3.1 Area under the curve, Part I: Find the probability of each of the following, if Z~N(μ = 0,σ = 1).

(please round any numerical answers to 4 decimal places)

a) P(Z < -1.35) =

b) P(Z > 1.48) =

c) P(-0.4 < Z < 1.5) =

d) P(| Z | >2)

The correct expanded form using Laws of exponents is:

Two-thirds times two-thirds times two-thirds times two-thirds

Some of the laws of exponents are:

1) When multiplying like bases, keep the base the same and add the exponents.

2) When raising a base with a power to another power, keep the base the same and multiply the exponents.

3) When dividing like bases, keep the base the same and subtract the denominator exponent from the numerator exponent.

Now, we want to solve the expression given as: (²/₃)⁴

When we expend this, we arrive at:

²/₃ × ²/₃ × ²/₃ × ²/₃

This among the options is Option A which is:

Two-thirds times two-thirds times two-thirds times two-thirds

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Answer: 18

Step-by-step explanation:

The probability of getting 2 or greater than 2 is 2/3.

Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.

Given, that I have cards numbered from 1 to 3.

∴ The probability of getting 2 is 1/3 and the probability of getting 3 is 1/3.

So, P(2 or greater than 2) is the sum of the probability of getting 2 and the probability of getting 3.

= 1/3 + 1/3.

= 2/3.

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Answer:

Probability = 9/25

This is 36%

Step-by-step explanation:

To find the probability take the total number of possibilities (25 marbles--all of them) put that number on the bottom of a fraction. Then put the number of ways that outcome can happen (9 blue and black) and put that on top of the fraction.

Probability(event)

= specific/total

Probability(blu&blk)

= 9/25

If the fraction can be simplified, do that. 9/25 cannot be simplified.

If you need a percent for your answer, divide then multiply by 100.

A fraction bar is a division symbol.

9/25 means 9÷25.

9/25 = .36

Percent means "per hundred" To convert a decimal to a percent, multiply by 100

.36×100 is 36%

Answer:

y = \(\frac{4}{3}\) x + 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (0, 2) and (x₂, y₂ ) = (6, 10) ← 2 points on the line

m = \(\frac{10-2}{6-0}\) = \(\frac{8}{6}\) = \(\frac{4}{3}\)

The line crosses the y- axis at (0, 2 ) ⇒ c = 2

y = \(\frac{4}{3}\) x + 2 ← equation of line

Answer:

34x=20*332

34x=6,640

x=6,640/34

x=195 ft. tall.

Step-by-step explanation:

You canAssuming he is lying on the ground then:

20/34=x/332

Answer:

there

Step-by-step explanation:

10.

TP = 20-12

TP = 8

SP = SQ

SP = 20

RQ = TP

RQ = 8

S-------15.5

20------12

12s = 310

s = 310/12

s =~25,8

11.

75--------46

100-------b

75b = 4600

b = 4600/75

b =~ 61,3

l² = 61,3² + 46²

l² = 3757,69 + 2116

l² = 5873,69

l = \(\sqrt{5873,69}\)

l =~ 76,7

Answer:

distributive

Step-by-step explanation:

a(b + c)=ab + ac

it's distributive one

Answer:

X=12

Step-by-step explanation:

The time and electricians it would take the remaining 3 electricians 8 hours to complete the job if one electrician does not report.

More people to do a task means less time it will take.

Less people to do a task means more time it will take.

Thus, they are inversely related.

If x men take y time for a work,

We can define a constant as "Manpower" needed for doing that specific work.

Let we define:

Manpower needed for a work = y + y + y + .. + y = Time per man × count of men

Manpower needed for a work = xy

We are given that;

Number of electricians= 4

Number of hours= 6

Now,

We can use the formula:

workers × time = work

where "workers" is the number of electricians, "time" is the number of hours they work, and "work" is the amount of work done.

In this case, we know that 4 electricians can complete the job in 6 hours. So:

4 × 6 = work

work = 24

This means that the total amount of work required to complete the job is 24 "units".

Now, if one electrician doesn't show up, we have only 3 electricians to do the work. Let's call the time it takes for the 3 electricians to complete the job "t".

So we have:

3 × t = 24

Dividing both sides by 3, we get:

t = 8

Therefore, by work and time answer will be 3 electricians and 8 hours.

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The way the flashback in these paragraphs advance the plot is C. It introduces Evan's motivation for working in the garden with Grandfather.

The technique of flashback in storytelling involves interrupting the chronological order of events to depict an earlier event or scene. It uses time travel to furnish the audience with necessary backstory, context, or a deeper understanding of the characters.

The technique of flashbacks is frequently employed as a means of divulging previous occurrences, recollections, or incidents that hold significance to the present narrative being conveyed.

Hence, it can be seen from the given text that the use of flashback helps show the motivation which Evans had for working in the garden with Grandfather

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Answer:

Step-by-step explanation:

12 tickets

The average yearly salary of an individual with each of these final degrees is,

Master's individual earns average of $66,000 while the Bachelor's individual earns $55,000.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The average yearly salary of an individual whose final degree is a​ master's is ​$44 thousand less than twice that of an individual whose final degree is a​ bachelor's.

And, Combined, two people with each of these educational attainments earn ​$121 thousand.

Now, The total amount earned by a Bachelor's person be $x:

And, amount earned by a masters person will be; $(2x - 44)

Hence, Total amount earned by the two individuals will be;

⇒ x + (2x - 44) = 121

Solve for x as;

⇒ x + 2x - 44 = 121

⇒ 3x - 44 = 121

⇒ 3x = 121 + 44

⇒ 3x = 165

⇒ x = 165/3

⇒ x = 55

And, (2x - 44) = 2 × 55 - 44

                     = 110 - 44

                     = 66

Therefore we conclude that; master's individual earns average of $66,000 while the Bachelor's individual earns $55,000.

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The Cookie Shop's profit at the end of January as a result of the 20% decrease was $12000.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let s represent the Cookie Shop's profit at the end of January. At the end of January, their profit had decreased by 20%:

Percentage decrease = 20% of 15000 = $3000

s = 15000 - 3000 = 12000

The Cookie Shop's profit at the end of January as a result of the 20% decrease was $12000.

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The value of the variable 'w' for the given equation 7 ( w + 7 )³ = 7(6³)  is equal to w = -1.

As given in the question,

Given equation is equal to :

7 ( w + 7 )³ = 7(6³)

Divide both the side of the equation by 7 we get,

⇒ 7 ( w + 7 )³ / 7 = 7(6³) /7

⇒( w + 7 )³ = (6³)  

Take cube root both the side of the equation we get,

⇒∛( w + 7 )³ = ∛(6³)  

⇒ w + 7 = 6

Now subtract 7 from both the side of the equation we get,

⇒w + 7 - 7 = 6 - 7

⇒ w = -1

Therefore, the value of the variable 'w' for the given equation is equal to w = -1.

The complete question is:

Solve this equation:

7 ( w + 7 )³ = 7(6³)

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Step-by-step explanation:

The total price of sneakers including tax will be equal to $20.75.

The Latin phrase "per centum," which means "by the hundred," is where the English word "percentage" comes from. Percentage segments are those with a numerator of 100. In other words, it is a connection where the whole is always deemed to be valued 100.

As per the given information in the question,

Price of sneakers = $20

Tax on sneakers = 3.75%

Then, the amount of tax will be,

(20 × 3.75)/100

= 75/100

= $0.75

Then, the total price of the sneakers will be,

$20 + $0.75

= $20.75

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Answer:

3,577

Step-by-step explanation:

Answer:

2.) AEB = DEC

Answer:

AEB = DEC

Step-by-step explanation:

SAS means Side-Angle-Side. So you need to find whats congruent with these triangles. Well, luckily, 2 of them are marked. DE is the same as EB because the two little lines show congruency. Well, that means AE is the same as EC because of the little lines. Well, that's two sides we found congruent so now all we need is an angle to complete Side-Angle-Side.

The angle we need is the one that conects the two triangles because if it were anywhere else it wouldn't be SAS. For example, if the angle you chose was angle B and D it would be SSA which isnt even a form to find congruency. Angles A and C are the same story which leaves us with AEB and DEC which are our congruent angles and our answer for this problem.

Answer:

20

Step-by-step explanation:

cause

Answer:

(100/500) *200 =40%

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

12:10 PM -   ( 1 + 1 ) hr = 10:10 AM    then subtract the 40 min to get 9:30 AM

Answer:

An increase of $0.94

Step-by-step explanation:

The solution to the system of equations y = 1/8x −1 and −5x + 4y = −13 is (2, −3/4). Option D is correct.

We are given:

y = 1/8 x − 1                 ..............equation i.

− 5x + 4y = − 13          ..............equation ii.

We will use the substitution method to solve the given equation.

substitute the value of y from equation i in equation ii, and we will get;

− 5x + 4(1/8 x − 1) = − 13

− 5x + 1/2 x − 4 = − 13

(-10 + 1) / 2 x = -13 + 4

-9/2 x = -9

x = -9 * 2 / -9

x = 2

Put the value of x in equation i, we will get;

y = 1/8 *2 − 1

y = 1/4 - 1

y = 1 - 4 / 4

y = -3 / 4

So, the value of x = 2 and the value of y = -3 / 4.

Thus, the solution to the system of equations y = 1/8x −1 and −5x + 4y = −13 is (2, −3/4). Option D is correct.

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The probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.

To find the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts, we need to use the concept of the Central Limit Theorem.

In this case, we know that the mean voltage of a single battery is 15 volts and the standard deviation is 0.2 volts. When batteries are connected in series, their voltages add up.

The combined voltage of four batteries connected in series is the sum of their individual voltages. The mean of the combined voltage will be 4 times the mean of a single battery, which is 4 * 15 = 60 volts.

The standard deviation of the combined voltage will be the square root of the sum of the variances of the individual batteries. Since the batteries are connected in series, the variance of the combined voltage will be 4 times the variance of a single battery, which is 4 * (0.2)^2 = 0.16.

Now, we need to calculate the probability that the combined voltage of four batteries is 60.8 or more volts. We can use a standard normal distribution to calculate this probability.

First, we need to standardize the value of 60.8 using the formula:

Z = (X - μ) / σ

Where X is the value we want to standardize, μ is the mean, and σ is the standard deviation.

In this case, the standardized value is:

Z = (60.8 - 60) / sqrt(0.16)

Z = 0.8 / 0.4

Z = 2

Next, we can use a standard normal distribution table or calculator to find the probability associated with a Z-score of 2. The probability of obtaining a Z-score of 2 or more is approximately 0.0228.

Therefore, the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.

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The posible numbers are:

So if we put the sign we can have:

and we can solve the equation to confirm it so:

Answer:

0.131

Step-by-step explanation:

you shouldn't be dividing anything if it has a + sign in between the problem. just add up the values and you'll get the right answer.

Answer:

It could be 0, is the question multiple choice?

a horizontal line always has a slope of 0, now, for the sake of a silly proof, let's do some rigamarole to get it.

to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below

\((\stackrel{x_1}{-3}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{7}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{7}-\stackrel{y1}{7}}}{\underset{\textit{\large run}} {\underset{x_2}{7}-\underset{x_1}{(-3)}}} \implies \cfrac{0}{7 +3} \implies \cfrac{ 0 }{ 10 } \implies \stackrel{ }{\text{\LARGE 0}}\)