Calculate the length of ED and BE

a) The standard deviation of T is the square root of the variance, which is SD(T) = sqrt(980) ≈ 31.3 months.

The rate of discovery of new beetle species can be modeled by a Poisson process with rate parameter λ = 1/7.0 new species per month. Let T be the time (in months) until 20 new species are discovered. Then T follows a gamma distribution with shape parameter k = 20 and rate parameter λ. The expected value of T is E(T) = k/λ = 20/(1/7.0) = 140 months. The variance of T is Var(T) = k/λ^2 = 20/(1/7.0)^2 = 980 months^2.

b) The probability that the supplement will be published within 10 years (120 months) is equal to the probability that T ≤ 120. Using the cumulative distribution function (CDF) of the gamma distribution, we can compute this probability as follows:

P(T ≤ 120) = F(120) = ∫[0,120] f(t) dt

where f(t) is the probability density function (PDF) of the gamma distribution, given by:

f(t) = λ^k * t^(k-1) * e^(-λt) / Gamma(k)

where Gamma(k) is the gamma function. Substituting the values of k, λ, and t, we get:

f(t) = (1/7.0)^20 * t^19 * e^(-t/7.0) / Gamma(20)

Using numerical integration or a software program, we can compute the integral:

P(T ≤ 120) ≈ 0.981

Therefore, the probability that the supplement will be published within 10 years is approximately 0.981, or 98.1%.

c) Alternatively, we can approximate the gamma distribution by a normal distribution using the central limit theorem, since the sample size (k = 20) is relatively large. The mean and standard deviation of the normal approximation are given by:

μ = E(T) = 140 months

σ = SD(T) = sqrt(980) ≈ 31.3 months

Using the standard normal distribution, we can standardize the random variable Z = (T - μ) / σ and compute the probability as follows:

P(T ≤ 120) = P(Z ≤ (120 - μ) / σ) ≈ P(Z ≤ (120 - 140) / 31.3) ≈ P(Z ≤ -0.64)

Using a standard normal table or a software program, we can find that the probability of Z being less than or equal to -0.64 is approximately 0.261. Therefore, the probability that the supplement will be published within 10 years using the normal approximation is approximately 0.261, which is lower than the exact probability obtained in part b). This is because the gamma distribution is not exactly symmetric and has a longer tail than the normal distribution, which makes the normal approximation less accurate in the tails of the distribution.

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To answer your question, Hailey is using the distributive property to simplify the calculation of 7(18). The distributive property allows us to break up a multiplication problem into smaller, more manageable parts.

Hailey has rewritten 18 as 10 + 8, and she will now use the distributive property to calculate 7 times each of these two numbers separately.
So, the two products that Hailey will add together to get the final product are 7 times 10 (which is 70) and 7 times 8 (which is 56).
To check her work, she can add these two products together:
70 + 56 = 126
So, using the distributive property and breaking up 18 into 10 and 8, Hailey can mentally compute the product of 7(18) as 126.
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The quadratic equation from the points is g(x) = x² + 5x + 4

From the question, we have the following parameters that can be used in our computation:

(-1,0), (-4, 0), and (1, 10).

A quadratic function is represented as

g(x) = a(x - x₁)(x - x₂)

Using the given points, we have

g(x) = a(x + 4)(x + 1)

Next, we have

a(1 + 4)(1 + 1) = 10

This gives

a = 1

So, we have

g(x) = (x + 4)(x + 1)

Expand

g(x) = x² + 5x + 4

Hence, the quadratic equation from the points is g(x) = x² + 5x + 4

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The given statement "The standard deviation can be negative" is false.

The standard deviation is a measure of dispersion or variability in a dataset. It represents the average amount of deviation or spread of the data points from the mean. By definition, the standard deviation is always a non-negative value or zero. It cannot be negative because it measures the distance of each data point from the mean, which is always a positive value.

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Required width is 29 millimeters and perimeter is 72 millimeters.

Given, Length of rectangle (L) = 7 millimeters

Area of the rectangle = 203 square millimeters

We know that, area of rectangle = Length × Width = L × W

According to the problem,

[tex]\sf L\times W = 203[/tex]

[tex]\sf \Rightarrow 7\times W=203[/tex]

[tex]\sf \Rightarrow W = \dfrac{203}{7}[/tex]

[tex]\sf \Rightarrow W = 29[/tex]

So, Width of rectangle = 29 millimeters

Perimeter of rectangle = 2 × (Length + Width)

[tex]\sf = 2\times(L+W)[/tex]

[tex]\sf = 2\times(7+29)[/tex]

[tex]\sf = 2\times36[/tex]

[tex]\sf = 72 \ millimeters[/tex]

So, perimeter of rectangle = 72 millimeters

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Check the picture below.

well, ∡CED is the same as ∡CEA and those are right-angles so those are pretty much given, now

[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{29}\\ a=\stackrel{adjacent}{20}\\ o=\stackrel{opposite}{CE} \end{cases} \\\\\\ CE=\sqrt{ 29^2 - 20^2}\implies CE=\sqrt{ 841 - 400 } \implies CE=\sqrt{ 441 }\implies \boxed{CE=21} \\\\\\ \stackrel{\textit{since we know the radius CB=29}}{CB-CE = EB\implies }\boxed{EB=8}[/tex]

Answer:

angle CED 90°. CE = 21. EB = 8.

Step-by-step explanation:

angle CED = 90° (right angle).

the radius (centre to edge) is the same right around the circle.

so that means that distance CD = 29.

draw a line from C to D. notice how that has just become an hypotenuse?

we know that DE = 20.

we have a right-angled triangle.

CE² = hypot² - DE²

       = 29² - 20²

       = 841 - 400

       = 441

CE = √441 = 21.

EB must be radius subtract CE. that is, 29 - 21 = 8.

The value of x is: x = 6, while the perimeter of the quadrilateral is calculated as: 52 units.

Based on the tangent theorem (two tangents meeting at the same point outside a circle have the length), we have:

x + 2 = 8

x + 2 - 2 = 8 - 2

x = 6

The value of x in the circumscribed quadrilateral is therefore, 6 units.

Using the same theorem the perimeter of the quadrilateral can be found by adding all sides of the quadrilateral as follows:

perimeter = 8 + 8 + 5 + 5 + 9 + 9 + 4 + 4

Perimeter = 52 units.

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Answer: YES, She is correct

Answer:

B. No. Both a and b are incorrect.

Step-by-step explanation:

Answer:The correct answer is: The 5th caller and the 16th caller are eligible for the prizes.

Step-by-step explanation:

The correct answer is: The 5th caller and the 16th caller are eligible for the prizes.

To find the eligible callers, we need to solve the absolute value equation:

|x - 111| = 5

This equation has two solutions:

x - 111 = 5 or x - 111 = -5

Solving for x in each case, we get:

x = 116 or x = 106

Therefore, the 5th caller is the one who calls in the 106th position, and the 16th caller is the one who calls in the 116th position.

Answer: The 6th caller and the 16th caller are eligible for the prizes.

Step-by-step explanation: correct for plato

the probability that the next customer that comes to the deli will order a ham sandwich is, 0.32

And,  the probability that the next customer that orders from the deli will NOT order a cheese sandwich is, 0.8

Given that;

The owner of a deli recorded the number of customers who ordered each of four sandwiches available.

Here, Total number of sandwiches = 160 + 100 + 180 + 60

= 500

Hence, the probability that the next customer that comes to the deli will order a ham sandwich is.,

⇒ 160 / 500

⇒ 16/50

⇒ 8/25

⇒ 0.32

And, the probability that the next customer that orders from the deli will NOT order a cheese sandwich is,

⇒ 1 - 100/500

⇒ 1 - 1/5

⇒ 4/5

⇒ 0.8

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Answer:

Let x = 6-2y/6

substitute into equation 2

6(6-2y/6)-2y = 6

6-4y = 6

-4y= -12

y = 3

From equation 2

6x-2y =6

substitute y=3

6x-2(3)= 6

6x = 12

x= 2

substitute both into the given equation

x+2y

2+2(3)= 8

Therefore x+ 2y= 8

The probability of obtaining 3 candies or fewer that are red in a random sample of 13 candies depends on the probability of selecting a red candy and follows a binomial distribution.

To calculate the probability, we can use the binomial probability formula and sum up the probabilities for each possible outcome (0, 1, 2, and 3 red candies) using the appropriate values for the number of trials, the probability of success (selecting a red candy), and the desired number of successes (3 or fewer). The result will provide the probability that the sample contains 3 or fewer red candies.

The probability of obtaining 3 candies or fewer that are red in a random sample of 13 candies can be calculated using the binomial probability formula. In this case, we are interested in the probability of success (selecting a red candy) and the desired number of successes (3 or fewer red candies) out of a fixed number of trials (13 candies).

The binomial probability formula is given by P(X = k) = C(n, k) * p^k * (1 - p)^(n - k), where P(X = k) is the probability of getting exactly k successes, n is the number of trials, p is the probability of success, and C(n, k) is the binomial coefficient.

To calculate the probability, we need to consider the cases of obtaining 0, 1, 2, and 3 red candies. We can then sum up the probabilities for each case.

For example, if the probability of selecting a red candy is p = 0.4, we can calculate the probabilities for 0, 1, 2, and 3 red candies using the formula and sum them up to find the overall probability.

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According to the given information, the friend's clock showed that 1 hour and 27 minutes had passed between the time we left and the time we arrived. The kitchen clock needs to be adjusted 1 hour and 5 minutes back, which is equal to 65 minutes.

When we left the house, the kitchen clock was showing 10:06, but according to the friend's clock, the correct time was 10:28.

Therefore, we left the house 22 minutes before the correct time. When we arrived at the friend's house, their clock showed 11:55, which means that 1 hour and 27 minutes had passed since we left our house.

However, the kitchen clock was only showing 10:28 + 22 minutes = 10:50, which means that the kitchen clock was slow by 1 hour and 5 minutes.

To adjust the kitchen clock to the correct time, we need to move it back by 1 hour and 5 minutes, which is equal to 65 minutes. Therefore, the correct time on the kitchen clock should be 10:06 - 1 hour and 5 minutes = 9:01. By adjusting the clock back by 65 minutes, it will now show the correct time of 11:55 when we return home.

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To find the value of x for which the two equations give the same value for y, we can set the expressions for y in both equations equal to each other and solve for x.

Given:

Equation 1: y = 3x + 6

Equation 2: 6x + 2y = 8

Substitute the expression for y from Equation 1 into Equation 2:

6x + 2(3x + 6) = 8

Simplify and solve for x:

6x + 6x + 12 = 8

12x + 12 = 8

12x = 8 - 12

12x = -4

x = -4/12

x = -1/3

Therefore, when x = -1/3, the two equations will have the same value for y.

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The options that have the same solution as the rewritten equation 2.3p - 10.1 = 6.49p - 4 are:

Option 2) 2.3p - 10.1 = 6.49p - 4

Option 5) 2.3p - 14.1 = 6.4p - 4

Both of these options are equivalent to the rewritten equation and have the same solution.

To rewrite the given equation, we can combine like terms and simplify:

2.3p - 10.1 = 6.5p - 4 - 0.01p

First, let's simplify the right side of the equation:

6.5p - 4 - 0.01p = 6.49p - 4

The equation becomes:

2.3p - 10.1 = 6.49p - 4

Now, we can compare the rewritten equation to the options provided:

2.3p - 10.1 = 6.4p - 42.3p - 10.1

= 6.49p - 4230p - 1010

= 650p - 400 - p23p - 101

= 65p - 40 - p2.3p - 14.1

= 6.4p - 4.

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Answer:

24

Step-by-step explanation:

Answer:

C. 20

Step-by-step explanation:

To find out how many students per teacher, we can divide the total number of students by the total number of teachers:

240 students / 12 teachers = 20 students per teacher.

Therefore, the answer is C. 20.

The maximum number of points that may not be on the line is given as follows:

A. 6.

To find the regression equation, which is also called called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator.

When we insert the points on a calculator, we get a linear function that is obtained using the mean and sum of squares of coefficients. This means that the line has on average the least distance to the points, but it can happen that none of the points is exactly on the line.

Hence option A is the correct option in the context of this problem.

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Answer:

YOUR ANSWER IS 0.139626

Step-by-step explanation:

HAVE A NICE DAY.

Answer:

EF ≈ 23.3

Step-by-step explanation:

given 2 secants drawn from an external point to the circle.

then the product of the measures of one secant's external part and that entire secant is equal to the product of the measures of the other secant's external part and that entire secant , that is

GF × GE = GH × GI

8 × GE = 10 × (10 + 15) = 10 × 25 = 250 ( divide both sides by 8 )

GE = 31.25

then

EF = GE - GF = 31.25 - 8 = 23.25 ≈ 23.3 ( to the nearest tenth )

A method to swap two array elements works correctly because it is designed to swap the entire elements at two different indexes in an array.

The method receives two integer values representing the indexes of the elements to be swapped and then proceeds to swap the elements themselves.
On the other hand, a method to swap two integer values does not work correctly because integers are passed by value, which means that the method receives a copy of the integer values rather than the original values themselves. Thus, the method only swaps the copies and not the original values, and as a result, the original values remain unchanged.
To overcome this issue, one can use a workaround such as passing the integer values as references instead of values. This way, the method receives a reference to the original value, and any changes made to the reference will affect the original value as well. However, this approach can be more complex and less efficient than simply swapping array elements.

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The factorized form of the expression[tex](x - y/xy)^3[/tex] is:

[tex]x^3 - 3x + 3/x - 1/x^3[/tex]

To factorize the expression [tex](x - y/xy)^3,[/tex] we can start by simplifying the expression inside the parentheses.

The term y/xy can be simplified to 1/x, so the expression becomes:

[tex](x - 1/x)^3[/tex]

Now, let's apply the cube of a binomial formula, which states that

[tex](a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3.[/tex]

Using this formula, we have:

[tex](x - 1/x)^3 = x^3 - 3x^2(1/x) + 3x(1/x)^2 - (1/x)^3[/tex]

Simplifying further, we get:

[tex](x - 1/x)^3 = x^3 - 3x + 3/x - 1/x^3[/tex]

Therefore, the factorized form of the expression[tex](x - y/xy)^3[/tex] is:

[tex]x^3 - 3x + 3/x - 1/x^3[/tex]

Please note that in this factorization, we simplified the term y/xy to 1/x based on the assumption that y is not equal to zero.

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The product of z1 and z2 is 81/2 + 27i*sqrt(6)/2 by using trigonometric identities.

To find the product of z1 and z2, we can use the formula for multiplying complex numbers:
z1 * z2 = (18*cos225 + 18i*sin225) * (3*cos240 + 3i*sin240)
Using trigonometric identities, we can simplify this expression:
z1 * z2 = 54*cos225*cos240 + 54i*sin225*cos240 + 54i*cos225*sin240 + 54*sin225*sin240
Now we can use the values of cosine and sine for 225 and 240 degrees:
cos225 = -sqrt(2)/2, sin225 = -sqrt(2)/2
cos240 = -sqrt(3)/2, sin240 = -1/2
Substituting these values, we get:
z1 * z2 = 54*(-sqrt(2)/2)*(-sqrt(3)/2) + 54i*(-sqrt(2)/2)*(-1/2) + 54i*(-sqrt(3)/2)*(-sqrt(2)/2) + 54*(-sqrt(2)/2)*(-1/2)
Simplifying this expression, we get:
z1 * z2 = 81/2 + 27i*sqrt(6)/2
Therefore, the product of z1 and z2 is 81/2 + 27i*sqrt(6)/2.

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The probability of experiencing exactly k delays in n days is given by:

P(X = k) = (nCk) * p^k * (1 - p)^(n - k)

To calculate the probability that Sasha will experience a delay due to traffic on at least 3 of the next 21 days, we need to consider the probability of experiencing a delay on each individual day and then use the binomial distribution.

Let's assume that the probability of experiencing a delay on any given day is p. The probability of not experiencing a delay on a single day is 1 - p.

Using the binomial distribution formula,

In this case, we want to find the probability of experiencing at least 3 delays, which means we need to calculate the probabilities for k = 3, 4, 5, ..., 21 and sum them up.

P(at least 3 delays) = P(X = 3) + P(X = 4) + P(X = 5) + ... + P(X = 21)

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The inequality is x + $318.67 + $12.89 + $30.57 + $78.20 ≤ $680. The value of 'x' is $226.78.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

Let 'x' be the remaining amount. Then the inequality is calculated as,

x + $318.67 + $12.89 + $30.57 + $78.20 ≤ $680

Simplify the inequality, then we have

x + $318.67 + $12.89 + $30.57 + $78.20 ≤ $680

x + $453.22 ≤ $680

x ≤ $226.78

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Triangle ABC ~ triangle DEF. triangle ABC with side AB labeled 11,.The length of fd is 2.28.

we can use the property that corresponding sides of similar triangles are proportional to find the length of side fd. let's set up the proportion:

ab/de = bc/ef = ac/df

plugging in the given values, we get:

11/3.3 = 7.9/ef = 7.6/fd

simplifying, we get:

fd = (7.6 x 3.3) / 11fd = 2.28 answer choice c. 2.28 is the correct answer.

Triangle ABC ~ triangle DEF. triangle ABC with side AB labeled 11, side CA labeled 7.6 and side BC labeled 7.9 and a second triangle DEF with side DE labeled

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To determine if the die is fair or not, we can perform a chi-square goodness-of-fit test. The null hypothesis for this test is that the observed frequencies match the expected frequencies, assuming the die is fair.

We can set the expected frequency for each face to be 50/6 = 8.33 (since there are six faces on the die and 50 total throws).

Next, we calculate the chi-square test statistic by comparing the observed frequencies to the expected frequencies. Using the formula:

χ² = ∑((O - E)² / E), where O is the observed frequency and E is the expected frequency.

Once we have the test statistic, we compare it to the critical value from the chi-square distribution with (number of categories - 1) degrees of freedom (in this case, 6 - 1 = 5) at a chosen significance level (e.g., 0.05). If the test statistic exceeds the critical value, we reject the null hypothesis and conclude that the die is not fair.

It's not possible to perform the chi-square test without the observed frequencies for each face of the die. Please provide the observed frequencies for each face, and I can help you analyze the data to determine if the die is fair or not.

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Answer:To completely fill in the basketball court, Glenwood High School will need 60 cubic yards of concrete.

Since one bag of concrete fills 0.5 cubic yards, we can calculate the number of bags needed by dividing the total cubic yards by the cubic yards per bag:

Number of bags = 60 cubic yards / 0.5 cubic yards per bag

Number of bags = 120 bags

Therefore, Glenwood High School needs to order at least 120 bags of concrete to completely fill in the basketball court. Since the school ordered more than enough concrete to completely fill in the court, they likely ordered more than 120 bags of concrete.

Step-by-step explanation:

Answer:

w=-4.5

Step-by-step explanation:

12÷3/8=4.5

-w= 4.5

w= -4.5

To solve the equation -3/8 w = 12 for w, you need to isolate w. You do this by dividing both sides by -3/8 which is equivalent to multiplying by -8/3 (the reciprocal). This gives w = -32.

To solve the given equation -3/8 w = 12 for w, we need to isolate w on one side of the equation. To do this, you can divide both sides of the equation by -3/8. In mathematics, dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of -3/8 is -8/3. So, when you multiply both sides of the equation by -8/3 you get:

w = 12 * (-8/3)

Simplify this further to get: w = -32

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The area of the actual plot of land, in acres is given by 320000 acres.

Here given the figure is a Trapezium.

We know that the area of the Trapezium with parallel sides of length ' a ' and ' b ' and height between them is ' d ' is given by = (1/2)*(1 + b)*d

We know that, 1 cm = 2 miles.

So, 10 cm = 20 miles

15 cm = 15*2 = 30 miles

Here in given trapezium the length of parallel sides are 10 cm and 15 cm. that is 20 miles and 30 miles respectively.

Height between them is = 10 cm = 20 miles.

So the area of the land is = (1/2)*(20 + 30)*20 = 50*10 = 500 square miles.

we know that 1 square miles = 640 acres

So the area in acres = 500*640 = 320000 acres.

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The question is incomplete. The complete question will be -

"The figure shown represents a plot of land and is drawn using a scale in which 1 cm equals 2 miles. one square mile is 640 acres. how large is the actual plot of land, in acres?"