(1,3) and (-3,-5)
write a linear equation

When dealing with the simultaneous occurrence of two events A and B, the probability can be determined by using the probability of one event and the conditional probability of the other event given that the first event has occurred. Both P(A) * P(B|A) and P(B) * P(A|B) are valid ways to calculate this probability.

The concept of probability is fundamental in various fields such as mathematics, statistics, and even in everyday life. The probability of the simultaneous occurrence of two events A and B is a critical concept in probability theory. According to the definition, the probability of A and B occurring at the same time is equal to the probability of A multiplied by the conditional probability of B given that A has occurred. This equation is also valid in the reverse case, where the probability of B and A occurring simultaneously is equal to the probability of B multiplied by the conditional probability of A given that B has occurred.

Understanding the relationship between the probability of two events and their conditional probabilities is essential in predicting the likelihood of these events happening together. In real-life situations, this concept can be used to determine the probability of two events such as the success of a product launch and the corresponding increase in sales. The probability of these two events occurring simultaneously can be predicted by analyzing the probability of the product launch's success and the conditional probability of sales increasing given that the product launch is successful.

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The volume of the pyramid is 30 inches cube.

The base of the pyramid is an equilateral triangle with an area of 6 inches².  The height of the pyramid is 15 inches.

Therefore, the volume of the pyramid can be calculated as follows:

volume of the pyramid = 1 / 3 BH

where

Therefore,

B = 6 inches²

H = 15 inches

Hence,

volume of the pyramid = 1 / 3 × 6 × 15

volume of the pyramid = 1 / 3 × 90

Therefore,

volume of the pyramid = 30 inches³

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Answer:

cylinder = 27π

cone =  9π

sphere = 36π

Step-by-step explanation:

volume of a cylinder = πr²h where r = radius and h = height

height of cylinder (h) = 3 and radius (r) = 3

so volume = π(3)²3

==> simplify exponent

volume = π9(3)

==> multiply 9 and 3

volume of cylinder = 27π

Volume of a cone = πr²(h/3) where r = radius and h = height

height of cone (h) = 3 and radius (r) = 3

so volume = π(3)²(3/3)

==> simplify exponent

volume = π9(3/3)

==> divide 3 by 3

volume = π9(1)

==> multiply 9 and 1

volume of cone = 9π

volume of a sphere = 4/3πr³ where r = radius

radius = 3

so volume = 4/3π(3)³

==> simplify exponent

volume = 4/3π27

==> multiply 4/3 and 27

volume of sphere = 36π

Answer:

60 ?

Step-by-step explanation:

Therefore, the student reads 2,436 pages on Thursday by the given equation.

According to the given information, the student reads three times as many pages on Thursday as on Wednesday. Let's say that the number of pages read on Wednesday is represented by the variable w. Then, we can write the equation:

Pages on Thursday = 3 * Pages on Wednesday

In this equation, we know that Pages on Wednesday = w. So we can substitute w into the equation and get:

Pages on Thursday = 3w

We are also given that on Wednesday, the student read 812 pages. So we can substitute 812 for w and get:

Pages on Thursday = 3 * 812

Simplifying, we get:

Pages on Thursday = 2,436

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Together, it will take the two machines 102 minutes to produce 5100 cans.

To solve this problem, we will use the work formula,

which is Work = Rate × Time.

1. First, let's find the rate of each machine.

New machine rate: 5100 cans / 170 minutes = 30 cans/minute

Old machine rate: 5100 cans / 255 minutes = 20 cans/minute

2. Now, let's find the combined rate of both machines. Combined rate: New machine rate + Old machine rate = 30 cans/minute + 20 cans/minute = 50 cans/minute

3. Finally, we will use the combined rate to find the time it takes for both machines to produce 5100 cans together.

Time = Work / Combined rate = 5100 cans / 50 cans/minute = 102 minutes

Together, it will take the two machines 102 minutes to produce 5100 cans.

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Answer:

hence ,

answer is R.s 360

Step-by-step explanation:

I=PTR/100

=1500×6×4/100

=360

Answer:17/4

Step-by-step explanation:

Solution:

Your problem → 2((1/8)+ 4) - ((3/6)*8)

2((18)+4)-((36)⋅8)

=2⋅(1/8)+4-((36)⋅8)

=2⋅(1+4×8)/8-((36)⋅8)

=2⋅(1+32)/8-((36)⋅8)

=2⋅(33/8)-((36)⋅8)

=2⋅(33/8)-((36)⋅8)

=(33/4)-((36)⋅8)

=(33/4)-(36⋅8)

=(33/4)-(12⋅8)

=(33/4)-12⋅8

=(33/4)-4

=(33/4)-4

=(33-4×4)/4

=(33-16)/4

=17/4

=4.25 (in decimal)

Step-by-step explanation:

To find the percentage, we can use the following formula:

Percentage = (Part / Whole) * 100

So, $131,701.32 is approximately 16.67% of $790,207.91.

In this case, the part is $131,701.32 and the whole is $790,207.91.

Percentage = ($131,701.32 / $790,207.91) * 100

Calculating the value:

Percentage ≈ 0.1667 * 100

Percentage ≈ 16.67%

Therefore, $131,701.32 is approximately 16.67% of $790,207.91.

Alternatively, we can calculate the percentage by dividing the part by the whole and multiplying by 100:

Percentage = ($131,701.32 / $790,207.91) * 100 ≈ 0.1667 * 100 ≈ 16.67%

So, $131,701.32 is approximately 16.67% of $790,207.91.

If you have any further questions, feel free to ask!

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The length of the short side x is 4.5 unit(s), the length of the short side x + 5 is 9.5 unit(s), and the length of the longer side x + 6 is 10.5 unit(s)

The given parameters from the question are:

Solving further, we make use of the Pythagoras theorem of a right triangle

Mathematically, this theorem states that:

Hypotenuse² = Adjacent² + Opposite²

This can also be represented as

Hypotenuse² = Leg² + Other leg²

So, we have

(x + 6)² = x² + (x + 5)²

Evaluate the exponents

x² + 12x + 36 = x² + x² +10x + 25

Evaluate the like terms

x² - 2x - 11 = 0

Solve for x using quadratic formula

\(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)

So, we have

\(x = \frac{2 \pm \sqrt{(-2)^2 - 4 * 1 * -11}}{2 * 1}\)

Evaluate

x = -2.5 and x = 4.5

The value of x cannot be negative

So, we have

x = 4.5

Recall that

So, we have

Hence, the side lengths are 4.5, 9.5 and 10.5 units

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That a full cut round brilliant diamond with a 6.50 mm girdle diameter typically weighs around 1.00 carat.

carat weight is determined by a combination of a diamond's size and density. A diamond's size is measured by its diameter, which is the distance across the widest part of the diamond, known as the girdle. Therefore, a diamond with a larger girdle diameter will generally weigh more than a diamond with a smaller diameter, assuming all other factors are equal.

the weight of a diamond can be estimated based on its girdle diameter, and a full-cut round brilliant diamond with a 6.50 mm girdle diameter typically weighs around 1.00 carat. However, it's important to note that other factors, such as depth, cut, and clarity, can also affect a diamond's weight and value.

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In these options, 0ption D that is, Multicollinearity, is not an assumption of the regression model.

The regression model is a statistical technique used to model the relationship between a dependent variable and one or more independent variables. There are several assumptions associated with the regression model, which should be satisfied for accurate and reliable results.

Option A, Linearity, assumes that there is a linear relationship between the independent variables and the dependent variable. It implies that the relationship can be represented by a straight line.

Option B, Independence, assumes that the observations or data points used in the regression model are independent of each other. This means that the value of one observation does not depend on or influence the value of another observation.

Option C, Homoscedasticity, assumes that the variance of the errors or residuals in the regression model is constant across all levels of the independent variables. It implies that the spread or dispersion of the residuals is consistent.

Option D, Multicollinearity, is not an assumption of the regression model. Multicollinearity refers to a high correlation between independent variables in the regression model, which can cause issues in estimating the individual effects of the independent variables.

Therefore, the correct answer is D) Multicollinearity, as it is not an assumption of the regression model.

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Therefore , the solution of the given problem of surface area comes out to be  240 tiles will cover the floor.

Calculating how much space would be needed to fully cover the outside will reveal its overall size. The surroundings are considered when determining the same surface with a rectangular form. The surface area of something determines its overall dimensions. The amount of edges present in the space between a cuboid's four trapezoidal corners determines how much water it can hold inside.

Here,

Let's first determine how many 6 inch squares are required to span the floor:

=> 80 square feet is the size of the floor (8 feet by 10 feet).

We require the following because each 6-inch square spans an area of => (1/2) ft x (1/2) ft = 1/4 square feet:

=>  80 square feet 1/4 square foot = 320 tiles in a row of 6 inch tiles.

Since a 12 inch square encompasses a space that is 1 foot by 1 foot, we require:

=>  80 square feet /  12 inch square tile,

which equals 80 tiles.

Using 12 inch squares rather than 6 inch squares allows us to save the following amount of tiles:

=> Number of 6 inch tiles - Number of 12 inch tiles = 320 - 80 = 240 tiles

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Answer:

The answer would be c) 8-14m

Answer:

C: 8-14m

Step-by-step explanation:

2(4-7m) = 8 - 14m

find this by distributing the 2 into the parenthesis: 2 * 4 and 2* -7m to get 8 and -7m

Answer:

THE answers to both questions are A

Step-by-step explanation:

Answer:

a for both

Step-by-step explanation:

just move point c on the graph where it tells u to. a translation only affects location

The equation of the line tangent to the curve at the point corresponding to the given value of t.

x = t²-23 and y = t³ + t, at t = 5 is

38x - 5y + 574 = 0

Given, a curve with the points represented by

x = t²-23 and y = t³ + t, at t = 5

we have to find an equation of the line tangent to the curve at the given point on the curve.

so, the given point is (x , y) = (5² - 23 , 5³ + 5)

(x , y) = (2 , 130)

Now, the slope of the curve at that point be,

dy/dx = (3t² + 1)/(2t)

dy/dx = 76/10

Now, on using the slope-intercept form, we get

(y - 130)/(x - 2) = 38/5

5(y - 130) = 38(x - 2)

5y - 650 = 38x - 76

38x - 5y + 574 = 0

Hence, the equation of the line tangent to the curve at the point corresponding to the given value of t.

x = t²-23 and y = t³ + t, at t = 5 is

38x - 5y + 574 = 0

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This is because angles 1 and 4 are vertical angles. Such angles form whenever we have an X shape like this. Vertical angles are always opposite one another and they are always the same measure. The fact that lines k and l are parallel has no relevance (so they could easily be not parallel and the two angles mentioned are still congruent).

The number of bottles of soda purchased are 4 and the number of bottles of juice purchased are 10.

Given,Parker went to the grocery store and bought bottles of soda and bottles of juice.

Each bottle of soda has 50 grams of sugar and each bottle of juice has 10 grams of sugar.

Parker purchased a total of 14 bottles of juice and soda which collectively contain 300 grams of sugar.

we are asked to determine  the number of bottles of soda purchased,x, and the number of bottles of juice purchased, y.

So, the total number of bottles:x+y=14

x=14-y ...eq(1)

As, Each bottle of soda has 50 grams of sugar and each bottle of juice has 10 grams of sugar.

50x+10y=300

Substituting the value of x from eq(1)

⇒ 50(14-y) + 10y = 300

⇒ 700 - 50y + 10y = 300

⇒ -40y = 300 - 700

⇒ -40y =-400

y = 400/40

y = 10

The number of juice bottles = 10.

Now, to get the number of bottle of soda by substituting the value of y  in equation (1):

x = 14-y

x = 14 - 10

x = 4

The number of soda bottles = 4.

Therefore, the number of bottles of soda purchased are 4 and the number of bottles of juice purchased are 10.

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Answer:

First, find any number that divides evenly into 360. Perhaps the number that comes to mind, since it ends in a 0, is 10. Since 10 divides into 360 and the result is 36, you can write 360 = 10*36.

Step-by-step explanation:

Sana makatulong

Step-by-step explanation:

I think option A is the correct answer

Because 48% of 9175 is 4771

The required solution to the given expression x⁵/x² is 8 for x = 2.

Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.

The expression is given as:

x⁵/x²

Substitute the value of x = 2 in the given expression,

(2)⁵/(2)²

Expand the terms in the above expression,

(2 x 2 x 2 x 2 x 2)/(2 x 2)

Apply the multiplication operation,

32/4

Apply the division operation, and we get

8

Thus, the required solution to the given expression is 8.

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Answer:

27/28

Step-by-step explanation:

2/7 - x =5/4

-2/7      -2/7

    x=27/28

Answer:

sorry its 2

Step-by-step explanation:

from 11 to 13 it is 2

Answer:

Sorry, I made a mistake

\(cos53° = \frac{y}{34} \)

cos53°=Adjacent / hypotenuse

Answer:

the answer is 20.46 or 20.5

Step-by-step explanation:

i hope this helps

The distance from the base of the stand to the campfire is 285.6 feet.

The angle of depression of 35 degrees.

Let's denote the distance from the base of the stand to the campfire as "x."

Since we know that,

The values of all trigonometric functions depending on the ratio of sides in a right-angled triangle are defined as trigonometric ratios. The trigonometric ratios of any acute angle are the ratios of the sides of a right-angled triangle with respect to that acute angle.

Using the tangent function, we have:

tan(35 degrees) = opposite/adjacent

tan(35 degrees) = 200/x

To find the value of x, we can rearrange the equation:

x = 200 / tan(35 degrees)

x ≈ 200 / 0.7002

x ≈ 285.6 feet

Therefore, the distance from the base of the stand to the campfire is 285.6 feet.

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Answer:

Step-by-step explanation:

As you can see in the venn diagram that is attached below, The individuals that drink milk are in green, those that drink curd are in yellow, and those that drink both are in light blue. Since the sum of those that drink milk with those that drink curd is 110 and a total of 120 students were surveryed. Then this means that 10 of the students neither drink milk nor curd. These students are represented outside of the venn diagram but within the box of surveyed students.

9514 1404 393

Answer:

  D.  52 ÷ 3 =17, with a remainder of 1

Step-by-step explanation:

There are only two answer choices that make a true statement: A and D. Of these, comparison with the diagram shows that you're looking for a statement where 17 and a remainder of 1 are involved. That's choice D.