What is the recursive formula for the perimeter of a square of side n(the nth perimeter) using the first number(perimeter) in the pattern?

Answer:

$134,061.09

Step-by-step explanation:

hope this helps

Answer:

134,061.09

Step-by-step explanation:

Divide 13,409,109 by 100

This can also be expressed as 134, 061 dollars, and 9 pennies.

Answer: 4

Step-by-step explanation:

Corresponding sides of similar triangles are proportional, so

\(\frac{y}{12}=\frac{5}{15}\\\\\frac{y}{12}=\frac{1}{3}\\\\y=4\)

Answer:

129

Step-by-step explanation:

Answer:

129

Step-by-step explanation:

180 - 51 = 129

Answer:

The  null hypothesis is  \(H_o : \mu = 445\)

The  alternative hypothesis  \(H_a : \mu < 445\)  (This is the original claim[ It is believed that the machine is under filling the bags] )

Step-by-step explanation:

From the question we are told that  

    The population mean is   \(\mu = 445 \ g\)

    The  sample size is  \(n = 12\)

    The  sample mean is  \(\= x = 442 \ g\)

     The  standard deviation is  \(\sigma = 20\)

     The  level of significance is  \(\alpha = 0.05\)

The  null hypothesis is  \(H_o : \mu = 445\)

The  alternative hypothesis  \(H_a : \mu < 445\)  (This is the original claim )

Answer:

456

Step-by-step explanation:

It is shared by 3 people so it will be multiplied by 3.

Answer:

5472

Step-by-step explanation:

If the mean between three people is 152 kilometers per month, the distance travelled in a month is 152 * 3 = 456.

Then we multiply 456 by 12 to get the number of km travelled in a year.

456 * 12 = 5472

Yes, the additional education costing $36,000 will pay for itself in less than 2 years based on the increased earning potential.

To determine whether the additional education costing $36,000 will pay for itself, we need to consider the time it takes to recover the investment through the increased earning potential.

The additional yearly earning potential is the difference between the post-education income ($39,746) and the pre-education income ($21,484), which is $18,262.

To calculate the payback period, we divide the cost of education ($36,000) by the annual increase in earning potential ($18,262).

Payback Period = Cost of Education / Annual Increase in Earning Potential

Payback Period = $36,000 / $18,262

The payback period is approximately 1.97 years, meaning that it would take approximately 1.97 years to recover the cost of education through the increased earning potential.

If the time required to recover the cost is less than the time in which the increased earning potential will be realized, then the additional education would be considered to have paid for itself.

In this case, since the payback period is less than 2 years and the increased earning potential will continue for subsequent years, it can be concluded that the additional education costing $36,000 will pay for itself over time.

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Answer:

0 hours.

Step-by-step explanation:

He finished at the same time than Kenrick finished last week. So, he/she did not delay in mowing the lawn. Hoped this helped.

The simplified form of -20/2(7 2/3) is -230/3.

To solve the expression -20/2(7 2/3), we need to follow the order of operations, which states that we should perform the operations inside parentheses first, then any multiplication or division from left to right, and finally any addition or subtraction from left to right.

First, let's convert the mixed number 7 2/3 to an improper fraction.

7 2/3 = (7 * 3 + 2) / 3 = 23/3

Now, let's substitute the value back into the expression:

-20/2 * (23/3)

Next, we simplify the multiplication:

-10 * (23/3)

To multiply a fraction by a whole number, we multiply the numerator by the whole number:

-10 * 23 / 3

Now, we perform the multiplication:

-230 / 3

Therefore, the simplified form of -20/2(7 2/3) is -230/3.

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Answer:

\(s \ne \±2\)

\(x_1 = \frac{3s - 2}{3(s^2 -4)}\)

\(x_2 = \frac{2(s- 6)}{5(s^2 - 4)}\)

Step-by-step explanation:

Given

\(3sx_1 +5x_2 = 3\)

\(12x_1 + 5sx_2 =2\)

Required

Determine the value of s

Express the equations as a matrix

\(A =\left[\begin{array}{cc}3s&5\\12&5s\end{array}\right]\)

Calculate the determinant

\(|A|= (3s*5s -5 *12)\)

\(|A|= (15s^2 -60)\)

Factorize

\(|A|= 15(s^2 -4)\)

Apply difference of two squares

\(|A|= 15(s -2)(s + 2)\)

For the system to have a unique solution;

\(|A| =0\)

So, we have:

\(15(s -2)(s+2) = 0\)

Divide both sides by 15

\((s -2)(s+2) = 0\)

Solve for s

\(s -2 = 0\ or\ s +2 = 0\)

\(s = 2\ or\ s = -2\)

The result can be combined as:

\(s =\±2\)

Hence, the system has a unique solution when \(s \ne \±2\)

Next, we solve for s using Cramer's rule.

We have:

\(mat\ x_1 = \left[\begin{array}{cc}3&5\\2&5s\end{array}\right]\)

Calculate the determinant

\(|x_1| = (3 * 5s - 5 *2)\)

\(|x_1| = 15s - 10\)

So:

\(x_1 =\frac{|x_1|}{|A|}\)

\(x_1 = \frac{15s - 10}{15(s -2)(s+2)}\)

Factorize

\(x_1 = \frac{5(3s - 2)}{15(s -2)(s+2)}\)

Divide by 5

\(x_1 = \frac{3s - 2}{3(s -2)(s+2)}\)

\(x_1 = \frac{3s - 2}{3(s^2 -4)}\)

Similarly:

\(mat\ x_2 =\left[\begin{array}{cc}3s&3\\12&2\end{array}\right]\)

Calculate the determinant

\(|x_2| = 3s * 2 - 3 * 12\)

\(|x_2| = 6s- 36\)

So:

\(x_2 =\frac{|x_2|}{|A|}\)

\(x_2 = \frac{6s- 36}{15(s -2)(s+2)}\)

Factorize

\(x_2 = \frac{6(s- 6)}{15(s -2)(s+2)}\)

Divide by 3

\(x_2 = \frac{2(s- 6)}{5(s -2)(s+2)}\)

\(x_2 = \frac{2(s- 6)}{5(s^2 - 4)}\)

The coordinates of point B are (-3, 17).

The given equation is M = I₁ + I₂ = 31 + 32.

Now let's substitute in our given values:

(-2, 2) = ((-5 + x₂) / 2, (-5 + 2 + y₂) / 2)

We will now set up two equations to solve for our two unknowns, x₂ and y₂:

Equation 1: (-5 + x₂) / 2 = -4

Multiply both sides by 2:

-5 + x₂ = -8

Add 5 to both sides:

x₂ = -3

This gives us the x-coordinate of point B.

Equation 2: (-5 + 2 + y₂) / 2 = 7

Simplify:

(-3 + y₂) / 2 = 7

Multiply both sides by 2:

-3 + y₂ = 14

Add 3 to both sides:

y₂ = 17

This gives us the y-coordinate of point B.

Therefore, the coordinates of point B are (-3, 17).

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Answer:

512 ft and 1,232 ft

Step-by-step explanation:

area is length x width

the pool's area can be calculated doing 32ft x 16ft

the area of the pool is 512 ft

the deck's area can be calculated doing 28ft x 44ft

the area of the deck is 1,232 ft

you're welcome<3

The annual interest rate is 7.5%.

What is Simple interest?

Simple interest is a type of interest that is calculated on the principal amount (or the initial amount) of a loan or investment, without taking into account any accumulated interest from previous periods.

The formula for simple interest is:

I = P × r × t

where I is the interest earned, P is the principal (initial amount), r is the annual interest rate as a decimal, and t is the time in years.

In this case, we know I = $562.50, P = $1500, and t = 5 years.

we ca substitute values into the formula,

562.50 = 1500× r ×5

Simplifying, we get:

r = 562.50 / (1500 ×5)

r = 0.075

r = 7.5%

Therefore, the annual interest rate is 7.5%.

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Answer: Addition

Step-by-step explanation:

x-7 = 15

x-7+7 = 15+7 ==> Addition

x=15+7

x=22

You'll lose on average $22 per roll.

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

Explanation:

Normally there is a 1/6 chance to land on any given side of a standard die, but your friend has loaded the die in a way to make it have a 40% chance to land on "1" and an equal chance to land on anything else. Since there's a 40% chance to land on "1", this leaves 100% - 40% = 60% for everything else.  

Let's define two events

So far we know that P(A) = 0.40 and P(B) = 0.60; I'm using the decimal form of each percentage.

The net value of event A, which I'll denote as V(A), is -100 since you pay $100 when event A occurs. So we'll write V(A) = -100. Also, we know that V(B) = 30 and this value is positive because you receive $30 if event B occurs.

To recap things so far, we have the following:

Multiply the corresponding probability and net value items together

Then add up those products:

-40+18 = -22

This is the expected value, and it represents the average amount of money you earn for each dice roll. So you'll lose on average about $22. Because the expected value is not zero, this means this game is not mathematically fair.

This does not mean that any single die roll you would lose $22; instead it means that if you played the game say 1000 or 10,000 times, then averaging out the wins and losses will get you close to a loss of $22.

Answer:

not sure what is the question

Step-by-step explanation:

We can write the scale factor for the table as {K} = y/x.

Given is to determine the scale for the given table.

Therefore, we can write the scale factor for the table as {K} = y/x.

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Answer:

l = 1.8 feet

Step-by-step explanation:

Given that,

The time period of the pendulum, T = 2.7 seconds

We need to find the length of the swing. The formula for the time period of a simple pendulum is given by :

\(T=2\pi \sqrt{\dfrac{l}{g}}\)

Where

l is the length of the swing.

\(T^2=\dfrac{4\pi^2l}{g}\\\\l=\dfrac{T^2g}{4\pi^2}\\\\l=\dfrac{(2.7)^2\times 9.8}{4\times 3.14^2}\\\\l=1.8\ \text{feet}\)

So, the length of the swing is 1.8 feet long.

Answer:5.4

Step-by-step explanation:

Answer:

X = 4

Y = 30

i think.

Step-by-step explanation:

1

Step

Multiple both numerator and both denominator

2

3

4

Answer:

Step-by-step explanation:

To find the area of the shaded region, we need to first find the x-coordinates of the points where the two functions intersect. We can set f(x) = g(x) and solve for x:

x^4 - 12x^3 + 48x^2 = 44x + 105

x^4 - 12x^3 + 48x^2 - 44x - 105 = 0

We can use a numerical method, such as the Newton-Raphson method, to approximate the roots of this equation. Using a graphing calculator or computer algebra system, we can find that the roots are approximately:

x = -1.932, x = 0.695, x = 4.149

Note that the root x = -1.932 is outside the given interval [3, 4], so we can ignore it.

The shaded region is bounded by the x-axis, the line y = 340, and the graphs of f(x) and g(x) between x = 3 and x = 4. To find the area of this region, we can integrate the difference between the two functions over this interval:

A = ∫3^4 [g(x) - f(x)] dx

A = ∫3^4 [44x + 105 - (x^4 - 12x^3 + 48x^2)] dx

A = ∫3^4 [-x^4 + 12x^3 - 48x^2 + 44x + 105] dx

We can integrate term by term using the power rule:

A = [-x^5/5 + 3x^4 - 16x^3 + 22x^2 + 105x]3^4

A = [-1024/5 + 192 - 192 + 22 + 105] - [-81/5 + 108 - 192 + 66 + 105]

A = 347.2

Therefore, the area of the shaded region is approximately 347.2 square units.

If you draw the bounded region in the x,y-plane, you'll find it to be somewhat ambiguous, but since y = 0 cuts the area between the parabola x = y ² and x = 4 perfectly in half, you can use either the top or bottom half. I'll use the top one, i.e. assume y ≥ 0.

For every x taken from the interval [0, 4], we can get a shell with height √x. The distance from x to the axis of revolution, x = 5, is 5 - x, which corresponds to the radius of the shell. The area of this shell is

2π (radius) (height) = 2π (5 - x) √x

Then the volume of the solid is the sum of infinitely many such shells made at every 0 ≤ x ≤ 4, given by the integral

\(\displaystyle 2\pi \int_0^4 (5-x)\sqrt x\,\mathrm dx = 2\pi \int_0^4 \left(5x^{1/2}-x^{3/2}\right)\,\mathrm dx \\\\ = 2\pi \left(\frac{10}3x^{3/2}-\frac25x^{5/2}\right)\bigg|_0^4 \\\\ = \boxed{\frac{416\pi}{15}}\)

Answer:

18cm

Step-by-step explanation:

Given:

- The length of AB is 9 centimeters

- A dilation with a scale factor of 2

The length of the image AB after the dilation is applied:

9 x 2 = 18

dilation is used to make an image or in this case AB, with a scale factor of 2 means that its doubling in size. If the scale factor was 1/2 that it would be decreasing in size since it will be half of the original size

Answer:

\(y=\frac{1}{3}x+7.6666\)

Step-by-step explanation:

First we must convert  \(3x+y=-7\) into slope-intercept form!

To do this we simply just need to subtract -3x from the 3x on the left and move it to the right side. This would result in: \(y = -3x-7\)

Now that we have our slope-intercept form for the equation remember that to find the equation that is perpendicular to the given equation, you need to use the opposite reciprocal of the slope. This would be \(\frac{1}{3}\) as that is the reciprocal and opposite of \(-\frac{3}{1}\)

Now in order to find the "b" variable of the equation that goes through the ordered pair (1, 8) we need to plug it in to the given equation!

That equation would be: \(y=\frac{1}{3}x-7\)

Given that x = 1 and y = 8 we can plug those in like so:

\(8=\frac{1}{3}(1)+b\)

(make sure to set the -7 to b as that's what we're solving for)

1 / 3 is 0.3333 (infinitely repeating)

Next we need to subtract 0.3333 from 8, which would be 7.6666 (infinitely repeating) Remember that the variable needs to be "alone"!

Now we have our "b" for the equation! Hence the equation would be:

\(y=\frac{1}{3}x+7.6666\)

(you can also use \(\frac{23}{3}\) for the b as that is the "exact form" of 1 / 3 but they both work)

Hope this helps! Feel free to ask questions!

Answer:

Answer: 90% of people marry there 7th grade love. since u have read this, u will be told good news tonight. if u don't pass this on nine comments your worst week starts now this isn't fake. apparently if u copy and paste this on ten comments in the next ten minutes you will have the best day of your life tomorrow. you will either get kissed or asked out in the next 53 minutes someone will say i love you.

Step-by-step explanation:

The perimeter of a rectangle is the sum of the lengths of its four sides. The perimeter is C. 28 units.

The perimeter of a two-dimensional shape is the total distance around its outer boundary. The formula for finding the perimeter depends on the shape you are dealing with.

Rectangle: Perimeter = 2(length + width)

The perimeter of a rectangle is the sum of the lengths of its four sides. In this case, the sides of the rectangle are 4 units, 10 units, 4 units, and 10 units. Therefore, the perimeter is:

= 4+10+4+10

= 28  units.

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Yes, Timothy is correct because triangle AKLM was dilated by using a scale factor of 1.5 centered at the origin.

In Mathematics, dilation can be defined as a type of transformation that is typically used for enlarging or reducing the size of a geometric object but not its shape, based on the scale factor.

For the given coordinates of the preimage triangle KLM, the dilation with a scale factor of 1.5 from the origin (0, 0) would be calculated as follows:

Coordinate K (-1, 3) → Coordinate K' (-1 × 1.5, 3 × 1.5) = Coordinate K' (-1.5, 4.5).

Coordinate L (8, 4) → Coordinate L' (8 × 1.5, 4 × 1.5) = Coordinate L' (12, 6).

Coordinate M (10, -3) → Coordinate M' (10 × 1.5, -3 × 1.5) = Coordinate M' (15, -4.5).

In conclusion, the coordinates of the image triangle K'L'M after a dilation with a scale factor of 1.5 from the origin are (-1.5, 4.5), (12, 6), and (15, -4.5) as shown in the graph above, therefore, Timothy is correct.

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Answer: 2*L - 5 = 11

Step-by-step explanation:

Suppose that we have a rectangle with length L and width W.

Now we know that:

" 5 less than twice the length equals 11"

Then we get:

"twice the length" is written as 2*L

5 less than that is:

2*L - 5

And this is equal to 11, then:

2*L - 5 = 11

This is the algebraic equation we wanted to find,

Answer:

-13, 8

Step-by-step explanation:

(x-3)(x+8) = 80

use FOIL to eliminate parenthesis

x² +8x - 3x - 24 = 80

combine like terms

x² + 5x - 24 = 80

move the constant to the left

x² + 5x - 104 = 0

factor x and then factor -8

x(x+13) - 8(x+13) = 0    factor (x+13)

(x+13)(x-8) = 0

separate into possible cases

x + 13 = 0

x - 8 = 0

solve

x = -13

x = 8

have a lovely day <3