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3 years ago

What is the theoretical probability of spinning an even number?

Mathematics

2 answers:

Zolol [24]3 years ago

7 0

4/9 probability get you a even number

Marina86 [1]3 years ago

5 0

Answer:

4/9 probability you will get an even number

Step-by-step explanation:

The theoretical probability of spinning an even number is 4/9, since there are 4 even numbers in the spinner

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What is the area of shaded section of the circle?

bazaltina [42]

Answer:

≈ 565.5 units²

Step-by-step explanation:

The area (A) of the shaded sector = area of circle × fraction of circle

A = πr² × $\frac{162}{360}$ ← r is the radius

= π × 20² × $\frac{162}{360}$

= 400π × 0.45 ≈ 565.5 units²

4 0

3 years ago

Find the sum of the first 25 terms in this geometric series:<br> 8 + 6 + 4.5...

Ksivusya [100]

Step-by-step explanation:

Given the geometric sequence

8 + 6 + 4.5...

A geometric sequence has a constant ratio and is defined by

$a_n=a_1\cdot r^{n-1}$

$\mathrm{Compute\:the\:ratios\:of\:all\:the\:adjacent\:terms}:\quad \:r=\frac{a_{n+1}}{a_n}$

$\frac{6}{8}=\frac{3}{4},\:\quad \frac{4.5}{6}=\frac{3}{4}$

$\mathrm{The\:ratio\:of\:all\:the\:adjacent\:terms\:is\:the\:same\:and\:equal\:to}$

$r=\frac{3}{4}$

$\mathrm{The\:first\:element\:of\:the\:sequence\:is}$

$a_1=8$

$\mathrm{Therefore,\:the\:}n\mathrm{th\:term\:is\:computed\:by}\:$

$a_n=8\left(\frac{3}{4}\right)^{n-1}$

$\mathrm{Geometric\:sequence\:sum\:formula:}$

$a_1\frac{1-r^n}{1-r}$

$\mathrm{Plug\:in\:the\:values:}$

$n=25,\:\spacea_1=8,\:\spacer=\frac{3}{4}$

$=8\cdot \frac{1-\left(\frac{3}{4}\right)^{25}}{1-\frac{3}{4}}$

$\mathrm{Multiply\:fractions}:\quad \:a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c}$

$=\frac{\left(1-\left(\frac{3}{4}\right)^{25}\right)\cdot \:8}{1-\frac{3}{4}}$

$=\frac{8\left(-\left(\frac{3}{4}\right)^{25}+1\right)}{\frac{1}{4}}$

$\mathrm{Apply\:exponent\:rule}:\quad \left(\frac{a}{b}\right)^c=\frac{a^c}{b^c}$

$=\frac{8\left(-\frac{3^{25}}{4^{25}}+1\right)}{\frac{1}{4}}$

$\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{\frac{b}{c}}=\frac{a\cdot \:c}{b}$

$=\frac{\left(1-\frac{3^{25}}{4^{25}}\right)\cdot \:8\cdot \:4}{1}$

$\mathrm{Multiply\:the\:numbers:}\:8\cdot \:4=32$

$=\frac{32\left(-\frac{3^{25}}{4^{25}}+1\right)}{1}$

$=\frac{32\cdot \frac{4^{25}-3^{25}}{4^{25}}}{1}$ ∵ $\mathrm{Join}\:1-\frac{3^{25}}{4^{25}}:\quad \frac{4^{25}-3^{25}}{4^{25}}$

$=32\cdot \frac{4^{25}-3^{25}}{4^{25}}$

$=\frac{\left(4^{25}-3^{25}\right)\cdot \:32}{4^{25}}$

$=\frac{2^5\left(4^{25}-3^{25}\right)}{2^{50}}$ ∵ $\mathrm{Factor}\:32:\ 2^5$ , $\mathrm{Factor}\:4^{25}:\ 2^{50}$

$=\frac{4^{25}-3^{25}}{2^{45}}$ ∵ $\mathrm{Cancel\:}\frac{\left(4^{25}-3^{25}\right)\cdot \:2^5}{2^{50}}:\quad \frac{4^{25}-3^{25}}{2^{45}}$

$\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a\pm \:b}{c}=\frac{a}{c}\pm \frac{b}{c}$

$=\frac{4^{25}}{2^{45}}-\frac{3^{25}}{2^{45}}$

$=32-\frac{3^{25}}{2^{45}}$ ∵ $\frac{4^{25}}{2^{45}}=32$

$=32-0.024$ ∵ $\frac{3^{25}}{2^{45}}=0.024$

$=31.98$

Therefore, the sum of the first 25 terms in this geometric series: 31.98

3 0

3 years ago

the pearl restaurant put a larger aquarium in its lobby. the base is 6 ft by 3 ft and the height is 4 ft how many more cubic fee

Anit [1.1K]

Well 6×12=72. I don't know what the original tank size was but subtract the original from this one to get your answer.

6 0

3 years ago

Lines x and y are parallel.

densk [106]

On the bottom line, the 106 and number 1 make a straight line and needs to equal 180 degrees.

This means number 1 = 180-106 = 74 degrees.

Because x and y are parallel, the top outside angle is the same as number 1.

6x +8 = 74

Subtract 8 from both sides:

6x = 66

divide both sides by 6:

x = 66 / 6

x = 11

Now you have x, replace x in the equation for 7x-2 to find that angle:

7(11) -2 = 77-2 = 75 degrees.

The three inside angles need to equal 180 degrees.

Angle 2 = 180 - 74 - 75 = 31 degrees.

7 0

2 years ago

Read 2 more answers

Write an equation for the parabola that passes through (-2, 7) , (1, 10) , and (2, 27) .

vlada-n [284]

(-2,7) (1,10) (2,27)

5 0

2 years ago