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3 years ago

A right angle has a league of 13 cm in the hypotenuse of 21 cm what is the length of the other leg

2 answers:

8 0

You can use c^2 = a^2 + b^2 to solve for the length of the other leg. Just substitute the values to the variable then transpose to get the value of the missing variable.

Given: a = 13; c = 21
Required: b - other leg
Solution:
c^2 = a^2 + b^2
21^2 = 13^2 + b^2
441 = 169 + b^2
b^2 = 272
√b = 16.49
b = 16.49 cm

Darya [45]3 years ago

5 0

For a Right Angled Triangle, according to the Pythagoras Theorem, the square of hypotenuse is equal to the sum of squares of its two legs.

One leg is 13cm long, hypotenuse is 21cm long. Let the other leg be x cm. So, we can write:

$21^{2} =13^{2} + x^{2} \\ \\ 
272= x^{2} \\ \\ 
x= \sqrt{272} \\ \\ 
x=16.49$

Rounding of to nearest hundredth, the length of other leg of the Triangle is 16.49

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Find the value of x

nataly862011 [7]

Answer:

x = 128°

Step-by-step explanation:

123 + 109 + x = 360

x = 360 - (123 + 109)

x = 360 - 232

x = 128°

7 0

3 years ago

A survey asked whether respondents favored or opposed the death penalty for people convicted of murder. Software shows the resul

pav-90 [236]

Answer:

95% confidence interval for the proportion of the adults who were opposed to the death penalty is (0.668, 0.704).

Step-by-step explanation:

We are given that a survey asked whether respondents favored or opposed the death penalty for people convicted of murder. Software shows the results below, where X refers to the number of the respondents who were in favor.

X = 1,790

N = 2,610

$\hat p$ = Sample proportion = X/N = 0.6858

Firstly, the pivotal quantity for 95% confidence interval for the population proportion is given by;

P.Q. = $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion = 0.6858

n = sample of respondents = 2,610

p = population proportion

Here for constructing 95% confidence interval we have used One-sample z proportion statistics.

So, 95% confidence interval for the population proportion, p is ;

P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at

2.5% level of significance are -1.96 & 1.96}

P(-1.96 < $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < 1.96) = 0.95

P( $-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < ${\hat p-p}$ < $1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.95

P( $\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} }$ < p < $\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.95

95% confidence interval for p = [ $\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} }$ , $\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} }$ ]

= [ $0.6858-1.96 \times {\sqrt{\frac{0.6858(1-0.6858)}{2610} }$ , $0.6858+1.96 \times {\sqrt{\frac{0.6858(1-0.6858)}{2610} }$ ]

= [0.668 , 0.704]

Therefore, 95% confidence interval for the population proportion of the adults is (0.668, 0.704).

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3 years ago

HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPP

RSB [31]

Answer:

7/8

Step-by-step explanation:

To find: number which represents the expression

Solution:

Integers refers to natural numbers, 0 together with negative of rational numbers.

A rational number is the number of the form where p and q are integers and .

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3 years ago

Simplify each algebraic axpression 4y+6y+5x-2y

Mkey [24]

Answer:

8y+5x

If in the case you need any other help , let me know. [ You need to pay me] :) Thanks!

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2 years ago

Read 2 more answers

The function f(x)=(x-5)^2 +2 is not one-to-one. Identify a restricted domain that makes the function one-to-one, and find the in

Anon25 [30]

We have been given a quadratic function $f(x)=(x-5)^{2} +2$ and we need to restrict the domain such that it becomes a one to one function.

We know that vertex of this quadratic function occurs at (5,2).

Further, we know that range of this function is $[2,\infty)$ .

If we restrict the domain of this function to either $(-\infty,5]$ or $[5,\infty)$ , it will become one to one function.

Let us know find its inverse.

$y=(x-5)^{2}+2$

Upon interchanging x and y, we get:

$x=(y-5)^{2}+2$

Let us now solve this function for y.

$(y-5)^{2}=x-2\\
y-5=\pm \sqrt{x-2}\\
y=5\pm \sqrt{x-2}\\$

Hence, the inverse function would be $f^{-1}(x)=5+\sqrt{x-2}$ if we restrict the domain of original function to $[5,\infty)$ and the inverse function would be $f^{-1}(x)=5-\sqrt{x-2}$ if we restrict the domain to $(-\infty,5]$ .

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3 years ago