Select the expression that is equivalent to 48 + 12.

The rule for the nth term of the sequence is: an = [tex]3 * 13.0^(n-1)[/tex]

An arithmetic progression is a list of numbers in which each term is obtained by adding a fixed number to the preceding term except the first term.

The rule for the nth term of a geometric sequence is given by:

an = a1 * rn-1

where:

an = the nth term of the sequence

a1 = the first term of the sequence

r = the common ratio of the sequence

n = the position of the term in the sequence

Using the given values, we can write the rule for the nth term of the sequence as:

an =[tex]a * r^(n-1)[/tex]

where:

a = 3 (given)

r = 13.0 (given)

Therefore, the rule for the nth term of the sequence is:

an =[tex]3 * 13.0^(n-1)[/tex]

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Answer:

[tex]\frac{1}{50}[/tex]

Step-by-step explanation:

[tex]\frac{54.5-55.5}{225-275}[/tex] = [tex]\frac{-1}{-50}[/tex] = [tex]\frac{1}{50}[/tex]

The baseball field's fence, soil and sod requirements will be-: Length of fencing ≈ 1410.5 feet, Area of the sod ≈ 118017.13 ft², Area of of the field covered with dirt ≈ 7,049.6 ft²

To find the area of a sector of a circle:

The amount of fencing, dirt, and sod can be found using the formula for finding the circumference of a circle and the area of a circle as follows;

Circle's Area can be given by, (A)= π × r²

Circle's Circumference can be given by, (C) = 2 × π × r

Where, 'r' denotes the radius of the circle

The area of a quarter of a circle is therefore= A ÷ 4

The perimeter of a quarter of a circle = C ÷ 4

Taking reference from the image,

Fencing; (1/4) × 2 × π × 380 + 2 × 15 + 2 × 380 + (1/4) × 2 × π × 15

Fencing = 190·π + 790 + 7.5·π = 197.5·π + 790 ≈ 1410.5

The fencing ≈ 1410.5 feet

Grass; π/4 × (380 - 6)² + 87² - π/4 × (87 + 30)² + 2 × 380 × 15 + π/4 × 15² - (3/4) × π × 10² - 25·π = 31528·π + 18969 ≈ 118017.13

The area covered by the sod is about 118017.13 square feet

Dirt; π/4 × 380² - π/4 × (380 - 6)² + π/4 × (87 + 30)²- 87² + π·100 = (18613·π - 30276)/4 ≈ 7049.6

The area occupied by the dirt is about 7049.6 square feet

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Complete Question:Find the amount of fencing, dirt, and sod needed to rebuild the baseball field?(refer to image attached for dimensions of field)

The number of possibilities in the given scenario are 144. The solution has been obtained by using permutations.

What is permutation?

Mathematical calculations are used to determine the number of different configurations for a given set, and this procedure is referred to as permutation. A permutation is a phrase that, simply put, refers to the variety of alternative configurations or orders. When employing permutations, the sequence of the arrangement is crucial.

We are given that a team of 12 lacrosse players need to choose a captain and co-captain.

This means that n is 12 and r is 2.

Using permutations, we get

⇒ Total possibilities = [tex]n^{r}[/tex]

⇒ Total possibilities = [tex]12^{2}[/tex]

⇒ Total possibilities = 144

Hence, the number of possibilities in the given scenario are 144.

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The assumption that AXB is a bounded angle is false, as a result, if AXB is a circumscribed angle of circle C, then AXB and ACB are supplementary.

To complete the proof of the Circumscribed Angle Theorem, use the fact that an inscribed angle of a circle is equal to half of the central angle that intercepts the same arc.

Since angle ∠AXB is circumscribed by the circle, point X lies on the circumference of the circle. Therefore, angles ∠CXA and ∠CXB are inscribed angles that intercept the same arc AB.

By the Inscribed Angle Theorem:

∠CXA = ½∠CAB

∠CXB = ½∠CAB

Adding these two equations:

∠CXA + ∠CXB = ½∠CAB + ½∠CAB

∠CXA + ∠CXB = ∠CAB

Now, observe that angles ∠CAB and ∠ACB form a linear pair, since they are adjacent angles that together make a straight line. Therefore, they are supplementary, which means:

∠CAB + ∠ACB = 180°

Substituting ∠CAB with ∠CXA + ∠CXB:

∠CXA + ∠CXB + ∠ACB = 180°

Finally, ∠AXB and ∠CXB form a linear pair, since they are adjacent angles that together make a straight line. Therefore, they are supplementary, which means:

∠AXB + ∠CXB = 180°

Substituting ∠CXB with ∠CAB - ∠CXA:

∠AXB + ∠CAB - ∠CXA = 180°

Adding ∠CXA to both sides:

∠AXB + ∠CAB = ∠ACB + 180°

Substituting ∠AXB + ∠CAB with 180° (since they are adjacent angles that together make a straight line):

180° = ∠ACB + 180°

Simplifying:

∠ACB = 0°

This is a contradiction, since we know that ∠ACB is a non-zero angle. Therefore, our assumption that ∠AXB is a circumscribed angle must be false. Hence, we have proved that if ∠AXB is a circumscribed angle of circle C, then ∠AXB and ∠ACB are supplementary.

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where t is measured in days, and A(t) represents the amount of flooded land at time t. This function has a B-value of -0.3118.

To model the situation of the flood, we can use an exponential decay function, which represents the decreasing amount of flooded land over time. The function can be written as:

[tex]A(t) = A0 * e^{(-kt)}[/tex]

where A(t) is the amount of flooded land at time t, A0 is the initial amount of flooded land, k is a constant representing the rate of decay, and e is the mathematical constant approximately equal to 2.718.

To determine the value of k, we can use the given information that after 2 days, only 3375 acres of land were under water. Substituting t = 2 and A(t) = 3375 into the equation above, we get:

[tex]3375 = A0 * e^{(-2k)[/tex]

We also know that initially, there were 6000 acres of land under water. Substituting A0 = 6000 into the equation above, we get:

Dividing both sides by 6000, we get:

ln(0.5625) = -2k[tex]ln(0.5625) = -2k[/tex]

Taking the natural logarithm of both sides, we get:

[tex]ln(0.5625) = -2k[/tex]

Solving for k, we get:

[tex]k = -ln(0.5625)/2[/tex]

k ≈ 0.3118

Therefore, the function to model the situation of the flood is:

[tex]A(t) = 6000 * e^{(-0.3118t)}[/tex]

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Thus, the density of the silver picture frame is found to be 10 grams / cubic centimeters.

We use the word "density" to indicate how much space (or "volume") an object or substance occupies in relation to the total quantity of matter contained therein (its mass).

Density can also be defined as the quantity of mass per unit of volume. A dense object is one that is both hefty and small. An object has a low density if it is light and occupies a large amount of space.

Density = mass / volume

given data:

mass of the silver picture frame = 100 grams

Volume = 10 cubic centimetres

Density = mass / volume

Density = 100 grams/ 10 cubic centimeters

Density = 10 grams / cubic centimeters

Thus, the density of the silver picture frame is found to be 10 grams / cubic centimeters.

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The volume of the trapezoidal prism is 180 cubic meters.

What are parallel lines?

Parallel lines are two lines in a plane that never intersect. This means that they maintain the same distance between each other at all points.

To find the volume of a trapezoidal prism, we need to multiply the area of the trapezoidal base by the height of the prism.

The trapezoidal base has a length of 10m and 8m, and a height of 4m. The formula for the area of a trapezoid is:

Area = (a + b) * h / 2

where a and b are the lengths of the parallel sides, and h is the height.

Using the formula, we can calculate the area of the trapezoidal base:

Area = (10m + 8m) * 4m / 2

Area = 36m²

Therefore, the volume of the trapezoidal prism is:

Volume = Area of base * Height

Volume = 36m² * 5m

Volume = 180 cubic meters

Therefore, the volume of the trapezoidal prism is 180 cubic meters.

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Answer:

19.5625

Step-by-step explanation:

Add up all of the x's (treating each place where an x is as if it's a number -- eg, there's twonumber 12's)

12+12+15+15+15+15+16+18+20+20+22+25+25+25+29 = 313

Divide by the number of x's

313 / 16 = 19.5625

The expression represents the height of the, rectangular prism has a square base with edge length, which is 3 cm.

The expression represents the height of the rectangular prism with a square base of edge length and volume .

To make this more concrete, let's assume some values for and . Let's say that the edge length of the square base is 4 cm, and the volume of the rectangular prism is 48 cubic cm.

Using the formula for the volume of a rectangular prism, we can write:

Volume = Base Area x Height

Since the base of the rectangular prism is a square with edge length 4 cm, its area is:

Base Area = 4 x 4 = 16 square cm

Substituting the given values into the formula for volume, we get:

48 cubic cm = 16 square cm x Height

To solve for the height, we can isolate it on one side of the equation by dividing both sides by 16 square cm:

48 cubic cm ÷ 16 square cm = Height

3 cm = Height

Therefore, in this scenario, the expression represents the height of the rectangular prism, which is 3 cm.

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The probability of the sample mean being less than 79 is 77.64%

In order to solve the given problem we have to take the help of Standard error mean

SEM = ∑/√(n)

here,

∑ = population standard deviation

n = sample size

hence, the z-score can be calculated as

z = ( x' - μ)/σ/√(n)

here,

x' = sample mean

μ = population mean

σ = population standard deviation

n = sample size

adding the values into the formula

SEM = σ / √(n)

= 21/√64

= 2.625

z = (x' - μ)/SEM

= (79-77)/2.625

= 0.76

now, using standard distribution table we find that probability of a z-score is less than 0.77 then converting it into percentage

0.77 x 100

= 77%

The probability of the sample mean being less than 79 is 77.64%

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We can use the equation y = 38.8x to find how many miles Camila can drive her car for each gallon of gas, and then use that information to find how many gallons of gas she would need to drive the same distance as Julieta.

Julieta drives 333 miles using 10 gallons of gas, so her car can travel 333/10 = 33.3 miles per gallon.

To find how many miles Camila's car can travel per gallon, we can use the equation y = 38.8x, where x is the number of gallons of gas. If Camila uses 1 gallon of gas, then y = 38.8(1) = 38.8 miles. Therefore, Camila's car can travel 38.8 miles per gallon.

To travel 333 miles like Julieta, Camila would need to use:

333 miles / 38.8 miles per gallon = 8.58 gallons of gas

Therefore, Camila would need to use 8.58 gallons of gas to travel the same distance as Julieta.

Answer:200.734

Step-by-step explanation:

150(1+0.06)^t

t=number of years

150(1.060)^5

200.73383664

round

200.734

The balance of this account after 5 years is $200.73

Compound interest is the interest earned on the principal and the interest previously accumulated. It is given by

Amount = [tex]P(1+r/n)^n^t[/tex] where P = Principal, r = annual rate of interest, n = number of times interest is compounded per year, & t = time in years.

The given principal is $150 for 5 years & annual interest rate is 6%.

To find the amount compunded annualy at 6% for 5 years substituting the given values in the above formula i.e.

Amount =  [tex]P(1+r/n)^n^t[/tex]

Amount = $[tex]150(1+0.06)^5[/tex]

Amount = $200.73

Hence, the total amount accumulated for 5 years will be $200.73

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It is true that a linear programming problem can have an optimal solution that is not a corner point.

In linear programming, the optimal solution represents the point where the objective function is optimized while still satisfying all the constraints.

In some cases, the optimal solution may occur at a corner point of the feasible region, where two or more of the constraints intersect.

However, it is possible for the optimal solution to occur at a point that is not a corner point, but rather lies on an edge or a line segment of the feasible region.

This can occur when the objective function is parallel to one of the constraint lines or when there are redundant constraints that limit the feasible region.

Therefore, it is true that a linear programming problem can have an optimal solution that is not a corner point.

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The probability that 3 of the 9 randomly selected subjects entered a profession closely related to their college major is approximately 0.1665, or 16.65%.

To find the probability that 3 out of 9 randomly selected subjects entered a profession closely related to their college major, we can use the binomial probability formula:
[tex]P(X = k) = (n choose k) * p^k * (1 - p)^{n - k}[/tex]
where:
- P(X = k) is the probability of k successes (in this case, 3 people entering a profession closely related to their major)
- n is the number of trials (9 subjects)
- k is the number of successes (3 people)
- p is the probability of success (53% or 0.53)
- (n choose k) is the number of combinations of n items taken k at a time, which can be calculated as C(n, k) = n! / (k! * (n - k)!)
Plugging in the values, we get:
[tex]P(X = 3) = C(9, 3) * (0.53)^3 * (1 - 0.53)^{9 - 3}[/tex]
First, calculate the combinations (n choose k):
C(9, 3) = 9! / (3! * (9 - 3)!)
C(9, 3) = 9! / (3! * 6!)
C(9, 3) = 362880 / (6 * 720)
C(9, 3) = 84
Now, calculate the probabilities:
[tex]P(X = 3) = 84 * (0.53)^3 * (0.47)^6[/tex]
P(X = 3) = 84 * 0.148877 * 0.013325
P(X = 3) ≈ 0.1665.

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the probability that a randomly selected passenger car gets more than 35 mpg is approximately 0.3665.

the probability that the average mpg of four randomly selected passenger cars is more than 35 mpg is approximately 0.087

the probability that all of the passenger cars get more than 35 mpg is approximately 0.015.

We need to find [tex]P(X > 35),[/tex] where X is the mpg rating of a randomly selected passenger car.

The standard normal distribution and Table 1, we have:

[tex]z = (35 - 33.8) / 3.5 = 0.34[/tex]

[tex]P(X > 35) = P(Z > 0.34) = 0.3665[/tex]

[tex]P(\bar X > 35)[/tex], were [tex]\bar X[/tex] is the sample mean mpg rating of four randomly selected passenger cars.

The population standard deviation, we use the t-distribution with [tex]n-1[/tex] degrees of freedom (were [tex]n = 4[/tex]) and Table 1. We have:

[tex]t = (35 - 33.8) / (3.5 / \sqrt(4)) = 1.83[/tex]

Using Table 1 with 3 degrees of freedom ([tex]n-1 = 4-1[/tex]), we find:

[tex]P(T > 1.83) = 0.087[/tex]

We need to find [tex]P(X1 > 35[/tex] and [tex]X2 > 35[/tex] and [tex]X3 > 35[/tex] and [tex]X4 > 35[/tex]), where X1, X2, X3, and X4 are the mpg ratings of four randomly selected passenger cars.

Since the mpg ratings of the four cars are independent and identically distributed, we have:

[tex]P(X1 > 35[/tex]and[tex]X2 > 35[/tex] and [tex]X3 > 35[/tex] and [tex]X4 > 35[/tex]) =[tex]P(X > 35)^4[/tex]

From part (a), we know that[tex]P(X > 35) = 0.3665.[/tex]

[tex]P(X1 > 35[/tex]and [tex]X2 > 35[/tex] and[tex]X3 > 35[/tex] and [tex]X4 > 35) = 0.3665^4 \approx 0.015[/tex]

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For the given statement after evaluating both the options the correct option is true under the condition that scores increase and null hypothesis is used to find out Treatment effect.

Here, null hypothesis clearly states that there is no significant difference is observed in comparison of sample mean and population mean.

Null hypothesis refers to statistical process which takes certain assumptions regarding two sets of different variables. In the branch of science it is used to find credibility regarding a sample data.

For the given case, the null hypothesis presents   that the population mean remains unchanged (m = 60) post  treatment, doesn't matter if it is greater than or equal to 60. The alternative hypothesis will be increases the mean  for the treatment (m > 60).

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True. Your statement is: A researcher administers a treatment to a sample from a population with a mean of m = 60. If the treatment is expected to increase scores and a one-tailed test is used to evaluate the treatment effect, then the null hypothesis would state that m ≥ 60.

The null hypothesis typically represents no effect or no difference. In this case, the null hypothesis would state that the population mean remains unchanged (m = 60) after the treatment, not that it is greater than or equal to 60. The alternative hypothesis would be that the treatment increases the mean (m > 60).

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2(4/3) represents the shaded area in the diagram as two rectangles of equal size, each with a length of 4 units and a width of 2/3 units.

4 * 2/3 represents the shaded area in the diagram as a rectangle with a length of 4 units and a width of 2/3 units.

4 * 2 * 1/3 represents the shaded area in the diagram as a rectangle with a length of 4 units, a width of 2 units, and a smaller rectangle with a length of 1 unit and a width of 1/3 units.

What is the area of the rectangle?

To find the area of a rectangle, we multiply the length of the rectangle by the width of the rectangle.

a. The diagram shows 3/5 by dividing the whole rectangle into 5 equal parts horizontally and shading 3 of those parts. This means that the shaded portion represents 3 out of 5 equal parts.

b. The diagram shows 3 * 1/5 by shading one-fifth of the rectangle, and then repeating this process three times. This means that the shaded portion represents three times one-fifth of the whole.

c. The value of 3/5 is equivalent to 0.6 or 60%. This means that if we divide a whole into 5 equal parts, and take 3 of those parts, we have 60% of the whole.

a. The expression 2(4/3) represents the shaded parts of the diagram by first finding the area of one shaded rectangle, which is 4/3. Then, we multiply this area by 2 because there are two shaded rectangles in the diagram. Therefore, 2(4/3) gives us the total shaded area.

b. The expression 4 * 2/3 represents the shaded parts of the diagram by multiplying the width of the shaded rectangle (2 units) by its height (2/3 units), and then multiplying that by the number of shaded rectangles (4). Therefore, 4 * 2/3 gives us the total shaded area.

c. The expression 4 * 2 * 1/3 represents the shaded parts of the diagram by multiplying the length of the shaded rectangle (4 units) by its width (2 units) by its height (1/3 units), and then multiplying that by the number of shaded rectangles (4). Therefore, 4 * 2 * 1/3 gives us the total shaded area.

Hence, 2(4/3) represents the shaded area in the diagram as two rectangles of equal size, each with a length of 4 units and a width of 2/3 units.

4 * 2/3 represents the shaded area in the diagram as a rectangle with a length of 4 units and a width of 2/3 units.

4 * 2 * 1/3 represents the shaded area in the diagram as a rectangle with a length of 4 units, a width of 2 units, and a smaller rectangle with a length of 1 unit and a width of 1/3 units.

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Emmy and Liam each played 4 games according to the given statement.

An equation is a claim that two expressions are equal, typically indicated by the equals symbol (=). In mathematics, equations are used to simulate real-world scenarios, solve problems, and depict relationships between variables.

Exponents, logarithms, and trigonometric functions can all be used in equations, in addition to basic operations like addition, subtraction, multiplication, and division.

Let us suppose the number of games played = x.

Thus, for Emmy we have:

E = 1 + 2x

For Liam the equation is:

L = 5 + 1x

Equating the two equations we have:

1 + 2x = 5 + 1x

x = 4

Hence, Emmy and Liam each played 4 games according to the given statement.

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Using the law of sines, the value of the indicated side x, is calculated to one decimal place as: 125.3.

The Law of Sines is a trigonometric formula used to relate the side lengths and angles of any triangle. It states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is equal for all three sides of the triangle. Mathematically, this can be represented as:

sin A/a = sin B/b = sin C/c

Thus, we have:

C = 180 - 102 - 28 = 50°

a = 160

A = 102°

c = x = ?

Applying the law of sines, we have:

sin 102/160 = sin 50/x

Cross multiply:

x = sin 50 * 160 / sin 102

x ≈ 125.3

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Answer:

Step-by-step explanation:

25

=

a

b

−

2

10

=

a

b

1

Answer:

236 cm^2  and  8 cm

Step-by-step explanation:

width=w

240=6(5)(w)

w=8 cm

area=2[(6)(5)+(6)(8)+(5)(8)]

area=236 cm^2

The ratio of the weight to the mass and the value of x in the table is B) The ratio is 10/98, x = 110.

The quantity of matter in an object is measured by its mass, which is commonly expressed in kilogrammes or grammes. Since mass is a scalar quantity, the gravitational field has no effect on it. The force of gravity acting on an object is quantified by weight, which is commonly expressed in newtons or pounds. Weight is a vector quantity that is influenced by the strength of the gravitational field. While an object's mass is constant, its weight might vary depending on the gravitational field.

The ratio of weight to mass according to the given table is:

weight / mass = 196 / 20 = 98/10

The ratio is constant thus for x we have:

1078 / x = 98 / 10

Using cross multiplication we have:

x = 1078 (10) / 98 = 110

Hence, the ratio of the weight to the mass and the value of x in the table is B) The ratio is 10/98, x = 110.

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The complete question is:

A) Their graphs will be different from the graph of the linear parent function. B) In real-world context, comparing functions can be useful in many scenarios, such as predicting sales or analyzing trends.

The y-intercept is the point where the graph of a function intersects with the y-axis. It is the point at which the value of x is 0.

Part A:

The linear parent function is represented by y = mx + b, where m is the slope and b is the y-intercept. The slope of the linear parent function is constant, while the y-intercept can vary.

In Jack's function, d = 0.05t, the slope is 0.05, which means that for every minute he runs, he travels 0.05 miles. The y-intercept is 0, which means that he starts at 0 miles.

In Jill's function, d = 0.04t + 0.5, the slope is 0.04, which means that for every minute she runs, she travels 0.04 miles. The y-intercept is 0.5, which means that she starts at 0.5 miles.

Both functions are linear, but they have different slopes and y-intercepts. Therefore, their graphs will be different from the graph of the linear parent function.

Part B:

Comparing Jack and Jill's functions to the linear parent function can give us insights into their race. The fact that their functions are linear means that they are running at a constant rate. However, the different slopes and y-intercepts mean that they are running at different rates and starting at different distances.

For example, we can see from their functions that Jack is running faster than Jill since his slope is larger. We can also see that Jill has a head start since her y-intercept is larger. By comparing their functions, we can make predictions about who will win the race or how far ahead one person will be at a certain time.

In real-world context, comparing functions can be useful in many scenarios, such as predicting sales or analyzing trends. By understanding the relationship between variables, we can make informed decisions and predictions.

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The total amount of the bill, including tax and gratuity, was $191.85.

What is the percentage?

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

The first step is to calculate the amount of tax and the amount of gratuity:

Amount of tax = 6% of $158.56 = $9.51

Amount of gratuity = 15% of $158.56 = $23.78

Next, we add the tax and the gratuity to the original bill:

Total bill = $158.56 + $9.51 + $23.78 = $191.85

Therefore, the total amount of the bill, including tax and gratuity, was $191.85.

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Answer:

The width is 4 inches

Step-by-step explanation:

Volume is the length x the width x height

84 = 7w3

84 = 21w  Divide both sides by 21

4 = w

Helping in the name of Jesus.

Answer:

The answer is B ([tex]x=\frac{6}{5}[/tex])

Step-by-step explanation:

We start with creating labels for the shapes that represent what they value -at first I tried multiplying the 5x by 4 but there wasn't an answer for that.

[tex]5x+4=10[/tex]

First we just simplify,

[tex]5x (-4)=10(-4)[/tex]

[tex]5x=6[/tex]

then divide,

[tex]\frac{5x}{5} =\frac{6}{5}[/tex]

and we end up with:

[tex]x=\frac{6}{5}[/tex]

or

B

Thus, the on average the contents weight for the transatlantic shipping is found as  24.7  pounds.

Given dimension of rectangular prism

Length l = 4ft

width w = 9.5 ft

height h = 13 ft

Volume of rectangular prism = l*w*h

V = 4*9.5*13

V = 494 ft³

Now,

1  ft³ = 0.05 pounds

So,

weight of  494 ft³ =  494*0.05 pounds

weight of 494 ft³ =  24.7  pounds

Thus, the on average the contents weigh for the transatlantic shipping is found as  24.7  pounds.

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