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1 year ago

a) The difference between the circumference and the diameter of a circle is 90cmFind the radius of the circle

Mathematics

1 answer:

Sveta_85 [38]1 year ago

8 0

Answer:

r=21.01 cm

Step-by-step explanation:

2r = diameter

Circumference of a circle = pi 2r

difference = 90

pi2r - 2r =90

2r (pi-1) =90

90/(2(pi-1) = r = 21.01 cm

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In a company 85% of the workers are men if 510 women work for the company how many workers are there in all

tester [92]

Answer:

3400 workers

Step-by-step explanation:

85% of men that means 15% are women

15% = 510

15/100= 510/x

100x510=51000

51000/15 =3400

x=3400

3 0

2 years ago

This figure is made up of a quadrilateral and a semicircle.

Arturiano [62]

Answer:

The correct option is B. The area of the figure is 40.4 units².

Step-by-step explanation:

The line AB divides the figure in two parts one is a rectangle and another is semicircle.

The distance formula is

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

The length of AB is

$AB=\sqrt{(2+3)^2+(4-2)^2}=\sqrt{25+4}=\sqrt{29}$

The length of AD is

$AD=\sqrt{(-1+3)^2+(-3-2)^2}=\sqrt{4+25}=\sqrt{29}$

Since AB=AD, therefore ABCD is a square. The area of the of square is

$A_1=a\times a=\sqrt{29}\times \sqrt{29} =29$

The area of square is 29 units².

The area of a semicircle is

$A_2=\frac{\pi}{2}r^2$

Since AB is the diameter of the semicircle, therefore the radius of the semicircle is

$r=\frac{d}{2}=\frac{\sqrt{29}}{2}$

The area of the semicircle is

$A_2=\frac{3.14}{2}(\frac{\sqrt{29}}{2})^2=40.3825$

The area of the figure is

$A=A_1+A_2=29+11.2825=40.3825\approx 40.4$

Therefore the area of the figure is 40.4 units². Option B is correct.

5 0

3 years ago

we believe that 42% of freshmen do not visit their counselors regularly. For this year, you would like to obtain a new sample to

Maksim231197 [3]

Answer:

A sample of 1077 is required.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

The margin of error is of:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

42% of freshmen do not visit their counselors regularly.

This means that $\pi = 0.42$

98% confidence level

So $\alpha = 0.02$ , z is the value of Z that has a pvalue of $1 - \frac{0.02}{2} = 0.99$ , so $Z = 2.327$ .

How large of a sample size is required?

A sample size of n is required, and n is found when M = 0.035. So

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.035 = 2.327\sqrt{\frac{0.42*0.58}{n}}$

$0.035\sqrt{n} = 2.327\sqrt{0.42*0.58}$

$\sqrt{n} = \frac{2.327\sqrt{0.42*0.58}}{0.035}$

$(\sqrt{n})^2 = (\frac{2.327\sqrt{0.42*0.58}}{0.035})^2$

$n = 1076.8$

Rounding up:

A sample of 1077 is required.

3 0

2 years ago

Kat is painting the edge of a triangular stage prop with reflective orange paint. The lengths of the edges of the triangle are (

Eva8 [605]

Plug 4 in for every x

(3*4)-4=8
(4^2)-1=15 [(4^2) is 4*4]
(2*(4^2))-15= 15 [because of PEMDAS the exponent comes first and then multiply by 2 then subtract]

Perimeter is the sum of the lengths so add up all the sides from above
8+15+15=38

3 0

2 years ago

Help pls i need it fast

sergij07 [2.7K]

The correct answer is C. Let’s break this down with the distributive property.

5(6x+6)

30x+30

5(9-x)

45-5x

Now add and subtract like terms.
30x-5x=25x

30+45=75

Put the remaining numbers together.
25x+75 and there you go.

3 0

2 years ago

a) The difference between the circumference and the diameter of a circle is 90cmFind the radius of the circle​

a) The difference between the circumference and the diameter of a circle is 90cmFind the radius of the circle