Sean is trying to decide between four Roth IRAs. The month after the required initial contribution (RIC), he wants to start contributing the minimum subsequent investment (MSI) each month. Compare the cost of the minimum initial investment and Sean's monthly contribution for each IRA over the next 10 years. Which Roth IRA would Sean put the most money in over those 10 years?

Answer: The quotient would be 30.6666 (goes on forever)

Step-by-step explanation: So, if In 1 week the group can explore 75 km, we need to find how many weeks it takes to complete. So, our equation would look like this:

2,300 / 75

You would get 30. 66666 (6 repeats forever) So, that means the team explores The Great Barrier Reef in around 30 days. The remainder would be 6. The line is a symbol that symbolizes the 6 repeats forever. There would be about 0.7 or .7 kilometers left. (Rounding the 6.6 up to 7) So, in the final week, the explorers would explore 30.6 kilometers or 29.6 (I say 29.6 because this is how much they explored before the week, and 30.6 because this is how much they explored at the end of the whole thing)

P.S. I just rounded to .6, but the 6 repeats forever.

Answer:

1. 70  2. 85  3. 63  4. 20  5. They are vertical angles

Step-by-step explanation:

Answer: 15.68

47.05/3=15.68

I hope this helps :

Answer:

if you are asking for the total of fiction books that were there then I think about 28 books were there.

The correct next step is C: Set the compass width equal to CZ, and draw two arcs, centered at Y, that intersect circle C.

What is a circumscribed circle?

The circumscribed circle or circumcircle of a polygon in geometry is a circle that passes through each of the polygon's vertices. This circle's circumcenter and circumradius are its center and radius, respectively.

It should be noted that an equilateral triangle simply means a triangle that has all the sides and angles to be equal.

The correct next step for Johann to find points W and X is option C: Set the compass width equal to CZ, and draw two arcs, centered at Y, that intersect circle C.

This is because an equilateral triangle can be inscribed in a circle by drawing two intersecting arcs that intersect the circle at three points. To find these points, the compass should be set to the length of one side of the equilateral triangle, which in this case is CZ, and two arcs should be drawn centered at Y and intersecting circle C. The two points where the arcs intersect the circle will be points W and X of the equilateral triangle inscribed in the circle.

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Answer:

Step-by-step explanation:

Replace g(x) with y, then switch the x and y variables:

\(x=\frac{-5y+5}{2}\)

Solve for the new y value, multiply by 2:

\(2x=-5y+5\)

Subtract 5 on both sides:

\(2x-5=-5y\)

Divide by -5 on both sides:

\(-\frac{2x-5}{5} =y\)

Distribute the negative sign and rearrange:

\(\frac{-2x+5}{5} =\frac{5-2x}{5} =g^-^1(x)\)

Answer:

Step-by-step explanation:

Substitute x with y and g(x) with x and  then solve for y:

Replace y with g⁻¹(x)

Correct choice is A

A

Step-by-step explanation:

I really don't know because like what's her expression like is A - D like the answers or are they the expressions but A looks right and if not A then c

Answer:

x = 2.5

Step-by-step explanation:

           y = -3x + 14   -----------(I)

3x - 5y = -25 -------------------(II)

Substitute y = -3x + 14 in equation (II),

             3x -5 ( -3x + 14) = -25

          3x  + 5 * 3x - 5*14 = -25

            3x  + 15x - 70      = -25    {Combine like terms}

                        18x - 70   = -25  

Add 70 to both sides,

                                 18x = -25 + 70

                                 18x = 45

Divide both sides by 18,

                                    x = 45 ÷ 18

                                   x = 2.5

Answer:

The value of x in the solution to the system of equations is x = 7.

Here's the explanation and verification:

Solve for X in the first equation:

Y = -3X + 14

X = (Y - 14) / -3

Substitute this expression for X into the second equation:

3X - 5Y = -25

3((Y - 14) / -3) - 5Y = -25

Simplify this expression:

Y + 42 / 3 + 5Y = -25

6Y + 42 / 3 = -25

Solve for Y:

6Y = -25 - 42 / 3

6Y = -25 - 14

6Y = -39

Y = -39 / 6

Y = -6.5

Substitute this value of Y back into the expression for X that you found in step 1:

X = (Y - 14) / -3

X = (-6.5 - 14) / -3

X = (-20.5) / -3

X = 6.83

Round the answer to the nearest integer, so X = 7.

Verification:

Now that you have found the values of X and Y, you can verify that they are a solution to the system of equations by plugging them back into the original equations and seeing if they make both sides equal.

Y = -3X + 14

Plug in X = 7 and Y = -6.5:

-6.5 = -3 * 7 + 14

-6.5 = -21 + 14

-6.5 = -7

3X - 5Y = -25

Plug in X = 7 and Y = -6.5:

3 * 7 - 5 * -6.5 = -25

21 + 32.5 = -25

53.5 = -25

Both equations evaluate to true, so X = 7 and Y = -6.5 is a solution to the system of equations.

Equate both

Put in first one

Graph attached

Answer:

x = -2,  y = 1

Step-by-step explanation:

Given system of equations:

\(\begin{cases}y=2x+5\\y=-3x-5 \end{cases}\)

Solve by Substitution

Substitute the first equation into the second equation and solve for x:

\(\implies 2x+5=-3x-5\)

Add 3x to both sides:

\(\implies 2x+5+3x=-3x-5+3x\)

\(\implies 5x+5=-5\)

Subtract 5 from both sides:

\(\implies 5x+5-5=-5-5\)

\(\implies 5x=-10\)

Divide both sides by 5:

\(\implies \dfrac{5x}{5}=\dfrac{-10}{5}\)

\(\implies x=-2\)

Substitute the found value of x into one of the equations and solve for y:

\(\implies y=2(-2)+5\)

\(\implies y=-4+5\)

\(\implies y=1\)

Therefore, the solution to the given system of equations is (-2, 1).

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The fractions with the least common denominator are 20/48 and 21/48 (Option D).

To express the pair of fractions 5/12 and 7/16 using the least common denominator (LCD),

follow these steps:
Find the least common multiple (LCM) of the two denominators, which are 12 and 16.

Rewrite the fractions using the LCM as the new denominator.

Simplify the fractions, if possible.

Find the LCM of 12 and 16.
- List the multiples of 12: 12, 24, 36, 48, 60...
- List the multiples of 16: 16, 32, 48, 64...
The LCM of 12 and 16 is 48.
Rewrite the fractions with the LCD of 48.
- For 5/12, multiply the numerator and denominator by 4: (5*4)/(12*4) = 20/48
- For 7/16, multiply the numerator and denominator by 3: (7*3)/(16*3) = 21/48
The fractions are already simplified.

Option D is correct.

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Answer:

a=4

b=1

c=2

d=3

Step-by-step  explanation:

Answer:

2.5x

Step-by-step explanation:

7.5 / 3 = 2.5

Answer:

2.5

Step-by-step explanation:

now to find the scale factor we do

7.5/3

=2.5

so the rectangle is increased by the scale factor of 2.5

I work hard on my answers

it would be very appreciated if you award me with a brainliest

Step-by-step explanation:

use the formula given

a is the first term

d is the differences between adjacent numbers

and then you substitute the value

Therefore, the tree is 78.14 feet tall. Rounded to the nearest hundredth of a foot, the answer is 78.14 feet.

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It is a fundamental part of geometry and is used in many areas of science, engineering, and technology.

by the question.

A represents the top of the tree, and the line segment AB represents the height of the tree, which we want to find. The angle of elevation, which is the angle between the ground and the line of sight to the top of the tree, is 54°. The distance from the point on the ground to the tree is 52 feet, which we'll call d. Finally, h represents the distance from the ground to the point where the line of sight intersects the tree.

Using trigonometry, we know that:

tan (54°) = h/d

We can rearrange this equation to solve for h:

\(h = d * tan (54)\)

Plugging in the values we know, we get:

\(h = 52 * tan (54) = 78.14\)

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Let, number of small and big pumpkin are x and y.

So, mathematical equation is given by :

x + y = 29    ...1)

3x + 5y = 105     ...2)

Putting value of x from equation 1 to equation 2, we get :

\(3(29-y ) +5y=105\\\\2y = 18\\\\y = 9\)

So, x = 20

Therefore, number of small and large pumpkins are 20 and 9 respectively.

Hence, this is the required solution.

Answer:

b 18 boys

Step-by-step explanation:

In order to solve this problem we must create a system of equations.

Creating a system of equations

Let x = number of boys and y = # of girls

We are given that in total there are 27 children which means # of boys + # of girls = 27 so we can say x + y = 27

We are also given that there are twice as many boys as girls so we can also say x = 2y ( as # of boys = twice the number of girls )

Solving the system

Now to find the # of boys and girls we must solve the system. To do so we are going to use the substitution method.

What is the substitution method?

The substitution method is where one of your variables ( x in this case ) is defined by an expression in which you can plug in or " substitute " it into the other equation ( we can substitute x = 2y into the other equation and solve for y )

Substitute equation 2 into equation 1

Equation 1 : x + y = 27

==> plug in x = 2y

y + 2y = 27

==> combine like terms

3y = 27

==> divide both sides by 3

y = 9

So there are 9 girls in the classroom

Solving for # of boys

To solve for the number of girls we plug in the # of girls (y=9) into one of the equations and solve for x

equation : x + y = 27

==> plug in y = 9

x + 9 = 27

==> subtract 9 from both sides

x = 18

There are 18 boys in the classroom

Checking our work:

Now that we have found the possible answers we can check our work. To do so we are going to want to plug in the values of x and y into both equations and if both are true our answer is correct

Equation 1 x + y = 27

==> plug in x = 18 and y = 9

18 + 9 = 27

==> simplify

27 = 27 ✓

equation 2 x = 2y

==> plug in x = 18 and y = 9

18 = 2(9)

==> multiply 2 and 9

18 = 18 ✓

Both are correct therefore we can conclude that there are 18 boys and 9 girls.

The correct option is B. $35,713. f someone saves $950.00 of their take home pay at the end of every six months for 15 years and invests in an account earning 3% compounded monthly, they will have accumulated $35,713.

To calculate how much money will be accumulated in 15 years, we need to apply the formula;A=P(1+r/n)^(n*t)where;A = the accumulated amount

P = principal (the initial amount) r = annual interest raten = number of times the interest is compounded in a year t = number of years.

In this case, the principal amount is $950, the annual interest rate is 3%, compounded monthly. We need to find out how much will be accumulated in 15 years.

Therefore;A = 950(1+0.03/12)ᵃ  (a=12*15)A = 35,713

Thus, the total accumulated amount in 15 years would be 35,713. Therefore, the correct option is B. 35,713.

In conclusion, if someone saves $950.00 of their take home pay at the end of every six months for 15 years and invests in an account earning 3% compounded monthly, they will have accumulated $35,713.

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The value of cv1, the lower critical value, is approximately 54.19.

To find the critical value (cv1) for a two-tailed hypothesis test at a 10% significance level, we need to divide the significance level (α) by 2.

Since α = 0.10, we divide it by 2 to get 0.10/2 = 0.05.

Next, we need to find the z-score associated with the cumulative probability of 0.05.

Using a standard normal distribution table or a calculator, we can find that the z-score for a cumulative probability of 0.05 is approximately -1.645.

Now, we can calculate the critical value by multiplying the z-score by the standard deviation (27) and adding it to the population mean (100).

cv1 = 100 + (-1.645 * 27)
cv1 ≈ 54.19 (rounded to two decimal places)

Therefore, the value of cv1, the lower critical value, is approximately 54.19.

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Answer:

In about 9 months the population of the towns will be equal.

Step-by-step explanation:

The population of both cities, after t months, can be modeled by linear functions.

Town A:

Population of 53330.

About 75 people move out of the town each month. Each​ month, 175 people on average move into town.

So, after t months, the population will be:

\(A(t) = 53300 + (175 - 75)t\)

\(A(t) = 53300 + 100t\)

Town B:

Population of 55,825.

An average of 175 people moving away every month.

So, after t months, the population will be:

\(B(t) = 55825 - 175t\)

In about how many months will the populations of the towns be​ equal?

This is t for which:

\(A(t) = B(t)\)

\(53300 + 100t = 55825 - 175t\)

\(275t = 2525\)

\(t = \frac{2525}{275}\)

\(t = 9.18\)

Rounding to the nearest number

In about 9 months the population of the towns will be equal.

Answer:

8.93h in³

Step-by-step explanation:

The circumference of the base of the cone is 8.5pi inches. What is the volume of the cone in terms of ne? Round to the nearest hundredth. Enter

Step 1

We find the radius of the cone

Base area = 8.5 π inches

Radius = √Area/π

Radius = √8.5 π /π

Radius = √8.5

Radius of the cone = 2.9154759474 inches

Approximately = 2.92 inches

Step 2

We find the volume of the cone

= πr²h/3

Height is not given, so we find in terms of h

= π × 2.92² × h/3

= 8.9288252005h in³

Approximately = 8.93h in³

The

Given a linear system of equations in unknowns x, y, and z with the following augmented matrix:{[1, -1, 0, 0, -7], [-2, 3, 0, 0, 2], [0, 0, 4, -2, 2]}Use Gauss-Jordan elimination to solve the system for x, y, and z.Solution:Step 1. The first step in solving this linear system of equations is to write the matrix in the form of an augmented matrix. In the following, we list the system of equations associated with the augmented matrix: 1x−1y=−72x+3y=24z−y=1  We begin by focusing on the first equation, which is:1x−1y=−7.

To get rid of the x-coefficient, we add one time the first equation to the second equation. This operation is written as follows:{[1, -1, 0, 0, -7], [-2, 3, 0, 0, 2], [0, 0, 4, -2, 2]}We add row1 to row2. -2r1 + r2 = r2{-2, 2, 0, 0, 14}r3 = r3This gives us the new augmented matrix.{[1, -1, 0, 0, -7], [0, 1, 0, 0, -5], [0, 0, 4, -2, 2]}Step 2Next, we focus on the second equation:0x+1y=−5.

The y-variable is isolated, and we now look at the third equation.4z−2y=1We can isolate the variable z by dividing the entire equation by 4 as follows:z−0.5y=0.25In order to eliminate y in the third row, we add 0.5 times the second row to the third row. This operation is written as follows:{[1, -1, 0, 0, -7], [0, 1, 0, 0, -5], [0, 0, 4, -2, 2]}We add 0.5 r2 to r3. r3 + 0.5r2 = r3{[1, -1, 0, 0, -7], [0, 1, 0, 0, -5], [0, 0, 4, -1, -1]}Step 3We can now solve for z using the third equation:4z−1y=−1z = (-1 + y) / 4.

Substituting this into the second equation gives:-2((1 - y) / 4) + 3y = 2y - 1 = 2y - 1Thus, y = 1/2.Substituting the value of y = 1/2 into the first equation gives:x - (1/2) = -7, so x = -13/2.Finally, we can substitute the values of x and y into the third equation to get the value of z: 4z - 1(1/2) = -1, so z = -3/2.The solution to the system of linear equations is: x = -13/2, y = 1/2, and z = -3/2.

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The inequality √17 > 239/58 correctly compares one rational number and one irrational number.

An Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

As per option (A),

4π/3 and √17

The values of the above number are 4.1887 and 4.1231

Thus, 4π/3 < √17

So, given inequality 4π/3 > √17 is not true.

As per option (B),

4.\(\bar{19}\) and 239/58

The values of the above number are 4.1919 and 4.1206

Thus, 4.\(\bar{19}\) < 239/58

So, given inequality 4.\(\bar{19}\) > 239/58 is not true.

As per option (C),

√17 and 239/58

The values of the above number are 4.1231 and 4.1206

Thus, √17 > 239/58

This inequality is true.

Therefore, the inequality √17 > 239/58 correctly compares one rational number and one irrational number.

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Hello!

\(\large\boxed{\frac{19}{30}}\)

There are 60 minutes in an hour, so:

38 / 60

Reduce the fraction by diving by the GCF, or 2:

(38/2) / (60/2) = 19 / 30.

Answer:

b- g(x)=7x+9

Step-by-step explanation:

the vertical compress is the slope so m

and the shifts up 9 is the y-intercept

hope this helps :)

The four levels of measurement in statistics are nominal, ordinal, interval, and ratio.

1. Nominal: The nominal level of measurement involves categorizing data into distinct categories or groups. Examples include gender (male or female), marital status (single, married, divorced), or types of fruits (apple, orange, banana).

2. Ordinal: The ordinal level of measurement allows for ranking or ordering of data based on a specific criterion. Examples include survey ratings (strongly agree, agree, neutral, disagree, strongly disagree) or educational levels (elementary, middle school, high school, college, postgraduate).

3. Interval: The interval level of measurement not only allows for ranking but also quantifies the intervals or differences between values.Examples include temperature measured in Celsius or Fahrenheit, where the intervals between values are equal but zero does not indicate the absence of temperature.

4. Ratio: The ratio level of measurement possesses all the properties of the interval level but also has a true zero point, which indicates the absence of the measured attribute. Examples include height, weight, or income, where zero represents the absence of the attribute and ratios between values are meaningful (e.g., someone twice as tall as another person).

Nominal: The nominal level of measurement involves categorizing data into distinct categories or groups. In this level, data are simply named or labeled without any quantitative value. Examples include gender (male or female), marital status (single, married, divorced), or types of fruits (apple, orange, banana).

Ordinal: The ordinal level of measurement allows for ranking or ordering of data based on a specific criterion. It indicates relative differences between the values but does not quantify the magnitude of those differences. Examples include survey ratings (strongly agree, agree, neutral, disagree, strongly disagree) or educational levels (elementary, middle school, high school, college, postgraduate).

Interval: The interval level of measurement not only allows for ranking but also quantifies the intervals or differences between values. However, it does not have a true zero point. Examples include temperature measured in Celsius or Fahrenheit, where the intervals between values are equal but zero does not indicate the absence of temperature.

Ratio: The ratio level of measurement possesses all the properties of the interval level but also has a true zero point, which indicates the absence of the measured attribute. It allows for comparisons of magnitude and ratios between values. Examples include height, weight, or income, where zero represents the absence of the attribute and ratios between values are meaningful (e.g., someone twice as tall as another person).

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The height of the tree is 13.2 m.

What is proportional ?

 The concept of proportionality in mathematics denotes the linear relationship between two quantities or variables. The size of one item increases by twofold, whereas the size of the other quantity decreases by one-tenth of the earlier amount.  

We can set up a proportion comparing the height of each object to the length of the shadow.

Then , \(\frac{h}{s}\).

=> \(\frac{3.8}{1.3} = \frac{h}{4.5}\)

=> h = \(\frac{3.8*4.5}{1.3}\)

=> 13.2 m.

Hence the height of the tree is 13.2 m.

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The power rule for logarithms states that logb(M^p) = p * logb(M). The logarithm of a number with an exponent is the product of the exponent and the logarithm of that number.

The power rule states that logb(M^p) = p * logb(M), where M, b, and p are positive real numbers.

To understand this rule, let's consider an example. Suppose we have log2(8^2). According to the power rule, this is equivalent to 2 * log2(8).

In this case, M is 8, b is 2, and p is 2. The power rule tells us that we can bring the exponent (p) down and multiply it with the logarithm of the base (b) raised to the number (M).

So, log2(8^2) can be simplified as 2 * log2(8), which is 2 * 3 = 6.

In general, the power rule allows us to simplify logarithmic expressions by bringing the exponent down and multiplying it with the logarithm of the base.

This rule is particularly useful when dealing with complex logarithmic expressions and simplifying them to a more manageable form.

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The equation line of the of the road in slope-intercept form is; y = 2·x - 10

The standard form of the equation of a line is Ax + Bx + C, where A, B, and C are constants and A and B are nonzero numbers.

The parameters for the new road are;

The road will be parallel to village way with points (0, 5), and (-4, -3)

The road will pass through the intersection  of Gray Dr and Canon Rd., which is the point with coordinates (3, -4)

Required; The equation of the road

Since the new road is parallel to Village Way, which has slope;

m = (5 - (-3))/(0 - (-4)) = 8/4 = 2

The slope of the new road will also be 2.

Let the equation of the new road be y = m·x + c, where m = 2 is the slope we just found. To find c, we use the fact that the road passes through the point (3, -4);

y - (-4) = 2 × (x - 3)

y = 2·x - 6 - 4 = 2·x - 10

y = 2·x - 10

Therefore, c = -10

Therefore, the equation of the new road in slope-intercept form, therefore is; y = 2·x - 10

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Therefore , the solution of the given problem of linear equation is  x's coefficient is -9.9,x's coefficient is 75  and  y's coefficient is 275.

A model of linear regression is one that applies the formula y=mx+b. B is the slope, and m is the y-intercept. Ignoring the fact that while both y and y are distinct components, the previous sentence is frequently referred as a "mathematical formula with two variables." Bivariate linear equations only have two variables. The application domains of linear equations have zero solutions in all cases.

Here,

Given :

=>0.8 (2x + x) + 3(7 - 4.1x) = __x + 21

=>0.8(3x) + 21 - 12.3x = __x + 21

=>2.4x + 21 - 12.3x = __x + 21

=>-9.9x + 21 = __x + 21

=> -9.9

=> 12 1/2 (6x + 22y) = x + y

=> 75x + 275y = x + y

Therefore , the solution of the given problem of linear equation is  x's coefficient is -9.9,x's coefficient is 75  and  y's coefficient is 275.

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