The distance across the body of water from point b (north end) to point c (south end) can be found using trigonometry and the sine ratio. Given that the angle is 30° and the distance from point A to point b is 17.5 m, the distance across the water (from point b to point c) is 8.75m.
Explanation:The problem at hand is a trigonometry problem which can be solved by using the sine ratio. In trigonometry, the sine of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. In this case, the angle is given as 30°, and we are asked to find the distance from point b (north end) to point c (south end), which is the side opposite to the 30° angle. Therefore, we can set up the following equation using the sine ratio: sin(30°) = opposite/hypotenuse.
In this instance, the hypotenuse is the distance from point A to point b, which is given as 17.5 m. Thus, the equation becomes sin(30°) = distance from point b to point c / 17.5 m. Solving this for the distance from point b to point c would mean multiplying both sides by 17.5 m, giving us: distance from point b to point c = sin(30°) * 17.5 m.
Upon calculation, we find that sin(30°) equals 0.5, so therefore the distance from point b to point c, which is the distance across the body of water is 0.5 * 17.5m = 8.75 m.
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fully expand the logarithm: log(x^3/z^5)
A line has a slope of 2 and a y intercept of (0,-4) what is the value of y when x=6
The question is about finding the y-value of a line when the x-value is given, knowing the slope and the y-intercept. By plugging the given slope, y-intercept and the provided x-value into the formula y = mx + b, we find that y equals 8 when x equals 6.
Explanation:If we know the slope (m) of a line and the y-intercept (b), we can use the formula y = mx + b to calculate the y-value for any x-value. In the given question, the slope (m) is 2 and the y-intercept (b) is -4. If we want to find the y-value when x = 6, we can substitute these values into the formula:
y = 2*6 - 4
So, y = 12 - 4 = 8. Therefore, when x = 6, the value of y is 8.
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graph of this ellipse
x^2 + y^2 =1
_ _
4 16
What is the equation of the circle shown in the graph ? (Blank)^2 + (Blank)^2 = blank
The equation of the circle shown in the graph is equal to [tex](x + 6)^2 + (y - 4)^2 = 36[/tex]
Form the graph, we can deduce the following points:
The center of the circle is denoted by the black dot and we can see that the values are -6 and 4 respectively.
Center (h, k) = (-6, 4)Also, the diameter of the circle is:
Diameter = 12 units
Radius = [tex]\frac{Diameter}{2} = \frac{12}{2} = 6 \;units[/tex]
Mathematically, the standard form of the equation of a circle is given by;
.....equation 1
Where;
h and k represents the coordinates at the center.r represents the radius of the circle.Substituting the values into eqn 1, we have:
[tex](x - [-6])^2 + (y - 4)^2 = 6^2\\\\(x + 6)^2 + (y - 4)^2 = 36[/tex]
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coordinate grid with plotted ordered pairs, point A at negative 5, 4 point B at 4, 7 point C at negative 2, 7 point D at negative 7, 1 point E at 4, negative 2 point F at 1, negative 6 point G at negative 3, negative 10 point H at negative 4, negative 4 point I at 9, 3 point J at 7, negative 4 and point K at 2, 3
The coordinate grid shows points A through K. Which points are solutions to the system of inequalities listed below?
2x + y ≤ 10
2x − 4y < 8
fresh raspberry contain 80% water.Dried raspberry contain only 20%.how many pounds do you get from 36lb fresh berries
The amount of fresh berries that contain 80% water is 7.2 pounds.
Amount of water in fresh raspberry = 80%
It means the amount of raspberry only in a fresh raspberry =20%
Amount of water in dry raspberry =20%
What is a percentage?A percentage is a value per hundred.
So, the amount of raspberry only in 36 lbs fresh berries = 20% of 36
20% of 36 = (20/100)*36 = 7.2 lbs
So, the amount of raspberry only in 36 lbs of fresh berries = 7.2 lbs
Therefore, we get 7.2 lbs from 36lb fresh berries.
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Of the 12,000 votes cast in an election, 42% of the votes were for Mr.Jones. How many votes were cast for all the other candidates?
The graph of y=|x| is transformed as shown in the graph below. Which equation represents the transformed function?
we have that
the original function [tex]y=\left|x\right|[/tex] has the vertex at point [tex](0,0)[/tex]
The transformed function has the vertex at point [tex](-3,-2)[/tex]
so
the rule of the translation is equal to
[tex](x,y)------> (x-3,y-2)[/tex]
That means
The translation is [tex]3[/tex] units to the left and [tex]2[/tex] units down
therefore
the answer is
the transformed function is [tex]y=\left|x+3\right|-2[/tex]
how many times does 15 go into 46
Given the least squares regression equation, = 1202 + 1,133x, when x = 4, what does equal?
Jackson goes to the gym 0, 2, or 3 days per week, depending on work demands. The expected value of the number of days per week that Jackson goes to the gym is 2.05. The probability that he goes 0 days is 0.1, the probability that he goes 2 days is , and the probability that he goes 3 days is .
In the number 7,777.777, how does the 7 in the hundreds place compare to the 7 in the place to its left?
A.
The 7 in the hundreds place represents of what the 7 to its left represents.
B.
The 7 in the hundreds place represents 10 times what the 7 to its left represents.
C.
The 7 in the hundreds place represents of what the 7 to its left represents.
D.
The 7 in the hundreds place represents 100 times what the 7 to its left represents.
After a comparison of the number 7 which is at hundreds of places to the number 7 left off it, it is 10 times of what the 7 to its left represents. Hence, option B is correct
What are arithmetic Operations?The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.
Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.
As per the data provided in the question,
The given number is 7,777.777
Now, we have to compare the number 7 which is at the hundreds place with the 7 in the place left to it.
So, the 7 which is left to the 7 at the hundredth place will be 10 times it. Also, the 7 which is the second left to the 7 at the hundredth place is 100 times and so on it will increase like this.
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Two thirds of the families in smithville own their own homes. The total number of home owning families there is 480. How many families live in smithville?
Al and Bill each have two bullets. They fire alternately at a glass bottle. Al has hitting probability 1/3 and Bill 1/4. What is the probability that Al smashes the bottle if he is the one who fires the first shot? (Note: Al can smash the bottle even if he misses with his first shot.)
Diana invested $3000 in a savings account for 3 years. She earned $450 in interest over that time period. What interest rate did she earn? Use the formula I=Prt to find your answer, where I is interest, P is principal, r is rate and t is time. Enter your solution in decimal form rounded to the nearest hundredth. For example, if your solution is 12%, you would enter 0.12.
Which point best approximates the root of 45
find the number of gallons in 6 liters of solution(1gal=3.79l)
To convert 6 liters of solution into gallons, given that 1 gallon is equivalent to 3.79 liters, you divide 6 by 3.79 which gives you 1.58 gallons of solution.
Explanation:The question is asking to find the number of gallons in 6 liters of a solution, given that 1 gallon is equivalent to 3.79 liters. The conversion from liters to gallons is a basic concept in measurement conversion. Here is a step-by-step explanation to help you understand the process:
You have 6 liters of solution which you want to convert to gallons. We know that 1 gallon is equivalent to 3.79 liters. So, to convert liters to gallons, we divide the number of liters by 3.79. Therefore, you have 6 / 3.79 = 1.58 gallons (rounded to two decimal places) of solution. Learn more about Unit Conversion here:
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hey can you please help me posted picture of question
What is the similarity ratio of the smaller to the larger similar pyramids? Enter your answer as a:b
A ball is thrown into the air with an upward velocity of 32 ft/s. Its height h in feet after t seconds is given by the function h = –16t2 + 32t + 6. a. In how many seconds does the ball reach its maximum height? Round to the nearest hundredth if necessary. b. What is the ball’s maximum height? 1 s; 54 ft 2 s; 6 ft 2 s; 22 ft 1 s; 22 ft
Answer: 22 ft, 1 s
Step-by-step explanation:
on a game show that are 10 keys in the bag and three of the key start a car and contest in randomly choosing the key it doesn't not start the car she returned to the bag the host mixed up the back she randomly selects another key this key does not start the car either what is the probability of this no start no start outcome
y = x3 - 3x On which intervals is this function increasing?
Part A: Factor 2x2b2 + 5xb2 + 2b2. Show your work. (4 points) Part B: Factor x2 − 8x + 16. Show your work. (3 points) Part C: Factor x2 − 49. Show your work. (3 points)
What is the equivalent of pi over 3 radians in degrees?
Terry uses 3 cups of pumpkin seeds to decorate the tops of 12 loaves if bread. She puts an equal amount of seeds on each loaf. How many cups of pumpkin seeds does she put on each loaf of bread?
What is the number of social security credits a worker needs to earn over his or her working lifetime to collect Social security benefits?
please help! i dont understand this.
a 25 gram sample substance that's used for drug research has a k-value of 0.1229. find the substances half-life, in days using the exponential decay formula. round your answer to the nearest tenth
With a k-value of 0.1229, the half-life is approximately 5.6 days.
The exponential decay formula is given by:
amount remaining = initial amount × e^-(k × t)
For a substance's half-life, the amount remaining is half of the initial amount. The formula to find the half-life (t1/2) is:
t1/2 = ln(2) / k
Here, ln(2) is approximately 0.693 and k is given as 0.1229. Substituting these values in:
t1/2 = 0.693 / 0.1229 ≈ 5.64 days
Rounding to the nearest tenth, the half-life of the substance is 5.6 days.
The net asset value of stock in a mutual fund had increased by $20 per share when an investor decided to redeem them. The investor had purchased 100 shares of the stock for $2,316 and redeemed them for $4,301. What can you conclude about the fund? a. The fund is a no-load fund. b. The offer price of the fund was $0.15 less than the net asset value when purchased. c. The offer price of the fund was $0.15 more than the net asset value when purchased. d. The offer price of the fund was $0.15 more than the net asset value when sold.
Instructions:Select the correct answer from each drop-down menu. The range of all real numbers x such that 2x − 5 < 7 and 4x + 10 > 6 is . The range of all real numbers x such that 2x − 5 < 7 or 4x + 10 > 6 is
Greg has an MP3 player called the Jumble. The Jumble randomly selects a song for the user to listen to. Greg's Jumble has 666 classical songs, 777 rock songs, and 999 rap songs on it. What is \text{P(not a rap song})P(not a rap song)P, left parenthesis, n, o, t, space, a, space, r, a, p, space, s, o, n, g, right parenthesis?
We have been given that Greg's Jumble has 666 classical songs, 777 rock songs, and 999 rap songs.
Therefore, total number of songs are
[tex]666+777+999\\ =2442[/tex]
The formula for probability is given by
[tex]P(E)=\frac{n(E)}{n(s)}[/tex]
Let us first find the probability for rap song
[tex]P(\text{rap song})= \frac{999}{2442} \\ P(\text{rap song})= \frac{9}{22}[/tex]\\
Therefore, we have
[tex]P(\text{ not rap song})=1- P(\text{rap song})\\ \\ P(\text{ not rap song})=1-\frac{9}{22} \\ \\ P(\text{ not rap song})=\frac{13}{22} =0.59[/tex]
Hence, we have
P(not rap song)=0.59