A retirement account is opened with an initial deposit of $6,500 and earns 5.12% interest compounded monthly. What will the account be worth in 25 years? (Round your answer to the nearest cent.)

Answer:

A)  \(B = \{\left[\begin{array}{ccc}1&0\\0&1 \end{array}\right], \left[\begin{array}{ccc}0&1\\1&0 \end{array}\right] \}\)

B) \(M_{B} = \left[\begin{array}{ccc}-2\\-7\end{array}\right]\)

Step-by-step explanation:

Let \(A = \left[\begin{array}{ccc}a&b\\c&d \end{array}\right]\) where a, b, c and d are real numbers

Since A is said to be a half magic square matrix, a = d, b = c.

The matrix A therefore becomes  \(A = \left[\begin{array}{ccc}a&b\\b&a \end{array}\right]\) where \(a,b \epsilon R\)

A can therefore be manipulated as:

\(A = a \left[\begin{array}{ccc}1&0\\0&1 \end{array}\right] + b \left[\begin{array}{ccc}0&1\\1&0 \end{array}\right]\)

The matrices \(\left[\begin{array}{ccc}1&0\\0&1 \end{array}\right]\) and \(\left[\begin{array}{ccc}0&1\\1&0 \end{array}\right]\) are apparently linearly independent and therefore form a basis B for V

\(B = \{\left[\begin{array}{ccc}1&0\\0&1 \end{array}\right], \left[\begin{array}{ccc}0&1\\1&0 \end{array}\right] \}\)

B) Find the coordinate vector [M]_B of M [-2 -7, -7 -2]

 \(M = \left[\begin{array}{ccc}-2&-7\\-7&-2 \end{array}\right]\)

\(M\) can be written in the form \(M = a\left[\begin{array}{ccc}1&0\\0&1 \end{array}\right] + b\left[\begin{array}{ccc}0&1\\1&0 \end{array}\right]\)

\(M = \left[\begin{array}{ccc}-2&-7\\-7&-2 \end{array}\right] = -2\left[\begin{array}{ccc}1&0\\0&1 \end{array}\right] -7\left[\begin{array}{ccc}0&1\\1&0 \end{array}\right]\)

The coordinate vector is therefore, \(M_{B} = \left[\begin{array}{ccc}-2\\-7\end{array}\right]\)

Step-by-step explanation:

d = √(15-10)²+(-6-3)²

=√5²+(-9)²

= √25+81

=√106

10.3 units

The probability that a simple random sample of 50 unemployed individuals will provide a sample mean within 1 week of the population mean is 0.92

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Let X the random variable that represent the avergae number of weeks an individual is unemployed of a population, and for this case we know the distribution for X is given by:

X = N(17.5)

Where μ = 17.5 and σ = 4

Since the distribution for X is normal then, the distribution for the sample mean  is given by:

X = N(17.5, σ/√n)

X =N(17.5.4/√50) = 0.566

We select a sample of n =50 people. And we want to find the following probability

P(16.5 < X < 18.5) = P((16.5 -17.5)/(4/√50) < Z < (16.5 -17.5)/(4/√50) )

And using the normal standard table or excel we find the probability:

P(-1.768 < Z 1.768) = P(Z < 1.768) - P(Z< -1.768) = 0.961 - 0.039 = 0.92

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Answer:

False

Step-by-step explanation:

1. The inverse function should have c(n) isolated
2. When finding the inverse of a function, the variables c(n) and n are interchanged (and then c(n) is isolated).
It would look like this --->c(n)=50+4n--->n=50+4(c(n)) ---> c(n)=(n-50)/4

The possible price for the items if the store sells $600 is (c) $40

From the question, we have the following parameters that can be used in our computation:

The supply-demand graph

If the store sells $600, then there is a supply worth of $600

The equation of the supply line is calculated as

y = mx + c

Where

c = y = 0

i.e. c = 100

So, we have

y = mx + 100

Using another point on the graph, we have

30m + 10 = 400

So, we have

m = 13

This means that

y = 13x + 100

For a supply of 600, we have

13x + 100 = 600

So, we have

13x = 500

Divide by 13

x = 38.4

Approximate

x = 40

Hence, the possible price for the items is (c) $40

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Answer:

h and k are simply variables that stand in for the x and y of a point. Math books could have easily have used x1, x2 y1 y2, etc, but h and k is the convention.

anyway, this is a guess n check question. Substitute the x value of the point for h, and y value for k, and whichever one gives you a true equation is the right one.

Answer:

Step-by-step explanation:

y = a(x-h)²+k is the “vertex-form equation” for a vertical parabola with vertex (h,k).

Since a>0, the parabola opens upwards. (If a<0, it opens downwards. If a=0, it is not a parabola at all.)

The parabola y = a(x-h)²+2k is the same shape as the first equation, but it is shifted vertically by k units.

Since (2,4) is a point on the first parabola, (2,4+k) is a point on the second parabola.

Answer:

21.47

Step-by-step explanation:

a^2 + b^2 = c^2

10^2 + 19^2 = c^2

100+361=c^2

461=c^2

21.4709

to the nearest hundredth, it is is 21.47

Answer:

5

Step-by-step explanation:

Slope is defined as rise over run, so it is (26-11)/(5-2) = 15/3 = 5

Answer:

slope is 5

Step-by-step explanation:

slope formula says m= y2-y1/x2-x1

m=26-11/5-2

m=15/3

m=5

Answer:

Its perimeter is 23 units

Step-by-step explanation:

The perimeter of any figure is the sum of the lengths of its outline sides

The rule of the distance between two points is:

In the given figure ABCD:

Its perimeter = AB + BC + CD + DE + EA

→ Find the length of each side using the rule above

A = (-4, -2), B = (-1, 2), C = (2, 2), D = (5, -1), E = (2, -4)

→ Substitute them in the rule above to find the lengths of its sides

\(AB=\sqrt{(-1--4)^{2}+(2--2)^{2}}=\sqrt{(-1+4)^{2}+(2+2)^{2}}\\\\=\sqrt{(3)^{2}+(4)^{2}}=\sqrt{9+16}=\sqrt{25}\)

∴ AB = 5

\(BC=\sqrt{(2--1)^{2}+(2-2)^{2}}=\sqrt{(2+1)^{2}+(0)^{2}}\\\\=\sqrt{(3)^{2}+0}=\sqrt{9+0}=\sqrt{9}\)

∴ BC = 3

\(CD=\sqrt{(5-2)^{2}+(-1-2)^{2}}=\sqrt{(3)^{2}+(-3)^{2}}\\\\=\sqrt{9+9}=\sqrt{18}\)

∴ CD = \(\sqrt{18}\)

\(DE=\sqrt{(2-5)^{2}+(-4--1)^{2}}=\sqrt{(-3)^{2}+(-4+1)^{2}}\\\\=\sqrt{(-3)^{2}+(-3)^{2}}=\sqrt{9+9}=\sqrt{18}\)

∴ DE = \(\sqrt{18}\)

\(EA=\sqrt{(-4-2)^{2}+(-2--4)^{2}}=\sqrt{(-6)^{2}+(-2+4)^{2}}\\\\=\sqrt{(-6)^{2}+(2)^{2}}=\sqrt{36+4}=\sqrt{40}\)

∴ EA = \(\sqrt{40}\)

→ Add them to find the perimeter of the figure ABCDE

∴ Its perimeter = 5 + 3 + \(\sqrt{18}\) + \(\sqrt{18}\) +\(\sqrt{40}\) ≅ 22.8098

→ Round it to the whole number

∴ Its perimeter = 23 units

Answer:

14√2

Step-by-step explanation:

This is a 45-45-90 triangle

Because both of the angles are the same all sides, but the hypotonouse are the same

this means that the other length is 14 too

we can use a²+b²=c² to solve

14²+14²=c²

=

392=c²

√392=c

√392=14√2

20 pages of Daniel's book had pictures.

If 1/12 of the pages in Daniel's book had pictures, we can calculate the number of pages with pictures by multiplying the total number of pages in the book by 1/12:

240 pages x (1/12) = 20 pages

To find the number of pages with pictures in the entire book, we need to determine how many groups of 12 pages there are in the book and then multiply that number by the number of pages with pictures in each group (which is one page). We can do this by multiplying the total number of pages in the book (240) by the fraction 1/12, which gives us 20 pages with pictures in the book.

Therefore, 20 pages of Daniel's book had pictures.

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Answer: -8

Since we are dividing the OPPOSITE of 4 then we are dividing 32÷-4

When multiplying or dividing a POSITIVE to a NEGATIVE you get a NEGATIVE

P/N=N

N/N=P

P*P=P

P=Positive

N=Negative

Divide

32/-4=-8

So your answer is -8

When 32 is divided by opposite of 4 the obtained result is - 8.

Additive inverse of a number is such a number when the original number and it's additive inverse is added we get zero.

4 + ( - 4 ) = 0.So the additive inverse of 4 is - 4.

According to the given question we have to obtain the result when 32 is divided by opposite of 4.

Here opposite of 4 means additive inverse of 4 which is -4.

∴ 32/-4

= - 8.

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Answer:

The probability that a resident reports high satisfaction while the resident is a renter is Option(a) \(13.7\%\)

Step-by-step explanation:

Given:

                               Levels of satisfaction

                      High      Medium     Low       Total

Owners          \(26\)             \(34\)               \(18\)           \(78\)

Renters           \(15\)            \(12\)                \(5\)            \(22\)

Total               \(41\)             \(46\)               \(23\)          \(110\)

The Resident is a renter.

Step 1:

To find the probability that a resident reports high satisfaction.

P(Renter- higher satisfaction)= Higher Satisfaction by render ÷ Total level of satisfaction

\(=\frac{15}{110}\)

\(=0.137\)

\(13.7\%\) is the probability that a resident reports high satisfaction.

Therefore, Option (a) is a correct answer.

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Answer:

A) 13.7%

Step-by-step explanation:

edge 2023

Answer:

3,952 ft

Step-by-step explanation:

Use the sine function since you need to find the hypotenuse but know the opposite side of the angle, since sine is equal to opposite/hypotenuse.

sin8°=\(\frac{550}{c}\)

csin8°=550

c=550/sin8°

c= 3,952

Answer:

angle ced is a right ange

so the m angels debate =135 m angle aeb =35

so the answer is 135+35 =170

180 is a all side sim

=180-170=10 answer

Answer:

∠CED is a right angle.

∠CEA is a right angle.

m∠CEB = m∠BEA

m∠DEB = 135°

The coordinates of point c on the coordinate plane are (4, 1)

From the question, we have the following parameters that can be used in our computation:

B = (10, 7)

M = (7, 4)

The midpoint formula for two points (x1, y1) and (x2, y2) is:

(x1 + x2) / 2 = x_midpoint

(y1 + y2) / 2 = y_midpoint

So, for points B and C, we have:

x_midpoint = 7

y_midpoint = 4

Also, we have

x_B = 10

y_B = 7

The coordinates of C are calculated as

x_C = 2 * x_midpoint - x_B = 2 * 7 - 10 = 4

y_C = 2 * y_midpoint - y_B = 2 * 4 - 7 = 1

The coordinates of point C are (4, 1).

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A graph of the resulting triangle after a rotation of -180° about the origin is shown below.

In Mathematics and Geometry, the rotation of a point 180° about the origin in a clockwise or counterclockwise direction would produce a point that has these coordinates (-x, -y).

Furthermore, the mapping rule for the rotation of triangle TOP 180° counterclockwise or -180° about the origin is given by this mathematical expression:

(x, y)                                            →            (-x, -y)

Coordinates of point T (6, 0)  →  Coordinates of point T' = (-6, 0)

Coordinates of point O (-2, -5)  →  Coordinates of point O' = (2, 5)

Coordinates of point P (-2, 5)  →  Coordinates of point P' = (2, -5).

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The first integral has a well-known beta function representation, so the second one should too. The beta function itself is defined as

\(B(x,y) = \displaystyle \int_0^1 t^{x-1} (1-t)^{y-1} \, dt\)

and satisfies the identity

\(\displaystyle B(x,y) = \frac{\Gamma(x) \Gamma(y)}{\Gamma(x+y)}\)

Later on, we'll also use the so-called reflection formula for the gamma function; for non-integer z,

\(\Gamma(z) \Gamma(1-z) = \dfrac{\pi}{\sin(\pi z)}\)

as well as the identity

\(\dfrac{\Gamma(z+1)}{\Gamma(z)} = z\)

Replace \(x\to\sin^{-1}(x)\) in both integrals, so that

\(\displaystyle \int_0^{\frac\pi2} \sqrt{\sin(x)} \, dx = \int_0^1 \frac{\sqrt x}{\sqrt{1-x^2}} \, dx\)

\(\displaystyle \int_0^{\frac\pi2} \frac{dx}{\sqrt{\sin(x)}} = \int_0^1 \frac{dx}{\sqrt x \sqrt{1-x^2}}\)

Now replace \(x\to\sqrt x\) :

\(\displaystyle \int_0^1 \frac{\sqrt x}{\sqrt{1-x^2}} \, dx = \frac12 \int_0^1 x^{-\frac14} (1-x)^{-\frac12} \, dx = \frac12 B\left(\frac34, \frac12\right) \)

\(\displaystyle \int_0^1 \frac{dx}{\sqrt x \sqrt{1-x^2}} = \frac12 \int_0^1 x^{-\frac34} (1-x)^{-\frac12} \, dx = \frac12 B\left(\frac14, \frac12\right)\)

So, the original integral (which I condense here to a double integral) is

\(\displaystyle \int_0^{\frac\pi2} \int_0^{\frac\pi2} \sqrt{\frac{\sin(x)}{\sin(y)}} \, dx \, dy = \frac14 B\left(\frac34, \frac12\right) B\left(\frac14, \frac12\right)\)

\(\displaystyle = \frac14 \frac{\Gamma\left(\frac14\right) \Gamma\left(\frac34\right) \Gamma\left(\frac12\right)^2}{\Gamma\left(\frac54\right) \Gamma\left(\frac34\right)}\)

\(\displaystyle = \frac14 \frac{\Gamma\left(\frac14\right) \Gamma\left(\frac34\right) \Gamma\left(\frac12\right)^2}{\frac14 \Gamma\left(\frac14\right) \Gamma\left(\frac34\right)}\)

\(\displaystyle = \Gamma\left(\frac12\right)^2 = \frac{\pi}{\sin\left(\frac\pi2\right)} = \boxed{\pi}\)

Answer:

\( g(x) = 2x+2\)

Let's find g(a+h):

\( g(a+h)=2*(a+h) +2= 2a +2h +2\)

And now let's find g(a)

\( g(a)= 2a+2\)

And now finally:

\( g(a+h) = 2a +2h +2 -2a-2 = 2h +2-2= 2h\)

Step-by-step explanation:

We have the following function given:

\( g(x) = 2x+2\)

Let's find g(a+h):

\( g(a+h)=2*(a+h) +2= 2a +2h +2\)

And now let's find g(a)

\( g(a)= 2a+2\)

And now finally:

\( g(a+h) = 2a +2h +2 -2a-2 = 2h +2-2= 2h\)

Answer:

Let's denote the number of football games Tommy started as "f" and the number of baseball games he started as "b."

We're given two pieces of information:

Tommy has started a total of 109 RHS games:

f + b = 109 (Equation 1)

The number of baseball games he started was five less than twice the number of football games he started:

b = 2f - 5 (Equation 2)

We can solve this system of equations to find the value of "f," which represents the number of football games Tommy started.

Substitute Equation 2 into Equation 1:

f + (2f - 5) = 109

Combine like terms:

3f - 5 = 109

Add 5 to both sides:

3f = 114

Divide both sides by 3:

f = 38

Therefore, Tommy started 38 football games.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Tommy started with 71

The slope of a line perpendicular to the line whose equation is x - 2y = -8 is -2.

In Mathematics and Geometry, perpendicular lines are two (2) lines that intersect or meet each other at an angle of 90° (right angles).

From the information provided above, the slope for the equation of line m is given  by:

x - 2y = -8

2y = x + 8

y = x/2 + 4

slope (m) of line m = 1/2

In Mathematics and Geometry, a condition that is true for two lines to be perpendicular is given by:

m₁ × m₂ = -1

1/2 × m₂ = -1

m₂ = -2

Slope, m₂ of perpendicular line = -2

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Answer: 36˚

Step-by-step explanation:

180 - 3x = 2x

180 = 5x

.: x = 36˚

Answer:

Q1. Answer: According to the guidelines, the ratio of the rise (height) to the run (length) of a wheelchair ramp should be no greater than 1:12.

Option A: A ramp with a length of 30 feet and a height of 3 feet. The ratio of the rise to the run is 3/30 = 1/10, which is less than 1:12, so this ramp follows the guidelines.

Option B: A ramp with a length of 20 meters and a height of 0.5 meters. The ratio of the rise to the run is 0.5/20 = 1/40, which is less than 1:12, so this ramp follows the guidelines.

Option C: A ramp with a length of 384 inches and a height of 32 inches. The ratio of the rise to the run is 32/384 = 8/96 = 2/24, which is less than 1:12, so this ramp follows the guidelines.

Option D: A ramp with a length of 1 feet and a height of 12 feet. The ratio of the rise to the run is 12/1 = 12, which is not less than 1:12, so this ramp does not follow the guidelines.

Therefore, the ramps that follow the guidelines are options A, B, and C.

Q2. Answer: The guidelines for a wheelchair ramp suggest that the ratio of the rise (height) to the run (length) of the ramp should be no greater than 1:12. In this case, the rise is 2.5 feet and the run is the length of the ramp (x feet). The ratio of the rise to the run is 2.5/x.

To follow the guidelines, the ratio of the rise to the run should be no greater than 1:12, or 1/12. Therefore, the length of the ramp (x) should be greater than or equal to 2.5/1/12 = 30 feet.

Therefore, the correct answer is C: X ≥ 30.

Step-by-step explanation:

The state spelled out with letter tiles depends on the probability of picking the letter O, and the possible states are Ohio,  Colorado and  Oregon respectively.

To solve this problem, we need to consider the frequency of the letter O in each state's name.

If the probability of picking the letter O is 1/2, then the state must have two O's in its name. The only state that meets this criteria is OHIO.

If the probability of picking the letter O is 3/8, then the state must have three O's in its name. The only state that meets this criteria is COLORADO.

If the probability of picking the letter O is 1/3, then the state must have at least three O's in its name. The only state that meets this criteria is OREGON.

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The current value of his Roth IRA is $215,658.00

What is Roth IRA retirement account?

Roth IRA retirement account is a retirement account where the contributions to the account are invested after taxes after have been deducted.

In other words, when the individual make contributions, taxes are first of all, deducted so as to invest the after-tax contribution into the Roth IRA account

The account lost 1/3 of its original value of $215,658

balance after the loss=$215,658-(1/3*$215,658)

balance after the loss=$ 143,772.00

Now the account regained 1/2 of its new balance of $ 143,772.00

balance now=$143,772.00+(1/2*$143,772.00)

balance now=$215,658.00

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Complete with the missing fractions:

michael wittry has been investing in his roth IRA retirement account for 20 years. Two years ago his account was worth $215,658. after losing 1/3 of its origiInal value, it then gained 1/2 of its new value back, what is the current value of his roth IRA?

linearity and relevant range include the use of cost behavior pattern data.

the existence of a chain of thoughts or actions wherein one directly follows another: True autobiographies rarely have a linear structure. We don't have a linear existence. Constantly thrown off balance is the narrative's traditional linearity.

The accounting phrase "relevant range" refers to the production or activity parameters that a company must adhere to in order to keep its fixed costs constant. Fixed costs in accounting are constant and unaffected by particular production rates.

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