Tikiro places a wrench on a nut and applies a downward force of 32 pounds to tighten the nut. If the center of the nut is at the origin, the force is applied at the point (.65,0,0.3) Find the torque. a. 18.4 ft-lb c. 21.2 ft-lb b. 20.8 ft-lb d. 22.1 ft-lb

Answer:

The area of the larger octagon is  [tex]236.18\ in^2[/tex]

Step-by-step explanation:

The question is

What is the area of the larger octagon?

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

so

Let

z ----> the scale factor

x ----> the area of the larger octagon

y ---> the area of the smaller octagon

[tex]z^2=\frac{x}{y}[/tex]

we have that

[tex]z=3.5[/tex]

Because, in similar figures the ratio of corresponding sides is proportional and this ratio is equal to the scale factor

we have

[tex]z=3.5[/tex]

[tex]y=19.28\ in^2[/tex]

substitute the given values

[tex]3.5^2=\frac{x}{19.28}[/tex]

[tex]x=12.25(19.28)=236.18\ in^2[/tex]

Answer:

the answer is D

Step-by-step explanation:

D) Westfield's data shows greater variability, since Westfield's MAD is approximately 2.9 times greater than Eastfield's MAD.  

Answer:

D) Westfield's data shows greater variability, since Westfield's MAD is approximately 2.9 times greater than Eastfield's MAD.

Step-by-step explanation:

Westfield's data shows greater variability, since Westfield's MAD is approximately 2.9 times greater than Eastfield's MAD.

Westfield's MAD = 6.56

Eastfield's MAD = 2.28

Therefore,

6.56

2.28

= 2.877

MAD =

∑|x − X|

n

, where x = Data value, X = Mean, and n = Number of values

Answer:

Refer below.

Step-by-step explanation:

The principal will have to increase the number of teachers next year.

We found out that the seventh grade enrollment was 120% of the number of eight graders, which is greater than 110%.

Answer:

x=29

Step-by-step explanation:

x-15=14

Add 15 to 14

x=29

Answer: the winnings are reduced

Step-by-step explanation:

Given 10 percent chance to win $1,000 for $100. That is

Gain = $900

Assuming diminishing marginal utility of dollars, when the utility of the gain and the money used for bet are considered, it is discovered that the utility of the $100 used to make the bet is greater than the $900 that you might gain if you win the bet.

this is not a fair bet in terms of utility because the winnings are reduced.

A mathematically fair bet does not account for the diminishing marginal utility of money. The expected utility calculated with a utility function might show a different picture, revealing the bet might not be fair in terms of utility. Samuelson's story illustrates statistical independence and that repeated gambles with positive expectations lead to better outcomes.

A "mathematically fair bet" is one where the expected value of the bet is equal to the cost of making the bet. In other words, if you bet $100 for a 10 percent chance to win $1,000, the mathematically calculated expectation would be $100, or 0.10 times $1,000. However, the concept of diminishing marginal utility suggests that the utility or satisfaction derived from each additional dollar decreases as one has more money. Thus, the utility of the potential win cannot simply be calculated by multiplying the probabilities by the monetary outcome.

Under the concept of expected utility, the expected utility of a bet should also be considered. To calculate this, one might use a utility function, like the von Neumann-Morgenstern utility function, to determine the utility of each possible outcome and then finding the average utility. For example, let's assume that the utility function is represented by the square root of the dollar amount (this is just an example, utility functions can take many forms). Hence, the expected utility of winning $1,000 would be the square root of $1,000, not just $1,000.

Paul Samuelson's story illustrates the idea of statistical independence and the law of large numbers, where repeated play of a gamble with positive expectation can lead to more stable and predictable results, as opposed to a single high-risk gamble. This idea reflects human behavior and the role of hope in encouraging smart risk-taking, even when each individual bet may not be favorable in terms of utility.

Answer: Riley will catch up with Lara after 6 seconds

Step-by-step explanation:

Let t represent the time it will take Riley to catch up with Lara. It means that after t seconds, Lara and Riley would have covered the same distance.

Distance = speed × time

​Lara can run 5 meters per second. It means that the distance covered by Lara in t seconds is 5t meters

​Mrs. Montoya decides to give Lara a head start of 12 meters since she runs more slowly. ​it means the total distance covered by Lara after t seconds is

5t + 12

Riley can run 7 meters per second. ​It means that the distance covered by Riley in t seconds is 7t meters.

Since the distance covered after t seconds is the same, then

7t = 5t + 12

7t - 5t = 12

2t = 12

t = 12/2

t = 6 seconds

Riley will have to run 42 meters to catch up to Lara.  It will take 6 seconds for Riley to catch up to Lara.

Given:

- Lara's speed [tex]\( v_L = 5 \)[/tex] meters per second

- Riley's speed [tex]\( v_R = 7 \)[/tex]meters per second

- Lara's head start [tex]\( d_{\text{head start}} = 12 \)[/tex] meters

Let's denote:

- t as the time it takes for Riley to catch up to Lara.

- d as the distance Riley needs to run to catch up to Lara.

1. Set up equations based on their speeds and the head start:

  - For Lara: [tex]\( d_L = v_L \cdot t \)[/tex]

  - For Riley: [tex]\( d_R = v_R \cdot t \)[/tex]

2. Account for Lara's head start:

  - Lara starts with a head start of 12 meters. Therefore, when Riley starts, Lara is already 12 meters ahead.

 [tex]\[ d_R = d_L + 12 \][/tex]

3. Substitute the expressions for [tex]\( d_L \)[/tex] and [tex]\( d_R \)[/tex]:

 [tex]\[ v_R \cdot t = v_L \cdot t + 12 \][/tex]

4. Solve for t:

[tex]\[ 7t = 5t + 12 \] \[ 7t - 5t = 12 \] \[ 2t = 12 \] \[ t = \frac{12}{2} \] \[ t = 6 \][/tex] seconds

5. Calculate the distance [tex]\( d_R \)[/tex] that Riley has to run:

[tex]\[ d_R = v_R \cdot t \] \[ d_R = 7 \cdot 6 \] \[ d_R = 42 \][/tex]

To find the value for each expression, substitute a = 3 and b = 5 into the given expressions. The values of the expressions are: 11, 13, 24, 17, 8.

To find the value for each expression, we substitute a = 3 and b = 5 into the given expressions. The expressions are:

1. 2a + b: Substituting a = 3 and b = 5, we have 2(3) + 5 = 6 + 5 = 11.
2. 2b + a: Substituting a = 3 and b = 5, we have 2(5) + 3 = 10 + 3 = 13.
3. (a + b)3: Substituting a = 3 and b = 5, we have (3 + 5)3 = 8 × 3 = 24.
4. 4b - a: Substituting a = 3 and b = 5, we have 4(5) - 3 = 20 - 3 = 17.
5. 6a - 2b: Substituting a = 3 and b = 5, we have 6(3) - 2(5) = 18 - 10 = 8.

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Final answer:

After substituting a = 3 and b = 5 into the given expressions, we calculate their values and order them from least to greatest: 6a - 2b = 8, 2a + b = 11, 2b + a = 13, 4b - a = 17, 3(a + b) = 24.

Explanation:

We are given the variables a = 3 and b = 5 and need to find the values of five expressions, then place them in order from least to greatest. Let's calculate each expression step by step:

Now placing them in order from least to greatest, we get:

Answer:

$24

Step-by-step explanation:

So the total number of hours John has worked after 4 hours plus another 2 hours is h = 4 + 2 = 6 hours.

Given that John's wage is modeled by the equation w = 4h, then his total wage within 6 hours of working is is

w = 4h = 4 * 6 = $24

John earns: [tex]\[\boxed{24}\][/tex] Dollars

To determine how much John earns, we can use the equation provided:  w = 4h , where w represents John's wages in dollars and h represents the number of hours worked.

John first worked for 4 hours. Using the wage equation:

[tex]\[w = 4 \times 4 = 16 \text{ dollars}\][/tex]

Next, John continues to work for another 2 hours. The total number of hours he works is now:

[tex]\[4 + 2 = 6 \text{ hours}\][/tex]

Using the wage equation for the total number of hours:

[tex]\[w = 4 \times 6 = 24 \text{ dollars}\][/tex]

Thus, John earns:

[tex]\[\boxed{24}\][/tex] Dollars

Answer:

I'm using algebra format ok so if u get it wrong pls dont kill me. 6(3+4) = 6*3 + 6*4 brackets in algebra means times so 6 times 3 + 6 times 4 done

Final answer:

In mathematics, when an operation involves an even number of signs, the result will be positive. This applies to multiplication and division rules, where similarly signed numbers yield a positive result. Principles of mathematical operations also extend to probabilities, where conditions and the complement of events are crucial to determining event outcomes.

Explanation:

If there is an even number of signs in a mathematical operation, such as multiplication or division, the solution will have a positive sign. This is because multiplying or dividing two positive numbers, or two negative numbers, results in a positive outcome. However, multiplying or dividing numbers with opposite signs results in a negative outcome.

For instance:

When two positive numbers multiply, the answer has a +ve sign, e.g., 2x3 = 6.

When two negative numbers multiply, the answer also has a +ve sign, e.g., (-4) x (-3) = 12.

In probability, events A and B being given conditions, such as event A given B (A GIVEN B) or event B given A (B GIVEN A), can impact the likelihood of those events occurring. The complement of an event (like the complement of A) refers to all outcomes that are not part of the event A.

Principles of Mathematical Operations and Probability

Understanding these principles helps solve many mathematical problems and assess probabilities, especially when working with equations with an unknown squared, which will typically result in two solutions, or when calculating the possibilities of a dice roll in probability exercises.

Answer:

Around 41 quarts

Step-by-step explanation:

Answer:

1675 ft

Step-by-step explanation:

For us to calculate how close the windmill is to the fire, if we imagine it as a triangle, the distance from watch tower to the fire will be:

tan θ= opposite/adjacent

opposite=140 ft

adjacent = x

θ=3°

Thus;

tan 3 = 140/x

x=140/tan 3

x = 2,671.359 ft

Now, the distance from watch tower to windmill will be:

tan θ=opposite/ adjacent

θ=8°

opposite=140 ft

adjacent=y

thus

tan 8 = 140/y

y = 140/tan8

y=996.15 ft

Now, the distance between fire and wind mill will be:

x - y = 2671.359 - 996.15

x - y = 1675.209 ≈ 1675 ft

Answer:

1675 feet

Step-by-step explanation:

Refer to the image attached for diagrams and better explanations

Answer:

The C.I. at 95% is 185±9.9583 or C.I.[175 to 195].

Step-by-step explanation:

Given:

Mean =185 mg

Standard deviation=17.6

Total number of samples=12

To Find:

95% of Confidence interval .

Solution:

We know that formula for C.I is given by ,

C.I.=mean±Z[standard deviation/Sqrt(Total no of samples)]

So using all above given values we get ,

Here Zscore at 95% is Z=1.96

So

C.I.=185±1.96[17.6/Sqrt(12)]

=185±1.96[17.6/3.464]

=185±1.965[5.0808]

=185±9.9583

In short C.I. is given as at 95% C.I.[175 to 195].

Answer:

The correct option is 90.2.

Step-by-step explanation:

The general form of a least square regression line is:

[tex]y=\alpha +\beta x[/tex]

Here,

y = dependent variable

x = independent variable

α = intercept

β = slope

The regression equation relating attitude rating (x) and job performance rating (y) for the employees of a company is:

[tex]y=11.7+1.02x[/tex]

In this case the dependent variable is the job performance rating for the employees of a company and the independent variable is their attitude rating.

This implies that the for an employee of the company the job performance rating is based on their attitude towards work.

Compute the value of y for x = 77 as follows:

[tex]y=11.7+1.02x[/tex]

  [tex]=11.7+(1.02\times 77)\\=11.7+78.54\\=90.24\\\approx90.2[/tex]

The predicted value of job performance rating for a person whose attitude rating is 77 is 90.2.

Thus, the correct option is 90.2.

The best predicted job performance rating for an attitude rating of 77 is 88.9.

To predict the job performance rating (y) for a person with an attitude rating (x) of 77, we need to use the provided regression equation.

Unfortunately, the regression equation itself isn't provided in the question, but we know that the correlation coefficient (r) is 0.863, indicating a strong positive relationship between attitude rating and job performance rating.

Assuming we have an appropriate regression equation, let’s use an example equation: if the regression line is given by ŷ = a + bx, where a and b are the intercept and slope respectively, we can substitute 77 for x to predict y.

For example, if the regression equation was of the form ŷ = 10 + 1.03x, substituting 77 would yield:

The closest option to 89.31 would be 88.9. Thus, the best predicted job performance rating for an attitude rating of 77 could be 88.9 given the options provided.

Answer:

11.45 miles

Step-by-step explanation:

you add

Answer:

21 inches

Step-by-step explanation:

In 1 rotation the angle at the centre = 360°

For 120° the fraction turned = [tex]\frac{120}{360}[/tex] = [tex]\frac{1}{3}[/tex], thus

distance travelled = [tex]\frac{1}{3}[/tex] × 63 = 21 inches

If the wheel rotates only 120° it travel 21 inches.

The angle at the center of one rotation is 360°.

The fraction for 120° changed[tex]=\frac{120}{360} =\frac{1}{3}[/tex]

Total 63 inches in one complete rotation of a wheel.

Thus distance travelled[tex]=\frac{1}{3}\times 63= 21[/tex]

The wheel travel on the bicycle is 21 inches.

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Answer:

10 cubes on each side

Step-by-step explanation:

The amount of cubes to make a square frame given was 36

If you start by putting ten cubes on one side then adding nine off of the the end cubes and continue that pattern you end up with 10 cubes on each side.

There will be 6 cubes on each side of the frame.

Explanation:

To understand the relationship between the number of cubes used and the length of the side of the square frame, let's first consider the given example with 12 cubes.

 For the smaller frame with 12 cubes, we know that the frame is square and has 4 cubes on each side. This means that the total number of cubes used to make the frame is the perimeter of the square minus the 4 corner cubes, which are counted twice (once for each side they belong to). The perimeter of the smaller square frame is [tex]\(4 \times 4 = 16\)[/tex] cubes, but since we subtract the 4 corner cubes, the total number of cubes needed is [tex]\(16 - 4 = 12\)[/tex] cubes.

Now, we are given that 36 cubes are used to make a larger square frame. Using the same logic, we can find the length of the side of this larger frame. Let \(n\) be the number of cubes on each side of the larger frame. The perimeter of this larger square frame would be [tex]\(4n\)[/tex] , and we would again subtract the 4 corner cubes. Therefore, the equation to find [tex]\(n\)[/tex] is:

 [tex]\[4n - 4 = 36\][/tex]

 Adding 4 to both sides gives us:

[tex]\[4n = 40\][/tex]

Dividing both sides by 4 gives us:

[tex]\[n = 10\][/tex]

So, there are 10 cubes on each side of the larger frame. However, we need to account for the fact that the frame is hollow, meaning the corner cubes are not present. Since there are 4 corners without cubes, we subtract 1 cube from each side to get the number of cubes actually used for each side:

[tex]\[n - 1 = 10 - 1 = 9\][/tex]

 Now, we can calculate the total number of cubes used for the frame with 9 cubes on each side:

[tex]\[4 \times 9 = 36\][/tex]

This confirms that with 9 cubes on each side, we indeed use 36 cubes to make the frame. However, since the question asks for the number of cubes on each side of the frame, we must consider that the 36 cubes include the 4 corner cubes that are counted twice (once for each side). Therefore, we add back the 4 corner cubes to the length of each side:

[tex]\[9 + 1 = 10\][/tex]

 Thus, there are 10 cubes on each side of the frame, but since we are considering the outer dimension of the frame (including the corners), we have to add the corner cubes that are shared by two sides. Since there are 4 corners, and each corner contributes 1 cube to 2 sides, we divide by 2 to avoid double counting:

[tex]\[10 + \frac{4}{2} = 10 + 2 = 12\][/tex]

 However, this calculation is incorrect because we've already accounted for the corner cubes when we subtracted 4 from the perimeter to get the number of cubes on each side. The correct number of cubes on each side is 9, as calculated previously. Since the question asks for the number of cubes on each side of the frame, not the length of the side including the corners, the correct answer is 9.

Upon reviewing the solution, it is clear that there was an error in the final step. The correct number of cubes on each side of the frame is indeed 9, not 12. Therefore, the final answer should be:

There will be 9 cubes on each side of the frame.

Answer:

The hip breadth for men that separates the smallest 99​% from the largest 1​% is 17.16 inches.

Step-by-step explanation:

We are given that the Men have hip breadths that are normally distributed with a mean of 14.6 in. and a standard deviation of 1.1 in.

We have to find the hip breadth for men that separates the smallest 99​% from the largest 1​%.

Let X = length of hip breadths

SO, X ~ Normal([tex]\mu=14.6,\sigma^{2} =1.1^{2}[/tex])

The z-score probability distribution for normal distribution is given by;

                               Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)

where, [tex]\mu[/tex] = mean hip breadth = 14.6 inches

            [tex]\sigma[/tex] = standard deviation = 1.1 inches

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

Now, we have to find the hip breadth for men that separates the smallest 99​% from the largest 1​%, which means;

       P(X > x) = 0.01   {where x is the required hip breadth}

       P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{x-14.6}{1.1}[/tex] ) = 0.01

        P(Z > [tex]\frac{x-14.6}{1.1}[/tex] ) = 0.01

So, the critical value of x in the z table which represents the largest 1% of the area is given as 2.3263, that is;

                       [tex]\frac{x-14.6}{1.1} =2.3263[/tex]

                         [tex]{x-14.6}{} =2.3263\times 1.1[/tex]

                          [tex]x[/tex] = 14.6 + 2.55893 = 17.16 inches

Hence, the hip breadth for men that separates the smallest 99​% from the largest 1​% is 17.16 inches.

Answer:3

Step-by-step explanation:

Answer:

8 ft

Step-by-step explanation:

Okay lets get our variables and notes down first, I'll use the most common terms for this.

Hypotenuse: 12 ft <-- The ladder is the hypotenuse

Leg: 9 <- The height of the top of the ladder on the house

Base: ? <- We need to solve for it.

Pythagorean Theorem says c²-a²=b²

c = Hypotenuse

a & b are both Legs and interchangeable

12²-9²=b²

144-81=b²

     63=b²

   [tex]\sqrt{63}[/tex]=[tex]\sqrt{b^{2} }[/tex]

   [tex]3\sqrt{7}[/tex]=b which is approximately 7.93 which rounds up to 8

Answer:

The answer to your question is 566 m²

Step-by-step explanation:

Data

length = 19 m

width = 4 m

height = 9 m

Process

1.- Calculate the area of the 6 faces

-Area of the bases

Area = 19 x 4 x 2 = 152 m²

-Area of the lateral faces

Area = 4 x 9 x 2 = 72 m²

-Area of the frontal and the opposite faces

Area = 19 x 9 x 2 = 342 m²

2.- Calculate the total area

Total area = 152 + 72 + 342

                 = 566 m²

Answer:

The 94% confidence interval is : ( 0.0867 , 0.1933 ) = ( 8.67 , 19.33 )%

Step-by-step explanation:

Solution:-

- The sample size, n = 150 visitors

- The proportion of visitors who hiked, p = 0.14

- We are to create a 94% confidence interval for the population proportion.

- We will determine the Z-critical value for the CI : 0.94 or significance level α = 0.06

- The critical value is defined and plucked from Z-score (standardized) tables as:

                        Z-critical = Z_α/2 = Z_0.03 = 1.88

- The confidence interval for the population proportion (p) is constructed as:

                         [tex]( p - Z-critical\sqrt{\frac{p*(1-p)}{n} } , p + Z-critical\sqrt{\frac{p*(1-p)}{n} } )\\\\( 0.14 - 1.88\sqrt{\frac{0.14*(1-0.14)}{150} } , p + 1.88\sqrt{\frac{0.14*(1-0.14)}{150} } )\\\\( 0.08673 , 0.19326 )[/tex]

- The 94% confidence interval is : ( 0.0867 , 0.1933 ) = ( 8.67 , 19.33 )%

Answer:

b. y = -7x + 4

   1.    y = -7(-5)+ 4 = 35+4= 39

   2. -24= -7x + 4

    -28 = -7x

       4 = x

    3. y = -7(0)+4= 4

    4. 0 = -7x+4

        -4= -7x

         4/7 = x

c. 3y - 5x = 15

 1. 3y - 5(6)

    3y-30=15

    3y=45

      y = 15

   2. 3(-10)-5x=15

        -30-5x=15

         -5x = 45

            x = -9

    3. 3y-5(0)=15

        3y=15

         y=5

    4. 3(0)-5x=15

         0-5x=15

          -5x=15

           x=-3

Step-by-step explanation:

Answer:

The slope of a line graphed to represent the volume of water in the pool can be described as negative.

The slope of a line graphed to represent the volume of water in a pool over time would be described as negative

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( 0 , 50 )

Let the second point be Q ( 5 , 20 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 50 - 20 ) / ( 0 - 5 )

m = 30 / -5

m = -6

Now , the slope of the line is negative and volume of water in the pool over time decreases at a rate of 6

Hence , the slope is negative

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The complete question is attached below :

The table shows the gallons of water in a pool over time. Choose the term that describes the slope of the line of a graph representing the data in the table. The slope of a line graphed to represent the volume of water in a pool over time would be described as___

The given expression 2(x − 7) + 10 matches with two times the difference of x and seven plus ten. Option B is correct.

Given that,
Which phrase matches the algebraic expression 2(x − 7) + 10 is to be determined.

In mathematics, it deals with numbers of operations according to the statements.

The procedure in mathematics to utilize and analyze the function or expression to make the function or expression uncomplicated or more coherent is called simplifying and the process is called simplification.

Here,
2(x − 7) + 10
When we turn the above algebraic expression into word phrase,

"two times the difference of x and seven plus ten"

Thus, the given algebraic expression 2(x − 7) + 10 matches with two times the difference of x and seven plus ten. Option B is correct.

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We have been given that the volume of a cone is 113.04 cubic mm. We are asked to find the approximate volume of a sphere that has the same height and a circular base with the same diameter.

We know that volume of cone is [tex]\frac{1}{3}\pi r^2\cdot h[/tex].

The height is equal to the diameter. We know that diameter is 2 times radius, so we can represent this information in an equation as:

[tex]h=2r[/tex]

Upon substituting [tex]h=2r[/tex] in volume of cone, we will get:

[tex]V=\frac{1}{3}\pi r^2\cdot 2r[/tex]

[tex]V=\frac{2}{3}\pi r^3[/tex]

We know that volume of sphere is [tex]V=\frac{4}{3}\pi r^3[/tex].

Upon comparing volume of cone with volume of sphere, we can see that volume of sphere is 2 times the volume of cone.

[tex]V=2(\frac{2}{3}\pi r^3)[/tex]

Since [tex]\frac{2}{3}\pi r^3=113.04[/tex], so volume of sphere would be:

[tex]V=2(113.04)[/tex]

[tex]V=226.08[/tex]

Therefore, volume of sphere would be 226.08 cubic mm.

Step-by-step explanation:

42° + x = 115° (alternate angles)

x = 115° - 42°

x = 73°

y = 180° - (115° + 42°) (by angle sum property of triangle)

y = 180° - 167°

y = 13°

z = 42° (corresponding angles)

Answer:

x=87.5

Step-by-step explanation:

40%=.4

.4x=35

x=35/.4

Answer:

that is pretty hard no cap but im hoping the other guy is right to help u out

Step-by-step explanation:

Answer:

#3

Step-by-step explanation:

Similar to the US highway system Rome realized if they wanted to control their territory they were going to need to be able to squash resistance that wasn't in the immediate area and move resources form place to place easily

Answer:

c

Step-by-step explanation:

i took the test

Answer:

5.7 MB

Step-by-step explanation:

1.9 + 3.8 = 5.7

Answer:

1.9+3.8=5.7 mb

Add the file sizes, and there's your answer!

:)