given the equation y = 2x - 8, what is the slope and the y-intercept?

When a person walks 5.0 kilometers north, they are moving in a straight line towards the north direction.

If they then walk 5.0 kilometers east, they are moving in a straight line towards the east direction. To find the person's displacement, we need to calculate the straight-line distance between their starting point and their ending point.

We can use the Pythagorean theorem to do this. If we draw a right-angled triangle with the northward distance as the vertical leg and the eastward distance as the horizontal leg,

The hypotenuse of the triangle will be the straight-line distance between the starting and ending points.

Using the Pythagorean theorem, we can calculate the hypotenuse as follows: hypotenuse^2 = (northward distance)^2 + (eastward distance)^2, hypotenuse^2 = (5.0 km)^2 + (5.0 km)^2, hypotenuse^2 = 50 km^2, hypotenuse = sqrt(50) km.

hypotenuse = 7.07 km (rounded to two decimal places), Therefore, the person's displacement is closest to 7.07 kilometers. This means that the straight-line distance between their starting and ending points is 7.07 kilometers, even though they walked a total distance of 10 kilometers.

The displacement can be found by using the Pythagorean theorem, as it represents the shortest distance between the initial and final points of the person's journey. In this case, we have a right triangle with legs of 5.0 kilometers north and 5.0 kilometers east.

Applying the Pythagorean theorem, we get:

Displacement^2 = (5.0 km)^2 + (5.0 km)^2
Displacement^2 = 25 km^2 + 25 km^2
Displacement^2 = 50 km^2

To find the displacement, take the square root:
Displacement ≈ √50 km ≈ 7.07 km
So, the person's displacement is closest to 7.07 kilometers in the northeast direction.

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a. The truth table for the standard POS expression (A + B)(A + C)(A + B + C) is generated by considering all possible combinations of inputs A, B, and C and evaluating the expression for each combination.

b. The truth table for the standard POS expression (A + B)(A + B + C)(B + C')(B + C + D)(A + B + C + D) is also generated by considering all possible combinations of inputs A, B, C, and D and evaluating the expression for each combination.

a. To generate the truth table for the expression (A + B)(A + C)(A + B + C), we consider all possible combinations of inputs A, B, and C. We evaluate the expression for each combination by applying the OR operation to the respective variables and then applying the AND operation to the resulting terms. The resulting truth table will have eight rows, representing all possible combinations of A, B, and C.

b. To generate the truth table for the expression (A + B)(A + B + C)(B + C')(B + C + D)(A + B + C + D), we consider all possible combinations of inputs A, B, C, and D. Similar to the previous case, we evaluate the expression for each combination by applying the OR and AND operations as needed. The resulting truth table will have sixteen rows, representing all possible combinations of A, B, C, and D.

By examining the truth tables, we can determine the output values of the expressions for all possible input combinations, which helps in understanding the behavior of the expressions and can be used for further analysis or decision-making purposes.

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The number of ways  5 puppies can be chosen from a litter of 8 puppies is 56 ways

Permutation has to do with arrangement while combination has to do with selection.

From the queston, since we are to select 5 puppies from a litter of 8 puppes, this can be done as shown:

8C5 = 8!/(8-5)!5!

8C5 = 8!/3!5!

8C5 = 8*7*6*5!/6*5!

8C5 = 8* 7

8C5 = 56ways

Hence the number of ways  5 puppies can be chosen from a litter of 8 puppies is 56 ways

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Answer:

1st option is correct .........

Answer:

y= 1/2x - 3

Step-by-step explanation:

identify two points on the line e.g

(6,0) and (2,-2)

gradient = change in Y over change in X

0--2/6-2

= 1/2

then pick any one known point eg (6,0) and one unknown (x,y)

use the points to obtain the equation of the line.......

The required experimental probability that the next batter will get a hit is 2/11.

A number that indicates how likely an event is to occur is called its probability. It is communicated as a number in the reach from 0 and 1, or, utilizing rate documentation, in the reach from 0% to 100 percent. The higher the probability, the more likely the event is to occur.

The experimental probability of an event happening is defined as the number of times the event occurs divided by the total number of trials or events.

In this case, we are given that 4 out of 22 batters have gotten a hit so far. Therefore, the experimental probability that the next batter will get a hit is:

P(hit) = Number of hits / Total number of batters

P(hit) = 4/22

Simplifying:

P(hit) = 2/11

Therefore, the experimental probability that the next batter will get a hit is 2/11.

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A zero-day exploit is an attack program that is created before patches or fixes are available from the software vendor.

It refers to a vulnerability or weakness in software that is unknown to the vendor or the general public. This means that the exploit takes advantage of a security flaw that has not yet been discovered or addressed by the software developer.

The term "zero-day" signifies that developers have had zero days to fix or patch the vulnerability. Zero-day exploits are particularly dangerous because they can be deployed by hackers to target systems before any defensive measures are in place, making them highly effective and difficult to defend against.

Therefore, a "zero-day" exploit is an attack program that is created before patches or fixes are available from the software vendor.

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Answer:

Option C is correct.

Step-by-step explanation:

Function is a Relation from set A to Set B whose every element of set A has one and only one image  in Set B.

Option A).

(0,2) , (2,3) , (0,-2) , (4,1)

here 0 has two image 2 and -2.

So, this is not function.

Option B).

(1,2) , (1,-2) , (3,2) , (3,4)

here 1 has two image 2 and -2.

So, this is not function.

Option C).

(1,6) , (2,7) , (4,9) , (0,5)

Here every element has only one image.

So, this is a function.

Option D).

(2,4) , (0,2) , (2,-4) , (5,3)

here 2 has two image 4 and -4.

So, this is not function.

Therefore, Option C is correct.

The volume of the biggest possible cube inside the right cylinder is approximately 1193.243 cubic centimeters.

Cubes are hexahedrons with one same side length and only right angles. In this case, the cube is constrained by cross area of right cylinder in accordance to image attached below. The maximum possible volume for a cube inside the cylinder is described by following expression:

V = (√2 / 2)³ · R³

Where:

If we know that R = 15 cm, then the volume of biggest possible cube is:

V = (√2 / 2)³ · (15 cm)³

V ≈ 1193.243 cm³

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Answer:

$75

Step-by-step explanation:

First divide 1,000 by 20 which gives you 50

Then Multiply 50 by $1.50 to get $75

Answer:75

Step-by-step explanation:

since there are 15 students and they each need 5 plates you just do 15x5 and get 75

The speed at which the pool is filling up is 0.744 litres/sec

To find the speed in litres/sec, we need to convert the rate at which the pool is filling up from gallons/day to litres/sec.

First, we can convert the number of gallons/day to litres/day by multiplying it by the conversion factor of 1 gallon = 3.785 litres:

1500 gallons/day * 3.785 liters/gallon = 5627.5 liters/day

Then, we can convert the number of litres/day to litres/sec by dividing it by the number of seconds in a day:

5627.5 liters/day / (24 hours/day * 60 minutes/hour * 60 seconds/minute) = 0.744 liters/sec

So the speed at which the pool is filling up is 0.744 litres/sec.

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Answer:

x^2 + 4xy + 4y^2

Step-by-step explanation:

hope this helps

Answer:

x² + 4xy + 4y²

Step-by-step explanation:

(x + 2y)²

= (x + 2y)(x + 2y)

Each term in the second factor is multiplied by each term in the first factor, that is

x(x + 2y) + 2y(x + 2y) ← distribute parenthesis

= x² + 2xy + 2xy + 4y² ← collect like terms

= x² + 4xy + 4y²

The BMI of an 118-lb adult who is 5 feet 4 inches tall is approximately 20.25.

BMI stands for Body Mass Index.

It's a measure of body fat based on height and weight that applies to both adult men and women.

BMI is an easy-to-perform screening tool for body fat levels that can help identify individuals who have health risks linked with excess body fatness.

It's important to keep in mind that the BMI measurement should not be used as a diagnostic tool for health conditions and is only one component in an overall evaluation of a person's health status.

Using the formula below, we can calculate the BMI of an 118-lb adult who is 5 feet 4 inches tall: BMI = (weight in pounds / (height in inches x height in inches)) x 703

First, we need to convert the height into inches:5 feet 4 inches = 64 inches

Next, we plug the values into the formula and solve for the BMI:

BMI = (118 / (64 x 64)) x 703BMI = (118 / 4,096) x 703BMI = 0.0288 x 703BMI = 20.2464

Therefore, the BMI of an 118-lb adult who is 5 feet 4 inches tall is approximately 20.25.

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Remember that

In a unit circle, the radius of the circle is 1

see the figure below to better understand the problem

we have that

and we know that

so

and we know that

so

therefore

the coordinates (x,y) are

Answer:

Answer:81

Step bye step

hope it really helps......!!!!!!

The radius of the basketball, in inches, is approximately 1.7206 inches.

We know that the volume of the basketball is 10 times larger than Susan's model. Let's denote the radius of Susan's model as r_s and the radius of the basketball as r_b.

The formula for the volume of a sphere is V = (4/3) * π * r^3, where V is the volume and r is the radius. We can set up the following equation to represent the given information:

(4/3) * π * r_b^3 = 10 * (0.3040)

Simplifying the equation, we have:

r_b^3 = (10 * 0.3040) / (4/3) * π

r_b^3 = 7.6 / (4/3) * π

r_b^3 = 7.6 * (3/4) * (1/π)

r_b^3 = 5.7 / π

Taking the cube root of both sides, we find:

r_b = (5.7 / π)^(1/3)

Evaluating this expression, we get r_b ≈ 1.7206 inches.

Therefore, the radius of the basketball, in inches, is approximately 1.7206 inches.

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Answer:

$15.70

Step-by-step explanation:

The total Cost is 101.40

The tax is               7.20    Subtract the tax

=====================

The cost of 6 CDs=94.20

1 CD costs 94.2 / 6

1 CD costs 15.70

Answer:

Rule is \(n^2+8\)

20th term is 408

Step-by-step explanation:

Notice that \(n^2=1,4,9,16,25,...\) so if we add 8 to each term, we get \(n^2+8=9,12,17,24,33\). Therefore, the 20th term would be \(20^2+8=400+8=408\)

n - 2.5 represent the Cost Price after a discount of 2.50

Given parameters,

Modeling of the total cost = 35 + 3(n - 2.5)

The general format of models like this is as follows;

Price + quantity (cost after coupon)

Coupon literally is a code that are used to obtain a discount on the current purchase

By comparison;

Price = 35 (i.e. current dress price).

Quantity = n (i.e. the number of shirts bought)

Lastly, cost after coupon = n - 2.5

It is stated that she applies a coupon on each T shirt

This can be interpreted to: removing a total discount of $2.50 from the three t-shirt.

By removing, the expression is given as negative $2.5

Hence,

n - 2.5 represent the total cost on each T shirt after coupon is applied

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Answer:

4/5 is the slope

Step-by-step explanation:

The line is written in the form

y = mx+b where m is the slope and b is the y intercept

y = 4/5x -3

4/5 is the slope and -3 is the y intercept

Answer:

yes

Step-by-step explanation:

The area of parallelogram ABCD is AB times CD, or 2 times CD squared. We can substitute the value of CD into the equation we found for the area of triangle CDF to solve for CD. Once we have CD, we can use it to find the area of ABCD.

The area of the parallelogram can be found by adding the area of triangle CDF and the area of parallelogram ABCD.

Let's first use the information given to find the area of triangle CDF. We know that CDF is a right triangle, so we can use the formula for the area of a triangle, which is 1/2 times base times height.

We are given that the area of CDF is 60m, so we can set up the equation 1/2 times CD times DF equals 60.

Next, we need to find the area of parallelogram ABCD. Since ABCD is a parallelogram, we know that its opposite sides are equal and parallel. We are given that CGF and DEF are straight lines, and that 2CG equals GF. This means that CG is half of GF, so we can use this information to find that CD is half of AB.

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Answer:

11

Step-by-step explanation:

(f/g)(5)=

f(5)=(5)2+1÷g(5)=5-4

10+1/1

11/1

(f/g)=11

The required simplified value of the given function as (f/g)(5)  is 26.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
f(x) = x² +1

f(5) = 5² + 1
f(5) = 26

g(x) = x - 4
g(5) = 5 - 4 = 1

f/g(5) = f(5) / g(5)
       = 26 / 1 = 26

Thus, the required simplified value of the given expression (f/g)(5)  is 26.

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Answer:

12.6

Step-by-step explanation:

Answer:9 miles

Step-by-step explanation:

5 working daya x 1.8 miles = 9 miles

Step-by-step explanation: 1.8 x  7