Answers
Answer:
901.1 km²
Step-by-step explanation:
The area of ∆WXY can be found using the formula, ½*a*b*sin(θ),
Where a and b, are two known sides of the triangle, and θ is the angle between both sides.
To find the area of ∆WXY, follow the steps below:
Step 1: Find XY using the law of sines.
m < W = 180 - (65 + 48) (sum of angles in a ∆)
W = 180 - (113) = 67°
X = 65°
WY = 49 km
XY = ?
[tex] \frac{XY}{sin(W)} = \frac{WY}{sin(X)} [/tex]
[tex] \frac{XY}{sin(67)} = \frac{49}{sin(65)} [/tex]
[tex] \frac{XY}{0.92} = \frac{49}{0.91} [/tex]
Cross multiply
[tex] XY*0.91 = 49*0.92[/tex]
Divide both sides by 0.91
[tex] \frac{XY*0.91}{0.91} = \frac{49*0.92}{0.91} [/tex]
[tex] XY = 49.54 [/tex]
XY ≈ 49.5
Step 2: find the area
Area = ½*WY*XY*sin(Y)
Area = ½*49*49.5*sin(48)
Area = ½*49*49.5*0.743
Area = 901.07325
Area = 901.1 km² (nearest tenth)
Related Questions
A square has diagonals of length 10 cm. Find the sides of the square
Answers
Answer:
5[tex]\sqrt{2}[/tex]
Step-by-step explanation:
The diagonal divides the square into 2 right triangles.
let s be the side of the square with the diagonal being the hypotenuse.
Applying Pythagoras' identity to one right triangle, gives
s² + s² = 10² , that is
2s² = 100 ( divide both sides by 2 )
s² = 50 ( take the square root of both sides )
s = [tex]\sqrt{50}[/tex] = [tex]\sqrt{25(2)}[/tex] = [tex]\sqrt{25}[/tex] × [tex]\sqrt{2}[/tex] = 5[tex]\sqrt{2}[/tex]
Using this data, what is the population proportion of semesters for which the number of student applications is less than 200,000?
Answers
Complete question :
The table shows the total number of student applications to universities in a particular state over a period of 12 semesters. States base their decisions on data like this. Suppose they decide that if fewer than 200,000 students apply during 6 or more semesters, the state will make a special effort to promote university education. Using this data, what is the population proportion of semesters for which the number of student applications is less than 200,000?
Semester Student Applications (in thousands)
1 106
2 137
3 285
4 120
5 202
6 195
7 327
8 139
9 307
10 318
11 212
12 217
Answer:
42%
Step-by-step explanation:
Given the above data in thousand :
Proportion of students
1 - - - - 106, 000
2 - - - -137, 000
3 - - - - 285, 000
4 - - - 120, 000
5 - - - 202, 000
6 - - - 195, 000
7 - - - 327, 000
8 - - - 139, 000
9 - - - 307, 000
10 - - - 318, 000
11 - - -212, 000
12 - - - 217, 000
Therefore, proportion of semesters with student application below 200,000
= (Number of semesters below 200,000 / total number of semesters)
Semesters below 200,000 :
(106000, 137000, 120000, 195000, 139000) = 5
(5 / 12) = 0.416666
= 0.42
In terms of percentage :
0.42 * 100 = 42%
Simplify. Your answer should contain only positive exponents.
9) 3^-1 • 3^0
Answers
Answer:
1 / 3^1
Step-by-step explanation:
3^-1 • 3^0
When multiplying exponents with the same base, we add the exponents
3^ (-1+0)
3 ^-1
We know that a^ - b = 1/a^b
3 ^ -1 = 1/3^1
HELPPPPPPPPPPPPPPPPPPPPPP
Answers
Answer:
x= 24, y= 33°
Step-by-step explanation:
MJ is part of the diameter of the circle and there is right angle between the diameter and HK
As the diameter and HK are perpendicular, HM=MK and mHJ= mJK
So,
x= 24and
y= 66°/2= 33°WNAE, an all-news AM station, finds that the distribution of the lengths of time listeners are tuned to the station follows the normal distribution. The mean of the distribution is 15.0 minutes and the standard deviation is 3.5 minutes. What is the probability that a particular listener will tune in:
Answers
Complete question :
WNAE, an all-news AM station, finds that the distribution of the lengths of time listeners are tuned to the station follows the normal distribution. The mean of the distribution is 15.0 minutes and the standard deviation is 3.5 minutes. What is the probability that a particular listener will tune in:
a. More than 20 minutes? b. For 20 minutes or less
Answer: 0.0764 ; 0.9236
Step-by-step explanation:
Mean (m) = 15 minutes
Standard deviation (sd) = 3.5
Z - score :
Z = (x - m) / sd
A) more than 20 minutes
P(X > 20) ; x = 20
Z > (20 - 15) / 3.5 = 5/3.5 = 1.429
P(z > 1.429) = 0.5 - P(0<z<1.43)
Using the z-table: 1.43 = 0.4236
0.5 - 0.4236 = 0.0764
2) 20 minutes or less :
P(X <= 20) ; x = 20
Z < (20 - 15) / 3.5 = 5/3.5 = 1.429
P(z < 1.429) = 0.5 + P(0<z<1.43)
Using the z-table: 1.43 = 0.4236
0.5 + 0.4236 = 0.9236
PLEASE help me with this question with solutions
Answers
Answer:
D
Step-by-step explanation:
the inscribed angle intersects an arc that twice the measure of the arc interested by the central angle. The inscribed angle's arc measures 144° and the central angle's arc measures 72°
>central angle and the arc the intersected arc are equal i.e they are both 72°
>the inscribed angle is half of the measure of the intersected arc i.e since the inscribed angle is 72° the arc interested is 144°
For one of the quadrilaterals: the corner are not the right angles, the quadrilateral has rotational symmetry of order 2 and the diagonals cross at the right angles. Write down the name of this quadrilateral
Answers
Answer:
Rhombus.
Step-by-step explanation:
A rhombus is a quadrilateral, meaning that it has four lateral sides. A Rhombus is a 2-dimensional shape, and has two lines of symmetry. A Rhombus has a rotational symmetry of order two, and the opposite sides are parallel. Also, the opposite angles in Rhombus are equal. Th diagonals of a Rhombus bisect each other at a right angle.
Other quadrilateral shapes includes the Rectangle, Parallelogram, and the Kite.
Find the measure of b.
Please help
Answers
Answer:
125 degrees
Step-by-step explanation:
Using a theorem, you know that angle a is half of 110. Also, in all quadrilaterals inscribed in a circle, the opposite angles are supplimentary. So then, knowing that angle a is 55 degrees, you can come to the conclusion that b is 125 degrees.
Hope this is helpful! :)
5. Over what interval is the following graph DECREASING? *
Answers
Answer:
(3, 13)
Step-by-step explanation:
The curve decreases from x = 3 to x = 13.
Answer: (3, 13)
In a scale drawing of a rectangular deck, the
length is 10 inches and the width is 8 inches. In
the drawing, 4 inches represents 3 yards. What
is the length of the actual deck, in yards?
Answers
Answer:
45
Step-by-step explanation:
10/4x3=7.5
8/4x3=6
6x7.5=45yards
John has 9 boxes of apples. Each box holds 16 apples. If 7 boxes are full, and 2 of the boxes are half full, how many apples does john have?
Answers
Answer:
128 Apples
Step-by-step explanation:
Answer:
128 apples
Elaborated:
Your first multiple 16 and 7 which is 112. Your than multiply 2 and 8 since the remaining boxes are half full which is 16. 112+16 is 128. Hope this helps!
We have 9 balls, numbered 1 through 9, and 27 bins. How many different ways are there to distribute these 9 balls among the 27 bins? Assume the bins are distinguishable (e.g., numbered 1 through 27).
Answers
Answer:
7625597484987 ways
Step-by-step explanation:
Given the following :
Number of ball(k) = 9
Number of bins (n) = 27
How many different ways are there to distribute these 9 balls among the 27 bins.
Here, the balls have different labels (1 to 9)
The bins are also distinguishable, therefore each ball can go into any of the 27 distinct bins.
Therefore, the different ways are there to distribute these 9 balls among the 27 bins equals = n^k
27^9 = 7625597484987 ways.
In a standard normal distribution, what is the probability of a z-score being less than 2.55?
Answers
Answer:
The probability is 0.0053861
Step-by-step explanation:
To answer this question, the best thing to do is to put the wordings in a mathematical expression.
Thus what we have is;
P(z < 2.55)
Now since we have the mathematical expression, the next thing to do here is to use the standard normal distribution table.
From the standard normal distribution table, we can get the probability value that equals the given z-score value
Mathematically this is;
P(z<2.55) = 0.0053861
It is 64º F at the 5000-foot level of a mountain, and 48º F at the 10,000-foot level of the mountain. Write a linear equation, in slope-intercept form, to find the temperature T at an elevation e on the mountain, where e is in thousands of feet.
Answers
Answer:
T = - 3.2e + 80
Step-by-step explanation:
Given the following :
e = elevation in thousands of feets
T = temperature (°F)
e1 = 5 ; e2 = 10 (in thousands of feet)
T1 = 64° ; T2 = 48°
y = mx + c ; T = me + c
y = ; m = slope, c = intercept
64 = m5 + c - - - - (1)
48 = m10 + c - - - - (2)
From (1)
c = 64 - m5
Substitute c = 64 - m5 into (2)
48 = m10 + c - - - - (2)
48 = m10 + 64 - m5
48 - 64 = 10m - 5m
-16 = 5m
m = - 16 / 5
m = - 3.2
Substitute the value of m into c = 64 - m5
c = 64 - 5(-3.2)
c = 64 - (-16)
c = 64 + 16
c = 80
Inserting our c and m values into T = me + c
T = - 3.2e + 80
Where e is in thousands of feet
T is in °F
PLEASE HELP THANK YOUUUU Your group has $120 available for the banquet. Any other costs must be covered from selling tickets for the event. You decided to take care of the major cost first–hall rental and caterer. Each caterer you approach is associated with a specific hall. Caterer One charges $45 per person. The cost of using the hall is inclusive. Caterer Two charges $250 for hall rental plus $28 per person. Cater Three charges $500 for hall rental plus $20 per person. 1. Write the equation to represent the cost of each caterer. Use C to represent cost and n to represent number of people. (3 marks)
Answers
Answer:
The cost C, of hosting the banquet with the services of Caterer One is;
C = $ 45·n
The cost C, of hosting the banquet with the services of Caterer Two is;
C = $250 + $ 28·n
The cost C, of hosting the banquet with the services of Caterer Three is;
C = $500 + $ 20·n
Step-by-step explanation:
The information includes;
The amount available to the group for the banquet = $120
The number of people attending the banquet = n
The cost incurred in hosting the banquet = C
The major costs in hosting the banquet are hall rental and caterer
The cost per caterer are as follows;
Caterer One
The cost per person including the hall = $45
Therefore, the cost incurred, C, in hosting the banquet using caterer one is equal;
C = n × $45 = $ 45·n
Caterer Two
The hall rental = $250
The cost per person = $28
Therefore, the cost incurred, C, in hosting the banquet using caterer two is equal;
C = $250 + n × $28 = $250 + $ 28·n
Caterer Three
The hall rental = $500
The cost per person = $20
Therefore, the cost incurred, C, in hosting the banquet using caterer three is equal;
C = $500 + n × $20 = $500 + $ 20·n.
Answer:
The cost C, of hosting the banquet with the services of Caterer One is;
C = $ 45·n
The cost C, of hosting the banquet with the services of Caterer Two is;
C = $250 + $ 28·n
The cost C, of hosting the banquet with the services of Caterer Three is;
C = $500 + $ 20·n
Step-by-step explanation:
The information includes;
The amount available to the group for the banquet = $120
The number of people attending the banquet = n
The cost incurred in hosting the banquet = C
The major costs in hosting the banquet are hall rental and caterer
The cost per caterer are as follows;
Caterer One
The cost per person including the hall = $45
Therefore, the cost incurred, C, in hosting the banquet using caterer one is equal;
C = n × $45 = $ 45·n
Caterer Two
The hall rental = $250
The cost per person = $28
Therefore, the cost incurred, C, in hosting the banquet using caterer two is equal;
C = $250 + n × $28 = $250 + $ 28·n
Caterer Three
The hall rental = $500
The cost per person = $20
Therefore, the cost incurred, C, in hosting the banquet using caterer three is equal;
C = $500 + n × $20 = $500 + $ 20·n.
Find the value of each trigonometric ratio.
Answers
Answer: 40/41
Step-by-step explanation:
The cosine can be represented as adjacent/hypotenuse. Thus, the cosine of C is 40/41
Answer:
[tex] \frac{40}{41} [/tex]Solution,
BC = 40
AC = 41
Now,
[tex]cos \: theta \: = \frac{adjacent}{hypotenuse} [/tex]
[tex]cos \: c \: = \frac{bc}{ac} [/tex]
Plugging the values
[tex]cos \: c \: = \frac{40}{41} [/tex]
Hope this helps..
Good luck on your assignment..
A waffle cone has a height of 7 inches and a diameter of 3 inches. What is the volume of ice cream that can be contained within the cone? Use 3.14 to for pi. Round your answer to the nearest hundredth.
15.43 in^3
16.49 in^3
17.86 in^3
18.89 in^3
Answers
Hey there! I'm happy to help!
To find the volume of a cone, we multiply the base by the height and then divide by three.
First, we find the area of the base, which is a circle. To find a circle, you square the radius and then multiply by pi (or 3.14 in our case).
Radius is half of the diameter.
3/2=1.5
We square this.
1.5²=2.25
We multiply by 3.14
2.25×3.14=7.065
Now, we multiply this base area by the height.
7.065×7=49.455
We divide by 3.
49.455/3=16.485
Therefore, if we round this, our answer is 16.49 in³.
Now you can find the volume of a cone! Have a wonderful day! :D
Answer:
16.49
Step-by-step explanation:
i need both answers pls !!
Answers
(y is -3 for both)
Natasha and her two dogs were walking on a perfectly straight road when her two dogs ran away from her in opposite directions. Her beagle is now \dfrac{25}{4} 4 25 start fraction, 25, divided by, 4, end fraction meters directly to her right, and her labrador is \dfrac{51}{20} 20 51 start fraction, 51, divided by, 20, end fraction meters directly to her left. Which of the following expressions represents how far apart the two dogs are?
Answers
Answer:
[tex]\dfrac{74}{20}=3.7 meters[/tex]
Step-by-step explanation:
Hello!
1) Since no other data has been given. Suppose Natasha is in the center and the beagle is to the right.
[tex]\dfrac{25}{4} \:meters[/tex]
2) The labrador is [tex]\dfrac{51}{20}\: to\: the\: left.[/tex]
[tex]\dfrac{25}{4} -\dfrac{51}{20} =\dfrac{(5*25)-51}{20} \\\dfrac{(125-51}{20} =\dfrac{74}{20}[/tex]
Answer:
The answer is B :D hope this helps
Step-by-step explanation:
A club elects a president, vice-president, and secretary-treasurer. How many sets of officers are possible if there are 12 members and any member can be elected to each position? No person can hold more than one office.
Answers
Answer:
1320 setsStep-by-step explanation:
This problem brothers on selection without repetition, so we will be using permutation to solve this problem.
Given
n= 12 ,which is the number we are choosing from
r= 3, which is the number of committee(president, vice-president, and secretary-treasurer.)
[tex]= \frac{n!}{(n-r)!}[/tex]
Substituting we have
[tex]= \frac{12!}{(12-3)!}\\\\ = \frac{12!}{(9)!}\\\\= \frac{12*11*10*9!}{9!}[/tex]
[tex]= 12*11*10= 1320[/tex]
You measure the sides of a pool and find that it is 20 yards wide and 50 yards long. Approximately, how far would it be diagonally between corners of the pool?
A. 54 yards
B. 58 yards
C. 62 yards
D. 66 yards
Answers
Answer:
[tex]\boxed{d = 54 yards}[/tex]
Step-by-step explanation:
Formula for diagonal is as follows:
[tex]d = \sqrt{l^2+w^2}[/tex]
Where d is diagonal, l is length (50 yards) and w is width (20 yards)
[tex]d = \sqrt{(50)^2+(20)^2}[/tex]
[tex]d = \sqrt{2500+400}[/tex]
[tex]d = \sqrt{2900}[/tex]
d = 53.85 yards
d ≈ 54 yards
Answer:
[tex]\boxed{\mathrm{54 \: yards}}[/tex]
Step-by-step explanation:
The shape of the pool is a rectangle.
The diagonal of a rectangle can be found through a formula by using Pythagorean theorem.
[tex]d^2=l^2 +w^2[/tex]
[tex]d=diagonal\\l=length\\w=width[/tex]
The length is given 50 yards, and width is given 20 yards. Find the diagonal.
[tex]d^2 =50^2 +20^2[/tex]
[tex]d^2 =2500+400[/tex]
[tex]d^2 =2900[/tex]
[tex]d=\sqrt{2900}[/tex]
[tex]d \approx 53.851648[/tex]
[tex]d \approx 54[/tex]
Samuel is solving the equation 3 (x minus 1) + 4 = 2 minus (x + 3). Which equivalent equations might Samuel use? Check all that apply.
3 x minus 3 + 4 = 2 minus x minus 3
3 x minus 1 + 4 = 2 minus x + 3
3 x minus 3 + 4 = 2 minus x + 3
3 x + 1 = negative x minus 1
3 x + 3 = negative x + 5
3 x + 1 = negative x + 5
Answers
Answer: 3 x minus 3 + 4 = 2 minus x minus 3
3 x + 1 = negative x minus 1
Step-by-step explanation:
A and D. Edge 2020
The required equation that Samuel used is 3x -3 + 4 =2- x -3. option A is correct.
Samuel is solving the equation 3 (x minus 1) + 4 = 2 minus (x + 3). Which equivalent equations might Samuel use, is to be determined.
The equation is the relationship between variables and represented as[tex]y = ax +b[/tex] is an example of a polynomial equation.
Given equation is [tex]3(x-1) +4 =2 -(x+3)[/tex]
Simplification of the above equation,
opening the parenthesis on both sides
step 1⇒ 3x - 3 + 4 = 2 - x - 3
step 2⇒ 3x + 1 = -x - 1
Transposition of -x to the left side and +1 to the right side
step 4 ⇒ 3x +x = -1 -1
4x = -2
Transposition of 4 to the denominator of -2.
step 5⇒ x = -2/4
x = -1/2
Thus , Step 1 3x -3 + 4 =2- x -3 is the equivalent equation used by the samuel.
Learn more about the equation here:
brainly.com/question/10413253
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Select the correct answer.
Which table shows a proportional relationship between x and y?
x y
1
5
2
6
3
7
x y
2
3
4
6
6
9
x y
4
16
8
64
12
144
x y
1
3
2
9
3
27
Answers
Answer:
I think
x y
2
3
4
6
6
9
Step-by-step explanation:
but i don't see any table
Benjamin decides to treat himself to breakfast at his favorite restaurant. He orders chocolate milk that
costs $3.25. Then, he wants to buy as many pancakes as he can, but he wants his bill to be at most $30
before tax. The restaurant only sells pancakes in stacks of 4 pancakes for $5.50.
Let S represent the number of stacks of pancakes that Benjamin buys.
1) Which inequality describes this scenario?
Answers
Answer:
[tex]\bold {3.25+5.50S \le 30}[/tex] is the correct answer.
Step-by-step explanation:
Given that
Chocolate milk already ordered for the cost of $3.25.
Maximum bill that Benjamin wants = $30
Cost of a stack pancake = $5.50
Number of stacks of pancakes bought = S
It is given that all the money available is to be spent on 1 chocolate milk and S number of stacks of pancakes.
Cost of 1 pancake = $5.50
Cost of S number of stacks of pancakes = [tex]\text{Number of stacks of pancakes} \times \text{Cost of each pancake}[/tex]
i.e. [tex]S \times 5.50 = 5.50S[/tex]
So, total money spent = $3.25+5.50S
Now, this money should be lesser than or equal to $30 because maximum bill that Benjamin wants is $30.
So, the inequality can be written as:
[tex]\bold{3.25+5.50S \le 30}[/tex]
Does this graph show a function? Explain how you know.
5
-5
-5
A. No; there are y-values that have more than one x-value.
B. No; the graph fails the vertical line test.
C. Yes; the graph passes the vertical line test.
D. Yes; there are no y-values that have more than one x-value.
Answers
Answer:
Option (C).
Step-by-step explanation:
To check a graph whether it's a function or not we use a vertical line test. In this test first we draw a vertical line on the given graph. If this line intersects the graph at more than one point, the graph is not a function.
In the given parabola, opening upwards passes the vertical line test.
Therefore, this graph shows a function.
Option (C) will be the answer.
Option (c) Yes; the graph passes the vertical line test. And
(d) Yes; there are no y-values that have more than one x-value are correct options. Hence, a given graph is a function.
This is a graph of [tex]y = x^2[/tex]
Which is a graph of parabola.
To determine the given graph is a function or not, we do a vertical line test.
The vertical line test says that if a vertical line intersects a graph more than once, then that graph is not a function. And in this case, y-values have more than one x-values.
Let’s draw a vertical line in the given graph (attached below)
We see that the vertical line touches the graph only at once. That’s why it is a function, and so there are no y-values that have more than one x-value.
Hence, the given graph is a function and option (3) and (4) are correct options.
Learn more about graphs here:
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A doctor prescribes a 100-mg antibiotic tablet to be taken every eight hours. Just before each tablet is taken, 20% of the drug remains in the body. (a) How much of the drug is in the body just after the sec- ond tablet is taken
Answers
Answer:
120 mg
Step-by-step explanation:
20% of 100 is 20 so that would be 20mg plus the 100mg they just took
100+20=120mg
i hope this helps you!
Tapiwa raked %5, percent more leaves than Adam raked. Tapiwa raked 357 liters of leaves. How many liters of leaves did Adam rake?
HELP!! DUE SOON
Answers
Answer:
340 liters
Step-by-step explanation:
357/1.05=340
divide 0.377 ÷ 2.9 dosto please solve it
Answers
ASAP!! Please help me. I will not accept nonsense answers, but will mark as BRAINLIEST if you answer is correctly with solutions.
Answers
Answer:
the numbers of cars pf various colors in a parking lot
Answer: The speed of a car as it changes during a time.
B is the best example of continuous data.
Step-by-step explanation: The contrast between the definitions of continuous data vs. discreet data is that discrete data is counted, continuous data is measured.
A speedometer measures speed continuously, time is measured continuously.
Time can, however, be reported as discreet measurements in situations where that kind of data is needed. (not in this question)
A Number of cars is discreet.
Data from different workers or different days is not continuous.
Which is the definition of a rhombus?
a. A quadrilateral with four right angles
b. A quadrilateral with four congruent sides
c. A quadrilateral with interior angles that sum to 360°
d. A quadrilateral with two pairs of opposite congruent sides
Answers
Answer:
a) A quadrilateral with 4 right angles
Answer:
I think the answer is b
I'm sorry if I'm not correct