Suppose that a 2 by 10 rectangular grid of seats is filled with people. On the
blow of a whistle, all 20 people get up from their current seat and move to an orthogonally adjacent seat. How many ways are there for everyone to do this so that at the end of the move, each seat is taken by exactly one person?

Answer:

1-21>151 and -2>5

I think so.

Answer:

2, x - 2, x + 4

Step-by-step explanation:

The factors of the given quadratic expression, 2x² - 4x - 16, are 2, (x +2), and (x -4)

From the question, we are to determine the each of the factors of the given quadratic expression

The given quadratic expression is

2x² - 4x - 16

Factoring

2x² - 4x - 16

First, factor out 2

That is,

2(x² - 2x - 8)

Now, we will factor x² - 2x - 8
x² - 2x - 8

x² - 4x + 2x - 8

x(x - 4) +2(x -4)

(x +2)(x -4)

Thus,

2x² - 4x - 16  = 2(x +2)(x -4)

Hence, the factors of the given quadratic expression, 2x² - 4x - 16, are 2, (x +2), and (x -4)

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Answer:

5/52

Step-by-step explanation:

There are 52 cards in a deck, with 26 red and 26 black cards. There are 2 red ones, 2 black threes, and 1 six of hearts. The # of favorable outcomes is 2 + 2 + 1 = 5, so the answer is 5/52.

The x value or observed value corresponding to  z-score, z = 1.50 is 130.

According to the question.

For a population with µ = 100 and σ = 20.

Since,  we know that

The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.

And it is given by

z = (x - μ) / σ

Where,

x is the observed value.

μ is the mean.

and, σ is the standard deviation.

Therefore, the x value or observed value corresponding to z = 1.50 is given by

[tex]1.50 = \frac{x -100}{20}[/tex]

⇒ 1.50 × 20 = x - 100

⇒ 30 = x - 100

⇒ x = 30 + 100

⇒ x = 130

Hence, the x value or observed value corresponding to  z-score, z = 1.50 is 130.

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The intervals which represents those in which case the function, f(x) is reducing are as follows; [–2.5, –2], [–2, –1.5], [1.5, 2], [2, 2.5].

It follows from the complete task content that the x-intervals between which the function value of f(x) is reducing are to be identified from the graph as attached.

On this note, by observation on the graph, it follows that from between the interval; [–2.5, –2], the function f(x) is decreasing.

Also, between the interval; [–2, –1.5], the function f(x) is decreasing.

Also, between the interval; [1.5, 2], the function f(x) is decreasing.

Also, between the interval; [2, 2.5], the function f(x) is decreasing.

Remark: The answer choices are as follows; [–2.5, –2] [–2, –1.5] [–1, 1] [1.5, 2] [2, 2.5) [2.5, 3]

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Answer:

A     [tex] \dfrac{2x^3}{3yw} [/tex]

Step-by-step explanation:

[tex] \dfrac{xy(24x^2y^3w)}{36y^5w^2} = [/tex]

[tex] = \dfrac{2 \times 12 x^3y^4w}{3 \times 12y^5w^2} [/tex]

[tex] = \dfrac{2x^3}{3yw} [/tex]

we can simply take the whole amount of 30 and divide it by (4 + 1), then distribute to each side accordingly, since they're in a 4 to 1 ratio.

[tex]\underset{\hspace{5em}4~\hfill to~\hfill 1\qquad }{\stackrel{\text{\LARGE 30}}{C\rule[0.35em]{18em}{0.25pt}E\rule[0.35em]{10em}{0.25pt}D}} \\\\\\ \stackrel{CE}{4\left( \frac{30}{4+1} \right)} ~~ : ~~ \stackrel{ED}{1\left( \frac{30}{4+1} \right)}\implies \stackrel{CE}{4\left( 6 \right)} ~~ : ~~ \stackrel{ED}{1\left( 6 \right)}\implies \stackrel{CE}{\text{\LARGE 24}} ~~ : ~~ \stackrel{ED}{\text{\LARGE 6}}[/tex]

The computation shows that the time before

they can no longer communicate will be 10 minutes

From the information, it was stated that two hikerd are wandering through heavy woods with walkie talkies and that the walkie talkies have a range c of 100 yards.

It should be noted that after t hours, the distance between the hikers will be:

d² = (0.24t)² + (0.17t)² - 2(0.24t)(0.17t) cos 109.10°

d = 0.0568

Therefore, we will find the time when d = 0.0568. This will give a time of 10 minutes.

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Answer: [tex]\Large\boxed{Total~area=586.17~cm^2}[/tex]

Step-by-step explanation:

Given information

[tex]Height=7~cm[/tex]

[tex]Base=18~cm[/tex]

Given formula

[tex]A=b\times h\times\dfrac{1}{2}[/tex]

[tex]A=Area\\b=base\\h=height\\[/tex]

Substitute values into the formula

[tex]A=(7)\times (18)\times\dfrac{1}{2}[/tex]

Simplify by multiplication

[tex]A=(7)\times 9[/tex]

[tex]A=63~cm^2[/tex]

Given information

[tex]Height = 18~cm[/tex]

[tex]Base=22~cm[/tex]

Given formula

[tex]A=b\times h[/tex]

[tex]A=Area\\b=base\\h=height\\[/tex]

Substitute values into the formula

[tex]A=(22)\times (18)[/tex]

Simplify by multiplication

[tex]A=396~cm^2[/tex]

Given information

Diameter = 18 cm

Given formula

[tex]A=(\dfrac{d}{2} )^2\times \pi \div2[/tex]

[tex]A=Area\\d=diameter[/tex]

Substitute values into the formula

[tex]A=(\dfrac{18}{2} )^2\times (3.14) \div2[/tex]

Simplify the fraction

[tex]A=(9 )^2\times (3.14) \div2[/tex]

Simplify the exponents

[tex]A=81\times (3.14) \div2[/tex]

Simplify by multiplication

[tex]A=254.34\div2[/tex]

Simplify by division

[tex]A=127.17~cm^2[/tex]

Given formula

[tex]Total~area=Triangle+Rectangle+circle~(half)[/tex]

Substitute values into the formula

[tex]Total~area=(63)+(396)+(127.17)[/tex]

Simplify by addition

[tex]Total~area=459+(127.17)[/tex]

[tex]\Large\boxed{Total~area=586.17~cm^2}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

The area of the missing slice is 15 inches ²

From the information given, we can see that the pizza takes the form of a circle;

Area of the missing slice takes the shape of a triangle

Area of a triangle = 1/ 2 base × height

base = 10 inches

height = 3 inches

Area of missing slice = 1/ 2 × 10 × 3

Area = 1/ 2 × 30

Area = 15 inches ²

Thus, the area of the missing slice is 15 inches ²

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Answer:

false

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

The net of a cylinder has a rectangle for the lateral area and 2 circles for the bases, so it has 3 parts.

Answer: False

Answer:

  50 miles/1 hour = 50 miles/hour

Step-by-step explanation:

The fraction is reduced by dividing numerator and denominator by their common factor of 2.

  100 miles / (2 hours) = 50 miles/ (1 hour) = 50 miles/hour

Answer:

1

Step-by-step explanation:

The slope of a function is equal to the coefficient of x when the equation is in standard form (y=mx+c)

In this case the equation is already in standard form and thusly we can see that the coefficient of x is 1 (the constant has no effect on the slope)

Answer:

4. 4.125 inches by 3.5 inches.

5. 8.4 hours.

Step-by-step explanation:

4. multiply 16.5 and 14 by .25 because each foot in the house is .25 of an inch on the paper.

5. 252 miles / 9 hours = 28 mph. Add 2 so you get 30 mph. 252 miles / 30 mph = 8.4 hours.

Formula for the circumference of a circle is

[tex]c = \pi \: d[/tex]

where c is the circumference, and d is the diameter.

When diameter is 27-in, then

[tex]c1 = \pi \times 27[/tex]

When diameter is 25-in, then

[tex]c2 = \pi \times 25[/tex]

.: 27π-in – 25π-in is the farther distance.

Finding the difference, we have:

2π ≈ 6.28

.: 6.28-in is our final answer.

The total amount spent by Elsa and her friends must not exceed RM 475; 475 ≤ x

Elsa + 3(her friends) ≤ Total

145 + 3(110) ≤ x

145 + 330 < x

475 ≤ x

Therefore, the total amount spent by Elsa and her friends must not exceed RM 475; 475 ≤ x

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Answer: 4096.

Step-by-step explanation:

[tex](8^3)^8\div(8^4)^5=\\8^{3*8}\div8^{4*5}=\\8^{24}\div8^{20}=\\8^{24-20}=\\8^4=\\4096.[/tex]

Answer:

48

Step-by-step explanation:

48 because you are multiplying it by -2 each time. -24 x -2 = 48

Answer:

Step-by-step explanation:

Use the distributive property.

Distributive property is a serving to distribute or allot or disperse.

Distributive property:

A(B+C)=AB+AC

A(B-C)=AB-AC

-10(1-9x)+6(x-10)

Expand.

-10(1-9x)

-10*1=-10

-10*9x=90x

[tex]\longrightarrow \sf{=-10+90x+6\left(x-10\right)}}[/tex]

6(x-10)

6*x=6x

6*10=60

6x-60

Rewrite the problem down.

= -10+90x+6x-60

Combine like terms.

90x+6x-10-60

Add the numbers from left to right.

90x+6x=96x

96x-10-60

Finally, subtract the numbers from left to right.

-10-60=-70

[tex]\Longrightarrow \boxed{\sf{96x-70}}[/tex]

Therefore, the final answer is 96x-70.

I hope this helps, let me know if you have any questions.

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Distributive Property :

[tex]-10(1-9x)+6(x - 10)[/tex]

[tex]-10(-9x+1)+6(x - 10)[/tex]

[tex]90x-10+6x-60[/tex]

[tex]90x-70+6x[/tex]

[tex]96x-70[/tex]

[tex]answer : \boxed{\pink\star\tt{96x-70}}[/tex]

━━━━━━━━━━━━━━━━━━━━━━━━

Common factor :

[tex]- 10(1 - 9x) + 6(x - 10)[/tex]

[tex]96x - 70[/tex]

[tex]2(48x - 35)[/tex]

[tex] answer : \boxed{ \pink \star\tt{2(48x - 35)}}[/tex]

The total surface area of the square pyramid (SA) = 144 yd².

A square pyramid is a solid shape that has a square base and four rectangular lateral faces.

The total surface area of a square pyramid is the sum of the area of its square base and four rectangular lateral faces. To find the total surface area, the following formula is used:

Total surface area of a square pyramid (SA) = A + 1/2(Pl), where:

Given the following:

Area of base (A) = 8² = 64 yd²

Perimeter of base (P) = 4(8) = 32 yds

Slant height of pyramid (l) = 5 yds

Plug in the values

Total surface area of a square pyramid (SA) = 64 + 1/2(32)(5)

Total surface area of a square pyramid (SA) = 64 + 80

Total surface area of a square pyramid (SA) = 144 yd².

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Answer:

following the (x,y) coordinate system,

(0,4) ; (1,1) ; (2,-2)

Step-by-step explanation:

youre given the value of the x variable in the table, so all you need to do is substitute x and follow pedmas!! hope this helps<3

The initial-value is  x(t)=F0/2w^2 (sin wt-wt cos wt)

An initial-value hassle is a differential equation wherein is an open set of, together with a point within the domain called the initial situation. A technique to an initial cost hassle is a function that is a technique to the differential equation and satisfies.

Inside the discipline of differential equations, preliminary cost trouble (additionally called Cauchy trouble by using a few authors) is a normal differential equation collectively with a detailed fee, called the preliminary situation, of the unknown function at a given factor in the domain of the solution.

In multivariable calculus, an initial-value hassle is a normal differential equation collectively with a preliminary circumstance that specifies the fee of the unknown characteristic at a given factor in the area. Modeling a system in physics or different sciences often amounts to fixing an initial cost problem.

Consider a differential equation x+x=F, sin wt, x(0) = 0,X(0) = 0

Apply Laplace transformation on both sides, and we get

(s²L{x(t)}-sy(0)-y'(0)) + w²L {x(t)} =·

Fow

Fow

(s² + w² ) { x(t)} = 3 + w²

L{x(t)}=

Fow

(5²+w²)²

x(t)=FwL

[(s² + w²)²]

Fow

x(t)=(sin wt-wt coswt)

2w

x(t)=

Fo

wtcos

2w (sin wt-wt cos wt),

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Answer: D

Step-by-step explanation:

If the leading coefficient is negative, then as [tex]x \to \infty[/tex], [tex]f(x) \to -\infty[/tex].

If the leading coefficient is negative, then as [tex]x \to -\infty[/tex], [tex]f(x) \to \infty[/tex].

This leaves D as the correct answer.

By using the digits 0 to 9, the boxes are filled with their respective numerical values to make the chart accurate as shown in the image attached below.

A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variables.

In Mathematics, there are different types of functions and these include the following;

A logarithm function can be defined as a type of function that represents the inverse of an exponential function. Mathematically, a logarithm function is written as follows:

y = logₐₓ

y = log₁₀10

y = log₁₀10 = 1.  

Therefore, if log₁₀x < 1, then, x < 10.  Also, if log₁₀x > 1, then, x > 10.

For this exercise, you should take note of this deductive points:

In conclusion, by using the digits 0 to 9, the boxes are filled with their respective numerical values to make the chart accurate as shown in the image attached below.

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D box plot correctly represents the data

A box plot or boxplot is a technique for illustratively displaying the localization, dispersion, and skewness groups of numerical data through their quartiles.

Using a five-number summary (the minimum, first quartile (Q1), median, third quartile (Q3), and "maximum"), a boxplot is a common method of visualizing data distribution.

The median value for the provided data will be the sixth data point's value, or 3.

The median of the data's lower half is now the first quartile. The third data point's value of 1 will therefore be in the lower quartile.

The median of the data's upper half is now referred to as the upper or third quartile. This means that the value of the ninth data point, which is 6, will represent the upper quartile.

Thus, box-plot D effectively displays the data from above.

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Answer:

The answer is D.

Edg 2023.

The solution to 0.5^(x + 2) > 9 is x  > -5.170

The inequality expression is given as:

0.5^(x + 2) > 9

Take the logarithm of both sides of the inequality expression

log(0.5^(x + 2)) > log(9)

Rewrite the inequality expression as

(x + 2)log(0.5) > log(9)

Divide both sides by log(0.5)

x + 2 > -3.170

Subtract 2 from both sides

x  > -5.170

Hence, the solution to 0.5^(x + 2) > 9 is x  > -5.170

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The amount saved in 10 years is = $1,04,461.13

The correct option is B.

An annuity is a series of payments that are distributed evenly over time.

One way to express the future value of an annuity of payment P for n years is,

Total salary is $65000

The interest rate is 5.32%

Trent save 8%  of his salary every year.

Company puts  4.6% of salary every year.

[tex]\text { Future Value }=\mathrm{P} \times \frac{\left(1+\frac{i}{n}\right)^{n t}}{\frac{i}{n}}[/tex]

Given:

Total salary is $65000

The interest rate is 5.32%

Trent save 8% of his salary every year.

Company puts  4.6%of salary every year.

The 8% of salary is calculated as:

[tex]\text { Amount } &=\frac{8}{100} \times 65000\\[/tex]

               [tex]&=\$ 5200[/tex]

The following information is available on the company's put:

[tex]\text { Amount } &=\frac{4.6}{100} \times 65000\\[/tex]

                [tex]&=\$ 2990[/tex]

Total amount as follows:

[tex]\begin{aligned}\text { Amount } &=5200+2990 \\&=\$ 8190\end{aligned}[/tex]

The future value can be obtained as follows

[tex]\begin{aligned}\mathrm{FV} &=8190 \times \frac{(1+0.053)^{10}-1}{0.053} \\&=8190 \times 12.75 \\&=1,04,461.13\ \\\end{aligned}[/tex]

Hence, the amount saved in 10 years is = $1,04,461.13

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Answer:

Graph b

Step-by-step explanation:

y = |x| is a "v"at x = 0

y = |x-1| is a "v" shifted to the right by 1 unit

X is the number of songs and Y the number of pics

our 2 equations will be - X+y=11 & 4x+2y=24

consider x=11-y

Lets replace x in 2:

=4(11-y) +2y=24

=44-4y+2y=24

=44-24= 4y-2y

=20= 2y

=Y=20/2

=Y=10

Lets replace y in 1

=X+10=11

=X=11-10

=X=1

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