Amelia flies her airplane through calm skies at a velocity v1. The direction of v1 is 15 degrees north of east, and the speed is 180 km/hr.
Eventually, however, she enters a windy part of the atmosphere and finds that her plane now moves at a velocity v2. The direction of v2 is due east, and the speed is 150 km/hr.

What is the speed of the wind?

In what direction is the wind blowing?
(between 0 and 360 degrees)

Answer:

95.44% probability that a sample of 100 steady smokers spend between $19 and $21

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

[tex]\mu = 20, \sigma = 5, n = 100, s = \frac{5}{\sqrt{100}} = 0.5[/tex]

What is the probability that a sample of 100 steady smokers spend between $19 and $21

This is the pvalue of Z when X = 21 subtracted by the pvalue of Z when X = 19. So

X = 21

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{21 - 20}{0.5}[/tex]

[tex]Z = 2[/tex]

[tex]Z = 2[/tex] has a pvalue of 0.9772

X = 19

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{19 - 20}{0.5}[/tex]

[tex]Z = -2[/tex]

[tex]Z = -2[/tex] has a pvalue of 0.0228

0.9772 - 0.0228 = 0.9544

95.44% probability that a sample of 100 steady smokers spend between $19 and $21

To find the probability that a sample of 100 steady smokers spend between $19 and $21, calculate the Z-score and use a standard normal distribution table or calculator. The probability is approximately 0.3413.

To find the probability that a sample of 100 steady smokers spend between $19 and $21, we can use the Z-score formula. The Z-score is calculated as the difference between the sample mean and the desired value (in this case, $20), divided by the population standard deviation, multiplied by the square root of the sample size.

Z = (x - μ) / (σ / √n)

Plugging in the values we have:

Z = (21 - 20) / (5 / √100) = 1

We can then use a standard normal distribution table or a calculator to find the probability associated with a Z-score of 1. The probability of obtaining a Z-score of 1 or less is approximately 0.8413. Since we want the probability between $19 and $21, we subtract the probability of getting a Z-score of less than 1 from the probability of getting a Z-score of less than or equal to 0. This gives us:

Probability = 0.8413 - 0.5000 = 0.3413

Answer:

5

Step-by-step explanation:

split 20 into 4 and find out how much is one portion the four

Plz mark brainliest

Answer:

c) Two sample t-test

Step-by-step explanation:

Given data

Golfer                          1             2                  3               4

Brand1 (x)                  93          88                112            79

Brand 2 (y)               95          86                 111            77

Mean of x =

                  [tex]\frac{93+88+112+79}{4} = 93[/tex]

            x⁻ = 93

Mean of y

                [tex]\frac{95+86+111+77}{4} = 92.25[/tex]

            y ⁻ = 92.25

Given data

Brand1 (x)         :         93            88                112            79

Brand 2 (y)       :        95             86                111             77

x- x⁻                 :        0                -5                19              -14

y -y ⁻                 :        2.75         -6.25           18.75        -15.25

(x- x⁻)²              :         0                 25             361            196

( y -y ⁻  )²         :       7.5625      39.0625      351.5625    232.5625

S² =     [tex]\frac{sum((x- x^{-} )^{2} +sum (y- y^{-} )^{2} }{n_{1}+n_{2} -2 }[/tex]

[tex]S^{2} = \frac{582+630.75}{4+4-2} = 202.125[/tex]

S = 14.21706

Null hypothesis: H₀: There is no significant difference between the means

Alternative hypothesis: H₁: There is significant difference between the means

Student's t test for difference for means

The test statistic

[tex]t = \frac{x^{-} -y^{-} }{\sqrt{S^{2}(\frac{1}{n_{1} } +\frac{1}{n_{2} } } }[/tex]

[tex]t = \frac{93 -92.25}{\sqrt{202.125(\frac{1}{4 } +\frac{1}{4 } } }[/tex]

on calculation , we get

t = 0.0746

Degrees of freedom ν = n₁ +n₂ -2 = 4+4-2 =6

[tex]t_{\frac{\alpha }{2} } = t_{\frac{0.05}{2} } = t_{0.025} = 2.447[/tex]

The calculated value t = 0.0746 < 2.447 at 0.05 level of significance

null hypothesis is accepted

Conclusion:-

There is no significant difference between the means

Final answer:

The matched pairs t-test is the correct method for analyzing the difference in golfers' scores with two different brands of clubs, as each golfer serves as their control.

Explanation:

The appropriate test to determine if the mean scores differ by brand of club is b. matched pairs t-test. Since the data consists of scores from the same golfers using two different brands of clubs in a controlled setting (meaning, the same golfer's scores are paired with each type of golf club), the analysis compares two related samples. In matched pairs designs, we test the differences by subtracting one measurement from the other. The golfers serve as their controls, eliminating variations between different individuals' performances, which could affect the scores. This is a classic scenario of a paired sample t-test, where each golfer's scores with Brand 1 are paired with their scores with Brand 2, and the difference in scores is analyzed.

Answer:

x=-6

Step-by-step explanation:

y=2x + 5

y= x -1

Plug in the equation for y

x-1=2x+5

Combine like terms

-1=x+5

-6=x

Hope this helps! Please mark brainliest :)

Willy is using a systematic sampling method by selecting every tenth person entering the school to understand milk consumption habits after cereal.

When Willy selects every tenth person who enters the school to determine what percent of students drink the milk after they finish their cereal, he is using a systematic sampling method. This type of sampling involves selecting subjects at regular intervals from an ordered list.

It's a form of probability sampling where the first unit is selected randomly and the subsequent units are selected using a fixed periodic interval.

In the context of the situation provided, this method could potentially provide a more representative sample compared to methods like convenience sampling, but there could be inherent biases if there are underlying patterns in the student arrivals at school that correlate with milk drinking habits after cereal.

Answer:

Domain: { -3,1,6}

Step-by-step explanation:

The domain is the input values

Domain: { 6,1,-3,-3}

We usually put them in numerical order and we do not list the same value twice

Domain: { -3,1,6}

Answer:

$1.50 per can

Step-by-step explanation:

6/4 = 1.5

to check your answer, do 1.50*4, and you get $6

hope this helps :)

Answer:

The unit rate is $1.50 per can.

Step-by-step explanation:

Price: $6

Number of Cans Purchased at This Price: 4

$6/4 cans=$1.50 per can

Answer:

186

Step-by-step explanation:

definition: a_n = a_1 + f × (n-1)

Common difference is 11

The sum of all numbers up through the 17th: 1666

Answer: 824

Step-by-step explanation:

This is problem on progression.

Considering the series/ sequence,

10, 21, 32, 43, 54, ........

To find the 75th term, we first of all find which of the sequence is it, is it, Arithmetic or Geometric sequence .

Now fro this, it is an AP sequence because, when the first term us subtracted from the second term and the common difference added to the second term it produces the third term and so on, . Haven't gotten this, we now apply the formula for finding the number if terms in an AP.

Tn = a + (n - 1 )d, where n = number of terms we are computing for = 75, a = first term = 10, and d = 21 - 10 = 11.

Now substitute for those values in the formula above

T75 = 10 + ( 75 - 1 )11

= 10 + 74 × 11

= 10 + 814

= 824.

Answer:

The height of the triangle, h, is 8 m

Step-by-step explanation:

The formula for the area of a triangle of base b and height h is A = (1/2)(b)(h).

Here b = 15 m and A = 60 m^2.  We want the measure of the height, h.

First we solve the area equation (above) for h:  2A = bh, or h = 2A/b,

and then substitute the given values for b and A:

       2(60 m^2)

h = ------------------ = 8 m

          15 m

The height of the triangle, h, is 8 m

Answer:

Answer is 8 because I did the quiz on my online school.

Hope it helps

Answer:

7

Step-by-step explanation:

THe Triangle Inequality Theorem states that the sum of the two least sides of a triangle must be greater than the third side. In this case, 2 and 6 are less than 10, 3 and 6 are less than 10, 6 and 10 are greater than 16, so the only number left is 7. The sum of seven and six is greater than ten so seven would be the correct answer.

Question:

Triangle D E F. Side D F is 6 inches, side F E is 10 inches, and side E D is question mark.

Which could be a possible length of side DE?

2 in.

3 in.

7 in.

Answer:

C.) 7 in.

Step-by-step explanation:

To calculate the perimeter of a triangle, add the length of its sides. For example, if a triangle has sides a, b, and c, then the perimeter of that triangle will be P = a + b + c. Remember the formula for finding the perimeter of a triangle. For a triangle with sides a, b and c, the perimeter P is defined as: P = a + b + c. What this formula means in simpler terms is that to find the perimeter of a triangle, you just add together the lengths of each of its 3 sides. Since all the three sides of the triangle are of equal length, we can find the perimeter by multiplying the length of each side by 3. 20 + 20 + 20 = 3 × 20 = 60 cm. Thus, the perimeter of an equilateral triangle is 3 times the length of each side. Area of a two-dimensional shape is the space occupied by the shape.

Have a Nice day! <3

Answer:

See explaination

Step-by-step explanation:

B. The equality relation on the real numbers is an equivalence relation.

This statement is true

C. If RR is a reflexive relation on a set S, then any two RR- related elements of S must also be R2R2 related.

This statement is true

F. The less than or equal relation on the real numbers fails to be an equivalence relation because it is reflexive and transitive but not symmetric

This statement is true

H. If RR is an equivalence relation, then R2

This statement is true

The measure of the portion of Earth that can be seen from an airplane 5.7 miles above the ground is approximately 0.163 degrees, when rounded to the nearest tenth. This is found using the formula for the angle subtended by an arc, and then converting from radians to degrees.

To solve this problem, we can use the properties of a circle, since the Earth is approximately spherical in shape. The formula to calculate the angle subtended by an arc (BD⌢) on the Earth's surface is as follows: θ = 2 * arcsin((distance_to_object)/(2 * radius_of_earth)).

So inserting the given values:

We get: θ = 2 * arcsin((5.7)/(2 * 4000)). This will give you an answer in radians, to convert this to degrees multiply by 180/π. In this case, the answer is approximately 0.163 degrees, rounded to the nearest tenth.

https://brainly.com/question/1364009

#SPJ12

Answer: 54 stitches

Step-by-step explanation:

12/2=6

6 stitches= 1 inch

X stitches=9 inches

X=54 stitches

Answer:

1/5 - 60 or b

Step-by-step explanation:

The expression that shows 20% of 60 is 1/5 * 60

The expression is given as:

20% of 60

Express of as *

20% * 60

Express the percentage as fraction

20/100 * 60

Simplify the fraction

1/5 * 60

Hence, the expression that shows 20% of 60 is 1/5 * 60

Read more about product expressions at

https://brainly.com/question/4344214

Answer:

2^-84

Step-by-step explanation:

First simplify inside the parentheses

2^-10 / 4^2

Rewriting 4 as 2^2

2^-10 / 4^2^2

We know that a^b^c = a^(b*c)

2^-10 / 2^(2*2) = 2^-10 / 2^4

We know that a^b / a^c = a^(b-c)

2^-10 / 2^4 = 2^(-10-4) = 2^-14

Replace the term in side the parentheses with 2^-14

2^-14 ^7

We know that a^b^c = a^(b*c)

2^(-14*7)

2^-84

Answer:

The histogram of the sample incomes will follow the normal curve.

Step-by-step explanation:

According to the Central Limit Theorem if we have an unknown population with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.

In this case the researches wants to determine the monthly gross incomes of drivers for a ride sharing company.

He selects a sample of n = 200 drivers and ask them their monthly salary.

As the sample selected is quite large, i.e. n = 200 > 30, the central limit theorem can be applied to approximate the sampling distribution of sample mean by the Normal distribution.

Thus, the histogram of the sample incomes will follow the normal curve.

Answer:

6

Step-by-step explanation:

The line in the middle of the box is the median

Answer:

n=9 10 11

Step-by-step explanation:

Answer: 10

Step-by-step explanation:

Answer:

[tex]\displaystyle \frac{dy}{dx} = \frac{66}{x}[/tex]

General Formulas and Concepts:

Calculus

Differentiation

Derivative Property [Multiplied Constant]:                                                           [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]

Derivative Property [Addition/Subtraction]:                                                         [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle y = 66 \ln x + 135[/tex]

Step 2: Differentiate

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

Answer: The distance of  Observer A from the radio antenna is what fraction  of the distance of Observer B from the radio  antenna?​

It is 1/4.

Step-by-step explanation:

We know that the intensity of electromagnetic waves decreases with the radius squared, this means that we can write a simple relation as:

Intensity(r) = A/r^2

Observer A measures 16 the intensity of observer B.

if Ia is the intensity that observer A measures and Ib is the intensity that observer B measures, we have that:

Ia = 16Ib

A/(ra)^2 = 16*A/(rb)^2

1/(ra)^2 = 16/(rb)^2

rb^2 = 16*ra^2

and we know that 16 = 4*4 = 4^2

rb^2 = (4*ra)^2

then rb = 4*ra

this means that the distance between observer B and the antenna is equal to 4 times the distance between observer A and the antenna.

The fraction is ra = rb/4

The distance of

Observer A from the radio antenna is what fraction of the distance of Observer B from the radio antenna?​

It is 1/4.

Observer A measures the intensity of the signal to be 16 times the intensity measured by Observer B. The distance of Observer A from the radio antenna is 4 times the distance of Observer B.

Observer A measures the intensity of the signal to be 16 times the intensity measured by Observer B. Let's denote the distance of Observer A from the radio antenna as dA and the distance of Observer B as dB.

We can use the inverse square law to relate the intensity to the distance: Intensity is inversely proportional to the square of the distance.

So, we have:

IntensityA/IntensityB = (dA/dB)^2 = 16

Solving for dA/dB, we find:

dA/dB = sqrt(16) = 4

Therefore, the distance of Observer A from the radio antenna is 4 times the distance of Observer B.

https://brainly.com/question/37247623

#SPJ3

Answer:

5/8 mile is less than 1 mile

Step-by-step explanation:

in this question, one could assume a mile is 8/8

5/8<8/8

Answer:

Step-by-step explanation: convert feet to inches then multiply all 3 numbers. 264 x 699x13 = 2398968. Then decide that by 12 the amount of inches in a foot and get 199,914 ft^3

Answer:

The correct option is (A).

Step-by-step explanation:

The p-value is well defined as the probability, [under the null hypothesis (H₀)], of attaining a result equivalent to or more extreme than what was truly observed.

From the provided options we can guess that the hypothesis was defined as follows:

H₀: There is no difference in the mean number of partners, i.e. μ₁ - μ₂ = 0.

Hₐ: There is difference in the mean number of partners, i.e. μ₁ - μ₂ ≠ 0.

The test is two tailed mean difference test.

A z-test or a t-test can be used to conclude the result.

In this case the p-value can be defined as the probability of obtaining a test statistic value equal to or more extreme that the results obtained from the sample, when the difference between the mean number of partners is 0.

Thus, the correct interpretation of the​ p-value is provided by statement (A).

The p-value represents the likelihood of obtaining a test statistic as extreme as our observed data, assuming the null hypothesis is true. The null hypothesis usually posits there's no difference or effect. A small p-value would suggest rejecting the null hypothesis in favor of the alternative hypothesis, indicating a significant effect or difference.

The correct interpretation of the ​p-value is: The p-value is the probability of getting a test statistic equal to or more extreme than the sample result if there is no difference in the mean number of partners.

In other words, the p-value measures how likely you are to get the observed data if the null hypothesis is true. The null hypothesis typically represents a theory that there is no effect or no difference between the groups you're comparing. Hence, if there's no difference in the mean number of partners (which is our null hypothesis here), then the p-value tells how likely we are to observe a test statistic as extreme as our sample result.

For example, if the p-value is very small, it might be less than our significance level (commonly 0.05 or 5%). In such a case, we have evidence to reject our null hypothesis in favor of the alternative hypothesis. The alternative hypothesis generally represents a theory that there is an effect or a difference between the groups. So, in this case, a small p-value would indicate a statistically significant difference in the mean number of partners.

https://brainly.com/question/28197808

#SPJ11

Answer:

a) The null and alternative hypothesis are:

[tex]H_0: \mu=23\\\\H_a:\mu> 23[/tex]

c) Test statistic t=1.53

P-value=0.064

d) The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that students who complete the core curriculum are ready for​ college-level mathematics.  That is that the true score for the group is not significantly higher than 23.

Step-by-step explanation:

The question is incomplete:

a) State the appropriate null and alternative hypotheses.

c) Use the P-value approach at the 0.05 level of significance to test the hypotheses in part (a). ldentify the test statistic. (Round to two decimal places as needed.) Identfy the P-value. P-value (Round to three decimal places as needed.)

d) Write a conclusion based on the results. Choose the correct answer below. ? the null hypothesis and claim that there ? sufficient evidence to conclude that the population mean is ? than 20.

This is a hypothesis test for the population mean.

The claim is that students who complete the core curriculum are ready for​ college-level mathematics.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=23\\\\H_a:\mu> 23[/tex]

The significance level is assumed to be 0.05.

The sample has a size n=150.

The sample mean is M=23.4.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=3.2.

The estimated standard error of the mean is computed using the formula:

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{3.2}{\sqrt{150}}=0.261[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{23.4-23}{0.261}=\dfrac{0.4}{0.261}=1.531[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=150-1=149[/tex]

This test is a right-tailed test, with 149 degrees of freedom and t=1.531, so the P-value for this test is calculated as (using a t-table):

[tex]P-value=P(t>1.531)=0.064[/tex]

As the P-value (0.064) is bigger than the significance level (0.05), the effect is  not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that students who complete the core curriculum are ready for​ college-level mathematics.

Answer:-19/7

Step-by-step explanation:

f varies directly as m

f=k x m

When f=-19,m=14

-19=k x 14

k=-19/14

Relationship is f=-19m/14

When m is 2

f=(-19x2) ➗ 14

f=-38 ➗ 14

f=-19/7

Answer:

16

Step-by-step explanation:

Number = x

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

3x/4 - x/2 = 4

3x - 2x / 4 = 4

x/4 = 4

x = 16

Answer:

a = 6.3mm

Step-by-step explanation:

Use Pythagoras theorem here

[tex]a^{2} + b^{2} = c^{2}[/tex]

Rearrange for a by subtracting [tex]b^{2}[/tex] from both sides of the equation

[tex]a^{2} + b^{2} -b^{2} = c^{2} -b^{2}[/tex]

Simplify

[tex]a^{2} = c^{2} -b^{2}[/tex]

Substitute in our numbers and solve for a

[tex]a^{2}[/tex] = [tex]8.3^{2} - 5.4^{2}[/tex]

[tex]a^{2}[/tex] = 68.89 - 29.16

[tex]a^{2}[/tex] = 39.73

a = [tex]\sqrt{39.73}[/tex]

a = 6.3mm

Final answer:

To find the length of leg a when b = 5.4 mm and c = 8.3 mm in a right triangle, we use the Pythagorean theorem a^2 + b^2 = c^2. We solve for a, yielding a ≈ 6.3 mm (rounded to the nearest tenth).

Explanation:

The student is asking how to find the length of leg a in a right triangle where the lengths of leg b and the hypotenuse c are given. Since b = 5.4 millimeters and c = 8.3 millimeters, we can use the Pythagorean theorem to find leg a.

First, we'll apply the theorem: a2 + b2 = c2. To solve for a, we rearrange it: a2 = c2 - b2.

Substitute the given values:

a2 = c2 - b2
= 8.32 - 5.42
= 68.89 - 29.16
= 39.73

Now, we take the square root of both sides to find a:

a =
√39.73

≈ 6.3 millimeters (rounded to the nearest tenth)

Therefore, the length of leg a is approximately 6.3 millimeters.

Answer:

The standard error of the mean (SE) is of 0.326lb.

Step-by-step explanation:

The standard error of the mean is given by the following formula:

[tex]SE = \frac{s}{\sqrt{n}}[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

In this problem, we have that:

[tex]s = 4.3, n = 174[/tex]

Then

[tex]SE = \frac{s}{\sqrt{n}} = \frac{4.3}{\sqrt{174}} = 0.326[/tex]

The standard error of the mean (SE) is of 0.326lb.

Answer:

3

Step-by-step explanation:

Range is the difference between

Answer: D

A is correct because when you convert 40% into a decimal the results will be .40 or .4

B is correct because 2/5 as a percent is 40%. It's like having 5 questions on a quiz and you get 2 right and 3 wrong. That means your grade is 40%.

C is correct because 40/100 means the decimal will be .4. 40÷100 will equal .4 which means 40/100 is also 40%.

D is incorrect due to the fact when you convert it to a fraction it'll be 4/25. When converting it to a percent the result will be 16%.

The number 40% in not equivalent to 0.04.

What is mean by Percentage?

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

The number is,

⇒ 40%

Now,

Since, The number is,

⇒ 40%

Hence, It can be written as;

⇒ 40% = 40/100

           = 4/10

           = 2/5

           = 0.4

Thus, The number 40% in not equivalent to 0.04.

Learn more about the percent visit:

https://brainly.com/question/24877689

#SPJ2