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3 years ago

Find the sum of a finite geometric series.

Mathematics

2 answers:

NNADVOKAT [17]3 years ago

3 0

Answer: 17 in.

Step-by-step explanation:

The sides of an equilateral triangle measure 16 inches. The midpoints of the sides of the triangle are joined to form another equilateral triangle with sides that are half the length of the outer triangle. This process is continued until three triangles are inscribed in the first triangle. The sum of the perimeters of all four triangles is 17 in.

Bumek [7]3 years ago

3 0

Answer with explanation:

⇒Side of largest equilateral triangle in which three equilateral triangles are inscribed = 16 inches

Perimeter of a triangle = Sum of three sides of triangle

Perimeter of equilateral triangle having side length 16 inches = 16 +16+16=48 inches

⇒→Second equilateral triangle which is inscribed in this equilateral triangle having side length half of that equilateral triangle in which it is inscribed

$=\frac{16}{2}\\\\=8$ inches

Perimeter of equilateral triangle having side length 8 inches = 8 +8+8=24 inches

⇒→Third equilateral triangle which is inscribed in this equilateral triangle having side length half of that equilateral triangle in which it is inscribed

$=\frac{8}{2}\\\\=4$ inches

Perimeter of equilateral triangle having side length 4 inches =4+4+4=12 inches

⇒→Fourth equilateral triangle which is inscribed in this equilateral triangle having side length half of that equilateral triangle in which it is inscribed

$=\frac{4}{2}\\\\=2$ inches

Perimeter of equilateral triangle having side length 2 inches =2+2+2=6 inches

→≡Total Perimeter of all four Equilateral Triangle

=48 +24+12+6

= 90 inches

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A poll of 793 adults aged 18 or older asked about purchases that they intended to make for the upcoming holiday season. One of t

Ira Lisetskai [31]

Answer:

(0.5793, 0.6363)

Step-by-step explanation:

Given that a poll of 793 adults aged 18 or older asked about purchases that they intended to make for the upcoming holiday season. One of the questions asked about what kind of gift they intended to buy for the person on whom they would spend the most. Clothing was the first choice of 482 people.

i.e. sample proportion p= $\frac{482}{793} =0.608$

$q=1-p = 0.392$

Std error of p = $\sqrt{pq/n} =0.0173$

For 90% Z crtiical = 1.645

Hence margin of error = 1.645 * std error = 0.0285

Confidence interval 90%

= proportion ±margin of error

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3 0

3 years ago

A circle with radius of \greenD{2\,\text{cm}}2cmstart color #1fab54, 2, start text, c, m, end text, end color #1fab54 sits insid

HACTEHA [7]

Answer:

119.43cm^2

Step-by-step explanation:

The computation of the area of the shaded region is shown below:

As we know that

= Area of the rectangle - Area of the circle

where,

Area of rectangle is

$= length \times breadth$

$= 11\times 12$

= 132 cm^2

And, the area of the circle is

$= \pi\times r^2\\\\ = \frac{22}{7} \times 2^2\\\\ = \frac{88}{7} cm^2$

Now the area of the shaded region is

$= 132 cm^2- \frac{88}{7}cm^2$

= 119.43cm^2

We simply deduct the area of the circle from the area of the rectangle so that the area of the shaded region.

7 0

3 years ago

Helpppppp please !!?

ch4aika [34]

Please refer to my image where it shows my work as I’m explaining.

Okay, for system 1:

1. I am using the elimination method to solve. So I check if all the terms are lined up and if any are the same. I found that 2X are common in both equations.

2. The goal is to “eliminate” the term hence the name. So I can choose to add or subtract. I chose subtraction because 2 - 2 equals 0 which is our goal. Solve for the rest of the terms. This will lead to getting y =4. Refer to image for the work.

3. Last step to to find the X value. We do this by picking any of the given equations,then substitute y with 4 and solve to eventually get x = 10. Refer to image for the work.

FOR SYSTEM 2:

1. Again, I am using the elimination method to solve. I noticed that NONE of the terms are in common so I will have to intervene. You can chose any term to create a match with but I chose Y since it was the one I could use the smallest number to multiply with. When multiplying, DONT just multiply Y, multiply ALL the terms in the equation or else everything will crash.

2. Now that I have terms in common I can choose to add or subtract. I chose subtraction because 2-2 equals zero which is what we want. Solve look at image for my process which lead to X = -8

3. Last step is to find the value of Y. Chose any of the given equations in system 2 then substitute x with -8. Refer to image to see process. It lead to y = 20

To check the validity of the answers, substitute the x and y values into both equations both side of the equal side should have the same number. Hope that helped!