What is the value of n when (9)^2n-1 =(27)^n+2

Answer:

The balance after 7 years would be $2,548.79

Step-by-step explanation:

We are given the following in the question:

P = $1800

r = 5% = 0.05

t = 7 years

The compound interest is given by:

[tex]A = p\bigg(1+\dfrac{r}{n}\bigg)^{nt}[/tex]

where A is the amount, p is the principal, r is the interest rate, t is the time in years and n is the nature of compound interest.

When compounded quarterly, n = 4

Putting values, we get,

[tex]A = 1800\bigg(1+\dfrac{0.05}{4}\bigg)^{28}\\\\A = \$2,548.79[/tex]

Thus, the balance after 7 years would be $2,548.79

Answer:

45.9ft/s

Step-by-step explanation:

Simply plug your given value into the function

[tex]f(26)=9\sqrt{26} = 45.9 (1.d.p.)[/tex]

Answer:

CI=[ 7.1302,7.2698]

we are 95% confident that the true mean sleeping time lies between the interval[ 7.1302,7.2698]

Step-by-step explanation:

-Given that the sample size, n=1546  the mean is 7.2 hrs and the standard deviation, [tex]\sigma=1.4[/tex]

-The 95% confidence interval can be calculated using the formula:

[tex]CI=\mu\pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}\\\\=\mu\pm z_{0.025}\times \frac{\sigma}{\sqrt{n}}\\\\=7.2\pm1.96\times \frac{1.4}{\sqrt{1546}}\\\\=7.2\pm 0.0698\\\\CI=[7.1302, \ 7.2698][/tex]

The confidence intervals is therefore 7.1302,7.2698]

Hence, we are 95% confident that the true mean sleeping time lies between the interval[ 7.1302,7.2698]

Answer:

Step-by-step explanation:

the answers for "in e^3" is 3

                          "in e^2y" is 2y

                          "e^in 1" is 1

                          "e^in 5x" is 5x

Answer: 3, 2y, 1, 5x.

We have to simplify the given expressions.

We use the formula: [tex]ln(e^a)=a[/tex].

So, [tex]ln(e^3)=3[/tex], here a = 3.

[tex]lne^{2y}=2y[/tex], here a = 2y.

We will use that: ln(1) = 0 and [tex]e^{ln(b)}=b[/tex]

[tex]e^{ln(1)}=e^0=1[/tex]

[tex]e^{ln(5x)}=5x[/tex], here b = 5x.

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Answer:

x/4 + 5 = 7

      -5    -5

x/4 = 2

*4     *4

x=8

Step-by-step explanation:

Answer:

its 8

Step-by-step explanation:

i know so big brains

Answer:

m= -7

Step-by-step explanation:

using the slope formula, plug in the variables and solve

m=rise/run

m=y2-y1 / x2-x1

(x1, y1) = coordinates of first point in the line

(x2, y2) = coordinates of second point in the line

Answer:

[tex]slope=-7[/tex]

Step-by-step explanation:

Use the slope formula for when you have two points:

[tex]\frac{y(2)-y(1)}{x(2)-x(1)}[/tex]

It is y over x because slope is rise over run : the change in the y-axis over the change in the x-axis. Plug in values:

(-4,6) (-3,-1)

[tex]\frac{-1-6}{-3-(-4)}[/tex]

Simplify

[tex]\frac{-1-6}{-3+4}=\frac{-7}{1}[/tex]

Simplify

[tex]\frac{-7}{1}=-7[/tex]

Done.

Answer:

y = 6

Step-by-step explanation:

if the triangles are congruent then the corresponding sides are equal.

so

4x + 1 = 13

4x = 13 -1

4x = 12

Therefore x = 3

Now

8x - 2y = 2x + y

y + 2y = 8x - 2x

3y = 6x

3y = 6 * 3

3y =18

Therefore y = 6

Answer:

y = 6

Step-by-step explanation:

Since the triangles are congruent then corresponding sides are congruent

4x + 1 = 13  ( hypotenuse are congruent )

Subtract 1 from both sides

4x = 12 ( divide both sides by 4 )

x = 3

Thus

8x - 2y = 2x + y ( substitute x = 3 )

8(3) - 2y = 2(3) + y, that is

24 - 2y = 6 + y ( subtract y from both sides )

24 - 3y = 6 ( subtract 24 from both sides )

- 3y = - 18 ( divide both sides by - 3 )

y = 6

Answer:

Step-by-step explanation:

hello :

Ax + 3x = bx + 5

Ax + 3x-bx = bx-bx + 5

x(A+3-b) =5

x= 5/(A+3-b)

Answer:

Quadrilateral

Explanation:

there are only for points,

triangle= three points

hexagon= 6 points

pentagon= 5 points

The   A(1, 2), B(4, 5), C(4, -3), and D(1, -1) forms a quadrilateral.

A quadrilateral is a closed object in geometry that is created by connecting four points, any three of which are not collinear. There are 4 sides, 4 angles, and 4 vertices in a quadrilateral.

The points A (1, 2), B (4, 5), C (4, -3), and D (1, -1) form a quadrilateral

as all four points are noncolinear.

These four points represent four vertices of a quadrilateral.

learn more about quadrilaterals here :

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Answer:

Car A and Car B are moving in opposite directions.

Car A is moving faster than Car B.

Car A and Car B pass each other at the crossover point on the graph.

Step-by-step explanation:

Hope that helps!

Answer:

see explanation

Step-by-step explanation:

Using the cosine and tangent trigonometric ratios and the exact values

cos30° = [tex]\frac{\sqrt{3} }{2}[/tex] and tan30° = [tex]\frac{1}{\sqrt{3} }[/tex] , then

cos30° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{6}{m}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )

[tex]\sqrt{3}[/tex] × m = 12 ( divide both sides by [tex]\sqrt{3}[/tex] )

m = [tex]\frac{12}{\sqrt{3} }[/tex] ← rationalise by multiplying numerator/ denominator by [tex]\sqrt{3}[/tex] )

m = [tex]\frac{12}{\sqrt{3} }[/tex] × [tex]\frac{\sqrt{3} }{\sqrt{3} }[/tex] = [tex]\frac{12\sqrt{3} }{3}[/tex] = 4[tex]\sqrt{3}[/tex]

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

tan30° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{n}{6}[/tex] = [tex]\frac{1}{\sqrt{3} }[/tex] ( cross- multiply )

[tex]\sqrt{3}[/tex] × n = 6 ( divide both sides by [tex]\sqrt{3}[/tex] )

n = [tex]\frac{6}{\sqrt{3} }[/tex] ← rationalise the denominator

n = [tex]\frac{6}{\sqrt{3} }[/tex] × [tex]\frac{\sqrt{3} }{\sqrt{3} }[/tex] = [tex]\frac{6\sqrt{3} }{3}[/tex] = 2[tex]\sqrt{3}[/tex]

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

Answer:

You would have -31 points left.  :)

196 - 227 = -31

Hope this helped!!

Answer:

-31

Step-by-step explanation:

196 - 227 = -31

Answer:

The answer to your question is the letter a

Step-by-step explanation:

 |    1    4    -1   |      |  2    -1   |

 |    3   2    2   |      |  0     3  |         Product  = 2 x 3   and 3 x 2  = 2 x 2

                              | 5     2  |          It is possible to do this product,

                                                      the result will be a 2 x 2 matrix

Process

1.- Multiply first row by first column and second row by second column.

2.- Multiply the second row by the first column and second row by the second column.

  = (1 x 2) + (4 x 0) + (-1 x 5) = 2 + 0 - 5 = -3

  = (1 x -1) + (4 x 3) + (-1 x 2) = -1 + 12 - 2 = 9

  = (3 x 2) + (2 x 0) + (2 x 5) = 6 + 0 + 10 = 16

  = (3 x -1) + (2 x 3) + (2 x 2) = -3 + 6 + 4 = 7

Result

             |  3   9  |

             | 16   7  |    

Answer:

Add 8x to both sides of the inequality

Step-by-step explanation:

took the quiz

The sample standard deviation of the given data set is approximately 20.72.

To find the sample standard deviation, we can use the following steps:

Answer:

7. x = -2 +/- [tex]4i\sqrt{5}[/tex]

8. x = 2 or x = 6

9. x = -2 +/- [tex]\frac{\sqrt{26} }{2} i[/tex]

10. t = -3 +/- [tex]\sqrt{35}[/tex]

Step-by-step explanation:

7. Subtract 320 from both sides: 4(x + 2)^2 = -320

Divide by 4: (x + 2)^2 = -80

Square root both sides: x + 2 = +/- [tex]\sqrt{-80}[/tex]. We need to add the imaginary i to this: +/- [tex]\sqrt{-80}[/tex] = +/- [tex]i\sqrt{80}[/tex] = +/- [tex]4i\sqrt{5}[/tex]

Subtract 2 from both sides: x = -2 +/- [tex]4i\sqrt{5}[/tex]

8. Add 18 to both sides: 7(x - 4)^2 = 28

Divide by 7: (x - 4)^2 = 4

Square root both sides: x - 4 = +/- 2

Add 4 to both sides: x = 4 +/- 2  ⇒  x = 2 or x = 6

9. Add 5 to both sides: -2(x + 2)^2 = 13

Divide by -2: (x + 2)^2 = -13/2

Square root both sides: x + 2 = +/- [tex]\sqrt{-13/2}[/tex]. We again need i: +/- [tex]\sqrt{-13/2}[/tex] = +/- [tex]i\sqrt{13/2} =[/tex] +/- [tex]\frac{\sqrt{26} }{2} i[/tex]

Subtract 2 from both sides: x = -2 +/- [tex]\frac{\sqrt{26} }{2} i[/tex]

10. Multiply by 5 on both sides: (t + 3)^2 = 35

Square root both sides: t + 3 = +/- [tex]\sqrt{35}[/tex]

Subtract 3: t = -3 +/- [tex]\sqrt{35}[/tex]

Hope this helps!

Answer:

7. -2 + 4sqrt(5) i, -2 - 4sqrt(5) i

8. x = 2, 6

9. x = -2 + sqrt(13/2) i, -2 - sqrt(13/2) i

10. t = -3 + sqrt(35), -3 - sqrt(35)

Step-by-step explanation:

7. 4(x + 2)² + 320 = 0

(x + 2)² = -80

x + 2 = +/- i × sqrt(80)

x + 2 = +/- i × 4sqrt(5)

x = -2 +/- i × 4sqrt(5)

8. 7(x - 4)² - 18 = 10

(x - 4)² = 4

x - 4 = +/- 2

x = 2, 6

9. -2(x + 2)² - 5 = 8

(x + 2)² = -13/2

(x + 2) = +/- i × sqrt(13/2)

x = -2 +/- i × sqrt(13/2)

10. 1/5(t + 3)² = 7

(t + 3)² = 35

t + 3 = +/- sqrt(35)

t = -3 +/- sqrt(35)

Answer:

36 Square Yards

Step-by-step explanation:

The Scale Drawing uses a ratio

2 Inches : 3 Yards

Therefore,

1 Inch = 3/2 Yards

If the area of the scale drawing is 16 Inch²

To get the area of the actual office, we multiply by the square of the scale factor.

Scale Factor=3/2

Therefore:

The area of the actual office space

=16X(3/2)² Square Yards

=36 Square Yards

Answer:

36 square yards.

Step-by-step explanation:

This question is solved with rule of three and ratios

We know that 2 inches is equivalent to 3 yards, and the area in the drawing is 16 square inches.

so if

2 inches ---- 3 yards then 1 inch is 3/2 yards.

Let's say that the office is 8 inches x 2 inches = 16 squared inches

Then, if we convert it to yards,

8 inches would be: [tex]8(\frac{3}{2})=12[/tex] yards

and 2 inches would be: [tex]2(\frac{3}{2})=3[/tex] yards

Then, the area of the office would be 12 x 3 = 36 squared yards.

Answer:

20 gallons per 180 miles

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

You distribute the 11 with the numbers in the parenthesis

Answer:

[tex]6x+2y=-2\\3x-2y=-5\\-------\\9x=-7[/tex]

Answer:

3:4

Step-by-step explanation:

Before we start to deal with the ratio, we need all lengths in the same units.

The width is 18 inches.

The height is 2 feet.

Let's convert the height to inches. Then we will have both dimensions in the same units, inches.

2 ft * (12 in.)/ft = 24 in.

Now we have:

width = 18 in.

height = 24 in.

ratio of width to height = 18 in. to 24 in. = 18/24 = 3/4 = 3:4

Final answer:

The ratio of the width to the height of the bonsai tree is 3:4 after converting both measurements to inches and simplifying. For the scale of a flower garden with a 1:12 scale and a plan width of 6 inches, the actual width of the garden is 6 feet.

Explanation:

The student asked about the ratio of the width to the height of a bonsai tree. First, it's important to have both measurements in the same units. Since the height is given in feet and the width in inches, we need to convert the height from feet to inches. There are 12 inches in a foot, so the height is 2 feet x 12 inches/foot = 24 inches. The resulting ratio of the width to the height is therefore 18 inches (width) to 24 inches (height). To simplify the ratio, we can divide both numbers by their greatest common divisor, which is 6 in this case. This gives us a simplified ratio of 3 to 4.

When calculating a scale for a flower garden, based on the available information where the plan shows 6 inches wide and the scale is 1:12, setting up the proportion would look like this: 1 inch on the plan equals to 12 inches in the actual garden. Therefore, to find the actual width of the flower garden, we multiply 6 inches (on the plan) by 12, resulting in an actual width of 72 inches or 6 feet.

Complete Question:

Justify the rationale behind Ms Calcutta's decision to use the circumcenter

Answer:

Check below for the answer and explanations.

Step-by-step explanation:

Ms Calcutta wants every occupant of the three office buildings to have equal easy access to the recycling station. The circumcenter of the three three office buildings, where the recycling station is located, has equal distance from the three offices, this means that all of Ms. Calcutta's workers in the three buildings can have to the recycling station equally without causing unnecessary inconvenience for occupants of any of the buildings.

Answer:

4

Step-by-step explanation:

As you only need the answer (•‿•)

Answer:

5 shirts

Step-by-step explanation:

First, subtract the shipping from her money. 45 - 2.50 = 42.50. Now divide this by the price of each shirt. 42.50 ÷ 8.50 = 5. The shipping fee only applies once because it is for the entire order.

The front wheel of the bicycle makes approximately 18 complete revolutions.

To find the number of complete revolutions the front wheel makes, we need to know the circumference of the wheel. Let's assume the diameter of the wheel is 0.7 meters. The circumference of the wheel can be calculated using the formula C = πd, where C is the circumference and d is the diameter. Substituting the given values, C = 3.14 * 0.7 = 2.198 meters.

Since the bicycle travels 40 meters, we can divide the distance traveled by the circumference of the wheel to find the number of complete revolutions. 40 / 2.198 = 18.19.

So, the front wheel of the bicycle makes approximately 18 complete revolutions.

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Answer:

Its D i did the question

Step-by-step explanation:

Answer:

  $26.0 million

Step-by-step explanation:

Use t=3 and do the arithmetic.

  S = 42e^(-0.16·3) = 42e^-0.48 ≈ 26.0

Three months after the end of the campaign, monthly sales are predicted to be $26.0 million.

Answer:

$26.0 million

Step-by-step explanation:

Answer:

communicating results

Step-by-step explanation:

hope this helps

Answer:

82.16 m²

Step-by-step explanation:

15.8 m x 5.2 m