The function that models this situation is f(n) = -3n + 24.
To find the function, we need to analyze the relationship between the number of meals dispensed (n) and the amount of pet food remaining (f(n)).
1. Observe the change in f(n) when n increases by 1 meal. From n=1 to n=3, f(n) decreases from 21 to 15, a change of -6. From n=6 to n=7, f(n) decreases from 6 to 3, a change of -3.
2. The decrease in f(n) is not constant, so the function is not linear. However, the decrease becomes smaller as n increases.
3. Consider the average rate of change in f(n) per meal: (-6/2) = -3, (-3/1) = -3.
4. Since the average rate of change is constant, the function is linear.
5. The function has the form f(n) = -3n + b. To find b, plug in the value of n and f(n) from the table: 21 = -3(1) + b, which gives b = 24.
6. Therefore, the function that models this situation is f(n) = -3n + 24.
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Which set of ordered pairs represents a proportional relationship? A. {(4, 1), (0, 0), (6, 2), (8, 4)} B. {(2, 1), (4, 3), (8, 9), (16, 27)} C. {(2, 3), (6, 9), (10, 15), (22, 33)} D. {(4, 9), (7, 12), (10, 15), (18, 23)}
Answer:
C.
Step-by-step explanation:
3 = 1.5 * 2
9 = 1.5 * 6
15 = 1.5 * 10
33 = 1.5 * 22
The equation y = –1.25x + 13.5
represents the gallons of water
y left in an inflatable pool after
x minutes. Select all the true
statements.
A. When the time starts, there
are 13.5 gallons of water in
the pool.
B. The tub is being filled at a rate
of 1.25 gallons per minute.
C. The water is draining at a rate
of 1.25 gallons per minute.
D. When the time starts, there
are 1.25 gallons of water in
the pool.
E. The water is draining at a rate
of 13.5 gallons per minute.
F. When the time starts, there
are 12.25 gallons of water in
the pool.
The two true statements are:
A "When the time starts, there are 13.5 gallons of water in the pool."
C "The water is draining at a rate of 1.25 gallons per minute."
Which statements are true?Here we have the linaer equation y = –1.25x + 13.5 that represents the gallons of water y left in an inflatable pool after x minutes.
And we want to see which of the given statements are true.
We can see that the slope is -1.25, this means that the volume of water is reducing (due to the negative sign) then the statement C is true.
We also can see that the y-intercept is 13.5, that would be the initial volume of water in the pool, then the statement A "When the time starts, there are 13.5 gallons of water in the pool." is also true.
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The volume of this cone is 339. 12 cubic feet. What is the height of the cone?
Answer:
Not enough info
Step-by-step explanation:
Volume of cone formula is: V = 1/3 π r²h
You did not give the radius so it is not possible to find the solution
If radius is given, isolate h by dividing the V by 1/3 π r²
Then simplify the left side of the equation and that is what h is
In the last hour, Ellie observed 32 monarchs, 56 gulf fritillaries and 8 giant swallowtails visit her butterfly garden. If 48 butterflies visit her garden, how many can we expect be giant swallowtails
We can expect 4 giant swallowtails to visit Ellie's garden.
In total, there were 96 butterfly visits (32 monarchs + 56 gulf fritillaries + 8 giant swallowtails).
Now, we can calculate the probability of a giant swallowtail visit:
Probability
= (number of giant swallowtails) / (total butterfly visits)
= 8/96
= 1/12
Given that 48 butterflies visit her garden, we can expect the number of giant swallowtails to be:
Expected giant swallowtails
= (total butterflies) × (probability of giant swallowtails)
= 48 × (1/12)
= 4
So, we can expect approximately 4 giant swallowtails to visit Ellie's garden out of the 48 butterflies.
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Use the drop down to answer the question about converting 0. 64 to a fraction.
How many repeating digits are in 0. 64 ?
What value is multiplied on both sides of the equals sign?
What fraction represents 0. 64 ?
The fraction value of 0.64 is 16/25 using the greatest common factor method to represent. There are no repeating digits in value.
The given decimal value = 0.64
There are no repeating numbers in the given decimal number 0.64.
To convert the given number into a fraction, we need to multiply the value with 10 on both sides to move the decimal point two places to the right.
0.64 × 100/100 = 64/100
Now simply this value by dividing both the numerator and denominator with the greatest common factor of both values. The greatest common factor is 4.
64/100 = 16/25
Therefore, we can represent the fraction value of 0.64 as 16/25.
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A bookstore conducted a survey to see how many books their customers bought in a year. 100 customers were chosen at random. 30% of customers bought 3 books per year, 25% of customers bought 5 books per year, and 45% of customers bought 6 books per year. What was the average number of books bought per year?
Question 1 options:
4. 50
5. 75
4. 85
The average number of books bought per year by customers in the survey is approximately 4.85 books.
To find the average number of books bought per year, we need to calculate the mean of the data set. We can do this by using the formula:
Average = (Sum of all data points) / (Number of data points)
However, we do not have the actual number of data points. Instead, we have percentages. Therefore, we need to convert the percentages into actual numbers.
Out of 100 customers surveyed:
30% bought 3 books, which is equal to 30/100 x 100 = 30 customers
25% bought 5 books, which is equal to 25/100 x 100 = 25 customers
45% bought 6 books, which is equal to 45/100 x 100 = 45 customers
Now, we can calculate the average number of books bought per year using the formula mentioned earlier:
Average = (30 x 3) + (25 x 5) + (45 x 6) / (30 + 25 + 45)
Simplifying the above equation, we get:
Average = (90 + 125 + 270) / 100
Therefore, the average number of books bought per year is:
Average = 485/100
Average = 4.85 books per year (rounded to two decimal places)
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As a contestant on a televised game show, lucy gets to spin the big prize wheel, which has a radius of 2 yards. what is the prize wheel's area?use 3.14 for .
The prize wheel's area is approximately 12.56 square yards.
The area of a circle can be calculated using the formula A = πr², where A represents the area, r represents the radius, and π is approximately 3.14. In Lucy's case, the big prize wheel has a radius of 2 yards.
To find the area of the prize wheel, we can plug the radius value into the formula:
A = π(2 yards)²
Squaring the radius (2 yards) gives us:
A = π(4 square yards)
Now, we can multiply by the given value of π (3.14):
A = 3.14 × 4 square yards
Finally, multiplying these values together, we get:
A = 12.56 square yards
Therefore, the area of the prize wheel is approximately 12.56 square yards. This calculation helps us understand the size of the prize wheel, which can be useful for various purposes such as determining the space required for the game show set or designing the prize sections on the wheel.
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Dado un triángulo equilatero de lado 4cm, calcula su altura. encuentra su área
The height of the triangle is given as follows:
[tex]h = 2\sqrt{3}[/tex] cm.
The area of the triangle is given as follows:
[tex]A = 4\sqrt{3}[/tex] cm².
What is the Pythagorean Theorem?The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
The theorem is expressed as follows:
c² = a² + b².
In which:
c is the length of the hypotenuse.a and b are the lengths of the other two sides (the legs) of the right-angled triangle.Considering an equilateral triangle, in which all the side lengths are of 4, we have a right triangle in which:
The sides are 2 cm and the height h.The hypotenuse is of 4 cm.Hence the height is obtained as follows:
h² + 2² = 4²
h² = 12
[tex]h = \sqrt{3 \times 4}[/tex]
[tex]h = 2\sqrt{3}[/tex] cm
The area of a triangle is given as half the multiplication of the base and of the height, hence:
[tex]A = 0.5 \times 4 \times 2 \sqrt{3}[/tex]
[tex]A = 4\sqrt{3}[/tex] cm².
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Hello, pleas help me with this geometry question. It’s about the area of sectors. Thanks :) (question in image below).
Answer:
39.27 square units
Step-by-step explanation:
In circle E with m∠DEF = 70∘ and DE=8, we want to find the area of sector DEF. To do this, we can use the formula for the area of a sector:
A_sector=1/2 r^2⋅
α
where r is the radius of the circle and α is the central angle in radians. In our case, r=8 and α=70 ∘ ⋅ π/180∘ = 7π/18 radians
Now, we can plug these values into the formula:
A_sector = 1/2(8^2) ⋅ 7π/18 = 32 ⋅ 7π/18 ≈ 39.27
So, the area of sector DEF is approximately 39.27 square units, rounded to the nearest hundredth.
The area of sector DEF in circle E is approximately 6.10 square units, rounded to the nearest hundredth.
To find the area of sector DEF in circle E, we need to use the formula for the area of a sector:
Area of sector = (Central angle / 360°) * π * r^2
where "Central angle" is the measure of angle DEF in degrees, "r" is the radius of the circle (DE in this case).
Given that m/DEF = 70° and DE = 8, we can calculate the area of sector DEF as follows:
Area of sector = (70° / 360°) * π * 8^2
Now, perform the calculations step by step:
Area of sector = (70/360) * π * 64
Area of sector = (7/36) * π * 64
Area of sector ≈ 3.14 * (7/36) * 64
Area of sector ≈ 3.14 * 1.9444
Area of sector ≈ 6.10 (rounded to two decimal places)
Therefore, the area of sector DEF in circle E is approximately 6.10 square units, rounded to the nearest hundredth.
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can someone help with this please
Answer:
shape a is 20 cm squared
Step-by-step explanation:
shape a is a parallogram, A =b×h. 5x4=20
shape b is a trapezoid. The picture is cut off but here are the steps for you to solve. A=0.5h(base1+base2) count the number of squares on the top and bottom of the shape. I can see the top is 2, you will need to tfind the length of the bottom base.then count the height, how far to get from the bottom to top, here it is 4.
area=0.5*4(2+bottom base) simply and that's your answer! Don't forget your units
Box plot percentage of data values are greater than 16?
The percentage of the data values that are greater than 16, as shown in the box plot is: 75%.
What is a Box Plot?A box plot shows how the data points of a data set are distributed, in such a way that, 25% of the data points lie below the lower quartile, % lie below the median, and 75% lie below the upper quartile.
In the box plot given, the values that are greater than 16 lie above the upper quartile, which equals about 75% of the data values.
Therefore, the percentage of the data values that are greater than 65, as shown in the box plot is: 75%.
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ldentify the relationship between the angles. y : x
Answer:
there both symmetrical
Answer:
Congruent
Step-by-step explanation:
When visualizing how two angles are related, try squashing the two parallel lines into each other. When you do that with these angles, they go from appearing like =\= to appearing like -\-, with x and y being catty-corner from each other.
Because the parallel lines are straight, x and y are both half of a pair that adds up to 180. However, x and y aren't sharing a straight line, so they cannot add up to 180 with each other. That leaves only one possibility, that x and y have the same angle measure.
For the pair of similar figures, use the given areas to find the scale factor from the figure on the left to the figure on the right. Write your answer as a fraction, if necessary.
scale factor =
Find the value of x to the nearest tenth. X= m
The value of x in the similar figures is 2.33
When two figures have the same shape but their sizes are different, then such figures are called similar figures
The two polygons are similar
We have to find the value of x
Let us form a proportional equation
4590/21=510/x
4590x=21×510
4590x=10710
Divide both sides by 4540
x=10710/4590
x=2.33
Hence, the value of x in the similar figures is 2.33
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please help!
Given YZ tangent to ⊙J at point Y and m∠WYZ = 104, what is mWXY?
The measure of the angle WXY is 152 degrees
Calculating the measure of the angle WXY?From the question, we have the following parameters that can be used in our computation:
Line segment YZ tangent to J at point Y The measure of m∠WYZ = 104,Using the above as a guide, we have the following:
m∠MYW = 104 - 90
m∠MYW = 14
The inscribed angle opposite to the same arc is half of the external angle
So, we have
mw = 2 * m∠MYW
mw = 2 * 14
mw = 28 degrees
Also, we have
my = 180 degrees
So, we have
Angle WXY = 180 - 28
Evaluate the difference
Angle WXY = 152
Hence, the measure of the angle is 152 degrees
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Fruit fly thorax lengths fruit flies are used frequently in genetic research because of their quick reproductive cycle. the length of the thorax (in millimeters) was measured for each fly in a random sample of 49 male fruit flies. the mean length was a=0.8004 mm, with a standard deviation of 8 = 0.0782 mm. a. construct and interpret a 90% confidence interval for the true mean thorax length of a male fruit fly.
The confidence level for length of the thorax of 49 fruit fly males is (0.7820 mm, 0.8188 mm).
Here the sample size (n=49), the sample mean (a=0.8004 mm), and the sample standard deviation (s=0.0782 mm), we can calculate the confidence interval as follows:
1. Determine the critical value (z-score) for a 90% confidence level. You can use a z-table or calculator to find the z-score, which is approximately 1.645.
2. Calculate the margin of error using the z-score, sample standard deviation, and sample size:
Margin of Error = z-score * (s / √n)
Margin of Error = 1.645 * (0.0782 / √49)
Margin of Error ≈ 0.0184 mm
3. Add and subtract the margin of error from the sample mean to obtain the confidence interval:
Lower Limit = a - Margin of Error = 0.8004 - 0.0184 ≈ 0.7820 mm
Upper Limit = a + Margin of Error = 0.8004 + 0.0184 ≈ 0.8188 mm
So, the 90% confidence interval for the true mean thorax length of a male fruit fly is approximately (0.7820 mm, 0.8188 mm). This means that we are 90% confident that the true mean thorax length of a male fruit fly falls within this range.
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Brooke bought a condominium for $413,600. She made a 9% down payment and financed the remaining amount using a 25-year fixed-rate mortgage at 5. 2%. The monthly payment is $2,244. Brooke will pay for one discount point, a 0. 75% origination fee, the brokerage fee, state documentary taxes on the deed and the mortgage, and the intangible tax. • Discount points equal 1% of the mortgage amount. Documentary stamp tax on deed is $0. 70 per $100 or portion thereof. • Documentary stamp tax on mortgage is $0. 35 per $100 or portion thereof. • Mortgage broker fee is $175 plus 5% of the mortgage amount. • Intangible tax is 0. 2% of the mortgage amount. What is the total amount of the principal, interest, down payment, and fees described for Brooke's condominium? (4 points) $743,687. 00 $807,569. 73 $481,369. 73 $740,969. 73
The total amount of the principal, interest, down payment, and fees described for Brooke's condominium is $1,154,091.59
Find out the total amount of the principal and interest down payment, and fees?The first step is to calculate the mortgage amount, which is the purchase price minus the down payment:
Mortgage amount = $413,600 - 9% of $413,600 = $376,576
Next, we need to calculate the total cost of the fees and charges:
Discount points = 1% of $376,576 = $3,766
Origination fee = 0.75% of $376,576 = $2,823.42
Documentary stamp tax on deed = $0.70 per $100 or portion thereof, so for $413,600 it would be:
$0.70 * ($413,600 / $100) = $2,895.20
Documentary stamp tax on mortgage = $0.35 per $100 or portion thereof, so for $376,576 it would be:
$0.35 * ($376,576 / $100) = $1,318.02
Brokerage fee = $175 + 5% of $376,576 = $19411.8
Intangible tax = 0.2% of $376,576 = $753.15
Now we can calculate the total cost of the principal and interest payments over the life of the mortgage. We'll use a mortgage calculator to do this, based on the mortgage amount, interest rate, and term:
Total mortgage payments = $2,244 * 12 months * 25 years = $673,200
Finally, we can add up all of these amounts to get the total cost of the principal, interest, down payment, and fees:
Total cost = Purchase price + Down payment + Mortgage payments + Discount points + Origination fee + Documentary stamp tax on deed + Documentary stamp tax on mortgage + Brokerage fee + Intangible tax
Total cost = $413,600 + $37,224 + $673,200 + $3,766 + $2,823.42 + $2,895.20 + $1,318.02 + $19,411.80 + $753.15
Total cost = $1,154,091.59
Therefore, we got a total cost of $1,154,091.59
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Rita and Jan are working on a school project together. Rita has completed 0.3 of her portion, and Jan has completed a portion as well. Use the model to complete the equation below and find how much of the total project Rita and Jan have completed.
answer the question.
Answer:
rita and john are susseful the job
js school
a specific combination lock has 3 numbers chosen out of 40 possible numbers (0-39). assuming that all lock combinations are possible (including repeated numbers) find the number of possible lock combinations.
The total number of possible lock combination using the 40 possible numbers for making lock of 3 numbers is equal to 64,000.
Possible number used for lock combination are 40.
Range is 0 - 39.
Total number chosen for lock combination is equal to 3.
Since there are 40 possible numbers to choose from for each of the three positions on the combination lock.
The total number of possible combinations is equal to ,
40 x 40 x 40
= 40^3
= 64,000
Therefore, there are 64,000 possible lock combinations when choosing 3 numbers out of 40 possible numbers, assuming repeated numbers are allowed.
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Helpppppppppppppppppppppp
there are 882 plastic beads and 18 metal beads on clearance. What percentage of the beads on clearance are plastic? Write your answer using a percent sign (%).
The percentage of plastic beads on clearance is 98.99%.
What percent of the clearance beads are plastic, if there are 882 plastic beads and 18 metal beads? express your answer in percent sign (%)?To calculate the percentage of plastic beads on clearance, you need to divide the number of plastic beads by the total number of beads and then multiply by 100 to get the percentage.
In this case, the total number of beads on clearance is the sum of plastic beads and metal beads:
In this question, you are given the number of plastic beads and metal beads on clearance, and you are asked to find the percentage of plastic beads.
To do this, you need to calculate the total number of beads on clearance by adding the number of plastic beads and the number of metal beads.
Once you have the total number of beads, you can find the percentage of plastic beads by dividing the number of plastic beads by the total number of beads.
And then multiplying by 100 to convert the answer into a percentage. This formula can be expressed as:
Percentage of plastic beads = (Number of plastic beads / Total number of beads) x 100%
Plugging in the given values, we get:
Total number of beads = 882 + 18 = 900
Percentage of plastic beads = (882 / 900) x 100% = 98.99%
So, the answer is that 98.99% of the beads on clearance are plastic.
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Please hurry I need it asap
Answer:
13 units
Step-by-step explanation:
To find the distance between the two points, use the distance formula.
[tex]\sqrt{(x-x)^{2}+(y-y)^{2} }[/tex]
Plug in the point values.
[tex]\sqrt{(-8--3)^{2}+(-6-6)^{2} }[/tex]
Simplify the parenthesis.
[tex]\sqrt{(5)^2+(-12)^2}[/tex]
Get rid of the parenthesis.
[tex]\sqrt{25+144}[/tex]
Simplify.
[tex]\sqrt{169}[/tex]
Solve.
13 units
Untitled Question
14 points
2 Chelsea sprinted 120 yards in 18. 5
seconds. One meter is approximately equal
to 1. 1 yards. Which measurement is closest
to the number of meters Chelsea sprinted?
F 109. 1 yd H 64. 9 yd
G 132 yd J 90. 6 yd
7. 4E
G
The measurement closest to the number of meters Chelsea sprinted is F) 109.1 yd.
To determine the number of meters Chelsea sprinted, we need to convert the distance she sprinted from yards to meters.
Given:
Chelsea sprinted 120 yards.
Conversion:
1 meter is approximately equal to 1.1 yards.
To convert yards to meters, we divide the distance in yards by the conversion factor:
120 yards / 1.1 yards/meter ≈ 109.1 meters.
Therefore, the measurement closest to the number of meters Chelsea sprinted is F) 109.1 yd.
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There are 100 dears within a circular area with a radius of 10. Find the density of deer for 400 square miles.
The density of deer for 400 square miles is around 1:4 based on stated number of deers.
The density of deer will be given by the formula -
Population density of deer = number of deer/ area
Population density is the amount or number of individuals of a population on land per unit area.
Keep the value in formula to find the population density
Population density = 100/400
Cancelling zero as common in both numerator and denominator
Population density = 1:4
Thus, there is 1 deer for every 4 square mile.
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Exl) Solve exercise 3 on the first page of the handout; that is, find y" if 2.23 – 3y = 8. Then, answer the following question. What equation did you obtain after differentiating both sides of the given equation with respect to x? ENTER dy/dx or y'where needed, enter a power using the symbol^, for example enter was x^3, NO SPACES: fill in blank
To solve exercise 3 on the first page of the handout, we need to first isolate y in the given equation 2.23 - 3y = 8, which gives us y = -1.59.
To find y", we need to differentiate both sides of the equation with respect to x twice. The first derivative gives us:
-3(dy/dx) = 0
Simplifying, we get dy/dx = 0.
Differentiating again, we get:
-3d^2y/dx^2) = 0
Simplifying, we get d^2y/dx^2 = 0.
Therefore, the equation we obtain after differentiating both sides of the given equation with respect to x is d^2y/dx^2 = 0, which is the second derivative of y with respect to x.
To solve the equation given on the first page of the handout, 2.23 - 3y = 8, first isolate y:
1. Subtract 2.23 from both sides: -3y = 5.77
2. Divide both sides by -3: y = -5.77/3
Your answer: y = -5.77/3
The original equation doesn't have any x terms, so differentiation with respect to x is not applicable in this case.
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How much would it cost to buy a cover for the pool that cost $0.30 per square foot
It would cost $735 to buy a cover for the pool at $0.30 per square foot
How much would it cost to buy a cover for the poolFrom the complete question (see attachment), we have the following parameters that can be used in our computation:
Unit rate = $0.30 per square foot
Dimensions = 10 inches by 20 inches
Scale = 2 inches : 7 feet
Using the above as a guide, we have the following:
Total cost = Unit rate * Area of pool
Where
Area of the pool = 10 inches * 20 inches
Using the scale, we have
Area of the pool = (10 * 7/2)* (20 * 7/2) square feet
Area of the pool = 2450 square feet
Substitute the known values in the above equation, so, we have the following representation
Total cost = $0.30 per square feet * 2450 square feet
This gives
Total cost = $735
Hence, it would cost $735 to buy a cover for the pool
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Complete question
The blueprint of a pool has a scale of 2 inches equals 7 feet. The scale drawing is shown below (see attachment)
How much would it cost to buy a cover for the pool that cost $0.30 per square foot
The sequence U is defined by: Un +2 = 2 * Un+1+1* Un for n > 2 with given up and u uo 3 U = 1 List the first four terms uo, 21, U2, U3. Enter your answer as: value of uo, value of u1, value of uz, value of uz Enter answer here
The given values for uo and u3 are uo = 1 and u3 = 21. We can use the recurrence relation Un+2 = 2 * Un+1+1* Un to find the remaining terms:
U1 = U3 - 2U2 - 1*U0
U1 = 21 - 2U2 - 1*1
U1 = 20 - 2U2
U2 = U1 - 2U0 + 1*U0
U2 = 20 - 2U0 + 1*1
U2 = 19 - 2U0
Therefore, the first four terms are: 1, 19, -17, -53
So, the answer is: 1, 19, -17, -53.
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5. Which model is most appropriate for the data shown in the graph below? (1 point)
O quadratic
O linear
O exponential
O line
Answer:
Ф Exponential.
Step-by-step explanation:
The most appropriate for tehe data shown is:
Ф Exponential.
...
After graduating from college, Herbert decided to join a new company. He agreed to a salary which will increase by 4. 5% each year and he will earn $63,417 for his tenth year of work
Herbert will earn $63,417 for his tenth year of work which is calculated using compound interest formula.
After graduating from college, Herbert decided to join a new company. He agreed to a salary which will increase by 4.5% each year. This means that every year, Herbert's salary will increase by 4.5% of his previous year's salary. For example, if his salary in the first year is $50,000, his salary in the second year will be $52,250, and so on.
To find out Herbert's salary for his tenth year of work, we need to use compound interest formula. The formula is:
A = P(1 + r)ⁿ
Where:
A = Final amount (salary in the tenth year)
P = Initial amount (salary in the first year)
r = Annual interest rate (4.5%)
n = Number of years (10)
Substituting the values in the formula, we get:
A = $50,000(1 + 0.045)¹⁰
A = $63,417
Therefore, Herbert will earn $63,417 for his tenth year of work. It is important to note that the increase in salary is a result of compound interest, which means that the salary growth rate accelerates over time. This is a good incentive for Herbert to stay with the company and work hard.
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There were 81 people sitting in a school auditorium of which 19 were teachers, while the rest were students. How many teachers were sitting in the auditorium?
There were 19 teachers sitting in the school auditorium.
The question provides us with the total number of people present in the auditorium, which is 81. It also tells us that 19 of them were teachers. Therefore, the number of students present in the auditorium can be found by subtracting the number of teachers from the total number of people, which is 81 - 19 = 62.
Since the question only asks about the number of teachers present in the auditorium, the answer is simply 19. This is because the question already provides us with the information that there were 19 teachers present.
Alternatively, we can use algebra to solve the problem. Let x be the number of students present in the auditorium. Then, we can write an equation based on the total number of people in the auditorium: x + 19 = 81. Solving for x, we get x = 81 - 19 = 62. Therefore, the number of teachers present in the auditorium is 19.
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15. sheila has an eye-height of 5.4 feet and is standing 33 feet from a building. the angle of elevation from her line of
sight to the top of the building is 71 degree how tall is the building? round to the nearest tenth.
The height of the building is approximately 102.3 feet, rounded to the nearest tenth.
Step 1: Draw a right triangle with Sheila's eye-height as the base, the building's height as the vertical side, and the distance between Sheila and the building as the horizontal side.
Step 2: We are given the angle of elevation (71 degrees) and the horizontal distance (33 feet). To find the vertical distance, we can use the tangent function in trigonometry. The formula is:
tan(angle) = (opposite side) / (adjacent side)
Step 3: Plug in the given values into the formula:
tan(71) = (vertical distance) / 33
Step 4: Solve for the vertical distance:
vertical distance = 33 * tan(71) ≈ 96.9 feet
Step 5: Add Sheila's eye-height to the vertical distance to find the total height of the building:
total height = eye-height + vertical distance
total height = 5.4 + 96.9 ≈ 102.3 feet
The height of the building is approximately 102.3 feet, rounded to the nearest tenth.
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