Answer:
The speed V = 194.03 mph
Direction = 3.6° northeast
Step-by-step explanation:
The distance of the trip = 291 miles
The direction of flight = 9.1 degrees northeast
Speed of the prevailing wind = 25 mph
Direction of wing = southeast = 45 degrees South of East
The speed heading to Ivy Cliffs = V₁
V×(sin(9.1) + cos(9.1)) + 25×(-sin(45) + cos(45)) × t₁ = 291 miles
V×(sin(9.1) + cos(9.1)) + 25×(sin(45) + -cos(45)) × t₂ = 291 miles
t₁ + t₂ = 3 hours
(V×(sin(9.1)-25×(sin(45))j + (V×cos(9.1) + 25×cos(45))i
The magnitude V² = V²+29.32·V +625= 291²/t₁²......(1)
Also on the return trip we have;
V²-29.32·V +625= 291²/(3-t₁)²..........................................(2)
Subtracting equation (2) from (1) gives;
58.64·V = 291²/t₁² - 291²/(3-t₁)² = 291²×(6·t-9)/(t²·(t-3)²)
V = 291²×(6·t-9)/(t²·(t-3)²)/58.64
Substituting the value of V in (2) with a graphing calculator gives;
t₁= 1.612 or 1.387
Given that magnitude of the speed going > return = V² for t₁ < t₂
t₁ = 1.387, t₂ = 1.612
From V²+29.32·V +625= 291²/t₁², we have
V²+29.32·V +625= 291²/1.387²
Which gives
V²+29.32·V -43336.5 = 0
(V + 233.35)(V-194.03) = 0
V = -233.35 mph or V = 194.03 mph
Given that V is a natural number, we have, V = 194.03 mph.
The direction is given by the relation;
V×(sin(9.1) + cos(9.1)) + 25×(-sin(45) + cos(45)) × t₁ = 291 miles
V×(sin(9.1) + cos(9.1)) + 25×(-sin(45) + cos(45)) × t₁ = 291 miles
194.03×sin(9.1 degrees)-25×sin(45 degrees)j + 194.03×cos(9.1 degrees) + 25×cos(45 degrees)i = 291/1.387
13j + 209.27i = 208.81 mph
The angle tan θ = 13/209 = 0.00622
θ = tan⁻¹(13/209.27) = 3.6°.
Find the (a) mean, (b) median, (c) mode, and (d) midrange for the data and then (e) answer the given question. Listed below are the weights in pounds of 11 players randomly selected from the roster of a championship sports team. Are the results likely to be representative of all players in that sport's league? 293 255 264 240 190 295 199 184 293 205 199
Answer:
A.) Mean = 237.9
B.) Median = 240
C.) Mode = 199
D.) Midrange = 239.5
Step-by-step explanation:
The given data are :
293 255 264 240 190 295 199 184 293 205 199
The mean = (sum of X) / f
Where frequency f = 11
X = 293 + 255 + 264 + 240 + 190 + 295 + 199 + 184 + 293 + 205 + 199
X = 2617
Substitute X and f into the formula
Mean = 2617/11
Mean = 237.9 approximately
B.) To get the median, you need to first rearrange the data, then pick the middle number.
184 190 199 199 205 240 255 264 293 293 295
The median = 240
C.) The mode is the highest frequency. That is the most occuring number
Mode = the two most occuring numbers are 199 and 293
D.) Range = highest number - lowest number
But midrange = (highest number + lowest number ) ÷ 2
Highest number = 295
Lowest number = 184
Substitute into the formula
Midrange = (295 + 184)/2
Midrange = 479/2
Midrange = 239.5
(05.02 LC)What is the area, in square inches, of the figure shown here? A parallelogram with a height of 4inches is shown. The height of the parallelogram is used to divide the side of the parallelogram into 5 inches, which is the length (or side) of the rectangle, and into 4 inches, which is the base of the triangle formed by the division. 20 in2 24 in2 32 in2 36 in2
Answer:
36 in²
Step-by-step explanation:
The figure that is been described is a Parallelogram.
The area of a Parallelogram is = Base × Height
From the question, the Height of the Parallelogram = 4 inches
The Base of the Parallelogram is calculated as the Length or base of the rectangle + base of the triangle
= 5 inches + 4 inches
= 9 inches
Area of the Parallelogram = 9 inches × 4 inches
= 36 square inches or 36 in²
Answer:
20 INCHES SQUARED
Step-by-step explanation:
PLEASE HELP Jane has twice as many cousins as James. Bryan has 5 cousins, which is 11 less that Jane has. How many cousins does James have?
Answer:
James has 8 cousins
Step-by-step explanation:
Bryan =5
Jane =Bryan + 11=5+11=16 ( Bryan has 11 cousins less than Jane)
James: 1/2 Jane=16/2=8 cousins ( Jane has twice as James)
4 ft
8 ft
3 ft
2 ft
6 ft
What is the volume of the composite figure
Which of the following statements is true
A. The relationship is a function because there are no two y-values corresponding to the same x-value
B. The relationship is not a function because there is more than one x value corresponding to y=2
C. The relationship is not a function because there are values of y that have no corresponding x- value
D. The relationship is not a function because each y has a corresponding x-value
Please answer this question now
Answer:
469.4ft²
Step-by-step explanation:
We have Triangle WXY
In the question, we are given already
Angle W = 27°
Angle X = ?
Angle Y = 40°
Side w =?
Side x = ?
Side y = 38ft
Area of the triangle= ?
Step 1
We find the third angle = Angle X
Sum of angles in a triangle = 180°
Third angle = Angle X= 180° - (27 + 40)°
= 180° - 67°
Angle X = 113°
Step 2
Find the sides w and x
We find these sides using the sine rule
Sine rule or Rule of Sines =
a/ sin A = b/ Sin B
Hence for triangle WXY
w/ sin W = x/ sin X = y/ sin Y
We have the following values
Angle W = 27°
Angle X = 113°
Angle Y = 40°
We are given side y = 38ft
Finding side w
w/ sin W= y/ sin Y
w/sin 27 = 38/sin 40
Cross Multiply
sin 27 × 38 = w × sin 40
w = sin 27 × 38/sin 40
w = 26.83879ft
w = 26.84ft
Finding side x
x / sin X= y/ sin Y
x/ sin 113 = 38/sin 40
Cross Multiply
sin 113 × 38 = x × sin 40
x = sin 113 × 38/sin 40
x = 54.41795ft
x = 54.42ft
To find the area of triangle WXY
We use heron formula
= √s(s - w) (s - x) (s - y)
Where S = w + x + y/ 2
s = (38 + 26.84 + 54.42)/2
s = 59.63
Area of the triangle = √59.63× (59.63 - 38) × (59.63 - 26.84 ) × (59.63 - 54.42)
Area of the triangle = √
Area of the triangle = 469.40772706541ft²
Approximately to the nearest tenth =469.4yd²
Please answer the question correct only if you know the answer
Use the law of cosines to solve for side g.
g^2 = e^2 + f^2 - 2*e*f*cos(G)
g^2 = 10^2 + 8^2 - 2*10*8*cos(57)
g^2 = 76.85775 ... make sure your calc is in degree mode
g = sqrt(76.85775)
g = 8.766855
g = 8.8
5/8 of the staff are male. 5/12 of the staff works part time at the aquarium.What fraction of the staff is female?
Answer:
3/8
Step-by-step explanation:
If 5/8 of the staff is male, then 8/8 is the total number of staff.
8/8 - 5/8 = 3/8
3/8 of the staff is female.
Hope this has helped. If the question has more to it, then please specify.
Jason considered two similar televisions at a local electronics store. The generic version was based on the brand name and was three eighths the size of the brand name. If the generic television set is 12 inches by 24 inches, what are the dimensions of the brand name television
Answer:
32 inches by 64 inches
Step-by-step explanation:
Since the generic television is [tex]\frac{3}{8}[/tex] the size of the brand name.
Then the brand name is [tex]\frac{8}{3}[/tex] the size of the generic, thus
[tex]\frac{8}{3}[/tex] × 12 = 32
[tex]\frac{8}{3}[/tex] × 24 = 64
Thus dimensions are 32 inches by 64 inches
Answer:
The dimensions are 32 inches by 64 inches
What is the simplified form of -9x+3x
Answer:
-6x
Step-by-step explanation:
you can combine numbers with the same coefficient like any other number
Answer:
-6x
Step-by-step explanation:
It would be doing the same thing as -9 + 3, but without a variable.
Together, two apples have 1/5 gram of fat. How many apples have a total of 4 grams of a
apples
Answer:
40 apples
Step-by-step explanation:
2 apples= [tex]\frac{1}{5}[/tex] grams
x apples= 4 grams
8/[tex]\frac{1}{5}[/tex] = 8 x 5/1=40
Answer:
40
Step-by-step explanation:
edu instruction correct
An annual salary is $45000. His tax free allowances total $13000. He has to pay a tax of 20% on his taxable income.
The tax payable is?
Answer:
6400
Step-by-step explanation:
Taxable amount=45000-13000=32000
tax=32000*20/100
=6400
what is 1 add 1 please help!!!!!!!!!!!!!!!PS first person to get it correct gets brainiest
Answer: 2
Step-by-step explanation:
Answer:
2...........
Step-by-step explanation:
1 + 1 = 2............
The solution to an inequality is given in set-builder notation as {x l x > two-thirds}. What is another way to represent this solution set?
Answer:
[tex](\frac{2}{3},\infty)[/tex]
Step-by-step explanation:
Set builder notation is a mathematical notation used to write the elements of a set stating the conditions that the elements of the set must satisfy. A solution set is also a way of defining solutions to equations and inequalities. A solution set contains a set of all variables for which the equation is true.
The notation {x l x > two-thirds} is a set of all real numbers greater than 2/3, it can also be represented as:
[tex](\frac{2}{3},\infty)[/tex]
Answer:
c) (two-thirds, ∞)
Step-by-step explanation:
edg2020
The right isosceles triangle shown is rotated about line k with the base forming perpendicular to k. The perimeter of the triangle is 58 units. Which best describes the resulting three-dimensional shape?
Answer:
The new shape will be cone with a radius of 17 units, tilt height 24 and units of height k.
Step-by-step explanation:
The image related to the exercise is necessary, to be able to solve therefore the attached one.
We have the following information:
Perimeter of the triangle = 58 units
Hypotenuse = 24 units
We have that the other two sides are equal and have x units, therefore we have the following:
x + x + 24 = 58
2 * x = 58-24
2 * x = 34
x = 34/2
x = 17
Now the triangle rotates around line k , and then it will result in a cone, which is a three-dimensional shape.
Therefore, the new shape will be cone with a radius of 17 units, tilt height 24 and units of height k.
Answer:
Cone with a radius of 17 units
if cos 0=2/3, what are the values of sin 0 and tan 0?
Answer:
Below
Step-by-step explanation:
● cos O = 2/3
We khow that:
● cos^2(O) + sin^2(O) =1
So : sin^2 (O)= 1-cos^2(O)
● sin^2(O) = 1 -(2/3)^2 = 1-4/9 = 9/9-4/9 = 5/9
● sin O = √(5)/3 or sin O = -√(5)/3
So we deduce that tan O will have two values since we don't khow the size of O.
■■■■■■■■■■■■■■■■■■■■■■■■■
●Tan (O) = sin(O)/cos(O)
● tan (O) = (√(5)/3)÷(2/3) or tan(O) = (-√(5)/3)÷(2/3)
● tan (O) = √(5)/2 or tan(O) = -√(5)/2
Explain how to solve the equation |2x-3| = x^2 graphically. Using a graphing calculator to find all real number solutions to the equation.
Answer:
x = -3 , x = 1
Step-by-step explanation:
Hello,
you need to draw the graph of the two functions and then find the intersection points.
please see below
So the solution is the two points A and B
(-3,9) and (1,1)
Hope this helps
Given the formula below, solve for x.
- Vi
ОА.
+ 11
B.
y – 9 + fi
O c.
Ử - VI
m
-fi
D.
mly – yy)
Answer:
Option (C)
Step-by-step explanation:
Given formula of a line passing through [tex](x_1, y_1)[/tex] and slope 'm' is,
[tex]y-y_1=m(x-x_1)[/tex]
Further solving this equation,
[tex]y-y_1=mx-mx_1[/tex] [By distributive property]
[tex]y-y_1+mx_1=(mx-mx_1)+mx_1[/tex] [By adding [tex]mx_1[/tex] on both the sides]
[tex]y-y_1+mx_1=mx[/tex]
[tex]\frac{y-y_1-mx_1}{m}=\frac{mx}{m}[/tex] [Divide the equation by m]
[tex]\frac{y-y_1}{m}-x_1=x[/tex]
Therefore, Option (C) will be the answer.
If a test has 40 questions and you get 200 points for the whole test, how many points are each question worth?
Answer:
5
Step-by-step explanation:
To find the points for each question, you must divide the number of points (200) by the number of questions (40) to get the number of points for each question
[tex]\frac{200}{40}[/tex]
Divide 200 by 40 to get
[tex]\frac{5}{1}[/tex] or [tex]5[/tex]
Hope this helps. If you have any follow-up questions, feel free to ask.
Have a great day!
Answer:
5 points
Step-by-step explanation:
200points / 40 questions = 5points/1question
then:
1 questión worths 5 points
Suppose you computed a 95% confidence interval for the difference in mean weight between two species of snakes in a large nature reserve (species #1 – species #2), and your interval is –3.6 to 61.6 ounces. What can you conclude?
Answer:
1. In a situation were we are willing to use 90% confidence, this means we could say that the observed difference that we have in the sample means tend to represents a real difference in the population means.
2. We cannot actually say because even with 95% confidence, that is the observed difference in sample means tend to as well represents a real difference in the population means.
3. Because the interval extends further in the positive direction than the negative direction this means that the evidence suggests that species #1 tend to weighs more than species #2 on average, but we can't actually say for sure.
Step-by-step explanation:
The following are what I will conclude about based on the information given in the question.
1. In a situation were we are willing to use 90% confidence, this means we could say that the observed difference that we have in the sample means tend to represents a real difference in the population means.
2. We cannot actually say because even with 95% confidence, that is the observed difference in sample means tend to as well represents a real difference in the population means.
3. Because the interval extends further in the positive direction than the negative direction this means that the evidence suggests that species #1 tend to weighs more than species #2 on average, but we can't actually say for sure.
Example 2
A black die and a white die are thrown at the same
time. Display all the possible outcomes. Find the
probability of obtaining:
a) a total of 5
b) a total of 11
c) a 'two' on the black die and a six' on the white die.
It is convenient to display all the possible outcomes
on a grid. This is called a possibility diagram
It’s example 2 please help:)
Answer:
Total possible outcomes = 6×6 = 36
a) P(5) = 1/9
b) P(11) = 1/18
c) P(two and six) = 1/36
Step-by-step explanation:
A black die and a white die are thrown at the same time.
Each die has six sides so total possible outcomes are
Total possible outcomes = 6×6 = 36
The possible outcomes are given below:
(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)
(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)
(3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)
(4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)
(5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)
(6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)
a) Find the probability of obtaining a total of 5
Number of ways to get a total of 5 = (1, 4) (2, 3) (3, 2) (4, 1)
Number of ways to get a total of 5 = 4
The probability is given by
P = Number of desired outcomes/total number of outcomes
P(5) = 4/36
P(5) = 1/9
b) Find the probability of obtaining a total of 11
Number of ways to get a total of 11 = (5, 6) (6, 5)
Number of ways to get a total of 11 = 2
The probability is given by
P(11) = 2/36
P(11) = 1/18
c) a 'two' on the black die and a six' on the white die.
There is only one way to get a two on the black die.
Probability of obtaining a two on the black die = 1/6
There is only one way to get a six on the white die.
Probability of obtaining a six on the white die = 1/6
P(two and six) = 1/6×1/6
P(two and six) = 1/36
how would you solve #81?
30. A rectangular prism has a volume of
285.6 cubic feet. The prism is
12 feet long and 3.4 feet wide. What is
the height of the prism?
A 7 ft
C 19 ft
B 15 ft
D 22 ft
Answer:
The answer is a
Step-by-step explanation:
my brother is very smart
Write the equations after translating the graph of y = |x|:
one unit up,
Answer:
y = | x | + 1
Step-by-step explanation:
Given y then y + c represents a vertical translation of y
• If c > 0 then a shift up of c units
• If c < 0 then a shift down of c units
Here the shift is 1 unit up, thus
y = | x | + 1
The pentagon ABCDE is dilated to the image A'B'C'D'E' with the center of the dilation at the origin.
Select all true statements
The scale factor of the dilation is 1/4
The line EA is parallel to the E’A’ because EA passes through the center of the dilation
Since the line C’D’ falls on the line CD, the scale factor is. It applied on the line CD
The scale factor of the dilation is 1/2
The line CD is not parallel to the line C’D’ because CD passes through the center of the dilation
Now I’m no genius but I‘m pretty sure the answers are “c” and “d”
Ya’ll have a good day or night, whichever one!
The true statement for the Pentagon in the given graph is
The scale factor of the dilation is 1/2 with the center at the origin(0,0).
Dilation:Dilation implies resize of any object.
It may increase or decrease the object by a particular value.The particular value is called the scale factor. Properties of Dilation of figure:Parallel lines in the dilated figure remain the same as in the original figure.The dilation of any figure does not vary from each angle of the figure.The midpoints of the dilated figure remain the same as that of the original figure.True statement:The scale factor of the dilation of the pentagon is 1/2.
Reason:The pentagon with vertices A(0.5,4.5), B(2,3), C(1,0), D(-2,0), E(-3,3) when multiplied by 1/2 we get The vertices of the dilated pentagon as A'(0.25,2.25), B'(1,1.5), C'(0.5,0), D'(-1,0), E(-1.5,1.5). When we plot the points A'B'C'D'E' in the graph, obtain the dilated pentagon with a center at the origin. Wrong statement with Reasons:The scale factor of the dilation is not 1/4 because when we multiply the vertices of pentagon ABCDE by 1/4 we are not getting the dilated points as in the graph.The line EA is parallel to E'A' but,1. The line EA does not passes through the center of the dilation
at origin(0,0), which can be clearly seen from the given graph.
2. For two lines to be parallel it is not necessary for one of the
lines to pass through the origin.
The line C'D' is parallel to CD as we should see the figure in a 3-dimensional way and it also follows the properties of dilation of a figure.Hence the scale factor of the given pentagon is 1/2.
To learn more about the Dilation of polygons:
https://brainly.com/question/3020085?referrer=searchResults
#SPJ2
write the expression in radical form. (88c)^2/3
Answer:
[tex]\sqrt[3]{88c^{2} }[/tex]
Step-by-step explanation:
If we have a term to a fractional power, that’s the same as finding the denominator root of the number - if the numerator of the fraction isn’t 1, then the term itself inside the root sign becomes the term to the numerator power.
So - since the denominator of this fraction is 3, we find the cube root of 88c. Since the numerator is 2, we square 88c.
[tex]\sqrt[3]{88c^{2} }[/tex].
Hope this helped! (By the way, this was my 100th answer!)
i need help with this please
Answer:
supplementary
Step-by-step explanation:
Since a and b form a straight line, they will add to 180 degrees
Two angles that add to 180 degrees are supplementary angles
PLEASEEE HELP JUST THE ANSWER I don’t to explain !!!
Find the length of a cube with a surface area of 850cm^2 rounded to the nearest tenth. I need a step by step solution pleaseeee:)
Answer:
11.9 cm.
Step-by-step explanation:
A cube has a SURFACE AREA of 850 cm^2.
A cube has six congruent sides. That means that each side measures 850 / 6 = 141.666666667 cm^2.
Since a side measures 141.66667 cm^2, a side length will be the square root of that (the area of a square is a side length times the side length, and they are the same).
[tex]\sqrt{141.666666666667}[/tex]
= 11.90238071
So, the side length of the cube is 11.9 cm.
Hope this helps!
A company has determined that its weekly profit is a function of the number of items that it sells. Which equation could represent the weekly profit in thousands of dollars, y, when the company sells x items? y squared = 4 x squared minus 100 y = negative x squared + 50 x minus 300 x = negative y squared minus 400 x squared = negative 6 y squared + 200
Answer:
B. y= -x^2 + 50x - 300
Step-by-step explanation:
Options given
A. y^2=4x^2 - 100
B. y= -x^2 + 50x - 300
C. x= -y^2 - 400
D. x^2= -6y^2 + 200
We are to find profits (y) function in thousands of dollars if the company sells x items.
We will use elimination method to eliminate the wrong options above in order to find the correct answer
Option A. y^2= 4x^2 - 100 is used to find the square of the profit function
Option B. y= -x^2 + 50x - 300 is used to calculate profit (y) function
Option C. x= -y^2 - 400 is for the calculation of the items x sold
Option D. x^2= -6y^2 + 200 is to find items x sold squared.
Since, we are required to find the profit (y) function, option A, C and D will be eliminated.
We are left with option B which is the correct answer to the question.
The weekly profits (y) function in thousands of dollars when the company sells x items is
B. y= -x^2 + 50x - 300
Answer:
B.
Step-by-step explanation:
I just took the quiz on edge