The building is perfectly vertical and the observer is at a consistent height above the ground.
A) Explain how the method of indirect measurement can be used to estimate the height of a building?The method of indirect measurement can be used to estimate the height of a building by using similar triangles and the principles of proportionality. First, the distance from the base of the building to the observer and the distance from the ground to a known point on the building are measured. By maintaining the same angle of sight, the observer can move back until the top of the building is in their line of sight. At this point, a second pair of measurements is taken: the distance from the new location to the base of the building and the height of the visible portion of the building from the ground. By using the principles of proportionality between similar triangles, the height of the entire building can be estimated.
Specifically, the ratio of the height of the known point on the building to the distance from the observer to that point can be set equal to the ratio of the height of the entire building to the distance from the observer to the base of the building. This proportion can be solved algebraically to find the estimated height of the entire building.
B) What are some potential sources of error or inaccuracy in this method of estimation?
There are several potential sources of error or inaccuracy in this method of estimation. One major source of error is the assumption that the two triangles being compared are similar. If the angle of sight is not maintained exactly or if the ground is not perfectly level, the triangles may not be similar and the estimated height may be incorrect.
Additionally, the accuracy of the estimated height depends on the accuracy of the distance measurements. If the distances are not measured precisely, the estimated height will be proportionally less accurate.
Finally, this method assumes that the building is perfectly vertical and that the observer is at a consistent height above the ground. If the building is not perfectly vertical or the observer's height above the ground changes, this can also affect the accuracy of the estimated height.
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Pythagorean Theorem answer quick please
Answer:
3.9
Step-by-step explanation:
pythagorean theorem states:
[tex]a^{2} +b^{2} =c^{2}[/tex]
We know that a is the height of the triangle, 2.
We also know that b is the base of the triangle, 3.
So, solve for c:
2²+3²=c²
simplify
4+9=c²
15=c²
take the square root of both sides
c=3.9
So, the spider and the fly are 3.9 ft apart from each other
Hope this helps :)
Answer:
3.6 feet
Step-by-step explanation:
The Pythagorean theorem states that a^2+b^2=c^2, where c is the hypotenuse, or longest side of the triangle opposite to the right angle, and a and b are the two legs of the triangle (the other two sides.)
In the question, sides a and b are given as 2ft and 3ft long. Plugging 2 and 3 into the equation, we will get that 2^2+3^2=c^2. 2 x 2 = 4 and 3 x 3 = 9, so 4 + 9 = c^2, or, c^2 = 13.
However, this is still c^2, not c, so we must take the square root of both sides. This is because the equation is now essentially saying that c x c = 13, so if we find a number that when multiplied by itself equals 13, that number will be c. to do this, we must take the square root of 13. This will give us an irrational number- approximately 3.605551275. The question asks to round it to the nearest tenth though, so this will simply become 3.6.
In the context of this question, it means that the spider and the fly are 3.6ft apart.
For what values of a and b will this equation have infinitely many solutions?
5(x + 3) = a(x + 4) + 3x + b
Answer: To have infinitely many solutions, the equation must be true for all values of x. In other words, the left side and right side of the equation must be equivalent, meaning that the coefficients of x on both sides of the equation must be equal, and the constant terms on both sides must be equal.
We can simplify the given equation as follows:
5(x + 3) = a(x + 4) + 3x + b
5x + 15 = ax + 4a + 3x + b
Simplifying further, we get:
8x + 4a + b = 5x + 15
Rearranging terms, we get:
3x + 4a + b - 15 = 0
For this equation to have infinitely many solutions, the coefficients of x on both sides must be equal to zero, meaning that:
3 = 0
This is not possible, so the equation cannot have infinitely many solutions for any values of a and b.
Therefore, there are no values of a and b for which the given equation will have infinitely many solutions.
Determine whether each situation can have only one value for the variable or more than one value for the variable.
select only one or more than one for each situation.
the total cost to buy t movie tickets for $8.50 each
o only one
more than one
the number of ounces of tomato juice, j, in 2 quarts
o only one
o more than one
the number of pizzas to order, p, if each person eats 2 slices
only one
more than one
the greatest number of $6 notebooks, n, ed can buy with $36
only one
0. more than one
the area, a, of a wall with a length of 5 meters and a height of 3 meters
o only one
o more than one
The total cost to buy t movie tickets for $8.50 each is o only one, the number of ounces of tomato juice, j, in 2 quarts o only one, the number of pizzas to order, p, if each person eats 2 slices more than one, the greatest number of $6 notebooks, n, ed can buy with $36 only one, and the area, a, of a wall with a length of 5 meters and a height of 3 meters o only one.
1. The total cost to buy t movie tickets for $8.50 each:
- Only one value for the variable
The cost to buy a specific number of movie tickets at a fixed price will have only one total cost value.
2. The number of ounces of tomato juice, j, in 2 quarts:
- Only one value for the variable
There are 32 ounces in a quart, so 2 quarts will always have 64 ounces.
3. The number of pizzas to order, p, if each person eats 2 slices:
- More than one value for the variable
The number of pizzas needed depends on the number of people attending, which can vary, leading to different values for p.
4. The greatest number of $6 notebooks, n, Ed can buy with $36:
- Only one value for the variable
Since each notebook costs $6, Ed can buy exactly 6 notebooks with $36 (36/6 = 6).
5. The area, a, of a wall with a length of 5 meters and a height of 3 meters:
- Only one value for the variable
The area of a rectangle is calculated by multiplying its length and height. In this case, the area will always be 15 square meters (5m x 3m = 15m²).
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A study was conducted by the Director of Parking and Transportation at a large university. One variable under study is the method of transportation to campus used by off-campus students. The choices for students on the survey were drive alone, carpool, public transportation, walk, or a paid driving service. Which type of variable is this?
The type of variable being studied in this case is a categorical variable, specifically a nominal variable.
What s the type of variable in the question?Categorical variables are variables that can be classified or grouped. The categories in this example are the various modes of transportation utilized by off-campus students (drive alone, carpool, public transportation, walk, or a paid driving service).
Nominal variables are categorical variables with no intrinsic order or numerical value. Because the various modes of transportation in this study have no numerical value or inherent order, they are classified as nominal variables.
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3. The insurance company also offers safety glass coverage. There is a 50% chance of no repairs ($0), a 30% chance of minor repairs ($50), and a 20% chance of full replacement ($300). Which plan for optional safety glass coverage has the lower expected cost?
Enter your answer.
Plan C has the lower expected cost, so, this is best to minimize costs for safety glass coverage.
How can we compare the plans?In order to compare expected cost of Plan C and D, we must calculate expected payout for each plan and add to the premium.
For Plan C, expected payout is:
= 0.5*(0) + 0.3*(50) + 0.2*(300)
= 15 + 60
= 75
The total expected cost of Plan C is:
= 75 + 50 + 20
= 145
For Plan D, expected payout is:
= 0.5*(0) + 0.3*(50) + 0.2*(300)
= 15 + 60
= 75
The total expected cost of Plan D is:
= 75 + 100 + 0
= 175
Therefore, the Plan C has the lower expected cost.
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. c) gordon has 4 cups of powdered sugar. he sprinkles 1/2 of the sugar onto a plate of lemon bars and the rest onto a plate of cookies. how much sugar does he sprinkle on the cookies?
Gordon sprinkles 2 cups of powdered sugar onto the plate of cookies after he sprinkles 1/2 of the sugar, or 2 cups, onto the plate of lemon bars.
Gordon has 4 cups of powdered sugar. He sprinkles 1/2 of the sugar onto a plate of lemon bars and the rest onto a plate of cookies. We want to find out how much sugar he sprinkles on the cookies.
If Gordon sprinkles 1/2 of the sugar onto the plate of lemon bars, he uses 1/2 x 4 = 2 cups of powdered sugar for the lemon bars.
This leaves him with 4 - 2 = 2 cups of powdered sugar remaining for the plate of cookies.
Therefore, Gordon sprinkles 2 cups of powdered sugar onto the plate of cookies.
We can also verify this answer by using subtraction. If Gordon uses 2 cups of powdered sugar for the lemon bars, he has 4 - 2 = 2 cups of powdered sugar remaining. This means that he must have used the remaining 2 cups of powdered sugar for the plate of cookies.
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The town of Knappville has a landmark, L, an amusement park, AP, a high school, HS, a city hall, CH, and a city park, P. Herberto is at the amusement park and wants to go to the city hall. Name a path he could travel
Herberto travelled through Amusement Park (AP), City Park (P), Landmark (L), High School (HS), City Hall (CH).
Herberto can take the following path to travel from the amusement park (AP) to the city hall (CH):
Amusement Park (AP) -> City Park (P) -> Landmark (L) -> High School (HS) -> City Hall (CH)
This path takes him through the city park, then to the landmark, followed by the high school, and finally to the city hall.
Please note that without a specific map or layout of Knappville, there could be multiple valid paths from the amusement park to the city hall. The path provided above is just one example.
When Herberto travels from the amusement park to the city hall, he can choose various paths depending on the specific layout of Knappville. The path mentioned earlier is just one example, but the actual paths could differ based on the town's infrastructure and the locations of the landmarks.
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The outside of a closed glass display case measures 22" x 15" x 12". The glass is half inch thick. How much air is contained in the case
The volume of the air in the container is: 3,585.125 in³
What is the Volume of the Box?The volume of a box or cuboid is given by the formula:
V = L * W * H
Where:
L is length
W is width
H is height
We are given the external dimensions as:
Length = 22 inches
Width = 15 inches
Height = 12 inches
Since the glass is 1/2 inch thick, then the interior dimensions are:
New length = 22 - 1/2 = 21.5 inches
New Width = 15 - 1/2 = 14.5 inches
New height = 12 - 1/2 = 11.5 inches
Thus:
Volume of air in container = 21.5 * 14.5 * 11.5
= 3,585.125 in³
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Statistics from Cornell's Northeast regional Climate Center indicate that Ithaca, NY, gets an average of 36. 1 inches of rain each year with a
standard deviation of 5. 2 inches,
My friend stayed in Ithaca, NY there for 10 years, she said that the average while she was there was less than 34 inches. What is her vscore for
the 10 years?
(Round to the thousandth place) (Use a Standard Deviation that is rounded to the thousandth place)
Rounded to the thousandth place, your friend's z-score for the 10 years is approximately -0.404.
To calculate your friend's z-score for the 10 years she stayed in Ithaca, NY, you can use the following formula:
z = (X - μ) / σ
where:
- z is the z-score
- X is the sample mean (in this case, 34 inches)
- μ is the population mean (in this case, 36.1 inches)
- σ is the standard deviation of the population (in this case, 5.2 inches, rounded to 5.200 for thousandth place)
Plugging in the values:
z = (34 - 36.1) / 5.200
z = -2.1 / 5.200
z = -0.404
Therefore, your friend's z-score for the 10 years is approximately -0.404, rounded to the thousandth place.
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Four tangents are drawn from E to two concentric circles A, B, C, and D are the points of tangency. 1. Name as many pairs of congruent triangles as possible 2. Tell how you can show each pair is congruent
1. Congruent triangles:
a) Triangle EAB and Triangle ECD
b) Triangle EAC and Triangle EBD
2. Triangle EAB ≅ Triangle ECD and Triangle EAC ≅ Triangle EBD by ASA Congruence Postulate.
In this scenario, we have two concentric circles and four tangents drawn from point E to these circles, creating points of tangency A, B, C, and D.
1. Pairs of congruent triangles:
a) Triangle EAB and Triangle ECD
b) Triangle EAC and Triangle EBD
2. Showing congruence for each pair:
a) To show that Triangle EAB and Triangle ECD are congruent, we can use the following information:
- EA and EC are both radii of the larger circle, so EA = EC (congruent radii).
- AB and CD are tangents to the smaller circle, so the segments are parallel and form corresponding angles at points A and C. Thus, Angle EAB and Angle ECD are congruent (alternate interior angles).
- EB and ED are both radii of the smaller circle, so EB = ED (congruent radii).
With this information, we can prove Triangle EAB ≅ Triangle ECD using the Angle-Side-Angle (ASA) Congruence Postulate.
b) To show that Triangle EAC and Triangle EBD are congruent, we can use the following information:
- EA and EB are both radii of the larger circle, so EA = EB (congruent radii).
- AC and BD are tangents to the larger circle, so the segments are parallel and form corresponding angles at points A and B. Thus, Angle EAC and Angle EBD are congruent (alternate interior angles).
- EC and ED are both radii of the smaller circle, so EC = ED (congruent radii).
With this information, we can prove Triangle EAC ≅ Triangle EBD using the Angle-Side-Angle (ASA) Congruence Postulate.
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Rewrite the expression using a single, positive exponent: 14^-3·14^12
Answer:
It's 14⁹.
Add the powers in the process of multiplying.
Which is -3 + 12 answer is 9.
Hope this helped!
Morgan bought a sofa for $216. 0. the finance charge was $25 and she paid for it over 15 months.
use the formula approrimate apr =
(finance charge: #months)(12)
amount financed
to calculate her approximate apr
round the answer to the nearest tenth.
The approximate APR for Morgan's sofa purchase is 1.7%.
To calculate the approximate APR (Annual Percentage Rate) for Morgan's sofa purchase, we can use the formula:
APR ≈ (finance charge / # of months) x 12 / amount financed
Here, the finance charge is $25, the number of months is 15, and the amount financed is the total cost of the sofa minus the finance charge, which is:
financed= $216.00 - $25.00 = $191.00
on substitution:
APR ≈ (25 / 15) x 12 / 191
APR ≈ 0.2778 x 0.06283
APR ≈ 0.01743
Rounding the answer to the nearest tenth, we get:
APR ≈ 1.7%
Therefore, the approximate APR for Morgan's sofa purchase is 1.7%.
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can someone help? asking for a friend (literally) I’d really appreciate it!
The graphs of the sinusoidal function for the question 1 to 4 created with MS Excel are attached
5. The function is; y = cos(θ) + 2
6. The function is; y = sin(2·θ) - 4
What is a sinusoidal function?A sinusoidal function is a smooth periodic or repetitive function based on the sine or cosine of an angle.
The equations for the graphs in the sinusoidal function indicates that we get;
The period = 2·π/B
The horizontal shift = -C/B
The vertical shift = D
Where;
B = The coefficient of the angle, θ
C = The constant within the parenthesis
D = The constant term outside the sine or cosine function parenthesis
1. y = 2·sin(2·θ + 1)
The function indicates that the amplitude is 2, the period is 2·π/2 = π, the vertical shift is 0, and the horizontal shift is -1/2
Please find attached the graph of the function, created with MS Excel
2. y = -cos(θ) - 2
The amplitude is 1
The period is 2·π
The horizontal shift is 0
The vertical shift is -2
Please find attached the graph of the function y = -cos(θ) - 2, created with ms Excel
3. y = 4·cos(3·θ -2)
The amplitude is 4
The period is 2·π/3
The horizontal shift is 0
The vertical shift is -2
Please find attached the graph of the function y = 4·cos(3·θ -2), created with MS Excel
4. y = 3·sin(6·θ) - 1
The amplitude is 3
The period is π/3
The horizontal shift is 0
The vertical shift is -1
Please find attached the graph of the function y = 3·sin(6·θ) - 1, created with MS Excel
5. The points on the graph are;
Peak; (0, 3)
The next adjacent trough; (180, 1)
The adjacent peak; (360, 3)
Therefore;
The amplitude is 1
The period is 360°
The horizontal shift is 2
The vertical shift is 0
The peak point at θ = 0, indicates;
The function is; y = cos(θ) + 2
6. The points on the graph are;
Peak; (45, -3)
The next adjacent trough; (135, -5)
The adjacent peak; (225, -3)
Therefore;
The amplitude is 1
The period is 180 = π radians
The horizontal shift is 0
The vertical shift is -4
The function is; y = sin(2·θ) - 4
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La familia de una de tus compañeras, que disponía de un terreno con 7 lotes colindantes, y se vieron en la necesidad de venderlos. Establecieron un precio por metro cuadrado de 800 pesos y tienen que calcular el costo, con base en los metros cuadrados que tiene cada lote. Determina el área de cada terreno, así como su precio
The area and cost of each of the lots is given below
What is the area?The area and cost of each of the lots is calculated below
To calculate the rectangle trapezoid, it will be:
B = 140m
h = 50m
b = 70m
Note that Area of Lot 1 : A =(B+b)h/2
Hence Height will be:
A= (140m+ 70m) 50m/2
A = 5250 m²
Cost: C = 5250m² *800 pesos = $4,200,000
Lot 2 is another rectangle trapezoid:
B = 150m
b = 80m
h = 50m
Area: A= (150m+ 80m)50m/2
A = 5750 m²
Cost: C = 5750m² x 800 pesos = $4,600,000
So, for Lot 3 which is a rectangle:
b = 70m
to = 50m
Area: A =a x b
W=50m x 70m
A = 3500 m²
Cost: C = 3500m² x 800 pesos = $2,800,000
Lot 4 is a right triangle:
b = 70m
h = 50m
Area: A =b x h/2
A= (50m x 70m)/2
A = 1750 m²
Cost: C = 1750 m² x 800 pesos = $1,400,000
So for Lot 5 that is a rhomboid:
b = 150 base meters
h=50m
Area: A=b x h
A= (150m x 50m
H = 7500 m²
Cost: C = 7500m² x 800 pesos = $6,000,000
So, for Lot 6 that is an isosceles triangle:
b = 140m
h= 50m
Area: A =b x h/2
A= (140m x 50m)/2
A = 3500 m²
Lastly, the Cost: C = 3500m² x 800 pesos = $2,800,000
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See transcribed text below
The family of one of your colleagues, who had a piece of land with 7 adjoining lots, and they found themselves in need of selling them. They established a price per square meter of 800 pesos and they have to calculate the cost, based on the square meters that each lot has. Before continuing, review the terrain sketch and answer the questions
What is the area and cost of each of the lots?
Customers arrive at a busy food truck according to a Poisson process with parameter λ. If there are i people already in line, the customer will join the line with probability 1/(i +1). Assume that the chef at the truck takes, on average, a minutes to process an order.
Required:
a. Find the long-term average number of people in line.
b. Find the long-term probability that there are at least two people in line
The required answer is P(at least 2) = P(at least 1) * (1/2) = (1 - e^(-λ * a)) * (1/2)
a. To find the long-term average number of people in line, we will use the following formula:
Average number of people in line = λ * a
Here, λ is the arrival rate of customers following a Poisson process, and a is the average time taken by the chef to process an order.
b. To find the long-term probability that there are at least two people in line, we first need to calculate the probability that there is at least one person in line. Then, we will subtract this probability from 1 to find the probability of having at least two people in line.
Probability of at least one person in line = 1 - Probability of no one in line
Since the arrival of customers follows a Poisson process, the probability of having no one in line is given by:
P(0) = e^(-λ * a)
Thus, the probability of at least one person in line is:
P(at least 1) = 1 - e^(-λ * a)
Now, we can calculate the probability of having at least two people in line by considering that the second person joins the line with probability 1/(1 + 1) = 1/2. So, the probability of at least two people in line is:
P(at least 2) = P(at least 1) * (1/2) = (1 - e^(-λ * a)) * (1/2)
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please help...................
I need to find the missing angle and arc measures.
please answer
Step by step
We will be sure to take your time and carefully consider the given information in order to find the missing angle and arc measures accurately.
To find the missing angle and arc measures, follow these steps:
1. Look at the given diagram to identify the angles and arcs involved.
2. Use the angle sum property of a circle to find the measure of the missing angle. This property states that the sum of the angles in a circle is equal to 360 degrees. So, if you know the measures of the other angles in the circle, you can subtract their sum from 360 to find the missing angle.
3. Use the arc angle formula to find the measure of the missing arc. This formula states that the measure of an arc is equal to the measure of its corresponding central angle. So, if you know the measure of the missing angle, you can use it to find the measure of the missing arc.
4. Check your answer by making sure that the sum of all the arc measures in the circle is equal to the circumference of the circle.
Overall, be sure to take your time and carefully consider the given information in order to find the missing angle and arc measures accurately.
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You and a group of friends want to know how many students in your school prefer rap music. There are 440 students in your school. Each person in the group randomly surveys 20 students. The table shows the results.
A. Use each sample to make and estimate for the number of students in your school who prefer rap music
B. Describe the center and variation of the estimates
The survey results show that the estimates for the number of students in the school who prefer rap music range from 110 to 154. The center of the estimates is around 121, with a variation of about 66.
To estimate the number of students who prefer rap music, multiply the proportion who prefer rap in each sample by the total number of students in the school (440)
Sample 1: 0.25 x 440 = 110
Sample 2: 0.20 x 440 = 88
Sample 3: 0.30 x 440 = 132
Sample 4: 0.35 x 440 = 154
The center of the estimates is the average of the four estimates: (110 + 88 + 132 + 154) / 4 = 121. Variability can be described using the range (154 - 88 = 66) or the standard deviation of the estimates, which requires additional calculations.
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Find the measure of angle D.
Answer:
Step-by-step explanation:
3x4
How can you use rational expressions and equations to describe relationship and solve problems?
Rational expressions and equations can be used to describe relationships and solve problems that involve proportions or rates of change.
They involve expressions that are fractions of polynomials, where the numerator and denominator can be thought of as values that change according to some variable.
For example, rational expressions can be used to represent rates of change in physics or finance, such as the speed of an object or the interest rate on a loan. By setting up equations with rational expressions, we can solve for unknown values or relationships between variables.
Rational equations can also be used to describe relationships between quantities that are proportional, such as the volume of a container and the amount of liquid it can hold. By solving for an unknown variable in a rational equation, we can determine the relationship between the two quantities and use it to make predictions or solve practical problems.
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40% of a smoothie from Blender Splendor is fruit juice. There are 20 ounces in a smoothie. How many ounces of fruit juice does a smoothie have?
A 20-ounce smoothie from Blender Splendor contains 8 ounces of fruit juice.
To find out how many ounces of fruit juice are in a 20-ounce smoothie from Blender Splendor, given that 40% of the smoothie is fruit juice, follow these steps:
1. Convert the percentage to a decimal: 40% = 0.40
2. Multiply the total ounces of the smoothie by the decimal: 20 ounces * 0.40 = 8 ounces
Your answer: A 20-ounce smoothie from Blender Splendor contains 8 ounces of fruit juice.
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What’s the answer? I need help please
Answer:
-√3/2
Step-by-step explanation:
sin(x) is equal to 1/2 when x=7π/6 or 11π/6
cos(7π/6) = -√3/2
cos(11π/6) = √3/2
In the question, it says that cos(x) is <0, which means that it has to be negative
So, the answer is -√3/2
Answer: C
Step-by-step explanation:
Think of a unit circle
sin x = -1/2 happens at 7[tex]\pi[/tex]/6 and 11[tex]\pi[/tex]/6, 3rd and 4th quadrant
Out of those 2 quadrants cos x is negative in the 3rd quadrant
So cos x= -√3/2
All of the training times of which person had the greatest spread? Explain how you know. (b) The middle 50% of the training times of which person had the least spread? Explain how you know. (c) What do the answers to Parts 2(a) and 2(b) tell you about Adam’s and Miguel’s training times?
(a) Miguel had the greatest spread in training times.
(b) The middle 50% of Adam's training times had the least spread.
(a) To find the greatest spread in training times, we need to calculate the range of each person's training times. Range is the difference between the maximum and minimum values. Comparing the ranges, we can say that Miguel had the greatest spread in training times since his range is the largest.
(b) The middle 50% of the training times refers to the interquartile range (IQR), which is the difference between the third quartile (Q3) and the first quartile (Q1).
To find the least spread in the middle 50% of the training times, we need to compare the IQRs of each person. Adam's IQR is the smallest, which means the middle 50% of his training times had the least spread.
(c) The answers to parts (a) and (b) indicate that Miguel had a wider range of training times compared to Adam. However, Adam's middle 50% of training times had the least spread. This suggests that while Miguel's overall training times varied more, Adam's training times were more consistent within the middle range.
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Find the inverse of the function
The inverse of the function f(x) = √(x+1) is [tex]f^-1[/tex](x) = x² - 1.
What is inverse function?Given a function f(x), its inverse function, denoted as [tex]f^-1[/tex](x), is a function that takes the output of f(x) and returns the original input. In other words, if y = f(x), then x = [tex]f^-1[/tex](y).
According to question:To find the inverse of the function f(x), we follow these steps:
Step 1: Replace f(x) with y:
y = √(x+1)
Step 2: Interchange x and y:
x = √(y+1)
Step 3: Solve for y:
x² = y+1
y = x² - 1
Step 4: Replace y with f^-1(x):
f^-1(x) = x² - 1
Therefore, the inverse of the function f(x) = √(x+1) is [tex]f^-1[/tex](x) = x² - 1.
To verify this, we can check that ([tex]f^-1[/tex] o f)(x) = x and (f o [tex]f^-1[/tex])(x) = x for all x in the domain of the functions:
([tex]f^-1[/tex] o f)(x) = [tex]f^-1[/tex](f(x)) = (√(x+1))² - 1 = x
(f o [tex]f^-1[/tex])(x) = f([tex]f^-1[/tex](x)) = √((x² - 1) + 1) = √(x²) = |x| + 1
Since the range of f(x) is [0, infinity), we restrict the domain of [tex]f^-1[/tex](x) to [1, infinity) to ensure that the inverse is a function.
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Victoria drove 76 miles, burning 4 gallons of gasoline. She knows the total number of miles she can drive is proportional to the number of gallons of gas she burns and wants to create an equation that can be used to predict the number of miles she can drive for any number of gallons of gas used. Drag the correct values to create an equation which will accurately represent the total number of miles, m, Victoria should expect to be able to drive if she uses g gallons of gasoline
The equation that represents the total number of miles, m, Victoria should expect to be able to drive if she uses g gallons of gasoline is m = (19g).
We can determine the proportionality constant by dividing the total number of miles driven (76) by the number of gallons of gasoline burned (4), which gives us 19 miles per gallon (76/4 = 19).
We can then use this proportionality constant to create the equation m = (19g), where m represents the total number of miles Victoria should expect to be able to drive if she uses g gallons of gasoline. This equation tells us that for every additional gallon of gasoline burned, Victoria should expect to be able to drive an additional 19 miles.
For example, if Victoria were to burn 6 gallons of gasoline, she should expect to be able to drive 114 miles (6 x 19 = 114). This equation assumes that Victoria's car has a constant fuel efficiency of 19 miles per gallon.
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consider the first month's sales data for the south region.
select the correct answer from each drop-down menu.
for the south region, the proportion of sales from current stores is approximately______ %.
a.63
b.37
c.58
d.24
because this proportion is_________
a. relatively close to
b. significantly different from
the sales director's statistical model, the data is______
a. inconsistent
b. consistent
with the model.
Answer is:
For the south region, the proportion of sales from current stores is approximately 58 %.
because this proportion is relatively close to the sales director's statistical model, the data is consistent with the model.
The given information states that the proportion of sales from current stores in the South region is approximately 58%. This value falls within the range of the sales director's statistical model, which could be an estimated value or a range of values based on past data or other sources. Since the proportion of sales falls within the expected range, the data is consistent with the model. This means that the actual value observed is not significantly different from the expected value, and there is no evidence to suggest that the model needs to be revised or updated.
Therefore, the answer to the second drop-down menu is "consistent". If the actual proportion of sales from current stores in the South region was significantly different from the expected value in the sales director's statistical model, then the answer would be "inconsistent". However, since the observed proportion is relatively close to the expected value, the data is consistent with the model.
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a man in a plane is looking down at a building below. if the man is 40,000 feet away from the building and the altitude of the man is 33,000 feel what is the angle of depression from the man to the building below
The angle of depression from the man to the building below is approximately 39.81°.
To find the angle of depression from the man to the building below, we'll use the tangent function and the given information.
Given:
- The man is 40,000 feet away from the building horizontally.
- The man's altitude is 33,000 feet.
Step 1: Identify the opposite and adjacent sides in relation to the angle of depression.
- The opposite side is the altitude (33,000 feet).
- The adjacent side is the horizontal distance (40,000 feet).
Step 2: Use the tangent function to find the angle of depression.
tan(angle) = opposite/adjacent
tan(angle) = 33,000/40,000
Step 3: Find the inverse tangent of the ratio to get the angle.
angle = arctan(33,000/40,000)
Step 4: Calculate the angle.
angle ≈ 39.81°
The angle of depression from the man to the building below is approximately 39.81°.
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if it's 9:45 am what time would it be in 9 hours?
Answer:
6:45pm
Step-by-step explanation:
Given: The time is currently 9:45am
To find: The time in 9 hours
To do this, we have to add 9 hours to 9:45am.
9:45am+9 hours=
6:45pm
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If the ratio of ambers miniature house to the original structure is 2:35 and the miniature requires 4 square feet of flooring how much flooring exists in the original house
The original house has 70 square feet of flooring.
If the ratio of the miniature house to the original structure is 2:35, then we can say that the miniature house is 2/35th the size of the original house in terms of floor area. Let's assume that the original house has x square feet of flooring. Then, we can set up a proportion based on the ratios:
2/35 = 4/x
Solving for x, we get:
x = 70
Therefore if the ratio of ambers miniature house to the original structure is 2:35 and the miniature requires 4 square feet of the flooring then original house has 70 square feet of flooring.
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the manager at the yellow rose diner needs to purchase silverware for the restaurant. the silverware cost $230 and the manager placed an order for silverware in a state with a sales tax of 6.5%
The manager will need to pay $244.95 to purchase the silverware, including sales tax.
What is decimal?
Decimals are numbers that have two parts: a whole number part and a fractional part separated by a decimal point.
According to the given information:
If the silverware costs $230 and the sales tax is 6.5%, we need to calculate the amount of tax that will be added to the cost of the silverware:
Tax = 6.5% of $230 = 0.065 x $230 = $14.95
So the total cost of the silverware including tax is:
$230 + $14.95 = $244.95
Therefore, the manager will need to pay $244.95 to purchase the silverware, including sales tax.
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