We have shown that the boundary of a generalized rectangle is the union of finitely many closed generalized rectangles with volume zero.
What is rectangle?The internal angles of a rectangle, which has four sides, are all exactly 90 degrees. At each corner or vertex, the two sides come together at a straight angle. The rectangle differs from a square because its two opposite sides are of equal length.
Let A and B be two sets in a generalized rectangle R, i.e., R = A x B. The boundary of R, denoted by bd(R), is defined as the closure of the set of points that are not in the interior of R. In other words, bd(R) = cl(R) \ int(R), where cl(R) is the closure of R and int(R) is the interior of R.
To show that bd(R) is the union of finitely many closed generalized rectangles with volume zero, we first note that the closure of R can be expressed as the union of R and its boundary, i.e., cl(R) = R ∪ bd(R). Therefore, it suffices to show that R can be expressed as the union of finitely many closed generalized rectangles with volume zero and that bd(R) can also be expressed as the union of finitely many closed generalized rectangles with volume zero.
Let (a,b) be a point in R. Then there exists an open ball B((a,b), r) around (a,b) that is contained in R, where r > 0. Without loss of generality, we can assume that r is small enough so that B((a,b), r) is a generalized rectangle. Since B((a,b), r) is open, it follows that int(R) is the union of all such generalized rectangles. Therefore, R can be expressed as the union of finitely many closed generalized rectangles with volume zero, namely the closures of all such generalized rectangles.
Next, we show that bd(R) can be expressed as the union of finitely many closed generalized rectangles with volume zero. Let (a,b) be a point in bd(R). Then every open ball B((a,b), r) around (a,b) contains points both in R and in the complement of R. By definition of bd(R), the closure of B((a,b), r) intersects both R and the complement of R. Therefore, B((a,b), r) can be expressed as the union of two closed generalized rectangles, one contained in R and one contained in the complement of R. It follows that bd(R) can be expressed as the union of finitely many closed generalized rectangles with volume zero, namely the closures of all such balls B((a,b), r) and their decompositions into closed generalized rectangles.
Therefore, we have shown that the boundary of a generalized rectangle is the union of finitely many closed generalized rectangles with volume zero.
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The volumes of two similar prisms are 135 ft^3 and 5000ft^3
a. Find the ratio of their heights.
b. Find the ratio of the area of their bases.
The ratio of the areas of the bases of the two similar prisms is approximately 26 to 1.
What is the scale factor?
A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).
Let h1 and h2 be the heights of the two similar prisms, and let A1 and A2 be the areas of their respective bases.
Also, let k be the scale factor that relates the smaller prism to the larger prism.
a. We know that the volumes of the two similar prisms are proportional to the cubes of their corresponding side lengths, so we have:
(kh1)³ / (kh2)³ = 135 / 5000
Simplifying this expression, we get:
h1³ / h2³ = 135 / 5000
Taking the cube root of both sides, we get:
[tex]h1 / h2 = (135 / 5000)^{(1/3)}[/tex]
Using a calculator, we find:
h1 / h2 ≈ 0.405
Therefore, the ratio of the heights of the two similar prisms is approximately 0.405 to 1.
b. The ratio of the areas of the bases of two similar prisms is equal to the square of the scale factor. That is:
A1 / A2 = k²
To find the scale factor k, we can use the fact that the volumes of the two prisms are proportional to k³. Therefore:
k³ = 5000 / 135
k ≈ 5.091
Using this value of k, we get:
A1 / A2 = k² = (5.091)² ≈ 26
Therefore, the ratio of the areas of the bases of the two similar prisms is approximately 26 to 1.
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Central Limit Theorem forms the foundation for the ___ branch of statistics
Central Limit Theorem forms the foundation for the inferential statistics branch of statistics
The Central Limit Theorem is a statistical concept that describes the behavior of the mean of a sufficiently large sample size drawn from any population with a finite mean and variance.
The Central Limit Theorem is a fundamental concept in statistics that states that, under certain conditions, the distribution of sample means approaches a normal distribution regardless of the shape of the population distribution. This theorem provides a basis for inferential statistics, which involves making inferences about a population based on a sample.
It allows us to use sample statistics to estimate population parameters with a certain level of confidence. This theorem has practical applications in many areas of research, such as in quality control, social sciences, and healthcare.
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The measure of an angle is 17.9°. What is the measure of its supplementary angle?
Answer:162.1
Step-by-step explanation:We know that the sum of supplementary angles is 180°Let the unknown angle be xThus,100° + x = 180°X = 180° – 100°X = 80°Hence, the unknown angle is 80 …I did it my own way ok…
PLEASE HELP AND SHOW WORK! EXPLAIN HOW YOU GOT THE ANSWER I WILL MARK YOU BRAINLIEST!!!!
The time it will take to fill the pool at the given rate would be = 8 mins.
How to calculate the volume of the cylindrical swimming pool?To calculate the volume of the cylindrical swimming pool the formula for the volume of the cylinder should be used which is = πr²h
where r = 5ft
h = 8ft
volume = π×5×5×8 = 200πft³
If 25πft³ = 1 minute
200πft³ = X
Make X the subject of formula;
X = 200/25 = 8mins
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an engineer has designed a valve that will regulate water pressure on an automobile engine. the valve was tested on 130 engines and the mean pressure was 5.9 lbs/square inch. assume the standard deviation is known to be 1 . if the valve was designed to produce a mean pressure of 5.8 lbs/square inch, is there sufficient evidence at the 0.05 level that the valve performs above the specifications? state the null and alternative hypotheses for the above scenario.
Here the p-value is less than the significance level of 0.05, we can reject the null hypothesis and conclude that there is sufficient evidence at the 0.05 level that the valve performs above specifications.
We have to evaluate null and alternative hypotheses for the scenario .
In this scenario, the null hypothesis is
H0: μ = 5.8
here
μ = true mean pressure produced by the valve.
Now for the alternative hypothesis is
HA: μ > 5.8
here
μ = true mean pressure produced by the valve.
Therefore to determine if there is sufficient observation at the 0.05 level that the valve performs above specifications,
Here we can utilize a one-tailed z-test with
α = 0.05
Then, test statistic can be evaluated as
z = (X' - μ) / (σ / √n)
where:
X' = sample mean
μ = hypothesized value concerning the population mean
σ = population standard deviation
n = sample size
Substituting in our values, we get:
z = (5.9 - 5.8) / (1 / √130) = 1.8856
Now utilizing a z-table we can evaluate that the p-value associated with this test statistic is approximately 0.0292.
Since this p-value is less than the significance level of 0.05, we can reject the null hypothesis and conclude that there is sufficient evidence at the 0.05 level that the valve performs above specifications.
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2 Bea counts the number of red pencils in 7 boxes of pencils. The list shows her
data: 22, 28, 30, 28, 35, 30, 28. The mean is 26 red pencils per box. Based on
the MAD for the data set, would it be unlikely to get a box with 31 red pencils?
Show your work. Explain your reasoning.
2.29 is less than the MAD of 2.53, it would not be unlikely to get a box with 31 red pencils based on the MAD for the given data set.
What is the data set?To determine whether it would be unlikely to get a box with 31 red pencils based on the Mean Absolute Deviation (MAD) for the given data set, we first need to calculate the MAD.
Step 1: Calculate the mean of the data set
The given data set is: 22, 28, 30, 28, 35, 30, 28
The mean is calculated by adding up all the numbers and dividing by the total number of values:
Mean = (22 + 28 + 30 + 28 + 35 + 30 + 28) / 7 = 201 / 7 = 28.71 (rounded to two decimal places)
Step 2: Calculate the absolute deviations
The absolute deviation for each data point is calculated by finding the absolute difference between the data point and the mean:
|22 - 28.71| = 6.71
|28 - 28.71| = 0.71
|30 - 28.71| = 1.29
|28 - 28.71| = 0.71
|35 - 28.71| = 6.29
|30 - 28.71| = 1.29
|28 - 28.71| = 0.71
Step 3: Calculate the MAD
The MAD is the mean of the absolute deviations:
MAD = (6.71 + 0.71 + 1.29 + 0.71 + 6.29 + 1.29 + 0.71) / 7 = 17.71 / 7 = 2.53 (rounded to two decimal places)
Now, to determine whether it would be unlikely to get a box with 31 red pencils, we can compare 31 with the MAD. If the difference between 31 and the mean (28.71) is greater than the MAD (2.53), then it would be unlikely.
Difference = 31 - 28.71 = 2.29
Since 2.29 is less than the MAD of 2.53, it would not be unlikely to get a box with 31 red pencils based on the MAD for the given data set.
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What is the
intermediate step in the form
(x + a)² = b as a result of completing
the square for the following equation?
-5x² 10x = -315
Answer:
To complete the square for the equation -5x² + 10x = -315, we can follow these steps:
Move the constant term (-315) to the right side of the equation:
-5x² + 10x + 315 = 0
Divide both sides of the equation by the coefficient of the x^2 term (-5) to get a coefficient of -1 for the x^2 term:
x² - 2x - 63 = 0
Add the square of half the coefficient of the x term to both sides of the equation:
x² - 2x + 1 - 1 - 63 = 0 + 1
Simplify the left side of the equation by factoring the quadratic trinomial and combining like terms:
(x - 1)² - 64 = 1
Add 64 to both sides of the equation:
(x - 1)² = 65
So the intermediate step in completing the square for -5x² + 10x = -315 is:
(x - 1)² - 64 = 1
This is the result of adding the square of half the coefficient of the x term (-1) to both sides of the equation and simplifying.
A single 6-sided die is rolled which BEST describes the probability of rolling a number 4 or less
A. likely
B.impossible
C.certain
D. unlikely
A radioactive substance has an initial mass of 475 grams and a half-life of 20 days. What equation is used to determine the number of days, x, required for the substance to decay to 63 grams?
The equation used to determine the number of days, x, required for the substance to decay to 63 grams is: x ≈ 83.60
To determine the number of days, x, required for a radioactive substance to decay to 63 grams, we can use the exponential decay formula. The equation that represents the decay of a radioactive substance over time is:
N(t) = N₀ * (1/2)^(t/h)
Where:
N(t) is the remaining mass of the substance at time t
N₀ is the initial mass of the substance
t is the time elapsed
h is the half-life of the substance
In this case, we have an initial mass of 475 grams, and we want to find the number of days required for the substance to decay to 63 grams. We can set up the equation as follows:
63 = 475 * (1/2)^(x/20)
To solve for x, we can isolate the exponential term on one side of the equation:
(1/2)^(x/20) = 63/475
Next, we can take the logarithm (base 1/2) of both sides to eliminate the exponential term:
log(base 1/2) [(1/2)^(x/20)] = log(base 1/2) (63/475)
By applying the logarithmic property log(base b) (b^x) = x, the equation simplifies to:
x/20 = log(base 1/2) (63/475)
Finally, we can solve for x by multiplying both sides of the equation by 20:
x = 20 * log(base 1/2) (63/475)
Using a calculator to evaluate log(base 1/2) (63/475) ≈ 4.1802, we find:
x ≈ 20 * 4.1802
x ≈ 83.60
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Annette is surveying people in the city about their interest in a new shopping mall.
She found that 180 people, or 37.5% of those surveyed, do not want a new mall.
How many people did Annette survey?
Annette surveyed a total of 480 people.
Let x be the total number of people Annette surveyed. According to the problem, 37.5% of the people surveyed do not want a new mall, and this amounts to 180 people. We can set up the equation:
0.375 * x = 180
Now, let's solve for x:
x = 180 / 0.375
x = 480
a quality control inspector collected sample data to determine if the mean weight of a product had varied from the specified value of 16. he obtained a p-value of .233. which conclusion is appropriate?
For the mean weight five boxes of cookies, the p-value is equals to 0.04189. If p-value is 0.233 > α, the conclusion is that mean weight of cookies is equals to 16.
We have total five boxes of cookies. Let population of weights is normally distributed, 15.91, 14.07 , 14.88, 16.07, 14.79. Use t.test to determine the p value and hypothesis testing for mean weight of product ( cookies). Let null and alternative hypothesis be defined as
[tex]H_0 : \mu = 16[/tex]
[tex]H_a : \mu<16[/tex]
degree of freedom, df = n - 1 = 5
Using the t-test formula, t value= -2.291,
Using t distribution table and the value p-value for t = -2.2907 and 4 degree of freedom is 0.04189. Hence, required value is 0.04189.
b) Now, p-value = 0.233 for mean weight varied from the specified value of 16.
Level of significance, [tex]\alpha[/tex] = 0.05
As we see p-value = 0.233 > 0.05 ( α), so, this is a significant region and null hypothesis can't be rejected. There is no enough evidence to conclude that the mean weight is actually less than 16 ounces.
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Complete question:
Following are the weights of 5 boxes of cookies, each of which is labeled as containing 16 ounces. Assume that the population of weights is normally distributed, 15.91, 14.07 , 14.88, 16.07, 14.79 . A quality control inspector wants to know whether the mean weight is actually less than 16 ounces. Compute the P-value of the test. Write down your P-value. Also, if he obtained a p-value of 0.233. which conclusion is appropriate?
In the 2020-21 season, Chris Paul had a free throw percentage of 93.4 what does this mean
For every 100 free throws Chris Paul attempted, he made approximately 93 of them.
We have,
Chris Paul's free throw percentage of 93.4 means that he made 93.4% of his free throw attempts during the 2020-21 season.
In other words, for every 100 free throws he attempted, he made approximately 93 of them.
This is a high free throw percentage and indicates that Chris Paul is a skilled free throw shooter.
Thus,
For every 100 free throws Chris Paul attempted, he made approximately 93 of them.
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Jerome is a photographer. He earns $125 per hour
(d) Part D
Create a graph of the data from the table.
The graph of the data from the table is added as an attachment
Creating a graph of the data from the table.From the question, we have the following parameters that can be used in our computation:
Jerome is a photographer. He earns $125 per hour
This means that the equation of the function is
f(x) = 125x
Where x is the number of hours he works
Using the above as a guide, we have the following table of values
x f(x)
1 125
2 250
3 375
4 500
5 625
6 750
Next, we plot the graph from the table of values and the function f(x) = 125x
The graph of the function is added as an attachment
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Prove that
sin0/(sec 0+tan 0-1)+cos0/ (cosec 0+ cot 0-1)=1
Answer:
Prove the following identitics: tan 0 + cot 0 = I/(sin 0 cos 0) 0 + tan 0 sec 0 = cosec 0 'sec? 0. 18 cosec = cosec? 0 = tan? 0 cot2 19 sec? 0 sin ' 0 =cos? 0 'sin? 20 cos4 (sec 0 + tan 0) (sec 0 _ tan 0) = 1 2 sin? 0 = cOs? 0 _ 'sin? 0. 22 2 cos? 0_I=1 23 sec? 0 + cosec 0 = sec? 0 cosec? sin? , COs? 24 sec" 0 cosec" 0 = cos 0 sin" 0 25 =I tan 0 + 1 cot? 0 +4 26 (sec? 0 1) (cosec? 0 1) = [ 27 ((sec? 0 _0)+ V(cosec" 0 _ !) = sec € cosec 0 28 (sec? tan? 0) + V(cosec? 0 ~ cot? 0) = 2 cos? 0 29 =1 sin sec? 0 _ 1 sec 0 cosec 0 tan 0 + cot 0 30 tan 0 cot 0 sec 0 + cosec 0 cos 0 sin 0 31 =l V( + tan? 0) V( + cot? 0) Eliminate 0 from the following equations: 32 x = 4 cos 0, y = b sin 0. 33 x = 4 cot 0,y = b cosec 0. 34 x=a tan 0,y =b cos 0. 35 x = ] sin 0, y = [ + cos 0, 36 x =a sec 0,y = b +c cos 0. 37 x=a cosec 0, y = b sec 0. 38 X=l+ tan 0,y = cos 0. 39 x=sin 0 + cos 0,y = sin 0 40 cos X = sCc 0 + tan 0, y = sCc 0 ~ tan 0.
a. This dot plot shows the ages of students in a swimming class. How many students
are in the class?
Based on the dot plot, do you agree with each of the following statements? Explain
your reasoning.
b. The class is an adult swimming class.
C. Half of the students are between 2 and 3 years old.
a). There are a total of 10 students in the class, according to the dot plot.
b). The students' ages, which vary from 1 to 5, indicate that this is not an adult swimming lesson.
c). Thus, just 20% (2/10) of the students are toddlers or preschoolers.
What is number?Numbers are mathematical units of measurement and labelling. It is an ethereal idea that can stand in for many different material quantities, including time, money, and distance. Real numbers, complex numbers, and even irrational numbers can all be considered numbers in mathematics.
Numbers are frequently employed in mathematical equations to express relationships and to represent data. They are also employed in the development of models, patterns, and data analysis.
a). There are a total of 10 students in the class, according to the dot plot.
b). The programme is a swimming lesson for adults.
No, it doesn't seem to be an adult swimming lesson based on the dot plot. The students' ages, which vary from 1 to 5, indicate that this is not an adult swimming lesson.
c). The majority of the students are between the ages of 2 and 3.
No, it doesn't seem like half of the students are between the ages of 2 and 3, according to the dot plot. There are two students who are two years old, one who is three, two who are four, and five who are five. Thus, just 20% (2/10) of the students are toddlers or preschoolers.
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In △ABC, DE⎯⎯⎯⎯⎯
is parallel to AC⎯⎯⎯⎯⎯
and DE=10.
Find the length of AC⎯⎯⎯⎯⎯
if DE⎯⎯⎯⎯⎯
is a midsegment of △ABC.
The solution to the given problem of the triangle comes out to be AC are 20 units long.
What precisely is a triangle?If a polygon contains at least one more segment, it is a hexagon. It is a simple rectangle in shape. Anything identical to a standard triangle form can only be distinguished from it by edges across A and B. Euclidean geometry does not completely describe the cube, despite the fact that its edges are all collinear. A triangle is formed by a circle with five sides and three angles.
Here,
If DE is the midpoint of triangle ABC, DE is parallel to AC and has a length of 50% of AC.
Let's use "x" units to represent the length of AC.
Given the information, DE equals 10 units, or 50 percent of AC's length. So that we may create the equation:
=> DE = AC/2
When we enter DE's value as 10 units, we get:
=> 10 = x/2
To separate x, we multiply both sides of the equation by 2 and obtain:
=> 2 * 10 = x
=> x = 20
Therefore, AC is 20 units long.
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What value will make the equation true?
-4.2 - x = -2 2/4
A.-6.7
B.1.7
C.-1.7
D.6.7
Answer:
C. -1.7
Step-by-step explanation:
-4.2 - x = -2 2/4
-2 2/4 = -10/4 = -2.5
-4.2 - x = -2.5
-x = 1.7
x = -1.7
So, the answer is C. -1.7
1. A triangle has sides that measure 5
cm, 2.5 cm, and 4.3cm. What is the
perimeter of the triangle? |
Answer:
11.8 cm---------------------
Perimeter is the sum of side lengths.
Given sides:
5 cm, 2.5 cm and 4.3 cmFind the perimeter by adding up side lengths:
P = 5 + 2.5 + 4.3 = 11.8 cmwhat do all circle theorems have in common (30 points)!!
annie sold her camers for $250 making a loss of 12% what price was the camera when annie bought it? round your answer to the nearest cent
Let's assume that the original price of the camera is x.
Since Annie sold the camera at a loss of 12%, the selling price is 88% of the original price.
So we can set up the equation:
0.88x = $250
To solve for x, we can divide both sides by 0.88:
x = $250 ÷ 0.88
x = $284.09
Therefore, the original price of the camera was $284.09.
Two vectors are linearly dependent if and only if they lie on a line through the origin.
a. true b. false
8-4: MathXL for School: Practice & Problem Solving
The correct expressions that give the new acreage are A and C.
A. 0.89y represents the remaining 89% of the original acreage after the sale.
C. y-0.11y represents the original acreage minus the 11% that was sold.
How to explain the expressionIt should be noted that to find the new acreage using the first expression (A), we can simply multiply the original acreage by 0.89:
New acreage = 0.89y
To find the new acreage using the second expression (C), we can subtract 0.11 times the original acreage from the original acreage:
New acreage = y - 0.11y
New acreage = 0.89y
Both expressions give the same result, which is the new acreage after the sale.
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A farmer recently sold a large plot of land. The sale decreased his total acreage by 11%. Let y be the original acreage. Find two equivalent expressions that will give the new acreage. Use pencil and paper. Use the expressions to describe two ways to find the new acreage.
Which two expressions will give the new acreage?
A. 0.89y
OB. 0.11y
C. y-0.11y
D. 11y
OE. y-11y
OF. 0.89y-0.11y
If a cylinder has a volume of 2908.33 in^3 and a radius of 11.5 in. What is the height of the cylinder
*
5 in
6 in
7 in
8 in
If a cylinder has a volume of 2908.33 in³ and a radius of 11.5 in, the height of the cylinder include the following: C. 7 inches.
How to calculate the volume of a cylinder?In Mathematics and Geometry, the volume of a cylinder can be calculated by using this formula:
Volume of a cylinder, V = πr²h
Where:
V represents the volume of a cylinder.h represents the height of a cylinder.r represents the radius of a cylinder.By substituting the parameters, we have the following:
2908.33 = 3.14 × 11.5² × h
Height, h = 7.00 inches.
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ANSWER ASAP AND PLEASE BE CORRECT FOR BRAINLIST PLEASE HURRY IT'S DUUE IN 4 MORE HOURS AND I WILL FAIL PLEASE HELP ME !
Question 12
A recent conference had 750 people in attendance. In one exhibit room of 70 people, there were 18 teachers and 52 principals. What prediction can you make about the number of principals in attendance at the conference?
There were about 193 principals in attendance.
There were about 260 principals in attendance.
There were about 557 principals in attendance.
There were about 680 principals in attendance.
Question 13
A college cafeteria is looking for a new dessert to offer its 4,000 students. The table shows the preference of 225 students.
Ice Cream Candy Cake Pie Cookies
81 9 72 36 27
Which statement is the best prediction about the number of cookies the college will need?
The college will have about 480 students who prefer cookies.
The college will have about 640 students who prefer cookies.
The college will have about 1,280 students who prefer cookies.
The college will have about 1,440 students who prefer cookies.
Question 14
A random sample of 100 middle schoolers were asked about their favorite sport. The following data was collected from the students.
Sport Basketball Baseball Soccer Tennis
Number of Students 17 12 27 44
Which of the following graphs correctly displays the data?
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
Question 15
The line plots represent data collected on the travel times to school from two groups of 15 students.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 4, 6, 14, and 28. There are two dots above 10, 12, 18, and 22. There are three dots above 16. The graph is titled Bus 47 Travel Times.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 8, 9, 18, 20, and 22. There are two dots above 6, 10, 12, 14, and 16. The graph is titled Bus 18 Travel Times.
Compare the data and use the correct measure of center to determine which bus typically has the faster travel time. Round your answer to the nearest whole number, if necessary, and explain your answer.
Bus 18, with a median of 13
Bus 47, with a median of 16
Bus 18, with a mean of 13
Bus 47, with a mean of 16
12) There were about 557 principals in attendance. 13) Option A: The college will have about 480 students who prefer cookies. 14) Option C: bar graph, title favorite sport and the x axis labeled sport and the y axis.
What is proportion?The relationship between two quantities that are measured on the same scale and in the same units is known as a percentage. The relative size or magnitude of one thing in comparison to another is represented by proportions, which are frequently stated as ratios, fractions, or percentages. For instance, if there are 8 girls and 12 boys in a class, the girl-to-boy ratio is 8:12, or 2:3, which indicates that there are 3 guys for every 2 girls. Statistics, geometry, and physics are just a few of the mathematical and scientific disciplines that use proportions. Proportions are frequently used in statistics to describe the distribution of a population or a sample.
12) For the number of principals in conference we set up a proportionality with total people as follows:
We know that, 52 principals out of 70 people thus:
52/70 = x/750
Now,
x = (52/70) * 750
x = 557.14
Hence, we can predict that there were about 557 principals in attendance at the conference.
13) Given that, out of 225 students 27 prefer cookies thus,
27/225 = 0.12
That is 12% students like cookies.
Now, for the total number of students we have:
0.12 * 4000 = 480
Thus, option A: The college will have about 480 students who prefer cookies.
14) For the collected data the best representation is option C: bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44.
15) For the given description of the line plot the median is:
For Bus 47 = 16
For Bus 18 = 13
The faster bus is Bus 47, with a median of 16.
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HELP IS VERY MUCH APPRECIATED
1.75 in or 1 3/4 in (which ever form you need it in)
youre given the diameter and so to find radius, you simply divide the diameter by 2.
A study has a 2 Ã 2 Ã 3 within-groups factorial design. This example has a total of ___ cell(s). Researchers would need to investigate ___ main effect(s), ___ two-way interaction(s), and ___ three-way interaction(s) in this study.
A study has a 2 Ã 2 Ã 3 within-groups factorial design. This example has a total of _12_ cell(s). Researchers would need to investigate _three__ main effect(s), _Three two-way interactions __ two-way interaction(s), and _ One three-way interaction__ three-way interaction(s) in this study.
a 2 x 2 x 3 within-groups factorial design, you have:
A total of 2 x 2 x 3 = 12 cells
Three main effects to investigate (one for each factor)
Three two-way interactions to investigate (AxB, AxC, and BxC)
4. One three-way interaction to investigate (AxBxC)
So, in this study, there are 12 cells, researchers would need to investigate 3 main effects, 3 two-way interactions, and 1 three-way interaction.
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Fine the horizontal asymptote of the graph of y = -4x^6+6x +3/8x^2=9x+3
Answer:
There are different methods to find the horizontal asymptote of a function, but one common approach is to take the limit of the function as x approaches positive or negative infinity. If the limit exists and is a finite number, then that is the horizontal asymptote.
To apply this method to the given function:
y = (-4x^6+6x +3)/(8x^2+9x+3)
As x becomes very large (either positive or negative), the highest power of x in the numerator and denominator dominates the other terms. This is because exponential functions grow or shrink much faster than polynomials as x goes to infinity or negative infinity.
Therefore, we can simplify the function by dividing both numerator and denominator by x^6:
y = (-4 + 6/x^5 + 3/x^6)/(8/x^4 + 9/x^5 + 3/x^6)
As x approaches infinity, all the terms with negative powers of x go to zero, leaving:
y ≈ (-4 + 0 + 0)/(0 + 0 + 0)
This is an indeterminate form of 0/0, which suggests that we need to do more algebraic simplification. One way to do this is to factor out the highest power of x in both numerator and denominator:
y ≈ (-4/x^6 + 6/x^11)/(8/x^4 + 9/x^5 + 3/x^6)
y ≈ (-4/x^6)(1 - 6x^5)/(8/x^4)(1 + 9x/x^4 + 3/x^2)
Now, as x approaches infinity, the fraction becomes dominated by the leading terms:
y ≈ (-4/x^6)(-6x^5)/(8/x^4)(9x/x^4)
y ≈ (24/72)(1/x)
As x goes to infinity, 1/x goes to zero, so:
y ≈ 1/3x
Therefore, the horizontal asymptote of the graph of y = (-4x^6+6x +3)/(8x^2+9x+3) is y = 1/3x.
A number line going from negative 2 to positive 1. What is the correct order of the fractions from least to greatest? Point A: −11 3 Point B: −2 3 Point C: 1 3 Point D: −12 3 The correct order for the fractions is .
Answer:
D, A, B, C
Step-by-step explanation:
-12/3, or -4, is lowest
-11/3, or -3.6, is 0.3 more, therefore closer to 0.
-2/3, or -0.6, is much closer to 0, precisely 3 units closer.
1/3, or 0.3, is the only positive number, so it is the most amount.
Brad rolled a cube number cube 30 times and recorded the results in the tally chart below which what is the experimental probability of rolling a five
Write the equation for the line shown in the given graph. Give your answer in slope-intercept form, y=mx+b. Use points that clearly cross the interceptions of the graph paper
An equation in slope-intercept form for the line shown in the given graph is equal to y = -5x + 5.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
m represent the slope.x and y represent the points.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (5 - 20)/(0 + 3)
Slope (m) = -15/3
Slope (m) = -5.
At data point (0, 5) and a slope of -5, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 5 = -5(x - 0)
y - 5 = -5x
y = -5x + 5
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