What is the slope of the line passing through (1, 2) and (3,8)?

Answer:

(0, -3, 2)

(0, -3, 0)

(-4, 0, 2)

Corner where 2 or more edges meet.

If the length of the diagonals are equal, then the vertices of a rhombus will form a square. Formula used: We will use the formula of distance between two points which is given

\(\[d = \sqrt {{{({x_2} - {x_1})}^2} + {{({y_2} - {y_1})}^2}} \], where \[({x_1},{y_1})\] and \[({x_2},{y_2})\]\)

be the two points.

To find the 75th percentile of X is A. 1.00, we need to find the value of x such that the probability of X being less than or equal to x is 0.75.

Let f(x) be the density function of X. We know that f(x) is proportional to (1+x^2)^(-1), which means we can write:
f(x) = k(1+x^2)^(-1)
where k is a constant of proportionality. To find k, we use the fact that the total area under the density function is 1:
∫f(x)dx = 1
Integrating both sides, we get:
k∫(1+x^2)^(-1)dx = 1
The integral on the left-hand side can be evaluated using a substitution u = x^2 + 1:
k∫(1+x^2)^(-1)dx = k∫u^(-1/2)du = 2k√(u)
Substituting back for u and setting the integral equal to 1, we get:
2k∫(1+x^2)^(-1/2)dx = 1
Using a trigonometric substitution x = tan(t), we can evaluate the integral on the left-hand side:
2k∫(1+x^2)^(-1/2)dx = 2k∫sec(t)dt = 2kln|sec(t) + tan(t)|
Substituting back for x and simplifying, we get:
2kln|1 + x^2|^(-1/2) = 1
Solving for k, we get:
k = √(2/π)
Now we can write the density function of X as:
f(x) = (√(2/π))(1+x^2)^(-1)
To find the 75th percentile of X, we need to solve the equation:
∫(-∞, x) (√(2/π))(1+t^2)^(-1) dt = 0.75
This integral does not have a closed-form solution, so we need to use numerical methods to approximate the value of x. One way to do this is to use a computer program or a graphing calculator that has a built-in function for finding percentiles of a distribution. Using a graphing calculator, we can enter the function y = (√(2/π))(1+x^2)^(-1) and use the "invNorm" function to find the x-value corresponding to the 75th percentile (which is the same as the z-score for a standard normal distribution).
Doing this, we get:
invNorm(0.75) ≈ 0.6745
Therefore, the 75th percentile of X is approximately:
x = tan(0.6745) ≈ 0.835

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Answer:

D

Step-by-step explanation:

To solve this question we can use the area formula for an octagon.

It is as follows:

A=2(1+√2)a^2

where "A" is the total area and "a" is the length of a side.

Plug in our side length a=10.4

A=2(1+√2)10.4^2

≈522.24268

Alternatively, you can split the octagon into 8 equal triangles.

The base of each triangle would be 10.4 and the height would be 12.5 since opposite sides are 25 feet apart. (25/2)

The area of a triangle would then be:

A=1/2bh

where "b" is base and "h" is height

A=125*10.4*1/2

=65

Since there are 8 we multiply that by 8 for the area of an octagon

65*8=520

The area of the octagon base is 520 square feet.

I'll use this value to do my calculations as it is more exact.

Now, using this area, we need to find the volume of the pool we are meant to fill.

To do this, we simply multiply the area of the base by the height.

520*3=1560

Now, we know that the volume of the pool is 1560 cubic feet.

Each cubic foot takes 7.5 gallons to fill.

1560*7.5=11700

Therefore, the pool takes 11700 gallons of water to fill.

Answer:

$15400

Step-by-step explanation:

1 year = 12 month

10 years = 120 months

12% = month

1440% = 120 months

1440% = 14.4

Take 1000 times 14.4 = $14400

So, we add the two numbers

1000 + 14400 = $15400

So, $15400 will be in the account at the end of 10 years.

Answer:

A4t = m - R²

A=m/4t-R²/4t or (m-R²)/4t or 1/4 +(m-R²)/t

Answer:

11

Step-by-step explanation:

On a fair six-sided die, there is a \(\frac{1}{6}\) chance of rolling each number. Therefore, for each of the rolls, the number 6 has a \(\frac{1}{6}\) chance of being rolled. This can be read as for every 6 rolls, one 6 should appear.

Since the die is being rolled 66 times, we have the following proportion:

\(\frac{1}{6}=\frac{x}{66}\), where \(x\) is the theoretical number of times a roll of "6" occurs.

Multiply both sides by 66:

\(x=\frac{1}{6}\cdot 66=\boxed{11}\)

Answer:

4. rise

match the following definition with the correct term:

the vertical distance between two points on a line

1. run

2. rate of run

3. slope

4. rise

Rounding up gives us a sample size of 7. Thus, we would require a sample size of 7 for 99 percent of the samples' means to be within 10 µmol/L of the population mean. Therefore, option B is correct.

The distribution of albumin levels in cerebrospinal fluid among adults in the US is roughly symmetric with a mean of 29.5 mg/100 ml and a standard deviation of 9.25 mg/100 ml. If repeated samples of size 20 are taken from this population and the mean is calculated for each, how large should the sample be for 99% of their means to lie within 10 µmol/L of the population mean.Solution:The mean of the population is 29.5 mg/100 ml and the standard deviation is 9.25 mg/100 ml, and we're looking for the number of samples required for 99 percent of the samples' means to be within 10 µmol/L of the population mean. The sample size formula is used for this problem.The sample size formula is:$$n

=\left(\d fraction{z*\sigma}{E}\right)^2$$Where, n is the sample size z is the level of significanceσ is the population standard deviation E is the margin of error The formula for margin of error is:E

= z*σ/√nWe require that the sample mean lies within 10 µmol/L of the population mean with a probability of 0.99.Using a standard normal distribution table, we find that the value of z for a 0.995 probability is 2.58.Accordingly, we have:E

= 10 µmol/Lz

= 2.58σ

= 9.25 mg/100 ml The formula for margin of error is:E

= z*σ/√n Solving for n by plugging in the above values we have:$$n

=\left(\dfraction{z*\sigma}{E}\right)^2$$$$n

=\left(\d fraction{2.58*9.25}{10}\right)^2$$$$n

=6.31$$.Rounding up gives us a sample size of 7. Thus, we would require a sample size of 7 for 99 percent of the samples' means to be within 10 µmol/L of the population mean. Therefore, option B is correct.

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Answer:

Solutions: (-5, 1), (-10, 1), (-10, 5)

Non-solutions: (0, 4), (5, 4), (10, 4)

Step-by-step explanation:

Solutions are in the shaded area. Non-solutions are in the non-shaded area and on the dashed line.

Solutions: (-5, 1), (-10, 1), (-10, 5)

Non-solutions: (0, 4), (5, 4), (10, 4)

Answer:

b ÷ 2 or b/2

Step-by-step explanation:

Quotient means division which is represented by "÷" or "/".

b ÷ 2 or b/2

Best of Luck!

In 120 different variations of this model car are possible.

One of the four fundamental mathematical operations, along with addition, subtraction, and division, is multiplication. Multiply in mathematics refers to the continual addition of sets of identical size. Let's use the ice creams as a multiplication example to help us comprehend. There are two such groupings, and each group has ice cream.

Calculating the sum of two numbers multiplied together is the process of multiplication. Simple tests in addition, subtraction, multiplication, and division will be given. 2. a noncount noun The process or occurrence of something of a certain kind multiplying occurs when their quantity or number increases.

Given,

There are five different ways to choose a car's color.

3 different car transmission selection options are available.

There are four different interior automobile selection options.

There are two different ways to pick a car's engine.

The potential number of car variations is thus:

Multiplying:

5 × 3 × 4× 2

120

In 120 different variations of this model car are possible.

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Answer:

pro video is my work and my

Step-by-step explanation:

vision is pro

The number of months Ben can be a member of the fitness club is 7 months .

In the question ,

it is given that Ben wants to join a fitness club ,

initial membership fees for fitness club is = $49.50

monthly fees for fitness club = $17.50

let the number of months be \(=\) x

the total fees that Ben paid = $172

So ,according to the question

the equation to represent the situation is  

49.50 + 17.50x = 172

17.50x = 172 - 49.50

17.50x = 122.5

x = 122.5/17.50

x = 7

Therefore , Ben can be a member of fitness club for 7 months .

The given question is incomplete , the complete question is

Ben wants to join a fitness club. The fitness club charges an initial membership fee of $49.50 and a monthly fee of $17.50 , Ben has $172 to spend on a membership at the fitness club . what is the number of months ben can be a member of the fitness club ?

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Answer:

U is Union

Step-by-step explanation:

In math, the symbol U represents the union of two sets.

Answer: $14708.14

Step-by-step explanation:

Amount = initial balance(1 + annual rate/periods per year)^(periods per year*years)

A = 6000(1+0.03/4)^4*30

A = 6000(1.0075)^120

A = 6000(2.451)

A = 14708.14

Hope this helps!

Answer: 26/12

Step-by-step explanation:

26 goes on top and 12 on bottom because it says “spotted fish to plain fish” telling you which comes first and which one second

Answer:

13:6

Step-by-step explanation:

To simplify the ratio 26:12, we find the greatest common divisor of 26 and 12, and then we divide 26 and 12 by the greatest common divisor.

The greatest common divisor that you can use to simplify 26:12 is 2. Which means the answer to ratio 26:12 simplified is:

13:6

have a good day c:

If altogether they spent a total of $71,  and a cap cost $5, then the price of a t-shirt is $8. Option A is correct

From the question, we are told that all caps cost $5 each

Let the cost of each shirt be x:

If Andy bought a t-shirt and a cap for each of his six friends, there will be 6 shirts and 6 caps

If Bob returned two caps and two t-shirts, there will be 4 caps and 4 shirts left

If Carl bought three t-shirts and returned a cap, the number of caps remaining will be 3 caps and the number of shirts remaining will be 7 shirts

If they spent a total of $71, this means;

3(5) + 7x = 71

15 + 7x = 71

7x = 71 - 15

7x = 56

x = 56/7

x = 8

This shows that the price of a t-shirt is $8

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Answer:

a = 32

b =  6

Step-by-step explanation:

Givens

a = number of 2 point baskets

b = number of 3 point baskets.

a + b = 38

2a + 3b = 82

Solution

a + b = 38                         (1)

2a + 3b = 82                     (2)

Multiply (1) by 2 and put the result under (2)

2a + 3b = 82

2a + 2b = 76                         Subtract

b = 6

a + b = 38

a + 6 = 38                             Subtract  6 from both sides

a + 6 - 6 = 38 - 6

a = 32

I dont remember that one sorry

Step-by-step explanation:

Answer:

y = 5/12 x + 2

Step-by-step explanation:

We need to find the equation of a line that passes through two given points.

y = mx + b

First, we find the slope.

m = slope = (y2 - y1)/(x2 - x1)

m = (7 - 2)/(12 - 0) = 5/12

Now we have

y = 5/12 x + b

To find the value of b, we use a point for x and y and solve for b.

y = (5/12)x + b

2 = (5/12)(0) + b

b = 2

The equation is

y = 5/12 x + 2

Answer:

The exact value of the given trigonometric expression is undefined.

Step-by-step explanation:

Given trigonometric expression:

\(\dfrac{\cos\left(\dfrac{2 \pi}{3}\right)}{\tan\left(-\dfrac{7 \pi}{4}\right)}+\csc(\pi)\)

To find the exact value of the given  trigonometric expression, begin by finding the exact values of each of the trigonometric functions in the expression

The exact value of cos(2π/3) is:

\(\implies \cos\left(\dfrac{2 \pi}{3}\right)=-\dfrac{1}{2}\)

The exact value of tan(-7π/4) is:

\(\implies \tan\left(-\dfrac{7 \pi}{4}\right)=1\)

Since the cosecant function is the reciprocal of the sine function, the exact value of csc(π) is:

\(\implies \csc (\pi)=\dfrac{1}{\sin(\pi)}=\dfrac{1}{0}=\textsf{unde\:\!fined}\)

Therefore:

\(\begin{aligned}\implies \dfrac{\cos\left(\dfrac{2 \pi}{3}\right)}{\tan\left(-\dfrac{7 \pi}{4}\right)}+\csc(\pi)&=\dfrac{-\dfrac{1}{2}}{1}+\dfrac{1}{0}\\&=-\dfrac{1}{2}+\dfrac{1}{0}\\\\&=\textsf{unde\:\!fined}\end{aligned}\)

It is true that the indexed variables (members) of an array must be integers.

The indexed variables or members of an array must be integers. This is because arrays are data structures that store elements in a contiguous block of memory, and each element is accessed using an index. Indexing allows us to uniquely identify and retrieve specific elements within the array. In most programming languages, including C, C++, Java, and Python, array indices are integers and must be whole numbers (positive or negative) without any fractions or decimals. Attempting to use non-integer values as indices would result in a compilation error or unexpected behavior.

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The area of the shaded regions is: 44π

Area of a circle where "r" is the radius is determined using the formula: πr².

The figure given has three circles, namely:

The area of the shaded regions = Area of circle A - Area of Circle B + Area of Circle C

Area of Circle A = (π)(8)² = 64π

Area of Circle B = (π)(4)² = 16π

Area of Circle C = (π)(2)² = 4π

Thus:

The area of the shaded regions = 64π - 16π + 4π

The area of the shaded regions = 44π

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Answer:

Figure A and B are still congruent to each other. the only change is the size of the shape.

Step-by-step explanation:

Yes, figure A and figure B similar because even though their side lengths are different, their internal angles are the same.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

Suppose figure A underwent a dilation to produce figure B.

Now, A dilation is a transformation that produces an image that is the same shape as the original, but is a different size

if Dilation factor  N then image Size is multiplied  by  N

if Scale factor  < 1 then image get reduced

if scale factor > 1  then image get enlarged

scale factor = 1 lead to Same size image

Hence, Figure A and figure B similar because even though their side lengths are different, their internal angles are the same.

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Answer:

Step-by-step explanation: 15

Mean means average, add all numbers and divide by amount

Mean= (15+12+14+19+x)/5

        =(60+x)/5

Median means to list numbers in order and pick the middle one

12 14 15 19       x is somewhere in the list in middle

Mode means the number that occurs the most, so 1 of these numbers is repeated

It must be 14 or 15 because the median must be the same as the mean

let's try both

(60+14)/5 =14.8                  (60+15)/15=15

The answer is 15.

The median of the data is M = 15 and the value of x = 15

The median is the value that's exactly in the middle of a data set when it is ordered. It's a measure of central tendency that separates the lowest 50% from the highest 50% of values. The steps for finding the median differ depending on whether you have an odd or an even number of data points

Arrange the data points from smallest to largest.

If the number of data points is odd, the median is the middle data point in the list.

If the number of data points is even, the median is the average of the two middle data points in the list.

Given data ,

The mean is calculated by summing all the numbers and dividing by the total count of numbers. In this case, we have 5 numbers, including x.

Mean = (15 + 12 + 14 + 19 + x) / 5

Since the mean is also equal to the median, we can rearrange the numbers in ascending order:

12, 14, 15, 19, x

The median is the middle number in a sorted list of numbers. In this case, the median is 15.

Since the mode is also equal to the mean and median, and we can see that 15 is the only number that appears more than once in the list, we can conclude that 15 is also the mode.

Setting the mean equal to 15 and solving for x:

15 = (15 + 12 + 14 + 19 + x) / 5

Multiplying both sides by 5 to eliminate the fraction:

75 = 15 + 12 + 14 + 19 + x

Subtracting the known numbers from both sides:

75 - (15 + 12 + 14 + 19) = x

15 = x

Hence , the value of x is 15 and median is 15

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To find the total number of balloons used, we need to add the quantities of white, yellow, blue, and red balloons together.

Let's break down the given information:
- The number of white balloons used is 1243.
- There are 7559 more yellow balloons than white balloons.
- The number of blue balloons is 1138 more than the number of white balloons.
- The number of red balloons is equal to the combined quantity of yellow and blue balloons.

First, let's determine the number of yellow balloons. Since there are 7559 more yellow balloons than white balloons, we add 7559 to the quantity of white balloons:
1243 + 7559 = 8802 yellow balloons.

Next, let's determine the number of blue balloons. As there are 1138 more blue balloons than white balloons, we add 1138 to the quantity of white balloons:
1243 + 1138 = 2381 blue balloons.

Now, let's calculate the number of red balloons. The number of red balloons is equal to the sum of yellow and blue balloons:
8802 + 2381 = 11183 red balloons.

Finally, to find the total number of balloons used, we add the quantities of white, yellow, blue, and red balloons:
1243 + 8802 + 2381 + 11183 = 23609 balloons in total.

In total, 23609 balloons were used for the party. For the party, a total of 23609 balloons were used. The breakdown of balloon colors is as follows: 1243 white balloons, 8802 yellow balloons, 2381 blue balloons, and 11183 red balloons. To arrive at these numbers, we followed the given information step by step. First, we determined the quantity of yellow balloons by adding 7559 (the number of yellow balloons that exceeded the white balloons) to the initial quantity of white balloons (1243). This gave us a total of 8802 yellow balloons. Then, we calculated the quantity of blue balloons by adding 1138 (the number of blue balloons that exceeded the white balloons) to the initial quantity of white balloons (1243). This resulted in 2381 blue balloons. Finally, we found the quantity of red balloons by adding the number of yellow balloons (8802) and the number of blue balloons (2381), resulting in 11183 red balloons. Adding up the quantities of white, yellow, blue, and red balloons, we obtained a total of 23609 balloons for the party.

In conclusion, the total number of balloons used for the party was 23609, consisting of 1243 white balloons, 8802 yellow balloons, 2381 blue balloons, and 11183 red balloons.

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Answer:

No. The input 1.2 has 2 outputs.

Step-by-step explanation:

See attachment for complete question

The first circle represents the domain while the second represents the range of the function.

For a mapping to be a function, it must either be a one to one relationship or a many to one relationship.

One to one, in the sense that; there can be only one entry in the domain points to one entry in the range of the function.

Many to one, in the sense that: there can be multiple domain entries that point to one entry in the range of the function

However, from the attachment it can be seen that an entry in the domain (1.2) points to two entries in the range (6 and 8).

Hence, this does not represent a function.

Answer: Exponents are like the multiplication of a number against itself that many times.

Step-by-step explanation: 2^4=2x2x2x2

3^3=3x3x3

Answer: You use exponents when you want to wright a number that is

being multiplied by itself one or more times. The number 3 is the number being multiplied. The smaller number 2, near the top, means that there are two 3s that are being multiplied.

Step-by-step explanation:

Answer:

115degrees

Step-by-step explanation:

Given the following angles

m<A=(7x+24)°

m<B=(7x-26)°

Since both angles are supplementary, their sum will be 180 degrees

Taking the sum of the angles

m<A + m<B = 180

7x+24 + 7x - 26 = 180

14x - 2 = 180

14x = 180+2

14x = 182

x = 182/14

x = 13

get m<A

m<A = 7x+24

m<A = 7(13) + 24

m<A = 91 + 24

m<A  = 115

Hence the measure of angle m<A is 115degrees