If p(a) = 0.25 and p(b) = 0.65, assuming independence of events, then p(a and
b.is:
The Independent events is 0.1625.Events A and B are considered independent if the likelihood of each event's occurrence is unaffected by the occurrence of the other.
Find the independent events?P(A/B) is equal to P(A.B)/P(B) by definition (A). P(A) = P(B) / P(B) (as A, B are Independent events).
Events A and B are considered independent if the likelihood of each event's occurrence is unaffected by the occurrence of the other. P(A) = P(AB) = 1/2, which suggests that the likelihood of event A occurring has not changed as a result of the occurrence of event B.
P(0.25) = P(0.25 * 0.65) = 1/2
P(0.25) = 0.1625.
The Independent events is 0.1625 .
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derivative of the (sqrt of t/4t-3)
Answer:
[tex]\displaystyle \frac{dy}{dt} = \frac{-3}{2(4t- 3)^2\sqrt{\frac{t}{4t - 3}}}[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative Rule [Quotient Rule]: [tex]\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]
Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = \sqrt{\frac{t}{4t - 3}}[/tex]
Step 2: Differentiate
Basic Power Rule [Derivative Rule - Chain Rule]: [tex]\displaystyle y' = \frac{1}{2\sqrt{\frac{t}{4t - 3}}} \cdot \frac{d}{dt} \bigg[ \frac{t}{4t - 3} \bigg][/tex]Derivative Rule [Quotient Rule]: [tex]\displaystyle y' = \frac{1}{2\sqrt{\frac{t}{4t - 3}}} \cdot \frac{(t)'(4t - 3) - t(4t - 3)'}{(4t - 3)^2}[/tex]Basic Power Rule [Derivative Properties]: [tex]\displaystyle y' = \frac{1}{2\sqrt{\frac{t}{4t - 3}}} \cdot \frac{(4t - 3) - 4t}{(4t - 3)^2}[/tex]Simplify: [tex]\displaystyle y' = \frac{-3}{2(4t- 3)^2\sqrt{\frac{t}{4t - 3}}}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Compare the decimals 17.20 and 17.2. Which comparison is correct? A. 17.20 > 17.2 B. 17.20 < 17.2 C. 17.20 = 17.2
A 6-ounce can of frozen juice costs 84. Give the unit price in cents per ounce.
one quart or one gram is greater
If you are adding two fractions that are both less than 1/2, What must be true about the sum? Give three examples to support your thinking.
if both fractions are less than 1/2 then the sum has to be less than 1
1/8 + 3/8 = 4/8 = 1/2 , less than 1
7/16 + 1/4 = 11/16, less than 1
3/16 + 1/16 = 4/16 = 1/4, less than 1
Anjali went to Citizens Bank and borrowed $7,000 at a rate of 8%. The date of the loan was September 20. Anjali hoped to repay the loan on January 20. Assuming the loan is based on ordinary interest, Anjali will pay back how much interest on January 20? A. $187.18 B. $187.17 C. $189.78 D. $188.22
Answer:
$189.78
Step-by-step explanation:
"The computation of the interest on January 20 is shown below:
= Principal × interest rate × number of days ÷ total number of days in a year
= $7,000 × 8% × 122 days ÷ 360 days
= $7,000 × 8% × 0.338
= $189.78
The 122 days are calculated below:
September - 10 days
October - 31 days
November - 30 days
December - 31 days
January - 20 days
Total - 122 days
And we assume the 360 days in a year"
Over a two hour time period a snail moved 76 inches. How far is this in yards? Write your answer as a whole number or a mixed number in simplest form. Include the correct unit in your answer.
Final answer:
The snail moved a total distance of 2 1/9 yards after converting 76 inches to yards using the conversion factor of 1 yard equals 36 inches.
Explanation:
To convert the distance a snail moved from inches to yards, we use the conversion factor that 1 yard equals 36 inches. Given that the snail moved 76 inches, we divide this number by 36 to find the distance in yards.
76 inches ÷ 36 inches/yard = 2 yards and 4 inches.
Since there are 36 inches in a yard, the remaining 4 inches must be converted to a fraction of a yard by dividing by 36:
4 inches ÷ 36 = 1/9 yard.
Therefore, the snail moved 2 yards and 1/9 yard, or 2 1/9 yards in total.
110% of 90 is what number a?
What does is a?
erica bougfht 3 1/2 yards of fabric if she uses 2/3 of the fabric for a curtain.how much will she have left?
17 ÷ 4520= what is the product
The student's question is related to dividing 17 by 4520. This is performed by a straight division resulting in a small decimal quotient, not a product. The calculation is best done using a calculator and rounding to the proper number of significant figures.
The equation given, 17 by 4520, is asking for the result of dividing 17 by 4520. To compute this, we simply perform the division, recognizing that since 4520 is much larger than 17, the answer will be a very small decimal value. The term 'product' in the student's question seems to be a mistake, as they are likely referring to the quotient obtained from the division.
When attempting to perform the computation mentally and simplify the process, one might attempt to find numbers that are more easily divisible or apply scientific notation to simplify calculations, much like re-expressing numbers to make them more manageable. However, for this division, no mental math trick simplifies it effectively, and using a calculator might be the best option.
When going through this process, it is also important to consider significant figures when giving the final answer, rounding as necessary based on the precision of the data provided.
Find the limit, if it exists. (if an answer does not exist, enter dne.) lim (x, y) → (0, 0) x4 − 20y2 x2 + 10y2
The limit of the expression as (x, y) approaches (0, 0) does not exist.
Explanation:To find the limit as (x, y) approaches (0, 0) of the expression \(\frac{x^4 - 20y^2}{x^2 + 10y^2}\), we can try approaching the limit along different paths. Let's consider approaching along the x-axis (y=0) and along the y-axis (x=0) separately.
Approaching along the x-axis: \(\lim_{{(x, 0) \to (0, 0)}} \frac{{x^4 - 20(0)^2}}{{x^2 + 10(0)^2}} = \lim_{{(x, 0) \to (0, 0)}} \frac{{x^4}}{{x^2}} = \lim_{{(x, 0) \to (0, 0)}} x^2 = 0.
Approaching along the y-axis: \(\lim_{{(0, y) \to (0, 0)}} \frac{{(0)^4 - 20y^2}}{{(0)^2 + 10y^2}} = \lim_{{(0, y) \to (0, 0)}} \frac{{-20y^2}}{{10y^2}} = \lim_{{(0, y) \to (0, 0)}} -2 = -2.
Since the limit approaches different values along different paths, the limit does not exist.
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A random variable x takes four possible values, 0, 2, a, and b, where a and b are unknown numbers. if pr[x = 0] = 0.2, pr[x=2] = 0.4, pr[x = a] = 0.3, e[x] = 2.8 and it is the case that a + b = 6, what is the missing value of a ?
a.-1.0
b.5.0
c.7.0
d.cannot be determined without more information
e.none of the above
Final answer:
The missing value of the random variable X can be determined by solving the equation e[x] = 2.8 and substituting the known values. By solving the equation, we find that the missing value is c. 7.
Explanation:
a. In words, X = A random variable that takes four possible values: 0, 2, a, and b.
b. X~ A missing value that represent an unknown number for the random variable X.
c. In words, X = The missing value of the random variable X, denoted by a.
d. X A missing value that we need to determine.
In this case, the missing value of a can be found by substituting the known values into the equation a + b = 6. Since b = 6 - a, we can substitute this expression into the equation e[x] = 2.8 and solve for a. From the equation, we get 0.2(0) + 0.4(2) + 0.3(a) + 0.3(6 - a) = 2.8.
Solving this equation gives us a = 7. Therefore, the missing value of a is 7, so the correct answer is c.
A closet measure 5 feet by 3 feet does the measurement of 15 square feet show the volume inside the closet
What is the y-intercept of the line given by the equation y = 5x - 21?
To find the y-intercept of y = 5x - 21, identify the constant term of the equation, which is -21, indicating the y-intercept is -21.
The y-intercept of the line given by the equation y = 5x - 21 can be found by analyzing the equation in the form y = mx + b, where m is the slope and b is the y-intercept.
Comparing the equation y = 5x - 21 with y = mx + b, we see that the y-intercept is -21 (b = -21).Therefore, the y-intercept of the line y = 5x - 21 is -21.Elizabeth has $252.00 in her account on Sunday. Over the next week, she makes the following changes to her balance via deposits and purchases: Day Debit ($) Credit ($) Monday 114.60 150.00 Tuesday 79.68 --- Wednesday 161.39 --- Thursday 57.40 --- Friday 22.85 75.00 Saturday 140.55 --- On what day does Elizabeth first get charged an overdraft fee?
Given:
Elizabeth has $252.00 in her account on Sunday and a table is given of her deposits and purchases over the following week.
To Find:
The day Elizabeth first gets charged an overdraft fee.
Answer:
Thursday's expenditure of $57.40 exceeds her bank balance at the time of transaction, and therefore Thursday is the day Elizabeth would first get charged with an overdraft fee.
Step-by-step explanation:
Elizabeth would first get charged with an overdraft fee when her expenditure exceeds her bank balance, i.e., the amount that is debited is more than what is in her bank account at that particular time.
So we analyse her transactions one by one.
On Sunday, we are given that she has $252.
On Monday, $114.60 is debited. So the remaining balance would be
$252 - $114.60 = $137.4
But on the same day, $150 is also credited to her account. So her balance would then be
$137.4 + $150 = $287.4
Next, on Tuesday, $79.68 is debited so the balance she is left with would be
$287.4 - $79.68 = $207.72
On Wednesday, $161.39 is debited so the balance she is left with would be
$207.72 - $161.39 = $46.33
On Thursday, $57.40 is debited so the balance she is left with would be
$46.33 - $57.40 = -$11.07
Thus, we see that Thursday's expenditure of $57.40 exceeds her bank balance and therefore Elizabeth would be charged with an overdraft fee as her bank balance after the transaction would be -$11.07.
factor the expression 10x−25y
Final answer:
To factor the expression 10x-25y, we find the greatest common factor, which is 5, and write the expression as 5(2x - 5y).
Explanation:
To factor the expression 10x−25y, we need to find the greatest common factor (GCF) that both terms share. In this case, both terms are divisible by 5. When we factor out the GCF, we get:
Identify the GCF of 10x and 25y, which is 5.
Divide both terms by the GCF: 10x/5 = 2x and 25y/5 = 5y.
Write the factored expression: 5(2x - 5y).
Thus, the expression 10x−25y factored is 5(2x - 5y)
A microwave is placed on top of two boxes. One box is 2 feet 5 inches tall the other box is 3 feet 11 inches tall and the other microwave is 3 feet 3 inches tall how tall are they combined?
simplify and reduce. show the work. ^= an exponent of 2 and 0
(-2 3/4 + 1 2/3)^2 - (-7/9)^0
Choose the true statement about the graph of x > -3.
closed circle on -3 and all numbers to the right shaded
open circle on -3 and all numbers to the right shaded
open circle on -3 and all numbers to the left shaded
Answer:
open circle on -3 and all numbers to the right shaded
What is the next letter a,z,e,b,I,y,o
Solve the system of linear equations. separate the x- and y- values with a coma. 20x=-58-2y
17x=-49-2y
please help me, solve for y 2x-y=5
Sam is a waiter at a local restaurant where he earns wages of $7 per hour. Sam figures that he also earns about $5 in tips for each person he serves. Sam works 6 hours on a particular day.
Answer:
y=5x+42
Where y is the money he earns and x is the number of person he serves.
Step-by-step explanation:
Let the number of person he serves =x
It is given that he earns $5 as tip for each person he serves.
Hence total tip earned for serving x person=5x
His fixed wages are $7 per hour and he works for 6 hours a day. Hence his wages per day are $7*6 =$42
Hence total money earned for a day , say y can be represented as
y=5x+42
Three boys share 28 toy cars equally. How many cars did each boy get and how many were left over
The sides of a triangle measure 76 mm, 8 CM, and 10 CM..What is the lengths of the two shorter sides
Evaluate each expression. Click on undefined as needed
Simply (8xto4) (4x to 3) \ 7x to 2
5 less than a third of a number is at most 15
Draw a garden with up to 5 rows and that has the same number of flowers in each row . Then two equation that match your array .