Answer:
Z and B are independent events because P(Z∣B) = P(Z).
Step-by-step explanation:
Z and B are independent events
When Z and B are independent events then
P(Z and B) = P(Z) * P(B)
P(Z∣B)= [tex]\frac{P(Z and B)}{P(B)}[/tex]
P(Z∣B)= [tex]\frac{P(Z)*P(B)}{P(B)}[/tex]
We cancel out P(B) on both sides
P(Z|B) = P(Z)
Problem Page
Lucy's shop sells
712
quarts of ice cream each day. How much is this in pints?
Write your answer as a whole number or a mixed number in simplest form. Include the correct unit in your answer.
Solve the following inequality: 2(x + 1) – (–x + 5) ≤ –18. A. x ≤ –9 B. x ≤ –20 C. x ≤ –37 D. x ≤ –5
Answer:
Solve the following inequality: 2(x + 1) – (–x + 5) ≤ –18. A. x ≤ –9 B. x ≤ –20 C. x ≤ –37 D. x ≤ –5
Step-by-step explanation:
2 (x + 1) - (-x + 5) ≤ -18
2x + 2 + x - 5 ≤ - 18
3x - 3 ≤ - 18
3x ≤ - 15
x ≤ - 15/3 ≤ - 5
The answer is: D. x ≤ - 5
A forest ranger can see for a distance of 12 miles from a firetower how many square miles can he observe?
using 3.14 for pi
area = pi x r^2
since he can see 12 miles in any direction 12 would be the radius
so 3.14 x 12^2 = 452.16 square miles
round the answer as needed.
Write the phrase as an algebraic expression 6 less than a number times 11
the oringinal cost of a lamp is $18.95. the lamp is on sale for 25% off. how much will you pay?
Davis Construction is building a new housing development. They begin by mapping the development out on a coordinate grid. They place one of the two swimming pools at (-4, -1) and another at (6, 3). If they want the clubhouse to be exactly halfway between the two pools, find the coordinates of the clubhouse.
Whats the quotient of 2 1/4 and 5/8
Is 703.005 is greater than or less than seven hundred three and five hundredths
A mountaineer climbed 1,000 feet at a rate of x feet per hour. He climbed an additional 5,000 feet at a different rate. This rate was 10 feet per hour less than twice the first rate. Which expression represents the number of hours the mountaineer climbed
The equation that represents the number of hours the mountaineer climbed is t = 1000/V1 + 2600(V1 - 5).
How to compute the equation?Based on the information given, V1 = 1000 and V2 = 2V1 - 10.
The time taken will be:
= 1000/V1 + 5000/V2
Well substitute the equations. This will be:
t = 1000/V1 + 5000//(2V1 - 10)
t = 1000/V1 + 5000/2(V1 - 5)
t = 1000/V1 + 2600(V1 - 5).
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One bag of Glizard wood chips covers a 215 square foot area. How many total bags of wood chips must be purchased to cover an area that is 42 feet by 61 feet?
42 x 61 = 2562
2562/215 = 11.92
12 total bags are needed
In a certain town 22 of voters favor a given ballot measure for groups of 21 voters find the variance for the number who favor the measure
Answer:
4.6
Step-by-step explanation:
Allow me to revise your question and hope it will be the same as the original one:
In a certain town 22% of voters favor a given ballot measure for groups of 21 voters find the variance for the number who favor the measure
a. 1.9
b. 13
c. 4.6
d. 3.6
Here is my answer:
Given:
22% of voters favor a given ballot = 0.22 Groups of 21 votersSo the variance is: 21*0.22 = 4.6
We choose B
2.8 meters linen divided into 45 cm pieces = # of pieces and waste
what is the equation to solve it
-7=7d-8
help me with the equation for that problem
If (h, •) and (k, •) are subgroups of (g, •), prove that (h n k, •) is a subgroup of (g, •). can the same be said for the union, hu k? prove or give a counterexample.
What is the simplified form of the expression? (2 – 9c)(–8)
A set of data with a mean of 62 and a standard deviation of 5.7 is normally distributed. what is the value that is −1 standard deviation from the mean
6/5 × 25/24 multiple
eliminate the parameter. x = 5 cos t, y = 5 sin t help please!
Final answer:
To eliminate the parameter 't' from the equations x = 5 cos t and y = 5 sin t, use the Pythagorean identity which leads to the non-parametric equation of a circle: x^2 + y^2 = 25.
Explanation:
To eliminate the parameter 't' from the parametric equations x = 5 cos t, y = 5 sin t, we can use the Pythagorean identity sin^2(t) + cos^2(t) = 1. Plugging in the given expressions for x and y:
(x/5) = cos(t)
(y/5) = sin(t)
We can square both sides of these equations and then add them together:
(x/5)^2 + (y/5)^2 = cos^2(t) + sin^2(t)
As cos^2(t) + sin^2(t) equals 1, the equation simplifies to:
(x/5)^2 + (y/5)^2 = 1
Thus, the eliminated parameter equation representing the same curve without the parameter 't' is:
x^2 + y^2 = 25
This is the equation of a circle with a radius of 5, centered at the origin.
A flat rectangular piece of aluminum has a perimeter of 66 inches. The length is 15 inches longer than the width. Find the width.
Let c be the curve of intersection of the parabolic cylinder x2 = 2y, and the surface 3z = xy. find the exact length of c from the origin to the point 4, 8, 32 3 .
To find the exact length of the curve c from the origin to a given point, we can parameterize the curve and use the formula for arc length. In this case, we need to solve for x, y, and z in terms of a parameter t. Then, we can integrate the arc length formula to obtain the exact length.
Explanation:To find the exact length of the curve c from the origin to the point (4, 8, 32/3), we need to first parameterize the curve. Given that x2 = 2y and 3z = xy, we can solve for x, y, and z in terms of a parameter t. Then, we can use the formula for arc length to calculate the length of the curve using integration.
Let's begin by solving for x, y, and z in terms of t:
From x2 = 2y, we have x = √(2t) and y = t2/2.Substituting these values into 3z = xy, we get 3z = √(2t) * (t2/2) or z = (t3√2)/6.Now, we can calculate the arc length using the formula:
L = ∫ sqrt((dx/dt)2 + (dy/dt)2 + (dz/dt)2) dt
Plugging in the values of x, y, and z in terms of t, we can evaluate the integral to find the exact length of curve c.
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It takes 8 minutes for Byron to fill the kiddie pool in the backyard using only a handheld hose. When his younger sister is impatient, Byron also uses the lawn sprinkler to add water to the pool so it is filled more quickly. If the hose and sprinkler are used together, it takes 5 minutes to fill the pool. Which equation can be used to determine r, the rate in parts per minute, at which the lawn sprinkler would fill the pool if used alone?
+ 5r = 8
+ 5r = 1
5() = r
= 5r
Let us say that the procedure of completely filling up the pool with water is called “1 job”. Therefore the rates of the equipment in doing the job would be:
Rate of handheld hose = 1 job / 8 minutes ---> 1
Rate of lawn sprinkler = r ---> 2
Rate of the two combines = 1 job/ 5 minutes ---> 3
So we are to find the equation to use, in this case, we simply have to add equations 1 and 2 to get 3:
1 / 8 + r = 1 / 5
Multiplying both sides by 5:
(5 / 8) + 5 r = 1 ---> ANSWER
Answer:
5/8 + 5r = 1
Step-by-step explanation:
Right on edge!
What percent of 645 is 187.05?
To find what percent 187.05 is of 645, one can use the following formula:
[tex]\[ \text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100 \][/tex]
In this case, the Part is 187.05 and the Whole is 645. Plugging these values into the formula gives:
[tex]\[ \text{Percentage} = \left( \frac{187.05}{645} \right) \times 100 \][/tex]
Now, calculate the fraction:
[tex]\[ \text{Percentage} = \left( \frac{187.05}{645} \right) \times 100 = \left( 0.29155 \right) \times 100 \][/tex]
[tex]\[ \text{Percentage} = 29.155 \][/tex]
Therefore, 187.05 is approximately 29.155% of 645. To express this as a fraction, one can write:
[tex]\[ \text{Percentage} = \frac{187.05}{645} \times 100 = \frac{18705}{645} \approx 29.155\% \][/tex]
To get the exact fraction, we can simplify:
[tex]\[ \text{Percentage} = \frac{187.05}{645} \times 100 = \frac{18705}{645} \times \frac{20}{20} = \frac{374100}{12900} \][/tex]
Simplifying the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 300, we get:
[tex]\[ \text{Percentage} = \frac{374100 \div 300}{12900 \div 300} = \frac{1247}{430} \][/tex]
So, the exact fraction representing the percentage is:
[tex]\[ \text{Percentage} = \frac{1247}{430} \times 100 \][/tex]
[tex]\[ \text{Percentage} = \frac{1247}{4.3} \][/tex]
[tex]\[ \text{Percentage} = 29.00 \% \][/tex]
Thus, 187.05 is exactly 29% of 645.
For what values of b will f(x)= log b^x be an increasing function?
Using logarithmic function concepts, it is found that for values of b > 1, [tex]f(x) = \log_b{x}[/tex] will be an increasing function.
What is an logarithmic function?A logarithmic function is modeled by:
[tex]f(x) = \log_b{x}[/tex]
The coefficient b determines the behavior of the function, as follows:
b > 1: The function is increasing.b < 1: The function is decreasing.Hence, for values of b > 1, [tex]f(x) = \log_b{x}[/tex] will be an increasing function.
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Use a triple integral to find the volume of the given solid. the solid enclosed by the cylinder x2 + y2 = 9 and the planes y + z = 14 and z = 2.
To find the volume of the solid enclosed by the given cylinder and planes, you convert to cylindrical coordinates. Then, you set up a triple integral with respect to these coordinates as ∫∫∫ dz dr dθ where the bounds of integration are 0<=θ<=2π, 0<=r<=3, and 2<=z<=14-r.
Explanation:The volume of the solid can be found using a triple integral in cylindrical coordinates. First, we need to identify the boundaries of the solid. From the cylinder equation, we see that x² + y² = 9, which in cylindrical coordinates converts to r^2 = 9, so 0<=r<=3. Then, from the plane equations y + z = 14 and z=2, we can determine that in cylindrical coordinates, 2<=z<=14-r.
Therefore, the volume V can be found by:
V = ∫∫∫ dz dr dθ
with bounds for integration being 0<=θ<=2π, 0<=r<=3, and 2<=z<=14-r.
Running this triple integral will provide the volume of the solid.
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For an analysis of variance, the term “one-way” refers to
A store has a $43.89 item on sale. The total discount of the sale is $9.66. What is the sale percentage off on this item?
$765.13 is deposited at the end of each month for 2 years in an account paying 12% interest compounded monthly. Find the amount of the account. Round your answer to the nearest cent.
The final amount is = $ 959.779
What is compound interest?
Compound interest is when you earn a hobby on both the cash we've got stored and the hobby we earn.
calculation:-
principal amount = $765.13
rate if interest = 12%
for 1st year:-
interest amount= $765.13*12/100
= $ 91.8156
final amount = $765.13 + $ 91.8156
= $ 856.9456
for 2nd year:-
principal amount = $ 856.9456
12% interest on $ 856.9456 = $ 102.833472
final amount = $ 856.9456+$ 102.833472
= $ 959.779 answer
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the following data values represents a population. What is the variance of the values? 6, 10, 14, 2
Answer:20 !
Step-by-step explanation:
Given the Arithmetic sequence A1,A2,A3,A4A1,A2,A3,A4
29, 39, 49, 59
What is the value of A33A33?