rectangle is 15 cm less than the length. The perimeter is

150 cm. Find the rectangle's dimensions.

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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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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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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:

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

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:

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:

$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]

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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Answer: 1.75

Step-by-step explanation:

13/4 = 3.25

5.00-3.25

1.75

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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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 :)

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

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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The smallest number of signs that he can sell to have an income of $300 in one week is 12.

The price of one sign is x

Number of signs he sells per week = 37-x

The total earning from selling these is  x(37-x)  which is given as $300

(37- x) x = 300

37x - x² = 300

x² - 37x + 300 = 0

As per formula to find base in a quadratic equation

[tex]x =\frac{37 - \sqrt{37^{2}-4 . 1 . 300 } }{2 . 1} \\x =\frac{37 - \sqrt{1369-1200 } }{2} \\x =\frac{37 - \sqrt{169 } }{2} \\x = \frac{37-13}{2}\\ x = \frac{24}{2}\\ x = 12[/tex]

The other base can be

[tex]x =\frac{37 + \sqrt{37^{2}-4 . 1 . 300 } }{2 . 1} \\x =\frac{37 + \sqrt{1369-1200 } }{2} \\x =\frac{37 + \sqrt{169 } }{2} \\x = \frac{37+13}{2}\\ x = \frac{50}{2}\\ x = 25[/tex]

Therefore  the smallest number of signs that he can sell to have an income of $300 in one week is 12.

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Given:

The given expression is,

Required:

To select the equivalent expression.

Explanation:

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:

He will cover 301.875 miles in 7.5 hours at a unit speed of 40.25 miles per hour.

A ratio that compares two amounts of different types of units is called a rate. When a unit rate is expressed as a fraction, the denominator is 1 unit.

Rate = Distance/Time

If Mr.Salcedo was driving at 120 3/4 miles in 3 hours, his unit rate will be calculated as:

Unit rate =[120 3/4]/3

Unit rate = 483/12

Unit rate = 40 1/4 miles/hr

This shows that he  drove 40 1/4 miles/hr.

The miles he drove in 7 1/2 hour is expressed as;

Miles driven = 161/4 * 15/2
Miles driven = 301.875 miles

Hence the miles that he will drive in 7.5 hours is 301.875miles and the unit rate is 40.25 miles/hr

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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

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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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

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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Drop Down 1

(2 in)(10 ft/1 in) = 20 ft

Drop Down 2

This means the scale factor is 1:2, and thus the new length will be 3 inches.