Look at the area models.

What is the product of the fractions represented by
these two area models?

4a) The direction of the vector A is 63.4° north of the x-axis.

4b) The direction of the vector B is -63.4° south of the x-axis.

4c) The direction of the vector C is 59.0° north of the x-axis.

4d) The direction of the vector A+B+C is 71.6° north of the x-axis.

4e) Direction = 71.6° north of the x-axis.

5a) 28.04 m/s

5b) 5.72 s

5c) The highest point of the projectile is 40.39 m.

5d) Range of the projectile: 220.9 m.

6a) 5.72 s

6b) 220.9 m

6c) The angle of the velocity vector with respect to the horizontal is given by: θ = tan⁻¹(Vy/Vx) = tan⁻¹(-22.51/(50 cos 35°)) = 308.4°.

7a) The box is in the air for 4.52 seconds.

7b) The distance from the edge of the table to the point of impact is 148.8 m.

7c) The components of the box's velocity vector when it strikes the floor are Vx = 40.97 m/s and Vy = 44.3 m/s.

7d) The height of the table is given by: H = d/tan 45° - v²/2g H = (261.2 m)/tan 45° - (40.97²)/(2*9.8) = 39.2 m .

4a) A=3x+6y magnitude = √(3^2+6^2) = √45 = 3√5. The direction of the vector A is 63.4° north of the x-axis.

b) B=2x−4y magnitude = √(2^2+(-4)^2) = √20 = 2√5. The direction of the vector B is -63.4° south of the x-axis.

c) C=−3x+5y magnitude = √((-3)^2+5^2) = √34. The direction of the vector C is 59.0° north of the x-axis.

d) A+B+C= (3x+6y)+(2x−4y)+(-3x+5y) = 2x+7y magnitude = √(2^2+7^2) = √53. The direction of the vector A+B+C is 71.6° north of the x-axis.

e) B=2x−4y magnitude = √(2^2+(-4)^2) = √20 = 2√5 Direction = -63.4° south of the x-axis.c) C=−3x+5y magnitude = √((-3)^2+5^2) = √34 Direction = 59.0° north of the x-axis.d) A+B+C= (3x+6y)+(2x−4y)+(-3x+5y) = 2x+7y magnitude = √(2^2+7^2) = √53 Direction = 71.6° north of the x-axis.

5a) Find the x and y components of the initial velocity:Initial velocity = 50 m/s at 35° x-component of the velocity = 50 cos 35° = 40.97 m/sy-component of the velocity = 50 sin 35° = 28.04 m/s

b) Time in air = Total time/2 = (2Voy)/g = 2*28.04/9.8 = 5.72 s

c) High point of projectile: At the highest point, the vertical component of the velocity is 0. Using the formula: Vfy = Voy + at Where Voy = 28.04 m/s, a = -9.8 m/s² (acceleration due to gravity) and t = time to reach the maximum height. 0 = 28.04 + (-9.8)t => t = 2.86 seconds. Using the formula: y = Voyt + (1/2)at² => y = 28.04(2.86) + (1/2)(-9.8)(2.86)² => y = 40.39 m The highest point of the projectile is 40.39 m

d) Range of the projectile: Time of flight = 2*28.04/9.8 = 5.72 seconds. Range = Horizontal velocity × time of flight Range = (50 cos 35°) × 5.72 = 220.9 m.

6a) Time of flight: Time of flight = (2Voy)/g = 2*28.04/9.8 = 5.72 s

b) Range of the projectile: Range = Horizontal velocity × time of flight Range = (50 cos 35°) × 5.72 = 220.9 m

c) Speed when it hits the ground: The velocity of the projectile when it hits the ground can be calculated using the formula: Vy = Voy + at, where Voy = 28.04 m/s, a = -9.8 m/s² and t = 5.72 s Vy = 28.04 + (-9.8)(5.72) = -22.51 m/s The magnitude of the velocity vector is given by: V = √[(Vx)² + (Vy)²] V = √[(50 cos 35°)² + (-22.51)²] = 53.04 m/s The angle of the velocity vector with respect to the horizontal is given by: θ = tan⁻¹(Vy/Vx) = tan⁻¹(-22.51/(50 cos 35°)) = 308.4°.

7a) Time in air: Time of flight can be calculated using the formula: h = Voyt + (1/2)at² => t = √(2h/a) = √(2*100/9.8) = 4.52 s The box is in the air for 4.52 seconds.

b) Distance from the edge of the table to the point of impact: Horizontal distance = Vox * t = 50 cos 35° × 4.52 = 148.8 m The distance from the edge of the table to the point of impact is 148.8 m.

c) Components of the box's velocity vector when it strikes the floor: At the moment of impact, the vertical component of the velocity is given by: Vfy = Voy + at = 0 + (9.8)(4.52) = 44.3 m/s The horizontal component of the velocity remains constant: Vx = Vox = 50 cos 35° = 40.97 m/s Therefore, the components of the box's velocity vector when it strikes the floor are Vx = 40.97 m/s and Vy = 44.3 m/s.

d) Height of the table: If the velocity vector when the box strikes the floor is 45°, then the horizontal and vertical components of the velocity are equal. Therefore, Vx = Vy = 40.97 m/s Using the formula: h = (1/2)at² => 100 = (1/2)(9.8)t² => t = √(100/4.9) = 6.37 s The time of flight is 6.37 seconds. Using the formula: d = Vx × t, the horizontal distance travelled is: d = 40.97 × 6.37 = 261.2 m Therefore, the height of the table is given by: H = d/tan 45° - v²/2g H = (261.2 m)/tan 45° - (40.97²)/(2*9.8) = 39.2 m.

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Answer: Choice C

\(0 \le d \le 2\)

Graph with filled in circles at d = 0 and d = 2, shading in between

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

Explanation:

d = amount downloaded in gigabytes

The smallest amount is d = 0. We cannot download a negative amount of data, so this is why d = 0 is the smallest.

The largest amount allowed is d = 2. This is the cap that the ISP has set up.

So basically d can be anything between d = 0 and d = 2, including both endpoints. This means \(0 \le d \le 2\)

We use filled in circles for both endpoints to show to the reader "include these endpoints". Shading is done in between to show the entire solution set of possible d values. For instance d = 1 is in that region so it is possible to have this solution. Something like d = 4 is outside the region and not possible.

If Ryan bought his house for $250300 and the value appreciate at 4.5% each year , then the future value of Ryan's home in 10 years is $388709  .   .

The price for the Ryan's house is = $250300 ,

the appreciation rate of the house is = 4.5% ,

the time after which the value is calculated is = 10 years ,

the predicted value of the house can be calculated as :

Amount = price × (1 + r/100)¹⁰ ,

substituting the value ,

we get ,

Amount = 250300 × (1 + 4.5/100)¹⁰

= 250300×(1 + 0.045)¹⁰ ,

= 250300×(1.045)¹⁰ ,

On simplifying ,

we get ,

= 388708.246

≈ 388709

Therefore , the predicted future value of Ryan's home in 10 years is $388709  .

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180g = 0.180 kg or there are 0.180 kilograms in 180 grams.

In mathematics, conversion is the process of changing the value of one form or unit to another. It can be changing ones unit of length, weight, volume or even currency to another.

A conversion factor is a number used to change one set of units to another, either by multiplying or dividing.

The sentence states an equality between a units of weight in grams (g) and kilograms (kg).

From there, we can say that we are asked how many kilograms are there in 180 grams.

Converting grams to kilograms, we must use the conversion

1 g = 0.001 kg

180g = 180 (0.001) kg

180g = 0.180 kg

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Answer:

Step-by-step explanation:the height of plant =133cm.

                after one week, height of plant =133+37=170cm.

new height of plant after three new weeks=238cm.

plant grow in three weeks =238-170=68cm.

Answer:

The inverse of f is \(f^{-1}\) =  (x -2)/4  

Step-by-step explanation:

To find the inverse of f(x) = 4x + 2 , interchange the variables and solve for y.

   Rewrite f(x) = 4x + 2  as  x = 4y + 2  then solve for y

                                             x -2 = 4y

                                           (x - 2)/4 = y  

The probability that represents the likelihood of a single event occurring by itself is called marginal probability.

Marginal probability refers to the probability of an individual event happening independently without considering any other events. It focuses on a single variable or outcome without considering the relationship or dependencies with other variables.

To calculate marginal probability, you divide the number of times the specific event occurs by the total number of observations. For example, if you have a bag of marbles with different colors and you want to find the marginal probability of drawing a red marble, you would count the number of red marbles and divide it by the total number of marbles in the bag.

Marginal probability is often used when working with categorical variables or when studying the probability of a single event without considering any other variables or conditions. It provides a fundamental understanding of the likelihood of an event occurring in isolation, independent of any other factors.

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you have the following inequality:

3 + 4x > -5

in order to solve for x, proceed as follow:

3 + 4x > -5 subtract 3 both sides

4x > - 5 - 3

4x > -8 divide by 4 both sides

x > -8/4

x > -2

Hence, the solution to the given inequality is x > -2

GCF: greatest common factor of any two (or more) numbers

Top left:

GCF of 24 and 60: 12

Top right:

GCF of 12 and 18: 6

Bottom left:

GCF of 18 and 42: 6

Right left:

GCF of 30 and 72: 6

Answer:5.68 dollars amirikan

Step-by-step explanation:

Given that price of the mouthwash is $4.39. It is currently on sale for 20% discount. You also have a store coupon for $1.00 off and a manufacturer's coupon for $1.25 off. The subtotal you need to pay is $1.262.

The term discount refers to the amount or percentage deducted from the normal selling price of something. The discount means a reduction in the price of a good or service.

Discount  = Marked price - Selling price

The mouthwash is at sale for 20% off.

Cost price = $4.39

Discount = 20% of $4.39 = $0.878

Total discount = 20% off + store coupon + manufacturer's coupon = $0.878 + $1.000 + $1.250 = $3.128

Selling price = Marked price - Discount = $4.39 - $3.128 = $1.262

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It will take Derrick 40 months or approximately 3 years and 4 months to save $2,000 for the down payment if he continues to add $50 every month.

A down payment is an initial payment made when purchasing an item or a property, typically used to cover a portion of the total cost. The size and frequency of down payment payments can vary depending on the item or property being purchased.

To determine how long it will take Derrick to save $2,000 for the down payment, we need to calculate how much he saves every month and divide the total amount he wants to save by the amount saved per month.

Given that Derrick adds $50 every month, the total amount he saves in a year can be calculated as:

$50 * 12 = $600

So, it would take Derrick to save $2,000 for the down payment is:

$2,000 / $600 = 3.33 years (approx. 4 years)

Therefore, It will take Derrick 40 months, or approximately 3 years and 4 months to save $2,000 for the down payment if he continues to add $50 every month.

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Answer:

c. is the answer

Answer:

21 and 34.

Step-by-step explanation:

21 is 13 less than 34 and the sum of them is 55.

Answer:

a. 24

b. 864

Step-by-step explanation:

a. The demand function is:

P = 60 - 2Q

When P = 12:

12 = 60 - 2Q

2Q = 60 - 12

2Q = 48

Q = 48/2 = 24

b. Consumer surplus is given as the integral of Demand function:

\(CS = \int\limits {[P(Q) - (p)(Q)] \ dQ\\\)

This implies that:

\(CS = \int\limits {60 - 2Q} \, dQ\\\\CS = 60Q - Q^2\\\\CS = (60 * 24) - 24^2\\\\CS = 1440 - 576\\\\CS = 864\)

The approximate measure of angle YZX is 39.4°. Option(B) is the correct answer.

we know that

In the right triangle XYZ

\(tan(Y Z X)= \frac{opposite side angle YZX}{adjacent side angle YZX}\)

In this problem,

Opposite side angle YZX= XY = 12.4cm

Adjacent side angle YZX= YZ = 15.1cm

substitute the values,

\(tan ( Y Z X) = \frac{12.4}{15.1}\)

\(Angle ( Y Z X) = arc tan( \frac{12.4}{15.1} )\)

Angle ( Y Z X) = 39.4°

So,  the approximate measure of angle YZX is 39.4°.

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The complete question is:

In right triangle XYZ, the right angle is located at vertex Y. The length of line segment XY is 12.4 cm. The length of line segment YZ is 15.1 cm. Which is the approximate measure of angle YZX?

A .34.8°

B .39.4°

C .50.6°

D. 55.2°

Answer:

it 180 degrees

Step-by-step explanation:

The formula is -900° × π/180 = -15.71rad

The dust particle is seen to have 400 times more mass than the pollen particle

We will use the scientific notation.

For example, 0, 002 can be written as:

2 × 10³

Where;

3 is the number of times the comma (,) must be run to the right to convert the quantity 0, 002 to 2.

0, 002

0| 0 0 2

0 0| 02 -----------1

0 0 0|2------------2

0 0 0 2| ----------3

Thus, for the given expression:

Powder particle 0.000000778 g

It can be written as: 0.0000008 g = 8 × 10⁻⁷

b = -7

In the same way

Pollen grain of 0.00000000155 g

It can be written as:

0.000000002 g = 2 × 10⁻⁹

To know how big the mass of the dust particle is with respect to the pollen, we have;

(8 × 10⁻⁷)/(2 × 10⁻⁹) = 400

Complete question is;

The table below shows the approximate masses of a dust particle and a grain of pollen.

Dust Particle 0.000000778 g

Grain of Pollen 0.00000000155 g

The mass of a dust particle can be estimated and written in the form a × 10^b, where a = 8 and b =

The mass of a grain of pollen can be estimated and written in the form a × 10^b, where a = 2 and b =

Based on the estimates, the mass of a dust particle is approximately BLANK

times larger than the mass of a grain of pollen.

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Answer:

1. -3

2. 0/4 or 0

3. -2/3

4. -4/-3

Step-by-step explanation:

Answer:

1. The slope is -3

2. The slope is -1

3. The slope is -1/2

4. The slope is 4/3

Answer:

71

Step-by-step explanation:

The slope of a line shows the distance of that line. This means it tells us how far the line moves each time you move over one unit on the x-axis for that line.

The slope of a line can be defined a number that describes the direction and steepness of the line.

It is also known as gradient

It is denoted by the letter 'm'

Thus, the slope of a line shows the distance of that line. This means it tells us how far the line moves each time you move over one unit on the x-axis for that line.

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What we need

A function which has atleast the below parameters

The simplest function is

\(\sf y=\dfrac{\sqrt{-x^2-1}}{2}\)

How can we prove ?

So -x²-1<0

the answer is 101

hope that helped

The probability that each player will have $1 after 2019 rings of the bell is: (c) 1/3.

To solve this problem, we need to think about the possible outcomes of the game. Each time the bell rings, each player has a 1/2 probability of giving $1 to one of the other two players. This means that after one ring of the bell, there are 2^3 = 8 possible outcomes, as each player can either give or not give money to each of the other players.

After two rings of the bell, there are 2^8 = 256 possible outcomes. After three rings, there are 2^12 = 4,096 possible outcomes. And so on.

To find the probability that after 2019 rings of the bell, each player will have $1, we need to find the total number of possible outcomes and the number of outcomes in which each player has $1.

The total number of possible outcomes after 2019 rings of the bell is 2^(3*2019) = 2^6057.

To count the number of outcomes in which each player has $1, we can use a combinatorial argument. We need to distribute 2019 dollars among the three players in such a way that each player ends up with exactly $1. This is equivalent to choosing two numbers between 0 and 2019, inclusive, and giving the first player the smaller amount, the second player the difference between the larger and smaller amounts, and the third player the remaining amount.

The number of ways to choose two numbers between 0 and 2019 is (2019+2) choose 2 = 2036 choose 2 = 2,066,530.

Therefore, the probability that each player will have $1 after 2019 rings of the bell is:

2,066,530 / 2^6057 = 1/3

So the answer is (c) 1/3.

In the game where Raashan, Sylvia, and Ted each start with $1 and a bell rings every 15 seconds, the probability that after the bell has rung 2019 times, each player will have $1 is (a) 1/7.

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Lines l and m are parallel; line l will map onto line m with a 90° rotation; line l can map onto line m with a vertical line of reflection.

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The approximate areas of the continents (excluding North America) are as follows:

- Australia: 11 million km^2

- Europe: 15 million km^2

- Antarctica: 18 million km^2

- South America: 26 million km^2

- Africa: 44 million km^2

- Asia: 66 million km^2

To find the approximate area of each continent, we will multiply the given percentages by the area of North America (220 million km^2).

1. Australia:

Percentage: 5%

Approximate area: 0.05 * 220 million km^2 = 11 million km^2

2. Europe:

Percentage: 7%

Approximate area: 0.07 * 220 million km^2 = 15.4 million km^2 (rounded to 15 million km^2)

3. Antarctica:

Percentage: 8%

Approximate area: 0.08 * 220 million km^2 = 17.6 million km^2 (rounded to 18 million km^2)

4. South America:

Percentage: 12%

Approximate area: 0.12 * 220 million km^2 = 26.4 million km^2 (rounded to 26 million km^2)

5. Africa:

Percentage: 20%

Approximate area: 0.20 * 220 million km^2 = 44 million km^2

6. Asia:

Percentage: 30%

Approximate area: 0.30 * 220 million km^2 = 66 million km^2

Note: These values are rounded to the nearest million square kilometers.

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The required canoeist's paddling rate in calm water is 3 mph.

Let's denote the canoeist's paddling rate in calm water as "x" mph.

When the canoeist paddles upstream against the current, their effective speed is the difference between their paddling rate and the current's rate, or (x - 3) mph. The distance traveled upstream is also 8 miles.

Using the formula:

distance = rate x time

We can set up two equations based on the distance traveled and the effective speed for each leg of the trip:

Downstream leg: 8 = (x + 3) * t1

Upstream leg: 8 = (x - 3) * t2

Since the total time for the round trip is 2 hours, we know that:

t1 + t2 = 2

Now we can solve for x by substituting t1 = 8/(x+3) and t2 = 8/(x-3) into the equation above:

8/(x+3) + 8/(x-3) = 2

Multiplying both sides by (x+3)(x-3) gives:

8(x-3) + 8(x+3) = 2(x+3)(x-3)

Simplifying this expression gives:

16x = 48

x = 3

Therefore, the canoeist's paddling rate in calm water is 3 mph.

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Answer:

i dont see anything

Step-by-step explanation:

Answer:

you didnt add a pic

Step-by-step explanation:

From of the pool to her friend's house, Andaya could bicycle in a straight line for a distance of 6.4 units.

The marked coordinates are:

A(1,2), (6,5), C(5,7)

AC is the distance between her friend's house and pool.

Using distance formula:

AC = √(x2 - x1)² + (y2 - y1)²

AC = √(5 - 1)² + (7 - 2)²

AC = √16 + 25

AC = √41

AC = 6.403

AC = 6.4 units

Thus, From of the pool to her friend's house, Andaya could bicycle in a straight line for a distance of 6.4 units .

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Answer:

The slope is 4

Step-by-step explanation:

basilly you add easy x(-1,-7) + y(3,9) = 2/2

make sure that you add x left and y right  first -1+3=2 and then -7+9=2 equal=2,2 together and just add both equal 4

Most easy just put you answer in a graht and count the squares

hope this helps ;)