Final answer:
Using trigonometry and the sine function, the maximum height that the ladder can reach when raised to a 75-degree angle with a length of 60 feet is approximately 58 feet.
Explanation:
To determine the maximum height that a fire truck ladder can safely reach when it is extended to 60 feet in length and raised to a maximum angle of 75 degrees with the horizontal, we would use trigonometry, specifically the sine function. The sine of an angle in a right triangle is equal to the opposite side (height in this case) divided by the hypotenuse (the length of the ladder).
Therefore, the maximum height (h) can be calculated using the formula:
h = Ladder Length × sin(Angle)
Where:
Ladder Length is 60 feet
Angle is 75 degrees
Plugging in our values we get:
h = 60 feet × sin(75 degrees)
Using a calculator, we find that:
sin(75 degrees) is approximately 0.9659.
Therefore:
h ≈ 60 feet × 0.9659
h ≈ 57.95 feet
The maximum height the ladder can safely reach when disregarding the height of the fire truck itself is approximately 58 feet.
a vertical pole 10 meters high, casts a shadow 8 meters long. at the same time, a nearby tree casts a shadow 40 meters long. find the height of the tree in meters
A fair number cube with sides labeled from 1 to 6 is rolled 20 times. the results of the simulation are shown in a dot plot. which dot plot models an unfair data-generating process?
The dot plot will be 1:4, 2:4, 3:0, 4:4, 5:4,6:4 and there is a face with 3 has not rolled option second is correct.
What is dot plot?A dot plot, also referred to as a dot chart or stripe graph, is a sort of simple histogram-like figure used in statistics for little data sets with values falling into a number of discrete bins.
Since the width of each "bar" of dots is equal to the number of items in a certain class, a dot plot is similarly to a bar diagram.
We have:
A fair number cube with sides labeled from 1 to 6 is rolled 20 times.
Total number on, a fair number of cubes = 6
So the dot plot can be shown as:
1:4, 2:4, 3:0, 4:4, 5:4,6:4
There is a face with 3 has not rolled.
Thus, the dot plot will be 1:4, 2:4, 3:0, 4:4, 5:4,6:4 and there is a face with 3 has not rolled option second is correct.
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Christine runs 7 miles in 60 minutes. at the same rate, how many miles would she run in 24 minutes?
Christine would run approximately 2.8 miles in 24 minutes at the same rate she runs 7 miles in 60 minutes.
Explanation:To find out how many miles Christine would run in 24 minutes, we can set up a proportion. We know that Christine runs 7 miles in 60 minutes, so we can write the proportion as:
7 miles / 60 minutes = x miles / 24 minutes
Now, we can cross-multiply and solve for x:
7 * 24 = 60 * x
168 = 60x
x = 168 / 60
x ≈ 2.8 miles
So, her speed would be 7/60 = 0.1167 miles per minute. Now, to find out the distance she would cover in 24 minutes at this speed, we multiply her speed per minute by 24 minutes. So, 0.1167 * 24 = approximately 2.8 miles. Therefore, at the same rate, Christine would run about 2.8 miles in 24 minutes.
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Amanda owns a clothing store that sells graphic t-shirts. n is the number of shirts she sells each month. the revenue function of her store is r = 25n. the cost function of her store is c = 10n + 900. using your calculator, what is the break-even point of amanda's store?
Answer:
n = 60 shirts
Step-by-step explanation:
The break-even point is the point where revenue is equal to cost. This means we take the equation for revenue, r = 25n, and set it equal to the equation for cost, c = 10n + 900:
25n = 10n + 900
Subtract 10n from each side:
25n - 10n = 10n + 900 - 10n
15n = 900
Divide both sides by 15:
15n/15 = 900/15
n = 60
WILL GIVE BRAINLIEST!!!! PLZ HELPPP!!!Which equation is the BEST fit for the data in the graph?
A) y = (1/4)x
B) y = (-1/4)x
C) y = (1/4)x-1
D) y = (1/4)x - 1
Of the following options, what could be a possible first step in solving the equation −7x − 5 = x + 3?
Adding 7x to both sides of the equation
Subtracting 5 from both sides of the equation
Adding x to both sides of the equation
Combining like terms, −7x + x = − 6x
add 7x to both of the sides
. Stephen deposited $1800 into a savings account for which interest is compounded weekly at a rate of 3.2%. How much interest will he earn after 10 years?
58.81
678.59
2478.59
im just putting this up to see if my answer was write. i did the math and unless i messed up writing i got the second answer
What is the measure of BAC
50
80
100
130
Find the x-intercepts for the parabola defined by the equation below. y=2x^2-6x+4
Given f(x)=x2+14x+40 .
Enter the quadratic function in vertex form in the box.
for the function d(x)=7x^3 - 6x^2 what is the vaule of d(4)
What is the exact volume of a cylinder whose radius is 21 centimeters and whose height is 30 centimeters?
answer in terms of pie
Explaining Factored Form The trinomial x2 + bx – c has factors of (x + m)(x – n), where m, n, and b are positive. What is the relationship between the values of m and n? Explain.
Sample Response: The value of m must be greater than the value of n. When you multiply the binomials, the middle term is the result of combining the outside and inside products. So, bx = –nx + mx, or bx = (–n + m)x. This means that b = –n + m. When adding numbers with opposite signs, you subtract their absolute values, and keep the sign of the number having the larger absolute value. Since b is positive, m must have the larger absolute value.
(on the assignment)
Which expression is equivalent to mc003-1.jpg?
Answer:
Option A is correct
The expression which is equivalent to [tex](f\cdot g)(5)[/tex] is [tex] f(5) \cdot g(5)[/tex]
Step-by-step explanation:
Using the formula:
[tex](f \cdot g)(x) = f(x) \cdot g(x)[/tex] .....[1]
Given the expression:
[tex](f\cdot g)(5)[/tex]
Substitute the value of x = 5 in [1]
we get;
[tex](f \cdot g)(5) = f(5) \cdot g(5)[/tex]
Therefore, the expression which is equivalent to [tex](f\cdot g)(5)[/tex] is [tex] f(5) \cdot g(5)[/tex]
Write the first 6 terms of an arithmetc sequence if the first number is 9 and the common diffrence is 5
A line of best fit predicts that when x equals 35, y will equal 34.785, but actually equals 37. What is the residual in this case?
How to find the shaded region of a circle with a rectangle inside?
Two large numbers of the Fibonacci sequence are F61 = 2,504,730,781,961 and F62 = 4,052,739,537,881. If these two numbers are added together, what number results?
A. F123
B. F60
C. F63
D. F64 - 1
What happens to correlation if you multiply every x in the data set by .5?
Simplify -62 ÷ 12 - 2(-7).
To simplify -62 ÷ 12 - 2(-7), evaluate the expression inside the parentheses first, then perform the division and subtraction.
Explanation:To simplify the expression -62 ÷ 12 - 2(-7), we need to follow the order of operations, which is PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) in this case. First, we need to evaluate the expression inside the parentheses: 2(-7) = -14. Then, we perform the division: -62 ÷ 12 = -5. Finally, "we subtract: -5 - (-14) = -5 + 14 = 9".
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Which of the following terms correctly describe the figure given below? Check all that apply.
I think its Polyhedron, pyramid, solid.
Answer:
Hence, the correct options are Polyhedron, Pyramid and Solid
Step-by-step explanation:
According to the options, we have,
1. Polyhedron is a solid figure in three dimensions having polygons as its faces along with sharp vertices and straight edges.
So, we can see that the given figure have polygonal faces with sharp vertices and straight edges.
Thus, it is a polyhedron.
2. Polygon is a closed two dimensional figure bounded by straight lines.
But, the given figure is not a 2-D figure and so is not a polygon.
3. Prism is a polyhedron with polygons as its faces along with a second base which is a translated copy of the first base.
Since, the given figure is a polyhedron but it does not have a second base which is a translated copy of the first base.
So, the given figure is not a prism.
4. Pyramid is 3-D figure having triangular outer surfaces converging to single point with polygonal base.
As, we can see that the given figure have polygonal base and triangular sides converging to a point.
So, the given figure is a pyramid.
5. Cube is a 3-D figure with all the six faces as squares.
But, the given figure does not have square faces and so is not a cube.
6. Solid is a figure having three dimensions.
Since, the given figure does have three dimensions.
So, it is a solid.
Hence, the correct options are Polyhedron, Pyramid and Solid.If you can buy 1⁄4 pizza for 5 dollars, how much can you purchase for 8 dollars? Write your answer as a fraction.
2/3 - 4x + 7/2 = -9x + 5/6
PLEASE HELP!
The center of a circle is at (2, −5) and its radius is 12.
What is the equation of the circle?
(x−2)2+(y+5)2=144
(x+2)2+(y−5)2=144
(x+2)2+(y−5)2=24
(x−2)2+(y+5)2=24
Pete is purchasing an mp3 player for 199.90 he gives the sales clerk 2 fifty dollar bills, 4 twenty dollar bills and 4 five dollar bills how much should he receive back
Write an equation to match each graph:
Write an equation to match each graph.
Solution:
The first graph is V shaped graph centered at origin, (0,0) and the graph is not shifted or translated. So, the equation of first graph is,
y=|x|
The second graph is V shaped graph centered at (1,0) and y=|x| is horizontally shifted right by 1 unit. So, the equation of second graph is,
y=|x-1|
The third graph is also V shaped but, it is inverted V graph centered at (0,1) . As, the graph is inverted V So, the graph must have y=-|x|. But, as the center is (0,1). So, the graph is shifted up by 1 unit. So, the equation of the third graph is,
y=-|x|+1
The fourth graph is shifted V graph, whose center is (1,-1). So, y=|x| is shifted right by 1 unit and down by 1 unit. So, the equation of fourth graph is,
y=|x-1|-1
The center of fifth graph is (-1,0), So, y=|x| graph is shifted left by 1 unit. So, the equation of fifth graph is
y=|x+1|
URGENT PLEASE HELP
Suppose 20% of all widgets produced at a factory are defective.
A simulation is used to model widgets randomly selected and then recorded as defective or working.
Which simulation best models the scenario?
Place 50 equally sized pieces of paper in a hat. Of the 50, 5 read “defective” and the rest read “working”.
Place 25 equally sized pieces of paper in a hat. Of the 25, 5 read “defective” and the rest read “working”.
Place 20 equally sized pieces of paper in a hat. Of the 20, 5 read “defective” and the rest read “working”.
Place 100 equally sized pieces of paper in a hat. Of the 100, 5 read “defective” and the rest read “working”.
What is the distance between point (3, 2) and line y = 1/4x-9
Maggie only wore sandals tracker on two of the days that she trained so from her fitness trackers she verified that on the third day she biked 20 miles and on the eighth day she biked 35 miles use these two data points to determine the equation of the line best of fit set for Maggie’s data
The number N is the produce of the first 1000 positive integers and can be written as 1000!.We say "1000 factorial."This is, N=1000!=1000x999x998x997x...x3x2x1.N is divisible by 5, 25, 125, 625,...Each of these factors is a power of 5.That is 5=5^1, 25=5^2, 125=5^3,625=5^4, and so on. Determine the largest power of 5 that divides N.