The volume of a paint can is 215 in. If the height of the can is 7.5 in, what is the radius to the nearest whole number

it has one value with x which is x^2 and it cn be easily solved without having to factorise, quadratic formula cant be used as it need ax^2+bx+c=0 format

B. factorising

$x^2-x-6=0\\x^2+2x-3x-6=0\\(x+2)(x-3)=0\\x+2=0 and x-3=0\\x= -2 \\x= 3$

i just felt like this was easier to factorise than the other 2 options left

C. Completing the square

$x^2-6x-7=0\\(x-3)^2=0\\x= -1\\x= 7$

same reason personal preference

D- Quadratic

$x^2-17x-7=0\\x=\frac{-(-17)+\sqrt{(-17)^2-4(1)(-7)} }{2(1)} \\x=\frac{-(-17)-\sqrt{(-17)^2-4(1)(-7)} }{2(1)}\\x=17.4\\x=-0.402$

the 17 kinda threw me off and i didnt wanna get on factorising or doing completing the square so quadratic formal

7 0

3 years ago

Determine the critical value or values for a one-mean z-test at the 1% significance level if the hypothesis test is right-tailed

kifflom [539]

Answer:

We need to conduct a hypothesis in order to determine if the mean is greater than specified value, the system of hypothesis would be:

Null hypothesis: $\mu \leq \mu_o$

Alternative hypothesis: $\mu > \mu_o$

For this case the significance is 1%. So we need to find a critical value in the normal standard distribution who accumulates 0.99 of the area in the left and 0.01 in the right and for this case this critical value is:

$z_{crit}= 2.326$

Step-by-step explanation:

Notation

$\bar X$ represent the sample mean

$\sigma$ represent the standard deviation for the population

$n=$ sample size

$\mu_o$ represent the value that we want to test

$\alpha$ represent the significance level for the hypothesis test.

z would represent the statistic (variable of interest)

State the null and alternative hypotheses.