What is the best approximate of the square root of 50

The balance in the fund at the end of 23 years, with monthly deposits of $1,150 and a 3.25% annual interest rate, is approximately $449,069.51. The amount of interest earned over the period is approximately $420,630.49.

a. The balance in the fund at the end of the 23-year period, considering a monthly deposit of $1,150 and an annual interest rate of 3.25% compounded annually, is approximately $449,069.51.

To calculate the balance, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where A is the accumulated balance, P is the monthly deposit, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.

In this case, we have monthly deposits, so we need to convert the annual interest rate to a monthly rate:

Monthly interest rate = (1 + 0.0325)^(1/12) - 1 = 0.002683

Using this monthly interest rate, we can calculate the accumulated balance over the 23-year period:

A = 1150 * [(1 + 0.002683)^(12*23) - 1] / 0.002683 = $449,069.51

Therefore, the balance in the fund at the end of the 23-year period is approximately $449,069.51.

b. The amount of interest earned over the 23-year period can be calculated by subtracting the total deposits from the accumulated balance:

Interest earned = (Monthly deposit * Number of months * Number of years) - Accumulated balance

Interest earned = (1150 * 12 * 23) - 449069.51 = $420,630.49

Therefore, the amount of interest earned over the 23-year period is approximately $420,630.49.

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Answer:

B

Step-by-step explanation:

The expression to represent the total volume of the two storage spaces is s³+12.

Volume is the measure of the capacity that an object holds.

Formula to find the volume of the object is Volume = Area of a base × Height.

Given that, the edge of the large cube s feet and the volume of the small cube is 12 ft³.

We know that, the formula to find the cube is side³.

Volume of large cube = s×s×s

= s³

Total volume of the two storage spaces =s³+12

If edge of large cube is 4 feet long, then the volume is

4³ = 64 ft³

Therefore, the expression to represent the total volume of the two storage spaces is s³+12.

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Answer:

y=1/2x=6 - linear, written as y=mx+b.

y=(x-5)^2 - nonlinear, x has an exponent greater than 1

y=2^x+8 - nonlinear, x is an exponent

y=3(x+7) - linear, can be written as y=mx+b (y=3x+21)

y=4x^3-1 - nonlinear, x has an exponent greater than 1

Step-by-step explanation:

The ordered pairs for the system of equations f(x) = x^2 -2x + 3 and f(x) = -2x + 12 are (3, 6) and (-3, 18)

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term. The first condition for an equation to be a quadratic equation is the coefficient of x2 is a non-zero term(a ≠ 0)

f(x) = x^2 -2x +3 and f(x) = -2x + 12

which means

x^2 -2x +3  = -2x + 12

x^2 -2x +3  + 2x - 12 = 0

x^2 -9 = 0

by factorizing we have

(x-3)(x+3) = 0

x = 3 or -3

when x = 3

f(x) = -2x + 12

f(3) = -2(3) + 12 which is 6

when x = -3

f(-3) = -2(-3) + 12 which is 18

ordered pairs are (3, 6) and (-3, 18)

In conclusion, (3, 6) and (-3, 18) are the ordered pairs

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The value if a such that CD is parallel to EF is

To find the value of "a" such that CD is parallel to EF, we need to use the slope formula.

The slope of the line CD is given by:

slope of CD = (y2 - y1)/(x2 - x1),

where

(x1, y1) = C (-7, 3) and

(x2, y2) = D (-1, 5)

slope of CD = (5 - 3)/(-1 - (-7)) = 2/6 = 1/3

The slope of the line EF is also given by:

slope of EF = (7 - 6)/(x - (-6)) = 1/(x + 6)

Since CD and EF are parallel, their slopes are equal. Therefore:

1/3 = 1/(x + 6)

Solving for x, we get:

x + 6 = 3

x = -3

Therefore, a = -3.

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Answer:

c (the third option)

Step-by-step explanation:

Answer:

-2/3x+1

Step-by-step explanation:

Our estimate for arctan(0.1) using a linear approximation at x = 0 is approximately 0.1.

To estimate the value of tan^(-1)(x), also known as arctan(x), using a linear approximation, we can utilize the fact that the derivative of arctan(x) is 1/(1+x^2).
First, let's choose a value of a that produces a small error. We can choose a = 0 as it simplifies the calculations and allows us to approximate tan^(-1)(x) around x = 0.
To start, we'll find the linear approximation of arctan(x) at x = a using the tangent line equation:
L(x) = f(a) + f'(a)(x - a)
In this case, f(x) represents arctan(x) and f'(x) represents the derivative of arctan(x), which is 1/(1+x^2).
Using a = 0, the equation becomes:
L(x) = arctan(0) + (1/(1+0^2))(x - 0)
Since arctan(0) is 0, the equation simplifies to:
L(x) = x
Now, we can use this linear approximation to estimate the value of arctan(x) for a given x.
For example, let's say we want to estimate arctan(0.1). Plugging 0.1 into the linear approximation equation, we get:
L(0.1) = 0.1
Therefore, our estimate for arctan(0.1) using a linear approximation at x = 0 is approximately 0.1.
By choosing a value of a that produces a small error, we are able to obtain a reasonably accurate estimation using the linear approximation method.

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Answer:

(X+6)(x-5) + (X-5)(X+6)

Answer:

\(2x ^{2} - 22x + 60\)

The error Justin made in his calculation is "He should have added the values in the numerator before dividing by 2".

The correct answer choice is option B

(x + y + 5) / 2

Where,

x and y are his parents’ current heights in inches,

Mom’s height = 54 inches

Dad’s height = 71 inches

Substitute into the expression

(71 + 54 + 5) / 2

= 130/2

= 65 inches

Justin's work:

( 71 + 54 + 5 ) / 2

= 71 + 27 + 5

= 103 inches

Therefore, Justin should have added the numerators before dividing by 2.

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Equation of a line

The equation of a line in point-slope form is:

Answer:

B) 6

Step-by-step explanation:

In a Scatter Plot you must plot all points given therefore you plot B) 6 points

Answer:

X+y over y

Step-by-step explanation:

X+y over y

Hope it helps

The line y = 4.08x + 63.13 is a good fit for this data because it accurately represents the positive relationship between median household income and the number of adults with bachelor's degrees in the 50 U.S. states.

Given that a scatter plot of median household income x and the number of adults per 1,000 people with bachelor's degrees y for 50 U.S. states. The line y = 4.08x + 63.13 is suggested to be a good fit for this data.

To understand why this line is a good fit, to consider its equation. In this case, y represents the number of adults per 1,000 people with bachelor's degrees, and x represents the median household income in thousands of dollars.

The equation of the line is y = 4.08x + 63.13. This means that for every increase of $1,000 in median household income, the number of adults with bachelor's degrees increases by 4.08 per 1,000 people. The intercept of the line is 63.13, which represents the number of adults with bachelor's degrees when the median household income is $0.

By analyzing the scatter plot, we can see that the points are roughly linear and show a positive correlation between median household income and the number of adults with bachelor's degrees. The line represents the best fit for this data because it minimizes the distance between the line and the points on the scatter plot.

Hence, the line y = 4.08x + 63.13 is a good fit for this data because it accurately represents the positive relationship between median household income and the number of adults with bachelor's degrees in the 50 U.S. states.

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a) The GCF of 63 and 36 is 9

b)

a) To find the GCF of 63 and 36, we do the following:

Write 63 and 36 as follows:

The common factors are:

Therefore, the Greatest Common Factor (GCF) is 9

b) To find the factor 63 - 36

The false statement is: "The researchers would come to the conclusion that the programme was successful if they used a significance level of 1%."

What is significance level?

A significance level, denoted by α, is the threshold chosen by researchers to determine the level of evidence required to reject the null hypothesis. It represents the maximum acceptable probability of making a Type I error (incorrectly rejecting the null hypothesis when it is true).

In this case, the given p-value is 0.003. If the null hypothesis is true, the p-value represents the likelihood of obtaining a test statistic that is equally extreme to or more extreme than the one that was observed. It offers proof that the null hypothesis is false.

We can conclude that there is strong evidence to reject the null hypothesis in favour of the alternative hypothesis because the p-value is 0.003, which is lower than any often used significance level like 0.05 or 0.01. Thus, if the researchers apply a 5% level of significance, they would draw the conclusion that the programme was successful.

However, if the researchers use a significance level of 1%, they would require even stronger evidence to reject the null hypothesis. Since the p-value of 0.003 is greater than 0.01, they would not be able to reject the null hypothesis at the 1% significance level and would not conclude that the program was effective.

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In the translation of the line segment to the pre-image only implies the change of position, but the slope never changes in translation.

Given that,
To write a true statement about the relationship between the line segments and angle measures when a translation is applied to a preimage.

The line is a curve showing the shortest distance between 2 points.

The angle can be defined as the one line inclined over another line.

Here,
The translation is a process, in which the same figure with the same orientation shifted its position which does not affect the orientation or size to the preimage,

Thus, in the translation of the line segment to the pre-image only implies the change of position, but the slope never changes in translation.

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Answer:

<XAW and <UAY are vertical angles

<XAW and <XAZ are complementary angles

Answer:

Slope is the ratio of the vertical and horizontal changes between two points on a surface or a line

Step-by-step explanation:

If coordinates of any two points of a line are given, then the rate of change is the ratio of the change in the y-coordinates to the change in the x-coordinates.

Answer:

The answer is true

Step-by-step explanation:

The rate of change of S for the weekly sales is :

-250 000e⁻°·⁵t

Given:

the sales of the product is :

S = 500,000e^-0.5t

where S is the weekly sales in the dollars and t is the number of weeks since end of the campaign.

we are asked to find the rate of sales dS/dt = ?

that is the rate of sales of delay.

Given:

S = 500,000e^-0.5t

dS/dt =(500,000)e^-0.5t + 500,00 (e^-0.5t)

= 0 +  500,00 (e^-0.5t)

= - 250 000 e^0.5t

therefore, dS/dt = - 250 000 e^0.5t

Hence we get the required answer.

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The number of laps that Kevin can run is 5 laps.

From the information, Kevin can run a lap around the field in 4-6 minutes and he has 30 minutes to run.

Therefore, the number of laps that he can run will be:

= Total minutes / Time taken for each lap

= 30 minutes / 6

= 5 laps.

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Answer:

a. \(\boxed{y=-3x+16}\)

b.\(\boxed{y=\frac{1}{3}x+1}\)

Step-by-step explanation:

a.\(y-10=-3(x-2)\)

\(\rightarrow y=-3x+6+10\\\rightarrow \boxed{y=-3x+16}\)

b. \(y-2=\frac{1}{3}(x-3)\\\rightarrow y=\frac{1}{3}x-1+2\\\rightarrow \boxed{y=\frac{1}{3}x+1}\)

Answer:

8

Step-by-step explanation:

Arrange the terms in ascending order.

\(-1, \frac{1}{3}, 4.5, 8\)

The maximum value is the largest value in the arranged data set.

8

Answer:18/35

Step-by-step explanation: 6*3 = 18

7*5 = 35

18 /35

Answer: 18/35

Step-by-step explanation:

6*3=18

7*5=35

18/35

The pair of equivalent radical expression is option D. √180 and 3√20.

Radicals are defined as the nth root of a number using the symbol  \(\sqrt[n]{x}\).

This is the opposite form of the exponential functions.

\(\sqrt[n]{x}\) can be written in the exponential form as \(x^{1/n\).

A.√45 can be written as the square root of (15 × 3).

√45 = √(15 × 3) ≠ 3√15

B. √75 cannot be written as 3√5, since, if we have to take 3 outside, inside he root there must be 3² = 9. But 75 is not a multiple of 9.

C. √54 = √(9 × 6) = 3√6 ≠ 9√6

D. √180 = √(9 × 20) = √9 × √20 = 3√20

Hence the correct option is D.

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The clear question is given below.

Which of the following is a pair of equivalent radical expressions?

A. √45 and 3√15

B. √ 75 and 3√5

C. √54 and 9√6

D. √180 and 3√20

Answer:

A.) 20

Step-by-step explanation:

These angles are complementary meaning they add up to 90°.

4x - 10 + x = 90

5x - 10 = 90

5x = 100

x = 20

Answer:

Hello! answer: x = 20

Step-by-step explanation:

This is a complementary angle meaning it will add up to 90 degrees so...

20 × 4 = 80 80 - 10 = 70

70 + 20 = 90 therefore x = 20

The four angles marked in the picture are equal, so they are congruent.

Congruent angles are angles that have the same measure or value. That is, two angles are congruent if they have the same angle measure.

When two angles are congruent, they have the same shape and size.

Let's call each of the angles formed by line L "a" and "b"

Let's call each of the angles formed by line M "c" and "d"

From the given parallel lines;

So angle a, angle b, angle c and angle d are equal, hence they are congruent.

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By using the concept of confidence interval, it is obtained that

We are 95% confident that the interval 15.75 < μ < 28.25 contains the population mean commute time in minutes using public transportation.

Second option is correct

What is Confidence interval?

Let the quantity which is to be estimated is \(\theta\).  A confidence interval for the parameter θ, with confidence level \(\alpha\) is the interval (a, b), where

P(a < \(\theta\) < b) = \(\alpha\), P is the probability

Here the  average commute time in minutes (\(\mu\)) is to be calculated

95% confidence interval for the average commute time in minutes using public transit is (15.75, 28.25)

This means that it is 95% confident that the interval (15.75, 28.25) contains the population mean commute time in minutes using public transit

So the correct interpretation is

We are 95% confident that the interval 15.75 < μ < 28.25 contains the population mean commute time in minutes using public transportation.

Second option is correct

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Complete Question

A researcher finds a 95% confidence interval for the average commute time in minutes using public transit is (15.75, 28.25). What is the correct interpretation of this interval?

A) There is a 95% chance commute time in minutes using public transit is between 15.75 and 28.25 minutes.

B) We are 95% confident that the interval 15.75 < μ < 28.25 contains the population mean commute time in minutes using public transportation.

C) We are 95% confident that all commute time in minutes for the population using public transit is between 15.75 and 28.25 minutes.

D) We are 95% confident that the interval 15.75 < μ < 28.25 contains the sample mean commute time in minutes using public transportation.