Answers
The height of the tree is 13.82 m
Step - by - Step Explanation
What to find? Height of the tree.
Given:
• Angle of elevation = 62,°
,• Eye-level above the ground =160cm
,• Distance away from the tree = 6.5m
We need to first sketch the problem, to have a clearer picture of the question.
Change 160cm to meter
160 cm = 160/100 = 1.6 m
Height of the tree = 1.6 + x
We need to find the value of x.
From the sketch above;
Opposite =x
Adjacent =6.5
θ= 62°
Using the trigonometric ratio;
[tex]\tan \theta=\frac{opposite\text{ }}{\text{adjacent}}[/tex]Substitute the values.
[tex]\tan 62=\frac{x}{6.5}[/tex]Cross-multiply.
x=6.5tan62°
x = 12.22 m
Height of the tree = 1.6 m + 12.22m
Height of the tree = 13.82 m
OR
Height of the tree = 1382 cm approximately.
Related Questions
A company produces 11 times as many rings on shift 1+ shift to if I total of 12,000 rings were produced how many were produced on each shift
Answers
Shift 1 produced 11000 rings and Shift 2 produced 1000 rings.
What does "parent company" mean and how Do Parent Companies Work?
A single firm that owns a majority stake in another company or groups of companies is known as a parent company.
Parent corporations are created through acquisition, merger, spin-off, or carving out of subsidiaries.
A parent company is a business that controls a significant portion of another business, giving it operational authority over that business.
Given :-
Production of Shift 1 = 11 times of Production of Shift 2
total production = 12,000 rings
production of ( Shift 1 + Shift 2 ) = Total production
on solving we get,
Production of Shift 1 = 11,000 rings
Production of Shift 2 = 1,000 rings
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Question
Refer to section 1.3.2, Credit scores, beginning on page 22 of the report.
Arrange the five tiers of credit scores in order, starting with the lowest tier of credit scores.
Answers
The five credit score tiers are listed in ascending order, starting with the lowest tier:
Deep Subprime < Subprime < near prime < prime < super prime
A consumer's credit score may have a big impact on their ability to receive credit. These interactive infographics show how lending practices have changed for borrowers with various credit score profiles.
We focus on the five credit score levels that are commercially available.
The range of subprime credit scores is 580 to 619.
The range of Prime's credit score is from 660 to 719.
Deep subprime credit scores fall below 580.
Near prime credit scores range from 620 to 659.
Super prime credit is defined as having a score of 720 or higher.
The following are the five credit scores, listed from lowest to highest:
Deep Subprime < Subprime < near prime < prime < super prime
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Use the graph of y = f (x) to find the following value of f. f(2) =
Answers
Answer:
f(2)=4
Explanation:
Consider the graph below:
When x=2, the value of f(x) = 4 (the poiny circled in blue above).
Therefore:
[tex]f(2)=4[/tex]The value of f(2) is 4.
Jan 10, 7:17:08 PM Which equation represents a line which is perpendicular to the line x - 2y = -14? Oy= -27 -1 Oy= 2x + 8 Submit Answer Oy=x+4 Oy = -x + 2
Answers
You need to determine which line is perpendicular to the line
[tex]x-2y=-14[/tex]For two lines to be considered perpendicular their slopes must be the inverse positive, that is, if, for example, you have the lines
[tex]y_1=mx_1+b[/tex][tex]y_2=nx_2+c[/tex]For them to be perpendicular one slope must be the inverse negative of the other such as
[tex]n=-\frac{1}{m}[/tex]The first step is to write the given line in slope-intercept form:
1) Pass the x term to the right side of the equal sign
[tex]\begin{gathered} x-2y=-14 \\ x-x-2y=-14-x \\ -2y=-x-14 \end{gathered}[/tex]2) Divide both sides of the expression by "-2"
[tex]\begin{gathered} -\frac{2y}{-2}=-\frac{x}{-2}-\frac{14}{-2} \\ y=\frac{1}{2}x+7 \end{gathered}[/tex]The slope of the line is
[tex]m=\frac{1}{2}[/tex]So the slope of a line perpendicular to it will be the inverse negative of it
[tex]\begin{gathered} n=-(\frac{1}{\frac{1}{2}}) \\ n=-2 \\ \end{gathered}[/tex]The correct option is the one that has slope -2
A focus group of 12 people is to be chosen randomly from among 24 right-handed people and 5 left-handed people. In order to find the probability that 3 of the people chosen are right-handed, you should use
Answers
Let 1 and 2 mean that a person is right-handed or left-handed, respectively.
Consider the probability space as the different groups of 12 people that can be formed with the 29 total people. {(1,1,1,1,1,...1),(2,1,1,1,1,...,1),...}
We need to use the binomial distribution in order to find the answer.
Consider X to be the number of right-handed people in the group.
The probability of X=3 is then:
[tex]Pr(X=3)=\text{ binomial coefficien(}12,3\text{)}(\frac{24}{29})^3(1-\frac{24}{29})^{12-3}[/tex]We used the formula
[tex]\begin{gathered} Pr(X=k)=\text{ binomial coefficient(n,k)}\cdot p^k(1-p)^{n-k} \\ \text{where } \\ k=3 \\ n=12 \\ p=\frac{24}{29} \end{gathered}[/tex]Finally, we need to simplify the expression, as shown below
[tex]\Rightarrow P(X=3)=220(\frac{24}{29})^3(\frac{5}{29})^9=0.0000167[/tex]This is the answer one obtains using the binomial distribution; nevertheless, the actual probability is equal to zero because it is not possible to form a group of 12 people that only contains 3 right-handed people as there are only 5 left-handed people (3+5=8).
which calculation does not show the surface area of the cube?
Answers
Given: A cube with side 6.5 cm
Required: Which calculation does not show the surface area of the cube.
Explanation:
Surface area of cube with side a is 6a².
So here the surface area of cube is
[tex]6(6.5)^2[/tex]Oprion 2, 3 and 4 reflects the calculation correctly.
But option A is actually the volume of the cube, it is not a correct way to show surface area of the cube.
Final Answer: option A is correct.
Find ca^2+b^2=c^2 3^2+2^2=c^29+4=13
Answers
Substituting with a = 3 and b = 2, we get:
[tex]\begin{gathered} 3^2+2^2=c^2 \\ 9+4=c^2 \\ 13=c^2 \\ \sqrt[]{13}=c \\ 3.6\approx c \end{gathered}[/tex]AcuveDetermining If a Number Is a SolutionQUICK CHECKWhich values are solutions to the inequality -3x – 4< 2? Check all of the boxes that apply.-4-2OOO03DONE
Answers
We have the next inequality given:
[tex]-3x-4<2[/tex]Solve the x variable:
Add both sides 4
[tex]\begin{gathered} -3x-4+4<2+4 \\ -3x<6 \end{gathered}[/tex]Divide both sides by 3
[tex]\begin{gathered} \frac{-3}{3}x<\frac{6}{3} \\ -x<2 \end{gathered}[/tex]Finally, multiply both sides by -1:
[tex]\begin{gathered} (-1)(-x)<2(-1) \\ x>-2 \end{gathered}[/tex]Hence, x can take any value greater than -2.
So, the solutions that apply are 0 and 3.
-353-0-- * GR-35-21-2700-3s 6 - 2y-6- - +28+82-80 -592-35-07-2+27-35-30 9815+ Seesters << RB- --3-1-1-12) 6-5-3= LG - 5+13-2225 SVE -3-5y+6=-24 -*- 4y +50=-21 5r - 55 - 5 = 3r-S-=
Answers
Explanation:
5x - 4y + 2z = 21 ...equation 1
-x - 5y + 6z = -24 ....equation 2
-x - 4y + 5z = -21 ...equation 3
Using elimination method:
multiply equation 2 by 5:
-5x - 25y + 30z = -120 ....equation 2a
add equation 2a from 1:
5x - 5x -4y -25y + 2z + 30z = 21 - 120
0 - 29y + 32z = -99
-29y + 32z = - 99 ....equation 4
multiply equation 3 by 5:
-5x - 20y + 25z = -105 ...equation 3a
add equation 1 and 3a
5x - 5x - 4y - 20y + 2z +25z = 21 - 105
0 - 24y + 27z = -84
-24y + 27z = -84 ...equation 5
-29y + 32z = - 99 ....equation 4 (×-24)
-24y + 27z = -84 ...equation 5 (×-29)
696y - 768x = 2376 ...(4a)
696y -783x = 2436 ...(5a)
subtract 5a from 4a
696y - 696y -768x -(-783x) = 2376 - 2436
0 - 768x + 783x = -60
15x = -60
x = -60/15
x = -4
substitute for x in equation 4a:
696y - 768(-4) = 2376
696y + 3072 = 2376
696y = 2376 -3072
696y = -696
y = -696/696
y = -1
substitute for y in equation 4:
-29(-1) + 32z = -99
29 + 32z = -99
32z = -99 - 29
32z = -128
z = -128/32
z = -4
solve for missing variable: 11y-36=63
Answers
The equation can be solved as,
[tex]\begin{gathered} 11y-36=63 \\ 11y=63+36 \\ 11y=99 \\ y=\frac{99}{11} \\ y=9 \end{gathered}[/tex]Therefore, the value of y is 9.
Which of the equations below could be the equation of this parabola? A. y = 1/2 x² B. x-1/2 y2 c. y = -1/2 x² D. x = 1/2 y2SUBMIT
Answers
The equation of the parabola is given as;
[tex]y=\frac{1}{2}x^2[/tex]The correct answer is option A.
Write 6.5123 x 10^8 in standard
Answers
The standard form is a standard method of writing numbers such that we have it in the form:
[tex]a\times10^b[/tex]where
[tex]0Therefore, 6.5123 x 10^8 in standard form is:[tex]6.5123\times10^8[/tex]- What is the closed linear form of the sequence 3, 4,5, 6, 7, ...?
Answers
Solve the system using the elimination method:2x - y + z = -26x + 3y - 4z = 8-3x + 2y + 3z = -6
Answers
multiply 2x - y + z = - 2 for 3
[tex]6x-3y+3z=-6[/tex]then sunstract the equation 1 and 2
[tex]\begin{gathered} 6x+3y-4z=8 \\ 6x-3y+3z=-6 \\ 6y-7z=14 \end{gathered}[/tex]multiply -3x+2y+3z=-6 for 2
[tex]-6x+4y+6z=-12[/tex]adding
[tex]\begin{gathered} -6x+4y+6z=-12 \\ \underline{6x-3y+3z=-6} \\ y+9z=-18 \end{gathered}[/tex]multiply y+9z=-18 for 6
[tex]6y+54z=-108[/tex]Subtracting
[tex]\begin{gathered} 6y+54z=-108 \\ \underline{6y-7z=14} \\ 61z=-122 \end{gathered}[/tex]then solve
[tex]\begin{gathered} 61z=-122 \\ \frac{61z}{61}=\frac{-122}{61} \\ z=-2 \end{gathered}[/tex][tex]\begin{gathered} 6y-7\mleft(-2\mright)=14 \\ 6y+14=14 \\ 6y+14-14=14-14 \\ 6y=0 \\ y=0 \end{gathered}[/tex][tex]\begin{gathered} 6x-3\cdot\: 0+3\mleft(-2\mright)=-6 \\ 6x-6=-6 \\ 6x-6+6=-6+6 \\ 6x=0 \\ x=0 \end{gathered}[/tex]answer is: x = 0, y = 0 and z = - 2
In a middle school with 300 students, there are 40% boys, 1/3 of the students wear glasses, and 15% of the girls wear glasses. What is the probability (= how many percent is it) that a randomly selected student does not wears glasses? (Round the percentage to the nearest hundredth) *
Answers
We know that
• There are 300 students.
,• 40% are boys (this means 60% are girls).
,• 1/3 of the students wear glasses.
If 1/3 of the students wear glasses, then 2/3 of the students don't wear glasses. Let's find 2/3 of 300.
[tex]\frac{2}{3}\cdot300=\frac{600}{3}=200[/tex]Therefore, 200 students don't wear glasses.
Then, we divide to find the probability.
[tex]P=\frac{200}{300}=0.6667[/tex]Then, we multiply by 100.
[tex]0.6667\cdot100=66.67[/tex]Therefore, the probability is 66.67%.| 5-6x | -12 = 0Solve the absolute. equation for 2 values of x
Answers
Given
[tex]|5-6x|-12=0[/tex]To solve this equation for both possible values of x, you have to separate it into two calculations.
1) One will be for the case that the values inside the absolute term are multiplied by "+1":
[tex]\begin{gathered} 1\cdot(5-6x)-12=0 \\ 5-6x-12=0 \\ -6x+5-12=0 \\ -6x-7=0 \\ -6x=7 \\ -\frac{6x}{-6}=\frac{7}{-6} \\ x=-\frac{7}{6} \end{gathered}[/tex]The first value of x is -7/6
2) The second will be the case that the absolute values are negative, that is as if they are multiplied by -1
[tex]\begin{gathered} (-1)(5-6x)-12=0 \\ -5+6x-12=0 \\ 6x-5-12=0 \\ 6x-17=0 \\ 6x=17 \\ \frac{6x}{6}=\frac{17}{6} \\ x=\frac{17}{6} \end{gathered}[/tex]The second value of x is 17/6
So for this absolute equation, the possible values of x are -7/6 and 17/6
Factor by grouping:y^3-5y^2+3y-15
Answers
we have the expression
y^3-5y^2+3y-15
Grouping terms
(y^3-5y^2)+(3y-15)
factor y^2
y^2(y-5)+(3y-15)
factor 3
y^2(y-5)+3(y-5)
factor (y-5)
(y-5)[y^2+3]absolute value of v-5>3
Answers
Answer: v=8
Step-by-step explanation:
-5+5=0
3+5=8
v=8
What is the inverse function of y = (x-4)^2+2
Answers
One way to find the inverse of a function is by first swapping x and y, then solving for y, like this:
[tex]\begin{gathered} y=(x-4)^2+2\text{ }\Rightarrow x=(y-4)^2+2 \\ \end{gathered}[/tex]Now, let's solve for y, like this:
[tex]\begin{gathered} x=(y-4)^2+2 \\ x-2=(y-4)^2+2-2 \\ (y-4)^2=x-2 \\ \sqrt[]{\mleft(y-4\mright)^2}=\sqrt[]{x-2} \\ y-4=\sqrt[]{x-2} \\ y-4+4=\sqrt[]{x-2}+4 \\ y=\sqrt[]{x-2}+4 \end{gathered}[/tex]Then, the inverse function of y = (x-4)^2+2 is:
[tex]y=\sqrt[]{x-2}+4[/tex]24. The base of a 13-foot ladder stands 5 feet from a house. Sketch a drawing to model this situation. How many feet up the side of the house does the ladder reach? Explain how drawing the picture helped you solve the problem.
Answers
The draw that describes this situation looks like this:
Drawing this helped us to know that the ladder forms a right triangle with one of the walls of the house.
When we have right triangles we can apply the Pythagoras theorem, from the Pythagoras theorem we can express:
[tex]13^2=5^2+h^2[/tex]Solving for h, we get:
[tex]\begin{gathered} 13^2-5^2=5^2-5^2+h^2 \\ 13^2-5^2=h^2 \\ h=\sqrt[]{13^2-5^2}=\sqrt[]{169-25}=\sqrt[]{144}=12 \end{gathered}[/tex]Then, the ladder reach 12 feet up the side of the house
2/5m = 1/2 what is the m stand for ?
Answers
we can interpret m as a constant of proportionality.
I will send u a picture of my equation
Answers
Answer:
where is the picture????
the triangle in the figure had a hypotenuse equal to 40 units what is the approximate length of x
25.7 units
30.6 units
47.7 units
52.2 units
(Srry I’m spamming I know nothing on this test)
Answers
If the triangle in the figure has a hypotenuse equal to 40 units, then the approximate length of x is 30.64 units
The length of the hypotenuse = 40 units
The angle = 50 degrees
Here we have to apply the trigonometric function
we know
sin θ = Opposite side / Hypotenuse
cos θ = Adjacent side / Hypotenuse
tan θ = Opposite side / Adjacent side
Here we have to use the equation of sin θ
Substitute the values in the equation
sin 50 = x/40
x = 40×sin 50
x = 30.64 units
Hence, if the triangle in the figure has a hypotenuse equal to 40 units, then the approximate length of x is 30.64 units
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A small company produces baseball and racquetball by the function B(x)=-6x^2+2,556x-106,878. The profit made from the racquetball products can be represented by the function R(x)=-x^2+293x-16,770. If x is the total number of products made, which function best describes P(x), the profit the company makes from these two products?
Answers
profit made from the baseball products
[tex]B(x)=-6x^2+2556x-106878[/tex]Profit made from the racquetball products
[tex]R(x)=-x^2+293x-16770[/tex]Profit made from those 2 products is
[tex]\begin{gathered} P(x)=-6x^2-x^2+2556x+293x-106878-16770 \\ P(x)=-7x^2+2849x-123648 \end{gathered}[/tex]the sum of the angle measures of a polygon with n sides is given find n1440
Answers
Given in the question:
a.) The sum of all angles of a polygon is 1,440 degrees.
To be able to determine what polygon has a total sum of angles of 1,440 degrees, we will be using the following formula:
[tex]\text{ }\Theta=(n-2)x180^{\circ}[/tex]We get,
[tex]\text{ 1},440^{\circ}=(n-2)x180^{\circ}[/tex][tex]\text{ 1},440^{\circ}=180n-360^{\circ}[/tex][tex]180n=1,440^{\circ}\text{ + 360}^{\circ}[/tex][tex]180n=1,800^{\circ}[/tex][tex]\frac{180n}{180}=\frac{1,800^{\circ}}{180}[/tex][tex]n\text{ = 10}[/tex]Therefore, that polygon is a decagon or a polygon with 10 sides.
Two ships are sailing across the Atlantic ocean at the equator. The dofference in solar time between them is two hours. How many degrees of longitude are they apart?
Answers
Answer:
30 degrees
Step-by-step explanation:
There are 360 degrees of longitude ( 360 degrees is a complete circle)
It takes 24 hours to complete a complete rotation of the earth
360 degrees / 24 hours = 15 degrees / hr
15 degrees/ hr * 2 hr = 30 degrees
You must show your work as you... determine whether QR and ST are parallel, perpendicular, or neither. Q(9, 10), R(-5, 2), S(-8, -2), T(-1, 2) Parallel Perpendicular Neither
WILL MARK BRAINLIEST
PLS HELP ASAP
Answers
Slope of QR = 4/7; Slope of ST = 4/7, therefore, the lines are parallel to each other.
How to Determine if Two Lines are Parallel or Perpendicular?To determine if two given lines are perpendicular to each other or parallel to each other, find their slopes.
Slope, m = change in y / change in x.
If they have the same slope, m, then they are parallel lines. If they have slopes that are negative reciprocal to each other, then they are perpendicular lines.
Given:
Q(9, 10)
R(-5, 2)
S(-8, -2)
T(-1, 2)
Find the slope of QR and ST:
Slope of QR = (10 - 2)/(9 -(-5)) = 8/14 = 4/7
Slope of ST = (-2 - 2)/(-8 -(-1)) = -4/-7 = 4/7
The slope are the same, therefore they are parallel to each other.
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Mario constructs a scale model of a building with a rectangular base. His model is 4.2 inches in length and 2 inches in width. The scale of the model is 1 inch = 15 feet What is the actual area, in square feet, of the base of the building?
Answers
First let's use two rules of three to determine the actual dimensions of the building.
For the length, we have:
[tex]\begin{gathered} 1\text{ inch}\to15\text{ feet} \\ 4.2\text{ inches}\to x\text{ feet} \\ \\ \frac{1}{4.2}=\frac{15}{x} \\ x=15\cdot4.2=63 \end{gathered}[/tex]For the width:
[tex]\begin{gathered} 1\text{ inch}\to15\text{ feet} \\ 2\text{ inches}\to x\text{ feet} \\ \\ \frac{1}{2}=\frac{15}{x} \\ x=15\cdot2=30 \end{gathered}[/tex]Now, calculating the area of the building base, we have:
[tex]\text{Area}=63\cdot30=1890\text{ ft2}[/tex]So the area of the building base is 1890 ft².
Lola needs 2/3 cup of lemon-lime soda for every 2 cups of punch. Find ____ cups of soda/cup of punch
Answers
We know that
• There are needed 2/3 cups of lemon soda for every 2 cups of punch.
To find the answer, we have to divide.
[tex]\frac{\frac{2}{3}}{2}=\frac{2}{6}=\frac{1}{3}[/tex]Therefore, the answer is 1/3 of soda/cup of punch.Can I get help w this pleaseThe dimensions of a rectangular prism are quadrupled.if the original surface area was 225ft^2 was is the new surface area?
Answers
Answer:
Concept:
Doubling the dimensions of a prism will increase the new area by 4 times the original area
Tripling the the dimensions of the prism will increase the new area by 9 times the original area
Quadrupling will increase the new area by 16 times the original area
Given that the original area given is
[tex]=225ft^2[/tex]The new area therefore will be
[tex]\begin{gathered} 16\times225 \\ =3600ft^2 \end{gathered}[/tex]Hence,
The final answer will be
[tex]\rightarrow3600ft^2[/tex]