Sam wants to measure the height of a tree. She walks 100 feet from the base of the tree and looks up. The angle of elevation from the ground to the top of the tree is 33°. How tall is the tree? Round your answer to the nearest hundredth.
Answers
The height of the tree from which Sam is standing 100 feet away from the base is 64.94 feet.
What is angle of elevation?The angle of elevation is an angle that is formed between the horizontal line and the line of sight.
To calculate the height of the tree , we use the formula below.
Formula:
tan∅ = H/B.............Equation 1Where:
∅ = Angle of elevation from the ground to the top of the treeH = Height of the treeB = Distance of the base of the tree to the point where Sam looks upFrom the question,
Given:
∅ = 33°B = 100 feetSubstitute these values into equation 1 and solve for H
tan33° = H/100H = tan33°×100H = 64.94 feetHence, the height of the tree is 64.94 feet.
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Related Questions
At May 31, Lily Company has net sales of $395,000 and cost of goods available for sale of $268,000.
Compute the estimated cost of the ending inventory, assuming the gross profit rate is 35%.
Answers
The estimated cost of the ending inventory, assuming the gross profit rate is 35% is; $11250
How to find Estimated Cost?Let us first calculate the gross profit;
Gross Profit = Sales * Profit%
Gross Profit = 395000 * 35%
Gross Profit = $138250
Cost of goods sold = Sales - Gross Profit
Cost of goods sold = 395000 - 138250
Cost of goods sold = $256750
Cost of ending inventory = Cost of goods available for sale - Cost of goods sold
Cost of ending inventory = 268000 - 256750
Cost of ending inventory = $11250
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How do you write
f(x)=-5x^2-100x+8
in vertex form?
Answers
f(x) = -5(x+10)^2 + 508
a cuboid has length 18.5 cm, width 9.4 cm a height 6.2 cm. Work out the area of the cuboid
Answers
Answer:
693.76 cm²Step-by-step explanation:
a cuboid has length 18.5 cm, width 9.4 cm a height 6.2 cm. Work out the area of the cuboid
assuming you are looking for thr surface area
Surface Area of a Cuboid ·
TSA = 2 (lw + wh + hl)
2*( 18.5 * 9.4 + 9.4 * 6.2 + 6.2 * 18.5) = (remember PEMDAS)
2 * 346.88 =
693.76 cm²
evaluate question 3 only
Answers
Step-by-step explanation:
(4²-x²)³/²
or,(4+X) (4-X)
Substitute [tex]x = 4 \sin(y)[/tex], so that [tex]dx = 4\cos(y)\,dy[/tex]. Part of the integrand reduces to
[tex]16 - x^2 = 16 - (4\sin(y))^2 = 16 - 16 \sin^2(y) = 16 (1 - \sin^2(y)) = 16 \cos^2(y)[/tex]
Note that we want this substitution to be reversible, so we tacitly assume [tex]-\frac\pi2\le y\le \frac\pi2[/tex]. Then [tex]\cos(y)\ge0[/tex], and
[tex](16-x^2)^{3/2} = 16^{3/2} \left(\cos^2(y)\right)^{3/2} = 64 |\cos(y)|^3 = 64 \cos^3(y)[/tex]
(since [tex]\sqrt{x^2} = |x|[/tex] for all real [tex]x[/tex])
So, the integral we want transforms to
[tex]\displaystyle \int (16 - x^2)^{3/2} \, dx = 64 \int \cos^3(y) \times 4\cos(y) \, dy = 256 \int \cos^4(y) \, dy[/tex]
Expand the integrand using the identity
[tex]\cos^2(x) = \dfrac{1+\cos(2x)}2[/tex]
to write
[tex]\displaystyle \int (16 - x^2)^{3/2} \, dx = 256 \int \left(\frac{1 + \cos(2y)}2\right)^2 \, dy \\\\ = 64 \int (1 + 2 \cos(2y) + \cos^2(2y)) \, dy \\\\ = 64 \int (1 + 2 \cos(2y) + \frac{1 + \cos(4y)}2\right) \, dy \\\\ = 32 \int (3 + 4 \cos(2y) + \cos(4y)) \, dy[/tex]
Now integrate to get
[tex]\displaystyle 32 \int (3 + 4 \cos(2y) + \cos(4y)) \, dy = 32 \left(3y + 2 \sin(2y) + \frac14 \sin(4y)\right) + C \\\\ = 96 y + 64 \sin(2y) + 8 \sin(4y) + C[/tex]
Recall the double angle identity,
[tex]\sin(2y) = 2 \sin(y) \cos(y)[/tex]
[tex]\implies \sin(4y) = 2 \sin(2y) \cos(2y) = 4 \sin(y) \cos(y) (\cos^2(y) - \sin^2(y))[/tex]
By the Pythagorean identity,
[tex]\cos(y) = \sqrt{1 - \sin^2(y)} = \sqrt{1 - \dfrac{x^2}{16}} = \dfrac{\sqrt{16-x^2}}4[/tex]
Finally, put the result back in terms of [tex]x[/tex].
[tex]\displaystyle \int (16 - x^2)^{3/2} \, dx \\\\ = 96 \sin^{-1}\left(\frac x4\right) + 128 \frac x4 \frac{\sqrt{16-x^2}}4 + 32 \frac x4 \frac{\sqrt{16-x^2}}4 \left(\frac{16-x^2}{16} - \frac{x^2}{16}\right) + C \\\\ = 96 \sin^{-1}\left(\frac x4\right) + 8 x \sqrt{16 - x^2} + \frac14 x \sqrt{16 - x^2} (8 - x^2) + C \\\\ = \boxed{96 \sin^{-1}\left(\frac x4\right) + \frac14 x \sqrt{16 - x^2} \left(40 - x^2\right) + C}[/tex]
In the fall, you charge people $8 for going to their house to rake leaves, then
$5 for every hour you rake. If you make $38 one day, how many hours did you
spend raking?
Answers
Reason
Using formula Y=mx + b
Y is your total $
M is your y/x rate
B is your y intercept, the starting point
38 = 5/1 x + 8
Solve
38 = 5x + 8 subtract 8 from both sides to isolate x
30 = 5x
now divide both sides by 5 to solve for x
X=6
Now check your work
38 = (5)(6) + 8
38 = 38
So it equals !
Consider all seven-digit numbers that can be created from the digits 0-9 where the first and last digits must be odd and no digit can
repeat. What is the probability of choosing a random number that starts with 5 from this group? Enter a fraction or round your answer to
4 decimal places, if necessary.
Answers
Answer:
1/4 or 0.25
Step-by-step explanation:
The total possibilities of any 7 digit number using 0-9 is :
9×10×10×10×10×10×10=9000000
To work out the total possibilities in this question :
We look at the conditions :
The first digit can only be 5 numbers :
1 , 3 , 5 , 7 , 9
Now we subtract 5 from 9 :
9-5 = 4
Since no repeats for 2 , 3 , 4, 5, 6:
9 , 8 , 7 , 6 , 5,
5 possibilities for the last digit :
Total possibilities for this code :
4 × 9 × 8 × 7 × 6 × 5 × 5 = 302400
If it begins with 5 that is only 1 possibility for the first digit
1 × 9 × 8 × 7 × 6 × 5 × 5 = 75600
Now we make a fraction :
75600÷302400
Dividing top and bottom by 75600 gives you 1/4 or 0.25
Hope this helped and have a good day
Answer:
Step-by-step explanation:
Comment
The first digit and the last digit are both odd. That tells you that so far what you have is one of 5 digits for the first digit and and one of 4 for the last digit. 4 because you can't repeat the first digit.
5, , , , , ,4
2 digits are gone 8 remain.
5* 8 * 7* 6* 5* 4* 4 = 134400
Part 2
Only one number can go at the beginning, and that is a 5. Everything else remains the same.
1 * 8 * 7 * 6 *5 * 4 * 4 = 26880
P(picking a number beginning with a 5 is 25880 /13440) = 0.2
Use the point–slope formula to write an equation of the line that passes through(-5, -16 )and has a slope of m=3. Write the answer in slope–intercept form (if possible).
Answers
Answer:
Slope-intercept form: y = 3x - 1
Step-by-step explanation:
We are given that a line passes through the point (-5, -16) and has a slope of 3
We want to write the equation in point-slope form, and simplify it to slope-intercept form (if it is possible to do so).
First, point-slope form is given as [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1, y_1)[/tex] is a point
We have both the slope and a point, but let's label the values of everything to avoid confusion + mistakes:
m = 3
[tex]x_1=-5\\y_1=-16[/tex]
Now substitute into the formula (remember: we have NEGATIVE numbers, and the formula uses SUBTRACTION):
[tex]y--16=3(x--5)[/tex]
The equation can be simplified
[tex]y+16=3(x+5)[/tex]
We can also write this in slope-intercept form
Start by distributing 3 to both x and 5 (multiply both x and 5 by 3)
[tex]y+16=3x + 15[/tex]
Subtract 16 from both sides
y = 3x - 1
The table shows values for a quadratic function.
X
y
0
2
3
18
4
32
50
6
72
What is the average rate of change for this function for the interval from x = 2
to x = 4?
16
A
5
Answers
The average rate of change for this function for the interval from x = 2
to x = 4 is 20
How to determine the average rate of change?The function is given as:
x y
0 18
2 32
3 50
4 72
The average rate of change at the interval from x = 2 to x = 4 is calculated using:
m = (f(4) - f(2))/(4 - 2)
Using the table values, we have:
m = (72 - 32)/(4 - 2)
Evaluate
m = 20
Hence, the average rate of change is 20
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Quadratic Functions graph
Answers
Answer:
y=-x^2-4x-1
Step-by-step explanation:
when it is an arch like an upside down U then its
-x^2
it passes through the y axis at -1
its vertex or high point is -2,3 so its
-4x
Answer:
See below
Step-by-step explanation:
Dome shaped parabola so 'a' is negative
'c' is determined where x = 0
this value is -1
Axis of symmetry is the x value of the vertex (which is the high point of the dome)
x = -2
What is another way to write the equation 7/8x3/4=-6
Answers
Another way to write the equation is 7x + 54 = 0
How to rewrite the equationGiven the equation;
[tex]\frac{7}{8}x + \frac{3}{4} = -6[/tex]
Find the LCM on the left side, which is 8
[tex]\frac{7x + 6}{8} = -6[/tex]
Cross multiply
[tex]7x + 6 = -6[/tex] × [tex]8[/tex]
[tex]7x + 6 = -48[/tex]
Collect like terms
[tex]7x = -48 - 6[/tex]
[tex]7x = -54[/tex]
Take all to one side
[tex]7x + 54 = 0[/tex]
Thus, another way to write the equation is 7x + 54 = 0
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Select the correct answer from each drop-down menu. Consider this system of equations: (equation A) (equation B) The solution for the system of equations is .
Answers
The solution for the system of equations is: (99/13, 150/13)
Given the two expression 2/3x+3/5y=12 and 5/2y-3x=6
We have to find solution of two given expression.
To find the value of x, we have to eliminate y by making y the subject of formula in any of the equations.
Multiply equation A by 5/3 t.o get,
5/3(2/3x) + 5/3(3/5y) = 5/3(12)
10/9x + y = 20
y = 20 - 10/9x
substituting for y into equation b, we have:
5/2(20 - 10/9x) - 3x = 6
50 - 25/9x - 3x = 6
52/9x = 44
52x = 396
The expression that gives the value of x is: 52x = 396
Hence, x = 396/52 = 99/13
y = 20 - 10/9(99/13) = 20 - 110/13 = 150/13
Hence The solution for the system of equations is: (99/13, 150/13)
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need help with this question for geometry
Answers
Answer:
[tex]31[/tex]
Step-by-step explanation:
It's 31 degrees, I hope it is the right answer
Jordan and Taylor are collecting canned foods for the homeless. They hope to collect 10 cans per day to reach their goal. They have already collected 120 cans. If the
function for this problem is f(c) = 10r+120, determine how many cans Jordan and Taylor will have collected after 8 days.
Answers
Answer:
200 cans.
Step-by-step explanation:
f(c)=10r + 120
Put t=8 into it
T(c) = 10 x 8 + 120
=200 cans
(Use substitution method)
Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. Round your answer to four decimal places.
P ( X > 2 ) , n = 5 , p = 0.7
Answers
The value of the probability P(x > 2) is 0.8369
How to evaluate the probability?The given parameters are:
n = 5
p =0.7
The probability is calculated as:
[tex]P(x) = ^nC_x *p^x * (1 - p)^x[/tex]
Using the complement rule, we have:
P(x > 2) = 1 - P(0) - P(1) - P(2)
Where:
[tex]P(0) = ^5C_0 *0.7^0 * (1 - 0.7)^5[/tex]
P(0) = 1 *1 * (1 - 0.7)^5 = 0.00243
[tex]P(1) = ^5C_1 *0.7^1 * (1 - 0.7)^4[/tex]
P(1) = 5 *0.7^1 * (1 - 0.7)^4 = 0.02835
[tex]P(2) = ^5C_2 *0.7^2 * (1 - 0.7)^3[/tex]
P(2) = 10 *0.7^2 * (1 - 0.7)^3 = 0.1323
Recall that:
P(x > 2) = 1 - P(0) - P(1) - P(2)
So, we have:
P(x > 2) = 1 - 0.00243 - 0.02835 - 0.1323
Evaluate
P(x > 2) = 0.83692
Approximate
P(x > 2) = 0.8369
Hence, the value of the probability P(x > 2) is 0.8369
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Ming drove to the lake and back. On the trip there she drove 30 km/h and on the return trip she went 24 km/h. How long did the trip there take if the return trip took five hours?
Answers
The trip to the lake took 4 hours.
How long did the trip to the lake take?The first step is to determine the distance of the trip.
Distance = average speed x time
24 km/h x 5 = 120 km
Time = distance / average speed
120 / 30 = 4 hours
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The table shows the percentage of students in each of three grade levels who list fishing as their favorite leisure activity
Fishing
6th Grade (38%) 48%
9th Grade (29%) 50%
11th Grade (33%) 32%
Total (100%) (0.38)(0.48) + (0.29)(0.5) + (0.33)(0.32) = 0.433 or 43.3%
Find the probability that a student is a 9th grader, given that fishing is their favorite leisure activity.
Answers
Using conditional probability, it is found that there is a 0.3349 = 33.49% probability that a student is a 9th grader, given that fishing is their favorite leisure activity.
What is Conditional Probability?Conditional probability is the probability of one event happening, considering a previous event. The formula is:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which:
P(B|A) is the probability of event B happening, given that A happened.[tex]P(A \cap B)[/tex] is the probability of both A and B happening.P(A) is the probability of A happening.In this problem, we have that the probabilities are given as follows:
[tex]P(A) = 0.433, P(A \cap B) = 0.29 \times 0.50 = 0.145[/tex]
Hence the conditional probability is:
[tex]P(B|A) = \frac{0.145}{0.433} = 0.3349[/tex]
0.3349 = 33.49% probability that a student is a 9th grader, given that fishing is their favorite leisure activity.
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Question 1 of 6
Read the problem below and find the solution. Draw a diagram on your own
paper to help solve it.
A group of 23 friends gets together to play a sport. First, people must be
divided into teams. Each team has to have exactly 4 players, and no one can
be on more than one team. How many teams can they make? (It is possible
that not everyone can be on a team.)
(Do not include units in your answer.)
Answer here
Answers
Answer:
They could make at most 5 teams and its not possible to make everyone on team.
Step-by-step explanation:
If there are 4 players on a team, then we use 23 ÷ 4 = 5.75, 0.75 is not enough for 1, so there are 3 players remaining after making 5 teams.
(a) Solve the following formula for b.
1
A = ab
(b) Evaluate b when A= 18 and a =
6/5
1
(a) The formula A = ab solved for b is b = 3X
6
(b) Evaluate b when A= 18 and a = 5
b = (Type an integer or a simplified fraction.)
Answers
Answer:
a. b = 2A/a
b. 30
Step-by-step explanation:
a. to solve for b:
[tex]A = 1/2 ab[/tex]
multiply both sides by 2
[tex]2A = ab[/tex]
divide both sides by a
[tex]2A/a=b[/tex]
so b = 2A/a
b. using the equation b = 2A/a
[tex]b = 2*18/(6/5)\\= 36/(6/5)\\= 30[/tex]
a) b = 2A/a
b) b = 30
Step-by-Step Solution:
a) Solve the following …
A = 1/2ab
A = a/2b
A * 2 = ab
2A = ab
2A/a = b
=> b = 2A/a
b) Evaluate b when A = 18 and …
=> b = 2A/a
=> A = 18
=> a = 6/5
Substitute the Values in the Equation :-
b = 2A/a
b = 2(18)/(6/5)
b = 36 ÷ 6/5
b = 36 * 5/6
b = 180/6
=> b = 30
Hence, b = 30 when A = 18 and a = 6/5
Solve for x. Please help me!!
Answers
Answer:
64 degrees
Step-by-step explanation:
90-32=58
180-58-58=64
Answer:
x = 64°
Step-by-step explanation:
supplementary angles is two angles whose sum is 180° (straight line)
90 + 32 = 122°
To find angle A,
A + 122 = 180
subtract 122 from both sides,
A + 122 - 122 = 180 - 122
A = 58°
This is an isosceles triangle, two angles are equal in measure (A and B). These angles lie opposite to the equal sides.
A triangles angles add up to 180°
58° + 58° + x° = 180°
116° + x = 180°
116 - 116 + x = 180 - 116
x = 64°
A 4. Which of the following statements is false?
All squares are rectangles.
All rectangles are parallelograms.
• All parallelograms are quadrilaterals.
All rhombuses are squares
Answers
Answer: Choice D) All rhombuses are squares
=============================================================
Explanation:
Let's go through the answer choices to see which are true and which are false.
A) This is a true statement since all squares have all four angles of 90 degrees each. Any square is a rectangle, but not the other way around. We can cross choice A off the list.B) This is also a true statement. The opposite sides of a rectangle are parallel, which by definition makes it a parallelogram. Any rectangle is a parallelogram, but not the other way around. Cross choice B off the list.C) Yet another true statement. Parallelograms have four sides, which means they are quadrilaterals. Cross choice C off the list.D) This is false. Yes some rhombuses are squares, but others are not. A rhombus has all four sides the same length. If all four angles were 90 degrees each, then we'd have a square. But if the rhombus has its angles that aren't 90 degrees, then we have a non-square rhombus. Any square is a rhombus, but not the other way around.Check out the venn diagram below showing the connection between the geometric shapes mentioned. The large outer rectangle represents the set of all quadrilaterals. Inside this is the oval representing all parallelograms. Then inside the oval is the set of rectangles and the set of rhombuses. The overlapping region of the rectangles and rhombuses is the set of squares, marked in blue.
As you can see, picking any square will get us a rhombus and a rectangle automatically. However, picking any rhombus will not guarantee it's a square.
The reverse of the number 129 is 921, and these add to 1050, which is divisible by 30.
How many three-digit numbers have the property that, when added to their reverse,
the sum is divisible by 30?
Answers
Answer:
Step-by-step explanation:
Write the number as [tex]abc[/tex] and use the divisibility rules for 10 and 3. From the rule for 10, we know that the last digit of [tex]abc+cba[/tex] is [tex]o[/tex], hence [tex]a+c=10[/tex]. Thus the options are [tex]a=1[/tex] & [tex]c=9[/tex], [tex]a=2[/tex], & [tex]c=8[/tex], etc.
From the rule for 3, namely that the digit sum must be divisible by 3, we find that [tex]2a+2b+2c=20+2b[/tex] is divisible by [tex]3[/tex]. By hand it's easy to check that [tex]b=2,5,8[/tex] are the only options that work.
So there are 9 choices for [tex]a[/tex] and [tex]c[/tex] and [tex]3[/tex] for [tex]b[/tex] , giving 27 total.
What is
162divide[6 multiply (7-4) to the second power]
help please
Answers
Answer:
please mark me brainlist
Step-by-step explanation:
i need it
Answer:
3^1 multiplied by 3^2 = 3^(1 + 2) = 3^3
162
Simplify ——————
(2•3^3)
Canceling out 2 as it appears on both sides of the fraction line
3^4 divided by 3^3 = 3^(4 - 3) = 3^1 = 3
Step-by-step explanation:
hope this helps you ♡
Suppose that you have a square pyramid like the one pictured. Which plane section will produce a trapezoid?
A. A cross section cut parallel with the bottom
B. A cut parallel to the vertical axis, but off the vertical axis
C. Cutting off one of the bottom corners
D. A cut parallel to the vertical axis, directly through the vertical axis
Answers
Work out the lengths of sides a and b.
Give your answers to 1 decimal place.
triangle a is a right angled triangle with a height | of 8cm base of 5cm and missing hypotenuse
triangle b is a right angled triangle with a height | of 12cm and a hypotenuse of 17cm with a missing base
Answers
The length of the missing sides of triangles A and B are 9.43 cm and 12.04 cm respectively.
Pythagoras theoremTriangle A:
Height = 8cmBase = 5cmHypotenuse = x cmHypotenuse² = height ² + base²
x² = 8² + 5²
= 64 + 25
x² = 89
x = √89
x = 9.43 cm
Triangle B:
Height = 12cmBase = x cmHypotenuse = 17 cmHypotenuse² = height ² + base²
17² = 12² + x²
17² - 12² = x²
289 - 144 = x²
145 = x²
x = √145
x = 12.04 cm
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What is the slope of the line that passes through the points (-7, -2)(−7,−2) and (-15, -14)(−15,−14)? Write your answer in simplest form.
Answers
Answer:
please help me find em ah and I will be able to do what I can
The sum of two numbers is ten. One number is twenty less than four times the other. Find the numbers
Answers
Answer:
6 and 4
Step-by-step explanation:
Let one number be x.
Then another will be : 4x - 20
In accordance with the question;
x + 4x - 20 = 10
5x = 10 + 20
x = 30/5
= 6
x = 6
4x - 20 = 4×6 - 20 = 4
So, the numbers are 6 and 4.
The graphs of three functions are shown. Which statements accurately compare the functions on the graph? Select two options. The square root and quadratic function share a y-intercept. The square root and absolute value function share an x-intercept. The range of the square root and quadratic function are the same. The range of the square root and absolute value function are the same. The quadratic function and the absolute value function have a minimum while the square root function has a maximum.
Answers
The following statements accurately compare the three functions on the graph: option A and C.
How to interpret the graph?In Geometry, the following statements are true about the graph of a function:
The x-intercepts of two or more functions are the same when their curves meet the x-axis at the same point. The y-intercepts of two or more functions are the same when their curves meet the y-axis at the same point. The ranges of two or more functions are the same when they all have the same vertical extension. The absolute value function and square root function both have the same minimum i.e at lower end of their range.By critically observing the graph of a function, we can logically deduce that the following statements accurately compare the three functions on the graph:
"The square root and quadratic function share a y-intercept.""The range of the square root and absolute value function are the same."Read more on function here: brainly.com/question/4246058
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Find the equation of the line using the given information.
(x, y) = (−3, 0)
and
(x, y) = (−3, 7)
are points on the line
Answers
Do you need to show your work ?
Please answer this for me
Answers
Step-by-step explanation:
all the details see in the attachment.
Solve 4|x + 6| = 16
Answers
Answer:
-10 and -2
Step-by-step explanation:
First, divide both sides by 4 to get |x+6| = 4
Then, Take the absolute vaule on both sides
x+6= 4 or -4
So, x could be 2 vaules
Your welcome!
4 | x + 6 | = 16
Divide both sides by 4.
[tex]\bf{\dfrac{4|x+6|}{4}=\dfrac{16}{4} }[/tex]
[tex]\bf{|x+6|=4 }[/tex]
Absolute value is solved.
[tex]\bf{|x+6|=4 }[/tex]
We know either x + 6 = 4 or x + 6 = -4.
x + 6 = 4 (Possibility 1)
x + 6 - 6 = 4 - 6 (Subtract 6 from both sides)
x=−2
x + 6 = -4 (Possibility 2)
x + 6 - 6 = -4 - 6 (Subtract 6 from both sides)
x=-10
Solution:
x=−2 or x=−10
[tex]\red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}[/tex]
