Given a sample of 36 male mosquitos of a species with a mean lifespan of 8.88 days and a standard deviation of 6.66 days, the probability of the sample mean lifespan exceeding 10 days is approximately 0.14. So, the correct choice is option B is P ( x ˉ > 10 ) ≈ 0. 14 P( x ˉ >10)≈0. 14P, left parenthesis, x, with, \bar, on top, is greater than, 10, right parenthesis, approximately equals, 0, point, 14.
The sampling distribution of the mean lifespan is approximately normal due to the Central Limit Theorem.
The standard error of the mean is 6.66 / sqrt(36) = 1.11. The z-score for a sample mean of 10 is (10 - 8.88) / 1.11 = 1.08. Using a standard normal distribution table or calculator, the probability of a z-score greater than 1.08 is approximately 0.14.
Therefore, the answer is Choice B is P(X > 10) ≈ 0.14.
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QUACKITY SUPREMACY ALSO I NEED HELP WITH MATH
Answer:
QUACKITY IS THE MOST POG PERSON EVER
Step-by-step explanation:
BECAUSE I SAID SO
Find (i) x ,y ,z and w (ii) x + y + z + w
Please lemme know with explanation
Answer:
x = 60°, y = 100°, z = 120°, w = 80°
Step-by-step explanation:
x and 120° are adjacent angles on a straight line and sum to 180°
x + 120° = 180° ( subtract 120° from both sides )
x = 60°
Similarly
y + 80° = 180° ( subtract 80° from both sides )
y = 100°
and
z + 60° = 180° ( subtract 60° from both sides )
z = 120°
--------------------------------------------------------------------
The sum of the interior angles in a quadrilateral = 360°
sum the interior angles of the quadrilateral and equate to 360°
60° + 80° + 120° + 4th angle = 360°
260° + 4th angle = 360° ( subtract 260° from both sides )
4th angle = 100°
w and 100° are adjacent angles on a straight line and sum to 180° , so
w + 100° = 180° ( subtract 100° from both sides )
w = 80°
hola me gusta la matematicas
Answer:
that is spanish for "hello, i like mathimatics"
Step-by-step explanation:
it is
Answer: Do you want a translation? If you do, it says, "Hello, I like Mathematics."
Step-by-step explanation: I know spanish.
What is the solution of 2x² 3x 2 0?
The solution of the function 2x² + 3x + 2 = 0 is the zeros obtained after factorizing them which is found to be as -2 and -1 / 2.
The given equation is , 2x² + 3x + 2 = 0
On factorizing this we will get ,
2x² +4x - x +2 = 0
=> 2x(x +2) - ( x + 2) = 0
=> (2x-1) (x + 2) = 0
Therefore , the zeroes are -2 and -1 / 2.
Factorization is a process in which we write a given equation in terms of their prime factors. The result of factorization is known as zeros off a polynomial and are the solution for the given equation.
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PLEASE HELP DUE TODAY
The back of Nico's truck is 7. 5 feet long, 4 feet wide, and 8 feet tall. He has several boxes of important papers that he needs to move. Each box of papers is shaped like a cube, measuring 2. 5 feet on each side.
How many boxes of papers can Nico pack into the back of his truck?
Show your work.
Answer:
15
Step-by-step explanation:
The volume of the back of his truck is equal to 7.5 X 4 X 8, this equals 240, the volume of each box is 2.5 X 2.5 X 2.5, this equals 15.625, that means that 15.36 boxes fit, but because you can't break a box into .36 pieces, only 15 will fit.
Answer fast
Which of the following is used to identify outliers in a set of data?
1.5(IQR)
1.5(range)
2(mean)
2(median)
The Interquartile range i.e 1.5 (IQR) is used to identify outliers in a set of data which is the correct answer would be option (A).
What is the Interquartile range (IQR)?We may build up a "fence" outside of Q1 and Q3 by using the Interquartile range (IQR) method of spotting outliers. Outliers are values that fall outside of this range.
To construct this barrier, we take 1.5 times the IQR, deduct it from Q1, and add it to Q3. This provides us with the lowest and maximum fence posts against which we will compare each observation.
Outliers are observations that are greater than 1.5 IQR below or above Q1. Minitab's default strategy for identifying outliers is this.
Therefore, the Interquartile range (IQR) is used to identify outliers in a set of data.
Hence, the correct answer would be option (A).
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what is the approach to test the hypotheses using the binomial distribution for both non-directional and directional cases
To test hypotheses using the binomial distribution, set up hypotheses, determine the significance level, calculate critical values or p-values, and compare them to the significance level to make a decision.
To test hypotheses using the binomial distribution, we can follow these approaches for both non-directional and directional cases:
Non-Directional (Two-Tailed Test):Set up the null hypothesis (H₀) and alternative hypothesis (H₁) based on the research question.
Determine the significance level (α) for the test.
Calculate the critical values or the rejection regions based on the significance level.
Collect the sample data and calculate the observed test statistic (such as the number of successes in a fixed number of trials).
Calculate the p-value, which is the probability of obtaining a test statistic as extreme as the observed one under the null hypothesis.
Compare the p-value to the significance level. If the p-value is less than or equal to α, reject the null hypothesis. Otherwise, fail to reject the null hypothesis.
Directional (One-Tailed Test):Set up the null hypothesis (H₀) and alternative hypothesis (H₁) based on the research question, specifying the direction of the expected effect.
Determine the significance level (α) for the test.
Calculate the critical value or the rejection region for the specified direction.
Collect the sample data and calculate the observed test statistic.
Calculate the p-value for the specified direction.
Compare the p-value to the significance level. If the p-value is less than or equal to α, reject the null hypothesis. Otherwise, fail to reject the null hypothesis.
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g a cylindrical can is to be made to hold 1.4 l of oil. find the dimensions that will minimize the cost of the metal to manufacture the can
The dimensions that will minimize the cost of the metal to manufacture the can are,
Radius = 4.08 cm
Height = 10.84 cm
To minimize the cost of the metal to manufacture the can, we need to minimize the surface area of the can. The surface area of a cylinder is given by
A = 2πrh + 2πr^2
where r is the radius of the cylinder, h is the height of the cylinder, and π is a constant equal to approximately 3.14159.
We are given that the can needs to hold 1.4 liters of oil. We can use this information to find the relationship between the radius and height of the cylinder. The volume of a cylinder is given by
V = πr^2h
Substituting the given volume of 1.4 liters (1400 cubic centimeters) and the constant π, we get
1400 = 3.14159r^2h
Solving for h, we get
h = 1400/(3.14159r^2)
Now we can substitute this expression for h in the formula for the surface area of the cylinder to get
A = 2πr(1400/(3.14159r^2)) + 2πr^2
Simplifying this expression, we get
A = (2800/πr) + 2πr^2
To minimize the surface area, we need to find the value of r that makes the derivative of A with respect to r equal to zero. Taking the derivative, we get
dA/dr = -2800/πr^2 + 4πr
Setting this equal to zero and solving for r, we get:
-2800/πr^2 + 4πr = 0
2800/πr^2 = 4πr
r^3 = 700/π
r ≈ 4.08 cm
Now we can use the formula for h in terms of r to find the corresponding value of h
h = 1400/(3.14159(4.08)^2) ≈ 10.84 cm
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the pearson correlation coefficient can be used as: group of answer choices a descriptive statistic. an inferential statistic. an analysis of cause through hypothesis testing. both a descriptive and inferential statistic.
The Pearson correlation coefficient can be used as both a descriptive statistic and an inferential statistic.
As a descriptive statistic, the Pearson correlation coefficient describes the strength and direction of the linear relationship between two variables. It provides a numerical measure between -1 and 1, where -1 indicates a perfect negative linear relationship, 1 indicates a perfect positive linear relationship, and 0 indicates no linear relationship.
As an inferential statistic, the Pearson correlation coefficient can be used to test hypotheses and make inferences about the population correlation based on a sample. Hypothesis testing allows you to determine whether the observed correlation in the sample is statistically significant or occurred by chance. By examining the p-value associated with the correlation coefficient, you can make inferences about the strength of the relationship in the population.
Therefore, the correct answer is that the Pearson correlation coefficient can be used as both a descriptive and an inferential statistic.
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find a power series representation for the function f(x) = ln(9 + x2)
The power series representation for the function f(x) = ln(9 + x²) is:
ln(9 + x²) = ln(9) + (∑ from n=1 to ∞) (-1)ⁿ * (x² - 9)ⁿ / (n * 9ⁿ)
How can we express the function f(x) = ln(9 + x²) as a power series?
To derive the power series representation for the function f(x) = ln(9 + x²), we start with the Taylor series expansion for ln(1 + t), where t = x² - 9:
ln(1 + t) = ∑ from n=1 to ∞ (-1)ⁿ * (tⁿ / n).
We substitute t = x² - 9 into the above equation:
ln(9 + x²) = ∑ from n=1 to ∞ (-1)ⁿ * ((x² - 9)ⁿ / n).
This gives us the power series representation for f(x) = ln(9 + x²). However, it's worth noting that this power series converges only within a certain interval of x values.
The radius of convergence can be determined using techniques such as the ratio test or the interval of convergence of the original function.
Therefore, the answer is ln(9 + x²) = ln(9) + (∑ from n=1 to ∞) (-1)ⁿ * (x² - 9)ⁿ / (n * 9ⁿ), but the convergence of the power series needs to be considered based on the interval of convergence.
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Enter the numerator and the denominator of the fraction in simplest form that is equal to 0.7¯¯¯
.
Answer:
7/10 is the answer
please give me brainlest
Answer: 7 / 9
Step-by-step explanation:
Sound will travel fastest in air at _____.
Answer: 15 degrees Celsius
Step-by-step explanation:
Sound travels fastest usually at 25 degrees Celsius when the air is hotter as physics professor Kim strong stated
• correct me if I'm wrong
an open-top box is to be made by cutting small congruent squares from the corners of a 10- in.-by-10-in. sheet of tin and bending up the sides. how large should the squares cut from thecorners be to make the box hold as much as possible? what are the dimensions of the box withthe largest volume?
the box with the largest volume has dimensions approximately 3.48 in. x 3.48 in. x 5.76 in.
Let x be the side length of the square cut from each corner of the tin sheet. Then the dimensions of the base of the box will be (10-2x) by (10-2x), and the height of the box will be x. Thus, the volume of the box is given by:
V = (10-2x)^2 * x = 4x^3 - 40x^2 + 100x
To maximize V, we take the derivative of this expression and set it equal to zero:
dV/dx = 12x^2 - 80x + 100 = 0
Solving for x using the quadratic formula, we get:
xx = (80 ± sqrt(80^2 - 4*12*100))/24 ≈ 1.74, 5.76
The solution x = 1.74 is extraneous, since it would result in negative dimensions for the box. Thus, the optimal size of the square to be cut from each corner is x = 5.76 inches.
The dimensions of the box with the largest volume are:
Length = Width = 10 - 2x = 10 - 2(5.76) ≈ 3.48 inches
Height = x = 5.76 inches
Therefore, the box with the largest volume has dimensions approximately 3.48 in. x 3.48 in. x 5.76 in.
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if the odds on a bet are 16:1 against, what is the probability of winning? express your answer as a fraction.
The probability of winning is 1/17, which can also be expressed as a decimal (approximately 0.059) or as a percentage (approximately 5.9%).
The odds on a bet represent the ratio of the probability of winning to the probability of losing. In this case, the odds are 16:1 against winning, which means that the probability of winning is 1 out of 16.
To express this probability as a fraction, we can use the formula:
Probability of winning = 1 / (odds + 1)
Plugging in the given odds, we get:
Probability of winning = 1 / (16 + 1)
Probability of winning = 1/17
In this case, the odds of 16:1 against winning correspond to a probability of 1/17, which represents the chance of winning the bet.
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How many positive odd integers less than 10,000 can be written using the digits
3, 4, 8, 9 and 0?
PLEASE HELP!!! 30+ POINTS
Use the following data to construct a frequency table and calculate the mean, mode, and median.
Answer:
A measure of average is a value that is typical for a set of figures. Finding the average helps you to draw conclusions from data. The main types are mean, median and mode. Data is also often grouped.
Step-by-step explanation:
To find the mean add all the ages together and divide by the total number of children.
If you type all those ages into a calculator it is easy to make an error.
Chen has an MP3 player called the Jumble. The Jumble randomly selects a song for the user to listen to. Chen's Jumble has
4
44 classical songs,
3
33 rock songs, and
2
22 rap songs on it. Chen is going to listen to
360
360360 songs.
What is the best prediction for the number of times Chen will listen to a classical song?
Choose 1 answer:
With probability=44/99, the number of times Chen will listen to a classical song is 160.
What exactly is probability?
Probability is the measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates that an event is impossible and 1 indicates that an event is certain. The probability of an event= number of favorable outcomes/ total number of possible outcomes.
Now,
The probability of Chen selecting a classical song is:
P(classical) = number of classical songs / total number of songs
P(classical) = 44 / (44 + 33 + 22)
P(classical) = 44 / 99
The expected value of the number of times Chen will listen to a classical song is:
E(X) = n * P(classical)
E(X) = 360 * 44 / 99
E(X) = 160
Therefore, the best prediction for the number of times Chen will listen to a classical song is 160.
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If a pumpkin weighs 2.7 kilograms and 1 pound is about 0.45 kilograms, how many pounds does the pumpkin weigh?
Answer:
6 pounds
Step-by-step explanation:
2.7/0.45 = 6
Questions are from: Gerald and Wheatly, Applied Numerical Analysis 1) 10. A sky diver jumps from a plane, and during the time before the parachute opens, the air resistance is propor- tional to the power of the diver's velocity. If it is known that the maximum rate of fall under these condi- tions is 80 mph, determine the diver's velocity during the first 2 sec of fall using the modified Euler method with Ar= 0.2. Neglect horizontal drift and assume an initial velocity of zero.
The diver's velocity during the first 2 sec of fall using the modified Euler method with Ar= 0.2 is 62.732 mph.
Given data: Initial velocity, u = 0 ft/sec
Acceleration, a = g = 32.2 ft/sec²
The maximum rate of fall, vmax = 80 mph
Time, t = 2 seconds
Air resistance constant, Ar = 0.2
We are supposed to determine the sky diver's velocity during the first 2 seconds of fall using the modified Euler method.
The governing equation for the velocity of the skydiver is given by the following:
ma = -m * g + k * v²
where, m = mass of the skydive
r, g = acceleration due to gravity, k = air resistance constant, and v = velocity of the skydiver.
The equation can be written as,
v' = -g + (k / m) * v²
Here, v' = dv/dt = acceleration
Hence, the modified Euler's formula for the velocity can be written as
v1 = v0 + h * v'0.5 * (v'0 + v'1)
where, v0 = 0 ft/sec, h = 2 sec, and v'0 = -g + (k / m) * v0² = -g = -32.2 ft/sec²
As the initial velocity of the skydiver is zero, we can write
v1 = 0 + 2 * (-32.2 + (0.2 / 68.956) * 0²)0.5 * (-32.2 + (-32.2 + (0.2 / 68.956) * 0.5² * (-32.2 + (-32.2 + (0.2 / 68.956) * 0²)))
v1 = 62.732 mph
Therefore, the skydiver's velocity during the first 2 seconds of fall using the modified Euler method with Ar= 0.2 is 62.732 mph.
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What is the solution of the inequality shown
below?
y+7≤-1
The solution to the inequality is y ≤ -8. This means that any value of y that is less than or equal to -8 will satisfy the original inequality.
To solve the inequality y + 7 ≤ -1, we need to isolate the variable y on one side of the inequality sign.
Starting with the given inequality:
y + 7 ≤ -1
We can begin by subtracting 7 from both sides of the inequality:
y + 7 - 7 ≤ -1 - 7
y ≤ -8
The solution to the inequality is y ≤ -8. This means that any value of y that is less than or equal to -8 will satisfy the original inequality.
In the context of a number line, all values to the left of -8, including -8 itself, will make the inequality true. For example, -10, -9, -8, -8.5, and any other value less than -8 will satisfy the inequality. However, any value greater than -8 will not satisfy the inequality.
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The following question may be like this:
What is a solution of the inequality shown below? y+7≤-1
Sarita deposits $1,00 in an account paying 3.4% annual interest compounded continuously. Use the formula to continuous compounded interest, A=Pe rt , where p is the principal, r is the annual interest rate, and t is the time in years.
A. What is the balance in Sarita's account after 5 years?
B.How long will it take the balance in Sarita's account to reach $2,000
Answer:
Step-by-step explanation:
a : 1,000
b : 350
Which is the equation of the function? f(x) = 3|x| + 1 f(x) = 3|x – 1| f(x) = 1/3|x| + 1 f(x) = 1/3|x – 1|
The equation of the function is −3<x<1. See the explanation below.
What is the solution to the above?Given the graph of function f is a parabola,
Thus, equation of parabola is y=(x+3)(x+1)
⇒y=x² +4x+3
⇒y−3+2²
= x²+2× x ×2+2²
⇒y+1=(x+2)²
We can rewrite this as
(x+2)² =4× (1/4) ×(y+1)
Comparing the above equation to the equation of a parabola, (x−h)² =4a(y−k), where (h,k) is the coordinates of vertex of parabola, we have,
(h,k)≡(−2,−1)
Hence, the x coordinate of the vertex is −2 which lies in the interval −3<x<1
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Ricky draws 24 cartoon Characters
every 3 minutes. Leo draws 28 cartoon
Characters every 4 minutes. Who draws
at a faster rate?
Answer:
Ricky
Step-by-step explanation:
24 divided by 3 equals 8 drawings per minute
28 divided by 4 equals 7 drawings per minute
Answer:
Ricky
Step-by-step explanation:
One way to solve this is finding out how many characters they draw per minute. In order to find this, you must divide the amount of cartoon characters by the time. For example, 24 divided by 3 is 8 and 28 divided by 4 is 7. Ricky draws 8 per min and Leo draws 7 per min. Therefore, Ricky draws at a faster rate. Hope this helps! :)
Please help me, I have no clue what its asking and I have to explain it in class tomorrow morning
its kinda blurry so;
The measurements for each side of the triangle:
side 1 (the vertical side): x-4
side 2 (the horizontal side on the top): x-1
side 3 (horizontal side on the bottom): 1/4x + 5
Answer:
The term was obtained by grouping and adding the all x terms in the expression.
Step-by-step explanation:
The example has already provided this step:
(x -4) +(x +1) +(¼x +5)= \( \frac{9}{4} x + 2\)
Thus, the question is asking how is \( \frac{9}{4} x\) derived from the expression.
The attached picture shows the intermediate working to arrive at the final perimeter expression.
This expression is later equated to 20 since it is given that the perimeter of the traingle is 20 inches.
Is the question ''how many cars were sold each day this month'' statistical or not?
simplify the expression
X - 4(3x + 2) + 8
Answer:
-11x
Step-by-step explanation:
X-4(3x+2)+8
multiply both 3x and 2
X-12x-8+8
x-12x
11x
What is an equation of the line that passes through the point (4,2)(4,2) and is perpendicular to the line 4x+3y=214x+3y=21?
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
\(4x+3y=21\implies 3y=-4x+21\implies y=\cfrac{-4x+21}{3} \\\\\\ y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{4}{3}}x+7\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill\)
\(\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{-4}{3}} ~\hfill \stackrel{reciprocal}{\cfrac{3}{-4}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{3}{-4}\implies \cfrac{3}{4}}}\)
so we're really looking for the equation of a line whose slope is 3/4 and it passes through (4 , 2)
\((\stackrel{x_1}{4}~,~\stackrel{y_1}{2})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{3}{4} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{ \cfrac{3}{4}}(x-\stackrel{x_1}{4}) \\\\\\ y-2=\cfrac{3}{4}x-3\implies {\Large \begin{array}{llll} y=\cfrac{3}{4}x-1 \end{array}}\)
true or false: a linear programming problem can have an optimal solution that is not a corner point. select one: true false
It is true that a linear programming problem can have an optimal solution that is not a corner point.
How given statement is true? Explain further?In linear programming, the optimal solution represents the point where the objective function is optimized while still satisfying all the constraints.
In some cases, the optimal solution may occur at a corner point of the feasible region, where two or more of the constraints intersect.
However, it is possible for the optimal solution to occur at a point that is not a corner point, but rather lies on an edge or a line segment of the feasible region.
This can occur when the objective function is parallel to one of the constraint lines or when there are redundant constraints that limit the feasible region.
Therefore, it is true that a linear programming problem can have an optimal solution that is not a corner point.
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Compare the fraction - 1/3 -1/2 100 points
Answer:
-1/3>-1/2
Step-by-step explanation:
-1/3>-1/2
Which of the following is a second degree trinomial? 3x + 8 -4x2 - 6x + 7 6x4 + 4x2 - 7 5x2 + 10
Answer:
the first one
Step-by-step explanation:
because it is