Identify the independent and dependent variables for this study. The independent variable is the ratio of students to faculty using the stairs, and the dependent variable is the length of time the signs were posted. The independent variable is whether the motivational signs were posted, and the dependent variable is the amount of use of the stairs. The independent variable is the amount of use of the stairs, and the dependent variable is whether the motivational signs were posted. The independent variable is the time when the motivational signs were posted, and the dependent variable is the amount of use of the stairs. What scale of measurement is used for the independent variable

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:

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.

Learn more about arithmetic progressions at

https://brainly.com/question/7882626

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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:

see below

Step-by-step explanation:

Let x be the original price

x* discount rate = discount

x * 60% = 30

Change to decimal form

x * .60 = 30

Divide each side by .60

x = 30/.60

x =50

The original price was 50 dollars

Answer:

A-30     B-20    C-50

Step-by-step explanation:

Answer:

k = -6

Step-by-step explanation:

hello

saying that (x-2) is a factor of [tex]x^2+x+k[/tex]

means that 2 is a zero of

[tex]x^2+x+k=0 \ so\\2^2+2+k=0\\<=> 4+2+k=0\\<=> 6+k =0\\<=> k = -6[/tex]

and we can verify as

[tex](x^2+x-6)=(x-2)(x+3)[/tex]

so it is all good

hope this helps

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:

-10, 40, -240, 1,920 and -19, 200

Step-by-step explanation:

Given the recurrence relation of the sequence defined as aₙ₊₁ = -2naₙ for n = 1, 2, 3... where a₁ = 5, to get the first five terms of the sequence, we will find the values for when n = 1 to n =5.

when n= 1;

aₙ₊₁ = -2naₙ

a₁₊₁ = -2(1)a₁

a₂ = -2(1)(5)

a₂ = -10

when n = 2;

a₂₊₁ = -2(2)a₂

a₃ = -2(2)(-10)

a₃ = 40

when n = 3;

a₃₊₁ = -2(3)a₃

a₄ = -2(3)(40)

a₄ = -240

when n= 4;

a₄₊₁ = -2(4)a₄

a₅ = -2(4)(-240)

a₅ = 1,920

when n = 5;

a₅₊₁ = -2(5)a₅

a₆ = -2(5)(1920)

a₆ = -19,200

Hence, the first five terms of the sequence is -10, 40, -240, 1,920 and -19, 200

Answer:

The answer to the equation from question 7 is 14.

Step-by-step explanation:

In question 7, we are given an equation.

2³ + (8 - 5)² - 3

First, subtract 5 from 8 in the parentheses.

2³ + 3² - 3

Next, solve the exponents for 2³ and 3².

8 + 9 - 3

Add 8 to 9.

17 - 3

Subtract 3 from 17.

14

So, the answer to this equation from question 7 is 14.

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:

[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

The discontinuity occurs when x is either -5 or 3.

That is determined by solving denominator = 0 quadratic equation for x.

Hope this helps.

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:

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%

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:

Step-by-step explanation:

Least common denominator = a²b²

[tex]\frac{3}{a^{2}}+\frac{2}{ab^{2}}=\frac{3*b^{2}}{a^{2}*b^{2}}+\frac{2*a}{ab^{2}*a}\\\\=\frac{3b^{2}}{a^{2}b^{2}}+\frac{2a}{a^{2}b^{2}}\\\\=\frac{3b^{2}+2a}{a^{2}b^{2}}[/tex]

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:

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.

Learn more about numbers here: https://brainly.com/question/13902300

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:

[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:

the answer is D

Step-by-step explanation:

Answer:

95°

Step-by-step explanation:

To get the value of n° we must get the values of the traingle angle's sides

and to do that :

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:

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:

  $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:

16$

Step-by-step explanation:

8*2=16

HOPE THIS HELPS :)

Answer: $16

Step-by-step explanation:

As the book was purchased for half its price plus 8 you can create the equation 1/2x + 8 = x.  Then, simplifying the expression you get x = 16.  Thus, the book costs 16 dollars.

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:  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

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

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:

No

Step-by-step explanation:

Let's check the first statement with an example. 2 and 3 are positive numbers and their sum (5) is also positive so his first statement is true.

To check the second statement let's look at the negative numbers -1 and -8 for example. Their sum (-9) is also negative so his second statement is true.

To check the third statement let's look at the numbers 9 and -5. One is positive and one is negative, but their sum (4) is positive, so his third statement is false. However if we look at the numbers 4 and -7, their sum is negative so the third statement is partially false.

Answers:

please see the attached picture for full solution..

Hope it helps....

Good luck on your assignment...