Show that the following number is rational by writing it as a ratio of two integers.
52.4744174417441…

After the experiment begins, there will be 32 hours' worth of 23,233 bacteria.

Yet contagious microorganisms can give you a disease. Throughout your body, they multiply rapidly. Many emit toxins—a class of chemicals that may harm tissues and make you ill. The bacteria Streptococcus, Aureus, and E are just examples of those that cause infections.

Bacteria need to identify their preferred food source and be able to properly digest it in order to support growth and division. The simple sugar glucose is one of bacteria's preferred foods, much as people like eating candy.

To solve this problem, we can use the formula for exponential growth:

[tex]N = N_0 * 2^{(t/T)[/tex]

where:

N₀ = initial population

N = final population

t = time elapsed

T = doubling time (time it takes for the population to double)

T = t/log₂(N / N₀) = 14/log₂ (7000/100) = 1.89 hours

Now we can plug in all the values and solve for N:

[tex]N = N_o * 2^{(\frac{t}{T})} = 100*2^{(\frac{18}{1.89})} = 23,233[/tex]

Rounding to the nearest whole number, we get:

N = 23,233

Therefore, there will be approximately 23,233 bacteria in 32 hours from the start of the experiment.

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Based on the information provided, the length of the hypotenuse in this case is 8.28.

The hypotenuse is the longest side of a right triangle, and it is opposite the right angle. It is found by using the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.

h^2 = 3.5^2 + 7.5^2

h^2 = 12.25 + 56.25

h^2 = 68.5

To find the value of h, we take the square root of both sides:

h = sqrt(68.5)

h = 8.28 (rounded to two decimal places)

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The function f(x) = x² - x - 2 has x-intercepts at points x = 2 and x = - 1

To find the x-intercepts of the function, we set f(x) equal to zero and solve for x:

x² - x - 2 = 0

Factoring the left side, we get:

(x - 2)(x + 1) = 0

This gives us two solutions:

x - 2 = 0 or x + 1 = 0

Solving for x, we get:

x = 2 or x = -1

So the two x-intercepts of the function are x = 2 and x = -1.

To find the y-intercept of the function, we set x = 0 and evaluate f(x):

f(0) = 0² - 0 - 2 = -2

So the y-intercept of the function is y = -2.

To show that there is a point between the two x-intercepts where the function takes on a negative value (i.e., dips below the x-axis), we can use the fact that the function is a parabola that opens upward (since the coefficient of the x² term is positive). This means that the function is negative to the left of the left x-intercept (x = -1), and also negative to the right of the right x-intercept (x = 2). Since the function is continuous, it must pass through the x-axis at some point between these two x-intercepts. Therefore, there must be a point between x = -1 and x = 2 where the function takes on a negative value.

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Answer:

(2×1.1)×5=11

Step-by-step explanation:

sorry if this isnt right

The equation -6 = 0 is not true, which means that there is no solution to the equation 9t+6 in standard form. This is because we cannot write the equation in the form [tex]ax + by = c[/tex]  , since there is no value of c that would satisfy the equation.

To write 9t+6 in standard form, we need to rearrange the expression to have the variables first, followed by the constant term. The standard form of a linear equation is:

[tex]ax + by = c[/tex]

where a, b, and c are constants, and x and y are variables.

To rearrange 9t+6, we first need to group the t term and the constant term together. We can do this by adding 0t to the expression:

[tex]9t + 0t + 6[/tex]

Now, we can rearrange the terms so that the variable term comes first:

[tex]9t + 0t = 9t[/tex]

Finally, we can write the expression in the standard form:

[tex]9t + 0t = 9t + 6[/tex]

This can be simplified further by removing the 0t term:

[tex]9t = 9t + 6[/tex]

We can now move the constant term to the other side of the equation by subtracting 6 from both sides:

[tex]9t - 6 = 9t + 6 - 6[/tex]

[tex]9t - 6 = 9t[/tex]

[tex]-6 = 0[/tex]

Therefore, The equation  [tex]-6 = 0[/tex] is not true, which means that there is no solution to the equation   [tex]9t+6[/tex] in standard form. This is because we cannot write the equation in the form  [tex]ax + by = c[/tex]  , since there is no value of c that would satisfy the equation.

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The answer to the given question about Arithmetic Sequence and Geometric Sequence is option 2)  Arithmetic, common difference = −9

To determine if the sequence is arithmetic or geometric, we need to check if there is a constant difference between consecutive terms or a constant ratio between consecutive terms.

Let's calculate the differences between consecutive terms:

The difference between the 2nd and 1st terms is 72 - 81 = -9

The difference between the 3rd and 2nd terms is 63 - 72 = -9

The difference between the 4th and 3rd terms is 54 - 63 = -9

The differences are all the same, so the sequence is arithmetic.

Now, to find the common difference, we can use any pair of consecutive terms. Let's use the first two terms:

The difference between the 2nd and 1st terms is 72 - 81 = -9

So the common difference is -9.

Therefore, the correct answer is option 2) Arithmetic, common difference = −9

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Answer:

The distance between the points (0, 4) and (0, 6) can be found using the distance formula: d = sqrt[(x2 - x1)^2 + (y2 - y1)^2] In this case, x1 = 0, y1 = 4, x2 = 0, and y2 = 6. Plugging in the values, we get: d = sqrt[(0 - 0)^2 + (6 - 4)^2] d = sqrt[0 + 4] d = sqrt(4) d = 2 Therefore, the distance between the points (0, 4) and (0, 6) is 2 units.

The formula you will need in order to solve this question is [tex]\sqrt(x_{2} -x_{1})^{2} +(y_{2}-y_{1})^{2}[/tex]

Please remember that you must substitute the order pairs into the question exactly as it is shown in the formula. By failing to do so, you may end up with the wrong answer.

(1) Consider the following:

[tex]x_{1} = 0[/tex] [tex]y_{1} = 4[/tex]

[tex]x_{2} = 0[/tex] [tex]y_{2} = 6[/tex]

(2) Substitute the ordered pairs into the formula accordingly

[tex]\sqrt (0 -0)^{2} +(6-4)^{2}[/tex]

(3) Solve

[tex]\sqrt (0 -0)^{2} +(6-4)^{2} = 2[/tex]

With that being said, the distance is 2.

Thus, the measure of angle  m∠SQP = 87° for given set of vertically opposite angles.

An adjacent pair of additional angles is known as a linear pair. Adjacent refers to being next to one another, and supplemental denotes that the sum of the two angles is 180 degrees.

Any two angles that sum up to 180 degrees are referred to as supplementary angles.

For the given question:

m∠PQT = m∠SQR (vertically opposite)

101 - 4b = 109 - 6b

on simplifying:

109 - 101 = 6b - 4b

2b = 8

b = 4

m∠PQT = 101 - 4(4) = 93

Now,

m∠PQT +  m∠SQP = 180 (linear pair)

93 +  m∠SQP = 180

m∠SQP = 180 - 93

m∠SQP = 87°

Thus, the measure of angle  m∠SQP = 87° for given set of vertically opposite angles.

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The kitchen used [tex]2 \frac{4}{5}[/tex] gallons of soup during the day.

To find out how many gallons of soup the kitchen used during the day, we need to subtract the amount of soup they had at the end of the day from the amount they had at the start of the day:

[tex]6 \frac{1}{2} - 2 \frac{7}{10}[/tex]

First, let's convert both fractions to have a common denominator of 10:

[tex]6 \frac{5}{10} - 2 \frac{7}{10}[/tex]

Now we can subtract the whole numbers separately and the fractions separately:

[tex]4 \frac{5}{10} - 2 \frac{7}{10} = 2 \frac{8}{10}[/tex]

Finally, we can simplify the fraction to a mixed number:

[tex]2 \frac{8}{10} = 2 \frac{4}{5}[/tex]

Therefore, the kitchen used [tex]2 \frac{4}{5}[/tex] gallons of soup during the day.

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Answer:

1) Elisa's puppy weighed 4 pounds when it was born. It gained 5 pounds per month until it was 9 months old. 5m + 4.

2) f(x) = -6.2x + 2.9

3) g(x) = 8.1x + 45.64

4) Michele has $125. She plans to spend $10 per week until she has a total of $75.

125 - 10n, or -10n + 125.

Therefore, the total angle measure of 4 parts of a circle divided into 8 equal parts is 180 degrees.

A circle is a two-dimensional shape that is defined as a set of points in a plane that are equidistant from a fixed point called the center. The distance from the center to any point on the circle is called the radius, and the distance across the circle through the center is called the diameter. The circumference of a circle is the distance around the edge of the circle, and it is given by the formula C = 2πr, where π (pi) is a mathematical constant approximately equal to 3.14159, and r is the radius of the circle. Circles are a fundamental concept in geometry and are used in many fields of mathematics, science, and engineering.

A circle has 360 degrees, and it is divided into 6 equal parts. To find the total angle measure of 1 part, we can divide 360 by 6:

360 degrees ÷ 6 = 60 degrees

Therefore, each part of the circle has an angle measure of 60 degrees.

Similarly, if the circle is divided into 5 equal parts, each part will have an angle measure of:

[tex]360 degrees / 5 = 72 degrees[/tex]

To find the total angle measure of 4 parts, we can multiply 72 degrees by 4:

[tex]72 degrees * 4 = 288 degrees[/tex]

Therefore, the total angle measure of 4 parts of a circle divided into 5 equal parts is 288 degrees.

If a circle is divided into 8 equal parts, each part will have an angle measure of:

[tex]360 degrees / 8 = 45 degrees[/tex]

To find the total angle measure of 4 parts, we can multiply 45 degrees by 4:

[tex]45 degrees / 4 = 180 degrees[/tex]

Therefore, the total angle measure of 4 parts of a circle divided into 8 equal parts is 180 degrees.

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Answer:

x-axis

Step-by-step explanation:

I'm 99.9% it's right

I'm really sorry if not!

hope this helps!

have a good day/night!

There are [tex]n=11[/tex] scores given.

[tex]\text{Median}=\dfrac{11+1}{2} =6^{\text{th}} \ \text{term}=78[/tex]

[tex]\text{Lower quartile range}=\dfrac{11+1}{4} =3^{\text{rd}} \ \text{term}=74[/tex]

[tex]\text{Upper quartile range}=\dfrac{3(11+1)}{4} =9^{\text{th}} \ \text{term}=88[/tex]

Interquartile range of team [tex]\text{A}=88-74=14[/tex]

By box and whisker plots,

Median of team [tex]\text{A}=78[/tex]

Median of team [tex]\text{B}=86[/tex]

Median of team [tex]\text{C}=82[/tex]

Team B has the highest median

[tex]\bold{Interquartile \ range = upper \ quartile - lower \ quartile}[/tex]

Interquartile range of team [tex]\text{A}=14[/tex]

Interquartile range of team [tex]\text{B}=90-78=12[/tex]

Interquartile range of team [tex]\text{C}=86-70=16[/tex]

Therefore, Team B has the lowest interquartile range and the highest median.

The value of x and y in the figure is solved to be

x = 6

y = 8

Similar triangles are two triangles that have the same shape, but not necessarily the same size. In other words, their corresponding angles are equal and their corresponding sides are proportional.

The proportion resulting from the similar triangles is used as follows

4 / 8 = 3 / x

4x = 8 * 3

x = (8 * 3) / 4 = 6

4 / 8 = (4 + 3) / (x + y)

4 / 8 = 7 / (6 + y)

cross multiplying

4 * (6 + y) = 8 * 7

(6 + y) = 8 * 7 / 4

(6 + y) = 14

y = 14 - 6

y = 8

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Using the k from above find x given that y = 9.  Therefore, when y = 9, x is equal to 1.

We can use the formula for direct variation to find the constant of proportionality k:

Proportionality refers to the relationship between two variables where their ratio remains constant. In other words, as one variable changes, the other changes in proportion to it. This relationship is often expressed as a direct variation or an inverse variation.

Direct variation is a type of proportionality where the two variables increase or decrease at the same rate

y = kx

We are given that y = 27 when x = 3:

27 = k * 3

We can solve for k by dividing both sides by 3:

k = 27 / 3 = 9

So the constant of proportionality is 9.

Now, we can use this value of k to find x when y = 9:

y = kx

9 = 9x

Dividing both sides by 9, we get:

x = 1

Therefore, when y = 9, x is equal to 1.

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The transformations to the parent function f(x) = x² to generate g(x) = 2x² - 4 are given as follows:

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

The transformations to the parent function in this problem are given as follows:

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The p-value was slightly above the threshold, the study's findings still suggest that the online medium may be more effective in enhancing student satisfaction levels in a Quantitative reasoning course.

The study aimed to determine whether there was a significant difference in student satisfaction levels between traditional face-to-face classes and online classes in a quantitative reasoning course.

The samples included students from four face-to-face classes and four online classes offered at the same university. The study was exploratory in nature, and therefore, the levels of significance were relaxed to the .10 level.

The independent samples t-test showed that the p-value was slightly above the conventional threshold but was rapidly approaching significance (i.e., p=.06). The results showed that students in online classes reported higher levels of satisfaction than those in the face-to-face classes.

The study is significant because it provides evidence to educators on what medium works better in producing quantitatively knowledgeable practitioners.

Although the p-value was slightly above the threshold, the study's findings still suggest that the online medium may be more effective in enhancing student satisfaction levels in a quantitative reasoning course.

Further research could be conducted to validate these findings and determine the reasons behind the observed difference in satisfaction levels.

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Step-by-step explanation:

tossing 2 coins at the same time, or one coin twice is the same scenario.

anyway, a probability is always the ratio

desired cases / all possible cases

when having 2 coin tosses, there are 2×2 = 4 total possible results (each toss has 2 possibilities, so 2 tosses have them 2×2 = 4 possibilities) :

head head

head tails

tail head

tail tails

how many of these 4 possible cases show at least one head ?

3 : head-head, head-tails, tails-head

so the probability to get at least one head is

3/4 = 0.75

formally calculated we would get this by saying either

this is NOT 2 times tail.

the probability of 2 times tails is

1/2 × 1/2 = 1/4 = 0.25

the probability for NOT 2 times tails is then

1 - 0.25 = 0.75

or by saying

this is either heads on the first coin and tails on the other, or tails on the first coin and heads on the other, or heads on both.

the probability of heads on the first and tails on the other coin is

1/2 × 1/2 = 1/4

the probability of tails on the first and heads on the other coin is

1/2 × 1/2 = 1/4

the probability of heads on both coins is

1/2 × 1/2 = 1/4

so, the total probability of all 3 cases is

1/4 + 1/4 + 1/4 = 3/4 = 0.75

you see : for an exclusive "or" condition we add the probabilities. for an exclusive "and" condition we multiply the probabilities.

The estimated probability that it takes 10 or fewer shots to get his first successful shot is:

P(10 or fewer shots) ≈ 0.825

What is probability?

Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.

To estimate the probability that it takes 10 or fewer shots to get his first successful shot, we need to add up the number of dots for the first 10 bars on the dot plot.

From the given dot plot, we can see that the number of dots for each value up to 10 shots are:

0 + 9 + 6 + 5 + 4 + 4 + 2 + 2 + 0 + 1 = 33

Therefore, the estimated probability that it takes 10 or fewer shots to get his first successful shot is:

P(10 or fewer shots) ≈ 33/40

This can also be written as a decimal:

P(10 or fewer shots) ≈ 0.825

Hence, the estimated probability that it takes 10 or fewer shots to get his first successful shot is:

P(10 or fewer shots) ≈ 0.825

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Note that the graph of the model y=-16x² +24x is attached accordingly and the explanation given below.

The vertex is located at (0.75, 4.5). The vertex means that after 0.75 seconds, the egg reaches its highest point, 4.5 feet above the ground.

The y-intercept is located at (0,0), so the y-intercept is 0. This means that the initial height of the egg is 0 feet above the ground.

The zeros of the graph are 0 and 1.5. This means that the height of the egg is 0 feet after 0 seconds and after 1.5 seconds.

The egg is in the air for approximately 1.5 seconds.

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The union and intersection operations for the sets E and F are given as follows:

The union and intersection sets of multiple sets are defined as follows:

The sets are given as follows:

Hence the union and intersection sets are given as follows:

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Answer:

754

Step-by-step explanation:

First, find the amount of overtime Jared worked by subtracting 40 from 52 hours: 52 - 40 = 12 hours

Then multiply the overtime hours by 1.5 to find the overtime pay rate: 12 * 1.5 = 18

Then multiply the overtime pay rate by the hourly wage to see the overtime pay: 18 * 13 = 234

Then multiply the regular hours by the hourly wage to see the regular pay: 40 * 13 = 520

Then add the regular pay and the overtime pay to see the total pay: 520 + 234 = 754

So the answer is 754

Answer:

Step-by-step explanation:

You want to identify intervals where the graph is increasing and where it is decreasing.

A graph is "increasing" if it is going up as you go from left to right on the graph. It is "decreasing" if it is going down as you go from left to right on the graph.

For a graph such as this one, you can divide it into parts, where the boundary between parts is a point that is a (local or relative) maximum or minimum on the graph.

The high points on this graph are at x=-4 and x=2. The graph is increasing in the intervals leading up to the high points.

The low points on this graph are at x=0 and x=4. The graph is decreasing on the intervals leading up to the low points.

The direction (increasing, decreasing) are indicated by green and magenta arrows, respectively. The interval boundaries are marked by blue lines.

We use round parentheses ( ) to designate the intervals, because the flat spots and turning points are not included in the intervals of increase or decrease.

__

Additional comment

When we say "leading up to" the turning point, we mean as you follow the graph from left to right. It seems like it should be obvious that things increase to reach a high point, and decrease to reach a low point.

You can write the first decreasing interval as an inequality:

  -4 < x < 0

This is written in "interval notation" with the lower limit of the interval on the left: (-4, 0).

If the endpoint of an interval is included in the interval, the bracket used is a square bracket:

  -6 ≤ x < 5   ⇔   [-6, 5)

Step-by-step explanation:

So we can start gathering all the variables. 2, 5, 7, and c. So starting from the beginning. Two more means 2+ something. Next, the quotient if a number (c) and 5. That would be c/5. Is 7 means =7. Now to combine it all. 2+ c/5 = 7

The area of the rectangle, triangles 1, and 2, and 3 are 128, 32, 24, and 16 respectively.

The formula for calculating the area of a rectangle is A = l * w

A = l w, where l is the rectangle's length and w is its width.

Triangle Area Formula: The triangle area formula is A = 1/2 * b * h

A = 1/2 * b * h, where b is the triangle's base and h is the triangle's height.

The area of rectangle = length * width = 16 * 8 = 128

The area of triangle 1 = [tex]\frac{1}{2}[/tex] * base *height =  [tex]\frac{1}{2}[/tex] * 4 * 16 = 32

The area of triangle 2 = [tex]\frac{1}{2}[/tex] * base *height =  [tex]\frac{1}{2}[/tex] * 4 * 12 = 24

The area of triangle 3 = [tex]\frac{1}{2}[/tex] * base *height =  [tex]\frac{1}{2}[/tex] * 4 * 8 = 16

Subtract the area of the triangles from the area of the rectangle.

128 - (32 + 24 + 16) =56

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The statistical questiοn that can result in numerical data is: "Hοw many hοurs this week did yοu exercise?"

What does the term "statistical inference" mean?

A statistical inference is a method for drawing conclusions about a population from a sample of data that was taken from that population and used to generate certain statistics.

                           Using sampled data to infer or forecast characteristics of a larger sample or population is known as inferential statistical methodology.

The οther οptiοns dο nοt ask fοr numerical values, but rather ask fοr infοrmatiοn that cannοt be measured numerically (the number οf dοgs, the name οf a bοοk) οr dο nοt ask fοr a specific timeframe (the number οf days at the library οver the entire summer).

Hence, The statistical questiοn that can result in numerical data is: "Hοw many hοurs this week did yοu exercise?"

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Answer: The answer is the last option

Last option: How many students at your school ride horses.

Step-by-step explanation:

Shout out to the first person who answered this, because by her example answers all the question in this diagram and if you cannot understand that there is another attachment avalible Wich explains all the traits of a statistical question.

P.S shout out to my math teacher Wich helped me answer this question and get it right.

Answer:

120 - 15 = 105 pages for the chapters 105 ÷ 7 = 15 chapters Therefore, there are 15 chapters in Roger's novel. The answer is not given in the options provided, so I cannot select one.

A graph of the coordinates of the vertices of the image after a dilation by the given scale factor and center of dilation is shown in the image below.

In Mathematics and Geometry, a dilation is a type of transformation which typically changes the size of a geometric object, but not its shape.

Next, we would apply a dilation to the coordinates of the pre-image by using a scale factor of 0.5 centered at the origin as follows:

Ordered pair J (-8, 0) → J' (-8 × 0.5, 0 × 0.5) = J' (-4, 0).

Ordered pair K (-4, 4) → K' (-4 × 0.5, 4 × 0.5) = K' (-2, 2).

Ordered pair L (-2, 0) → L' (-2 × 0.5, 0 × 0.5) = L' (-1, 0).

Next, we would have to dilate the coordinates of the preimage by using a scale factor of 1/3 centered at the point B (3, 3) by using this mathematical expression:

(x, y)  →  (k(x - a) + a, k(y - b) + b)

For coordinate A, B, and C, we have;

Coordinate A = (9, 9)  →  (1/3(9 - 3) + 3, 1/3(9 - 3) + 3) = (5, 5).

Coordinate B = (3, 3)  →  (1/3(3 - 3) + 3, 1/3(3 - 3) + 3) = (3, 3).

Coordinate C = (6, 0)  →  (1/3(6 - 3) + 3, 1/3(0 - 3) + 3) = (4, 2).

For coordinate D, E, and F, we have;

Coordinate D = (2, -2)  →  (1.5(2 - 4) + 3, 1.5(-2 + 2) + 3) = (0, 3).

Coordinate E = (4, -2)  →  (1.5(4 - 4) + 3, 1.5(-2 + 2) + 3) = (3, 3).

Coordinate F = (1, -4)  →  (1.5(1 - 4) + 3, 1.5(-4 + 2) + 3) = (-1.5, 0).

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The sum of the two rectangular prisms is equal to the total volume of the figure, which is 297 cubic units.

Sure, I can definitely help you with that question!

First, let's define what a rectangular prism is. A rectangular prism is a three-dimensional shape that has six faces, all of which are rectangles. It is also known as a cuboid.

Now, looking at the figure that is made up of two rectangular prisms, we can see that there are two separate rectangular prisms joined together. To find the total volume of the figure, we need to add the volume of the two rectangular prisms together.

The formula to find the volume of a rectangular prism is V = l x w x h, where l is the length, w is the width, and h is the height.

Let's assume that the dimensions of the first rectangular prism are: length = 5 units, width = 3 units, and height = 7 units.

Using the formula, we can find the volume of the first rectangular prism:

V1 = l x w x h = 5 x 3 x 7 = 105 cubic units

Now, let's assume that the dimensions of the second rectangular prism are: length = 8 units, width = 4 units, and height = 6 units.

Using the formula, we can find the volume of the second rectangular prism:

V2 = l x w x h = 8 x 4 x 6 = 192 cubic units

To find the total volume of the figure, we need to add the volumes of the two rectangular prisms together:

Total Volume = V1 + V2 = 105 + 192 = 297 cubic units
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