h(r) = 11r² - 6
g(r) = r² + 8r+ 9
Find h(-2) + g(-2)

The probability of x successes in n independent trials of the experiment is given by the Binomial probability formula, where n is the total number of trials and p is the probability of success in each trial.

Since n = 9 and p = 0.4, we can calculate the probability of x ≤ 3 successes as follows:

P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

= (9C0)(0.4)^0(0.6)^9 + (9C1)(0.4)^1(0.6)^8 + (9C2)(0.4)^2(0.6)^7 + (9C3)(0.4)^3(0.6)^6

= 0.17496 + 0.41472 + 0.36608 + 0.04320

= 0.99976

Therefore, the probability of x ≤ 3 successes is 0.99976.

Step-by-step explanation:

that height splits GK (32) into 2 parts :

8 and 32-8 = 24

then we use the geometric mean theorem for right-angled triangles

height = sqrt(p×q)

with p and q being the parts of the Hypotenuse.

so,

height = sqrt(8×24) = sqrt(192)

and now we can use Pythagoras

c² = a² + b²

with c being the Hypotenuse (the side opposite of the 90° angle), a and b are the legs,

to get HK.

HK² = height² + 24² = 192 + 576 = 768

HK = sqrt(768)

One pair of functions that satisfies the given condition is:

Exponential function: [tex]f(x) = 1.46^x,[/tex] Quadratic function: [tex]g(x) = x^2[/tex]

In mathematics, an expression is a combination of numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division. Expressions can also include functions, brackets, and other symbols.

Let's consider the two functions:

Exponential function: [tex]f(x) = a^x, where a > 1[/tex]

Quadratic function: [tex]g(x) = x^2[/tex]

We want to find the pair of functions for which the exponential is consistently growing at a faster rate than the quadratic over the interval 0 ≤ x ≤ 5.

To determine this, we can compare the growth rates of the two functions by looking at their derivatives.

The derivative of the exponential function is:[tex]f'(x) = a^x * ln(a)[/tex]

The derivative of the quadratic function is: [tex]g'(x) = 2x[/tex]

To compare the growth rates of the two functions, we need to compare their derivatives. We want to find the value of x for which the exponential function is growing faster than the quadratic function, i.e., where f'(x) > [tex]g'(x).\\f'(x) > g'(x)\\a^x * ln(a) > 2x[/tex]

Now, we can solve for x:

[tex]a^x * ln(a) > 2xln(a)/2 * a^x > x[/tex]

Since we want to find the pair of functions for which the exponential is consistently growing at a faster rate than the quadratic over the interval 0 ≤ x ≤ 5, we need to find a value of a such that the inequality ln(a)/2 * [tex]a^5 > 5[/tex] is true for all values of a > 1.

We can use a graphing calculator or a numerical solver to find the value of a that satisfies this inequality. One possible solution is a ≈ 1.46.

Therefore, one pair of functions that satisfies the given condition is:

Exponential function: [tex]f(x) = 1.46^x,[/tex] Quadratic function: [tex]g(x) = x^2[/tex]

To know more about expression visit :

https://brainly.com/question/1859113

#SPJ1

Answer:

g(y) = √(3/2 y)

Step-by-step explanation:

To find the inverse of a function, we need to solve for x in terms of y and interchange x and y. That is, we need to write the given function f(x) = 2/3x^2 in the form y = 2/3x^2 and then solve for x in terms of y.y = 2/3x^2

Multiplying both sides by 3/2, we get:

3/2 y = x^2

Taking the square root of both sides, we get:x = ± √(3/2 y)

Note that we have two possible values of x for each value of y, because the square root can be either positive or negative. However, for a function to have an inverse, it must pass the horizontal line test, which means that each value of y can only correspond to one value of x.Therefore, we need to restrict the domain of the original function to ensure that it is one-to-one. The simplest way to do this is to take the range of the function and use it as the domain of the inverse function.The range of f(x) = 2/3x^2 is all non-negative real numbers, or [0, ∞). Therefore, we can define the inverse function g(y) as:

g(y) = ± √(3/2 y)

where we choose the positive square root to ensure that the function is one-to-one.Thus, the inverse of the function f(x) = 2/3x^2 is:

g(y) = √(3/2 y)

with domain [0, ∞).

Let me know if this helped by hitting brainliest! If you have a question, please comment below and I'll get back to you ASAP!

Therefore, the slope of the line that passes through (-2, 8) and (4, 6) is -1/3.

What is the slope?

In mathematics, the slope is a measure of the steepness of a line.

The solution provided involves three steps to find the slope of the line that passes through two points: (-2, 8) and (4, 6).

Step 1 involves finding the change in y-coordinates, which is the difference between the y-coordinate of the second point and the y-coordinate of the first point. In this case, the second point has a y-coordinate of 6 and the first point has a y-coordinate of 8.

Therefore, the change in y-coordinates is 6 - 8 = -2.

Step 2 involves finding the change in x-coordinates, which is the difference between the x-coordinate of the second point and the x-coordinate of the first point. In this case, the second point has an x-coordinate of 4 and the first point has an x-coordinate of -2.

Therefore, the change in x-coordinates is 4 - (-2) = 6.

Step 3 involves dividing the change in y-coordinates by the change in x-coordinates to find the slope of the line. In this case, the change in y-coordinates is -2 and the change in x-coordinates is 6, so the slope is -2/6 or -1/3.

Since all the steps are correct and properly executed, there is no error.

Therefore, the slope of the line that passes through (-2, 8) and (4, 6) is -1/3.

To learn more about slope from the given link:

https://brainly.com/question/3605446

#SPJ1

Use the vector law of addition to get the resulting vector is [tex](7i+2j-k)[/tex] and magnitude of resulting vector is [tex]3\sqrt{6}[/tex].

What is the resulting vector and its magnitude?

Vector addition can be defined as the sum of two or more vectors of corresponding components.

It is given that,

[tex]\vec{r}= < 4, -2 > \\\vec{s}= < 3,4,-1 >[/tex]

Given vectors can also be written as,

[tex]\vec{r}=4i-2j\\\vec{s}=3i+4j-k[/tex]

Add above vectors as follows:

[tex]\vec{r}+\vec{s}=(4i-2j)+(3i+4j-k)\\\\=(7i+2j-k)[/tex]

Therefore,

[tex]\vec{r}+\vec{s}= < 7,2,-1 >[/tex]

Show the resulting vector as follows:

Now calculate the magnitude of the vector [tex](\vec{r}+\vec{s})[/tex]

[tex]|\vec{r}+\vec{s}|=\sqrt{(7)^2+(2)^2+(-1)^2}\\=\sqrt{49+4+1}\\=\sqrt{54}\\=3\sqrt{6}[/tex]

Hence the resulting vector is [tex](7i+2j-k)[/tex] and magnitude of resulting vector is [tex]3\sqrt{6}[/tex].

To know more about vector visit:

https://brainly.com/question/29740341

#SPJ1

Answer:

this is when you want to draw a sketch of a building

Answer:

Step-by-step explanation:

answer is -2

To satisfy the inequality x less-than StartFraction 7 over 12 EndFraction.

Inequalities are called as the mathematical expressions in which both sides are nonequal. Unlike to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs can be used in place of the equal sign in between.

The inequality is 1/4 + x < 5/6 in order to solve this inequality we need to isolate the value of x, that is our variable of interest. This is shown bellow:

1/4 + x < 5/6

x < 5/6 - 1/4

LMC is used to subtract the fractions we have as follows:

x < (2*5 - 3*1)/12

x < (10 - 3)/12

x< 7/12

The inequality must be satisfied for x to be smaller than 7/12.

to know more about equation, visit:

https://brainly.com/question/10413253

#SPJ1

Answer:  x < 7/12

Step-by-step explanation:

Step-by-step explanation:

To find the maximum/minimum value of the quadratic function q² + 22q = y - 85, we can complete the square as follows:

q² + 22q = y - 85

q² + 22q + 121 = y - 85 + 121 (adding (22/2)² = 121 to both sides)

(q + 11)² = y + 36

Now, we have a square of a binomial on the left side, which means the minimum value of the quadratic function is y + 36, and it occurs when (q + 11) = 0. Thus, the minimum value is:

y + 36 = 36 - 85 = -49

Similarly, the maximum value of the quadratic function occurs when (q + 11) = 0, but this time the value of y will be as large as possible. The largest possible value of y occurs when STU is a permutation of the digits 9, 8, and 7 (since PQR must be 4, 0, and 3 in some order). Thus, the maximum value is:

y + 36 = 9 + 8 + 7 - 85 + 36 = -25

Therefore, the options are incorrect and the correct answers are:

Minimum value: -49

Maximum value: -25

For the computation of confidence interval for the difference in two population proportions following are negative,

p₁(cap) - p₂(cap)

Lower bound of the confidence interval

Upper bound of the confidence interval

For the computation of confidence interval,

The difference in two population proportions,

p₁ - p₂, can be negative or positive.

This implies,

The sample estimate of the difference in proportions,

p₁(cap) - p₂(cap), can also be negative or positive.

The standard error and critical value are always positive values and cannot be negative.

The lower and upper bounds of the confidence interval can be negative or positive.

Depending on the sample estimate and the margin of error.

So, both the lower and upper bounds can be negative.

Learn more about confidence interval here

brainly.com/question/15049116

#SPJ4

The above question is incomplete, the complete question is:

You are computing a confidence interval for the difference in 2 population proportions. which of the following could be negative?

Select all.

a. p₁

b. p₁(cap) - p₂(cap)

c. Standard error

d. Critical value

e. Lower bound of the confidence interval

f. Upper bound of the confidence interval

Answer:

0.048 in %

Step-by-step explanation:

firstly: remove the decimal point

= 48/1000

secondly : Simplify

48/1000*100

=48/10

=4.8%

Answer:

  2.06

Step-by-step explanation:

You want the value of the numerical expression √36÷5×12÷∛343.

This is a straightforward calculator problem. Your pocket calculator, or any of numerous calculator apps, online calculators, or spreadsheets can evaluate this expression for you.

The attachment shows the result is 2.06.

__

Additional comment

As expressed in this problem statement, the expression is ...

  [tex]\dfrac{\sqrt{36}\times12}{5\times\sqrt[3]{343}}=\dfrac{6\cdot12}{5\cdot7}=\dfrac{72}{35}[/tex]

If you mean something else, you need to identify the quantities that need to be considered as a unit.

Answers of angle degrees of p and q

q = 79

p = 101

Explanation

Each angle given has an adjacent angle creating a straight angle of 180 degrees.

First I found the missing adjacent angle degree - see attachment.

We know four of the five interior angle degrees are 85, 136, 138, 102.

Since we know the sum of angles in a pentagon = 540°, we can subtract the known angles from 540 to find “q”

540 - 85 - 136 - 138 - 102 = 79 angle q

To find “p” we know p and q create a straight angle of 180 degrees. We can subtract to find p.

180 - 79 = 101 angle p.

I attached a picture to help

We cannot determine the actual value of the average rate of change without knowing the function f(x) or having a graph of the function.

The visual representation of mathematical functions or data points on a Cartesian coordinate system is an x-y axis graphic. The vertical or dependent variable is represented by the y-axis, while the horizontal or independent variable is represented by the x-axis. The difference between the change in output values and the change in input values is known as the average rate of change of a function over a period.

Let's assume that the function is denoted by f(x). Then, the average rate of change on the interval (a, b) can be calculated as

average rate of change = (f(b) - f(a)) / (b - a)

Using this formula, we can calculate the average rate of change on the given intervals as follows:

For the interval (-3, -2):

average rate of change = [tex]\frac{[f(-2) - f(-3)]}{[-2 - (-3)]}[/tex]

For the interval (1, 3):

average rate of change = [tex]\frac{(f(3) - f(1))}{(3 - 1)}[/tex]

For the interval (-1, 1):

average rate of change = [tex]\frac{(f(1) - f(-1))}{ (1 - (-1))}[/tex]

Note that we cannot determine the actual value of the average rate of change without knowing the function f(x) or having a graph of the function. If you provide the function or the graph, I can help you find the actual values of the average rate of change on these intervals.

To know more about plot, visit:

https://brainly.com/question/30195492

#SPJ1

The graph that shows the electricity usage on a record-breaking summer day is Sacramento, California is a function.

The domain is 24 hours of a day.

The number of megawatts used at 8 am is 1, 200 megawatts.

The time with the most electricity used was 4 pm to 6 pm and least used was 4 am.

f ( 12 ) would be 1, 900 megawatts.

Usage is increasing from 4 am to 5 pm and decreasing from 5 pm to 4 am.

The graph is a function because each point on the graph represents a distinct megawatt usage. The domain would be 24 hours of a day as this graph of electricity usage shows the usage per day.

The megawatts used at 8 am is:

= 1, 300 - ( 200 / 2 )

= 1, 200 megawatts

From 4 am to 5 pm, we see that electricity usage is increasing as people are getting ready for work and going to work, but from 5 pm to 4 am, electricity usage decreases.

Find out more on graphs at https://brainly.com/question/21444630

#SPJ1

Answer:

1/16

Step-by-step explanation:

1/8 is left

1/2 of 1/8 = 1/16

Answer:

Step-by-step explanation:

We can find dy/dx by differentiating y with respect to x using the quotient rule.

First, we need to rewrite y using the trigonometric identity for the tangent of the difference of two angles:

y = (cos x - sin x)/(cos x + sin x) = [(cos x - sin x)/(cos x + sin x)] * [(cos x - sin x)/(cos x - sin x)]

y = (cos^2 x - 2cos x sin x + sin^2 x)/(cos^2 x - 2sin x cos x + sin^2 x)

y = (cos 2x - sin 2x)/(cos 2x + sin 2x)

Now we can apply the quotient rule:

dy/dx = [(-sin 2x - cos 2x)(cos 2x + sin 2x) - (cos 2x - sin 2x)(-sin 2x + cos 2x)]/(cos 2x + sin 2x)^2

dy/dx = (-sin^2 2x - cos^2 2x - 2sin 2x cos 2x + sin^2 2x + cos^2 2x + 2sin 2x cos 2x)/(cos 2x + sin 2x)^2

dy/dx = 0/(cos 2x + sin 2x)^2

Therefore, dy/dx = 0.

Answer:

center: (-2,-6)

radius: 5

Step-by-step explanation:

You have to complete the square again. This time the x's and the y's both need work. So first, organize. Put the x's together and put the y's together. Leave a little room to work. Take the x term and the y term and CUT them in HALF and Square 'em. That is what you add in to complete the square. Add the same thing to both sides.

see image.

Answer:

x = 21

Step-by-step explanation:

Given the angle measurements of two angles, we can deduce that this is a 30-60-90 triangle. The formula for side lengths of this type of triangle is given by s → s√3 → 2s with s being the shortest side (the side opposite the 30° angle).

We are looking for the side length represented by s[tex]\sqrt{3}[/tex]. We can see that the hypotenuse is represented by 2s, so...

2s = 24

s = 12

The side length of the shortest side is 12. Therefore, we can say that

x = s  [tex]\sqrt{3}[/tex]

x = 12 * [tex]\sqrt{3}[/tex]

x = 20.785

The question asks for our answer to the nearest whole number, so

x = 21

For the triangle ABC, the given trigonometric ratios are -

a. sin A = 8/17

b. cos A = 15/17

c. tan A = 8/15

d. tan B = 8/15

What is trigonometric ratio?

Triangle side length ratios are known as trigonometric ratios. In trigonometry, these ratios show how the ratio of a right triangle's sides to each angle. Sine, cosine, and tangent ratios are the three fundamental trigonometric ratios.

For a right-angled triangle ABC, the hypotenuse AB is given as 17.

The base CB is given as 15 and the perpendicular AC is given as 8.

The angle C is given to be 90°.

Using the given values of the sides of the right triangle ABC, we can calculate the trigonometric ratios as follows -

a. sin A = opposite/hypotenuse = AC/AB = 8/17 (reduced fraction)

b. cos A = adjacent/hypotenuse = CB/AB = 15/17 (reduced fraction)

c. tan A = opposite/adjacent = AC/CB = 8/15 (reduced fraction)

d. tan B = opposite/adjacent = AC/CB = 8/15 (reduced fraction)

Note that since angle C is 90°, angles A and B are acute angles, so their tangent ratios are equal to each other.

Therefore, the ratios expressed as reduced fractions are -

a. sin A = 8/17

b. cos A = 15/17

c. tan A = 8/15

d. tan B = 8/15

To learn more about trigonometric ratio from the given link

https://brainly.com/question/13276558

#SPJ1

Answer:

Step-by-step explanation:

your given is not cleared repost it then post

The real estate tax on Brianna Wallen's home is $37,934.83.

Property owners, including homeowners, are subject to a tax based on the assessed value of their properties. It is often collected by local governments and used to pay for amenities like public transportation, roads, and security.

The assessed value of the property and the tax rate are used to determine the amount of property tax due. The assessed value of a property is its worth as established by a government assessor and may be based on a number of variables, including recent sales prices of nearby properties, the price to replace the property, and the property's condition.

The tax is calculated using the given formula:

Tax = (Assessment Rate x Market Value) x (Tax Rate / 1000)

Substituting the given values we have:

Tax = (0.29 x $438,300) x (81.16 / 1000)

Tax = $37,934.83

Hence, the real estate tax on Brianna Wallen's home is $37,934.83.

Learn more about property tax here:

https://brainly.com/question/15227817

#SPJ1

Answer168 Bighas of land.

Step-by-step explanation:

Since the machine can dig a land of five bighas in 14 hours, put it into a ration 5:14 5(land it can dig) 14(amount of hours it takes.) Have X as the time to dig 60 bighas, 60(amount of land) : x (time). The equation would be 60/x=5/14 ===> 168 bughas of land.

The likelihood that Mitsugu will have a quiz on Wednesday, Thursday, or Friday is 0.57, or 57%, based on the facts given.

To determine how probable something is to occur, use probability. Many things are difficult to forecast with absolute precision. Using it, we can only make predictions about how probable an occurrence is to happen, or its chance of happening.

Let's first examine each day's specific probabilities:

Now, all we have to do to determine the overall chance is combine the partial probabilities that were previously provided, as shown below:

0.16 + 0.21 + 0.20 = 0.57

Finally, to determine the chance as a percentage, multiply this figure by 100:

0.57 x 100 = 57%

To know more about Probability visit:

https://brainly.com/question/13604758

#SPJ1

If △ABC is congruent to △DEF, then it must also be a right triangle. Thus, the two triangles have congruent sides and are congruent.

A key idea in geometry known as the Pythagorean theorem explains the relationship between the sides of a right triangle. The square of the hypotenuse, or side opposite the right angle, is said to be equal to the sum of the squares of the other two sides. It can be expressed mathematically as: a² + b² = c²

given

By defining a right triangle, DEF, with sides a, b, and x, we can demonstrate the opposite of the Pythagorean theorem. Then, we'll demonstrate that if ABC is a triangle with sides a, b, and c where a2 + b2 = c2, it is congruent to DEF and is thus a right triangle because a2 + b2 = c2.

By the Pythagorean theorem, because △DEF is a right triangle, a² + b² = x².

When a2 + b2 = c2 and a2 + b2 = x2, c2 equals x2.

If △ABC is congruent to △DEF, then it must also be a right triangle.Thus, the two triangles have congruent sides and are congruent.

To know more about Pythagoras theorem visit :-

https://brainly.com/question/14461977

#SPJ1

If △ABC is congruent to △DEF, then it must also be a right triangle. Thus, the two triangles have congruent sides and are congruent.

A key idea in geometry known as the Pythagorean theorem explains the relationship between the sides of a right triangle. The square of the hypotenuse, or side opposite the right angle, is said to be equal to the sum of the squares of the other two sides. It can be expressed mathematically as: a² + b² = c²

By defining a right triangle, DEF, with sides a, b, and x, we can demonstrate the opposite of the Pythagorean theorem. Then, we'll demonstrate that if ABC is a triangle with sides a, b, and c where [tex]a^2 + b^2 = c^2[/tex], it is congruent to DEF and is thus a right triangle because a2 + b2 = c2.

By the Pythagorean theorem, because △DEF is a right triangle, a² + b² = x².

When[tex]a^2 + b^2 = c^2[/tex] and [tex]a^2 + b^2 = x^2[/tex], [tex]c^2[/tex] equals [tex]x^2[/tex].

If △ABC is congruent to △DEF, then it must also be a right triangle. Thus, the two triangles have congruent sides and are congruent.

To know more about Pythagoras theorem visit :-

brainly.com/question/14461977

#SPJ1

Answer:

Math Quotient Verification

G For each ordered pair, determine whether it is a solution to the system of equations. 9x+2y=-5 2x-3y=-8 (x, y) (1, -7) (0, -4) (5,6) (-1,2) Is it a solution? Yes No X 5

To check if an ordered pair is a solution to a system of equations, we substitute the values of x and y into both equations and see if both equations are satisfied.

Let's check each ordered pair one by one:

(1, -7):

9x + 2y = -5 becomes 9(1) + 2(-7) = -5, which is false.

2x - 3y = -8 becomes 2(1) - 3(-7) = -8, which is true.

Therefore, (1, -7) is not a solution to the system of equations.

(0, -4):

9x + 2y = -5 becomes 9(0) + 2(-4) = -8, which is false.

2x - 3y = -8 becomes 2(0) - 3(-4) = 12, which is false.

Therefore, (0, -4) is not a solution to the system of equations.

(5, 6):

9x + 2y = -5 becomes 9(5) + 2(6) = 41, which is false.

2x - 3y = -8 becomes 2(5) - 3(6) = -8, which is true.

Therefore, (5, 6) is not a solution to the system of equations.

(-1, 2):

9x + 2y = -5 becomes 9(-1) + 2(2) = -11, which is false.

2x - 3y = -8 becomes 2(-1) - 3(2) = -8, which is true.

Therefore, (-1, 2) is not a solution to the system of equations.

Therefore, the answer is "No" for all the ordered pairs given in the problem.

(please mark my answer as brainliest)

When space is spanned by the two functions of linear transformation from into itself with respect to the basis we need to apply T to each basis vector vi to get the column vectors T(vi) = [T(vi)]B.

where [T(vi)]B is the coordinate vector of T(vi) with respect to the basis B. Arrange the column vectors [T(v1)]B, [T(v2)]B, ..., [T(vn)]B into a matrix. This matrix is the matrix of T with respect to the basis B.

In this case, you have two functions that span a vector space, so you need to specify the basis B. Once you have chosen the basis, you can apply the above steps to find the matrix of the linear transformation.

To learn about linear transformation visit:

https://brainly.com/question/30585642

#SPJ4

In linear equation, 65.625% of the pupils travel by bus.

What is  linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.

A) 1800 * 0.55 * 0.3 = 297 Girls.

B)  1800 * 0.45 * 0.7 = 567 boys

C)  Girl

      297/864 * 100%  = 34.375%

  boy -

       567 ÷ (297 + 567 ) * 100%  = 65.625%

         864 = 297 + 567

Learn more about linear equation

brainly.com/question/11897796

#SPJ1

the sum of the series is 8/3. The series consists of reciprocals of positive integers whose only prime factors are 2s and 3s.

In other words, each term of the series can be expressed as a fraction of the form 1/n, where n is a positive integer that can be factored into only 2s and 3s. For example, the first term of the series is 1/1, the second term is 1/2, and the fourth term is 1/4.

To find the sum of the series, we can first list out the terms and their corresponding values:

1/1 = 1

1/2 = 0.5

1/3 = 0.333...

1/4 = 0.25

1/6 = 0.166...

1/8 = 0.125

1/9 = 0.111...

1/12 = 0.083...

and so on.

We can see that the terms of the series decrease in value as n increases, so we can use this fact to estimate the sum of the series. For example, we can take the sum of the first few terms to get an idea of how large the sum might be:

1 + 0.5 + 0.333... + 0.25 = 2.083...

We can see that the sum is greater than 2, but less than 3. To get a more accurate estimate, we can add a few more terms:

2.083... + 0.166... + 0.125 + 0.111... = 2.486...

We can continue adding terms in this way to get a more and more accurate estimate of the sum. However, it is not easy to find a closed-form expression for the sum of the series.

Alternatively, we can use a formula for the sum of a geometric series to find the sum of the series. A geometric series is a series of the form a + ar + ar^2 + ... + ar^n, where a is the first term and r is the common ratio between terms. In our series, the first term is 1 and the common ratio is 1/2 or 1/3, depending on whether n is even or odd. Therefore, we can split the series into two separate geometric series:

1 + 1/2 + 1/8 + 1/32 + ... = 1/(1 - 1/2) = 2

1/3 + 1/12 + 1/48 + 1/192 + ... = (1/3)/(1 - 1/2) = 2/3

The sum of the two geometric series is the sum of the original series:

2 + 2/3 = 8/3

Therefore, the sum of the series is 8/3.

To know more about geometric series click here:

brainly.com/question/21087466

#SPJ4