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Related Questions
In 2010, the number of houses built in Town A was 25 percent greater than the number of houses built in Town B. If 70 houses were built in Town A during 210, how many were built in Town B
Answers
Answer:
The number of houses built in Town B is 56.
Step-by-step explanation:
We are given that in 2010, the number of houses built in Town A was 25 percent greater than the number of houses built in Town B.
Also, 70 houses were built in Town A during 210.
Let the number of houses built in Town B be 'x'.
So, according to the question;
Number of houses built in Town A = Number of houses built in Town B + 25% of the houses built in Town B
\(70 = x + (25\% \times x)\)
\(70 = x(1+0.25)\)
\(x=\frac{70}{1.25}\)
x = 56
Hence, the number of houses built in Town B is 56.
take all coins that are still on tails and keep flipping them until they land on heads. what is the expected number of total flips until all coins are on heads?
Answers
The probability that all coins show heads up is 1/16.
How to calculate the probabilityThe probability of one is 1/2: Half of the time (on average, as all numbers in this answer will be) it will show heads.
Of those times it shows heads, only half of the time will the second coin also show heads. We're down to a quarter of the time now.
Of those times the second coin shows heads, only half of the time will the third coin also show heads. This is 1/8.
And, of the times the third coin also shows heads, only half of the time will the fourth coin also show heads. Half of 1/8 is 1/16.
You can simplify this by calculating (1/2)^4.
= 1/16
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Take all coins that are still on tails and keep flipping them until they land on heads. We flip 4 coins simultaneously. What is the probability that all coins show heads up?
What is the slope of the line on the graph?
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Complete the function for this graph.
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y = | x - -2 | + 3
suppose that a and b are independent events with p(a) = 0.2 and p(b) = 0.4. p(a ∩ bc) =What is P (A and not B)?
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the probability of event A and not B (A ∩ Bc) is 0.12.
To find the probability of event A and not B (A ∩ Bc), we can use the formula:
P(A ∩ Bc) = P(A) - P(A ∩ B)
Given that events A and B are independent, we know that P(A ∩ B) = P(A) * P(B).
We are given that:
P(A) = 0.2
P(B) = 0.4
So, substituting the values into the formula, we have:
P(A ∩ Bc) = P(A) - P(A ∩ B)
= P(A) - P(A) * P(B)
= 0.2 - (0.2 * 0.4)
= 0.2 - 0.08
= 0.12
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Which of the following graphs represents a function that has a positive
leading coefficient? Check all that apply.
A + N N N
A.
D.
B.
Click here for long description
A. Graph A
B. Graph B
C. Graph C
D. Graph D
+
Answers
The graphs represents a function that has a positive leading coefficient are Options B, C, and D.
Now, By the given graphs;
The first graph is a parabola. Since it opens downwards, it means the leading coefficient is negative.
And, The third graph is also a parabola. Since it opens upwards, it means it has a positive leading coefficient.
And, The second and fourth graphs represents a polynomial with an odd degree. Since both polynomial goes rises on the left and keeps rising on the right, their leading coefficients are positive.
Thus, The correct options are:
B, C , and D
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A forestry study found that the diameter of the trees in a forest is normally distributed with mean 34 cm with a standard deviation of 8 cm. A group of 4 trees will be used as timber if the average of the 4 trees diameter is not too thick or thin. Specifically it is desired for the mean diameter to be between 30 and 40 cm in diameter. Find the probability that a randomly chosen group of 4 trees can be used as timber
Answers
Answer:
The probability that a randomly selected group of four trees can be used as timber is 4.5 × 10⁻⁵
Step-by-step explanation:
The given parameters are;
Mean = 34 cm
The standard deviation = 8 cm
The mean
The Z score is \(Z=\dfrac{x-\mu }{\sigma }\), which gives;
For x = 30 we have;
\(Z=\dfrac{30-34 }{8 } = -0.5\)
P(x>30) = 1 - 0.30854 = 0.69146
For x = 40, we have
\(Z=\dfrac{40-34 }{8 } = 0.75\)
P(x < 40) = 0.77337
Therefore, the probability that the mean of four trees is between 30 and 40 is given as follows;
P(30 < x < 40) = 0.77337 - 0.69146 = 0.08191
The probability that a randomly selected group of four trees can be used as timber is given as follows;
Binomial distribution
\(P(X = 4) = \dbinom{4}{4} \left (0.08191\right )^{4}\left (1-0.08191 \right )^{0} = 4.5 \times 10^{-5}\)
major league baseball game durations are normally distributed with a mean of 180 minutes and a standard deviation of 25 minutes. what is the probability of a game duration of more than 195 minutes?
Answers
The probability of a game duration of more than 195 minutes is approximately 0.2743 or 27.43%.
What is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.
We can use the standard normal distribution to answer this question by transforming the given data to a standard normal variable (Z-score).
First, we find the Z-score corresponding to a game duration of 195 minutes:
Z = (195 - 180) / 25 = 0.6
Now, we need to find the probability of a game duration being more than 195 minutes, which is the same as finding the probability of a Z-score greater than 0.6.
Using a standard normal distribution table or calculator, we can find that the probability of a Z-score greater than 0.6 is approximately 0.2743.
Therefore, the probability of a game duration of more than 195 minutes is approximately 0.2743 or 27.43%.
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Based on data obtained from the Census Bureau, the number of Americans over age 100 is expected to beP(t) = 0.07e0.54t (0 ≤ t ≤ 4). Where P(t) is measured in millions and t is measured in decades, with t = 0, corresponding to the beginning of 2000.†How fast was the population of americans over age 100 changing at the beginning of 2000? million people/decade
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The population of Americans over age 100 was changing at a rate of 0.0378 million people/decade at the beginning of 2000.
To find how fast the population of Americans over age 100 was changing at the beginning of 2000, we need to take the derivative of the function P(t) with respect to t. The derivative of P(t) with respect to t is given by:
P'(t) = 0.54*0.07e0.54t
At the beginning of 2000, t = 0. So, we need to plug in t = 0 into the derivative to find how fast the population was changing at that time:
P'(0) = 0.54*0.07e0.54*0 = 0.0378
Therefore, the answer will be 0.0378.
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Sarah Fuller is a female soccer player who played as a placekicker for the Vanderbilt Commodores football team a few years ago.She madehistory by becoming the first woman to score points in a Power 5 college football game. During one kick, she kicked the football with an upward velocity of 80 feet per second. The following function gives the height,h(in feet) after t seconds. h(t)=-16^t+80t+1 What is the initial height of the football? How do you know? Is there something in the equation that represents this value? How long did it take the football to reach its maximum height? Please show your work! What was the maximum height of the football? Please show your work! How long did it take the football to reach the ground? Please show your work and round to the nearest whole number.
Answers
It akes 2.5 seconds for the football to reach its maximum height.
How to calculate the valueIt should be noted that to find the initial height of the football, we need to determine the height when t=0. We can substitute t=0 into the equation:
h(0) = -16(0)² + 80(0) + 1
h(0) = 1
We can find the time at which the vertical velocity is zero by finding the vertex of the parabolic function. The vertex can be found using the formula:
t = -b/2a
where a = -16 and b = 80. Substituting these values into the formula gives:
t = -80/(2(-16)) = 2.5
Therefore, it takes 2.5 seconds for the football to reach its maximum height.
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8 less than the sum of u and 2
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Answer: u < 6
Step-by-step explanation: 2 + u < 8
u < (8-2)
u < 6
let x[t] be a parametric motion and denote speed v[t]=|v[t]|=sqrt[v[t]\[bullet]v[t]], where velocity is v[t]=(x^\[prime])[t].
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a) We have shown an example where A[t] · V[t] = 0, indicating that the speed is not changing at that specific time, but the velocity is changing.
b) We have proved that dy/dt = "the scalar component of A[t] in the direction of V[t]" for this particular motion where the speed is constant.
To demonstrate that a motion could have A[t] · V[t] = 0, where A[t] represents acceleration and V[t] represents velocity, we can consider an example where the motion occurs along a curved path.
Let's assume the motion of an object on a circle with a constant radius r.
In polar coordinates, we can express the position vector as x[t] = r(cos(t), sin(t)), where t is the parameter representing time. Taking the derivative of x[t] with respect to time, we obtain the velocity vector:
v[t] = (dx/dt, dy/dt)
= (-r sin(t), r cos(t)).
The speed, denoted by v[t], is the magnitude of the velocity vector:
|v[t]| = \(\sqrt{((-r sin(t)}^2 + (r cos(t))^2) = \sqrt{(r^2 (sin^2(t) + cos^2(t)))}\)
= r.
As we can see, the speed is constant and equal to r, which means it does not change with time.
Now let's calculate the acceleration vector A[t]:
A[t] = (dv/dt)
=\((d^2x/dt^2, d^2y/dt^2).\)
Differentiating the velocity vector v[t] with respect to time, we obtain:
(dv/dt) = (-r cos(t), -r sin(t)).
The dot product of A[t] and V[t] is given by:
A[t] · V[t] = (-r cos(t), -r sin(t)) · (-r sin(t), r cos(t))
= \(r^2\) (cos(t) sin(t) - cos(t) sin(t))
= 0.
Therefore, we have shown an example where A[t] · V[t] = 0, indicating that the speed is not changing at that specific time, but the velocity is changing.
Now let's prove the derivative of speed satisfies dy/dt = "the scalar component of A[t] in the direction of V[t]."
We have already established that the speed v[t] is constant (let's denote it as v) in this case. So, we can write:
v[t] = v.
Differentiating both sides with respect to time, we get:
dv[t]/dt = 0.
Now, let's express the velocity vector v[t] in terms of its components:
v[t] = (dx/dt, dy/dt).
Taking the derivative of v[t] with respect to time, we have:
dv[t]/dt = \((d^2x/dt^2, d^2y/dt^2)\).
The magnitude of the acceleration vector A[t] is the derivative of speed:
|A[t]| = \(\sqrt{((d^2x/dt^2)^2 + (d^2y/dt^2)^2)}\)
Since we know that dv[t]/dt = 0 (from the constant speed), the acceleration vector A[t] is orthogonal to the velocity vector V[t].
Now, let's consider the scalar component of A[t] in the direction of V[t]. We can calculate it by taking the dot product of A[t] and V[t] and dividing it by the magnitude of V[t]:
(A[t] · V[t]) / |V[t]| = (A[t] · V[t]) / v.
But we have established that A[t] · V[t] = 0, so the numerator is zero:
(A[t] · V[t]) / |V[t]| = 0 / v = 0.
Thus, we have shown that the derivative of speed, dy/dt, is equal to the scalar component of A[t] in the direction of V[t], which is 0 in this case.
Therefore, we have proved that dy/dt = "the scalar component of A[t] in the direction of V[t]" for this particular motion where the speed is constant.
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Complete Question:
let x[t] be a parametric motion and denote speed v[t]=|V[t]|=\(\sqrt{[v[t].v[t]]}\), where velocity is v[t]=\(x^{'}[t]\). a) Show by example that a motion could have A[t] V[t] = 0, so the speed is not changing (at least at that time), but the velocity is changing (at that time.)
b) Prove that the derivative of speed satisfies dy/dt = "the scalar component of A[t] in the direction of V[t]"
A parabola has a vertex at (0,0). The focus of the parabola is located on the positive y-axis.
In which direction must the parabola open?
up
down
left
right
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Based on the given information, the parabola must direction open upward.
To determine the direction in which the parabola must open, we need to consider the location of the vertex and the focus.
Given that the vertex of the parabola is at (0,0), this means that the parabola opens either upward or downward. If the vertex is at (0,0), it is the lowest or highest point on the parabola, depending on the direction of opening.
Next, we are told that the focus of the parabola is located on the positive y-axis. The focus of a parabola is a point that is equidistant from the directrix and the vertex. In this case, since the focus is on the positive y-axis, the directrix must be a vertical line parallel to the negative y-axis.
Now, let's consider the possible scenarios:
1. If the vertex is the lowest point and the focus is located above the vertex, the parabola opens upward.
2. If the vertex is the highest point and the focus is located below the vertex, the parabola opens downward.
In our given information, the vertex is at (0,0), and the focus is located on the positive y-axis. Since the positive y-axis is above the vertex, it indicates that the focus is above the vertex. Therefore, the parabola opens upward.
In summary, based on the given information, the parabola must open upward.
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If the interaction between two factors is not significant, the next tests to be done are:
A. None, the analysis is complete.
B. None, gather more data.
C. Tests about the population means of factor A or factor B using two-way ANOVA without interaction. D. Tukey's confidence intervals.
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The next tests to be done if the interaction between two factors is not significant are tests about the population means of factor A or factor B using two-way ANOVA without interaction. The correct option is C.
Tests about the population means of factor A or factor B using two-way ANOVA without interaction. If the interaction between two factors is not significant, then the next tests to be done are tests about the population means of factor A or factor B using two-way ANOVA without interaction.There are three types of interactions: no interaction, interaction, and crossover. When there is no interaction, the effect of factor A is the same for each level of factor B, or the effect of factor B is the same for each level of factor A. If there is an interaction, the effect of factor A depends on the level of factor B, or the effect of factor B depends on the level of factor A. If there is a crossover, the effect of factor A changes direction across the levels of factor B, or the effect of factor B changes direction across the levels of factor A.
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What is the factored form of 6x²+13x+5?
Answers
If you need help with math I suggest using an app called Photomath :)
Answer:
x1=-1/3 and x2=-1/5
3(3x+1)+2(5x+1)
3x+1=0,5x+1=0
×=-1/4 x=-1/5
The area of a rectangle is 60 square inches.
The length is x - 3, and the width is x +8.
Find the value of x, and the dimensions of the rectangle.
A = lw
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Any nice math experts I have 5 unanswered questions on my profile where you can get more points please consider answering them this is my offering for your time and knowledge.
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Answer:
I´m not an expert but I´ll look at it :3
Step-by-step explanation:
What is the result when 8x3 + 10x² + 23x + 15 is divided by 4x + 3 ?
Answers
Hope this helps
1. Solve for x. Show your solution and justify every step.
Equation. Justification
4(x - 3) + 5 = 17. Given
Answers
Given:
The equation is
\(4(x-3)+5=17\)
To find:
The solution of given equation.
Solution:
We have,
\(4(x-3)+5=17\)
Using distributive property, we get
\(4(x)+4(-3)+5=17\)
\(4x-12+5=17\)
\(4x-7=17\)
Adding 7 on both sides, we get
\(4x-7+7=17+7\)
\(4x=24\)
Divide both sides by 4.
\(x=\dfrac{24}{4}\)
\(x=6\)
Therefore, the value of x is 6.
Find the equation to the line above.
Answers
The equation of line given in the graph is, y = -4/3x.
What is equation of line?
How to calculate the equation of a line starting from two points:
The slope formula can be used to determine the slope.
The y-intercept (b) can be calculated using the slope and one of the points.
When you have the values for m and b, you can use them to solve for the line's equation in the slope-intercept form (y = mx + b).
The given line passes through the points (0, 0) and (3, -4)
So, the slope of the line is,
\(m = \frac{y_2-y_1}{x_2-x_1} = \frac{-4-0}{3-0} = -\frac{4}{3}\)
Now y - intercept is the point where line crosses the y - axis.
Line crosses the x - axis at (0, 0)
Hence, the y - intercept is b = 0.
Plug m = -4/3 and b = 0 in equation y = mx + b
⇒ y = -4/3x + 0
y = -4/3x
Hence, the equation of line given in the graph is, y = -4/3x.
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two years ago, paul was 7 times as old as matt was. two year from now, paul will be five times as old as matt will be. find the present age of each
Answers
The present age of Paul is 52 years and the present age of Matt is 10 years.
We are given that two years ago, Paul = 7 times as Matt
Let the current age of Matt be x and of Paul be y
2 years ago, we will have that:
Age of Matt = x - 2
So, we get the equation as:
Age of Paul = 7 ( x - 2) = 7 x - 14
y - 2 = 7 x - 14
y = 7 x - 14 + 2
y = 7 x - 12
Also, we are given that to year from now, Paul = five times Matt
We get that:
y + 2 = 5 ( x + 2)
y + 2 = 5 x + 10
y = 5 x + 10 - 2
y = 5 x + 8
So, we get:
7 x - 12 = 5 x + 8
7 x - 5 x = 8 + 12
2 x = 20
x = 20 / 2
x = 10
y = 5 (10) + 2
y = 50 + 2
y = 52
Therefore, the present age of Paul is 52 years and the present age of Matt is 10 years.
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What is the domain of F(x) = 1/x ?
Answers
Step-by-step explanation:
The domain is the possible x values of a function.
Since our function is a reciprocal function, our denominator can't equal 0. Note x=0, is a vertical asymptote.
So our domain is
All Reals except 0,
or (-oo,0) U (0, oo).
A recently televised broadcast of a popular television show had a 15 share, meaning that among 5000 monitored households with TV sets in use, 15% of them were tuned to the show. A 0.01 significance level is used to test an advertiser’s claim that among the households with TV sets in use, less than 20% were tuned in to the show. Find the P-value.
1.9998
0.9999
0.0001
0.0002
Answers
The p-value of the given hypothesis is; 0.9999
How to find the p-value of the statistics?The formula for the z-score of proportions is;
z = (p^ - p)/√(p(1 - p)/n)
where;
p^ is sample proportion
p is population proportion
n is sample size
We are given;
p^ = 15% = 0.15
p = 20% = 0.2
n = 5000
Thus;
z = (0.15 - 0.2)/√(0.2(1 - 0.2)/5000)
z = -8.8388
From p-value from z-score calculator, we have;
P(Z < -8.8388) = 1 - 0.0001 = 0.9999
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Evaluate f(-3), show all work:
F(x) = 2/3x + 8
Answers
Answer:
f(-3) = 6
Step-by-step explanation:
\(f(-3)=\frac{2}{3} (-3)+8=\frac{2(-3)}{3} +8=-\frac{6}{3}+8= -2+8=6\)
Hope this helps.
Answer:
f(x) = 6
Step-by-step explanation:
f(-3) means replace the x in f(x) with a -3, and replace every x in the equation with -3.
f(-3) = (2/3)x + 8
= (2/3) (-3) + 8
= (2 X -3)/3 + 8
= -6/3 + 8
= - 2 + 8
= 6
choose between rational and irrational for the real number 4.6 repeating
Answers
Answer:
Rational
Step-by-step explanation:
While the number never terminates since it repeats it qualifies as rational. Also since it can be put in fraction form it is a rational number.
ANOVA
printers (significance level=0.05). [30\%] (c) State two assumptions that are necessary in order for the above ANOVA to be valid. \( [20 \%] \) (d) The company uses leaflets that are of four different
Answers
(c) Two assumptions necessary for the validity of the ANOVA are:
1. Independence: The observations within each group and between groups should be independent of each other. This means that the value of one observation should not be influenced by or related to the value of another observation.
2. Homogeneity of variances: The variances within each group should be roughly equal. This assumption, also known as homoscedasticity, ensures that the variability in the dependent variable is similar across all groups.
(d) The company uses leaflets of four different designs to promote its printers. To assess the impact of leaflet design on sales, an ANOVA is performed. The null hypothesis states that the mean sales are equal across all leaflet designs, while the alternative hypothesis suggests at least one mean is different.
By comparing the computed F-statistic with the critical F-value at a significance level of 0.05, the ANOVA determines whether there is sufficient evidence to reject the null hypothesis. If the p-value is less than 0.05, it indicates a significant difference among the leaflet designs.
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A spinner is divided into 11 equal sections numbered from 0 to 10. You spin the spinner once. What is P(not even)
Answers
I hope this helps
The probability of not getting an even number when spinning the spinner once is \(\frac{5}{11}\).
You want to know the probability of not getting an even number when spinning a spinner divided into 11 equal sections numbered from 0 to 10.
Step 1: Identify the even numbers in the given range (0 to 10). The even numbers are 0, 2, 4, 6, 8, and 10.
Step 2: Count the number of even numbers. There are 6 even numbers in the given range.
Step 3: Calculate the total number of possible outcomes when spinning the spinner. There are 11 possible outcomes (0 to 10).
Step 4: To find the probability of not getting an even number (P(not even)), subtract the number of even numbers from the total number of outcomes. This will give you the number of odd numbers: 11 - 6 = 5.
Step 5: Now, divide the number of odd numbers by the total number of outcomes to find the probability: P(not even) = 5/11.
So, the probability of not getting an even number when spinning the spinner once is \(\frac{5}{11}\).
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The set of life spans of an appliance is normally distributed with a mean = 48 months and a standard deviation = 8 months. what is the z-score of an appliance that stopped working at 64 months?
Answers
The z-score of an appliance that failed after 64 months is 2.
What is mean?In mathematics, particularly statistics, there are several types of means. Each mean is used to summarize a specific set of data, often in order to better understand the overall value (magnitude and sign) of a given data set.The arithmetic mean, also known as "arithmetic average," of a data set is a measure of the central tendency of a finite set of numbers: specifically, the sum of the values divided by the number of values.To find the z-score:
The given parameters are:
Mean, \(\mu\) = 48 monthsStandard deviation, \(\sigma\) = 8 monthsThe z-score is then computed as follows:
\(z=\frac{x-\mu}{\sigma}\)We have the following for an appliance that stopped working after 64 months:
x = 64So, the equation becomes:
z = 64 - 48/8Compare and contrast the differences:
z = 16/8Calculate the quotient:
z = 2Therefore, the z-score of an appliance that failed after 64 months is 2.
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1. A lifeguard marks off a rectangular swimming area at the beach with 200m of rope. What is the greatest area of water she can enclose?
Answers
Answer:
20l 10w or it could be the other way around
The greatest area of water she can enclose is 2500 m².
A rectangle is a 2-dimensional quadrilateral with four right angles.
Perimeter of a rectangle = 2 x (length + width)
Area of a rectangle = length x width
In order to determine the greatest area of water the lifeguard can enclose, we have t determine the sum of the dimensions.
200m = 2( l + b)
l + b = 200m / 2
l + b = 100m
The second step is to determine the pair of dimensions that add up to 100.
90 x 10 = 900
80 x 20 = 1600
70 x 30 = 2100
60 x 40 = 2400
50 x 50 = 2500
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e. now say two robots are going to attempt the same task. the robots operate independently from one another. what is the probability that both robots succeed less than or equal to 80 times out of 100?
Answers
The probability of one robot succeeding in a task less than or equal to 80 times out of 100 can be calculated using a binomial distribution formula. Assuming the probability of success for one robot is p, the probability of success for both robots is p^2. Using the binomial distribution formula, we can calculate the probability of success for each robot and then multiply them together to find the probability of both robots succeeding less than or equal to 80 times out of 100. The formula is P(X<=80) = sum of P(X=k) from k=0 to k=80, where X is the number of successes in 100 attempts.
To calculate the probability of both robots succeeding less than or equal to 80 times out of 100, we need to first find the probability of success for one robot. Let's assume the probability of success for one robot is p = 0.7. The probability of success for both robots is then p^2 = 0.7^2 = 0.49.
Next, we need to use the binomial distribution formula to calculate the probability of success for each robot. The formula is P(X=k) = (n choose k) * p^k * (1-p)^(n-k), where n is the number of attempts, k is the number of successes, and (n choose k) is the binomial coefficient.
Using this formula, we can calculate the probability of one robot succeeding less than or equal to 80 times out of 100. P(X<=80) = sum of P(X=k) from k=0 to k=80 = sum of [(100 choose k) * 0.7^k * 0.3^(100-k)] from k=0 to k=80.
We can use a calculator or a software program like Excel to calculate this sum. The result is 0.9899, which means the probability of one robot succeeding less than or equal to 80 times out of 100 is almost 99%.
To find the probability of both robots succeeding less than or equal to 80 times out of 100, we just need to multiply the probability of one robot succeeding by itself: 0.9899 * 0.9899 = 0.9799. So the probability of both robots succeeding less than or equal to 80 times out of 100 is about 98%.
The probability of both robots succeeding less than or equal to 80 times out of 100 can be calculated using the binomial distribution formula. Assuming the probability of success for one robot is p, the probability of success for both robots is p^2. Using the formula P(X<=80) = sum of P(X=k) from k=0 to k=80, we can calculate the probability of one robot succeeding less than or equal to 80 times out of 100. Multiplying this probability by itself gives us the probability of both robots succeeding less than or equal to 80 times out of 100. For the given values, the probability is about 98%.
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