To calculate the probability of getting exactly 7 tails in 16 tosses of a fair coin, use the binomial probability formula with p = 0.5, q = 0.5, n = 16, and k = 7. Calculate C(16, 7) and then multiply it by (0.5^7) × (0.5^9) to find the probability.
Explanation:Calculating Probability of Exactly 7 Tails in 16 Coin Tosses
To find out the probability of getting exactly 7 tails when a fair coin is tossed 16 times, you can use the binomial probability formula. The formula for the binomial probability of getting exactly k successes (in our case, tails) in n trials (coin tosses) is given by:
P(X = k) = C(n, k) × (p^k) × (q^(n-k))
Where:
Here, the probability of getting a tail p is 0.5, the probability of not getting a tail q is also 0.5, n is 16, and k is 7. Substituting these values into the formula, we can calculate the probability of getting exactly 7 tails in 16 tosses of a fair coin.
The combination C(16, 7) can be calculated using the binomial coefficient formula or by using a calculator with binomial functions. Once we have the value of C(16, 7), we multiply it by (0.5^7) × (0.5^9) to get the probability. The final answer represents the probability of getting exactly 7 tails when a fair coin is tossed 16 times.
5x - 10y = 15 if 3x + 7y = 31
a 23 gram sample of a substance thats a by-product of fireworks has a K-value of .13. whats the substances half life in days
Answer:
5.3 is the right answer.
Step-by-step explanation:
Suppose a rectangular garden has a length of 3c + 15 feet and a width of 4c feet. write an expression for the area of the garden in square feet.
The area of the rectangle is given by the equation A = 12c² + 60c
What is the Area of a Rectangle?
The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle
Area of Rectangle = Length x Width
Given data ,
Let the area of the rectangle be represented as A
Now , the equation will be
Let the length of the rectangle L = ( 3c + 15 ) feet
Let the width of the rectangle W = 4c feet
Now , the area of the rectangle A = length of the rectangle L x width of the rectangle W
Substituting the values in the equation , we get
Area of Rectangle A = ( 3c + 15 ) ( 4c )
On simplifying the equation , we get
Area of Rectangle A = ( 3c ) ( 4c ) + 15 ( 4c )
Area of Rectangle A = 12c² + 60c
Therefore , the value of A is 12c² + 60c
Hence , the area of the rectangle is A = 12c² + 60c
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Two cards are drawn at random from a standard deck of cards without replacement. What is the probability that both cards will be from the clubs suit?
Answer:
The answer is 1/17.
Step-by-step explanation:
You will draw one club which will be 13/52. You will NOT replace it so you will draw a second card 12/51.
You will need to multiply them to find the probability.
First simplify your two fractions.
13/52 = 1/4 AND 12/51= 4/17
Multiply the two together and you will get 4/68 = 1/17
Hope this helps :)
at right is graph of this situation predict how the line would change to present the average cost of gas in dicember of 2005 when gas cost $2.20 per gallon on average
at maximum speed, an airplane travels 1680 miles against the wind in 5 hours. Flying with the wind, the plane can travel the same distance in 4 hours.
The speed of the airplane with the wind is 420 mph, and against the wind is 336 mph. The speed of the wind is 84 mph.
To find the speed of the wind, we use the following formulas:
Against the wind, the airplane travels 1680 miles in 5 hours. So, the speed against the wind is : [tex]\( S_a = 1680 \div 5 = 336 \)[/tex] mph
With the wind, the airplane travels the same distance of 1680 miles in 4 hours. So, the speed with the wind is: [tex]\( S_w = 1680 \div 4 = 420 \)[/tex]mph
Let W be the speed of the wind.
Against the wind: [tex]\( S_a = S_w - W \)[/tex]
[tex]\[ 336 = 420 - W \]\[ W = 420 - 336 = 84 \][/tex]
So, the speed of the wind is 84 mph.
1/2(6x-4)=2/3x How do i solve this?
Joseph pays $20 for his base phone in addition to the $0.10 per text. Micki pays $10 for her phone plan plus the $0.15 per text. Write a function for Joesph's phone plan and for Micki's phone plan.
Provide the number of text messages in which the plans are the same plan.
By using the equations Cj = 20 + 0.10x for Joseph's phone cost and Cm = 10 + 0.15x for Micki's phone cost, we find their costs would both be the same if 200 text messages were sent.
Explanation:The question is asking us to create an equation for both Joseph's and Micki's texting plans. In mathematical terms, the cost for each plan would be represented by the equation Cost = base rate + (cost per letter)x, where x represents the number of texts.
So for Joseph, the equation would be Cj = 20 + 0.10x and for Micki the equation would be Cm = 10 + 0.15x.
To find out when both plans cost the same, we set the two equations equal to each other and solve for x.
20 + 0.10x = 10 + 0.15x
By subtracting 0.10x from both sides and then subtracting 10 from both sides we get:
x = 200.
This means that both plans would cost the same if both parties sent 200 texts.
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Use 1% or 10% to estimate 8% of 310
D: region D helppppppppp
A solution of phosphoric acid has a boiling point of 158 degrees Celsius. What is the boiling point of the solution in degrees Fahrenheit?
The boiling point of a phosphoric acid solution that is 158 degrees Celsius is 316.4 degrees Fahrenheit. This is found by using the formula F = C * 9/5 + 32.
Explanation:To convert the boiling point of a solution from degrees Celsius to Fahrenheit, we use the formula F = C * 9/5 + 32, where F represents the temperature in Fahrenheit and C represents the temperature in Celsius.
In this case, the temperature in Celsius that you want to convert is 158 degrees. So you can substitute this value in the formula as follows:
F = 158 * 9/5 + 32
When you perform the calculation, you find that the boiling point of the phosphoric acid solution is 316.4 degrees Fahrenheit.
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.help me with this please thanks
Find the product of (2x + 5y)2.
What is the length of diagonal ac in parallelogram ABCD if the diagonal BD = 10cm which is twice the diagonal AC?
The length of the diagonal AC in parallelogram ABCD is 5 cm.
Explanation:Given that the diagonal BD is twice the length of diagonal AC, we can represent the length of diagonal AC as x. So, the length of diagonal BD would be 2x. From the given information, we know that BD = 10 cm. Therefore, we can write the equation 2x = 10 to solve for x. Dividing both sides of the equation by 2 gives x = 5. So, the length of diagonal AC is 5 cm.
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In the given parallelogram, the length of the diagonal AC is 5 cm, given that the length of the diagonal BD is twice that of AC.
Explanation:The question pertains to the properties of a parallelogram. In this case, it has been provided that diagonal BD (10 cm) is twice the length of the other diagonal AC. This implies that the length of diagonal AC is half the length of BD. Therefore, to find the length of AC, take the length of BD and divide by 2:
AC = BD / 2 = 10 cm / 2 = 5 cm
So, the length of diagonal AC is 5 cm.
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Two pools are being filled with water. To start, the first pool contains 2200
liters of water and the second pool contains 1840
liters of water. Water is being added to the first pool at a rate of 21.25
liters per minute. Water is being added to the second pool at a rate of 32.5
liters per minute.
(PLEASE ANSWER QUICK)
2200 + 21.25X = 1840 +32.50X
subtract 1840 from each side
360+ 21.25X= 32.50X
subtract 21.25x from each side
360=11.25X
x= 360/11.25 = 32 minutes pool will have the same amount
21.25*32 = 680+2200 = 2880 liters
32.5*32 = 1040 + 1840=2880 liters
it will take 32 minutes and they will have 2880 liters each
ROUND 43.0810194943 TO THE NEAREST TEN-THOUSANDTH HELP!
Which property is demonstrated by this equation? 3 + 2x = 2x + 3
Determine the number of possible triangles, abc, that can be formed given c = 85°, a = 10, and c = 13.
A quadratic equation is shown below:
25x2 + 10x + 1 = 0
Part A: Describe the solution(s) to the equation by just determining the radicand. Show your work. (5 points)
Part B: Solve 4x2 − 4x + 1 = 0 by using an appropriate method. Show the steps of your work, and explain why you chose the method used. (5 points)
hello :
help :
the discriminat of each quadratic equation : ax²+bx+c=0 ....(a ≠ 0) is :
Δ = b² -4ac
1 ) Δ > 0 the equation has two reals solutions : x = (-b±√Δ)/2a
2 ) Δ = 0 : one solution : x = -b/2a
3 ) Δ < 0 : no reals solutions
Find the surface area of each figure to the nearest tenth. Show your work, please
Find the sum of the geometric sequence. (1 point) 1, one divided by two, one divided by four, one divided by eight, one divided by sixteen
Answer:
31/16
Step-by-step explanation:
The hypotenuse of a right triangle is 3 times as long as the shorter leg. find the measure of the angle between the shorter leg and the hypotenuse
The measure of the angle between the shorter leg and the hypotenuse, [tex]\theta[/tex] = 70.53 °
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between the sides and angles of triangles.
Given that:
Let us consider the shorter leg be 'x'.
and, the Hypotenuse be '3x '.
Using trigonometric functions,
[tex]cos \theta= \frac{Base}{Hypotenuse}[/tex]
cos [tex]\theta[/tex] = x /3x
cos [tex]\theta[/tex] = 1/3
[tex]\theta[/tex] = [tex]cos^{-1}[/tex] (1/3)
[tex]\theta[/tex] = 70.53 °
Hence, the measure of the angle between the shorter leg and the hypotenuse 70.53 °
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Draw a model to represent the problem 6/12 divided by 1/4
The expression 6/12 divided by 1/4 is 2 and the model is attached
Drawing a model to represent the problem
From the question, we have the following parameters that can be used in our computation:
6/12 divided by 1/4
This can be expressed as
6/12 multiplied by 4
So, we have
0.5 multiplied by 4
When the product is evaluated, we have
2
Hence. 6/12 divided by 1/4 is 2 and the model is attached
If y varies directly with x and y = 10 when k = 10, what is the value of x?
y = k *x
y=10 ; k=10
10 = 10*x
x = 10/10 = 1
x =1
express 3/4, 7/16,and 5/8 with the LCD
ROUND 3.05947821031 TO THE NEAREST WHOLE NUMBER HELP
What is the length of a square
I need help with all of these
HELP!!!!
Use the following data set and a separate piece of paper to make a line plot that will help you to answer questions 2-7.
(6, 4, 4, 5, 1, 8, 10, 7, 8, 6, 6, 7, 5, 4, 6)
Add a box and whisker plot to the graph. Clearly mark the ends of box by drawing vertical lines and labeling their values on the horizontal axis. What are the ends of the box and whisker plot?
A. 1 and 6
B. 4 and 7
C. 4 and 8
D. 5 and 7
The original value of the car is $18,000 and it depreciates by 50% each year what is the value of the car after three years
value = 18000*(1-0.50)^3 = 2250
value after 3 years = $2250