A coin is tossed 72 times. Find the standard deviation for the number of heads that will be tossed
The standard deviation for the number of heads that will be tossed is [tex]\boxed{4.24}.[/tex]
Further Explanation:
The random variable X follows binomial distribution.
[tex]\boxed{X \sim {\text{Bin}}\left( {n,p} \right)}[/tex]
Here, n represents the total number of experiments and p denotes the probability of the event.
Apply central limit theorem.
[tex]\boxed{X \sim {\text{Normal}}\left( {np,np\left( {1 - p} \right)} \right)}[/tex]
The mean of the binomial distribution can be calculated as follows,
[tex]\boxed{{\text{Mean}} = n \times p}[/tex]
The standard deviation of binomial distribution can be calculated as follows,
[tex]\boxed{{\text{Standard deviation}} = \sqrt {np\left( {1 - p} \right)} }[/tex]
Given:
Coin is tossed 72 times.
Explanation:
Consider X is the random variable that head will occur.
The probability of head occur is [tex]p = \dfrac{1}{2}.[/tex]
The mean can be calculated as follows,
[tex]\begin{aligned}{\text{Mean}}&= 72\times \frac{1}{2}\\&= 36\\\end{aligned}[/tex]
The standard deviation of the number of heads can be calculated as follows,
[tex]\begin{aligned}{\text{Standard deviation}}&= \sqrt {72 \times \frac{1}{2}\left( {1 - \frac{1}{2}} \right)} \\&= \sqrt {72 \times\frac{1}{2} \times \frac{1}{2}}\\&=\sqrt{\frac{{72}}{4}}\\&= \sqrt {18}\\&= 4.24\\\end{aligned}[/tex]
Hence, the standard deviation for the number of heads that will be tossed is [tex]\boxed{4.24}.[/tex]
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Answer details:
Grade: College
Subject: Statistics
Chapter: Binomial Distribution
Keywords: coin, tossed 72 times, number of heads, binomial distribution, standard normal distribution, standard deviation, test, measure, probability, low score, mean, repeating, indicated, normal distribution, percentile, percentage, proportion, empirical rule.
A carpenter is assigned a job of installing a spa into a pre-existing deck. The dimensions of the deck are (5x + 2) wide by (3x + 1) long. The dimensions of the spa are (2x + 3) wide by (x + 2) long.
Write the polynomial that represents the remaining area of the deck after the carpenter cut the hole out for the spa.
Find the area of the new deck if x = 2 feet.
I REALLY NEED HELP ON THESE EQUATIONS THE LAST PIC AND THIS ONE PLEASEEE IM IN DANGER OF FAILING
Write the set of points greater than or equal to −5−5 but strictly less than 44, excluding 00, as a union of two intervals (if you're having trouble with this, try drawing a number line):
Use cavalieri's principle to a circular pillar candle is 2.8 inches wide & 6 inches tall. find the volume of the candle.
Daniella wrote the equation shown to represent “four less than – 3.7 times a number is –11.9.” 4n – (–3.7) = 11.9 Explain her error, include the correct equation in your response.
Answer:
The correct equation is [tex]-3.7n-4=-11.9[/tex]
Step-by-step explanation:
Let
n-------> the number
we know that
The equation that represent the expression “four less than [tex]-3.7[/tex] times a number is [tex]-11.9[/tex] " is equal to
[tex]-3.7n-4=-11.9[/tex]
The equation that Daniella wrote represents the expression "[tex]-3.7[/tex] less than four times a number is [tex]11.9[/tex] "
Answer:
The coefficient of the variable should be -3.7 because of the word “times.” The words “four less than” mean that 4 will be subtracted from 3.7n. “Is” represents the equals sign, and “-11.9” is the second expression. The correct equation is -3.7n – 4 = -11.9.
Step-by-step explanation:
Edg math
Jane Marko buys a car for $43,900. In three years, the car depreciates 48% in value. How much is the car worth in 3 years
The sides of a triangle are in the ratio 5:12:13. what is the length of each side of the triangle if the perimeter of the triangke is 15 inches
Use the distributive property to expand the following expression. -3(6.3x + 7y - 2.5)
The expression -3(6.3x + 7y - 2.5) expands to -18.9x - 21y + 7.5 using the distributive property by multiplying each term inside the parentheses by -3.
To use the distributive property to expand the expression -3(6.3x + 7y - 2.5), you multiply each term inside the parentheses by -3. The distributive property lets you reverse the distributive law and turn it into factors (multiples).
-3 × 6.3x = -18.9x
-3 × 7y = -21y
-3 ×-2.5 = 7.5
Once each term is multiplied, the expanded expression is: -18.9x - 21y + 7.5
What is the final transformation in the composition of transformations that maps pre-image ABCD to image A"B"C"D"?
Bella made a drawing of her rectangular bedroom with the scale of 1 inch = 3 feet. The drawing was 6 inches long by 4 inches wide. What are the dimensions of Bella's room? What is the actual area? Show your work.
Bella's actual room dimensions are 18 feet by 12 feet, resulting in an actual area of 216 square feet. This was determined by applying the scale factor from the drawing to the actual room size.
To determine the actual dimensions of Bella's room based on her drawing, we first need to use the provided scale factor. According to the scale, 1 inch on the drawing is equal to 3 feet in actual size. We can calculate the actual dimensions by multiplying the length and width of the drawing by the scale factor.
The drawing is 6 inches long by 4 inches wide.
Actual length: 6 inches × 3 feet/inch = 18 feet
Actual width: 4 inches × 3 feet/inch = 12 feet
Now, to determine the actual area of Bella's room, we multiply the actual length by the actual width:
Actual area = actual length × actual width
Actual area = 18 feet × 12 feet = 216 square feet
solve The quantity 2 x minus 10 divided by 4 = 3x
To solve the equation 2x - 10 / 4 = 3x, multiply both sides by 4, simplify, and solve for x to find its value as -1.
Step 1: Multiply both sides of the equation by 4 to get rid of the fraction:
4 * (2x - 10) / 4 = 4 * 3x
Step 2: Simplify the equation:
2x - 10 = 12x
Step 3: Rearrange the equation to solve for x:
2x - 12x = 10
-10x = 10
x = -1
In the past ten years, the population of a city decreased from 90,000 to 75,000 Find the percent decrease.
Please HELP. Thank you
Point C to Point B appears to have a slope of 2/3, 3 blocks apart (in width) and 2 blocks apart (in height). Using a^2 + b^2 = c^2 will help where ^2 means (squared).
(2 x 2) + (3 x 3) = 13
Line CB is (square root) of 13.
Point A and B are 2 blocks apart (width) and 3 blocks apart (height), so using what we did in the last step...
(3 x 3) + (2 x 2) = 13
Line AB is (square root) of 13.
So now... With Line AB and Line CB being the square root of 13, the line AC should be (square root) (13 + 13), so (square root) 26. If it does equal this, then it is a right-triangle.
Point C and A are 1 block apart (width) and 5 blocks apart (height) so...
(1 x 1) + (5 x 5) = 26
Square root of 26...
In conclusion, the Triangle IS a Right-angle and you should pick "D"
What is the area of the triangle?
Identify the property that justifies the statement: If 4x-3=7, then 4x=10
The equation shown above is showing the Addition Property of Equation where the number “3” is added to both of its sides. This is shown below,
4x - 3 = 7
4x - 3 + 3 = 7 + 3
4x = 10
What is the distance between the points (3,8) (-9,8)
A)5
B)10
C)15
D)20
The distance between the points (3,8) and (-9,8) is 12. The correct answer is option B) 10.
Explanation:The distance between two points can be found using the distance formula: d = √((x2 - x1)^2 + (y2 - y1)^2). In this case, the coordinates of the two points are (3,8) and (-9,8). Plugging these values into the formula, we get:
d = √((-9 - 3)^2 + (8 - 8)^2)
d = √((-12)^2 + (0)^2)
d = √(144 + 0)
d = √144
d = 12
Therefore, the distance between the points (3,8) and (-9,8) is 12. The correct answer is option B) 10
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Jorge bought a car for $41,902 . He paid for the car with a check. Round the price to the nearest:
What is the degree of each monomial -9
The degree of a monomial is the sum of the exponents of the variables.
For example:
monomial: 257 x^3 y^5 z^21.
The degree is the sum of the exponents of x, y and z, this is 3 + 5 + 21 = 29.
When a monomial is just a number, it means that the exponents of the variables are zero. For example:
- 9 x^0 y^0 z^0 = - 9 * 1 * 1 * 1 = - 9.
This is your case, the monomial -9 has degree 0, which is the option B.
an arc that lies between the two sides of a cental angle is called a_____.
A. minor arc
B. major arc
C. semicircle
Sasha sets a goal to read 5 minutes longer than each previous day for 30 days. On the first day, Sasha reads for 20 minutes. The expression mc018-1.jpg represents the total number of minutes Sasha reads during the 30 days. How many total minutes does she read?
Final answer:
Sasha reads a total of 2775 minutes over 30 days, calculated using the formula for the sum of an arithmetic sequence.
Explanation:
To calculate the total number of minutes Sasha reads over 30 days, we note that she starts with 20 minutes on the first day and reads 5 minutes more each subsequent day. This is an arithmetic sequence where the first term (a1) is 20 minutes, the common difference (d) is 5 minutes, and the number of terms (n) is 30.
We can use the formula for the sum of an arithmetic sequence: Sn = n/2 (2a1 + (n - 1)d).
Plugging in the given values gives us S30 = 30/2 (2(20) + (30 - 1)(5)).
Now we calculate: S30 = 15(40 + 29(5)) = 15(40 + 145) = 15(185) = 2775 minutes.
Therefore, Sasha reads a total of 2775 minutes over the course of 30 days.
Because the car that has a terrible oil leak not only as a new battery for the van but also slows him down because he needs the Atwell after every hundred miles of driving he drives 100 miles every two hours it takes him 15 minutes to add oil how long should it take him to drive 500 miles
To drive 500 miles, taking into account both driving time and oil stop time, it would take 11 hours and 15 minutes.
He drives 100 miles every 2 hours, so to drive 500 miles he would take 10 hours (5 segments of 100 miles each).He needs to add oil every 100 miles, which takes 15 minutes each time. Therefore, for the 500-mile trip, he would spend an additional 75 minutes (5 segments x 15 minutes each).Adding the driving time and oil stop time, he would take 10 hours (driving) + 1 hour 15 minutes (oil stops) = 11 hours 15 minutes to drive 500 miles.You have 12 balloons to blow up for a party. You blow up 1313 of them, and your friend blows up 5 of them. What fraction of the balloons still need blowing up?
Answer:
The Answer Is 1/4
Step-by-step explanation:
Ur brain xd
The formula a = 118e^0.024t models the population of a particular city, in thousands, t years after 1998. when will the population of the city reach 140 thousand?
Final answer:
To find when the population of the city will reach 140 thousand, the formula a = 118e⁰.⁰²⁴t must be solved, resulting in approximately 3.52 years after 1998.
Explanation:
The formula a = 118e^0.024t models the population of a city, in thousands, t years after 1998. To find when the population reaches 140 thousand, set the formula equal to 140 and solve for t:
a = 118e⁰.⁰²⁴t
140 = 118e⁰.⁰²⁴t
t = (ln(140/118)) / 0.024 ≈ 3.52 years after 1998.
How do you use the slope to prove lines are parallel or perpendicular?
How do you write an equation of a line so that it is parallel or perpendicular to a given point?
Final answer:
To prove lines are parallel, their slopes must be equal, and to prove they are perpendicular, their slopes must be negative reciprocals. To write an equation for a parallel line, use the same slope as the original; for a perpendicular line, use the negative reciprocal of the original line's slope. Manipulating a line involves changing either its slope or intercept.
Explanation:
To use slope to prove that lines are parallel or perpendicular, you need to compare their slopes. Two lines are parallel if their slopes are equal. Conversely, two lines are perpendicular if their slopes are negative reciprocals of each other, meaning that one slope is the negative inverse of the other (e.g., the slope of one line is 2 and the other is -1/2).
To write an equation of a line so that it is parallel to a given line, you must use the same slope as the given line. If the equation of the given line is y = mx + b, then the equation of a parallel line will be y = mx + c, where c is a different y-intercept. To write an equation of a line so that it is perpendicular to a given line, you use the negative reciprocal of the slope of the given line. If the slope of the given line is m, then the slope of the perpendicular line will be -1/m.
For example, consider a line with the equation y = 3x + 9, which signifies a slope of 3 and a y-intercept of 9 based on Figure A1. A parallel line would have a slope of 3 but could have a different y-intercept, such as y = 3x + 4. A perpendicular line would have a slope of -1/3, so it could be something like y = -1/3x + 5.
Manipulating a line involves changing its slope (m) or intercept (b). Changing the slope will tilt the line, while changing the intercept will shift the line up or down on the graph. Understanding how to read and manipulate a graph is crucial for visualizing these changes.
Each triangle is a 30-60-90 triangle, and the hypotenuse of one triangle is the longer leg of an adjacent triangle. the hypotenuse of the larger triangle is 16 centimeters. what is the number of centimeters in the length of the longer leg of the smaller triangle?
The length of the longer leg of the smaller triangle is 8[tex]\sqrt{3}[/tex] centimeters.
In a 30-60-90 triangle, the ratio of the lengths of the sides is as follows:
- The length of the shorter leg is x.
- The length of the longer leg is x[tex]\sqrt{3}[/tex].
- The length of the hypotenuse is 2x.
Given that the hypotenuse of the larger triangle is 16 centimeters, we can set up the equation:
2x = 16
Solving for x:
x = [tex]\frac{16}{2}[/tex] = 8
Now, we know that the length of the longer leg of the larger triangle is x[tex]\sqrt{3}[/tex] = 8[tex]\sqrt{3}[/tex] centimeters.
Since the hypotenuse of the larger triangle becomes the longer leg of the smaller triangle, the longer leg of the smaller triangle is 8[tex]\sqrt{3}[/tex] centimeters.
The question is:
There are two triangles. Each triangle is a 30-60-90 triangle, and the hypotenuse of one triangle is the longer leg of an adjacent triangle. the hypotenuse of the larger triangle is 16 centimeters. What is the number of centimeters in the length of the longer leg of the smaller triangle?
What does 6× mean in math
A gardener has 27 pansies and 36 daisies he ants an equal number of each type of flower in each row what is the greatest possible number of pansies in each row
For a daily airline flight between two cities, the number of pieces of checked luggage has a mean of 380 and a standard deviation of 20. What number of pieces of checked luggage is 3 standard deviations above the mean?
Answer:
The answer is 440 pieces of checked luggage
Step-by-step explanation:
Mean = 380
Standard deviation = 20
No. of pieces of checked luggage for 1 standard deviation = 20 pieces
Therefore, Mean for 3 standard deviations above the mean = 3 × 20 = 60
Now, number of pieces of checked luggage 3 standard deviations above the mean = Mean for 1 standard deviation + Mean for 3 standard deviations above the mean
⇒ 380 + 60 = 440 pieces
If M is the midpoint of FG and MG = 7x-15, FG = 33, X = ?
The given expression gives x = 4.5.
If M is the midpoint of FG, this means that M divides FG into two equal segments. Therefore, FM = MG. We are given that MG = 7x - 15 and the total length of FG = 33. Hence, FM = MG = (1/2) * (FG).
Step-by-step solution:
Set up the equation for FM: FM = MG = (1/2) * 33.
This simplifies to FM = MG = 16.5.
Since MG = 7x - 15, we set 7x - 15 equal to 16.5.
Solve for x: 7x - 15 = 16.5.
First, add 15 to both sides: 7x = 31.5.
Finally, divide both sides by 7: x = 4.5.
Therefore, the value of x is 4.5.