Calculate the partial sum S for the sequence 243,81,27,....

Hope this helps!!!!!!!!!

Answer:

Refer to the image attached

Step-by-step explanation:

[tex]z_0=3-2i\\\\z_{n+1}=2z_n+i\\\\z_1=z_{0+1}=2z_0+i\to z_1=2(3-2i)+i=6-4i+i=6-3i\\\\z_2=z_{1+1}=2z_1+i\to z_2=2(6-3i)+i=12-6i+i=12-5i\\\\z_3=z_2+1}=2z_2+i\to z_3=2(12-5i)+i=24-10i+i=24-9i\\\\Answer:\ \boxed{6-3i;\ 12-5i;\ 24-9i}[/tex]

Final answer:

To determine the sale price with a 65% markup on a skirt bought for $4.50, calculate the markup in dollars, add it to the original cost, and round to the nearest cent to get the final price of $7.43.

Explanation:

To find the sale price of the skirt after a markup of 65%, we first calculate the amount of the markup by multiplying the cost by the markup rate. The markup on the skirt that costs $4.50 would be:

$4.50 times 0.65 = $2.925.

Now, add the markup to the original cost to find the sale price:

$4.50(original cost) + $2.925(markup) = $7.425

However, prices are not typically listed with three decimal places, so we would round to the nearest cent, making the final sale price of the skirt $7.43.

Answer:

B

Step-by-step explanation:

= 6cos ([tex]\frac{5\pi }{6}[/tex]) + 6i sin ([tex]\frac{5\pi }{6}[/tex])

the related acute angle of [tex]\frac{5\pi }{6}[/tex] is [tex]\frac{\pi }{6}[/tex]

= - 6 cos ([tex]\frac{\pi }{6}[/tex]) + 6i sin ([tex]\frac{\pi }{6}[/tex])

= - 6 × [tex]\frac{\sqrt{3} }{2}[/tex] + 6 i × [tex]\frac{1}{2}[/tex]

= - 3[tex]\sqrt{3}[/tex] + 3i → B

Answer:

We are given eqaution: e=\frac{17}{20}d , where e the amount of euros and d is the value as U.S. Dollars.

We need to find number of euros for 1 U.S. Dollar.

Plugging d=1 in the given equation

We get

e=\frac{17}{20}(1)

On simplfying , we get

e=\frac{17}{20}

Dividing 17 by 20, we get 0.85.

Therefore, there would be 0.85 euro have the same value as 1 U.S. Dollar.

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Step-by-step explanation:

Answer:

Step-by-step explanation:

There is missing information, the complete question is:

We can calculate e, the amount of euros that has the same value as d U.S. Dollars, using the equation [tex]e=\frac{17}{20}d[/tex], in words, e equals, start fraction, 17 divided by 20, end fraction, d. How many euros have the same value as 1 U.S. Dollar?

Basically, the problem offer a equation that allows to transform certain amount of American dollars into euros. In the expression given, e is the amount of euros and d is the amount of dollars. Now, the problem is asking how many euros would be 1 U.S. Dollar, to do that we have to use the equation and replace values:

[tex]e=\frac{17}{20}d\\e=\frac{17}{20}(1 USD)= 0.85[/tex]

Therefore, one dollar equals 0.85 euros.

Answer:

660

Step-by-step explanation:

first you multiply the first 10,000 by 5%. 10,000*5%=500 or 10,000*0.05=500. after you do that, you multiply the money left over by 8%, in this case the money left over is 2,000 dollars. 2,000*8%= 160. Then you add the two numbers together. 500+160= 660. and there you have your answer. Hope it helped!

Final answer:

To calculate the commission on a $12,000 car sale, compute 5% of the first $10,000 and 8% of the remaining $2,000, then add these to find the total commission of $660.

Explanation:

The question is about calculating the commission on a car sale given a two-tiered commission structure. The salesperson receives 5% commission on the first $10,000 of the sale and 8% commission on any amount over $10,000.

Step-by-step Calculation:

Calculate the commission on the first $10,000 at 5%: $10,000 * 0.05 = $500.

Calculate the commission on the remaining $2,000 at 8%: $2,000 * 0.08 = $160.

Add the two commission amounts together to get the total commission: $500 + $160 = $660.

The salesperson's total commission for selling a $12,000 car would be $660.

Expand

12x - 48 + 4x + 28

Collect like terms

(12x + 4x) + (-48 + 28)

Simplify

16x - 20

Answer:

16x - 20

Step-by-step explanation:

12(x-4)+4(x+7)

Applying the distributive law to both parentheses:-

= 12x - 48 + 4x + 28

= 16x - 20  

Answer:

Number 95 is bigger than number 85.

Step-by-step explanation:

If we want to find which number is the bigger one; we subtract the numbers in  two orders:

95 - 85 = 10

and

85 - 95 = -10

Since the first order (95 - 85) gives a positive answer;

Then it implies that number 95 is bigger than number 85.

Since the second order (85 - 95) gives a negative answer;

Then it implies that number 85 is smaller than number 95.

Answer:

64pi

Step-by-step explanation:

So the volume of a sphere is 4/3pi r^3. So the total area would be 6*4/3*8*pi. So that’s 64pi.

Answer:

201.06 cubic centimeters.

Step-by-step explanation:

Hello

I think   I can help you with this

the volume of a sphere is given by:

[tex]V=\frac{4*\pi*r^{3}  }{3}[/tex]

where r is the radius of the sphere

to solve this question you just have to put the values into the formula and multiply by the number of spheres in the  ice cube tray

Let

the number of spheres in the  ice cube tray=6

radius =  2 cm

the total volume is

[tex]V=6*(\frac{4*\pi*r^{3} }{3})\\V=6*(\frac{4*\pi*(2cm)^{3} }{3})\\v=\frac{192\pi }{3} \\v=201.06\ cubic\ centimeters[/tex]

Have a good day.

Answer:

The correct answer is The second table.

Step-by-step explanation:

1x5= 5

2x5= 10

3x5= 15

4x5= 20

5x5= 25

Hope this helps!! (:

Answer:

r 5 10 15 20 25

s 1 2 3 4 5

Step-by-step explanation:

1x5= 5

2x5= 10

3x5= 15

4x5= 20

5x5= 25

Answer: #5 is 10 student tickets and 20 adult tickets

Step-by-step explanation:

Answer:

20 adult tickets sold and 15 student tickets sold

Step-by-step explanation:

Answer:

23% of 432 is 99.36

That rounds to 99

So, 99 students picked teacher for a career.

Answer:

the answer here is B

Step-by-step explanation:

Step  1  :

           b10

Simplify   ———

           b2  

Dividing exponential expressions :

1.1    b10 divided by b2 = b(10 - 2) = b8

Final result :

 b8

Answer:

B)  [tex]b^{8}[/tex].

Step-by-step explanation:

Given  : [tex]\frac{b^{10}}{b^{2}}[/tex].

To find : simplify.

Solution : We have given  [tex]\frac{b^{10}}{b^{2}}[/tex].

By the quotient property of exponential  :  [tex]\frac{x^{a}}{x^{c}} = x ^{a -c}[/tex].

Here , x = b , a = 10 , c = 2.

[tex]\frac{b^{10}}{b^{2}}[/tex] = [tex]b^{10 -2}[/tex].

[tex]\frac{b^{10}}{b^{2}}[/tex] =  [tex]b^{8}[/tex].

Therefore, B)  [tex]b^{8}[/tex].

The pair of polygons in the image are not similar. Although they are both rectangles, they do not have the same corresponding side ratios.

A rectangle is defined by having four right angles and two pairs of parallel sides. The corresponding sides of similar rectangles are in proportion. In the image, the rectangle on the left has side lengths of 11 ft and 10 ft, while the rectangle on the right has side lengths of 9.4 ft and 8.4 ft.

The ratio of the corresponding sides is not the same for both pairs of sides. The ratio of the left side lengths is 11 ft / 9.4 ft, which is about 1.17. The ratio of the right side lengths is 10 ft / 8.4 ft, which is about 1.19. Because the corresponding side ratios are not the same, the rectangles are not similar.

Here are some additional points to note:

Answer:

25.38

Step-by-step explanation:

Its a 3-D block, so you have to find the distance from on corner to the opposite corner of the roof, but first find the distance from corner to corner on the floor.

20^2+12^2=c^2

400+144=544=c^2

c=[tex]\sqrt{544}[/tex]

then find corner of floor to opposite roof corner.

100+544=644=c^2

c=[tex]\sqrt{644}[/tex]

so its about 25.38 feet

Answer:

25.4 ft  

Step-by-step explanation:

Let D1 be the distance from one corner to the diagonally opposite one and D2 be the  diagonal distance from one corner to the ceiling.

D1² = 20² + 12²

D2² = D1² + 10²            Substitute the value of D1²

D2² = 20² + 12² + 10²

D2² = 400 + 144 + 100

D2² = 644

D2 = √(644)

D2 = 2√(161)

D2 ≈ 25.4 ft

Answer:

12 dollars

Step-by-step explanation:

"95% off" means Charlie pays 5% of the original price (5% + 95% = 100%)

5% = 5/100 = 0.05

Multiply 0.05 with the original price $240 and we get our answer to be 0.05*240 = 12

Answer: 9

Step-by-step explanation: This is the answer because you would subtract so the equation would be 24-15=9. Hope this helps!

Hey there!

[tex](3^2)^2[/tex] [tex]*[/tex] [tex](10^3)^2[/tex]

Good luck on your assignment and enjoy your day!

~[tex]LoveYourselfFirst:)[/tex]

Answer:

81000000

Step-by-step explanation:

(3^2)^2 x (10^3)^2

PEMDAS says do what is inside the parentheses first

3^2 = 9

10^3 = 1000

3^2)^2 x (10^3)^2

9^2 * 1000^2

Now we need to do the exponents

81 * 1000000

Mow we multiply

81000000

Answer:

r>0 and V(r)>0

Step-by-step explanation:

Number one: There arent no negative volumes

Number two: There aren't Negative radi

Thus V(r) and r must be greater than one. I attach the graph V(r)=5 Pi r^2

The domain would be (0,infinity)

The range would be (0, infinity)

The domain of a function is [tex]$r \geq 0$[/tex] and range of a function is [tex]$V(r) \geq 0$[/tex].

The formula for the volume of a cylinder with a height of 5 units is:

[tex]V(r)=5 \pi r^{2}$$[/tex]

Where [tex]$\mathrm{r}$[/tex] is the radius of the cylinder and [tex]$\mathrm{r}$[/tex] cannot be in negative

Let [tex]$r \geq 0$[/tex] here, [tex]$\mathbf{r}$[/tex] is the independent variable and [tex]$\mathbf{V}(\mathbf{r})$[/tex] is the dependent variable by definition of domain and range.

The domain of the given function is: [tex]$r \geq 0$[/tex] or in the interval [tex]$=[0, \infty)$[/tex]

The range of the function [tex]$(\mathrm{V}(\mathrm{r}))$[/tex] is: [tex][0, \infty)$$[/tex].

Therefore the correct answer is r > 0, V(r) > 0.

Learn more about the domain and range of this function

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The next number in the sequence 16, 4, 20, 24, 44 is 68 and in the sequence 6, 5, 15, 10, 70 is 61.

A sequence's series is the total number of terms in the sequence.

A series follows some pattern for example if you take data set of natural numbers then there will be a sequence of that data and something will be due to that we can form that series.

Now the given series are,

16, 4, 20, 24, 44

and 6, 5, 15, 10, 70

Now the difference between the two terms of the series 16, 4, 20, 24, 44

4 - 16 = 12 = 4*3

20 - 4 = 16 = 4*4

24- 20 = 4 = 4*1

44 - 24 = 20 = 4*5

So let x be the next term; hence it can be written as

x - 44 = 4*6

x = 24 + 44

x = 68

Now for the series 6, 5, 15, 10, 70, it is an alternative series,

6 - 1 = 5

5 x 3 = 15

15 - 5 = 10

10 x 7 = 70

So the next term is given as,

70 - 9 = 61

Hence, The next number in the sequence 16, 4, 20, 24, 44 is 68 and in the sequence 6, 5, 15, 10, 70 is 61.

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[tex]49-c\leq45\qquad\text{subtract 49 from both sides}\\\\-c\leq-4\qquad\text{change the signs}\\\\\boxed{c\geq4}[/tex]

[tex]12x+4>16\qquad\text{subtract 4 from both sides}\\\\12x>12\qquad\text{divide both sides by 12}\\\\\boxed{x>1}\\\\or\\\\3x-5<-14\qquad\text{add 5 to both sides}\\\\3x<-9\qquad\text{divide both sides by 3}\\\\\boxed{x<-3}\\\\Answer:\ \boxed{x<-3\ or\ x>1}[/tex]

The inequalities 12x + 4 > 16 and 3x - 5 < -14 simplify to x > 1 and x < -3 respectively. In graphical form, both inequalities represent lines extending from the points x = 1 and x = -3, with x > 1 going towards the right and x < -3 moving leftward.

To solve this inequality problem, we first isolate the variable on one side of the inequality for both expressions. Let's begin with 12x + 4 > 16. We can start by subtracting 4 from both sides to get 12x > 12, then divide each side by 12, resulting in x > 1.

Solve 12x + 4 > 16:

Subtract 4 from both sides to isolate 12x:

12x > 16 - 4

12x > 12

Divide both sides by 12:

x > 1

Solve 3x - 5 < -14:

Add 5 to both sides to isolate 3x:

3x < -14 + 5

3x < -9

Divide both sides by 3:

x < -3

Now, you have two separate solutions:

For the first inequality, x > 1.

For the second inequality, x < -3.

This means the solution graph includes all values of x that are greater than 1 or less than -3. In graphical terms, it's the union of two intervals:

Solution Graph: (-∞, -3) ∪ (1, ∞)

This represents all real numbers less than -3 and all real numbers greater than 1.

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Answer: A. 7.84

Step-by-step explanation:

1. According to the problem given in the image attached, the total energy used was 98 quadrillion Btu.

2. Therefore, if you want to know how many quadrillion Btu of energy were consumed in 2010 from renewable energy sources, you must multiply the percentage given in the circle graph, as following:

[tex]8[/tex]%[tex]=0.08[/tex]

Then:

[tex]98*0.08=7.84[/tex]

3. Therefore, the answer is the option A.

Answer: The three sides are 14, 14, 20

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

x = length of the two equal sides

x+6 = length of the third longer side

add up the three lengths x, x, x+6. Set it equal to the perimeter 48. Solve for x

x+x+x+6 = 48

3x+6 = 48

3x+6-6 = 48-6 ... subtract 6 from both sides

3x = 42

3x/3 = 42/3 ... divide both sides by 3

x = 14

If x = 14, then x+6 = 14+6 = 20

The three sides are 14, 14, 20

We can check this by adding up the three sides 14+14+20 = 28+20 = 48 and we get the right perimeter.

Answer:

the answer is 77a8b7

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

I took the test

Answer:

x² - 8x + 65 = 0

x² - 8x + 16 = -49

(x - 4)² = -49

x - 4 = ±7i

x = 4 ± 7i

Answer:

Price after discount = 2.4 (1-.3)

Price after discount = 2.4 (.7)

Step-by-step explanation:

We know the cost after the discount.

Price after discount = original price - original price * discount rate

Factoring out the original price

Price after discount = original price (1- discount rate)

We know the discount rate = .3 and the original price is 2.4

Price after discount = 2.4 (1-.3)

Price after discount = 2.4 (.7)

Price after discount = 1.68

Answer:

The function is an exponential,

f(x) = A exp(log(3)x) = 2×3^x = 2(3)^x

The first point you graph for any exponential is (0,A), here (0,2). After (1,6), the next point might be (2,18).

Step-by-step explanation:

(0,2×3^0) = (0,2)

(1,2×3^1) = (1,6)

(2,2×3^2) = (2,2×9) = (2,18)

2(3)^x ought to be written 2×3^x, that is, two times three raised to the x power. x can be any real number.

Since 3 = exp(log(3)), we can substitute for 3 and write 2×exp(log(3))^x. Since exp(p)^q = exp(p×q), the function is also written 2×exp(log(3)x).

exp(x) is also written e^x. exp(x) is the unique function with exp(0)=1, and with the slope of the tangent line at exp(x) equal to exp(x). For instance, the slope at exp(0) is 1, the slope at exp(1) = e is e, slope at exp(2) is exp(2).

for A exp(b x), the slope at x is A b exp(b x).

For 3^x = exp(log(3)x), we have

3^0=1, slope log(3)

3^1=3, slope 3log(3),

3^2=9, slope 9log(3).

Step-by-step explanation: Put 2 as the exponent to get 3x3=9, then do 9x2=18. So x = 2 is y = 18 = (2,18).

Answer:

3 2/4 is your answer.

Step-by-step explanation:

8 1/4 - 4 3/4

Subtract. Note that one whole number = 4/4 (1 = 4/4)

Now, change the first fraction by breaking down one whole number into fraction form.

8 1/4 = 7 4/4 + 1/4 = 7 5/4

Subtract.

7 5/4 - 4 3/4 = 3 2/4

3 2/4 is your answer.

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