As per the given probability, the values of
(a) E (X) is 17.4 ft³, E (X²) is 323.2 ft⁶, and V (X) is 2.16 ft⁶.
To calculate the expected value of X (E(X)), we multiply each possible value of X by its probability and add up the results. Using the probability mass function given, we have:
E(X) = (16)(0.3) + (18)(0.5) + (20)(0.2) = 17.4
This means that on average, the rated capacity of a freezer sold at this store is 17.4 ft³.
To calculate the expected value of X squared (E(X²)), we follow a similar process, but instead of multiplying each possible value of X by its probability, we square each possible value of X and multiply it by its probability before adding up the results. Using the probability mass function given, we have:
E(X²) = (16²)(0.3) + (18²)(0.5) + (20²)(0.2) = 323.2
This means that on average, the square of the rated capacity of a freezer sold at this store is 323.2 ft⁶.
To calculate the variance of X (V(X)), we then add up the results to obtain the variance. Using the probability mass function given, we have:
V(X) = (16 - 17.4)²(0.3) + (18 - 17.4)²(0.5) + (20 - 17.4)²(0.2) = 2.16
This means that the variance of the rated capacity of a freezer sold at this store is 2.16 ft⁶. The square root of the variance is known as the standard deviation, which gives us a measure of the spread of the distribution of X.
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Complete Question:
A certain brand of upright freezer is available in three different rated capacities: 16 ft³, 18 ft³ , and 20 ft³ . Let X = the rated capacity of a freezer of this brand sold at a certain store. Suppose that X has the following probability mass function:
x 16 18 20
p(x) 0.3 0.5 0.2
(a) Compute E (X) , E (X²) , and V (X) .
consider a markov chain with the following probability transition matrix: what is the period of this chain?
The period of the Markov chain is 2.
The period of this Markov chain is determined by the number of times you have to go through the probability transition matrix before you return to the same state. The period for this Markov chain is 2, as you can see from the probability transition matrix below:
P(i,j) State 0 State 1 State 0 0.5 0.5 State 1 0.3 0.7
Starting from State 0, the probability of transitioning to State 0 is 0.5, and the probability of transitioning to State 1 is 0.5. If we start from State 1, the probability of transitioning back to State 0 is 0.3, and the probability of transitioning back to State 1 is 0.7.
Therefore, it takes two steps for the chain to return to its original state and the period of this Markov chain is 2.
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A 95 percent confidence interval for the mean time, in minutes, for a volunteer fire company to respond to emergency incidents is determined to be (2.8. 12.3). Which of the following is the best interpretation of the interval? Five percent of the time, the time for response is less than 2.8 minutes or greater than 12.3 minutes. B The probability is 0.95 that a randomly selected time for response will be between 28 minutes and 12.3 minutes Ninety-five percent of the time the mean time for response is between 2.8 minutes and 12.3 minutes. (D) We are 95% confident that the mean time for response is between 2.8 minutes and 12.3 minutes We are 95% confident that a randomly selected time for response will be between 2.8 minutes and 12.3 minutes.
The best interpretation of the interval is: We are 95% confident that the mean time for response is between 2.8 minutes and 12.3 minutes. Option D is correct
A confidence interval is a measure of how accurately an estimate (such as the sample average) corresponds to the actual population parameter. It is a range of values that the researcher believes is very likely to include the actual value of the population parameter.
Here, a 95 percent confidence interval for the mean time, in minutes, for a volunteer fire company to respond to emergency incidents is determined to be (2.8. 12.3). Thus, we can say that we are 95% confident that the mean time for response is between 2.8 minutes and 12.3 minutes. Therefore, option D is correct.
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Evaluate f(x)=1/2x-3 for each value of x. Show your work. (a)f(-8)
(b)f(0)
(c)f(3)
(d)f(10)
Answer:
To evaluate f(x)=1/2x-3 for each value of x, we substitute each value into the function and simplify:
(a) f(-8) = (1/2)(-8) - 3 = -4 - 3 = -7
(b) f(0) = (1/2)(0) - 3 = 0 - 3 = -3
(c) f(3) = (1/2)(3) - 3 = 1.5 - 3 = -1.5
(d) f(10) = (1/2)(10) - 3 = 5 - 3 = 2
Therefore, the values of the function for each value of x are:
(a) f(-8) = -7
(b) f(0) = -3
(c) f(3) = -1.5
(d) f(10) = 2
if 2 chickens can lay 3 eggs in eight days how many days can 5 chickens lay in 6 days?|continental math league ml
Answer:
8
Step-by-step explanation:
2=3
3÷2=1.5
1.5×5=7.5
round up to get 8
PLEASE ANSWER ASAP!!
The graph that would have x - intercepts if the functions are graphed on the xy- coordinate plane, is C) y = 3 sec x.
How to find the graph with x - intercepts ?An x-intercept is a point where the graph intersects the x-axis, which means the value of y is 0 at that point.
We can analyze the functions randomly.
y = csc x + 3
The cosecant function is the reciprocal of the sine function, so csc x = 1 / sin x. For this function to have x-intercepts, we need 1 / sin x + 3 = 0. However, this equation cannot be satisfied since the minimum value of 1 / sin x + 3 is greater than 0. Therefore, there are no x-intercepts for this graph.
y = 3 sec x
The secant function is the reciprocal of the cosine function, so sec x = 1 / cos x. For this function to have x-intercepts, we need 3(1 / cos x) = 0. This equation can be satisfied when cos x = 0, which occurs at x = (2n + 1)π/2, where n is an integer. Therefore, this graph has x-intercepts.
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Rewrite the following equation in slope-intercept form. 16x − 5y = 16
Write your answer using integers, proper fractions, and improper fractions in simplest form
Slope intercept form of the given equation is y=16/5x-16/5
What is a line's Slope Intercept Form?The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. where, m and c are real integers in the slope-intercept form of the linear equation.
The slope, m, refers measure of how steep a line is. Sometimes, the gradient of a line is referred to as its slope. A line's y-intercept, ab, the y-coordinate of the location where the line's graph crosses the y-axis.
Given equation16x-5y=16
Writing equation in slope intercept form
16-5y=16
-5y=16-16x
y=16/-5 +16/5x
y=16/5x-16/5.
hence, Slope intercept form of the given equation is y=16/5x-16/5
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In a chemistry lab there are 9. 52 g of powdered substance in a container max needs to place an equal amount of the powdered substance into each of three glass plates the amount of powdered substance he places into each glass glass plate is 1. 98 g
No, the given statement about the lab experiment is not reasonable.
If Max places 1.98 grams of powdered substance into each glass plate and he needs to place the substance into 3 glass plates, then the total amount of the powdered substance he needs is 1.98 x 3 = 5.94 grams. This is greater than the amount Max estimates to be in the container (4.5 grams).
Therefore, it is not reasonable to assume that there are only 4.5 grams of the powdered substance in the container when Max needs to use more than that amount for his experiment.
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Complete Question:
In chemistry lab, there are 9.52 grams of powdered substance in a container. Max needs to place substance into each of 3 glass plates. The amount of powdered substance he places into each glass plate is 1.98 grams. Max estimates that there are 4.5 grams of the powdered substance in the container. Is the statement reasonable?
The functions f(x), g(x), and h(x) are shown below. Select the option that
represents the ordering of the functions according to their average rates of change on
the interval 1
HELP!!!
Arrange the functions according to the average rate of change in the interval 1<1. ×< 3 is: g(x) < f(x) = h(x)
In other words, g(x) has the smallest average rate of change, while f(x) and h(x) have the same largest average rate of change.
What is function?A function is a mathematical rule that takes an input (or inputs) and produces a corresponding output.
It describes a relationship between two quantities, where each input is associated with exactly one output.
Since the interval of interest is not provided, I will assume that the interval is 1 < x < 3, based on the graphs of the functions given.
To determine the ordering of the functions according to their average rates of change on the interval 1 < x < 3, we can use the following formula:
Average rate of change = (f(b) - f(a)) / (b - a)
where a and b are the endpoints of the interval.
Using this formula, we can calculate the average rates of change of the three functions on the interval 1 < x < 3. Here are the results:
f(x): average rate of change = (f(3) - f(1)) / (3 - 1) = (2 - (-2)) / 2 = 2
g(x): average rate of change = (g(3) - g(1)) / (3 - 1) = (-3 - (-1)) / 2 = -1
h(x): average rate of change = (h(3) - h(1)) / (3 - 1) = (0 - (-4)) / 2 = 2
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The complete question is given below:
Arrange the functions in the period 1 according to the average rate of change. 3 is: g(x) f(x) = h(x)
In other words, g(x) has the lowest average rate of change, whereas f(x) and h(x) both have the highest average rate of change.
What is a Function?A function is a mathematical rule that accepts an input (or inputs) and generates an output.
It defines a relationship among two quantities in which each input corresponds to only one output.
Because the interval of interest is not specified, I will assume that it is 1 x 3 based on the graphs of the functions supplied.
We can use the formula that follows to find the ordering of the functions based on their average frequencies of change on the interval 1 x 3:
Change at an Average Rate = (f(b) - f(a)) / (b - a)
where a and b are the interval's ends.
We can compute the average rates of change of all three functions on the interval 1 x 3 using this formula. Here are the outcomes:
f(x): average rate of change = (f(3) - f(1)) / (3 - 1)
= (2 - (-2)) / 2
= 2
g(x): average rate of change = (g(3) - g(1)) / (3 - 1)
= (-3 - (-1)) / 2
= -1
h(x): average rate of change = (h(3) - h(1)) / (3 - 1)
= (0 - (-4)) / 2
= 2
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Find the x- and y-intercepts of the graph of -7x + 3y = 21. State each answer as
an integer or an improper fraction in simplest form.
x-intercept:
Submit Answer
Terms
Use
y-intercept:
The x-intercept and y-intercept of the graph of -7x + 3y = 21 are -3 and 7 respectively.
How to find the x-intercept and y-intercept of a graph?The x-intercept of a graph is the point where a line crosses the x-axis, while the y-intercept of a graph is the point where a line crosses the y-axis.
Therefore, the x-intercept is the value of x when y = 0 while the y-intercept is the value of y when x = 0.
Hence, let's find the x and y-intercept of -7x + 3y = 21
x-intercept
-7x + 3(0) = 21
-7x = 21
x = 21 / -7
x = -3
Y-intercept
-7x + 3y = 21
-7(0) + 3y = 21
3y = 21
y = 21 / 3
y = 7
Therefore,
x-intercept = (-3, 0)
y -intercept = (0, 7)
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What is the area of the parallelogram
Base is 8 height is 5 and width is 5.1:
I NEED AN ASWER ASAP
What would be the new coordinates of W' after a dilation of 3? W
The new coordinates would be
W' (12 , 6)
X'( 24 , 18 )
Z'(24 ,6 )
What exactly does coordinate geometry mean?
The term "coordinate geometry" refers to the study of geometry using coordinate points (or analytic geometry). Calculating distances between points, segmenting lines into m:n pieces, finding a line's midpoint, figuring out a triangle's area in the Cartesian plane, and other operations are all achievable with coordinate geometry.
Remember that the rule for a dilation by a factor of k about the origin is
(x,y) = (kx, ky)
Identify the coordinates of the points W, X and Z. Then, apply a dilation by a factor of 3 about the origin to find W', X' and Z', the new coordinates after the dilation.
w = (4,2)
x = ( 8, 6 )
z = ( 8,2)
Apply a dilation by a factor of 3:
W(4,2) ⇒ W'(3 * 4, 3 * 2) = W' (12 , 6)
X(8 ,6 ) ⇒ X'(3 * 8 , 3 * 6 ) = X' ( 24 , 18 )
Z(8 , 2 ) ⇒ Z'(3*8 , 3 * 2) = Z'(24 ,6 )
Therefore, the new coordinates would be
W' (12 , 6)
X'( 24 , 18 )
Z'(24 ,6 )
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I NEED HELP ON THIS ASAP!
Answer:
Step-by-step explanation:
The solution (16, 2) means 16 small gloves and 2 large gloves can be made in less than or equal to 16 hours and cost less than or equal to $40 in materials to make.
9. What is the volume of the triangular prism
below?
5 cm
3 cm
4 cm
3 cm
Answer:
Step-by-step explanation:
The radical form for each expression is given as follows:
How to obtain the radical form of each expression?
The general format of the exponential expression is given as follows:
To obtain the radical form, we have that:
a is the radicand.
n is the exponent.
m is the root.
Hence the radical form of the exponential expression is given as follows:
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What is an equation of the line that passes through the point (6,6)(6,6) and is parallel to the line 3x-2y=43x−2y=4?
The equation of the line that passes through (6,6) and is parallel to 3x - 2y = 4 is y = (3/2)x - 3.
What is an equation of the line parallel to the given line?The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
To find the equation of the line passing through (6,6) that is parallel to 3x - 2y = 4.
We need to find the slope of the given line first.
3x - 2y = 4
-2y = -3x + 4
y = (3/2)x - 2
The slope of the given line is 3/2.
Since the line we want to find is parallel to this line, it will have the same slope.
Therefore, we can use the point-slope form of the equation of a line to write the equation:
y - y1 = m( x - x1 )
Plug in m = 3/2 and (x1,y1) : (6,6)
y - 6 = (3/2)(x - 6)
Simplifying:
y - 6 = (3/2)x - 9
y = (3/2)x - 3
Therefore, the equation of the parallel line is y = (3/2)x - 3.
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Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).
The statement "The graph cοntains the pοint (0, 0)" is true.
What is a Quadratic Functiοn?Quadratic functiοns are used in different fields οf engineering and science tο οbtain values οf different parameters. Graphically, they are represented by a parabοla.
The statements that are true abοut the functiοn and its graph are:
1.The graph οf the functiοn is a parabοla.
2.The graph οf the functiοn οpens dοwn.
3.The graph cοntains the pοint (0, 0).
The functiοn [tex]f(x) = x^2 - 5x + 12[/tex] is a quadratic functiοn, which means its graph is a parabοla. The leading cοefficient οf the functiοn is pοsitive, which means the parabοla οpens dοwn.
Tο find the value οf f(-10), we can substitute -10 fοr x in the functiοn and evaluate:
[tex]f(-10) = (-10)^2 - 5(-10) + 12 = 100 + 50 + 12 = 162[/tex]
Therefοre, the statement "The value οf f(–10) = 82" is false.
The pοint (20, -8) is nοt οn the graph οf the functiοn, because if we substitute x = 20 in the functiοn, we get:
[tex]f(20) = 20^2 - 5(20) + 12 = 200 - 100 + 12 = 112[/tex]
Therefοre, the statement "The graph cοntains the pοint (20, –8)" is false.
On the οther hand, the pοint (0, 0) is οn the graph οf the functiοn, because if we substitute x = 0 in the functiοn, we get:
[tex]f(0) = 0^2 - 5(0) + 12 = 12[/tex]
Therefοre, the statement "The graph cοntains the pοint (0, 0)" is true.
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At a science exhibition, students learnt that it takes 5 hours for a block of ice to melt at 32° C.
Determine the time taken to melt a similar-sized block of ice at 20° C.
I've been waiting to order your cupcakes all day!
I'll have 4 Nom-Nom-Nom cupcakes -- that's
80% of my order. The rest of the order are Wow.
Using fraction, the total number of cupcakes is obtained to be 5.
What is fraction?
In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.
If 4 cupcakes represent 80% of the order, then we can use proportional reasoning to find the total number of cupcakes.
Specifically, if x is the total number of cupcakes, then we can write -
4/x = 80/100
where the left-hand side represents the fraction of the order that is Nom-Nom-Nom cupcakes, and the right-hand side represents the percentage of the order that is Nom-Nom-Nom cupcakes.
Solving for x, we get -
x = 4 / (80/100) = 5
So the total number of cupcakes is 5. Since 4 of them are Nom-Nom-Nom cupcakes, the remaining 1 cupcake must be a Wow cupcake.
Therefore, in total there are 5 cupcakes.
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I've been waiting to order your cupcakes all day! I'll have 4 Nom-Nom-Nom cupcakes -- that's 80% of my order. The rest of the order are Wow.
Find the total number of cupcakes.
the perimeter of an isosceles triangle is 56 in. the ratio of the sides is 5:4. find the lengths of the sides and the base of the triangle
The perimeter of an isosceles triangle is the sum of the length of the sides. In this case, the perimeter is 56 inches. The ratio of the sides is [tex]5:4.[/tex]
To calculate the lengths of the sides and base, we need to first calculate the lengths of the two equal sides. To do this, divide the perimeter (56 inches) by the sum of the ratio (5 + 4) which is 9. This gives us a result of 6.2 inches for the two equal sides.
To calculate the length of the base, multiply the two equal sides by the ratio of 5:4, which gives us a result of 7.5 inches for the base.
Therefore, the lengths of the sides and the base of the triangle are: two equal sides of 6.2 inches, and a base of 7.5 inches.
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Tough problem: Aisha bought a rectangular field. The perimeter of
the field is 240m. If the length of the field is increased by 8m and the
width is decreased by 5m, the area is decreased by 42m2
. Find the
length and the width of the field. Hint: If you set things right one of the
equations you get is not actually a linear equation, however it is
solvable.
Answer:
let W =with of field (M)
L=length of field=(7/5)×W
P=perimeter of field =2×(L+W) =240m
substiting L as fungtion of w in last equation:
2×(7/5)×W+W=240m
(12/5×w=120m
W=(5×+20m)/12=50m
L=(7/5×50m)=70m
f(x)=x^2
shifted 5 units left
reflect over x-axis
shift 3 down
vertically stretch by a factor of 2
The transformed function is f(x)=(-2*((x+5)²)-3) and green is graph.
The vertical shift depends on the value of k. The vertical shift is described as follows:
g(x) = f (x) + k - The graph is shifted up k units.
g(x) = f (x) − k - The graph shifts down units.
we have,
f(x)=x²
reflected in the x-axis
f(x)=-(x)²
vertically stretched by a factor of 2
f(x)=2*x²
shifted five units to the left
f(x)=(x+5)²
shifted three units to dawn
f(x)=x²-3
we can write all together
f(x)=(-2*((x+5)²)-3)
graphing red original function green is transformed function.
the complete question is-
The graph of f(x) = x^2 is reflected in the x-axis, vertically stretched by a factor of 2, shifted five units to the left, and shifted three units down.
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assume that the heights of women in a population follow a normal distribution with a mean of 64.3 and a standard deviation of 2.6. (a) a woman is chosen at random from this population. what is the probability that she is more than 67 inches tall? g
The probability that a woman chosen at random from this population is more than 67 inches tall is approximately 0.1492 or 14.92%.
To find the probability that a woman chosen at random from this population is more than 67 inches tall, we need to calculate the z-score for this height and then find the corresponding probability from the standard normal distribution.
The z-score is calculated as:
z = (x - μ) / σ
where x is the value we want to find the probability for, μ is the mean of the distribution, and σ is the standard deviation.
In this case, x = 67, μ = 64.3, and σ = 2.6. Substituting these values into the formula, we get:
z = (67 - 64.3) / 2.6
= 1.04
Next, we look up the probability corresponding to a z-score of 1.04 in a standard normal distribution table or using a calculator. The probability of a z-score being less than 1.04 is 0.8508.
Since we are interested in the probability of a woman being more than 67 inches tall, we need to subtract this probability from 1:
P(x > 67) = 1 - P(z < 1.04)
= 1 - 0.8508
≈ 0.1492
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the equation y equals 20 times 3 to the power of t shows the number of infected people from an outbreak of whooping cough. the variable y represents the number of infected people, and t represents time in weeks. in how many weeks will the number of infected people reach 1,000?
An exponential equation, y = (20) 3ᵗ, shows the number of infected people from an outbreak of whooping cough. The number of Infected people reach 1000 after 3.56 weeks.
We have an equation that shows the number of people infected from a whooping cough outbreak. This equation is y is equal to 20 times 3 to the power of t, i.e. y = (20) 3ᵗ -- (1)
where y--> number of infected people
t--> time in weeks
An exponential equation is an equation with exponents where either the exponent or part of the exponent is a variable. As we see 't' is variable so, eqution (1) is an exponential equation. We have to determine time in weeks when the number of infected people count reach 1,000. Substitute, y = 1000 in (1)
=> 1000 = (20)3ᵗ
Dividing by 20 both sides
=> 1000/20 = 3ᵗ
=> 50 = 3ᵗ
Taking natural logarithm both sides,
=> ln(50) = ln( 3ᵗ)
=> ln(50) = t ln(3)
=> t = ln(50)/ln(3)
=> t = 3.56
Hence, required value of t is 3.56 weeks.
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maple has 4 identical loaves of bread that weigh a total of 6.6 pounds how much does 1 loaf of bread weigh ;show your work:
Answer:
1.45 pounds
Step-by-step explanation:
6.6 divided by 4
Use the following information to answer questions 10 - 13. (You will be following the steps to calculate the finance charge on an unpaid balance, and find the new balance.)
• Previous Balance: $678.98
• Payment: $150
• Purchases: $147.20
• APR: 14.24%
• Period: Monthly
10. What is the unpaid balance?
11. What is the periodic rate?
12. What is the finance charge?
13. What is the new balance?
The periodic rate is the annual percentage rate (APR) divided by the number of periods per year. The periodic rate is 1.1867%
What is the finance charge?The finance charge is the cost of borrowing money, and it is typically expressed as a percentage of the outstanding balance. In the given scenario, the finance charge is the interest that is charged on the unpaid balance.
According to question:10) The unpaid balance is the previous balance minus the payment, which is:
Unpaid balance = Previous balance - Payment
= $678.98 - $150
= $528.98
Therefore, the unpaid balance is $528.98.
11) The periodic rate is the annual percentage rate (APR) divided by the number of periods per year. Since the period is monthly, we divide the APR by 12. The periodic rate is:
Periodic rate = APR / 12
= 14.24% / 12
= 1.1867%
Therefore, the periodic rate is 1.1867%.
12) The finance charge is the unpaid balance multiplied by the periodic rate. The finance charge is:
Financial charge = Unpaid balance times the periodic rate
= $528.98 × 1.1867%
= $6.28 (rounded to the nearest cent)
Therefore, the finance charge is $6.28.
13) The new balance is the sum of the unpaid balance, the finance charge, and the purchases. The new balance is:
New balance = Unpaid balance + Finance charge + Purchases
= $528.98 + $6.28 + $147.20
= $682.46
Therefore, the new balance is $682.46.
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Camile walked 1/2 of a mile from school to Tom's house and 2/5 of a mile from Tom's house to her own house how many miles did Camile walk in all
Answer: 0.9 or 9/10
Step-by-step explanation:
The question asks how many miles did Camila walk in all, so we have to add 1/2 mile and 2/5 of a mile.
1/2 + 2/5 = 9/10
Answer:
9/10 of a mile
Step-by-step explanation:
1/2 + 2/5
= 5/10 + 4/10
=9/10
in a certain shipment of 18 18 computers, 6 6 are defective. 9 9 of the computers are selected at random without replacement. what is the probability that 4 4 of the 9 9 computers are defective? express your answer as a fraction or a decimal number rounded to four decimal places.
The probability that 4 of the 9 computers are defective is given by expression 0.3665.
It may be calculated by dividing the number of positive outcomes by the total number of potential outcomes. It is the attribute or state of being probable, the degree to which something is likely to happen. In other words, it is a way to gauge how likely an event is to occur.
out of 18 phones, 6 are defective. 9 of the phones are selected at random without replacement.
the probability that 4 of the 9 phones are defective
18 phones- 6 defective , 12 non-defective
9 phones- 4 defective , 5 non-defective
Required probability = [tex]\frac{^6 C_4*^1^2C_5 }{^1^8C_9}[/tex]
= 15x1188 / 48620
P = 0.3665
after rounding we get 0.3665.
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Complete question:
in a certain shipment of 18 computers, 6 are defective. 9 of the computers are selected at random without replacement. what is the probability that 4 of the 9 computers are defective? express your answer as a fraction or a decimal number rounded to four decimal places.
State the coordinates of the point.
Answer:
Step-by-step explanation:
look get 8 then 7 then you get 5 and luh tyler.
Hellppppppppppppppppp
find the probability that among 250 randomly selected subjects treated with the drug, exactly 10 of them experience nausea.
The probability that among 250 randomly selected subjects treated with the drug, exactly 10 of them experience nausea is 0.1317, or 13.17%
The number of subjects experiencing nausea follows a binomial distribution with parameters n=250 (number of trials) and p=0.1 (probability of success, i.e., experiencing nausea). The probability of exactly k subjects experiencing nausea is given by the probability mass function:
P(X=k) = (n choose k) * [tex]p^k[/tex] * [tex](1-p)^{(n-k)[/tex]where (n choose k) is the binomial coefficient "n choose k", which represents the number of ways to select k subjects out of n.
Using this formula with n=250, p=0.1, and k=10, we get:
P(X=10) = (250 choose 10) * (0.1)^10 * [tex](0.9)^{240[/tex]This gives a probability of approximately 0.1317, or 13.17%.
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Identify the asymptotes, domain, and range of each function.
The function f(x) = 5/(x+3), vertical asymptote at x = -3, domain of the function is all real numbers except x = -3, range is all real numbers except 0.
Describe Function?A function is a mathematical object that takes one or more inputs (usually represented as variables) and produces a single output. In other words, a function is a relation between sets of inputs and outputs that associates each input value with exactly one output value.
A function can be represented by an equation or a graph. The most common way to write a function is in the form f(x) = y, where x is the input variable and y is the output variable. The function f maps each value of x to a corresponding value of y.
Functions can be classified based on their properties, such as their domain (set of allowable input values), range (set of output values), and behavior (e.g., increasing, decreasing, constant, etc.). Some common types of functions include linear, quadratic, exponential, trigonometric, and logarithmic functions.
The function f(x) = 5/(x+3) has a vertical asymptote at x = -3, since the denominator becomes zero at that point.
The domain of the function is all real numbers except x = -3, since division by zero is undefined.
To find the range, we can consider what happens to the function as x approaches -3 from both sides. As x approaches -3 from the left (i.e., as x gets closer and closer to -3 from values less than -3), the function becomes increasingly negative. As x approaches -3 from the right (i.e., as x gets closer and closer to -3 from values greater than -3), the function becomes increasingly positive. This means that the range of the function is all real numbers except 0.
Therefore, the asymptote is x = -3, the domain is all real numbers except x = -3, and the range is all real numbers except 0.
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