Michael plans to make contributions to his retirement account for 12 years. After the last contribution, he will start withdrawing $10,000 a quarter for 10 years. Assuming Mike's account earns 8% compounded quarterly, how large must his quarterly contributions be during the first 12 years, in order to accomplish his goal?

F and G are inverse if both of them satisfy the condition h(x)=x. f(g(x))=g(f(x))=x, as we discovered. The argument f(x) and g(x) are inverse functions is thus established.

If f (x) and g (x) are inverse functions, it can be determined using one of two ways. For more information, see the explanation.

Explanation:

Instance 1

Inverse functions of both functions can be found using the first method.

Example.

Inverse of f (x) = x + 7 is what we're looking for.

We attempt to determine x using the equation y = x + 7.

y = x + 7

Inferring that g (x) is the inverse of f (x) from the fact that x = y 7

Finding g (x inverse )'s is now necessary.

g( x ) = x − 7

y = x − 7

x = y + 7

As a result, we discovered that f (x) is the inverse function of g (x).

f and g are equal if g is inverse of f and vice versa.

The second approach entails locating the compound functions f ( g ( x ) ) and g ( f ( x ) ). In this case, f and g are inverse if they are both h (x ) = x.

Example:

f ( g ( x ) =  [ x − 7 ] + 7

G ( x ) placed as x is the expression in brackets.

f ( g ( x ) ) = x − 7  + 7 = x

g (f ( x ) =  [ x + 7 ] − 7

f ( x ) inserted as x is the expression in brackets.

g ( f ( x ) ) = x + 7 − 7 = x

The equation f ( g ( x ) ) = g ( f ( x ) ) = x was what we discovered. The argument f (x) and g (x) are inverse functions is thus established.

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Answer:

98 cm²

Step-by-step explanation:

Lateral surface area = surface area of the sides ONLY of the object

⇒ lateral SA = B + C + D = 35 + 28 + 35 = 98 cm²

For finding surface area we will add them all.

Surface area

\(\\ \rm\hookrightarrow A+B+C+D+E\)

\(\\ \rm\hookrightarrow 10+35+28+35+10\)

\(\\ \rm\hookrightarrow 118cm^2\)

As we need LSA so let out A and E

We cannot conclude that whether a subject lies or does not lie is independent of the polygraph test indication.

The test statistic needed to test the claim that whether a subject lies or does not lie is independent of the polygraph test indication is the chi-square statistic.

In this case, the grand total is 90. The row totals are 57 and 33, and the column totals are 42 and 48. The expected frequencies are as follows:

The chi-square statistic is calculated as 0.177. The p-value for the chi-square statistic is calculated using a chi-square table. The degrees of freedom for the chi-square table are the number of rows minus 1, multiplied by the number of columns minus 1.

Since the p-value is greater than 0.05, we fail to reject the null hypothesis. We cannot conclude that whether a subject lies or does not lie is independent of the polygraph test indication.

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The baker can only make peanut butter cookies and cannot make any chocolate chip cookies with the given amount of ingredients.

Let's denote the number of batches of peanut butter cookies as "x" and the number of batches of chocolate chip cookies as "y."

From the given information, we can set up the following system of equations:

For the flour:

2x + 3y = 26

For the butter:

34x + y = 9

To solve this system of equations, we can use the substitution method or the elimination method. Let's use the elimination method:

Multiply the first equation by 17 (to make the coefficients of x in both equations the same):

34x + 51y = 442

Now we have the system of equations:

34x + y = 9

34x + 51y = 442

Subtract the first equation from the second equation:

34x + 51y - (34x + y) = 442 - 9

50y = 433

Divide both sides by 50:

y = 433/50

Since the number of batches of cookies cannot be fractional, we need to find a whole number solution for y. However, in this case, y is a fraction, indicating that the given amount of butter is not sufficient to make even one batch of chocolate chip cookies.

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The surface area of the cylinder will be \(968feet^{2}\)

The surface area of ​​a cylinder is the area occupied by its surface in three-dimensional space. It has no peaks. The area is shown in square units. For example cm2, m2, and so on. A cylinder can be seen as a set of circular disks that are stacked on top of each other. Since a cylinder is a three-dimensional body, it has both a surface and a volume.

The area of ​​the cylinder is defined as the sum of the curved surface and the area of ​​the two circular bases of the cylinder.

The surface area of ​​the cylinder = curved area + area of ​​circular bases

SA = \(2\)πr (h + r) square unit

Where, π (Pi) = \(3.142\) or = \(22/7\)

r = Radius of the cylinder

h = Height of cylinder

As we know, a cylinder has two types of surfaces, one is a curved surface and the other is a circular base. So the total area will be the sum of the curved area and the two circular bases.

Now if the cylinder has h=\(15\) feet and d=\(14\) feet or r=\(7\) feet

The surface area of cylinder will be:

SA=\(2\)π*\(7(15+7)\) \(feet^{2}\)

Hence the surface area of cylinder will be:

\(SA=2*22/7*7*22=968feet^{2}\)

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The length of side AB in right angled triangle ABC  will be 48 cm.

Every triangle with one 90° angle is said to have a right angle. The triangle with a right angle is known as a right triangle because a right angle is 90 degrees.The longest side of a right angle is known as the hypotenuse, and it is opposite the right angle.

Given,

∠B= 90°, AC = 96 cm, ∠C = 30°

Now, we know, Trignometric ratio sin θ in triangle can be given by-:

sin θ = \(\frac{perpendicular}{hypotenuse}\)

From given figure,

Perpendicular= AB= ?

and Hypotenuse= AC = 96

and θ= 30°

Hence,

sin 30° =\(\frac{perpendicular}{hypotenuse}\)= \(\frac{AB}{96}\)

\(\frac{1}{2} = \frac{AB}{96}\)                                      (∵ sin 30°= 1/2)

\(AB=\frac{96}{2}\)

\(AB= 48 cm\)

Thus, AB= 48 cm

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Correct Question:ABC is a right angled triangle. if B = 90°, AC = 96 cm, C = 30°. Find AB = ?

Answer:

C

Step-by-step explanation:

Plz mark as brainliest

Answer:

It’s D

Step-by-step explanation:

Step-by-step explanation:

-8x + 4 > 5 - 3x

-8x + 3x > 5 - 4

-5x > 1

x > 1 / - 5

To match the graphs of cylinders a and b to cylinders P and Q, we need to analyze the relationship between the height of the water and the volume of water in each cylinder.

Cylinder P would correspond to graph b, while Cylinder Q would correspond to graph a.

The reasoning behind this is as follows:

Cylinder P, corresponding to graph b, shows a steeper increase in height with increasing volume. This indicates that the water level rises quickly as more volume is added, suggesting that the cylinder has a smaller cross-sectional area. Since height is directly proportional to volume for a cylinder, a smaller cross-sectional area would result in a higher rise in height for the same volume of water.

Cylinder Q, corresponding to graph a, shows a slower increase in height with increasing volume. This implies that the water level rises more gradually as more volume is added, indicating a larger cross-sectional area. A larger cross-sectional area would result in a smaller increase in height for the same volume of water.

In summary, the steeper graph b matches Cylinder P with a smaller cross-sectional area, while the gentler graph a matches Cylinder Q with a larger cross-sectional area.

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Answer:

Step-by-step explanation:

\( \frac{5}{ {3b}^{3} - {2b}^{2} - 5 } = \frac{2}{ {b}^{3} - 2 } \\ 5( {b}^{3} - 2) = 2( {3b}^{3} - {2b}^{2} - 5) \\ {5b}^{3} - 10 = {6b}^{3} - {4b}^{2} - 10 \\ 10 - 10 = {6b}^{3} - {5b}^{3} - {4b}^{2} \\ 0 = {b}^{3} - {4b}^{2} \\ 0 = {b}^{2} (b - 4) \\ \)

b = 0 or b - 4 = 0

b = 0

b = 4

Answer:

37 million

Step-by-step explanation:

Answer:

Oh lord, what is this-

Step-by-step explanation:

Answer:

By examining the line plot, we find the number with the maximum number of crosses or occurrences. This gives the mode of the data set. We find the smallest and the largest number from the data set and find their difference and this difference is the range of the given data set.

6x1/6=6/6=1

---

hope it helps

Answer:

Of the total 31 + 20 + 6 + 6 + 6 = 69 medals, the USA won 31 of them. 31/69 as a percentage is about 45%. Since there are 360° in a full circle, 45% of that is 0.45 * 360 = 162°.

Answer:

How many degrees will the USA section be in a circle graph?

31°

162°

45°

184°

Step-by-step explanation:

162° THIS ONE IS RIGHT

PLEASE GIVE ME A Brainiest PLEASE AND THX

HOPE IT HELP

The inequality expression that corresponds to the solution of the inequality graph is x² + 3x - 3 < 0.

option B.

The inequality expression that corresponds to the solution of the inequality graph is determined by simplifying the equations as follows;

The solution of the graph,

x > -4 and x < 1

The first equation with "≥" is ruled out because the graph doesn't have a thick dot.

Let's simplify the second expression;

x² + 3x - 3 < 0

solve using quadratic formula;

x > -3.79 or x < 0.79

The third expression is ruled out since its solution will be complex.

For the last expression;

x² + 3x - 3 > 0

x < -3.79 or x > 0.79

Thus, the correct inequality expression is x² + 3x - 3 < 0.

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Answer: The answer is D. 1/16

Step-by-step explanation: If you think about it, 2 to the 4th power is 16. But in this situation, you have a negative exponent. To solve an exponent situation with a negative situation, put a 1 as the numerator and put the answer of the expression but with the exponent's positive value as the denominator. Hope this helps :D

We want to find the motion equation for the two horses and then use these equations to find how far would run each horse in 12 minutes.

The motion equations are:

And in 12 minutes horse A moves 3 miles while horse B moves 4.8 miles

We can see that both equations pass through the point (0, 0), thus both equations are proportional equations of the form:

y = k*x

Then to get the equations we just need one point on each line, for example for horse A we can use the point (8 min, 2 mi)

Replacing that in the general equation we get:

2 mi = k*8min

Now we can solve that for k

(2 mi)/(8 min) = k

(1/4) mi/min = k

Notice that this is a speed.

For horse B we can use the point (5 min, 2 mi), in the same way than above we will get:

2 mi = k*5 min

(2mi/ 5 min) = k

(2/5) mi/min = k

Then the two equations are:

Now we want to see how far would each horse run in 12 minutes, we get this by evaluating bot equations in x = 12 min

For horse A we get:

y = (1/4) mi/min*12min = 3mi

For hose B we get:

y = (2/5) mi/min*12min = 4.8 mi

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To make the fractions equivalent, we need to find the missing numerators that would make them equal. Let's fill in the missing numerators:

1/2 and __/8

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 4:

1/2 and 4/8

Now, the fractions are equivalent.

---

4/12 and __/60

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 5:

4/12 and 20/60

Now, the fractions are equivalent.

---

2/3 and __/12

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 4:

2/3 and 8/12

Now, the fractions are equivalent.

---

4/4 and __/8

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 2:

4/4 and 8/8

Now, the fractions are equivalent.

The quartic function with only two real zeros of x=0 and x=4 is x² - 4x = 0

A quartic function is a quartic polynomial, that is, a polynomial with integer coefficients whose highest degree is four. The coefficient of the variable to the fourth degree cannot be zero. Examples of quartic functions include

From the roots;

a = 0 ; b = 4

From the polynomial expressions

x² - (a +b)x + ab = 0

x² - (0 +4 )x + 0*4 = 0

x² - 4x = 0

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9.3 ft³

use the rule:

\(\rightarrow \sf (\dfrac{V_1}{V_2} )= (\dfrac{h_1}{h_2} )^3\)

solve:

\(\rightarrow \sf (\dfrac{74\frac{2}{5} }{V_2} )= (\dfrac{10\frac{1}{3} }{5\frac{1}{6} } )^3\)

\(\rightarrow \sf (\dfrac{74\frac{2}{5} }{V_2} )= (2 )^3\)

\(\rightarrow \sf \dfrac{74\frac{2}{5} }{V_2} =8\)

\(\rightarrow \sf V_2 = \dfrac{74\frac{2}{5} }{8}\)

\(\rightarrow \sf V_2 = 9.3 \ ft^3\)

Answer:

Given:

\(\sf Height \ of \ Prism \ X = 10\frac13=\dfrac{(10 \times 3)+1}{3}=\dfrac{31}{3}\)

\(\sf Height \ of \ Prism \ Y = 5\frac16=\dfrac{(5 \times 6)+1}{6}=\dfrac{31}{6}\)

\(\sf Volume\ of \ Prism \ X = 74\frac25=\dfrac{(74 \times 5)+2}{5}=\dfrac{372}{5}\)

Prism X is a dilation of Prism Y.

⇒ Scale factor of dilation = height of Prism X ÷ height of Prism Y

                                          \(\sf =\dfrac{31}{3} \div \dfrac{31}{6}\)

                                          \(\sf =\dfrac{31}{3} \times \dfrac{6}{31}\)

                                          \(\sf =\dfrac63\)

                                          \(\sf =2\)

If Prism X is a dilation of Prism Y by scale factor 2, then Prism Y is a dilation of Prism X by scale factor \(\frac12\).

To find the volume of Prism Y, we simply need to multiply the volume of Prism X by the cube of scale factor \(\frac12\), since volume is measured in cubic units.

\(\sf \implies volume \ of \ Prism \ Y = volume \ of \ Prism \ X \times (scale \ factor)^3\)

                                    \(\sf = \dfrac{372}{5} \times \left(\dfrac12\right)^3\)

                                    \(\sf = \dfrac{372}{5} \times \dfrac18\)

                                    \(\sf =\dfrac{372}{40}\)

                                    \(\sf =\dfrac{93}{10}\)

                                    \(\sf = 9 \frac{3}{10} \ ft^3\)

Answer:

x = -3, y = -14

Step-by-step explanation:

Graph it

Answer:

\(g(x)=2x^2-10\)

Step-by-step explanation:

The function f(x) is given by

\(f (x) = 2x^2 - 8\)

The quadratic function g(x) is obtained by translating f(x) 2 units down.

We use the below rule to find the equation for g (x)

Rule:- If a function f(x) is translated 'c' units down then the equation of the translated function be f(x)-c

Here, f(x) is translated 2 units down to obtain g(x).

Hence, we have

\(g(x)=f(x)-2\)

\(g(x)=2x^2-8-2\)

\(g(x)=2x^2-10\)

Answer:

I would say 3n-8=n+2

Step-by-step explanation:

First it says the difference of three times a number. N is serving as the unknown number so, so far we have 3n then 8 so 3n-8 and then put an = and then it says 2 more than the number so put the n + 2

your answer should be 3n-8=n+2

i also took the test  :)

hope this helps

The expression representing the given word sentence is 3n-8 = n+2

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given that, a statement the difference of three times a number and eight is two more than the number.

We need to convert it into a mathematical expression,

Therefore,

First it is saying, the difference of three times a number n, and 8

= 3n-8

Then, it says 2 more than the number so put the n + 2

Therefore,

3n-8 = n+2

Hence, the expression representing the given word sentence is 3n-8 = n+2

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Answer:

a straight line from the centre to the circumference of a circle or sphere.

OR

half of a diameter

Answer:

A radius is a straight line from the center of a circle to the circumference of a circle. If you have two or more of them, they are referred to as radii. All radii in a circle will be the same length. If you put two radii together, edge to edge, going through the center of a circle, you would get a diameter.

Step-by-step explanation:

Answer:

43% probability of being moderate

Step-by-step explanation:

Since the formating is a little messed up, I assumed that the first column was liberal, second was moderate, and the third was conservative.

(a). The graph of y = -f(x) is shown in the image below.

(b). The graph of y = g(-x) is shown in the image below.

By reflecting the parent absolute value function g(x) = |x + 2| - 4 over the x-axis, the transformed absolute value function can be written as follows;

y = -f(x)

y = -|x + 2| - 4

Part b.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = rise/run

Slope (m) = -2/4

Slope (m) = -1/2

At data point (0, 5) and a slope of -1/2, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 5 = -1/2(x - 0)

g(x) = -x/2 + 5, -4 ≤ x ≤ 4.

y = g(-x)

y = x/2 + 5, -4 ≤ x ≤ 4.

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we have the following:

speed 8 miles every 6 minutes:

therefore, the speed is 1.34 mi/m, now to complete it would be:

therefore, the answer is:

Time (minutes) Distance (miles)

3 4

15 20

60 80

Answer:

Step-by-step explanation:

x/4.8 < 1.25                             Multiply both sides by 4.8

4.8 x /  4.8 < 1.25*4/8

x < 6

What this means is that every every number less than 6 is a solution to this inequality.

Graph 32 (shown below is a red area. The important thing to note is that the boundary at 6 is dotted which means it is not included in the solution.

What you want is more closely related to a number line and sort of looks like this

-----o-----o-----o-----o-----o-----o-----o-----o

    -1      0      1       2      3      4      5     6

<===============================o                                                              

Explanation

The top line is the actual number line or the graph

o------- is the way it is made.

The second line are the number divisions of the number line

The third line shows which way the inequality goes and that it is open at 6. Open means that you can get close to 6 but you can't touch 6.