Name a Linear Pair.
​

the distance from the plane to the radar station is increasing at a rate of approximately 30.84 kilometers per minute.

A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The total of the other two angles is 90 degrees. Perpendicular and the triangle's base are the sides that make up the right angle. The longest of the three sides, the third side is known as the hypotenuse.

Given, A plane flying with a constant speed of 25 km/min passes over a ground radar station at an altitude of 12 km and climbs at an angle of 30 degrees.

We can use the law of cosines to find d:

d² = 12² + (h + 12)² - 2(12)(h + 12)cos(θ)

Since the plane is climbing at an angle of 30 degrees, we can use trigonometry to find h:

sin(30) = h / (25 km/min * 2 min)

h = 25 km/min

Now we can substitute this value of h into the equation for d and simplify:

d² = 12² + (25 + 12)² - 2(12)(25 + 12)cos(θ)

d² = 12² + 37² - 2(12)(37)cos(θ)

d² = 144 + 1369 - 888cos(θ)

d² = 1513 - 888cos(θ)

To find the rate at which d is changing, we can take the derivative of both sides of this equation with respect to time:

2dd/dt = -888(d(cos(θ))/dt)

Since the plane is flying with a constant speed of 25 km/min, we can use trigonometry to find d(cos(θ))/dt:

cos(θ) = 12/d

d(cos(θ))/dt = -(12/d²)(dd/dt)

d(cos(θ))/dt = -(12/d²)(25 km/min)

Now we can substitute these values into the equation for the rate of change of d:

2dd/dt = -888(-(12/d²)(25 km/min))

2dd/dt = (888*12)/(d²)(25 km/min)

dd/dt = (5328)/(d²) km/min

Finally, we can substitute the value we found for d into this equation to get the rate at which d is changing 2 minutes later:

d = sqrt(1513 - 888cos(θ))

θ = 30 degrees

dd/dt = (5328)/(d²) km/min

dd/dt = (5328)/(1513 - 888cos(30)) km/min

dd/dt ≈ 30.84 km/min

Therefore, the distance from the plane to the radar station is increasing at a rate of approximately 30.84 kilometers per minute.

Learn more about right-angle triangles here:

https://brainly.com/question/3770177

#SPJ1

Alright! Let's imagine the farmer's land as a huge pizza, with the western fields being on one half, and the eastern fields being on the other half. Imagine the crops are like the toppings scattered across this pizza.

Now, when the farmer takes a random sample of 12 crops from the western fields, it's like picking 12 toppings from the left half of the pizza. Similarly, taking a sample of 12 crops from the eastern fields is like picking 12 toppings from the right half of the pizza.

Now, let's talk about the term "independent". When we say that two samples are independent, we mean that picking items from one sample doesn't affect what might be picked in the other sample. Imagine if you had a bag of red marbles and a bag of blue marbles. If you pick some red marbles, it doesn’t change what's in the bag of blue marbles. They're independent.

Back to the pizza analogy: since the western and eastern fields are two separate halves of the land (like two halves of the pizza), picking crops from the western fields doesn't affect the crops in the eastern fields, and vice versa. They are like two separate bags of marbles.

This is why we can say that the samples the farmer takes from the western and eastern fields are independent. It’s because the health or the state of the crops in the western fields doesn’t change what’s going on with the crops in the eastern fields, and picking 12 crops from one side doesn't change what you could pick from the other side. The two groups of crops are doing their own thing, like dancers in two separate dance studios.

In summary, when the farmer takes 12 crops from the western fields and 12 crops from the eastern fields, these samples are considered independent because what happens in one field doesn’t mess with what happens in the other field. They are like two separate pizzas with their own toppings, or like two bags of marbles minding their own business.

Answer:

the answer is C......

Step-by-step explanation:

!!!!!!!!!!!

The probability that the card selected is a heart is P(heart) = 13/52 = 1/4.

Since there are 13 hearts in the deck of 52 cards. The probability that the card selected is an Ace is P(Ace) = 4/52 = 1/13, since there are 4 Aces in the deck of 52 cards.

To find the probability that the card selected is a heart or an Ace, we can use the formula P(heart or Ace) = P(heart) + P(Ace) - P(heart and Ace), where P(heart and Ace) is the probability of selecting a card that is both a heart and an Ace.

Since there are only 1 Ace of Hearts in the deck, P(heart and Ace) = 1/52. Therefore, P(heart or Ace) = 1/4 + 1/13 - 1/52 = 17/52.

Therefore, the probability that the card selected is a heart or an Ace is 17/52.

For more questions like Probability click the link below:

https://brainly.com/question/30034780

#SPJ11

Answer:

-2 ≤ x ≤ 2

Step-by-step explanation:

x values will be somewhere between -2 and 2 and include -2 and 2

Answer:

1.6 hours so 96 minutes

Step-by-step explanation:

The  sum of the links of the two parallel sides is 5cm

The formula for calculating the area of a trapezoid is expressed as:

A = 0.5(a+b)h

where

h is the height of the trapezoid

a+b is the sum of the sides

Substitute

20 = 0.5(a+b)8

40 = 8(a+b)

a+b = 40/8

a+b = 5cm

Hence the  sum of the links of the two parallel sides is 5cm

Learn more on area of trapezoid here: https://brainly.com/question/1410008

#SPJ1

Answer:

0.000025

two point five times ten to the power of negative five

a. So the function is not continuous at x = 0. Also, since lim_{x→0} (1/sin(x)) does not exist, the function is not differentiable at x = 0.

b. This function is continuous everywhere, including x = 0. However, it is not differentiable at x = 0 because the derivative is undefined (the limit does not exist).

c. This limit exists and is equal to cos(log(2)) / 2, so h(x) is differentiable at x = 0.

d. Therefore, the correct option is (D): P2, Q1; R4; S3, where P, Q, R, and S correspond to the functions (a), (b), (c), and (d) respectively.

Function and determine if it is continuous and differentiable at x = 0.

(a) f(x) = 4(1-sin(πx)), 1/sin(x), tan(x), if x = 0, 12(x) otherwise

For x ≠ 0, the function is a combination of continuous and differentiable functions, so it is itself continuous and differentiable. For x = 0, we have:

f(0) = 4(1-sin(0)) = 4

lim_{x→0} f(x) = lim_{x→0} (1/sin(x)) = ∞ (since sin(x) approaches 0 from both sides)

(b) g(x) = sin(x), if x = 0, 1 otherwise

This function is continuous everywhere, including x = 0. However, it is not differentiable at x = 0 because the derivative is undefined (the limit does not exist).

(c) h(x) = sin(log(x+2))

This function is continuous and differentiable for all x > -2. At x = 0, we have:

h(0) = sin(log(2)) ≈ 0.693

h'(x) = cos(log(x+2)) / (x+2)

Taking the limit as x approaches 0, we get:

lim_{x→0} h'(x) = cos(log(2)) / 2

(d) k(x) = [x] sin(x), if x = 0, 0 otherwise

For x ≠ 0, the function is a combination of continuous and differentiable functions, so it is itself continuous and differentiable. For x = 0, we have:

k(0) = [0] sin(0) = 0

lim_{x→0} k(x) = lim_{x→0} ([x] sin(x)) = 0

So the function is continuous at x = 0. Also, since lim_{x→0} ([x] sin(x))/x = lim_{x→0} sin(x) = 0, the function is differentiable at x = 0 and its derivative is 0.

Learn more about Differentiable visit: brainly.com/question/30760662

#SPJ4

Answer: 0.6763 cm∧2

Step-by-step explanation: Variance is one of the measures of dispersion which is the the second central moment in probability. It is defined as a measure of by how much the values in a data set differs from the mean of the values. Thus it is the average of the squares of the deviations from the mean as this ensures that both the negative and positive deviations do not cancel each other out.

The sample variance would be calculated as follows:

Population size is 7 (5.6 4.9 6.0 5.1 5.5 5.1 7.5)

Mean: Sum of samples / population size ;

(5.6 4.9 6.0 5.1 5.5 5.1 7.5) / 7 = 5.67

Applying the formula for variance: [ Summation (x - mean) ] / population size =( |5.6 - 5.67| + |4.9 - 5.67| + |6.0 - 5.67| + (|5.1 - 5.67|) * 2 + | 5.5 - 5.67| + |7.5 - 5.67|) / 7 = 0.6763 cm^2

The expected monetary value of your lottery ticket is £60.

To calculate the expected monetary value of the lottery ticket, we need to multiply each outcome by its probability and then sum the products:

Expected Monetary Value = (Probability of winning £500 × £500) + (Probability of winning £25 × £25) + (Probability of winning £0 × £0)

EMV = (0.1 × 500) + (0.4 × 25) + (0.5 × 0)

EMV = 50 + 10 + 0

EMV = £60

Therefore, the expected monetary value of your lottery ticket is £60. This means that if you were to buy many tickets over time, you could expect to win an average of £60 per ticket. However, keep in mind that this is just an average and does not guarantee that you will win this amount on any particular ticket.
Therefore, the expected monetary value of your lottery ticket is £60.

Learn more about expected monetary value:https://brainly.com/question/14909520

#SPJ11

Answer:

Step-by-step explanation:

Step as below:

Answer: 2.4

Step-by-step explanation: just use a calculator???

Answer:

2.4

Explanation:

- The rate of the jet in still air is 615 miles per hour.
- The rate of the Jetstream is -40 miles per hour.

The rate of the jet in still air can be found by averaging the speeds of the jet against and with the Jetstream.

Let's calculate the rate of the jet in still air step-by-step:

1. First, find the average distance traveled against and with the Jetstream:
  - Distance traveled against the Jetstream: 2875 miles
  - Distance traveled with the Jetstream: 3275 miles
  - Average distance: (2875 + 3275) / 2 = 6150 / 2 = 3075 miles

2. Next, find the average time taken against and with the Jetstream:
  - Time taken against the Jetstream: 5 hours
  - Time taken with the Jetstream: 5 hours
  - Average time: (5 + 5) / 2 = 10 / 2 = 5 hours

3. Now, calculate the rate of the jet in still air:
  - Rate = Distance / Time
  - Rate = 3075 miles / 5 hours = 615 miles per hour

The rate of the jet in still air is 615 miles per hour.

To find the rate of the Jetstream, subtract the rate of the jet in still air from the rate of the jet with the Jetstream:
  - Rate of the Jetstream = Rate with Jetstream - Rate in still air
  - Rate of the Jetstream = 615 miles per hour - 3275 miles / 5 hours
  - Rate of the Jetstream = 615 miles per hour - 655 miles per hour
  - Rate of the Jetstream = -40 miles per hour

Therefore, the rate of the Jetstream is -40 miles per hour.

In summary:
- The rate of the jet in still air is 615 miles per hour.
- The rate of the Jetstream is -40 miles per hour.

to learn more about distance

https://brainly.com/question/33716087

#SPJ11

Answer:

\(\angle BDC=80^{\circ}\)

Step-by-step explanation:

We are given that

\(\angle ABC=69^{\circ}\)

\(\angle ACB=31^{\circ}\)

We have to find the angle BDC.

In triangle ABC

Sum of interior angles of triangle=180 degrees

\(\angle ABC+\angle ACB+\angle BAC=180^{\circ}\)

\(69+31+\angle BAC=180\)

\(100+\angle BAC=180\)

\(\angle BAC=180-100\)

\(\angle BAC=80^{\circ}\)

\(\angle BAC=\angle BDC=80{\circ}\)

Angles subtended on the same are ac are equal.

\(\angle BDC=80^{\circ}\)

The probability that the mean number of moths in a sample of size 50 is greater than or equal to 0.6 is 8.08%

The CLT states that the distribution of the sample means of a random variable with a finite mean and standard deviation approaches a normal distribution as the sample size increases.

In this case, the population mean is 0.5, and the population standard deviation is 0.7. Since we have a sample size of 50, the standard deviation of the sample means would be

=> 0.7 / √(50) = 0.099.

Next, we need to calculate the z-score, which measures the number of standard deviations from the mean.

In this scenario, we want to find the probability that the mean number of moths in a sample of size 50 is greater than or equal to 0.6. So, we would plug in x = 0.6, μ = 0.5, σ = 0.7, and n = 50 into the z-score formula. This gives us

=> (0.6 - 0.5) / (0.7 / √(50)) = 1.41.

Using a standard normal distribution table or calculator, we can find that the probability of a z-score of 1.41 or higher is approximately 0.0808. Therefore, the estimated probability that the mean number of moths in a sample of size 50 is greater than or equal to 0.6 is 0.0808 or about 8.08%.

To know more about standard deviation here.

https://brainly.com/question/16555520

#SPJ4

Complete Question:

The gypsy moth is a serious threat to oak and aspen trees. A state agriculture department places traps throughout the state to detect the moths. Each month, an SRS of 50 traps is inspected, the number of moths in each trap is recorded, and the mean number of moths is calculated. Based on years of data, the distribution of moth counts is discrete and strongly skewed, with a mean of 0.5 and a standard deviation of 0.7. Estimate the probability that the mean number of moths in a sample of size 50 is greater than or equal to 0.6.

Answer:

29x+8 is the answer

Step-by-step explanation:

12x-4+17x+8

=12x+17x-4+8

=29x+8

Hope it will help ^_^

The point estimate of the difference between the mean number of miles that Buffalo residents travel per day and the mean number of miles that Boston residents travel per day is 4.3 miles/day. The 95% confidence interval for the difference between the two population means is (2.08, 6.52) miles/day.

a)

The point estimate of the difference between the mean number of miles that Buffalo residents travel per day and the mean number of miles that Boston residents travel per day can be calculated as:

Point estimate = Mean of Buffalo residents - Mean of Boston residents

Point estimate = 22.5 miles/day - 18.2 miles/day

Point estimate ≈ 4.3 miles/day

Therefore, the point estimate of the difference between the mean number of miles that Buffalo residents travel per day and the mean number of miles that Boston residents travel per day is 4.3 miles/day.

b)

To calculate the 95% confidence interval for the difference between the two population means, we can use the formula:

Confidence interval = (Point estimate) ± (Critical value) * (Standard error)

The critical value depends on the desired confidence level and the sample size. Since the sample sizes are relatively large (70 and 40), we can approximate the critical value using a Z-distribution.

For a 95% confidence level, the critical value for a two-tailed test is approximately 1.96.

The standard error can be calculated as:

Standard error = sqrt((s1^2 / n1) + (s2^2 / n2))

where s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.

Standard error = sqrt((8.5^2 / 70) + (7.1^2 / 40))

Standard error ≈ 1.1307

Now, we can calculate the confidence interval:

Confidence interval = 4.3 ± 1.96 * 1.1307

Confidence interval ≈ (2.08, 6.52)

Therefore, the 95% confidence interval for the difference between the two population means is (2.08, 6.52) miles/day.

To learn more about mean: https://brainly.com/question/1136789

#SPJ11

Answer:

The formula for circumference of s circle is pi x diameter.

If the circumference is 28 we can divide it by pi to get the Diameter.

28/ pi = 8.9126768131461388030574907488608042739297 rounded to 8.91 (2dp)

The radius is half of the diameter, so this means 8.91 / 2 = 4.46 ft (rounded to 2dp)

Answer:

\(Width\ of\ the\ rectangle\ is\ 20x^4y\)

Step-by-step explanation:

\(We\ know\ that,\\Area\ of\ a\ rectangle=Length*Width\\Here,\\Let\ the\ width\ of\ the\ rectangle\ be\ b\\20x^6y^4=x^2y^3b\\b=\frac{20x^6y^4}{x^2y^3} \\b=20x^{(6-2)}y^{(4-3)}\\b=20x^4y\)

Answer: Option A.

Step-by-step explanation:

The function for the volume of a sphere is given by V(r) = (4/3)πr^3.

The radius of the sphere is increasing at a rate of 2 mm per second, which means that the radius at time t seconds is given by r(t) = 2t mm.

To find the volume of the sphere at time t, we can substitute the expression for r(t) into the formula for the volume of the sphere:

V(t)  = (4/3)πr(t)^3

      = (4/3)π(2t)^3

      = (4/3)π(8t^3)

      = (32/3)πt^3

V(t)= (32/3)πt^3

(V ∘ r)(t) = V(r(t))

              = V(2t)

              = (32/3)πt^3

Therefore, the function that gives the volume of the sphere at time t is option A.

According to the question, the four consecutive numbers can be written as :

First = \(x\); Second = \(x+2\);  Third = \(x+4\); Fourth = \(x+6\)

As per the question, the final expression is :

\(2((x+2)+(x+4)) = 3(x)+32\)

\(4x+12 = 3x+32\)

\(x = 20\)

Therefore, the four values can be calculated by substituting the above value:

\(x=20; x+2=22; x+4=24; x+6=26\)

The four consecutive numbers are: \(20,22,24,26\)

Substitute the calculated values in the final expression, to check whether the answer is correct or not.

\(2(22+24) = 3(20)+32\)

\(92=92\)

Therefore, the calculated values are correct.

What are consecutive terms?

Consecutive terms are those terms which follow one sequential order.

To learn more about the consecutive terms from the given link:

https://brainly.com/question/28350604

#SPJ4

minutes of long-distance calls in a month make plan A the better deal= 300.

you are choosing between two long-distance telephone plans. Plan A has a monthly fee of $15 with a charge of $0.08 per minute for all long-distance calls. Plan B has a monthly fee of $3 with a charge of $0.12 per minute for all long-distance calls.

f(x)=15+0.08x

g(x)=3+0.12x

The costs for the two planes be the same when f(x)=g(x),

15+0.08x=3+0.12x

12=0.04x

x=300 minut.

f(x)=15+0.08*300=15+24=39.

g(x)=3+0.12*300=3+36=39.

 minutes of long-distance calls in a month make plan A the better deal= 300.

learn more about long-distance,

https://brainly.com/question/332039

#SPJ4

She can run 3 miles within her time limit.

The formula for distance, if you know the time and the average speed, is:

d = v x t

where v is the velocity (average speed)

t is the time and d is the distance,

so you can read it as Distance = Speed x Time.

for example, if speed is given in mph, the result will be in miles

if it is given in km/h, the result will be in kilometers.

Suzie is going to run for 32 minutes. She runs 1 mile in 5 minutes and she cools off for 7 minutes

5+7=12 minutes

she runs 1 mile and needs 12 minutes total

32÷12=2⋯8

8-5=3 minutes

2+1=3      3×1=3 miles

She can run 3 miles within her time limit.

To know more about Distance:

https://brainly.com/question/26550516

#SPJ4

If segment BD is congruent to segment BC, and BD = 4x - 18, BC = x + 3, and AC = 34, then AB = 31/x.

Let the equation be AB + BC = AC

substitute the values in the above equation, we get

AB + x + 3 = 34

simplifying the value of x,

Subtract A B from both sides AB + x + 3 - AB = 34 - A B

x + 3 = 34 - AB

Subtract 3 from both sides,

x + 3 - 3 = 34 - AB - 3

x = -AB + 31

Plug in this value of x into the line segments to find BC and AC.

Where, BC = x + 3

substitute the value of x in the above equation, we get

BC = [-AB + 31 ] + 3

BC = -AB + 34

Then, AB + BC = AC

x = -AB + 31

AB = 31/x

Hence, If segment BD is congruent to segment BC, and BD = 4x - 18,

BC = x + 3, and AC = 34, then AB = 31/x.

To learn more about Congruent angles, refer to:

https://brainly.com/question/28262429

#SPJ1

Answer:

The first statement is correct(15+(-7)+4+8)=20

\(\frac{AB}{A"B"} = \frac{1}{4}\)  equation clearly illustrates how AABO and AA"B"C relate to one another.

An equation is, for instance, 3x - 5 = 16. We can solve this equation and determine that the value of the variable x is 7.

The three main types of linear equations are the slope-intercept form, standard form, and point-slope form.

Considering the data:

Dilation by a scale factor of 4 from the origin in the form of an A'B'C' reflection over x = 1

<=> The two triangles are comparable to one another since triangles can have the same shape but differ in size, so A′′B′′C′′ is 4 times larger than ABC.

=> the connection between "ABC" and "A"B"C" .

\(\frac{AB}{A"B"} = \frac{1}{4}\)

We settle on C.

\(\frac{AB}{A"B"} = \frac{1}{4}\)  equation clearly illustrates how AABO and AA"B"C relate to one another.

To know more about equation visit:-

https://brainly.com/question/29657992

#SPJ1

The equation most closely models the line of best fit for the scatter plot is y = 2.5x

A line is the distance between two points. The equation of a line in point-slope form is given as y =mx + b

Using the coordinate points on the line (3, 5000) and (9, 20000)

Get the slope

Slope = 20000-5000/9-3
Slope = 15000/6 = 2500

Determine the y-intercept

5000 = 2500(3) + b

b = 5000 - 7500
b = -2500

Determine the equation

y = 2.5x - 2.5

Hence the equation most closely models the line of best fit for the scatter plot is y = 2.5x

Learn more on line plot here: https://brainly.com/question/8989301

#SPJ1