A rectangular solid has edges that are 10, 8, and 3 units long.
1. Draw the solid, showing the 10 x 8 face as the base. Find:
a. The lateral area
b. The total area
c. The volume
2. Repeat Exercise 1, but show the 10 x 3 face as the base.
a.
b.
c.
We are adjusting the original rectangular solid and here is what we have:
1. Rectangular solid showing 10x8 face as the base(a) The lateral area is the sum of the areas of the four sides, which are all rectangles. The two sides with dimensions 8 x 3 have an area of 8 x 3 = 24 square units each, and the two sides with dimensions 10 x 3 have an area of 10 x 3 = 30 square units each. Therefore, the lateral area is:
2(24) + 2(30) = 48 + 60 = 108 square units
(b) The total area is the sum of the areas of all six faces. The two faces with dimensions 10 x 8 have an area of 10 x 8 = 80 square units each, the two faces with dimensions 8 x 3 have an area of 8 x 3 = 24 square units each, and the two faces with dimensions 10 x 3 have an area of 10 x 3 = 30 square units each. Therefore, the total area is:
2(80) + 2(24) + 2(30) = 160 + 48 + 60 = 268 square units
(c) The volume is the product of the length, width, and height of the rectangular solid. Therefore, the volume is:
10 x 8 x 3 = 240 cubic units
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Directions: Use the information in the charts to answer the questions. Show your
work and include equations to show how you solved each problem. Refer to the unit
glossary terms to remind yourself of the measurement conversions.
Beverages
at the Store
2 pints of
milk
2 quarts of
orange juice
16 cups of
chocolate
milk
32 ounces of
lemonade
1. Julius is buying beverages for brunch. He needs to buy a total of 5
gallons of beverages. He decides to buy two containers of each
beverage. How many gallons of beverages did he buy?
Therefore , the solution of the given problem of equation comes out to be Julius thus purchased a total of 2 gallons of beverages.
What is an equation?In intricate algorithms, variable words are typically employed to demonstrate consistency between two opposing arguments. Equations are academic phrases that are used to demonstrate the equality of different academic figures. Consider the specifics associated with the x + 7 suggestions.
Here,
Julius needs to purchase a total of 5 gallons of beverages, therefore let's begin by converting the given measurements to gallons.
2 quarts of milk were given.
Orange juice, 2 quarts
16 cups of milk, chocolate
Lemonade, 32 ounces
The following conversion factors are available to us:
1 Pints = 1/8 gallon.
1/4 gallon = 1 quart.
1 cup = 1/16 gallon
1 ounce = 1/128 gallon.
2 pints of milk are equal to 1/8 gallon each pint, or
=> 2 pints * 1/8 gallon/pint = 1/4 gallon
2 quarts of orange juice converted to gallons:
=> 2 quarts * 1/4 gallon/quart = 1/2 gallon
16 cups of chocolate milk converted to gallons:
=> 16 cups * 1/16 gallon/cup = 1 gallon
How many litres of lemonade are in 32 ounces?
=> 32 ounces * 1/128 gallon/ounce = 1/4 gallon
Let's now calculate the total number of gallons of beverages Julius purchased:
=> 1/4 gallon (milk) + 1/2 gallon (orange juice) + 1 gallon (chocolate milk) + 1/4 gallon (lemonade) = 2 gallons
Julius thus purchased a total of 2 gallons of beverages.
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3√b in exponential form
^4√p7
in exponential form.
Answer:1111
Step-by-step explanation:
2298/24 what is the quotient step by step
2298 divided by 24 using long division shows what is the quotient and remainder while 2298 divided by 24 and the complete steps for how to find it.
Question:
2298/24 = (?)
what is 2298 divided by 24?
Answer:the quotient is 95 and the remainder is 18 when 2298 is divided by 24.
A convenience store collected data on its customers to determine the most popular items purchased. The manager of the convenience store created a table of the data they gathered.
Convenience Store Item Number of Purchases
Candy 75
Snacks 125
Automotive Supplies 100
Beverages 200
Which of the following circle graphs correctly represents the data in the table?
circle graph titled convenience store purchases, with four sections labeled candy 15 percent, snacks 20 percent, auto supplies 40 percent, and beverages 25 percent
circle graph titled convenience store purchases, with four sections labeled candy 30 percent, snacks 40 percent, auto supplies 20 percent, and beverages 10 percent
circle graph titled convenience store purchases, with four sections labeled snacks 20 percent, candy 40 percent, beverages 25 percent, and auto supplies 15 percent
circle graph titled convenience store purchases, with four sections labeled snacks 25 percent, candy 15 percent, beverages 40 percent, and auto supplies 20 percent
Candy accounts for 15% of the total purchases, snacks account for 25%, automotive supplies account for 20%, and beverages account for 40%.
Which of the following circle graphs correctly represents the data in the table?The correct circle graph representing the data in the table is:
circle graph titled convenience store purchases, with four sections labeled candy 15 percent, snacks 25 percent, auto supplies 20 percent, and beverages 40 percent.
This graph accurately represents the proportion of each item's purchases out of the total number of purchases. Candy accounts for 15% of the total purchases, snacks account for 25%, automotive supplies account for 20%, and beverages account for 40%.
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NASA is conducting an experiment to find out the fraction of people who black out at G forces greater than 6
. In an earlier study, the population proportion was estimated to be 0.33
.
How large a sample would be required in order to estimate the fraction of people who black out at 6
or more Gs at the 95%
confidence level with an error of at most 0.03
? Round your answer up to the next integer.
We need to select at least 754 people for the experiment to estimate the fraction of people who black out at G forces greater than 6 with an error of at most 0.03 and a 95% confidence level.
How to determine how large a sample would be required in order to estimate the fraction of people who black out at 6or more Gs
We can use the formula for the sample size required to estimate a population proportion with a specified margin of error and confidence level:
n = (Z^2 * p * (1-p)) / E^2
where:
Z = the z-score corresponding to the desired confidence level (95% confidence level corresponds to a z-score of 1.96)
p = the estimated population proportion from the earlier study
E = the desired margin of error
Substituting the given values, we get:
n = (1.96^2 * 0.33 * (1-0.33)) / 0.03^2
n = 753.69
Rounding up to the next integer, we need a sample size of 754. Therefore, we need to select at least 754 people for the experiment to estimate the fraction of people who black out at G forces greater than 6 with an error of at most 0.03 and a 95% confidence level.
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1. All numbered streets runs parallel to each other. Both 3rd and 4th Streets are intersected by King Ave. as shown:
(a) Suppose a car is traveling east on 4th Street and turns onto King Avenue heading northeast. What is the measure of the angle created by the car's turning? Explain your answer.
(b) Suppose a car is traveling southwest on King Avenue and turns left onto 3rd Street. What is the measure of the angle created by the car's turning? Explain your answer.
(c) Suppose a car is traveling northeast on King Avenue and turns right onto 3rd Street. What is the measure of the angle created by the car's turning? Explain your answer.
When the car travels east on 4th Street and turns onto King Avenue heading northeast, the angle created by the car's turning is a 45-degree angle.
When the car travels southwest on King Avenue and turns left onto 3rd Street, the angle created by the car's turning is a 135-degree angle.
When the car travels northeast on King Avenue and turns right onto 3rd Street, the angle created by the car's turning is a 45-degree angle.
How to get the Angle?(a) When the car travels east on 4th Street and turns onto King Avenue heading northeast, the angle created by the car's turning is a 45-degree angle. This is because the intersection of 4th Street and King Avenue creates a right angle, and the car turns northeast, creating another 45-degree angle with the horizontal 4th Street.
(b) When the car travels southwest on King Avenue and turns left onto 3rd Street, the angle created by the car's turning is a 135-degree angle. This is because the intersection of King Avenue and 3rd Street creates a right angle, and the car turns left, creating an additional 90-degree angle. Therefore, the total angle is 90 degrees + 45 degrees = 135 degrees.
(c) When the car travels northeast on King Avenue and turns right onto 3rd Street, the angle created by the car's turning is a 45-degree angle. This is because the intersection of King Avenue and 3rd Street creates a right angle, and the car turns right, creating another 45-degree angle with the horizontal 3rd Street.
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4x+3y=-23and-x+y=-8 algebra elimination
I hope this helps you.
you can check your ans. by sub. in the value of x and y into both the equation which must give you the same answer.
If P(A)=0.3, P(B)=0.2 and P(A∩B)=0.2 determine the following probabilities:
(a) P(A')
(b) P(A∪B)
(c) P(A'∩B)
(d) P(A∩B')
(e) P[(A∪B)']
The probabilities are as follows:
(a) P(A')= 0.7
(b) P(A∪B) = 0.3
(c) P(A'∩B) = 0
(d) P(A∩B') = 0.1
(e) P[(A∪B)'] = 0.7
What is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.
(a) P(A') = 1 - P(A) = 1 - 0.3 = 0.7
(b) P(A∪B) = P(A) + P(B) - P(A∩B) = 0.3 + 0.2 - 0.2 = 0.3
(c) P(A'∩B) = P(B) - P(A∩B) = 0.2 - 0.2 = 0
(d) P(A∩B') = P(A) - P(A∩B) = 0.3 - 0.2 = 0.1
(e) P[(A∪B)'] = 1 - P(A∪B) = 1 - 0.3 = 0.7
Note: P(A) represents the probability of event A occurring, P(B) represents the probability of event B occurring, and P(A∩B) represents the probability of both events A and B occurring simultaneously. The symbol '∪' represents the union of two events, and the symbol '∩' represents the intersection of two events. The complement of an event A is represented by A'.
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Find the area of a shaded region
Answer:
40 cm²
Step-by-step explanation:
you have to multiply the top of the triangle by the base(40) which is 80 then you divide by two since it's a triangle then you get 40 again since your finding the area you have to put the 2 above the cm
2. The designers need to know the total surface area of the
entire robot in order to determine painting costs. If it costs
$0.02 per square centimeter, determine the cost to paint
each action figure.
12 cm
3. The designers also need to determine the total amount
of plastic to be used in the molds for each robot. If each cubic centimeter of
plastic costs $0.03, determine the total cost to mold each action figure.
4. The designers are discussing the best figure to use for the neck of the robot.
They have narrowed their decision to three options: a right circular cone with
a radius of 1 cm and a height of 2 cm, a square pyramid with base edge 2 cm
and a height of 2 cm, and a right hexagonal pyramid with base edges of 1 cm
and a height of 2 cm. Which figure will cost the least amount to produce?
Justify your answer.
Answer:
it's complex but i will justify wait me
The diameter of a circle is 5 centimeters. What’s the radius? Give the exact answer in simplest form
Answer:
2.5cm
Step-by-step explanation:
you half the diameter to get the radius
Convert the following General Form Equations into Standard Form and then find the center and radius
Answer:
good luck
Step-by-step explanation:
Ricky would like to retire with an amount of 200,000 she found a bank that offers 9% interest compounded yearly and has an initial investment of 20,000.how much time will Ricky have to wait until she attains the 200,000 in this situation?
Ricky will have to wait for 26.78 years to have 200,000 in her account with this investment.
How do you calculate how long Ricky will wait for her investment to reach 200,000?In order to determine the time it takes for Ricky's initial investment to grow to the desired amount, we can use the compound interest formula: A = P(1 + r/n)^(nt)
Where:
A is the final amount in the account (in this case, 200,000)
P is the initial investment (in this case, 20,000)
r is the annual interest rate (in this case, 0.09 for 9%)
n is the number of times interest is compounded per year (in this case, 1 for yearly compounding)
t is the number of years
We are trying to solve for t, so we can rearrange the formula to:
t = ln(A/P) / (n * ln(1 + r/n))
Plugging in the values:
t = ln(200,000/20,000) / (1 * ln(1 + 0.09/1))
t = ln(10) / ln(1.09)
t ≈ 2.303 / 0.086
t ≈ 26.78
Ricky will have to wait approximately 26.78 years to have 200,000 in her account with this investment.
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Hurry help Greg plants a seed and as soon as the plant sprouts, he measures its height each day and records his data for two weeks. If the plant continues to grow the whole two weeks, what would a line graph of Greg's data look like?
It would be flat.
It would move downward.
It would go up and down.
It would move upward.
The line graph of Greg's data wood look like "It would move upward."
What is graph?A graph is a visual representation of data that shows the relationship between two or more variables. There are several types of graphs that can be used to display data
If Greg is measuring the height of the plant each day and the plant is continuing to grow for two weeks, then the line graph of his data would move upward. The graph would show an increasing trend as the plant grows taller each day. Therefore, the correct answer is "It would move upward."
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3. How many ways can you line up 7 books on a shelf?
Answer:
There are 5040 different ways to arrange the 7 books on a shelf.------------------------------
Use the formula for permutations:
n! = n × (n - 1) × (n - 2) × ... × 1, where n is the number of objects and ! denotes a factorial.The number of objects is n = 7 books.
Calculate the factorial:
7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040A savings account earns an interest rate of 1.625 % compounded quarterly for an account with an initial deposit of $ 2 , 225 . How much money will be in the account after 6 years? Round your answer to the nearest hundredth.
The balance in the account after 6 years is $2,466.69.
What is compound interest?
Compound interest is when you earn interest on both the money you've saved and the interest you earn.
We can use the formula for compound interest to find the balance in the savings account after 6 years:
[tex]A = P(1 + r/n)^{(nt)}[/tex]
where:
A is the balance in the account after t years
P is the initial deposit, which is $2,225
r is the annual interest rate, which is 1.625%
n is the number of times the interest is compounded per year, which is 4 (since it's compounded quarterly)
t is the number of years, which is 6
Plugging in these values, we get:
[tex]A = 2,225(1 + 0.01625/4)^{(4*6)}\\A = 2,225(1.0040625)^{24}[/tex]
A = 2,225(1.108227)
A = 2,466.69
Hence, the balance in the account after 6 years is $2,466.69.
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Hello, I am confused on how to answer this question.
Answer: x=14
Step-by-step explanation:
cb=10.
ac=14
The value of X will be 14.
This is a simple mathematics problem that can be solved by using ratios.
Given, AC : BC : AB = 7 : 5 : 8
AC = X ; BC = 10 ; AB = X + 2
AC/ BC = X/ 10 = 7/5 (Ratios can also be represented as fractions)
X/10 = 7/5
On Transposing,
5X = 70
X = 70/5
X = 14
Alternatively,
BC/AB = 5/8 = 10/ (X + 2)
5/8 = 10/ (X + 2)
On Transposing,
80 = 5X + 10
5X = 70
X = 14
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Pls help with this question
The plane degrees off course is 6.79 degrees off at a speed of 541. 92 km / hr relative to the ground.
How to find the degrees off course ?To find the airplane's course deviation and its ground speed, we need to first determine the velocity vectors of the airplane and the wind.
W x = W x cos(225) = 90 x cos(225) = -63.64 km/hr
Wy = W x sin(225) = 90 x sin(225) = -63.64 km/hr
Magnitude: |R| = sqrt(Rx^2 + Ry^2) = √(536.36^2 + (-63.64)^2) = 541.92 km/hr
Direction: θ = arctan(Ry / Rx) ≈ arctan (-63.64 / 536.36) = -6.79 degrees
So, the airplane is 6.79 degrees off course, and its ground speed is 541.92 km/hr.
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The first three terms of a sequence are given. Round to the nearest thousandth (if necessary). 12 , 17 , 22 36th term
Answer:
the 36th term is 187.
Step-by-step explanation:
To find the 36th term of a sequence, we need to know the rule that generates the sequence. Without that rule, we cannot find the 36th term.
However, if we assume that the sequence is an arithmetic sequence (meaning that there is a common difference between consecutive terms), we can use the given terms to find the common difference and then find the 36th term.
The common difference is found by subtracting the second term from the first term, or the third term from the second term.
Using the first and second terms, we get:
17 - 12 = 5
Using the second and third terms, we get:
22 - 17 = 5
Since both calculations give the same result, we can be confident that the common difference is 5.
Therefore, to find the 36th term, we can use the formula for the nth term of an arithmetic sequence:
an = a1 + (n - 1)d
where an is the nth term, a1 is the first term, n is the term number, and d is the common difference.
Using a1 = 12, d = 5, and n = 36, we get:
a36 = 12 + (36 - 1)5
a36 = 12 + 175
a36 = 187
So, if the sequence is an arithmetic sequence with a common difference of 5, then the 36th term is 187.
6. Two out of every five Canadians read at least 10 books a year. What percent of Canadians read at least 10 books a year?
Answer:
40%
Step-by-step explanation:
2/5=x/100
cross multiply and you get 5x=200
by isolation the variable you will get x=40
therefore, 40% of Canadians read at least 10 books a year
Michelle is building a car for the local soap box derby. The floor boards of her car need to be 2.2 meters long. If she has 13.2 meters of wood, how many floor boards can she make? 20 boardo
Michelle can make 6 floor boards for her car.
How many times does 2.2 meters fit into 13.2 meters?To determine how many floor boards Michelle can make, we need to divide the total length of wood she has (13.2 meters) by the length of each floor board (2.2 meters).
The number of floor which boards Michelle can make is:
= 13.2 meters / 2.2 meters/floor board
= 6 floor boards
Therefore, Michelle can make 6 floor boards for her car using the 13.2 meters of wood she has.
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(6x^2+10x-7) + (-x^2-8x)
For the given expression, the addition of coefficients is [tex]5x^2 + 2x - 7[/tex].
What are coefficients?In algebra, a coefficient is a numerical or constant quantity placed before and multiplying the variable in an algebraic expression. In other words, it is the number that is being multiplied by the variable.
What is addition?Addition is a basic mathematical operation that combines two or more numbers or quantities to produce a sum. It is denoted by the plus sign (+). When two or more numbers are added, the result is called the sum or total.
According to given information:First, we need to combine like terms by adding the coefficients of terms with the same variable(s) raised to the same power.
[tex](6x^2 + 10x - 7) + (-x^2 - 8x)[/tex]
[tex]= 6x^2 + (-x^2) + 10x + (-8x) - 7[/tex] (grouping like terms together)
[tex]= (6x^2 - x^2) + (10x - 8x) - 7[/tex] (rearranging terms)
[tex]= 5x^2 + 2x - 7[/tex] (combining the coefficients)
Therefore, the final answer for the addition of coefficients is [tex]5x^2 + 2x - 7.[/tex]
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please help me answer this
The prompt that examines linear functions and ordered pairs are given below.
What is the explanation for the above response?1) Here are the ordered pairs for each point:
Point A: (4, 9)
Point B: (6, 3)
Point C: (1, 3)
Point D: (8, 7)
Point E: (8, 9)
See the attached graph.
2) Part A: The completed table and graph for Derek is given as attached.
Part B: Derek makes 10 bracelets in 5 hours.
3) The ordered pairs are given in the labelled graph accordingly.
4) Deanna's coordinates plane is labelled and attached accordingly. The correct answer is Option B (5,8)
5) The other ordered pairs that could be the vertext are Options A - E. See the attached image (Miguel's Squre
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. (Adapted from Terence Blows, Northern Arizona University.) Classify as in Exercise 6 but for the following circumstances. a. The amount of caffeine in the bloodstream decreases by 50% every 5 hours or so after stopping drinking coffee. b. The amount of trash in a landfill increases by 350 tons per week. c. The amount of alcohol in the bloodstream decreases by 10 grams (the amount in a standard drink) per hour after stopping drinking. d. Your age increases every day.
The statements are classified as Exponential decay and Linear growth.
What are the classification of the statements?
a. Exponential decay: The amount of caffeine in the bloodstream decreases by 50% every 5 hours, which indicates an exponential decay process where the quantity decreases at a constant percentage rate over time.
b. Linear growth: The amount of trash in a landfill increases by 350 tons per week, which indicates a linear growth process where the quantity increases by a constant amount over time.
c. Exponential decay: The amount of alcohol in the bloodstream decreases by 10 grams (the amount in a standard drink) per hour after stopping drinking, which indicates an exponential decay process where the quantity decreases at a constant percentage rate over time.
d. Linear growth: Your age increases every day, which indicates a linear growth process where the quantity (age) increases by a constant amount (1 day) over time.
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If 1 US dollar in 1860 had the same purchasing power as $28.95 in 2018, what is the yearly average inflation rate during that time?
A. 2.15%
B. 2.75%
C. 3.15%
D. 3.75%
Step-by-step explanation:
From 1860 to 2018 is 158 years
Use compounding formula
$ 28.95 = $ 1 ( 1 +i) ^158 where i is decimal inflation rate %
[tex]\sqrt[158]{28.95}[/tex] = 1 + i
i = .0215 = 2.15 %
coordinate plane with points at A 0 comma 2 and B 2 comma 0 intersected by line f Dilate line f by a scale factor of one half with the center of dilation at the origin to create line f′. Where are points A′ and B′ located after dilation, and how are lines f and f′ related? The locations of A′ and B′ are A′ (0, 2) and B′ (0, 0); lines f and f′ intersect at point A. The locations of A′ and B′ are A′ (0, 1) and B′ (1, 0); lines f and f′ are parallel. The locations of A′ and B′ are A′ (0, 0) and B′ (2, 0); lines f and f′ intersect at point B. The locations of A′ and B′ are A′ (0, 2) and B′ (2, 0); lines f and f′ are the same line.
The answer of the given question based on the graph is , The locations of A′ and B′ are A′ (0, 1) and B′ (1, 0); lines f and f′ are parallel.
What is Scale factor?A scale factor is a number that scales, or multiplies, a quantity by some factor. It is used in mathematics to describe the relationship between corresponding measurements of two similar figures, such as triangles or rectangles.
To dilate line f by scale factor of one half with center of dilation at origin, we multiply coordinates of each point on line f by 1/2.
The equation of line f can be found by using the points A and B:
slope of line f = (0 - 2)/(2 - 0) = -1
y-intercept of line f = 2
Therefore, the equation of line f is y = -x + 2.
To find the coordinates of A' and B' after dilation, we can apply the dilation factor to each point:
A' = (0, 2)*1/2 =(0, 1)
B' = (2, 0)*1/2 =(1, 0)
So A' is located at (0, 1) and B' is located at (1, 0) after dilation.
Now let's analyze the relationship between lines f and f'. The dilation was centered at the origin, so the origin is a fixed point of the dilation. This means that the point where lines f and f' intersect must be the origin.
If we plug in x = 0 into the equation of line f, we get y = 2. This means that point A is located at (0, 2) and intersects with line f at y = 2. After dilation, point A' is located at (0, 1), which means that lines f and f' intersect at point A.
To determine the relationship between lines f and f', we can compare their equations. The equation of f' can be found by using the points A' and B':
slope of f' = (0 - 1)/(1 - 0) = -1
y-intercept of f' = 0
Therefore, the equation of f' is y = -x.
Comparing the equations of f and f', we can see that they have the same slope of -1, which means they are parallel. Therefore, the correct answer is: The locations of A′ and B′ are A′ (0, 1) and B′ (1, 0); lines f and f′ are parallel.
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Can someone help me with this problem, and explain how to solve it?
Thus, the height of flagpole from the ground is found as 23.34 feet.
Explain about the angle of elevation:The measurement of the angle between a person's eyes' line of sight to anything above and the horizontal line is known as the angle of elevation.
The movement of the observer's eyes determines the elevation angle. The angle of elevation is the angle formed by the line of sight and the horizontal line when a viewer is looking up at an object.
Given data:
height of boy = 5 ftDistance of boy from flagpole = 30 ft angle of elevation = 35 degreesLet the height of pole above the boy be 'h'feet.Using the trigonometric ratios in the right triangle ABE.
tan 35 = h / 30
h = 30* tan(35)
h = 18.34
Height of flagpole = 18.34 + 5 = 23.34 feet
Thus, the height of the flagpole from the ground is found as 23.34 feet.
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i have 60 square feet of paper to wrap a box in the shape of a right rectangular prism the height of the box is 1 2/3 feet the width is 4 feet and the length is 5 1/2 feet what percent of the box will remain unwrapped if i use all the paper i has available
The percent of the box that will remain unwrapped by the 60 square feet of paper is about 20.70%
What is a percentage?A percentage is a proportion of a number expressed as fraction of a 100
The dimensions in mixed fractions can be expressed as follows;
Height of the box = 1 2/3 feet = 5/3 feet
Width of the box = 4 feet
Length of the box = 5 1/2 feet = 11/2 feet
Surface area of the box, A = 2 × (5/3) × 4 + 2 × 4 × 11/2 + 2 × (5/3) × 11/2 = 227/3 = 75 2/3 square inches
The percent of the box that will remain unwrapped is therefore;
Percentage = 60/(227/3) × 100 ≈ 79.3%
The percentage of the box that will remain unwrapped is about (100 - 79.3)% = 20.70%
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