ABCD is a trapezium<br><br> Calculate the area of ABCD

Find an explicit rule for the nth term of the sequence.The second and fifth terms of a geometric sequence are 18 and 144, respec

vova2212 [387]

Given:

second term = 18

fifth term = 144

The nth term of a geometric sequence is:

$\begin{gathered} a_n\text{ = ar}^{n-1} \\ Where\text{ a is the first term} \\ r\text{ is the common ratio} \end{gathered}$

Hence, we have:

$\begin{gathered} \text{ar}^{2-1}\text{ = 18} \\ ar\text{ = 18} \\ \\ ar^{5-1}=\text{ 144} \\ ar^4\text{ =144} \end{gathered}$

Divide the expression for the fifth term by the expression for the second term:

$\begin{gathered} \frac{ar^4}{ar}\text{ = }\frac{144}{18} \\ r^3\text{ = }\frac{144}{18} \\ r\text{ = 2} \end{gathered}$

Substituting the value of r into any of the expression:

$\begin{gathered} ar\text{ = 18} \\ a\text{ }\times\text{ 2 = 18} \\ Divide\text{ both sides by 2} \\ \frac{2a}{2}\text{ =}\frac{18}{2} \\ a\text{ = 9} \end{gathered}$

Hence, the explicit rule for the sequence is:

$a_n\text{ = 9\lparen2\rparen}^{n-1}$

5 0

2 years ago

The percent, X , of shrinkage o n drying for a certain type of plastic clay has an average shrinkage percentage :, where paramet

never [62]

Answer:

a) $t=\frac{18.4-17.5}{\frac{2.2}{\sqrt{45}}}=2.744$

The degrees of freedom are given by:

$df=n-1=45-1=44$

The critical value for this case is $t_{\alpha}=1.68$ since the calculated value is higher than the critical we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 18.4

b) $p_v =P(t_{(44)}>2.744)=0.0044$

Step-by-step explanation:

Information given

$\bar X=18.4$ represent the sample mean

$s=2.2$ represent the sample standard deviation

$n=45$ sample size

$\mu_o =17.5$ represent the value to verify

$\alpha=0.05$ represent the significance level

t would represent the statistic

$p_v$ represent the p value

Part a

We want to test if the true mean is higher than 17.5, the system of hypothesis would be:

Null hypothesis: $\mu \leq 17.5$

Alternative hypothesis: $\mu > 17.5$

The statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

And replacing we got:

$t=\frac{18.4-17.5}{\frac{2.2}{\sqrt{45}}}=2.744$

The degrees of freedom are given by:

$df=n-1=45-1=44$

The critical value for this case is $t_{\alpha}=1.68$ since the calculated value is higher than the critical we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 18.4

Part b

The p value would be given by:

$p_v =P(t_{(44)}>2.744)=0.0044$

5 0

4 years ago

ANSWER HELP SHOW WORK 15 POINTS

azamat

Answer:

m<-2

Step-by-step explanation:

-4m-3.65>4.35

-4m>4.35+3.65

-4m>8

4m<-8 (the greater than or less than sign flips when you multiply or divide by the - sign)

m<-2 (divide both sides by 4)

7 0

3 years ago

What is the inequality?

True [87]

Option A, x < 0

When looking at line graphs, it's relatively easy to figure out how they work.

Start by locating where the point is. In this case, the point is on 0. Now, is the point hollow? If it is, then you know that the inequality is either < or > (if it's hollow, it means that the integer isn't included). However, if the circle's filled in, you know that it's either ≥ or ≤ (if the circle's filled in, the integer is included)

Now, check to see which way the line goes. Does the number get smaller or bigger as you go across the line? If the number gets bigger, then x > 0. If the number gets smaller, then x < 0.

-T.B.

6 0

4 years ago

Which relation is a function

liq [111]

Answer:

the first one

Step-by-step explanation:

6 0

4 years ago

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ABCD is a trapezium Calculate the area of ABCD