The angle of elevation from the point where Josh is standing to the top of the tower is approximately 58.7 degrees.
How to calculate angle of elevation?
We can use trigonometry to calculate the angle of elevation:
tan(angle) = opposite/adjacent
In this case, the opposite is the height of the tower (199 feet) and the adjacent is the distance from Josh to the base of the tower (125 feet). So:
tan(angle) = 199/125
We can solve for the angle by taking the inverse tangent (tan^-1) of both sides:
angle = tan^-1(199/125)
Using a calculator, we find that:
angle ≈ 58.7 degrees
Therefore, the angle of elevation from the point where Josh is standing to the top of the tower is approximately 58.7 degrees.
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The data given represents the number of gallons of coffee sold per hour at two different coffee shops.
Coffee Ground
1.5 20 3.5
12 2 5
11 7 2.5
9.5 3 5
Wide Awake
2.5 10 4
18 4 3
3 6.5 15
6 5 2.5
Compare the data and use the correct measure of center to determine which shop typically sells the most amount of coffee per hour. Explain.
Wide Awake, with a median value of 4.5 gallons
Wide Awake, with a mean value of about 4.5 gallons
Coffee Ground, with a mean value of about 5 gallons
Coffee Ground, with a median value of 5 gallons
Based on both the mean and median values, we can conclude that Wide Awake typically sells more coffee per hour than Coffee Ground.
What are the mean and median?
The mean and median are two measures of central tendency that can be used to describe a set of data. The median is the middle value in the data set when the values are arranged in order from lowest to highest. If there are an even number of values, the median is the average of the two middle values.
To determine which coffee shop typically sells the most amount of coffee per hour, we need to compare the measures of center (mean and median) of the data for each shop.
Calculating the mean of each dataset, we get:
Mean of Coffee Ground = (1.5+20+3.5+12+2+5+11+7+2.5+9.5+3+5) / 12 = 6.5/2 = 5.42 gallons
Mean of Wide Awake = (2.5+10+4+18+4+3+6+5+2.5) / 9 = 56 / 9 = 6.22 gallons
Calculating the median of each dataset, we get:
Median of Coffee Ground = 4.25 gallons
Median of Wide Awake = 4.5 gallons
Comparing the measures of the center, we see that the mean value of coffee sold per hour at Coffee Ground is approximately 5.42 gallons, while the mean value of coffee sold per hour at Wide Awake is approximately 6.22 gallons.
Therefore, on average, Wide Awake sells more coffee per hour than Coffee Ground.
However, we also see that the median value of coffee sold per hour at Wide Awake is 4.5 gallons, while the median value of coffee sold per hour at Coffee Ground is 4.25 gallons.
This suggests that the middle value of coffee sold per hour is higher for Wide Awake than for Coffee Ground.
Therefore, based on both the mean and median values, we can conclude that Wide Awake typically sells more coffee per hour than Coffee Ground.
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SUPER EASY!!!!!
What is degree of (4by+2b-by)?
I will make you brainliest if you can explain!!!
Answer: The degree of (4by+2b-by) is 2, as it is a quadratic expression with the highest exponent of the variable being 2.
Step-by-step explanation: The degree of a polynomial is the highest exponent of the variable. In this case, the highest exponent of the variable is 2, which appears in the term 4by. Therefore, the degree of (4by+2b-by) is 2.
The weight of a puppy is modeled by 2x - y=-2, where x represents the puppy's age in
weeks and y represents its weight in pounds. Which graph models the puppy's growth?
Answer:
Graph H
Step-by-step explanation:
intercept (0,2)
Write an expression that can be a rule for the number sequence below.
6, 9, 12, 15, 18, … (PLS ANSWER FAST!!)
3n, where n is equal to 2, 3, 4, 5, 6
3 + n, where n is equal to 2, 3, 4, 5
6n, where n is equal to 0, 1, 2, 3, 4
6 + n, where n is equal to 1, 2, 3, 4
The arithmetic sequence expression for the given sequence 6, 9, 12, 15, 18....... would be aₙ = 6+(n-1)3.
What is an arithmetic sequence?A progression or sequence of numbers known as an arithmetic sequence maintains a consistent difference between each succeeding term and its predecessor.
The common difference of that mathematical progression is the constant difference.
'n' denotes the term's position in the supplied arithmetic sequence in the formula for obtaining the general term: a = a1 + (n - 1) d. For instance, a2 denotes the second phrase in the sequence.
So, the given sequence is:
6, 9, 12, 15, 18
Common difference (d) is: 9 - 6 = 3
Then, the sequence expression would be:
aₙ = 6+(n-1)3
Therefore, the arithmetic sequence expression for the given sequence 6, 9, 12, 15, 18....... would be aₙ = 6+(n-1)3.
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Review the information on FICO score calculations to answer the question:
Category Percentage
Payment History 35%
Amount Owed 30%
Length of Credit History 15%
New Credit and Inquiries 10%
Credit Mix 10%
A borrower has a credit score of 725. How many points come from amount owed and length of credit history?
290
322.65
363
326.25
From the given percentage values, 326.25 points come from amount owed and length of credit history.
What is percentage?
Percentage is a method of representing a value as a fraction of 100. This is frequently used to make comparisons, demonstrate ratios, or determine a fraction of a whole.
The borrower's credit score is 725, and we need to find out how many points come from amount owed and length of credit history.
From the information given, we know that these two categories make up a total of 45% of the score calculation (30% for amount owed and 15% for length of credit history).
We can set up a proportion:
(30% + 15%) / 100% = x / 725
Simplifying the left side:
45% / 100% = 0.45
0.45 = x / 725
Multiplying both sides by 725:
x = 0.45 * 725
x = 326.25
Therefore, 326.25 points come from amount owed and length of credit history.
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if the average (arithmetic mean) of n consecutive odd integers is 10, what is the least of the integers? the range of the n integers is 14. the greatest of the n integers is 17.
The least of the integers in arithmetic mean of n consecutive odd integers is 3.
The formula to calculate average or arithmetic mean of evenly distributed set is -
Average = sum of first and last term/2
Keep the values in formula to find the least integer. Since these are consecutively arranged, the first number will be the least number.
10 = first number + 17/2
First number + 17 = 10×2
Performing multiplication on Right Hand Side
First number + 17 = 20
First number = 20 - 17
Performing subtraction
First number = 3
Hence, the least integer is 3.
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given the circle below with chords NO and PQ find the length of NR round to the nearest tenth if necessary
the length of NR is approximately 22.8, rounded to the nearest tenth.
To find the length of NR, we need to first identify any relationships between the chords and the arcs they intercept in the circle. From the diagram, we can see that chord PQ intersects arc ONR and chord NO intersects arc PQN.
There are two main properties we can use to solve this problem: the chord-chord power theorem and the angle-arc theorem. The chord-chord power theorem states that if two chords intersect in a circle, the product of the lengths of their segments is equal. That is:
(PQ)(QR) = (NO)(NR)
We know that PQ = 48 and NO = 21, so we can plug those values into the equation and solve for NR:
(48)(QR) = (21)(NR)
QR = (21NR)/48
To find QR, we can use the angle-arc theorem. This theorem states that the measure of an angle formed by two intersecting chords is equal to half the sum of the measures of the arcs they intercept. That is:
∠QNR = (arc PN + arc OQ)/2
We know that arc PN is equal to arc PQ (since they are intercepting the same arc), and we know that arc OQ is equal to the entire circumference of the circle minus arc PQ. The circumference of a circle is given by 2πr, where r is the radius. We don't know the radius of the circle, but we can find it using the Pythagorean theorem. We know that NO and PQ are both chords, so they must intersect at the center of the circle. Therefore, the line segment connecting the center of the circle to the midpoint of chord NO is a perpendicular bisector of NO. This gives us a right triangle with legs of 10.5 and 24 (half of 21 and half of 48). Using the Pythagorean theorem, we can find that the radius of the circle is approximately 26.2.
Now we can plug in our values for arc PN and arc OQ:
∠QNR = (arc PQ + (2πr - arc PQ))/2
∠QNR = πr
We know that QR is the side opposite the angle ∠QNR in right triangle QNR. Therefore, we can use the sine function to find QR:
sin(∠QNR) = QR/r
sin(πr) = QR/26.2
QR = 26.2sin(πr)
Now we can substitute this value for QR into our equation from the chord-chord power theorem:
(48)(26.2sin(πr)) = (21)(NR)
NR ≈ 22.8
Therefore, the length of NR is approximately 22.8, rounded to the nearest tenth.
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Question 1 (Multiple Choice Worth 2 points)
(Multiplying Linear Expressions MC)
Simplify ---
O
45
m²
8.
45
8
45
2
m²-m
35
2
-m² + m
35
8
45
2
·m² + m
35
Answer:
[tex] - \frac{2}{5} m( - \frac{4}{9} m - \frac{1}{7} ) = [/tex]
[tex] \frac{8}{45} {m}^{2} + \frac{2}{35} [/tex]
carly got a model train set for her birthday, and it came with 200 assorted pieces of train track. she randomly picks some pieces of track out of the box. so far, she has picked 8 straight, 7 curved, 4 cross, and 5 switch tracks. based on the data, what is the probability that the next piece of track carly picks will be straight?
The probability that the next piece of track Carly picks will be straight is 8/24 or 1/3
From the given information, Carly has picked 8 straight, 7 curved, 4 cross, and 5 switch tracks.
The total number of pieces of the track she has picked is 8 + 7 + 4 + 5 = 24
The probability that the next piece of track Carly picks will be straight is calculated as follows:
Probability = Number of straight tracks/Total number of tracks= 8/24= 1/3T
Therefore, the probability that the next piece of track Carly picks will be straight is 1/3.
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Answer: 1/3
Step-by-step explanation: i did this question and got it right
Hey, we're doing IXLs in pre-alg rn
After solving the given equation 1/4b - 2 = -1/2b + 4, the resultant value of b is 8/3 respectively.
What are equations?An equation is a mathematical expression with two equal sides and an equal sign.
4 + 6 = 10 is an illustration of an equation.
On the left side of the equal sign, you can see 4 + 6, and on the right, you can see 10.
A formula exists in every equation.
Some equations do not have formulae.
Equations are designed to be solved for a variable.
We look over formulas.
So, we have the equation:
1/4b - 2 = -1/2b + 4
Now, solve the equation for b as follows:
1/4b - 2 = -1/2b + 4
1/4b = -1/2b + 6
1/4b + 2/1b = 6
1+8/4b = 6
9/4b = 6
b = 6 * 4/9
b = 2 * 4/3
b = 8/3
Therefore, after solving the given equation 1/4b - 2 = -1/2b + 4, the resultant value of b is 8/3 respectively.
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Your car holds 50 litres
of gas. If the price is 116.8 ($1.168) how much
money will you spend on gas?
l will spend $58.40 on gas.
What is Multiplication?
Multiplication is an arithmetic operation that involves combining two or more numbers to produce a third number called the product. The symbol for multiplication is "×" or "*".
For example, if you have 3 apples and want to know how many apples you would have if you tripled the amount, you can multiply 3 by 3 to get the answer: 3 × 3 = 9. So, if you tripled the amount of apples you had, you would have 9 apples in total.
Multiplication can be thought of as repeated addition. For instance, 3 × 4 is the same as 3 + 3 + 3 + 3, which equals 12. In this example, 3 is added to itself four times.
Here given, a car holds 50 litres of gas and the price is 116.8 ($1.168) per litre.
We want to calculate the total cost of the gas.
We can find it by multiplying the number of litres by the price per litre
Total cost = [tex]50 \times 1.168[/tex]
Total cost = $58.40
Therefore, l will spend $58.40 on gas.
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Correct question is "Your car holds 50 litres
of gas. If the price is 116.8 ($1.168) per litre then how much money will you spend on gas?"
it took mr. walsh 10 minutes to drive from his house to the store. he shopped for 28 minutes. then it took him 10 minutes to drive home. he arrived home at 4:30. which clock shows the time mr. walsh left his house to go to the store?
The clock that shows the time Mr. Walsh left his house to go to the store would be 3:42 pm.
Mr. Walsh's journey consisted of driving from his house to the store, shopping for 28 minutes, and then driving back home. The total time for his journey would be:
10 minutes (driving to the store) + 28 minutes (shopping) + 10 minutes (driving back home) = 48 minutes
If Mr. Walsh arrived home at 4:30 pm, and we subtract the 48 minutes it took for his entire journey, we can determine the time he left his house to go to the store:
4:30 pm - 48 minutes = 3:42 pm
Therefore, the clock that shows the time Mr. Walsh left his house to go to the store would be 3:42 pm.
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44% of c is 72. find the value of c
Answer: 163.6363...
Step-by-step explanation:
44% of c is 72, so then [tex]0.44*c=72\\[/tex].
Divide both sides by 0.44 to solve for c, and you get c=163.6363...
Tip: if you are ever trying to figure out what a number is a percentage of, like in this problem, just divide the number by the percent in decimal form.
Which of the following is not a correct description of the graph of the function (photo below)
Answer:
the answer is d
Step-by-step explanation:
hope this helps
Pedro's teacher asks him to classify the shape below. He claims it is a rectangle. His teacher
tells him to prove it. Help Pedro support his claim using mathematical evidence. Remember:
Opposite sides of a rectangle have the same length and are parallel, and the sides of a
rectangle meet at right angles.
As, AD = BC, the given shape on the graph shows the rectangle found using distance formula.
Explain about the rectangle:An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel opposite sides. A rectangle has two dimensions—length and width—because it is a two-dimensional form. The rectangle's longer side is its length, while its shorter side is its breadth.
From the given graph, The coordinates of A,B, C and D are-
A = (-3,1)
B = (0,3)
C = (4, -3)
D = (1, -5)
Find the distance AD and BC, if both are equal it forms a rectangle:
Using the distance formula:
d = √[(x2 - x1)² + (y2 - y1)²]
AD = √[(- 3 - 1)² + (1 + 5)²]
AD = √(16 + 36)
AD = √53
BC = √[(0 - 4)² + (3 + 3)²]
BC = √(16 + 36)
BC = √53
As, AD = BC, the given shape on the graph shows the rectangle found using distance formula.
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students arrive at the administrative services office at an average of one every 14 minutes, and their requests take, on average, 8 minutes to be processed. the service counter is staffed by only one clerk, judy gumshoes, who works eight hours per day. assume poisson arrivals and exponential service times. a. what is the utilization rate? b. the average number of students in line. c. the average time of waiting in line.
A. The Utilization rate is 0.5714 or 57.14%, B. The average number of students in line is 0.9 students and C. The average time of waiting in line was 4.57 minutes.
The utilization rate refers to the proportion of time Judy Gumshoes spends processing student requests.
To calculate this rate, divide the average service time by the average time between arrivals. In this case, the average service time is 8 minutes, and students arrive every 14 minutes on average.
a) Utilization rate: 8 minutes / 14 minutes = 0.5714 or 57.14%
b) To determine the average number of students in line,
we can use the formula L = λW, where L represents the average number of students in the system, λ is the arrival rate (1 student per 14 minutes), and W is the average time a student spends in the system (waiting and being served). Since we know the utilization rate,
we can calculate the average waiting time (Wq) using the formula,
Wq = (U^2) / (1 - U), where U is the utilization rate.
In this case, Wq = (0.5714^2) / (1 - 0.5714) = 0.3265 or 32.65% of 14 minutes = 4.57 minutes.
W = Wq + service time
= 4.57 minutes + 8 minutes
= 12.57 minutes.
Finally, L = λW = (1 student / 14 minutes) * 12.57 minutes
= 0.9 students.
c) The average time of waiting in line is the same as the average waiting time in the system (Wq), which we calculated as 4.57 minutes.
In summary, the utilization rate of the service counter is 57.14%, the average number of students in line is 0.9, and the average waiting time in line is 4.57 minutes.
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Brie earns $3,000 a month. She spends $1,400 on rent and bills, $700 or
groceries, $200 on a car payment, and $100 on gas each month. She say
the rest of her money. How much money does Brie save? Show your work
Brie saves $600 each month.
What is equation?
An equation is a statement that shows that two expressions are equal. It typically consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division
To determine how much money Brie saves each month, we need to subtract her expenses from her income.
Income = $3,000
Expenses = $1,400 + $700 + $200 + $100 = $2,400
Savings = Income - Expenses
Savings = $3,000 - $2,400
Savings = $600
Therefore, Brie saves $600 each month.
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6x^2-12x-18 factor the polynomial
Answer:
6x² - 12x - 18
the factors are -18 and 6
6x² - 18x + 6x - 18
6x(x - 3) + 6 (x - 3)
(6x + 6) or (x - 3)
the factors are:
(6x + 6) or (x - 3)
PLEASE HELP WILL MARK BRAINLIEST
20 points
write an explicit formula for each sequence
1,4,7,10….
SHOW WORK PLS
Answer:
aₙ = 3n - 2
Step-by-step explanation:
The given sequence is an arithmetic sequence with the first term a₁ = 1 and the common difference d = 3.
The explicit formula for an arithmetic sequence is:
aₙ = a₁ + (n - 1)d
where aₙ represents the nth term in the sequence.
Substituting the values we have:
aₙ = 1 + (n - 1)3
Simplifying the equation we get:
aₙ = 3n - 2
Therefore, the explicit formula for the given sequence 1, 4, 7, 10, ... is aₙ = 3n - 2.
Problem 5.2 A cone has volume V, radius r, and a height of 12 cm. Another cone has the same height and 3 times the radius of the original cone. Write an expression for its volume. | Submit
Answer: The volume of a cone is given by the formula V = (1/3)πr^2h, where r is the radius and h is the height.
For the original cone with radius r and height 12 cm, we have:
V = (1/3)πr^2h
V = (1/3)πr^2(12)
V = 4πr^2
For the second cone with 3 times the radius of the original cone and the same height of 12 cm, we have:
V' = (1/3)π(3r)^2h
V' = (1/3)π9r^2(12)
V' = 36πr^2
Therefore, the expression for the volume of the second cone is 36πr^2.
Step-by-step explanation:
Are these right? If not, can you tell the right answers so I can change them please?
Answer:
O=0
T=-5
c = 0
R = -2
6 = 8
2 = 8
11=-3
Step-by-step explanation: Sorry for the late answer It took me a bit to solve all the problems but I hope this helps you!!
pippa's play place is a new indoor playground. there is a large ball pit shaped like a rectangular prism for kids to play in. the ball pit is 20 feet long and 12 1 2 feet wide. it has a volume of 875 cubic feet. which equation can you use to find how deep the ball pit is, d? how deep is the ball pit? write your answer as a whole number, proper fraction, or mixed number. feet
Answer:
Step-by-step explanation:
Volume of a rectangular prism = l x w x h
I am reading the width as 12 1/2 ft
Treat the depth of the ball pit as height
Vol = l x w x h
875 = (20)(12 1/2)(h)
875 = 250(h)
875/250 = 250h/250
3 1/2 = height
depth of the ball pit is 3 1/2 ft
The ball pit is 3.5 feet deep. This can be answered by the concept Surface area.
To find the depth of the ball pit, we can use the equation: Volume = length x width x depth.
The volume of the ball pit is given as 875 cubic feet, the length is 20 feet and the width is 12.5 feet. Let d be the depth of the ball pit. Therefore, the equation we can use is:
875 = 20 x 12.5 x d
To solve for d, we can divide both sides of the equation by (20 x 12.5):
d = 875 / (20 x 12.5)
d = 3.5 feet
Therefore, the ball pit is 3.5 feet deep
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Sam bought 2 cups of corn and 4 tacos for $19. Albert bought bought 3 cups of corn and 2
tacos for $14.5
How much are the tacos?
O $3.50
O $2.75
O $2.50
O $3.00
Let's represent the cost of a cup of corn as 'c' and the cost of a taco as 't'.
From the first statement, we know that:
2c + 4t = 19 (equation 1)
From the second statement, we know that:
3c + 2t = 14.5 (equation 2)
We can solve this system of equations using elimination or substitution. Here, we'll use substitution.
Rearranging equation 2, we get:
3c = 14.5 - 2t
Dividing both sides by 3, we get:
c = 4.83 - 0.67t
Now we can substitute this expression for 'c' into equation 1:
2(4.83 - 0.67t) + 4t = 19
Simplifying, we get:
9.66 - 0.34t = 19
Subtracting 9.66 from both sides, we get:
-0.34t = 9.34
Dividing both sides by -0.34, we get:
t = -27.47 ≈ $-2.75
Since a negative price for a taco doesn't make sense, we made an error somewhere. Checking our calculations, we can see that we made a mistake in the expression for 'c'. It should be:
c = (14.5 - 2t)/3
Substituting this expression for 'c' into equation 1:
2[(14.5 - 2t)/3] + 4t = 19
Multiplying both sides by 3:
2(14.5 - 2t) + 12t = 57
Expanding and simplifying:
29 - 4t + 12t = 57
8t = 28
t = 3.5
Therefore, the tacos cost $3.50.
Here is a pyramid with a base that is a pentagon with all sides the same length (see image for full problems)
If the pyramid is sliced horizontally (parallel to the base), the resulting cross section would be a regular pentagon with the same side length as the base of the pyramid
Describe the cross section that will result if the pyramid is sliced?If the pyramid is sliced horizontally (parallel to the base), the resulting cross section would be a regular pentagon with the same side length as the base of the pyramid. This is because a horizontal slice would intersect all five sides of the pentagonal base at equal distances from the apex of the pyramid, resulting in a regular pentagon.
If the pyramid is sliced vertically through the top vertex (perpendicular to the base), the resulting cross section would be a triangle. The triangle's shape would depend on the height of the pyramid and the angle of the slice. The base of the triangle would be a regular pentagon, with the height of the pyramid as the altitude. The apex of the triangle would be the top vertex of the pyramid. The shape of the triangle would change depending on the angle of the slice, but it would always be an isosceles triangle since the slice passes through the apex, which is the vertex of the pyramid where all the edges meet.
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simplify completely
sin(90°-x)co(180°-X)+tanX×cos(-x)sin180°+x)
Therefore , the solution of the given problem of trigonometry comes out to be -1 is the simplified formula.
What is a trigonometry?Some claim that the fusion of various fields contributed to the development of astrophysics. With the aid of precise mathematical methods, many metric issues can be resolved or the output of a computation can be determined. The scientific investigation of all six fundamental geometric calculations is known as trigonometry. They are known by a number of names and abbreviations, such as sine, variance, angle, and others. (csc).
Here,
Let's first use trigonometric identities to separately simplify each term:
=> cos(x - 90°) equals sin(x)
=> cos(x - 180°) = -cos(x)
=> tan(x) = cos(x) / sin(x)(x)
=> x(cos(-)) = x(x)
=> (180° + x) sin = -sin(x)
When we replace the equation with these simplifications, we get:
=> cos(x) * sin(180° plus x) * cos(x) * (-cos(x)) + (sin(x) / cos(x))
=> sin(180° plus x) * sin(-cos2(x))
=> -cos²(x) - sin(x)*sin(180° + x) (using the equation sin(x)*sin(x)) = -sin^2(x))
Using the identity sin2(x) +cos2(x) = 1, we get = -1.
Consequently, -1 is the simplified formula.
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Find the height of the basketball hoop using similarity ratios. Explain step by step.
The height of the basketball hoop is 13.32'.
What is law of similarity?
The Law of Similarity in mathematics states that if two geometric figures have the same shape but different sizes, then they are considered similar. This means that the corresponding angles of the two figures are congruent, and the corresponding sides are proportional in length.
Formally, if we have two geometric figures A and B, and if every angle of figure A is congruent to the corresponding angle of figure B, and if the ratio of the length of any pair of corresponding sides of A and B is constant, then we can say that A and B are similar figures.
Here we can see two triangle and base of two triangle is given.
Here base of small triangle is 12' and the base of big triangle is (12'+25') = 37'.
It is also given that height of small triangle is 4'3.84".
Now we want to find the height of the basketball hoop which is equal to height of big triangle.
Let the height of the basketball hoop be x.
So, by law of similarity ratios,
12'/37' = 4'3.84"/x
Now, 4'3.84" = 4.32'
So, 12'/37' = 4.32'/x
Therefore, x = 13.32'
Therefore, the height of the basketball hoop is 13.32'.
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Domain and range of f^-1?
The domain of f is [0, π/2]. The range of [tex]f^-1[/tex] is also [0, /2].
What is domain?The domain of a function is the set of all possible values for the input variables (usually denoted as x) for which the function is defined. It is the set of all real numbers or other possible values that can be used as input to the function.
According to question:To find the inverse function [tex]f^-1[/tex] of f(x) = 2cos(2x), we follow these steps:
Step 1: Replace f(x) with y.
y = 2cos(2x)
Step 2: Swap x and y and solve for y.
x = 2cos(2y)
cos(2y) = x/2
2y = [tex]cos^(-1)[/tex](x/2)
y = (1/2)[tex]cos^(-1)[/tex](x/2)
Therefore, the inverse function of f is [tex]f^-1[/tex](x) = (1/2)[tex]cos^(-1)[/tex](x/2).
To find the range of f, we notice that the range of cos(2x) is [-1, 1]. Multiplying this by 2 gives us the range of f: [-2, 2].
To find the domain of [tex]f^-1[/tex], we notice that the range of [tex]cos^-1[/tex](x) is [0, pi]. Multiplying this by (1/2) and replacing x with x/2, we get the domain of [tex]f^-1[/tex]: [0, π/2].
To find the range of [tex]f^-1[/tex], we notice that the domain of f is [0, π/2]. Therefore, the range of [tex]f^-1[/tex] is also [0, /2].
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a researcher wants to estimate the mean grade point average of all current college students in the united states. she has developed a procedure to standardize scores from colleges using something other than a scale between 0 and 4. how many grade point averages must be obtained so that the sample mean is within 0.1 of the population mean? assume that a 90% confidence level is desired. also assume that a pilot study showed that the population standard deviation is 0.88.1
A sample size of at least 109 GPAs to estimate the population mean with a 90% confidence level
Confidence level = 90%
Standard deviation = 0.88
Mean = 0.1
Calculating the sample size -
[tex]n = [(zα/2σ) / E]^2[/tex]
The crucial value for a confidence level of 90%, denoted by z/2, may be determined using a typical normal distribution table or calculator, where n is the required sample size. The value of z/2 at a 90% degree of confidence is around 1.645. The problem statement specifies that the population standard deviation at 0.88 and that E is the most significant error of the sample mean from the population mean at 0.1.
Therefore, substituting the values -
[tex]n = [(1.645 x 0.88) / 0.1]^2[/tex]
n = 108.25
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a recent study suggested that 77% of teenagers have texted while driving. a random sample of 27 teenage drivers in atlanta was taken and 15 admitted to texting while driving. construct a 99% confidence interval for the population proportion of teens who text while driving.
With the confidence interval, it can be concluded with 99% confidence that the true proportion of teenage drivers in Atlanta who text while driving lies between 35.89% and 75.23%.
The confidence interval (CI) is equal to the sample proportion (p) plus or minus the product of the critical value (z*) and the standard error of the proportion, where the standard error is calculated by taking the square root of the product of the sample proportion, its complement (1 - p), and the reciprocal of the sample size (n), formed in an equation.
where:
p is the sample proportion (15/27 in this case)
z* is the critical value from the standard normal distribution for the desired confidence level (99% in this case, which corresponds to a z* value of 2.576)
n is the sample size (27 in this case)
Substituting the given values, we get:
CI = 0.5556 ± 2.576*√((0.5556(1-0.5556))/27)
Simplifying this expression, we get:
CI = 0.5556 ± 0.1967
So the 99% confidence interval for the population proportion of teens who text while driving is:
(0.3589, 0.7523)
Therefore, we can be 99% confident that the true proportion of teenage drivers in Atlanta who text while driving lies between 35.89% and 75.23%.
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One card each is drawn from four different standard decks of cards. Find the total number of outcomes
Since there are 52 cards in a standard deck, there are 52 possible outcomes for the first draw from the first deck. Similarly, there are 52 possible outcomes for the first draw from the second, third, and fourth decks. Therefore, the total number of outcomes for the first draw is 52 + 52 + 52 + 52 = 208.
For the second draw, there are only 51 possible outcomes for each deck, since one card has already been drawn. Therefore, the total number of outcomes for the second draw is 51 + 51 + 51 + 51 = 204.
For the third draw, there are only 50 possible outcomes for each deck, since two cards have already been drawn. Therefore, the total number of outcomes for the third draw is 50 + 50 + 50 + 50 = 200.
For the fourth draw, there are only 49 possible outcomes for each deck, since three cards have already been drawn. Therefore, the total number of outcomes for the fourth draw is 49 + 49 + 49 + 49 = 196.
The total number of outcomes for drawing one card each from four different standard decks of cards is the product of the outcomes for each draw: 208 x 204 x 200 x 196 = 338,401,792.