a. ~0.442, b. ~0.221, c. 0, d. ~0.221. Calculated using combinations: [tex]\( \frac{C(n, k)}{C(12, 5)} \)[/tex].
To solve this problem, we can use the concept of combinations, which is a way to calculate the number of possible outcomes when order doesn't matter.
Let's define:
- [tex]\( n \)[/tex] as the total number of finalists (12 in this case)
- [tex]\( k \)[/tex] as the number of positions to be filled (5 in this case)
- [tex]\( n_F \)[/tex] as the number of female finalists (7 in this case)
- [tex]\( n_M \)[/tex] as the number of male finalists (5 in this case)
We'll use the formula for combinations:
[tex]\[ C(n, k) = \frac{n!}{k!(n - k)!} \][/tex]
where [tex]\( n! \)[/tex] represents the factorial of [tex]\( n \)[/tex], which is the product of all positive integers up to [tex]\( n \)[/tex].
a. Probability of selecting 3 females and 2 males:
[tex]\[ P(3 \text{ females, } 2 \text{ males}) = \frac{C(7, 3) \times C(5, 2)}{C(12, 5)} \][/tex]
[tex]\[ = \frac{\frac{7!}{3!4!} \times \frac{5!}{2!3!}}{\frac{12!}{5!7!}} \][/tex]
[tex]\[ = \frac{\frac{7 \times 6 \times 5}{3 \times 2 \times 1} \times \frac{5 \times 4}{2 \times 1}}{\frac{12 \times 11 \times 10 \times 9 \times 8}{5 \times 4 \times 3 \times 2 \times 1}} \][/tex]
[tex]\[ = \frac{35 \times 10}{792} \][/tex]
[tex]\[ = \frac{350}{792} \][/tex]
[tex]\[ \approx 0.442\][/tex]
b. Probability of selecting 4 females and 1 male:
[tex]\[ P(4 \text{ females, } 1 \text{ male}) = \frac{C(7, 4) \times C(5, 1)}{C(12, 5)} \][/tex]
[tex]\[ = \frac{\frac{7!}{4!3!} \times \frac{5!}{1!4!}}{\frac{12!}{5!7!}} \][/tex]
[tex]\[ = \frac{\frac{7 \times 6 \times 5}{3 \times 2 \times 1} \times \frac{5}{1}}{\frac{12 \times 11 \times 10 \times 9 \times 8}{5 \times 4 \times 3 \times 2 \times 1}} \][/tex]
[tex]\[ = \frac{35 \times 5}{792} \][/tex]
[tex]\[ = \frac{175}{792} \][/tex]
[tex]\[ \approx 0.221\][/tex]
c. Probability of selecting 5 females:
Since there are only 7 female finalists, it's impossible to select 5 females out of them for 5 positions. So, the probability is 0.
d. Probability of at least 4 females:
This includes the cases of selecting 4 females and 5 females.
[tex]$\begin{aligned} & P(\text { at least } 4 \text { females })=P(4 \text { females, } 1 \text { male })+P(5 \text { females }) \\ & =\frac{175}{792}+0 \\ & =\frac{175}{792} \\ & \approx 0.221\end{aligned}$[/tex]
So, the probabilities are:
a. Approximately 0.442
b. Approximately 0.221
c. 0
d. Approximately 0.221
In a typical start for his baseball team, Rick throws 120 total pitches with a ratio of 3 fastballs thrown for every 2 curveballs. If Rick makes a relief appearance of 30 pitches using the same ratio, how many fastballs will he throw in the relief appearance?
Answer:
18 fastballs
Step-by-step explanation:
Let x represent each throw
fastball : curve ball = 3:2
For fastball we have 3x while for curve ball we have 2x
If Rick makes a relief appearance of 30 pitches with the same ratio,
3x + 2x = 30
5x = 30
x = 30/5
x = 6
fastball, 3x= 3*6
= 18
curveball = 2x = 2*6
= 12
Rick will throw 18 fast balls
At the beginning of the year, a sporting goods store had $250,000 worth of inventory. The store’s buyers purchased an additional $115,000 worth of inventory during the year. At year’s end, the value of the inventory was $185,000. What was the store’s cost of goods sold?
Answer:
180000
Step-by-step explanation:
Which statements are true about the ordered pair (−4, 0) and the system of equations?
{2x+y=−8
x−y=−4
Select each correct answer.
The ordered pair (−4, 0) is a solution to the first equation because it makes the first equation true.
The ordered pair (−4, 0) is a solution to the second equation because it makes the second equation true.
The ordered pair (−4, 0) is not a solution to the system because it makes at least one of the equations false.
The ordered pair (−4, 0) is a solution to the system because it makes both equations true.
Answer:
first, second, and fourth are correct
Step-by-step explanation:
2(-4) + 0 = -8; this is correct because -8 + 0 = -8
(-4) - 0 = -4; this is correct because -4 - 0 = -4
We know that they are both true, so the fourth choice is true as well.
Statements first, second, and fourth are true about the ordered pair (−4, 0) and the system of equations, 2x+y=−8 and x−y=−4.
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
It is given that,
2x+y=−8
x−y=−4
The correct statements for the ordered pair (−4, 0) are,
Because it makes the first equation true, the ordered pair (4, 0) is a solution to the first equation.
⇒2(-4) + 0 = -8
⇒-8 + 0 = -8
Because it makes the second equation true, the ordered pair (4, 0) is a solution to the second equation.
⇒(-4) - 0 = -4
⇒-4 - 0 = -4
The ordered pair (4, 0) makes both equations true, making it a solution to the problem.
Thus, statements first, second, and fourth are true about the ordered pair (−4, 0) and the system of equations, 2x+y=−8 and x−y=−4.
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Look at the graph of this system of equations: y = - x2 + 1 and y = x2. At which approximate points are the two equations equal? There more than one answer.
A.(-0.7, 0.5)
B.(0.5, 0.7)
C.(0.7, 0.5)
D.(-0.5, 0.7)
Answer:
option A and C, (-0.7, 0.5) and (0.7, 0.5)
Step-by-step explanation:
The two equations are equal means, the points at which the two graphs meet.
In that case the x and y coordinates satisfy both the graphs.
let the coordinates at the intersection point be (a,b).
Inserting in first equation,
[tex]b = -a^{2} + 1[/tex]
Inserting in second equation,
[tex]b = a^{2}[/tex]
Inserting value of b from second to first equation, we get
[tex]b = -b + 1[/tex]
[tex]b = \frac{1}{2} = 0.5[/tex]
Now inserting the value of b second equation, we get
[tex]\frac{1}{2} = x^{2}[/tex]
[tex]x = \sqrt{\frac{1}{2} } = +\frac{1}{1.414} or -\frac{1}{1.414} = +0.7 or -0.7[/tex]
Thus points are, (-0.7, 0.5) and (0.7, 0.5)
What is the value of h for the parallelogram?
Answer:
9.6 units
Step-by-step explanation:
The area of the parallelogram is the product of the base length and distance between parallel sides, either way you figure it.
16 × 6 = area = 10 × h
96 = 10h
h = 96/10 = 9.6 . . . . units
Find the values of x and y using trig
Answer:
Step-by-step explanation:
The triangle is a right angle triangle. This is because one of its angles is 90 degrees.
Let us determine x
Taking 47 degrees as the reference angle,
x = adjacent side
11 = hypotenuse
Applying trigonometric ratio,
Cos # = adjacent side / hypotenuse
# = 47 degrees
Cos 47 = x/11
x = 11cos47
x = 11 × 0.6820
x = 7.502
Let us determine y
Taking 47 degrees as the reference angle,
y = opposite side
11 = hypotenuse
Applying trigonometric ratio,
Sin # = opposite side / hypotenuse
# = 47 degrees
Sin 47 = y/11
x = 11Sin47
x = 11 × 0.7314
x = 8.0454
How many terms are in this equation?
Answer:
2
Step-by-step explanation:
Terms are products separated by +'s and −'s. Here, there are 2 terms:
2 tan(1/t) / (1/t)
sec²(1/t)
Owen earns a base salary plus a commission that is a percent of his total sales. His total weekly pay is described by f(x)=0.15x+325, where x is his total sales in dollars. What is the change in Owen's salary plan if his total weekly pay function changes to g(x)=0.20+325?
Answer:
0.05x
This is equivalent to 5% of the total amount of sales.
Step-by-step explanation:
Previous Weekly pay function for Owen; f (x) = 0.15x +325-------------------- (1)
Current Weekly pay function for Owen; g(x) = 0.20x +325--------------------(2)
Change in Owen's Salary plan is equation (2) minus equation (1)
g(x) - f(x) = (0.20x+325)-(0.15x+325)
= 0.05x
The new change in Owen's salary is 5% of the total amount of sales
Kylie explained that (negative 4 x + 9) squared will result in a difference of squares because (negative 4 x + 9) squared = (negative 4 x) squared + (9) squared = 16 x squared + 81. Which statement best describes Kylie’s explanation?
Answer:
C. Kylie did not understand that this is a perfect square trinomial, and she did not determine the product correctly.
just passed on edge-nuity
Step-by-step explanation:
Kylie's explanation is incorrect. The simplified expression for (negative 4x + 9) squared is 16x squared - 72x + 81.
Explanation:Kylie's explanation is incorrect.
The statement that (negative 4x + 9) squared results in a difference of squares is incorrect.
To simplify (negative 4x + 9) squared, we need to multiply the expression by itself. Using the formula (a + b) squared = a squared + 2ab + b squared, we can expand (negative 4x + 9) squared as follows:
(negative 4x + 9) squared = (negative 4x) squared + 2(negative 4x)(9) + (9) squared
= 16x squared - 72x + 81
So, the correct simplification of (negative 4x + 9) squared is 16x squared - 72x + 81, not 16x squared + 81.
A stretch of highway that is 12 1 4 12 4 1 12, start fraction, 1, divided by, 4, end fraction kilometers long has speed limit signs every 7 8 8 7 start fraction, 7, divided by, 8, end fraction of a kilometer. How many speed limit signs are on this stretch of highway?
Answer:
7
Step-by-step explanation:
Answer:
its 14 signs
Step-by-step explanation:
A jar contains 800 red and green jelly beans. Of those, 320 are red and the rest are green. What is the ratio of red and green jelly beans?
Answer:
The ratio is 2 to 3.
Step-by-step explanation:
The jar is comprised of only red and green jelly beans. We are given the number of total beans and the number of red beans. We calculate the number of green beans by doing 800-320 = 480.
The problem is asking for the ratio of red to green jelly beans, which is 320 to 480, or 320/480. Simplified, this is 2/3.
The ratio of red to green jellybeans will be 1/3.
What are ratios and proportion?Ratio is a quantitative relation between two amounts showing the number of times one value contains or is contained within the other. A statement expressing the equality of two ratios A:B and C:D is called a proportion. We can express proportion as -
A : B ∷ C : D
AND
A x D = B x C
Product of extremes equal to product of means
We have a jar that contains 800 red and green jelly beans. Of those, 320 are red and the rest are green.
Number of red beans = 320
Number of green jelly beans = 800 - 320 = 480
Ratio of red to green jellybeans = 320/480 = 1/3
Therefore, the ratio of red to green jellybeans will be 1/3.
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Shawn bought fruit last week, consisting of 2.26 pounds of bananas, 1.5 pounds of grapes, and a watermelon that weighed 6.78 pounds. What is the total weight, in pounds, of the fruit that Shawn bought last week?
Answer:
10.54 pounds is right answer
Step-by-step explanation:
bananas 2.26 pounds
Grapes 1.5 pounds
water melon 6.78 pounds
total weight = 10.54 pounds
Answer:
10.54 pounds
Step-by-step explanation:
An inspector inspects large truckloads of potatoes to determine the proportion p in the shipment with major defects prior to using the potatoes to make potato chips. If there is clear evidence that this proportion is less than 0.10, she will accept the shipment. To reach a decision, she will test the hypotheses H0: p = 0.10, Ha: p < 0.10. To do so, she selects a simple random sample of 150 potatoes from the more than 3000 potatoes on the truck. Only eight of the potatoes sampled are found to have major defects. What is the value of the large-sample z test statistic?
Answer: z=1.9065
Step-by-step explanation:
As per given , we have
[tex]H_0: p=0.10\\\\ H_a: p<0.10[/tex]
Sample size : n= 150
No. of potatoes sampled are found to have major defects = 8
The sample proportion of potatoes sampled are found to have major defects :
[tex]\hat{p}=\dfrac{8}{150}=0.0533[/tex]
The test statistic for population proportion is given by :-
[tex]z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}\\\\ [/tex] , where p=population proportion.
n= sample size.
[tex]\hat{p}[/tex] = sample proportion.
[tex]z=\dfrac{0.0533-0.10}{\sqrt{\dfrac{0.10\times0.90}{150}}}\\\\=\dfrac{-0.0467}{0.02449}\\\\=-1.90651951647\approx1.9065[/tex]
Hence, the value of the large-sample z test statistic is z=1.9065 .
There are 24 basketball teams competing in a tournament. After each round half the teams are eliminated. This situation can be modeled by the function
Answer:
b(x)=24(1/2)x
Step-by-step explanation:
The situation can be modeled by the exponential function will be y = 24 (0.5)ˣ.
What is an exponent?Let a be the initial value and x be the power of the exponent function and b be the increasing factor.
The exponent is given as
y = a(b)ˣ
There are 24 ball groups contending in a competition. After each round around 50% of the groups is dispensed with.
Then the value of the b will be 1/2 and the value of the variable 'a' will be 24. Then the exponential equation is given as,
y = 24 (1/2)ˣ
y = 24 (0.5)ˣ
The situation can be modeled by the exponential function will be y = 24 (0.5)ˣ.
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A recipe Uses 1 1/4 cups of milk to make 10 servings if the same amount of milk is used for each serving how many servings can be made using one gallon of milk
Answer:
128
Step-by-step explanation:
There are a couple of ways to go at this. One is to use a proportion:
(10 servings)/(1.25 cups) = (x servings)/(16 cups)
160/1.25 = x = 128 . . . . . . . multiply by 16 and simplify
1 gallon of milk will make 128 servings.
__
Another way to go at this is to figure out how much milk is used in one serving. It is ...
1.25 cups/(10 servings) = 0.125 cups/serving = 1/8 cup/serving
Now, you can work with several different conversion factors:
1 cup = 8 oz
1 gal = 128 oz
1 gal = 16 cups
Obviously 1/8 cup is 1 oz. Since there are 128 oz in a gallon, the gallon will make 128 servings.
__
Or, you can divide 16 cups by (1/8 cup/serving) to find the number of servings:
(16 cups/gal)/(1/8 cup/serving) = 16·8 servings/gal = 128 servings/gal
Answer:
128
Step-by-step explanation:
I can do math yay
Help please??.... I don’t understand
Answer:
0.50 m²9.8 in²Step-by-step explanation:
Whole Circle
The formula for the area of a circle is ...
A = πr² . . . . . where r is the radius and π is the value given
The radius of the circle is half the diameter, so is 0.4 m. Putting the numbers into the formula, we get ...
A = (314)(0.4 m)² = 0.5024 m²
Rounding to the nearest tenth, the area is ...
0.5 m²
__
Area of Sector CTM
As above, the area of the circle is ...
A = πr² = (3.14)(3 in)² = 28.26 in²
A whole circle has a central angle of 360°. The sector of interest has a central angle of 125°, so its area is the fraction 125/360 of the area of the whole circle.
sector area = (125/360)(28.26 in²) = 9.8125 in²
Rounding to the nearest tenth, the sector area is ...
9.8 in²
The sum of the ages of Berma, her mother Rinna and her father Erwin is 80. Two years from now, Rinna’s age will be 13 less than the sum of Erwin’s age and twice Berma’s age. Three years ago, 15 times Berma’s age was 5 less than the age of Rinna. How old are they now?
Answer: Berma is 5 years old
Rinna is 38 years old
Erwin is 37 years old
Step-by-step explanation:
Let x represent Berma's age
Let y represent Rinna's age
Let z represent Erwin's age
Since the sum of their ages is 80,
x + y + z = 80 - - - - - - -1
Two years from now, Rinna’s age will be 13 less than the sum of Erwin’s age and twice Berma’s age. This means that
y +2 = [ (z+2) + 2(x+2) ] - 13
y +2 = z + 2 + 2x + 4 - 13
2x - y + z = 13 + 2 - 4 -2
2x - y + z = 9 - - - - - - -2
Three years ago, 15 times Berma’s age was 5 less than the age of Rinna. It means that
15(x - 3) = (y - 3) - 5
15x - 45 = y - 3 - 5
15x - y = - 8 + 45
15x - y = 37 - - - - - - - -3
From equation 3, y = 15x - 37
Substituting y = 15x - 37 into equation 1 and equation 2, it becomes
x + 15x - 37 + z = 80
16x + z = 80 + 37 = 117 - - - - - - 4
2x - 15x + 37 + z = 9
-13x + 2 = -28 - - - - - - - - -5
subtracting equation 5 from equation 4,
29x = 145
x = 145/29 = 5
y = 15x - 37
y = 15×5 -37
y = 38
Substituting x= 5 and y = 38 into equation 1, it becomes
5 + 38 + z = 80
z = 80 - 43
z = 37
In a game of poker a hand of five cards is dealt to each player from a deck of 52 cards. find the probablility of a hand containing a spade flush.
Answer:
0.00597
Step-by-step explanation:
Given,
Total number of cards = 52,
In which flush cards = 20,
Also, the number of spade flush cards = 5,
Since,
[tex]\text{Probability}=\frac{\text{Favourable outcomes}}{\text{Total outcomes}}[/tex]
Thus, the probability of a hand containing a spade flush, if each player has 5 cards
[tex]=\frac{\text{Ways of selecting a spade flush card}}{\text{Total ways of selecting five cards}}[/tex]
[tex]=\frac{^{20}C_5}{^{52}C_5}[/tex]
[tex]=\frac{\frac{20!}{5!15!}}{\frac{52!}{5!47!}}[/tex]
[tex]=\frac{15504}{2598960}[/tex]
= 0.00597
Find the positive number such that the sum of 8 times this number and 7 times its reciprocal is as small as possible.
Answer:
√56/8
Step-by-step explanation:
Let the number be x
f(x) = 8x + 7(1/x)
f(x) = 8x + 7/x
Differentiate f(x) with respect to x
f'(x) = 8x - 7/x = 0
8 - 7/x^2 = 0
(8x^2 - 7)/2 = 0
8x^2 - 7 = 0
8x^2 = 7
x^2 = 7/8
x = √7/8
x = √7 /√8
x = (√7/√8)(√8/√8)
x = (√7*√8) / √8*√8)
x = √56/8
the volume of a cylindrical can is 500cm^3. The materail used to make the top and bottom costs 0.012 cent/cm^2 the material used for the sides costs 0.01 cent?cm^2, and the seam joining the top and bottom to the sides costs .015 cent/cm. what size can would cost the least to produce?
Answer:
radius: 3.671 cmheight: 11.810 cmStep-by-step explanation:
The total cost of producing a cylindrical can with radius r and height h will be ...
cost = (lateral area)×(side cost) +(end area)×(end cost) +(seam length)×(seam cost)
__
The lateral area (LA) is ...
LA = 2πrh
Since the volume of the can is fixed, we can write the height in terms of the radius using the volume formula.
V = πr²h
h = V/(πr²)
Then the lateral area is ...
LA = 2πr(V/(πr²)) = 2V/r = 2·500/r = 1000/r
__
The end area (EA) is twice the area of a circle of radius r:
EA = 2×(πr²) = 2πr²
__
The seam length (SL) is twice the circumference of the end:
SL = 2×(2πr) = 4πr
__
So, the total cost in cents of producing the can, in terms of its radius, is ...
cost = (1000/r)(0.01) +(2πr²)(.012) +(4πr)(0.015)
We can find the minimum by setting the derivative to zero.
d(cost)/dr = -10/r² +0.048πr +.06π = 0
Multiplying by r² gives the cubic ...
0.048πr³ +0.06πr² -10 = 0
r³ +1.25r² -(625/(3π)) = 0 . . . . . . divide by .048π
This can be solved graphically, or using a spreadsheet to find the value of r to be about 3.671 cm. The corresponding value of h is ...
h = 500/(π·3.671²) ≈ 11.810 . . . cm
The minimum-cost can will have a radius of about 3.671 cm and a height of about 11.810 cm.
_____
A graphing calculator can find the minimum of the cost function without having to take derivatives and solve a cubic.
Based on the Polynomial Remainder Theorem what is the value of the function below when x = 3.
Answer:
Remainder = 64
Step-by-step explanation:
Given equation,
[tex]x^4+3x^3-6x^2-12x-8[/tex]
Remainder theorem says a polynomial can be reset in terms of its divisor (a) by evaluating the polynomial at x=a
Plug x=3,
[tex]=3^4+3(3)^3-6(3)^2-12(3)-8\\=81+81-54-36-8\\=162-54-36-8\\=64[/tex]
Thus the remainder is 64 at x=3 ,using polynomial remainder theorem.
How would I solve this?
Answer:
It is rotated by 72 degrees.
Step-by-step explanation:
Since it is a regular polygon,when u connect all the corners of it to the middle of the polygon, they will meet at a point i.e, CENTER.
The sum of the angles subtended by all the sided at the center will be 360 degrees.As there are 60 sides, the angle subtended by each side at the center will be 6 degrees.Because,
[tex]\frac{360}{60} = 6[/tex]
As the polygon rotates every minute and it is rotated for 12 minutes,[tex]12*6 = 72[/tex]
( For every minute, it will be rotated by 6 degrees.
so, for 12 minutes it should be rotated by 12 times 6 ( 12*6) = 72 degrees)
So, after 12 minutes it will be rotated by 72 degrees.A boat leaves the entrance to a harbor and travels 150 miles on a bearing of Upper N 56 degrees Upper E. How many miles north and how many miles east from the harbor has the boat traveled?
Answer:
83.9 miles north124.4 miles eastStep-by-step explanation:
It can be helpful to draw a diagram. In the attached diagram, point H represents the harbor, point B represents the position of the boat, and point N represents a point directly north of the harbor and west of the boat.
The bearing N56E means the direction of travel is along a path that is 56° clockwise (toward the east) from north.
__
The mnemonic SOH CAH TOA reminds you of the relationships between the sides of a right triangle. Here, we are given the length of the hypotenuse, and we want to know the lengths of the sides opposite and adjacent to the angle. One of the useful relations is ...
Sin = Opposite/Hypotenuse
In our diagram, this would be ...
sin(56°) = BN/BH
We want to find length BN, so we can multiply by BH to get ...
BN = BH·sin(56°) = 150·0.829038 = 124.4 . . . . miles (east)
__
For the adjacent side, we use the relation ...
Cos = Adjacent/Hypotenuse
cos(56°) = HN/HB
HN = HB·cos(56°) = 150·0.559193 = 83.9 . . . . miles (north)
The boat has traveled 124.4 miles north and 83.9 miles east of the harbor entrance.
Mikayla is a waitress who makes a guaranteed $50 per day in addition to tips of 20% of all her weekly customer receipts, t. She works 6 days per week. Which of the following functions best represents the amount of money that Mikayla makes in one week?
A) f(t) = 50 + 20t
B) f(t) = 300 + 20t
C) f(t) = 50 + 0.2t
D) f(t) = 300 + 0.2t
Answer:
D. [tex]f(t)=300+0.20t[/tex]
Step-by-step explanation:
We have been given that Mikayla is a waitress who makes a guaranteed $50 per day.
Since Miklaya works 6 days per week, so the guaranteed income for one week would be [tex]\$50\times 6=\$300[/tex]
We are also told that she gets tips of 20% of all her weekly customer receipts, t. So amount earned from tips would be 20% of t, that is [tex]\frac{20}{100}t=0.20t[/tex].
Total amount earned in one week would be guaranteed income for 1 week plus 20% of t:
[tex]300+0.20t[/tex]
Therefore, our required function is [tex]f(t)=300+0.20t[/tex] and option D is the correct choice.
This Venn diagram shows the pizza topping preferences for 9 students. Let event A = The student likes pepperoni. Let event B = The student likes olives. What is P(A or B)?
Answer:
[tex]P(A\ or\ B)=\frac{7}{9}[/tex]
Step-by-step explanation:
We need to use the formula to calculate the probability of (A or B) where
A=Probability a student likes pepperoni
B=Probability a student likes olive
A and B =Probability a student likes both toppings in a pizza
A or B =Probability a student likes pepperoni or olive (and maybe both), a non-exclusive or
The formula is
[tex]P(A\ or\ B)=P(A)+P(B)-P(A\ and\ B)[/tex]
Since 6 students like pepperoni out of 9:
[tex]P(A) = \frac{6}{9}[/tex]
Since 4 students like olive out of 9:
[tex]P(B) = \frac{4}{9}[/tex]
Since 3 students like both toppings out of 9
[tex]P(A\ and\ B) = \frac{3}{9}[/tex]
Then we have
[tex]P(A\ or\ B)=\frac{6}{9}+\frac{4}{9}-\frac{3}{9}[/tex]
[tex]P(A\ or\ B)=\frac{7}{9}[/tex]
A farmer is using a barn as one side of a fence to enclose his cattle. If the barn is 80 feet long what is the width of the rectangular enclosure if the farmer has 260 ft. Of fencing to complete the project?
Answer:
90 feet
Step-by-step explanation:
The perimeter is the sum of the side lengths of the enclosure. The length is given as 80 ft, but only one side that long counts as part of the 260 ft of fence. So, we have ...
260 ft = 2×W + L = 2×W + 80 ft . . . . . length of fence for 3 sides
180 ft = 2×W . . . . . . subtract 80
90 ft = W . . . . . . . . . divide by 2
The width of the enclosure is 90 feet.
Final answer:
To find the width of the farmer's rectangular enclosure, we subtract the length of the barn (80 ft) from the total amount of fencing available (260 ft) to get the length available for the other three sides. Dividing this by two (because there are two widths), we find that the width of the enclosure will be 90 feet.
Explanation:
The question asks about creating a rectangular enclosure using a fixed length of fencing and a barn as one of the sides. With 260 feet of fencing available and the barn covering one side of 80 feet, the farmer must use the remaining fencing for the other three sides of the rectangle.
To find the width of the rectangular enclosure, we need to subtract the length of the barn side from the total amount of fencing available, and then divide by two (because there are two widths in a rectangle), as follows:
260 ft - 80 ft = 180 ft for both widths, so each width will be
180 ft / 2 = 90 ft.
Therefore, the width of the rectangular enclosure will be 90 feet.
A modified roulette wheel has 36 slots. One slot is 0, another is 00, and the others are numbered 1 through 34, respectively. You are placing a bet that the outcome is an odd number. (In roulette, 0 and 00 are neither odd nor even.)
Answer:0.472
Step-by-step explanation:
Given
there are 36 slots with 0 and 00 as two slots which are neither odd nor even
i.e. there are 34 remaining slots numbered 1 to 34
there are 17 odd terms and 17 even terms
thus Probability of getting a odd number is [tex]=\frac{17}{36}=0.472[/tex]
Answer:
P(odd#'s) = number of odd numbers/total number of outcomes = 18/38 = 9/19
Step-by-step explanation:
Please answer quick guys! 3. Given LJ ≅ MK, and LK ≅ MJ, prove ∠L ≅ ∠M (Picture is below)
Answer:
The Proof is given below.
Step-by-step explanation:
Given:
LJ ≅ MK
LK ≅ MJ
To Prove:
∠ L ≅ ∠ M
Proof:
In Δ LKJ and Δ MJK
LK ≅ MJ ……….{Given}
KJ ≅ KJ ………..{Reflexive Property}
LJ ≅ MJ ……….{Given}
Δ LKJ ≅ Δ MJK ....….{Side-Side-Side test}
∴∠ KLJ ≅ ∠ JMK .....{corresponding angles of congruent triangles (c.p.ct)}
i.e ∠ L ≅ ∠ M ............Proved.
Asha invests rs 8000 at a certain rate for three yrs compounded annually . She finds at the end of the first year it amounts to rs 9200. Calculate(1) R%(2)interest acquired in second year (3)amount at the end of the third year
Answer:
= 12169 rs
Step-by-step explanation:
Asha invest total=rs 8000
Total years = 3
Amount after 1 year= 9200 rs
Interest on first year =9200-8000= 1200 rs
So for second and third years
A= P (1 + R/100)ⁿ
9200= 8000( 1+ R/100)¹
9200= 8000( 100+ R/100)
115= 100 +R
R = 15
So amount after second year
A= 8000 (1 +15/100)²
A= 10580
Interest on second is = 10580 –P-interest on ist
=10580-8000-1200
= 1380 rs
So total amount at the end
A = 8000 ( 1 +15/100) ³
=12169 rs
In a swim-and-run biathlon, An Athlete must get to a point on the other side of a 50 meter wide river, 100 meters downstream from her starting point. Ann can swim 2 m/sec and run 5 m/sec. What path should Ann take in order to minimize her total time?
Answer:
running distance = 78,18 m
swimmingdistance = 92m
Step-by-step explanation:
Ann has to run a distance 100 - x and swim √ (50)² + x²
at speed of 5 m/sec and 2 m/sec
As distance = v*t t = d/v
Then running she will spend time doing d = ( 100-x)/5
and √[(50)² + x² ] / 2 swimming
Therefore total time of biathlon
t(x) = ( 100 - x )/5 + √[(50)² + x² ] / 2
Taking derivatives both sides of the equation we get
t´(x) = - 1/5 + [1/2 ( 2x)*2] / 4√[(50)² + x²]
t´(x) = - 1/5 + 2x / 4√[(50)² + x²] t´(x) = - 1/5 + x/2√(50)² + x²
t´(x) = 0 - 1/5 + x/2√(50)² + x² = 0
- 2√[(50)²+ x²] + 5x = 0
- 2√(50)²+ x² ) = -5x
√(50)²+ x² = 5/2 *x
squared
(50)² + x² = 25/4 x²
2500 - 21/4 x² = 0
x² = 2500*4/21
x = 21,8 m
Therefore she has to run 100 - 21,82 = 78,18 m
And swim √(50)² + (78,18)² = 92m
The question pertains to Physics and involves calculating the optimal path in a swim-and-run biathlon to minimize total time, which would typically involve physics and calculus. However, the scenario is incomplete and lacks necessary information for a precise solution.
Explanation:The subject of this question is Physics, as it involves concepts of speed, velocity, and optimization of travel paths in a biathlon, which includes both swimming and running. To answer the question on the optimal path Ann should take in the swim-and-run biathlon, we would use principles of physics and calculus to find the path that minimizes the total time. The calculation would involve deriving the functional relationship between swimming and running speeds, and the distances covered in each stage, then determining the point at which Ann should exit the water to reach the end point in the shortest total time. However, since the problem in the question is incomplete and requires additional information, such as the current of the river or whether Ann swims at a constant speed relative to the water, we cannot solve it without making assumptions that may be incorrect.
Learn more about Optimization in Biathlon here:https://brainly.com/question/32822211
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