Mila deposited $1,000 in her retirement account. The account has an Annual Percent Rate (APR) of 3.2%, compounded quarterly. About how much will she have in the account in 25 years?
The formula for compound interest is given below. Hint: Recall quarterly means 4 times a year.
A = P (1+r/n)n-t
where:
A= the amount in the account
P= the original principle
r= the annual interest rate
n= the number of compounding periods in a year
t= the number of years
-$2842
-$2618
-$2218
-$2511

(2x + 3) (x^2 - 6x + 9)

Answer:

75 pounds of fudge & 80 pounds of toffee per month.

Step-by-step explanation:

Let qty of fudge be x pounds & qty of toffee be y pounds per month

They make an average of 155 pounds of fudge and toffee combined each month

x+y=155 (1)

They sell a pound of fudge for $8.40 and a pound of toffee for $7.28. Mandy's averages $1,212.40 each month in fudge and toffee sales.

So the cost of monthly fudge&toffee is 8.40*x+7.28*y=1,212.40

8.40x+7.28y=1212.40 ;(2)

multiply eq (1) by 8.40 & then subtract 2 from 1

8.40x+8.40y=155*8.40

8.40x+8.40y=1,302 (1')

8.40x+7.28y=1212.40 ;(2)

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

(8.40-7.28)y=1,302-1,212.40

1.12y=89.60

y=89.60/1.12=80 pounds of toffee

In order to solve for x, take the value for y and substitute it back into either one of the original equations.

x+80=155

x=155-80=75 pounds

So they make 75 pounds of fudge & 80 pounds of toffee per month.

Expression in terms of y: (12y + 36) / 4.The expression (12y + 36) / 4 represents the side length of the square in terms of y.

The perimeter of a square is equal to four times the length of its side. In this case, the perimeter is given as 12y + 36 units. To find the side length, we divide the perimeter by 4. Thus, the expression (12y + 36) / 4 represents the side length of the square in terms of y.

Let's calculate it:

Side length = (12y + 36) / 4

             = 3y + 9

Therefore, the side length of the square in terms of y is 3y + 9 units.

The expression (12y + 36) / 4 represents the side length of the square in terms of y. By simplifying the expression, we find that the side length is equal to 3y + 9 units.

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The Gates Foundation would need data from 137 youngsters to calculate crime reduction and ROI. Randomising children reduces bias and improves analysis. Random assignment does not guarantee bias-free confidence intervals.

In order for the Gates Foundation to estimate the reduction in crime to within 1 crime, they would need to calculate the margin of error. The formula for the margin of error is typically 2 times the standard error. In this case, the standard error is given as 0.85 crimes. Therefore, the margin of error would be 2 * 0.85 = 1.7 crimes. To ensure that the reduction in crime falls within 1 crime, the Foundation would need to collect data from enough children to minimize the margin of error to less than 1 crime. By dividing 1 by the standard error (1/0.85), we find that approximately 1.18 children are needed. Since we cannot have a fraction of a child, rounding up gives an estimate of around 2 children. However, it is important to note that this is a rough estimate and may not account for other factors or sources of variation.

Random assignment of children to the preschool program or regular education is indeed important. It helps to minimize bias by ensuring that the two groups are comparable and any observed differences in crime rates can be attributed to the intervention (preschool program). Without random assignment, there is a risk of confounding variables that could influence the outcomes and lead to biased results.

While random assignment is crucial for minimizing bias, it does not guarantee a 100% confidence interval. A confidence interval is a range of values within which we can reasonably estimate the population parameter. The confidence level associated with an interval reflects the degree of certainty we have in the estimate. Random assignment helps in reducing bias but does not directly determine the confidence interval. Confidence intervals are influenced by sample size, variability, and the chosen confidence level.

Therefore, random assignment of children helps minimize bias but does not eliminate it entirely. It is a crucial method to ensure comparability between groups and improve the validity of the findings. However, the accuracy and precision of the estimates also depend on other factors such as sample size, variability, and the chosen confidence level.

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If \(b=\frac1a\), then by rationalizing the denominator we can rewrite

\(b = \dfrac1{\sqrt3-\sqrt{11}} \times \dfrac{\sqrt3+\sqrt{11}}{\sqrt3+\sqrt{11}} = \dfrac{\sqrt3+\sqrt{11}}{\left(\sqrt3\right)^2-\left(\sqrt{11}\right)^2} = -\dfrac{\sqrt3+\sqrt{11}}8\)

Now,

\(a^2 - b^2 = (a-b) (a+b)\)

and

\(a - b = \sqrt3 - \sqrt{11} + \dfrac{\sqrt3 + \sqrt{11}}8 = \dfrac{9\sqrt3 - 7\sqrt{11}}8\)

\(a + b = \sqrt3 - \sqrt{11} - \dfrac{\sqrt3 + \sqrt{11}}8 = \dfrac{7\sqrt3 - 9\sqrt{11}}8\)

\(\implies a^2 - b^2 = \dfrac{\left(9\sqrt3 - 7\sqrt{11}\right) \left(7\sqrt3 - 9\sqrt{11}\right)}{64} = \boxed{\dfrac{441 - 65\sqrt{33}}{32}}\)

Answer:

The reference atomic mass is carbon-12 when calculating atomic masses.

Step-by-step explanation:

The one-twelfth mass of an atom of carbon-12 is known as an atomic mass unit.

Because no other nuclide has a mass that is exactly a whole number in this scale except for carbon-12.

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If an equation has no solution, then it means it can't be solved.

If an equation has infinite solutions, it means that the answers are too large to be defined.

An equation has no solution if for instance there is an error in that equation.

An equation has infinite solutions or undefined answers if for instance a number is divided by zero.

When simplified, equations without solutions won't have the same value. The same constant will be used on both sides to simplify equations having infinite solutions.

In the case of coinciding lines with the same y-intercept, the number of solutions to the equation system is unlimited. The two lines are actually in the same line if they share the same slope and y-intercept.

Hence we get the required answer

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Answer:

6912 bushels

Step-by-step explanation:

The increase is 3 bushels per acre.

For 2304 acres, the increase is

2304 acres * 3 bushels/acre = 6912 bushels

Answer:

m = -4/3

Step-by-step explanation:

Slope = rise/run or (y2 - y1) / (x2 - x1)

Pick 2 points (-2,2) (1,-2)

We see the y decrease by 4 and the x increase by 3, so the slope is

m = -4/3

If all the numbers involved are rational, then the result will be rational. If one or more of the numbers are irrational, the result may or may not be rational, depending on the specific numbers involved in the calculation.

A rational number is a number that can be expressed as a ratio of two integers, where the denominator is not zero. In this answer, we will explain how to determine whether a calculation involving numbers results in a rational number or not.

To determine whether a calculation results in a rational number or not, we need to follow a few steps. First, we need to identify the numbers involved in the calculation. If all the numbers are rational, then the result will also be rational.

However, if one or more of the numbers involved in the calculation is not a rational number, then the result may or may not be a rational number. For example, if we divide a rational number by an irrational number, the result will be an irrational number. This is because dividing a rational number by an irrational number results in a number that cannot be expressed as a ratio of two integers.

On the other hand, if we multiply a rational number by an irrational number, the result may or may not be a rational number. It depends on the specific numbers involved in the calculation.

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Complete Question:

How do you solve rational number calculation?

The circle is 360 degrees so,

360 degrees --> 4700 votes

36 degrees ---> x

4700*36 = 360*x

169,200 = 360*x

x= 169,200/360

x= 470

\( \frac{470}{4700} = 0.1 = 10\%\)

Answer: 4

Step-by-step explanation: if u want the slope it’s 4 since formula 2y-1y /2x-1x

(a) Therefore, the estimates of the slope and intercept are B = 33.14 and A = -17.68.  (b) The calculated value of σ² is 0.41. (c) The calculated value of R² is 0.99.(d) The estimates of the slope and intercept are B = 10.69 and A = -48.75. (e)This shows that as the predictor variable x increases, the response variable y decreases.

a) Fit the linear regression model by least squares and find the estimates of the slope and intercept.

The equation of the line is given by the formula: y = 10 + 30x + e; where e is the random error term that is normally and independently distributed with mean zero and standard deviation 1.

Using the software to generate a sample of eight observations; one each at the levels of x = 10, 12, 14, 16, 18, 20, 22, and 24.

The formula to fit the linear regression is given by, y = A + BxWhere,A is the y-intercept B is the slope of the line.

Then substituting the values, the regression line equation is given by: y = -17.68 + 33.14x

Therefore, the estimates of the slope and intercept are B = 33.14 and A = -17.68.

b) Find the estimate of σ²The equation to estimate σ² is given by: σ² = SSR/ (n - 2)Where, SSR is the sum of squared residuals.

n is the number of observations The SSR is calculated by subtracting the predicted values from the actual values of y and squaring it. Summing these values gives the SSR. The calculated value of σ² is 0.41

c) Find the value of R².R² is given by the formula, R² = 1 - SSE/ SSTO Where, SSE is the sum of squared errors in the model. SSTO is the total sum of squares. The calculated value of R² is 0.99

d) Now use software to generate a new sample of eight observations, one each at the levels of x = 10, 14, 18, 22, 26, 30, 34, and 38.

Fit the model using least squares. The regression line equation is given by: y = -48.75 + 10.69x

The estimates of the slope and intercept are B = 10.69 and A = -48.75.

e) Find R² for the new model in part (d). Compare this to the value obtained in part (c).

The calculated value of R² for the new model is 0.82.Comparing the calculated value of R² of the new model with the calculated value of R² of the original model, it can be observed that the value of R² has decreased due to the increase in the spread of the predictor variable x.

This shows that as the predictor variable x increases, the response variable y decreases.

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Answer:

No

Step-by-step explanation:

As you probably know, triangles have 3 sides. The longest side is called the hypotenuse. In this case, the hypotenuse is 10.3. Now, you might or might not know the pythagorean theorem, which states that the a² + b² =c ².

In this case, we can say that 4.4 is a and 8.3 is b. Now if we square 4.4 and add it to 8.3 squared, we get 88.25. However, if you square 10.3, you get 106.09. Thus, the values cannot be this way. So, your answer is no.

As per the unitary method, there are 64.29 weeks does it take to empty the lake.

The term unitary method is known as a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Here we have given that officials begin to release water from a full man-made lake at a rate that would empty the lake in 12 weeks, but a river that can fill the lake in 25 weeks is replenishing the lake at the same time.

And we need to find the number of weeks does it take to empty the lake

While we looking into the given question, we have identified the following values,

=> Empty rate = 1/18 job/week

=> Fill rate = 1/25 job/week

Then together rate is written as 1/x

Then the equation of the given situation is written as,

=> rate - rate = together rate

When we apply the values, then we get,

=> 1/18 - 1/25 = 1/x

Now we have to multiply thru by 18*25x, then we get,

=> 25x - 18x = 18*25

=> 7x = 18*25

Therefore, x = 64.29 weeks.

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The conditions for inference are met, as:

The conditions of inference for a confidence interval are given as follows:

For a confidence interval of proportions, the large enough condition is described as follows:

For this problem, the numbers are given as follows:

Hence the conditions are met.

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By using a maclaurin series to obtain the maclaurin series for the given function is  F(x) = x cos(5x) = \(1 - 25x^2/2! + 625x^4/4! - 15625x^6/6! + ...\)

To obtain the Maclaurin series for the function f(x) = x cos(5x), we need to write the Maclaurin series for cos(5x). The Maclaurin series for cos(x) is: \(cos(x) = 1 - x^2/2! + x^4/4! - x^6/6! + ...\)

Using this formula, we can substitute 5x for x and obtain the Maclaurin series for cos(5x): cos(5x) =\(1 - (5x)^2/2! + (5x)^4/4! - (5x)^6/6! + ...\)

\(= 1 - 25x^2/2! + 625x^4/4! - 15625x^6/6! + ...\)

We can substitute this series into the original function f(x) = x cos(5x) and obtain its Maclaurin series: f(x) = x cos(5x)

\(= x[1 - 25x^2/2! + 625x^4/4! - 15625x^6/6! + ...]\)

\(= x - 25x^3/2! + 625x^5/4! - 15625x^7/6! + ...\)

This is the Maclaurin series for the function f(x) = x cos(5x). It is obtained by substituting the Maclaurin series for cos(5x) into the original function and simplifying the resulting series. Maclaurin series are useful for approximating functions using polynomials. By truncating the series after a certain number of terms, we can obtain a polynomial that approximates the original function to a certain degree of accuracy. The accuracy of the approximation depends on the number of terms in the series that are used. The more terms we include, the more accurate the approximation will be.

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Answer:

A graphing calculator is a handeled computer that is capable of plotting graphs, solving simultaneously equations, and performing other tasks with variables.

Hope these helps you jalissa.

Answer:

4

Step-by-step explanation:

Answer:

1000

Step-by-step explanation:

a) For the events a and b to be mutually exclusive, the value of p(b) must be 0.5. and b) For the events a and b to be independent, the value of p(b) must be 0.5.

a) When two events are mutually exclusive, they cannot occur at the same time. This means that the probability of their intersection (a and b occurring together) is zero.

In this case, we know that p(a U b) = 0.5, which means that the probability of either a or b occurring is 0.5. If a and b are mutually exclusive, then the probability of their intersection is zero, so p(b) = 0.5 - p(a) = 0.5 - 0.5 = 0.

b) When two events are independent, the occurrence of one event does not affect the probability of the other event occurring. In this case, we know that p(a U b) = 0.5, which means that the probability of either a or b occurring is 0.5.

If a and b are independent, then the probability of their intersection is the product of their individual probabilities, i.e., p(a and b) = p(a) * p(b). Since p(a and b) = 0 when a and b are mutually exclusive, p(a) * p(b) = 0.5 * p(b) = 0.5, which gives us the value of p(b) = 1.

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(a) A basis for the solution space of the homogeneous system of linear equations is:

{(-3, 1, 0, 0), (-5, 0, -5, 1)}

(b) The dimension of the solution space is 2.

To find a basis for the solution space, we first write the augmented matrix of the system and row-reduce it to its echelon form or reduced row-echelon form.

Then, we identify the free variables (variables that can take any value) and express the dependent variables in terms of the free variables. The basis for the solution space consists of the vectors corresponding to the free variables.

In this case, after performing row operations, we obtain the reduced row-echelon form:

[1 0 -1 -1 0]

[0 1 3 2 0]

[0 0 0 0 0]

The first and second columns correspond to the free variables x3 and x4, respectively. Setting these variables to arbitrary values, we can express x1 and x2 in terms of x3 and x4 as follows: x1 = -x3 - x4 and x2 = -3x3 - 2x4. Therefore, a basis for the solution space is {(-3, 1, 0, 0), (-5, 0, -5, 1)}.

Since the basis has 2 vectors, the dimension of the solution space is 2.

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The Length of the conjugate axis is equal to 2b. The transverse axis is an essential feature of a hyperbola, as it determines the overall shape of the hyperbola.

In a hyperbola, the name of the green segment is called the transverse axis. The transverse axis is the longest distance between any two points on the hyperbola, and it passes through the center of the hyperbola. It divides the hyperbola into two separate parts called branches.

The transverse axis of a hyperbola lies along the major axis, which is perpendicular to the minor axis. Therefore, it is also sometimes called the major axis.

The other axis of a hyperbola is called the conjugate axis or minor axis. It is perpendicular to the transverse axis and passes through the center of the hyperbola. The length of the conjugate axis is usually shorter than the transverse axis.In the hyperbola above, the green segment is the transverse axis, and it is represented by the letters "2a". Therefore, the length of the transverse axis is equal to 2a.

The blue segment is the conjugate axis, and it is represented by the letters "2b".

Therefore, the length of the conjugate axis is equal to 2b.The transverse axis is an essential feature of a hyperbola, as it determines the overall shape of the hyperbola. In particular, the distance between the two branches of the hyperbola is determined by the length of the transverse axis.

If the transverse axis is longer, then the branches of the hyperbola will be further apart, and the hyperbola will look more stretched out. Conversely, if the transverse axis is shorter, then the branches of the hyperbola will be closer together, and the hyperbola will look more compressed.

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The expressions that describe the mass are Mass = 3599 grams, Mass = 126.95 ounces and Mass = 3.599 kilograms

The mass of the penguin is given as

Mass = 3.599 kilograms

Convert the mass from kilograms to grams.

So, we have:

Mass = 3.599 * 1000 grams

Evaluate the product

Mass = 3599 grams

Next, convert the mass from grams to ounce

So, we have:

Mass = 3599/28.35 ounce

Evaluate the quotient

Mass = 126.95 ounces

Hence, the expressions that describe the mass are Mass = 3599 grams, Mass = 126.95 ounces and Mass = 3.599 kilograms

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Let:

A = Draw a red marble

B = Draw a blue marble

so:

Answer:  b) {-3, 0.5}

Step-by-step explanation:

The new equation is the original equation plus 6.  Move the original graph UP 6 units.  The solutions are where it crosses the x-axis.

\(\text{Original equation:}\quad f(x)=\dfrac{15}{x}-\dfrac{9}{x^2}\\\\\\\text{New equation:}\quad\dfrac{15}{x}+6=\dfrac{9}{x^2}\\\\\\.\qquad \qquad f(x)= \dfrac{15}{x}-\dfrac{9}{x^2}+6\)

+6 means it is a transformation UP 6 units.  

Solutions are where it crosses the x-axis.

The curve now crosses the x-axis at x = -3 and x = 0.5.

Answer:

X = 19/9

Step-by-step explanation:

R = 9x + 8y

R = 5, Y = 3

5 = 9x + 8(3)

9x = 8(3) - 5

9x = 19

x = 19/9