Find the slope of the line that connects these points.

The second term in a geometric sequence is 20. The fourth term in the same sequence is 45/4 or 11.25. What is the common ratio i

kati45 [8]

$\bf \begin{array}{ccll}
n&term&value\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
2&a_2&20\\
3&a_3&20r\\
4&a_4&20rr\\
&&20r^2\\\\
&&\frac{45}{4}
\end{array}\implies \stackrel{4^{th}~term}{20r^2=\cfrac{45}{4}}\implies r^2=\cfrac{45}{80}
\\\\\\
r^2=\stackrel{simplified}{\cfrac{9}{16}}\implies r=\sqrt{\cfrac{9}{16}}\implies r=\cfrac{\sqrt{9}}{\sqrt{16}}\implies r=\cfrac{3}{4}$

4 0

3 years ago

Each year, all final year students take a mathematics exam. It is hypothesised that the population mean score for this test is 1

Yuri [45]

Answer:

90% confidence interval for the population mean test score is [95.40 , 106.59]

Step-by-step explanation:

We are given that the population mean score for mathematics test is 115. It is known that the population standard deviation of test scores is 17.

Also, a random sample of 25 students take the exam. The mean score for this group is 101.

The, pivotal quantity for 90% confidence interval for the population mean test score is given by;

P.Q. = $\frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, X bar = sample mean = 101

$\sigma$ = population standard deviation

n = sample size = 25

So, 90% confidence interval for the population mean test score, $\mu$ is ;

P(-1.6449 < N(0,1) < 1.6449) = 0.90

P(-1.6449 < $\frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } }$ < 1.6449) = 0.90

P(-1.6449 * $\frac{\sigma}{\sqrt{n} }$ < ${Xbar-\mu}$ < 1.6449 * $\frac{\sigma}{\sqrt{n} }$ ) = 0.90

P(X bar - 1.6449 * $\frac{\sigma}{\sqrt{n} }$ < $\mu$ < X bar + 1.6449 * $\frac{\sigma}{\sqrt{n} }$ ) = 0.90

90% confidence interval for $\mu$ = [ X bar - 1.6449 * $\frac{\sigma}{\sqrt{n} }$ , X bar + 1.6449 * $\frac{\sigma}{\sqrt{n} }$ ]

= [ 101 - 1.6449 * $\frac{17}{\sqrt{25} }$ , 10 + 1.6449 * $\frac{17}{\sqrt{25} }$ ]

= [95.40 , 106.59]

Therefore, 90% confidence interval for the population mean test score is [95.40 , 106.59] .

7 0

3 years ago

Help me!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

ahrayia [7]

Answer:

9. x=-6, y=0

10. x=-9, y=-10

11. x=3, y=-1

Step-by-step explanation:

$2x-9y=-12\\3x+18y=-18$

Multiply the first equation by 2.

$4x-18y=-24\\3x+18y=-18$

Add the equations.

$7x=-42$

$x=-6$

We figured out x now we have to figure out y. To figure out y plug in x into any equation.

$2(-6)-9y=-12$

$-12-9y=-12$

$-9y=0$

$y=0$

Your answer is x = -6 and y = 0 for number nine.

$6x+3y=24\\2x+3y=-12$

Change the signs of the second equation becuase 3y and 3y are both positive. We need one of them to be negative.

$6x+3y=24\\-2x-3y=12$

Add them.

$4x = 36$

$x=9$

Now we have to figure out y.

$2(9)+3y=-12$

$18+3y=-12$

$3y=-30$

$y=-10$

x=-9 and y=-10 is your answer to number ten.

$10x+5y=25\\-7x-3y=-18$

$30x+15y=75\\-35x-15y=-90$

$-5x=-15$

$x=3$

$-7(3)-3y=-18$

$-21-3y=-18$

$-3y=3$

$y=-1$

x=3 and y=-1 is the answer to number eleven. I hope this helps! Let me know if I got anything wrong.

4 0

2 years ago

Read 2 more answers

The length of a rectangle is 4cm more than the width and the perimeter is 48cm. What is the width?

Karolina [17]

Answer:

12cm

Step-by-step explanation:

4 0

3 years ago

Sorry for the computer quality lol but can someone please help ?

xenn [34]

Answer:

a=(-1,0) b=(0,3) c=(-2,2)

Step-by-step explanation:

7 0

3 years ago