(a) The distance between the airport and the pilot's final landing point is 300 miles.
(b) the bearing from the airport to the pilot's final landing point is approximately 300.7684°.
(a) The distance between the airport and the pilot's final landing point can be calculated by finding the sum of the two distances traveled in the given directions.
First, let's calculate the distance traveled in the direction N 20° E for one hour at a speed of 200 mi/h. The formula to calculate distance is:
Distance = Speed × Time
Distance = 200 mi/h × 1 h = 200 miles
Next, let's calculate the distance traveled in the direction N 40° E for half an hour at the same speed. Since the time is given in hours, we need to convert half an hour to hours:
0.5 hours = 1/2 hours
Using the same formula, we can calculate the distance:
Distance = 200 mi/h × (1/2) h = 100 miles
To find the total distance, we add the two distances:
Total Distance = 200 miles + 100 miles = 300 miles
Therefore, the distance between the airport and the pilot's final landing point is 300 miles.
(b) To find the bearing from the airport to the pilot's final landing point, we can use trigonometry.
First, let's consider the triangle formed by the airport, the pilot's final landing point, and the point where the pilot made the course correction. The angle between the first leg (N 20° E) and the second leg (N 40° E) is 20°.
Using the Law of Cosines, we can find the angle between the first leg and the line connecting the airport and the final landing point:
cos(angle) = (a^2 + c^2 - b^2) / (2ac)
where a = 200 miles, b = 100 miles, and c is the distance between the airport and the final landing point (300 miles).
cos(angle) = (200^2 + 300^2 - 100^2) / (2 × 200 × 300)
Solving for angle, we find:
angle ≈ 39.2316°
The bearing from the airport to the final landing point is the angle measured clockwise from due north. Since the pilot initially flew in the direction N 20° E, we need to subtract 20° from the angle we calculated.
Bearing = 360° - 20° - angle
Bearing ≈ 360° - 20° - 39.2316° ≈ 300.7684°
Therefore, the bearing from the airport to the pilot's final landing point is approximately 300.7684°.
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5) (3a + 1) - (4 + 2a)
Answer:
5a - 3
Step-by-step explanation:
3a + 2a = 5a
1 - 4 = -3
5a + (-3) or 5a - 3
A photo of a beetle in a science book is increased to 655% as large as the actual size. In the
beetle is 16 millimeters, what is the size of the beetle in the photo?
The size of the beede in the photo
Answer:
104.8
Step-by-step explanation:
16 x 6.55 = 104.8
Answer:
104.8 millimeters
Step-by-step explanation:
16 x 6.55 = 104.8
Find the profit function if cost and revenue are given by C(x)=150+5.8x and R(x)=9x-0.01x² The profit function is P(x)
The profit function if the cost and revenue is given P(x) = -0.01x² + 3.2x - 150.
To find the profit function P(x), we subtract the cost function C(x) from the revenue function R(x). This gives us the expression for P(x) as P(x) = R(x) - C(x).
The profit function P(x) represents the difference between the revenue R(x) and the cost C(x). To find P(x), we subtract C(x) from R(x):
P(x) = R(x) - C(x)
Substituting the given expressions for R(x) and C(x), we have:
P(x) = (9x - 0.01x²) - (150 + 5.8x)
Simplifying this expression, we get:
P(x) = 9x - 0.01x² - 150 - 5.8x
Combining like terms, we have:
P(x) = -0.01x² + 3.2x - 150
Thus, the profit function is given by P(x) = -0.01x² + 3.2x - 150. This function represents the profit made as a function of the quantity of goods sold, x. It allows us to analyze the relationship between revenue, cost, and profit for different values of x.
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The following set of data is from a sample of n = 6. 4 9 10 4 3 12 a, Compute the mean, median, and mode. b. Compute the range, variance, and standard deviation. a. Compute the mean, median, and mode. Mean=(Type an integer or decimal rounded to four decimal places as needed.) Compute the median Median-(Type an integer or a decimal. Do not round.) What is the mode? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The mode(s) is/are (Type an integer or a decimal. Do not round. Use a comma to separate answers as needed.) B. There is no mode for this data set 5. Compute the range, Range-(Type an integer or a decimal. Do not round.) ompute the variance.
a. The mean of the data set is 6.3333, the median is 4.5, and there is no mode. b. The range of the data set is 9, and the variance is 11.8667.
a. To compute the mean, we sum up all the values in the data set and divide it by the number of data points. In this case, the sum is 4 + 9 + 10 + 4 + 3 + 12 = 42. Dividing this by 6 (the number of data points), we get a mean of 42/6 = 6.3333.
To compute the median, we arrange the data set in ascending order: 3, 4, 4, 9, 10, 12. Since the number of data points is even, we take the average of the middle two values, which are 4 and 9. The median is (4 + 9) / 2 = 4.5.
The mode is the value(s) that appear most frequently in the data set. In this case, none of the values are repeated, so there is no mode.
b. The range is the difference between the largest and smallest values in the data set. In this case, the largest value is 12 and the smallest value is 3, so the range is 12 - 3 = 9.
The variance measures the variability of the data set. It is calculated by taking the average of the squared differences between each data point and the mean. Using the formula for sample variance, the calculations are as follows:
[tex](4 - 6.3333)^2 + (9 - 6.3333)^2 + (10 - 6.3333)^2 + (4 - 6.3333)^2 + (3 - 6.3333)^2 + (12 - 6.3333)^2 = 71.2[/tex]
Dividing this sum by n-1 (where n is the number of data points) gives us the sample variance: 71.2 / 5 = 14.24.
Therefore, the variance is 14.24.
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The center of a circle is located at (4, 2). A point on the circle is located at (1, 2). What is the approximate area of the circle?
Answer: 9π≈28.26 squared units
Step-by-step explanation: The distance between the two points, 3 units, is the radius. And then we use that to find the area by squaring and multiplying by pi.
Please Help!!! Unit 8: Right Triangles & Trigonometry Homework 6: Trigonometry Review
The value of x from the figure is [tex]cos^-1(\frac{14}{13} )[/tex]
Triangles and AnglesFrom the given diagram, we have the following
Adjacent = 14Hypotenuse = 13The required angle is x
Using the SOH CAH TOA identity
[tex]cos \theta =\frac{adj}{hyp}\\ cos \theta =\frac{14}{13}\\ \theta = arccos(\frac{14}{13} )[/tex]
Hence the value of x from the figure is [tex]cos^-1(\frac{14}{13} )[/tex]
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As reported in Runner's World magazine, the times of the finishers in the New York City 10-km run are normally distributed with mean 60 minutes and standard deviation 9 minutes. Determine the percentage of finishers who have times between 55 and 75 minutes.
The mean of the finishers in the New York City 10-km run is 60 minutes and standard deviation is 9 minutes.
To determine the percentage of finishers who have times between 55 and 75 minutes, we need to find the Z-scores for both of these values as follows:
Z1 = (55 - 60) / 9 = -0.56Z2 = (75 - 60) / 9 = 1.67
Now, we need to find the area under the standard normal distribution curve between these two Z-scores as follows:
P(-0.56 < Z < 1.67) = P(Z < 1.67) - P(Z < -0.56) Using a standard normal distribution table,
we can find the probabilities as:
P(Z < 1.67) = 0.9525P(Z < -0.56) = 0.2881
Therefore , P(-0.56 < Z < 1.67) = P(Z < 1.67) - P(Z < -0.56)= 0.9525 - 0.2881= 0.6644Therefore, the percentage of finishers who have times between 55 and 75 minutes is 66.44%.
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Find the missing side
Answer:
72
Step-by-step explanation:
Answer:
72 units
Step-by-step explanation:
The Pythagorean Theorem states that [tex]a^2+b^2=c^2[/tex] in a right triangle when a and b are the two legs and c is the hypotenuse (the longest side).
[tex]a^2+b^2=c^2[/tex]
In the diagram, 30 measures one of the legs and 78 measures the hypotenuse. Plug these in as a and c.
[tex]30^2+b^2=78^2\\900+b^2=6084[/tex]
Subtract 900 from both sides
[tex]900+b^2-900=6084-900\\b^2=5184[/tex]
Take the square root of both sides
[tex]900+b^2-900=6084-900\\\sqrt{b^2} =\sqrt{5184}\\b=72[/tex]
Therefore, the length of the missing side is 72 units.
I hope this helps!
PLEASE SHOW YOUR WORK!!! WILL MARK BRAINLIEST!!!
On a youth soccer team 3 out of 12 team members have played in previous years. Based on this information, if 180 kids are in the youth soccer league, then how many could be expected to have played the year before?
Answer:
45
Step-by-step explanation:
3 out of 12 is 1/4, or 0.25, so if you divide 180 by 4, then using the same logic, you can expect 45 kids to have played last year.
3 = 1/4 OR .25 of 12, 12 divided by 4 = 3
180 divided by 4 = 45
Answer:
yes its 45 i did the test and i got an 100
Step-by-step explanation:
heres proof
PLEASE MARK BRAINLIEST!!!!!!Children's recall of TV ads. Marketing professors at Robert Morris and Kent State Universities examined children's recall and recognition of television advertisements. (Journal of Advertising, Spring 2006.) Two groups of children were shown a 60-second commercial for Sunkist FunFruit Rockn-Roll Shapes. One group (the AN group) was shown the ad with both audio and video; the second group (the video only group) was shown only the video portion of the commercial. Following the viewing, the children were asked to recall 10 specific items from the ad. The number of items recalled correctly by each child is summarized in the accompanying table. The researchers theorized that "children who receive an audiovisual presentation will have the same level of mean recall of ad information as those who receive only the visual aspects of the ad."
Video-Only Group
n1= 20
x1_bar = 3.70
s1 = 1.98
A/V Group
n2 = 20
x2-bar = 3.30
s2 = 2.13
a. Set up the appropriate null and alternative hypotheses to test the researchers' theory.
b. Find the value of the test statistic.
c. Give the rejection region for ? = 0.10
d. Make the appropriate inference. What can you say about the researchers' theory?
e. The researchers' reported the p-value of the test as p-value = 0.62. Interpret this result.
f. What conditions are required for the inference to be valid?
a. The null hypothesis (H0) would state that the mean recall of ad information for children who receive an audiovisual presentation is equal to the mean recall.
a.The alternative hypothesis (Ha) would state that the mean recall of ad information differs between the two groups.
b. To find the test statistic, we can use the two-sample t-test formula:
t = (x1_bar - x2_bar) / sqrt((s1^2/n1) + (s2^2/n2))
Substituting the given values:
t = (3.70 - 3.30) / sqrt((1.98^2/20) + (2.13^2/20))
c. The rejection region for a significance level of α = 0.10 in a two-tailed test can be determined using a t-table or a t-distribution calculator. Since the alternative hypothesis is two-tailed, we need to split α equally between the two tails. In this case, the rejection region would be t < -1.734 or t > 1.734.
d. Based on the test statistic value calculated in part (b), we can compare it to the rejection region. If the test statistic falls within the rejection region, we reject the null hypothesis. If it falls outside the rejection region, we fail to reject the null hypothesis. In this case, we would fail to reject the null hypothesis since the test statistic does not fall within the rejection region. Therefore, we cannot conclude that the mean recall of ad information differs between the two groups, supporting the researchers' theory.
e. The p-value is a measure of the strength of evidence against the null hypothesis. In this case, the researchers reported a p-value of 0.62. Since this p-value is greater than the significance level of α = 0.10, it indicates that the observed data is likely to occur by chance alone assuming the null hypothesis is true. Therefore, we fail to reject the null hypothesis and cannot conclude that there is a significant difference in the mean recall of ad information between the two groups.
f. For the inference to be valid, certain conditions must be met. These conditions include random sampling, independence between observations, approximately normal distributions of the populations or large sample sizes, and equal variances between the groups. Without information about the sampling method and data characteristics, we cannot determine if these conditions were met. It is important to note that if the conditions for inference are not met, the validity and reliability of the test results may be compromised.
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Solve the equation using either addition or substitution. Show all your work
Answer:
(x1, y1) = (1, 3)
(x2, y2) = (4, 12)
Step-by-step explanation:
y= x^2 - 4
y= 5x - 8
(substitute the value for y)
x^2 - 4 = 5x - 8
(solve the equation)
x = 1
x = 4
(substitute the values)
y = 5 × 1 - 8
y = 5 × 4 - 8
(solve the equations)
y = -3
y = 12
( the possible solutions are)
x1, y1 = 1, -3
x2, y2 = 4, 12
(check the solutions)
-3 = 1^2 - 4
-3 = 5 × 1 - 8
12 = 4^2 - 4
12 = 5 × 4 - 8
(simplify)
-3 = -3
-3 = -3
12 = 12
12 = 12
(the ordered pairs are the solutions)
PLEASE HELPP, DONT SCAM!! The table below represents a function. Which of the following equations could be its function rule?
Step-by-step explanation:
From the table, let's extract a set of data.
let's take x = 3, y = -9.
Let's substitute x into each of the equation to check.
A.
[tex]y = \frac{x}{ - 3} \\ y = \frac{3}{ - 3} \\ = - 1[/tex]
From here we can see the calculated y is not equal to the y in the table, therefore this cannot be the answer.
B.
[tex]y = x \\ y = - 3[/tex]
From here we also can see the calculated y is not equal to the y in the table, therefore this also cannot be the answer.
C.
[tex]y = 3x \\ = 3( - 3) \\ = - 9[/tex]
From here we can see the calculated y is equal to the y in the table , therefore this is the answer.
D.
[tex]y = - 3x \\ = - 3( - 3) \\ = 9[/tex]
From here we can see the calculated y is not equal to the y in the table, therefore this is not the answer.
I WILL GIVE BRAINLIEST!!!
Answer:
F(x)=h(x)-8
I think
Step-by-step explanation:
Can someone help me please?
Answer:
81
Step-by-step explanation:
81
Answer:
6+3=9x9=81 final answer 81.
Step-by-step explanation:
Is (2, 7) the answer to the equation 5x = y?
If not, what should y be?
Answer:
[see below]
Step-by-step explanation:
[tex]5(2)=7\\\\10\neq 7[/tex]
No, (2, 7) is not the answer to the equation 5x = y.
[tex]5x=y\\\\5(2)=y\\\\\boxed{10=y}[/tex]
The value of y should be 10.
Hope this helps.
Gary buys a 3 and 1/2 - pound bag of cat food every 3 weeks. Gary feeds his cat the same amount of food each
day. Which expression can Gary use to determine the number of pounds of cat food his cat eats each
year? (1 year = 52 weeks)
Answer:
546
Step-by-step explanation:
3 1/2 times 3 equals 10 1/2. 10 1/2 times 52 equals 546.
A video store has 6 new comedies, 4 new action movies, and 2 new dramas available to rent. If you choose 1 of each type of movie, how many combinations are there?
Answer:
48
Step-by-step explanation:
Number of comedy = 6
Number of action = 4
Number of drama = 2
Selecting one of each ; total Number of possible combinations ;
nCr
Comedy = 6C1
Action = 4C1
Drama = 2C1
6C1 * 4C1 * 2C1 = 6 * 4 * 2 = 48
A 4 pack of 12-ounce bottles of water costs $4.40. What is the cost per ounce?
Answer:
5
Step-by-step explanation:
please help asapppppp
Answer:
45 degree
Step-by-step explanation:
can someone check my answer make sure it's right, if it's wrong can you please explain thanks ❤️❤️
Answer:
it is wrong
Step-by-step explanation:
the reason it is wrong is because I said so
Answer:
I am going to say no BECAUSE there are two y values, on the same point. For it to be linear it should only have one point per value. I think... good luck.
What’s the answer????
Answer:
I believe its 10 but forgive me if I'm wrong
Given the angles in the diagram below what is m<2?
Answer: 98
Step-by-step explanation: According to the corresponding angles theorem m<1=82. Then according to the linear supplements theorem m<2=98. Hope this helps!
Answer:
98°
Step-by-step explanation:
Angle 1 also measures 82° because it is a corresponding angle to the given angle. Angles 1 and 2 are supplementary and therefore must add up to 180°.
Andrea reads 36 pages each night. How many pages does Andrea read in 42 nights?
A 1,502pages
B 1,512pages
C 1,552pages
D 1,582pages
Answer:
1,512
Step-by-step explanation:
36x42
Help meeeeeeeeeeeeeee pls
Answer:
-3.5
all u have to do is get the 2 and the 7 and just subtract and the 8 and 10
helpppppp pleaseeeeee
Answer:
50°
Step-by-step explanation:
We are to find m ∠2
And lines A and B are parallel
m ∠2 and 50° are Vertical angles. This means m ∠2 is the same as 50°
Hence,
m ∠2 = 50°
Therefore, m ∠2 = 50°
Fifty people put there name
into a two different drawings
(30 males and 20 females).
One drawing is for an iPad and
the other is for a flat screen
TV. What is the probability
that a male will win both
drawings.
Possible answers ⇒
13%
27%
36%
49%
WILL GIVE BRAINLIST
Answer:
36%
Step-by-step explanation:
30/2500 x 30/2500=
900/2500=0.36
0.36*100=36%
PLS HELP ILL MARK U BRAINLIEST
I DID THE FIRST 1 I NEED HELP WITH THE SECOND <3
Answer:
7m and 49 m^2
Step-by-step explanation:
i am not sure on the second answer
Can someone plzzz helpppp!!!!
Answer:
[tex] m\angle SXW =113\degree [/tex]
Step-by-step explanation:
In circle with center X, VS is diameter.
So [tex] \widehat {SWV} [/tex] is a semicircular arc.
[tex] \therefore m\widehat{SWV} = 180\degree [/tex]
[tex] \therefore (12x+7)\degree + (21x +8)\degree = 180\degree [/tex]
[tex] \therefore (33x+15)\degree = 180\degree [/tex]
[tex] \therefore 33x+15 = 180 [/tex]
[tex] \therefore 33x = 180-15 [/tex]
[tex] \therefore 33x = 165 [/tex]
[tex] \therefore x =\frac{165}{33} [/tex]
[tex] \therefore x =5 [/tex]
[tex] m\angle SXW =m\widehat{SW} [/tex]
(Measure of central angle is equal to the measure of its corresponding minor arc)
[tex] m\angle SXW =(21x + 8)\degree [/tex]
[tex] m\angle SXW =(21\times 5+ 8)\degree [/tex]
[tex] m\angle SXW =(105+ 8)\degree [/tex]
[tex] m\angle SXW =113\degree [/tex]
An object is acted upon by the forces F1=(10,6,3), and F2=(0,4,9). Find forces F3 that must act on the object so that the sum of the forces is zero.
The forces [tex]F_3[/tex] that must act on the object so that the sum of the forces is zero are [tex]F_3[/tex] = (-10, -10, -12).
To find the forces [tex]F_3[/tex] that must act on the object so that the sum of the forces is zero, we need to find a vector [tex]F_3[/tex] that satisfies the equation
[tex]F_1 + F_2 + F_3 = 0.[/tex]
Given the forces:
[tex]F_1[/tex] = (10, 6, 3)
[tex]F_2[/tex] = (0, 4, 9)
We can rearrange the equation to solve for [tex]F_3[/tex]:
[tex]F_3 = -F_1 - F_2[/tex]
Now, let's calculate [tex]F_3[/tex]:
[tex]F_3[/tex] = -(10, 6, 3) - (0, 4, 9)
= (-10, -6, -3) - (0, 4, 9)
= (-10-0, -6-4, -3-9)
= (-10, -10, -12)
Therefore, the forces [tex]F_3[/tex] that must act on the object so that the sum of the forces is zero are [tex]F_3[/tex] = (-10, -10, -12).
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on the graph of f(x)=sinx and the interval [0,2π), for what value of x does f(x) achieve a maximum? choose all answers that apply.
On the graph of f(x) = sin(x) on the interval [0, 2π), the function achieves a maximum value at x = π/2.
The function f(x) = sin(x) is a periodic function with a period of 2π. Within one period, the function oscillates between the values of -1 and 1. The maximum value of sin(x) is 1, and it occurs when the angle x is π/2.
In the given interval [0, 2π), the function f(x) = sin(x) completes one full period. Starting from x = 0, the function increases and reaches its maximum value of 1 at x = π/2. After that, it starts decreasing and goes through one complete cycle by the time it reaches x = 2π.
Therefore, on the graph of f(x) = sin(x) on the interval [0, 2π), the function achieves a maximum value at x = π/2.
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