A biologist tags 25 birds with a band on their foot and lets them go back into the wild. The next year 100 total birds are captured and 5 of them have the foot bands. Enter an estimate of the total bird population. 20

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⨠ add 8 and 6

\(\sf{2x^2+14}\)

⨠ factor the 2 out

\(\sf{2(x^2+7)}\)

Since we cannot simplify this more, we know that we've simplified completely.                                                                                   \(\small\pmb{\sf{Frozen \ melody}}\)

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The researchers have increased the power of their analysis by increasing the sample size.

The number of subjects involved in a sample size is referred to as the sample size in market research.

Examine 15 randomly selected groups of subjects.

There are five main ways to increase the power of an experiment or study: increase the alpha level, decrease random error, conduct a one-tailed test, expand the sample size, or increase the effect size. Of these, only the first option, which increases the sample size, will increase power.

Thus, the researchers have increased the power of their analysis by increasing the sample size.

Complete question: As one step in the statistical analysis of the effectiveness of CHW intervention, researchers calculated the average percentage of postnatal care use found in 10 randomly selected groups of 50 mothers. How could the researchers have increased the power of their analysis?

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Answer:

B

Step-by-step explanation:

So we have the two functions:

\(f(x)=-2x^2-5x+1\text{ and } h(x)=3(x+3)^2-11\)

And we want to find:

\(h(f(-1))\)

So, find f(-1) first. Substitute -1 into f(x):

\(f(-1)=-2(-1)^2-5(-1)+1\)

Square:

\(f(-1)=-2(1)-5(-1)+1\)

Multiply:

\(f(-1)=-2+5+1\)

Add:

\(f(-1)=4\)

Now, substitute this into h(f(-1)):

\(h(f(-1))=h(4)\)

So, substitute 4 into h(x):

\(h(4)=3(4+3)^2-11\)

Add:

\(h(4)=3(7)^2-11\)

Square:

\(h(4)=3(49)-11\)

Multiply:

\(h(4)=147-11\)

Subtract:

\(h(4)=136\)

So, our answer is B.

And we're done!

The standard deviation for the given data is 7.5668.

To calculate the standard deviation, we need to follow these steps:

Calculate the mean (average) of the data. The sum of the products of each class midpoint and its corresponding frequency is 625.

Calculate the deviation of each class midpoint from the mean. The deviations are as follows: -15, -10, -5, 0, 5, 10, 15.

Square each deviation. The squared deviations are 225, 100, 25, 0, 25, 100, 225.

Multiply each squared deviation by its corresponding frequency. The products are 675, 300, 75, 0, 225, 300, 675.

Sum up all the products of squared deviations. The sum is 2250.

Divide the sum by the total frequency minus 1. Since the total frequency is 50, the denominator is 49.

Take the square root of the result from step 6. The square root of 45.9184 is approximately 7.5668.

Therefore, the standard deviation for the given data is 7.5668.

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Answer:

2.4 ft tall

Step-by-step explanation:

If the Taj Mahal is 240 ft tall and the model is 1/100th of that then you would multiply 1/100 by 240. That give us our answer: 2.4 ft.

Answer:

------------

The value of the truck decreases by a fixed percentage (16%) each year.

The function can be represented as:

where x represents the number of years and y represents the value of the truck.

It is therefore an exponential decay function

This function will provide the value of the truck (y) after x number of years, given the initial value of $45,000 and a depreciation rate of 16% per year.

The depreciation of the truck's value over time can be modeled using an exponential decay function. An exponential decay function is suitable when the value decreases by a fixed percentage over a given time period.

In this case, the value of the truck depreciates by 16% per year. We start with the initial value of $45,000 and multiply it by (1 - 0.16) for each year of depreciation.

The exponential decay function can be represented as:

y = a(1 - r)^x

Where:

y represents the value of the truck at a given time (in dollars),

a represents the initial value of the truck (in dollars),

r represents the rate of depreciation (as a decimal), and

x represents the number of years.

Applying it to this situation, the function that best models the depreciation of the truck's value would be:

y = 45,000(1 - 0.16)^x

This function will provide the value of the truck (y) after x number of years, given the initial value of $45,000 and a depreciation rate of 16% per year.

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The equation we should solve to find b is option A:sin 55°/b = sin 30°/8

What is trigonometry?

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles.

We can use the law of sines to solve for the missing side length of the triangle. The law of sines states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is constant for all sides of the triangle. In other words:

a/sin A = b/sin B = c/sin C

where a, b, and c are the side lengths of the triangle, and A, B, and C are the angles opposite those sides.

Using this formula, we can write:

b/sin B = a/sin A

Substituting the given values, we get:

b/sin 30° = 8/sin 55°

Now, we can solve for b by cross-multiplying:

b = 8(sin 30° / sin 55°)

Therefore, the equation we should solve to find b is option A:

sin 55°/b = sin 30°/8

Note that options B and C have the sine and cosine terms reversed, respectively, and option D uses the law of cosines, which is not necessary to solve this problem.

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Answer:

7/24

Step-by-step explanation:

two minuses make a +,

meaning this equation is basically

-1/12+3/8

find a common denominator by LCM.

8,16,24,32

12,24,36,48

they share 24

denominator is 24

12*2 is 24, -1*2 = -2. 8*3 = 24 so we do 3*3 = 9

-2+9/24

7/24

y = -1/3x + 1

y = -2x - 3

We can compare the equations to the graphs and see which graph represents the intersection point of the two equations.

The first equation, y = -1/3x + 1, has a negative slope (-1/3) and a y-intercept of 1.

The second equation, y = -2x - 3, also has a negative slope (-2) and a y-intercept of -3.

Based on the slopes and y-intercepts, we can identify the correct graph by finding the point where the two lines intersect.

Unfortunately, since the graphs are not provided, I am unable to determine which specific graph shows the solution to the system of linear equations. I recommend referring to the graph representation of the equations and identifying the intersection point to determine the correct graph.

Answer:

B and C

Step-by-step explanation:

Answer: B and C

Step-by-step explanation:

For the 2-parameters, m and n, both the functions \(m^{ln(n)}\) and \(n^{ln(m) }\) have the same θ-complexity.

In order to find the θ-complexity of the function,

We let, f(m,n) = \(m^{ln(n)}\)  , and g(m,n) = \(n^{ln(m) }\) ;

To simplify, we take "ln" for both sides,

we get,

ln(f(m,n)) = ln(\(m^{ln(n)}\)),

ln(f(m,n)) = ln(n)×ln(m),    ...equation(1)

and for g(m,n),

We have,

ln(g(m,n)) = ln(\(n^{ln(m) }\) ),

ln(g(m,n)) = ln(m)×ln(n),     ...equation(2)

On comparing both equation(1) and equation(2), we observe that both f(m,n) and g(m,n) are reducible to exactly same forms, thus, f(m,n) = g(m,n);

Therefore, both functions have same θ-complexity.

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The given question is incomplete, the complete question is

Suppose we have two parameters, m and n, with m → ∞ and n → ∞, perhaps at different rates independent of one another. Which has larger θ-complexity: \(m^{ln(n)}\) or \(n^{ln(m) }\) ?

12 cm, 35 cm, 37 cm measurements could not represent the side lengths of a right triangle. So the option C is correct.

The Pythagorean Theorem states that the sum of the squares of the two shorter sides of a right triangle must equal the square of the longest side.

The Pythagorean Theorem states that in a right triangle, the sum of the squares of the two legs (the sides that make the right angle) is equal to the square of the hypotenuse (the side opposite the right angle). Mathematically, this can be written as a² + b² = c².

So the sides of option C "12 cm, 35 cm, 37 cm" could not represent the side lengths of a right triangle because 12 cm² + 35 cm² ≠ 37 cm², these side lengths could not represent a right triangle.

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Step-by-step explanation:

Using a calculator, if you typed in 7 divided by 8, you'd get 0.875. You could also express 7/8 as a mixed fraction: 0 7/8. If you look at the mixed fraction 0 7/8, you'll see that the numerator is the same as the remainder (7), the denominator is our original divisor (8), and the whole number is our final answer (0).

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Answer:  Y = 4

the output is 4

Step-by-step explanation:

substitute the given input value, 3, for x and solve

Y= 10 -2x

Y = 10 -2(3)  multiply -2 × 3 to get -6

Y = 10 -6 . subtract

Y = 4

Answer:

Input is always x and output is always y.

Just substitute the 3 for y.

y= 10-2(3)

y= 10-6

y= 4

Answer:

2 digits in the quotient are overlined

Answer:

a or b

Step-by-step explanation:

Assuming the Bacteria count grows the exponential initial size of the culture is 400.

At t = 0, the initial population size is given by:

P(0) = 400

The doubling period can be found using the following formula:

T = ln2/r

Where r is the exponential growth rate.

Using the data from the question, we can calculate the exponential growth rate:

r = [ln(1300) - ln(400)]/(30 - 10) = 0.12

The doubling period is then given by:

T = ln2/r = 5.7 minutes

The population at t = 95 minutes can be calculated using the equation:

P(95) = P(0) * (2^(r*95))

P(95) = 400 * (2^(0.12*95)) = 7114

The time taken to reach a population of 15000 can be found using the equation:

t = (ln(15000/P(0))/r

t = (ln(15000/400))/0.12 = 97.2 minutes

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The value of y in the equation -3y+2y = 10 is y = -10

A linear equation is an algebraic equation where each term has an exponent of 1 and when this equation is graphed, it always results in a straight line. A linear equation can have a variable or two variables. Examples of linear equation with two variables is 2x+2y = 5 and example of linear equation with a variable is 2x+5 = 12. The variables here are x and y

-3y + 2y = 10 is an example of linear equation with a variable

-3y + 2y = 10

-y = 10

divide both sides by -1

y = -10

therefore the value of y is -10

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Answer:

i could  be wrong but B

Step-by-step explanation:

I assume it's D

S shows a variable you need to find to find how many students are in Social Studies class.

Answer:

x = -1

Step-by-step explanation:

The vertex is halfway between the focus and the directrix.

So here the directrix is  a vertical line  to the left of the vertex and passing through the point (2-3, 9) = (-1, 9)

It is x = -1.

The population of Somerville is approximately 35047 after a depreciation of of 3% every year .

Depreciation is economics refers to two different aspects of the same idea: first, the actual decline in an asset's fair value as it is used and worn, such as the annual decline in value of factory equipment; and second, the allocation in accounting statements of the asset's original cost to the periods during which it is used.

Here depreciation is the gradual decline in population each year in the town.

The rate of depreciation or decline is the percentage amount of population that decreases every year.

The formula used to calculate depreciation is given by:

\(A=P(1-r)^t\)

Given the rate of depreciation as 3%.

Population at present = 38400

Population after 3 years:

= 38400 (1 - 0.03 )³

= 38400 ( 0.97 )³

= 35046.6432

≈ 35047

Hence the population after 3 years will be approximately 35047.

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Answer: =35047

Step-by-step explanation:

The most appropriate hypothesis test to determine whether there is support for the claim that the average of the predicted charges is more than $500 greater than the average actual charges would be: c. Two-sample T-test assuming unequal variances (upper-tailed).

In this case, we have two independent samples: one for the predicted charges and another for the actual charges. We want to compare the means of these two samples to determine if there is a significant difference.

Unequal variance refers to the situation where the variances of two groups or populations being compared are not assumed to be equal. In statistical hypothesis testing, it is important to consider the assumption of equal variances, as violating this assumption can affect the accuracy of the results.

Since we are specifically interested in whether the average of the predicted charges is more than $500 greater, we would perform an upper-tailed test.

Assuming unequal variances is appropriate when the variances of the two samples are not assumed to be equal. This test allows for a more accurate assessment of the difference between the means when the variances differ between the groups.

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The smallest possible inside length of the cubical steel tank that can hold 600 L of water is approximately X meters. This calculation is based on the assumption that 1 liter of water occupies 1 cubic decimeter.

To determine the smallest possible inside length of the tank, we need to calculate the volume of the tank and then find the side length of the cube. Given that the tank needs to hold 600 L of water, we can convert this volume to cubic meters by dividing by 1000 (since 1 cubic meter is equal to 1000 liters). So, the volume of the tank in cubic meters is 600/1000 = 0.6 cubic meters.

Since the tank is cubic in shape, the volume can be calculated by raising the length of any side to the power of 3. Let's denote the side length of the cube as 's'. Therefore, we have the equation s^3 = 0.6.

Taking the cube root of both sides, we find s = ∛0.6. Evaluating this expression, we get s ≈ 0.824 m (rounded to three decimal places).

Therefore, the smallest possible inside length of the cubical steel tank that can hold 600 L of water is approximately 0.824 meters.

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Answer:

Options (B) and (C)

Step-by-step explanation:

The given expression is \((d^{\frac{1}{8}})^5\)

By simplifying this expression,

\((d^{\frac{1}{8}})^5\)

= \((\sqrt[8]{d})^{5}\)

Option (B)

Similarly,

\((d^{\frac{1}{8}})^5\)

= \(d^{\frac{5}{8}}\)

= \((d^{5})^{\frac{1}{8}}\)

Option (C)

Therefore, Options (B) and (C) will be the correct options.

Answer:

what do we have to simplify?

Answer:

8 = 16

Step-by-step explanation:

1/4  =  4 /8

Cross multiply:

1 * 8 = 4 * 4

Simplifying

1 * 8 = 4 * 4

Multiply 1 * 8

8 = 4 * 4

Multiply 4 * 4

8 = 16

Solving

8 = 16

Answer:

115%, 1.15, 115/100

Step-by-step explanation: