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2 years ago

11

An election ballot asks voters to se4five city commissioners from a group of fifteen candidates. In how many wsys can this be do

ne

1 answer:

svp [43]2 years ago

8 0

That's "15 choose 5"

$\displaystyle{15 \choose 5} = \dfrac{15! }{5! 10!} = \dfrac{15 \cdot 14 \cdot 13 \cdot 12 \cdot 11}{5 \cdot 4 \cdot 3 \cdot 2 \cdot 1} = (15/(5(3))(14/2)(13)(12/4)(11)\\\\= 7(13)(3)(11)=231(13)=3003$

Answer: 3003 ways

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Please help me with number 1 to 6 please

Ugo [173]

1.) 144
2.) 8
3.) 262.5
4.) 36
5.) 630
6.) 440

8 0

2 years ago

From a random sample of size 18, a researcher states that (11.1, 15.7) inches is a 90% confidence interval for mu, the mean leng

alexandr402 [8]

Complete Question

From a random sample of size 18, a researcher states that (11.1, 15.7) inches is a 90% confidence interval for mu, the mean length of bass caught in a small lake. A normal distribution was assumed. Using the 90% confidence interval obtain:

a. A point estimate of $\mu$ and its 90% margin of error.

b. A 95% confidence interval for $\mu$ .

Answer:

a

$\= x = 13.4$ . $E = 2.3$

b

$10.7 < \mu < 16.1$

Step-by-step explanation:

From the question we are told that

The sample size is n = 18

The 90% confidence interval is (11.1, 15.7)

Generally the point estimate of $\mu$ is mathematically evaluated as

$\= x = \frac{11.1 + 15.7 }{2}$

=> $\= x = 13.4$

Generally the margin of error is mathematically evaluated as

$E = \frac{15.7 - 11.1}{2 }$

=> $E = 2.3$

From the question we are told the confidence level is 90% , hence the level of significance is

$\alpha = (100 - 90 ) \%$

=> $\alpha = 0.10$

Generally from the normal distribution table the critical value of $\frac{\alpha }{2}$ is

$Z_{\frac{\alpha }{2} } = 1.645$

Generally the equation for the lower limit of the confidence interval is

$\= x - Z_{\frac{\alpha }{2} } * \frac{s}{\sqrt{18} } = 11.1$

=> $13.4 - 0.3877 s = 11.1$

=> $s = 5.932$

From the question we are told the confidence level is 95% , hence the level of significance is

$\alpha = (100 - 95 ) \%$

=> $\alpha = 0.05$

Generally from the normal distribution table the critical value of $\frac{\alpha }{2}$ is

$Z_{\frac{\alpha }{2} } = 1.96$

Generally the margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }$

=> $E = 1.96 * \frac{5.932}{\sqrt{18} }$

=> $E = 2.7$

Generally 95% confidence interval is mathematically represented as

$\= x -E < \mu < \=x +E$

=> $13.4 - 2.7 < \mu < 13.4 + 2.7$

=> $10.7 < \mu < 16.1$

3 0

2 years ago

In triangle ABC, line A.B.=CB Angle ABC equals 4X -3, and angle CAB equals X -3, what is angle ACB

Soloha48 [4]

Answer:

∠ACB = 28.5

Step-by-step explanation:

In triangle ABC,

angle CAB = x-3

angle ABC = 4X-3

It is also given that AB=CB

We know that if two sides of any triangle are equal then corresponding sides must also be equal.

Hence

angle ACB = angle CAB

angle ACB = x-3 {Given that angle CAB = x-3 }

We know that sum of all three angles of a triangle is 180 degree so let's add given angles

angle ACB + angle CAB + angle ABC = 180

(x-3) + (x-3) + (4x-3) = 180

x-3 + x-3 + 4x-3 = 180

6x-9 = 180

6x = 180+9

6x = 189

x = 189/9

x= 31.5

Now plug value of x into

angle ACB = x-3 = 31.5-3 = 28.5

Hence final answer is

∠ACB = 28.5

3 0

2 years ago

The nurse needs to mix 2% solution with 10% solution to get 10 ml of the prescribed 6% solution. What amount of each solution do

xenn [34]

<em>Volumes of 2% Solution = </em><em>5 ml</em>

<em>Volumes of 10% Solution = </em><em>5 ml</em>

$\texttt{ }$

<h3>Further explanation</h3>

Simultaneous Linear Equations could be solved by using several methods such as :

<em>Elimination Method</em>
<em>Substitution Method</em>
<em>Graph Method</em>

If we have two linear equations with 2 variables x and y , then we need to find the value of x and y that satisfying the two equations simultaneously.

Let us tackle the problem!

$\texttt{ }$

<em>Let:</em>

<em>Volumes of 2% Solution = x</em>

<em>Volumes of 10% Solution = y</em>

$\texttt{ }$

<em>Total Volume = 10 ml</em>

$\boxed{x + y = 10}$ → <em>Equation 1</em>

$\texttt{ }$

<em>The nurse needs to mix 2% solution with 10% solution to get 10 ml of the prescribed 6% solution</em>.

$2 \% x + 10 \% y = 6 \% (10)$

$2x + 10y = 6(10)$

$\boxed{x + 5y = 30}$ → <em>Equation 2</em>

$\texttt{ }$

<em>Equation 1 - Equation 2:</em>

$( x + y ) - ( x + 5y ) = 10 - 30$

$-4y = -20$

$y = -20 \div -4$

$y = 5 \texttt{ ml}$

$\texttt{ }$

$x + y = 10$

$x + 5 = 10$

$x = 5 \texttt{ ml}$

$\texttt{ }$

<h2>Conclusion:</h2>

<em>Volumes of 2% Solution = </em><em>5 ml</em>

<em>Volumes of 10% Solution = </em><em>5 ml</em>

$\texttt{ }$

<h3>Learn more</h3>

Perimeter of Rectangle : brainly.com/question/12826246
Elimination Method : brainly.com/question/11233927
Sum of The Ages : brainly.com/question/11240586

<h3>Answer details</h3>

Grade: High School

Subject: Mathematics

Chapter: Simultaneous Linear Equations

Keywords: Simultaneous , Elimination , Substitution , Method , Linear , Equations

6 0

2 years ago

Can anyone help me on this please

vazorg [7]

Answer:

201.06

Step-by-step explanation:

hope this helps!!!!

3 0

2 years ago