The possible total number of boys and girls in the class is 21, and
the answer is b).
Let's denote the number of girls in the class as 'g' and the number of
boys as 'b'.
We know that all students in the class study either French or German,
but not both.
Therefore, the total number of students in the class is equal to the sum
of the number of students who study French and the number of students
who study German
From the given information, we can write the following equations:
g + b = total number of students(1/3)g = (1/3)b (one third of the girls and the same number of boysstudy German
2(1/3)g = b (twice as many boys as girls study French)We can simplify the second equation by multiplying both sides by 3:g = bSubstituting this into the first equation, we get:
2g = total number of studentsSubstituting the second equation into the third equation, we get:2g = b (twice as many boys as girls study French)Substituting this into the first equation, we get:
3g = total number of studentsTherefore, the total number of students in the class must be a multiple
of 3.
Let's try the answer choices:
a) 15 students (total number of students is not a multiple of 3)
b) 21 students (total number of students is a multiple of 3 and the
number of girls is a multiple of 3, so this is a possible solution)
c) 24 students (total number of students is a multiple of 3 and the
number of girls is not a multiple of 3)
d) 30 students (total number of students is a multiple of 3 but the
number of girls is not a multiple of 3)
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In △PQR, what is the length of segment QR? Right triangle PQR with PR measuring 56 and angles P and R measure 45 degrees. 28 28radical 2 56radical 3 56radical 2
Answer:
[tex]\overline{\sf QR}=28\sqrt{2}[/tex]
Step-by-step explanation:
If ΔPQR is a right triangle, where angles P and R both measure 45°, then the triangle is a special 45-45-90 triangle.
The measure of the sides of a 45-45-90 triangle are in the ratio 1 : 1 : √2.
This means that the length of each leg is equal, and the length of the hypotenuse is equal to the length of a leg multiplied by √2.
The legs of ΔPQR are segments PQ and QR.
The hypotenuse of ΔPQR is segment PR.
Therefore, to find the length of the leg QR, divide the length of the hypotenuse PR by √2.
[tex]\begin{aligned}\implies \overline{\sf QR}&=\dfrac{\overline{\sf PR}}{\sqrt{2}}\\\\&= \dfrac{56}{\sqrt{2}} \\\\&=\dfrac{56}{\sqrt{2}}\cdot \dfrac{\sqrt{2}}{\sqrt{2}}\\\\&=\dfrac{56\sqrt{2}}{2}\\\\&=28\sqrt{2}\end{aligned}[/tex]
Therefore, the length of segment QR is 28√2.
. 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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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
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!
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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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.
Plot all of the existing five features of the following rational function (some may not
be needed). if you get a fraction or decimal then plot as close to the true location as
possible.
f(x)
5x + 20
x2
- - 20
plot rational function
vertical asymptote
horizontal asymptote
x-intercept y-intercept hole
click on a feature then drag it into place,
to
5
4
5
8
9 10
Answer:
Step-by-step explanation:
To plot the given rational function f(x) = (5x+20)/(x^2 - 20), we need to find the vertical asymptote, horizontal asymptote, x-intercepts, y-intercepts, and holes.
Vertical asymptote:
The denominator of the rational function cannot be zero. Therefore, we need to find the value of x when the denominator equals zero.
x^2 - 20 = 0
x^2 = 20
x = ±√20
The vertical asymptotes are x = √20 and x = -√20.
Horizontal asymptote:
To find the horizontal asymptote, we need to compare the degree of the numerator and denominator. The degree of the numerator is 1, and the degree of the denominator is 2. Therefore, the horizontal asymptote is
y = 0.
X-intercepts and y-intercept:
To find the x-intercepts, we need to set the numerator equal to zero.
5x + 20 = 0
x = -4
Therefore, the x-intercept is (-4,0).
To find the y-intercept, we need to set x equal to zero.
f(0) = (5(0) + 20) / (0^2 - 20)
f(0) = -1
Therefore, the y-intercept is (0,-1).
Hole:
We can factor the numerator and denominator of the rational function to find if there is a hole. Factoring 5x + 20, we get 5(x+4). Therefore, there is a hole at x = -4.
To summarize, the features of the rational function f(x) = (5x+20)/(x^2 - 20) are:
Vertical asymptotes at x = √20 and x = -√20
Horizontal asymptote at y = 0
X-intercept at (-4,0)
Y-intercept at (0,-1)
Hole at x = -4
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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
Hope this helps! :)
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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Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar.
Lab tests of a new drug indicate a 70% success rate in completely curing the targeted disease. The doctors at the lab created the random data in the table using a representative simulation. The letter E stands for "effective," and N stands for "not effective. "
EEEE NEEE EEEE EEEN NEEN
NEEE EENE NNNE NEEN EENE
NENE EEEE EEEE NNNE ENEE
NEEN ENEE EENN ENNE NEEE
ENEN EEEE EEEN NEEE EENN
EENE EEEN EEEE EENE EEEE
ENEE ENNN EENE EEEE EEEN
NEEE ENEE NEEE EEEE EEEE
NENN EENN NNNN EEEE EEEE
ENNN NENN NEEN ENEE EENE
The estimated probability that it will take at least five patients to find one patient on whom the medicine would not be effective is BLANK The estimated probability that the medicine will be effective on exactly three out of four randomly selected patients is BLANK.
PLEASE HELP I NEED HELP :(
50 POINTS
To find the estimated probability that it will take at least five patients to find one patient on whom the medicine would not be effective, we need to find the probability of getting NNNNN as the first five patients. Since the success rate is 0.3 and the failure rate is 0.7, the probability of getting NNNNN is:
0.7 x 0.7 x 0.7 x 0.7 x 0.7 = 0.16807
Therefore, the estimated probability that it will take at least five patients to find one patient on whom the medicine would not be effective is 0.16807.
To find the estimated probability that the medicine will be effective on exactly three out of four randomly selected patients, we need to count the number of ways we can select three patients out of four and multiply it by the probability of getting EEE and NEEE for the selected patients and non-selected patients, respectively. The number of ways to select three patients out of four is:
4C3 = 4
The probability of getting EEE and NEEE for the selected patients and non-selected patients, respectively, is:
(0.7)^3 x (0.3) x (0.7) = 0.1029
Therefore, the estimated probability that the medicine will be effective on exactly three out of four randomly selected patients is 4 x 0.1029 = 0.4116 (rounded to 4 decimal places).
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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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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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A candlemaker prices one set of scented candles at $10 and sells an average of 200 sets each week. He finds that when he reduces the price
by $1, he then sells 50 more candle sets each week. A function can be used to model the relationship between the candlemaker's weekly
revenue, R(x) after xone-dollar decreases in price.
R(x)
R(x)
6,000+
4,000+
6,000+
1,000+
2. 000
2,000+
2,000
2,000+
-4,000
4,000
6,000+
-6,000
Graph w
R(x)
Graph X
R(x)
6,000+
1,000+
6,000+
1,000+
2,000+
2,000
-2,000+
2,000
1,000+
4,000
-6,000
6,000
Graph Y
Graph Z
This situation can be modeled by the equation y =
x +
x +
and by graph
Next
The equation of demand of candle sticks can be modeled by
y = 14 - 0.02x while the revenue function will be xy = 14x - 0.02x².
Here we are given the information that
200 candles are sold for $10 and,
250 candles are sold for $9
Let the Price be y while the Quantity sold be x
Hence, by one unit decrease in price P, the quantity sold is increased by 50 units.
Here the slope of the function will be
(10 - 9)/(200 - 250)
= - 1/50
= - 0,02
Now we will use the formula of the equation of a straight line
(y - y₁) = m(x - x₁)
where, m is the slope and x₁ , y₁ are some point on line
Hence we get
(y - 10) = -0.02(x - 200)
or, y - 10 = -0.02x + 4
or, y = 14 - 0.02x
The revenue function will be xy = 14x - 0.02x²
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Correct Question
A candlemaker prices one set of scented candles at $10 and sells an average of 200 sets each week. he finds that when he reduces the price by $1, he then sells 50 more candle sets each week. a function can be used to model the relationship between the candlemaker's weekly revenue, r(x), after one-dollar decrease in price. this situation can be modeled by the equation y =
Find the value of m if third quartile (Q3) of the data given below is 128. (Income Rs. ) 0-30, 30-60, 60-90, 90-120, 120-150, 150-180 (No. Of Labour) 2, 8 ,22 ,24 ,m ,9
The value of median m that makes Q₃ equal to 128 is approximately 18.75.
What is median?The median is the value that divides the higher half of a population, a probability distribution, or a sample of data from the lower half. It can be conceptualised as a data set's "middle" value to put it simply.
To find the value of m, we need to first calculate the median and third quartile of the data.
To calculate the median, we need to find the value that splits the data into two halves. Since the data is already sorted into intervals, we can find the cumulative frequency for each interval and use it to determine the median interval. The median interval is the interval that contains the median. We can then use the formula for the median of grouped data to calculate the median value.
Cumulative frequency for each interval:
- Interval 0-30: 2
- Interval 30-60: 2+8=10
- Interval 60-90: 10+22=32
- Interval 90-120: 32+24=56
- Interval 120-150: 56+m
- Interval 150-180: 56+m+9=65+m
Since there are 6 intervals, the median interval is the 3rd interval, which is 60-90. The lower limit of this interval is 60, and the cumulative frequency up to this interval is 32. The frequency of this interval is 22. Using the formula for the median of grouped data:
Median = L + ((n/2 - CF) / f) * w
where L is the lower limit of the median interval, CF is the cumulative frequency up to the median interval, n is the total sample size, f is the frequency of the median interval, and w is the width of the interval.
Plugging in the values, we get:
Median = 60 + ((50 - 32) / 22) * 30
Median = 60 + (18 / 22) * 30
Median = 60 + 15.45
Median ≈ 75.45
Now, to find the third quartile (Q₃), we need to find the value that splits the upper 50% of the data. Since Q₃ is the 75th percentile, the cumulative frequency up to Q₃ is 0.75 times the total sample size:
Q₃ = L + ((0.75 * n - CF) / f) * w
We know that Q₃ is 128, and we can plug in the values for L, n, CF, f, and w that correspond to the interval that contains Q₃:
128 = 120 + ((0.75 * 85 - 56 - m) / (24)) * 30
Simplifying and solving for m, we get:
m = 120 + ((0.75 * 85 - 56) / (24)) * 30 - 128
m ≈ 18.75
Therefore, the value of m that makes Q₃ equal to 128 is approximately 18.75.
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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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WITHIN FIVE MINS PLEASE
Point B has rectangular coordinates (-5, 12)
Write the coordinates (r, θ) for point B. (θ in degrees)
The polar coordinates (r, θ) for point B with rectangular coordinates (-5, 12) are (13, 112.62°).
The polar coordinates (r, θ) for point B with rectangular coordinates (-5, 12) can be determined as follows.
1. Calculate the radius r:
r = √(x² + y²) = √((-5)² + 12²) = √(25 + 144) = √169 = 13.
2. Calculate the angle θ in radians:
θ = arctan(y/x) = arctan(12/-5) ≈ -1.176 radians.
3. Convert θ from radians to degrees:
θ = (-1.176 * 180) / π ≈ -67.38 degrees.
4. Adjust the angle to the proper quadrant (since point B is in the second quadrant):
θ = 180 - 67.38 = 112.62 degrees.
So, the polar coordinates (r, θ) for point B are (13, 112.62°).
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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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The following information pertains to Rainey Inc. For 2020. Jan. 1 Number of common share issued and outstanding, 200,000
Feb. 1 Number of new common shares issued, 8,000
July 31 100% common stock dividend
Dec. 31 Reported net income of $560,000
What is the company’s earnings per share reported in its financial statements for the year ended December 31, 2020?
Select one:
a. $1. 35
b. $1. 90
c. $1. 45
d. $1. 3
The company’s earnings per share reported in its financial statements for the year ended December 31, 2020 is $1.45. The correct option is c.
To calculate earnings per share, we need to take the company's net income and divide it by the weighted average number of shares outstanding during the year.
First, let's adjust for the stock dividend on July 31. Since the dividend was 100%, we can double the number of shares outstanding to 416,000:
Jan. 1: 200,000 shares
Feb. 1: 8,000 new shares
July 31: 200,000 shares doubled to 400,000 shares
Dec. 31: 416,000 shares
Next, we need to calculate the weighted average number of shares outstanding during the year. We can do this by taking the number of shares outstanding for each period and multiplying it by the number of months those shares were outstanding:
Jan. 1 to Jan. 31: 200,000 shares x 1 month = 200,000
Feb. 1 to July 31: (200,000 + 8,000) shares x 6 months = 1,248,000
Aug. 1 to Dec. 31: 416,000 shares x 5 months = 2,080,000
Total weighted average shares outstanding: 3,528,000
Finally, we can divide the net income of $560,000 by the weighted average shares outstanding of 3,528,000 to get earnings per share of $0.1585. Multiplying this by 9 (since there are 9 months of the year remaining after February 1) gives us earnings per share of $1.4265. Rounded to the nearest penny, the answer is $1.45.
Thus, The correct option is c.
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A table titled inequality symbols contains the symbols for less-than and greater-than.
Check all that are inequalities.
-3 = y
t > 0
-4. 3 < a
g = 5 and one-half
k less-than Negative Start Fraction 5 Over 7 End Fraction
x = 1
The inequalities in the given table are "t > 0" and "3 < a."
To identify the inequalities from the provided options, we need to understand the meaning of the symbols and check if they represent a comparison between two values.
-3 = y: This is not an inequality symbol but rather an equality symbol. It represents that -3 is equal to y, not greater or less than.
t > 0: This is an inequality symbol. The symbol ">" represents "greater than." Therefore, t is greater than 0.
-4. 3 < a: This is another inequality symbol. The symbol "<" represents "less than." Hence, 3 is less than a.
g = 5 and one-half: This is an equality symbol. The symbol "=" denotes equality, indicating that g is equal to 5 and one-half, not greater or less than.
k less-than Negative Start Fraction 5 Over 7 End Fraction: This is also an inequality symbol. The phrase "less than" indicates a comparison. The fraction "Negative Start Fraction 5 Over 7 End Fraction" represents -5/7. Therefore, k is less than -5/7.
x = 1: This is an equality symbol. The symbol "=" indicates that x is equal to 1, not greater or less than.
In summary, the inequalities in the table are "t > 0" and "3 < a."
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4 Il y f(x, y) da = Sot Shot Sot Staf (x, y) dxdy x D
Characteristics of the drawing of D, you can choose several answers:
1. It is the region in the first quadrant that is bounded from the right by the line x = 2
2. It is the region in the first quadrant that is bounded above by y = x
3. It is the region in the first quadrant that is bounded from the left by the line x = 0
4. It is the region in the first quadrant that is bounded above by y = x2
5. It is the region in the first quadrant that is bounded below by y = 0
6. It is the region in the first quadrant that is bounded below by y = 2
which of these 6 options is correct?
The correct option is option 3.
How to determine the boundaries of the region?Based on the given integral, region D is in the first quadrant, and its boundaries are not explicitly given. However, we can deduce the boundaries of D by looking at the integrand. Since the integrand is f(x,y), we can see that we are integrating over the entire region D, which means that D must be the rectangle that contains all the other regions mentioned in the options.
Therefore, option 1 is not correct, as D is not bounded from the right by x=2, but rather extends indefinitely to the right. Option 2 is also not correct, as D extends beyond the line y=x. Option 4 is not correct either, as D is not bounded above by y=x^2, but rather extends beyond it. Options 5 and 6 are also not correct, as D extends beyond the lines y=0 and y=2.
Therefore, the correct option is option 3, which states that D is the region in the first quadrant that is bounded from the left by the line x=0. This is correct, as D extends indefinitely to the right, and is bounded from the left by x=0.
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The function f(x)=8x+3x^−1 has one local minimum and one local maximum.
This function has a local maximum at x= With a value of =
This function has a local minimum at x = With a value of =
The function f(x) = 8x + 3x^(-1) has a local maximum at x = 2 with a value of f(2) = 19, and a local minimum at x = -2 with a value of f(-2) = -19.Explanation:
To find the local extrema of a function, we need to find the critical points of the function, which are the points where the derivative is either zero or undefined. In this case, the derivative of f(x) is f'(x) = 8 - 3x^(-2), which is undefined at x = 0.Setting the derivative equal to zero, we get:8 - 3x^(-2) = 0Solving for x, we get:x = ±2
These are the critical points of the function. To determine whether each critical point is a local maximum or a local minimum, we need to examine the second derivative of the function.
The second derivative of f(x) is f''(x) = 6x^(-3), which is negative for x > 0 and positive for x < 0.Therefore, x = 2 is a local maximum of the function with a value of f(2) = 19, and x = -2 is a local minimum of the function with a value of f(-2) = -19. These are the only local extrema of the function, since the function is increasing for x < -2 and decreasing for -2 < x < 0, and then increasing again for x > 0.
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Find the reduction formula for the following integrals
In = ∫cot^n dx, then find I4
The reduction form is [tex]I_4 i= cot^3 x =ln |sin x| - 3 cot x + 3x + C[/tex].
To find the reduction formula for ∫cot^n x dx, we can use integration by parts. Let u = cot^(n-1) x and dv = cot x dx, then[tex]du = (n-1)cot^(n-2) x csc^2[/tex]x dx and v = ln |sin x|. By the formula for integration by parts, we have:
∫cot^n x dx = ∫u dv = uv - ∫v du
= [tex]cot^(n-1) x ln |sin x| - (n-1) ∫cot^(n-2) x csc^2 x ln |sin x| dx.[/tex]
This gives us the reduction formula:
[tex]I_n = ∫cot^n x dx = cot^(n-1) x ln |sin x| - (n-1) I_(n-2).[/tex]
Using this formula, we can find I_4 as follows:
[tex]I_4 = ∫cot^4 x dx = cot^3 x ln |sin x| - 3 I_2\\= cot^3 x ln |sin x| - 3 ∫cot^2 x dx\\= cot^3 x ln |sin x| - 3 (cot x - x) + C,\\[/tex]
where C is the constant of integration. Therefore, the solution for I_4 is [tex]cot^3 x ln |sin x| - 3 cot x + 3x + C.[/tex]
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Find the measure of angle D.
Answer:
Step-by-step explanation:
3x4
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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WILL GIVE BRAINLYES, 5 STARS, AND A THANKS
Choose an amount between $50.00 and $60.00 to represent the cost of a meal for a family. Be sure to include dollars and cents.
Part A: If the family has a 15%-off coupon, calculate the new price of the meal. Show all work or explain your steps. (2 points)
Part B: Calculate a 20% tip using the new price. What is the final cost of the meal? Show all work or explain your steps. (2 points)
Answer:
The price of the meal after the discount was (A)$48.11 and the final price of the meal was (B)$57.73.
Step-by-step explanation:
Let us consider the amount of money $56.60 as the cost of the meal.
So the amount of money is 56 dollars and 60 cents.
A: The family has a 15% off coupon.
Discount = 15% of 56.60=0.15x56.60=8.49
Now we subtract the discount amount from the original amount.
Cost of the meal = 56.60-8.49=48.11
So the final price of the meal for the family is $48.11 or 48 dollars and 11 cents.
B: The family gave a tip of 20%.
Amount of money tipped= 20% of 48.11=0.20 x 48.11=9.622
To get the final amount we add the tip to the discounted price.
The final cost of the meal= 48.11+9.622=57.732=57.73
Therefore the family paid a total of 57 dollars and 73 cents for the final cost of the meal after the discount and tip.
Hope this helps :)
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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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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A rectangular field is 63 yards long and 21 yards wide. A fence is needed for the perimeters of the field. Fencing is also needed to divide the field into three square sections. How many feet of fencing are needed? Show step-by-step.
Answer: 210 yards of fencing will be needed
Step-by-step explanation: well the perimeter of this rectangular field is 21 + 63 + 21 + 63 yards or 2(21) + 2(63) yards which equals 168 yards.
To divide the field into 3 equal parts, u need to divide the length (63 yards) into 3 parts which also requires two more lines of fencing.
63/3=21 which means u get squares perfect squares when u divide. now that means that's an additional 21*2 yards of fencing since you need two more rows of fencing in the middle of the field to divide the length into three equal parts. 21*2 = 42 so thats an additional 42 yards. The total amount of fencing is 168 + 42 = 210 yards.
Mia is participating in a kite-flying competition. She wanted to find out how long is the string needed for fly her kite 33 meters from the ground if she is 56 meters away from the kite.
how do i do this assignment while showing the work?
The length of the string needed is 65 meters
What is an equation?An equation is an expression that shows how numbers and variables using mathematical operators.
Pythagoras theorem shows the relationship between the sides of a right angle triangle.
To find the length of string, Mia needs. A triangle is formed with hypotenuse (l) represent the length of string. The height of the kite (h) = 33 m which is the triangle height; while the 56 m is the base of the triangle (b). Hence:
l² = b² + h²
l² = 33² + 56²
l = 65 meters
The length of the string needed is 65 meters
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PLEASE ANSWER QUICKLY FOR THE LOVE OF EVERYTHING
Mrs. Robinson surveyed her class about what flavor cake and ice cream they wanted for their class party. The results were split evenly between the cake with 15 choosing chocolate cake and 15 choosing yellow cake. Of the students who chose chocolate cake, 12 also chose vanilla ice cream. There were 7 students in all that chose strawberry ice cream. Construct a two -way table summarizing the data
The two-way table is of the class survey is:
Vanilla Ice Cream | Strawberry Ice Cream | Total
Chocolate Cake | 12 | 3 | 15
Yellow Cake | 11 | 4 | 15
Total | 23 | 7 | 30
A two-way table summarizing the data from Mrs. Robinson's class survey on cake and ice cream preferences can be constructed as follows.
1: Create a table with rows for Chocolate Cake and Yellow Cake, and columns for Vanilla Ice Cream, Strawberry Ice Cream, and Total.
2: Fill in the given information:
15 students chose Chocolate Cake and 15 students chose Yellow Cake, so put 15 in the Total column for both rows.12 students who chose Chocolate Cake also chose Vanilla Ice Cream, so put 12 in the intersection of Chocolate Cake and Vanilla Ice Cream.There were 7 students in all that chose Strawberry Ice Cream, so put 7 in the Total row of the Strawberry Ice Cream column.3: Complete the table using the given information:
Since 12 students who chose Chocolate Cake also chose Vanilla Ice Cream, 3 students chose Chocolate Cake and Strawberry Ice Cream (15 total - 12).There are 7 students in total who chose Strawberry Ice Cream, so 4 students chose Yellow Cake and Strawberry Ice Cream (7 total - 3).The remaining 11 students chose Yellow Cake and Vanilla Ice Cream (15 total - 4).So, the completed two-way table is:
Vanilla Ice Cream | Strawberry Ice Cream | Total
Chocolate Cake | 12 | 3 | 15
Yellow Cake | 11 | 4 | 15
Total | 23 | 7 | 30
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