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3 years ago

A. 16

Mathematics

1 answer:

kogti [31]3 years ago

6 0

9514 1404 393

Answer:

C. 8√3/3

Step-by-step explanation:

It can be useful to remember that the ratio of sides in a 30°-60°-90° triangle are ...

1 : √3 : 2

That is the short leg is 1/√3 times the length of the longer leg.

8(1/√3) = 8(√3/3) . . . . . matches choice C

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A survey of 73 students found that 37% were in favor of raising tuition to pave new parking lots. The standard deviation of the

KatRina [158]

Answer:

The value is $n_2 = 317$

Step-by-step explanation:

From the question we are told that

The sample size is n = 73

The proportion that in favor of raising the tuition is $\^{p} = 0.37$

The standard deviation is $s_1 = 0.098$

The required standard deviation $s_2 = 0.047$

Generally the requires standard deviation is mathematically represented as

$s_2 = s_1 * \sqrt{\frac{n_1}{n_2} }$

=> $\frac{s_2}{s_1} = \sqrt{\frac{n_1}{n_2} }$

=> $\frac{n_1}{n_2} =[\frac{s_2}{s_1} ]^2$

=> $\frac{73}{n_2} =[\frac{0.047}{0.098} ]^2$

=> $\frac{73}{n_2} =0.2300$

=> $n_2 = \frac{73}{0.2300}$

=> $n_2 = 317$

3 0

3 years ago

Solve for x: −6 < x − 1 < 9

shtirl [24]

Answer:

$-5$

Step-by-step explanation:

$-6$

If $a$ than $a$ and $u$

$-6$

⇒ Switch sides:-

 $x-1>-6$

⇒ Add 1 to both sides:-

 $x-1+1>-6+1$

$x>-5$

And...

$\:x-1$

⇒ Add 1 to both sides:-

$x-1+1$

$x$

⇒ Now, Combine the intervals:-

 $-5$

OAmalOHopeO

3 0

3 years ago

You are given a 16-bit binary integer X= (1110 0100 0111 1010)2 . Convert X to decimal if:

podryga [215]

Step-by-step explanation:

a). The decimal numbers is equal to the sum of binary numbers $(b_n)$ times their powers of $2(2^n) .$

That is,

$b_n \times 2^n + b_{n-1} 2^{n-1}+ ..... + b_02^0$

$\therefore (1110 \ \ 0100 \ \ 0111 \ \ 1010)_2$

= $(0 \times 2^0) + (1 \times 2^1) + (0 \times 2^2) + (1 \times 2^3) + (1 \times 2^4) + (1 \times 2^5) + (1 \times 2^6) + ( 0 \times 2^7) + (0 \times 2^8) + (0 \times 2^9) + (1 \times 2^{10} )$ $+ (0 \times 2^{11}) + (0 \times 2^{12}) + (1 \times 2^{13}) + (1 \times 2^{14})+ (1 \times 2^{15})$

= 58490

b).

The left most bit of the number represents the sign of the number. If bit = 1, the number is negative else if the bit is 0, the number is positive.

All the remaining bits (i.e all the bits except the leftmost bit) represent the magnitude of the number.

Now, X = 1110 0100 0111 1010

left most bit = 1 => number is negative

remaining bits Y = 110 0100 0111 1010

converting Y to decimal => Y = 25722

c).

Check the leftmost bit(lmb) of the number

if leftmost bit is 0 => convert do the binary to decimal conversion

if leftmost bit is 1, follow the following steps

1. Flip the bits (convert the 0's into 1's and the vice versa)

2. convert the new number from binary to decimal.

3. Add a negative sign / multiply by -1

Now, X = 1110 0100 0111 1010

left most bit = 1;

flipping the bits => Y = 0001 1011 1000 0101

converting Y into decimal => Y = 7045

multiplying Y with -1 => Y = -7045

Therefore, one's complement of X to decimal is -7045

Thus, X = -25722 in decimal.

d).

Check the leftmost bit(lmb) of the number

if leftmost bit is 0 => convert do the binary to decimal conversion

if leftmost bit is 1, follow the following steps

1. Flip the bits (convert the 0's into 1's and the vice versa)

2. convert the new number from binary to decimal.

3. Add 1 to the converted number

4. Add a negative sign / multiply by -1

Now, X = 1110 0100 0111 1010

left most bit = 1;

flipping the bits => Y = 0001 1011 1000 0101

converting Y into decimal => Y = 7045

Adding 1 to Y => Y = 7046

multiplying Y with -1 => Y = -7046

Thus, two's complement of X to decimal is -7046

7 0

3 years ago

B is decreased by 40% and decreased again by 40%. What is the result?

skelet666 [1.2K]

Answer:

result is 20%

Step-by-step explanation:

initially B was 100%

therefore 100% - 40%

=60% remaining

60% - 40%

= 20%

3 0

2 years ago

Jessica has a circular birdbath in her backyard with a radius of 1.25 feet. She wants to place a decorated border around the cir

Alexxandr [17]

Answer:

The total cost is 28.26.

Step-by-step explanation:

The radius of the birdbath is 1.25 feet.

The cost per foot is 3.6 .

The formula for perimeter of circle is given by,

= 2πR , where R is the radius of circle.

Inserting the above value of radius in the equation above,

circumference = 2(π)(1.25) = 2(3.14)(1.25) = 7.85 $ft^{2}$

Thus the total cost is,

= (7.85)(3.6) = 28.26

4 0

3 years ago