We have designed a situation where the probability of one event (event A) is 1/5 and the probability of another event (event B) is 1/10.
How to quantify probability?To quantify the probability of each event, we can define the following events:
Event A: selecting a unit of product A at random and finding that it is defective.Event B: selecting a unit of product B at random and finding that it is defective.Then, the probability of event A is 1/5, since 1 in every 5 units of product A is defective. Similarly, the probability of event B is 1/10, since 1 in every 10 units of product B is defective.
Now, let's consider a scenario where the company receives an order for 100 units of products, with 60 units of product A and 40 units of product B. The company wants to determine the probability of the following events:
Event C: selecting a unit from the order at random and finding that it is defective.Event D: selecting a unit from the order at random and finding that it is not defective.To calculate the probability of event C, we need to consider the probability of selecting a defective unit from product A and from product B, and the proportion of each product in the order. Since the order has 60 units of product A and 40 units of product B, the probability of selecting a unit of product A is 60/100 = 3/5, and the probability of selecting a unit of product B is 40/100 = 2/5.
Using the probabilities of event A and event B, we can calculate the probability of selecting a defective unit from product A or from product B as follows:
Probability of selecting a defective unit from product A: 1/5Probability of selecting a defective unit from product B: 1/10Therefore, the probability of event C can be calculated as follows:
P(C) = P(A) * P(A in order) + P(B) * P(B in order)
= (1/5 * 3/5) + (1/10 * 2/5)
= 3/25
So the probability of selecting a defective unit from the order is 3/25.
To calculate the probability of event D, we can use the complement rule, which states that the probability of an event and its complement (i.e., the event not happening) add up to 1. Therefore, the probability of event D can be calculated as follows:
P(D) = 1 - P(C)
= 1 - 3/25
= 22/25
So the probability of selecting a unit from the order at random and finding that it is not defective is 22/25.
In summary, we have designed a situation where the probability of one event (event A) is 1/5 and the probability of another event (event B) is 1/10. We have also calculated the probability of two other events (event C and event D) in a scenario where a manufacturing company produces two types of products, with different probabilities of defects, and receives an order with a certain proportion of each product.
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Factor the expression completely. x^3 y^4 −x^4 y^4
The algebraic expression x³y⁴ - x⁴y⁴ is factorized to be x³y⁴(1 - x) using their highest common factor HCF
What is HCFThe H.C.F. defines the highest common factor present in between given two or more numbers or mathematical expression.
The two terms x³y⁴ and x⁴y⁴ of the algebraic expression x³y⁴ - x⁴y⁴ have their highest common factor to be x³y⁴ such that:
x³y⁴ × 1 = x³y⁴
x³y⁴ × x = x⁴y⁴
and
x³y⁴ - x⁴y⁴ = x³y⁴ × 1 - x³y⁴ × x
x³y⁴ - x⁴y⁴ = x³y⁴(1 - x)
Therefore, the algebraic expression x³y⁴ - x⁴y⁴ is factorized to be x³y⁴(1 - x) using their highest common factor HCF
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Please help
Nancy purchased a hot tub at a total price of $6995.
She made a $1200 down
payment and financed the rest at 10. 4% compounded monthly.
Nancy can repay
the loan in 36 months or 48 months.
How much interest will Nancy save is she
repays the loan in 36 months instead of 48 months?
First, we need to calculate the remaining balance after the down payment of $1200. The remaining balance is: $6995 - $1200 = $5795
To calculate the total interest for 36 months, we can use the formula:
I = P * r * t
Where:
I = total interest
P = remaining balance ($5795)
r = interest rate (10.4%/12)
t = number of months (36)
So the total interest for 36 months would be:
$5795 * (0.104/12) * 36 = $2,199.40
To calculate the total interest for 48 months, we can use the same formula but with a different value for t (48 months):
$5795 * (0.104/12) * 48 = $2,932.80
To find out how much Nancy will save by repaying the loan in 36 months instead of 48 months, we can subtract the total interest for 36 months from the total interest for 48 months:
$2,932.80 - $2,199.40 = $733.40
So, Nancy will save $733.40 in interest if she repays the loan in 36 months instead of 48 months.
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Determine the slope of a line that is perpendicular to a line with the slope 2/7
Answer:
-7/2
Step-by-step explanation:
The slopes of perpendicular lines are negative reciprocals of each other.
To find the reciprocal of a fraction, flip the fraction.
For the negative part, change the sign.
Slope of line: 2/7
Slope of perpendicular line: -7/2
There are 28 students in a class. Fourteen of those students are men.
What percent of the class are men ?
Answer: 50%
Step-by-step explanation:
If fourteen are men, and there are twenty-eight in the class, then the fraction that are men are -
14/28.
14/28 is 1/2 which is equal to 0.5
0.5 converted to percent is 50%
I took a random sample of size 49 students score from their sampling distribution test. The
score was selected from the Regular Statistics class. The mean of the score of the population of
Regular statistics is 63 and standard deviation is 14. What is the probability in the sample selected will have mean score more than 65.
The probability of a sample mean more than 65 is given as follows:
0.1587 = 15.87%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The parameters for this problem are given as follows:
[tex]\mu = 63, \sigma = 14, n = 49, s = \frac{14}{\sqrt{49}} = 2[/tex]
The probability of a sample mean above 65 is one subtracted by the p-value of Z when X = 65, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (65 - 63)/2
Z = 1
Z = 1 has a p-value of 0.8413
1 - 0.8413 = 0.1587 = 15.87%.
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oshua is 12 years old and his sister is three times as old as he. when joshua is 23 years old, how old will his sister be?
His sister will be 47 years old.
Now, According to the question:
To find Joshua's sisters age when Joshua is 23 years old. We are given that Joshua is currently 12 years old and that his sister is three times as old as he is.
3 × 12 = 36
We have that his sister's current age is 36 years old.
We want to know how old she will be when Joshua is 23 years old. Since Joshua is currently 12 years old,
23 - 12 = 11
We have that in 11 years, Joshua will be 23 years old.
So we want to know what his sister's age will be in 11 years.
To find this, we simply add 11 to her current age of 36.
36 + 11 = 47
We get that in 11 years, his sister will be 47 years old, so when Joshua is 23 years old, his sister will be 47 years old.
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I really need help with rate of change!!! Please helpppppp
Answer:
zero
Step-by-step explanation:
You want the rate of change between the points (3, 1) and (4, 1).
Rate of changeThe "rate of change" is also known as the "slope" of the line between the points. That is given by the formula ...
m = (y2 -y1)/(x2 -x1)
For your points, this is ...
m = (1 -1)/(4 -3) = 0/1 = 0
The rate of change is zero.
__
Additional comment
The y-value is constant. That means the equation of the line is y=1, a horizontal line. It does not rise or fall. Its rate of change is zero.
(a) how many paths are there from the point (0, 0) to the point (110, 111) in the plane such that each step either consists of going one unit up or one unit to the right? (b) how many paths are there from (0,0) to (210, 211), where each step consists of going one unit up or one unit to the right, and the path has to go through (110, 111)?
(a) The number of pathways in the plane from point (0, 0) to point (110, 111) when each step consists of walking one unit up or one unit to the right is known as the number of ways to go to a point in a grid using just right and up moves.
This is a classic combinatorial problem known as a binomial coefficient. The binomial coefficient C(110+111, 110) = C(221, 110) = 221!/(110!111!) is the number of ways to travel from (0, 0) to (110, 111).
(b) The number of paths from (0, 0) to (210, 111) where each step consists of walking one unit up or one unit to the right and the path must pass through (110, 111) is the product of two binomial coefficients.
First, as calculated in section 1, the number of pathways from (0, 0) to (110, 111) is C(110+111, 110) = C(221, 110). Second, there are C(210+211, 210) ways to get from (110, 111) to (210, 111). (210, 211). (421, 210). C(221, 110) * C is the total number of paths found by multiplying these two binomial coefficients (421, 210).
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Determine the solution to the inequality.
one third times the absolute value of the quantity x plus 1 end quantity is greater than or equal to 3
x ≤ −8 or x ≥ 8
x ≤ −10 or x ≤ 9
x ≤ −2 or x ≥ 2
x ≤ −10 or x ≥ 8
The solution of the inequality |x + 1| ≥ 3 is:
x ≥ 2 or x ≤ -4
How to solvethe inequality?Here we want to solve the absolute value inequality:
|x + 1| ≥ 3
The absolute value can be decomposed into two inequalities, these are:
(x + 1) ≥ 3
(x + 1) ≤ -3
Now we can solve these two inequalities to get:
x ≥ 3 - 1 = 2
x ≤ -3 - 1 = -4
Then the solution is:
x ≥ 2 or x ≤ -4
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Answer: Its D
Step-by-step explanation:
I looked up the answer
Rectangle J'K'L'M' shown on the grid is the image of rectangle JKLM after transformation. The same transformation will be applied on trapezoid STUV.
What will be the location of T' in the image trapezoid S'T'U'V'?
answers
12,6
12,7
16,7
16,6
Point T becomes (18, 2), which equals T', when we transform STUV using the technique above.
What is meant by transformation?Four distinct approaches to modify the position and/or shape of a point, line, or geometric figure are collectively referred to as transformations. The Pre-Image of the object is its initial shape, while the Image, after transformation, is the final shape and location of the thing.
The movement of two-dimensional figures about a plane or coordinate system is described by mathematical transformations. A preimage, also known as an inverse image, is a two-dimensional shape that exists without any change. After transformation, the figure is shown in the image.
If we pay attention to the transformation, it is obvious that every point in the rectangle JKLM is changed to a point that is 13 units to the right and 3 units to the bottom.
The T in STUV is currently at (5, 5).
When we transform STUV using the formula above, point T becomes (5 + 13, 5 - 3) (18, 2), which equals T'.
Therefore, the correct answer is option b. (18, 2).
The complete question is:
Rectangle J'K'L'M' shown on the grid is the image of rectangle JKLM after transformation. The same transformation will be applied to trapezoid STUV.
What will be the location of T' in the image trapezoid S'T'U'V'?
a. (18, −2)
b. (18, 2)
c. (15, −2)
d. (15, 2)
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Which inequality describes the relationship between points A and B on the number line?
A. A > B
B. B ≤ A
C. B > A
D. B = A
From the Number in the graph , the inequality that describes the relationship between points A and B on number line is (c) B > A .
In the Number Line we can see that , Both the points A and B are between 0 and 1 on the number line ,
We know that , On a number line , the further right we move the higher numerical values we get ;
On the number line the point B is further to the right , as well as closer to 1 than A , So , we can conclude that B is greater than A .
Therefore , The point B is greater than point A .
The given question is incomplete , the complete question is
Which inequality describes the relationship between points A and B on the number line ?
(a) A > B
(b) B ≤ A
(c) B > A
(d) B = A
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A local pizza shop has a membership program for frequent buyers. The membership costs $20 per month and members get a discounted price of $1.25 per slice of pizza. Jaya purchased a membership to this pizza shop. How much would Jaya have to pay the pizza shop if she bought 16 slices of pizza this month? What would be the monthly cost for
�
x slices of pizza?
Answer:
Step-by-step explanation:
a couple slices of pizza
Let us assume that you started a job on 08/21/2019. You graduated on 05/20/2022. How many days have you been working at the job as a student?Group of answer choices121512879051003
I began my job as a student on 08/21/2019 and worked for a total of 905 days until my graduation on 05/20/2022. This is calculated by taking the total number of days between the start and end date - 3 years - which is 1095, and then subtracting the weekends and holidays - 190 days - during that period. This demonstrates my commitment to my job as a student.
08/21/2019 - 05/20/2022
= 3 years
= 1095 days
- 190 days (weekends and holidays)
= 905 days
Starting on 08/21/2019, I have been working at my job as a student for 905 days as of 05/20/2022. This is determined by taking the total number of days - 3 years - between the start date and end date, which is 1095 days, and then subtracting 190 days for the weekends and holidays during that period. This leaves me with 905 days of work as a student.
I began my job as a student on 08/21/2019, and my graduation was on 05/20/2022. After calculating the total number of days between the two dates - 3 years - which is 1095, and then subtracting the weekends and holidays during that period - 190 days - I have worked as a student for 905 days up until my graduation date. This demonstrates the commitment and dedication I had to my job as a student.
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Find the area of a circle with radius, r = 7.27m. Give your answer rounded to 2 DP.
The area of a circle is given by the formula:
A = πr^2
Where A is the area of the circle, π is approximately 3.14 and r is the radius of the circle.
Given the radius, r = 7.27m, we can substitute this into the formula and calculate the area of the circle.
A = π * 7.27^2 = π * 52.5129
A = 165.9 m^2
The area of the circle is 165.9 m^2. Rounded to 2 decimal places, the area of the circle is 165.90 m^2
Hi,please help ! (see image!)
The following algebraic expressions are factorized using their highest common factor HCF:
a) x² - 2x = x(x - 2)
b) 6x² + 12x = 6x(x + 2)
c) 3x³ - 9x = 3x(x² - 3)
d) 4x² + 28x³ = 4x²(1 + 7x)
What is HCFThe H.C.F. defines the highest common factor present in between given two or more numbers or mathematical expression.
x² and 2x have HCF as x such that;
x² - 2x = x × x - 2 × x
x² - 2x = x(x - 2)
6x² and 12x have HCF as 6x such that;
6x² + 12x = x × 6x + 2 × 6x
6x² + 12x = 6x(x + 2)
3x³ and 9x have HCF as 3x such that;
3x³ - 9x = x² × 3x - 3 × 3x
3x³ - 9x = 3x(x² + 3)
4x² + 28x³ have HCF as 4x² such that;
4x² + 28x³ = 1 × 4x² + 7x × 4x²
4x² + 28x³ = 4x²(1 + 7x)
Therefore, the algebraic expressions are factorized using their highest common factor HCF to be:
a) x² - 2x = x(x - 2)
b) 6x² + 12x = 6x(x + 2)
c) 3x³ - 9x = 3x(x² - 3)
d) 4x² + 28x³ = 4x²(1 + 7x)
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If a mechanic rotates the octagonal nut shown clockwise around its center, what is the angle of rotation that will moves position 5 to position 8?
The angle of rotation that will move the clockwise position of 5 to 8 is 225 degrees.
What is rotation?The circular movement of an item about a center is referred to as rotation. Different forms can be rotated by an angle about their central point. A rotation is a map in mathematics. The rotation group of a certain space is made up of all the rotations that revolve around a fixed point and form a group beneath a structure.
The given nut is in the shape of an octagon.
The total angle of a polygon is 360 degrees.
An octagon has 8 sides, so each rotation of the nut will result in an angle of:
Rotation = 360 / 8
Rotation = 45 degrees.
To move the position of 5 to 8, a total of 5 rotations are required.
Total rotation = (45)(5)
Total rotation = 225 degrees.
Hence, the angle of rotation that will move the position of 5 to 8 is 225 degrees.
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1. Whitney buys a latte in a cylindrical cup that has a cardboard sleeve, so the cup isn't too hot to hold. If the sleeve has a diameter of 9 cm and a height of 5 cm, find the number of square centimeters of the cup covered by the sleeve
Please help immediately!!!
The number of square centimeters of the cup covered by the sleeve is 141.42 square cm
How to find the number of square centimeters of the cup covered by the sleeveFrom the question, we have the following parameters that can be used in our computation:
Height, h = 5 cm
Diameter, d = 9 cm
This means that the radius, r is
r = 9/2
r = 4.5 cm
Since the sleeve is a cylinder, we can use the formula for the lateral area of a cylinder to calculate the area of the sleeve:
Lateral area = 2 * pi * r * h
So in this case, the lateral area of the sleeve is:
2 * pi * (4.5) * 5 = 141.42 square cm
This is the area of the cup covered by the sleeve.
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question is on the picture
Answer:
C. √5 =2.236.
Step-by-step explanation:
it's the sq root of 2²+1² = 5.
Adam writes a number. The number is greater than 50 and less than 54. What numbers could Adam have written?Explain
The numbers is greater than 50 and less than 54 are 51, 52 and 53.
Now, According to the question:
A number is an arithmetic value used for representing the quantity and used in making calculations. A written symbol like “3” which represents a number is known as numerals. A number system is a writing system for denoting numbers using digits or symbols in a logical manner.
Adam writes a number.
The number is greater than 50 and less than 54.
Based on the given condition:
A number is > and < .
Then,
51, 52, and 53 are all greater than 50, but less than 54
Hence, The numbers is greater than 50 and less than 54 are 51, 52 and 53.
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Simplify 4(7 - 3) + 11.
Answer:
27
Step-by-step explanation:
First do the () part which is (7-3) equal 4×4 equal 16 so then u will add 16+11 getting 27
what is the dependent variable? what is the independent variable in this study? a. calorie resctrition b. weight loss c. randomized control trial d. body composition
A dependent variable is the variable that being check in a scientific experiment.
The dependent variable is "dependent" on the other independent variable. As the experimenter alter the independent variable, the change in the dependent variable is observed and recorded. When you take data in an experiment, the dependent variable is the one being advised.
A scientist is testing the effect of light and dark on the efforts of moths by turning a light on and off. The independent variable is the amount of light and the moth's reply is the dependent variable.
A change in the independent variable (total amount of light) straight source a change in the dependent variable (moth behavior).
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a population is a. always the same size as the sample. b. the same as a sample. c. the collection of all items of interest in a particular study. d. the selection of a random sample.
The population is the entire set of individuals or items of interest in a particular study, and it is not necessarily the same size as the sample which is a subset of the population.
Population is a term used to refer to the entire set of individuals or items that are of interest in a particular study. Population size is not necessarily the same as sample size. Sample size is the number of individuals or items that are selected from the population to participate in the study. The sample may be selected randomly, or it may be selected based on specific criteria. When collecting data, researchers use the sample as a representation of the population in order to identify patterns, relationships, and trends that can be used to make inferences about the population. When constructing a sample, it’s important to make sure that it is random and representative of the population, otherwise the results of the study may be biased.
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Determine if the given point is a solution of the system of inequalities.
Help please.
The inequality equations is
a) The point ( -9 , 4 ) lies on the inequality relation
b) The point ( 6 , -2 ) lies on the inequality relation
c) The point ( 0 , -4 ) does not lie on the relation
What is an Inequality Equation?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the inequality equation be represented as A
a)
Now , let the first point be represented as P ( -9 , 4 )
The shaded region is below 4 in the y axis and less than -4 in the x axis
So , the point ( -9 , 4 ) does lies on the inequality equation graph
b)
Now , let the first point be represented as Q ( 6 , -2 )
The shaded region is below -8 in the y axis and less than 8 and more than 4 in the x axis
So , the point ( 6 , -2 ) does lies on the inequality equation graph
c)
Now , let the first point be represented as R ( 0 , -4 )
The shaded region is above -8 in the y axis and more than -4 in the x axis and less than -1
So , the point ( 0 , -4 ) does not lie on the inequality equation graph
Hence , the inequality equations is solved
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a normal blood sugar range for someone without diabetes, 2 hours after eating, is less than 140 mg/dl. james is concerned about his health and measures and records his blood sugar 4 times a day for a week. the results are in the boxplot above. what is the minimum blood sugar reading james measured?
The minimum blood sugar reading that James measured was 92 mg/dl. This is based on the boxplot shown above, which shows the range of blood sugar readings that James recorded over the course of a week.
The boxplot shown above provides a graphical representation of the range of blood sugar readings that James measured over the course of a week. A boxplot is composed of five different components: the minimum, the first quartile (Q1), the median, the third quartile (Q3), and the maximum. The minimum is the lowest value in the dataset, and in this case, it is represented by the lowermost point of the boxplot. This point indicates that the minimum blood sugar reading that James measured was 92 mg/dl. This value is lower than the normal blood sugar range for someone without diabetes, which is less than 140 mg/dl, two hours after eating. This indicates that James's blood sugar levels are within a healthy range.
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how to graph
y=-1/2x + 3
y=5
Answer:
The graph would look like this
Step-by-step explanation:
Answer the question In the picture.
Concept of limits
For the trigonometric function lim x→(π/2) tan (x), the RHL and LHL are not equal to f(a), hence the limit does not exist.
What is trigonometric function?
Simply put, trigonometric functions also referred to as circular functions are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle.
The given trigonometric function is -
lim x→(π/2) tan (x)
To find the value of trigonometric function use x = π/2.
First deduce the right hand limit (RHL).
Right Hand Limit = lim h→0^+ tan [(π/2) + h]
= lim h→0^+ -cot h
= lim h→0^+ [(-cot h)/h] × h
= -1 × 0 = 0
Now deduce the left hand limit (LHL).
Left Hand Limit = lim h→0^- tan [(π/2) - h]
= lim h→0^- cot h
= lim h→0^- [(cot h)/h] × h
= 1 × 0 = 0
Thus, LHL = RHL.
Left hand limit = right hand limit = f(a)
If the above condition is satisfied then limit exists.
f(π/2) = lim x→(π/2) tan (x)
= tan (π/2)
= ∞
Left hand limit = right hand limit ≠ f(a)
Therefore, the limit does not exist.
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The teacher gave a true and false quiz where P(true) = 0.5 for each question. Interpret the likelihood that the first question will be true.
Likely
Unlikely
Equally likely and unlikely
This value is not possible to represent probability of a chance event.
Answer: Don't trust me on this.
Step-by-step explanation:
I want to say it will be equally unlikely and equally likley, because it's 0.5, which is half. (Tell me if im right.)
suppose the probability is 0.25 that a certain athlete wins in each race. find the expected number of races until she needs to run to win a race.
Answer:
4 races
Step-by-step explanation:
Four races is expected to win
P = 0.25 = 25% = 1/4
Hope this helps
the angle of elevation from the tip of a building's shadow to the top of the building is 63 degrees and the distance is 220 feet. find the height of the building to the nearest foot
The angle of elevation from the tip of a building's shadow to the top of the building is 63⁰. The height of the building is 432 ft.
The tip of the building's shadow, the top of the building, and the base of the building form a right triangle.
Angle of elevation is the angle formed an object is placed above the observer. It is the angle between the the line of sight and the horizontal line.
If we know the angle of elevation and the distance, we can compute the height of the building using trigonometric function.
tan α = y/x
Since it is a right triangle, using the trigonometric formula
height of the building / distance = tan 63⁰
height of the building / 220 = 1.96
height of the building = 220 x 1.96 = 432 feet.
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The length of a rectangle is 6 less than twice its width. The perimeter is 90. Find the dimensions of the rectangle
The length of the rectangle is 20 and the width is 13.
What are the dimensions?The perimeter of a rectangle = 2(length + width)
Width = w
Length = 2w - 6
90 = 2(w + 2w - 6)
In order to determine the value of w, take the following steps:
Divide both sides of the equation by 2
90/2 = w + 2w - 6
45 = w + 2w - 6
Combine and add similar terms:
45- 6 = w + 2w
39 = 3w
Divide both sides of the equation by 3
w = 39/3
w = 13
In order to determine the length, substitute for w in the equation that represents the length.
Length = 2(13) - 6
= 26 - 6
= 20
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