Solve the inequality 6 is greater or equal than m- 1

There is a L-shaped sidewalk that is 158 meters long. By cutting across the lawn, the

NikAS [45]

Answer:

Each side of the L-shaped sidewalk is 126 m and 32m respectively.

Step-by-step explanation:

Given:

Total length of the sidewalk = 158 meters

Cutting across the lawn the distance = 130 meters

The L-shaped lawn will be treated as a right angled triangle.

So the 130 m distance is the hypotenuse here.

Let one side of the L-shaped lawn be 'x' meter so the another side will be (158-x) meters.

Applying Pythagoras formula.

$(Hypotenuse)^2=(height)^2+(base)^2$

So,

⇒ $(130)^2=x^2 +(158-x)^2$

⇒ $(130)^2=x^2+(158-x)(158-x)$

⇒ $16900=x^2+24964-158x-158x+x^2$

⇒ $16900 =2x^2-316x+24964$

⇒ $2x^2+316x+24964-16900=0$

⇒ $2x^2-316x+8064=0$

⇒ $x^2-158x+4032=0$

Applying quadratic formula;

Quadratic formula : $\frac{\pm b \sqrt{b^2-4ac} }{2a}$ where a=1 and b=-158 and c=4032

So the value of x= 126 and 32.

The length of each side of the sidewalk is 'x'= 126 m and '(158-x)'='(158-126)'=32 m

7 0

3 years ago

What is the scale factor of figure b to a

viktelen [127]

Answer:

C. 2:5

Step-by-step explanation:

Find perimeter of each...

a. 10+25+21.5=56.5

b. 4+10+8.6=22.6

b:a

22.6:56.6

simplify

11.3 will go into both for..

2:5

7 0

3 years ago

g You are planning an opinion study and are considering taking an SRS of either 200 or 600 people. Explain how the sampling dist

Katen [24]

Answer:

By the Central Limit Theorem, both would be approximately normal and have the same mean. The difference is in the standard deviation, since as the sample size increases, the standard deviation decreases. So the SRS of 600 would have a smaller standard deviation than the SRS of 200.

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For the sampling distribution of size n of a sample proportion p, the mean is p and the standard deviation is $s = \sqrt{\frac{p(1-p)}{n}}$

Differences between SRS of 200 and of 600

By the Central Limit Theorem, both would be approximately normal and have the same mean. The difference is in the standard deviation, since as the sample size increases, the standard deviation decreases. So the SRS of 600 would have a smaller standard deviation than the SRS of 200.

6 0

3 years ago

What is the degree of angle YQR

katovenus [111]

Answer: Angle is 3

Step-by-step explanation:

16x - 27 = 5x + 6

-5x -5x

______________

11x - 27 = 6

+ 27 +27

___________

11x = 33

__ __

11 11

x = 3

4 0

3 years ago

which of the following properties could be used to rewrite the expression (2/3•1/5)•5/2 as 2/3•(5/2•(5/2•1/5) sorry to ask Su ma

slamgirl [31]

The original expression is given by:
$( \frac{2}{3}*\frac{1}{5})*\frac{5}{2}$
The correct way to rewrite the expression is given by:
$\frac{2}{3}*(\frac{5}{2}*\frac{1}{5})
$
For this, we use two properties:

Associative property:
The way of grouping the factors does not change the result of the multiplication:
$\frac{2}{3}*(\frac{1}{5}*\frac{5}{2})$

Commutative property:
The order of the factors does not vary the product:
$\frac{2}{3}*(\frac{5}{2}*\frac{1}{5})$

8 0

3 years ago