The sum of the m integers between ai and aj is si - s(i-1) + s(i-1) - s(j-1) = si - sj, which is divisible by m since si, sj have same remainder. So, there exists a consecutive subsequence of the original sequence with a sum divisible by m, namely the integers between ai and aj.
We can prove this using the Pigeonhole Principle.
Consider the sequence of m integers a1, a2, ..., am. Let's compute the prefix sums of this sequence, which we'll denote by s0, s1, s2, ..., sm. That is, we define si = a1 + a2 + ... + ai-1 for i = 1, 2, ..., m, and s0 = 0.
Note that there are m + 1 prefix sums, but only m possible remainders when we divide a sum by m (namely, 0, 1, 2, ..., m-1).
Therefore, by the Pigeonhole Principle, at least two of the prefix sums must have the same remainder when divided by m. Let's say these are si and sj, where i < j.
Then, the sum of the m integers between ai and aj (inclusive) is si - s(i-1) + s(i-1) - s(j-1) = si - sj, which is divisible by m since si and sj have the same remainder when divided by m.
Therefore, there exists a consecutive subsequence of the original sequence with a sum divisible by m, namely the integers between ai and aj.
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What is the volume of the cylinder? Round to the nearest hundredth and approximate using π = 3.14.
cylinder with a segment from one point on the circular base to another point on the base through the center labeled 2.8 feet and a height labeled 4.2 feet
10.39 cubic feet
25.85 cubic feet
36.93 cubic feet
73.85 cubic feet
Answer:
(b) 25.85 cubic feet
Step-by-step explanation:
You want the volume of a cylinder with diameter 2.8 feet and height 4.2 feet, using π = 3.14.
VolumeThe volume of a cylinder is given by the formula ...
V = πr²h
The radius (r) is half the diameter, so is (2.8 ft)/2 = 1.4 ft. Using the given values in the formula, we have ...
V = 3.14·(1.4 ft)²(4.2 ft) ≈ 25.85 ft³
The volume of the cylinder is about 25.85 cubic feet.
te Spring 2014 922 Stat 100 students responded to this survey question: *20 years down the road, what do you expect your income to be? Are there differences between the 5 ethnic groups (White Back Hispanic, Asian, Mixed/Other) on how much they expect to be caring 20 years from now? Here are the results Level of Ethnicity Average SD a Expected Income white 114700 45780 475 Expected Income Back 136800 50840 106 Expected Income Hispank 110900 43400 112 Expected Income Asian 125100 53200 190 Expected Income Other 117800 49960 39 First do an overall test to see if any of the differences are significant in the population given that R20.02670 a. Compute the Chi Square Statistic www Ties 0/2 ts. b. How many degrees of freedom 4 Computers are now shown bove. You are correct. Your receipt no 159-6257 Previous Tries p-value =_______(Use this this online calculator) Anne Tries 0/3
c. Now Compute the F Statistic SA Tries 0/2 d. d. How many degrees of freedom in the numerator? ____
Submit Answer Tries 0/2 denominator? _____
Submit Answer Tries 0/2 p-value=______ % (Use this this online calculator.) Submit Answer Tries 0/3
A p-value less than 0.05 indicates that there is a significant difference between the average expected incomes of the different ethnic groups.
We will perform an ANOVA (Analysis of Variance) test to determine if there are any significant differences between the average expected incomes of the 5 ethnic groups.
a. Compute the Chi Square Statistic: The Chi Square Statistic is not applicable in this case, as it is used for categorical data. Instead, we will use the F Statistic for ANOVA.
b. Degrees of freedom: For ANOVA, there are two degrees of freedom to calculate: - df_between (numerator): This is the degrees of freedom between groups, which is equal to the number of groups minus 1. There are 5 ethnic groups, so df_between = 5 - 1 = 4. - df_within (denominator): This is the degrees of freedom within groups, which is equal to the total number of observations minus the number of groups. The total number of observations is 922, so df_within = 922 - 5 = 917.
c. Compute the F Statistic: Use an ANOVA calculator or software to input the data and calculate the F Statistic.
d. Degrees of freedom in the numerator and denominator: - Numerator degrees of freedom: 4 (as calculated in part b) - Denominator degrees of freedom: 917 (as calculated in part b) After computing the F Statistic, use an online calculator or software to find the p-value.
A p-value less than 0.05 indicates that there is a significant difference between the average expected incomes of the different ethnic groups.
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Which of the following is a line of symmetry for the figure shown?
Figure shows an arrow shape pointing up and down on a dot grid. Lines AB and CD run horizontally and parallel across the arrow. Line EF runs vertically through the center of the arrow.
A.
←→
A
B
B.
←→
C
D
C.
←→
E
F
D.
None of the above
Answer:
The line of symmetry for the given figure is EF which runs vertically through the center of the arrow. Therefore, the answer is C.
Step-by-step explanation:
An element of the sample space is a(n) _____.
a. sample point
b. outlier
c. estimator
d. event
An element of the sample space is a sample point. Your answer: a. sample point. In this context, an "element" refers to an individual outcome within the "sample space," which is the set of all possible outcomes. A "sample point" is a single outcome in the sample space. Therefore, an element of the sample space is a sample point.
An element of the sample space is a sample point. A sample point represents the most basic outcome of an experiment or observation. For example, if we roll a dice, the sample space would be {1, 2, 3, 4, 5, 6}, and each number in the sample space would be a sample point.
Similarly, in a coin toss experiment, the sample space would be {heads, tails}, and each outcome would be a sample point. The sample space is the set of all possible outcomes of an experiment or observation, and each element in the sample space represents a unique sample point. Understanding the sample space is essential in probability theory as it forms the basis for defining events and calculating probabilities.
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Pleaese help me! Thank you!
The angle ∠ABC is 83 degrees.
How to find the angle of a cyclic quadrilateral?A cyclic quadrilateral is a quadrilateral which has all its four vertices lying on a circle.
The opposite angles of a cyclic quadrilateral have a total of 180°.
Using the theorem for cyclic quadrilateral angles and arc angles,
67 = 1 / 2 (78 + x)
where
x = ∠DC
67 = 39 + 0.5x
67 - 39 = 0.5x
28 = 0.5x
divide both sides by 0.5
x = 28 / 0.5
x = 56 degrees
Hence,
Arc ∠AC = 110 + 56 = 166 degrees
Therefore,
∠ABC = 1 / 2 (166)
∠ABC = 83 degrees
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On a track and field team, 8% of the members run only long-distance, 32% compete only in field events, and 12% are sprinters only. Find the probability that a randomly chosen team member runs only long-distance or competes only in field events.
The probability a randomly chosen team member runs only long-distance or competes only in field events is 40%
Finding the probability that of randomly chosen team memberFrom the question, we have the following parameters that can be used in our computation:
8% of the members run only long-distance, 32% compete only in field events, 12% are sprinters only.The probability a randomly chosen team member runs only long-distance or competes only in field events is
P = run only long-distance + field events,
So, we have
P = 8% + 32%
Evaluate
P = 40%
Hence, tthe probability os 40%
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You are required to setup a predictive equation involving variable 1 and variable 2. First, you plot the DATA to determine if linear regression applies. You decide
A) Linear regression is not applicable because the point patter is curvilinear (has a curve).
B) Linear regression Is not useful because the points have no discernible pattern.
C) You need more information before deciding to use linear regression.
D) Linear regression is not applicable because it appears that there are two linear patterns indicating that the data came from two populations.
E) The linear regression equation will be very useful because the points have a strong linear pattern.
variable1 variable2
3.06470 44.98382
-9.69073 -22.93531
-4.20144 -18.19409
4.30225 12.39010
4.48845 55.39978
8.39173 15.67437
5.89874 16.51967
-9.46846 -34.45667
1.54090 -7.82248
5.92418 58.17744
-6.81619 -32.24022
-7.69106 -17.85516
-0.72913 22.13627
9.13267 14.72200
-2.15342 -14.33373
6.11798 24.94679
7.00841 70.46126
1.32124 34.80144
-2.35173 13.57464
-9.46731 -23.94740
9.94412 75.11078
0.60205 -6.82526
-5.68710 -4.79326
8.84593 83.90314
A) Linear regression is not applicable because the point pattern is curvilinear (has a curve).
In statistical analysis, linear regression is a powerful tool used to model the relationship between two variables. It is commonly used to identify and quantify the linear association between a dependent variable and one or more independent variables. However, it is important to verify whether the relationship between the two variables is indeed linear before applying linear regression.
To determine whether linear regression is appropriate for a given set of data, we should start by creating a scatterplot of the data, with one variable on the horizontal axis and the other variable on the vertical axis. The scatterplot will help us visualize the pattern of the data points and identify any outliers or nonlinear patterns.
Looking at the scatterplot of variable1 against variable2 provided in this question, we see a curvilinear pattern instead of a linear pattern. The data points do not appear to follow a straight line, but instead seem to curve upwards in a parabolic shape. This means that there is no linear relationship between the two variables, and we cannot use linear regression to model the relationship.
Therefore, we can conclude that the correct answer is A) Linear regression is not applicable because the point pattern is curvilinear (has a curve). We would need to explore other regression models, such as quadratic or exponential regression, to see if they fit the data better.
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The diagram shows three streets that form the perimeter of a park. How far is it from the corner of Oak and Ridgewood to the corner of Oak and Savannah?
Round to the nearest tenth of a yard.
The distance from the corner of Oak and Ridgewood to the corner of Oak and Savannah is given as follows:
276 yd.
What is the law of sines?Suppose we have a triangle in which:
Side with a length of a is opposite to angle A.Side with a length of b is opposite to angle B.Side with a length of c is opposite to angle C.The lengths and the sine of the angles are related as follows:
[tex]\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}[/tex]
Then the ratio for this problem is given as follows:
sin(38º)/d = sin(42º)/300
The distance is obtained as follows:
d = 300 x sine of 38 degrees/sine of 42 degrees
d = 276 yd.
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SAT Scores: A college admissions officer sampled 116 entering freshmen and found that 45 of them scored more than 590 on the math SAT. Part 1 of 3 (a) Find a point estimate for the proportion of all entering freshmen at this college who scored more than 590 on the math SAT. Round the answer to at least three decimal places The point estimate for the proportion of all entering freshmen at this college who scored more than 590 on the math SATIS 0.388 Part 2 of 3 (b) Construct a 98% confidence interval for the proportion of all entering freshmen at this college who scored more than 590 on the math SAT. Round the answer to at least three decimal places. A 9896 confidence interval for the proportion of all entering freshmen at this college who scored more than 590 on the math SAT IS 0.283
The 98% confidence interval for the proportion of all entering freshmen at this college who scored more than 590 on the math SAT is approximately 0.283 to 0.493.
To find the point estimate for the proportion of all entering freshmen at this college who scored more than 590 on the math SAT, we divide the number of freshmen who scored more than 590 by the total sample size.
Point Estimate = Number of freshmen who scored more than 590 / Total sample size
In this case, the number of freshmen who scored more than 590 on the math SAT is 45, and the total sample size is 116.
Point Estimate = 45 / 116 ≈ 0.388
Rounded to three decimal places, the point estimate for the proportion of all entering freshmen at this college who scored more than 590 on the math SAT is approximately 0.388.
To construct a 98% confidence interval for the proportion of all entering freshmen at this college who scored more than 590 on the math SAT, we can use the following formula:
Confidence Interval = Point Estimate ± (Critical Value * Standard Error)
The critical value corresponds to the desired confidence level and is obtained from the standard normal distribution. For a 98% confidence level, the critical value is approximately 2.326.
The standard error can be calculated using the following formula:
Standard Error = sqrt((Point Estimate * (1 - Point Estimate)) / Sample Size)
Using the point estimate from part (a) as 0.388 and the sample size as 116, we can calculate the standard error:
Standard Error = sqrt((0.388 * (1 - 0.388)) / 116) ≈ 0.050
Now we can construct the confidence interval:
Confidence Interval = 0.388 ± (2.326 * 0.050)
Lower Bound = 0.388 - (2.326 * 0.050) ≈ 0.283
Upper Bound = 0.388 + (2.326 * 0.050) ≈ 0.493
Rounded to three decimal places, the 98% confidence interval for the proportion of all entering freshmen at this college who scored more than 590 on the math SAT is approximately 0.283 to 0.493.
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write the equation of write the equation of a parabola with the given focus and directrix (2 points). please show all work, and make sure that your final answer is in x-equals or y-equals form (the way we learned in class).
The parabola has its vertex at (h, k), and the focus is located at (h + p, k). The directrix line is represented by the equation x = h - p.
The equation of a parabola with a given focus and directrix can be derived using the geometric definition of a parabola. Let's consider a parabola with a focus F and a directrix line d. The parabola is defined as the set of all points P such that the distance from P to the focus F is equal to the perpendicular distance from P to the directrix line d. The equation of the parabola can be expressed in terms of either x or y, depending on the orientation of the parabola.
To derive the equation, we can assume that the focus F is located at (h, k + p), where (h, k) represents the vertex of the parabola, and p is the distance from the vertex to the focus. Let's also assume that the directrix line is given by the equation y = k - p.
If we consider a generic point P(x, y) on the parabola, we can calculate the distance between P and the focus F using the distance formula:
√((x - h)² + (y - (k + p))²)
Similarly, we can calculate the perpendicular distance from P to the directrix line d, which is simply the difference in y-coordinates:
|y - (k - p)|
According to the definition of a parabola, these distances should be equal. Therefore, we can set up the equation:
√((x - h)² + (y - (k + p))^2) = |y - (k - p)
To simplify this equation, we square both sides to eliminate the square root:
(x - h)² + (y - (k + p))² = (y - (k - p))²
Expanding and simplifying, we get:
(x - h)² + (y - k - p)² = (y - k + p)²
Further simplifying, we obtain:
(x - h)² = 4p(y - k)
This is the equation of a parabola with its vertex at (h, k) and the focus at (h, k + p). The directrix line is given by the equation y = k - p.
Therefore, the equation of the parabola in x-equals form is:
(x - h)² = 4p(y - k)
Alternatively, if you prefer the y-equals form, you can rearrange the equation as follows:
y = (1/(4p))(x - h)² + k
In this form, the parabola has its vertex at (h, k), and the focus is located at (h + p, k). The directrix line is represented by the equation x = h - p.
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You want to obtain a sample to estimate how much parents spend on their kids birthday parties. Based on previous study, you believe the population standard deviation is approximately σ=53.9σ=53.9 dollars. You would like to be 95% confident that your estimate is within 1.5 dollar(s) of average spending on the birthday parties. How many parents do you have to sample?
n =
You need to sample 4949 parents to be 95% confident that your estimate is within 1.5 dollars of the average spending on birthday parties.
To calculate the required sample size (n) for your study, you can use the following formula:
n = (Z^2 * σ^2 * E^2)
where:
n = sample size
Z = Z-score, which corresponds to the desired confidence level (1.96 for a 95% confidence interval)
σ = population standard deviation (53.9 dollars)
E = margin of error (1.5 dollars)
Now, plug in the values and solve for n:
n = (1.96^2 * 53.9^2) / 1.5^2
n = (3.8416 * 2905.21) / 2.25
n = 11133.69936 / 2.25
n = 4948.31104
Since you cannot have a fraction of a parent in your sample, round up to the nearest whole number:
n = 4949
So, you need to sample 4949 parents to be 95% confident that your estimate is within 1.5 dollars of the average spending on birthday parties.
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ASAP help need help with questions
The component form and magnitude of the vector are;
v = 3·i - 2·j
||v|| = √(14)
What is the component form of a vector?The component form of a vector is expressed as <x, y>, which indicates the distance of the vector to the right or left, x-component, and the distance up or down of the y-component.
The coordinate points on the vector are; (0, 0), and (3, -2)
The component form of the vector consists of the horizontal and vertical components, which can be found as follows;
Horizontal component = (3 - 0)·i = 3·i
The vertical component = (-2 - 0)·j = -2·j
The component form of the vector is therefore;
v = ⟨3, -2⟩
The magnitude of the vector can be obtained as follows;
||v|| = √((3 - 0)² + (-2 - 0)²) = √(14)
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Weekly Expenses Per Person for Tyler, Texas
Housing $243 Utilites $97 Insurance $192
Transportation $194 Other $149 Taxes $124
If there are 4 weeks in a month, what is the minimum monthly amount
needed per person to live in Tyler, Texas?
PLS HELP
It’s just 7th grade math
Last one I promise.
Make everything simple.
The area of a circle can be obtained from the use of formula πr^2
What is the circumference of the circle?The circumference of a circle is the distance around the circle, which can be found using the formula; C = 2πr
where "C" is the circumference, "π" (pi) is a mathematical constant approximately equal to 3.14, and "r" is the radius of the circle.
Area of the circle = 3.14 * (3)^2 = 28.26 cm^2
C = 2 * 3.14 * 3 = 18.84
2) A = 3.14 * (17)^2 = 907.46
C = 2 * 3.14 * 17 = 106.76
3) A = 3.14 * (324)^2 = 329.624.64
C = 2 * 3.14 * 324 = 2034.72
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In a flower garden, there are 6 tulips for every 7 daisies. If there are 48 tulips, how many daisies are there?
Answer:
56, There are 56 daisies.
Step-by-step explanation:
For the matrix 「-2-3 31 A -6-99 4 6 -6 the row space C(AT) and the null space N(A) are spanned by the bases: 2 3 3 0 2 Write the vector 18 uniquely in the form v=VC+VN with VC in C(AT) and VN in N(A): vc= , VN
We can express the vector 18 as v = VC + VN =
[tex](1/14)*[-3, 3, 3]^T + [47/28, -41/28, 3, 0, 0]^T.[/tex]
To express the vector 18 in the form v = VC + VN with VC in the row space C(AT) and VN in the null space N(A), we need to first find the components of v in both spaces.
The basis for the row space is given as {2, 3, 3, 0, 2}, we can use these vectors as rows to form a matrix C. We then compute the orthogonal complement of C, which gives us the null space of A.
We can find that the row space C(AT) is spanned by the basis vectors {2, 3, 3} and the null space N(A) is spanned by the basis vector {0, -2, 1, 0, 0}.
To express the vector 18 as a sum of a vector in C(AT) and a vector in N(A), we first project v onto the row space C(AT) using the formula VC =
[tex](C(AT)C)^(-1)C(AT)v[/tex]
This gives us VC =
[tex](1/14)*[-3, 3, 3]^T[/tex]
We find the projection of v onto the null space N(A) using the formula VN =
[tex]v - A(A^T A)^(-1)A^T v[/tex]
This gives us VN =
[tex] [47/28, -41/28, 3, 0, 0]^T[/tex]
To express a vector in the form v = VC + VN, where VC is in the row space C(AT) and VN is in the null space N(A), we first need to find the basis vectors for both spaces. Then, we can use the projection formulas to find the components of v in each space and combine them to obtain the desired expression.
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Question 9
In an educational study, the researchers hypothesised that older students tend to make more complaints over minor details (e.g. spelling mistakes and grammar) compared to their younger counterparts.
Which of the statistical tests below would be the most appropriate to utilise in addressing this hypothesis?
1.Paired t-test 2.Correlation 3.Binomial
4.Chi-square
If the chi-square test shows that there is a significant association, then it can be concluded that older students tend to make more complaints over minor details compared to their younger counterparts.
The most appropriate statistical test to utilize in addressing the hypothesis that older students tend to make more complaints over minor details compared to their younger counterparts would be the chi-square test.
The chi-square test is used to analyze the categorical data and determine whether there is a significant association between two categorical variables. In this case, the two categorical variables would be the age group of the students (older vs. younger) and the frequency of complaints over minor details.
The researchers could collect data by randomly selecting a sample of older and younger students and recording the number of complaints made by each student over minor details. This data could then be organized into a contingency table with rows representing the age group of the students and columns representing the frequency of complaints.
Once the data is organized in this way, the chi-square test can be used to determine if there is a significant association between age group and frequency of complaints. If the chi-square test shows that there is a significant association, then it can be concluded that older students tend to make more complaints over minor details compared to their younger counterparts.
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A research group developed the following mathematical model relating systolic blood pressure and age: P(x)=a+ bln(x+1). Where P(x) is pressure, measured in millimeters of mercury, and x is age in years. By examining Guilford County hospital records, they estimate the values for Guilford County to be a=43 and b=25. Using this model, estimate the rate oI change of pressure with respect to time after 31 years. Round to the nearest hundredth ( 2 decimal places). ____ millimeters per year
Rounding to two decimal places, the rate of change of blood pressure with respect to time after 31 years is approximately 0.81 millimeters per year.
The mathematical model relating systolic blood pressure and age is given as P(x)=a+b*ln(x+1), we can differentiate it with respect to time (t) to find the rate of change of pressure with respect to time:
dP/dt = dP/dx * dx/dt
Here dx/dt is the rate of change of age with respect to time, which is simply 1 year per year or 1.
Taking the derivative of P(x) with respect to x, we get:
dP/dx = b/(x+1)
Substituting the given values for a and b, we have:
P(x) = 43 + 25ln(x+1)
dP/dx = 25/(x+1)
Therefore, the rate of change of pressure with respect to time after 31 years is:
dP/dt = dP/dx * dx/dt = (25/(31+1)) * 1 = 0.8065
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Directions: Complete the following problems. Do your best and show all work. Partial credit will be
determined for partial answers.
1. Complete the table with the components of the following quadratic equation. Then sketch the
function on the graph.
Equation in Standard
Form:
Equation in Factored
Form:
x-intercepts:
y-intercepts:
Leading Coefficient
Axis of Symmetry:
Point symmetric to the
y-intercept:
Parabola opens which
way:
Does the graph have a
Minimum or Maximum?
Vertex:
f(x) =
2)
(-8,0)
3)
5)
6)
7)
Algebra 1 Unit 10
Flipped Math
Ms. Crow
8)
9)
x² + 2x - 8
-11-0)-4-4----4--
1
+10
24 1 A
A
*
<9 10 11
Please help me YALL
The table should be completed with the components of the quadratic equation as follows;
Equation in Standard Form: f(x) = x² + 2x - 8.Equation in Factored Form: (x + 4)(x - 2)x-intercepts: x = -4 and x = 2y-intercepts: (0, -8)Leading Coefficient: 1.Axis of Symmetry: -1Point symmetric to the y-intercept: (0, 8)Parabola opens which way: up.Does the graph have a Minimum or Maximum: minimum.Vertex: (-1, -9).What is the general form of a quadratic function?In Mathematics and Geometry, the general form of a quadratic function can be modeled and represented by using the following quadratic equation;
y = ax² + bx + c
Where:
a and b represents the coefficients of the first and second term in the quadratic function.c represents the constant term.Axis of symmetry, Xmax = -b/2a
Axis of symmetry, Xmax = -(2)/2(1)
Axis of symmetry, Xmax = -2/2
Axis of symmetry, Xmax = -1
For the vertex, we have:
f(-1) = (-1)² + 2(-1) - 8 = -9.
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Which number is divisible by both 5 and 6?
A.132.359
B.142.645
C.164.780
D.193.560
The only option that has a number that is divisible by both 5 and 6 is: D.193.560
How to find a divisible number?We want to find a number that is divisible by both 5 and 6.
Now, looking at the options, since they are all decimals, the one that would be the most appropriate is the one that does not contain a recurring decimal.
Thus:
A) 132.359/5 =26.4718
132.359/6 = 22.0598333..
B) 142.645/5 = 28.529
142.645/6 = 23.77416666666..
C) 164.780/5 = 32.956
164.780/6 = 27.46333333
D) 193.560/5 = 38.712
193.560/6 = 32.26
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How does mL=(M+m)D simplify to m=M * (D/L - D)?
To begin, we can expand mL=(M+m)D by distributing the D:
mL = MD + mD
Next, we can isolate m by subtracting MD from both sides:
mL - MD = mD
We can then factor out m on the right side:
m(L - D) = MD
Finally, we can solve for m by dividing both sides by (L-D):
m = MD / (L-D)
And since M = mL/D, we can substitute this into the equation:
m = (mL/D) * D / (L-D)
Simplifying, we get:
m = M * (D/L - D)
So, mL=(M+m)D simplifies to m=M * (D/L - D).
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The double dot plot shows the values in two data sets.
Double dot plot shows the values of two data sets. It shows the number line ranges from 10 to 70 showing the following values that appear as dots above the line. For data set A. Two dots above 10. Three dots above 20. Four dots above 30. Two dots above 40. One dot above 50. For data set B. One dot above 30. Three dots above 40. Four dots above 50. Two dots above 60. Two dots above 70.
Compare the data sets using measures of center and variation.
Data set A Data set B
Median $=$
Median $=$
IQR $=$
IQR $=$
The median for Data Set A is 30, and
median for Data Set B is 50.
The IQR for Data Set A is 20 (from 20 to 40), also the IQR for Data Set B is also 20 (from 40 to 60).
What is the explanation for the above ?To find the median we say ......
For data set A, the median is:
The 6th value is the middle value, since there are 12 total values.
The 6th value = 30 on the number line,
since there are 2 dots above 10, 3 above 20, and 4 above 30.
Therefore, the median of data set A is 30.
For data set B, the median is:
The 7th and 8th values are the middle values, since there are 14 total values.
The 7th and 8th values = 50 on the number line,
since there are 4 dots above 50 and 2 dots above 60.
Hence, the median of data set B is 50.
To find the IQR, we need to find the range of the middle 50% of each data set.
For data set A, the IQR is:
The lower quartile is the 3rd value, which = 20 on the number line.
The upper quartile is the 9th value, = 40 on the number line.
The IQR is the difference between the upper and lower quartiles: 40 - 20 = 20.
For data set B, the IQR is:
The lower quartile is the 4th value, = 40 on the number line.
The upper quartile is the 11th value, = 70 on the number line.
Thus,
The IQR = 70 - 40 = 30.
Thus, data set B has a higher median than data set A,
And see that data set B has a larger IQR than data set A.
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Use a fraction or mixed number to represent the time on a number line. Let 0 represent noon. 12:15 P. M
The time 12:15 PM is 1 BY 4 hours after noon. The fraction that represents 12:15 AM is +1/4.
According to the question, we have to represent time 12: 15 PM in fraction and we are given that noon is represented by 0. As we have a fixed number of minutes in an hour, we can convert any number of minutes into a fraction of an hour by dividing it by 60.
The time is given as:
Time = 12:15 PM
It is given that 0 represents noon.
It means that time before noon would be represented with a negative value and time after noon would be represented with a positive value.
12:15 PM is 15 minutes after noon which means 1/4 th of an hour. So, we have:
12:15 PM = + 1/4
Hence, the fraction that represents 12:15 PM is +1/4.
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A bag contains seven red balls numbered 2, 4, 5, 6, 7, 8, 10 and three white balls numbered 1, 3, and 9. If a ball is drawn, what is the probability the ball is white or less than 3? Show all work.
The probability of drawing a ball that is white or less than 3 is 3/10 or 0.3.
We have,
There are 10 total balls in the bag.
The probability of drawing a white ball is 3/10 since there are three white balls out of ten total balls.
The probability of drawing a ball that is less than 3 is 1/10 since there is only one ball less than 3 (the white ball numbered 1) out of ten total balls.
To find the probability of drawing a ball that is white or less than 3, we need to add the probabilities of these two events occurring:
P(white or less than 3)
= P(white) + P(less than 3) - P(white and less than 3)
Since there is only one ball that satisfies both conditions (the white ball numbered 1), we can calculate P(white and less than 3) as 1/10.
P(white or less than 3) = 3/10 + 1/10 - 1/10
P(white or less than 3) = 3/10
Therefore,
The probability of drawing a ball that is white or less than 3 is 3/10 or 0.3.
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The top of square table has an area of 24 square feet. What is the length of 1 edge of the tabletop?
The length of one edge of the tabletop is 4.89 feet.
We know that square is a shape that has all the side equal. Based on this using the formula to find the length of edge of the tabletop.
The area of square table is given by the formula -
Area of square table = side²
We will keep the value of area of square table to find the value of side which will be length of edge
24 = side²
Side = ✓24
Taking square root for the value on right side of the equation
Side = 4.89
Hence, the length of one edge of the tabletop is 4.89 feet.
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u=a-k+b, solve for a
To solve for a in terms of other variables, a = u + k - b
Subject of formula.Subject of formula is a topic in mathematics that involves expressing a required variable in terms of other variables in a given equation. This requires the application some mathematical principles so as to get the final expression.
From the given question, we have;
u = a - k + b
to solve for a, add k and -b to the two sides of the equation.
Thus we have;
u + k -b = a - k + b + k - b
u + k - b = a
Therefore,
a = u + k - b
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In a round robin tournament, each team plays every other team once. The formula G - the number of games G that must be scheduled for n teams. How many games must be scheduled for 7 teams? Show your work.
The number of games that must be scheduled for a round-robin tournament with 7 teams is :
21
A round-robin tournament is a competition in which each team or player plays against every other team or player once. In a round-robin tournament, each team or player is given an equal opportunity to compete against every other team or player, ensuring a fair and balanced competition.
To determine the number of games (G) that must be scheduled for a round-robin tournament with 7 teams (n), you can use the formula:
G = n(n - 1) / 2
Step 1: Replace n with 7 in the formula:
G = 7(7 - 1) / 2
Step 2: Calculate the value inside the parentheses:
G = 7(6) / 2
Step 3: Multiply 7 by 6:
G = 42 / 2
Step 4: Divide 42 by 2:
G = 21
So, 21 games must be scheduled for a round-robin tournament with 7 teams.
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a city department of transportation studied traffic congestion on a certain highway. to encourage carpooling, the department will recommend a carpool lane if the average number of people in passenger cars on the highway is less than 2 2 . the probability distribution of the number of people in passenger cars on the highway is shown in the table. number of people 1 1 2 2 3 3 4 4 5 5 probability 0.56 0.56 0.28 0.28 0.08 0.08 0.06 0.06 0.02 0.02 based on the probability distribution, what is the mean number of people in passenger cars on the highway? responses 0.28 0.28 0.28 0.56 0.56 0.56 1.7 1.7 1.7 2 2 2 3
The mean number of people in passenger cars on the highway is 1.7.
The mean is a measure of central tendency that represents the average value of a set of data. In the context of probability distributions, the mean is also referred to as the expected value. It is calculated by multiplying each possible value of the random variable by its probability of occurrence and summing up the products
To find the mean number of people in passenger cars on the highway, we need to multiply each possible number of people by its corresponding probability, and then add up these products.
So,
mean = (1 * 0.56) + (2 * 0.28) + (3 * 0.08) + (4 * 0.06) + (5 * 0.02)
mean = 0.56 + 0.56 + 0.24 + 0.24 + 0.1
mean = 1.7
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Based on the table, the linear equation that represents the change in water’s boiling point for every 1,000-foot change in altitude has a slope of
units.
The linear equation that represents the change in water’s boiling point for every 1,000-foot change is y = -1.8x + 212.
We have,
From the table,
Take two ordered pairs.
(0, 212) and (0.5, 211.1)
Now,
The slope can be calculated as,
= (211.1 - 212) / (0.5 - 0)
= -0.9/0.5
= -1.8
Now,
The equation can be written as,
y = mx + c
(0, 212) = (x, y)
So,
212 = -1.8 x 0 + c
c = 212
Now,
y = mx + c
y = -1.8x + 212
Thus,
The linear equation that represents the change in water’s boiling point for every 1,000-foot change is y = -1.8x + 212.
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Use the figure to find the Area of Segment AXB.
9
12 - 18
9 - 18
The area of the segment is 9π - 18.
Option C is the correct answer.
We have,
Area of sector = 360/360 x πr²
Radius = 6
The area of sector AOB.
= 90/360 x π x 6²
= 1/4 x π x 36
= 9π
= 9π
Now,
The area of the triangle.
= 1/2 x base x height
= 1/2 x 6 x 6
= 18
Now,
Area of segment AXB.
= Area of the sector - Area of triangle
= 9π - 18
Thus,
The area of the segment is 9π - 18.
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