Explain why when multiplying powers you add rather than multiply the exponents.

The expected value for the number of times Danny goes swimming during a week is 0.65.

Given that:-

Percentage of time Danny went swimming twice a week = 15 %

Percentage of time Danny went swimming once a week = 35 %

Percentage of time Danny doesn't go swimming at all in a given week = 50%

The expected value is calculated by multiplying each of the possible outcomes by the likelihood each outcome will occur and then summing all of those values.

Hence, based on the data given in the question, we can write,

Expected value n how many times Danny will go to swimming in a week = 15 %*2 + 35 % * 1 + 50 % *0 = 0.3 + 0.35 + 0 = 0.65

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Answer:

Hope it helps you

Step-by-step explanation:

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

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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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

The graph of the linear function t(m) = -0.2m + 6 is given at the end of the answer.

A linear function, in slope-intercept format, is modeled according to the following rule:

y = mx + b

In which:

In this problem, the function is defined by:

t(m) = -0.2m + 6.

Hence:

To graph the function, we have to consider the constraint that the time cannot be negative, hence the domain is:

t ≥ 0.

Thus, the graph is given by the image at the end of the answer.

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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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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:

The measure of the angles for the given parallel lines are-

For the given question;

The set of parallel lines are given;

Thus,

∠1 + 80 = 180 (linear pair)

∠1 = 100°

Now, two set of parallel line form a parallelogram.

Thus, in parallelogram opposite angles are equal.

∠1 = °∠3 = 100°

So, ∠3 = 100°

And, ∠2 = 80° (opposite angle of 80)

Thus, the measure of the angles are calculated.

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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

Solution:

Given that a livestock company reports that the mean weight of a group of young steers is 1123 pounds with a standard deviation of 84 pounds, this implies that

A) Percentage of steers that weigh over 1300 pounds.

Step 1: Evaluate the z score value.

The z score value is expressed as

In this case, x equals 1300.

Thus, the z score value is evaluated as

Step 2: Evaluate the probability that the steer would weigh over 1300 pounds.

Using the normal distribution table, we have

thus,

The percentage of young steers that weigh over 1300 pounds is thus evaluated as

B) Percentage of steers that have weights under 1050 pounds.

Step 1: Evaluate the z score value.

Thus, we have

Step 2: Evaluate the probability that the steer would have weights under 1050 pounds.

Using the normal distribution table, we have

thus,

Thus, the percentage of young steers that would have weight under 1050 pounds is evaluated as

C) Percentage of young steers that weigh between 1000 and 1200 pounds.

Step 1: Evaluate the z score value.

Step 2: Evaluate the probability that the steer would weigh between 1000 and 1200 pounds.

Using the normal distribution table, we have

thus, we have

1) Alternate interior angles

2) Corresponding angles

3) Alternate exterior angles

4) Same-side interior angles

5) Vertical angles (angles opposite of each other)

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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Given:

The given expression is,

Required:

To select the equivalent expression.

Explanation:

From a total of 8 books, she has a choice of 2 in 28 different ways.

When things are of diverse kinds, the term "permutation" is used to describe the various arrangements that could be made. Combination, meanwhile, is the quantity of smaller groups or sets that can be created from the components of a bigger set.

The member must select 2 books from a group of 8 books in the scenario that is provided. It is not important what sequence you select your books in. If a member chooses books A and B or books B and A, for instance, she is choosing the same books from the list of available titles (A,B,C,D,E,F,G, and H). By extension, this is a problem of combinations since the order of the selections is irrelevant in this situation.

Eight books, two at a time, must be combined to produce

The general formula of combination is :

[tex]nC_{r} = \frac{n!}{r!(n-r)!}[/tex]

Using the values of n=8 and r=2, we get:

[tex]8C_{2}[/tex] = [tex]\frac{8!}{2!(8-2)!}[/tex]

=28

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[tex]x^2=16\\\sqrt{x^2}=\sqrt{16}\\x=\lm+/-4[/tex]

x = 4, x = -4

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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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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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:

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 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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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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La maxima velocidad lineal de la masa con la que se puede girar la masa es igual a 40 newtons.

En este problema tenemos el caso de una masa (m), en kilogramos, conectada a una cuerda y que experimenta un movimiento circular uniforme, en donde la partícula describe un movimiento a velocidad lineal constante (v), en metros por segundo, debido a una aceleración radial que está en la forma de tensión (T), en newtons, a través de la cuerda. En consecuencia, la velocidad máxima permitida es determinada a partir de las leyes de Newton:

T = m · (v² / R)

Donde:

Si sabemos que m = 2 kg, R = 5 m y T = 40 N, entonces la maxima velocidad lineal permitida es:

40 N = (2 kg) · v² / (5 m)

v = 10 m / s

La maxima velocidad lineal permitida es igual a 10 metros por segundo.

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The rate of change is      [tex]\frac{1}{2\sqrt{x} }[/tex]

The link between one quantity changing in respect to another is given by the rate of change formula.can be used to calculate the rate of change from y coordinates to x coordinates (x2 - x1 ). The rate of change m for a linear function is written as y=mx+b in the slope-intercept form for a line, whereas the rate of change for a function is written as (f(b)-f(a))/b-a. It is said that the rate at which one quantity changes in relation to another is known as the rate of change function. The amount of change in one item is simply divided by the comparable amount of change in another when calculating the rate of change.

Given that : The function f (x)=[tex]\sqrt{x}[/tex]

f (x)=[tex]\sqrt{x}[/tex]

[tex]f^{'} x = \frac{1}{2\sqrt{x} }[/tex]

The rate of change is      [tex]\frac{1}{2\sqrt{x} }[/tex]

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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.

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

A statement of order that shows the relation of the in-town speed limit to the highway speed limit is that the in-town speed limit is less than or equal to 30 and the highway speed limit is less than or equal to 60.

A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numbers (numerical values) that are placed at equal intervals along its length.

In Mathematics, these four rules are generally used to write an inequality:

Now, we would apply the aforementioned inequality rules to write the solution to the compound inequality shown in the graph above:

30 ≤ x ≤ 60.

In conclusion, x represent the speed limit for in-town and highway.

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