y=\ 4\cdot2\ ^{x}\left\{-5\le x\le1.5\right\}

The magnitude of the average velocity vector is approximately 3.651 m/s.

To find the magnitude of the average velocity vector, we need to calculate the displacement and divide it by the time taken.

Representation:

Initial position: D1 = (50 m North, 10 m East)

Final position: D2 = (5 m North, 35 m East)

Time taken: t = 15 seconds

Equations:

Displacement vector (ΔD) = D2 - D1

Average velocity vector (\(V_{avg}\)) = ΔD / t

Algebra work:

ΔD = D2 - D1

   = (5 m North, 35 m East) - (50 m North, 10 m East)

   = (-45 m North, 25 m East)

|ΔD| = √((-45)^2 + 25^2)  [Magnitude of the displacement vector]

\(V_{avg}\) = ΔD / t

       = (-45 m North, 25 m East) / 15 s

       = (-3 m/s North, 5/3 m/s East)

|\(V_{avg}\)| = √((-3)^2 + (5/3)^2)  [Magnitude of the average velocity vector]

Symbolic answer:

The magnitude of the average velocity vector is approximately 3.651 m/s.

Units check:

The units for displacement are in meters (m) and time in seconds (s). The average velocity is therefore in meters per second (m/s), which confirms the units are consistent with the calculation.

Therefore, the magnitude of the average velocity vector is approximately 3.651 m/s.

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Answer:

The equation of the given circle is (x-2)^2 + (y+3)^2 = 9, which is in the standard form of a circle: (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius.

Comparing the given equation with the standard form, we can see that the center of the circle is (2, -3) and the radius is 3.

Therefore, the radius of the circle is 3 units.

Answer:

The answer is -5<x

Step-by-step explanation:

-3<2x+7

Subtract 7 from both sides

-10<2x

Isolate x by divided both sides by 2

-5<x

Answer:

x = 1 and y =5

Step-by-step explanation:

\(8x -2y= -2\\Divide by -2\\-4x+y = 1\\add 4x\\y= 1+4x\\\)

Substitute this value of y in the next equation.

\(9x+5(1+4x) = 34\\9x+5+20x=34\\29x+5=34\\29x=29\\x=1\)

Solve for y using x.

\(y=4x+1\\y=4(1)+1\\y=5\)

Answer:

-3

Step-by-step explanation:

3 x 6 - 42/2 =

18 - 42/2 =

18 - 21 =

-3

Answer:

18-21=x

Step-by-step explanation:

18-21=x

x= -3(this is just extra)

The statement that knowing the value of x tells you nothing about the value of y can be explained by several scenarios. One possible scenario is when the values of x and y are not related in any way. In other words, there is no mathematical or logical connection between them.

Another scenario where knowing the value of x tells you nothing about the value of y is when there are multiple possible values of y for a given value of x. This occurs when the relationship between x and y is not one-to-one. For instance, if x represents a person's age and y represents their height, knowing someone's age does not determine their height since there are different heights for different ages.

Furthermore, it is possible that there is a relationship between x and y, but the value of y is affected by other factors besides x. For example, if x represents the amount of time a student spends studying and y represents their grade on a test, knowing the value of x does not completely predict the value of y because other factors like natural ability and test-taking skills may also play a role in determining the grade.

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a) "You will get an A in this course if and only if you learn how to solve discrete mathematics problems."
b) "You will be informed if and only if you read the newspaper every day."
c) "It will rain if and only if it is a weekend day."
d) "You can see the wizard if and only if the wizard is not in."
e) "My airplane flight will be late if and only if I have to catch a connecting flight."

These propositions are written in the form "p if and only if q" in English, which means that both p and q must be true for the entire statement to be true.

This form is also known as a biconditional statement, and it is often used in logic and mathematics to express the relationship between two propositions.

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Step-by-step explanation:

what is the ratio of softballs to the total number of balls if there are 3 softballs and 184 is the total?

Ratio will be according to given units.

So, Softball : Total Balls

3: 184

Since it cannot be simplified further this is the answer.

Hope it helps ☃️

As a car dealer lowers a vehicle that was worth 18300 to 16000 by applying the formula of change in percentage we get that by 12.569 percentage (approximately) the price gets lowered .

The initial price of the car is set at P = 18300 (units)

The price after lowering drom P becomes A= 16000 (units)

Hence the change in price (or value) of the car, that is the price of the car is lowered by, C = (initial price - lowered price) = (P - A) = (18300 - 16000) units = 2300 units.

The formula for calculating percentage change is given as follows,

Change in percentage = [(Change in value)/ ( Initial value) ]*100

⇒Change in percentage = (C/ P)*100

⇒ Change in percentage =( 2300/ 18300)*100 = 12.569% (approximately)

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Answer:

A : 8 , 0 , -8 , -16

Step-by-step explanation:

Answer:

RM 300

Step-by-step explanation:

Let's assume that the cost price of the merchandise is "C" in RM.

According to the problem, the marked price of the merchandise is 20% higher than the cost price. Therefore, the marked price can be calculated as:

Marked price = Cost price + 20% of Cost price

Marked price = C + 0.2C

Marked price = 1.2C

The merchandise is sold at 90% of the marked price, which means the selling price can be calculated as:

Selling price = 90% of Marked price

Selling price = 0.9 × 1.2C

Selling price = 1.08C

We are given that the profit after selling the merchandise is RM 24. Profit is calculated as the difference between selling price and cost price. Therefore, we can write:

Profit = Selling price - Cost price

24 = 1.08C - C

24 = 0.08C

Solving for C, we get:

C = 24/0.08

C = 300

Therefore, the cost price of the merchandise is RM 300.

Solving an inequality, we will see that there is less than $280 in the pile of money.

Let's say that the amount of money is defined by the variable.

First, we know that Jeri keeps $80, so now in the pile we have:

M - $80.

Now she gives one third of that, then the leftover is:

(2/3)*(M - $80) + $80

We know that this is more than:

M - $200

Then we have the inequality:

(2/3)*(M - $80) + $80 > M - $200

And we can solve this for M.

(2/3)*M  - (2/3)*$80 + $80 > M - $200

(1/3)*$80 + $200 > M - (2/3)*M

(1/3)*$80 + (1/3)*$200 > (1/3)*M

$280 > M

Then we conclude that there is less than $280 in the pile of money.

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Answer:

Answer

Step-by-step explanation:

OK, there are 360 students in the whole school and 15 classes there, too.

Each class has an EVEN amount of students, so simply, all you need to do is divide (360 divided by 15)

i) The counting numbers which are multiples of 5 and less than 50 can be represented using the roster method as:

{5, 10, 15, 20, 25, 30, 35, 40, 45}

ii) The set of all-natural numbers x for which x+6 is greater than 10 can be represented as:

{5, 6, 7, 8, 9, 10, 11, 12, 13, ...}

iii) The set of all integers x for which 30/x is a natural number can be represented as:

{-30, -15, -10, -6, -5, -3, -2, -1, 1, 2, 3, 5, 6, 10, 15, 30}

Note that in the third set, we include both positive and negative integers that satisfy the condition.

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Answer:

14/27

Step-by-step explanation:

7/3 ÷ 9/2

7/3 x 2/9 = 14/27

The given quadrilaterals are not congruent but are similar and have a scale factor of \(\frac{1}{3}\).

Congruent figures are figures where one of the figure's sides and angles are equivalent to other  figure's corresponding sides and angles.

Clearly, the quadrilateral are not congruent because their size is not equal. Quadrilateral WXYZ is bigger than quadrilateral LMNO.

Similar triangles are triangles which are of same shape. There is no need for the same size.

So the given triangles are similar.

Here the coordinates of quadrilateral LMNO are L (1, 2), M (4, 2), N (3, 3) and 0 (1, 3).

LM = √[(4 - 1)² + (2 - 2)²] = 3

MN = √[(3 - 4)² + (3 - 2)²] = √2

N0 = √[(1 - 3)² + (3 - 3)²] = 2

OL = √[(1 - 1)² + (2 - 3)²] = 1

Coordinates of the quadrilateral WXYZ are W (-6, 6), X (3, 6), Y (0, 9) and Z (-6, 9).

WX = √[(3 - -6)² + (6 - 6)²] = 9

XY = √[(0 - 3)² + (9 - 6)²] = √18

YZ = √[(-6 - 0)² + (9 - 9)²] = 6

ZW = √[(-6 - -6)² + (6 - 9)²] = 3

Now, \(\frac{LM}{WX}\) =  \(\frac{MN}{XY}\) =  \(\frac{NO}{YZ}\) =  \(\frac{OL}{ZW}\) =  \(\frac{1}{3}\)

Hence the figure shown here are similar and the scale factor is  \(\frac{1}{3}\).

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According to the information, Samuel can stain the deck in 4 hours, and Julio can do it three times faster, in 4/3 hours or 1 hour and 20 minutes.

Let's assume that Samuel can stain the deck in x hours. Then, Julio can do the same job in x/3 hours (since he is three times faster).

Working together, they can stain the deck in 3 hours. Using the concept of work, we can set up the following equation:

1/x + 1/(x/3) = 1/3

Simplifying this equation by finding a common denominator, we get:

3/(3x) + x/(3x) = 1/3

Combining like terms, we get:

4x/(3x) = 1/3

Cross-multiplying, we get:

12x = 3x

Solving for x, we get:

x = 4

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Answer:

22r-1

Step-by-step explanation:

5(2r+1)-3(-4r+2) Distribute the terms

10r+5+12r-6 Combine like terms

22r-1

Answer:

5 ×( 2r +1) - 3 × ( -4r +2)

= 10r +5 +12r -6

= 22r -1

Answer:

I believe the correct answer is D

Answer:

it has to be among us, i love that game

Step-by-step explanation:

Answer:

The best game ever created is either call of duty or Halo

The procedure that can be used to show the converse of the Pythagorean theorem using side lengths chosen from 2 cm, 3 cm, 4 cm, and 5 cm is option C.

Knowing that 3^2 +4^2 = 5^2, draw the 3 cm side and the 4 cm side with a right angle between them. The 5 cm side will fit to form a right triangle.

The Pythagorean Theorem is a relationship that exists between the sides of a right triangle, which is a triangle with one interior angle of 90 degrees. According to the Pythagorean Theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

The Converse of the Pythagorean Theorem is an inverse statement that implies that if a triangle's sides satisfy the relationship described in the Pythagorean Theorem, then the triangle is a right triangle.

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Answer:

4%/ a interest compounded semi-annually

Step-by-step explanation:

The option that gives the lower interest rate payment would be more appropriate. to determine this calculate the effective interest rate

Effective annual rate = (1 + APR / m ) ^m - 1

M = number of compounding

(1 + 0.04/2)^2 - 1 = 4.04%

(1 + 0.04/12)^12 - 1 = 4.07%

the choice should be 4%/ a interest compounded semi-annually

Answer: single random sample

Step-by-step explanation:

In the trapezium OABC, the value of y will be 1.

To find the value of y in the trapezium OABC, we can use the fact that O(0,0), A(2,-1), B(4,3), and C(0,y). Since OABC is a trapezium, we know that the line segments OA and BC are parallel.

Therefore, their slopes are equal. The slope of OA is (0 - (-1))/(0 - 2) = 1/2. The slope of BC is (y - 3)/(0 - 4) = (3 - y)/4. Setting these slopes equal to each other, we get:

1/2 = (3 - y)/4

Multiplying both sides by 4, we get:

2 = 3 - y

Subtracting 3 from both sides, we get:

y = 1

Therefore, the value of y in the trapezium OABC is 1.

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Answer:

The median of the lower half of the data was determined to be 67 while the median of the upper half of the data was determined to be 92.

Step-by-step explanation:

Step 1:  Order from least to greatest

51, 56, 62, 72, 79, 81, 82, 85, 89, 95, 97, 98

Step 2:  Determine the median of the lower half of the data

There are 12 numbers which means that there is going to be 6 numbers on both sides of the data.  So using the first 6 numbers we will be able to determine the median of the lower half of the data.

51, 56, 62, 72, 79, 81

Since there is an even amount of numbers, that means that we will need to find the middle between the 3rd and 4th number.  We can do that by adding them up together and dividing by 2.

(62 + 72) / 2 = 67

Step 3:  Determine the median of the upper half of the data

So using the first 6 numbers we will be able to determine the median of the upper half of the data.

82, 85, 89, 95, 97, 98

Since there is an even amount of numbers, that means that we will need to find the middle between the 3rd and 4th number.  We can do that by adding them up together and dividing by 2.

(89 + 95) / 2 = 92

Answer: The median of the lower half of the data was determined to be 67 while the median of the upper half of the data was determined to be 92.

Answer:

The answer is -164.37 dollars in there bank account.

Step-by-step explanation:

you subtract the two fees first and then you subtract the two deposits from the bank and then you have your answer. I hope that this helps you :)