a plane is flying away from you at a speed of 750 mph at an altitude of 2 miles. how fast is the plane's distance from you increasing at the moment when the plane is flying over a point on the ground 9 miles from you?

The direction of the hike from the given vectors represented by the vector C is approximately -26.57° with respect to the positive x-axis.

To find the sum of the displacement vectors A and B, you simply add their respective components.

Vector A = (2.0i + 2.0j) m

Vector B = (2.0i - 4.0j) m

To find the sum (vector C), add the corresponding components,

C = A + B

= (2.0i + 2.0j) + (2.0i - 4.0j)

= 2.0i + 2.0j + 2.0i - 4.0j

= 4.0i - 2.0j

So, the vector representing the sum of A and B is (4.0i - 2.0j) m.

The components of the resulting vector C are 4.0 in the x-direction (i-component) and -2.0 in the y-direction (j-component).

To determine the direction of the hike,

Calculate the angle of the resulting vector with respect to the positive x-axis.

The angle (θ) can be found using the arctan function,

θ = arctan(-2.0/4.0)

θ = arctan(-0.5)

θ ≈ -26.57° (rounded to two decimal places)

Therefore, the direction of the hike represented by the vector C is approximately -26.57° with respect to the positive x-axis.

learn more about vectors here

brainly.com/question/32643529

#SPJ4

Step-by-step explanation:

y = 2x + b ---> 3 = 2(1) + b ---> b = 1

Therefore, y = 2x + 1

Part a.)

The probability model is:

P(R) = 1/5

P(B) = 3/25

P(G) = 4/25

P(Y) = 4/25

P(P) = 1/5

P(W) = 4/25

part b.)

all possible outcomes are included in the probability model.

part c.)

The probability model is non-uniform.

For part a

Let R =the event of selecting a red balloon,

Let B = the event of selecting a blue balloon,

G = the event of selecting a green balloon,

Y =  the event of selecting a yellow balloon,

P = the event of selecting a purple balloon,

W = the event of selecting a white balloon.

We can write the  probability model as:

P(R) = 5/25 = 1/5

P(B) = 3/25

P(G) = 4/25

P(Y) = 4/25

P(P) = 5/25 = 1/5

P(W) = 4/25

Part B:  we check that the sum of the probabilities of all possible outcomes is equal to 1 in order to verify.

We have:

P(R) + P(B) + P(G) + P(Y) + P(P) + P(W) = (1/5) + (3/25) + (4/25) + (4/25) + (1/5) + (4/25) = 1

All possible outcomes are included in the probability model.

Part C: The probability model is non-uniform because the probabilities of selecting each color of balloon are not equal.

Learn more about probability models at:

https://brainly.com/question/25688842

#SPJ1

The value of the index at the end of the day is $46,400. The value of the index at the end of the day can be calculated by considering the initial values of each stock and the percentage increase of the index.

To calculate the value of the index at the end of the day, we need to determine the total value of all the stocks at the beginning of the day and then apply the percentage increase.

Let's calculate the total value of each stock at the beginning of the day:

- Stock X: 5000 shares * $4.10/share = $20,500
- Stock Y: 2000 shares * $4.50/share = $9,000
- Stock Z: 4000 shares * $3.60/share = $14,400

Now, let's calculate the total value of all the stocks at the beginning of the day:

$20,500 + $9,000 + $14,400 = $44,900

Next, we need to apply the 3.4% increase to the total value of all the stocks:

3.4% of $44,900 = 0.034 * $44,900 = $1,526.60

Finally, we add the increase to the initial value:

$44,900 + $1,526.60 = $46,426.60

Rounding to the nearest hundred, the value of the index at the end of the day is approximately $46,400.

Therefore, the value of the index at the end of the day is $46,400.

For more information on percentage visit:

brainly.com/question/32197511

#SPJ11

For a person to be able to create a coordinate proof to show that the two triangles are congruent by the SSS Triangle Congruence Theorem one can simply use the distance formula.

Given that the distance formula =

\(\sqrt{(x_{2} -x_{1})^{2} + (y_{2} - y_{1}^{2} )}\)

Let say that Angle ABC has the vertices of A (-4, -2),  B (-5,1). C (0,2) and Angle DEF   has the vertices of D (7, -4), E (4,-5), F (3,0)

So lets prove it:

AC = \(\sqrt{(x_{2} -x_{1})^{2} + (y_{2} - y_{1}^{2} )}\)

=\(\sqrt{(-4-0)^2 + (-2-2)^2}\)

=\(\sqrt{32}\)

= 4\(\sqrt{2}\)

Do the same for DF:

DF = \(\sqrt{(x_{2} -x_{1})^{2} + (y_{2} - y_{1}^{2} )}\)

= \(\sqrt{(7-3)^2 + (-4-0)^2}\)

=\(\sqrt{32}\)

= 4\(\sqrt{2}\)

Looking at the above, one can see the values are the same and as such this proves that AC is the same to DF. If you do the same for the other part of the angles, you will see that they are congruent.

Therefore, For a person to be able to create a coordinate proof to show that the two triangles are congruent by the SSS Triangle Congruence Theorem one can simply use the distance formula.

Learn more about congruent Angle from

https://brainly.com/question/2938476

#SPJ

Answer:

1.5 dollars

Step-by-step explanation:

24/16=1.5

Answer:

if 16 tickets cost 24 dollars how about one

if 16tkts = 24 dollars

how about 1 tkt = ?

1×24=24

24÷16 = 1.5 dollars or you round off to the nearest 5 cents Making the answer to be 2 Dollars per ticket

Bill spent less than $20 on the composition books which can be written as x < 20.

The relation between two unequal expressions is defined as inequality.

Given that, Bill spent less than $26 on a game and some composition books.

Let the cost of composition books be x.

Then, the total cost is represented by:

6 + x < 26

x < 26 - 6

x < 20

Hence, Bill spent less than $20 on the composition books which can be written as x < 20.

To learn more about inequalities, click here:

https://brainly.com/question/28823603

#SPJ1

The effective interest on £2000 at a 3% interest rate compounded quarterly over a period of 4 years is approximately £245.15.

To calculate the effective interest, we need to use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = the future value of the investment (including interest)

P = the principal amount (initial investment)

r = the annual interest rate (as a decimal)

n = the number of compounding periods per year

t = the number of years

In this case, the principal amount (P) is £2000, the annual interest rate (r) is 3% (or 0.03 as a decimal), the compounding is done quarterly (n = 4), and the investment period (t) is 4 years.

Plugging the values into the formula:

A = £2000(1 + 0.03/4)^(4*4)

= £2000(1 + 0.0075)^16

= £2000(1.0075)^16

≈ £2000(1.126825)

Calculating the future value:

A ≈ £2253.65

To find the effective interest, we subtract the principal amount from the future value:

Effective Interest = £2253.65 - £2000

≈ £253.65

Therefore, the effective interest on £2000 at a 3% interest rate compounded quarterly after 4 years is approximately £253.65.

Learn more about compound interest here:

https://brainly.com/question/22621039

#SPJ11

Answer:

y= 30 + 3.50

Step-by-step explanation:

lol I think you're Giselle for my school but that's what the answer it im pretty sure.

Answer:

first answer

Step-by-step explanation:

Hi, this is correct because repeating decimals are rational numbers.

Rational numbers can be written by a fraction of integers.

If there is a pattern, it means that this is the division of two integers.

hope this helps

Answer:

yes

Step-by-step explanation:

If the two cylinders are similar, that means that the ratio between the diameter and the height will be the same in both solids.

In the bottom cylinder, we have a ratio of 3ft to 12ft. This is a ratio of 3:12, or 1:4, where the 1 is the height and 4 is the diameter.

The top cylinder has a height of 8 inches, meaning that the 8 corresponds to the 1 in the ratio. Thus, we can set up the equation like this:

\(\frac{1}{4} =\frac{8}{x}\)

To get from 1 to 8, we have to multiply by 8. But because we don't want to change the ratio, we have to multiply the denominator by 8 as well:

\(\frac{1}{4}*\frac{8}{8}=\frac{8}{32}\)

That means the top cylinder has a diameter of 32. But we can't forget our units. Because we used 8 inches in our ratio, that means the diameter is 32 inches.

Answer:

4. Circumference = diameter × π

8× 3. 14= 25. 12 ~25. 1

5. 13×3. 14= 40. 82 ~40. 8

6. Diameter= radius ×2

3. 5×2=7

Diameter = 7

7× 3. 14= 21. 98 ~22

Answer:

24

Step-by-step explanation:

I think you meant PQRS not ABCD?

If so, perimeter is the sum of all four sides of a square. Since square has same side lengths,

Perimeter = 4(2x+8)

96=8x+32

64=8x

x=8

So plugging this back into expression,

2(8)+8= 24

Richard's net pay for the week, considering Social Security, Medicare, and FIT deductions, can be calculated by subtracting the total deductions from his gross earnings.

First, let's determine the amount deducted for Social Security. The Social Security rate is 6.2%, and the maximum earnings subject to this deduction are $118,500. Since Richard is $1,000 below the maximum level, the amount subject to Social Security deduction is $1,000. Therefore, the Social Security deduction is 6.2% of $1,000.

Next, we calculate the Medicare deduction. The Medicare rate is 1.45%, and it is applied to the entire earnings of $1,700.

To calculate the FIT deduction, we need additional information about Richard's taxable income, tax brackets, and exemptions. Without this information, we cannot provide an accurate calculation for the FIT deduction.

Finally, we subtract the total deductions (Social Security, Medicare, and FIT) from Richard's gross earnings of $1,700 to obtain his net pay for the week.

Learn more about subtract here: brainly.com/question/28008319

#SPJ11

Answer:

401

Step-by-step explanation:

Answer:

-14 -8

Step-by-step explanation:

Answer

-14,-8

i did this on ttm and got it correct

Answer: ( 4 , 8 )

Step-by-step explanation:

3x - 2y = -4

y = 2x

Substitute the second equation into the first

3x - 2(2x) = -4
3x - 4x = -4
-1x = -4
x = 4

y = 2(4)
y=8

( 4 , 8 )

Note that  it is important to remember when converting a music file from analog data to digital data to use:

The greater the sample rate, the more snapshots of the audio stream are captured. The audio sample rate, measured in kilohertz (kHz), defines the frequency range sampled in digital audio. under most DAWs, you may change the sample rate under the audio options.

Continuous variables are numerical variables with an endless number of possible values between any two values. A continuous variable can be either numeric or date/time based.

Learn more about higher sampling rate:
https://brainly.com/question/31390480
#SPJ1

Answer:

45

Step-by-step explanation:

A number consists of 2 digits whose sum is 9 => x + y = 9

If the order of the numbers is inverted, the result is equal to the given number plus 9 units => (10*y + x) + 9 = (10*x + y)

Thus:

x + y = 9  => multiply by -9 => 9*y + 9*x = 81

10*y + x + 9 = 10*x + y =>  9*y - 9*x = -9

We are left then that:

9*y + 9*x = 81  (1)

9*y - 9*x = -9  (2)

we add both equations

18y = 72

y = 72/18 = 4

replacing

x + y = 9

x + 4 = 9

x = 5

Therefore the number is (10y + x) => (10 * 4 + 5) => 45

The answer is: a. Yes, the forecast fails the bias test.

To determine whether the forecast fails the bias test, we need to compare the Average Error (AE) with zero.

If the AE is significantly different from zero, it indicates the presence of bias in the forecast. If the AE is close to zero, it suggests that the forecast is unbiased.

In this case, the Average Error (AE) is -2.0, which means that, on average, the forecast is 2.0 units lower than the actual values. Since the AE is not zero, we can conclude that there is a bias in the forecast.

Therefore, the answer is:

a. Yes, the forecast fails the bias test.

Learn more about bias test from

https://brainly.com/question/32000527

#SPJ11

The answer to this question is less coping strategies.

What are coping strategies?

Coping strategies are ways through which an individual gains some control over their emotions

Yes research has proved that the   Younger adults use more coping strategies than Older adults because now a days so methods for coping strategies like Cigerrate, alcohol, drugs etc things are easily being available to them and they use that to overcome their emotions

where as older adults have already seen most of their life so they are less likely to use these things to overcome their emotions

TO learn more about coping strategies click below

https://brainly.com/question/990775

#SPJ4

Answer:

0.84 m^2

Step-by-step explanation:

Long: 1200 millimeter = 1.2 meter

Wide: 700 millimeters = 0.7 meter

Area of rectangle: L x W

1.2 x 0.7 = 0.84 m^2

Answer:

Let's start by translating the sentence into an equation using algebra.

Let's say the number is represented by "x".

According to the problem:

"Twice a number" can be written as "2x".

"If twice a number is decreased by 13" can be written as "2x - 13".

"The result is 9" can be written as "= 9".

Putting it all together, we get the equation:

2x - 13 = 9

Now we can solve for x:

2x = 22

x = 11

Therefore, the number is 11.

The prοbabiIity οf the spinner stοpping at green and a yeIIοw card being seIected is 1/18.

PrοbabiIity is a measure οf the IikeIihοοd οf an event οccurring, expressed as a number between 0 and 1. It is caIcuIated as the number οf favοrabIe οutcοmes divided by the tοtaI number οf pοssibIe οutcοmes.

The prοbabiIity οf the spinner stοpping at green is 1/3 since there are three equaI parts.

The prοbabiIity οf seIecting a yeIIοw card frοm the six cards is 1/6 since there is οne yeIIοw card οut οf six cards in tοtaI.

Tο find the prοbabiIity οf bοth events happening, we muItipIy the individuaI prοbabiIities:

P(green and yeIIοw) = P(green) * P(yeIIοw)

= (1/3) * (1/6)

= 1/18

Therefοre, the prοbabiIity οf the spinner stοpping at green and a yeIIοw card being seIected is 1/18.

Tο learn more about Probability from the given link

https://brainly.com/question/24756209

#SPJ1

The sample space of rolling a six-faced dice is {1, 2, 3, 4, 5, 6}.

The sample space of an experiment is the set of all possible outcomes of the experiment. In the experiment of rolling a six-faced dice, the sample space is the set of all possible values that the dice can show when it is rolled.

Since a dice has six faces, each with a distinct number (1, 2, 3, 4, 5, or 6), the sample space of the experiment of rolling a six-faced dice is {1, 2, 3, 4, 5, 6}. This means that any time the dice is rolled, it can only show one of these six values.

It's important to note that the sample space is a finite set, as there are only a limited number of possible outcomes. In this case, the sample space contains only six elements, each representing one of the faces of the dice that can show up when it is rolled.

To know more on sample space

https://brainly.com/question/30206035

#SPJ4

Answer:

y = 125°

Step-by-step explanation:

the sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

here n = 5 , then

sum = 180° × (5 - 2) = 180° × 3 = 540°

sum the interior angles and equate to 540°

y + 86° + 142° + 72° + 115° = 540°

y + 415° = 540° ( subtract 415° from both sides )

y = 125°

Answer:

125°

Step-by-step explanation:

First you find the value of total interior angles

Since it's a Pentagon

\((5- 2) \times 180\)

Then you arrive at 540°

When you sum all the angles in the Pentagon together they should be equal to 540

\(540 = 86 + 142 + 72 + 115 + y\)

\(540 = 415 + y\)

\(540 - 415 = y\)

\(y = 125\)