A flagpole 8m high cast a shadow of 12m, while a nearby building cast a shadow of 60m. How high is a building?
Answers
Answer:
40 m
Step-by-step explanation:
8/12=x/60
x=(8*60)/12
x=40
The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. The height of the building when it cast a shadow of 60 meters is 40 m.
What is Tangent (Tanθ)?The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. it is given as,
\(\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}\)
where,
θ is the angle,
Perpendicular is the side of the triangle opposite to the angle θ,
The base is the adjacent smaller side of the angle θ.
As it is given that the height of the pole is 8m, while the shadow cast by the pole is 12 m. If we use the ratio of trigonometry then the height of the building can be written as,
\(\rm Tan(\theta)= \dfrac{\text{Height of the pole}}{\text{Shadow of the pole}}= \dfrac{\text{Height of the building}}{\text{Shadow of the pole}}\)
\(\dfrac{8}{12}= \dfrac{\text{Height of the building}}{\text{60}}\\\\\dfrac{8 \times 60}{12}= {\text{Height of the building}}\\\\\text{Height of the building}=40\ \rm m\)
Hence, the height of the building when it cast a shadow of 60 meters is 40 m.
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Related Questions
write a definite integral that yields the area of the region f(x)= 25-x^2
Answers
This integral will give us the desired area of the region bounded by the curve f(x) = 25 - x^2 and the x-axis within the interval [-5, 5].
To calculate the area of the region bounded by the curve f(x) = 25 - x^2, we can set up a definite integral over the desired interval.
The function, f(x) = 25 - x^2, represents a downward-opening parabola centered at the origin with a vertex at (0, 25).
To get the area, we need to consider the portion of the curve that lies above the x-axis. This corresponds to the region we want to find the area of.
Since the curve is symmetric about the y-axis, we can focus on the positive x-values.
To determine the interval, we need to get the x-values where the curve intersects or touches the x-axis. Solving the equation 25 - x^2 = 0 gives x = ±5.
Therefore, the interval we are interested in is [-5, 5], which represents the portion of the curve above the x-axis.
The definite integral that yields the area of the region is:
∫[from -5 to 5] (25 - x^2) dx
Evaluating this integral will give us the desired area of the region bounded by the curve f(x) = 25 - x^2 and the x-axis within the interval [-5, 5].
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Gayle has a piece of plywood that is twelve feet long. Gayle is using the piece of plywood to saw off pieces of wood needed to build shelves in her room. First, Gayle saws off 3/10 of the wood. Next, Gayle saws off 6/10 of the wood. Last, Gayle saws off 2/10 of the board. Gavin says she has 2/10 of the wood left to use for another shelf. Is Gayle correct? Show all your mathematical thinking
Answers
Based on the calculations, we find that Gayle is not correct. Instead of having 2/10 of the wood left, she actually ends up with a negative fraction (-1/10), which doesn't make sense in this context.
To determine if Gayle is correct, we need to calculate the remaining fraction of the wood after each sawing off operation.
First, Gayle saws off 3/10 of the wood. This leaves her with 1 - 3/10 = 7/10 of the wood remaining.
Next, Gayle saws off 6/10 of the wood. This is equivalent to 3/5. So, she now has 7/10 - 3/5 = (7/10) - (6/10) = 1/10 of the wood remaining.
Lastly, Gayle saws off 2/10 of the wood. This is equivalent to 1/5. So, she is left with 1/10 - 1/5 = (1/10) - (2/10) = -1/10.
Based on the calculations, we find that Gayle is not correct. Instead of having 2/10 of the wood left, she actually ends up with a negative fraction (-1/10), which doesn't make sense in this context. Therefore, Gayle's claim that she has 2/10 of the wood left for another shelf is incorrect.
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What is the probability of selecting a green shirt
Answers
the probaility of selecting a green shirt
9. Marry plays a game of throwing a ball at a target.
The table shows information about the probability of each possible score.
0
1
*
2
3
4
Score
0.09
Probability
X
3x
0.16
0.21
Marry is three times more likely to score 2 points than to score 1 point.
a) Work out the value of x.
b) Mary plays the game twice.
Work out the probability of Mary scoring a total of 8.
5
0.30
6.......
Answers
Answer:
6.97%
Step-by-step explanation:
a) To work out the value of x, we can use the information given that "Marry is three times more likely to score 2 points than to score 1 point". We know that the probability of scoring 1 point is x, and the probability of scoring 2 points is 3x.
So we can set up the equation:
3x = probability of scoring 2 points
x = probability of scoring 1 point
We know that 3x = probability of scoring 2 points = 0.16
So we can solve for x by dividing both sides by 3:
x = 0.16 / 3 = 0.05333
b) To work out the probability of Mary scoring a total of 8, we can use the information from the table and the formula for the probability of a specific outcome when playing the game twice.
We know that the probability of scoring 4 points in one game is 0.21, so the probability of scoring 4 points twice is (0.21)^2 = 0.0441
We also know that the probability of scoring 2 points in one game is 3x = 3(0.05333) = 0.16, so the probability of scoring 2 points twice is (0.16)^2 = 0.0256
We can add these probabilities together to find the total probability of scoring 8 points:
0.0441 + 0.0256 = 0.0697 or 6.97%
So the probability of Mary scoring a total of 8 is 6.97%.
At a school, the average of the number of boys, girls, male teachers, and female teachers is 117. The average of the number of boys, girls, and male teachers is 151At a school, the average of the number of boys, girls, male teachers, and female teachers is 117. The average of the number of boys, girls, and male teachers is 151. There are 6 fewer male teachers than there are female teachers. The number of female teachers is 1/16 the number of girls. How many boys are there at the school? boys
Answers
Using a system of equations, it is found that there are 204 boys at the school.
What is a system of equations?A system of equations is when multiple variables are related, and equations are built to find the values of each variable, according to the relations given in the problem.
For this problem, the variables are given as follows, considering the situation described:
Variable x: number of boys in the school.Variable y: number of girls in the school.Variable z: number of male teachers in the school.Variable w: number of female teachers in the school.The average of the number of boys, girls, male teachers, and female teachers is 117, hence:
(x + y + z + w)/4 = 117
x + y + z + w = 468.
The average of the number of boys, girls, and male teachers is 151, hence:
(x + y + z)/3 = 151
x + y + z = 453.
Then:
x + y + z + w = 468.
453 + w = 468
w = 15.
There are 6 fewer male teachers than there are female teachers, hence:
z = w - 6 = 15 - 6 = 9.
So:
x + y + z = 453.
x + y = 444.
The number of female teachers is 1/16 the number of girls, hence:
y = 16w = 16 x 15 = 240.x = 444 - y = 444 - 240 = 204.There are 204 boys at the school.
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Analyze the proportion below and complete the instructions that follow.
2x+5 x-5
3
4
Solve the proportion for x
A. -7
B. -4
C-2
D. -1
Answers
Answer:
A
Step-by-step explanation:
(2x + 5)/(3) = (x - 5)/(4)
Multiplying both sides by 12 to eliminate the fractions, we get:
4(2x + 5) = 3(x - 5)
Expanding the brackets, we get:
8x + 20 = 3x - 15
Subtracting 3x and 20 from both sides, we get:
5x = -35
Dividing both sides by 5, we get:
x = -7
Therefore, the solution to the proportion is x = -7.
So, the correct option is A) -7.
What is the volume of this cube?
4 cubic feet
») 3 cubic feet
1 ft
6 cubic feet
1 ft
1 ft
>) 1 cubic foot
Answers
Answer:
it's 6 cubic feet look you must count all the sides together also I took the test this cube has 6 sides so your answer will be 6 cubic feet ;)
Step-by-step explanation:
Write 567.4892 correct to (I)the nearest ten (II)2 decimal places
Answers
Step-by-step explanation:
(I) To the nearest ten, we need to determine the multiple of 10 that is closest to 567.4892. Since 567.4892 is already an integer in the tens place, the digit in the ones place is not relevant for rounding to the nearest ten. We only need to look at the digit in the tens place, which is 8.
Since 8 is greater than or equal to 5, we round up to the next multiple of 10. Therefore, 567.4892 rounded to the nearest ten is 570.
(II) To 2 decimal places, we need to locate the third decimal place and determine whether to round up or down based on the value of the fourth decimal place. The third decimal place is 9, and the fourth decimal place is 2. Since 2 is less than 5, we round down and keep the 9. Therefore, 567.4892 rounded to 2 decimal places is 567.49.
The answers are:
567.5567.49Work/explanation:
Before we start rounding, let me tell you about the rules for doing this.
Rounding RulesHow do we round a number correctly to the required number of decimal places? Where do we start? Well, there are two rules that will help us:
#1: if the number/decimal place is followed by a digit that is less than 5, then we simply drop that digit. This can be illustrated in the following example:
1.431 to the nearest tenth : 1.4
because, we need to round to 4, and 4 is followed by 3 which is less than 5, so we simply drop 3 and move on.
4.333 to the nearest hundredth : 4.33
because, the nearest hundredth is 2 decimal places.
#2: if the number/decimal place is followed by a digit that is greater than or equal to 5, then we drop the digit, but we add 1 to the previous digit. Let me show you how this actually works.
5.87 to the nearest tenth.
We drop 7 and add 1 to the previous digit, which is 8.
So we have,
5.8+1
5.9
________________________________
Now, we round 567.4892 to the nearest tenth:
567.5
because, the nearest tenth is 4, it's followed by 8, so we drop 8 and add 1 to 4 which gives, 567.5.
Now we round to 2 DP (decimal places):
567.49
Hence, the answer is 567.49
ASAP! what type of angles are <3 and <10
A. Consecutive interior angles
B. Alternate exterior angles
C. alternative interior angles
D. Corresponding angles
Answers
Answer:
∠3 and ∠10 are;
B. Alternate exterior angles
Step-by-step explanation:
From the given diagram, we have;
∠3 and ∠10 are angles on the same transversal
The location of ∠3 and ∠10 are on the outer (exterior) part of the two lines crossed by the transversal that forms ∠3 and ∠10 such that the two lines comes between the angles
∠3 and ∠10 are on the alternate sides of the transversal such that ∠3 is below the transversal and ∠10 is above the transversal
Therefore, ∠3 and ∠10 are alternate exterior angles.
Help me please. shoe steps
Answers
what is the probability that a randomly chosen return shows an adjusted gross income of $50,000 or more?
Answers
The probability that a randomly chosen return shows an adjusted gross income of $50,000 or more is 33.2%.
For mutually exclusive events, use the following addition rule:
P(A or B) = P(A) +P(B)
The corresponding probabilities is :
P( income > $50000) = P( >50)
= P(50 - 90) +P( 100 - 499) +P( ≥ 500)
= 0.215 + 0.100 +0.006
= 0.321
Therefore, the probability of a random selection returning is
P( income > 50000) = 0.321
Now ,
P( income ≥ 50000 and ≥ 100000 ) = P( > 100000)
= 0.100 + 0.006
= 0.106
The Probability Condition is:
P(A/B) = P(A and B) / P(B)
Therefore,
P( ≥ $100000 / $ $50000)
= P( ≥ $100000 and $ $50000)/ P( ≥ $50000)
= 0.106/ 0.321
≈ 0.3302
= 33.2%
Therefore, the conditional probability of earning at least $50000 and more is 33.2%
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Jacob and his 6 friends are at restaurant and split the bill evenly. If ecah person paid $20, what was the bill total?
Answers
Complete the statements.
f(4) is
f(x) = 4 when x is
Answers
F(x)=4 when x is 8
Hope this helps:)
The answer X is 8
Hope I helped
What is 2+2.2*46-13(41+3 x)-16x
Answers
Answer:
7912.8x
Step-by-step explanation:
First do what in the parenthesis (41+3x)=44x
Then what to the left of the ()
2+2.2*46-13=180.2
then multiply what you got in the () to what we just got
180.2*44x=7928.8x
finally we subtract it to the -16x
7928.8x-16x=7912.8x
If PQRS is a kite, find m angle Q
Answers
Answer:
Q = 35
Step-by-step explanation:
1. You add both (m)x values and y values making them equal to 180 creating a 2 step-equation: (7x+2) + (10x-31) making that 17x-33= 180
2. Now you have a 2 step-equation to solve: 17x-33 = 180-33=147
+-33 +-33
__________
17x = 147/17=21
/17 /17
3. From here with 21, knowing the kite must equal to 180, you add 21 to the other angle 124: 124+21=145
4. Seeing that you don't have a total of 180, you now subtract 145 from 180 in order to get the value of Q: 180-145= 35
Q= 35
Step-by-step explanation:
7x + 2 = 10x - 31
33 = 3x
x = 11
so, 7x + 2 = 7( 11 ) +2 = 79°
10x - 31 = 10( 11 ) - 31 = 79°
ΔP + ΔQ + ΔR + ΔS = 360°
79° + ΔQ + 79° + 124° = 360°
ΔQ + 282° = 360°
ΔQ = 360° - 282°
ΔQ = 78°
when the temperature is 35°C there are 7 million bacteria. How many millions of bacteria are there when the temperature is 38°C 
Answers
The number of millions of bacteria when the temperature is 38°C is 7, 600, 000 bacteria
What is proportion?Proportion can simply be defined as a mathematical comparison of numbers.
The different types of proportion in mathematics are;
Direct ProportionInverse ProportionCompound ProportionContinued ProportionFrom the information given, we have that;
When the temperature was 35 degree Celsius, the number was 7 million
Then, we have the representation given as;
35°C = 7, 000, 000
Then 38°C = x
cross multiply, we get;
x = 7, 000, 000 × 38/35
divide the values
x = 7, 600, 000 bacteria
Hence, the value is 7, 600, 000 bacteria
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1. below is a side-by-side bar chart of the data. descriptively, does the data suggest that there is an association between whether a penguin is banded and survival rate?
Answers
The complete question is :
What statistical tests and analysis can be conducted to determine whether there is a significant association between being banded and penguin survival rates, given a dataset with information on the number of banded and non-banded penguins that survived and did not survive?
Banded Not Banded
Survived 75 100
Did Not Survive 25 50
To determine if there is a significant association, statistical tests such as chi-squared test or Fisher's exact test can be used, to compare the observed proportions of survival and non-survival in banded and non-banded penguins to the expected proportions under the assumption of no association.
To answer the question of whether there is an association between being banded and survival rate, we can calculate the proportions of penguins that survived or did not survive in each group:
Banded Not Banded
Survived 0.75 0.67
Did Not Survive 0.25 0.33
From this table, it seems that a higher proportion of banded penguins survived compared to non-banded penguins. However, we cannot conclude that there is a definite association between being banded and survival rate based on this limited data. To make more definitive conclusions, we would need to conduct statistical tests and analysis.
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Which of the following statements are true?(Choose all correct answers)Methods cannot be written with parameters.Parameter values can never be used within the method code block.Methods can be written with any number of parameters.Methods can never be written with more than four parameters.Parameter values can be used within the method code block
Answers
The true statement is, Parameter values can be used within the method code block. (option e).
In computer programming, methods are used to group a set of instructions together that can be executed repeatedly. Parameters are used to pass values to a method so that the method can perform specific actions based on the values passed. Let's discuss the given statements one by one to determine which ones are true.
Parameter values can be used within the method code block.
This statement is true. Parameter values can be used within the method code block to perform specific actions. The parameter values can be manipulated or combined with other values to produce the desired result.
In summary, methods can be written with any number of parameters, and parameter values can be used within the method code block to perform specific actions. The number of parameters needed will depend on the specific task the method is designed to perform.
Hence the option (e) is correct.
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Pop is on sale at Save-U-Lots. Which pack has the lowest cost per unit?
A. 6- pack for $2. 49
B. 12-pack for $3. 99
C. 24-pack for $5. 49
Answers
In the case of a 24-pack for $5. 49, the cost of the unit is the lowest.
The cost per item is nothing to the amount of money invested in buying one item.
As we have 3 different scenarios:
Case A. 6- pack for $2. 49
As here. cost of 6 packs is $2.49, so for determining the cost of one pack we will divide $2.49 by 6.
So, the cost of 1 pack will be = 2.49/6 = 0.415 $/pack
B. 12-pack for $3. 99
As here. cost of 12 packs is $3.99, so for determining the cost of one pack we will divide $3.99 by 12.
So, the cost of 1 pack will be = 3.99/12 = 0.3325 $/pack
C. 24-pack for $5. 49
As here. cost of 24 packs is $4.49, so for determining the cost of one pack we will divide $5.49 by 24.
So, the cost of 1 pack will be = 5.49/6 = 0.22875 $/pack
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John works 40 hours per week at a rate of $20 per hour. He earns 1 1/2 times his regular pay for every hour worked over 40. What is his pay, in $, for a 46 hour work week?
Answers
what is 4h divided by 5?
Answers
5.30085603 × 10-34 m2 kg / s
Answer:
5.30085603 × 10-34 m2 kg / s
Step-by-step explanation:
30% × 750 =
(30 ÷ 100) × 750 =
(30 × 750) ÷ 100 =
22,500 ÷ 100 =
225;
Answers
Answer:
1.250
2.225
3.225
4.225
The radius of a circle is 17 m. Find its area in terms of pi.
Answers
Answer:
289m²
Step-by-step explanation:
Area of circle =πr²=π×17²=289m² when r=radius =17m
Find the slope of the line passing through the points(-3, 7) and (2, -6).
Answers
Answer:
-13/5
Step-by-step explanation:
The formula for slope is [ y2-y1/x2-x1 ].
-6-7/2-(-3)
-13/5
Best of Luck!
Solve the equation. y + 3 = –y + 9
Answers
Answer:
3
Step-by-step explanation:
y + 3 = –y + 9
=> y + y = 9 - 3
=> 2y = 6
=> y = 6/2
=> y = 3
Hope you understood!!
a(b+c/2)=x solve for a
Answers
Answer:
Divide each term in
a(b+c2) = x by b+c2
and simplify. a=2x2b+c
Step-by-step explanation:
Find the vector of the points p which divide Ac in the ratio 1:4
Answers
Answer:
Where is the points p and ration?
Step-by-step explanation:
Example: $2.21 + 8% tax = $2.3868, rounds to __________.
Answers
The equation in percentage given by, $2.21 + 8% tax = $2.3868 rounds to $2.4 to the nearest tenth.
Given an equation,
$2.21 + 8% tax = $2.3868
This is an equation which relates the cost including the percentage of tax.
When 2.21 is added to the tax amount, we get $2.3868.
2.21 + (0.08 × 2.21) = 2.3868
Here it is not mentioned up to what decimal we have to round the figure.
If 2.3868 is rounded to the nearest whole number, it becomes 2.
If 2.3868 is rounded to the tenth, it becomes 2.4.
If 2.3868 is rounded to the hundredth, it becomes 2.39.
Hence the rounded amount to the nearest tenth is $2.4.
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Jared is creating a flower garden in the shape of a triangle. Which could be the dimensions of the garden in feet?
Answers
Answer:
3 by 7 by 9
Step-by-step explanation:
What is an equation in standard form of an ellipse centered at the origin with vertices (± 13,0) and foci (± 12,0) ?
Answers
The equation of the ellipse in standard form, centered at the origin, with vertices (±13,0) and foci (±12,0), is: x^2/169 + y^2/25 = 1
To find the equation of an ellipse in standard form centered at the origin, we can use the following equation:
x^2/a^2 + y^2/b^2 = 1
where (a,0) are the coordinates of the vertices and (c,0) are the coordinates of the foci.
Given that the vertices are (±13, 0) and the foci are (±12, 0), we can determine the values of a and c as follows:
The distance between the origin and the vertices is equal to the value of 'a', so a = 13.
The distance between the origin and the foci is equal to the value of 'c', so c = 12.
Now we can substitute these values into the equation to obtain the final equation:
x^2/13^2 + y^2/b^2 = 1
Since the ellipse is centered at the origin, the value of 'b' would be equal to the square root of (a^2 - c^2):
b = √(13^2 - 12^2) = √(169 - 144) = √25 = 5
Therefore, the equation of the ellipse in standard form, centered at the origin, with vertices (±13,0) and foci (±12,0), is:
x^2/169 + y^2/25 = 1
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