MATHEMATICS HIGH SCHOOL

If the radius of a circle is increased by 50 %, what will be the percent increase in the circumference of the circle? (Circumference 2*pi *r)

Answers

Answer 1
Answer: If the radius is increased by 50 per cent,
then R = r+ r/2
= 3r/2 = 1.5r
thus, increase in circumference = 2 pi r = 2 x pi x 1.5 r
= 3 pi r.
Thus initial c = 2 pi r, final c = 3 pi r.
thus increase percent = change in c/ initial c x 100 = 1/2 x 100 = 50 percent.
Thus, the circumference will also increase by 50 % 

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The perimeter of a square garden is to be at least 30 feet but not more than 64 feet. Find all possible values for the length of its sides.

Answers

Answer:

7.5\leq x\leq 16

Step-by-step explanation:  

Let x be the length of each side of square.

Since the perimeter of the square is 4 times the length of each side, so perimeter of our given circle will be 4x.

We have been given that the perimeter of a square garden is to be at least 30 feet but not more than 64 feet.

This means the perimeter of the garden should we greater than or equal to 30 feet and less than or equal to 64 feet.

We can represent this information in an equation as:

30\leq 4x\leq64

Let us divide our inequality by 4 to solve for x.

(30)/(4)\leq (4x)/(4)\leq(64)/(4)

7.5\leq x\leq 16

We can represent our answer in interval notation as: [7.5,16]

Therefore, the length of the square's side can be any number between 7.5 feet and 16 feet including both 7.5 and 16 as well.
4x \in <30.64>/:4 \n x \in <7.5,16>

The value of 3.6 - 2.4 ÷ (-0.8) is _____.
6.6
0.6
-1.5
3

Answers

I hope this helps you

Answer:

6.6

Step-by-step explanation:

Solve for x. Round to the nearest tenth of a degree, if necessary.

Answers

Sin (angle) = opposite leg / hypotenuse

Sin(x) = 2.1/4

x = arcsin(21./4)

x = 31.7 degrees

A hypothesis will be used to test that a population mean equals 10 against the alternative that the population mean is more than 10 with known Ï. What is the critical value of z-score for the following significance levels?A) 0.01
B) 0.05
C) 0.10

Answers

Answer:

A) 2.58

B) 1.96

C) 1.65

Step-by-step explanation:

A hypothesis used to test that

H_o : \mu  = 10

against the alternatives H1 : \mu not equal to 10

if null hypothesis is true, then distribution of test statics follow

Zo = (\bar x - \mu)/((\sigma)/(√(n)))

for two sided alternatives  hypothesis ( H1: \mu \neq 7), then P value is

P = 2[1- \phi(\left | Zc \right |)]                          (1)

a)significance level  \alpha = 0.01

from 1 eq we get

\pi (\left | Zc \right |) = P(Zo<\left | Zc \right |) = 1 - (0.01)/(2)  = 0.995

Therefore  \left | Zc \right | = 2.58    FROM Z TABLE

B) significance level  \alpha = 0.05

from 1st equation we get

\pi (\left | Zc \right |) = P(Zo < \left | Zc \right |) = 1 - (0.05)/(2)  = 0.975

Therefore  \left | Zc \right | = 1.96    FROM Z TABLE

C) significance level  \alpha = 0.10

from 1 eq we get

\pi (\left | Zc \right |) = P(Zo<\left | Zc \right |) = 1 - (0.10)/(2)  = 0.95

Therefore  \left | Zc \right | = 1.65    FROM Z TABLE

Which fraction converts to a repeating decimal number 1/12 7/8 14/25 17/20 6/10

Answers

The fraction converts a repeating decimal number is 1/12 is a repeating decimal.

What is fraction?

Fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.

Parts of a Fraction

All fractions consist of a numerator and a denominator and they are separated by a horizontal bar known as the fractional bar.

  • The denominator indicates the number of parts in which the whole has been divided into. It is placed in the lower part of the fraction below the fractional bar.
  • The numerator indicates how many sections of the fraction are represented or selected. It is placed in the upper part of the fraction above the fractional bar.

Given:

  • 1/12= 0.0833333333
  • 7/8= 0.875
  • 14/25= 0.56
  • 17/20= 0.85
  • 6/10=.6

As, we can see that the approximately every fraction is non repeating except 1/12

Learn more about fraction here:

brainly.com/question/10354322

#SPJ5
Hey there! :D 

Let's try it out. 

1/12= 0.0833333333

7/8= 0.875

14/25= 0.56

17/20= 0.85

6/10=.6

So, 1/12 is a repeating decimal. 

I hope this helps!
~kaikers 

1)If (x-2) is a factor of x2+ 3ax -2a, then find the value of a

Answers

Answer:

x - 2 => x = 2

x² + 3ax - 2a

=> 2² + 3 × a × 2 - 2 × a

=> 4 + 6a - 2a

=> 4 + 4a

=> 4 ( 1 + a )

★ 1 + a = 0

a = -1

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