The probability that x is either less than 3 or greater than 8 is 0.375 .
In the question ,
it is given that ,
a continuous random variable X , is uniformly distributed between 2 and 10 ,
So , alpha(α) = 2 and beta(β) = 10 .
the probability that x is either less than 3 or greater than 8 can be calculated by :
P(X < 3 or X > 8) = 1 - (8 - 3)/(β - α)
= 1 - (8 - 3)/(10 - 2)
= 1 - 5/8
On simplifying further ,
we get ,
= 0.375
Therefore , the probability P(X < 3 or X > 8) is = 0.375 .
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An entomologist can model the number of mosquitos in a forest as a function of
rainfall. In a similar way, they can also model the number of bats in the forest.
The function f(x) = 5x
22
gives the number of mosquitos in the forest (in
millions), and the function g(x) = 3a 0.5a² gives the number of bats (in millions
-
In both equations z represents rainfall (in centimeters). Here are the graphs of f and
G
The interpretation of the point of intersection of the curves is (c) they give a solution to the equation 5x - x^2 = 3x - 0.5x^2
How to interpret the points of intersection?The graph of the two functions alongside their equations are the given parameters of this question
The functions are given as:
f(x) = 5x - x^2
g(x) = 3x - 0.5x^2
When the graphs of two curves or lines intersect on a coordinate plane, it means that the point of intersection represents where the graphs have equal value
In this case, it represents
f(x) = g(x)
Substitute the known values in the above equation
5x - x^2 = 3x - 0.5x^2
So, the interpretation of the point of intersection of the curves is (c) they give a solution to the equation 5x - x^2 = 3x - 0.5x^2
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What is the slope of (1,2) and (5,2) (remember to use the slope formula y1-y2/x1-x2 and
reduce) 1
Answer:
Zero slope
Step-by-step explanation:
When it is reduced you end up with 0/4 which is a zero slope.
Marcus and Jeremy both evaluated the expression −52 + 3. Marcus said the answer was −22. Jeremy said the answer was 28. Who is correct? Explain the error in the other student's work.
Step-by-step explanation:
Sample response: Marcus is correct. Jeremy squared -5 instead of 5. The negative is not within parentheses, so it is not squared.
Answer:
sup
Step-by-step explanation:
Marcus is correct. Jeremy squared -5 instead of 5. The negative is not within parentheses, so it is not squared.
sample response on edge
see ya
pls answer this as soon as possible no wrong answers pls
Answer:
The answe is b
Step-by-step explanation:
Because when u calculat,you’ll only get 1 answer.
pls mark BRAINLIEST
(x-2)3
nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn
Briefly describe the criterion used to obtain the ordinary least square estimator.
The criterion used to obtain the ordinary least square (OLS) estimator is to minimize the sum of the squared differences between the observed values and the predicted values.
In OLS, the goal is to find the line that best fits the given data points. The estimator minimizes the sum of the squared residuals, which are the differences between the observed values and the predicted values. The squared residuals are used to ensure that both positive and negative differences contribute to the overall error measure.
The OLS estimator achieves this by calculating the coefficients of the linear regression model that minimize the sum of the squared residuals. It finds the intercept and slope of the line that minimizes the total squared distance between the data points and the regression line. This minimization process is based on the principle of least squares, which aims to find the best-fitting line by minimizing the overall error.
By minimizing the sum of the squared residuals, the OLS estimator provides a measure of how well the regression line represents the data points. It allows for the determination of the line's slope and intercept, which can be used for predicting values and understanding the relationship between the variables.
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Liam is standing on a cliff that is 2km tall, he looks out towards the sea from the top of a cliff and notices two cruise liners on is 5km away at a diagonal and the other is 6. 8km away at a diagonal. What is the distance between the two cruise liners?
To find the distance between the two cruise liners, we can use the Pythagorean theorem. Let's assume Liam is standing at the vertex of a right triangle, with the cliff being the vertical side and the distances to the cruise liners being the diagonal sides.
Let's denote the distance between Liam and the first cruise liner as x, and the distance between Liam and the second cruise liner as y.
For the first cruise liner, we have a right triangle with one leg measuring 2 km (the height of the cliff) and the hypotenuse measuring 5 km. Using the Pythagorean theorem, we can calculate x:
x^2 + 2^2 = 5^2
x^2 + 4 = 25
x^2 = 21
x ≈ √21
Similarly, for the second cruise liner, we have a right triangle with one leg measuring 2 km and the hypotenuse measuring 6.8 km. Using the Pythagorean theorem, we can calculate y:
y^2 + 2^2 = 6.8^2
y^2 + 4 = 46.24
y^2 = 42.24
y ≈ √42.24
Now, to find the distance between the two cruise liners, we subtract the two distances:
Distance between the two cruise liners = y - x ≈ √42.24 - √21
Calculating the approximate values:
Distance between the two cruise liners ≈ 6.5 km
Therefore, the approximate distance between the two cruise liners is 6.5 km.
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please help me i promise it is school related
Answer:
$100 (rounding)
Step-by-step explanation:
Morning
in- 8 am
out- 12 pm
hours worked= 12-8
= 4hrs
After-noon
In- 12:45 pm
Out- 17:30 pm
hours worked= 4hrs 45min
Total working time= 8hrs 45 mins
$11 per hour
So, 8hrs wage= 11*8
=$88
60 min- $11
1 min - 11/60
45 min- (11*45)60
=$8.25
Total, wage= $(88+8.25)
=$ 96.25
Divide (18x^3+9x^2)/(3x)
Answer:
6x^2 + 3x
Step-by-step explanation:
Dividing (18x3+9x2)/(3x) gives
Suppose $m$ is a two-digit positive integer such that $6^{-1}\pmod m$ exists and $6^{-1}\equiv 6^2\pmod m$. What is $m$
The value of $m$ is $43$.
The equation $6^{-1}\equiv 6^2\pmod m$ implies that $6^{-1}$ is a valid inverse of $6$ modulo $m$. This means that multiplying $6^{-1}$ by $6$ must result in the remainder $1$ when divided by $m$.
To find the value of $m$, we can then set up the equation:
$0\equiv 215\pmod m$
and find all possible values of $m$ that make this equation true.
Multiplying $6^{-1}\equiv 6^2\pmod m$ by $6$, we get $1\equiv 6^3\pmod m$, so $0\equiv 215\pmod m$. So, $m$ must be a divisor of $215$. The only 2-digit divisor of $215$ is $43$.
Therefore, $m$ is a two-digit number, the only possible value of $m$ is $43$.
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toms water bottle can hold up to 32 ounces of water. each day he drinks more than 2 full bottles of water. which inequality correctly describes the number of ounces of water, w, that tom drinks each day?
The inequality that correctly describes the number of ounces of water, w, that tom drinks each day is d. 64<w.
Amount of water that the bottle can hold = 32 ounces
Bottles of water consumed = 2
A mathematical comparison and representation of the connection between two expressions is known as an inequality. It can be regarded as a generalisation of an equation and is denoted by signs such as <, > and =.
Tom consumes more than two complete bottles of water every day. Since each bottle can carry up to 32 ounces of water, we can describe Tom's daily water consumption as -
= w > 2 × 32
Therefore,
Simplifying the right side of the inequality:
w > 64
Complete Question:
Toms water bottle can hold up to 32 ounces of water. each day he drinks more than 2 full bottles of water. which inequality correctly describes the number of ounces of water, w, that tom drinks each day?
a. w>2
b. 32<w
c. w = 64
d. 64<w
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You text your friend for 15 minutes on friday night and for 25 minutes on saturday night. what is the percent of increase? (round to nearest whole percent)
Answer:
66%
Step-by-step explanation:
This doesn't really require any equations, it's just brain work.
15 can be easily divided into 3 parts, each part consisting of 5 units. Here, it will be 5 minutes, then, if it's 5 minutes for each 33%(this number is rounded), then, that means that for 10 minutes, it will be 66%. You can understand this because the amount of increase in minutes is 10 minutes, and if each 5 minutes = 33% of increase, then 33+33=66, so hence, our answer is 66%.
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A cola-dispensing machine is set to dispense 8 ounces of cola per cup, with a standard deviation of 1.0 ounce. The manufacturer of the machine would like to set the control limit in such a way that, for samples of 47, 5% of the sample means will be greater than the upper control limit, and 5% of the sample means will be less than the lower control limit.
If the population mean shifts to 7.8, what is the probability that the change will be detected? (Round your intermediate calculations to 2 decimal places and final answer to 4 decimal places.)
If the population mean shifts to 8.6, what is the probability that the change will be detected? (Round your intermediate calculations to 2 decimal places and final answer to 4 decimal places.)
1. When the population mean shifts to 7.8, the probability of detecting the change is approximately 0.0495 (or 4.95%).
2. The probability of detecting the change is 0.0495 or 4.95%.
To solve this problem, we'll use the concept of control limits and the sampling distribution of the sample means.
When the population mean shifts to 7.8: First, let's calculate the standard deviation of the sampling distribution, also known as the standard error (SE). The formula for SE is given by SE = σ / sqrt(n), where σ is the standard deviation of the population (1.0 ounce) and n is the sample size (47).
SE = 1.0 / sqrt(47) ≈ 0.145
Next, we need to determine the z-score corresponding to the lower and upper tails of the sampling distribution that capture 5% each. Since the total probability in both tails is 10%, each tail will have a probability of 5%. We can find the z-scores using a standard normal distribution table or calculator.
The z-score corresponding to the lower tail of 5% is approximately -1.645.
The z-score corresponding to the upper tail of 5% is approximately 1.645.
Now, let's calculate the lower and upper control limits:
Lower Control Limit (LCL) = Population Mean - (z * SE)
Upper Control Limit (UCL) = Population Mean + (z * SE)
LCL = 7.8 - (-1.645 * 0.145) ≈ 8.026
UCL = 7.8 + (1.645 * 0.145) ≈ 9.574
To find the probability of detecting the change, we need to calculate the area under the sampling distribution curve that falls beyond the control limits. In this case, we're interested in the area above the upper control limit.
Since the distribution is assumed to be normal, we can use the standard normal distribution's cumulative distribution function (CDF) to calculate this probability.
Probability of detecting the change = 1 - CDF(z-score for UCL)
Using the z-score for the upper control limit (UCL), we can calculate the probability.
Probability of detecting the change ≈ 1 - CDF(1.645) ≈ 0.0495
Therefore, when the population mean shifts to 7.8, the probability of detecting the change is approximately 0.0495 (or 4.95%).
When the population mean shifts to 8.6: We'll follow the same steps as before.
SE = 1.0 / sqrt(47) ≈ 0.145
The z-score corresponding to the lower tail of 5% is still approximately -1.645.
The z-score corresponding to the upper tail of 5% is still approximately 1.645.
LCL = 8.6 - (-1.645 * 0.145) ≈ 8.926
UCL = 8.6 + (1.645 * 0.145) ≈ 10.274
Probability of detecting the change = 1 - CDF(z-score for UCL)
Probability of detecting the change ≈ 1 - CDF(1.645) ≈ 0.0495
Therefore, when the population mean shifts to 8.6, the probability of detecting the change is also approximately 0.0495 (or 4.95%).
In both cases, the probability of detecting the change is 0.0495 or 4.95%.
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define a function substitute which takes three parameters, x, y, and z. it returns a new list which replaces all occurrences of x in y with z.
A function is a block of code that performs a specific task and can be reused throughout a program. In this case, the function `substitute` is designed to replace all occurrences of one element (`x`) in a list (`y`) with another element (`z`).
Here is the definition of the function `substitute` in Python:
```python
def substitute(x, y, z):
# Create a new list to hold the modified values
new_list = []
# Loop through each element in the original list
for element in y:
# If the element is equal to x, replace it with z
if element == x:
new_list.append(z)
# Otherwise, keep the original element
else:
new_list.append(element)
# Return the new list
return new_list
```
Here is an example of how to use the function:
```python
>>> original_list = [1, 2, 3, 4, 1, 2, 3, 4]
>>> print(substitute(1, original_list, 5))
[5, 2, 3, 4, 5, 2, 3, 4]
```
In this example, all occurrences of the number 1 in the original list are replaced with the number 5 in the new list.
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I need help pleaseeeeee
Answer: Angle 3
Step-by-step explanation:
Find the product.
(4x2 + x - 5)(2x + 1)
Why is x = 6 a solution to the proportion StartFraction 192/36=32/x?
Answer:
C
Step-by-step explanation:
When you cross multiply 192 times 6 it equals 1152 and if you multiply 32 times 36 you get 1152 and 1152 is equal to 1152.
(a-3b)^3 write the factors
Answer:
(-a×9b)2 taetaetaetaetae
Is this a function or no
Answer:
No
Step-by-step explanation:
It is not properly done.
Find the value of x so that l || m. State the converse used. (please help asap)!!!
Answer:
Corresponding Angles; x=35
Step-by-step explanation:
These are corresponding angles.
To solve this, make the two angles equal to each other.
4x+7 = 6x-63
Push the variables to one side and the numbers to the other
4x-4x+7+63= 6x-4x-63+63
7+63=6x-4x
70 = 2x
x=35
Now, plug it into one of the angles. It does not matter which, both angles are the same.
4(35)+7 = 147
(It was at this point i realize that you were looking for the x value, not the angles, but I guess this is a bit extra.)
Use the point (0, 500)and (6, 740) to write an equation for the best line of best fit
Answer:
y = x(40) + (500)
Step-by-step explanation:
slope = 40
y-in.. = 500
slope =
500 - 740 = -240
_______
0 - 6 = -6
slope = 240/6 or 40
A car slows down at -5.00 m/s2 until it comes to a stop after traveling 15.0 m. How much time did it take to stop.
Answer:
2.45 seconds to the nearest hundredth.
Step-by-step explanation:
Acceleration a = -5, distance s = 15, time = ?.
Final velocity = v = 0.
We need to use the equations of motion under constant acceleration.
v^2 = u^2 + 2as where u is the initial velocity
0 = u^2 + 2*-5*15
u^2 = 150
so u = √150
Now we use v = u + at:
0 = √150 - 5t
t = √150/5
t = 2.45 seconds.
Kimaya decided to by mangos and pineapples for her snack this week.
Mangos, m, cost $1.50 each. Pineapples, p , cost $3.00 each. She wants to spend $18
Here is Kimaya's work to solve 1.5m+3p=18:
1.5m+3p-3p=18-3p
1.5m/1.5=18-3p/1.5
m=12-2p
1. What does the 12 and -2 say about the situation
2. Solve 1.5m+3p=18 for p
If Kimaya does not buy any Pineapple then the cost of the Mangos will be 12 and for p the equation is p = 6 - 0.5m.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
Mangos, m, cost $1.50 each. Pineapples, p, cost $3.00 each. She wants to spend $18
1.5m+3p=18
After solving:
m = [1/1.5](18 - 3p)
m = 12 - 2p
If Kimaya does not buy any Pineapple then the cost of the Mangos will be 12 and -2 represents the slope.
m = 12 - 2p
p = 6 - 0.5m
Thus, if Kimaya does not buy any Pineapple then the cost of the Mangos will be 12 and for p the equation is p = 6 - 0.5m.
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i need help with this
What percent of 30 is 16.5 ?
..........
Answer: 0.55
Step-by-step explanation:
16.5 ÷ 30 = 0.55
In conclusion, 0.55 is 16.5 of 30.
Hope this helps!
Can y’all please help ASAP.
A fish is located 5 feet below sea level.
A bird is flying 10 feet above sea level.
A shark is swimming at 18 feet below sea level.
A balloon is floating at 7 feet above sea level.
What is the furthest from sea level (zero)?
Answer: A shark is swimming at 18 feet below sea level.
Step-by-step explanation: because it just asked that which one is the furthest from sea level it don’t say above zero or below zero!
what is the missing side of the triangle if one side is 12 and the other is 13?
Therefore, the missing side of the triangle is 5.
To determine the missing side of a triangle, you can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, if one side of the triangle is 12 and the other side is 13, we can label the missing side as x. Using the Pythagorean theorem, we have:
\(x² = 13² - 12²
x² = 169 - 144
x² = 25\)
Taking the square root of both sides, we find:
\(x = √25
x = 5\)
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What is the value of the expression below when y = 5?
y? – 3y + 6
Step-by-step explanation:
y-3y+6
when y is equal to 5
=5 - 3(5) + 6
=5 - 15 + 6
=5 - 9
= -4
If a+b+c = 9 and ab+bc+ca = 40, find a^2 + b^2 + c^2
Explanation
By definition.
\(\begin{gathered} (a+b+c)^2=a^2+b^2+c^2+2((ab)+(bc)+(ac)) \\ \end{gathered}\)so
Let
\(\begin{gathered} (a+b+c)=9 \\ ab+bc+ac=40 \\ \text{now, replace} \end{gathered}\)\(\begin{gathered} (a+b+c)^2=a^2+b^2+c^2+2((ab)+(bc)+(ac)) \\ 9^2=a^2+b^2+c^2+2(40) \\ 81=a^2+b^2+c^2+80 \\ \text{subtract 80 in both sides} \\ 81-80=a^2+b^2+c^2+80-80 \\ 1=a^2+b^2+c^2 \end{gathered}\)hence
\(a^2+b^2+c^2=1\)I hope this helps you
Will mark brainliest. Add 2√2+ 5√3 and √2 – 3√3.
Answer:
3√2 + 2√3
Step-by-step explanation:
2√2 + 5√3 + (√2 - 3√3)
(2√2 + √2 ) + (5√3 - 3√3)
(2+1) √2 + (5-3) √3
3√2 + 2√3
The answer is 7.70674230227