Write the equation of a line passing through the points (5,5) and (8,11).
1. y = 2x + 5
2. y = 1/3 x + 7
3. y = 2x - 5
4. y = -2x + 15

Events, of randomly drawing a King OR a card with an even number describe by a) Mutually Exclusive.

The events of randomly drawing a King and drawing a card with an even number are mutually exclusive. This means that the two events cannot occur at the same time.

In a standard deck of 52 playing cards, there are no Kings that have an even number.

Therefore, if you draw a King, you cannot draw a card with an even number, and vice versa.

The occurrence of one event excludes the possibility of the other event happening.

It is important to note that mutually exclusive events cannot be both independent and conditional. If two events are mutually exclusive, they cannot occur together, making them dependent on each other in terms of their outcomes.

The correct option is (a) Mutually Exclusive.

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Using the given percentage we can see that there are 78 filled pages.

We know that there are 800 cards and each page holds 8 cards, then the number of pages is:

N = 800/8 = 100

And we know that 22% of the album is empty, then 78% (the complement) of the album is filled, this means that the number of filled pages is given by the formula below.

F = 100*(78%/100%) = 100*0.78 = 78

We divide the percentage by 100% to make it a decimal number, so we can use it in the operation.

There are 78 filled pages in the album.

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The instantaneous velocity is v(t) = 3t² - 30t

To find the velocity function, we need to take the derivative of the position function with respect to time.

The velocity function represents the rate of change of position with respect to time. Let's find the derivative of the position function step by step:

Given: s(t) = t³ - 15t² + 631

Take the derivative of each term with respect to time (t):

  s'(t) = d/dt(t³) - d/dt(15t²) + d/dt(631)

Apply the power rule of differentiation:

  Recall that the power rule states that d/dx(x^n) = nx^(n-1).

  s'(t) = 3t² - 30t + 0

Simplify the derivative:

  s'(t) = 3t² - 30t

The velocity function, v(t), is given by the derivative of the position function. Therefore, the velocity function for the given position function s(t) = t³ - 15t² + 631 is:

v(t) = 3t² - 30t

This represents the instantaneous velocity of the crazy cat at any given time t between 0 and 8 seconds.

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The exponent of 3 in the simplified expression is -3.

The expression you've provided is \((3^{10)} / (3^5 * 3^8)\).

This can be simplified by using the properties of exponents, particularly the rule that says when you divide with the same base, you subtract the exponents.

Moreover, if you have a common base and want to multiply, you simply sum the corresponding exponents.

Thus, it is possible to alter your wording into the following form:

\(3^(10) / 3^{(5+8)\)

Then, this simplifies to:

\(3^{(10)} / 3^{(13)}\)

Now you subtract the exponents:

= \(3^{(10-13)\)

= \(3^{(-3)\)

So the exponent of 3 in the simplified expression is -3.

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Answer:

x=55°

Step-by-step explanation:

x=90-35

x=55°

(because its x+35=90°)

Answer:

The angle of x equals to be 45 degrees.

Step-by-step explanation:

Since the angle is a right angle that equals to 90. The you subtract 90 by your second angle, 35. 90 - 35 = 45

The answer is systematic

Here, at first, a house is randomly selected and then every eighth house in the neighbourhood was interviewed. So, after selecting the starting point, the interviewer uses a sampling interval of 8 and interviews accordingly.

Which is the concept of linear systematic sampling. So, the answer is Systematic.

What is Linear systematic sampling ?

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The population of interest in this study is the youth population aged 15-24 years in British Columbia.

b) The sampling frame in this study is the list of colleges and high schools that were visited by the police department.

c) The bias in this survey is called social desirability bias.

Many students who have used cannabis may be afraid or hesitant to admit it to a uniformed police officer due to social stigma, fear of legal consequences, or other reasons.

This can lead to underreporting or inaccurate reporting of cannabis use.

d) The bias that can result from the sampling frame used is known as selection bias.

The sample of students selected may not be representative of the entire youth population in British Columbia.

For example, if certain schools or colleges were excluded from the sampling frame, it may not provide a comprehensive representation of all youth in the province.

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Complete question :

The line plot shows the weights of packages of meat that members of a club bought. The meat will be mixed with vegetables to make stew for a club dinner. Each serving of the stew contains 1/4 pound of meat. How many servings of the stew can the club make?

Answer:

36 servings

Step-by-step explanation:

From the plot ; we take the sum of total weight of meat packages :

(5/8 * 2) + 6/8 + 1 + (9/8 * 3) + 10/8 + 11/8

10/8 + 6/8 + 8/8 + 27/8 + 10/8 + 11/8 = 72 / 8 = 9 meat packages

Each serving of meat = 1/4

Number of servings the club can make :

Total meat package / pound of meat per serving

(9 ÷ 1/4)

9 * 4/1

= 36 servings

Answer:

36 hope this help

Step-by-step explanation:

he required solution is \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

where \(c_1,c_2,c_3\) and \(c_4\) are constants.

Let’s assume the general solution of the given differential equation is,

y=e^{mx}

By taking the derivative of this equation, we get

\(\frac{dy}{dx} = me^{mx}\\\frac{d^2y}{dx^2} = m^2e^{mx}\\\frac{d^3y}{dx^3} = m^3e^{mx}\\\frac{d^4y}{dx^4} = m^4e^{mx}\\\)

Now substitute these values in the given differential equation.

\(\frac{d^4y}{dx^4}-2\frac{d^2y}{dx^2}-8y\\=0m^4e^{mx}-2m^2e^{mx}-8e^{mx}\\=0e^{mx}(m^4-2m^2-8)=0\)

Therefore, \(m^4-2m^2-8=0\)

\((m^2-4)(m^2+2)=0\)

Therefore, the roots are, \(m = ±\sqrt{2} and m=±2\)

By applying the formula for the general solution of a differential equation, we get

General solution is, \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

Hence, the required solution is \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

where \(c_1,c_2,c_3\) and \(c_4\) are constants.

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The answer is choice 1 because when you divide 2 numbers with the same base and different exponents you subtract the second exponent from the first.

p^-m / p^-n = p^(-m - (-n))

CHOICE 1

Hope this helps

There were 360 students surveyed who liked exactly one of the three types of music means that out of the total number of students surveyed, 360 of them expressed a preference for only one of the three music types.

To find the number of students who liked exactly one of the three types of music, we need to subtract the students who liked two or three types of music from the total number of students who liked each individual type of music.

Let's define:

R = Number of students who like rock

C = Number of students who like country

J = Number of students who like jazz

Given the information from the survey:

R = 204

C = 164

J = 129

We also know the following intersections:

R ∩ C = 24

R ∩ J = 29

C ∩ J = 29

R ∩ C ∩ J = 9

To find the number of students who liked exactly one type of music, we can use the principle of inclusion-exclusion.

Number of students who liked exactly one type of music =

(R - (R ∩ C) - (R ∩ J) + (R ∩ C ∩ J)) +

(C - (R ∩ C) - (C ∩ J) + (R ∩ C ∩ J)) +

(J - (R ∩ J) - (C ∩ J) + (R ∩ C ∩ J))

Plugging in the given values:

Number of students who liked exactly one type of music =

(204 - 24 - 29 + 9) + (164 - 24 - 29 + 9) + (129 - 29 - 29 + 9)

= (160) + (120) + (80)

= 360

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Answer:

x=3

Step-by-step explanation:

The steps are in the picture below.

Answer:

8 rectangles

Step-by-step explanation:

I just folded a piece of paper three times and I counted 8 rectangles!

Answer:

8

Step-by-step explanation:

Answer:

the formula for a square pyramid is \(a^{2}\)\(\frac{h}{3}\) so I THINK its B please do not base ur answer from my opinion

Step-by-step explanation:

Answer:

it is b

Step-by-step explanation:

Answer:

\(2\frac{6}{7}\)

Step-by-step explanation:

-5(-4/7)

First:

A negative multiplied by a negative is positive, so we can remove the negative symbols.

5(4/7)

Multiply:

\(\frac{5(4)}{7}\)

20/7

Convert into a mixed number:

2 6/7

Answer:

528,672

Step-by-step explanation:

A=P(1+r)^t

360,000(1+.03)^13 = 528,672.1368

Rounded: 528,672

A measure of central tendency refers to a statistical measure that summarizes or represents the center or typical value of a dataset. It provides a single value that represents the central or average value of the data.

In more detail, option b is the correct answer. A measure of central tendency, such as the mean, median, or mode, allows a reader to summarize a dataset with one datum point. These measures provide information about the typical value or the central position of the data distribution.

The mean is calculated by summing all the values in the dataset and dividing by the number of data points. The median is the middle value when the data is arranged in order, and the mode is the value that appears most frequently in the dataset.

By using a measure of central tendency, readers can gain insight into the overall trend or central value of a dataset without having to examine every individual data point. It simplifies the understanding and interpretation of data by providing a concise summary that represents the central tendency of the data distribution.

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The anti-federalist assumed that using the constitution will increase the oppression of the people by those in power but regardless, the constitution was ratified

The Anti-Federalists were a group of individuals who opposed the ratification of the Constitution. They believed that the Constitution granted too much power to the central government and did not adequately protect the rights of individual states and citizens. They argued that the Constitution should include a bill of rights to safeguard individual liberties and that the government should be more closely modeled after the Articles of Confederation. Additionally, some Anti-Federalists believed that the Constitution would lead to the rise of an aristocracy and the oppression of the common people. Despite their opposition, the Constitution was ultimately ratified in 1788 with the support of Federalists.

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Given statement solution is :-Time cannot be negative in this context, we discard the solution t = -1,  the book will hit the ground after approximately 2.5 seconds.

To find the time when the book hits the ground, we need to determine when the height (h) becomes zero. We can set up the equation and solve for t.

The equation given is:

h = -\(16t^2 + 24t + 40\)

Setting h = 0, we have:

0 = \(-16t^2 + 24t + 40\)

Now we can solve this quadratic equation. There are a few methods to solve quadratic equations, such as factoring, completing the square, or using the quadratic formula. In this case, we'll use the quadratic formula:

t = \((-b ± √(b^2 - 4ac)) / (2a)\)

For our equation, a = -16, b = 24, and c = 40. Plugging these values into the quadratic formula, we get:

t = \((-24 ± √(24^2 - 4*(-16)40)) / (2(-16))\)

t = \((-24 ± √(576 + 2560)) / (-32)\)

t = (-24 ± √3136) / (-32)

t = (-24 ± 56) / (-32)

Now we have two possible solutions:

t = (-24 + 56) / (-32) = 32 / (-32) = -1

t = (-24 - 56) / (-32) = -80 / (-32) = 2.5

Since time cannot be negative in this context, we discard the solution t = -1. Therefore, the book will hit the ground after approximately 2.5 seconds.

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Answer:

smell my feet nnnnnnnnnsdsdsdnnnsdsdnigdsga

Step-by-step explanation:

Answer:

The GCF is 4

Explain:

Answer:

When  x =  -16, y = -1.

Step-by-step explanation:

Let's plug in y = -1 into this equation

-1 = 1/4x + 3

Now, we need to solve the equation for x. To do so, we want x to be by itself on one side of the equation. We will use inverse operations to get the x by itself. First, subtract 3 from either side to under the +3 on the right side of the equation.

-1 - 3 = 1/4x + 3 - 3

-4 = 1/4x

Next, we will divide by 1/4 to undo the *1/4. Dividing by 1/4 is the same as multiplying by 4, so we will multiply each side by 4.

-4 * 4 = 1/4x * 4

-16 = x

bye now

im tyler

The probability that exactly 5 out of the first 12 customers buy a magazine is 0.139.

The probability that exactly 5 out of the first 12 customers buy a magazine assuming his suspicion that 7.5% of his customers buy a magazine is correct is 0.139.

Here's how to solve it:

First, we note that we have a binomial distribution since we are counting the number of "successes" (people buying magazines) out of a fixed number of trials (12 customers).

We can use the formula:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

where

P(X = k) is the probability of getting k successes,

n is the number of trials,

p is the probability of success, and

C(n, k) is the binomial coefficient "n choose k".

We can plug in the values we have:

P(X = 5) = C(12, 5) * 0.075^5 * (1 - 0.075)^(12 - 5)

where

C(12, 5) = 792 is the number of ways to choose 5 out of 12 customers.

Evaluating this expression gives:

P(X = 5)

≈ 0.139

So the probability that exactly 5 out of the first 12 customers buy a magazine is 0.139.

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The sample space can be represented as S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

The sample space for rolling a fair 10-sided die represents all possible outcomes when rolling the die.

In this case, each outcome corresponds to a number that can appear on the face of the die.

Since the die has 10 sides, the numbers 1 to 10 are the possible outcomes.

Therefore, the sample space for rolling a fair 10-sided die can be listed as {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.

Each element in the sample space represents a distinct possibility and covers all the potential results of rolling the die.

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In step 1, y was made the subject of the second equation to get:

y=5x-4

To proceed, the next step is to substitute the expression into the other equation, not the equation we solved for y.

8x+2y=-12

8x+2(5x-4)=-12

8x+10x-8=-12

18x=-12+8

18x=-4

x=-\(\frac{4}{18}\)

x=\(\frac-{2}{9}\)

answer=  the value of x is -2/9

Answer:

$53.22

Step-by-step explanation:

$53.22

Sorry If I am wrong