Name an event that would be measured in days.

X^2 + 3x = 24

completing the square
(x + 1.5)^2 - 2.25 = 24

(x + 1.5)^2 = 26.25

x + 1.5 = +/- sqrt26.25 = +- 5.123

x = -1.5 + 5.123 = 3.62 to nearest hundredth and

x = -1.5 - 5.123 = -6.62 to nearest hundredth

solution set is {-6.62, 3.62}

7 0

3 years ago

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Find the critical values: a. Determine the critical value z????/2 that corresponds to a level of confidence of 87%. (2 pts). b.

larisa86 [58]

Answer:

a) $z_{\alpha/2}=-1.51$ and $z_{\alpha/2}=1.51$

b) $t_{\alpha/2}=-1.89$ and $t_{\alpha/2}=1.89$

c) $t_{\alpha/2}=-2.11$

d) $z_{\alpha/2}=-1.75$ and $z_{\alpha/2}=1.75$

Step-by-step explanation:

Part a

On this case the confidence is 87% or 0.87 so the significance level is $\alpha=1-0.87=0.13$ and $\alpha/2 =0.065$ . On this case we can assume that is a bilateral test or a confidence interval so we will have two critical values.

We need values a,b on the normal standard distribution such that:

$P(Z$ or $P(Z>b)=0.065$ and in order to find it we can use the following code in excel:

"NORM.INV(0.065,0,1)" or "NORM.INV(1-0.065,0,1)", and we see that the critical values $z_{\alpha/2}=-1.51$ and $z_{\alpha/2}=1.51$

Part b

On this case the confidence is 92% or 0.92 so the significance level is $\alpha=1-0.92=0.08$ and $\alpha/2 =0.04$ . On this case we can assume that is a bilateral test or a confidence interval so we will have two critical values.

First we need to calculate the degrees of freedom given by:

$df=n-1=15-1=14$

We need values b,c on the t distribution with 14 degrees of freddom such that:

$P(t_{(14)}$ or $P(t_{(14)}>c)=0.04$ and in order to find it we can use the following code in excel:

"T.INV(0.04,14)" or "T.INV(1-0.04,14)", and we see that the critical values $t_{\alpha/2}=-1.89$ and $t_{\alpha/2}=1.89$

Part c

The significance level is $\alpha=0.025$ and is a left tailed test. On this case we know that is a left tailed test so then we have just one critical value.

First we need to calculate the degrees of freedom given by:

$df=n-1=18-1=17$

We need a value c on the t distribution with 17 degrees of freddom such that:

$P(t_{(17)}$ , and in order to find it we can use the following code in excel:

"T.INV(0.025,17)", and we see that the critical values $t_{\alpha/2}=-2.11$

Part d

The significance level is $\alpha=0.08$ and $\alpha/2 =0.04$ . On this case we know that w ehave a two tailed proportion test, so we will have two critical values.

We need values a,b on the normal standard distribution such that:

$P(Z$ or $P(Z>b)=0.04$ and in order to find it we can use the following code in excel:

"NORM.INV(0.04,0,1)" or "NORM.INV(1-0.04,0,1)", and we see that the critical values $z_{\alpha/2}=-1.75$ and $z_{\alpha/2}=1.75$

6 0

3 years ago

This question is really had wallahy bufff

Evgesh-ka [11]

Answer:

x = 0, - 2

Step-by-step explanation:

To find f(g(x)) , substitute x = g(x) into f(x)

f(x²) = 2x² + 1

To find g(f(x)) , substitute x = f(x) into g(x)

g(2x + 1) = (2x + 1)²

Then equating

(2x + 1)² = 2x² + 1 ← expand left side using FOIL

4x² + 4x + 1 = 2x² + 1 ( subtract 2x² + 1 from both sides )

2x² + 4x = 0 ← factor out 2x from each term on the left side

2x(x + 2) = 0

Equate each factor to zero and solve for x

2x = 0 ⇒ x = 0

x + 2 = 0 ⇒ x = - 2

solutions are x = 0, - 2

6 0

2 years ago

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