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Explanation:
The given statement is claiming something like [tex]P(X < 2)[/tex] produces a different result compared to [tex]P(X \le 2)[/tex]. The subtle difference of course is the "or equal to".
When talking about continuous random variables, the two values are the same. Why? Because probability of selecting *exactly* X = 2 is going to be zero. Think of a very very thin strip of height P(X = 2) and the width is approaching zero. The width is doing this because we're trying to pinpoint X = 2 itself. As you can see, this skinny rectangle will have its area approach 0. Ultimately, whether we compute [tex]P(X < 2)[/tex] or [tex]P(X \le 2)[/tex], it doesn't matter. They both produce the same result.
If you are a visual learner, consider the standard normal distribution. Now consider the task if shading to the left of z = 2. This area describes both probabiltiies mentioned above.
If X is a continuous random variable, then [tex]P(X < 2) = P(X \le 2)[/tex] and we can change the "2" to any number we want to have the same outcome.
Therefore, the original claim is false.
-------------------------
Extra info:
Now if X was discrete (say from the binomial distribution), then the two probabilities would be different. This is because
[tex]P(X < 2) = P(0) + P(1)\\\\P(X \le 2) = P(0) + P(1) + P(2)\\\\P(X < 2) \ne P(X \le 2) \ \text{only if X is discrete}[/tex]
We can see in this case that the second line has P(2) while the first one does not.
So the original claim would be true if we changed "continuous" to "discrete".
Where does most regular lightning occur?
A. The stratosphere
B. The troposphere
C. The Mesosophere
Rollie borrowed some money from his sister. Their brother wanted to know how much Rollie borrowed, but Rollie wouldn’t tell him. Instead, Rollie gave his brother a riddle.
“Each month, I paid our sister one-third of the amount I still owed her plus an additional $3. At the end of 3 months, I still owed her $3.”
Solve the riddle to find out how much money Rollie borrowed from his sister.
Explain how you arrived at your solution.
By working with fractions, we will see that the amount that Rollie borrowed from his sister is $31.50.
How much Rollie borrowed?Let's say that Rollie borrowed a quantity x.
The first month, Rollie returns one third of x + $3, so now he owes:
x - x/3 - 3 = (2/3)*x - 3
the second month returns another third of what he owes plus $3, so now he returns:
(1/3)*((2/3)*x - 3) + 3 = (2/9)*x + 2
So no he owes:
(2/3)*x - 3 - (2/9)*x - 2 = (4/9)*x - 5
Finally, on the third month he returns:
(1/3)*((4/9)*x - 5) + 3 = (4/27)*x - 5/3 + 3 = (4/27)*x + 4/3
Now he owes:
(4/9)*x - 5 - (4/27)*x - 4/3 = (8/27)*x - 19/3
And that is equal to $3, what he owes at the end of the third month, so we need to solve:
(8/27)*x - 19/3 = 3
(8/27)*x = 3 + 19/3 = 28/3
Solving for x, we get:
x = (27/8)*(28/3) = 31.5
So Rollie borrowed $31.5 from his sister.
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graph the line y= 4/3x
Answer:
RISE/RUN
Step-by-step explanation:
You start at (0,0)move up 4move right 3Select the reason that best supports statement both 2 and 8 in the given proof.
Find a polynomial f(x) of degree 3 that has the following zeros. 8 ( multiplicity 2) , -4
Polynomial is an expression that consists of indeterminates(variable) and coefficient. The polynomial f(x) is x³-12x²+256=0.
What are polynomial?
Polynomial is an expression that consists of indeterminates(variable) and coefficient, it involves mathematical operations such as addition, subtraction, multiplication, etc, and non-negative integer exponentials.
As the zeros of the polynomial are 8(multiplicity 2), -4. Therefore, the factors of the polynomial can be written as,
[tex]x = 8\\x-8=0[/tex]
[tex]x =-4\\x+4=0[/tex]
Now, the polynomial f(x) which is a third-degree polynomial can be written as,
[tex](x-8)(x-8)(x+4)=0\\\\(x-8)^2(x+4)=0\\\\(x^2-16x+64)(x+4)=0\\\\x^3-16x^2+64x+4x^2-64x+256 = 0\\\\x^3-12x^2+256=0[/tex]
Hence, the polynomial f(x) is x³-12x²+256=0.
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What is the diameter of a sphere with a volume of 397\text{ m}^3,397 m
3
, to the nearest tenth of a meter?
REsponse: 9.1
PLEASE CHOOSE CORRECT OPTION AND WITH EXPLANATION 25 POINTS
Answer:
d
Step-by-step explanation:
Each point has been moved 2 spaces to the right and 5 units down.
Moving 2 spots to the right means x updates to x+2
Moving 5 units down tells us to change y to y-5
Therefore, [tex](x,y) \to (x+2, y-5)[/tex]
What is the solution to the system of equations below?
(Hint: Solve using substitution!)
−5x−y=5
x=7y−1
(
Answer:
x = -1, y = 0 or (-1, 0)Step-by-step explanation:
We have two equations :
-5x - y = 5x = 7y - 1Take the value of x in Equation 2 and substitute in Equation 1.
-5(7y - 1) - y = 5-35y + 5 - y = 5-36y = 0y = 0Now, take the value of y and substitute in Equation 2.
x = 7(0) - 1x = -1Solution
x = -1, y = 0 or (-1, 0)Answer:
The lines intersect at the point (-1, 0)
Step-by-step explanation:
−5( )−y=5
-5(7y-1) - y = 5 substitute the x=7y-1 into first equation
-35y + 5 - y =5 multiply -5
-36y + 5 = 5 combine like terms
-36y = 0 subtract 5
y=0 divide by -36
x=7(0)-1 substitute 0 for y in x=7( )-1
=-1 simplify
The lines intersect at the point (-1, 0)
What is the value of x in the equation 1/3x − 2/3 =− 18?
Answer:
x = -52
Step-by-step explanation:
[tex]\frac{1}{3}x-\frac{2}{3}=-18[/tex]
Let us solve for x.
[tex]\frac{1}{3}x=-18+\frac{2}{3}[/tex]
[tex]\frac{1}{3}x=-\frac{18*3}{1*3} +\frac{2}{3}[/tex]
[tex]\frac{1}{3}x=-\frac{54}{3} +\frac{2}{3}[/tex]
[tex]\frac{1}{3}x=\frac{-54+2}{3}[/tex]
[tex]\frac{1}{3}x=\frac{-52}{3}[/tex]
Use cross multiplication to find the value of x.
[tex]\frac{1x}{3}=\frac{-52}{3}[/tex]
[tex]3*1x=3*-52[/tex]
[tex]3x=-156[/tex]
Divide both sides by 3.
x = - 52
Please help! Will mark brainlyest.
Answer:
the letter d does not have symmetry
Step-by-step explanation:
Brian invests £990 into his bank account. He receives 2.6% per year simple interest. How much will Brian have after 3 years? Give your answer to the nearest penny where appropriate
Answer:
£1067.22.
Step-by-step explanation:
Interest I= PRT/100 where P = Initial investment, R = % rate, T = time.
So I = 990*2.6* 3 / 100
= £77.22
So total he will have in the bank
= 990+77.22
= £1067.22.
the base of the rectangular prism is shaded what is the lateral surface area ( show work pls )
LSA
2×H(L+B)2(4.5)(11+3)9(14)126ft²solve each logarithmic equation. Round your answer to two decimal places.
log4 16 = x
my attempt:
log4 16 (x+x) = x
--
x
log 4 (x+16) = 1
(x + 16) = 1
x + 16/1 =17
x+ 16 = 17
x= 8/9
Answer:
x = 2Step-by-step explanation:
Given equation
[tex]log_416=x[/tex]Use the property of logarithm
[tex]log_ab=c[/tex] ⇒ [tex]b = a^c[/tex]Apply to the given equation
[tex]16 = 4^x[/tex][tex]4^2=4^x[/tex][tex]2 = x[/tex][tex]x=2[/tex]Let's see
[tex]\\ \rm\Rrightarrow log_416=x[/tex]
[tex]\\ \rm\Rrightarrow 16=4^x[/tex]
[tex]\\ \rm\Rrightarrow 4²=4^x[/tex]
[tex]\\ \rm\Rrightarrow x=2[/tex]
Done!
which is greater - 3/4 or - 5/6
Answer:
-3/4
Step-by-step explanation:
see picture below
Answer:
[tex]-3/4~ > -5/6[/tex]
Step-by-step explanation:
Using the given inputs
[tex]3/4~and~5/6[/tex]
The least common denominator (LCD) is 12.
Rewriting as equivalent fractions with the LCD:
[tex]-\frac{3}{4} ~becomes-\frac{9}{12}[/tex]
And
[tex]-\frac{5}{6}~becomes-\frac{10}{12}[/tex]
Comparing the numerators of the equivalent fractions we have
[tex]-9/12 > -10/12[/tex]
Therefore, the comparison shows:
[tex]-3/4~ > -5/6[/tex]
Hope this Helps! :3
have a great day! :3
Norberto received the following scores on his last five spelling tests 93, 66, 78, 85, and 98. Which of the following statements
is true?
A) The median of the set of scores is 78.
B) The mean of the set is less than the median.
C) The mode of the set of scores is 93
D) The mean of the set is more than the median.
The mean of the set is less than the median. Option B is correct.
Given that,
Norberto received the following scores on his last five spelling tests 93, 66, 78, 85, and 98.
The mean of the values is the ratio of the total sum of values to the number of values.
Here,
Marks scored by Norberto in 5 spelling tests are 93, 66, 78, 85, and 98.
Mean of marks score = total marks scored / total spelling test
Mean of marks score = (93 + 66 + 78 + 85 + 98) / 5
Mean of marks score = 420 / 5 = 84
Now,
In order to get the median,
Arrange the marks in ascending order,
66, 78, 85, 93, 98
n = 5
median = (n + 1) / 2th term
= (5 + 1) / 2th term
= 6 / 2 = 3 th term
Median = 85
Here, 85 > 84 implies the median is more than the mean.
Thus, the mean of the set is less than the median. Option B is correct.
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Which of the following is an example of a linear system of equations?
5
x
2
+
6
y
=
13
6
x
−
12
y
=
14
5
x
+
6
y
=
13
6
x
−
12
y
2
=
14
5
x
+
6
y
=
13
6
x
2
−
12
y
=
14
5
x
+
6
y
=
13
6
x
−
12
y
=
14
Yw :D pls mark me brainiest
hElp me I need help with this question
Answer:
Jackie divided the number of quarts by 2. There are 2 pints in each quart. She should have multiplied by 2; so Jackie made 20 pints of lemonade.
What is the five-number summary of this data set? {403, 276, 649, 786, 274, 189, 654, 652, 572} Drag the numbers into the boxes to correctly complete the five-number summary.
Answer:
Minimum: 189
Maximum: 786
Median: 572
Lower quartile: 275
Upper quartile: 653
Step-by-step explanation:
Listing the numbers in order from least to greatest, we have: 189, 274, 276, 403, 572, 649, 652, 654, 786.
From this, we can see that the smallest (minimum) value is 189, and the largest (maximum) value is 786.
We can find the the median by taking off a number from each side of the number set one by one. When done, we can see that the number in the middle is 572, so that is our median.
To find the upper and lower quartiles, split the number set in half where the median lies and find the median of those two sections.
Q1: 189, 274, 276, 403
274 + 276 = 550
550 ÷ 2 = 275
--------------------------
Q3: 649, 652, 654, 786
652 + 654 = 1306
1306 ÷ 2 = 653
So, the lower quartile range is 275, and the upper quartile range is 653.
hope this helps!
help thanksSSSSSSSSSS
Answer:
[tex]\boxed{\sf{x=24}}[/tex]Step-by-step explanation:
GIVEN:
To find the missing number in the proportion, you have to isolate it the term of x from one side of the equation.
[tex]\sf{\dfrac{8}{7}=\dfrac{x}{21} }[/tex]
First, thing you do is switch sides.
[tex]\sf{\dfrac{x}{21}=\dfrac{8}{7} }[/tex]
Multiply by 21 from both sides.
[tex]\Longrightarrow: \sf{\dfrac{21x}{21}=\dfrac{8*21}{7} }[/tex]
Solve.
Multiply the numbers from left to right.
Use the order of operations.
PEMDAS stands for:
ParenthesesExponentsMultiplyDivideAddSubtract[tex]\Longrightarrow: \sf{\dfrac{8*21}{7}=\dfrac{168}{7}=24 }[/tex]
[tex]\Longrightarrow: \boxed{\sf{x=24}}[/tex]
Therefore, the final answer is x=24.I hope this helps. Let me know if you have any questions.
For the transformation to be a translation, which statements must be true? Select four options.
Answer:
A, B, C, and E.
Step-by-step explanation:
I don’t know how to explain what I did very well.
((454 x 344)/4) + 4854
Solve order of operations
Answer:
43,898
Step-by-step explanation:
1. 454 x 344 = 156,176
2. 156,176 / 4 = 39,044
3. 39,044 + 4,854 = 43,898
Tulong bwhahahhahahaha
can u guys please help a poor soul
1/root 5 - root 3
hope it really helps......!!!!!!
how to graph y = x + 10
Answer:
if you use desmos graphing calculator it will make graphing equations like this easier.
Step-by-step explanation:
by easier i mean it just graphs it for you. hope this helps:)
a department store has guft boxes that are 20 inches long, 12 1/2 inches wide, and 5 1/2 inches high what is the volume
The diameter of a circle is 8 inches. What is the angle measure of an arc 37 pie inches long?
Answer:
135 degrees.
Step-by-step explanation:
Circumference of the circle
= 8pi inches.
8pi equals 360 degrees
So 3pi = (3pi / 8pi) * 360
= 3/8 * 360
= 135 degrees.
A coin jar contains 12 quarters, 15 dimes, and 23 nickels. Find the probability that a Karen will choose a dime from the jar and then Mikah will choose a quarter from the jar.
Write the probability as a fraction in simplest form.
6/25 is incorrect
Answer:
18/245.
Step-by-step explanation:
Total number of coins = 12+15+23 = 50.
Prob(Karen chooses a dime) = 15/50 = 3/10.
Prob(Mikah then chooses a quarter) = 12/49. ( Karen has already removed one coin)
Prob(of Karen choosing a dime then Mikah a quarter)
= 3/10 * 12/49
= 36/490
= 18/245.
Which of the following numbers is a multiple of 7?
Answer:
You have to share number too
Mr. Sims bought 9 tickets to a puppet show and spent $57. He bought a combination of child tickets for $3 each and adult tickets for $9 each.
Which system of equations below will determine the number of adult tickets, a, and the number of child tickets, c, he bought?
Answer:
x =number of child tickets
y=number of adult tickets
x + y = 9
3x +9y = 57
x = 9-y
3(9-y) + 9y =57
27 - 3y + 9y = 57
6y = 30
y=5 adult tickets
x = 4 child tickets
Answer:
adult's tickets a=5
child's tickets c=4
Step-by-step explanation:
a+c=9
9a+3c=57
c=9-a
3a+c=19
3a+9-c=19
2a=10
a=5
c=9-a=9-5=4
You decide that you are going to flip a coin, and a six sided die.
What is the probability of the following events?
Tails and an even number? (Round to two decimal places)
Tails and the number 9?
Heads or a number bigger than 4? (Round to two decimal places)
Heads or the number 2? (Round to two decimal places)
Probability helps us to know the chances of an event occurring. The probability of getting a tail and an even number is 0.25.
What is Probability?
Probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
Since a coin has two faces, therefore, the probability of getting either of the sides of the coin is (1/2). While a die has six faces, so the probability of getting any side of the die is (1/6).
A.) The probability of getting a tail and an even number can be written as,
[tex]\text{Probability of getting a tail} = \dfrac{1}{2}[/tex]
[tex]\text{Probability of Even Number(2,4,6) } = \dfrac{3}{6} = \dfrac{1}{2}[/tex]
[tex]\text{Probability (Tails and an even number)} = \dfrac12 \times \dfrac12 = 0.25[/tex]
B.) The Probability of getting tails and the number 9 can be written as,
[tex]\text{Probability of getting a tail} = \dfrac{1}{2}[/tex]
[tex]\text{Probability of Number 9} = \dfrac{0}{6} = 0[/tex]
[tex]\text{Probability of the tails and the number 9} = 0[/tex]
C.) The Probability of getting Heads or a number bigger than 4 can be written as,
[tex]\text{Probability of getting a Head} = \dfrac{1}{2}[/tex]
[tex]\text{Probability of a number bigger than 4 (5,6) } = \dfrac{2}{6} = \dfrac{1}{3}[/tex]
[tex]\text{Probability (Heads or a number bigger than 4 )} = \dfrac12 + \dfrac13 = \dfrac{5}{6} = 0.83333[/tex]
D.) The Probability of getting Heads or the number 2 can be written as,
[tex]\text{Probability of getting a Head} = \dfrac{1}{2}[/tex]
[tex]\text{Probability of the number 2} = \dfrac{1}{6}[/tex]
[tex]\text{Probability (Heads or the number 2 )} = \dfrac12 + \dfrac16 = \dfrac{8}{12} = 0.6666[/tex]
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