Write an expression, using an exponent, that is equivalent to 9 x 9 x 9 x 9 x 9 x 9 x 9.

Answer:

[tex]s=\sqrt{\frac{\sum (x_{i} -\mu)^{2} }{N-1} }[/tex]

Step-by-step explanation:

In statistics, the standard deviation is a measure about the amount of variation of a dataset.

The variation is measured through comparison between each data and the mean of the dataset. This way, we could get a numerical information about how far are those values form the mean (which represents the central value).

The formula to find the standard deviation of a sample is

[tex]s=\sqrt{\frac{\sum (x_{i} -\mu)^{2} }{N-1} }[/tex]

Where [tex]\mu[/tex] is the sample mean and [tex]N[/tex] is the total number of values there are.

In the formula you can notice the difference between each value ([tex]x_{i}[/tex]) and the mean ([tex]\mu[/tex]), That's why the standard deviation is commonly use to measure variation.

Therefore, the answer is

[tex]s=\sqrt{\frac{\sum (x_{i} -\mu)^{2} }{N-1} }[/tex]

Answer:

d) All of the above

Step-by-step explanation:

A one way analysis of variance (ANOVA) test, is used to test whether there's a significant difference in the mean of 2 or more population or datasets (minimum of 3 in most cases).

In a one way ANOVA the critical value of the test will be a value obtained from the F-distribution.

In a one way ANOVA, if the null hypothesis is rejected, it may still be possible that two or more of the population means are equal.

This one way test is an omnibus test, it only let us know 2 or more group means are statistically different without being specific. Since we mah have 3 or more groups, using post hoc analysis to check, it may still be possible it may still be possible that two or more of the population means are equal.

The degrees of freedom associated with the sum of squares for treatments is equal to one less than the number of populations.

Let's say we are comparing the means of k population. The degree of freedom would be = k - 1

The correct option here is (d).

All of the above

The correct answer is all of the statements are true in a one-way ANOVA: the test uses the F-distribution, rejecting the null can mean two or more population means are equal, and degrees of freedom for treatment sum of squares is the number of groups minus one.

The correct answer to which statement is true in a one-way ANOVA is d. All of these.

One-way ANOVA is used to determine if there are any statistically significant differences between the means of three or more independent (unrelated) groups. The F statistic in ANOVA is always right-tailed because larger F values fall in the right tail of the F-distribution curve, leading to the rejection of the null hypothesis.

Answer:16

Step-by-step explanation:

prime factors of 16=2x2x2x2

Prime factors of 48=2x2x2x2x3

Their greatest common factor is:2x2x2x2=16

The greatest common factor of 16 and 48 is determined by listing the factors of each number and identifying the largest factor they share. In this case, the GCF of 16 and 48 is 16.

The greatest common factor (GCF) is the highest number that divides exactly into two or more numbers. To find the GCF of 16 and 48, you can list the factors of each number and find the highest factor they share.

The factors of 16 are 1, 2, 4, 8, 16. The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. The largest number that appears in both lists is 16. Therefore, the GCF of 16 and 48  is 16.

https://brainly.com/question/35541703

#SPJ3

Answer:

Brother read 8 books

Sophia read 32

Step-by-step explanation:

Number of book Sophia and her brother read is 32 and 8.

Given that;

Total number of books = 40 books

Number of book Sophia read = 4[Number of book Sophia's brother read]

Find:

Number of books each person read

Computation:

Assume;

Number of book Sophia's brother read = a

So,

Number of book Sophia read = 4a

So,

a + 4a = 40

5a = 40

a = 8

Number of book Sophia's brother read = 8 books

So,

Number of book Sophia read = 32 books

Find out more information about 'Distribution'.

https://brainly.com/question/10006924?referrer=searchResults

Answer:

87

Step-by-step explanation:

The expected value is the product of the probability and the outcome.

E = 0.98 (89)

E = 87.22

Rounded to the nearest integer, the expected number of classes is 87.

Answer:

Given:

mean, u = 6.2

sample size, n = 180

Sample mean, X' = 6.3

s.d [tex] \sigma [/tex] = 0.9

Significance level = 0.05

The null and alternative hypothesis will be:

H0 : u = 6.2

H1 : u > 6.2

Degree of freedom = 180 - 1 = 179

Using t table, the t critical value,

t> t(0.05, 179) = 1.6534

The test statistic:

[tex] t = \frac{X' - u}{\frac{\sigma}{\sqrt{n}}} [/tex]

[tex] T = \frac{6.3 - 6.2}{\frac{0.9}{\sqrt{180}}} = 1.4907 [/tex]

Since the test statistic(t calculated value) 1.4907 < t critical value (1.6534), we fail to reject the null hypothesis H0.

Answer:

$390,900

Step-by-step explanation:

Given:

Initial payment = $965

New rapayment = $925 when she decided to refinance her ballon payment with a 30 year mortgage

In this case, a 5/25 ballon mortgage simply means loan repayment for the first 5 years is at a fixed rate.

Which means the total amount she paid in the first five years was=

12 * 5 * $965 = $57,900

When she refinanced the payment with a 30 year mortgage, her total payment = $925 * 12 * 30years = $333,000

Total financed cost Patricia paid =

$57,900 + $333,000 = $390,900

Answer:

3 x 12 = 36

Step-by-step explanation:

We have been given that Maria put trim around a banner that is the shape of a triangle. Each side is 21 inches long.

The amount of trim will be equal to perimeter of triangle. The perimeter of given triangle will be 3 times each side length that is [tex]3\times 21=63[/tex] inches.

Now we need to convert 63 inches into feet.  

12 inches = 1 feet

63 inches = [tex]\frac{63}{12}[/tex]  feet = 5.25 feet.

We are also told that Maria has [tex]\frac{3}{4}[/tex] foot of trim left, so total length of trim would be trim used plus trim left that is [tex]5.25+\frac{3}{4}=5.25+0.75=6[/tex] feet.

Since we need to find length of trim in yards, so we will convert 6 feet into yards.

3 feet = 1 yard

6 feet = [tex]\frac{6}{3}[/tex] yards = 2 yards

Therefore, the length of the trim was 2 yards.

Answer:

The weight of pears is 3.08 kg

Step-by-step explanation:

A farmer sells 7.7 kilograms of apples and pears.

3/5 of this weight is apples.

This means that the weight of apples is:

3/5 of 7.7

=> [tex]\frac{3}{5} * 7.7 = 4.62kg[/tex]

The weight of apples is 4.62 kg.

The weight of pears will therefore be:

[tex]7.7 - 4.62 = 3.08 kg[/tex]

The weight of pears is 3.08 kg.

Angle 3 = 60°

Angle 4 = 60°

Step-by-step explanation:

To find angle 3 we have to use the straight angle that is formed with angle C. Angle C is the same value as angle 2 (120°) so all we have to do now is make an equation by subtracting angle C (120°) from 180°. 180°-120°=60°. So 60° is the value of angle 3.

Angle 4 is also 60° because it is the same angle as angle 3. So the value of angle 4 is 60°.

Another way to solve this problem (shown in the picture) is using the value of angle 1 (60°) and when you have the value 60° and there are triangles formed within the angle (highlighted in the picture) you know that all the angles within the triangle are going to be 60° because all angles within a triangle add up to 180°. So if we were to use this rule the equation would look like 60°+60°+60°=180°. Angle 3 in the green triangle would be equal to 60° because of the fact that one angle was already confirmed as being 60° so because of that all the angles in the triangle have to add up to 180° so the all the angles must be 60°. Angle 4 in the red triangle would also be equal to 60° for the same reason mentioned above.

So therefore the answer to this question is Angle 3 = 60° and Angle 4 = 60°

Hope this helps! If you have any more questions or you need further clarification please comment down below or message me! Good luck!

Answer:

[tex]y=0.259 x +10.447[/tex]

Now we can find the residulls like this:

[tex] e_1 = 17.3 - 17.375 = -0.075[/tex]

[tex] e_2 = 17.1 - 17.052 = 0.049[/tex]

[tex] e_3 = 17.3 - 17.311 = -0.011[/tex]

[tex] e_4 = 17.5 - 17.440 = 0.06[/tex]

[tex] e_5 = 16.9 - 16.922 = -0.022[/tex]

So then we can see that the residuals are not with an specified pattern (alternating sign) so then we can conclude that are distributed normally

Step-by-step explanation:

We have the following data given:

Height​ (inches), x 26.75 25.5 26.5 27 25

Head Circumference​ (inches), y 17.3 17.1 17.3 17.5 16.9

We need to find a linear model [tex] y = mx +b[/tex]

For this case we need to calculate the slope with the following formula:

[tex]m=\frac{S_{xy}}{S_{xx}}[/tex]

Where:

[tex]S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}[/tex]

[tex]S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}[/tex]

So we can find the sums like this:

[tex]\sum_{i=1}^n x_i =130.75[/tex]

[tex]\sum_{i=1}^n y_i =86.1[/tex]

[tex]\sum_{i=1}^n x^2_i =3422.06[/tex]

[tex]\sum_{i=1}^n y^2_i = 1482.85[/tex]

[tex]\sum_{i=1}^n x_i y_i =2252.28[/tex]

With these we can find the sums:

[tex]S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=3422.06-\frac{130.75^2}{5}=2.95[/tex]

[tex]S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}=2252.28-\frac{130.75*86.1}{5}=0.765[/tex]

And the slope would be:

[tex]m=\frac{0.765}{2.95}=0.259[/tex]

Nowe we can find the means for x and y like this:

[tex]\bar x= \frac{\sum x_i}{n}=\frac{130.75}{5}=26.15[/tex]

[tex]\bar y= \frac{\sum y_i}{n}=\frac{86.1}{5}=17.22[/tex]

And we can find the intercept using this:

[tex]b=\bar y -m \bar x=17.22-(0.259*26.15)=10.447[/tex]

So the line would be given by:

[tex]y=0.259 x +10.447[/tex]

Now we can find the residulls like this:

[tex] e_1 = 17.3 - 17.375 = -0.075[/tex]

[tex] e_2 = 17.1 - 17.052 = 0.049[/tex]

[tex] e_3 = 17.3 - 17.311 = -0.011[/tex]

[tex] e_4 = 17.5 - 17.440 = 0.06[/tex]

[tex] e_5 = 16.9 - 16.922 = -0.022[/tex]

So then we can see that the residuals are not with an specified pattern (alternating sign) so then we can conclude that are distributed normally

Answer:

y = (-5/3)x + 3

Step-by-step explanation:

slope intercept form: y = mx + b

Isolate the variable, y. Note the equal sign, what you do to one side, you do to the other.

First, add 9 to both sides:

3y - 9 (+9) = -5x (+9)

3y = -5x + 9

Next, divide 3 from both sides:

(3y)/3 = (-5x + 9)/3

y = (-5/3)x + 3

y = (-5/3)x + 3 is your answer.

~

Answer:

-3/4

Step-by-step explanation:

9/10 ÷ (-6/5)

Copy dot flip

9/10 * -5/6

Rewriting

-5/10 * 9/6

-1/2 * 3/2

-3/4

Answer: -3/4

Step-by-step explanation: Remember that dividing by a fraction is the same thing as multiplying by the reciprocal of that fraction or that fraction flipped.

In other words we can rewrite 9/10 ÷ -6/5 as 9/10 · -5/6.

Before multiplying however, notice that we can cross-cancel

the 9 and 6 to 3 and 2 and the 5 and 10 to 1 and 2.

So we now have 3/2 · -1/2.

Now multiplying across the numerators

and denominators we get -3/4.

Answer:

[tex]\displaystyle A = \int\limits^{33}_{5} {\frac{1}{x}} \, dx[/tex]

[tex]\displaystyle A = \ln \frac{33}{5}[/tex]

General Formulas and Concepts:

Algebra II

Calculus

Integration

Integration Rule [Fundamental Theorem of Calculus 1]:                                     [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]

Area of a Region Formula:                                                                                     [tex]\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle y = \frac{1}{x}[/tex]

Bounds: [5, 33]

Step 2: Find Area

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

Answer:

18.66

Step-by-step explanation:

2.41 + 15.8 + 0.45

Rectangle square rhombus

Step-by-step explanation:

Answer:

The 90% confidence interval for the population proportion of all train travelers who do not buy a ticket is (0.08, 0.16).

Step-by-step explanation:

The (1 - α)% confidence interval for the population proportion is:

[tex]CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]

The information provided is:

n = 200

X = 24

Confidence level = 90%

Compute the value of sample proportion as follows:

[tex]\hat p=\frac{X}{n}=\frac{24}{200}=0.12[/tex]

Compute the critical value of z for 90% confidence level as follows:

[tex]z_{\alpha/2}=z_{0.10/2}=z_{0.05}=1.645[/tex]

Compute the 90% confidence interval for the population proportion of all train travelers who do not buy a ticket as follows:

[tex]CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]

     [tex]=0.12\pm 1.645\times\sqrt{\frac{0.12(1-0.12)}{200}}\\\\=0.12\pm0.038\\=(0.082, 0.158)\\\approx (0.08, 0.16)[/tex]

The 90% confidence interval for the population proportion of all train travelers who do not buy a ticket is (0.08, 0.16).

The 90% confidence interval (0.08, 0.16) for the population proportion of all train travelers who do not buy a ticket implies that there is a 0.90 probability that the true proportion lies in this interval.

Or if 100 such intervals are computed then 90 of those intervals will consist of the true proportion.

Answer:

100-x represents the distance that Serena hit with her 9-iron. 2(100-x) represents the distance she can hit using her driver.

When the distance is given for the 9-iron, use the distributive property to find the simplified equation, so it will be much easier to solve after you are given the information on the 9-iron. Unsolvable without 9-iron distance.

Step-by-step explanation:

Hence, it is unsolvable without [tex]9[/tex] iron distance.

What is the yards?

A yard is a unit of length in both US Customary and British Imperial Systems of Measurement.

It is equivalent to [tex]3[/tex] feet or [tex]36[/tex] inches. Its symbol is yd. It is often used to measure the length of medium-sized objects.

Here, [tex]100-x[/tex] represents the distance that Serena hit with her [tex]9[/tex]-iron, and [tex]2(100-x)[/tex]  represents the distance she can hit using her driver.

Now using the distributive property, it will be easier to solve about the information of nine-iron.

Hence, it is unsolvable without [tex]9[/tex] iron distance.

To know more about the yards

https://brainly.com/question/14516546

#SPJ5

Answer:

The production level that will maximize the revenue is 1800 (in thousands of phones produced), that is, production of 1,800,000 phones will maximize the revenue.

Step-by-step explanation:

The price per unit of phone is given as

p = 45 - 0.0125x

where x is in thousands of phones produced

Revenue = (price per unit) × (number of units)

Revenue = (45 - 0.0125x) × x

= (45x - 0.0125x²)

To find the maximum revenue, we need to obtain the maximum value of the revenue function.

R(x) = (45x - 0.0125x²)

At maximum point, (dR/dx) = 0 and (d²R/dx²) < 0

R(x) = (45x - 0.0125x²)

(dR/dx) = 45 - 0.025x

at maximum point, (dR/dx) = 0

(dR/dx) = 45 - 0.025x = 0

0.025x = 45

x = (45/0.025) = 1800

Hence, the production level that will maximize the revenue is 1800 (in thousands of phones produced)

That maximum revenue is thus

R(x) = (45x - 0.0125x²)

R(1800) = (45×1800) - (0.0125×1800²)

= 40,500

Hope this Helps!!!

To find the production level that will maximize revenue, we need to find the critical point of the revenue equation and determine if it is a maximum or minimum. Then we can find the corresponding production level.

To find the production level that will maximize revenue, we need to find the value of x that maximizes the revenue equation R(X)=X*p. The revenue equation can be written as R(X) = X*(45 - 0.0125x). To maximize revenue, we can find the x-value where the derivative of the revenue equation is equal to zero. After finding this critical point, we can check if it is a maximum or minimum by analyzing the second derivative. Finally, we can substitute this x-value back into the original equation to find the corresponding production level.

https://brainly.com/question/34073789

#SPJ11

Answer:

2 1/4 hours

Step-by-step explanation:

Each night, he read for 3/4 hours = 3*60/4 = 45 minutes.

He read for 3 days.

So in total, he read for:

3*45 = 135 minutes.

135 minutes is 2 hours and 15 minutes. 15 minutes is 1/4 of an hour.

So the correct answer is:

2 1/4 hours

To find the expected number of white marbles in future pulls, calculate the probability of pulling a white marble from the current results, then multiply this probability by the number of new pulls.

To solve this problem, we will first identify the probability of pulling a white marble out of the bag based on Maria's results. Then, we will multiply this probability by the number of new marbles being pulled out (20) to determine the expected number of white marbles.

Note: Since the outcomes are being replaced, the probabilities don't change after each pull.

https://brainly.com/question/37190983

#SPJ12

Answer:

a) 1,518,000

b) 2,284,880

c) 60,720

Step-by-step explanation:

a) a. if the first letter must be Upper C comma Upper X comma Upper T comma or Upper M and no letter may be​ repeated?

We draw 5 boxes, and based on that we will see the total possible cases. There are 26 alphabets

The first box should have C or X or T or M .No letter may be repeated.

Any                    Any             Any                 Any                    Any

5 alphabets    of the            of the              of the                 of the

C,X , T , M      remaining     remaining       remaining          remaining

                   25 alphabets   24 alphabets   23 alphabets   22 alphabets

Therefore; total possible call letters = 5 × 25 × 24 × 23 × 22 = 1,518,000

b)

The first box should have C or X or T or M Repeats as allowed

Any                    Any             Any                 Any                    Any

5 alphabets    of the            of the              of the                 of the

C,X , T , M      remaining     remaining       remaining          remaining

                   26 alphabets   26 alphabets   26 alphabets   26 alphabets

Therefore Total possible call letters = 5 × 26 × 26 × 26 × 26 = 2,284,880

c)   The first box should have   C,X , T , M  and end with S

So the last place if fixed, and we now have 25 alphabets. The first box can go in 5 ways. The next box then will have only 24 letters to choose from, as the first box has taken a letter and the last box already has S in it. Repetition not allowed

Any                    Any             Any                 Any                       S

5 alphabets    of the            of the              of the                  is fixed

C,X , T , M      remaining     remaining       remaining           here

                   24 alphabets   23 alphabets   22 alphabets  

Therefore Total possible call letters = 5 × 24 × 23 × 22  × 1 =  60,720

a. 30,240 different call letters can be made if the first letter must be C, X, T, or M and no letter may be repeated. b. 11,881,376 different call letters can be made if repeats are allowed. c. 22,464 different call letters can be made if the call letters start with C, X, T, or M, have no repeats, and end with S.

a. If the first letter must be C, X, T, or M, and no letter may be repeated, the options for the first letter are 4. For the remaining 4 positions, we can choose from 25 letters (all except the first letter chosen). Therefore, the total number of different 5-letter radio station call letters is 4 * 25 * 24 * 23 * 22 = 30,240.

b. If repeats are allowed, including the first letter being C, X, T, or M, we still have 26 options for each position (including the possibility of repeating the first letter chosen). Therefore, the total number of different 5-letter radio station call letters is 26 * 26 * 26 * 26 * 26 = 26^5 = 11,881,376.

c. To have no repeats and end with the letter S, we have 24 options for the first position (all letters except C, X, T, or M) and 1 option for the last position (the letter S). For the remaining 3 positions, we can choose from 24 letters (all except the first and last position chosen). Therefore, the total number of different 5-letter radio station call letters starting with C, X, T, or M and ending with S is 4 * 24 * 24 * 24 * 1 = 22,464.

https://brainly.com/question/32730304

#SPJ3

Answer:560

Step-by-step explanation:

Let a be the number of students the school have last year

135% of a=756

135/100 x a=756

135a/100=756

Cross multiplying we get

135a=756 x100

135a=75600

Divide both sides by 135

135a/135=75600/135

a=560

Answer:

Check the explanation

Step-by-step explanation:

(a) The appropriate test is the matched-pairs test because a student’s score on Try 1 is certainly correlated with his/her score on Try 2. Using the differences, we have xbar =  29 and s = 59.

(b) To test H0: mu=0 vs.  H1 mu > 0, we compute

[tex]t = (29-0)/((59/sqrt(427))=10.16[/tex]

with df = 426. This is certainly significant, with P < 0.0005. Coached students do improve their scores on average

(a) H0: μ1 = μ2 vs. Ha: μ1 > μ2, where μ1 is the mean gain among all coached students and μ2 is the mean gain among uncoached students. H0 and Ha. Using the conservative approach, df = 426 is rounded down to df = 100 in  (t table) and we obtain 0.0025 < P < 0.005. Using software, df = 534.45 and P = 0.004. There is evidence that coached students had a greater average increase.

(b) 8 ± t*(3.0235) where t* equals 2.626 (using df = 100 with (t table) ) or 2.585 (df = 534.45 with software). This gives either 0.06 to 15.94 points, or 0.184 to 15.816 points, respectively.

(c) Increasing one’s score by 0 to 16 points is not likely to make a difference in being granted admission or scholarships from any colleges.

Answer:

The 98% confidence interval for the population proportion p is (0.4149, 0.6695).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 83, \pi = \frac{45}{83} = 0.5422[/tex]

98% confidence level

So [tex]\alpha = 0.02[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.02}{2} = 0.99[/tex], so [tex]Z = 2.327[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5422 - 2.327\sqrt{\frac{0.5422*0.4578}{83}} = 0.4149[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5422 + 2.327\sqrt{\frac{0.5422*0.4578}{83}} = 0.6695[/tex]

The 98% confidence interval for the population proportion p is (0.4149, 0.6695).

Answer:

116

Step-by-step explanation:

8.2 / 2 = 4.1

a = [tex]\sqrt{7^{2}-4.1^{2} } = 5.6736[/tex]

0.5 x 8.2 x 5.6736 = 23.2618

23.2618 x 5 = 116.309 = 116

Answer:

4x + 7 = x + 10: x = 1!

Step-by-step explanation:

Not sure if you wanted me to solve as well; but I figured I would do it just in case!

To solve this, use the following steps!:

[tex]4x+7=x+10\\-7\\4x=x+3\\-x\\3x=3\\x=1![/tex]

x = 1 Should be the correct answer!

The sum of four times a number and seven is ten more than the number can be express as follows:

4x - 3

let

the number = x

Therefore,

Four times the number = 4x

Seven is ten more than the number is as follows:

Therefore, the sum of four times a number and seven is ten more than the number is as follows:

learn more on variable here: https://brainly.com/question/18681264

Answer: It should be used 2 for type-A and 3 for type-B to minimize the cost.

Step-by-step explanation: As it is stipulated, x relates to type-A and y to type-B.

Type-A has 60 deluxe cabins and B has 80. It is needed a minimum of 360 deluxe cabins, so:

60x + 80y ≤ 360

For the standard cabin, there are in A 160 and in B 120. The need is for 680, so:

160x + 120y ≤ 680

To calculate how many of each type you need:

60x + 80y ≤ 360

160x + 120y ≤ 680

Isolating x from the first equation:

x = [tex]\frac{360 - 80y}{60}[/tex]

Substituing x into the second equation:

160([tex]\frac{360 - 80y}{60}[/tex]) + 120y = 680

-3200y+1800y = 10200 - 14400

1400y = 4200

y = 3

With y, find x:

x = [tex]\frac{360 - 80y}{60}[/tex]

x = [tex]\frac{360 - 80.3}{60}[/tex]

x = 2

To determine the cost:

cost = 42,000x + 51,000y

cost = 42000.2 + 51000.3

cost = 161400

To keep it in a minimun cost, it is needed 2 vessels of Type-A and 3 vessels of Type-B, to a cost of $161400