Gabe rolls a six sided die twenty times, and records the result in the table below. How many times did Gabe roll above the average?

__________
3 6 2 3 4
__________
5 1 4 2 3
__________
2 2 2 3 1
__________
5 6 1 3 2
__________

A. 2
B. 3
C. 5
D. 6

Answer:

736 Newtons

Step-by-step explanation:

Given

Pressure = [tex]\frac{Force}{Area}[/tex]

Multiply both sides by Area

Area × Pressure = Force

Area = 2.3 × 1.6 = 3.68 m², hence

Force = 3.68 × 200 = 736 Newtons

Answer:True

Step-by-step explanation:

Given Fran earn [tex]\$ 225[/tex] per week working 15 hr

i.e. in 7 days he earn [tex]\$ 225[/tex]

in 1 day [tex]\frac{225}{7}[/tex]

i.e. in 15 hr he earns [tex]\frac{225}{7}[/tex]

in 1 hr  [tex]\$ \frac{15}{7}[/tex]

he has to earn [tex]\$600 [/tex]extra to make [tex]\$1400[/tex]

i.e. he needs to work [tex]\frac{600\times 7}{15}[/tex]hr extra

For 20 weeks he needs to work 2 hr extra

i.e. total 17 hr per day to save [tex]\$ 1400[/tex]

she needs to work atleast 17 hr

Answer:

B on edgenuity

Step-by-step explanation:

Answer:

[tex]8\frac{19}{20}[/tex] in.

Step-by-step explanation:

To find your answer, subtract.

[tex]12\frac{3}{4}[/tex] may be rewritten as [tex]\frac{51}{4}[/tex] and [tex]3\frac{4}{5}[/tex] may be rewritten as [tex]\frac{19}{5}[/tex]

Establish a common denominator, which would be the lowest common multiple of 4 and 5, which is 20. Multiply both parts of your first fraction by 5 to get a denominator of 20, and both parts of your second fraction by 4 to get a denominator of 20.

[tex]\frac{51}{4} *\frac{5}{5} =\frac{255}{20}[/tex]

and

[tex]\frac{19}{5} *\frac{4}{4} =\frac{76}{20}[/tex]

Subtract.

[tex]\frac{255}{20} -\frac{76}{20} =\frac{179}{20}[/tex]

This fraction may be rewritten as [tex]8\frac{19}{20}[/tex].

Answer:

[tex]8\frac{19}{20}[/tex] inches.

Step-by-step explanation:

Average rainfall of Tucson = [tex]12\frac{3}{4}[/tex] inches

                                              or  [tex]\frac{51}{4}[/tex] inches

Average rainfall of Yuma =  [tex3\frac{4}{5}[/tex] inches

                                              or  [tex]\frac{19}{5}[/tex] inches

Now we have to find the fifference of average rainfall in Tucson as compared to Yuma.

Difference =  [tex]\frac{51}{4}[/tex] -  [tex]\frac{19}{5}[/tex]

                  =  [tex]\frac{255-76}{20}[/tex]

                  =  [tex]\frac{179}{20}[/tex]

                  =  [tex]8\frac{19}{20}[/tex] inches.

Answer:

1. reflection across x-axis

2. translation 6 units to the right and 3 units up (x+6,y+3)

Step-by-step explanation:

The trapezoid ABCD has it vertices at points A(-5,2), B(-3,4), C(-2,4) and D(-1,2).

First transformation is the reflection across the x-axis with the rule

(x,y)→(x,-y)

so,

Second transformation is translation 6 units to the right and 3 units up with the rule

(x,y)→(x+6,y+3)

so,

Answer:

Step-by-step explanation:

In all of these problems, the key is to remember that you can undo a trig function by taking the inverse of that function.  Watch and see.

a.  [tex]sin2\theta =-\frac{\sqrt{3} }{2}[/tex]

Take the inverse sin of both sides.  When you do that, you are left with just 2theta on the left.  That's why you do this.

[tex]sin^{-1}(sin2\theta)=sin^{-1}(-\frac{\sqrt{3} }{2} )[/tex]

This simplifies to

[tex]2\theta=sin^{-1}(-\frac{\sqrt{3} }{2} )[/tex]

We look to the unit circle to see which values of theta give us a sin of -square root of 3 over 2.  Those are:

[tex]2\theta =\frac{5\pi }{6}[/tex] and

[tex]2\theta=\frac{7\pi }{6}[/tex]

Divide both sides by 2 in both of those equations to get that values of theta are:

[tex]\theta=\frac{5\pi }{12},\frac{7\pi }{12}[/tex]

b.  [tex]tan(7a)=1[/tex]

Take the inverse tangent of both sides:

[tex]tan^{-1}(tan(7a))=tan^{-1}(1)[/tex]

Taking the inverse tangent of the tangent on the left leaves us with just 7a.  This simplifies to

[tex]7a=tan^{-1}(1)[/tex]

We look to the unit circle to find which values of a give us a tangent of 1.  They are:

[tex]7\alpha =\frac{5\pi }{4},7\alpha =\frac{\pi }{4}[/tex]

Dibide each of those equations by 7 to find that the values of alpha are:

[tex]\alpha =\frac{5\pi}{28},\frac{\pi}{28}[/tex]

c.  [tex]cos(3\beta)=\frac{1}{2}[/tex]

Take the inverse cosine of each side.  The inverse cosine and cosine undo each other, leaving us with just 3beta on the left, just like in the previous problems.  That simplifies to:

[tex]3\beta=cos^{-1}(\frac{1}{2})[/tex]

We look to the unit circle to find the values of beta that give us the cosine of 1/2 and those are:

[tex]3\beta =\frac{\pi}{6},3\beta  =\frac{5\pi}{6}[/tex]

Divide each of those by 3 to find the values of beta are:

[tex]\beta =\frac{\pi }{18} ,\frac{5\pi}{18}[/tex]

d.  [tex]sec3\alpha =-2[/tex]

Let's rewrite this in terms of a trig ratio that we are a bit more familiar with:

[tex]\frac{1}{cos(3\alpha) } =\frac{-2}{1}[/tex]

We are going to simplify this even further by flipping both fraction upside down to make it easier to solve:

[tex]cos(3\alpha)=-\frac{1}{2}[/tex]

Now we will take the inverse cos of each side (same as above):

[tex]3\alpha =cos^{-1}(-\frac{1}{2} )[/tex]

We look to the unit circle one last time to find the values of alpha that give us a cosine of -1/2:

[tex]3\alpha =\frac{7\pi}{6},3\alpha  =\frac{11\pi}{6}[/tex]

Dividing both of those equations by 3 gives us

[tex]\alpha =\frac{7\pi}{18},\frac{11\pi}{18}[/tex]

And we're done!!!

Answer:

1.5

2.11

3.4

4.10

Step-by-step explanation:

We are given that store the following vectors of 15 values as an object in your workspace :

6,9,7,3,6,7,9,6,3,6,6,7,1,9,1

We have to find the number of elements

1.equal to  6

2. equal  or greater than 6

3.less than 6

4.not equal to 6

The 15 vectors are arrange in increasing order then we get

1,1,3,3,6,6,6,6,6,7,7,7,9,9,9

1.6,6,6,6,6

There are five elements which is equal to 6.

2.Number of elements equal or greater than 6=6,6,6,6,6,7,7,7,9,9,9=11

There are eleven elements which is equal or greater than 6.

3. Number of elements which is less than 6=1,1,3,3=4

There are four elements which is less than 6.

4.Number of elements which is not equal to 6=1,1,3,3,7,7,7,9,9,9=10

There are ten elements which is less than 6.

Answer:

(4,0)

Step-by-step explanation:

The object is first at (0,0)

It is reflected across line x=-2, this means you draw the mirror line at x=-2 and count 2 equal units backwards to get the image.The image will be at ;[tex]y=0\\\\x=-2-2=-4\\\\\\=(-4,0)[/tex]

The image (-4,0) is then reflected on the y-axis

You know reflection on the y-axis, the y-coordinate remains the same but the x-coordinate is changed to its opposite sign.

Hence;

(- -4,0)= (4,0)

The image will move 8 units towards positive x-axis.This is the same as moving 4 units from the mirror line at (0,0) and land at (4,0)

For this case we have the following expression:

[tex]\sqrt [3] {5x-2} - \sqrt [3] {4x} = 0[/tex]

If we add to both sides of the equation [tex]\sqrt [3] {4x}[/tex] we have:

[tex]\sqrt [3] {5x-2} = \sqrt [3] {4x}[/tex]

To eliminate the roots we must raise both sides to the cube:

[tex](\sqrt [3] {5x-2}) ^ 3 = (\sqrt [3] {4x}) ^ 3\\5x-2 = 4x[/tex]

So, the correct option is the option c

Answer:

Option C

Answer:

C

Step-by-step explanation:

By the conditional property we have:

If A and B are two events then A and B are independent if:

                  [tex]P(A|B)=P(A)[/tex]

                               or

                 [tex]P(B|A)=P(B)[/tex]

( since,

if two events A and B are independent then,

[tex]P(A\bigcap B)=P(A)\times P(B)[/tex]

Now we know that:

[tex]P(A|B)=\dfrac{P(A\bigcap B)}{P(B)}[/tex]

Hence,

[tex]P(A|B)=\dfrac{P(A)\times P(B)}{P(B)}\\\\i.e.\\\\P(A|B)=P(A)[/tex] )

Based on the diagram that is given to us we observe that:

Region A covers two parts of the total area.

Hence, Area of Region A= 72/2=36

Hence, we have:

[tex]P(A)=\dfrac{36}{72}\\\\i.e.\\\\P(A)=\dfrac{1}{2}[/tex]

Also,

Region B covers two parts of the total area.

Hence, Area of Region B= 72/2=36

Hence, we have:

[tex]P(B)=\dfrac{36}{72}\\\\i.e.\\\\P(B)=\dfrac{1}{2}[/tex]

and A∩B covers one part of the total area.

i.e.

Area of A∩B=74/4=18

Hence, we have:

[tex]P(A\bigcap B)=\dfrac{18}{72}\\\\i.e.\\\\P(A\bigcap B)=\dfrac{1}{4}[/tex]

Hence, we have:

[tex]P(A|B)=\dfrac{\dfrac{1}{4}}{\dfrac{1}{2}}\\\\i.e.\\\\P(A|B)=\dfrac{2}{4}\\\\i.e.\\\\P(A|B)=\dfrac{1}{2}[/tex]

Hence, we have:

[tex]P(A|B)=P(A)[/tex]

         Similarly we will have:

[tex]P(B|A)=P(B)[/tex]

bearing in mind that perpendicular lines have negative reciprocal slopes, let's find firstly the slope of AC.

[tex]\bf (\stackrel{x_1}{2}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{6}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{6-1}{1-2}\implies \cfrac{5}{-1}\implies -5 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{\cfrac{-5}{1}}\qquad \qquad \qquad \stackrel{reciprocal}{\cfrac{1}{-5}}\qquad \stackrel{negative~reciprocal}{\cfrac{1}{5}}}[/tex]

so, we're really looking for the equation of a line whose slope is 1/5 and that passes through (3,3)

[tex]\bf (\stackrel{x_1}{3}~,~\stackrel{y_1}{3}) ~\hspace{10em}slope = m\implies \cfrac{1}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-3=\cfrac{1}{5}(x-3) \implies y-3=\cfrac{1}{5}x-\cfrac{3}{5} \\\\\\ y=\cfrac{1}{5}x-\cfrac{3}{5}+3\implies y=\cfrac{1}{5}x+\cfrac{12}{5}[/tex]

Answer:

det(A) = (-6)(-2) - (-4)(-7)

Step-by-step explanation:

The determinat of the following matrix:

[tex]\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right][/tex]

Is given by: Determinant a*d - b*c

In this case, a=-6, b=-7, c=-4 and d=-2.

Therefore the determinant is: (-6)(-2) - (-7)(-4).

Therefore, the correct option is the third one:

det(A) = (-6)(-2) - (-4)(-7)

Answer:

C det(A) = (–6)(–2) – (–4)(–7)

Step-by-step explanation:

EDGE 2020

~theLocoCoco

Answer:

Let X be the event of feeling secure after saving $50,000,

Given,

The probability of feeling secure after saving $50,000, p = 40 % = 0.4,

So, the probability of not  feeling secure after saving $50,000, q = 1 - p = 0.6,

Since, the binomial distribution formula,

[tex]P(x=r)=^nC_r p^r q^{n-r}[/tex]

Where, [tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]

If 8 households choose randomly,

That is, n = 8

(a) the probability of the number that say they would feel secure is exactly 5

[tex]P(X=5)=^8C_5 (0.4)^5 (0.6)^{8-5}[/tex]

[tex]=56(0.4)^5 (0.6)^3[/tex]

[tex]=0.12386304[/tex]

(b) the probability of the number that say they would feel secure is more than five

[tex]P(X>5) = P(X=6)+ P(X=7) + P(X=8)[/tex]

[tex]=^8C_6 (0.4)^6 (0.6)^{8-6}+^8C_7 (0.4)^7 (0.6)^{8-7}+^8C_8 (0.4)^8 (0.6)^{8-8}[/tex]

[tex]=28(0.4)^6 (0.6)^2 +8(0.4)^7(0.6)+(0.4)^8[/tex]

[tex]=0.04980736[/tex]

(c) the probability of the number that say they would feel secure is at most five

[tex]P(X\leq 5) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5)[/tex]

[tex]=^8C_0 (0.4)^0(0.6)^{8-0}+^8C_1(0.4)^1(0.6)^{8-1}+^8C_2 (0.4)^2 (0.6)^{8-2}+8C_3 (0.4)^3 (0.6)^{8-3}+8C_4 (0.4)^4 (0.6)^{8-4}+8C_5(0.4)^5 (0.6)^{8-5}[/tex]

[tex]=0.6^8+8(0.4)(0.6)^7+28(0.4)^2(0.6)^6+56(0.4)^3(0.6)^5+70(0.4)^4(0.6)^4+56(0.4)^5(0.6)^3[/tex]

[tex]=0.95019264[/tex]

Answer:

$6750 in the bank account and $20,250 in the stock fund

Step-by-step explanation:

If B is the money they put in the bank and S is the amount they put in the stock fund, then:

B + S = 27000

1.024 B + 1.072 S = 1.06 × 27000

Solving the system of equations:

1.024 (27000 − S) + 1.072 S = 28620

27648 − 1.024 S + 1.072 S = 28620

0.048 S = 972

S = 20250

B = 27000 − S

B = 6750

They should put $6750 in the bank account and $20,250 in the stock fund.

The only thing you can do with this expression is to factor a 5 out of the two terms: we have

[tex]15n-20 = 5(3n-4)[/tex]

Answer:

5(3n-4)

Step-by-step explanation:

because(5*3n)-(5*4)=15n-20

Answer:

let the equal sides of the triangle be of length "a"  . let the angle between these two sides be " x  ". Then drop a perpendicular from the vertex to the base.  now u have 2 similar triangles  .the angle between the perpendicular and one of the equal sides is now (x/2)  . length of perpendicular = a cos(x/2)  length of base = 2a sin(x/2)  . area of triangle = (1/2) 2sin(x/2) cos(x/2) a-square  

= (1/2) (sin x) a-square

Answer:

At q=6.8 the revenue is maximum. So, q=6.8 thousand units.

Step-by-step explanation:

The revenue function is

[tex]R(q)=-q^3+140q[/tex]

where q is thousands of units and R ( q ) is thousands of dollars.

We need to find for what value of q is revenue maximized.

Differentiate the function with respect to q.

[tex]R'(q)=-3q^2+140[/tex]

Equate R'(q)=0, to find the critical values.

[tex]0=-3q^2+140[/tex]

[tex]3q^2=140[/tex]

Divide both sides by 3.

[tex]q^2=\frac{140}{3}[/tex]

Taking square root both the sides.

[tex]q=\pm \sqrt{\frac{140}{3}}[/tex]

[tex]q=\pm 6.8313[/tex]

[tex]q\approx \pm 6.8[/tex]

Find double derivative of the function.

[tex]R''(q)=-6q[/tex]

For q=-6.8, R''(q)>0 and q=6.8, R''(q)<0. So at q=6.8 revenue is maximum.

At q=6.8 the revenue is maximum. So, q=6.8 thousand units.

Answer:

30 and 150

Step-by-step explanation:

Whether these are same side interior or same side exterior, the sum of them is 180 when they are on the same side of a transversal that cuts 2 parellel lines.  If angle A is 5 times smaller than angle B, then angle B is 5 times larger.  So angle A is "x" and angle B is "5x".  The sum of them is 180, so

x + 5x = 180 and

6x = 180 so

x = 30 and 5x is 5(30) = 150

Answer:

30 and 150

Step-by-step explanation:

YOUR WELCOME!

Answer:

11≤√134≤12

Step-by-step explanation:

11^2 is 121

and 12^2 is 144

so √134 would have to fall between these numbers

Answer:

  (x +8)^2 +(y -15)^2 = 289

Step-by-step explanation:

The numbers 8, 15, 17 are a Pythagorean Triple, so we know the radius of the circle is 17. Filling in the given information in the standard equation of a circle, we get ...

  (x -h)^2 +(y -k)^2 = r^2 . . . . . . circle with center (h, k) and radius r

  (x +8)^2 +(y -15)^2 = 289 . . . . . circle with center (-8, 15) and radius 17

_____

Once you have identified the center (h, k)=(-8, 15) and a point you want the circle to go through (x, y)=(0, 0), evaluate the equation for the circle to find the square of the radius:

  (0 +8)^2 +(0 -15)^2 = r^2 = 64+225 = 289

Final answer:

The equation of the circle with center at (-8, 15) that passes through the origin is (x + 8)² + (y - 15)² = 289.

Explanation:

The equation of a circle is given in the form (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius. In this case, the center of the circle is at (-8, 15). Since the circle passes through the origin (0,0), we can find the radius by calculating the distance between the origin and the center using the distance formula: √[(-8 - 0)² + (15 - 0)²] = [tex]\sqrt{(64 + 225)}[/tex] = [tex]\sqrt{289}[/tex] = 17.

Now that we have the radius, we can substitute our values into the circle's equation. The equation becomes (x + 8)² + (y - 15)² = 17² or (x + 8)² + (y - 15)² = 289.

Answer:

The first option:

Vertices: A, B, C, D, E, F, G, H;

Edges: AB, BC, CD, DA, BE, EF, FG, GH, HE, AH, CF, and DG;

Bases: rectangle ABEH and rectangle DCFG

Hope this helps C:

The correct option is option A:

    rectangular prism

The point where 2 or more side intersects is called vertices.

The individual flat surface of the solid object is the face.

The line segment where 2 faces intersect each other.

The prism whose bases are rectangular and are connected by line segment is called a rectangular prism.

As Rectangular prism has 2 rectangular bases at top and bottom position of the prism, 8 vertices, 6 faces, and 12 sides.

From the definition, It is clear that,

This figure is a rectangular prism whose

8 vertices are: A, B, C, D, E, F, H, G.

12 edges are: AB, BC, CD, DA, BE, EF, FG, GH, HE, AH, CF, and DG

2 rectangular bases are: ABEH and DCFG

Learn more about Rectangular prism

here: https://brainly.com/question/3890207

#SPJ2

Final answer:

The answer explains how to calculate the probability of not receiving one's own ID card using the inclusion-exclusion principle and provides the limit of this probability as n approaches infinity.

Explanation:

Inclusion-Exclusion Principle:

(a) To calculate the probability that no one receives their own ID card back, we use the principle of inclusion-exclusion. The probability is given by 1 - 1/1! + 1/2! - 1/3! + ... + (-1)^n * 1/n!.

(b) As n approaches infinity, the probability approaches e-1 which is approximately 0.3679.

Answer:

7

Step-by-step explanation:

I am assuming that the division problem looks like this:

-2|  1   2   -3   1

Going off that assumption, we will work this problem.  The first thing you always do in the execution of synthetic division is to bring down the first number.  Then multiply that number by the one "outside", which is -2, then put that number up under the next number in the line:

-2|  1   2   -3   1

         -2

     1

Now add the 2 and -2 and bring that down as a 0 and multiply the -2 times the 0:

-2|   1   2   -3   1

          -2    0

      1    0

Now add -3 and 0 to get -3 and multiply that -3 times the -2 and put the product up under the next numbe in line;

-2|   1   2   -3   1

           -2   0  6

      1     0   -3

Now add the 1 and the 6 to get the remainder:

7

Answer: 7

Step-by-step explanation:

A

P

E

X

Answer:

  3/10

Step-by-step explanation:

Bonnie has completed 0.5 + 0.2 = 0.7 of her art project. 1 - 0.7 = 0.3 of her art project remains to be completed.

_____

1/2 = 5/10 = 0.5

1/5 = 2/10 = 0.2

Step-by-step explanation:

You are close.  When calculating the radius and angle, you use the magnitudes of the real and imaginary terms.  In other words, you leave out the i in the calculation.

r = √((-8)² + (√3)²)

r = √(64 + 3)

r = √67

θ = π + atan((√3) / (-8))

θ ≈ 2.928

Answer:

The price per pound of bananas is $0.5 and the price per pound of apples is $0.6

Step-by-step explanation:

Let

x -----> the price per pound of bananas

y -----> the price per pound of apples

we know that

12x+10y=12 -----> equation A

8x+5y=7 ----> equation B

Solve the system of equations by graphing

Remember that the solution is the intersection point both graphs

The intersection point is (0.5,0.6)

see the attached figure

therefore

The price per pound of bananas is $0.5

The price per pound of apples is $0.6

To find the price per pound of bananas and apples, we set up and solved a system of equations based on two purchases. We found that bananas are $0.50 per pound and apples are $0.60 per pound.

To determine the price per pound of bananas and apples, we need to set up a system of equations based on the information given. Henrietta's purchase can be represented by the equation 12b + 10a = 12, where b is the cost of bananas per pound and a is the cost of apples per pound. Gustavo's purchase can be represented by the equation 8b + 5a = 7.

Now, let's solve the system of equations:

Multiplying Equation 2 by 2 gives us 16b + 10a = 14, which can be compared to Equation 1 to eliminate the apple's cost:

Subtracting Equation 1 from the doubled Equation 2:

16b - 12b + 10a - 10a = 14 - 12

4b = 2

b = 0.50

Now that we have the cost of bananas per pound, we can substitute b = 0.50 into either Equation 1 or 2 to find the cost of apples per pound. Using Equation 2:

8(0.50) + 5a = 7

4 + 5a = 7

5a = 3

a = 0.60

The price per pound of bananas is $0.50, and the price per pound of apples is $0.60.

Answer:

  (a) 720 -2x

  (b) 0 ≤ x ≤ 360

  (c) A = x(720 -2x)

  (d) (30.334, 68.645) ∪ (291.355, 329.666) (two disjoint intervals)

  (e) x = 180 ft, the other side = 360 ft; total area 64,800 ft²

Step-by-step explanation:

(a) The two parallel sides of the fenced area are each x feet, so the remaining amount of fence available for the third side is (720 -2x) ft. Then ...

  length = 720 -2x

__

(b) The two parallel sides cannot be negative, and they cannot exceed half the length of the fence available, so ...

  0 ≤ x ≤ 360

__

(c) Area is the product of the length (720-2x) and the width (x). The desired function is ...

  A = x(720 -2x)

__

(d) For an area of 20,000 ft², the values of x will be ...

  20000 = x(720 -2x)

  2x² -720x +20000 = 0

  x = (-(-720) ±√((-720)² -4(2)(20000)))/(2(2)) = (720±√358400)/4

  x = 180 ±40√14 = {30.334, 329.666} . . . feet

For an area of 40,000 ft², the values of x will be ...

  x = 180 ±20√31 ≈ {68.645, 291.355} . . . feet

The values of x producing areas between 20,000 and 40,000 ft² will be values of x in the intervals (30.334, 68.645) or (291.355, 329.666) feet.

__

(e) The vertex of the area function is at the axis of symmetry: x = 180. The corresponding dimensions are ...

  180 ft × 360 ft

and the area of that is 64,800 ft².

The length of the remaining side to be fenced is 4x - 720 ft. The restrictions on x are that it must be greater than 180 ft. The area function A(x) is (4x - 720) * x. The values of x that give an area between 20,000 and 40,000 ft2 are 30 ft to 42 ft. The dimensions that give a maximum area are 42 ft by 42 ft, with an area of 17,640 ft2.

(a) Express the length of the remaining side to be fenced in terms of x:

The perimeter of a rectangle is the sum of all its sides. Since we know the width is x and there are two parallel sides of length x, we can express the perimeter as 2x + x + x = 4x. The remaining side to be fenced can be expressed as 4x - 720 ft.

(b) What are the restrictions on x:

The length of each side, x, cannot be negative or zero since it represents a physical length. Additionally, the remaining side to be fenced must be positive, so 4x - 720 > 0. Combining these restrictions, x > 180 ft.

(c) Determine a function A that represents the area of the parking lot in terms of x:

The area of a rectangle is given by length multiplied by width. In this case, the length is the remaining side to be fenced, so the function A representing the area is A(x) = (4x - 720) * x.

(d) Determine the values of x that will give an area between 20,000 and 40,000 ft2:

To find the values of x that give an area between 20,000 and 40,000 ft2, we can set A(x) between those values and solve for x. We get the inequality 20,000 ≤ (4x - 720) * x ≤ 40,000. Solving this inequality, we find that 30 ft ≤ x ≤ 42 ft.

(e) What dimensions will give a maximum area, and what will this area be:

To find the dimensions that will give a maximum area, we can maximize the area function A(x). We can do this by finding the critical points of A(x) by taking its derivative and setting it equal to zero. After solving this equation, we find that x = 30 ft and x = 42 ft are the critical points. Evaluating A(x) at these critical points, we find that the dimensions that give a maximum area are 42 ft by 42 ft, with an area of 17,640 ft2.

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Answer:

a) The probability of being dealt a blackjack hand

[tex]= \frac{64}{1326}[/tex]

b) Approximate percentage of hands winning blackjack​ hands

[tex]4.827%[/tex]

Step-by-step explanation:

It is given that -

Winning Black Jack means -  getting 1 of the 4 aces and 1 of 16 other cards worth 10 points

Thus, in order to win a "black jack" , one is required to pull 1 ace and 1 of 16 other cards

Number of ways in which an ace card can be drawn from a set of 4 ace card is [tex]C^4_1[/tex]

Number of ways in which one card can be drawn from a set of other 16 card is [tex]C^16_1[/tex]

Number of ways in which two cards are drawn from a set of 52 cards is [tex]C^52_2[/tex]

probability of being dealt a blackjack hand

[tex]= \frac{C^4_1* C^16_1}{C^52_2} \\= \frac{4*16}{\frac{51*52}{2} }\\ = \frac{64}{1326} \\[/tex]

Approximate percentage of hands  winning blackjack​ hands

[tex]= \frac{64}{1326} * 100\\= 4.827[/tex]%

After completing this question, I got the calculation that the probability of being dealt a blackjack hand is 32/663. The percentage is 4.83%, or as a decimal ~0.0483

Answer:

61 steps per minute

3,660 steps per hour

Step-by-step explanation:

To find how many steps she walks in a minute, you have to divide 1830 by 30.

So, 1830/30 = 61

So she takes 61 steps per minute.

She walks 1830 in 30 minutes, and there are 60 minutes in an hour. 30 is also half of 60, so you would multiply 1830 by 2 to find out how many steps she walks in an hour.

So, 1830*2 = 3,660

So she takes 3,660 steps per hour.

Answer:

  8184 vocalists sang in total

Step-by-step explanation:

The number needed is ...

  8 + 16 + 32 + 64 + 128 + 256 + 512 + 1024 + 2048 + 4096

You can add these up to get a total of 8184, or you can use the formula for the sum of a geometric series:

  Sn = a1(r^n -1)/(r -1) . . . . where a1 is the first term and r is the common ratio

  S10 = 8(2^10 -1)/(2 -1) = 8(1024 -1)/1 = 8184

Answer:

6,138

Step-by-step explanation:

Number of vocalist needed on the first day = 6

Each day after that, the number of vocalists needed doubles

To Find:

The total number of vocalist found on the 10th day = ?

Solution:

By using the geometric series

Where

a is the first term

r is the ratio

n is the number of terms

On substituting the values

That is

The first day = 6 vocalist

Second day = 12 vocalist

third day =24 vocalist

Fourth day   =48 vocal list

Fifth day = 96 vocalist

Sixth day = 192 vocalist

Seventh day = 384 vocalist

eight day = 768 vocalist

Ninth day = 1536 vocalist

Tenth day = 3072 vocalist

So

6+12+24+48+96+192+384+768+1536+3072 = 6138 vocalist sang in total on the  end of tenth day.

Answer:

11.8 feet

Step-by-step explanation:

The given situation is represented in the figure attached below. Note that a Right Angled Triangle is being formed.

We have an angle which measures 28 degrees, a side opposite to the angle which measure 6.3 feet and we need to calculate the side adjacent to the angle. Tan ratio establishes the relation between opposite and adjacent by following formula:

[tex]tan(\theta)=\frac{Opposite}{Adjacent}[/tex]

Using the given values, we get:

[tex]tan(28)=\frac{6.3}{x}\\\\ x=\frac{6.3}{28}\\\\x=11.8[/tex]

Thus, the distance from the pole is 11.8 feet