The answer to this problem is "The population is the total number of people who go to the mall, and the sample is the first 75 people at the mall".
What is true about this situation?
When conducting a survey, it's important to carefully define the population of interest and the sample being surveyed. The population is the entire group that you want to draw conclusions about, while the sample is the group of individuals that you actually survey. In this situation, the population of interest is the total number of people who go to the mall, as this is the group that we want to make inferences about.
The sample is the first 75 people who entered the mall and were asked about their favorite restaurant in the food court. This sample was likely selected in a way that is meant to be representative of the larger population of mall-goers. However, it's worth noting that the sample is still a subset of the population, and therefore there is some risk of sampling error. For example, if the first 75 people who entered the mall were all from the same demographic group, the survey results might not be representative of the larger population.
Overall, it's important to be clear about the population and sample when conducting a survey, as this helps to ensure that the results are meaningful and accurate.
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Not sure how to go about tackling this question?
Should I try to get [tex]y= \frac{x(k+1)}{k-1}[/tex] into the form of the ratio first then simplify?
The proof for the given proportion or two equivalent ratios given as (y+x):(y-x) = k:1 is shown below
What is a proportion?
On ratio and fractions, proportion is based. Two ratios are equal when they are represented as a fraction (a/b), a ratio (a:b), and then a proportion. A and B are two integers. Two sets of supplied numbers are said to be directly proportional if they increase or decrease in the same ratio for both sets. The symbols "::" or "=" are used to indicate proportions. If the ratio between the first and second is equal to the ratio between the second and third, then any three quantities are in continuing proportion.
Given that (y+x) : (y-x) = k : 1
We know that product of extremes = product of means
Extremes=(y+x) and 1
Means=(y-x) and k
(y+x) . 1 = (y-x) . k
y + x = ky - kx
y - ky = -kx - x
y - ky = - x(k + 1)
-(y - ky) = x(k + 1)
ky - y = x(k + 1)
y(k - 1) = x(k + 1)
y=[tex]\frac{x(k+1)}{(k-1)}[/tex]
Hence proved.
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Find the length of the arc on a circle with the radius of 2. 4 km and is intercepted by a central angle measuring 150°. Leave your answer in terms of pi
The length of the arc on a circle with the radius of 2. 4 km and is intercepted by a central angle measuring 150° is 2π km.
The length of an arc on a circle with radius "r" intercepted by a central angle of "θ" degrees is given by the formula:
L = (θ/360) * 2πr
In this case, the radius is 2.4 km and the central angle is 150 degrees, so we have to put the values in the formula above to find the answer:
L = (θ/360) * 2πr
L = (150/360) * 2π(2.4)
L = (5/12) * 4.8π
L = 2π
Therefore, the length of the arc is 2π km (or approximately 6.28 km) when rounded to two decimal places.
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9) all of the following are required of a binomial distribution except: a) each trial has exactly two outcomes. b) the number of trials is fixed. c) all trials have the same probability of success. d) there must be at least 30 trials.
d) there must be at least 30 trials.
1) 4/10=
2) 2/3=
3) 5/10=
4) 3/8=
5) 2/11 =
6) 3/7 =
7) 1/6 =
8) 4/6 =
9) 11/12 =
10) 1/4 =
You select a marble from two different bags. You have a 30% chance of choosing a blue marble from the first bag and 70% chance of choosing blue from the seconf bag. Desigin a simulation to estimate the probbility that you choose a blue marble from both bags
The probability of choosing a blue marble from both bags is 0.21 or 21%.
What is probability?Probability is a measure of the likelihood or chance that a particular event will occur. It is typically expressed as a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain to occur.
According to given information:Let B1 and B2 denote the events of choosing a blue marble from bag 1 and bag 2, respectively. We want to find the probability of the event B1 ∩ B2, which is the probability of choosing a blue marble from both bags.
We know that:
P(B1) = 0.3 (the probability of choosing a blue marble from bag 1)
P(B2) = 0.7 (the probability of choosing a blue marble from bag 2)
Assuming that the events B1 and B2 are independent, we can use the formula for the intersection of two independent events:
P(B1 ∩ B2) = P(B1) * P(B2)
Substituting the values we know, we get:
P(B1 ∩ B2) = 0.3 * 0.7 = 0.21
Therefore, the probability of choosing a blue marble from both bags is 0.21 or 21%.
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9. A parenteral medication is to arrive through the mail. The label on the box states that the medication cannot be exposed to temperatures higher than 47. 8° C. The current outdoor temperature is 100. 2° F
The current outdoor temperature is 37.89°C, which is less than the highest temperature limit, i.e., 47.8°.
Both Celsius and Fahrenheit have different zero points and the temperature increments also vary quite differently. 100 degrees separate freezing and boiling on the Celsius scale, but for Fahrenheit the difference is 180 degrees. This means Celsius is 1.8 times larger than Fahrenheit.
To determine whether the medication has been exposed to temperatures higher than 47.8°C, we need to convert the outdoor temperature from Fahrenheit to Celsius. The conversion formula is:
°C = (°F - 32) x 5/9
Using this formula, we can get the temperature in Celsius form,
°C = (100.2 - 32) x 5/9
= 37.89°C
Since the outdoor temperature is lower than the maximum temperature the medication can be exposed to, it is safe to assume that the medication has not been exposed to temperatures higher than 47.8°C.
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Mrs. Hanson is filling containers in her bakery with flour. How much flour will fit into two of the containers?
The flour will fit into two of the container is 144 inches.
What is the volume of cuboids?
A cuboid is a six-sided solid known as a hexahedron. Quadrilaterals make up its faces. Cuboid is short for "like a cube". A cuboid is similar to a cube in that a cuboid can become a cube by varying the lengths of the edges or the angles between the faces.
Here, we have
Given: Mrs. Hanson is filling containers in her bakery with flour.
we have to find how much flour will fit into two of the containers.
Volume of cuboid = length × breadth × height
Length = 6 inches
Breadth = 3 inches
Height = 8 inches
The flour will fit into two of the containers = length × breadth × height
= 6 ×3 × 8
= 144 inches
Hence, The flour will fit into two of the container 144 inches.
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an analysis of future events performed by the probability of those events and the potential outcomes is called
An analysis of future events performed by the probability of those events and the potential outcomes is called probabilistic analysis.
Probabilistic analysis involves using mathematical models and statistical techniques to estimate the likelihood of different outcomes, given a set of assumptions and inputs. It is commonly used in risk management, financial analysis, and project management to evaluate the potential impact of different scenarios and make informed decisions. By quantifying the probabilities of different outcomes, probabilistic analysis helps decision-makers identify the best course of action and manage uncertainty and risk.
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what is the effect of the interaction of the number of pages and cover type on cost? (round your answers to four decimal places.)
To determine the effect of the interaction of the number of pages and cover type on cost, a statistical analysis would need to be performed using data on the number of pages, cover type, and cost. The analysis would likely involve running a regression model that includes both the number of pages and cover type as predictor variables, as well as an interaction term between the two.
To answer your question, the effect of the interaction between the number of pages and cover type on the cost can be determined through a step-by-step process:
1. Identify the base cost of each cover type (e.g., hardcover, paperback, etc.).
2. Determine the cost per additional page for each cover type.
3. Calculate the cost for a specific number of pages and cover type by adding the base cost and the cost of additional pages.
For example:
- Base cost for hardcover: $5.00
- Base cost for paperback: $3.00
- Cost per additional page for hardcover: $0.10
- Cost per additional page for paperback: $0.05
Now, let's say you want to find the cost of a 100-page hardcover book:
1. Start with the base cost of a hardcover: $5.00
2. Multiply the number of pages (100) by the cost per additional page for hardcover ($0.10): 100 * $0.10 = $10.00
3. Add the base cost and the cost of additional pages: $5.00 + $10.00 = $15.00
So, the cost of a 100-page hardcover book is $15.00.
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in table 9.1, the marginal cost of producing the seventh unit of output is equal to _____.
In table 9.1, the marginal cost of producing the seventh unit of output is equal to $8.
Marginal cost refers to the additional cost incurred when producing one more unit of output. To find the marginal cost of producing the seventh unit of output, follow these steps:
1. Locate the total cost column in table 9.1.
2. Identify the total cost of producing 6 units of output.
3. Identify the total cost of producing 7 units of output.
4. Subtract the total cost of producing 6 units from the total cost of producing 7 units.
The difference you get from step 4 is the marginal cost of producing the seventh unit of output.
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BRAINLIST!
PLS SHOW ALL STEPS!! WE ARE DOING A CLASS JAM BOARD AND I NEED THIS DONE! I WILL MAKE YOU A BRAINLIST!
Step-by-step explanation:
Ok do what you need to do is label the line opposite the square angle as H for the hypotenuse. Then label the line opposite the circular angle as O for the opposite. And finally, the last line remaining should be labelled as A for Adjacent. Does this help?
Add parentheses to make expression true
5×6-3+4 = 19
Correct expression would be, 5*(6-3)+14=19
What is expression?
An expression consists of one or more numbers or variables along with one more operation.
Given Expression:
5×6-3+4 = 19
To make expression true we will add parentheses between 6 and 3
The correct expression would be, 5*(6-3)+14=19
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Find the perimeter of ΔNOP. Round your answer to nearest tenth if necessary. Figures are not necessarily drawn to scale ML = 5 MK = 4 KL = 7
ON = x NP = 6.4 OP = 8
The perimeter of ΔNOP is equal to 25.6 units.
What is the basic proportionality theorem?In Mathematics, the basic proportionality theorem states that when any of the two (2) sides of a triangle is intersected by a straight line which is parallel to the third (3rd) side of the triangle, then, the two (2) sides that are intersected would be divided proportionally and in the same ratio.
By applying the basic proportionality theorem to the given triangles, we have the following:
ΔNOP ≅ ΔKLM
OP/ML = x/KL
x = (OP × KL)/ML
x = (8 × 7)/5
x = ON = 11.2 units.
For the perimeter of ΔNOP, we have;
Perimeter of ΔNOP = OP + NP + ON
Perimeter of ΔNOP = 8 + 6.4 + 11.2
Perimeter of ΔNOP = 25.6 units.
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what is the probability that at least one customer arrives at the shop during a one-minute interval? 0.736 0.368 0.632 0.264
Probability about at least one customer arrives at the shop while a one-minute interval is almost 0.632 or 63.2%.
How to calculate probability?The probability that at least one customer arrives at the shop during a one-minute interval can be calculated using the Poisson distribution, which is commonly used to model the arrival of events over a given time period.
Let's assume that the average number of customers arriving at the shop per minute is [tex]l[/tex]. Poisson probability mass function is;
[tex]P(X = k) = (e^{-l} * l^k) / k![/tex]
where X is the random variable representing the number of customers arriving in a one-minute interval, and k is the number of customers that arrive.
To find the probability of at least one customer arriving, we need to calculate the probability of X being greater than or equal to 1. That is,
[tex]P(X > = 1) = 1 - P(X = 0)[/tex]
When [tex]l[/tex] is relatively small, we can use approximation:
[tex]P(X = 0) = e^{-l[/tex]
Therefore,
[tex]P(X > = 1) = 1 - P(X = 0)[/tex]
[tex]≈ 1 - e^{-l[/tex]
We don't have the value of [tex]l[/tex], but assuming an average arrival rate of 1 customer per minute (i.e., [tex]l[/tex] = 1), we get:
[tex]P(X > = 1) = 1 - e^{-1[/tex]
≈ 0.632
Therefore, the probability about at least one customer arrives at the shop while a one-minute interval is almost 0.632 or 63.2%.
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16 mi c. john started a carpool with his coworkers to save money. he and his three passengers split the cost of the toll. if each person pays about $0.81 , which includes their contribution to the toll lane entry fee, how many miles do they travel on the toll lane?
John and his three passengers travel a total of 20.25 miles on the toll lane.
To solve this problem, we can use the fact that each person pays about $0.81, which includes their contribution to the toll lane entry fee. This means that the total amount of money paid by John and his three passengers is 4 times $0.81, or $3.24.
We can then use this information to find the cost per mile of the toll lane. If they traveled a total of x miles on the toll lane, then the cost per mile would be:
$3.24 / x
We can set this equal to the given cost of 16 cents per mile:
$0.16 = $3.24 / x
Multiplying both sides by x, we get:
x * $0.16 = $3.24
Dividing both sides by $0.16, we get:
x = $3.24 / $0.16
x = 20.25 miles
In summary, to find the distance they traveled on the toll lane, we used the fact that they split the cost of the toll, and that each person paid about $0.81. We then set the cost per mile equal to the given cost of 16 cents per mile, and solved for the distance traveled on the toll lane, which turned out to be 20.25 miles.
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A small juice company spends $1200 per day on business expenses plus $1. 10 per bottle of juice them make. They charge $2. 50 for each bottle of juice they produce. How many bottles of juice must the company sell in a day for the company to break-even?
The company must produce and sell at least 857 bottles of juice in a day to break-even, given the given expenses and selling price per bottle.
Let's denote the number of bottles of juice sold in a day as "x".
The total cost of production and business expenses :
Total cost = Business expenses + (Cost per bottle of juice) x (Number of bottles produced and sold)
Total cost = $1200 + $1.10x
The revenue generated from selling "x" bottles :
Revenue = (Selling price per bottle of juice) x (Number of bottles produced and sold)
Revenue = $2.50x
The company will break-even when revenue equals total cost, so we can set two expressions equal to each:
[tex]\\$2.50x = $1200 + $1.10x\\$2.50x - $1.10x = $1200\\$1.40x = $1200\\x = $1200 / $1.40\\[/tex]
x ≈ 857
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The graph of a linear function is shown on the coordinate grid.
What is the y-intercept of the graph of this function?
PLEASE HELP! WILL GIVE BRAINLY ANSWER
Answer:
[tex]\dfrac{4}{3}[/tex]
Step-by-step explanation:
We can find the y-intercept of this line by:
1) finding the slope using the given points
[tex]m = \dfrac{8-(-7)}{4-(5)}[/tex]
[tex]m = \dfrac{8+7}{4+5}[/tex]
[tex]m = \dfrac{15}{9}[/tex]
[tex]m=\dfrac{5}{3}[/tex]
2) forming an equation for the line using point slope form
[tex]y - b = m(x - a)[/tex] where [tex](a,b)[/tex] is a point on the line
... using the point (4,8)
[tex]y - 8 = \frac{5}{3}(x - 4)[/tex]
3) plugging 0 in for x to get the y-intercept
[tex]y - 8 = \frac{5}{3}(0 - 4)[/tex]
[tex]y - 8 = \frac{5}{3}(-4)[/tex]
[tex]y = 8 -\frac{20}{3}[/tex]
[tex]y = \frac{24}{3} -\frac{20}{3}[/tex]
[tex]\boxed{y=\dfrac{4}{3}}[/tex]
8. an unfair coin, when tossed 7 times, has the same probability of obtaining 2 heads out of 7 as it does of obtaining 3 heads out of the 7 tosses. what is the probability the coin lands heads on a single toss?
The probability the coin lands heads on a single toss is 0.625
Let's assume that the probability of getting heads on a single toss is denoted by p.
The probability of getting 2 heads out of 7 tosses is given by the binomial distribution
P(2 heads) = (7 choose 2) × p^2 × (1-p)^5
Similarly, the probability of getting 3 heads out of 7 tosses is
P(3 heads) = (7 choose 3) × p^3 × (1-p)^4
We are given that P(2 heads) = P(3 heads), so we can set these two equations equal to each other:
(7 choose 2) × p^2 × (1-p)^5 = (7 choose 3) × p^3 × (1-p)^4
Simplifying this equation, we get
21 × p^2 × (1-p)^5 = 35 × p^3 × (1-p)^4
Dividing both sides by p^2 * (1-p)^4, we get
21/(1-p) = 35/p
Solving for p, we get:
p = 35/(21+35) = 35/56 = 0.625
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What is the solution to 9/x+81 > 45?
Answer:
I dont know the answer to be honest..
JUST KIDDING.. ill answer this step by step lol
To solve the inequality 9/x + 81 > 45, we can follow these steps:
Step 1: Subtract 81 from both sides of the inequality to isolate the fraction on the left-hand side:
9/x + 81 - 81 > 45 - 81
9/x > -36
Step 2: Take the reciprocal of both sides of the inequality to eliminate the fraction:
1 / (9/x) < 1 / (-36)
x/9 < -1/36
Step 3: Multiply both sides of the inequality by 9 to get rid of the fraction in the numerator:
9 * (x/9) < 9 * (-1/36)
x < -1/4
So, the solution to the inequality 9/x + 81 > 45 is x < -1/4. This means that x must be less than -1/4 for the inequality to be true.
Please use Triangle Inequality to solve. I'm quite confused... Or at least help me with this T T
The value of 'x' evaluated on the basis of angle sum property is 31 & arranged length of sides of given triangle ΔEBD from longest to shortest is DE > BD > BE
What is a triangle?
A triangle is a three-sided polygon with three vertices that is constructed using segments of straight lines. The triangle's angles are created by connecting the three line segments that make up its sides end to end at a single point. Angle sum attribute states that the sum of the triangle's three angles is 180 degrees. Triangle inequality asserts that the third side is greater than or equal to the sum of any two triangle sides.
Given that
∠ABC=(4x)°
∠BED=(5+x)°
∠BDF=160°
a)Find 'x'
consider ΔBED,
∠ABC=∠EBD {vertically opposite angles}
∴∠EBD=(4x)°
∠BDF+∠BDE=180° {angles on straight line}
∠BDE=180-160
∠BDE=20°
We know that ∠EBD+∠BDE+∠DEB=180° {angle sum property}
4x + 20 + (5+x)=180°
4x + 20 + 5 + x = 180°
5x + 25 = 180°
5x = 180 - 25
5x = 155
x = 31
b)Arrangement of sides from the longest to the shortest:
Based on the value of 'x', the angles of triangle ΔEBD:
∠EBD=4x=4 . 31 = 124°
∠BED=5 + x= 5 + 31 = 36°
∠BDE=20°
We know that the side opposite to the larger angle is the longest and that of the least angle is the shortest.
∴Side opposite to the largest angle ∠EBD=124° is DE
side opposite to the least angle ∠BDE=20° is BE
∴Descending order of sides of ΔEBD is DE > BD > BE
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1. In a survey, it was found that the ratio of the people who liked modern songs and folk songs is 8:9, out of which 50 people like both songs, 40 liked folk songs only and 80 liked none of the songs.i) Represent the above information in a Venn - diagram. ii) How many people like folk song? iii) How many people like Modern song? iv) Find the number of people in the survey.
According to the information, the number of people who likes folk song is 90, and the number of people who likes modern song 80. So, the total number of people in the survey is 250.
How to calculate how many people like folk song?Let the number of people who like modern songs be 8x, and the number of people who like folk songs be 9x.
From the given information, we know that:
50 people like both modern and folk songs
40 people like only folk songs
The total number of people who like at least one type of song is (8 + 9)x - 50 = 17x - 50
80 people like none of the songs
Therefore, we can write the following equation:
(8x + 9x) - 50 - 40 + 80 = 17x
Simplifying this equation, we get:
17x - 10 = 17x
Thus, x = 10.
So, the number of people who like folk songs is 9x = 9(10) = 90.
How to calculate how many people like modern song?Similarly, the number of people who like modern songs is 8x = 8(10) = 80.
How to calculate the number of people in the survey?The total number of people in the survey is the sum of the number of people who like modern songs, the number of people who like folk songs, and the number of people who like none of the songs.
So, the total number of people in the survey is:
80 + 90 + 80 = 250.
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The floor of a storage unit is 3 meters long and 4 meters wide. What is the distance between two opposite corners of the floor?
The distance between two opposite corners of the floor is 5 meters.
What is Pythagoras Theorem?
Pythagoras' theorem is a fundamental principle in geometry that states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Using the Pythagorean theorem, the distance between two opposite corners of the floor can be found by calculating the length of the hypotenuse of a right triangle whose legs are the length and width of the floor. Therefore,
c² = a² + b²
where c is the length of the hypotenuse, a is the length of the floor (3 meters), and b is the width of the floor (4 meters).
Substituting the values, we get:
c² = 3² + 4²
c² = 9 + 16
c² = 25
Taking the square root of both sides, we get:
c = √(25)
c = 5
Therefore, the distance between two opposite corners of the floor is 5 meters.
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Can someone help me asap? It’s due tomorrow.
Answer:
it A or B
Step-by-step explanation:
the other two C and D dont make sense to what the question is asking
the minimum, or lowest value, of the data set is 2. move the leftmost blue dot back and forth. how does this relate to the position of the leftmost point of the box-and-whisker plot?
The minimum value, or lowest value, of the data set is the same value as the leftmost point of the box and whisker plot.
We know that a box-and-whisker plot is nothing but a graph summarising a set of data. This plot shows how the data is distributed. It also shows any outliers.
In box-and-whisker plot, the median is in the middle of the box. The minimum value in the dataset is displayed at the far left end of the plot. The first quartile (Q1 or the 25th percentile) is in between the minimum value and median. The third quartile (Q3 i..e, the 75th percentile) at the right side, between the median and the maximum value. Latsly the maximum value in the dataset is displayed at the far right end of the plot.
Therefore, the minimum value is the same value as the leftmost point of the plot.
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The complete question is:
Holly and Brian’s social studies teacher gives them quizzes worth up to 20 points. Holly received the following scores: 5, 11, 17, 18, and 20. Brian’s scores were 16, 16, 17, 19, and 19
The box-and-whisker plot is shown below. The minimum, or lowest value, of the data set is 2. Move the leftmost blue dot back and forth. How does this relate to the position of the leftmost point of the box-and-whisker plot?
Quadrilateral ABCD is inscribed in a circle. Find the measure of x and the measure of each of the angles of the quadrilateral. You must use the fact that opposite angles in a quadrilateral are supplementary. (a) supplementary equation used to solve for x: (1 point)
(a) all math used to calculate for x:
(c) correct value for x:
(d) plugging x into expressions for angles A, C, D:
(e) show all math used to calculate the measures of angles A, C, D:
(f) all math used to calculate the measure of angle B:
For quadrilateral ABCD x=85 and angle B= 23°.
What is quadrilateral?A quadrilateral is a polygon with four sides and four angles. It is a closed figure and can have different shapes and sizes, depending on the length of its sides and the angles between them.
According to given information:(a) Supplementary equation used to solve for x:
∠A + ∠C = 180°
(b) All math used to calculate for x:
∠A + ∠C = 180°
(x - 5) + (x + 15) = 180 (substitute the given values for ∠A, ∠C)
2x - 10 = 180
2x = 170
x = 85
(c) Correct value for x:
x = 85
(d) Plugging x into expressions for angles A, C, D:
∠A = x - 5 = 2(85) - 5 = 165
∠C = x + 15 = 85 + 15 = 100
∠D = x - 13 = 85 - 13 = 72
(e) All math used to calculate the measures of angles A, C, D:
∠A + ∠B + ∠C + ∠D = 360° (sum of angles in a quadrilateral)
165 + ∠B + 100 + 72 = 360
∠B = 23
Therefore, the measures of the angles are:
∠A = 165°
∠B = 23°
∠C = 100°
∠D = 72°
(f) All math used to calculate the measure of angle B:
∠B = 360 - ∠A - ∠C - ∠D
∠B = 360 - 165 - 100 - 72
∠B = 23°
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Jack draws a rainbow which is a parabola that has the equation y =-0. 1(x-1) 2+6, where x and y are measured in centimeters. If the height of the rainbow is 6 cm, how far away are the endpoints of the rainbow from one another?
The endpoints of the rainbow are 2√60 cm apart.
The given equation for the rainbow is in vertex form, which is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.
In this case, the vertex is (1, 6), which means that the parabola is shifted horizontally by 1 unit to the right and vertically by 6 units upwards from the standard parabola y = ax^2.
Since the height of the rainbow is 6 cm, this means that the highest point of the parabola is at y = 6, which occurs at the vertex (1, 6).
To find the distance between the endpoints of the rainbow, we need to find the x-intercepts of the parabola. These occur where y = 0. Therefore, we need to solve for x in the equation:
0 = -0.1(x - 1)^2 + 6
-6 = -0.1(x - 1)^2
-6/-0.1 = (x - 1)^2
60 = (x - 1)^2
±√60 = x - 1
x = 1 ± √60
Since we are looking for the distance between the endpoints, we need to subtract the smaller x-value from the larger one:
Distance between endpoints = (1 + √60) - (1 - √60)
Distance between endpoints = 2√60
Therefore, the endpoints of the rainbow are 2√60 cm apart.
The given equation in the question is wrong, the correct equation is:
y = -0.1(x - 1)^2 + 6.
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A rod of length L is placed along the X-axis between X=0 and x=L. The linear density (mass/length) rho of the rod varies with the distance x from the origin as rho=a+bx. (a) Find the SI units of a and b. (b) Find the mass of the rod in terms of a,b and L.
(a) The linear density (mass/length) rho has SI units of kg/m. Since rho = a + bx, the SI units of a must be kg/m and the SI units of b must be kg/m^2.
(b) To find the mass of the rod, we need to integrate the linear density function over the length of the rod:
m = ∫₀ᴸ ρ(x) dx
Substituting in ρ(x) = a + bx:
m = ∫₀ᴸ (a + bx) dx
m = [ax + (1/2)bx²] from 0 to L
m = aL + (1/2)bL²
Therefore, the mass of the rod in terms of a, b, and L is m = aL + (1/2)bL².
(a) In this problem, rho (ρ) represents linear density, which has units of mass per length. In SI units, mass is measured in kilograms (kg) and length in meters (m). Therefore, the units of linear density are kg/m. Since ρ = a + bx, the units of a and b must be consistent with this equation. The units of a are the same as those of ρ, so a has units of kg/m. For b, since it is multiplied by x (which has units of meters), b must have units of kg/m² to maintain consistency in the equation.
(b) To find the mass of the rod, we need to integrate the linear density function over the length of the rod (from x=0 to x=L). Let's set up the integral:
Mass (M) = ∫(a + bx) dx, with limits from 0 to L
Now, we can integrate:
M = [a * x + (b/2) * x²] evaluated from 0 to L
Substitute the limits:
M = a * L + (b/2) * L²
So, the mass of the rod in terms of a, b, and L is:
M = aL + (bL²)/2
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Which sum is equivalent to 9c-12-15c-8-3c
The equivalent sum to the given equation is -9c - 20.
An algebraic expression is consists of variables, numbers with various mathematical operations.
Equivalent sums refers to addition or subtraction from the other number to maintain the same total value.
= 9c-12-15c-8-3c
To find the equivalent sum, first we can simplify this expression by first combining like terms:
= 9c - 15c - 3c - 12 - 8
= (9c - 15c - 3c) - (12 + 8) (grouping the like terms)
Solving the expression for terms c and for constant terms,
= -9c - 20
Therefore, the equivalent sum is -9c - 20.
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19
Points Scored
74 82 84
122 193
21
53
103
108 116
a. Find the range and interquartile range of the data.
The range is [172 points.
The interquartile range is 42 points.
93
b. Use the interquartile range to identity the outlier(s) in the data set. Find the range and the interquartile range of the data set without
the outier(s).
The outier is 21 points.
The range without the outlier is 140 points
The interquartile range without the outlier is points.
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Therefore, the range is 172 points and the interquartile range is 42 points. Therefore, the range without the outlier is 140 points and the interquartile range without the outlier is 40 points.
What is range?In statistics, the range is the difference between the largest and smallest values in a dataset. It is a measure of dispersion that indicates the spread of the data. The range provides a quick and simple way to get an idea of the variability of the data, but it can be affected by outliers and is therefore not always a reliable measure of dispersion. To calculate the range, you simply subtract the smallest value from the largest value in the dataset.
Here,
a. To find the range, we subtract the smallest value from the largest value:
Range = 193 - 21 = 172
To find the interquartile range, we first need to find the first and third quartiles.
Arrange the data in order from smallest to largest:
21, 53, 74, 82, 84, 103, 108, 116, 122, 193
Find the median (middle value) of the lower half of the data (Q1):
Q1 = median(21, 53, 74, 82, 84) = 74
Find the median (middle value) of the upper half of the data (Q3):
Q3 = median(103, 108, 116, 122, 193) = 116
Subtract Q1 from Q3 to get the interquartile range:
IQR = Q3 - Q1 = 116 - 74 = 42
b. To identify the outlier(s), we can use the rule that any value less than Q1 - 1.5 x IQR or greater than Q3 + 1.5 x IQR is considered an outlier.
Q1 - 1.5 x IQR = 74 - 1.5 x 42 = 11
Q3 + 1.5 x IQR = 116 + 1.5 x 42 = 181
The value 21 is less than the lower bound of 11, so it is an outlier.
To find the range and interquartile range without the outlier, we need to remove it from the data set:
74 82 84 122 193 53 103 108 116
The range without the outlier is:
193 - 53 = 140
To find the interquartile range without the outlier, we need to find the first and third quartiles of the new data set:
Q1 = median(53, 74, 82, 84, 108) = 82
Q3 = median(116, 122, 193) = 122
IQR = Q3 - Q1 = 122 - 82 = 40
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What is the Y-intercept of boundary line of y 4x + 2 ?