Find the slope of the line that passes
through these two points.
(3,2)
(4,6)
У2-У1
X2-X1
m =
m = [?]
Simplify Completely.
Enter

Answer:

im not very good at math so maybe 202.5 but that might be a little high

Step-by-step explanation:

The distance traveled by the particle is 4 units (approximately).

The distance traveled by a particle with position (x, y) as t varies in the given time interval is 4 units (approximately).Given,x = 2 sin^2(t),y = 2 cos^2(t),0 ≤ t ≤ 3To find the distance, we can use the formula for distance between two points in a plane which is as follows: Distance = √(x₂ − x₁)² + (y₂ − y₁)²where (x₁, y₁) and (x₂, y₂) are the initial and final points respectively. Substituting the given values, we get;x₁ = 2 sin²(t₁),y₁ = 2 cos²(t₁),x₂ = 2 sin²(t₂),y₂ = 2 cos²(t₂)∴ Distance = √(2 sin²(t₂) − 2 sin²(t₁))² + (2 cos²(t₂) − 2 cos²(t₁))²= 2 √sin⁴(t₂) − sin⁴(t₁) + cos⁴(t₂) − cos⁴(t₁)Now, we can simplify this equation by using trigonometric identities.Sin²x + cos²x = 1⇒ sin⁴x + cos⁴x + 2(sin²x cos²x) = 1-2 sin²x cos²x⇒ sin⁴x + cos⁴x = 1- 2(sin²x cos²x)Substituting these values in the above equation, we get;Distance = 2√(1-2 sin²(t₁) cos²(t₁)) - 2(sin²(t₂) cos²(t₂))= 2√(cos⁴(t₁) - sin²(t₁) cos²(t₁)) - (cos⁴(t₂) - sin²(t₂) cos²(t₂)))= 2√(cos²(t₁)(1 - sin²(t₁))) - cos²(t₂)(1 - sin²(t₂)))= 2 cos(t₁) sin(t₁) - cos(t₂) sin(t₂)≈ 4 units (approximately).

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We have the following equations to compute the distance traveled by a particle with position (x, y) as t varies in the given time interval:

The content describes the position of a particle as it moves over a specific time interval. The particle's position is defined by two equations: x = 2 sin^2(t) and y = 2 cos^2(t), where t represents time. The given time interval is 0 ≤ t ≤ 3.

To find the distance traveled by the particle in this time interval, we can use the concept of arc length. The arc length formula for a parametric curve is given by:

s = ∫√((dx/dt)^2 + (dy/dt)^2) dt,

where dx/dt and dy/dt represent the derivatives of x and y with respect to t, respectively.

In this case, let's calculate the derivatives:

dx/dt = d(2 sin^2(t))/dt = 4 sin(t) cos(t),

dy/dt = d(2 cos^2(t))/dt = -4 sin(t) cos(t).

Now, substitute these derivatives into the arc length formula and integrate it over the given time interval (0 ≤ t ≤ 3) to find the distance traveled by the particle.

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Given below is the table that has the details of weights and ROIs of three companies:

A (30% weight): 15% ROIB (50% weight): 20% ROIC (20% weight): 10% ROI

Using the formula of weighted average, we get,

WAVG = ((30% * 15%) + (50% * 20%) + (20% * 10%)) / (30% + 50% + 20%)= (4.5% + 10% + 2%) / 100%= 16.5%

Therefore, the correct option is c. 16.5%.

Weighted average is the average of all the values of a given data set, where each value has a different weight, that is different importance assigned to it. It is the product of each value multiplied by its respective weight divided by the sum of all the weights.

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Answer:

$181.25

Step-by-step explanation:

Given data

Amount=  $7250

The amount the parent will pay

=70/100*7250

=0.7*7250

= $5075

Hence the balance left for her to pay is

=7250 -5075

=$2175

Hence the least monthly amount is

=2175/12

=$181.25

adddddddddddddddddddddddddddddddddddddddddddddddddddddd

Answer:

B

Step-by-step explanation:

The color of your eyes doesn't depend on your shoe size, and your shoe size doesn't depend on the color of your eyes. All the other examples have a clear independent and dependent variable.

Answer:450

Step-by-step explanation:

Answer:

2,292/3 = x/12

Step-by-step explanation:

if you were to solve

2,292/3 finds you how many people per hour

and multiply that by 12 to find how many people for 12 hours.

Step-by-step explanation:

\(\frac{2292}{3} =\frac{x}{12}\)  

cross multiply divide.

x=9168

To answer this question we need to remember that:

then:

now we need to remember that:

hence:

Therefore:

and the asnwer is A.

To maintain the original volume of the pond, Talisa needs to increase the radius by a factor of √(30/36), which is approximately 0.9129.

If Talisa hits rock at 30 feet, then the depth of the pond will be limited to 30 feet. Therefore, she needs to modify the radius of the pond to maintain the original volume.

To do this, Talisa can use the formula for the volume of a circular cylinder, which is:

V = πr^2h

where V is the volume of the cylinder, r is the radius, and h is the height (or depth) of the cylinder.

Since Talisa wants to maintain the original volume of the pond, she can set the equation for the new cylinder equal to the equation for the original cylinder, and solve for the new radius, r2:

πr1^2h1 = πr2^2h2

where r1 is the original radius (unknown), h1 is the original height (36 ft), r2 is the new radius (unknown), and h2 is the new height (30 ft).

Simplifying this equation, we can cancel out the π and h1 terms:

r1^2 = r2^2(30/36)

Taking the square root of both sides, we get:

r1 = r2(√(30/36))

Thus, to maintain the original volume of the pond, Talisa needs to increase the radius by a factor of √(30/36), which is approximately 0.9129. In other words, she needs to multiply the original radius by 0.9129 to get the new radius.

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The sum of the infinite geometric series –288 –216 –144 –72 is -1152.

The sum of an infinite number of terms having a constant ratio between successive terms is called as infinite geometric series.

Given series, -288, -216, -144, -72, ...

The sum of the infinite geometric series can be calculated as:

Sum = \(\dfrac{a}{1 -r}\)

Here, 'a' is the first term of the series and 'r' is the common ratio.

a = -288

The common difference can be calculated as:

r = \(\dfrac{(-216)}{(-288)}\)

= \(\dfrac{3}{4}\)

Substitute the values in the sum formula:

Sum = \(\dfrac{-288}{1 - \dfrac{3}{4}}\)

It can be simplified as:

Sum =  -288 \(\times\) 4

             = -1152

So, the sum of the infinite geometric series is -1152.

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Answer:

i believe it is c:50 if you add pi to the radius and of 8

Step-by-step explanation:

Answer:

C) 50 inches

Step-by-step explanation:

C = 2(3.14) x r

C = 6.28 x r

C = 6.28 x 8

C = 50.24

50.24 ≅ 50

Answer:

Step-by-step explanation:

2a.

The remaining 50.4% of the variance has not been accounted for, and it could be due to other factors that are not captured by the two variables being studied.

If the correlation between two variables is .496, it means that 49.6% of the variance has been accounted for. This is because the correlation coefficient measures the strength and direction of the linear relationship between the two variables, and it ranges from -1 to 1.

A correlation of 1 indicates a perfect positive linear relationship, while a correlation of -1 indicates a perfect negative linear relationship. In this case, a correlation of .496 indicates a moderate positive linear relationship.

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based on the confidence interval and the hypothesis test, there is evidence to support the alternative hypothesis that μ is not equal to 16.

In hypothesis testing, the significance level (α) is the probability of rejecting the null hypothesis when it is actually true. In this case, the significance level is 0.05, which means that you are willing to accept a 5% chance of making a Type I error, which is rejecting the null hypothesis when it is true.

Since the 95% confidence interval for μ does not include the value of 16, and the null hypothesis assumes μ = 16, we can conclude that the null hypothesis is unlikely to be true. The confidence interval suggests that the true value of μ is between 10 and 15, which does not overlap with the value of 16. Therefore, we have evidence to reject the null hypothesis and accept the alternative hypothesis that μ is not equal to 16.

In conclusion, based on the 95% confidence interval and the hypothesis test, we would reject the null hypothesis H0: μ = 16 and conclude that there is evidence to support the alternative hypothesis H1: μ ≠ 16.

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The minimum amount of paper that Trevor needs to cover the entire cylindrical can is approximately 565.2 square centimeters, which is closest to 565 square centimeters.

The minimum amount of paper that Trevor needs to cover the entire cylindrical can can be calculated by using the formula for the lateral surface area of a cylinder. Here's how to solve this problem: Given that the can is 18 centimeters tall and has a radius of 5 centimeters. Therefore, the diameter of the can be calculated as follows:

Diameter = 2 x Radius = 2 x 5 = 10 centimeters

The lateral surface area of the cylinder is given by:

Lateral surface area of cylinder = 2πrh

where, π is the mathematical constant pi (3.14)

r is the radius of the base

h is the height of the cylinder

Substituting the given values, we get:

Lateral surface area of cylinder = 2 x 3.14 x 5 x 18 = 565.2 square centimeters (rounded to one decimal place)

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Answer:

B. $35.50/hr and \$6,079.38 in total income

Step-by-step explanation:

Given the following :

Total regular pay earning for the year = $73,840

Let basic salary = b

Overtime = 1.5b

Regular earning per week :

Regular year earning / number of weeks per year

$73840 / 52 = $1420

Regular hours = 40

Regular earning per week = $1420

Regular earning per hour = $1420 / 40

Regular earning per hour = $35.50

Number of overtime hours :

4 hours + 3.5hours = 7.5hours

Overtime pay per hour = 1.5 * regular earning

Overtime pay per hour = 1.5 * 35.5 = $53.25

Total overtime pay = Overtime pay per hour * Number of overtime hours

Total overtime pay = $53.25 * 7.5

Total overtime pay = 399.375

Total pay for the month :

160 regular hours + 7.5 overtime hours

(160 * 35.5) + $399.375

$5,680 + 399.375 = $6,079.375

= $6,079.38

Answer:

The length is 40 units.

Step-by-step explanation:

You need to use a triangle for the base then use the hypotenuse of the base as the base of the diagonal shown in the prism.

\(0.5*8*2=\\4*2=\\16\)

The hypotenuse of the triangle of the base is 16.

\(0.5*16*5=\\8*5=\\40\)

The diagonal shown in the prism is 40 units.

The least distance between P and (50,0) is 25sqrt(10) units.

The line y=3x can be expressed in the form y=mx+b, where m is the slope and b is the y-intercept. In this case, m=3 and b=0, so the equation of the line can be written as y=3x.

Let P=(x,y) be the point on the line y=3x that is closest to the point (50,0). Then the vector from P to (50,0) is orthogonal to the line y=3x. The direction vector of the line y=3x is (1,3), so the direction vector of the vector from P to (50,0) is (-3,1).

Let Q=(50,0) and R=(x,y) be the two points. The vector from Q to R is given by:

v = R - Q = (x-50, y-0) = (x-50, y)

Since the vector v is orthogonal to the direction vector (-3,1) of the line y=3x, their dot product is zero:

v . (-3,1) = 0

Substituting v and the equation y=3x, we get:

(x-50, 3x) . (-3,1) = 0

Expanding the dot product, we get:

-3(x-50) + 3x = 0

Simplifying the equation, we get:

x = 25

Substituting x=25 into the equation y=3x, we get:

y = 75

Therefore, the point P on the line y=3x that is closest to the point (50,0) is (25,75), and the least distance between P and (50,0) is the length of the vector v:

|v| = sqrt((x-50)^2 + y^2) = sqrt((25-50)^2 + 75^2) = sqrt(6250) = 25sqrt(10)

So the least distance between P and (50,0) is 25sqrt(10) units.

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a. The determinant of the given matrix is -1116.

b. The determinant is 0.

(a) We can simplify this matrix using row operations:

R2 = R2 - 2R1, R3 = R3 - 3R1

101 201 301

102 202 302

103 203 303

->

101 201 301

0 -2 -2

0 -3 -6

Expanding along the first row:

101 | 201 301

-2 |-202 -302

-3 |-203 -303

Det = 101(-2*-303 - (-2*-203)) - 201(-2*-302 - (-2*-202)) + 301(-3*-202 - (-3*-201))

Det = -909 - 2016 + 1809

Det = -1116

Therefore, the determinant is -1116.

(b) We can simplify this matrix using row operations:

R2 = R2 - tR1, R3 = R3 - t^2R1

1 t t^2

t 1 t^2

t^2 t^2 1

->

1 t t^2

0 1 t^2 - t^2

0 t^2 - t^4 - t^4 + t^4

Expanding along the first row:

1 | t t^2

1 | t^2 - t^2

t^2 | t^2 - t^2

Det = 1(t^2-t^2) - t(t^2-t^2)

Det = 0

Therefore, the determinant is 0.

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The answer is  True, the percentile rank identifies the percentile of a particular value within a set of data.

The percentile rank is a measure that identifies the percentage of scores in a distribution that are equal to or lower than a given score. It is calculated by dividing the number of scores that are equal to or lower than the given score by the total number of scores in the distribution, and multiplying the result by 100 to obtain a percentage. The percentile rank can be used to compare individual scores to the rest of the distribution, and can provide useful information about the relative standing of a score within a particular group or population. Therefore, it is true that the percentile rank identifies the percentile of a particular value within a set of data.

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Based on the coordinates of the vertices of the quadrilateral ABCD, the perimeter is 18.64 units and the area is 18.96 units².

First, find the distance between the points of the quadrilateral:

Distance formula is:

d = √( (x₂ - x₁)² + (y₂ - y₁)²)

Distance for AB:

= √( (6 - 3)² + (5 - 5)²)

= 3

Distance for BC:

= √( (4 - 6)² + (-1 - 5)²)

= 6.32

Distance of CD:

= √( (1 - 4)² + (-1 - (-1)²)

= 3

Distance of AD:

= √( (1 -3)² + (-1 -5)²)

= 6.32

Perimeter is:

= 6.32 + 6.32 + 3 + 3

= 18.64 units

The area of the quadrilateral would be:

= 3 x 6.32

= 18.96 units²

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Answer:

32, 40, 48, 56

Step-by-step explanation:

\(a_n= 8(n+3)...(given) \\\\ a_1= 8(1+3) = 8 \times 4 = 32 \\ \\ \: a_2= 8(2+3) = 8 \times 5 = 40 \\ \\ a_3= 8(3+3) = 8 \times 6 = 48 \\ \\ a_4= 8(4+3) = 8 \times 7 = 56 \\ \)

The information about the how to open a comic book store should be included in the b. organizational plan.

An organizational plan serves as a way that can be used to plan for the future events to achieve the desire goals of the institution.

Therefore, option B is correct, because with the organizational plan, Korey can note all information required for the business and how the business will grow.

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Answer:

Basic Cable Company A= 30x + 75

Basic Cable Company B= 40x

After 7.5 months, it's more economical to go with Company A. Before 7.5 months, Company B is cheaper

Step-by-step explanation:

When graphing an exponential function, a T-chart is commonly used to determine the values. The correct answer is option A.

The T-chart employs positive real numbers since this is the most typical form of exponential function.

Exponential functions are utilized to represent processes that increase or decrease exponentially, as well as to model phenomena in many different disciplines, including science, economics, and engineering.

The exponential function can be represented by the following equation:

\(y=a^x\), where a is the base, x is the exponent, and y is the outcome.

When a is a positive number greater than one, the function is called exponential growth, while when a is a fraction between 0 and 1, the function is called exponential decay.

The T-chart is used to determine the values to use in the graph and connect the dots as required. Positive real numbers are used as the values in the T-chart in order to effectively graph the exponential function.

Therefore, the correct answer is option A.

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Answer:

x+54°=90° ( Given)

x=36°

x+y°=90°

y=90°-36°

y=54°

Hope this help!

Answer:

12

Step-by-step explanation:

To evaluate 3(w*8)+x, replace 'w' with (1/3) and 'x' with 4:

3([1/3]*8) + 4

We can multiply 3, [1.3] and 8 in any order, then add 4:

1*8 + 4, or            8 + 4 = 12

Answer:

10

Step-by-step explanation:

Harvey drove a total of 2(x + y) = 240 miles altogether. We can calculate it in the following manner.

Let's start by finding out how many miles Harvey drove in the city and on the highway separately.

Let x be the number of miles he drove on the highway, and y be the number of miles he drove in the city.

Given that the car travels 28 miles per gallon on the highway and 20 miles per gallon in the city, we can write:

x/28 + y/20 = 34

This equation represents the fact that Harvey used 34 gallons of gasoline in total for his trip.

We also know that he drove twice as many miles as he did the first time, so the total distance he drove is:

2(x + y)

Now, we need to use the information that Harvey paid $400 for the car. We can assume that this cost includes the price of the car and any gas he used during his trip.

Let's assume that the car has already used up some gas before Harvey bought it, and that he filled up the tank before his trip. Let's also assume that the car has a fuel efficiency of 24 miles per gallon on average (the average of the highway and city fuel efficiencies).

Then, the cost of the gas he used during his trip is:

34 - 400/($2.50/gallon) = 20

The cost of the gas is equal to the number of gallons used (34) minus the cost of the car ($400) divided by the price per gallon ($2.50/gallon).

Using the fuel efficiency of 24 miles per gallon, we can write:

x/28 + y/20 = 34

x/24 + y/24 = 20

Simplifying these equations, we get:

x/7 = 34 - y/5

x/6 + y/6 = 20

Multiplying the second equation by 6, we get:

x + y = 120

Substituting this into the first equation, we get:

x/7 = 34 - (120 - x)/5

Multiplying both sides by 35, we get:

5x = 1190 - 7(120 - x)

Simplifying, we get:

12x = 770

x = 64.17

Substituting this into x + y = 120, we get:

y = 55.83

Therefore, Harvey drove a total of 2(x + y) = 240 miles altogether.

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