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Vinvika [58]
3 years ago
6

If n,6 M are in geometric sequence n,7.5, m are in arithmetic sequence ,then find the value of n and m?​

Mathematics
1 answer:
hjlf3 years ago
3 0

Answer:

if  n,6,m are in geometric sequence

=> 6/n = m/6

⇔ mn = 36       (1)

if n,7.5, m are in arithmetic sequence

=> 7.5 - n = m - 7.5

<=> m + n = 15     (2)

from (1)(2), we have the equations:

\left \{ {{mn=36} \atop {m+n=15}} \right.\\\\\left \{ {{mn=36} \atop {m=15-n}} \right.\\\\\left \{ {{(15-n)n=36} \atop {m=15-n}} \right.\\\\\left \{ {{n^{2}-15n+36 =0} \atop {m=15-n}} \right.\\\\\left \{ {{n=12orn=3} \atop {m=15-n}} \right.

with n = 12 => m = 3

       n = 3 => m = 12

=> (m;n) = {(3;12),(12;3)}

Step-by-step explanation:

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Answer:

The bag contains $5.14

Step-by-step explanation:

18% of 50 = (.18)(50) = 9 pennies

40% of 50 = (.40)(50) = 20 dimes

2 more nickels than pennies = 9 + 2 = 11 nickels

40 coins so far, so 50 - 40 = 10 quarters

Total value:

9 x ($0.01) = $0.09  for pennies

20 x ($0.10) = $2.00 for dimes

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10 x ($0.25) = $2.50 for quarters

Grand total value = $5.14

7 0
3 years ago
The average spending at Neco's salad bar is $9.03 with a standard deviation of $3.26. The distribution follows t-distribution. T
arlik [135]

Answer:

The difference between these cut-offs is of $1.9.

Step-by-step explanation:

In this question, we have to find the 90% confidence interval, using the t-distribution.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 41 - 1 = 40

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 40 degrees of freedom(y-axis) and a confidence level of 1 - \frac{1 - 0.9}{2} = 0.95. So we have T = 1.684

The margin of error is:

M = T\frac{s}{\sqrt{n}} = 1.684\frac{3.26}{\sqrt{41}} = 0.95

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 9.03 - 0.95 = $8.08.

The upper end of the interval is the sample mean added to M. So it is 9.03 + 0.95 = $9.98.

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The difference between these cut-offs is of $1.9.

8 0
3 years ago
The dimensions of the scale drawing of a rectangle are 8cm and 11cm. If the scale factor is 4, what is the length of the origina
jeyben [28]

Answer:

Length of the original rectangle is 2.75 cm

Step-by-step explanation:

The dimensions of the scale drawing of rectangle are 8 cm and 11 cm respectively.

This implies that the width of the rectangle is 8 cm while the length of the rectangle is 11 cm.

The scale factor is given as 4. This means that the dimensions of the original rectangle are 1/4 times the given dimensions.

So the length of the original rectangle = \[\frac{1}{4}*11\]

= \[2.75\]

6 0
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seropon [69]
The 5 in the thousands place is greater than the 5 in the hundreds place
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