You choose to invest $600 a year in a 401k which invests in an international stock mutual fund. Assuming an annual rate of turn of 9 percent, how much will this fund worth if retiring in 40 years?

Answer:

Step-by-step explanation:

Surface area of a triangular prism: The surface area of a triangular prism is given by A=bh+(b1+b2+b3)l units2 A = b h + ( b 1 + b 2 + b 3 ) l units 2 where b is the base of a triangular face, h is the height of a triangular face, b1 , b2 , and b3 are the sides of the triangular base, and l is the length of the prism.

Answer:

Step-by-step explanation:

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-2x - 4 is not greater than 14

Step-by-step explanation:

I don't understand the question but I hope this helps

(-2 × X) + (-2 × 2)

Answer:

5175 7 ehsjdjdrusjskskekrirr

Answer:

Step-by-step explanation:

Well when rotating 90° RSTU counterclockwise we get MNPQ.

When rotating 90° RSTU clockwise we get it the reflection across the y-axis.

Answer: Yes

Step-by-step explanation:

Well, since 6+2, 6+2+3 does equal 8 plus 3 because 6+2+3 is basically saying 8+3, but just broken up.

The box volume, entrance volume and building volume are 50x², y³ and 50x² - y³ respectively

An equation is an expression that shows the relationship between numbers and variables using mathematical operations like exponents, addition, subtraction, multiplication and division.

a) The volume of the whole box is:

Volume = length * width * height = x * x * 50 = 50x²

b) The volume of the entrance is:

Volume = length * width * height = y * y * y = y³

c) Volume of building is:

Building volume = volume of the whole box - volume of the entrance

Building volume = 50x² - y³

The building volume is 50x² - y³

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Answer: 390

Step-by-step explanation:

m

Isabel is in a hot air balloon that has just taken off and is now floating 140 meters above

its launching point. Debbie is standing on the ground, 147 meters away from the

launching point. How many meters apart are Isabel and Debb

Answer:

Isabel and Debbie are 203m apart.

Step-by-step explanation:

Since Isabel went straight up in the balloon and Debbie is straight over presumably on flat ground, they make a right triangle with the third point being the launching spot.

It is a right triangle. See image. Use the Pythagorean Theorem.

140^2 + 147^2 = d^2

Where d is the distance between Isabel and Debbie.

see image for work shown.

Solving the inequalities for x and y, we have x > 3 and y > 1

Inequalities are mathematical expressiοns that cοmpare twο quantities οr values and indicate their relative sizes. Inequalities are represented using symbοls such as < (less than), > (greater than), ≤ (less than οr equal tο), and ≥ (greater than οr equal tο).

Here Given that the twο inequalities are:

x + 5 < 8y

And

x + 5 > 8

x > 8 - 5

x > 3

Substate the value of x in x + 5 < 8y:

x + 5 < 8y

x < 8y - 5

3 < x < 8y - 5

3 < 8y - 5

3 + 5 < 8y

8 < 8y

y > 8/8

y  > 1

Thus, Solving the inequalities for x and y, we have x > 3 and y > 1

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Complete question:

Solve the for x and y.

a. x + 5 < 8y

   x + 5 > 8

​

From the equation x²+ (y-5)² = 64, the coordinates of the center of the circle are (0, 5), and the radius of the circle is 8 units.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

The given equation of the circle is in the standard form -

(x - h)² + (y - k)² = r²

where (h, k) is the center of the circle and r is the radius.

Comparing this standard form with the given equation, we get -

(x - 0)² + (y - 5)² = 8²

So the center of the circle is (0, 5) and the radius is 8.

Therefore, the center of the circle is (0, 5), and the radius is 8 units.

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The radius of the circle E is 27/5.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

Let X be the intersection of the circles with centers B and E, and Y be the intersection of the circles with centers C and E.

Since the radius of B is 3, AX = 4.

Assume AE = p.

Then EX and EY are radii of circle E and have length 4 + p.

AC = 8, and ∠CAE = 60° because we are given that triangle T is equilateral.

Using the Law of Cosines on Δ CAE, we obtain

(6+p)² =p² + 64 - 2(8)(p) cos 60

The 2 and the cos 60 terms cancel out:

p² + 12p + 36 = p² + 64 - 8p

12p+ 36 = 64 - 8p

p = 28/20

= 7/5

The radius of circle E is 4 + (7/5)

= 27/5

Hence, the radius of the circle E is 27/5.

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The value of b from the given hyperbolic equation is 10. Therefore, option A is the correct answer.

In mathematics, a hyperbola is an important conic section formed by the intersection of the double cone by a plane surface, but not necessarily at the center. A hyperbola is symmetric along the conjugate axis, and shares many similarities with the ellipse. Concepts like foci, directrix, latus rectum, eccentricity, apply to a hyperbola.

Given that, the equation x²/24² -y²/b² =1 represents a hyperbola centered at the origin with a directrix of x=576/26.

Here, a=24

Then c²=a²+b²

c²= 24²+b²

c=√(576+b²)

We know that, directrix = x =± a²/c

Now, 576/26 = 576/√(576+b²)

√(576+b²)=26

576+b²=26²

576+b²=676

b²=100

b=10

Therefore, option A is the correct answer.

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Answer:

in photo I provided :)

Step-by-step explanation:

hope this helps <3

The given data does not belong to the function.

A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.

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

In simple words, a function is a relationship between inputs where each input is related to exactly one output.

Every function has a domain and codomain or range.

Since in the given data,

at the different values of y, the value of x is the same. that is the first violation of the rule of function.

Therefore, the given data does not belong to the function.

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Answer:

The first question asks which variable Amari used to construct a bar graph. It is not specified which variable she used, so we cannot determine the answer.

The second question asks which graph correctly displays the data collected from the customers about their favorite topping. The data is nominal, so a bar graph would be appropriate. The correct answer is:

c) a bar graph titled favorite topping with the x axis labeled topping and the y axis labeled number of customers, with the first bar labeled chocolate chips going to a value of 17, the second bar labeled hot fudge going to a value of 12, the third bar labeled nuts going to a value of 27, and the fourth bar labeled sprinkles going to a value of 44

The third question asks which stem-and-leaf plot correctly graphs the data set of points scored by the Riverside Red Dragons during the 2021 football season. The correct answer is:

c)

2021 Riverside Red Dragon Football Season Points

0 0 4

1 1 3 3

2 0 0 6 7 7 7

3 0 0 0 0 1

Key 1|1 = 11

The fourth question asks which graphical representation would be best for a principal interested in the number of hours slept per night by 14-year-olds in a particular town. The data is quantitative, so a histogram would be appropriate. The correct answer is:

b) Histogram

Answer:

Step-by-step explanation:

1 gallon= 4 liters

2gallons=8liters

8liters answered

But exactly: 7.57082 liters

The inverse function of the given is y^-1=x/2 -4.

The domain of the original function becomes the range of the inverse function, and the range of the given function becomes the domain of the inverse function. The inverse function is denoted by the notation f-1 in relation to the original function f. Swapping (x, y) with (y, x) with reference to the line y = x yields the graph of the inverse function. Only when f is both a one-one and an onto function does it have an inverse, indicated by the symbol f-1. Keep in mind that f-1 is NOT f's inverse. The domain value of x is given by combining the function f and the reciprocal function f-1.

Here the given function is,

=> y = 2x+8

Now interchange x and y then

=> x=2y+8

Now simplify the expression with respect to y then,

=> x-8=2y

=> y =x/2 -4

=>y^-1=x/2 -4

Hence inverse function is, y^-1=x/2 -4

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Answer:

Moving the decimal 3 places to the left.

Step-by-step explanation:

Take the number 3000 and divide it by 1000 in your calculator.  You will get the answer 3.  Although we do not write it, the decimal in the number 3000 is at the end of the number (after the last zero).  When we divide by 1000, we move the decimal 3 places to the let.  The decimal in the number 3 is at the end or to the right of the 3, we just do not write the decimal.

Helping in the name of Jesus.

Check the picture below.

[tex](x+18)(18)=(24+16)(16)\implies 18x+324=640 \\\\\\ 18x=316\implies x=\cfrac{316}{18}\implies x=\cfrac{158}{9}\implies x=17\frac{5}{9}[/tex]

Answer:

5 3/4

Hope this is what you're looking for

Answer:

A. 62 units

Step-by-step explanation:

To find the perimeter of the rectangle, you have to use the Pythagorean theorem.

a^2 + b^2 = c^2 - Formula

24^2 + b^2 = 25^2 - Plug in values

576 + b^2 = 625 - Simplify

b^2 = 49 - Isolate the variable

b = 7 - Solve

After finding the height, find the perimeter.

P = 2b + 2h

P = 2(24) + 2(7)

P = 48 + 14

P = 62 units

The graph of the two functions is different from each other.

The expression that established the relationship between the dependent variable and independent variable is referred to as a function.

In the function as the value of the independent variable varies the value of the dependent variable also varies.

When we plot the graph of the function [tex]f(x) = \dfrac{x + 2 }{x^2-4}[/tex] and the function g(x) = |(x + 2 )} - 6.

Both graphs are different in nature and shape from each other. The graph of both functions is attached with the answer below.

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Answer:

Step-by-step explanation:

Blue shirts: [tex]\frac{1}{6}[/tex]×[tex]12=2[/tex]

White shirts: [tex]\frac{2}{3}[/tex]×[tex]12=8[/tex]

∴ there are 2 students(12-2-8=2) wearing a different shirt.

The exponential function is a decay, and it can be written as:

f(x) = 1,200*( 0.875)^x

The general exponential function can be written as:

f(x) = A*(b)^x

Where A is the initial value and b is the base.

Here we have a decay rate, so this is an exponential decay, and we can write:

b = 1 - r

Where r is the decay rate in decimal form:

b = 1 - 0.125 = 0.875

And the initial value is 1,200, so the exponential function is:

f(x) = 1,200*( 0.875)^x

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The polynomial expressions when simplified are 2g² + 3g - 1, 24c⁵d - 8cd² + 12c³d³ + 4cd, (m² + 5m + 4) ÷ (m + 1) = m + 4.

Others are added below

Expression 1

The expression is given as

(14g³ + 21g² - 7g)/7g

Divide the numerator by the denominator

So, we have

2g² + 3g - 1

Expression 2

Here, we have

24c⁵d - 8cd² + 12c³d³ + 4cd

The expression is in its simplified state

Expression 3

Given that

(m² + 5m + 4) ÷ (m + 1)

By long division, we have

           m + 4

m + 1 | m² + 5m + 4

           m² + m

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

              4m + 4

              4m + 4

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

                0

This means that (m² + 5m + 4) ÷ (m + 1) = m + 4

Expression 4

Given that

(c² - 2c - 15)(c + 3)⁻¹

By long division, we have

           c - 5

c + 3 | c² - 2c - 15

          c² + 3c

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

              -5c - 15

              -5c - 15

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

                0

This means that (c² - 2c - 15)(c + 3)⁻¹ = c - 5

Expression 5

Here, we have

(2y² + 10y + 17) ÷ (y + 3)

By synthetic division, we have

-3 | 2  10  17

    |__-6_-12______

      2  4   5

This means that (2y² + 10y + 17) ÷ (y + 3) = 2y + 4 + 5/(y + 3)

Expression 6

Here, we have

(2p³ - p² - 10p + 8)(p - 2)⁻¹

By synthetic division, we have

2 | 2    -1   -10    8

    |___4__6__-8____

      2    3   -4     0

This means that (2p³ - p² - 10p + 8)(p - 2)⁻¹ = 2p² + 2p - 4

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The number 7234 can be rounded to the nearest multiple of and it is 7235.

Check the value of the remainder:

If the remainder is less than 2.5, round down to the nearest multiple of 5

If the remainder is 2.5 or greater, round up to the nearest multiple of 5

Rounding off 7234 to the nearest 5 means we need to find the multiple of 5 that is closest to 7234.

Divide 7234 by 5 and get the quotient and remainder

= 7234 ÷ 5

= 1446 with a remainder of 4

Multiply the quotient by 5 and add the value determined.

Using this method, we can see that the nearest multiple of 5 to 7234 is 7235, since the remainder is 4 which is less than 2.5. Therefore, rounding off 7234 to the nearest 5 results in 7235.

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The complete question:

What will be the value when 7234 rounded off to the nearest 5(which will be divisible by 5)?

Answer:

Step-by-step explanation:

[tex]I=Prt[/tex]  P=principal, r =interest rate, t=time

[tex]I=1,320[/tex] × [tex]\frac{3.2}{100}[/tex] × [tex]5[/tex]

 [tex]= 211.20[/tex]

He will earn $211.20 interest.

Answer: 0.94

Step-by-step explanation: This is the same as saying subtract 0.954 from 1.894.

1.894 - 0.954 = 0.94

The percentage of annual returns is 25.63% and total return is $5400.

A percentage is a way of expressing a portion or part of a whole as a fraction of 100. The word "percent" comes from the Latin per centum, which means "per hundred". Percentages are commonly used to represent rates of change, such as growth rates or inflation rates, and to express proportions, such as the percentage of people in a population who have a certain characteristic or the percentage of a product's ingredients that are natural.

To calculate a percentage, you can use the following formula:

percentage = (part / whole) x 100

Now,

To calculate the total return on your investment, we need to find the profit made over the 4-year period.

Total return = final value of investment - initial investment

Total return = $8400 - $3000 = $5400

To calculate the annual return, we can use the formula:

Annual return = ((1 + total return percentage)^(1/number of years)) - 1

We can find the total return percentage by dividing the total return by the initial investment and multiplying by 100:

Total return percentage = (total return / initial investment) x 100

Total return percentage = ($5400 / $3000) x 100 = 180%

Using the formula for annual return, we get:

Annual return = ((1 + 1.8)¹/⁴-¹

Annual return = 0.2563 or 25.63%

Therefore, your total return on the investment was $5400 and the annual return averaged 25.63% over the 4-year period.

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