A bus company took a tour bus on the ferry when there were 30 people aboard. The ferry charged the bus company $180. The following week, the bus had 50 people on board and the ferry charged them $220. How much is the "base rate" for the empty bus? hint: look at the difference between number of people and cost to get cost per person and then cost without people
How much does each person cost?
Write an equation to show cost, c, of a bus with x number of people on it.

Answer:

8

Step-by-step explanation:

6/3 + 2 x 3

6/3 + 6

2 + 6=8

Answer:

\(2/3\)

Step-by-step explanation:

\(\frac{6}{3x}\)

\(\frac{6}{3(3)}\)

\(\frac{6}{9} =\frac{2}{3}\)

Answer:

19.99%

Step-by-step explanation:

hope this helps

here you go

Answer: subtraction property of equality

Step-by-step explanation:

88 kilometers per hour in miles per hour is 54.68 mi/hr

Note that:

1 km = 0.6214 miles

The measurement to convert is 88 kilometers per hour

Multiply 88 kilometers per hour by 0.6214 to convert to miles per hour

88 kilometers per hour = 88 x 0.6214 miles per hour

88 kilometers per hour = 54.6832 miles per hour

88 kilometers per hour =  54.68 mi/hr

Therefore, 88 kilometers per hour in miles per hour is 54.68 mi/hr

Learn more on speed conversion here: https://brainly.com/question/7716790

#SPJ1

Step-by-step explanation:

The steam-powered locomotive revolutionized commercial transportation by providing a durable, faster, cheaper way to move goods. The Governor Stanford was the first train on the Central Pacific, which became the first transcontinental railroad line in 1869 when it was joined with the Union Pacific.

Answer: 8ft

Step-by-step explanation:

the are of a square is 64

A=l x l or A=l^2

64= l^2

l=sqrt64=8

The output value of (g/f)(x) is 9x/(7x + 28).

The domain of g/f is (-∞, -4) U (-4, ∞)..

In this exercise, we would determine the corresponding composite function of f(x) and g(x) under the given mathematical operations in simplified form as follows;

(g/f)(x) = (9/(x + 4)) ÷ 7/x

By rearranging the mathematical expression using the multiplication operation, we have the following:

(g/f)(x) = (9/(x + 4)) × x/7

(g/f)(x) = 9x/(7x + 28)

For the restrictions on the domain, we would have to equate the denominator of the rational function to zero and then evaluate as follows;

7x + 28 ≠ 0

7x ≠ -28

x ≠ -4

Domain = (-∞, -4) U (-4, ∞).

Read more on domain here: brainly.com/question/17440903

#SPJ1

The sides of the triangle in order from shortest to longest are b < a < c

In triangle ABC, the side opposite angle A is denoted by a,

To determine the order of the sides from shortest to longest, we need to use the triangle inequality theorem which implies that

The side opposite the largest angle is the largest side and vice versa

So, we have

b from B = 38 degrees

a from A = 54 degrees

c from C = 88 degrees

Therefore, the order of the sides from shortest to longest is: b < a < c

In other words, the side opposite angle B is the shortest, followed by the side opposite angle A, and the side opposite angle C is the longest.

Read more about truangle inequality theorem at

https://brainly.com/question/11416388

#SPJ1

1a) The total direct manufacturing cost incurred to make 14,000 units is $187,600.

1b) The total indirect manufacturing cost incurred to make 14,000 units is $74,200.

2a) The total manufacturing cost directly traceable to the Manufacturing Department is $187,600.

2b) The total manufacturing cost, which is an indirect cost, that cannot be easily traced to the Manufacturing Department is $74,200.

3a) When the company sells 14,000 units, the total direct selling expense, which can be readily traced to individual sales representatives, is $18,200.

3b) When the company sells 14,000 units, the total indirect selling expense, which cannot be readily traced to individual sales representatives, is $14,000.

4a) The total manufacturing cost directly traceable to the Manufacturing Department per unit is $13.40.

4b) The total manufacturing cost, which is an indirect cost, that cannot be easily traced to the Manufacturing Department per unit is $5.30.

2a. Direct material cost per unit is $7.30.

2a. Direct labor cost per unit is $4.30.

2a. The Variable manufacturing overhead per unit is $1.80.

2a. The Fixed manufacturing overhead per unit is $5.30.

2a. The total manufacturing cost per unit is $18.70 ($13.40 + $5.30)

2a. The number of units produced and sold is 14,000 units.

2a. Total direct costs are $217,000 (14,000 x $13.40 + 14,000 x $2.10).

2b. Total indirect costs are $166,600 (14,000 x $5.30 + 14,000 x $6.60).

Relevant production range = 12,000 to 16,000 units

Production and sales units = 14,000 units

                                                  Average Cost

                                                       per Unit

Direct materials                                $ 7.30

Direct labor                                      $ 4.30

Variable manufacturing overhead  $ 1.80

Direct cost per unit                         $13.40

Fixed manufacturing overhead     $ 5.30

Total manufacturing cost per unit $18.70

Fixed selling expense                   $ 3.80    $53,200 ($3.80 x 14,000)

Fixed administrative expense      $ 2.80     $39,200 ($2.80 x 14,000)

Total fixed costs per unit               $6.60     $92,400 ($6.60 x 14,000)

Variable selling and admin:

Sales commissions                        $ 1.30

Variable administrative expense $ 0.80

Total variable selling and admin per unit = $2.10

1a) The total direct manufacturing cost incurred to make 14,000 units is $187,600 ($13.40 x 14,000).

1b) The total indirect manufacturing cost incurred to make 14,000 units is $74,200 ($5.30 x 14,000).

2a) The total manufacturing cost directly traceable to the Manufacturing Department is $187,600 ($13.40 x 14,000).

2b) The total manufacturing cost, which is an indirect cost, that cannot be easily traced to the Manufacturing Department is $74,200 ($5.30 x 14,000).

3) Fixed selling expenses =  $53,200 ($3.80 x 14,000)

Advertising expenses = $39,200

Sales Compensation = $14,000 ($53,200 - $39,200)

Sales Commission = $18,200 ($1.30 x 14,000)

Total Salespersons' compensation = $32,200

a) When the company sells 14,000 units, the total direct selling expense, which can be readily traced to individual sales representatives, is $18,200.

b) When the company sells 14,000 units, the total indirect selling expense, which cannot be readily traced to individual sales representatives, is $14,000.

4a) The total manufacturing cost directly traceable to the Manufacturing Department per unit is $13.40.

4b) The total manufacturing cost, which is an indirect cost, that cannot be easily traced to the Manufacturing Department per unit is $5.30.

2a. Direct material cost per unit is $7.30.

2a. Direct labor cost per unit is $4.30.

2a. The Variable manufacturing overhead per unit is $1.80.

2a. The Fixed manufacturing overhead per unit is $5.30.

2a. The total manufacturing cost per unit is $18.70 ($13.40 + $5.30)

2a. The number of units produced and sold is 14,000 units.

2a. Total direct costs are $217,000 (14,000 x $13.40 + 14,000 x $2.10).

2b. Total indirect costs are $166,600 (14,000 x $5.30 + 14,000 x $6.60).

Learn more about classifying manufacturing costs at https://brainly.com/question/13767214

#SPJ1

The approximately 99.7% of the students have commute distances between 13.9 miles and 24.1 miles, the area within two standard deviation is 95%

It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.

a) We have:

mean u = 19.0 miles,

\(\rm \sigma = 5.1 \ miles\)

According to the empirical rule, the area between \(\mu - \sigma\) and \(\mu + \sigma\) is 99.7%

\(\mu - \sigma = 19- 5.1 = 13.9\)

\(\mu + \sigma = 19+5.1 = 24.1\)

b) = P(8.8 < X < 29.2)

\(\rm P(\dfrac{8.8-\mu}{\sigma } < \dfrac{X-\mu}\sigma < \dfrac{29.2-\mu}{\sigma})\)

\(\rm P(\dfrac{8.8-19}{5.1} < Z < \dfrac{29.2-19}{5.1})\)

P(-2 < Z < 2)

Thus, the approximately 99.7% of the students have commute distances between 13.9 miles and 24.1 miles, the area within two standard deviation is 95%

Learn more about the standard deviation here:

brainly.com/question/12402189

#SPJ1

Answer:

Blue is 16.6667%

Green is 21.875%

Yellow is 28.5714%

Red is 10.7143%

Step-by-step explanation:

Set up a ratio for each amount to the total, make it a fraction, simplify or try to get to 100 with a common factor, and convert to a decimal.

Answer:

Part A) \(\frac{5}{25} or \frac{1}{5}\)

Part B) \(\frac{10}{25} or \frac{2}{5}\)

Part C) \(\frac{20}{25} or \frac{4}{5}\)

Step-by-step explanation:

First of all, the total number of tiles is 25.

For part A, all you need to do is make a fraction, like this:

# of blue tiles

# of total tiles

Now, make your fraction.

\(\frac{5}{25}\) = \(\frac{1}{5}\)

So, the probability is 5/25 or 1/5.

For part B, they are asking for both green and red. So, add the number of both green and red together, and put them as a fraction like this:

# of green and blue tiles

      # of total tiles

Make your fraction.

\(\frac{3+7}{25} = \frac{10}{25} = \frac{2}{5}\)

So, the probability is 10/15 or 2/5.

For part C, they are asking for all the colors except blue. So, add all colors (red, green, yellow) together, and put them as a fraction like this:

# of red, green, yellow tiles

      # of total tiles

Make your fraction.

\(\frac{7+10+3}{25} = \frac{20}{25} = \frac{4}{5}\)

So, the probability is 20/25 or 4/5.

Hope this helps!

Answer:

1:92

Step-by-step explanation:

that's how you write scale

pls mark brainliest

Answer:

4000+0+80+2×0.1

Step-by-step explanation:

after expanding, /means division so you diving

Answer:

Step-by-step explanation:

(a)

From the given information; we can compute the null and the alternative hypothesis as follows:

\(H_o : \mu = 38\)  

\(H_1 : \mu < 38\)

Level of significance ∝ = 1% = 0.01

The critical values of t distribution since the sample size n = 20 is:

n - 1

= 20 - 1

= 19 degree of freedom

Assuming the population  is normally distributed:

The t test can be computed by using the EXCEL FUNCTION

  = TINV(0.01, 19 )

  = 2.539483

\(t_{0.01,19} = 2.539483\)

However;

we were also given the sample mean X to be = 35 minutes

the standard deviation SD = 5 minutes

Thus; the test statistics can be computed as;

\(t = \dfrac{\bar X - \mu}{\dfrac{s}{\sqrt{n}}}\)

\(t = \dfrac{35- 38}{\dfrac{5}{\sqrt{20}}}\)

\(t = \dfrac{-3}{\dfrac{5}{4.472}}\)

\(t_o = -2.6833\)

The P-value P ( t < \(t_o\)) = P(  t < - 2.633)

= 0.007355

P-value \(\approx\) 0.0074

Decision Rule: If P - value is less than the level of significance; we are to reject the null hypothesis.

Conclusion: P-value < level of significance ; i.e 0.0074 < 0.01; so we reject the null hypothesis and accept the alternative hypothesis.

Thus; we conclude that the average time for assembling the computer board is less than 38 minutes at 0.01 level of significance.

b).

Given that:

Sample size n = 20

level of significance = 0.05

The population variance σ² is more than 22

Thus null hypothesis and the alternative hypothesis can be computed as follows:

\(H_0 : \sigma^2 = 22\)

\(H_1 : \sigma^2 < 22\)

From above;

degree of freedom  df = 19

The critical value of \(X^2\) at df = 19 and ∝ = 0.05 is = 30.14353  at the right tailed region.

\(X^2_{0.05,19} =\) 30.14353

The test statistics \(X^2\)  for the sample variance is computed as:

\(X^2= \dfrac{(n-1 )s^2}{\sigma^2}\)

\(X^2= \dfrac{(20-1 )25}{22}\)

\(X^2= \dfrac{(19)25}{22}\)

\(X^2= \dfrac{475}{22}\)

\(X^2\) = 21.5909

The P-value for the test statistics is :

= 1 - P( \(X^2\) < 21.5909)

= 1 - 0.694914

= 0.305086

The P-value = 0.305086

Decision Rule: If P - value is less than the level of significance; we are to reject the null hypothesis.

Conclusion:  SInce the P-value is greater than the level of significance ; i.e

0.305086  > 0.05 ; Therefore; we  do not reject the null hypothesis.

Therefore the data does not have sufficient information to conclude that the population variance is more than 22 at 5% level of significance.

I hope that helps a lot.

Daniela's graph of the function describing Monday's storm depicted the storm's temporal evolution, showcasing the changing intensity of rainfall, intermittent spikes, shifting wind direction, and overall duration. Analyzing the graph allowed Daniela to gain insights into the storm's behavior and better understand its impact on the area.

Daniela graphed the function describing Monday's storm and observed several key features. The graph displayed a rapid increase in precipitation during the early morning hours, with rain intensifying steadily until reaching its peak around midday. Afterward, the precipitation gradually subsided, leading to a decline in rainfall amounts throughout the afternoon and evening.

The graph exhibited a distinct pattern of fluctuation, reflecting the storm's dynamic nature. Intermittent spikes in rainfall were visible, indicating periodic bursts of heavy precipitation throughout the day. These spikes were followed by brief periods of relative calm, during which the rainfall decreased temporarily before resuming its intensity.

Furthermore, Daniela noticed a gradual shift in wind direction as the storm progressed. Initially, the wind blew from the east, but it gradually veered towards the south as the storm system moved across the region. The change in wind direction was evident on the graph, showing a gradual rotation of the wind vector over time.

The graph also revealed the storm's duration, spanning from the early morning hours until late evening. The rainfall accumulation steadily increased during the storm's initial phase and reached a maximum before gradually tapering off towards the end of the day.

for more questions on Daniela's graph

https://brainly.com/question/28699268

#SPJ8

The equation does not hold true, the ordered pair (3, 10) is not a solution of the equation y = 2x + 6.In this way, we can determine whether an ordered pair is a solution of the given equation or not.

Given the equation y = 2x + 6To determine if an ordered pair is a solution of this equation or not, substitute the values of x and y in the equation. If the equation holds true, then the ordered pair is a solution.

If it is not true, then the ordered pair is not a solution.For example, let's consider the ordered pair (1, 8).

Here, x = 1 and y = 8.Substituting these values in the given equation,

we get: y = 2x + 6 => 8 = 2(1) + 6 => 8 = 8 Since the equation holds true,

the ordered pair (1, 8) is a solution of the equation y = 2x + 6.

Now, let's consider another ordered pair, say (3, 10). Here, x = 3 and y = 10.Substituting these values in the given equation, we get: y = 2x + 6 => 10 = 2(3) + 6 => 10 = 12

To learn more about : equation

https://brainly.com/question/17145398

#SPJ8

After 4 half-lives, only 1/16th (or 0.0625) of the initial amount of the radioactive isotope will remain.

The amount of a radioactive isotope remaining after a certain number of half-lives can be calculated using the formula:

Amount remaining = Initial amount × (1/2)^(number of half-lives)

In this case, we are given the initial amount as "grams" and we want to find out the amount remaining after 4 half-lives.

So, the equation becomes:

Amount remaining = Initial amount × (1/2)^4

Since each half-life reduces the quantity to half, (1/2)^4 represents the fraction of the initial amount that will remain after 4 half-lives.

Simplifying the equation:

Amount remaining = Initial amount × (1/16)

Therefore, after 4 half-lives, only 1/16th (or 0.0625) of the initial amount of the radioactive isotope will remain.

for such more question on radioactive isotope

https://brainly.com/question/20596678

#SPJ8

Answer:

Disagree

Step-by-step explanation:

X+y equals 9 if 4 replaces x and 5 replaces y not 10.

Answer:

Solution given:

5x-6=29.

5x=29+6

x=35/5=7

x=7 is your answer

Answer:

x=7

Step-by-step explanation:

The inputs 4 and 8 have more than one out, the relation is not a function.

A relation is said to be a function if one input is mapped to one output.

that is, each x-value can only have one y-value.

From the table;

Input, output

4 ----- 1

8 ----- 3

4 ------5

8 ----- 4

4  is an input, it has an output of 1.

4 appeared again as input but this time has an output of 5.

This means one input has more than one output.

Also, 8 is an input, it has an output of 3.

8 appeared again as input but this time has an output of 4.

Which also means one input has more than one output.

Therefore, the relation is not a function.

Learn more about functions here: brainly.com/question/2541698

#SPJ1

The mean distance increased by a factor of 2^(²/₃)

The given equation for the relationship between a planet's orbital period, T and the planet's mean distance from the sun, A is;

T² = A³.

Let the orbital period of planet X = T(X).

Let the orbital period of planet Y = T(Y).

Let the mean distance of planet X from the sun = A(X).

Let the mean distance of planet Y = A(Y).

Thus;

A(Y) = 2A(X)

Therefore;

[T(Y)]² = [A(Y)]³ = [2A(X)]^3

However, [T(X)]² = [A(X)]³

Thus;

[T(Y)]² = 2³[T(X)]² * [T(Y)]²/[T(X)]² = 2³T(Y)/T(X) = 2^(³/₂)

That's for orbital period but the mean distance will increase by 2^(²/₃)

Thus we conclude that, the mean distance increased by a factor of 2^(²/₃)

Read more about factor of increase at; https://brainly.com/question/1638294

#SPJ1

Answer:

2 Superscript three-halves

Step-by-step explanation:

Edge

Answer:

Option A is the right answer mate...

Answer:

skewed to the right

Step-by-step explanation:

Given that

the mean household income for the last year was $46,200

And, the median was $37,800

In the case when the historgram is prepared so the income would be skewed to the right as the mean i..e $46,200 is more tha the median i.e. $37,800

So, the distribution would be right skewed

Hence, the same would be considered and relevant

Answer:

B) 2≤x≤8.

Step-by-step explanation:

Add 6 to all sides of the inequality.

0+6≤3x-6+6≤18+6

6≤3x≤24

Divide all sides by 3.

2≤x≤8

The correct answer is B) 2≤x≤8.

Answer:

5.4

Step-by-step explanation:

square of 29 = 5.385164807

5.385164807 estimated is 5.4

Answer:

8 and 3; 56 and 21; 896 and 336 all have the same ratio i.e. 8:3

The union of sets A and B is {1, 2, 3, 4, 5, 6, 7, 8}.

The union of two sets A and B is the set of all elements that are in A, or B, or both. In this case, the elements in set A are {1, 2, 3, 4, 5} and the elements in set B are {5, 6, 7, 8}.

To find the union of these sets, we simply combine all the elements from both sets but remove any duplicates.

Therefore, the answer that shows the union of sets A and B is {1, 2, 3, 4, 5, 6, 7, 8}, since it contains all the elements from both sets without any duplicates.

Learn more about union of sets on:

brainly.com/question/2166579

#SPJ1