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3 years ago

Set G is the set of positive integers divisible by 4 and Set F is the set of perfect

Mathematics

1 answer:

Natalka [10]3 years ago

4 0

Greetings from Brasil...

G = {4; 8; 12; 16; 20; 24; 28; 32; 36; 40; 44; 48; 52; 56; 60; 64; 68; 72; 76; 80; 84; 88; 92; 96; 100; 104; ...}

F = {1; 4; 9; 16; 25; 36; 49; 64; 81; 100; ...}

So, according to the statement, it is desired:

G ∩ F - the intersection between the 2 sets, that is, which numbers are present simultaneously in the 2 sets....

Looking at the sets we conclude that

OBS: note that in truth G are the multiples of 4

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3 years ago

Can someone answer this question answer it correctly please and show work please

3241004551 [841]

Answer:

42) 254.47 ft²

43) 56 pendants

Step-by-step explanation:

42)

The radius of a circle is equal to half of its diameter.

Diameter = 18 feet

Radius = Diameter ÷ 2 = 18 ÷ 2 = 9 feet

Area of a circle = π $r^{2}$

Substitute in known value of r

Area = π $9^{2}$

Substitute in pi

Area = 3.14 * $9^{2}$

Solve exponent

Area = 3.14159265359 * 81

Area = 254.4690049408

(Rounds to 254.47)

254.47 ft²

43)

$1\frac{1}{2} =$ 1.5 ounces per pendant

3 pieces of silver:

$1\frac{7}{8}$ pounds

14 ounces

$2\frac{1}{2}$ pounds

Convert to improper fractions (1 lb = 16 ounces)

$\frac{15}{8}$ pounds

$\frac{14}{16}$ pounds

$\frac{5}{2}$ pounds

Find a common denominator for the fractions

$\frac{30}{16}$ pounds

$\frac{14}{16}$ pounds

$\frac{40}{16}$ pounds

Add

$\frac{30}{16}$ + $\frac{14}{16}$ + $\frac{40}{16}$

$\frac{84}{16}$ pounds

Find how many pendants can be made out of this amount

$\frac{84}{16}$ pounds

Convert back to ounces (1 lb = 16 ounces)

84 ounces

Amount to make one pendant:

$1\frac{1}{2}$ ounces

Convert to decimal

1.5 ounces

Divide 84 by amount of silver per pendant

84 ÷ 1.5

The maximum number the pendants that the manufacturer can make is 56

Hope this helps :)

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Step-by-step explanation:

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3 years ago

What is the first term in a geometric sequence if the common ratio is − 2 and the sum of the first six terms is −105?

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$\bf \qquad \qquad \textit{sum of a finite geometric sequence}
\\\\
S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
r=\textit{common ratio}\\
----------\\
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\end{cases}$

$\bf -105=a_1\left( \cfrac{1-(-2)^6}{1-(-2)} \right)\implies -105=a_1\left( \cfrac{1-(64)}{1+2} \right)
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3 years ago