Rearrange the following steps in the correct order to locate the last occurrence of the smallest element in a finite list of integers, where the integers in the list are not necessarily distinct.
Rank the options below.
if min > ai then
procedure last smallest a1,a2,....,an: integers)
return location
min = a1 and location = 1
min ai and location = i
for i = 2 to n

Answer:

0.07

Step-by-step explanation:

The number of sophmores is 2+25+3 = 30.

Of these sophmores, 2 drive to school.

So the probability that a student drives to school, given that they are a sophmore, is 2/30, or approximately 0.07.

Answer:

[tex]\large \boxed{0.07}[/tex]

Step-by-step explanation:

The usual question is, "What is the probability of A, given B?"

They are asking, "What is the probability that you are driving to school if you are a sophomore (rather than taking the bus or walking)?"

We must first complete your frequency table by calculating the totals for each row and column.

The table shows that there are 30 students, two of whom drive to school.

[tex]P = \dfrac{2}{30}= \mathbf{0.07}\\\\\text{The conditional probability is $\large \boxed{\mathbf{0.07}}$}[/tex]

Answer:

Yes, he can buy 8 donuts and 4 energy drinks.

Step-by-step explanation:

If Tension is able to buy 8 donuts and 4 energy drinks, then both inequalities would be valid when we use these numbers as inputs. Let's check each expression at a time:

[tex]0.75*d + 2*e \leq 25\\0.75*8 + 2*4 \leq 25\\6 + 8 \leq 25\\14 \leq 25[/tex]

The first one is valid, since 14 is less than 25. Let's check the second one.

[tex]360*d + 110*e \geq 1000\\360*8 + 110*4 \geq 1000\\2880 + 440 \geq 1000\\3320 \geq 1000[/tex]

The second one is also valid.

Since both expressions are valid, Tension can buy 8 donuts and 4 energy drinks and achieve his goal of having a caloric surplus of at least 1000 cal.

Answer:

[tex] L= x[/tex]

And the width for this case is:

[tex] W= 5x^3 +4 -x^2[/tex]

And we know that the perimeter is given by:

[tex] P= 2L +2W[/tex]

And replacing we got:

[tex] P(x) = 2x +2(5x^3 +4 -x^2)= 2x +10x^3 +8 -2x^2[/tex]

And symplifying we got:

[tex] P(x)= 10x^3 -2x^2 +2x+8[/tex]

Step-by-step explanation:

For this problem we know that the lenght of the rectangle is given by:

[tex] L= x[/tex]

And the width for this case is:

[tex] W= 5x^3 +4 -x^2[/tex]

And we know that the perimeter is given by:

[tex] P= 2L +2W[/tex]

And replacing we got:

[tex] P(x) = 2x +2(5x^3 +4 -x^2)= 2x +10x^3 +8 -2x^2[/tex]

And symplifying we got:

[tex] P(x)= 10x^3 -2x^2 +2x+8[/tex]

Answer:

[tex] 5.10 X +9.00 Y = 831.60[/tex]

We also know that for Wedneday we have two times tickets for adults compared to child so we have

[tex] Y =2x[/tex]

And using this condition we have:

[tex] 5.10 X + 18 X = 831.60[/tex]

And solving for X we got:

[tex] X= \frac{831.60}{23.1}=36[/tex]

So then the number of tickets sold for child are 36

Step-by-step explanation:

For this problem we can set upt the following notation

X = number of tickets for child

Y= number of tickets for adults

And we know that the total revenue  for Wednesday was 831.60. So then we can set up the following equation for the total revenue

[tex] 5.10 X +9.00 Y = 831.60[/tex]

We also know that for Wedneday we have two times tickets for adults compared to child so we have

[tex] Y =2x[/tex]

And using this condition we have:

[tex] 5.10 X + 18 X = 831.60[/tex]

And solving for X we got:

[tex] X= \frac{831.60}{23.1}=36[/tex]

So then the number of tickets sold for child are 36

Answer:

[tex]n=(\frac{2.58(58.2)}{1})^2 =22546.82 \approx 22547[/tex]

So the answer for this case would be n=22547 rounded up to the nearest integer

Step-by-step explanation:

Let's define some notation

[tex]\bar X[/tex] represent the sample mean

[tex]\mu[/tex] population mean (variable of interest)

[tex]\sigma=58.2[/tex] represent the population standard deviation

n represent the sample size  

[tex] ME =1[/tex] represent the margin of error desire

The margin of error is given by this formula:

[tex] ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]    (a)

And on this case we have that ME =+1 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

[tex]n=(\frac{z_{\alpha/2} \sigma}{ME})^2[/tex]   (b)

The critical value for 99% of confidence interval now can be founded using the normal distribution. The significance would be [tex]\alpha=0.01[/tex] and the critical value [tex]z_{\alpha/2}=2.58[/tex], replacing into formula (b) we got:

[tex]n=(\frac{2.58(58.2)}{1})^2 =22546.82 \approx 22547[/tex]

So the answer for this case would be n=22547 rounded up to the nearest integer

Answer:

46 logs on the 5th row.

Step-by-step explanation:

Number of logs on the nth row is

n =  50 - (n-1)

 n = 51 - n    (so on the first row we have  51 - 1 = 50 logs).

So on the 5th row we have 51 - 5 = 46 logs.

The given relation is an arithmetic progression, which can be solved using the recursive formula: aₙ = aₙ₋₁ + d.

The 5th row has 46 logs.

An arithmetic progression is a special series in which every number is the sum of a fixed number, called the constant difference, and the first term.

The first term of the arithmetic progression is taken as a₁.

The constant difference is taken as d.

The n-th term of an arithmetic progression is found using the explicit formula:

aₙ = a₁ + (n - 1)d.

The recursive formula of an arithmetic progression is:

aₙ = aₙ₋₁ + d.

In the question, we are informed that logs are stacked in a pile. The bottom row has 50 logs and the next bottom row has 49 logs. Each row has one less log than the row below it.

The number of rows represents an arithmetic progression, with the first term being the row in the bottom row having 50 logs, that is, a₁ = 50, and the constant difference, d = -1.

We are instructed to use the recursive formula. We know the recursive formula of an arithmetic progression is, aₙ = aₙ₋₁ + d.

a₁ = 50.

a₂ = a₁ + d = 50 + (-1) = 49.

a₃ = a₂ + d = 49 + (-1) = 48.

a₄ = a₃ + d = 48 + (-1) = 47.

a₅ = a₄ + d = 47 + (-1) = 46.

Hence, the 5th row will have 46 logs.

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Answer:

Solution,

Let the points be A and B

A(7,-1)--->( X1,y1)

B(6,-4)---->(x2,y2)

Now,

[tex] slope = \frac{y2 - y1}{x2 - x1} \\ \: \: \: \: \: \: = \frac{ - 4 - ( - 1)}{6 - 7} \\ \: \: \: \: \: \: = \frac{ - 4 + 1}{ - 1} \\ \: \: \: \: \: = \frac{ - 3}{ - 1} \\ \: \: \: \: = 3[/tex]

Hope this helps..

Good luck on your assignment..

Answer:

-1/3  (given that the first co-ordinate is the initial point)

Step-by-step explanation:

slope of a line is basically the change in y divided by the change in x.

we have the 2 co-ordinates (7,-1) , (6,-4)

lets find the change in x  = 7 - 6 (the difference of the x - values of both the coordinates)

change in y = -1 - (-4)

change in x  = -1

change in y  = 3

now, slope is change in y / change in x

slope  = -1/3

Answer

X= 64.8 gives the minimum average cost

Explanation:

The question can be interpreted as

C(x)= 5x^3 -40^2 + 21000x

To find the minimum total cost, we will need to find the minimum of

this function, then Analyze the derivatives.

CHECK THE ATTACHMENT FOR DETAILED EXPLANATION

Step-by-step explanation:

given,

base( b) = 6cm

height (h)= 11cm

now, area of parallelogram (a)= b×h

or, a = 6cm ×11cm

therefore the area of parallelogram (p) is 66cm^2.

hope it helps...

Answer:

x < 11.5

Step-by-step explanation:

2x + 9 < 32

(2x + 9) - 9  < 32 - 9

2x < 23

2x/2 < 23/2

x < 11.5

Answer:

x < 11 1/2

Step-by-step explanation:

2x+9<32

Subtract 9 from each side

2x+9-9 < 32-9

2x<23

Divide by 2

2x/2 <23/2

x < 11 1/2

X is any number less than 11 1/2

Answer:

[tex]\hat p=\frac{48}{64}= 0.75[/tex] represent the estimated proportion successfull

The standard error for this case is given by this formula:

[tex] SE= \sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]

And replacing we got:

[tex] SE= \sqrt{\frac{0.75*(1-0.75)}{64}}= 0.0541[/tex]

Step-by-step explanation:

We have the following info:

[tex] n= 64[/tex] represent the sample size

[tex] X= 48[/tex]  represent the number of people classified as successful

[tex]\hat p=\frac{48}{64}= 0.75[/tex] represent the estimated proportion successfull

The standard error for this case is given by this formula:

[tex] SE= \sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]

And replacing we got:

[tex] SE= \sqrt{\frac{0.75*(1-0.75)}{64}}= 0.0541[/tex]

Answer:

16.7%

Step-by-step explanation:

Each of the six faces of a six-faced die shows one of the numbers: 1, 2, 3, 4, 5, 6.

A roll of a die is equally likely to land on any face, so the total number of possible outputs is 6, corresponding to the number of faces on the die.

The desired outcome here is 3, meaning the face that shows the number 3. Only one face has the number 3, so the number of desired outcomes is 1.

p(event) = (number of desired outcomes)/(total number of possible outcomes)

p(3) = 1/6 = 0.16666... = 16.7%

Answer:

Side 1: 40 feet

Side 2: 20 feet

Side 3: 22 feet

Step-by-step explanation:

Side 1 is twice the length of side 2 and side 2 is 20 feet, which means side 1 is 40 feet. Side 3 is the the length of the second side plus 2, which means it has a length of 22 feet.

Answer:

If our random variable of interest for this case is X="the number of teenagers between 12-17 with smartphone" we can model the variable with this distribution:

[tex] X \sim Binom(n=234, p=0.75)[/tex]

And the mean for this case would be:

[tex] E(X) =np = 234*0.75= 175.5[/tex]

And the standard deviation would be given by:

[tex] \sigma =\sqrt{np(1-p)}= \sqrt{234*0.75*(1-0.75)}= 6.624[/tex]

Step-by-step explanation:

If our random variable of interest for this case is X="the number of teenagers between 12-17 with smartphone" we can model the variable with this distribution:

[tex] X \sim Binom(n=234, p=0.75)[/tex]

And the mean for this case would be:

[tex] E(X) =np = 234*0.75= 175.5[/tex]

And the standard deviation would be given by:

[tex] \sigma =\sqrt{np(1-p)}= \sqrt{234*0.75*(1-0.75)}= 6.624[/tex]

Answer:

(a) Yes, there are 10 independent trials, each with exactly two possible outcomes, and a constant probability associated with each possible outcome.

(b) The probability that exactly 6 out of 10 randomly sampled 18- 20-year-olds consumed an alcoholic drink is 0.203.

(c) The probability that exactly 4 out of 10 randomly sampled 18- 20-year-olds have not consumed an alcoholic drink is 0.203.

(d) The probability that at most 2 out of 5 randomly sampled 18-20-year-olds have consumed alcoholic beverages is 0.167.

Step-by-step explanation:

We are given that data collected by the Substance Abuse and Mental Health Services Administration (SAMSHA) suggests that 69.7% of 18-20-year-olds consumed alcoholic beverages in 2008.

(a) The conditions required for any variable to be considered as a random variable is given by;

So, in our question; all these conditions are satisfied which means the use of the binomial distribution is appropriate for calculating the probability that exactly six consumed alcoholic beverages.

Yes, there are 10 independent trials, each with exactly two possible outcomes, and a constant probability associated with each possible outcome.

(b) Let X = Number of 18- 20-year-olds people who consumed an alcoholic drink

The above situation can be represented through binomial distribution;

[tex]P(X = r) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r}; x = 0,1,2,......[/tex]

where, n = number of trials (samples) taken = 10 people

            r = number of success = exactly 6

            p = probability of success which in our question is % 18-20

                  year-olds consumed alcoholic beverages in 2008, i.e; 69.7%.

So, X ~ Binom(n = 10, p = 0.697)

Now, the probability that exactly 6 out of 10 randomly sampled 18- 20-year-olds consumed an alcoholic drink is given by = P(X = 6)

           P(X = 3) =  [tex]\binom{10}{6}\times 0.697^{6} \times (1-0.697)^{10-6}[/tex]

                         =  [tex]210\times 0.697^{6} \times 0.303^{4}[/tex]

                         =  0.203

(c) The probability that exactly 4 out of 10 randomly sampled 18- 20-year-olds have not consumed an alcoholic drink is given by = P(X = 4)

Here p = 1 - 0.697 = 0.303 because here our success is that people who have not consumed an alcoholic drink.

           P(X = 4) =  [tex]\binom{10}{4}\times 0.303^{4} \times (1-0.303)^{10-4}[/tex]

                         =  [tex]210\times 0.303^{4} \times 0.697^{6}[/tex]

                         =  0.203

(d) Let X = Number of 18- 20-year-olds people who consumed an alcoholic drink

The above situation can be represented through binomial distribution;

[tex]P(X = r) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r}; x = 0,1,2,......[/tex]

where, n = number of trials (samples) taken = 5 people

            r = number of success = at most 2

            p = probability of success which in our question is % 18-20

                  year-olds consumed alcoholic beverages in 2008, i.e; 69.7%.

So, X ~ Binom(n = 5, p = 0.697)

Now, the probability that at most 2 out of 5 randomly sampled 18-20-year-olds have consumed alcoholic beverages is given by = P(X [tex]\leq[/tex] 2)

        P(X [tex]\leq[/tex] 2) = P(X = 0) + P(X = 1) + P(X = 3)

= [tex]\binom{5}{0}\times 0.697^{0} \times (1-0.697)^{5-0}+\binom{5}{1}\times 0.697^{1} \times (1-0.697)^{5-1}+\binom{5}{2}\times 0.697^{2} \times (1-0.697)^{5-2}[/tex]

=  [tex]1\times 1\times 0.303^{5}+5 \times 0.697^{1} \times 0.303^{4}+10\times 0.697^{2} \times 0.303^{3}[/tex]

=  0.167

Answer:

The pair of numbers is (3,3) while the maximum product is 9

Step-by-step explanation:

The pairs of numbers whose sum is 6 starting from zero is ;

0,6

1,5

2,4

3,3

Kindly note 2,4 is same as 4,2 , so there is no need for repetition

So the maximum product is 3 * 3 = 9 and the pair is 3,3

The pair of the numbers where the sum is 6 should be 3 and 3 and the maximum product is 9.

Since the sum of the pairs is 6

So, here are the following probabilities

0,6

1,5

2,4

3,3

Now if we multiply 3 and 3 so it comes 9 also it should be large

Therefore, The pair of the numbers where the sum is 6 should be 3 and 3 and the maximum product is 9.

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Answer:

[tex]3\frac{4}{5}[/tex]

Step-by-step explanation:

You first need to make the denominators the same and the LCM (least Common Multiple of this equation is 10.

10/10-->1

1/2--> 5/10

2--> 20/10

3/10, the denominator is already 10, so don't need to change.

10/10+5/10+20/10+3/10=38/10=[tex]3\frac{8}{10}[/tex]=[tex]3\frac{4}{5}[/tex]

Answer:

3 4/5

Step-by-step explanation:

hopefully this helped :3

CHECK THE ATTACHMENT FOR COMPLETE QUESTION

Answer:

We can show that ΔABC is congruent to ΔA'B'C' by a translation of 2 unit(s) Left and a Reflection across the x axis.

Step-by-step explanation:

We were given triangles ABC and A'B'C' of which were told are congruents,

Now we can provide the coordinates of A and A' from the given triangles ΔABC and ΔA'B'C' ,if we choose a point of A from ΔABC and A' from ΔA'B'C' we have these coordinates;

A as (8,8) and A' (6,-8) from the two triangles.

If we shift A to A' , we have (8_6) = 2 unit for that of x- axis

If we try the shift on the y-coordinates we will see that there is no translation.

Hence, the only translation that take place is of 2 units left.

It can also be deducted that there is a reflection

by x-axis to form A'B'C' by the ΔABC.

BEST OF LUCK

Answer:

GCF - 2

Step-by-step explanation:

24 - 1, 2, 3, 4, 6, 8, 12, 24

36 - 1, 2, 23, 46

Hope this helps! :)

The Greatest Common Factor of 24 and 46 is 2

What is Greatest Common Factor?

Greatest Common Factor is the highest number that divides exactly into two or more numbers.

Given data ,

The two numbers are 24 and 46

Factors of 24 = 1 , 2 , 3 , 4 , 6 , 12 , 24

Factors of 46 = 1 , 2 , 23 , 46

The common factor is 1 and 2

And the greatest among them is 2

Hence , the greatest common factor of 24 and 46 is 2

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Answer:

Width = 8 ft

Length = 53 ft

Height = 9 ft

Step-by-step explanation:

Let width be x

Length will be 8x-11

Height will be x + 1

Volume = width x height x length

=

x * (8x-11) * (x+1) = 3816

(8x^2 - 11x) * (x+1) = 3816

8x^3 + 8x^2 - 11x^2 - 11x = 3816

8x^3 -3x^2 - 11x = 3816

8x^3+64x^2-61x^2-488x +477x-3816= 0

8x^2 (x-8)+61x(x-8)+488(x-8)

(x-8)(8x^2 + 61x + 477) = 0

x-8

8x^2 + 61x + 477 = 0

Solve the equations:

x = 8

Length = 8x -11 = 64-11 = 53

Height = 8+1 = 9

Answer:

8w^3-3w^2-11w=3816

Step-by-step explanation:

Find the equation, in terms of w, that could be used to find the dimensions of the trailer in feet. Your answer should be in the form of a polynomial equals a constant.

Answer:

  27 years

Step-by-step explanation:

The formula for the number of payments can be used:

  N = -log(1 +0.05(1 -1000000/65000))/log(1.05) +1 = 27.03

There will be a couple thousand dollars left after the 27th payment.

The winnings will last 27 years.

Answer:

84 Ibs. 8 oz.

Step-by-step explanation:

1 pound equals 16 oz

so u add 3 to 13 which gives u 1 pound which is 9

so u subtract 93 by 9 which is 84

plus the 5 oz which is 84 pounds 8 oz

to check it u add 8 lbs and 13 by 84 lbs and 8 oz

which is 93 and 5 lbs

hope this helps

Answer:

A) [tex]\boxed{m<VYW = 47 degrees}[/tex]

B) [tex]\boxed{XY = 77 degrees}[/tex]

Step-by-step explanation:

a) According to Outside Angles theorem:

=> m∠VYW = [tex]\frac{1}{2} (VW-VX)[/tex]

Where mVX = 79, VW = 173

=> m∠VYW = (173-79)/2

=> m<VYW = 94/2

=> m∠VYW = 47 degrees

b) According to Angles of Intersecting Chords Theorem:

=> m∠VZW = [tex]\frac{1}{2} (VW+XY)[/tex]

Where m∠VZW = 64, VW = 51

=> 64 = 1/2(51+XY)

Multiplying both sides by 2

=> 64*2 = 51+XY

=> 128 = 51+XY

=> XY = 128-51

=> XY = 77 degrees

Answer:

1.7 m²

Step-by-step explanation:

Given a ∆ABC with side AB = 8 ft, side AC = 8 ft, and the angle (θ) between both sides = 35°

Thus, we can find the area of ∆ABC using the formula below:

Area of ∆ABC = ½*AB*AC*sin(θ)

Length of AB = AC = 8 ft = 2.4384 m

(Note: you must convert from ft to m since we are told to find the area in m²)

Area = ½*2.4384*2.4384*sin(35)

Area = ½*5.95*0.5736

Area = ½*3.41292

Area = 3.41292/2

Area of ∆ABC = 1.7065

Area of ∆ABC ≈ 1.7 m² (to nearest tenth)

Answer:

[tex]2\sin{\frac{x}{2}}\cos{\frac{x}{2}} = \sin{x}[/tex]

Step-by-step explanation:

The double angle formula states that:

[tex]\sin{2a} = 2\sin{a}\cos{a}[/tex]

In this question:

[tex]2\sin{\frac{x}{2}}\cos{\frac{x}{2}}[/tex]

So

[tex]a = \frac{x}{2}[/tex]

Then

[tex]2\sin{\frac{x}{2}}\cos{\frac{x}{2}} = \sin{\frac{2x}{2}} = \sin{x}[/tex]

Answer:

Step-by-step explanation:

Identify the variable in each term. If two or more terms have the same variable, they are "like" terms.*

1) Like terms are found in selection b. They are 7r and r.

__

2) The variables in selection d are u and y, not the same. Only unlike terms are found in selection d. (Selection b has variables x, b, x. The x-terms are like terms and can be combined.)

_____

* Strictly speaking, it is the constellation of variables you want to match. For example, terms 3xy, 4xy², and -5x²y all have variables x and y, but the powers of those variables don't match from term to term. For terms to be "like", the variables and their powers need to match.

Answer:

See below.

Step-by-step explanation:

There are 3 edges and 3 faces  projecting out from a vertex of a cube.

So the polygon produced would be a triangle.

Answer:

A triangle.

Step-by-step explanation:

As shown above, the plane which slices a corner intersects the polyhedron in [tex] n [/tex] faces which depend on the particular polyhedron.

Here it is a cube, and it intersects three faces. Since the intersection of two planes is a line and there are three planes to intersect with, there are three sides of the polygon.

Hence the polygon is a triangle.

Answer:

  $11,991.60

Step-by-step explanation:

An appropriate formula is ...

  A = P(1 +r/n)^(nt)

where r is the annual rate, n is the number of time per year interest is compounded, and t is the number of year. P is the principal invested.

Filling in the given numbers, we have ...

  A = $2000(1 +0.12/12)^(12·15) = $2000(1.01^180) ≈ $11,991.60

The account balance after 15 years will be $11,991.60.

Answer:  width = 300

Step-by-step explanation:

Area (A) = Length (L) x width (w)

Given: A = 268,500

           L = 3w - 5

           w = w

268,500 = (3w - 5) x (w)

268,500 = 3w² - 5w

            0 = 3w² - 5w - 268,500

            0 = (3w + 895) (w - 300)

   0 = 3w + 895        0 = w - 300

  -985/3 = w             300 = w

Since width cannot be negative, disregard w = -985/3

So the only valid answer is: w = 300

Answer:

-(14 - 7x)

7(x - 2)

3x - 14 + 4x

Step-by-step explanation:

The expressions have to equal 7x - 14.

-(14 - 7x)

-14 + 7x

7(x - 2)

7x - 14

3x - 14 + 4x

7x - 14

The equivalent expression for the given expression 7x - 14 will be 7(x – 2) and 3x – 14 + 4x.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression is 7x – 14. The equivalent expression to 7x - 14 will be,

E = 7(x – 2)

E = 7x - 14

E = 3x - 14 + 4x

E = 3x+ 4x - 14

E = 7x - 14

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