To find the distance between two radar installations a UFO calculates the distance to installation A to be 119 mi, the distance to installation C to be a = 77 mi, and the angle between them 6 = 34.6°. Find the distance between the installations.
Answers
Distance to A= 119mi
Disy¿tance to C=77mi
angle=34.6°
We have to find h, the angle that curts h will be half of 34.6, is a bisector
Using trigonometric to find h:
\(Cos(\theta)=\frac{c.a}{119mi}=\frac{h}{119mi}\)Isolating h:
\(\begin{gathered} cos(\frac{34.6}{2})*119mi=h \\ \\ h=113.61 \end{gathered}\)Using the Pythagorean theorem we calculate x:
\(\begin{gathered} 119^2=h^2+x^2 \\ x=\sqrt[\placeholder{⬚}]{119^2-h^2}=\sqrt[\placeholder{⬚}]{119^2-113.6^2}=35.4 \end{gathered}\)Now, we will use tan function:
\(\begin{gathered} tan\theta=\frac{b-x}{h} \\ \\ h*tan\theta=b-x \\ \\ b=h*tan\theta+x=113.61*tan(\frac{34.6}{2})+35.4=70.78 \end{gathered}\)The answer is: 70.78 mi.
Related Questions
A window in the shape of a semi-circle has a radius of 40 cm. The window is shown below.Find the area of the window. (Use pi = 3.14)
Answers
In order to calculate the area of a semi-circle, we can use the formula below:
\(A=\frac{\pi r^2}{2}\)For pi = 3.14 and r = 40 cm, we have:
\(\begin{gathered} A=\frac{3.14\cdot40^2}{2} \\ A=\frac{3.14\cdot1600}{2} \\ A=3.14\cdot800 \\ A=2512\text{ cm}^2 \end{gathered}\)Therefore the window area is 2512 cm².
The ratio of Val's savings to Dan is 2:3 at first. After Dan spent P3000.00, Val's saving became 11/3 more of that Dan's remaining savings. What is the total amount of saving the two had at first
Answers
Answer:
P.7500.00
Step-by-step explanation:
We are told that:
The ratio of Val's savings to Dan is 2:3 at first.
Now, Dan spent P3000.00 and Val's saving became 1⅓ more of that Dan's remaining savings.
Let's say the total amount of savings they had at first was x.
Thus;
Val had: 2x/5
Dan had: 3x/5
Now, Dan spent P3000.00.
So amount Dan has left = (3x/5) - 3000
We are told Val's savings is now 1⅓ = 4/3 times that of Dan's remaining savings
Thus; 2x/5 = (4/3)((3x/5) - 3000)
2x/5 = 12x/15 - 4000
Multiply through by 15 to get;
6x = 12x - (3000 × 15)
6x = 12x - 45000
Rearranging, we have;
12x - 6x = 45000
6x = 45000
x = 45000/6
x = P.7500
The total amount of saving the two had at first is P7500 and this can be determined by using the arithmetic operations and given data.
Given :
The ratio of Val's savings to Dan is 2:3 at first.After Dan spent P3000.00, Val's saving became 4/3 more of that Dan's remaining savings.Given that the ratio of Val's savings to Dan is 2:3 at first. Now, assume that the total amount of savings they had at first was x. So:
Val's had - 2x/5
Dan's had - 3x/5
Now, it is also given that Dan's spent P3000. So, the amount left is:
\(\rm =\dfrac{2x}{5}-3000\)
It is given that Val's saving became 4/3 more of that Dan's remaining savings. That is:
\(\dfrac{2x}{5} = \dfrac{4}{3} \times\left( \dfrac{3x}{5}-3000 \right)\)
\(\dfrac{6x}{20} = \dfrac{3x}{5}-6000\)
\(x = \dfrac{45000}{6}\)
x = P.7500
The total amount of saving the two had at first is P7500.
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Find the percent change from the first value to the second.
40; 70
Answers
Answer:
75%
Step-by-step explanation:
Answer:
75% increase
Step-by-step explanation:
The following are the ages (years) of 5 people in a room: 13 , 22 , 15 , 14 , 15 A person enters the room. The mean age of the 6 people is now 16. What is the age of the person who entered the room?
Answers
Answer:
17
Step-by-step explanation:
Add up the values (13, 22, 15, 15, 14) and subtract from the product of 16 and 6
Answer:
17
Step-by-step explanation:
the mean is calculated as
mean = \(\frac{sum}{count}\)
let x be the age of the person entering the room, then sum of 6 is
sum = 13 + 22 + 15 + 14 + 15 + x = 79 + x
\(\frac{79+x}{6}\) = 16 ( multiply both sides by 6 to clear the fraction )
79 + x = 96 ( subtract 79 from both sides )
x = 17
the age of the person who entered the room is 17
Billy took 5 tests in his math class. He scored an 89,88,93,90 and 81. What is the variance of his grades in these test? If necessary, round to the nearest hundredth.
Answers
The variance of Billy's grades obtained from his test scores is 15.76
What is variance?The variance is a measure of variability or spread a dataset. The variance can be calculated from the sum of the square of the differences of the data points from the mean divided by the number or count of the data points.
The variance of Billy's test scores can be calculated by finding the mean or the average of the scores, then finding the sum of the squares of the differences of each score from the mean as follows;
The mean score = (89 + 88 + 93 + 90 + 81)/5 = 88.2
The square of the differences of the values from the mean can be calculated as follows;
(89 - 88.2)² = 0.64, (88 - 88.2)² = 0.04, (93 - 88.2)² = 23.04, (90 - 88.2)² = 3.24, and (81 - 88.2)² = 51.84
The sum of the square of the differences is therefore;
0.64 + 0.04 + 23.04 + 3.24 + 51.84 = 78.8
The variance is therefore; 78.8/5 = 15.76Learn more on the variance of a set of data here: https://brainly.com/question/30701163
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Audrey is growing basil. On February 1st, her plant was 5 inches tall. A week later, the plant was 9 inches tall. By what percent did the plant grow?
Answers
Answer:
80%
Step-by-step explanation:
We know that the plant was 5 inches and it grew 4 inches to become 9 inches, so now we just need to figure out what percentage 4 is of 5. An easy way to do this is by multiplying 5 by 2 to get 10 and since 4 is 40% of ten we know that 4 is 80% of 5 because we have to multiply 4 by 2 because we did 5.
the plant grew by 80%.
Step-by-step explanation:
Which expression represents twice the sum of w and 6?
A) 2 +6w
B) 20 + 6
C) 20 + 60
D) 2 (w+6)
QC 261
Answers
What is the coefficient of determination for Data Set B? Full Data Set: Data Set A Data Set B Data Set C x y x y x y 3.6 8.9 3.1 8.9 2.8 8.9 8.3 15.0 9.4 15.0 8.1 15.0 0.5 4.8 1.2 4.8 3.0 4.8 1.4 6.0 1.0 6.0 8.3 6.0 8.2 14.9 9.0 14.9 8.2 14.9 5.9 11.9 5.0 11.9 1.4 11.9 4.3 9.8 3.4 9.8 1.0 9.8 8.3 15.0 7.4 15.0 7.9 15.0 0.3 4.7 0.1 4.7 5.9 4.7 6.8 13.0 7.5 13.0 5.0 13.0 (This is a reading assessment question. Be certain of your answer because you only get one attempt on this question.) The coefficient of determination for Data Set B is nothing%. (Type an integer or decimal rounded to the
Answers
Answer: the coefficient determination of dataset B is 1.00
Step-by-step explanation:
Given Dataset B
x y xy x² y²
3.1 8.9 27.59 9.61 79.21
9.4 15.0 141 88.36 225
1.2 4.8 5.76 1.44 23.04
1 6 6 1 36
9 14.9 134.1 81 222.01
5 11.9 59.5 25 141.61
3.4 9.8 33.32 11.69 96.04
7.4 15.0 111 54.76 225
0.1 4.7 0.47 0.01 22.09
7.5 13 97.5 56.25 169
∑x=47.1, ∑y=104, ∑xy=616.24, ∑x²=329.12, ∑y²=1239
Now to find the coefficient determination ( r² )
we need to first find r
r = { n(∑xy) - (∑x)(∑y) } / { √( [n∑x² - (∑x)²] [n∑y² - (∑y)²] )
so we substitute
r = { 10(616.24) - (47.1)(104)} / { √( [10(329.12) - (47.1)²] [10(1239) - (104)²] )
r = 1264 / 1299.45
r = 0.97
now the coefficient determination is ( r² )
so coefficient determination = r²
= (0.97)²
= 0.9409 ≈ 1.00 (integer)
Therefore the coefficient determination of dataset B is 1.00
the sum of 6 and the product of 8 and x" into mathematical expression
Answers
Answer:
6=8x
Step-by-step explanation:
Answer:
6+8x
Step-by-step explanation
We are going to make sure we can do this as best as possible. We need to make sure that the words that you are reading are making sense.
Sum can be taken out because its just 6. We do not know what adds to 6, it could be 1 +5, 2+4, 3+3, -3 and 9, WE DO NOT KNOW. So don't put extra information into the expression, when it is not given.
The and would be an addition to something, because when we are speaking and say the word AND, we want to add to that sentence. So, and is the plus sign.
6+
Then product is multiplication. So 8 times x.
Put it all together and you get the expression:
6+8x
I really hoped that helped you!
Researchers are studying the distribution of subscribers to a certain streaming service in different populations. From a random sample of 200 people in City C, 34 were found to subscribe to the streaming service. From a random sample of 200 people in City K, 54 were found to subscribe to the streaming service. Assuming all conditions for inference are met, which of the following is a 90 percent confidence interval for the difference in population proportions (City C minus City K) who subscribe to the streaming service?
A. (0.17 – 0.27) + 1.65, 0.27 0.17 V 200
B. (0.17 – 0.27) 1.96 V (0.17)(0.83)+(0.27)(0.73) 400
C. (0.17 – 0.27) + 1.657 (0.17)(0.83)+(0.27)(0.73) 400
D. (0.17 – 0.27) + 1.96V (0.17)(0.83)+(0.27)(0.73) 200
E. (0.17 – 0.27) + 1.657 (0.17)(0.83)+0.27)(0.73) 200
Answers
Answer:
\(CI = (0.17 - 0.27)\± 1.65\sqrt{\frac{(0.17)*(0.83) + (0.27)*(0.73)}{200}}\)
Step-by-step explanation:
Given
\(n = 200\)
\(x_1 = 34\) -- City C
\(x_2 = 54\) --- City K
Required
Determine the 90% confidence interval
This is calculated using:
\(CI = \bar x \± z\frac{\sigma}{\sqrt n}\)
Calculating \(\bar x\)
\(\bar x = \bar x_1 - \bar x_2\)
\(\bar x = \frac{x_1}{n} - \frac{x_2}{n}\)
\(\bar x = \frac{34}{200} - \frac{54}{200}\)
\(\bar x = 0.17 - 0.27\)
For a 90% confidence level, the z-score is 1.65. So:
\(z = 1.65\)
Calculating the standard deviation \(\sigma\)
\(\sigma = \sqrt{(\bar x_1)*(1 - \bar x_1) + (\bar x_2)*(1 - \bar x_2) }\)
So:
\(\sigma = \sqrt{(0.17)*(1 - 0.17) + (0.27)*(1 - 0.27) }\)
\(\sigma = \sqrt{(0.17)*(0.83) + (0.27)*(0.73)}\)
So:
\(CI = (0.17 - 0.27)\± 1.65\frac{\sqrt{(0.17)*(0.83) + (0.27)*(0.73)}}{\sqrt {200}}\)
\(CI = (0.17 - 0.27)\± 1.65\sqrt{\frac{(0.17)*(0.83) + (0.27)*(0.73)}{200}}\)
Write the phrase "the product of 19 and a number" as a mathematical expression.
A 19 + x
B) 19/x
C) 19 x
(D) 19 -x
Answers
Answer:
19x
Step-by-step explanation:
product means multiply
19*x
19x
Answer:
The answer is C.
Step-by-step explanation:
if a number and a variable are next to each other, it is assumed they will be multiplied.
solve for x using the picture
a. 180
b. 70
c. 60
d. 110
Answers
Answer:
D. 110
Step-by-step explanation:
First let's start by finding the measure of Angle ACB. Since angles in a triangle add up to 180 degrees:
ACB=180-(50+60)
ACB=180-110
ACB=70
We can also see that Angle X is supplementary/linear pair with Angle ACB. This means that Angle X+Angle ACB is equivalent to 180 degrees.
So...
x=180-ACB
x=180-70
x=110 degrees
40 POINTS In a region where 48% of the population is male, there are 11 boys and 14 girls in a sample of children. Find p and ρˆ (p-hat).
p =
ρˆ (p-hat) =
Answers
The values of p and ρˆ (p-hat) in the sample are
p = 0.48 and ρˆ (p-hat) = 0.44
How to determine the values of p and ρˆ (p-hat)?From the question, we have the following parameters that can be used in our computation:
Proportion of male = 48%
Boys = 11
Girls = 14
The proportion of male represents the variable p
So, we have
p = Proportion of male = 48%
This gives
p = 48%
Express as decimal
p = 0.48
The variable ρˆ (p-hat) is then calculated as
ρˆ = x/n
In this case,
x = Boys = 11
n = Boys + Girls = 11 + 14 = 25
So, we have
ρˆ = 11/25
Evaluate
ρˆ = 0.44
Hence, the values are 0.48 and 0.44, respectively
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There are 30 students in a class. 20 study Chemistry (C), 18 study Biology (B) and 4 study neighther Chemistry nor Biology.
(a) Show this information in the venn diagram.
(b) Find the number of students who study both Chemistry and Biology.
Answers
Answer:
(a) Venn Diagram attached
(b) 12 students study both Chemistry and Biology
Step-by-step explanation:
Denote n(C) as the number of students studying Chemistry
Denote n(B) as the number of students studying Chemistry
n(C) = 20
n(B) = 18
There are 4 students who do not study either Chemistry or Biology
Total number of students who study either Chemistry or Biology or both indicated in set notation as n(C ∪ B)
n(C ∪ B) = n(C) + n(B) - n(A and B)
we subtract n(A and B) because we count it twice when adding n(A) and n(B)
In numbers:
n(C ∪ B) = 20 + 18 - n(C and B)
Rearranging terms:
n(C and B) = 38 - n(C U B)
We know that 4 students study neither
So total number of students who study either Chemistry or Biology or both = 30 - 4 = 26
n(C and B) = 38 - 26 = 12
2x + 8 > -4. 2.find the solution set of x and express the solutions set in number form
Answers
The solution set of this inequality is {x| x > -6.1}
How to find the solution set?Here we have the inequality:
2x + 8 > -4.2
To find the solution set, we need to isolate the variable x in one of the sides of the inequality. Doing that we will get:
2x + 8 > -4.2
2x > -4.2 - 8
2x > -12.2
x > -12.2/2
x > -6.1
So the set of all numbers larger than -6.1, this in number form is:
{x| x > -6.1}
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Cheetahs have been clocked at a top speed of approximately 102.6 ft/s. Gazelles are a main
part of a cheetah's diet. Gazelles have been clocked at a top speed of approximately 73.3 ft/s.
Suppose a cheetah sees a gazelle across the plains of Africa, 500 feet away, and begins to
run after it. The gazelle spots the cheetah and begins running at the same time the cheetah
does.
Determine how many seconds later the cheetah catches the gazelle. How many feet did the
cheetah have to run to catch the gazelle? Round to the nearest tenth of a foot. Show all your work.
DO NOT PUT ANY LINKS TO A FILE OR ANYTHING LIKE THAT. Help ASAP pls.
Answers
9514 1404 393
Answer:
17.1 seconds1750.9 feetStep-by-step explanation:
The distance from the cheetah's starting point (in feet) can be modeled by ...
for the cheetah
c = 102.6t
for the gazelle
g = 73.3t +500
When these are equal, the cheetah will have caught the gazelle:
c = g
102.6t = 73.3t +500
29.3t = 500
t = 500/29.3 ≈ 17.1 . . . . . . seconds
The distance at that time is ...
c = 102.6(17.0648) ≈ 1750.9 . . . . feet
_____
Additional comment
The cheetah can maintain top speed only for about 10 seconds. At 500 ft distance, the gazelle is pretty safe.
To solve a(b + c) = d for a in 1 step:
Answers
Answer:
a = \(\frac{d}{b+c}\)
Step-by-step explanation:
a(b + c) = d
isolate a by dividing both sides by b + c
a = \(\frac{d}{b+c}\)
Please help fast!! What is the domain of the relation?
Please explain the answer!
Answers
The domain of the relation include the following: C. {-5, -2, 0, 1, 4}.
How to determine of this relation?In Mathematics, the horizontal extent of any graph of a function represents all domain values and they are always read and written from smaller to larger numerical values, and from the left of the graph to the right.
By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain:
Domain = {-5, -2, 0, 1, 4}.
In conclusion, the domain of this relation are all the x-values (independent value) that are located on the x-axis of the graph, which include {-5, -2, 0, 1, 4}.
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Solve this here
3x^2-27
Answers
Answer:Factor 3x^2-27. Step 1. Factor out of . Tap for more steps... Step 1.1. Factor out of . Step 1.2. Factor out of . Step 1.3. Factor out of . Step 2. Rewrite as . Step 3. Factor. Tap for
Step-by-step explanation:
Solution:
3(x-3)x(x+3)
or
3, -3
Which of the following is an equivalent
simplified expression for
3(2x + 1) - 2(4x - 1)
A. 2x + 1
B. -2x + 5
C. -X + 5
D. 14x + 1
E. 14x - 1
Answers
Answer:
B. -2x + 5
Step-by-step explanation:
First, distribute the 3 and 2 to the parentheses:
3(2x + 1) - 2(4x - 1)
6x + 3 - 8x + 2
Add like terms:
-2x + 5
So, the simplified expression is -2x + 5
B is the correct answer
Answer:
it is B
Step-by-step explanation:
3*2x=6x
2*4x=8x
1*3=3
1*2=2
6x-8x= -2x
3+2=5
i got the +2 because there are two negative signs and that makes it positive
Find the surface area
Answers
Answer: 120 yds
Step-by-step explanation:
48+30+24+18+120 yds
which cannot represent a proportional relationship select all that apply.
Answers
To represent a proportional relationship between y and x, the center of coodinates has to be part of the equation, as:
\(y=k\cdot x\)Graph A: Although the center of coordinates is not marked, we see that the line that fits all the points goes through the center of coordinates.
We can test that all the quotients y/x are constant, so the relation is proportional.
Graph B: the line has value y=5 for x=0. This is not possible for a proportional relationship, so this graph does not represent a proportional relationship.
Graph C: in this case, we see that y has a value of 0 for x=1. That is not possible for a proportional relationship. We can test 2 points and see that the quotient y/x is not constant.
This is not a proportional relationship.
Graph D: the line includes the center of coordinates, so it is a proportional relationship.
Answers: the ones that does not represent a proportional relationship are B and C.
NEED HELP ASAP 25 POINTS HELP A GIRL GET HER GEOMETRY GRADE UP
Answers
The angle measure of x, y and z are 104, 76 and 104 degrees respectively
Determining the angles in a parallelogramThe given. figure is a parallelogram with 4 interior angles. In a parallelogram, the sum of its adjacent angle is 180 degrees and its opposite angles are equal.
<A = <C
x = 104 degrees
For the measure of y:
x + y = 180
104 + y = 180
y = 180 - 104
y = 76 degrees
Since the sum of angles on a straight line is 180 degrees, hence;
y + z = 180
76 + z = 180
z = 104 degrees
Hence the measure of x, y and z are 104, 76 and 104 degrees respectively
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what are 3 different equations that have x=5 as a solution
Answers
Answer:
1) x+y=50
2) 5x+2y=200
3)2x+4y=200
Hope this helps!
Answer:
x+3=8, 2x-8=2, and 4x-4=16
Step-by-step explanation:
Jessica needs to rent a moving truck for one day. She can choose to rent a moving truck from Rentals Plus or from Speedy Move. At Rentals Plus, it costs $5.24 to rent a moving truck for one day, plus $4.46 per mile driven. At Speedy Move, it costs $85.24 to rent a moving truck for one day, plus $0.46 per mile driven. How many miles would Jessica have to drive for the cost to rent a moving truck for one day to be the same at Rentals Plus and Speedy Move?
Answers
Jessica would have to drive 20 miles for the cost to rent a moving truck for one day to be the same at Rentals Plus and Speedy Move.
How find how many miles would Jessica have to driveLet's assume the number of miles driven is represented by 'm'. The cost of renting a moving truck for one day at Rentals Plus can be calculated using the equation:
Cost at Rentals Plus = $5.24 + $4.46 * m
Similarly, the cost of renting a moving truck for one day at Speedy Move can be calculated using the equation:
Cost at Speedy Move = $85.24 + $0.46 * m
To find the number of miles that makes the costs equal, we can set up the equation:
$5.24 + $4.46 * m = $85.24 + $0.46 * m
By rearranging the equation, we can solve for 'm':
$4.46 * m - $0.46 * m = $85.24 - $5.24
$4 * m = $80
m = $80 / $4
m = 20
Therefore, Jessica would have to drive 20 miles for the cost to rent a moving truck for one day to be the same at Rentals Plus and Speedy Move.
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Solve by the method of your choice 6x-2y= 16, 5x+y=24
Answers
(5x+y=24)*2
__________
6x-2y=16
10+2y=48 Add the equations”+”
—-
16x=64
X=4
So y=1
suppose you have 20 consecutive even numbers. What is the difference between the sum of the last 10 numbers and the sum of the first 10 numbers
plz answer
Answers
Explanation: First start out with 20 even numbers:
2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40
As stated, you have to add the first ten together, and then add the last ten together
First ten:110 Last ten:310
Then subtract:
310-110=200
The difference between the sum of the last 10 numbers and the sum of the first 10 numbers will be 200.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
Let a₁ be the first term, L be the last term, n be the number of terms, and d be a common difference.
Then the sum of the arithmetic sequence will be
Sₙ = (n / 2)[a₁ + L]
The 20 consecutive even numbers are given below.
2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40
The sum of the first 10 numbers will be given as,
⇒ (10 / 2)[2 + 20]
⇒ 5 x 22
⇒ 110
The sum of the last 10 numbers will be given as,
⇒ (10 / 2)[22 + 40]
⇒ 5 x 62
⇒ 310
Then the difference between the numbers is given as,
⇒ 310 - 110
⇒ 200
The difference between the sum of the last 10 numbers and the sum of the first 10 numbers will be 200.
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Help me please???????????
Answers
Answer:
I believe it is 6.
I hope this helps
In an examination, 80% of candidates passed in English, and 85% passed in Math. If 73% of
candidates passed in both subjects, then what percent of candidates failed in both subjects?
a. 27
X
b. 15
C. 8
d. 35
Answers
Answer:
8%
Step-by-step explanation:
Using set notation
M is mathematics
E is English
n(M) = 85%
n(E) = 80%
n(M n E) = 73%
n(M U E)' are percentage of people that failed both subnets
Hence n(U) = n(M U E) + n(M U E)'
n(MUE) = n(M) + n(E) - n(MuE)
n(MUE) = 85 + 80 - 73
n(MUE) = 92%
Since n(U) = n(M U E) + n(M U E)'
100 = 92 + n(M U E)'
n(M U E)' = 100 - 92
n(M U E)' = 8%
Hence 8% of candidates failed in both subjects
1/3 + 3/5 + 7/9 + 13/15
Answers
Answer:
116 / 45
Step-by-step explanation:
To add fractions with unlike denominators, we need to find their common denominator.
One way to do this is by finding the least common multiple (LCM) of the denominators.
The LCM of 3, 5, 9 and 15 is 45.
We then convert each fraction so that its denominator is 45:
1/3 = 15/45
3/5 = 27/45
7/9 = 35/45
13/15 = 39/45
Now we can add the fractions:
15/45 + 27/45 + 35/45 + 39/45
To simplify, we can add the numerators and keep the common denominator:
(15 + 27 + 35 + 39) / 45
Which gives us:
116 / 45
Therefore, the sum of the fractions 1/3 + 3/5 + 7/9 + 13/15 is, 116 / 45.