The answer is yes, events A and B are independent to each other when A random card is chosen from a 52-card standard deck.
Given that,
We have to identify the independence of the events a and b. A random card is chosen from a 52-card standard deck. Then it is changed, and a second card is chosen at random. event a: The initial draw selects a club event b: The second draw yields an ace.
We know that,
Here a card is selected randomly from the deck of 52 cards. Then this card is replaced, that means the deck has again 52 cards. Now, Second card is then selected randomly from the deck.
Here as we are replacing the first drawn card that means probability of drawing first card doesn't affect the probability of drawing second card. So here the given events A and B are independent.
P(A and B) = P(A) P(B)
Therefore, The answer is yes, events A and B are independent to each other when A random card is chosen from a 52-card standard deck.
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The function g(x) is graphed below. According to the graph, what is the
value of g(4)?
Answer:
6
Step-by-step explanation:
g(4) tells us that we need to look for the y coordinate when g(x) reaches 4 on the x axis.
6 is the answer
What number is 0.1 less than 15.2?
Answer:
15.1
Step-by-step explanation:
Indicate whether a binomial distribution is a reasonable probability model for the random variable X. give your reasons in each case.
joey buys a virginia lottery ticket every week. x is the number of times in a year that he wins a prize.
The given statement is a reasonable probability model because it fulfills the 4 conditions of binomial distribution.
How to identify binomial distribution model?The conditions for binomial distribution are;
1: The number of observations n must be fixed.
2: Each observation must be independent.
3: Each observation must represent one of two outcomes ("success" or "failure").
4: The probability of "success" p must be the same for each outcome.
Now, we are given the statement;
Joey buys a Virginia lottery ticket every week. x is the number of times in a year that he wins a prize.
From that statement, we can tell that the number of observations is fixed at 52 weeks since a year is made up of 52 weeks.
Secondly, we can say that there could be success by winning a price or failure by not winning the price.
Each weekly observation is independent.
The probability is the same for each outcome.
Thus, we conclude that since it fulfills all the four conditions then it is a binomial model.
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collect at least 50 observations from a data source of your choice. the observations you collect may be discrete data or continuous data but cannot be categorical in nature. you can generate or collect the observations yourselves, but you may not use mass emailing to the class to do so. you can obtain the data from internet sites, but you must include where you collected the data from as a reference
The discrete data can be number of legs, number of teeth.
The continuous data can be the length of tail, and the height of dog.
Consider the provided information.
The discrete data is a data whose value is obtained by counting and they can be described by an integer value.
So, the discrete data can be number of legs, number of teeth.
A continuous data is a variable whose value is obtained by measuring.
The continuous data can be the length of tail, and the height of dog.
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Frosty the Snowman thought he could last in a greenhouse for 2 hours before melting. Unfortunately, it only took him 1 12
hours to melt.
Percent error is a way to describe error, expressed as a percentage of the actual amount. What is the percentage error in this situation?
The percentage error in this situation will be 33%.
How to calculate the percentage?It's important to note that Percent error is a way to describe error, expressed as a percentage of the actual amount.
Since Frosty the Snowman thought he could last in a greenhouse for 2 hours before melting but it only took him 1 1/2 hours to melt. The percentage error in this situation will be:
= (2 - 1 1/2) / 1 1/2 × 100
= 1/2 ÷ 1 1/2 × 100
= 1/3 × 100
= 33.33%
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Please Help
Have a close look at the diagram below. What is the probability of selecting the following marbles in order: red - blue - blue - blue ? Show your work and explain your thinking.
The probability of selecting the following marbles in order: red - blue - blue - blue will be 3 / 40.
How to calculate the probability?Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1. In this case, 0 denotes the impossibility of the event and 1 represents certainty.
From the diagram Illustrated, it should be noted that that there are 2 blue balls and 3 red balls. The total number of balls will be 5.
The probability of selecting the following marbles in order: red - blue - blue - blue will be:
= 3/5 × 2/4 × 1/4 × 0/3
= 6 / 80
= 3 / 40
The probability is 3 / 40.
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The given point is reflected across the line indicated. Find the coordinates of the image.
R across y = -2
If the given point R is reflected across the line y = -2, the image is
(Type an ordered pair.)
Researchers in the Hopkins Forest (see Problem 7-16 from) also count the number of maple trees (genus
acer) in plots throughout the forest. The following is a histogram of the number of live maples in 1002 plots
sampled over the past 20 years. The average number of maples per plot was 19.86 trees with a standard
deviation of 23.65 trees.
a). If we took the mean of a sample of eight plots, what would be the standard error of the
mean?
b). Using the central limit theorem, what is the probability that the mean of the eight would be
within 1 standard error of the mean?
c). Why might you think that the probability that you calculated in (b) might not be very
accurate?
Read the following prompt and type your response in the space provided.
Kim's teacher has marked this problem as one to recheck, but Kim cannot determine what she has done incorrectly. Identify Kim's error and write a correct solution.
Six less than 2 times a number is 50. What is the number?
2x – 6 = 50 (line 1)
2x – 6 – 6 = 50 – 6 (line 2)
2x = 44 (line 3)
2x ÷ 2 = 44 ÷ 2 (line 4)
x = 22 (line 5)
A random sample of n measurements was selected from a population with unknown mean and standard deviation o = 20 for each of the situations in parts a through d. Calculate a 95% confidence interval for ju for each of these situations. a. n=70, X = 27 b. n = 150, x= 115 c. n= 80. x = 18 d. n = 80, x=5.33
The 95% confidence interval for this situation is (0.95, 9.71).
What is the Standard deviation?
The standard deviation of a random variable, sample, statistical population, data set, or probability distribution is the square root of its variance.
The formula for Confidence Interval for Population Mean When Population Standard deviation is known
[tex]\bar{x} \pm Z_{a/2} * \frac{\sigma}{\sqrt{n} }[/tex]
α for 95% confidence level = (100-95)/100 =0.05
[tex]Z_{\alpha/2}[/tex] = 0.05/2=0.025
[tex]Z_{\alpha/2}[/tex] = Z0.025 = 1.96
σ = 20
95% Confidence Interval for Population Mean When Population Standard deviation is known
[tex]\bar{x} \pm 1.96* \frac{20}{\sqrt{n} }[/tex]
a.
n=70 ; [tex]\overline{x}=27[/tex]
[tex]\bar{x} \pm 1.96* \frac{20}{\sqrt{n} }[/tex]
27 ± 1.96 × (20/√70)
= 27 + 1.96 x 2.3905
= 27 + 4.6853 = (22.31.31.69)
(22.31, 31.69)
b.
n=150 ; [tex]\overline{x}=115[/tex]
[tex]\bar{x} \pm 1.96* \frac{20}{\sqrt{n} }[/tex]
= 115 + 1.96 x
= 115 +1.96 x 1.633 = 115 + 3.2007 = (111.8, 118.2)
(111.8, 118.2)
c.
n=80 , [tex]\overline{x}=18[/tex]
[tex]\bar{x} \pm 1.96* \frac{20}{\sqrt{n} }[/tex]
= 18 + 1.96 x 2.2361 = 18 + 4.3827 = (13.62.22.38) V8018+
(13.62, 22.38)
d.
n=80, [tex]\overline{x}=5.33[/tex]
[tex]\bar{x} \pm 1.96* \frac{20}{\sqrt{n} }[/tex]
= 5.33 1.96 x 2.2361 = 5.33 4.3827 = (0.95, 9.71)
(0.95, 9.71)
e.
No. Since Sample sizes are large [tex](n\small \geq30)[/tex] and randomly selected from the target population, the condition guarantees that the sampling distribution of [tex]\overline{x}[/tex] is approximately normal.
Hence, the 95% confidence interval for this situation is (0.95, 9.71).
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Write the
slope-intercept form of the equation of
the line that passes through the point (1, 2) and
has the slope of 6.
Calculate the difference and enter below. 3-9
Answer: -6
Step-by-step explanation: Since 9 is being subtracted from 3, we know that it will be a negative number. So, 9-3 = 6, and a greater number subtracted from a smaller number is a negative number. So, that results in this being -6. I hoped this helped.
[tex]3-9[/tex]
[tex]3+(-9)[/tex]
[tex]=\fbox{-6}[/tex]
[tex]3+(-9)[/tex] on a number line:
when max and evie were counting their items of candy after trik or treating. the total humber of items was at least 90 and at most 115. If Evie had 42 items of candy, which of the following inequalities represents all possible number of items, m, that Max could have had?
Answer:
48 ≤ m ≤ 73
Step-by-step explanation:
Evie has 42, Max has x.
Total candy = x + 42
90 ≤ x+42 ≤ 115
48 ≤ m ≤ 73
Max can have 48 or more, but no more than 73
A linear relationship is given in the table below. Determine the slope of the relationship.
-1 / -3/ 2/3/4/7/8/15/10/19
The slope of the linear relationship will be 2.
What is Equation of line?The equation of line passing through the points (x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
A linear relationship is given in the table.
Now,
Let two point on the table are (- 1, - 3) and (2, 3).
So, We need to find the slope of the line.
Hence, Slope of the line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (3 - (-3)) / (2 - (-1))
m = 6 / 3
m = 2
Thus, The slope of the linear relationship = 2.
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Test of Independence 6. Are the factors that contribute to a person's wellbeing, (ie: Friendship and social life, job or primary activity, and health and physical condition), Independent of a person's marital status. See the chart. Marital married Widowed/divorced totals 42 132 49 Factors contribution to a 50 33 110 person's wellbeing. 21 25 58 100 300 a. a. b. b. C. C. d. d. e. e. status single Friendship 41 and social life Job or 27 primary activity Health and physical condition totals 80 120 State the null and alternative hypothesis State the observed values State the expected values Give the p-value Give a conclusion for the hypothesis test. 12
The conclusion of the hypothesis test is 0.342112
What is meant by hypothesis?
In statistics, hypothesis means an assumption, an idea that is proposed for the sake of argument so that it can be tested to see if it might be true.
Here we have given that the factors that contribute to a person's wellbeing, That is Friendship and social life, job or primary activity, and health and physical condition), Independent of a person's marital status.
And we need to find the null and alternative hypothesis and the conclusion of the hypothesis test.
As per the given table of data we have to calculated the p value in order to find the null and alternative hypothesis,
For that we gathered the value of the following,
Number of samples = 9
Then the mean value of data = 83.63
And the standard deviation of the data = 80.475
Then the p - value is calculated as,
p-value ≈ 0.342112
This decision is made at significance level α = 0.05.
Therefore, the result is not statistically significant: there is not enough evidence to reject the null hypothesis.
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The least expensive
buttons cost
$0.28 each. Yellow bought all of
the buttons she could for $1.40 and
wore them proudly.
The number of buttons that she can wear proudly will be 5.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another.
As per the given,
Cost of one button = $0.28
The cost of buttons that she can wear = $1.40
A number of buttons = $1.40/$0.28 = 5
Hence "She will be able to wear five buttons with pride.".
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An evergreen nursery usually sells certain shrub after 6 years of growth and shaping: The growth rate during those 6 years is approximated by dh/dt = 1.2t + 2, where t is the time in years and h is the height in centimeters. The seedlings are 15 centimeters tall when planted (t = 0). (a) Find the height after years h(t) (b) How tall are the shrubs when they are sold? cm
(a) After t years, the height is 18t² + 3t + 10
(b) The shrubs are847 cm tall when they are sold.
Given growth rate
dh/dt = 1.8t + 3
dh = (18t + 3)dt
Integrating this, we have
h = 18t² + 3t + C
When t = 0, h = 10cm
Then
10 = C
So
(a) h = 18t² + 3t + 10
(b) Because they are sold after every 9 years, then at t = 9
h = 18(9)² + 3(9) + 10
= 810 + 27 + 10
= 847 cm
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Simplify (-3x^4) (-4x^2)
Step-by-step explanation:
(-3x⁴)(-4x²)
as multiplication is commutative (that means the sequence of the factors is irrelevant), we get
-3×-4×x⁴×x²
we can combine everything of the same type (constants or variable names).
-3×-4 = 12
remember, -×- = +
x⁴×x² = x⁶
remember, when multiplying terms with the same base variable, we can simply add the exponents.
why ? because an exponent is a short way of saying that the base variable has to be multiplied by itself that many times.
e.g.
a³ = a×a×a
a⁷ = a×a×a×a×a×a×a
a³×a⁷ = a×a×a × a×a×a×a×a×a×a = a¹⁰
that's why.
so, the complete simplified expression is
12x⁶
Here are the shopping times (in minutes) for each of fifteen shoppers at a local grocery store. Shopping times (in minutes) 29 35 27 26 24 20 37 34 24 33 24 36 32 18 31 (b) Construct a histogram for the data. (a) Complete the grouped frequency distribution for the data. (Note that the class width is 5.) Frequency Shopping times (in minutes) Frequency 18 to 22 23 to 27 OOOO 28 to 32 33 to 37 18 to 22 23 to 27 28 to 32 Shopping times in minutes) 33 to 37 X 5 ? xo?
Frequency is the number of occurrences of a repeating event.
What do you mean by frequency?The frequency of an occurrence or a value is the number of times it happens. A frequency table is a list of objects with the frequency of each item shown in the table.
The information that is gathered is called data. The quantity of occurrences of an event or value is referred to as its frequency. A frequency table is a table that lists items and displays how frequently each item happens.
The number of times a specific data value occurs is the frequency of that data. We use f to symbolise the frequency of a data value.
As an illustration, the grade A is said to occur frequently if five students received an A in science.
Here we have the events:
shopping time between occurrences frequency
18 to 22: 20, 18 2
23 to 27: 27, 24, 26, 24, 24 5
28 to 32 29, 31 2
33 to 37 37, 34, 35, 33, 36, 32 6
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(100 points plus brainliest) A proportional relationship between the number of pounds of potatoes (x) and the price in dollars (y) is graphed, and the ordered pair (4, 3) is on the graphed line
what is the price of 1 pound of potatoes? SHOW YOUR WORK
Answer: $0.75
Step-by-step explanation:
-We know that the line must also contain the point (0,0), as 0 pounds of potatoes would cost $0. Thus we can find the slope of the line and write an equation:
slope = Δy/Δx = (3-0)/(4-0) = 3/4
y = (3/4)x
(The y-int (aka b) is 0 since the line passes through (0,0))
Plugging in 1 yields $0.75
Answer:
$0.75 per pound-------------------------------------------------------
Proportional relationship equation:
y = kx, where k-constant of proportionalityGiven point (4, 3).
Use its coordinates to find the value of k:
3 = 4kk = 3/4k = 0.75This is representing the price of 1 pound of potatoes.
Brainly please don't delete my question it's not even breaking your guideline I even checked I just need my questions answered!
Answer:
Hey
you are correct
18x – 40
Step-by-step explanation:
2( x + 4 (2x – 5) )
= 2( x + 8x – 20)
= 2x + 16x – 40
= 18x – 40
Dont forget to rate the answer as brainliest
Have a good day
Answer: 18x-40
Step-by-step explanation: First, you have to isolate the 2, so now it would look like this:
=(2)(x+4(2x−5))
Now, You have to isolate the x, along with the 2 again, so it would look like this:
=(2)(x)+(2)(4(2x−5))
Now, you would combine the like terms of 2x & x, and all the numbers that don't have a variable, so it would look like this:
2x+16x−40
Now, finally, we can combine 2x + 16x, because they are like terms, so that is how we get 18x - 40
I hoped this helped friend!
-Shining Dream
A local university offers a review course for those who are planning to take the GRE exam. Thirty
percent of the people who took the exam had attended the university's GRE review course. The results
of the test showed that 60% of those who attended the review passed the exam, while among those who
did not attend the course, only 20% passed the exam. An individual has passed the exam. Knowing this,
what is the probability that he attended the review course?
The probability that an individual attended the course given he passed
is 37.5%.
What is conditional probability?Conditional probability is a term used in probability theory to describe the likelihood that one event will follow another given the occurrence of another event.
We know the probability of A given B is P(A/B) = P(A∩B)/P(B).
Let, The number of students be 100.
Given, Thirty percent of the people who took the exam had attended the university's GRE review course which is 30 and hence 70 people did not attend the review course.
60% of those who attended the review passed the exam,
= (60/100)×30.
= 18 people.
20% who passed the exam did not attend the review course.
= (20/100)×70.
= 14.
So, The no. of people who passed is (18 + 14)/100 = 32/100 = 0.32.
The probability that a student passed and taken the course is (18/30)×(14/70) = 0.12.
Therefore, Given that he passed, the likelihood that someone took the course is = (0.12/0.32) = 0.375 Or 37.5%.
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Please help will mark Brainly
Answer:
Below
Step-by-step explanation:
The solution set is the point(s) where the two plotted graphs intersect:
Krystal is considering job offers from two companies. Company A offered her a starting salary of $45,000 with a $2100 raise at the end of each year. Company B offered her a starting salary of $45,000 with a 4.2% raise at the end of each year. Let f(t) represent Carissa's salary at Company At years after accepting a position at Company A, and let g(t) represent Carissa's salary at Company B t years after accepting a position at Company B. a. Find a function formula for f. b. Find a function formula for g. c. If Carissa was expecting to work for 5 years before going back to school, which company do you think she should work for? Use your functions to justify your answer. I d. If Carissa was expecting to work for 10 years before going back to school, which company do you think she should work for? Use your functions to justify your answer.
The function formula for f and g are f(t) = $45000+$2100t and g(t) = $45000(1+0.042) to the power of t when Krystal is weighing two job offers from various organizations.
Given that,
Krystal is weighing two job offers from various organizations. She received a $45,000 beginning salary from Company A, with annual raises of $2100. Company B gave her a $45,000 beginning salary with an annual rise of 4.2%. Let f(t) stand for Carissa's pay at the company. Let g(t) stand in for Carissa's pay at Company B at Years after Accepting a Position at Company B, and at Years after Accepting a Position at Company A.
We have to find the function formula for f and g.
We know that,
Company A has
f(t) = $45000+$2100t
And
Company B has
g(t) = $45000(1+0.042) to the power of t.
Therefore, The function formula for f and g are f(t) = $45000+$2100t and g(t) = $45000(1+0.042) to the power of t when Krystal is weighing two job offers from various organizations.
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Hey WRLD... 999
Match each polynomial with its factorization. Type the number of the corresponding polynomial on the line of it’s factorization on the right.
1.
x2 – 2x – 48
_____ (x + 2)(9 – x)
2.
-3x2 + 14x - 8
____ (2 – 3x)(x – 4)
3.
X2 – 10x – 25
_____ (x + 6) (x – 8)
4.
-x2+7x+18
____ 3(x – 7) (x + 7)
5.
X4 – 16
_____ (x – 5)2
6.
3x2 – 147
_____ ( x – 2)( x + 2)( x2 + 4)
Each equation is expressed and mentioned in its factorized form are given above.
What is a mathematical function, equation and expression?function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given are the polynomials along with their factorized forms.
The polynomials along with their correct factorized forms are as follows -
x² - 2x - 48 → (x + 6) (x – 8)-3x² + 14x - 8 → (2 – 3x)(x – 4)x² – 10x + 25 → (x - 5)²- x² + 7x + 18 → (x + 2)(9 – x)x⁴ - 16 → (x – 2)(x + 2)(x² + 4)3x² – 147 → 3(x – 7) (x + 7)Therefore, each equation is expressed and mentioned in its factorized form are given above.
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elementary surveying two ridges b and c forms a valley having a at the bottom part in between the ridges. elevation difference between b nad c is 111..356 m. observing at point a, the angle of elevation is
the difference of elevation between a and b.Let AB = x, tan 36 = x/111.356 ,x = 111.356 tan 36= 64.39 m and Difference in elevation = 64.39m
We are given that two ridges B and C form a valley with a point A at the bottom part with an elevation difference of 111.356m between the ridges and and angle of elevation of 36 degrees at point A. To find the difference of elevation between A and B, we use the formula of tangent which is tan θ = Opposite/Adjacent. We substitute the values and solve for x, which is the elevation difference between A and B. So the difference in elevation between A and B is 64.39m.
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Claim: all natural numbers are either even or odd. Proof: By induction. Base case:0 is even, since 0 = 2.0. Now suppose that n - 1 is either even or odd, and we must show that n is either even or odd. Case 1: If n - 1 is even, then n - 1 = 2k for some k, so n = 2k + 1, showing n must be odd. Case 2: If n - 1 is odd, thenn - 1 = 2k +1 for some k, so n = 2k + 2 = 2(k+1), showing n must be even. Is this proof correct?
• Yes • No
No. The proof is wrong.
Here we are asked to prove all Natural numbers are either even or odd.
Natural numbers start from 1 to infinity.
Hence to prove by mathematical induction, we need to take the base case to be n = 1.
here, 1 = 2X0 + 1, therefore 1 is odd
Then we need to assume that for any integer m < n, m is either even or odd.
Now n > 1
Therefore,
n -1 > 0
Hence n - 1 will be a natural number.
Hence by our earlier assumption where any number smaller than is either even or odd
n - 1 has to be either even or odd.
case 1
here n - 1 is odd
if n - 1 is odd then
n-1 + 1 is a sum of two odd numbers, hence n is even
Case 2- If n - 1 is even
then, n-1 + 1 is a sum of an even and n odd number hence n is odd
Therefore n will either be even or odd.
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sylvia went on a trip. The number of shirts she packed was 2 fewer than twice the number of pants she packed. The total number of pairs of pants and shirts was 16
Answer:
She packed 6 pairs of pants and 10 shirts.
Step-by-step explanation:
Say the number of pants is x. Then, the number of pants is 2x-2. Now you have the equation:
x+ (2x-2)=16
Solving this equation gives x=6.
Therefore, she packed 6 pairs of pants and 10 shirts.
give an example of a continuous map with x and y connect that is one to one and honto but is not a homemorphism g
Let X be the integers with the topology created by declaring a set to be open if either it is a subset of N or it is the entire set Z. Then, we define a map f: X --> X such that f(x) = x- 1 is an example of continuous map is one to one and honto but is not a homemorphism .
What is a bijective function?A function f: A --> B is said to be bijective or bijection if it satisfies both injective (one-to-one function) and surjective (over-function) properties. Let X be the integers with the topology created by declaring a set to be open if either it is a subset of N or it is the entire set Z. Then, we define a map
f : X--> X such that f(x) = x- 1 ; x∈X (domain)
Now, we show that it is bijective, so
One to One : let x₁ and x₂ belongs to X such that f(x₁) = f(x₂) we have to show x₁= x₂
f(x₁) = f(x₂) => x₁ - 1 = x₂ - 1
=> x₁ = x₂ -1 + 1
=> x₁ = x₂
So, f(x) is one to one.
Onto : let y be a element of X ( co-domain) We can show that there exists x∈A such that f(x)=y. Choose x= f⁻¹(y) and so f(f⁻¹(y))=y. So for all y∈B, there exists an x∈A such that f(x)=y. Therefore, it is onto. Thus, f(x) is one to one and onto and continus( due to polynomial nature) i.e it is a continuous bijection from X to itself, but it is not a
homeomorphism, since the image of N is not open.
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how do you prove 6^7-6^6+6^5 is divisible by 31
Step-by-step explanation:
I don't know if this is valid but
We can think of this problem like
(6^7-6^6+6^5)/31 = x
Where x is a whole number so 6^7-6^6+6^5 is divisible by 31
Multiply each side with 31 :
6^7-6^6+6^5 = 31x
We can turn 6^7 into 6^5 x 6^2
We can also turn 6^6 into 6^5 x 6
So the equation turns into this :
(6^5 x 6^2) - (6^5 x 6) + (6^5 x 1) = 31x
We can factor out the 6^5 out of the left side of the equation, which turns into :
(6^5) x (6^2 - 6 + 1) = 31x
Which is also :
(6^5) x (31) = 31x
Divide each side with 31
6^5 = x
X is obviously a whole number