Answer: There is a 0.88% chance of pulling three red marbles in a row.
Step-by-step explanation:
First pull = 4/15 (26.67%)
second pull = 3/14 (21.43%)
Third pull = 2/13 (15.38%)
You need to multiply these three fractions to get the probability of pulling three reds in a row, doing that will get you 4/455 or 0.88%
Which answer choice contains only equations? 2 + h = 14 and k minus 25 = 2 c minus 14 and d + 134 10 = 3 + s and 22 minus y 15 + x and 55 = r minus 1
Answer:
2 + h = 14 and k - 25 = 2
Step-by-step explanation:
An equation has an equal sign.
Apparently, your answer choices are of the form ...
(math expression) and (math expression)
In order for this to be "only equations", each "math expression" must contain an equal sign. That is, you must have ...
( ... = ... ) and ( ... = ... )
Something like ...
c -14 and d +134
contains no equal signs, so has no equations.
It looks like your appropriate choice is ...
2 + h = 14 and k - 25 = 2
Answer:
the answer is a
Step-by-step explanation:
i took the test
:)
note: have a wonderful day!
Marcus states that angle ORP and angle LRP are a linear pair. Which best describes his statement?
Answer:
He is incorrect. Ray RO and ray RL are not opposite rays.
Step-by-step explanation:
Two angles are linear pair if they are supplementary and share a leg.
∠ORP and ∠LRP are not supplementary, because ray RO and ray RL are not opposite rays.
Therefore, ∠ORP and ∠LRP are not linear pair.
correct me if this is wrong
A shopkeeper buys 1 dozen of pens at Rs 15 each and sells them at Rs 18
ch. Find his profit and profit percent.
Answer:
20%
Step-by-step explanation:
Cost price (C. P.) of each pen = ₹ 15
Selling price (S. P.) of each pen = ₹ 18
Profit = S. P. - C. P. = 18 - 15 = ₹3
[tex]profit \: percent \\ \\ = \frac{profit}{c.p.} \times 100 \\ \\ = \frac{3}{15} \times 100 \\ \\ = \frac{3}{3} \times 20 \\ \\ = 20\%[/tex]
WILL GIVE BRAINLIEST HURRY
Answer: C
Step-by-step explanation:
To get all the constant terms on one side and variable terms on another, all we have to do is to add or subtract them on both sides.
3x+2x=10+5
Now that the like terms are on one side, we can combine them.
5x=15
To get x alone, we divide both sides by 5.
x=3
Now, we notice that x=3 is not an answer choice, but the next option that is equivalent to x=3 is C.
For C, if you divide both sides by -5, you still get x=3.
-15=-5x
x=3
A group of neighbors are constructing a community garden that is 80 m wide and 40 m long the top to vertex are plotted below at 10, 70 and 90, 70 what are the coordinates from the bottom to vertex of the garden
Question Correction
A group of neighbors are constructing a community garden that is 80 meters wide and 40 meters long. The top two vertices are plotted below at (10, 70) and (90, 70). What are the coordinates for the bottom two vertices of the garden?
Answer:
(10,30) and (90,30)
Step-by-step explanation:
The community garden is 80 m wide and 40 m long.
The top two vertex are plotted at: (10, 70) and (90, 70).
Horizontal Distance =90-10=80
This serves as the Width of the garden.
Since the length is 40m, the bottom two vertex can be derived by the transformation: (x,y-40).
(x,y-40)-->(10, 70)=(10,30); and
(x,y-40)-->(90, 70)=(90,30)
The coordinates for the two bottom vertices are (10,30) and (90,30).
Complete the equation of the line through (−10,3), (−10,3) and (−8,−8) ,(−8,−8).
Answer:
(y + 8) = -5.5(x + 8)
or
y = -5.5x - 52
Step-by-step explanation:
So find the slope first:
[tex]\frac{-8-3}{-8+10}=\frac{-11}{2} =-5.5[/tex]
Point - Slope Form: (y + 8) = -5.5(x + 8)
Slope - Intercept Form: y = -5.5x + b
-8 = 44 + b
b = -52
y = -5.5x - 52
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
B. 4x² - 20x + 26
Step-by-step explanation:
→Set it up, like so:
(2x - 5)² + 1
4x² - 20x + 25 + 1
→Add like terms (25 and 1):
4x² - 20x + 26
The functions f(x) and g(x) are graphed.
On a coordinate plane, a curved red line with an upward arc, labeled g of x, crosses the y-axis at (0, 4) and the x-axis at (2, 0). A straight blue line with a negative slope, labeled f of x, crosses the y-axis at (0, 4) and the x-axis at (2, 0).
Which represents where f(x) = g(x)?
f(2) = g(2) and f(0) = g(0)
f(2) = g(0) and f(0) = g(4)
f(2) = g(0) and f(4) = g(2)
f(2) = g(4) and f(1) = g(1)
Answer: first answer choice
Step-by-step explanation:
They give us that f(0) and g(0) = 4 and f(2) = g(2) = 0, so the answer is simply the first one. When x=0, y=4 for both and when x=2, y=0 for both.
Hope that helped,
-sirswagger21
Answer:
A
Step-by-step explanation:
on edge
Please answer this correctly
Answer:
# of broken crayons # of boces
1-5 1
6-10 4
11-15 5
16-20 3
21-25 1
Step-by-step explanation:
1-5: 4 (1 number)
6-10: 6, 6, 8, 9 (4 numbers)
11-15: 12, 13, 14, 14, 15 (5 numbers)
16-20: 17, 17, 19 (3 numbers)
21-25: 24 (1 number)
Answer:
Number of broken crayons Number of boxes
1-5 = 4
6-10 = 9
11-15 = 14
16-20 =19
21-25 =24
Step-by-step explanation:
To find the number of boxes compared to the number of broken crayons you have to find 5 consecutive (hence there being five boxes to fill in) numbers with a constant rate of change. Start with the largest number possible that you can pick and then find the second largest so 24 and 19 the rate of change is 5. Compared to 17 and 19 the rate of change is 2 so it doesn’t have the same rate of change but if you try 19-5 you get 14 which is an option if you subtract 14-5 you get 9 which is another option 9-5 is 4 the lowest number you could possibly pick and they all have a constant rate of change of 5 so the answer is correct.
Patricia can buy individual songs for $1.00 to download. Also, an entire album costs $10.00 to download. She can spend no more than a total of $80. She wants to buy no more than four albums, and at least 30 individual songs. The following system of inequalities represents this situation, where x is the number of individual songs and y is the number of albums.
Answer:
The system of inequalities is:
[tex]x\geq30\\\\y\leq4\\\\10x+1y\leq80[/tex]
Step-by-step explanation:
We will write each of the conditions stated in this problem
Patricia wants to buy at least 30 individual songs.
[tex]x\geq30[/tex]
She wants to buy 4 albums at most.
[tex]y\leq4[/tex]
The total expenditure has to be equal or less than $80, when each album cost $10 and each individual song cost $1.
[tex]10x+1y\leq80[/tex]
The system of inequalities is:
[tex]x\geq30\\\\y\leq4\\\\10x+1y\leq80[/tex]
The width of the rectangle is 2 more than the length. The area of the rectangle is 63 square inches. How long is the width?
Answer:
9 inches
Step-by-step explanation:
Area of rectangle= length ×width
Let the length of the rectangle be x inches.
Width of rectangle= (x +2) inches
since the width is 2 more than the length.
63= x(x+2)
63= x(x) +2x
Bringing constant to one side,
x² +2x -63= 0
(x +9)(x-7) = 0 (factorise)
x+9= 0 or x-7= 0
x= -9 or x= 7
(reject)
width of rectangle
= 7+2
= 9 inches
*We reject x= -9 since the length of the rectangle cannot be a negative number.
Simplify
6x^-2. ....
Answer:
6/x^2
Step-by-step explanation:
6x^-2
6*x^-2
6*(1/x^2)
6/x^2
Solve for w: 2w<9+5w
Answer:
w > -3
Step-by-step explanation:
2w<9+5w
Subtract 5w from each side
2w-5w<9+5w-5w
-3w <9
Divide each side by -3 remembering to flip the inequality
-3w/-3 > 9/-3
w > -3
Answer:
w>-3
Step-by-step explanation:
what the product of the reciprocals of 2/3, 1/8, and 5
Answer:
12/5
Step-by-step explanation:
Reciprocal of 2/3 is 3/2
Reciprocal of 1/8 is 8/1
Reciprocal of 5 is 1/5
[tex]\frac{3}{2} \times \frac{8}{1} \times\frac{1}{5} = \frac{24}{10} \\[/tex]
Can be simplified to
[tex]\frac{12}{5}[/tex]
4. The Navarro family uses an average of 225 gallons of water per day, 5 gallons of water per day, 5 gallons of water which goes through the family’s water filter. The Navarros’ water filter can process 450 gallons before it needs to be replaced. After how many days of average water use will the family need to replace their filter?
Answer:
90
Step-by-step explanation:
The family filters 5 gallons per day, so can expect to use the filter for ...
(450 gal)/(5 gal/day) = 90 day
After 90 days of average water use, the family will need to replace the filter.
A box on a 20 degree incline is shown with vectors radiating from a point in the center of the box. The first vector points up and parallel to the surface of the incline, labeled F Subscript f s Baseline. A second vector points toward the center of the earth, labeled F Subscript g Baseline = 735 N. A third vector is perpendicular to and away from the surface of the incline from the point, labeled F Subscript N Baseline. A fourth vector is broken into 2 components, one parallel to the surface and down the incline, labeled F Subscript g x Baseline, and one perpendicular to the surface and into the surface, labeled F Subscript g y Baseline.
A box at rest on a ramp is in equilibrium, as shown.
What is the force of static friction acting on the box? Round your answer to the nearest whole number. N
What is the normal force acting on the box? Round your answer to the nearest whole number.
The images to solve this problem is in the attachment.
Answer: [tex]F_{fs}[/tex] = 671.0 N; [tex]F_{N}[/tex] = 300 N
Step-by-step explanation: From the image in the attachment and knowing that the box is in equilibrium, i.e., the "sum" of all the forces is 0, it is possible to conclude that:
[tex]F_{fs}[/tex] = [tex]F_{gx}[/tex] and [tex]F_{N}[/tex] = [tex]F_{gy}[/tex]
Using trigonometry, shown in the second attachment, the values for each force are:
Force of Static Frictionsin 20° = [tex]\frac{F_{gx} }{F_{g} }[/tex]
[tex]F_{gx}[/tex] = [tex]F_{g}[/tex]. sin(20)
[tex]F_{gx}[/tex] = 735.0.913
[tex]F_{gx}[/tex] = 671.0
Normal Forcecos 20° = [tex]\frac{F_{gy} }{F_{g} }[/tex]
[tex]F_{gy}[/tex] = [tex]F_{g}[/tex]. cos (20)
[tex]F_{gy}[/tex] = 735.0.408
[tex]F_{gy}[/tex] = 300
The force of static friction is 671N and normal force is 300N
Answer:
Static force is 251 and the Normal force is 691.
Step-by-step explanation:
Hope this helps!! Have a great day!! :)
Na figura abaixo estão representadas cinco ruas do bairro onde moram João, Marcos, Pedro, Vitor e Samuel. A localização da casa de cada menino é identificada pela inicial de seu nome. Na esquina das ruas A e D fica a escola onde todos estudam. Sabe-se que as ruas A, B e C são paralelas e que todos os meninos vão a pé para a escola, sempre pelo caminho mais curto. Se Samuel caminha 100 m até a escola, Vitor caminha 260 m, João caminha 180 m e Marcos, 270 m, qual é a distância, em metros, que Pedro percorre de sua casa até a escola?
280m
300m
340m
460m
320m
Answer:
340 m
Step-by-step explanation:
Assume the figure looks like the one below.
We have three parallel lines cut by two transversals.
1. Lengths of segments
(a) Segment VS
If Vitor walks 260 m,
VS + SE = 260
VS + 100 = 260
VS = 260 - 100 = 160 m
(b) Segment MJ
If Marcos walks 270 m,
MJ + JE = 270
VS + 180 = 270
VS = 270 - 180 = 90 m
(c) Segment PV
The segments on the transversals are proportional.
[tex]\begin{array}{rcl}\dfrac{x}{90} & = & \dfrac{160}{180} \\\\x & = & 90 \times \left (\dfrac{160}{180}\right )\\\\& = &\textbf{80 m}\\\end{array}\\\textbf{PV = 80 m}[/tex]
2. Distance travelled by Pedro
Distance = PV + VS + SE = 80 m + 160 m + 100 m = 340 m
Pedro walks 340 m to school.
Select the correct answer. Meg deposited a $3,000 bonus check in a new savings account. The account has an interest rate of 3% for 5 years. The interest is compounded daily. How much money did Meg have at the end of the account term? (Round your answer to the nearest dollar.)
Answer:
$3,485.48
Step-by-step explanation:
For computing the money required at the end of the account term we need to apply the Future value formula i.e be to shown in the attachment below:
Given that,
Present value = $3,000
Rate of interest = 3% ÷ 365 days = 0.00821917
NPER = 5 years × 365 days = 1,825
PMT = $0
The formula is shown below:
= FV(Rate;NPER;PMT;PV;type)
So, after applying the above formula
the amount of future value is $3,485.48
The data from the data sample o 10 paired observations are shown:
Pair Population 1 Population 2
1 19 24
2 25 27
3 31 36
4 52 53
5 49 55
6 34 34
7 59 66
8 47 51
9 17 20
10 51 55
1. If you wish to test whether these data are sufficient to indicate that the mean for population 2 is larger than that for population 1, what are the appropriate null and alternative hypotheses?
2. Assuming that the within-pair differences are approximately normally distributed, conduct
the test using α = 0.1. What is your decision.
3. Find a 90% confidence interval for µd.
Answer:
Step-by-step explanation:
Corresponding means for population 1 and population 2 form matched pairs.
The data for the test are the differences between the mean for population 1 and mean for population 2.
μd = the mean for population 1 minus the mean for population 2.
Population 1 population 2 diff
19 24 - 5
25 27 - 2
31 36 - 5
52 53 - 1
49 55 - 6
34 34 0
59 66 - 7
47 51 - 4
17 20 - 3
51 55 - 4
Sample mean, xd
= (- 5 - 2 - 5 - 1 - 6 + 0 - 7 - 4 - 3 - 4)/10 = - 3.7
xd = - 3.7
Standard deviation = √(summation(x - mean)²/n
n = 10
Summation(x - mean)² = (- 5 + 3.7)^2 + (- - 2 + 3.7)^2 + (- 5 + 3.7)^2+ (- 1 + 3.7)^2 + (- 6 + 3.7)^2 + (0 + 3.7)^2 + (- 7 + 3.7)^2 + (- 4 + 3.7)^2 + (- 3 + 3.7)^2 + (- 4 + 3.7)^2 = 73.7
Standard - eviation = √(73.7/10
sd = 2.71
For the null hypothesis
H0: μd ≥ 0
For the alternative hypothesis
H1: μd < 0
The distribution is a students t. Therefore, degree of freedom, df = n - 1 = 10 - 1 = 9
The formula for determining the test statistic is
t = (xd - μd)/(sd/√n)
t = (- 3.7 - 0)/(2.71/√10)
t = - 4.32
We would determine the probability value by using the t test calculator.
p = 0.00097
Since alpha, 0.1 > than the p value, 0.00097, then we would reject the null hypothesis. Therefore, at 0.1 level of significance, we can conclude that these data are sufficient to indicate that the mean for population 2 is larger than that for population 1.
3) for population 1,
Mean = (19 + 25 + 31 + 52 + 55 + 34 + 59 + 47 + 17 + 51)/10 = 38.4
Summation(x - mean)² = (19 - 38.4)^2 + (25 - 38.4)^2 + (31 - 38.4)^2+ (52 - 38.4)^2 + (49 - 38.4)^2 + (34 - 38.4)^2 + (59 - 38.4)^2 + (47 - 38.4)^2 + (17 - 38.4)^2 + (51 - 38.4)^2 = 2042.4
Standard deviation, s1 = √2042.4/10 = 14.3
for population 2,
Mean = (24 + 27 + 36 + 53 + 55 + 34 + 66 + 51 + 20 + 55)/10 = 42.1
Summation(x - mean)² = (24 - 42.1)^2 + (27 - 42.1)^2 + (36 - 42.1)^2 + (53 - 42.1)^2 + (55 - 42.1)^2 + (34 - 42.1)^2 + (66 - 42.1)^2 + (51 - 42.1)^2 + (20 - 42.1)^2 + (55 - 42.1)^2 = 2248.9
Standard deviation, s2 = √2248.9/10 = 15
The formula for determining the confidence interval for the difference of two population means is expressed as
Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)
For a 90% confidence interval, we would determine the z score from the t distribution table because the number of samples are small
Degree of freedom =
(n1 - 1) + (n2 - 1) = (10 - 1) + (10 - 1) = 18
z = 1.734
x1 - x2 = 38.4 - 42.1 = - 3.7
√(s1²/n1 + s2²/n2) = √(14.3²/10 + 15²/10)
= 6.55
Margin of error = 1.734 × 6.55 = 11.4
The 90% confidence interval is
- 3.7 ± 11.4
2(x+3)+5 simplified expression
Answer:
2x+11
Step-by-step explanation:
2(x+3)+5
Distribute
2x+ 6 +5
Combine like terms
2x+11
Answer:
2x + 11
Step-by-step explanation:
First distribute 2 to the x + 3
2x + 6 + 5
Combine the constants
6+5=11
2x + 11
The simplified expression is 2x + 11
Which of the following is the solution to 1 x1 +9 $7?
A XS -2
B. All values are solutions
C. 3-2 and 2-16
D. No solution
Answer:
d. no solution
Explanation:
Step 1 - Subtract nine from both sides of the equation
[tex]|x| + 9 \leqslant 7 \\ |x| + 9 - 9 \leqslant 7 - 9 \\ |x| \leqslant - 2[/tex]
Step 2 - Remove the absolute value
[tex] |x| \leqslant - 2 \\ 2 \leqslant x \leqslant - 2 \\ 2 \leqslant - 2[/tex]
Therefore, since positive two is not less than or equal to negative two, there is no solution.
7. How much alcohol must be added to 480 grams of hand sanitizer that is 24% alcohol to
make it a hand sanitizer that is 40% alcohol? Correct your answer to the nearest whole
number
Answer:
the amount of alcohol to be added is 128 grams
Step-by-step explanation:
Given that:
The initial mass of the hand sanitizer = 480 grams
The initial strength of the hand sanitizer = 24 %
The new strength of the hand sanitizer = 40%
The objective here is to determine the final amount of alcohol that is to be added to get the new strength of the alcohol
First; let's find the mass of alcohol in the initial hand sanitizer;
SO;
= 24 % of 480
[tex]=\dfrac{24}{100}*480[/tex]
= 115.2 grams
If y should represent the mass of the alcohol added to have 40%; we have
The new amount of the alcohol to be[tex](115.2 + y) \ grams[/tex]
The new amount of the hand sanitizer will be[tex](480 + y) grams[/tex]
∴
For the new strength of sanitizer:
40 % of (480 + y) = (115.2 + y)
[tex]0.4 *(480 + y) = (115.2 + y) \\ \\ 192 + 0.4 y = 115.2 + y \\ \\ y (1 - 0.4) = 192 - 115.2 \\ \\ y= \dfrac{76.8}{0.6} \\ \\ y = 128 \ grams[/tex]
Thus ; we can conclude that the amount of alcohol to be added is 128 grams
if a propane tank has the shape of a cylindrical tank with a height of 4.2m and a radius of 1.3m how many cubic metres of propane is in the tank if it's only 50% full
Answer:
11.1 cm³
Step-by-step explanation:
V=πr²h / 2 (for half full)
V = (3.14)(1.3)²(4.2)/2
V = 11.1 cm³
ANSWER QUICK!!! Need 2 people to answer with the same answer to make sure! in the fridge there are 7 apples and 5 oranges. which of the following does NOT represent a ratio in the fridge? 7:5 5:7 5:12 7:12 6:7
You have two numbers to work with 7 and 5.
To keep the ratios the same using different numbers they would have to increase or decrease by the same multiple.
The answers would be 5:12, 7:12 and 6:7 do not represent a ratio in the fridge.
find the circumference of the circle use 3.14 for pi when the radius is 13 cm
Answer:
C =81.64 cm
Step-by-step explanation:
The circumference of a circle is given by
C = 2*pi*r
C = 2 * 3.14 * 13
C =81.64 cm
_______________________________
Radius(r)=13 cm
Circumference of circle=?
Now,
Circumference of circle=2 pi r
=2*3.14*13
=81.64 cm
Hope it helps..
Good luck on your assignment
________________________________
I wanted to compare my 5 hamsters’ average intelligence to see if they are different from the average intelligence of the 6 hamsters of another faculty member at a different university. Assume α = .01, then the cutoff for my hypothesis testing is ______.
Answer:
Step-by-step explanation:
The test to use is the t-test of independent means.
To determine the cutoff for the study then you need to find the degree of freedom and the alpha level. After the hypothesis testing, the calculated t value is then compared to the critical t value from the t distribution table using the degrees of freedom.
Find the point of diminishing returns (x comma y )for the function R(x), where R(x) represents revenue (in thousands of dollars) and x represents the amount spent on advertising (in thousands of dollars).
Complete Question
The complete question is shown on the first uploaded image
Answer:
The point of diminishing returns (x , y ) is (11, 21462)
Step-by-step explanation:
From the question we are told that
The function is [tex]R(x) = 10,000 -x^3 - 33x^2 + 800x , \ \ 0 \le x \le 20[/tex]
Here R(x) represents revenue (in thousands of dollars) and x represents the amount spent on advertising (in thousands of dollars).
Now differentiating R(x) we have
[tex]R'(x) = -3x^2 +66x + 800[/tex]
Finding the second derivative of R(x)
[tex]R''(x) = -6x +66[/tex]
at inflection point [tex]R''(x) = 0[/tex]
So [tex]-6x +66 = 0[/tex]
=> [tex]x= 11[/tex]
substituting value of x into R(x)
[tex]R(x) = 10,000 -(11)^3 - 33(11)^2 + 800(11) ,[/tex]
[tex]R(x) = 21462[/tex]
Now the point of diminishing returns (x , y ) i.e (x , R(x) ) is
(11, 21462)
A cylindrical metal pipe has a diameter of 8.4 millimeters and a height of 10 millimeters. A hole cut out of the center has a diameter of 6 millimeters.
A smaller cylinder is cut out of a larger cylinder. The smaller cylinder has a diameter of 6 millimeters. The larger cylinder has a diameter of 8.4 millimeters. Both cylinders have a height of 10 millimeters.
What is the volume of metal in the pipe? Use 3.14 for and round the answer to the nearest tenth of a cubic millimeter.
Answer:
[tex]271.3 mm^3\\[/tex]
Step-by-step explanation:
We have to find the volume of the hole and subtract it from the volume of the cylinder.
The volume of a cylinder is given as:
[tex]V = \pi r^2h[/tex]
where r = radius
h = height
A cylindrical metal pipe has a diameter of 8.4 mm and a height of 10 mm.
Its radius is 4.2 mm. Therefore, its volume is:
[tex]V = 3.14 * 4.2^2 * 10 = 553.9 mm^3[/tex]
A hole cut out of the center has a diameter of 6 mm. Its height is also 10 mm.
Its radius is 3 mm. Therefore, its volume is:
[tex]V = 3.14 * 3^2 * 10 = 282.6 mm^3[/tex]
Therefore, the volume of metal in the pipe is:
[tex]553.9 - 282.6 = 271.3 mm^3[/tex]
Answer:
B
Step-by-step explanation:
Two positive, consecutive, odd integers have a product of 143.
Complete the equation to represent finding x, the greater integer.
x(x –
) = 143
What is the greater integer?
Answer:
The answer is 13
Step-by-step explanation:
Two positive and consecutive old numbers are x and x - 2.
=> x(x - 2) = 143
=> x^2 - 2x - 143 = 0
=> x^2 + 11x - 13x - 143 = 0
=> x(x + 11) - 13(x + 11) = 0
=> (x + 11)(x - 13) = 0
=> x = -11 (invalid)
or x = 13 (valid), the remaining number is 13 - 2 = 11
=> The two numbers are 11 and 13, and the greater number is 13.
Hope this helps!
:)
Answer:
top: 2
bottom: 13
Step-by-step explanation:
step
by
step
explanation
An aeroplane X whose average speed is 50°km/hr leaves kano airport at 7.00am and travels for 2 hours on a bearing 050°. It then changes its course and flies on a bearing 1200 to an airstrip A. Another aeroplane Y leaves kano airport at 10.00am and flies on a straight course to the airstrip A. both planes arrives at the airstrip A at 11.30am. calculate the average speed of Y to three significant figures. the direction of flight Y to the nearest degree
Answer:
(a)123 km/hr
(b)39 degrees
Step-by-step explanation:
Plane X with an average speed of 50km/hr travels for 2 hours from T (Kano Airport) to point U in the diagram.
Distance = Speed X Time
Therefore: Distance from T to U =50km/hr X 2 hr =100 km
It moves from Point U at 9.00 am and arrives at the airstrip A by 11.30am.
Distance, UA=50km/hr X 2.5 hr =125 km
Using alternate angles in the diagram:
[tex]\angle U=110^\circ[/tex]
(a)First, we calculate the distance traveled, TA by plane Y.
Using Cosine rule
[tex]u^2=t^2+a^2-2ta\cos U\\u^2=100^2+125^2-2(100)(125)\cos 110^\circ\\u^2=34175.50\\u=184.87$ km[/tex]
Plane Y leaves kano airport at 10.00am and arrives at 11.30am
Time taken =1.5 hour
Therefore:
Average Speed of Y
[tex]=184.87 \div 1.5\\=123.25$ km/hr\\\approx 123$ km/hr (correct to three significant figures)[/tex]
b)Flight Direction of Y
Using Law of Sines
[tex]\dfrac{t}{\sin T} =\dfrac{u}{\sin U}\\\dfrac{125}{\sin T} =\dfrac{184.87}{\sin 110}\\123 \times \sin T=125 \times \sin 110\\\sin T=(125 \times \sin 110) \div 184.87\\T=\arcsin [(125 \times \sin 110) \div 184.87]\\T=39^\circ $ (to the nearest degree)[/tex]
The direction of flight Y to the nearest degree is 39 degrees.
