Let X be the number of tail when a coin is flipped n number of times. Let n is the number of times a coin is flipped. Let p be the probability of getting tail on any flip of coin.
Here as coin is fair coin the chance of getting head or tail at any flip is 1/2.
n=75, p =0.5
From given information X follows Binomial distribution with n=75 and p=0.5
The probability that getting tail 35 or fewer times is
P(X ≤ 35) = P(X=35) + P(X=34) + P(X=33) + ....+ P(X=2) + P(x=1)
The Binomial probability is calculated using probability function
[tex] P(X=k) = (nCk) p^{k} (1-p) ^{n-k} [/tex]
For given parameters n=75 and p=0.5 the probability of getting X=k is
[tex] P(X=k) = (75Ck) 0.5^{k} (1-0.5) ^{75-k} [/tex]
Using excel function to find cumulative binomial probability for x=1 to 35 is
=BINOM.DIST(35,75,0.5,1) = 0.322
The probability there will be 35 or fewer tails is 0.322
The percentage of getting 35 or fewer tails is 32.2%
Zack borrowed $1,087 for 12 months at 11 percent interest. If he must pay 11.00 per $100, what is Zack's monthly payment?
How is the interquartile range calculated? HELP WITH APEX PLEASE!
By definition the interquartile range or IQR is obtained when the 25th percentile or [tex] Q_{1} [/tex] is subtracted from the 75th percentile or [tex] Q_{3} [/tex].
Thus, from the above definition, the formula for IQR is:
[tex] IQR=Q_{3}-Q_{1} [/tex]
As we can see from the provided options that the definition of IQR matches the expression provided in Option A and thus, Option A is the correct answer.
Quartile 3 (Q3) minus quartile 1 (Q1) is right for apex.
Doug can paint the living room in 4 hours. it would take elaine 6 hours to paint the same room. how long would it take doug and elaine, working together, to paint the living room?
If I get 3 problems wrong on a 12 question math paper, what grade would I get?
If you got 3 questions wrong on a 12 problem math paper, to figure out how many you got right you must subtract the number you got incorrect (3) from the total number (12).
12-3=9
To figure out your grade, you have to divide how many you got correct (9-see above) by the total number of questions (12).
9/12 = 0.75
If you multiply this decimal by 100, you get the equivalent percentage of 75%.
Therefore, you would have gotten a 75% on the paper.
Hope this helps!
Use the following information to answer the next two questions
simplify: 10(6y+x)=4
The sales tax in the city of Taxemalot is 8.1%. What is the growth factor for any item purchased at your local Tarmart? a.8.1 c.1.081 b.0.81 d.81
Please help:
In a right triangle ABC, tan(A) = 3/4. Find sin(A) and cos(A).
In a right triangle ABC with angle A equal to 90 degrees, find angle B and C so that sin(B) = cos(B).
Which group of values makes the expression 3x2y−2z UNDEFINED? A) x = –1; y = 0; z = 3 B) x = –1; y = 3; z = 0 C) x = 0; y = −1; z = 3 D) x = 0; y = 3; z = −1 E) x = –1; y = 2; z = 1
Answer:
The answer is A
Step-by-step explanation:
sadly i dont have the work of it just by looking it up you can get the answer tho. Answer is A
A waitress works 1.75 hours less in the afternoon than in the evening. If she works 5 1/8
hours in the afternoon, how many hours does she work in the evening?
Answer: The waitress works:[tex]\[{6 \frac{7}{8}}[/tex] hours in the evening
Let us denote the number of hours the waitress works in the evening as E and the number of hours she works in the afternoon as A.
Given that:
[tex]\[A = 5 \frac{1}{8} \text{ hours}\][/tex]
We can convert the mixed number to an improper fraction:
[tex]\[5 \frac{1}{8} = 5 + \frac{1}{8} = \frac{40}{8} + \frac{1}{8} = \frac{41}{8}\][/tex]
So, [tex]\( A = \frac{41}{8} \)[/tex] hours.
The waitress works 1.75 hours less in the afternoon than in the evening. Thus, we have:
[tex]\[A = E - 1.75\][/tex]
[tex]\[\frac{41}{8} = E - 1.75\][/tex]
Converting 1.75 to a fraction:
[tex]\[1.75 = \frac{7}{4} = \frac{14}{8}\][/tex]
Now, the equation becomes:
[tex]\[\frac{41}{8} = E - \frac{14}{8}\][/tex]
[tex]\[E = \frac{41}{8} + \frac{14}{8}\]\[E = \frac{41 + 14}{8} = \frac{55}{8}\][/tex]
Convert the improper fraction back to a mixed number:
[tex]\[\frac{55}{8} = 6 \frac{7}{8}\][/tex]
Therefore, the waitress works:
[tex]\[{6 \frac{7}{8}}[/tex] hours in the evening
An in-ground pond has the shape of a rectangular prism. The pond has a depth of 24 inches and a volume of 72,000 cubic inches. The length of the pond is two times its width. Find the length and width of the pond to the nearest tenth.
The length of the pond is 77.4 inches, and the width of the pond is 38.7 inches.
What is the rectangular prism?In geometry, a rectangular prism can be defined as a 3-dimensional solid shape that has six faces that are rectangles. A rectangular prism is also a cuboid.
Let,a be the length of the pond and b be the width of the pond.
The volume of the pond is;
[tex]\rm Volume \ of \ the \ pond= Area\ of\ the\ base\times deep\\\\Area\ of\ the\ base=\dfrac{Volume \ of \ the \ pond}{base}\\\\Area\ of\ the\ base=\dfrac{72000}{24}\\\\Area\ of\ the\ base=3000 in^2[/tex]
The length of the pond is two times its width.
a = 2b
The area of the base = a × b
3000 = ab
ab = 3000
Substitute the value of a in equation 2
[tex]\rm ab=3000\\\\2b \times b = 3000\\\\b^2=\dfrac{3000}{2}\\\\b^2=1500\\\\b=38.7[/tex]
Substitute the value of b in equation 1
[tex]\rm a=2b\\\\a=2 \times 38.7\\\\a=77.4[/tex]
Hence, the length of the pond is 77.4 inches, and the width of the pond is 38.7 inches.
To know more about rectangular prism click the link given below.
https://brainly.com/question/22534870
#SPJ3
The width of the pond is approximately 38.7 inches and the length is approximately 77.4 inches.
Explanation:To find the length and width of the pond, we can use the formula for the volume of a rectangular prism: length × width × depth. We are given that the depth is 24 inches and the volume is 72,000 cubic inches.
Let's denote the width as w.
Since the length is two times the width, we can express the width as w and the length as 2w.
Therefore, the equation for the volume becomes:
2w × w × 24 = 72,000
48w^2 = 72,000
w^2 = 1,500
w ≈ 38.7
Therefore, the width is approximately 38.7 inches and the length is approximately 77.4 inches.
Learn more about Rectangular prism here:https://brainly.com/question/32444543
#SPJ3
jane's salary is increased by 2% to £39474. how much is her salary before the rise?
The perimeter of a rectangular garden is 100 feet (ft). the area of the rectangular garden area is 600 ft2. find the length and width of the garden. let the length of the garden be the shorter side, of necessary.
The length of the garden is 20 feet and the width is 30 feet.
To solve this problem, we will use the formulas for the perimeter and area of a rectangle. The perimeter (P) of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. The area (A) of a rectangle is given by the formula A = lw.
Given the perimeter of the garden is 100 feet, we can set up the following equation:
[tex]\[ 2(l + w) = 100 \][/tex]
[tex]\[ l + w = 50 \][/tex]
[tex]\[ w = 50 - l \][/tex]
This equation relates the length and width of the garden.
Next, we are given that the area of the garden is 600 square feet:
[tex]\[ lw = 600 \][/tex]
Substituting the expression for w from the first equation into the area equation, we get:
[tex]\[ l(50 - l) = 600 \][/tex]
[tex]\[ 50l - l^2 = 600 \][/tex]
Rearranging the terms, we have a quadratic equation:
[tex]\[ l^2 - 50l + 600 = 0 \][/tex]
To solve this quadratic equation, we can factor it:
[tex]\[ (l - 20)(l - 30) = 0 \][/tex]
This gives us two possible solutions for the length: l = 20 feet or l = 30 feet.
Since we are asked to let the length be the shorter side, if necessary, we choose the smaller value for the length:
[tex]\[ l = 20 \text{ feet} \][/tex]
Now we can find the width by substituting the length back into the equation for the perimeter:
[tex]\[ w = 50 - l \][/tex]
[tex]\[ w = 50 - 20 \][/tex]
[tex]\[ w = 30 \text{ feet} \][/tex]
Therefore, the length of the garden is 20 feet and the width is 30 feet.
You have a bag of chocolate candy. Ten of them are red, 7 are brown, 12 are green, and 9 are blue. What is the probability that you pick a red candy, given that you have already picked a red candy and have not replaced it?
9/37 is the correct answer.
Urgent!! Need an answer ASAP!
Professor Scott has 84 students in his college mathematics lecture class. The scores on the midterm exam are normally distributed with a mean of 72.3 and a standard deviation of 8.9. How many students in the class can be expected to receive a score between 63.4 and 81.2? Express the answer to the nearest student.
Answer: 57
=====================================================
Explanation:
Convert each raw score to a z score
If x = 63.4, then
z = (x-mu)/sigma
z = (63.4-72.3)/8.9
z = -1
if x = 81.2, then
z = (x-mu)/sigma
z = (81.2-72.3)/8.9
z = 1
So P(63.4 < x < 81.2) is the same as P(-1 < z < 1)
Through the empirical rule (aka the 68-95-99.7 rule), we know that roughly 68% of the data values are within one standard deviation of the mean. In other words
P(-1 < z < 1) = 0.68 approximately (see note below)
Multiply 0.68 by the total 84 to get
0.68*84 = 57.12
which rounds to 57 people
Note: we can use a calculator to get a more accurate result of 0.68268949; a data table works as well but it won't be as accurate. For the purposes of this problem, the value 0.68 is good enough
What is the center of the circle with the equation (x-1)2 + (y-3)2= 9?
A summer camp manager wants to order 500 bag lunches for a field trip. Each lunch will have a piece of fruit. The manager is deciding on ordering apples, oranges, bananas, or plums. The camp manager surveys 50 random campers, and the results are given in this table.
Based on the results, which fruit should the manager order?
A- Apples
B- Oranges
C- Plums
D- Bananas
The number of tropical fish that an aquarium can hold depends on the volume of the fish tank. the interior dimensions of the fish tank are 25 cm, 30 cm, and 39 cm. each fish requires 10,000 cubic centimeters of water. how many tropical fish will this fish tank hold?
Circle 1 is center at (-4,5) and has a radius of 2 centimeters. Circle 2 is centered at (2,1) and has a radius of 6 centimeters. What transformations can be applied to Circle 1 to prove the circles are similar?
How do you write an equation for a circle with center (2,4) and passes through point (5, 9)?
A large truck and a small car have a head-on collision. Which scenario is true?
A) The truck has the greater acceleration because it has the greater mass
B) The car has the greater acceleration because it has the smaller mass
C) Both the truck and car have the same magnitude of acceleration
(Edit: This was meant to go in the Physics section, I'm so sorry about this, if anyone here could still answer that's be amazing)
In a collision, both the car and truck experience the same force due to Newton's Third Law. However, due to Newton's Second Law, the car, with its smaller mass, experiences a greater acceleration.
Explanation:According to Newton's Third Law of Motion, 'for every action, there is an equal and opposite reaction', both the truck and the car would experience the same magnitude of force. However, let's recall Newton's Second Law, 'force equals mass times acceleration' (F=ma). Using these physics principles, we can deduce that the car with the smaller mass would experience a greater acceleration, and the large truck would experience a lesser acceleration. This is because when the same force is applied to both objects, an object with a smaller mass will have a greater acceleration compared to an object with a larger mass. Hence, option B) 'The car has the greater acceleration because it has the smaller mass' would be the correct answer based on Newton's laws of motion.
Learn more about Acceleration in head-on collision here:https://brainly.com/question/32323129
#SPJ2
Phillip watched a beach volleyball game from 1:45pm to 2:00pm.how many degrees did the minutes hand turn?
Answer:
90 degrees
Step-by-step explanation:
Two mechanics worked on a car. the first mechanic worked for 20 hours, and the second mechanic worked for 15 hours. together they charged a total of $1775 . what was the rate charged per hour by each mechanic if the sum of the two rates was $100 per hour?
16. Supposes that y varies inversely with x and that y-10 whenx-7. Which of the following equations models this relationship?
A. Y=70x
B. Y=-10x
C. Y=x/70
D. Y=70/x
The equation that models this relation is y = 70/x. So, option (D) is the correct answer.
What is constant of proportionality?The constant of proportionality is the ratio of two proportional values at a constant value. Two variable values have a proportional relationship when either their ratio or their product gives a constant.
For the given situation,
The values are y = 10 and x = 7
y varies inversely with x.
⇒ [tex]y[/tex] ∝ [tex]\frac{1}{x}[/tex]
To remove proportionality we introduce a constant 'k'.
⇒ [tex]y=\frac{k}{x}[/tex]
Substitute the values of x and y,
⇒ [tex]10=\frac{k}{7}[/tex]
⇒ [tex]k=70[/tex]
Now substitute the value of k = 70 in y,
⇒ [tex]y = \frac{70}{x}[/tex]
Hence we can conclude that the equation that models this relation is y = 70/x. So, option (D) is the correct answer.
Learn more about constant of proportionality here
https://brainly.com/question/21328304
#SPJ2
Chris took a vacation trip to maine, where sales tax on taxable items is 5%. in maine, prepared food and lodging are taxed an additional 2%, for a total of 7% tax, while auto rentals are taxed an additional 5%, for a total of 10% tax.chris bought $70 worth of souvenirs, taxable at the general rate. he also spent $580 on prepared food and lodging and $620 for a rental car, all before tax. how much did he spend in total after tax was included?
a.$1333.50
b.$1316.10
c.$1270.00
d.$1376.10
For anyone with the “TRICIA” problem: $1202.30
Calculate the area of the shaded sector in square inches.
What is the greatest common factor of 60x4y7, 45x5y5and 75x3y?
Answer:
15x^3·y
Step-by-step explanation:
The numbers 60, 45, 75 are all multiples of 15, so 15 is their greatest common factor.
The least power of the factor x is 3; the least power of the factor y is 1, so the GCF is ...
GCF = 15·x^3·y
At sea, the distance to the horizon is directly proportional to the square root of the elevation of the observer. if a person who is 36 feet above the water can see 7.4 miles, find how far a person 64 feet above the water can see.
The person 64 feet above the water can see 9.84 miles.
It is given in the question that the distance to the horizon is directly proportional to the square root of the elevation of the observer.
if the elevation of the observer be h and distance to the horizon be x then:
[tex]x=k\sqrt{h}[/tex] where k is the constant of proportionality
from the given data:
[tex]7.4= k\sqrt{36}\\\\7.4=6k\\\\k=1.23[/tex]
So, if h = 64 feet then,
[tex]x=k\sqrt{h}\\\\x=1.23\sqrt{64}\\\\x=9.84 miles[/tex] is how far the person 64 feet above the water can see.
Learn more:
https://brainly.com/question/16998607
A bag of uninflated balloons contains 10 red, 12 blue, 15 yellow and 8 green balloons. A balloon is drawn at random, what is the probability of drawing a red balloon?
We have been given that a bag of uninflated balloons contains 10 red, 12 blue, 15 yellow and 8 green balloons.
We need to find the probability of drawing a red balloon.
We know that probability is given by
[tex]\\ \text{Probability =} \frac{\text{Favorable outcomes}}{\text{Total outcomes}}[/tex]
Since we know that there are 10 red balloons. Therefore, our number of favorable outcomes is 10.
In order to find the total number of outcomes, we will add balloons of all colors.
Therefore, total outcomes are = [tex]10+12+15+8 = 45[/tex]
We can now substitute the values of favorable outcomes and total outcomes in order to find the required probability.
[tex]\\ \text{Probability =} \frac{\text{10}}{\text{45}} = \frac{2}{9}[/tex]
8 MIN LEFT anyone know this?