Find the angle and round it to the nearest hundredth

The number of ways in which we can make a sitting arrangements to meet the requirement is 1440.

= 5!⋅4⋅3

= 120⋅12

= 1440

Combinations are ways to choose things from a collection where the order of the choices is irrelevant. Let's say we have a trio of numbers: P, Q, and R. Then, combination determines how many ways we can choose two numbers from each group.

It is easy to count the number of combinations in smaller cases, but the likelihood of a set of combinations is also higher in cases with many groups of components or sets. As a result, a formula has been developed to determine the number of items that could be chosen which is nCr.

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Answer:

Step-by-step explanation:

I'm assuming you're looking for the age of the mammal hide, since there's no question here, but there's also nothing else to solve for. Remember a few things before we move on. First, if we are not told the initial amount with which we start, we have to assume that it's 100%. Second, remember that natural log and e are inverses of each other so they eliminate each other in application. Now to set up the problem. It looks like this:

\(71=100e^{-.0001t}\) and begin by dividing both sides by 100 to get

\(.71=e^{-.0001t}\) and take the natural log of both sides. The other important thing to remember about the rules for logs and natural logs is that when you take the natural log of something, you are "allowed" to move the exponent down out front, which is why we do this. We cannot currently solve for t when it's stuck up there where it is right now. Taking the natural log allows us to bring that exponent down AND eliminate both the natural log and the e at the same time:

ln(.71) = -.0001t and we divide to solve for t:

\(\frac{ln(.71)}{-.0001}=t\) and

\(\frac{-.3424903089}{-.0001}=t\) so

t = 3424.9 years, or rounded, 3425 years.

Given:

The expression is:

\(\left(\dfrac{11}{19}n-8\right)+\left(\dfrac{1}{19}n+10\right)=\left(\_\_\_+\dfrac{1}{19}n\right)+\left(-8+\_\_\_\right)\)

                                          \(=\_\_\_n+\_\_\_\)

To find:

The missing values.

Solution:

We have,

\(\left(\dfrac{11}{19}n-8\right)+\left(\dfrac{1}{19}n+10\right)\)

It can be written as

\(\left(\dfrac{11}{19}n-8\right)+\left(\dfrac{1}{19}n+10\right)=\left(\dfrac{11}{19}n+\dfrac{1}{19}n\right)+\left(-8+10\right)\)

So, the values for the first two boxes are \(\dfrac{11}{19}n\) and 10 respectively.

On simplification, we get

\(\left(\dfrac{11}{19}n-8\right)+\left(\dfrac{1}{19}n+10\right)=\left(\dfrac{11+1}{19}n\right)+\left(2\right)\)

\(\left(\dfrac{11}{19}n-8\right)+\left(\dfrac{1}{19}n+10\right)=\dfrac{12}{19}n+2\)

So, the values for third and fourth boxes are \(\dfrac{12}{19}\) and 2 respectively.

Answer:

.53

Step-by-step explanation:

Answer:

0.5294 is a decimal and 52.94/100 or 52.94% is the percentage for 9/17.

Answer:

tomas is 10

Step-by-step explanation:

Hey there!

\(Answer:\boxed{10}\)

\(Explanation:\)

Since Tomas's grandfather is 100 and he is 10 times older than Tomas, let's divide 100 by 10.

\(100/10=10\)

Now let's try multiplying 10 by 10 to see if it is equal to 100.

\(10\times10=100\)

So that means that Tomas is 10.

Hope this helps!

1 gallon is equivalent to 3.785 liters, so 5 liters is equivalent to approximately 1.32 gallons.

Here,

In math, two values are equivalent if they have the same numerical value or represent the same amount or quantity. For example, the fractions 1/2 and 2/4 are equivalent because they represent the same amount or quantity (one-half of a whole).

Similarly, the expressions 3x and 6x/2 are equivalent because they have the same numerical value (both simplify to 3x). In general, we can say that two values are equivalent if they can be transformed or manipulated in a mathematically valid way to obtain the same result.

In the given question,

In math, two values are equivalent if they have the same numerical value or represent the same amount or quantity. For example, the fractions 1/2 and 2/4 are equivalent because they represent the same amount

The customary unit that a measurement of 5 liters could be converted to is gallons.

1 gallon is equivalent to 3.785 liters, so 5 liters is equivalent to approximately 1.32 gallons.

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complete question;

Which customary unit could a measurement of 5 liters be converted to?

gallons

ounces

pounds

feet

The marked price of the radio is Rs 10000.

From the question, we have the following parameters that can be used in our computation:

Discount = 10%

VAT = 13%

VAT - Selling price = 1170

Represent the price of the radio with x

Using the above as a guide, we have the following:

Discount = 10% implies 0.9x

VAT = 13% implies 0.9x * 1.13 = 1.017x

So, the difference is

1.017x - 0.9x = 1170

This gives

0.117x = 1170

Divide

x = 10000

Hence, the price of the radio is Rs 10000.

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Answer: 45

Step-by-step explanation:

Let's call the number of students in the yearbook club "x". Since the drama club has 12 more students, the number of students in the drama club would be "x+12".

We know that the total number of students in both clubs is 78, so we can set up an equation:

x + (x+12) = 78

Simplifying the equation:

2x + 12 = 78

Subtracting 12 from both sides:

2x = 66

Dividing both sides by 2:

x = 33

So there are 33 students in the yearbook club.

To find the number of students in the drama club, we can substitute x = 33 into the equation we set up earlier:

x + 12 = 33 + 12 = 45

Therefore, there are 45 students in the drama club.

Answer:

year book club= 33 people

drama club = 45 people

Step-by-step explanation:

78 students in total

drama : year book

x+12 x

x+12+x=78

2x+12=78

2x=66

x=33

year book= 33

drama= 45

Answer:

2x-3y=-5

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

bc it is

Here are all possible rolls:  Count them, there are 36

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)  

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)  

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

Answer:

Step-by-step explanation:

Rolling 2 dice gives a total of 36 possible outcomes.

Here is the sample space when we roll 2 dice:

Answer:

250

Step-by-step explanation:

1000 divided by 4, is 250

The unit rate would be 250 calories per mile which is the slope of the given linear function.

The unit rate of a linear function is defined as the slope of the linear function.

The slope is denoted by m

Slope m = (y₂ - y₁)/(x₂ -x₁ )

Consider two points on a line—Point 1 and Point 2. Point 1 has coordinates (x₁,y₁) and Point 2 has coordinates (x₂, y₂)

The given graph represents the number of miles he ran and the number of calories burned.

Taking two points as per the given graph :(2, 500), (6, 1500)

Let

x₁ = 2, y₁ = 500

x₂ = 6, y₂ = 1500

Substitute values in the formula to get

unit rate = (1500 - 500)/(6 - 2)

unit rate = (1000)/(4)

Apply the division operation,

unit rate = 250

Therefore, the unit rate would be 250 calories per mile

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Answer:

(x4+1)(x2-2)

Step-by-step explanation:

x6-2x4+x2-2

separate them into two different expressions

(x6-2x4)+(x2-2)

factor out the common factor for each expression. For (x6-2x4), it would be x4, and for (x2-2), it would just be 1

x4(x2-2)+1(x2-2)

since there both expressions have the same factor, you can do a reverse of the distribution property and factor it like

(x4+1)(x2-2)

Answer:

(x4+1)(x2-2)

Step-by-step explanation:

Answer:

\(g(x) = - 3x + 2 \\ g( - 2) = - 3 \times - 2 + 2 \\ = 8 \\ g( - 1) = - 3 \times - 1 + 2 = 5\)

Answer:

60

Step-by-step explanation:

60

The average speed of the train was 80mph.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.

Here, Given that, Station A and Station B are 120 miles apart.

And, a train traveling from station A to station B travels exactly 1/3 of the distance when it is held up and stops for 16 minutes.

Let, its average speed was x mph.

Then, Total time if didn't stop = 120/x h

Now, before stop it took time =( 1/3×120)/x h =40/x h

After stop it took time = 80/(x+15) h

i.e. 40/x +16/60+ 80/(x+15) = 120/x

⇒80/(x+15)+8/30= 80/x

⇒80(1/x-1/(x+15))=8/30

⇒10×(15/x^2+15x)=1/30

⇒x^2+15x=10×15×30

⇒x^2+15x-450=0

⇒x^2+75x-60x-450=0

⇒(x+75)(x-60)=0

⇒x=60 or, x= -75

Hence. the required speed was 60mph.

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Answer:

\(15m^{3} +9m-8\)

Step-by-step explanation:

Answer:

p(m) = 15m3 + 0m2 + 8m - 8

Step-by-step explanation:

Answer:

lol

Step-by-step explanation:

to get x in quadratic equations, factor it

There are 720 ways the first three positions of the order of finish can occur assuming no ties in a race with 10 horses.

To calculate the number of ways the first three positions can occur, we use the permutation formula:

nPr = n! / (n - r)!

where n is the total number of objects and r is the number of objects we are choosing.

In this case, we have 10 horses and we want to choose the first three positions, so we get:

10P3 = 10! / (10 - 3)! = 10! / 7! = (10 x 9 x 8) / (3 x 2 x 1) = 720

Therefore, there are 720 ways the first three positions of the order of finish can occur assuming no ties.

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Answer:

Step-by-step explanation:

Given

Natoy's rectangular swimming pool has the length of 3m more than thrice its

width.

Width=w

Length =3w+3

So

Area of the rectangular swimming pool=length×width

216=(3w+3)×w

216=3w^2+3w

3w^2+3w-216=0

3(w^2+w-72)=0

W^2+w-72=0

W^2+(9-8)w-72=0

W^2+9w-8w-72=0

W(w+9)-8(w+9)=0

(W+9)(w-8)=0

Sotwo value of w are 8,-9

We take positive value for rectangular swimming so we take w=8m

Width=8m

Length=3×8+3

= 24+3

=27m

The total price of 4 pounds of apples this week at the grocery store is $5.76

Total price of apples this week = Last week price of apples per pound × Quantity of apples

= $1.60 × 4

= $6.4

Actual price paid = Total price of apples this week - (Discount × Total price of apples this week)

= $6.4 - (10% × $6.4)

= 6.4 - (0.1 × 6.4)

= 6.4 - 0.64

= $5.76

In conclusion, 4 pounds of apples cost $5.76 this week at the grocery store.

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Therefore, the solutions to the quadratic equation x² - 14x - 49 = 0 are x = 7 + 7√2 and x = 7 - 7√2.

A quadratic equation is a second-degree polynomial equation in a single variable. In other words, it is an equation of the form ax² + bx + c = 0, where x is the variable, and a, b, and c are constants. The goal of solving a quadratic equation is to find the values of x that make the equation true. There are several methods for solving quadratic equations, including factoring, completing the square, and using the quadratic formula.

In the given question,

To solve the quadratic equation x² - 14x - 49 = 0 , we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

where a = 1, b = -14, and c = -49.

Plugging in these values, we get:

x = (-(-14) ± √((-14)² - 4(1)(-49))) / 2(1)

Simplifying this expression, we get:

x = (14 ± √(196 + 196)) / 2

x = (14 ± √392) / 2

x = (14 ± 14√2) / 2

x = 7 ± 7√2

Therefore, the solutions to the quadratic equation x² - 14x - 49 = 0 are x = 7 + 7√2 and x = 7 - 7√2.

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Answer:

quadriatlan is the correct answer

Step-by-step explanation:

Answer:

288.4m

Step-by-step explanation:

This track is split into a rectangle and two semi-circles.

We can find the length of the semi-circles by finding its circumference with the formula \(2\pi r\).

\(2\cdot3.14\cdot30\\188.4\)

However this is half a circle, so:

\(188.4\div2=94.2\).

There are two semi-circles.

\(94.2\cdot2=188.4\)

Since there are two legs of 50m each, we add 100 to 188.4

\(188.4+100=288.4\)m

Hope this helped!

Answer:

Step-by-step explanation:

To solve for the perimeter, we first look at the rectangle in the middle. the length is 50m, and there are two sides to it, so: 50 * 2 = 100m for the top and bottom of the track.

For the circle, we can see the diameter is 30m. To solve for the circumference, we need to use the formula 2πr.

15 * 2π ≈ 94.2477796077

We add that to 100m and get:

194.2477796077

Answer:

Statistical Inference

Step-by-step explanation:

Statistical analysis has two main focuses: descriptive statistics and infernetial statistics.

Descriptive statistics summarise data using graphs and summary values such as the mean and interquartile range. Descriptive statistics can help us identify relationships and patterns. Descriptive statistics do not draw conclusions beyond the data we already have. Inferential statistics anaylsis does allow us to make conclusions beyond the data we have.

A defintion of inference is:
The process of drawing conclusions.

The values of b and a for the logarithmic function in this problem are given as follows:

The logarithmic function in the context of this problem has the format given as follows:

\(y = b\log_3{x + a}\)

The vertical asymptote is at x = -4, hence:

\(y = b\log_3{x - 4}\)

When x = 5, y = -1, hence the parameter b is obtained as follows:

\(-1 = b\log_3{5 - 4}\)

0.477b = -1

b = -1/0.477

b = -2.1.

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Answer:

The first one is 14 the second is 30 and the last one is 10

Answer:

1. d = 14

2. d = 30

3. d = 10

Ex. Divide 6d by 6 and you get d. Divide 84 by 6 and you get 14. d = 14

The matrix A of the linear transformation t that rotates any vector through an angle of 30 degrees counterclockwise can be found using the standard rotation matrix formula.

A = [cosθ -sinθ; sinθ cosθ]

where θ is the angle of rotation in radians.

Converting 30 degrees to radians gives θ = π/6, so we can substitute this value into the formula to get:

A = [cos(π/6) -sin(π/6); sin(π/6) cos(π/6)]

Simplifying this, we get:

A = [√3/2 -1/2; 1/2 √3/2]

So the matrix A of the linear transformation t that rotates any vector through an angle of 30 degrees counterclockwise is:

A = [√3/2 -1/2; 1/2 √3/2]

This matrix can be used to rotate any vector in R2 by multiplying it with matrix A. The resulting vector will be the original vector rotated counterclockwise by 30 degrees.

In other words, if v is a vector in R2, then the rotated vector r can be found as:

r = Av

where A is the rotation matrix we found above.

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Answer:

i believe the answer is A 90

Step-by-step explanation: