1) Alternate interior angles
2) Corresponding angles
3) Alternate exterior angles
4) Same-side interior angles
5) Vertical angles (angles opposite of each other)
A) What is the probability that a 13-card bridge hand contains i) All 13 hearts? ii) 13 cards of the same suit? iii) Seven spades and six clubs?
Using the hypergeometric distribution, the probabilities are given as follows:
a) All 13 hearts: [tex]1.57 \times 10^{-12}[/tex]
b) 13 cards of the same suit: [tex]6.30 \times 10^{-12}[/tex]
c) Seven spades and six clubs: [tex]5.4 \times 10^{-9}[/tex]
What is the hypergeometric distribution formula?The formula is:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
Parameter x is the number of successes.Parameter N is the size of the population.Parameter n is the size of the sample.Parameter k is the total number of desired outcomes.The general parameters in this problem are given as follows:
N = 52, as a standard deck has 52 cards.n = 13, as 13 cards will be chosen.In item i, there are 13 hearts in a standard deck, hence k = 13 and the probability is P(X = 13), hence:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 13) = h(13,52,13,13) = \frac{C_{13,13}C_{39,0}}{C_{52,13}} = 1.57 \times 10^{-12}[/tex]
For item ii, we consider the same context of item i, just now we can consider any of the four types of cards, hence:
[tex]p = 4 \times 1.57 \times 10^{-12} = 6.30 \times 10^{-12}[/tex]
For item iii, we want:
Seven spades from a set of 13.Six clubs from a set of 13.Hence the probability is given as follows:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 7) = h(7,52,13,13) = \frac{C_{13,7}C_{13,6}}{C_{52,13}} = 5.4 \times 10^{-9}[/tex]
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Need help with Stats homework, Picture has been uploaded of the question
Solution:
Given that a livestock company reports that the mean weight of a group of young steers is 1123 pounds with a standard deviation of 84 pounds, this implies that
[tex]\begin{gathered} \mu=1123 \\ \sigma=84 \\ \end{gathered}[/tex]A) Percentage of steers that weigh over 1300 pounds.
Step 1: Evaluate the z score value.
The z score value is expressed as
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ where \\ x\Rightarrow sample\text{ value} \\ \mu\Rightarrow mean\text{ value} \\ \sigma\Rightarrow standard\text{ deviation of the sample} \end{gathered}[/tex]In this case, x equals 1300.
Thus, the z score value is evaluated as
[tex]\begin{gathered} z=\frac{1300-1123}{84} \\ \Rightarrow z=2.107142857 \end{gathered}[/tex]Step 2: Evaluate the probability that the steer would weigh over 1300 pounds.
Using the normal distribution table, we have
thus,
[tex]\begin{gathered} Pr(z>1300)=0.0175525991947 \\ \end{gathered}[/tex]The percentage of young steers that weigh over 1300 pounds is thus evaluated as
[tex]\begin{gathered} 0.0175525991947\times100 \\ =1.7552991947\% \\ \approx1.8\%\text{ \lparen1 decimal place\rparen} \end{gathered}[/tex]B) Percentage of steers that have weights under 1050 pounds.
Step 1: Evaluate the z score value.
Thus, we have
[tex]\begin{gathered} z=\frac{1050-1123}{84} \\ =-0.869047619 \end{gathered}[/tex]Step 2: Evaluate the probability that the steer would have weights under 1050 pounds.
Using the normal distribution table, we have
thus,
[tex]Pr(z<1050)=0.192410542709[/tex]Thus, the percentage of young steers that would have weight under 1050 pounds is evaluated as
[tex]\begin{gathered} 0.192410542709\times100 \\ =19.2410542709\% \\ \approx19.2\%(\text{ 1 decimal place\rparen} \end{gathered}[/tex]C) Percentage of young steers that weigh between 1000 and 1200 pounds.
Step 1: Evaluate the z score value.
[tex]\begin{gathered} z_1=\frac{1000-1123}{84} \\ =-1.464285714 \\ z_2=\frac{1200-1123}{84} \\ =0.9166666667 \end{gathered}[/tex]Step 2: Evaluate the probability that the steer would weigh between 1000 and 1200 pounds.
Using the normal distribution table, we have
thus, we have
[tex]Pr(1000Thus, the percentage of young steers that weigh between 1000 and 1200 pounds is evaluated as[tex]\begin{gathered} 0.748783381404\times100 \\ =74.8783381404\% \\ \approx74.9\% \end{gathered}[/tex]If 343 is the third proportional of A and B, where a:b= 1:7 then the value of a+b will be
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9. Find an infinite set A such that a. A is finite and b. A is infinite. Use the real numbers R as the universal set.
Please show work.
An infinite set is infinite from start to end, but both sides can have continuity, unlike a finite set, which has both start and end elements. The finite() function in R Language is used to determine whether or not the elements of a vector are Finite values. It returns a Boolean value for each vector element.
What exactly is a finite number?A countable number less than infinity that is the cardinality of a finite set - that is, some natural number, possibly zero. A genuine number, such as the result of a measurement (of time, length, area, etc.)In other words, it is a set that can be finished counting. 1,3,5,7, for example, is a finite set with four elements. The finite set element is a natural number, i.e. a non-negative integer. A set is infinite if it has an infinite number of elements; finite if the elements can be counted.In R, there are two kinds of infinity. Inf and -Inf represent positive and negative infinity, respectively, whereas NaN stands for 'Not a Number.'Hence, The finite() function in R Language is used to determine whether or not the elements of a vector are Finite values.
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Simplify the expression:
a^-2
1/[tex]a^{2}[/tex] is the answer.
How to simplify the expression?Given,
a^-2
Solution:
a^-2
Expand it
a^-2 = 1/a^2
= 1/[tex]a^{2}[/tex]
Therefore,
a^-2 = 1/[tex]a^{2}[/tex]
1/[tex]a^{2}[/tex] is the answer.
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HELPPPPP
How can we guarantee that a polynomial is not a perfect square, considering just the constant term? For instance, in 4, the constant term is -121, in 2, the constant term is 36. Which of them cannot be a perfect square and why, based only on the constant term?
Answer:
Polynomials with a negative constant term are not perfect squares, hence polynomial 4, with constant term of -121, is not a perfect square.
What are perfect square expressions?
Perfect square expressions are formed in two ways, either with the square of the sum or the square of the subtraction, as follows:
Square of the sum: (a + b)² = a² + 2ab + b².
Square of the subtraction: (a - b)² = a² - 2ab + b².
The constant term is the final term. Since this term is squared, it will always be positive for perfect squares, hence if the constant term is negative, it will guarantee that the polynomial is not a perfect square.
For the expressions in this problem, we have that:
The expression with a constant term of 36 can be a perfect square, as 36 is a positive number.
The expression with a constant term of -121 cannot be a perfect square, as -121 is a negative number.
Hope this helps :)
Step-by-step explanation:
a final exam in math 160 has a mean of 73 with standard deviation 7.2. if 22 students are randomly selected, find the probability that the sample mean of their test scores is less than 75
The probability is that the mean of their test scores is less than 70.
What is probability?
A probability is a number that reflects tha chance of particular event will occur.
Sol-
As per the question given-
Mean = 73
Standard daviation=7.2
Number of students randomly selected =22
Let's take n number for experiment of outcomes.
The number of favorable outcomes can be denoted by x.
The formula to calculate the probability is -
probability = favorable
Outcomes/total outcomes =x/n
The number of standard daviation form the mean is called z.
Z = (x-¥)/€
Z=(75-73)(7.2/√22)
Z= -37.0582965
P(z<-37.05)
= 37.05
There for the probability is 37.05.
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the expression 2x squared minus -x squared is equivalent to
2x² - x²
Factor:
x²(2 - 1)
x²(1)
x²
--------------------------------------------
(3x² + x + 8) + (x² - 9)
Add like terms:
(3x² + x²) + x +(8 - 9)
4x² + x - 1
-----------------------------------------------
-3x² - 7x + 9 - 5x² + 6x - 4
Add like terms:
(-3x² - 5x²) + (-7x + 6x) + (9 - 4)
-8x² - x + 5
Jessica makes $24,000 a year, butreceives weekly paychecks. If 12% ofher check is withheld for federaltaxes, what is her required weeklydeduction, including FICA?
The weekly deduction, including FICA is a $60
Define percentage.
A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%"
Given,
Jessica makes in a year = $24000
She receives weekly pay checks is = 12%
We know, in 1 month there are 4 weeks and for 12 months there are 48 weeks.
so, Jessica makes per week = $24000 / 48
= $500
And, we know Jessica receives 12% paychecks then,
find, 12% of weekly payment
⇒12% of 500
⇒ (12 * 500) / 100
⇒$60
Hence, The weekly deduction, including FICA is a $60
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A metal sculpture has a total volume of 1250 cm³ and a mass of 9.2 kg.
Work out its density, in grams per cubic centimetre (g/cm³).
Give your answer to 2 d.p
Answer:
7.36 g/cm3
Step-by-step explanation:
Density = mass ÷ volume
Mass in grams = 9200g
Volume in cm3 = 1250cm3
9200 ÷ 7850 = 7.36
7.36 is already in 2 d.p.
Jacob and Diego are racing to see who can get his community service hours for scouting completed first. Jacob, who has already completed 50 hours, plans to volunteer for 5 hours per week going forward. Diego hasn't started yet, but plans to dedicate 6 hours per week to his volunteer project from now on. Before too long, the boys will be tied, with the same number of volunteer hours. How long will that take?
Number of weeks required before Jacob and Diego will be tied in the race to complete community service hours for scouting is equal to 50 weeks.
As given in the question,
Let number of weeks be represented by a variable x.
Jacob plans to devote 5 hours per week from now onwards. Hence his volunteer hours will cumulate to 5x+50 as he has already completed 50 weeks.
Diego plans to devote 6 hours per week from now onwards. Hence his volunteer hours will cumulate to 6x.
For Jacob and Diego to tie in the race, their volunteer hours should be equal. Translating this into a linear algebraic equation,
6x = 5x+50
=> 6x-5x = 50
=> x = 50
Therefore, number of weeks required before Jacob and Diego will be tied in the race to complete community service hours for scouting is equal to 50 weeks.
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4. Solve the quadratic equation x² = 16.
[tex]x^2=16\\\sqrt{x^2}=\sqrt{16}\\x=\lm+/-4[/tex]
x = 4, x = -4
How would I answer and what would be the answer?
Given the exression:
[tex]\frac{x-1}{x+4}-\frac{4x-11}{x+4}[/tex]Let's solve the expression and identify the error.
Since both expressions have the same denominator, let's combine the numerators:
[tex]\frac{(x-1)-(4x-11)}{x+4}[/tex]Apply distributive property:
[tex]\begin{gathered} \frac{x-1-4x-(-11)}{x+4} \\ \\ \frac{x-1-4x+11}{x+4} \end{gathered}[/tex]Combine like terms in the numerator:
[tex]\begin{gathered} \frac{x-4x-1+11}{x+4} \\ \\ \frac{-3x+10}{x+4} \end{gathered}[/tex]The error in the problem was that distributive property was not applied when the numerators were combined.
ANSWER:
[tex]\frac{-3x+10}{x+4}[/tex]A theater group made appearances in two cities. The hotel charge before tax in the second city was $500 higher than in the first. The tax in the first city was 6.5% and the tax in the second city was 6% The total hotel tax paid for the two cities was $748.75. How much was the hotel charge in each city before tax?
Based on the taxes in the first city and the tax in the second city as well as the total hotel tax paid in the two cities, the hotel charge for each city before taxes was:
First city - $5,750Second city - $6,250How to find the hotel charge?The hotel charge before taxes was $500 higher in the second city than in the first. Assuming the charge in the first city was x, the charge in the second city was:
= x + 500
The total charge in the first city would be:
0.065x + 0.06(x + 500) = 748.75
0.065x + 0.06x + 30 = 748.75
0.125x + 30 = 748.75
0.125x = 748.75 - 30
0.125x = 718.75
x = 718.75/0.125
x = $5,750
The total charge in the second city would be:
= 5,750 + 500
= $6,250
In conclusion, the charges in the first and second cities are $5,750 in the first city and $6,250 in the second city.
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Can you solve this please.
The simplified expression of (x¹² ÷ x⁴). x³ is x¹¹
How to solve expression?The expression can be solved as follows:
(x¹² ÷ x⁴). x³
The law of indices can be used to solve the expression.
Therefore,
[tex]\frac{x^{a} }{x^{b} } = x^{a - b}[/tex] and [tex](x^{a} )^{b} = x^{ab}[/tex] and [tex]x^{a} .x^{b} = x^{a+b}[/tex]
Hence,
(x¹² ÷ x⁴) = x¹² / x⁴ = x¹²⁻⁴ = x⁸
Therefore,
(x⁸). x³ = x⁸⁺³
Finally,
x⁸⁺³ = x¹¹
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Round to the place value of the underlined digit 698, 07 to the underline number is six
The place value of the underlined digit (6) is tens of thousands and should be rounded to 70,000.
What is a place value?A place value simply refers to a numerical value (number) which denotes a digit based on its position in a given number and it includes the following:
TenthsHundredthsThousandthsUnitTensHundredsThousands.Tens of thousands.Hundred of thousandsIn this scenario, the place value of the underlined digit (6) is tens of thousands and 9 is the next digit to six (6). Therefore, we would add one (1) to the underlined digit (6) and then change all of the other digits to zero (0) as follows:
69,807 = 70,000
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Which of the following is LEAST associated with human capital?
a)medical treatment that reduces time off of work due to illness or injury.
b)maintenance of fully automated production facilities
c)a college course in accounting
d)an on-the-job training course in the latest production methods.
Answer:
Hope it helps you
Step-by-step explanation:
(a) medical treatment that reduces time off of work due to illness or injury.
Pedro has scores of 81, 80, 82, 88 after four tests. What score must he make on his fifth test to have an average of 76 or greater?
Answer:
he must make sure he gets up to 49 and higher to obtain an average of 76 or greater
Step-by-step explanation:
logically from 49 - 100 :)
Newton had 15 baseball cards. Today he bought 3 packs of baseball cards. Now he has a total of 45 baseball cards. Write and solve an equation to determine how many baseball cards were in each pack
Answer:
15 I did 15+15+15 or 15x3 and it equals 45
Step-by-step explanation:
Brainliest?
15
Divide 45 by 3 because newton has 15 base ball cards and each card has fifteen card in each pack
find slope of the line that passes through each pair of points 4,3 -1,6
Answer:
Formula for slope is given as (y2-y1) ÷ (x2-x1) or (y1-y2) ÷ (x1-x2), where x and y are the coordinates of the points.
Slope = (6 - 3)÷(- 1 - 4)
= -3/5
Find the measure of <1, <2, and <3.
The measure of the angles for the given parallel lines are-
∠1 = 100°∠2 = 80°∠3 = 100°What is defined as the term linear pair?Once two lines intersect at a single point, a linear pair of angles is formed. If the angles are adjacent to one another after the two lines intersect, they are referred to as linear. The sum of the angles of a linear pair always is 180°. These angles are also referred to as supplementary angles. The adjacent angles include those that share a vertex. As a result, the linear angles get a common vertex here as well.For the given question;
The set of parallel lines are given;
Thus,
∠1 + 80 = 180 (linear pair)
∠1 = 100°
Now, two set of parallel line form a parallelogram.
Thus, in parallelogram opposite angles are equal.
∠1 = °∠3 = 100°
So, ∠3 = 100°
And, ∠2 = 80° (opposite angle of 80)
Thus, the measure of the angles are calculated.
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According to a 2017 survey conducted by the technology market research firm The Radicati Group, U.S. office workers receive an average of 121 e-mails per day (Entrepreneur magazine website). Assume the number of e-mails received per hour follows a Poisson distribution and that the average number of e-mails received per hour is five.
a) Probability of receiving no e-mails during an hour = 0.0067
b) Probability of receiving at least three e-mails during an hour = 0.8754
c) Expected number of e-mails received during 15 minutes = 1.25
d) Probability that no e-mails are received during 15 minutes = 0.2865
Given that five emails are typically received every hour. If X represents the number of emails received in an hour, then X is poisoned with the given parameter, λ = 5.
⇒ P (X = x) = [tex]\frac{e^{ -x} X^{x}}{x!} = \frac{e^{-5} 5^{x}}{x!}[/tex]
(a) Likelihood of not receiving any emails for an hour = p (x = 0)
= (e⁻⁵5⁰) / 0! = (e⁻⁵ * 1) / 1 = e⁻⁵ = 0.00674 ≈ 0.0067
(b) Likelihood of receiving three or more emails in a single hour P(x ≥ 3)
= 1 - [P (x < 3) = 1 - [P(x = 0) + P(x = 1) + P(x = 2)]
= 1 - [(e⁻⁵5⁰) / 0! + (e⁻⁵5¹) / 1! + (e⁻⁵5²) / 2!]
= 1 - [0.00674 + 0.03369 + 0.08422]
= 1 - 0.12465
= 0.87535 ≈ 0.8754
(c) The number of emails that should be received in the next 60 minutes = an hour's worth of emails on average = 5
As a result, the anticipated quantity of emails received in 15 minutes = 5 / 4 = 1.25
(d) Number of emails received on average every 15 minutes = Number of emails that should be received in the next 15 minutes = 1.25
Let X represent how many emails were received in 15 minutes. X then proceeds with a parameterized Poisson distribution, λ = 1.25
⇒ P (x = X) = [tex]\frac{e^{-x} X^{x} }{x!} = \frac{e^{-1.25}1.25^{x} }{x!}[/tex]
The likelihood that no emails will be received during the next 15 minutes = [tex]\frac{e^{-1.25}* (1.25)^{0} }{0!} = \frac{e^{-1.25}*1 }{1} = e^{-1.25} = 0.2865[/tex]
COMPLETE QUESTION: According to a 2017 survey conducted by the technology market research firm The Radicati Group, U.S. office workers receive an average of 121 e-mails per day (Entrepreneur magazine website). Assume the number of e-mails received per hour follows a Poisson distribution and that the average number of e-mails received per hour is five.
a. What is the probability of receiving no e-mails during an hour (to 4 decimals)?
b. What is the probability of receiving at least three e-mails during an hour (to 4 decimals)? For this question, if calculating the probability manually make sure to carry at least 4 decimal digits in your calculations.
c. What is the expected number of e-mails received during 15 minutes (to 2 decimals)?
d. What is the probability that no e-mails are received during 15 minutes (to 4 decimals)?
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if a population has a mean of 30, if 3 points are added to each score how do you calculate the mean for the new distribution
When the population has a mean of 30, if 3 points are added to each score, the mean for the new distribution is 33.
How to illustrate the information?It should be noted that mean simply means the average of a given set of numbers that are given. The entire group about whom you want to make conclusions is referred to as a population. The particular group from which you will gather data is known as a sample. The sample size is always smaller than the population as a whole. A population in research doesn't usually refer to humans.
In this case, the population has a mean of 30 a and 3 points are added to each score.
In this case, the new mean will be the addition of the numbers. This will be illustrated as:
= 30 + 3
= 33
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Y=x when x increases by 5 what does y increase by
pleaseee helpp meeee
Given:
The given expression is,
[tex]25^x[/tex]Required:
To select the equivalent expression.
Explanation:
Annalise buys a pair of sunglasses for 30% off and saves $15. What is the original price of the pair of sunglasses?
*
Answer:
$50
Step-by-step explanation:
We will call x the original price of the sunglasses.
We can create the equation below using the information given.
[tex]x*\frac{30}{100} =15[/tex]
Now solve for x.
[tex]x = 15*\frac{100}{30}[/tex]
[tex]x = \frac{100}{2}[/tex]
[tex]x=50[/tex]
6 plus 8 divided by 2
Using the PEMDAS ( In order to know the order of the operations)
P = Parentheses
E = Exponents
M = Multiplication
D = Division
A = Addition
S = Subtraction
Accordint to this, we need to divide first, and then we need to add the resultant number, so:
[tex]\begin{gathered} 6+8\div2=6+4=10 \\ \\ \end{gathered}[/tex]Answer:
10
What’s the slope of this line?
X
6
9
15
21
у
-5
-7
-11
-15
Slope is [tex]\frac{-2}{3}[/tex] of coordinates (6,5) and (9,-7).
What is slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. [1] The letter m is frequently used to represent slope; however, there is no obvious reason for this. The slope of a curve at a point in differential calculus is defined as the slope of the tangent line at that point as a generalization of this practical definition. The slope can be determined between any two locations when the curve is represented by a series of points in a diagram or list of point coordinates. Maybe when the curve is represented as a continuous function.
Given Data
coordinates - (6,-5) and (9,-7)
slope of the line denoted as m
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
m = [tex]\frac{-7-(-5)}{9-6}[/tex]
m = [tex]\frac{-2}{3}[/tex]
Slope is [tex]\frac{-2}{3}[/tex]
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