We have to use pigeonhole principle to find balls from bowl. From 75 balls at least one out of 31 balls will be of black color, out of 23 balls will be red, out of 25 will be blue, out of 27 balls will be green, out of 29 will be yellow.
out of 75 balls for each ball to be chosen at least once then we have to compute each color of ball separately,
By using the pigeonhole principle's formula n(r - 1) + 1
For red ball,
N=11, k=1, [N/2]≥3
= 11(3-1)+1
= 23
Hence, out of 23 balls from 75 balls at least one will be of red color
For, blue ball
N=12, k=1, [N/2]≥3
= 12(3-1)+1
= 25
Hence, out of 25 balls from 75 balls at least one will be of blue color
For green color,
N=13, k=1, [N/2]≥3
= 13(3-1)+1
= 27
Hence, out of 27 balls from 75 balls at least one will be of green color
For yellow ball,
N=14, k=1, [N/2]≥3
= 14(3-1)+1
= 29
Hence, out of 29 balls from 75 balls at least one will be of yellow color
For black ball,
N=15, k=1, [N/2]≥3
= 15(3-1)+1
= 31
Hence, out of 31 balls from 75 balls at least one will be of black color
The pigeonhole principle states that if n items are put into m containers, where n > m, at least one container must contain more than one item. If there are k+1 or more pigeons dispersed throughout the k pigeonholes, at least one pigeonhole will have two or more pigeons. Proof. The statement's converse is that there can only be a maximum of k pigeons if each slot can only accommodate one bird.
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Kelli walks no more than 25 dogs on Mondays. Ms. Lincoln has 5 dogs that Kelli walks. The inequality shown can be used to find x, the number of dogs Kelli can walk on Monday in addition to Ms. Lincoln's dogs. x + 5 25 Which inequality represents all possible values of x?
The inequality x ≤ 20 represents the all possible values of x.
What is inequality?Inequality shows relation between two expression which are not equal to each others.
Given that,
Kelli walks not more than 25 dogs on Mondays,
Also,
Kelli walks 5 dogs that belongs to Ms. Lincoln
The inequality to find the number of dogs Kelli walks on Monday x, in addition to Ms. Lincoln's dogs, can be written as,
x+5 ≤ 25
Subtract 5 from both the sides,
x + 5 - 5 ≤ 25 - 5
x ≤ 20
The required inequality is x ≤ 20.
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the margin of error is: a. the largest possible sampling error for a specified level of confidence; b. the critical value times the standard error of the sampling distribution; c. the difference between the point estimate and the parameter. a only b only c only a and b b and c a and c all of the above none of the above
The correct is b i.e; the critical value times the standard error of the sampling distribution
Given options are :
a. The biggest sampling error that can be made while maintaining a certain level of confidence.
b. the critical value multiplied by the sampling distribution's standard error
c. the discrepancy between the parameter and the point estimate.
Margin of error
= C * SE
Where C is critical value of on
of is the Standard error
The multiple of Critical Value and Standard error is the margin of error
Correct Option is b i. e the critical value times the Standard error of Sampling distribution
Therefore, The margin of error is the product of Critical Value and Standard Error.
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Uppose there are three pipes filling a tank. The first pipe can fill the tank in 5 hours. The second pipe can fill the tank in 8 hours. The third pipe can fill the tank in 11 hours. How much of the tank can the first pipe fill in one hour? how much of the tank can the second pipe fill in one hour? how much of the tank can the third pipe fill in one hour?
Answer:
Step-by-step explanation:
in this fulcrum, the weights are perfectly balanced. how far must the fulcrum be located from the 40 lb. weight if the bar is 9 feet long?
The distance of 40 lb will be 5ft, according to the question.
What do you mean by distance?
Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.
According to the given question,
We have the given information:
The fulcrum be located from the 40 lb.
The weight of bar is 9ft long.
Now, we will calculate the distance,
40x = 50(x-1)
40x = 50x - 50
40x - 50x = -50
-10x = -50
x = 5
Therefore, the required answer is 5ft.
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this exercise involves the formula for the area of a circular sector. the area of a sector of a circle with a central angle of 5????/11 rad is 15 m2. find the radius of the circle. (round your answer to one decimal place.) incorrect: your answer is incorrect. m
The radius of the circle will be 4.6m.
What is area of a circle?
The measurement of the circle's boundaries is called as the circumference or perimeter of the circle. whereas the circumference of a circle determines the space it occupies. The circumference of a circle is its length when it is opened up and drawn as a straight line. Units like cm or unit m are typically used to measure it. The circle's radius is considered while calculating the circumference of the circle using the formula. As a result, in order to calculate the circle's perimeter, we must know the radius or diameter value. The area of the circle will be A = [tex]\pi r^{2}[/tex].
The area of the circle given is = 15 m²
Sector of a circle with a central angle of 5π/11 rad
The area will be (1/2) * r² * Ф
15 = (1/2) * r² * (5π/11)
⇒r² = 30 * (11/5π)
⇒r² = 21.00
⇒r=4.6m
Hence, the radius of the circle will be 4.6m.
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a rancher has 720 feet of fencing with which to enclose two adjacent rectangular corrals (see figure). what dimensions should be used so that the enclosed area will be a maximum?
If a rancher has 720 feet of fencing with which to enclose two adjacent rectangular corrals, the dimensions are 90 feet and 120 feet
From the figure
4x + 3y = 720
3y = 720 - 4x
y = 240 - (4/3)x
The area = l × w
Where l is the length
w is the width
Substitute the values in the equation
A = 2x × y
= 2x (240 - (4/3)x)
Apply the distributive property
= 480x - (8/3)x^2
Differentiate the values
0 = (-16/3)x + 480
(16/3) x = 480
x = 480 / (16/3)
x = 90 feet
Then,
y = 240 - (4/3)(90)
= 120 feet
Hence, the dimensions are 90 feet and 120 feet
I have answered the question is general, as the given question is incomplete.
The complete question is
A rancher has 720 feet of fencing with which to enclose two adjacent rectangular corrals (see figure). what dimensions should be used so that the enclosed area will be a maximum?
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PLS HELP!!! CHOICES FOR ANSWERS ARE THE SAME FOR BOTH! 50 PTS
The two-column proof shown above should be completed with the following theorems:
Statements Reasons
ΔADB ≅ ΔCDB HL.
AD ≅ CD CPCTC.
What are the types of triangle?In Geometry, there are five (5) major types of triangle based on the length of their sides and angles, and these include the following;
Equilateral triangleScalene triangleIsosceles triangleObtuse triangleRight-angled triangleWhat is CPCTC?In Mathematics, CPCTC is an acronym for corresponding parts of congruent triangles are congruent and it can be defined as a theorem which states that the corresponding angles and side lengths of two (2) or more triangles are congruent if they are both congruent.
By applying the corresponding parts of congruent triangles are congruent (CPCTC) theorem to triangle ABC (ΔABC), we have the following;
Statement Reason
AD ≅ CD CPCTC.
What is HL?In Mathematics, HL is an acronym for hypotenuse leg and it can be defined as a theorem which states that if the hypotenuse and one (1) leg in a right-angled triangle are congruent to the hypotenuse and leg of another right-angled triangle, then the two (2) triangles would be congruent i.e ΔADB ≅ ΔCDB.
By applying the hypotenuse leg (HL) theorem to triangle ABC (ΔABC), we have the following;
Statement Reason
ΔADB ≅ ΔCDB HL.
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9 2 8 7 6 5 1 4 3 show the contents of the array above each time an insertion sort changes it while sorting the array into ascending order.
The array that has been sorted using insertion sorting 1 2 3 4 5 6 7 8 9.
A straightforward sorting algorithm called insertion sort functions like how you might arrange playing cards in your hands.
Initial Pass: 2 9 8 7 6 5 1 4 3
The array's first two members are initially compared using an insertion sort.
Since 9 is bigger than 2, they are not arranged in ascending order, and 2 is not in the proper place. So, switch 9 and 2.
Therefore, 2 is currently kept in a sorted sub-array.
Second Pass: Continue with the next two elements and compare them.
2 8 9 7 6 5 1 4 3
Here, 9 is bigger than 8, therefore both items appear to be in ascending order; as a result, there won't be any switching. Along with 8, 9 is also kept in a sorted sub-array.
Third pass: Currently, the sorted sub-array has two entries, which are 2 and 8.
Moving on to the following two components, which are 9 & 7,
2 7 8 9 6 5 1 4 3
Continue sorting similarly; the results would be 1 2 3 4 5 6 7 8 9.
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flipping a fair two-sided coin, the probability of getting heads is equal to the probability of getting tails. if the coin is flipped three times consecutively, what is the probability of getting heads at least twice?
The probability of getting heads at least twice is 0.5
Since we are given two-sided coin, where the probability of getting heads is equal to the probability of getting tails.NO of outcomes in this case is 2,The probability of getting a head = 1/2, similarly probability of getting a tail is =1/2 .So when a coin is flipped three times, the sample space for the event will be (HHH, HHT, HTH, HTT, THH, THT, TTH, TTT), H stands for head and T stands for tails, here for tossing the coin the number of outcomes is 8 .So the probability of getting at least two heads is: 4/8= 1/2 =0.5
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You pend 2/3 hour reading a book daily. How many hour did you pend reading after a week?
The total number of hours spent on reading in a week is 14/3 hours.
Define the term fraction of a number?A fraction is a number that is a component of a whole. By breaking a whole into a number of parts, it is evaluated.The components of a whole or group of items are described by fractions. The numerator is the figure only at top of the line. It details the number of equal portions which have been taken from the total or collection. The denominator is the figure that appears below the line.For the given question-
Number of hours spent of reading = 2/3 hours.
Total number of days in a week = 7.
Total number of hours spent on reading = 2/3 x 7
Total number of hours spent on reading = 14/3
Thus, the total number of hours spent on reading in a week is 14/3 hours.
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If Veronica has 4 more nickels than quarters and they have a combined value of 170 cents, how many of each coin does she have?
The total number of nickels and quarters with Veronica are 5 and 9, respectively.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Let the number of nickels be represented by x, while the number of quarters be represented by y.
It is known that a nickel is worth 5 cents, while a quarter is worth 25 cents. Therefore, the given statements can be written in the form of equations as,
Veronica has 4 more nickels than quarters,
x = y + 4
Coins have a combined value of 170 cents,
5x + 25y = 170
Substitute the value of x from the first equation in the second,
5x + 25y = 170
5(y + 4) + 25y = 170
5y + 20 + 25y = 170
30y = 170 - 20
30y = 150
y = 150/30
y = 5
Therefore, the number of quarters are 5.
Since, Veronica has 4 more nickels than quarters,
x = y + 4
x = 5 + 4
x = 9
Hence, the total number of nickels and quarters are 5 and 9, respectively.
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which point on the unit circle corresponds to −π? responses (1, 0) begin ordered pair 1 comma 0 end ordered pair (0, −1) begin ordered pair 0 comma negative 1 end ordered pair (0, 1) begin ordered pair 0 comma 1 end ordered pair (−1, 0) begin ordered pair negative 1 comma 0 end ordered pair
(-1 , 0) is the point that represents the point on the unit circle and corresponds to -π.
Option (D) is the correct one.
Given, a unit circle
and we have to mention the point on the unit circle that corresponds to -π.
As, the equation of a unit circle is
x² + y² = 1
now -π is represented by the left side of the x-axis
therefore to represent the given point we have to take a point on x-axis that will be at the left side of the origin and at the unit distance from the origin.
So, (-1 , 0) is the point that represents the point on the unit circle and corresponds to -π.
Hence, (-1 , 0) is the point that represents the point on the unit circle and corresponds to -π.
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Your question is incomplete kindly find the complete question below.
Which point on a unit circle corresponds to -π ?
(a) (1 , 0)
(a) (0 , -1)
(c) (0 , 1)
(d) (-1 , 0)
Answer:
(-1,0)
Step-by-step explanation:
I just took the quiz :)
you and a friend are riding your bikes to a restaurant that you think is east; your friend thinks the restaurant is north. you both leave from the same point, with you riding mph east and your friend riding mph north. after you have travelled mi, at what rate is the distance between you and your friend changing? after you have travelled mi, the distance between you and your friend is changing at a rate of mph.
The distance between you and your friend is changing at a rate of 20 miles per hour.
What is the Pythagorean theorem?
A right triangle's three sides are related in Euclidean geometry by the Pythagorean theorem, also known as Pythagoras' theorem. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
Here, we
Let the east direction is denoted by x and
the north direction is denoted by y.
dx / dt = 16 miles per hour
dy / dt = 12 miles per hour
x = 4 miles
Let the distance between both the friends be s.
Time is taken by you to travel 4 miles,
time = distance / speed = 4 / 12 = 1/4 hour
Distance traveled by your friend in time t,
y = speed x time = 12 x 1/4 = 3 miles
By Using the Pythagorean theorem,
x² + y² = s² ..... (1)
Substitute, x = 4 mile, y = 3 mile
s² = 16 + 9 = 25
s = 5 miles
Now, Differentiate equation (1) with respect to t, we get
2x dx/dt + 2y dy/dt = 2s ds/dt
4 (16) + 3 (12) = 5 ds/dt
ds/dt = 20 miles per hour
Hence, the distance between you and your friend is changing at a rate of 20 miles per hour.
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I need help, please answer this?
The Answer is A: 50
just remember that the line in the middle is half of the one on the outside of the triangle
What is the value of the expression below when x=3? i need help on evaluating expressions.
7x^2 -2x+2
The value of the expression 7x² - 2x + 2 when x = 3 is 59.
What is an expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.
Based on the information given, the expression is:
7x² - 2x + 2
Put x = 3
= 7x² - 2x + 2
= 7(3)² - (2 × 3) + 2
= 63 - 6 + 2
= 59
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How do you find the distance between these two integers? Complete the following statement that answers this question. Count the units between integer and zero. There is______ unit(s) between 0 and 1. There are______ unit(s) between 0 and 1. There are0 and -3. So, the sum of these two values is______ units.
Answer: (A) There is 1 unit between 0 and 1.
(B) There are 1 units between 0 and 1
(C) There are 0 and -3 so the sum of these two values is 3 units.
Step-by-step explanation:
How to find a distance between two integers? Easy!
First find the absolute value! Its gonna help a lot!
Please help! Lots of points and brainliest!
4 bracelets and 3 Necklaces are made by the Jeweler.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let us represent Bracelet as B and Necklace as N
B+N=7..(1)
7B+18N=82..(2)
From equation 1,
B=7-N
Now plug in B value in equation 2
7(7-N)+18N=82
49-7N+18N=82
49+11N=82
Subtract 49 on both sides
11N=33
N=3
Now we have to find B
B+N=7
B+3=7
Subtract 3 on both sides
B=4
Hence, 4 bracelets and 3 Necklaces are made by the Jeweler.
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write a function that computes a hask key for a string. the hash key is the average of the position of each letter in the alphabet divided by the size of the table. you can use the charposition() defined in the previous exercise in your calculation, this correct implementation was provided for you in this exercises.
a function that determines a string's hask key. The average position of each letter in the alphabet divided by the size of the table yields the hash key.
def char_position(char):
alphabet = list("abcdefghijklmnopqrstuvwxyz")
return alphabet.index(char)
def hash_key(string):
total = 0
for char in string.lower():
total += char_position(char)
return total / len(string)
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Suppose that a One-way ANOVA is being performed to compare the means of 4 populations and that the sample sizes are 14, 16, 19, and 13. Determine the degrees of freedom for the F-statistic. (a) the degree of freedom of the numerator (b) the degree of freedom of the denominator
The degrees of freedom for the F- statistic is:
(a) the degree of freedom of the numerator= 3
(b) the degree of freedom of the denominator= 58
What is Analysis of Variance (ANOVA)?
The statistical analysis tool known as analysis of variance (ANOVA) divides the observed aggregate variability present in a data set into two categories: systematic variables and random components. The random factors have no statistical impact on the presented data set, whereas the systematic factors do.
The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean".
If we assume that we have [tex]p[/tex] groups and on each group from [tex]j=1,...,p[/tex]we have [tex]n_{j}[/tex] individuals on each group we can define the following formulas of variation.
We know, we have this property
[tex]SST=SS_{between} +SS_{within}[/tex]
The degrees for the numerator are [tex]df_{num}=k-1=4-1=3[/tex], where k represents the number of groups (k = 4)
The degrees for the denominator are [tex]df_{den} =N-K=62-4=58[/tex], where N represent the total number of people (N = 14+16+19+13=62)
And the total degrees of freedom are given by:
[tex]df_{tot} =df_{num} +df_{den} =3+58=61[/tex]
Hence, degree of freedom of the numerator is 3 and the degree of freedom of the denominator is 58.
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Educational Technology, Inc. sells software to provide guided homework problems for a statistics course. They would like to know if students who use the software score better on exams. A sample of students who used the software had the following scores: 86, 78,66,83, 84, 81, 84, 109, 65, and 102. Students who did not use the soft-ware had the following scores:91, 71, 75,76, 87, 79, 73, 76,79, 78, 87, 90, 76, and 72. Assume the population standard deviations are not the same. At the .10 significance level, can we conclude that there is a difference in the mean scores for the two groups of students
a. What are the three assumptions for CASE C?
b. State the null and alternative hypothesis for this problem.
c. State the level of significance for this problem.
d. Which distribution (normal or t) should be used in this problem? Explain why.
e. Create a decision rule for this problem. Include the critical value. (USE TEXTBOOK TABLE.) Make sure it agrees with the excel printout.
f. Calculate the test statistic. (BY HAND). Make sure it agrees with the excel printout.
g. What is your conclusion? EXPLAIN IN DETAIL.
h. Estimate the p-value for this problem. Restate the conclusion. What is the actual p-value from the excel printout?
The assumptions are- Sample of students are independent and samples are simple random samples. Distribution is normal (t distribution). The independent variable measures on interval scale.
What is Statistics?The study and development of techniques for gathering, processing, interpreting, and presenting empirical data are within the purview of statistics, a branch of natural science. Research in stats has application in almost all scientific domains, and software concerns in the many science disciplines inspire the creation of new statistical methods and theories. Statistics is a very multidisciplinary field. Statisticians use a range of mathematical and computational techniques while creating new approaches and researching the concept that supports such methods.
Uncertainty and variation are two cornerstones of the statistical profession. In science, as well as more broadly in life, there are numerous circumstances where the result is unknown. Sometimes the uncertainty is caused by the fact that the result is still up in the air.
How to solve?
ts < tc Do not reject H0
P value > α Do not reject H0
There is insufficient data to determine that the mean scores of the two groups of pupils differ.
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The Seinfeld family pays $60 per month for electricity under balanced billing. At the end of the year, they had used less electricity than the balanced billing covered, and the utility company owed them a credit of $35.
What are their total electricity expenses for the year?
Answer:
685
Step-by-step explanation:
they would normally pay 720
but they got 35 credit
720-35 is 685
Let the random variable x represent the amount of money won or lost for a player who pays $1 to play a certain carnival game. The following table shows the probability distribution of x.
The best interpretation of the mean of X is in the long run, a player will lose an average of $0.15 per carnival game played.
What do you mean by Mean?
The average of the specified collection of numbers is what is referred to as mean. It indicates a data set's values are distributed equally.
Given:
Amount = $1 $1 $10
Probability = 0.80 0.15 0.05
In mathematics and statistics, the arithmetic mean is the sum of a set of integers divided by the total number of the numbers in the set. When the context is clear, it is also referred to as the mean or average. A set of experiments or survey findings are typically included in the collection.
Hence, the correct option is (A) In the long run, a player will lose an average of $0.15 per carnival game played.
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How do I find slope?
The graph of a line is shown on the grid. The
coordinates of both points indicated on the graph of the
line are integers.
What is the rate of change of y with respect to x for
this line?
Answer:
4/5
Step-by-step explanation:
The two points are (5, 7) and (-5, -1). The slope is the difference of y over the difference in x, or [tex](7--1)/(5--5)[/tex]. This simplifies to 8/10, or 4/5.
5x+4y-2x+3x+3y simplify
12. A clothing store has 621 blouses.
they place these on 9 racks. About the
same number of blouses were placed on
each rack. About how many blouses are
on each rack? (equation & sentence
Answer:
you have to divide
Step-by-step explanation:
621/9=69 so there are 69 blouses on each of the 9 racks
f a 90% confidence interval for the difference in the two population means contains zero, then the null hypothesis of zero difference between the two population means cannot be rejected at a 0.10 level of significance. true false
True , the null hypothesis of zero difference between the two population means cannot be rejected at a 0.10 level of significance.
Given :
f a 90% confidence interval for the difference in the two population means contains zero, then the null hypothesis of zero difference between the two population means cannot be rejected at a 0.10 level of significance.
at 10 % significance:
z score = 1.282
at 90 % confidence interval :
z score = 1.645
[tex]H_0 :[/tex] differences between population mean = 1.282
so true the null hypothesis of zero difference between the two population means cannot be rejected at a 0.10 level of significance.
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Grafica y aproxima el area bajo la curva de f(x)=x³+1 en el intervalo x€[0,2]
The total area bounded by curve f(x)=x³+1 between (0,2) will be 6 units.
What is Integration ?The summing of discrete data is indicated by the integration. To determine the given functions that will characterize the area, displacement, and volume that result from a combination of small data that cannot be measured separately and integrals are calculated. The concept of limit is employed broadly in calculus whenever algebra and geometry are applied.
Given Graph = x³+1
Area between interval x€[0,2]
To get the desired area we have to integrate between x€[0,2]
[tex]\int\limits^2_0 {(x^3 + 1)} \, dx[/tex]
∫x³dx + ∫1dx
[tex]\frac{x^4}{4}[/tex] + x + c
We can find the area by lower limit - upper limit
Putting x = 0
we get result as c
Putting x = 2
We get result as 6+c
So desired area will be ( 6+c ) - c = 6
Hence the total area bounded by curve between (0,2) will be 6 units.
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Sue wants to leave her grandson a nice inheritance. She has decided to deposit
$350.00 each month into an ordinary annuity that earns 4% compounded monthly.
How much will be in the account after 30 years rounded
The amount that would be in the account in 30 years will be $245,371.
How much will be in the account?An ordinary annuity is when a series of payment is made at the end of the period over a number of years.
The formula that can be used to determine the future value of an ordinary annuity is: monthly deposit x annuity factor
Annuity factor = {[(1+r)^n] - 1} / r
Where:
r= monthly interest rate = 4/12 = 1/3%n = number of periods = number of years x number of compounding : 30 x 12 = 360$350 x (1.0033)^360 - 1} / 0.0033 = $245,371
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What are the missing angle measures in parallelogram rstu? m∠r = 70°, m∠t = 110°, m∠u = 110° m∠r = 110°, m∠t = 110°, m∠u = 70° m∠r = 110°, m∠t = 70°, m∠u = 110° m∠r = 70°, m∠t = 110°, m∠u = 70°
∠R= 110°, ∠U= 70°, ∠T= 110° are the missing angle measures in parallelogram RSTU.
A parallelogram is a simple quadrilateral with two pairs of parallel sides in Euclidean geometry. A parallelogram's opposite or facing sides are of equal length, and its opposite angles are of equal measure.
Because RSTU is a parallelogram, we may use parallelogram characteristics to calculate S=U=70° ( Opposite angles of parallelogram are equal).
Using the property, sum of adjacent angles is equal to 180°, therefore,
⇒∠S+∠R= 180°
⇒70°+∠R= 180°
⇒∠R= 180°- 70°
⇒∠R=110°
Also, ∠R= ∠T= 110° (Opposite angles of parallelogram are equal).
Thus, ∠R=110°, ∠T= 110° and ∠U=70°
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It is more than 7+3
It is less than 8+5
Answer:
11 or 12 ....?
Step-by-step explanation:
This seems simple... so simple i feel like im overthinking it (x_x)