(a) The probability is [tex]\[\boxed{0.464}\][/tex]. (b) The probability is [tex]\[\boxed{0.763}\][/tex]. (c) The probability is [tex]\[\boxed{0.585}\][/tex]. (d) The probability is [tex]\[\boxed{0.921}\][/tex]. (e) No, because 205 females are frequently involved in charity work. The option (A) is correct.
To address the given questions based on the provided table, let's go through each question step-by-step:
(a) Find the probability that the person is frequently or occasionally involved in charity work.
First, we need the total number of people who are frequently or occasionally involved in charity work. This is the sum of people in the "Frequently" and "Occasionally" columns.
[tex]\[\text{Total frequently or occasionally involved} = 432 + 904 = 1336\][/tex]
Now, we divide this by the total number of people surveyed:
[tex]\[P(\text{frequently or occasionally involved}) = \frac{1336}{2881} \approx 0.464\][/tex]
So, the probability is [tex]\[\boxed{0.464}\][/tex].
(b) Find the probability that the person is female or not involved in charity work at all.
To solve this, we need to find the number of females and those not involved in charity work at all.
[tex]\[\text{Total females} = 1402\][/tex]
[tex]\[\text{Total not involved at all} = 1545\][/tex]
We need to subtract the overlap (females not involved in charity work) to avoid double-counting. From the table, the number of females not involved at all is 747.
[tex]P(\text{female or not involved at all}) = \frac{\text{Total females} + \text{Total not involved at all} - \text{Females not involved}}{\text{Total}}[/tex]
[tex]= \frac{1402 + 1545 - 747}{2881} = \frac{2200}{2881} \approx 0.763[/tex]
So, the probability is [tex]\[\boxed{0.763}\][/tex].
(c) Find the probability that the person is male or frequently involved in charity work.
[tex]\[\text{Total males} = 1479\][/tex]
[tex]\[\text{Total frequently involved} = 432\][/tex]
We need to subtract the overlap (males frequently involved) to avoid double-counting. From the table, the number of males frequently involved is 227.
[tex]P(\text{male or frequently involved}) = \frac{\text{Total males} + \text{Total frequently involved} - \text{Males frequently involved}}{\text{Total}}[/tex]
[tex]= \frac{1479 + 432 - 227}{2881} = \frac{1684}{2881} \approx 0.585[/tex]
So, the probability is [tex]\[\boxed{0.585}\][/tex].
(d) Find the probability that the person is female or not frequently involved in charity work.
[tex]\[\text{Total females} = 1402\][/tex]
[tex]\[\text{Total not frequently involved} = 2881 - 432 = 2449\][/tex]
We need to subtract the overlap (females not frequently involved) to avoid double-counting. From the table, the number of females not frequently involved is 1197 (450 + 747).
[tex]P(\text{female or not frequently involved})=\frac{1402 + 2449 - 1197}{2881} = \frac{2654}{2881} \approx 0.921[/tex]
So, the probability is [tex]\[\boxed{0.921}\][/tex].
(e) Are the events "being female" and "being frequently involved in charity work" mutually exclusive?
Two events are mutually exclusive if they cannot occur at the same time.
From the table, 205 females are frequently involved in charity work.
Since there are females who are frequently involved in charity work, the events "being female" and "being frequently involved in charity work" are not mutually exclusive.
So, the answer is A. No, because 205 females are frequently involved in charity work.
The complete question is:
The table below shows the results of a survey that asked 2881 people whether they are involved in any type of charity work. A per selected at random from the sample. Complete parts (a) through (e).
(a) Find the probability that the person is frequently or occasionally involved in charity work.
P(being frequently involved or being occasionally involved) - (Round to the nearest thousandth as needed.)
(b) Find the probability that the person is female or not involved in charity work at all.
P(being female or not being involved) (Round to the nearest thousandth as needed.)
(c) Find the probability that the person is male or frequently involved in charity work.
P(being male or being frequently involved) (Round to the nearest thousandth as needed.)
P(being male or being frequently involved) - (Round to the nearest thousandth as needed.)
(d) Find the probability that the person is female or not frequently involved in charity work.
P(being female or not being frequently involved) = (Round to the nearest thousandth as needed.)
(e) Are the events "being female" and "being frequently involved in charity work" mutually exclusive? Explain.
A. No, because 205 females are frequently involved in charity work.
B. Yes, because no females are frequently involved in charity work.
C. Yes, because 205 females are frequently involved in charity work.
D. No, because no females are frequently involved in charity work.
For the function f(x) = x + 4, what is the ordered pair for the point on the graph when x = 3p? a. (x, x + 4) b. (x, 3p + 4) c. (3p, x + 4) d. (3p, 3p + 4)
plz help me so confused
Marcel is planning a vacation. The travel agent says the average high temperature at the resort is 20 degrees Celsius. What is the equivalent Fahrenheit temperature
The equivalent Fahrenheit temperature for 20 degrees Celsius is 68 degrees Fahrenheit.
Explanation:To convert Celsius to Fahrenheit, you can use the formula: F = (C × 9/5) + 32
Using this formula, we can calculate the equivalent Fahrenheit temperature for 20 degrees Celsius:
F = (20 × 9/5) + 32 = 68 degrees Fahrenheit
which simplified fraction is equal to 0.17...?
A. 9/17
B. 8/45
C. 17/9
D. 16/90
find f(-2) for f(x)=2×3^x
a.-18
b.1/18
c.-36
d.2/9
given that 2/3a=16, which of the following illustrates how the multiplicative inverse property can be used to find the value of a?
Step-by-step explanation:
We have been given that [tex]\frac{2}{3}a=16[/tex].
Since multiplicative inverse property states that any number multiplied by its reciprocal is equal to one.
[tex]\frac{2}{3}\times \frac{3}{2} =1[/tex]
To solve for a let us divide 16 by [tex]\frac{2}{3}[/tex].
[tex]a=16\div \frac{2}{3}[/tex]
Since dividing a number by fraction is same as multiplying the number by the reciprocal of fraction. So we will multiply 16 by [tex]\frac{3}{2}[/tex].
[tex]a=16\times\frac{3}{2}[/tex]
[tex]a=8\times 3[/tex]
[tex]a=24[/tex]
We can see that to solve for a we have multiplied 16 by [tex]\frac{3}{2}[/tex] and [tex]\frac{3}{2}[/tex] is reciprocal of [tex]\frac{2}{3}[/tex].
Let us verify our answer by substituting a=24 in our given equation.
[tex]\frac{2}{3}\times 24=16[/tex]
[tex]2\times 8=16[/tex]
[tex]16=16[/tex]
Hence, to find the value of a we used multiplicative inverse property.
If x = -2 and y = 2, then which of the following statements is false?
Consider a point on the trans-australian highway, where two old wombats live. arrivals of cars at this point follow a poisson distribution; the average rate of arrivals is 1 car per 12 seconds.
) find the solution of y"+2y'=64sin(2t)+64cos(2t) with y(0)=9 and y'(0)=9
What is 7 divided by 28
7 divided by 28 is 1/4 or 0.25.
To calculate 7 divided by 28.
What is simplification?
Simplification is defined as solving mathematical problems using arithmetic operators.
7 divided by 28 = 7/28
= 1/4
= 0.25
Thus, 7 divided by 28 is 1/4 or 0.25.
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162x + 731 = −y − 9x-2 vertex form
To write the given equation in vertex form, we need to complete the square for the x terms. The vertex form of a quadratic equation is y = a(x-h)^2 + k, where (h, k) is the vertex of the parabola. After completing the square and rearranging the equation, we find that the equation in vertex form is y = 171(x + 7391/4) - 17113/4.
Explanation:To write the given equation in vertex form, we need to complete the square for the x terms. The vertex form of a quadratic equation is given by y = a(x-h)^2 + k, where (h, k) is the vertex of the parabola.
Let's rearrange the equation to isolate the x terms on one side and the y term on the other side: 162x + 9x + y = -731 - 2
Combine like terms: 171x + y = -733
Now, we can complete the square for the x terms. Divide the coefficient of x by 2 and square the result. Add this value to both sides of the equation: 171x + y + (171/2)^2 = -733 + (171/2)^2
Simplify: 171x + y + 7391/4 = 17113/4
Finally, we can rewrite the left side as a binomial squared and simplify the right side: 171(x + 7391/4) + y = 17113/4
Therefore, the equation in vertex form is: y = 171(x + 7391/4) - 17113/4
A school employs 30 teachers.how many will there be if there is a 10% reduction
If a school has 30 teachers and there is a 10% reduction, there will be 27 teachers remaining.
Explanation:If a school employs 30 teachers and there is a 10% reduction, we can calculate the number of teachers after the reduction by multiplying the initial number of teachers by (100% - 10%) = 90%. So, there will be 30 * 0.90 = 27 teachers after the reduction.
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Samuel order four did from an online music stores. Each dvd cost 9.99$. He has a 20% discount code and sales tax is 6.75%. What is the total cost of the order
multiply 4 by 9.99 for cost of the 4 dvd's
9.99 *4 = 39.96
20% discount is: 39.96 *0.20 = 7.99
39.96 - 7.99 = 31.97
now add the sales tax:
31.97 * 1.0675 = 34.13
total cost is $34.13
can anyone help me in pre-cal
tan^2 x = tan x
sin^2 x = sin x
P(4,13);Q(13,13) find the slope
Evaluate (1/2^-2) + 1/2
Find the greatest common factor of 36 and 72
Answer:
36
Step-by-step explanation:
36 is a factor of both numbers
_____
If the smaller divides the larger with no remainder, then the smaller number is the greatest common factor.
If there is a remainder, replace the larger number with that and repeat the process.
Which property is represented by the number sentence shown below?
6+(4+5) = (6+4)+5
A. Commutative property of multiplication
B. Associative property of addition
C. Commutative property of addition
D. Associative property of multiplication
If you can also explain how you got the I’ll appreciate it.
Which function has a vertex at the origin?
f(x) = (x + 4)^2
f(x) = x(x – 4)
f(x) = (x – 4)(x + 4)
f(x) = –x^2
Answer:
fdx = x-4 2
Step-by-step explanation:The test was right
in which number does the 6 have a value that is one tenth the value of the 6 in 34, 761
The 6 in 600 has a value one tenth the value of the 6 in 34, 761.
Explanation:The question asks in which number does the 6 have a value that is one tenth the value of the 6 in 34, 761.
To find the answer, we need to compare the place value of the 6 in both numbers. In 34, 761, the 6 is in the thousands place, and its value is 6,000. To have a value that is one tenth of 6,000, the 6 would need to be in the hundreds place in the other number.
So, the number in which the 6 has a value one tenth the value of the 6 in 34, 761 would be 600.
Final answer:
The number 6 in 2,001.06 is one-tenth the value of the 6 in 34,761.
Explanation:
The number 6 in 34,761 has a value that is one-tenth the value of the 6 in the number 2,001.06.
To find this, we can compare the place values of the two 6's. The 6 in 34,761 is in the ones place, while the 6 in 2,001.06 is in the tenths place.
Since the tenths place is one place to the right of the ones place, the value of the 6 in 2,001.06 is one-tenth the value of the 6 in 34,761.
Abe is going to plant 54 oak trees and 27 pine trees. Abe would like to plant the trees in rows that all have the same number of trees and are made up of only one type of tree. What is the greatest number of trees Abe can have in each row?
Answer:
27 trees in each row
Step-by-step explanation:
Abe is going to plant 54 oak trees and 27 pine trees
greatest number of trees Abe can have in each row =?
54 = 2 x 27
27 = 1 x 27
Now 27 is the common in both numbers and also is the greatest number
So, there are 2 rows of oak trees and 1 row of pine trees and all the rows have 27 number of trees.
Help Dana find the sum 346 421 152
For numbers 13a-13d, select yes or no to tell Dana when to regroup
Derivative of y = cos(x-1)/(x-1)
Answer:
[tex]\displaystyle y' = \frac{- \cos (x - 1)}{(x - 1)^2} - \frac{\sin (x - 1)}{x - 1}[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative 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 = \frac{\cos (x - 1)}{x - 1}[/tex]
Step 2: Differentiate
Derivative Rule [Quotient Rule]: [tex]\displaystyle y' = \frac{\Big( \cos (x - 1) \Big)'(x - 1) - \cos (x - 1)(x - 1)'}{(x - 1)^2}[/tex]Trigonometric Differentiation [Derivative Rule - Chain Rule]: [tex]\displaystyle y' = \frac{- \sin (x - 1)(x - 1)'(x - 1) - \cos (x - 1)(x - 1)'}{(x - 1)^2}[/tex]Basic Power Rule [Derivative Properties]: [tex]\displaystyle y' = \frac{- \sin (x - 1)(x - 1) - \cos (x - 1)}{(x - 1)^2}[/tex]Simplify: [tex]\displaystyle y' = \frac{- \cos (x - 1)}{(x - 1)^2} - \frac{\sin (x - 1)}{x - 1}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Can the leaves of an ordered rooted tree have the universal address 1.1, 1.2.1, 1.2.2, 1.2.3, 2.1, 2.2.1, 2.3.1, 2.3.2, 2.4.2.1, 2.4.2.2, 3.1, 3.2.1, 3.2.2? if so, identify such an ordered rooted tree.
a picnic start at 12:10 pm .kevin arrives at 1:40 pm the picnic continues until 3 pm.how much time elapsed betwwen the picinic and keven arrivals
Final answer:
To determine the time elapsed between the start of the picnic and Kevin's arrival, subtract the start time (12:10 pm) from Kevin's arrival time (1:40 pm), which results in 1 hour and 30 minutes.
Explanation:
To find out the amount of time that elapsed between the start of the picnic and Kevin's arrival, we subtract the start time of the picnic from the time Kevin arrived. The picnic started at 12:10 pm and Kevin arrived at 1:40 pm.
Step-by-step calculation:
Convert the times into a 24-hour format to avoid any confusion.12:10 pm is 12:10 in 24-hour format.There are 46 kids in the After-school Club. Today they're going to the pool at the Community Center. If each minivan can take 6 kids, they'll need 8 minivans for all the kids. Do you agree or disagree? Explain your thinking.
Alan is building a garden shaped like a rectangle with a semicircle attached to one short side. If he 21) has 20 feet of fencing to go around it, what dimensions will give him the maximum area in the garden?
Let the short side be W
The half circumference of the semi-circle = .5 * pi *W
2Lengths + width + semicircle = 20 ft
2L + W + (.5*pi*W) = 20
2L + W + 1.57W = 20
Combine like terms
2L + 2.57W = 20
Simplify divide by 2
L + 1.285W = 10
L = (10 - 1.285W); for substitution:
Get the area equation:
Rectangle area + semicircle area
A = L * W + (.5*pi*(.5W) ^2)
A = LW + (1.57*.25W^2)
A = LW + .3925W^2
Replace L with (10-1.285W)
A = W(10-1.285W) + .3925W^2
A = -1.285W^2 + .3925W^2 + 10W
A = -.8925W^2 + 10W
Find W by finding the axis of symmetry of this equation a=-.8925, b=10
W = -10 / 2 * (-.8925)
W = -10 / -1.785
W = 5.60 is the width for max area
then we solve for the length
L = 10 - 1.285(5.60)
L = 10 – 7.20 = 2.8 ft is the length
Then, Check the perimeter
2(2.8) + 5.60 + 1.57(5.60) = 20ft
5.6 + 5.6 + 8.736 = 20ft
Rectangle: 2.8 by 5.60 has semicircle circumference 8.736 has a maximum area: (2.8*5.60)
+ (.5 * pi * 2.8 ^ 2)
=15.68 + 12.31
=28 sq/ft
After a power failure, the temperature in a freezer increased an average rate of 2.5 Fahrenheit per hour. The total increase was 7.5 Fahrenheit. Right and solve any Quetion to find the number of hours until the power was restored.
A circle with a central that measures 1° has a radius of 10 inches. Find the length of the intercepted .
There is a value of $a$ such that subtracting $a-4$ from $4a+16$ gives an answer of $-25$. What is that value of $a$?
Answer:
a = -15
Step-by-step explanation:
Let's rewrite the exercise in math language.
We have to subtract a-4 from 4a+16 to get -25, that is
4a+16 - (a-4) = -25
The minus sign that is just before the parenthesis changes all the signs inside it. Therefore, if we want to delete the parenthesis, we need to change the signs before.
4a + 16 - a + 4 = -25
Now we can associate the terms with an a between them and the terms without it from the left side of the equation.
3a + 20 = -25
Let's subtract 20 on both sides.
3a + 20 - 20 = -25 - 20
3a = -45
Finally, we divide by 3 on both sides
3a/3 = -45/3
a = -15