Answer:
55.95 ft²
Step-by-step explanation:
Circumference formula: C = 2πr => r = C / (2π)
Area formula: A = πr²
Substituting C / (2π) for r in the above equation, we get:
C 47 ft
A = π( ----------- )² = π ( -------------- )²
2π (2π)
or ...
π(47 ft)² 2209 ft²
A = ---------------------- = -------------------- = 55.95 ft²
4π² 4(3.14159)²
A corporation must appoint a president, chief executive officer (CEO), chief operating officer (COO), and chief financial officer (CFO). It must also appoint a planning committee with five different members. There are 15 qualified candidates, and officers can also serve on the committee. Complete parts (a) through (c) below. There are nothing different ways to appoint the officers. b. How many different ways can the committee be appointed? There are nothing different ways to appoint the committee. c. What is the probability of randomly selecting the committee members and getting the five youngest of the qualified candidates? P(getting the five youngest of the qualified candidates)equals nothing (Type an integer or a simplified fraction.)
Answer:
(a) There are 32,760 different ways to appoint the officers.
(b) 3003 different ways can the committee be appointed.
(c) Probability of getting the five youngest of the qualified candidates is 0.00033.
Step-by-step explanation:
We are given that a corporation must appoint a president, chief executive officer (CEO), chief operating officer (COO), and chief financial officer (CFO). It must also appoint a planning committee with five different members.
There are 15 qualified candidates, and officers can also serve on the committee.
(a) The number of officers are 4, i.e; A president, chief executive officer (CEO), chief operating officer (COO), and chief financial officer (CFO).
There are 15 qualified candidates.
To find the number of ways to appoint the officers, we will use permutation because here the order of selecting the officer's matters.
So, the number of ways to appoint the officers = [tex]^{15}\text{P}_4[/tex]
= [tex]\frac{15!}{(15-4)!}[/tex] {[tex]\because ^{n}\text{P}_r = \frac{n!}{(n-r)!}[/tex] }
= [tex]\frac{15!}{11!}[/tex] = 32,760 ways
(b) The number of committee numbers to appoint include five members.
There are 15 qualified candidates.
To find the number of ways in which the committee can be appointed, we will use combination because here the order of selecting the members doesn't matter.
So, the number of ways to appoint the committee = [tex]^{15}\text{C}_5[/tex]
= [tex]\frac{15!}{5! \times (15-5)!}[/tex] {[tex]\because ^{n}\text{C}_r = \frac{n!}{r! \times (n-r)!}[/tex] }
= [tex]\frac{15!}{5! \times 10!}[/tex] = 3003 ways
(c) The probability of randomly selecting the committee members and getting the five youngest of the qualified candidates is given by;
Number of ways of selecting the committee = 3003
Selecting the five youngest of the qualified candidates = 1
So, the required probability = [tex]\frac{1}{3003}[/tex]
= 0.00033
A linear function has a slope of -7 /9 and a y-intercept of 3. How does this function compare to the linear function that is represented by the equation y + 11 = -7/9 (x minus 18)?
Answer:
both functions have the same graph
Step-by-step explanation:
The first function is described in terms of its slope and y-intercept, so can be written in slope-intercept form as ...
y = mx + b . . . . m = slope (-7/9); b = y-intercept (3)
y = -7/9x +3
__
The second function is written in point-slope form:
y -k = m(x -h) . . . . m = slope (-7/9), point = (h, k) = (18, -11)
y +11 = -7/9(x -18)
If we rearrange the second equation to the form of the first, we get ...
y = -7/9x +14 -11 . . . . eliminate parentheses, subtract 11
y = -7/9x +3 . . . . . . . matches the equation of the first function
__
Both functions describe the same relation.
ABC transforms to produce A’ B’C’ which transformation did NOT take place. A. Rotation 180° counterclockwise about the origin
B. Reflection across the origin
C. Rotation 180 clockwise about the origin
D. Reflection across the Line y=x
Please answer this correctly
Answer:
13 2/3 cm
Step-by-step explanation:
To find the perimeter, add up all the sides
2 1/2 + 3 1/3+ 4 1/2 + 3 1/3
Add up the whole numbers
2+3+4+3 = 12
Add up the fractions
1/2+1/3+1/2+1/3
2/2 + 2/3
1 +2/3
Put them together
12+1+2/3
13 2/3
Answer: 13 2/3 cm
Step-by-step explanation:
1. Turn mixed fractions into improper fractions:
2 1/2 = 5/2
3 1/3 = 10/3
3 1/3 = 10/3
4 1/2 = 9/2
2. Formula for perimeter: left side + right side + upper base + lower base
3. Put your numbers in replace: 10/3 + 10/3 + 5/2 + 9/2
4. Solve: 41/3
5. Simplify into mixed fraction: 41/3 = 13 2/3
6. Don't forget to add the unit!
Find in degrees the numeric value of the acute angle of rotation that eliminates the product term from the equation 7x2+24xy−34x+24y−185=07x2+24xy−34x+24y−185=0
Rotating the graph of [tex]Ax^2+Bxy+Cy^2+Dx+Ey+F=0[/tex] with [tex]B\ne0[/tex] counterclockwise by [tex]\theta[/tex] eliminates the [tex]xy[/tex] term, where [tex]\cot2\theta=\frac{A-C}{B}.[/tex] Plugging in, we have [tex]\cot2\theta=\frac{7}{24},[/tex] since [tex]C=0.[/tex] Solving, we have [tex]\theta=\frac{1}{2}\cot^{-1}(\frac{7}{24})\approx\boxed{36.9^\circ}.[/tex]
. In a sale, there is twenty-five per cent off all prices.
A chair costs £45 in the sale.
How much was it before the sale?
Answer:
€60
Step-by-step explanation:
€45 = 75%
100% (original) = (100/75)
[tex](100 \div 75) \times 45 = 60[/tex]
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
A. [tex]F(x) = (\frac{3}{4}x )^2-1[/tex]
Step-by-step explanation:
The correct answer is "A," because the function F(x), shifted downwards 1 unit. This means that the function has to have a -1 being subtracted. Note that when the number in front of x is less than one, the function widens. In this case, [tex]\frac{3}{4}[/tex] is less than one, making it grow bigger as shown on the graph above.
Four expressions are shown below which expression are equivalent A:10 (10 +5y) B:5(20x + 25y) C:5 (2x + y) D: 0.25(400x + 500y)
Answer:
Step-by-step explanation:
remove parentheses by multiplying factors.
use exponent rules to remove parentheses in terms with exponents.
combine like terms by adding coefficients.
combine the constants.
A hotel wants to know if there's a relationship between gender and the way customers make room reservations. A manager takes a random sample of 160 reservations. She records whether they were made by a man or a woman, and also records how the reservation was made. She gets the following data: Phone 28 Men Women Fax 9 12 Email 37 29 45 Perform a chi-square significance test of association with a = .05. Be sure to include your null and alternative hypotheses, a justification for the use of this test, your test statistic calculations, your P-value, and your conclusion.
Answer:
Step-by-step explanation:
Here,
H_o: The way of reservation is independent of gender.
H_a: The way of reservation is not independent of gender.
We use a chi square test because we can calculate the expected frequencies for this chart.
Doing an Expected Value Chart,
33.7625 9.7125 30.525
39.2375 11.2875 35.475
Using chi^2 = Sum[(O - E)^2/E],
chi^2 = 4.482385929
With df = (a - 1)(b - 1), where a and b are the number of categories of each variable,
a = 3
b = 2
df = 2
Thus, the critical value is
significance level = 0.05
chi^2(critical) = 5.991464547
Also, the p value is
P = 0.106331579
Thus, comparing chi^2 and chi^2(critical) [or, p and significance level], we FAIL TO REJECT THE NULL HYPOTHESIS.
Thus, there is no significant evidence that the way of reservation is dependent of gender. [CONCLUSION]
For each problem clearly describe the conditional distribution of each coordinate given the others. Then describe the procedure for running Gibbs sampling to sample from the joint distribution. Assume that Gibbs sampling works for continuous densities as well as discrete distributions. Guess the conditional from the structure of the joint distribution. Avoid doing integration as much as possible. Use your knowledge of the all the named one dimensional distributions/ densities.
a. Sample from the mixed joint pmf/pdf:
f(p, n) = p(1 - p)^-1, 0
Answer:
Step-by-step explanation:
The dot plots below show rainfall totals in the Highlands and Lowlands areas of a certain region.
Which statement comparing the shapes of the dot plots is true?
Options:
A. Both the Highlands and the Lowlands data points are evenly distributed around the center.
B. Both the Highlands and the Lowlands data points are clustered toward the left of the plot.
C. The Highlands data points are evenly distributed around the center, while the Lowlands data points are clustered toward the left of the plot.
D. The Highlands data points are clustered toward the left of the plot, while the Lowlands data points are evenly distributed.
Answer:
B. Both the Highlands and the Lowlands data points are clustered toward the left of the plot.
Step-by-step Explanation:
From the dot plots displaying rainfall totals for highland and lowland areas as shown in the diagram attached below, we can clearly observe that most of the dots on the plot tend to be more concentrated towards the left of the plot, compared to the concentration of dots toward the right of the plot.
Invariably, we can infer that data points for lowlands and Highlands are clustered toward the left of the plot.
Therefore, the statement that is true, comparing the shapes of the dot plot is B. "Both the Highlands and the Lowlands data points are clustered toward the left of the plot."
Answer:B
Step-by-step explanation: I took the edge quiz
daryl hit a home run 8 out of 32 times.if he is at bat 224 times how many home runs will he hit
Answer:
56 out of 224 times
Step-by-step explanation:
8 out of 32 = 1 out of 4
56 out of 224 = 1/4
Answer:56
Step-by-step explanation:
The zeros of the function p(x) = x2 – 2x– 24 are
1) -8 and 3
3) -4 and 6
2) -6 and 4
4) -3 and 8
Can u show work too
Answer:
3) -4 and 6
Step-by-step explanation:
I find it easiest to solve these by factoring. Here, you're looking for factors of the constant (-24) that have a sum equal to the coefficient of the linear term (-2). You know the divisors of 24 are ...
-24 = 1(-24) = 2(-12) = 3(-8) = 4(-6)
The sums of these factors are, respectively, -23, -10, -5, -2. So, the last pair of factors are the ones we're looking for. These are the constants that go into the binomial factors of the function:
p(x) = x^2 -2x -24
p(x) = (x +4)(x -6)
Then the zeros are the values of x that make these factors zero:
x +4 = 0 ⇒ x = -4
x -6 = 0 ⇒ x = 6
The zeros of the function are -4 and 6.
____
The graph of the function confirms these values.
Find the perimeter of the figure when l = 15 m, w = 9 m, x = 3 m, and y = 6 m
Answer:
54
Step-by-step explanation:15+15+9+9+3+3=54
plifying a Radical
Find the values for a, b, and c that complete the simplificatio
12.95
Y Z
12
y8 .y . z. z = x y z Syz
a =
I
b =
Answer: answer is D
Step-by-step explanation:
Answer: The correct answer is 6,4,2
Step-by-step explanation: Doing a 100 point giveaway stay tuned!
I need this asap
Rectangle ABCD is graphed in the coordinate plane. The following are the vertices of the rectangle:
A(2,-3) B(4, -3) C(4, 5) D(2,5)
What is the perimeter of the rectangle ABCD?
Answer:
20
Step-by-step explanation:
The rectangle is 2 x 8.
2 + 2 + 8 + 8 = 20
Perimeter=8+8+2+2
=20
orly uses 2 cups of raisins for every 12 cups of trail mix she makes. How many cups of trail mix will she make if she uses 8cups of raisins
Answer:
Step-by-step explanation:
48 cups of trail mix
A city doubles its size every 50 years. If the population is currently 500,000, what will the
population be in 200 years?
______ people?
Answer:
8,000,000 or 2,000,000
Step-by-step explanation:
For 8,000,000=
1st 50 years= 500,000+500,000= 1,000,000
2nd 50 years= 1,000,000+1,000,000= 2,000,000
3rd 50 years= 2,000,000+2,000,000= 4,000,000
4th 50 years= 4,000,000+4,000,000= 8,000,000
For 2,000,000=
200 years ÷ 50 years= 4
500,000×4= 2,000,000
I can't decide
What is the value of X?
The number of hours of daylight measured in one year in Ellenville can be modeled by a sinusoidal function. During 2006, (not a leap year), the longest day occurred on June 21 with 15.7 hours of daylight. The shortest day of the year occurred on December 21 with 8.3 hours of daylight. Write a sinusoidal equation to model the hours of daylight in Ellenville.
Answer:
[tex]f ( t ) = 3.7*sin ( 0.01736*t ) + 12[/tex]
Step-by-step explanation:
Solution:-
- We are to model a sinusoidal function for the number of hours of daylight measured in one year in Ellenville.
- We will express a general form of a sinusoidal function [ f ( t ) ] as follows:
[tex]f ( t ) = A*sin ( w*t ) + c[/tex]
Where,
A: The amplitude of the hours of daylight
w: The angular frequency of occurring event
c: The mean hours of daylight
t: The time taken from reference ( days )
- We are given that the longest day [ [tex]f ( t_m_a_x )[/tex] ] occurred on June 21st and the shortest day [ [tex]f ( t_m_i_n )[/tex] ] on December 21st.
- The mean hours of daylight ( c ) is the average of the maximum and minimum hours of daylight as follows:
[tex]c = \frac{f(t_m_a_x ) +f(t_m_i_n ) }{2} \\\\c = \frac{15.7 + 8.3}{2} = \frac{24}{2} \\\\c = 12[/tex]
- The amplitude ( A ) of the sinusoidal function is given by the difference of either maximum or minimum value of the function from the mean value ( c ):
[tex]A = f ( t_m_a_x ) - c\\\\A = 15.7 - 12\\\\A = 3.7[/tex]
- The frequency of occurrence ( w ) is defined by the periodicity of the function. In other words how frequently does two maximum hours of daylight occur or how frequently does two minimum hours of daylight occur.
- The time period ( T ) is the time taken between two successive maximum duration of daylight hours. We were given the longest day occurred on June 21st and the shortest day occurred on December 21st. The number of days between the longest and shortest day will correspond to half of the time period ( 0.5*T ):
[tex]0.5*T = 7 + 31 + 31 + 30 +31 +30 +21\\\\T = 2* [ 181 ] \\\\T = 362 days[/tex]
- The angular frequency ( w ) is then defined as:
[tex]w = \frac{2\pi }{T} = \frac{2\pi }{362} \\\\w = 0.01736[/tex]
- We will now express the model for the duration of daylight each day as function of each day:
[tex]f ( t ) = 3.7*sin ( 0.01736*t ) + 12[/tex]
What is the value of y?
Answer:
65
Step-by-step explanation:
The exterior angle is equal to the sum of the opposite interior angles
130 = y+y
130 = 2y
Divide by 2
130/2= 2y/2
65=y
Answer:
D. 65
Step-by-step explanation:
I agree with the above reasoning
The value of homes in Baltimore, Maryland is dropping by 2.5% each month. If a house
costs $215,000 now, how much is it expected to be worth in 6 months
Answer:
The house will be worth $184,699.6847 in 6 months.
Step-by-step explanation:
Since the cost of the houses is dropping by 2.5 % per month, then it is decreasing exponentially and can be modeled by the following formula:
[tex]cost(x) = 215000*(1 - \frac{2.5}{100})^t\\cost(x) = 215000*(1 - 0.025)^t\\cost(x) = 215000*(0.975)^t\\[/tex]
After 6 months:
[tex]cost(6) = 215000*(0.975)^6\\cost(6) = 184699.6847[/tex]
The house will be worth $184,699.6847 in 6 months.
At 5 \text{ p.m.}5 p.m.5, start a text, space, p, point, m, point, end text, the temperature is halfway between the temperature at 2 \text{ p.m.}2 p.m.2, start a text, space, p, point, m, point, end text and the temperature at 8 \text{ p.m.}8 p.m.8, start a text, space, p, point, m, point, end text
What coordinates represent the temperature at 5 \text{ p.m.}5 p.m.5, start a text, space, p, point, m, point, end text?
Answer:
(5,2)
Step-by-step explanation:
From the graph attached below:
The coordinate for the temperature (in degree Celsius) at 2 p.m. is (2,7) The coordinate for the temperature (in degree Celsius) at 8 p.m. is (8,-3)Since the temperature at 5 p.m. is halfway between the temperature at 2 p.m. and 8 p.m. , the coordinate of the temperature at 5 p.m. is the midpoint of (2,7) and (8,-3).
For two coordinate points [tex]A(x_1,y_1)$ and B(x_2,y_2)[/tex]
[tex]\text{Midpoint of AB }=\dfrac{1}{2} \left( x_1+x_2,y_1+y_2 \right)[/tex]
Therefore, the coordinates for 5p.m.
[tex]=\dfrac{1}{2} \left( 2+8,7+(-3) \right) \\=\dfrac{1}{2} \left( 10,4 \right)\\\\=(5,2)[/tex]
A firm can produce only 2500 units per month. The monthly total cost is given by C(x) = 400 + 200x dollars, where x is the number produced. If the total revenue is given by R(x) = 350x − 1 100 x2 dollars, how many items, x, should the firm produce for maximum profit?
Answer:
2500
Step-by-step explanation:
Monthly total cost, C(x) = 400 + 200x dollars
Monthly total revenue, R(x) = [tex]350x -\dfrac{1}{100}x^2[/tex] dollars
Profit = Revenue - Cost
[tex]=R(x)-C(x)\\=(350x -\dfrac{1}{100}x^2)-(400 + 200x)\\=350x -\dfrac{1}{100}x^2-400 - 200x\\P(x)=150x-\dfrac{1}{100}x^2-400[/tex]
To determine how many items, x, the firm should produce for maximum profit, we maximize P(x) by taking its derivative and solving for its critical points.
[tex]P(x)=150x-\dfrac{1}{100}x^2-400\\P'(x)=150-\dfrac{x}{50}\\\\$Set $ P'(x)=0\\150-\dfrac{x}{50}=0\\150=\dfrac{x}{50}\\$Cross multiply\\x=150*50\\x=7500[/tex]
Next, we check if the point x=7500 is a maxima or a minima.
To do this, we find the second derivative of P(x).
[tex]P''(x)=-\dfrac{1}{50} $ which is negative[/tex]
Hence, the point x=7500 is a point of maxima. However, since the firm can only produce 2500 units per month.
Therefore, the company needs to produce 2500 units to maximize profit.
What are two decimals equivalent to 9.60
Answer:
9.600
9.6
Step-by-step explanation:
These two decimals above are equivalent to 9.60 because no matter the amount of zeroes there are, as long as the numbers before the zeroes maintain the same location (in this case, ones and tens place) the decimals will be equivalent. For example, 9.60 is also equivalent to 9.600000000000000000000000...
In the diagram provided line L is parallel to line M. Select which of the following statements could be used to prove that the interior angles of a triangle have a sum of 180°. You may choose More than one correct answer
Answer:
1 and 4 are alternate interior angles.
m5 + m1 = 180
m5 = m3 + m2
Question:
The complete version of your question as found in other site is stated below:
In the diagram provided, line l is parallel to line m. Select which of the following statements could be used to prove that the interior angles of a triangle have a sum of 180°. You may choose more than one correct answer.
1 and 4 are alternate interior angles.
m4 + m5 + m6 = 180.
m5 + m1 = 180.
m5 = m3 + m2
Step-by-step explanation:
Given: line l is parallel to line m
We need prove that the interior angles of a triangle have a sum of 180°. In order to do that, the angles in the triangle = 180°
∠1 + ∠2 + ∠3 = 180°
Alternate angles:
∠1 = ∠4
∠6 = ∠2
∠5 = ∠3 + ∠6
Checking the options and inserting the values above in them:
a) 1 and 4 are alternate interior angles
∠1 = ∠4
This gives one of the side of the interior angles. The alternate angles enables us to find the sum of the interior angles. It is correct
b) m4 + m5 + m6 = 180
∠4 + ∠5 + ∠6 = 180°
∠1 + (∠3 + ∠6) + ∠2 = 180°
The above option wont give ∠1 + ∠2 + ∠3 = 180°. Hence it is wrong.
c) m5 + m1 = 180
(∠3 + ∠6) + ∠1 = 180°
∠5 = (∠3 + ∠6) = ∠3 + ∠2
∠3 + ∠2 + ∠1 = 180°
This option is correct
d) m5 = m3 + m2
∠5 = ∠3 + ∠2
From the diagram, ∠5 + ∠1 = 180° (angles on a straight line)
∠5 = ∠3 + ∠2
This option can be used to get sum of interior angles.
Staples sells boxes of pens ($10) and rubber bands ($5). Leona ordered a total of 24 cartons for $200. How many boxes of each did Leona order? Hint: Let P = Pens.
Answer:
number of box of pen = 16
number of box of ribbon bands = 8
Step-by-step explanation:
Let
number of boxes of pen = p
number of boxes of rubber bands = r
He ordered 24 boxes of both items. Therefore,
p + r = 24...............(i)
The total cost of what he ordered is $200 . Therefore,
10p + 5r = 200.......(ii)
combine the equations
p + r = 24...............(i)
10p + 5r = 200.......(ii)
from equation (i)
p = 24 - r
insert the value of p in equation (ii)
10(24 - r) + 5r = 200
240 - 10r + 5r = 200
240 - 200 = 5r
40 = 5r
divide both sides by 5
r = 40/5
r = 8
insert the value of r in equation(i)
p + 8 = 24
p = 24 - 8
p = 16
number of box of pen = 16
number of box of ribbon bands = 8
The general form of a circle is given as x^2+y^2+4x-10y-7=0.
What are the coordinates of the center of the circle?
What is the length of the radius of the circle?
Answer:
center: (-2, 5)radius: 6Step-by-step explanation:
We can complete the squares of the x- and y-terms by adding the square of half the linear term coefficient.
(x^2 +4x) +(y^2 -10y) = 7
(x^2 +4x +4) +(y^2 -10x +25) = 7 + 4 + 25
(x +2)^2 +(y -5)^2 = 6^2
Compare to ...
(x -h)^2 +(y -k)^2 = r^2 . . . . . standard form equation of a circle
We see that the center is ...
(h, k) = (-2, 5)
and the radius is ...
r = 6
What is imaginary 34
Answer:
raising a number to the 34th power
Step-by-step explanation:
What’s the correct answer for this question?
Answer:
[tex] \frac{11}{24} [/tex]
Answer:
D. 11/24
Step-by-step explanation:
Total students' reading preferences = 240
Using electronic device = 110
Probability of having electronic device = 110/240
= 11/24
