The wildlife conservation group is interested in the health of reproducing female wallabies. The wildlife group has established that 83% of female wallabies have a joey in their pouch. The group also know that 68% of wallabies in the region are female. You may assume that the sex and joey status of wallabies are independent wallaby to wallaby.
a) Use an appropriate limiting distributio to estimate the probability that at least 600 wallabies from a sample of 1000 have a joey.
b) From birth, joeys spend an average of 280 days in their mothers pouch. To answer the following, you may assume that the time a joey spends in the pouch is exponentially distributed.

Answer: The answer is 81x

Step-by-step explanation:

1. You have to apply the exponet rule.  so 3 to the 2nd power +2x

2. You then have to add the numbers 2+2=4  so your answer is 81x

Millimeters can be converted into centimeters by dividing the value by 10. The solution has been obtained by using the unit conversion.

What is unit conversion?

A unit conversion is used to express the same property in a different unit of measurement. For instance, you could use minutes instead of hours to represent time or feet instead of miles to indicate distance. It commonly occurs when measurements are provided in one system of units, such as feet, but are required in a different system, such as chains.

We are required to convert millimeters to centimeters.

We know that 1 centimeter = 10 millimeters

So, for converting millimeters to centimeters, we need to divide the value by 10.

Hence, millimeters can be converted into centimeters by dividing the value by 10.

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it would take approximately 0.0004 seconds (or 0.4 milliseconds) to determine the activity with a statistical uncertainty of 2%.

To determine the activity with a statistical uncertainty of 2%, we need to calculate the time interval that would provide sufficient data to achieve this level of precision.

The statistical uncertainty is typically expressed as the standard deviation or the relative standard deviation (coefficient of variation). In this case, let's assume the 2% uncertainty refers to the relative standard deviation.

The relative standard deviation (RSD) is calculated as the standard deviation divided by the mean, expressed as a percentage:

RSD = (Standard Deviation / Mean) * 100%

Given that the mean number of decays in 10 minutes is 1000, we can use this information to calculate the standard deviation:

Standard Deviation = (RSD / 100%) * Mean

                 = (2% / 100%) * 1000

                 = 0.02 * 1000

                 = 20

Now, to determine the time interval required to achieve the desired statistical uncertainty, we can use the following formula:

Time Interval = (Standard Deviation / Mean)²

Time Interval = (20 / 1000)²

             = 0.02²

             = 0.0004

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Answer:

900 people

Step-by-step explanation:

540 / 60 = 9

10% = 9

9 x 100 = 900 people

Hope that helps!

One ounce (oz) and milliliter (ml) are different units of measurement

An ounce (oz) is a unit of weight that is commonly used in the United States, while a milliliter (ml) is a unit of volume that is commonly used in the metric system. One ounce is equal to approximately 28.35 grams, while one milliliter is equal to one cubic centimeter.

So, 1 oz is not the same as 15 ml, because oz is a unit of weight and ml is a unit of volume. 1 oz is roughly equal to 28.35 grams and 15 ml is equal to 15 cubic centimeters. These measurements are not equal to each other and it's not possible to convert them directly.

In summary, that are used to measure different things. 1 oz is not the same as 15 ml, because oz is a unit of weight and ml is a unit of volume.It's important to remember that when cooking or measuring ingredients, it is important to use the appropriate unit of measurement for the task at hand.

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Every 30th person on a list of county residents, is the most representative sample of the population of interest.  Option A

A representative sample is a small group of individuals who, as closely as possible, reflect a larger group.

The best representative sample will be obtained by taking every 30th person on a list of county residents.

This is due to the fact that it requires choosing people from the entire county's resident population as opposed to only those who frequent a certain region (options B and C) or a particular group (option D, high school students).

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Answer:

Supplementary and Linear pair

The interval notation for the solution to the given inequality is:

(6,∞).

The inequality is solved similarly to an equality, applying the operations to isolate the variable.

For this problem, the inequality is given by:

3(3a - 6) > 12.

Dividing both sides by 3:

3a - 6 > 12.

Then:

3a > 18

a > 18/3

a > 6.

In interval notation, the solution is:

(6,∞).

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The area of the base of the gift box is 660 square inches.

We have to find the area of the base.

As we observe the bases, there are two rectangles.

One rectangle which has length of 24 in and width of 20 in.

Area of rectangle is length times width:

Area =24×20

Area = 480 square inches.

second rectangle which has length of 18 in and width of 10 in.

Area =18×10

=180 square inches.

Area of base =180+480

=660 square inches.

Hence, the area of the base of the gift box is 660 square inches.

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Answer

x = 6°

Explanation

The key to solving this is shown in the attached image below

So, we can see that the relation between all of this is that

5x + 17 = ½ [(37x + 5) - (23x - 5)]

5x + 17 = ½ (37x + 5 - 23x + 5)

5x + 17 = ½ (37x - 23x + 5 + 5)

5x + 17 = ½ (14x + 10)

5x + 17 = 7x + 5

5x - 7x = 5 - 17

-2x = -12

Divide both sides by -2

(-2x/-2) = (-12/-2)

x = 6°

Hope this Helps!!!

The scenario described is best described as a randomized block design experiment.

In a randomized block design experiment, the sample is divided into blocks based on certain characteristics (in this case, age, size, and soil type) to ensure that plants with similar characteristics are grouped together. Within each block, one plant is randomly assigned to receive the pesticide, while the other plant serves as a control. This design helps control for the potential effects of confounding variables and increases the precision of the experiment by reducing variability within each block.

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The expression that is equivalent to 734 + 356 - 134 using addition instead of subtraction is:

734 + 356 + (-134)

Answer:

706+350 = 956

Answer: False

Step-by-step explanation:

Researchers typically report the adjusted R-squared value in addition to the regular R-squared value, not because they lack confidence in the actual R-squared, but because the adjusted R-squared provides additional information about the goodness of fit of a statistical model. The regular R-squared value measures the proportion of the variance in the dependent variable that is explained by the independent variables in the model. However, it can be biased and increase as more predictors are added to the model, even if the additional predictors do not contribute significantly to the prediction.

The adjusted R-squared, on the other hand, takes into account the number of predictors in the model and penalizes the addition of irrelevant predictors. It provides a more conservative measure of the goodness of fit by adjusting for the number of predictors and the sample size. Researchers often use the adjusted R-squared to evaluate and compare different models with varying numbers of predictors or to assess the overall explanatory power of a model while considering its complexity.

In summary, researchers report the adjusted R-squared value to address the limitations of the regular R-squared and to provide a more accurate assessment of the model's goodness of fit.

Answer:

2.91 mph

Step-by-step explanation:

To find the unit rate you just divided 35 miles into 12.

35 ÷ 12 = 2.91

To find the magnitude and direction of a vector using trigonometry, you can follow these steps:

1. Identify the components of the vector: A vector can be represented by its horizontal (x) and vertical (y) components. For example, if we have a vector A with components Ax and Ay, we can express it as A = (Ax, Ay).

2. Calculate the magnitude of the vector: The magnitude of a vector is the length of the vector. To find the magnitude of a vector A, you can use the Pythagorean theorem. The formula is:
  magnitude(A) = √(Ax^2 + Ay^2)

3. Find the direction of the vector: The direction of a vector can be given in different forms, such as angles or degrees. Two common ways to express the direction of a vector are:
  a. Angle with the positive x-axis: This angle is measured counterclockwise from the positive x-axis to the vector. You can use trigonometric functions to find this angle. The formula is:
     angle = arctan(Ay / Ax)
  b. Angle with the positive y-axis: This angle is measured counterclockwise from the positive y-axis to the vector. To find this angle, you can subtract the angle obtained in step 3a from 90 degrees (or π/2 radians).

4. Convert the direction to degrees or radians, depending on the required format.

Let's consider an example to illustrate these steps:

Suppose we have a vector A with components Ax = 3 and Ay = 4.

1. Identify the components: A = (3, 4).

2. Calculate the magnitude:
  magnitude(A) = √(3^2 + 4^2) = √(9 + 16) = √25 = 5.

3. Find the direction:
  angle = arctan(4 / 3) ≈ 53.13 degrees.

4. Convert the direction:
  angle with positive y-axis = 90 degrees - 53.13 degrees ≈ 36.87 degrees.

So, the magnitude of vector A is 5, and its direction is approximately 36.87 degrees with a positive y-axis.

Remember, trigonometry can be used to find the magnitude and direction of a vector when you have its components.

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The complement of the empty set is the set of all possible elements in the universal set U, which is the English alphabet in this context.

The universal set U is defined as the set of all possible elements or values under consideration for a given context. On the other hand, the complement of a set A is defined as the set of all elements that are not in A but are in U.

The complement of the empty set is defined as the set of all elements in U since the empty set is a subset of every set.

Therefore, the complement of the empty set in this context would be the entire set of all letters in the English alphabet.

This is because the empty set contains no elements, and therefore, its complement would be the set of all possible elements in U, which in this case is the English alphabet.

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Given:

The objective is to find the probability of drawing a face card from a deck of card.

The number of cards in a deck is, N = 52.

The number of face cards in a deck is, n(E) = 12.

Then, the required probability can be calculatad as,

Hence, option (A) is the correct answer.

The frequency of a class is the number of data points that fall within the class is 1.

To determine the frequency of each class in the table shown, we must first divide the data points into the respective classes. The classes are 1003, 1062, 1063, 1122, 1123, 1182, 1183, 1242, 1243, 1302, 1303, and 1362.

For the class 1003, the frequency is 1, since there is only one data point (1003) in this class.

For the class 1062, the frequency is also 1 since there is only one data point (1062) in this class.

For the class 1063, the frequency is also 1 since there is only one data point (1063) in this class.

For the class 1122, the frequency is 1 since there is only one data point (1122) in this class.

For the class 1123, the frequency is 1 since there is only one data point (1123) in this class.

For the class 1182, the frequency is 1 since there is only one data point (1182) in this class.

For the class 1183, the frequency is 1 since there is only one data point (1183) in this class.

For the class 1242, the frequency is 1 since there is only one data point (1242) in this class.

For the class 1243, the frequency is 1 since there is only one data point (1243) in this class.

For the class 1302, the frequency is 1 since there is only one data point (1302) in this class.

For the class 1303, the frequency is 1 since there is only one data point (1303) in this class.

For the class 1362, the frequency is 1 since there is only one data point (1362) in this class.

Therefore, the frequency of each class in the table shown is 1.

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Probability that the number of speeding cars is at least 9: 0.009 Expected number of speeding cars, E[X]: 4.5 Variance of the distribution of X: 2.25 Standard deviation of the distribution of X: 1.5 Expected fines generated by the next 9 cars: R19566.

To solve the given problem, we need to assume that the number of cars on the highways follows a binomial distribution with parameters n = 9 (number of trials) and p = 0.5 (probability of a car being above the speed limit).

Probability that the number of speeding cars is at least 9:

Since the probability of a car being above the speed limit is 0.5, the probability of a car not being above the speed limit is also 0.5.

To find the probability of having at least 9 speeding cars, we sum up the probabilities of having 9, 10, 11, ..., up to 9 cars. Mathematically, it can be represented as P(X ≥ 9) = P(X = 9) + P(X = 10) + P(X = 11) + ... + P(X = 9).

Using the binomial probability formula, P(X = k) = (n choose k) * p^k * (1 - p)^(n - k), we can calculate the probabilities for each value of k and then sum them up:

P(X ≥ 9) = P(X = 9) + P(X = 10) + P(X = 11) + ... + P(X = 9)

= [C(9, 9) * 0.5^9 * 0.5^(9 - 9)] + [C(9, 10) * 0.5^10 * 0.5^(9 - 10)] + [C(9, 11) * 0.5^11 * 0.5^(9 - 11)] + ...

Evaluating this expression, we find that P(X ≥ 9) ≈ 0.009 (rounded to 3 decimal places).

Expected number of speeding cars, E[X]:

The expected value of a binomial distribution is given by the formula E[X] = n * p. Therefore, in this case, the expected number of speeding cars is E[X] = 9 * 0.5 = 4.5 (rounded to one decimal place).

Variance of the distribution of X:

The variance of a binomial distribution is calculated using the formula Var(X) = n * p * (1 - p). Substituting the values, we get Var(X) = 9 * 0.5 * (1 - 0.5) = 2.25 (rounded to one decimal place).

Standard deviation of the distribution of X:

The standard deviation is the square root of the variance. Therefore, the standard deviation of the distribution of X is sqrt(2.25) = 1.5 (rounded to one decimal place).

Expected fines generated by the next 9 cars:

Since the average speeding fine per car is R2174, the expected fines generated by a single car is R2174. Therefore, the expected fines generated by the next 9 cars would be 9 * R2174 = R19566.

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When we subtract 3 from 22, the simplified answer is 19. The subtraction operation involves removing or deducting one value from another, resulting in the difference between the two quantities.

To subtract 3 from 22, we can perform the subtraction operation as follows:

22

3

19

We align the numbers vertically and subtract each corresponding place value from right to left. In this case, subtracting 3 from 2 requires borrowing or regrouping. However, since 2 is greater than 3, we can directly subtract 3 from 2 and write the difference, which is 1, in the one's place.

Therefore, the simplified answer is 19.

The subtraction process involves taking away or removing a certain quantity from another. In this case, we subtracted 3 from 22, resulting in a difference of 19. The process of simplifying the answer is simply expressing the result in its most concise and reduced form.

By subtracting 3 from 22, we removed 3 units from the original value of 22, leaving us with 19. This can be visualized as taking away three objects from a group of 22 objects, resulting in a remaining count of 19.

In summary, when we subtract 3 from 22, the simplified answer is 19. The subtraction operation involves removing or deducting one value from another, resulting in the difference between the two quantities.

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Answer:

4/8 or 1/2

Step-by-step explanation:

Convert all size to x/8

1/4=2/8 and 1/2=4/8

Multiply size of beaker by how many there are filled

1/8 * 2= 2/8

2/8*7= 14/8

4/8*3 =12/8

then add all of them together = 28/8

convert 4 liters to 32/8

Subtract 32/8 - 28/8 = 4/8

Declan's reasoning does make sense. This is because 3/4 and 1/2 have the same denominator, and 3/4 is a larger fraction than 1/2.

Therefore, it is reasonable to assume that 3/4 is greater than 6/12 because 6/12 simplifies to 1/2. Simplifying fractions means dividing the numerator and denominator by the same number, in this case, 6 is divisible by 2, so we can reduce the fraction to 1/2.

So, Declan is correct in his reasoning that 3/4 is greater than 6/12. It is important to understand the relationship between fractions and their denominators to make such comparisons accurately.

3/4 = 9/12

1/2 = 6/12

6/12 = 6/12

Since 9/12 (which is equivalent to 3/4) is greater than 6/12 (which is equivalent to 1/2), we can say that 3/4 is indeed greater than 6/12.

Therefore, Declan's reasoning is correct.

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Answer:

g(x)= 9 cos (x - \(\frac{\pi}{3}\)) +7

Step-by-step explanation:

What is given is f(x) = g cos (x - pi/2) + 3

Note that the standard form of cosine function is a cos (bx + c) + d

a= amplitude

-c/b = phase shift

d = vertical shift

After moving pi/6 to the left --

x = pi/2 - pi/6 = pi/3

once moving pi/6 left, it is at pi/3

moving 4 units up just means adding 4 + 3, and that equals 7, that would be the vertical shift once applied.

So the equation that represents g(x) is C. 9 cos (x - pi/3) + 7

The equation that represents the function g(x) is \(g(x)=9 \cos (x- \frac{\pi}{3})+7\)

The function is given as:

\(f(x)=9 \cos (x-\frac{\pi}{2})+3\)

The function f(x) is first translated \(\frac{\pi}{6}\) units left.

The rule of this translation is:

\((x,y) \to (x + \frac{\pi}{6},y)\)

So, we have:

\(f'(x)=9 \cos (x+ \frac{\pi}{6}-\frac{\pi}{2})+3\)

Take LCM

\(f'(x)=9 \cos (x+ \frac{\pi - 3\pi}{6})+3\)

\(f'(x)=9 \cos (x- \frac{2\pi}{6})+3\)

Divide 2 by 6

\(f'(x)=9 \cos (x- \frac{\pi}{3})+3\)

Next, we translate f'(x) 4 units up.

The rule of this translation is:

\((x,y) \to (x,y+4)\)

So, we have:

\(g(x)=9 \cos (x- \frac{\pi}{3})+3 +4\)

\(g(x)=9 \cos (x- \frac{\pi}{3})+7\)

Hence, the equation that represents the function g(x) is \(g(x)=9 \cos (x- \frac{\pi}{3})+7\)

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Answer

Thats how you do it really hope it helps

Step-by-step explanation:

y=10x−1

Swap sides so that all variable terms are on the left hand side.

10x−1=y

Add 1 to both sides.

10x=y+1

Divide both sides by 10.

10

10x

​

=

10

y+1

​

Dividing by 10 undoes the multiplication by 10.

x=

10

y+1

​

SOLVE FOR Y

y=10x−1

Answer: Number 1: 3/4 = 21/28

Need any more help? I am usually available mon - fri 9 a.m. to 3:50 p.m.

Answer: 161+7n

Explanation: Let the number be n.

7(23+n)

=161+7n

Hope this helps you! Have a great day!!!!! :) :D

You can use the given data to find out how many miles does the van travels for 1 gallon of gas. This will help you get the distance van can travel for full tank (16.2 gallons) of gas.

The considered van with full tank(16.2 gallons) can travel 362.88 miles

Since the considered van traveled 241.92 miles in 10.8 gallons, then we can take equal in dimension of input and output relation.

\(10.8 \: \rm gallons = 241.92 \: miles\\\\\text{Dividing both quantities by 10.8 to get miles traveled per gallon}\\\\\dfrac{10.8}{10.8} \: gallon = \dfrac{241.92}{10.8} \: miles\\\\ 1 \: gallon = 22.4 \: miles\)

Thus, the considered van travels 22.4 miles per gallon of gas.

Now, since full tank consists of 16.2 gallons, thus, multiplying by 16.2 on both the sides, we  get

\(\rm 1 \: gallon = 22.4 \: miles\\\\16.2 \: gallons = 16.2 \times 22.4 \: miles = 362.88 \: miles\)

Thus,

The considered van with full tank(16.2 gallons) can travel 362.88 miles

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Answer:

it's law

Step-by-step explanation:

i think it is law of mathematics. isn't it?

Answer:

C 3.5t + 15, where t is the number

of days