Events $A$ and $B$ are disjoint. Find $P\left(A\ \text{or}\ B\right)$ when $P(A)=\frac{2}{3}$
and $P\left(B\right)=\frac{1}{5}$
. Express your answer as a fraction in simplest form.

The limit of the series is a finite, nonzero number, the series converges by the ratio test.

We have,

We can use the ratio test to determine whether the series

Σn = 1 (2n +1) 2n/(5n+3) 3n is convergent or divergent.

Using the ratio test, we take the limit as n approaches infinity of the absolute value of the ratio of the (n+1)th term to the nth term:

lim n→∞ |((2(n+1) +1)^(2(n+1))/(5(n+1)+3)^(3(n+1))) / ((2n +1)^(2n)/(5n+3)^(3n))|

Simplifying this expression, we get:

lim n→∞ |(2n+3)^2 (5n+3)^3 / ((5n+8)(2n+1)^2)|

We can further simplify this expression by dividing both the numerator and denominator by n^5, which gives:

lim n→∞ |(2+3/n)^2 (5+3/n)^3 / ((5+8/n)(2+1/n)^2)|

Taking the limit as n approaches infinity, we can see that the leading term in the numerator is (5^n)/(n^5) and the leading term in the denominator is (5^n)/(n^5).

Therefore, the limit evaluates to:

lim n→∞ |(2+3/n)^2 (5+3/n)^3 / ((5+8/n)(2+1/n)^2)| = 25/4

This is a finite number.

Thus,

The limit is a finite, nonzero number, the series converges by the ratio test.

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Answer:

All the sides of the square are equalso the squares are congruent.. Are congruent shapes? Two shapes that are the same size and the same shape are congruent.

hope this helps

mark me brainliest

Step-by-step explanation:

(a) The coefficient of y² is -3x

(b) The constant value of the expression is -4

(c) There are 4 terms in the expression

From the question, we have the following parameters that can be used in our computation:

9y - 3xy² - 4 + x

Consider an expression ax where the variable is x

The coefficient of the variable in the expression is a

Using the above as a guide, we have the following:

The coefficient of y² is -3x

Consider an expression ax + b where the variable is x

The constant of the variable in the expression is b

Using the above as a guide, we have the following:

The constant value of the expression is -4

Consider an expression ax + b where the variable is x

The terms of the variable in the expression are ax and b

Using the above as a guide, we have the following:

There are 4 terms in the expression

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Answer:

can you write these in proper way

A linear inequality that is represented by the graph include the following: C. y > 2/3(x) + 3.

In Mathematics, there are two (2) main rules that are generally used for writing and interpreting an inequality or system of inequalities that are plotted on a graph and these include the following:

here, we have,

The line on a graph should be a solid line when the inequality symbol is (≥ or ≤).

The line on a graph should be a dashed (dotted) line when the inequality symbol is (> or <).

The line on a graph should be shaded above the line when the inequality symbol is (>).

Since the line on this graph was shaded above the line and it passes through the point (0, 3), it ultimately implies that 3 is part of its solution and as such, it is represented by this inequality equation:

y > 2x/3 + 3.

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36.99. It says total and out of all those numbers I just added.

Answer:

36.99

Step-by-step explanation:

The acceleration of gravity on the surface of planet Nos'kere is about 21.16 m/s².

Since we know that,

The formula for the period of a pendulum is,

⇒ T = 2π√(L/g)

where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity.

We can rearrange this formula to solve for g,

⇒ g = 4π²L/T²

Substituting the given values, we get,

⇒ g = 4π²(3.4 m)/(2.9 s)²

⇒ g ≈ 21.16 m/s²

Therefore,

On the surface of the planet Nos'kere, gravity accelerates at a rate of around 21.16 m/s².

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In a study of happiness 100 people rate the level of happiness on 1 to 10 scale; the kind of variable is this "quantitative".

The numbers you enter when collecting quantitative data represent real quantities which can be added, subtracted, divided, and so on. There are two kinds for quantitative variables: discrete variables and continuous variables.

Some characteristics of variables are-

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Answer:

a = 18

Step-by-step explanation:

3(x+6)-x = 2x + a

Distribute

3x +18 -x = 2x+a

2x +18 = 2x+a

Subtract 2x from each side

18 = a

Answer:

Step-by-step explanation:

Answer:

3

Step-by-step explanation: there is 3 lolllllllllllllllllllllllllllllllllllllll

Step-by-step explanation:

A o option

-(-45)

hope it helps

Answer:

x+6=y and 3x=12

Step-by-step explanation:

Let x be the distance traveled by Bryan and let y be the distance traveled by Sam then the first equation would be:

x+6=y (x plus 6 is equal to y, Bryan's distance plus 6 is equal to Sam's distance) and the second one is:

3x=12 (3 times x is 12, 3 times the distance travelled by Bryan is 12)

So our statements/equations are:

x+6=y and

3x=12 (we dont write this as x=4 as it asks us to give the statements we got from the information given, we only start simplifying once it tells us to solve)

Answer: \(h=8.33\ cm\)

Step-by-step explanation:

Given

The length of a cuboid is \(l=15\ cm\)

breadth is \(b=12\ cm\)

Total surface area is \(S.A.=900\ cm^2\)

Surface area is given by \(2(lb+hl+bh)\)

Insert the values

\(\Rightarrow 900=2(15\times 12+15h+12h)\\\Rightarrow 450=225+27h\\\Rightarrow 225=27h\\\Rightarrow h=8.33\ cm\)

Answer:

10

Step-by-step explanation:

plug in the variable

2 (6 + 4) - 10

distribute

12 + 8 - 10

add

20 - 10

subtract

10

Answer: (x+1)(x+4) is the solution

Step-by-step explanation:

Use the sum-product pattern

Common factor from the two pairs

Rewrite in factored form

Answer:

(x+1)(x+4)

Step-by-step explanation:

x²+5x+4

x²+4x+x+4

x(x+4)+1(x+4)

(x+1)(x+4)

Answer:

slope = - 14

Step-by-step explanation:

calculate the slope m using the slope formula

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

with (x₁, y₁ ) = (- 92, 21 ) and (x₂, y₂ ) = (- 93, 35 )

m = \(\frac{35-21}{-93-(-92)}\) = \(\frac{14}{-93+92}\) = \(\frac{14}{-1}\) = - 14

Answer:

-14

Step-by-step explanation:

In this type of question we solve the multiplication first then the subtraction.

3-4*3-5=

3-12-5=

= -14

Hope this helps!

(pls mark as brainiest) :)

The number of rides is the dependent variable, while the total cost is the independent variable.

In mathematical modeling, statistical modeling, and experimental sciences, there are dependent and independent variables. Dependent variables get their name because, during an experiment, their values are investigated under the presumption or requirement that they are dependent on the values of other variables according to some law or rule.

The variable that the researcher modifies or manipulates in an experiment is known as the independent variable. The measured reaction is the dependent variable. The dependent variable is dependent on the change in the independent variable, to put it another way.

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Using proportions, it is found that the amounts are given as follows:

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

James' amount decreased by 15%, that is, it is multiplied by 0.85, hence:

0.85 x 22 = 18.7 super balls.

Becky's amount is increased by 3%, that is, 103% of the original amount, which is multiplied by 1.03, hence:

1.03 x 1645 = 1694.35.

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1. An event that is likely to happen, but not certain, for the number Kenisha calls is that it is a prime number. While there are several prime numbers between 1 and 75, it is not guaranteed that the number she calls will be prime. However, given the range of numbers, the probability of calling a prime number is relatively high.

2. An event that is unlikely to happen, but not impossible, for the number Kenisha calls is that it is a perfect square. Perfect squares are numbers that can be expressed as the square of an integer. In the range of 1 to 75, there are only a few perfect squares, so the chances of calling one as the bingo number are relatively low, but not impossible.

3. An event that is certain to happen for the number Kenisha calls is that it will be an integer. Since the game is played with whole numbers from 1 to 75, the number called will always be an integer, as it represents a specific whole number in the given range.

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

The solution is given below.

1. An event that is likely to happen, but not certain, for the number Kenisha calls is that it will be an odd number. Since there are 75 numbers in total and half of them are odd, there is a higher probability that the number called will be odd.

2. An event that is unlikely to happen, but not impossible, for the number Kenisha calls is that it will be a perfect square. There are only a few perfect square numbers between 1 and 75, so the chances of calling a perfect square number are lower compared to other numbers.

3. An event that is certain to happen for the number Kenisha calls is that it will be a number between 1 and 75. Since the numbers in the game range from 1 to 75, any number called by Kenisha will definitely fall within this range.

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Given information: 461 households were surveyed, 318 households have internet fiber cable, and we need to find out the sample proportion of households without fiber cable.

To find the sample proportion of households without fiber cable, we need to subtract the households with fiber cable from the total surveyed households and divide the result by the total surveyed households.

Total households surveyed - households with fiber cable = households without fiber cable

461 - 318 = 143

Now, we can calculate the sample proportion of households without fiber cable by dividing the households without fiber cable by the total surveyed households.

Sample proportion of households without fiber cable = households without fiber cable / total surveyed households

=> 143 / 461 = 0.31 (rounded to 3 decimal places)

Therefore, the sample proportion of households without fiber cable is 0.31 (rounded to 3 decimal places).

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Answer:

2000 percent.

Step-by-step explanation:

First we find the calculation of the equation, this will be equal to 100 percent.

1/8 * 16 = 2

Next we divide 2 by 100, to find how much is 1 percent.

2 / 100 = 0.02

Finally, we divide 40 by 0.02 to find out the total percent it it made up of.

40 / 0.02 = 2000

The final answer is 2000 percent.

this is just a quick additon to "24mhomme" good posting above

\(\cfrac{1}{8}\cdot 16 \implies \cfrac{16}{8}\implies 2 \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{ccll} Amount&\%\\ \cline{1-2} 2 & 100\\ 40& x \end{array} \implies \cfrac{2}{40}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{ 1 }{ 20 } ~~=~~ \cfrac{ 100 }{ x }\implies x=\stackrel{ \% }{2000}\)

For the function f(x), the practical domain will be [0 min, 165 min]

We define the practical domain as the section of the domain that has practical meaning.

In this case, the part of the domain that we care about is only when the rock climber is on the mountain.

After that, the function does not work anymore, then the practical domain will be [0 min, 165 min]

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The sample space is 4845.Therefore, option C is correct.

Given: The mayor of a city randomly chooses 4 of the 20 wards in her city and surveys all the voters in those selected wards.

Solution: We have a sample size of 4 wards out of a total of 20 wards. The mayor has chosen all the voters in those 4 wards. So, the sampling method used here is stratified sampling as the mayor chose the voters of specific 4 wards.

Sample space = Total number of ways to select 4 wards out of 20 wards= C(20,4) = 20!/(4!(20 - 4)!) = 4845

Hence, the sample space is 4845.Therefore, option C is correct.

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Answer:

Inequality:  125x + 55 < 600

Solution of inequality: x < 4.36

Final answer: 4 hours

Step-by-step explanation:

Let the number of hours be x.

1 hour costs $125.

2 hours cost $125 × 2

3 hours cost $125 × 3

x hours cost $125 × x or simple 125x.

The assistant costs $55.

The total cost is 125x + 55.

The cost must be under $600, so

125x + 55 < 600

Subtract 55 from both sides.

125x < 545

Divide both sides by 125.

x < 4.36

In theory he can be hired for any amount of hours under 4.36 hours, but he probably works only full hours, so you need to round down to 4 hours.

4 hours

The underlined part of the sentence "the lecture lasted for _two hours_" is known as a prepositional phrase. Understanding different sentence components enhances our grasp of grammar and sentence structure.

In sentence analysis, identifying the various parts of a sentence is crucial to understanding its structure and meaning. Let's explore the underlined part of the sentence and determine its classification.

The underlined part, "for two hours," functions as a prepositional phrase. A prepositional phrase consists of a preposition (in this case, "for") followed by a noun phrase (here, "two hours"). It provides additional information about time, location, direction, or other relationships within the sentence.

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Answer:

A chemist mixes a 10% saline solution with a 20% saline solution to make 500 milliliters of a 16% saline solution.

Step-by-step explanation:

Answer: 7. 35, 8. 42.50

Step-by-step explanation:

7. First, convert 4 3/8 to an improper fractoin.

4 3/8 = 35/8

Now divide 35/8 by 1/8 and you get 35.

8. Each ounce increased 5 dollars, so 8.5 ounces increased 8.5*5 dollars = $42.50