the length of a rectangle is 4x meters and its width is 5x meters determine the value of x and the width if the perimeter of the rectangle is 54 meters.

x=
width=

If an auditorium has 20 rows of seats. there are 20 seats in the first row, 21 seats in the second row, 22 seats in the third row, and so on. then,  there are 39 seats present in the 17th row.

The given data is as follows:

Number of rows of seats = 20

Number of seats in the first row = 20

Number of seats in the second row = 21

Number of seats in the third row = 22 and so on.

Let's calculate the common difference between the seats,

common difference = 21-20 = 1 or 22-21 = 1

Therefore common difference = 1

Then the number of the seats in 17th row will be

The number of the seats = 20 + (20 - 1)* 1

The number of the seats= 39 seats.

Therefore, there are a total of 39 seats present in the 17th row.

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Answer: ITS C (2) trust me my guy

The slope of the function is,

⇒ m = 4

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The ordered pairs in the table below represent a linear function are,

(2, 5) and (3, 9)

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (9 - 5) / (3 - 2)

m = 4 / 1

m = 4

Thus, The slope of the function is,

⇒ m = 4

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For the given data of population of two cities Sudbury and Victoria , the ratio of the population of the two cities in the beginning of 1996 is given by :

Sudbury (x) / Victoria (y)  = 57 /47.

As given in the question,

Let us consider population of Sudbury city be 'x'

And population of Victoria be 'y'

Given:

Population of Sudbury decreased by 6%

= x - ( 6%of x)

= x - (6x/100)

= 94x/100

Population of Sudbury increased by 14%

= y + ( 14%of y)

= y + (14y/100)

= 114y/100

Ratio of the population of the two cities in the beginning of 1996 is given by:

Population of two cities were equal

94x/100 = 114y/100

⇒ x / y = 114 /94

⇒ x / y = 57 /47

Therefore, for the given data of population of two cities Sudbury and Victoria , the ratio of the population of the two cities in the beginning of 1996 is given by :

Sudbury (x) / Victoria (y)  = 57 /47.

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Answer: 137 degrees

Step-by-step explanation:

It's in the sentences, the angle is 137 degrees

Answer:

A dilation by 2 and a rotation about the origin at 90 degrees counter-clockwise

Step-by-step explanation:

Already taken geometry.

The probability sum of the dice is 2/11.

Let A be the event that the sum of dots is 5, then

A={(1,4), (2,3), (3,2), (4,1)}

n(A)=4

And, B is the event that one die shows a "one"

B={(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (3,1), (4,1), (5,1), (6,1)}

n(B)=11

The Event that some of the dots are five and one of the die shows "one".

A intersection B = {(1,4), (4,1)}

Since n(A) = 36 (thirty-six possible samples of two dice)

P(A)=4/36

P(B)=11/36

P(A intersection B)=2/36

So, the required probability is

P(A|B)=P(A intersection B)/P(B) =2/11

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According to the ratio test, the series is divergent.

Using the ratio test, we can determine if a series is convergent or divergent. Given the series ∑\((9n^{n})\) where n starts from 1 to infinity, we need to first identify the general term \(a_n\), which in this case is \(9n^{n}\).
To apply the ratio test, we need to find the limit of the absolute value of the ratio of consecutive terms: \(\lim_{n \to \infty} |a_{n+1} / a_n|\)

Let's calculate this limit:
\(\lim_{n \to \infty} |(9(n+1)^{(n+1))} / (9n^{n})|\)
After simplifying, we get:
\(\lim_{n \to \infty} |((n+1)^{(n+1))} / (n^{n})|\)
To evaluate this limit, we can use L'Hopital's Rule or express the limit in the form of \(e^{ \lim_{n \to \infty} f(n)}\):
\(\lim_{n \to \infty} |e^{(ln((n+1)^{(n+1)} - ln(n^n))}|\)
Now, apply properties of logarithms:
\(\lim_{n \to \infty} |e^{((n+1)ln(n+1)) - (nln(n))}|\)
We can rewrite this as:
\(\lim_{n \to \infty} |e^{(n(ln(n+1) - ln(n) + ln(n+1)))}|\)
Now, observe that as n approaches infinity, the difference (ln(n+1) - ln(n)) approaches 0, and ln(n+1) becomes significant. Hence, the limit is:
\(\lim_{n \to \infty} |e^{(n(ln(n+1)))}| = \infty\)
Since the limit is greater than 1, the series is divergent according to the ratio test.

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The researchers used a sample of mice in a maze experiment to study learned behavior. They timed each mouse on its first run through the maze and again on its tenth run through the maze, recording the difference in times for each mouse.

The maze experiment is a common method used by researchers to study the learned behavior of animals, including mice. In this experiment, a maze is set up with food placed at the end to motivate the mouse to find its way through the maze. The researchers time the mouse on its first run through the maze to establish a baseline for the mouse's performance. They then repeat the experiment by timing the mouse on its tenth run through the maze to see if the mouse has learned and improved its performance. By subtracting the time of the first run from the time of the tenth run, the researchers can measure the difference in time and assess how much the mouse has learned.

The difference in time between the first and tenth run can be used as a measure of learning, and statistical analysis can be applied to identify significant changes in the mouse's performance. This type of experiment can be useful for studying the effects of different variables on learning, such as different training methods or drug treatments. The maze experiment can also be adapted to study other aspects of animal behavior, such as memory and decision-making.

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Among the given values, the smallest value is 0.01

A number is an arithmetic value that is used to calculate and represent a quantity. Numerical symbols, such as "3," are written to represent numbers. A number system is a logical way of writing numbers that use digits or symbols to represent them.

The different Types of Numbers that exist are as follows

Natural Numbers.

Whole Numbers.

Integers.

Rational Numbers.

Irrational Numbers.

Real numbers.

Complex numbers.

According to the given value, the smallest number is

0.01

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Answer:

21 stations

Step-by-step explanation:

1 1/4 = 5/4

26.2 / 5/4 = 20.96

rounded up to 21

Answer: X=5 AB=12 BC=16 AC=28

hope this helps

Answer:

130

Step-by-step explanation:

26/2 = 13

10 x 13 = 130

====================================================

Explanation:

We start off with 16 seats in the first row. Then we have 16+3 = 19 seats in the next row and 19+3 = 22 seats in the third row, and so on.

The pattern is this: 16, 19, 22, ...

We add on 3 each time we need to get another row of seats. We keep doing this until we have 25 rows in all.

We need to determine how many seats are in row n, where n is some positive whole number, aka n is a natural number.

--------------------

Going back to the sequence {16,19,22,...} we can see that this is arithmetic because we have the same gap between the adjacent numbers. That gap being 3. This is the common difference, so d = 3.

The start term is a = 16

The nth term is...

f(n) = a + d(n-1)

f(n) = 16 + 3(n-1)

f(n) = 16 + 3n - 3

f(n) = 3n + 13

This function f(n) will quickly tells us how many seats are in a given row.

For instance, if n = 3, then,

f(n) = 3n + 13

f(3) = 3*3 + 13

f(3) = 9 + 13

f(3) = 22

This matches from the third term in {16, 19, 22, ...}. I recommend you try other values of n to help show why that function works the way it does.

--------------------

We did all that work to find the nth term f(n) so that we can then use the formula below to sum all the terms from 1 to n

Sn = sum of the first n terms

Sn = first term + second term + ... + nth term

Sn = (n/2)*(first term + nth term)

Sn = (n/2)*( a + f(n) )

Sn = (n/2)*(16 + 3n+13)

Sn = (n/2)*(3n + 29)

Let's try n = 2 and we get

Sn = (n/2)*(3n + 29)

S2 = (2/2)*(3*2 + 29)

S2 = 35

Then note how the first two terms of {16, 19, 22, ...} add to 16+19 = 35 to help confirm that we have the correct Sn formula.

I should point out that this trick only works for arithmetic sequences.

--------------------

We have one more step from here. Plug in n = 25 to find the sum of the first 25 terms of the arithmetic sequence {16,19,22,...}

Sn = (n/2)*(3n + 29)

S25 = (25/2)*(3*25 + 29)

S25 = 1300

Therefore, this theater has a total of 1300 seats which is the final answer.

--------------------

You could list out all the first 25 terms of {16,19,22,...}, and then add them up, and you should get 1300 as the result. Doing such a check is tedious and often something I recommend you would use computer software for.

I used computer software to get the following

16+19+22+25+28+31+34+37+40+43+46+49+52+55+58+61+64+67+70+73+76+79+82+85+88 = 1300

This confirms the correct final answer. This part is optional in my opinion. It's just there if you're curious. Note how each term in that long sum above is incrementing by 3 each time.

Answer:6.85565

Step-by-step explanation:

Answer:I think the answer is d.25

Step-by-step explanation:

The prompt on fractions is given as follows:

1 ) (1/2) ÷ 4 = 1/8
2) ( 1/5) ÷ 2 = 1/10

3) (1/3) ÷ 5 = 1/15

4) (1/4) ÷ 4 = 1/16
5) The solution to the puzzle for (1/2) ÷ 3 is given below.

The calculations are given as follows;

1 )

= (1/2) x (1/4) [dividing by a number is the same as multiplying by its reciprocal]

= 1/8

2) (1/5) ÷ 2

= (1/5) x (1/2)

= 1/10

3)

(1/3) ÷ 5

= (1/3) x (1/5)

= 1/15

4) (1/4) ÷ 4

= (1/4) x (1/4)

= 1/16

5) Mary had 1/2 of a pie that she wanted to share with 3 of her friends. She decided to divide it equally among them. Each friend got 1/6 of the pie. To check, Mary multiplied 1/6 by 3 and got 1/2. This shows that (1/2)/3 equals 1/6, since dividing by 3 is the same as multiplying by its reciprocal, 1/3.


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The differences between two samples are more likely to be statistically significant if the samples are and the standard deviations of the samples are: large and the standard deviations of the samples are small.

Now,

Hence, The differences between two samples are more likely to be statistically significant if the samples are and the standard deviations of the samples are: large and the standard deviations of the samples are small.

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We have that there are 8 participants and 4 prizes, in this problem, it's important the order of the prizes too.

Now, for the first time, there are 8 possibilities for awarding the winner prize.

For the second moment, there are just 7 possibilities for awarding the first runner-up.

Then, we have that there are 6 possibilities for awarding the second runner-up.

And, finally, we have 5 possibilities for awarding the third runner-up.

So, we have that all the ways are represented as:

And since the order of the 4 prizes is important to get a specific prize, we have:

Then the correct answer would be 70.

Para calcular el área de un rectángulo multiplicamos el largo por el ancho.

The area is the space inside a two-dimensional figure. We can also consider the area as the amount of space that surrounds the figure. Reaction of the Right Angle: Long and Sharp

Area = largo anchostart text, A, with, ', on top, r, e, a, end text, equals, start text, l, a, r, g, o, end text, times, start text, a, n, c, h, o, end text =62Area = largo anchostart text, empty space, equals, 6, times, 2=12 cuadradas

Area equals 12 square units

start text, space, u, n, I d, a, d, e, s, space, c, u, a, d, r, a, d, a, s, end text, empty space, equals,

Example 2: "Area=largo"anchostart text, "A," "with," "on top," "equals," "l," "a," "r," "g," "o," "end text," "times," and "l".

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Answer:

133

Step-by-step explanation:

The solution is, b. x² = 12(y + 3) equation represents a parabola that has a focus of (0, 0) and a directrix of y = −6

The parabola is a plane curve which is mirror symmetrical and is approximately U-shaped. It fits several superficial different mathematical descriptions.

here, we have,

If the focus is (0,0) and the  directrix  is y=-6, the equation will be found as follows:

Let (x,y) be any point on the parabola. Find the distance between (x,y) and the directrix, then find the distance between (x,y) and the focus. Equate these two distance equations and the simplified equation in x and y is equation of the parabola.

The distance between (x,y) and (0,0) is √(x²+y²)

The distance between (x,y) and the directrix, y=-6 is ly+6l

Equate the two distance expressions and square on both sides

√(x²+y²)=ly+6l

x²+y²=(y+6)²

simplifying and bringing terms together we get:

x²-12y-36=0

make x² the subject:

x²=12y+36

x²=12(y+3)

Hence, Answer :b. x² = 12(y + 3)

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complete question:

Which equation represents a parabola that has a focus of (0, 0) and a directrix of y = −6 ?

a. x² = 12y

b. x² = 12(y + 3)

c. x² = −3y

d. x² = −3(y + 3)

Answer:

C

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

33=9.8x-7.6x

33=2.2x

33/2.2=x

15=x

Answer:

x=-15

Step-by-step explanation:

8+9.8x+9=3.8x-16+3.8x

8+9=17

17+9.8x=7.6x-16

   -7.6x  -7.6x

17+2.2x=-16

-17 .          -17

-16-17= -33

2.2x=-33

/2.2    /2.2

x=-15

To analyze the open intervals of increasing and decreasing for g(x) on the interval [1/2, √3/2], we need to consider the derivative of g(x). Let's calculate it step by step:

1. Calculate f'(x):

Since f(x) is given, we can differentiate it to find f'(x). However, you haven't provided the expression for f(x), so I cannot compute f'(x) without that information. Please provide the function f(x) to proceed further.

Once we have the expression for f'(x), we can continue with the rest of the problem, including finding the absolute extrema for g(x).

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Answer:

Step-by-step explanation:

The average density of the red supergiant star Betelgeuse is 1.45 × 10⁻¹¹ kg/m³.

To calculate the average density of the red supergiant star Betelgeuse,

we need to use the formula for average density, which is:

Average density = Mass/VolumeHere,

Betelgeuse has 16 times the mass of our sun.

Therefore, its mass (M) is given by:

M = 16 × (2 × 10²³) kg

M = 32 × 10²³ kg

M = 3.2 × 10²⁴ kg

Betelgeuse has a radius (r) of 500 million km.

We need to convert it to meters:r = 500 million

km = 500 × 10⁹ m

The volume (V) of Betelgeuse can be calculated as:

V = 4/3 × π × r³V = 4/3 × π × (500 × 10⁹)³

V = 4/3 × π × 1.315 × 10³⁵V = 2.205 × 10³⁵ m³

Therefore, the average density (ρ) of Betelgeuse can be calculated as:

ρ = M/Vρ = (3.2 × 10²⁴) / (2.205 × 10³⁵)

ρ = 1.45 × 10⁻¹¹ kg/m³

Thus, the average density of the red supergiant star Betelgeuse is 1.45 × 10⁻¹¹ kg/m³.

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The inequalities x≤2 or x<5 are unequal expressions

The common points of both inequalities are {.......0,1,2}

Inequalities are expressions that have unequal values

Number lines are lines that are used to represent numbers and expressions at regular intervals

The inequalities are given as;

x≤2 or x<5

This means that:

x is less than or equal to 2

And

x is less than 5

So, we have:

x≤2 = {.......0,1,2}

x<5 = {.......0,1,2,3,4}

The common points of both inequalities are:

x≤2 or x<5 = {.......0,1,2}

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Answer:

\((3x^2-5x-19)$ Square feet of brick\)

Step-by-step explanation:

\(\text{The total area of the brick and pool }=6x^2 - 21\\\text{The area of the pool }= 3x^2 + 5x - 2. \\\)

The total area of the brick and pool =Area of the Brick + Area of the Pool

Therefore:

Area of the Brick=Total area of the brick and pool-Area of the Pool

\(=(6x^2 - 21)-(3x^2 + 5x - 2)\\=6x^2-21-3x^2-5x+2\\$Collect like terms\\=6x^2-3x^2-5x-21+2\\$Simplify\\=(3x^2-5x-19)$ Square feet\)

Answer:

The speaker is a child who cannot understand the concept of a shadow or what it is, that it isn't another person, and instead looks at his shadow in a new way, showing the reader how to think past the mere science of it. rhuman being.

Step-by-step explanation:

Answer:

Oliver walked 3 miles in 2 hours and he walked 24 miles in 16 hours.

Step-by-step explanation:

Divide 9 by 6 and you'll get 1.5. 1.5 goes into 3 two times, so the first answer is 2 and then do 16 times 1.5 and you'll get 24.

Hope this helps.  

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