Answers
The z-scores are given as follows:
Josh: Z = -1.79. -> more convincing.Rita: Z = -1.58.How to obtain the z-scores?The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution of the data-set, depending if the obtained z-score is positive(above the mean) or negative(below the mean).The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure X in the distribution. -> this means that the higher the absolute value of the z-score, the more convincing it is.Josh's z-score is given as follows:
Z = (185.16 - 185.81)/0.363
Z = -1.79.
Rita's z-score is given as follows:
Z = (109.89 - 110.1)/0.133
Z = -1.58.
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Related Questions
How do I write this in a function?? And then also how do I graph this function?? Thank you.
Answers
To find the length of a row of bookshelves, we can use the square root function, as the length of a row of bookshelves will be proportional to the square root of the area of the space that Isabel rents.
Mathematically, we can express f(x) as: f(x) = √(x)
Where x represents the area of the space that Isabel rents, and f(x) represents the total length of a row of bookshelves.
What is the square root function?The above function takes the square root of the area x, which gives us the length of a row of bookshelves in feet, assuming that the area is in square feet. As x increases, f(x) will also increase, indicating that the length of the row of bookshelves will also increase as Isabel rents a larger area in the warehouse.
To find the length of a row of bookshelves, we can use the square root function, denoted as √(x), where x represents the area of the space that Isabel rents.
Determine the area of the space that Isabel rents, denoted as x. This could be obtained from the rental agreement or by measuring the area of the space using appropriate units (e.g., square feet).Take the square root of x using a calculator or by using a mathematical formula. The square root of x, denoted as √(x), represents the positive value which, when multiplied by itself, gives x.The resulting value of √(x) represents the total length of a row of bookshelves in feet (assuming that the area is in square feet), as per the requirement given in the problem statement.For example, if Isabel rents an area of 324 square feet, we can find the length of a row of bookshelves as follows:
x = 324
f(x) = √(x) = √(324) = 18
So, the length of a row of bookshelves would be 18 feet in this case.
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See full text below
Part 2: Solve a real-world problem using a square root function.
When Isabel began her book-selling business, she stored her inventory in her garage. Now that her business has grown, she wants to rent warehouse space. Lisa owns a large warehouse nearby and can rent space to Isabel. The area of the warehouse is 8,100 square feet. Lisa is willing to rent Isabel as little as 100 square feet of the space or up to as much as the entire warehouse. Her only requirement is that all spaces must be square.
The total length of each row of bookshelves will be of the length of the storage space.
Let x be the area of the space that Isabel rents and f(x) represent the total length of a row of bookshelves. How would you find the length of a row of bookshelves? (3 points)
Write a function that expresses f(x). (10 points)
Does anybody know what 3,600 is as 1 unit less than 4,000???
Answers
Answer:
Amount of change: 4,000 - 3,600 = 400
Percent of change: 400/4,000 = 1/10 = 10%
There was a 10% decrease in the number of visitors:
Find the value of x in the triangle shown below.
X=
4.5
56°
4
4
X°
Answers
Answer:
68.9 degrees
Step-by-step explanation:
To find this we can use the rule of sines.
It states [tex]\frac{sinA}{a}=\frac{sinB}{b}=\frac{sinC}{c}[/tex]
We will use 56 degrees and its complementary measurement, which is discovered by observing the opposite side from the angle, which is 4. Then, we will find the side that compliments x, which is 4.5. Then we can plug those values into the rule of sines.
[tex]\frac{sin56}{4}=\frac{Sinx}{4.5}[/tex]
Then, we want to get Sin x by itself.
[tex]\frac{sin56}{4}*4.5=sinx[/tex]
Then, we can solve for sin x.
[tex]0.932667269124=sinx[/tex]
finally, we need to take the inverse of sin to find our solution.
[tex]sin^{-1} (0.932667269124)=sin^-^1(sinx)\\x=68.85\\[/tex]
Which can be rounded to 68.9.
A spinner has 10 equally sized sections, 3 of which are green and 7 of which are yellow. The spinner is spun and, at the same time, a fair coin is tossed. What is the probability that the spinner lands on green and the coin toss is heads?
Answers
Okay, here are the steps to solve this problem:
* There are 10 sections on the spinner, 3 of which are green and 7 of which are yellow.
* So there is a 3/10 = 0.3 probability that the spinner will land on green.
* A fair coin has a 1/2 probability of landing on heads.
* For the spinner and coin toss to both have the desired outcome (green and heads), we multiply their individual probabilities:
* 0.3 * 1/2 = 0.15
Therefore, the probability that the spinner lands on green and the coin toss is heads is 0.15.
A normal distribution has a mean of 33 and a standard deviation of 4. Find the probability that a randomly selected x-value from the distribution is in the given interval. a. between 29 and 37 b. between 33 and 45 c. at least 29 d. at most 21
Answers
Step-by-step explanation:
We can use the standard normal distribution to calculate probabilities for a normal distribution with mean 33 and standard deviation 4. We just need to standardize the intervals using the formula:
z = (x - mu) / sigma
where x is the specific value in the interval, mu is the mean, sigma is the standard deviation, and z is the corresponding z-score.
a. Between 29 and 37:
z1 = (29 - 33) / 4 = -1
z2 = (37 - 33) / 4 = 1
Using a standard normal distribution table, the cumulative probability of z being between -1 and 1 is approximately 0.6827.
So the probability that a randomly selected x-value from the distribution is between 29 and 37 is approximately 0.6827.
b. Between 33 and 45:
z1 = (33 - 33) / 4 = 0
z2 = (45 - 33) / 4 = 3
The cumulative probability of z being between 0 and 3 is approximately 0.4987.
So the probability that a randomly selected x-value from the distribution is between 33 and 45 is approximately 0.4987.
c. At least 29:
z = (29 - 33) / 4 = -1
The cumulative probability of z being less than -1 is approximately 0.1587. So the probability that a randomly selected x-value from the distribution is at least 29 is approximately 1 - 0.1587 = 0.8413.
d. At most 21:
z = (21 - 33) / 4 = -3
The cumulative probability of z being less than -3 is very close to 0. So the probability that a randomly selected x-value from the distribution is at most 21 is approximately 0.
5. Scott planted 20% of a garden with roses. What is the area of
the section of the garden that is planted with roses?
Answers
If Scott planted 20% of a garden with roses then the area of
the section of the garden that is planted with roses is 10 square feet
The garder is in rectangle shape
We have to find the area of the garden
The length of the garden is 10 ft and width of garden is 5 ft
Area of garden = 10×5
=50 square feet
Now Scott planted 20% of a garden with roses
Convert 20% to decimal by dividing 20 by 100
Area of garden which has roses = 50×0.2
=10 square feet
Hence, if Scott planted 20% of a garden with roses then the area of
the section of the garden that is planted with roses is 10 square feet
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The average daily balance of a credit card for the month of March was $1900 and the unpaid balance at the end of the month was $1700. If the annual percentage rate is 32.4% of the average daily balance, what is the total balance on the next billing date, April 1?
Round your answer to the nearest cent.
Answers
Using the average daily balance, the total balance on the next billing date, April 1 is $5,059.73.
What is the average daily balance?The average daily balance is a credit card method of computing finance charges.
To determine the average daily balance, the sum of the daily balances over your billing cycle is divided by the number of days in the billing cycle.
The finance charge is then the product of the average daily balance multiplied by the APR and the number of days involved, divided by 365 days.
Average daily balance = $1,900
Unpaid balance at month-end = $1,700
APR = 32.4%
The finance charge for the month = $9.73 ($1900 x 32.4% x 30/365)
The total balance on the next billing date, April 1 = $5,059.73 ($5,050 + $9.73)
Thus, on April 1, the next billing cycle, the balance on the card is $5,059.73.
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HELP FAST PLEASE!!
Which of the following are parts of a pyramid?
altitude
vertex
lateral edges
sides
lateral faces
Answers
The part of a pyramid include the following: E. lateral faces.
How to calculate the volume of a pyramid?In Mathematics and Geometry, the volume of a pyramid can be calculated by using the following formula:
Volume = 1/3 × b × h
Where:
h represent the height of a pyramid.b represent the base area of a pyramid.Generally speaking, a pyramid is composed of three main parts and these include the following:
ApexLateral faceBaseIn conclusion, we can reasonably infer and logically deduce that lateral face is a part of any pyramid.
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Danny works at the hunting and fishing supply store. At the end of each month he earns a commission on all of his sales for that month.
He earns a 2.5% commission on his first $4000 in sales.
He earns a 7.5% commission on any amount of sales beyond $4000. Lastmonthheworkedhardandearned$1000commission. How much,in dollars,did he have in sales last month?
(The answer is 16,000 I just need to figure out how to do it)
Answers
Danny had the sales of total $16,000.
We have,
He earns a 2.5% commission on his first $4000 in sales.
He earns a 7.5% commission on any amount of sales beyond $4000.
Commission earned = $1000
So, 6.25% of x = 1000
6.25/10 x = 1000
0.0625x = 1000
x= 1000/ 0.0625
x= $16,000
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Danny had the sales of total $16,000.
We have,
He earns a 2.5% commission on his first $4000 in sales.
He earns a 7.5% commission on any amount of sales beyond $4000.
Commission earned = $1000
So, 6.25% of x = 1000
6.25/10 x = 1000
0.0625x = 1000
x= 1000/ 0.0625
x= $16,000
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Help with this math please.
Answers
The actual distance between the two cities is given as follows:
17 miles.
How to obtain the actual distance?The actual distance between the two cities is obtained applying the proportions in the context of the problem.
The scale factor is given as follows:
1 inch = 17 miles.
The length of the drawing is given as follows:
1 inch.
Hence the actual distance between the two cities is given as follows:
1 x 17 = 17 miles.
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A group of students was to clean up to two areas in their school. area a was 1 1 2 times of area b. in the morning (half of a day), the number of students cleaning area a was 3 times that of the number of students in area b. in the afternoon (another half of a day), 7/12 of the students worked in area a while the rest of them in area b. at the end of the day, area a was done, but area b still needed 4 students to work one more day before it was done. how many were there in this group of students?
Answers
There were 24 students working in area B in the morning, and 3 times as many, or 72 students, working in area A. The total number of students is then 24 + 72 = 96.
What is an area?In geometry, an area is the measurement of the amount of space inside a two-dimensional flat surface such as a square, rectangle, triangle, circle, or any other shape. It is usually expressed in square units, such as square centimeters (cm²) or square meters (m²), and is calculated by multiplying the length and width of a rectangular shape or by using specific formulas for different geometric shapes such as the base times the height divided by 2 for a triangle or pi times the radius squared for a circle. The concept of area is fundamental in many branches of mathematics, physics, engineering, and other fields where the measurement of the extent of a surface is important.
According to the given equationLet's assume that the number of students working in area b is x. Then the number of students working in area A is 3x (since there are three times as many students working in area A as in area b in the morning).
Let A be the area of area a, and B be the area of area b. We know that A = 1.5B (since area a is 1 1 2 times the area of area b).
In the morning, the total number of students is x + 3x = 4x.
In the afternoon, 7/12 of the students work in area a, and the rest work in area b. So, the number of students working in area A in the afternoon is 7/12 * 4x = 7x/3, and the number of students working in area b is (1 - 7/12) * 4x = 5x/12.
Since area a was finished at the end of the day, we know that the total area cleaned by the students is A + B = 1.5B + B = 2.5 B. This means that the number of students working in area b is enough to finish 0.5B (since area a was already finished), but 4 more students are needed to finish the remaining 0.5B.
So, we can set up the following equation:
(5x/12) / x = 0.5 / (0.5 + 4/x)
Simplifying this equation, we get:
5x = 6x + 24
x = 24
Therefore, there were 24 students working in area b in the morning, and 3 times as many, or 72 students, working in area A. The total number of students is then 24 + 72 = 96.
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Form a polynomial f(x) with real coefficients having the given degree and zeros.
Degree 4; zeros: 6 (Multiplicity 2); 3i
Enter the expanded polynomial. Let a represent the leading coefficient.
f(x) = a( )
Answers
Answer:
Step-by-step explanation:
The polynomial f(x) with real coefficients, degree 4, and zeros 6 (multiplicity 2), 3i can be formed as follows:
Since the zero 6 has a multiplicity of 2, it appears twice in the factored form of f(x), i.e., (x-6)(x-6) = (x-6)^2.
The other zero is 3i, which means its complex conjugate, -3i, is also a zero. Therefore, the factored form of f(x) can be written as:
(x-6)^2(x-3i)(x+3i)
Expanding this expression, we get:
f(x) = (x-6)^2(x^2 + 9)
Multiplying this out, we get:
f(x) = x^4 - 12x^3 + 81x^2 - 216x + 324
Therefore, the polynomial f(x) with real coefficients, degree 4, and zeros 6 (multiplicity 2), 3i can be written as:
f(x) = x^4 - 12x^3 + 81x^2 - 216x + 324.
f(x) = a(x - 6)^2(x - 3i)(x + 3i)
To expand this polynomial, we can use the fact that (a + b)(a - b) = a^2 - b^2. Substituting a = x - 6 and b = 3i, we get:
(x - 6 + 3i)(x - 6 - 3i) = (x - 6)^2 + 9
Therefore, the expanded polynomial is:
f(x) = a(x - 6)^2(x - 3i)(x + 3i)
f(x) = a(x - 6)^2(x^2 + 9)
f(x) = a(x^4 - 12x^3 + 57x^2 - 108x + 81)
So, the expanded polynomial is f(x) = a(x^4 - 12x^3 + 57x^2 - 108x + 81).
3800 people attended a football game. If 4% of the people who attended were
teenagers, how many teenagers attended the game?
Answers
4% of 3800 is 152
Answer:
152 teenagers attended the game.
Step-by-step explanation:
Write the formula:
4% of 3800 people = total teens
Evaluate:
4/100 x 3800
Calculate:
4 x 38
= 152 teens
What is (1/4) to the second power
Answers
Answer:
1/16
Step-by-step explanation:
(1/4)x(1/4)= 1/16
The expression (cscx + cotx)? is the same as____.
Answers
The expression (cscx + cotx)² is the same as csc²x + 2(cscx)(cotx) + cot²x. (option a).
The given expression is (cscx + cotx)². To simplify this expression, we can use the formula for squaring a binomial, which is (a + b)² = a² + 2ab + b². In this case, a = cscx and b = cotx. Therefore, we can substitute these values into the formula to get:
(cscx + cotx)² = csc²x + 2(cscx)(cotx) + cot²x
So the expression (cscx + cotx)² is the same as csc²x + 2(cscx)(cotx) + cot²x.
Hence the correct option is (a).
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Paul bakes raisin bars in a pan shaped like a rectangular prism. The volume of the pan is 252 cubic inches. The length of the pan is 12 inches, and its width is 10-1/2 inches. What is the height of the pan? Enter your answer in the box
Answers
Answer:
The volume of a rectangular prism is given by the formula V = lwh, where l, w, and h are the length, width, and height of the prism, respectively. We are given that the volume of the pan is 252 cubic inches, the length is 12 inches, and the width is 10-1/2 inches.
So, 252 = 12 x 10.5 x h
Simplifying the right side of the equation, we get:
252 = 126h
Dividing both sides by 126, we get:
h = 2
Therefore, the height of the pan is 2 inches.
The height of the pan can be found by dividing the volume of the pan by the area of the pan's base.
Step 1: Find the area of the base.
The area of the base is the length multiplied by the width:
Area = Length * Width = 12 inches * 10.5 inches = 126 inches²
Step 2: Divide the volume of the pan by the area of the base:
Height = Volume / Area = 252 cubic inches / 126 inches² = 2 inches
33.3/11=_____ (round to the nearest hundredth)
Answers
33.3/11 = 3.02727272727...
Then, rounding to the nearest hundredth means keeping only two decimal places. The third decimal place is 7, which is greater than or equal to 5, so we round the second decimal place up:
3.03
Therefore, 33.3/11 rounded to the nearest hundredth is 3.03.
Hannah is working in England for 3 months on a project for her company. One weekend Hannah decides to go to France with her car on the ferry, then explore the French countryside. In England, speed limit signs are posted in miles per hour (mph) and Hannah's rental car only shows the speed in miles per hour. In France, speed limit signs are posted in kilometers per hour (kph). Hannah looks up the conversion and learns that 1 kph = 0.62 mph.
On the road that Hannah is currently on, the posted speed limit is 130 kilometers per hour. What is the maximum whole-number speed, in miles per hour, that Hannah can drive without exceeding the speed limit??
A. 82 mph
B. 79 mph
C. 209 mph
D. 80 mph
Answers
Answer:
To convert 130 kph to mph, we can use the conversion factor 1 kph = 0.62 mph:
130 kph × 0.62 mph/kph ≈ 80.6 mph
So the maximum whole-number speed that Hannah can drive without exceeding the speed limit is 80 mph (option D).
Step-by-step explanation:
Explanation: I was doin sth like this last year
An island is located 48 miles N23°38'W of a city. A
freighter in distress radios its position as N11°26'E of the
island and N12° 16'W of the city. How far is the freighter
from the city?
Answers
The freighter is approximately 164.33 miles from the city.
How to determine how far is the freighter from the city?We can use the Law of Cosines to solve this problem. Let's label the distances as follows:
d: distance between the city and the freighter
x: distance between the city and the island
y: distance between the island and the freighter
First, we need to find x using the given coordinates:
N23°38'W is equivalent to S23°38'E, so we have:
cos(23°38') = x/48
x = 48cos(23°38') ≈ 42.67 miles
Next, we can use the coordinates of the freighter to find y:
N11°26'E is equivalent to E11°26'N, and N12°16'W is equivalent to S12°16'E. This means that the angle between the island and the freighter is:
23°38' + 11°26' + 12°16' = 47°20'
cos(47°20') = y/d
We can rearrange this equation to solve for y:
y = dcos(47°20')
Now we can use the Law of Cosines to solve for d:
d² = x² + y² - 2xy cos(90° - 47°20')
d² = 42.67² + (d cos(47°20'))² - 2(42.67)(d cos(47°20')) sin(47°20')
d² = 1822.44 + d² cos²(47°20') - 2(42.67)(d cos(47°20')) sin(47°20')
d² - d² cos²(47°20') = 1822.44 - 2(42.67)(d cos(47°20')) sin(47°20')
d² (1 - cos²(47°20')) = 1822.44 - 2(42.67)(d cos(47°20')) sin(47°20')
d² sin²(47°20') = 1822.44 - 2(42.67)(d cos(47°20')) sin(47°20')
d² = (1822.44 - 2(42.67)(d cos(47°20')) sin(47°20')) / sin²(47°20')
d ≈ 164.33 miles
Therefore, the freighter is approximately 164.33 miles from the city.
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FIND THE SPACE SAMPLE AND TOTAL POSSIBLE OUTCOMES
Sunscreen
SPF 10, 15, 30, 45, 50
Type Lotion, Spray, Gel
Answers
The space sample would include the lotion, spray and gel, with the SPF and there are 15 possible outcomes.
How to find the sample space ?The enumeration of sample space and all potential results can be achieved by duly considering various combinations of SPF and sunscreen variety. It is achievable to list the entire gamut of possibilities when each type of sunscreen is matched with every value of SPF:
The sample space would look like this:
SPF 10 LotionSPF 10 SpraySPF 10 GelSPF 15 LotionSPF 15 SpraySPF 15 GelSPF 30 LotionSPF 30 SpraySPF 30 GelSPF 45 LotionSPF 45 SpraySPF 45 GelSPF 50 LotionSPF 50 SpraySPF 50 GelThis shows that there are 15 possible outcomes in the sample space.
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Help Please Be Fast
Answers
The maximum value of the objective functions are 2600, 27 and 1980
Solving the objective function graphicallyGiven that
Max Z = 8x + 16y
Where the constraints are
3x + 6y ≤ 900
x + y ≤ 200
y ≤ 125
x, y ≥ 0
Plotting the constraints 3x + 6y ≤ 900, x + y ≤ 200 and y ≤ 125 on the same graph, the coordinates of the feasible region are:
(x, y) = (100, 100), (75, 125) and (50, 125)
So, we have
Z = 8(100) + 16(100) = 2400
Z = 8(75) + 16(125) = 2600
Z = 8(50) + 16(125) = 2400
Hence, the maximum value is 2600
Solving the objective function graphicallyGiven that
Max Z = 6x + 3y
Where the constraints are
2x + y ≤ 8
3x + 3y ≤ 18
y ≤ 3
x, y ≥ 0
Plotting the constraints 2x + y ≤ 8, 3x + 3y ≤ 18 and y ≤ 3 on the same graph, the coordinates of the feasible region are:
(x, y) = (3, 3), (2.5, 3) and (2, 4)
So, we have
Z = 6(3) + 3(3) = 27
Z = 6(2.5) + 3(3) = 24
Z = 6(2) + 3(4) = 24
Hence, the maximum value is 27
Solving the objective function by simplexGiven the objective function, the constraints and the final simplex tableau
We have the final values to be
Z = 1980
This means that the maximum value is 1980
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PLEASE HELP IT'S FOR MY TEST
Use long division to rewrite this rational function in transformation form, then graph.
[tex]f(x) = \frac{x-1}{4x-16} \\[/tex]
Answers
The graph of f(x) = (x - 1)/(4(x - 4)) is plotted to represent f(x) = (x - 1)/(4x - 16)
Rewriting the rational functionFrom the question, we have the following parameters that can be used in our computation:
f(x) = (x - 1)/(4x - 16)
Factor out 4 from the denominator
So, we have
f(x) = (x - 1)/(4(x - 4))
This means that
f(x) = (x - 1)/(4(x - 4)) is equivalent to f(x) = (x - 1)/(4x - 16)
So, we can plot the graph of f(x) = (x - 1)/(4(x - 4)) to represent f(x) = (x - 1)/(4x - 16)
See attachment for the graph
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What is the length of the unknown leg
of the right triangle?
2 ft
3 ft
(The figure is not drawn to scale.)
The length of the unknown leg of the right triangle is ft.
(Round to one decimal place as needed.)
Answers
Thus, the unknown leg x of the right angled triangle is found as 2.2 ft.
Explain about the right triangle:A right triangle is one that has an interior angle of 90 degrees. The hypotenuse, which is also the side of the right triangle that faces the right angle, is its longest side. The height and base make up the two arms of the right angle.
What a Right Triangle Looks Like
In a right triangle, the right angle is often the biggest angle.The longest side is the hypotenuse, which is the side that faces the right angle.A right triangle cannot include any obtuse angles.For the given right triangle:
Let the unknown length be 'x'.
Using the Pythagorean theorem:
3² = 2² + x²
x² = 3² - 2²
x² = 9 - 4
x² = 5
x = 2.2
Thus, the unknown leg x of the right angled triangle is found as 2.2 ft.
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What is the image of point (-6,1) after the reflection over the line x=2
Answers
Answer:
(-6,3)
Step-by-step explanation:
reflect over x=2, so you. move Y up by 2. 1+2 =3
Find inverse of the following f(x)=x^3+9
Answers
as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solving for "y", let's do so.
[tex]\stackrel{f(x)}{y}~~ = ~~x^3+9\hspace{5em}\stackrel{\textit{quick switcheroo}}{x~~ = ~~y^3+9} \\\\\\ x-9=y^3\implies \sqrt[3]{x-9}=y=f^{-1}(x)[/tex]
This year's property taxes on a parcel are $1,743.25. If a sale of the property is to be closed on
August 12, what is the approximate tax proration that will be charged to the seller based on a 360-day
year?
Answers
Answer:
$1070.16
Step-by-step explanation:
You want the prorated amount of taxes if the annual amount is $1743.25 and the sale closes August 12, based on a 360 day year.
Months and daysA 360-day year assumes months are 30 days. The tax charged to the seller will be that for 7 months plus 11 days:
(7·30 +11)/360 × $1743.25 = $1070.16
The seller will pay $1070.16 of the tax bill.
__
Additional comment
We have presumed the buyer pays the taxes for August 12, the first day they own the property.
Using the following conversions between the metric and U.S. systems, convert the measurement.
Round your answer to 6 decimal places as needed
1 meter≈ 3.28 feet
1 Lite≈ 0.26 gallons
1 kilogram≈ 2.20 pounds
15.048 dL≈ qt
Answers
15.048 deciliters is equivalent to 1 quart.
What is conversion?Conversion is the process of changing a quantity from one unit of measure to another unit of measure using a conversion factor or a formula.
We have:
To convert meters to feet, multiply by 3.28.
To convert liters to gallons, multiply by 0.26.
To convert kilograms to pounds, multiply by 2.20.
To convert deciliters to quarts, divide by 15.048.
Let's use these conversions to convert the given measurement:
15.048 dL = qt
Dividing both sides by 15.048, we get:
1 dL = qt/15.048
Multiplying both sides by 0.946353, which is the number of quarts in a liter, we get:
0.946353 dL = qt/15.048 * 0.946353
Simplifying the right-hand side, we get:
0.946353 dL = qt/15.961
Multiplying both sides by 3.78541, which is the number of liters in a gallon, we get:
3.78541 * 0.946353 dL = 3.78541 * qt/15.961
Simplifying the left-hand side, we get:
3.58702 L = qt/4.22676
Multiplying both sides by 4.22676, we get:
15.1485 L = qt
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bird was sitting 33 feet from the base of an oak tree and flew 65 feet to reach the top of the tree. How tall is the tree?
Answers
Thus, the height of the oak trees of found to be 98 feet.
Explain about the addition:In maths, addition is the process of adding two or more numbers together. The numbers that added are known as addends, while the outcome of the addition process, or the final response, is known as the sum.
In general, the definition of addition is the coming together of two or so more groups of items into one group. According to mathematics, addition is an arithmetic operation that determines the total or sum of two or more numbers.The plus (+) addition symbol is placed between the two integers being added. One of the fundamental numerical operations is addition.Given data:
Height of the bird from the base of the oak tree: 33 feet.
Height flew by the bird to reach at the top of the tress: 65 feet.
So,
Height of the oak tree = 33 + 65
Height of the oak tree = 98 feet
Thus, the height of the oak trees of found to be 98 feet.
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Determine the intervals in which the function is decreasing
Answers
The intervals in which the function is decreasing. [tex][-\pi , -\frac{\pi }{3} ], [\frac{\pi }{3}, \pi ][/tex]. Option 3
How do you find the interval in which the function is decreasing?We're given a function f(x) = 2 sin x - x, which describes a curve on a graph. We want to find the intervals where this curve is decreasing (going down) within the range of -π to π.
To find when the function is decreasing, we look at its slope. The slope tells us if the curve is going up or down. We find the slope by taking the first derivative of the function: f'(x) = 2 cos x - 1.
We now have an equation for the slope, f'(x) = 2 cos x - 1. A negative slope means the function is decreasing. So, we want to find where f'(x) is less than 0 (negative).
We set up the inequality: 2 cos x - 1 < 0. We solve it to find the x-values where the slope is negative. The solution is cos x < 1/2.
From the inequality cos x < 1/2, we find the intervals within the range of -π to π where the function is decreasing. These intervals are [-π, -π/3] and [π/3, π].
The above answer is in response to the question below as seen in the picture.
Determine the interval(s) in [tex][-\pi, \pi ][/tex] on
which f(x) = 2 sin x - x
is decreasing.
1. [tex][-\frac{\pi }{3}, \frac{\pi }{3} ][/tex]
2. [tex][-\frac{\pi }{6}, \frac{\pi }{6} ][/tex]
3. [tex][-\pi , -\frac{\pi }{3} ], [\frac{\pi }{3}, \pi ][/tex]
4. [tex][-\pi , -\frac{-2\pi }{3} ], [\frac{2\pi }{3}, \pi ][/tex]
5. [tex][-\pi , - \frac{5x}{6} ], [\frac{\pi }{6}, \pi ][/tex]
6. [tex][-\frac{\pi }{6}, \frac{5\pi }{6} ][/tex]
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Twelve people apply for a teaching position in mathematics at a local college. Six have a PhD and five have a master’s degree. If the department chairperson selects five applicants at random for an interview, find the probability that all three have a PhD
Answers
Answer:
0.3788
Step-by-step explanation:
12 people want to teach math at a college.
6 people have a PhD.
5 people have a master's degree.
boss wants to interview 5 people for the job.
chance that all 5 of the people interviewed have a PhD.
total number of ways to select 5 applicants out of 12 is given by the combination:
combinations formula :
nCr = n! / r! * (n – r)!
C(12, 5) = 12! / (5! * 7!) = 792
number of ways to select 3 applicants with a PhD out of the 6 available is:
C(6, 3) = 6! / (3! * 3!) = 20
remaining 2 applicants can be selected from the remaining 6 applicants with a master's degree:
C(6, 2) = 6! / (2! * 4!) = 15
total number of ways to select 5 applicants with 3 having a PhD is:
20 * 15 = 300
P(3 PhDs) = 300 / 792
P(3 PhDs) = 0.3788 (rounded to four decimal places)
So, the probability of selecting five applicants for an interview where all three applicants have a PhD is approximately 0.3788
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