In a class experiment, Sean finds that the probability that a student plays soccer is . If the school population is 300, how many students would we expect to play soccer, based on Sean's experiment?
How to find the sum of the squares of the lengths of the legs of a triangle of a=(-6,11) b=(2,8) c=(-1,0)?
To find the sum of the squares of the lengths of the legs of a triangle, use the distance formula to calculate the length of each leg and then square these lengths, summing the squares of the two legs that do not form the hypotenuse.
Explanation:To find the sum of the squares of the lengths of the legs of a triangle with vertices A=(-6,11), B=(2,8), and C=(-1,0), we first calculate the length of each leg using the distance formula, which is √((x2-x1)² + (y2-y1)²). For AB, AC, and BC we find distances:
AB = √((-6-2)² + (11-8)²)AC = √((-6+1)² + (11-0)²)BC = √((2+1)² + (8-0)²)Then, we square each leg's length:
AB² = ((-6-2)² + (11-8)²)AC² = ((-6+1)² + (11-0)²)BC² = ((2+1)² + (8-0)²)Finally, we sum up the squares of AB and AC because they represent the legs of the triangle:
Σ(leg squares) = AB² + AC²The sum of the squares of the lengths of the legs has now been found.
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Anna has leaned a ladder against the side of her house. The ladder forms a 72º angle with the ground and rests against the house at a spot that is 6 meters high. What length is the best approximation for the distance along the ground from the bottom of the ladder to the wall?
Answer:
The best approximation of AB is 2 meters.Step-by-step explanation:
Notice that this situation models a right triangle, when the height, which is a leg of the triangle, is 6 meters.
Also, we know the angle between the ladder and the ground, which is 72°.
To find the distance from A to B, which from the bottom of the ladder to the bottom of the wall, we just need to use trigonometric reasons.
[tex]tan(72\°)=\frac{opposite \ leg}{adjacent \ leg}[/tex]
Why we use tangent? Because it relates both legs where we just need to find the adjacent one.
[tex]tan(72\°)=\frac{6}{AB}\\AB=\frac{6}{tan(72\°)} \\AB \approx \frac{6}{3} \\AB \approx 2 \ m[/tex]
Therefore, the best approximation of AB is 2 meters.
The length of a train is about 1,700 meters. If there are approximately 3.28 feet in one meter, what is the length of the train in feet?
0.002 feet
557,600 feet
5,576 feet
518 feet
To convert 1,700 meters to feet, we multiply by the conversion factor of 3.28 feet per meter, resulting in a length of 5,576 feet for the train.
Explanation:To find the length of the train in feet, we need to convert meters to feet using the conversion factor provided. Given that 1 meter is approximately 3.28 feet, we can calculate the length of the train in feet by multiplying the length of the train in meters (1,700 meters) by the conversion factor (3.28 feet per meter).
The calculation would be as follows:
1,700 meters × 3.28 feet/meter = 5,576 feet
Therefore, the length of the train is 5,576 feet.
Betty makes pies. To make 6 pies, she uses 127 cups of flour. How many cups of flour are needed to make 1 pie?
order them from least to greatest, with the least at the top.
6\pi -6
\pi 3
\sqrt{99}
Arranging the numbers in ascending order is: √99 < 6π - 6 < π³
How to arrange the numbers in ascending order?Arranging numbers in ascending order simply means arranging them from smallest to the biggest.
Now, the given numbers are:
6π - 6
π³
√99
Let us simplify the numbers to get:
6π - 6 = 6(3.14) - 6 = 12.85
π³ = 3.14³= 31
√99 = 9.95
Thus, arranging in ascending order is:
√99 < 6π - 6 < π³
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Due tomorrow help please
Wha is the greatest common factor of 1 and 27
need help i havent done this since 2015 :// lolz
Answer:
2w+4 = 5w-6 . . . . w = 10/3
12 = 3x-3 . . . . . . . x = 5
6y = 4y+6 . . . . . . . y = 3
27 = (5/4)z +2 . . . z = 20
107 and 73
Brian invests $10,000 in an account earning 4% interest, compounded annually for 10 years. Five years after Brian's initial investment, Chris invests $10,000 in an account earning 7% interest, compounded annually for 5 years. Given that no additional deposits are made, compare the balances of the two accounts after the interest period ends for each account. (round to the nearest dollar)
Compound interest formula is [tex]A = P(1+r)^t[/tex]
Where P is the principal amount
r is the rate of interest
t is number of years
Brian invests $10,000 in an account earning 4% interest, compounded annually for 10 years
P = 10,000 , r= 4% = 0.04 , t =10
Plug in all the values
[tex]A = 10000(1+0.04)^{10}[/tex] = 14,802.44
Chris invests $10,000 in an account earning 7% interest, compounded annually for 5 years.
P = 10,000 , r= 7% = 0.07 , t =5
Plug in all the values
[tex]A = 10000(1+0.07)^5[/tex] = 14,025.52
Brian balance after the interest period = $ 14,802.44
Chris balance after the interest period = $ 14,025.52
Balance in Brian's account is more than Chris account
HELP ME PLEASE THIS IS IMPORTANT
Help on both 13 and 14. Show work please
The cylinder below has a volume of 785 ft^3. and the cone has a volume of 314 ft^3.
(please see attached picture)
Which explains which figure has the greater height?
The cylinder has a greater height because the bases are the same, but the cylinder has a greater volume.
The cylinder has a greater height because the volume of the cylinder is greater than twice the volume of the cone.
The cone has a greater height because the bases are the same, but the volume of the cylinder is less than 3 times the volume of the cone.
The cone has a greater height because the bases are the same, but the volume of the cylinder is less than 4 times the volume of the cone.
Answer:
The cone has a greater height because the bases are the same, but the volume of the cylinder is less than 3 times the volume of the cone.
Step-by-step explanation:
Just did the quiz
What is the expected value of the game if 3 hits pay $6, 2 hits pays $4, 1 hit pays $2, and 0 hits pays costs $4?
ABC Bookstore sells new books, n, for $12, and used books, u, for $8. The store earned $112 revenue last month. The store sold 4 more used books than new books. Using the substitution method, how many new and old books did ABC bookstore sell?
A.n = 4; u = 8
B.n = 8; u = 4
C.n = 8; u = 12
D.n = 12; u = 8
What are the inputs of the function below?
Please help
Answer:
Input of the function are -8,2,4,6
Step-by-step explanation:
Input of a function are the domain .
Domain is the values of x. So inputs are the value of x in the table
Input of the table is x and output is f(x)
Input are the values that gives the output f(x)
From the table the x values are -8,2,4 and 6
Input of the function are -8,2,4,6
Jacob drove from town a to town b at an average rate of x miles per hour, then returned along the same route at y miles per hour. if he then drove back to town b at z miles per hour along the same route, what was jacob's average rate of speed for the entire trip, in miles per hour?
Compare the exponential and logarithmic models of population growth
Find the volume of the given prism. round to the nearest tenth if necessary.
a. 2,511.5 yd to the power of 3b) 1,255.7 yd to the power of 3c) 1,025.3 yd to the power of 3d) 1,450.0 yd to the power of 3
A plane intersects a double-napped cone such that the plane intersects both nappes through the cone's vertex.
Which terms describe the degenerate conic section that is formed?
Select each correct answer.
pair of intersecting lines
degenerate ellipse
degenerate hyperbola
line
point
degenerate parabola
Answer:
degenerate hyperbola
pair of intersecting lines
Step-by-step explanation:
Point X is the center of regular pentagon RSTUV. What is the measure of the angle of rotation that will map S onto U?
Final answer:
The measure of the angle of rotation that will map vertex S onto vertex U in a regular pentagon is 72 degrees.
Explanation:
The student is asking about an angle of rotation in a geometric context, specifically concerning mapping one vertex of a regular pentagon onto another through rotation about the center of the shape. In a regular pentagon, the angles between adjacent vertices are all equal, as it is a symmetrical shape. Since there are five vertices in a pentagon, you can divide the full rotation of 360 degrees by the number of vertices to find the angle of rotation that will map one vertex onto the next.
To map vertex S onto vertex U in a regular pentagon, you will need to rotate the pentagon by 360 degrees divided by 5 vertices, which is 72 degrees. Therefore, a rotation of 72 degrees around the center point X of the pentagon will map S onto U.
what is the height of the beach sign?
and what is the height of the beach umbrella?
I'm not sure if both images were attached, oops. but please help! I'll mark as brainliest! thank you!
2. Which of the following is equivalent to 5455 cm3?
(
0.5455 L
5.455 L
54.55 L
5455 L
What is the 12th term of the sequence?
3, −9, 27, −81, 243, ...
The 12th term of the sequence 3, -9, 27, -81, 243, ... is 177,147.
Explanation:The given sequence is: 3, -9, 27, -81, 243, ...
To find the 12th term, we can observe that the sequence alternates between positive and negative, and each term is obtained by multiplying the previous term by -3. Starting with 3 as the first term, we can find the 12th term using the formula:
an = a1 * (-3)n-1
Substituting the values, we have:
a12 = 3 * (-3)12-1a12 = 3 * (-3)11a12 = 3 * (-32)5a12 = 3 * 95a12 = 3 * 59049a12 = 177,147Final answer:
The 12th term of the geometric sequence is -531441, found by using the formula for the nth term of a geometric series with a first term of 3 and a common ratio of -3.
Explanation:
The sequence given is geometric with each term being multiplied by -3 to obtain the next term. To find the 12th term of the sequence, we can use the formula for the nth term of a geometric sequence: Tn = a * rn-1, where a is the first term, r is the common ratio, and n is the term number.
For the given sequence, the first term a is 3 and the common ratio r is -3. The 12th term is found by placing these values into the formula:
T12 = 3 * (-3)12-1
T12 = 3 * (-3)11
T12 = 3 * (-177147)
T12 = -531441
Therefore, the 12th term of the sequence is -531441.
A student takes a 15 question
a. True
b. False quiz and guesses at every answer. what is the probability that the student gets exactly 10 questions right, given that the student got the first question right?
Tan α = - 4/3 lies in quad 2, and cos β = 2/3 lies in quad 1 find
a. cos(α + β)
b. sin( α+β)
c. t...
Given the following sets: A={ 2, 4, 6, 8, 10} B={ 3, 5, 7, 9} C={ 2, 3, 5, 7} N={ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} Match the following Unions and intersections to the correct set.
a) {2, 3, 5, 7, 9}
b){3, 5, 7, 9}
ｃ）{2, 3, 4, 5, 6, 7, 8, 10}
ｄ）{ }
ｅ）{2, 4, 6, 8, 10}
1.
What is A U C?
2.
What is A ∩ B?
3.
What is A ∩ N?
4.
What is B ∩ N?
5.
What is B U C?
Divide. Give the quotient and remainder.
55 Divided by 8
The day started at 48 degrees. by 3:00 p.m., the temperature has increased by 17 degrees. by nightfall, the temperature fell 17 degrees. what was the net change in temperature
Final answer:
The net change in temperature over the day is 0 degrees. After increasing by 17 degrees in the afternoon, the temperature fell by 17 degrees by nightfall, returning it to the starting temperature.
Explanation:
The student has asked about calculating the net change in temperature over the course of a day starting at 48 degrees. By 3:00 p.m., the temperature increased by 17 degrees, making it 65 degrees. But by nightfall, the temperature decreased by the same amount, falling back down to 48 degrees. The calculation of net change in this scenario is simple: subtract the starting temperature from the final temperature after all changes have occurred. In this case, the starting temperature was 48 degrees, it went up to 65 degrees, and then back to 48 degrees.
The net temperature change is therefore 48 degrees (final temperature) - 48 degrees (starting temperature), which equals 0 degrees. This means there was no net change in temperature over the course of the day. It is important to recognize that even though there was a temporary increase and subsequent decrease, the net effect cancels out, leaving the temperature the same as it started.
do 5, 4, 3 represent the side lengths of a triangle