An investment of $1800 earned $60.75 at a simple-interest rate of 4.5% per year. For how long was the investment held? Question 1 options: a) Nine years b) Three years c) Three months d) Nine months

The extent to which the researcher can refer that findings with a sample from which it was drawn is referred to as generalizability.

Generalizability refers to the ability to extrapolate study findings from a sample to the entire population. It also refers to the capacity to apply findings from one study to a similar environment in a different investigation.

Generalizability and transferability are two research traits that are related. When considering generalizability in research, there are two features or dimensions to consider: generalizability as it relates to the specific population on which the research is conducted, and generalizability on a global scale.

Such studies will be easier to generalize if the researcher uses adequate sampling approaches, sample sizes, and exact processes.

In general, a study has strong generalizability when the findings apply to a wide range of persons or situations. The study has weak generalizability if the results can only be applied to a subset of the population or in a very specific circumstance.

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Answer:

All the none-zero digits given should be included when written in scientific notation. But also any trailing zeros written after non-zero digits should also be included.

For example in 0.00900 the 900 is significant because the person who included the trailing zeros is saying look I measured this far and these zeros are significant.

Cosecant (csc) can be expressed as 1 divided by the tangent (tan) function: csc(x) = 1/tan(x).

To express cosecant (csc) in terms of tangent (tan), we can utilize the reciprocal relationship between the trigonometric functions.

First, let's consider a right triangle where the angle of interest is x. The cosecant of an angle is defined as the reciprocal of the sine of that angle: csc(x) = 1/sin(x).

Next, we can rewrite the sine of an angle in terms of the tangent of the same angle. Using the Pythagorean identity, sin(x) = opposite/hypotenuse = (1/tan(x))/√(1 + tan^2(x)).

Substituting this expression into the equation for cosecant, we get: csc(x) = 1/[(1/tan(x))/√(1 + tan^2(x))] = √(1 + tan^2(x))/tan(x).

Therefore, we can express cosecant in terms of a tangent as: csc(x) = √(1 + tan^2(x))/tan(x).

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Answer:

Options A,B and D are correct.

Step-by-step explanation:

I have attached a photo. that might help you out.

If he p-value is used for hypothesis testing , then the Null Hypothesis is rejected if (a) p-value ≤ α .

In a hypothesis testing, the p-value represents the probability of observing a test statistic as extreme or more extreme than the one observed, provided that the null hypothesis is True.

The significance level, represented by "α" , is a pre-determined threshold which determines the level of evidence required to reject the null hypothesis.

If the p-value is less than or equal to α, this indicates that the observed test statistic is sufficiently unlikely to occur under the null hypothesis, and therefore the null hypothesis is rejected.

Therefore , the Null hypothesis is rejected if (a) p-value ≤ α .

The given question is incomplete , the complete question is

When the p-value is used for hypothesis testing, the null hypothesis is rejected if

(a) p-value ≤ α

(b) α < p-value

(c) p-value ≥ α

(d) p-value = 1 - α

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The correct answer is a) p-value ≤ α. In hypothesis testing, the null hypothesis is typically assumed to be true initially. The p-value is used to determine the probability of observing a test statistic as extreme or more extreme than the one obtained from the data, assuming that the null hypothesis is true.

The significance level (α) is chosen beforehand and represents the maximum acceptable probability of rejecting the null hypothesis when it is actually true.

If the p-value is less than or equal to the significance level (p-value ≤ α), then the result is considered statistically significant and the null hypothesis is rejected. This implies that the observed effect is unlikely to have occurred by chance alone and that the alternative hypothesis is more likely to be true.

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Answer:

A 26

Step-by-step explanation:

4(x - y) + 2                     x = 7 and y = 1

4(7 - 1) + 2

= 4(6) + 2

= 24 + 2

= 26

So, the answer is A 26

The volume of one penny is 0.36 mL if the volume of 50 pennies is 18.0 mL.

To find the volume of one penny if the volume of 50 pennies is 18.0 mL, we use the concept of proportionality as follows:

We can find the volume of one penny by dividing the volume of 50 pennies by 50 since we know that 50 pennies occupy a volume of 18.0 mL.

Therefore, the volume of one penny can be calculated as:Volume of one penny = Volume of 50 pennies / 50= 18.0 mL / 50= 0.36 mL

Hence, the volume of one penny is 0.36 mL if the volume of 50 pennies is 18.0 mL.

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The two options to define increase in subscribers per amount of content is:

1)A Number of new subscribers divided by number of writers

2)Number of new subscribers divided by number of posts

Based on the fact that charlotte has launched two new websites and want to understand how to measure the increase in subscribers per amount of content.

The four options given to us are:

(Choice A) Number of new subscribers divided by number of writers (Choice B) Number of new subscribers divided by number of likes (Choice C) Number of new subscribers divided by number of posts (Choice D) Number of new subscribers divided by number of words

The only two choices which quantify content are number of writers and number of post. Hence A and C are the correct options.

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The complete question is given below:

Charlotte owns two entertainment websites. Charlotte wants to know which website gains more new subscribers per amount of content. Charlotte thought of two different ways to define this quantity. Identify these two definitions among the following options.

(Choice A)  Number of new subscribers divided by number of writers (Choice B)  Number of new subscribers divided by number of likes (Choice C)  Number of new subscribers divided by number of posts (Choice D)  Number of new subscribers divided by number of words

Answer:

The equation of the line is y = 4x/7 - 1

Step-by-step explanation:

The equation of a straight line can be represented by

y = mx + c

where m represents the slope and c represents the y-intercept

So for;

4x - 7y = 9

7y = 4x - 9

y = 4x/7 - 9/7

The slope here is 4/7

Since the line we are trying to form is parallel, then the slope of the line is 4/7 also, since parallel lines have equal slope

So the equation of the new line will be;

y = 4x/7 + c

To get c, just put the point x = 7 and y = 3

3 = 4/7(7) + c

3 = 4 + c

c = 3-4

c = -1

So the equation of the line is;

y = 4x/7 - 1

Answer:

50.27 ft

Step-by-step explanation:

hope this helps :)

Answer:

y = 3/x

Step-by-step explanation:

Answer:

The bird had to fly \(12\sqrt{5}\) feet to reach the top.

Step-by-step explanation:

Assuming that the tree is perpendicular to the ground, then the given problem forms a right triangle. The tree's height is one of the legs (sides of the right triangle that is adjacent to the right angle), and the distance that Kami is from the tree is the other leg. The distance from where Kami is to the top of the tree is the hypotenuse (side of the right triangle that is opposite from the right angle). Since this is a right triangle, one can apply the Pythagorean theorem. The Pythagorean theorem states;

\(x^2 + y^2 = z^2\)

Where (x) and (y) are the legs, and (z) is the hypotenuse. One can substitute in the given values from the problem, and solve for the hypotenuse.

\(x^2 + y^2 = z^2\)

Substitute

\(12^2 + 24^2 = z^2\\\)

Simplify,

\(144 + 576 = z^2\\\\720 = z^2\)

Inverse operations,

\(720 = z^2\\\\\sqrt{720}=z\\\\12\sqrt{5}=z\)

Answer:

Kami's bird had to fly 26.8 feet

Step-by-step explanation:

Using the given formula and the values in the table, we will get the probability:

P(bus | junior)  = 0.57

Here we just need to use the little formula that is already in the image, it says taht:

P(B|A) = P(A ∩ B)/P(A)

We want to get:

P(bus | junior)

First let's get P(junior), there are 100 students, and there are 35 juniors, so the probability that a student is a junior is:

P(junior) = 35/100 = 0.35

Now, the probability that a student is a junior and goes in bus  P(A ∩ B) is equal to the quotient between the number of juniors that go in bus and the total number of students, here we have:

P(junior ∩  bus) = 20/100 = 0.2

Now we take the quotient between these:

P(bus | junior) = 0.2/0.35 = 0.57

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Answer:

20.8 ft²

Step-by-step explanation:

area = (ab sin C)/2

area = (6 ft × 8 ft × sin 60°)/2

area = 20.8 ft²

The toy cars Anna must sell for her revenue to equal her expense is 4 toy cars. The result is obtained by using the concept of calculating algebra.

To calculate the algebra with one variable, sum up all the same variable and count the value.

Anna want to sell toy car at a craft fair. Each car is sold at a price of $ 12. The material for each car cost $ 3.50 and the table rental at the fair is 34 dollar for the day.

Find the toy cars must Anna sell for her revenue to equal her expense!

We have

Let's say

Revenue = Expense

a × $12 = (a × $3.5) + $34

12a = 3.5a + 34

12a - 3.5a = 34

8.5a = 34

a = 4 toy cars

Hence, Anna must sell 4 toy cars so that her revenue is equal to expense.

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The number of burger sam bought = x

Let the number of burgers for mike be = y

the equation for the total number of burgers will be

Mike brought 5 more than 2 times as many burgers as sam will be represented as

By substituting Eqn 2 in Eqn 1 we will have

Therefore,

The value of x= 15

To calculate the number of burgers mike brought to the BBQ =y,

We will substitute the value of x in (Eqn 1) above

The first derivatives for the given functions are:

For \(y = 3x^2 + 5x + 10,\) the first derivative is dy/dx = 6x + 5.

For  \(y = 100200x + 7x,\) the first derivative is dy/dx = 100207.

For \(y = ln(9x^4),\) the first derivative is dy/dx = 4/x.

To find the first derivative for each of the given functions, we'll use the power rule, constant rule, and chain rule as needed.

For the function\(y = 3x^2 + 5x + 10:\)

Taking the derivative term by term:

\(d/dx (3x^2) = 6x\)

d/dx (5x) = 5

d/dx (10) = 0

Therefore, the first derivative is:

dy/dx = 6x + 5

For the function y = 100200x + 7x:

Taking the derivative term by term:

d/dx (100200x) = 100200

d/dx (7x) = 7

Therefore, the first derivative is:

dy/dx = 100200 + 7 = 100207

For the function \(y = ln(9x^4):\)

Using the chain rule, the derivative of ln(u) is du/dx divided by u:

dy/dx = (1/u) \(\times\) du/dx

Let's differentiate the function using the chain rule:

\(u = 9x^4\)

\(du/dx = d/dx (9x^4) = 36x^3\)

Now, substitute the values back into the derivative formula:

\(dy/dx = (1/u) \times du/dx = (1/(9x^4)) \times (36x^3) = 36x^3 / (9x^4) = 4/x\)

Therefore, the first derivative is:

dy/dx = 4/x

To summarize:

For \(y = 3x^2 + 5x + 10,\) the first derivative is dy/dx = 6x + 5.

For y = 100200x + 7x, the first derivative is dy/dx = 100207.

For\(y = ln(9x^4),\) the first derivative is dy/dx = 4/x.

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In order to determine the sensitivity, if the optimal value of x2  is positive, we know that increasing c2 will increase the optimal solution, while if the optimal value of x2 is negative, we know that decreasing c2 will increase the optimal solution.

To determine the sensitivity of the optimal solution to a change in c2 using the objective function 25x1 c c2x2, we need to perform a sensitivity analysis. This involves finding the range of values for c2 that will not change the optimal solution, as well as the range of values that will change the optimal solution.

Assuming we have a linear programming problem with the objective function 25x1 c c2x2 and constraints, we can use the simplex method to solve the problem and find the optimal solution. Once we have the optimal solution, we can then perform the sensitivity analysis by calculating the shadow price for the constraint involving c2.

The shadow price for a constraint is the amount by which the objective function would increase or decrease with a one-unit increase in the right-hand side of the constraint, while all other variables are held constant at their optimal values. In this case, the constraint involving c2 is the coefficient of x2 in the objective function, so the shadow price for c2 is simply the optimal value of x2.

If the optimal value of x2 is positive, this means that the objective function is sensitive to changes in c2, and that increasing c2 will increase the optimal solution. Conversely, if the optimal value of x2 is negative, this means that the objective function is also sensitive to changes in c2, but that decreasing c2 will increase the optimal solution.

Therefore, to determine the sensitivity of the optimal solution to a change in c2, we need to calculate the optimal value of x2 and determine whether it is positive or negative. If it is positive, we know that increasing c2 will increase the optimal solution, while if it is negative, we know that decreasing c2 will increase the optimal solution.

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Answer:

(x)=(x-7)(x-4)

g(x)=x(2)+7x - 2

Now find a common denominator. (x+10)(x-4) is a good one.

x-16/(x+10)(x-4)+x-4/(x+10)(x-4)

2x-20/(x+10)(x-4)

The value of function g(f(-1)) is -70.

What is Function?

A relation between a set of inputs having one output each is called a function.

Given that;

The value of functions,

f (x) = -4x - 7

g (x) = x² + 7x - 2

Now, Value of function g(f(-1)) as;

g(f(x)) = g(-4x - 7)

        = (-4x - 7)² + 7(-4x - 7) - 2

        = (4x + 7)² + 7 × -4 × x - 7 × 7 - 2

        = 16x² + 49 + 56x + 28x - 49 - 2

        = 16x² + 84x - 2

Thus, g(f(x)) = 16x² + 84x - 2

Now, To find value of g(f(-1)) we can substitute x = -1,

g(f(-1)) = 16(-1)² + 84(-1) - 2

        = 16 - 84 -2

        = -70

Thus, The value of function g(f(-1)) is -70.

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For any value of t greater than 5 minutes spent running in Routine #2, Routine #1 will burn more calories than Routine #2.

To determine the amount of time spent running in which Routine #1 burns more calories than Routine #2, we need to compare the calorie burn rates of the two routines.

Routine #1:

Calories burned per minute = 8.5 calories

Routine #2:

Calories burned while walking = 21 calories

Calories burned per minute of running = 4.3 calories

Let's assume t represents the number of minutes spent running in Routine #2.

In Routine #1, the total number of calories burned can be calculated as 8.5t.

In Routine #2, the total number of calories burned is the sum of the calories burned while walking (21 calories) and the calories burned during running (4.3t calories).

To find the time spent running at which Routine #1 burns more calories than Routine #2, we set up the following inequality:

8.5t > 21 + 4.3t

Simplifying the equation, we get:

8.5t - 4.3t > 21

Combining like terms:

4.2t > 21

Finally, we divide both sides by 4.2 to isolate t:

t > 21 / 4.2

Simplifying further, we find:

t > 5

Therefore, for any value of t greater than 5 minutes spent running in Routine #2, Routine #1 will burn more calories than Routine #2.

In summary, if Henry spends more than 5 minutes running in Routine #2, it is more effective in terms of burning calories to choose Routine #1 instead.

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Explanation:

The sign of the product of any odd number of negative integers is positive because when two minuses are multiplied with each other, it will result in a positive number.

For example:

Hoped this helped!

Answer: 154

Step-by-step explanation: trust

The area of the customer's yard is 580π.

The distance formula is given as -

d = √(x₂ - x₁)² + (y₂ - y₁)²

Given is that this grid represents the customer’s yard. The bottom left corner is the origin point  O(0, 0), and the x- and y- axes represent the two fences. The rose bush is at point P(16, 18).

We can write the area of the customer's yard -

A = πr²

Here -

r = d

r² = d²

We can write -

A = πd²

A = π {(x₂ - x₁)² + (y₂ - y₁)²}

A = π{16 x 16 + 18 x 18}

A = 580π

Therefore, the area of the customer's yard is 580π.

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Answer:

Distributive property is verified.

Step-by-step explanation:

Verifying distributive property:

  a * (b +c) = a*b + a*c

a = -3/11 ;   b = 9/5 ;   c = 1/5

LHS  = a * (b + c)

First Slove that is inside the parenthesis, (b +c)

        \(\sf = \dfrac{-3}{11}*\left(\dfrac{9}{5}+\dfrac{1}{5}\right)\\\\=\dfrac{-3}{11}*\dfrac{10}{5}\\\\= \dfrac{-3}{11}*2\\\\=\dfrac{-6}{11}\)

                  RHS = a * b + a*c

                          \(\sf = \dfrac{-3}{11}*\dfrac{9}{5} +\dfrac{-3}{11}*\dfrac{1}{5}\\\\=\dfrac{-27}{55}-\dfrac{3}{55}\\\\=\dfrac{-30}{55}\\\\=\dfrac{-30 \div 5}{55 \div 5}\\\\=\dfrac{-6}{11}\)

LHs = RHS

Hence, verified

Answer:

C: 2

Step-by-step explanation:

\({ \purple{purple \: line}} \: \: and \: \: { \green{green \: line}}\)

There are two numbers of proportional relationships are shown in the coordinate plane which is correct option (C).

A graph can be defined as a pictorial representation or a diagram that represents data or values.

A proportional relationship between two quantities is the one in which the rate of change is constant or one in which the ratio of one quantity to the other is constant.

In this graph, We'll analyze the graph of proportional relationships. If the graph of a relationship is a straight line, it is a proportional relationship.

Since, there are two straight lines in the graph.

So, there are two proportional relationships are shown in the graph.

Hence, there are two numbers of proportional relationships are shown in the coordinate plane.

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The standard error of the sample mean of 200 fill-ups by one driver is 0.2213.

The 2015 Subaru Outback is rated by the EPA at μ=28.0 mpg and a standard deviation of σ=3.13 mpg.

To calculate the standard error of the sample mean of 200 fill-ups by one driver, we can use the formula for standard error:

Standard error = σ/√n

Where,σ = standard deviation of the population (in mpg)n = sample size

To find the standard error of the sample mean of 200 fill-ups by one driver, we need to substitute the given values into the formula:

Standard error = σ/√n= 3.13/√200= 0.2213 (rounded to four decimal places)

Therefore, the standard error of the sample mean of 200 fill-ups by one driver is 0.2213.

Hence, the correct option is 0.2213.

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Answer:

Solve what's in the parentheses

Step-by-step explanation:

You always solve what's in the parentheses first.

Step-by-step explanation:

Second option is the answer

Answer:

x= 130 degrees

Step-by-step explanation:

Answer:

Brainliest???

Step-by-step explanation: