Flying against the wind, an airplane travels 4720 kilometers in 8 hours. Flying with the wind, the same plane travels 4040 kilometers in 4 hours. What is the rate of the plane in still air and what is the rate of the wind?

2) P(did not exercise | did not catch a cold) = 1/16

3) P(did not catch a cold | did not exercise) = 1/6

4) The events "did not exercise" and "did not catch a cold" are dependent events.

"Probability is a branch of mathematics which deals with finding out the likelihood of the occurrence of an event."

P(A) = n(A) / n(S)  

where, n(A) is the number of favorable outcomes and n(S) is the total number of events in the sample space.

For events A, B,

P(A|B) means, event A and event B are depends on each other.

P(A | B) = n(A ∩ B) / P(B)

For given situation:

the total number of doctor’s patients: 8 + 30 + 10 + 2 =50

⇒ n(S) = 50

Let event A: did not exercise

⇒ n(A) = 10 + 2

⇒ n(A) = 12

⇒ P(A) = 12/50

event B: did not catch cold

⇒ n(B) = 30 + 2

⇒ n(B) =32

⇒ P(B) = 32/50

patient who did not catch a cold as well as who did not exercise = A ∩ B

⇒ n(A ∩ B) = 2

⇒  P(A ∩ B) = 2/50

2) To find: P(did not exercise | did not catch a cold)

⇒ P(A | B) = P(A ∩ B) / P(B)

⇒ P(A | B) = [tex]\frac{\frac{2}{50} }{ \frac{32}{50} }[/tex]

⇒ P(A | B) = 2/32

⇒ P(A | B) = 1/16

3) To find: P(did not catch a cold | did not exercise)

⇒ P(B | A) = P(B ∩ A) / P(A)

⇒ P(B | A) = [tex]\frac{ \frac{2}{50} }{ \frac{12}{50} }[/tex]

⇒ P(B | A) = 2/12

⇒ P(B | A) = 1/6

4) Since P(B | A) ≠ P(B)

i.e., P(did not catch a cold | did not exercise) ≠ P(did not catch a cold)

This means, the events "did not exercise" and "did not catch a cold" are dependent.

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Answer:

I found a calculator that does the work for you it's called calculator soup

Step-by-step explanation:

here's the link https://www.calculatorsoup.com/calculators/statistics/quartile-calculator.php

Therefore, the number of stickers David has in terms of d is d+10 and the number of stickers Matt has in terms of d is 2d-10.

A term is a phrase or statement that is used to convey a certain meaning. Rap, punk, grunge, and heavy metal are examples of words used to characterize certain musical genres. To the majority of people, at least, "sweetie" is a word of affection.

A phrase is a collection of words with significance but which is not usually a complete sentence. A set of words that form a sentence must have a topic.

We know that Matt has twice as many stickers as David, so if David has d stickers, then Matt has 2d stickers.

When Matt gives David 10 stickers, David has d+10 stickers and Matt has 2d-10 stickers.

So the number of stickers David has in terms of d is d+10 and the number of stickers Matt has in terms of d is 2d-10.

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Answer:

33.46

Step-by-step explanation:

Using the cosine rule;

b² = a²+c²-2accosB

b² = 51²+38²-2(51)(38)cos41

b² = 2601+1444-2(51)(38)cos41

b² = 4045-2,925.25

b² = 1,119.74

b = √1,119.74

b = 33.46

Hence the value of b to nearest hundredth is 33.46

Answer:

sine: 5:13

cosine: 12:13

tangent: 5:12

Step-by-step explanation:

sine is opposite:hypotenuse

cosine is adjacent:hypotenuse

tangent is opposite:adjacent

Answer:

y < -5

Step-by-step explanation:

The catch for this problem is remembering that when you divide by a negative number, your > or < will switch, so in this case, our > sign will become a < sign, otherwise its not too complicated!

-2y > 10

y < -5

Answer:

[tex]x^{4}[/tex] + 8x³ + 12x² - 16x + 4

Step-by-step explanation:

Given

[(x² + 4x) - 2 ]² ← simplify contents of bracket

= (x² + 4x - 2)² = (x² + 4x - 2)(x² + 4x - 2)

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

x²(x² + 4x - 2) + 4x(x² + 4x - 2) - 2(x² + 4x - 2) ← distribute parenthesis

= [tex]x^{4}[/tex] + 4x³ - 2x² + 4x³ + 16x² - 8x - 2x² - 8x + 4 ← collect like terms

= [tex]x^{4}[/tex] + 8x³ + 12x² - 16x + 4

Answer:

a)

The margin of error is of 0.33 years.

b)

The margin of error is of 0.67 years.

c)

INCREASES

Step-by-step explanation:

In this question, we have that:

Sample of 109 means that [tex]n = 109[/tex]

The standard deviation of time with the company for all general managers is 2.7 years, which means that [tex]\sigma = 2.7[/tex]

Question a:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.8}{2} = 0.1[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.1= 0.9[/tex], so Z = 1.28.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

So

[tex]M = 1.28\frac{2.7}{\sqrt{109}} = 0.33[/tex]

The margin of error is of 0.33 years.

Question b:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.99}{2} = 0.005[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.005= 0.995[/tex], so Z = 2.575. So

[tex]M = 2.575\frac{2.7}{\sqrt{109}} = 0.67[/tex]

The margin of error is of 0.67 years.

(c) In general, increasing the confidence level the margin of error (width) of the confidence interval.

We have that:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

That is, M and z are direct proportional, and since z increases when the confidence level increases, the marign of error will increase. So the answer is INCREASES.

Answer:

fixed order

Step-by-step explanation:

Answer:

Step-by-step explanation:

It’d be C

The solution for the question found using the double angle formula for cosine is -[tex]\frac{7}{25}[/tex].

What are double angle formulae?

There are some trigonometric formulas that are known as double angle formulae because they contain double angles, such as Sin 2x, Cos 2x, and Tan 2x.

The double angle formula for cosine is

Cos 2θ = Cos²θ - Sin²θ

           =2Cos²θ – 1

            = 1 – 2Sin²θ

Given sinθ = [tex]\frac{4}{5}[/tex]

         cos(2θ) = 1-2sin²θ = [tex]1-2[/tex]×( [tex]\frac {4}{5}[/tex])² = [tex]1-[/tex] [tex]\frac{32}{25}[/tex] = [tex]\frac{-7}{25}[/tex]

Therefore Cos(2θ) fund using double angle formula is -[tex]\frac{7}{25}[/tex]

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The solution for the question found using the double angle formula for cosine is -.7/-25

There are some trigonometric formulas that are known as double angle formulae because they contain double angles, such as Sin 2x, Cos 2x, and Tan 2x.

An angle is a measure of the amount of rotation between two rays or lines that share a common endpoint, called the vertex of the angle. The two rays or lines are called the sides of the angle, and the endpoint is called the vertex. The size of an angle is typically measured in degrees or radians, with one full rotation around a point (360 degrees or 2π radians) being equal to a full circle.

The double angle formula for cosine is

Cos 2θ = Cos²θ - Sin²θ

          =2Cos²θ – 1

           = 1 – 2Sin²θ

Given sinθ = 4/5

        cos(2θ) = 1-2sin²θ = 1-2×(4/5 )² =  1-32/25 = -7/25

Therefore Cos(2θ) fund using double angle formula is -

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Answer: Mr. Sink bought 7 calves for a total of $3,500, and he later bought another calf for $600, for a total of $4,100.

In total, Mr. Sink bought 7 + 1 = 8 calves.

The mean cost for all of the calves is equal to the total cost of all of the calves divided by the number of calves.

Therefore, the mean cost for all of the calves is 4,100 / 8 = $512.50.

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Its B

Answer:

(3,5,4)

Step-by-step explanation:

B

Answer:

7

Step-by-step explanation:

hope you have a great day!

Answer:

6x6=36 so 36+$6 discount, 42

Step-by-step explanation:

42

Answer:

In the quadratic function "y = -x^2q - 2x + 10", the term "-x^2q" is the coefficient of the quadratic term and is represented by the letter "A". The term "-2x" is the coefficient of the linear term and is represented by the letter "B". The constant term "10" is the coefficient of the constant term and is represented by the letter "C".

The axis of symmetry of the graph of this quadratic function is the line that divides the graph into two congruent halves. It can be found by using the formula "x = -B / 2A". In this case, the axis of symmetry is "x = -(-2) / 2(-x^2q) = x^2q / x".

So in the function "y = -x^2q - 2x + 10", the coefficient of the quadratic term is "A = -x^2q", the coefficient of the linear term is "B = -2x", the coefficient of the constant term is "C = 10", and the axis of symmetry is "x = x^2q / x".

Answer:

There are two. <CEB and <AED. You could put either one.

Step-by-step explanation:

There are two. <CEB and <AED. You could put either one.

Answer: A scale is a ratio of the size of the representation (such as a drawing) to the size of the real-world object being represented. In this case, Patty's drawing uses a scale of 1 inch = 45 feet, and Jamie's drawing uses a scale of 2 inches = 35 feet.

In order to find the side length of Jamie's drawing of one of the side length we need to use a proportion:

Jamie's side length / Patty's side length = Jamie's scale / Patty's scale

So if we know one of the side length of Patty's drawing we can find the side length of Jamie's drawing. Let's assume that the side length of Patty's drawing is x

x / Jamie's side length = 45 / 35

So we can isolate Jamie's side length by multiplying both sides by Jamie's scale of 35ft/2 inches

Jamie's side length = (x*35)/45

This is the length of one side length in Jamie's drawing using the scale of 2 inches = 35 feet. If you don't have the length of one side in patty's drawing you can't find the side length of Jamie's drawing.

Step-by-step explanation:

Answer:

5/7

Step-by-step explanation:

5,6,7,1, and 3 would have to be rolled, which is 5 out of the 7 numbers that can possibly be rolled

9514 1404 393

Answer:

  y = -1/12x² +2

Step-by-step explanation:

For vertex (h, k) and vertex-to-focus distance p, the vertex form equation is ...

  [tex]y=\dfrac{1}{4p}(x-h)^2+k[/tex]

Here, the vertex-to-focus distance is -1-2 = -3 units. The vertex is (h, k) = (0, 2). So, the equation of the parabola is ...

  [tex]\boxed{y=-\dfrac{1}{12}x^2+2}[/tex]

Answer:

A 50% chance.

Step-by-step explanation:

After subtracting 1 yellow sock and 1 blue sock, there are 11 blue and 11 yellow socks left.

So a 22 sock total.

The probability of picking another blue sock on the third try is the ratio of blue socks to total socks:

11/22 = 1/2=50%

Answer:

In the form of y=mx+b:

y = -5/6x-5

Step-by-step explanation:

I'm not that good at explaining, but I'll try:

Slope intercept is y=mx+b, M is the slope of the line which is rise over run, the rise is -5 (distance traveled along y-axis) and the run is 6 (distance traveled along x-axis) found from two points: (-6, 0) and (0, -5). Using this data -5/6 can be plugged in for M, and b is the y variable at (0, _) in this case the y variable is -5. The final answer after plugging everything in is y=-5/6x-5, I hope this wasn't too confusing.

Answer:

No the conditions for this test are not met, as 20% of the data has expected value less than 5. And 37.5% data is equal to 5.

Step-by-step explanation:

The conditions for the chi square test independence are

1) the sample is a random sample

2) the variable under study is categorical

3) all expected value of the number of sample observations are greater or equal to 5.

A)The observations must be independent

B) for 2 categories the expected values must be at least 5

C) for the 3 categories the expected values must be at least 1 and no more than 20% may be smaller than 5

The observations given have equal chances of occurrences or are dependent on each other.

The sample collected has 20 % of data having expected values less than 5.

And 37.5% data is equal to 5.

We cannot use a chi-square test to determine whether these two distributions differ significantly because the expected value for some cells is less than 5.

For the considered case, the sample is not large enough.

Although the sample was taken randomly and values are categorical, expected values are sometimes less than 5 for some cells of the contingency table.

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Answer: outlier

Step-by-step explanation:

It is way lower than the rest of the data.

Answer:

Outlier

Step-by-step explanation:

An outlier is a number that lies significantly out of the range of all the other numbers.

I also took the quiz, and this was correct.

Answer:

mode-6

median-5.5

range-7

Answer:

A

Step-by-step explanation:

The greater the range the greater the variability of the numbers

Answer: A

Box plot A because it has a greater median.

Step-by-step explanation:

Hope this help!

Answer: B) 45 minutes.

Step-by-step explanation:

5 minutes * 9 = 45 minutes.

Answer: No

Step-by-step explanation: a rectangle can be a parallelogram because it qualifies to be a parallelogram however a parallelogram can’t be a rectangle because a rectangle has all 90 degree angles and that opposite sides can be equal and parallelograms come in different forms

Answer:

C

Step-by-step explanation: