Barney has a biased coin. When the coin is thrown once, the probability that the coin will land heads is 0.3 Barney throws the coin 4 times. Work out the probability that the coin will land heads exactly 3 times. (3 marks)
Answers
The probability that the coin will land heads exactly three times in four throws is approximately 0.0756 or 7.56%. We can use the binomial probability formula, which is P(X=k) = (n choose k) * p^k * (1-p)^(n-k), where X is the number of successes, n is the total number of trials, k is the number of successes we're interested in, p is the probability of success on a single trial, and (n choose k) is the binomial coefficient.
In this case, n=4, k=3, and p=0.3. So the probability of getting exactly three heads is: P(X=3) = (4 choose 3) * 0.3^3 * (1-0.3)^(4-3)
= 4 * 0.027 * 0.7
= 0.0756
Therefore, the probability that the coin will land heads exactly three times is 0.0756.
To calculate the probability of the coin landing heads exactly three times out of four throws, we will use the binomial probability formula. The formula is: P(X=k) = (nCk) * (p^k) * (q^(n-k))
In this case, n=4 (number of throws), k=3 (number of heads), p=0.3 (probability of heads), and q=0.7 (probability of tails, which is 1-p). Using the formula, the answer to the probability of the coin landing heads exactly three times in four throws is: P(X=3) = (4C3) * (0.3^3) * (0.7^(4-3))
P(X=3) = 4 * (0.027) * (0.7)
P(X=3) ≈ 0.0756
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Related Questions
Which of the following is divisible by 3?
a) 10
b) 24
c) 67
d) 555
Answers
Answer:
24, 555 are answer of this question.
Step-by-step explanation:
2+4=6 (3×8)
5+5+5=15 (15 is divisible by 3 ).
Answer:
B and D
Step-by-step explanation:
24 divided by 3 equals 8
555 divided by 3 equals 185
3 does not divide equally into 24 or 67
HOPE THIS HELPS <33333
-Silver
part 2e. what is the probability that a randomly selected hotel general manager makes more than $66,000?
Answers
The probability that a randomly selected hotel general manager makes more than $66,000 can be calculated using the standard normal distribution. We need to calculate the z-score for the value $66,000 using the formula z = (x - μ) / σ, where x is the value we want to find the probability for, μ is the mean salary, and σ is the standard deviation. Assuming a normal distribution with a mean salary of $60,000 and a standard deviation of $8,000, we get z = (66,000 - 60,000) / 8,000 = 0.75. Using the standard normal distribution table, the probability of finding a z-score of 0.75 or more is approximately 0.2266.
The z-score is a measure of how many standard deviations a value is from the mean. In this case, a z-score of 0.75 means that the value $66,000 is 0.75 standard deviations above the mean salary of $60,000. The standard normal distribution table provides the probabilities for different values of z-score. To find the probability of a value greater than $66,000, we need to find the area under the standard normal distribution curve to the right of the z-score of 0.75.
The probability that a randomly selected hotel general manager makes more than $66,000 is approximately 0.2266 or 22.66%. This means that out of 100 randomly selected hotel general managers, we would expect 22 to have a salary greater than $66,000.
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the base of a triangle is shrinking at a rate of 2 cm/min and the height of the triangle is increasing at a rate of 3 cm/min. find the rate (in cm2/min) at which the area of the triangle changes when the height is 38 cm and the base is 32 cm.
Answers
When the height is 38 cm and the base is 32 cm, the rate at which the area of the triangle changes is 10 cm²/min.
The rate at which the area of a triangle changes can be found by multiplying the rate at which the base is shrinking by the rate at which the height is increasing.
Given:
Rate of shrinking of the base = -2 cm/min
Rate of increasing of the height = 3 cm/min
Height of the triangle = 38 cm
Base of the triangle = 32 cm
To find the rate at which the area of the triangle changes, we use the formula for the area of a triangle:
Area = (1/2) * base * height
Differentiating the area formula with respect to time gives us:
dA/dt = (1/2) * (db/dt) * height + (1/2) * base * (dh/dt)
Substituting the given values, we have:
dA/dt = (1/2) * (-2) * 38 + (1/2) * 32 * 3
Simplifying, we get:
dA/dt = -38 + 48
dA/dt = 10 cm²/min
Therefore, when the height is 38 cm and the base is 32 cm, the rate at which the area of the triangle changes is 10 cm²/min.
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You buy a stock for $100. In one year its price rises to $114, and it pays a $1 dividend. Your capital gains yield is _____
Answers
Answer:
Step-by-step explanation:
$13
Kiara peeled 2 oranges every 4 hours. At that rate, how many would she peel in 12 hours?
please put an explanation, thank you!
Answers
The diagonals of rectangle qrst intersect at point p. given that m angle pts = 30 degrees, qs = 12, and qt = 6, find the following,
Answers
find the following what?
What is the НСF of
4725
5850
Answers
Answer:
433345344 Answer
Step-by-step explanation:
(Will mark Brainliest)Function g can be thought of as translated(shifted)version of f(x)=x²
Write The equation for g(x)
g(x)=__?__
Answers
Answer:
g(x) = (x + 2)² + 1
Explanation:
Given parent function: f(x) = x²
If the function translates two units right
g(x) = (x + 2)²If the function translates one units up
g(x) = (x + 2)² + 1 ← final function.uh can someone help me with this please I'm confused ughhh I missed school for two weeks and dk how to do this
Answers
Answer:
35
Step-by-step explanation:
Top box equals 10
(5x2)
Middle box equals 15
(5-2+2) x 3
Bottom box equals 10
(5x2)
Answer:
35 in sq.
Step-by-step explanation:
Find the area of each rectangle and add them together.
Area of a rectangle = length*height
Top rectangle: This one is easy. Length=2 Width=5
5*2=10
Middle rectangle: There's a missing segment in the width but we can find it. Notice the bottom rectangle's width includes the missing segment + 2 (look at the top rectangle). 5-2 is 3. Add the 2 of the known segment to the 3 of the previously unknown segment.
Length=3 Width=5
5*3=15
Bottom rectangle: This one is also easy. Length=2 Width=5
2*5=10
10+15+10=35 in sq.
Determine if the following statements are true or false.
If the null hypothesis that the means of four groups are all the same is rejected using ANOVA at a significance level a = 0.05, then...
a. The standardized variability between the groups is higher than the standardized variability within the groups.
b. The appropriate a* to be used in pairwise comparisons of group means is 0.05/4 = 0.0125 because there are four groups.
c. We can then conclude that all of the group means are different from one another.
Answers
a. The statement is true.
b. The statement is false.
c. The statement is false.
a. When the null hypothesis of equal means for four groups is rejected using ANOVA at a significance level of 0.05, it implies that there is sufficient evidence to suggest differences between the group means. ANOVA compares the variability between groups to the variability within groups. If the null hypothesis is rejected, it means that the standardized variability between the groups is higher than the standardized variability within the groups.
b. The appropriate significance level for pairwise comparisons of group means, also known as post hoc tests, is not simply divided by the number of groups. Dividing the significance level by the number of groups, as stated in option b, is not a valid approach. To appropriately account for multiple comparisons, adjustments like the Bonferroni correction, Tukey's HSD, or the Sidak correction are commonly used. These methods ensure that the overall Type I error rate is controlled.
c. Rejecting the null hypothesis using ANOVA only indicates that there are differences between at least two group means. It does not provide information about which specific group means differ from each other. To identify which group means are significantly different, additional post hoc tests or pairwise comparisons are required. These tests allow for a more detailed analysis of specific group differences and provide insights into which pairs of group means are statistically significant.
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An isosceles triangle in which the two equal sides, labeled a, are longer than the base, labeled b.
This isosceles triangle has two sides of equal length, a, that are longer than the length of the base, b. The perimeter of the triangle is 15.7 centimeters. The equation can be used to find the side lengths.
If one of the longer sides is 6.3 centimeters, what is the length of the base?
cm
Answers
If one of the longer sides of the Isosceles triangle is 6.3 centimeters, the length of the base is 3.1 centimeters.
Let's solve the problem step by step:
1. Identify the given information:
- The triangle is isosceles, meaning it has two equal sides.
- The two equal sides, labeled "a," are longer than the base, labeled "b."
- The perimeter of the triangle is 15.7 centimeters.
- One of the longer sides is 6.3 centimeters.
2. Set up the equation based on the given information:
Since the triangle is isosceles, the sum of the lengths of the two equal sides is twice the length of the base. Therefore, we can write the equation:
2a + b = 15.7
3. Substitute the known value into the equation:
One of the longer sides is given as 6.3 centimeters, so we can substitute it into the equation:
2(6.3) + b = 15.7
4. Simplify and solve the equation:
12.6 + b = 15.7
Subtract 12.6 from both sides:
b = 15.7 - 12.6
b = 3.1
5. Interpret the result:
The length of the base, labeled "b," is found to be 3.1 centimeters.
Therefore, if one of the longer sides of the isosceles triangle is 6.3 centimeters, the length of the base is 3.1 centimeters.
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if f is a differentiable function and y=sin(f(x2)) what is dy dx when x = 3
Answers
To find dy/dx when x = 3, we need to use the chain rule. The derivative dy/dx evaluates to cos(f(x2)) * f'(x2) * 2x, where f'(x) represents the derivative of the function f with respect to x.
Let's break down the problem step by step. We start with the function y = sin(f(x2)), where f is a differentiable function. To find dy/dx, we need to apply the chain rule. According to the chain rule, if we have a composite function, say g(h(x)), then the derivative with respect to x is given by g'(h(x)) * h'(x).
In our case, we have y = sin(f(x2)), where h(x) = f(x2) and g(x) = sin(x). Applying the chain rule, we find that dy/dx = cos(f(x2)) * f'(x2) * 2x.
To evaluate dy/dx at x = 3, we substitute x = 3 into the expression. Thus, dy/dx when x = 3 becomes cos(f(32)) * f'(32) * 2(3). Since the function f and its derivative f' are not explicitly given, we cannot determine their exact values or simplify the expression further without additional information.
In summary, to find dy/dx when x = 3 for the function y = sin(f(x2)), we apply the chain rule. The derivative evaluates to cos(f(x2)) * f'(x2) * 2x, but without further information about f and f', we cannot calculate the numerical value of dy/dx at x = 3.
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ATH CHALLENGE
The seats on the right side of the
10
school bus seat two students each.
The seats on the left side of the school bus
can seat three students each. There are 14
rows of seats. Eight students can fit in the
very back seat. How many people can ride
the bus at one time (remember to count
every person)?
Answers
Answer:
78
Step-by-step explanation:
for the right side we can just do 14*2 since there are two people per seat and 14 rows
14 *2 is 28
for the left side we just do 14*3 since there are three people per seat and 14 rows
14*3 is 42
Then we have to add the 8 students that can fit in the very back seat
42 + 28 + 8
28 + 8 is 36
42 + 36 = 78
Polygon with four sides, and the sum of the interior angles is equal to 360 degrees
Answers
Answer: I'm assuming your asking the length of each side. If so, each side is 90 degrees. If not, you should be more specific
Step-by-step explanation:
360 degrees divided by 4 sides equals 90 degrees for each side.
Alice,barbra, and carol are sisters. alice is 3 years younger then barbara is 5 years younger then carol. together the sisters are 68 years old. how old is barbara?
Answers
The age of Barbra is 22 years.
What is method of substitution?The algebraic method for solving simultaneous linear equations is the substitution method. A quantity of one variable through one expression is replaced in the second equation, as the name implies.
Now, according to the question.
Let 'a' be the age of Alice.
Let 'b' be the age of Barbra
Let 'c' be the age of Carol.
The sum of age of all three sisters is 68 years.
Thus, a + b + c = 68
Now, as Alice is three years younger than Barbra.
a = b - 3
and, Barbra is 5 years younger than Carol.
b = c - 5
c = b + 5
By substitution of values of a and c in total age.
(b - 3) + b + (b + 5) = 68
3b - 3 + 5 = 68
On solving the expression.
b = 22
Therefore, the age of Barbra is 22 years.
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Two angles are supplementary. One measures 7x - 9 and the other measures 4x + 3. Find x and the measure of the smaller angle
Answers
Answer:
Supplementary angles add up to 180°
180=7x-9+4x+3
180=7x+4x-9+3
180=11x-7
180+7=11x
187=11x
11x=187
x=187/11
x=17
Therefore x = 17
If 500 calories adds 1 pound to your weight how many 1000 calorie banana splits would you need to eat to gain 10 pounds
Answers
1000cal=2lbs
2x5=10
1000x5=5000
Answer: 10 banana splits
Answer: 5
Step-by-step explanation:
each banana split is equal to 2 lbs. therefore, to gain 10 lbs. you need to eat 5 banana splits.
500cal = 1 lb.
1000cal = 1 banana split
1 banana split = 2lbs.
to gain 10lbs, divide 10lbs by 2lbs = 5 banana splits
HELP! will give brainliest if you show work on how to get this answer below!
Solve for x. Check for extraneous solutions.
2+ sq root (x+18)=x
answer should be:
7(-2 is extraneous)
Answers
Kekskekeke
Step-by-step explanation:njbnmmk
Answer:
It should be 7! :)
Step-by-step explanation:
Isolate the radical, then raise each side of the equation to the power of its index.
Solve the inequality. |x − 3| + 8 > 6
Answers
The inequality expression given has a solution of 1 < x < 5.
Solving inequalities
Inequality are expressions not separated by an equal sign. Given the inequality expression below;
|x − 3| + 8 > 6
The expression can be divided into x − 3 + 8 > 6 and -(x - 3) + 8 > 6
For the inequality x − 3 + 8 > 6
x - 3 > 6 - 8
x - 3 > -2
x > 1
For the inequality -(x - 3) + 8 > 6
-(x - 3) > 6 - 8
-(x - 3) > - 2
x - 3 < 2
x < 5
Hence the solution to the given inequality is 1 < x <5
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HELP MEE PLEASEEEEEE
Answers
The third term in the recursive sequence is 9
How to find the third term in the recursive sequence?
A recursive sequence is a sequence of numbers where each term is defined by a formula that uses one or more of the previous terms in the sequence. In other words, each term depends on the term(s) that come before it.
Since a₁ = 3 and \(a_{k+1}\)= 2a\(_{k}\) - 1
a₂ = 2a₁ - 1
a₂ = 2(3) - 1 = 6 - 1 = 5
a₃ = 2a₂ - 1
a₃ = 2(5) - 1 = 10 - 1 = 9
Thus, the third term in the recursive sequence will be 9
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Your credit card charges an interest rate of 2% per month. You have a current balance of $1,000, and want to pay it off. Suppose you can afford to pay $100 per month. What will your balance be at the end of one year? You will still owe $72.97 after one year. (Round to the nearest cent.) X x That's incorrect. We want to compute the future value of our account balance. Here is the cash flow timeline over the next 12 months: Month 0 1 2 11 12 Cash flow $1,000 - $100 - $100 - $100 -$100 From the timeline we can see that we need to combine the FV of our current balance with the FV of our annuity payments of $100 per month. The FV of our current balance is: FV = PV x (1 + r)" The FV of the annuity payments is: FV=cxı((1+y)+ - 1) We can also compute this result using a spreadsheet. OK Your credit card charges an interest rate of 2% per month. You have a current balance of $1,000, and want to pay it off. Suppose you can afford to pay $100 per month. What will your balance be at the end of one year?
Answers
After calculating the future value of the current balance, You will still owe $72.97 after one year.
Calculate the future value of the current balance: FV = PV x (1 + r)
Where, FV = Future Value, PV = Present Value (the current balance of $1,000), and r = interest rate of 2% per month.
Thus, FV = 1,000 x (1 + 0.02) = 1,020
Calculate the future value of the annuity payments of $100 per month:
FV = c x ı((1 + y)+ - 1)
Where, c = $100, y = interest rate of 2% per month.
Thus, FV = 100 x ı((1 + 0.02)12 - 1) = 1,246.24
Calculate the future value of the account balance: FV = 1,020 + 1,246.24 = 2,266.24
Finally, calculate the balance at the end of one year:
Balance at the end of one year = Future Value - Annuity Payments
Thus, Balance at the end of one year = 2,266.24 - (12 x 100) = 72.97.
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Compared to quantitative research, qualitative studies tend to have _________samples. A. larger B. more representative C. smaller D. more statistically valid E. none of the above
Answers
Compared to quantitative research, qualitative studies tend to have smaller samples.
Qualitative research is a form of research that relies on non-numeric data like behaviors, feelings, language, and symbols. Qualitative research is used to research social phenomena by making use of qualitative approaches.
Quantitative research is a form of research that relies on numeric data and mathematical models for statistical analysis. Quantitative research is used to test and verify theories by making use of a systematic and empirical approach.
Samples in research are the smaller groups taken from the larger population being studied. In qualitative research, researchers use a smaller number of individuals and usually choose them intentionally to better understand the phenomena they are studying. In quantitative research, samples are typically larger and randomly selected to help researchers get a more accurate representation of the population being studied.
In conclusion, the statement, Compared to quantitative research, qualitative studies tend to have smaller samples is correct. Therefore, the answer to your question is option C. smaller.
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A square and a regular hexagon have sides of the same length. the perimeter of the square increased by 32 units will be equal to the perimeter of the hexagon. what is x, the length of a side of the hexagon or square?
Answers
The length of a side of the hexagon or square is - 16 units
A square has four equal sides and four equal angles. The angles of squares are at right angles or 90°.If all six sides are equal, then it is called a regular hexagon. The perimeter of the regular hexagon is defined as the sum of all the sides of a hexagon.The length of a side of the hexagon or square = x
The perimeter of the square = 4 × lengths of its side
= 4x
The perimeter of the hexagon = 6 × lengths of its side
= 6x
According to the question,
4x + 32 = 6x
⇒ 6x - 4x = 32
⇒ 2x = 32
⇒ x = 16
So, the length of a side of the hexagon or square is - 16 units.
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someone please help me
Answers
Answer:
A. 20ft
Step-by-step explanation:
Answer:
d. 98.5
Step-by-step explanation:
Triangles:
5 x 4 = 20/2 = 10
Circle:
5² x 3.14 = 78.5
Add both of them 98.5
Solve for q. 4. 3 9 + 2 Stuck? Watch a video or use a hint.
Answers
Answer:
-2/3
Step-by-step explanation:
q + 4/3 = 2/3
q = 2/3 - 4/3
q = -2/3
Steps:
Step 1: Simplify both sides of the equation.
3(q+/3 )=2
(3)(q)+(3)( 4 /3 )=2(Distribute)
3q+4=2
Step 2: Subtract 4 from both sides.
3q+4−4=2−4
3q=−2
Step 3: Divide both sides by 3.
3q /3 = −2 /3
How to solve for q?
1: Divide Both sides by the first number in this case it will be 3.
2: Then simplify the equation in this case our answer will lead up to 2/3
3: Subtract the value from both sides (4/3). The answer will lead up to -2/3.
Answer: q= −2 /3
Which of the following is not a standard metric unit? a. kilogram b. meter c. second d. gram
Answers
Exactly D
well i dont know why gram is non standard
hope it helps.
The correct answer is d. gram. The gram is indeed a metric unit; however, it is not considered a standard metric unit in the International System of Units (SI).
It is equal to one thousandth of a kilogram. The kilogram (a), meter (b), and second (c) are all standard metric units and form the basis of the International System of Units (SI). The kilogram is the unit of mass, the meter is the unit of length, and the second is the unit of time. These units are universally recognized and used in scientific, engineering, and everyday measurements.
Therefore, the gram (d) is the correct option as it is not considered a standard metric unit.
The rest of the options are as follows:
a. kilogram: The kilogram is the standard unit for mass in the International System of Units (SI). It is defined as the base unit for mass.
b. meter: The meter is the standard unit for length in the SI. It is defined as the base unit for length and is commonly used to measure distances.
c. second: The second is the standard unit for time in the SI. It is defined as the base unit for time and is commonly used to measure durations and intervals.
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w
Which graph represents the function 9x)= x21 +4
)
-
?
Answers
Answer:
Which ever graph equals y=9x
or has one line going through the 0 and where the two lines intersect just to the left of the (0,-4) mark
Step-by-step explanation:
I dont see any photo so this is all i can do. Hope it works
1) Given the vectors a \( =[-1,2,0], b=[-1,1,1], e=[3,0,-3] \). Find the thind component of the vector \( v=a-2 b+(1 / 3) c \) 2)
Answers
The third component of the vector v is -3.
The third component of the vector \(\(v=a-2b+\frac13c\)\) can be found by using the given vectors a, b, and e.
We know that the vectors a, b, and e are given as:
\($$a=[-1,2,0], b=[-1,1,1], e=[3,0,-3]$$\)
Now we can substitute these values in the expression for v to get:
\($$v=a-2b+\frac13e$$$$= \begin{bmatrix}-1\\2\\0\end{bmatrix} - 2\begin{bmatrix}-1\\1\\1\end{bmatrix}+\frac13 \begin{bmatrix}3\\0\\-3\end{bmatrix}$$$$=\begin{bmatrix}-1\\2\\0\end{bmatrix} - \begin{bmatrix}-2\\2\\2\end{bmatrix} + \begin{bmatrix}1\\0\\-1\end{bmatrix}$$$$=\begin{bmatrix}2\\0\\-3\end{bmatrix}$$\)
Therefore, the third component of the vector v is -3.
An alternative method is to simply calculate the third component of each vector and then substitute those values in the expression for v. Using this method, we get:
\($$v_3=a_3-2b_3+\frac13e_3$$$$=0-2(1)+\frac13(-3)$$$$=-3$$\)
So, the third component of the vector v is -3.
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hey hi hello whats up can someone help me with this please??........ thank you! :)
Answers
6.79
Step-by-step explanation:
the 9 in the thousand makes the 8 in the hundredth place go up
Sure!
The hundredths place is the second in a decimal.
with rounding, if the number is greater than or equal to 5, you round up, if not, you round down.
In this case we round up because 9 is bigger than 5.
So, it becomes 6.79
Therefore your answer is B
Add. Enter your answer in scientific notation.
4.25 x 10^*3 + 4.50 x 10^*3 +0.25 x 10^*3=
Answers
\(▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪\)
\(4.25 \times 10 {}^{3} + 4.50 \times 10 {}^{3} + 0.25 \times 10 {}^{3} \)\((4.25 + 4.50 + 0.25) \times 10 {}^{3} \)\(9 \times 10 {}^{3} \)Answer:
\(9 .0 \times {10}^{3} \)
Step-by-step explanation:
Hey there,
\(4.25 \times {10}^{3} + 4.50 \times {10}^{3} + 0.25 \times {10}^{3} \\ 4250 + 4500 + 250 \\ 8750 + 250 \\ 9000 \\ = 9.0 \times {10}^{3} \)
Hope this helps you.
Let me know if you have any other questions :-):-)