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3 years ago

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the first, second and fifth term of a linear sequence (A. P) is /are three consecutive terms of an exponential sequence (G. P),

if the first term of the linear sequence is 7. Find the common difference.

1 answer:

vredina [299]3 years ago

8 0

Answer: common difference is 14

Step-by-step explanation:

a,a+d,a+4d

7,7+d,7+4d

(7+d)/7=(7+4d)/(7+d)

(7+d)(7+d)=7(7+4d)

49+14d+d^2=49+28d

d^2-14d=0

d(d-14)=0

d=0 or d-14=0

d=14

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How do I do 8b(ii) ? Please help me thank you!

Mila [183]

Step One
======
Find the length of FO (see below)

All of the triangles are equilateral triangles. Label the center as O
FO = FE = sqrt(5) + sqrt(2)

Step Two
======
Drop a perpendicular bisector from O to the midpoint of FE. Label the midpoint as J. Find OJ

Sure the Pythagorean Theorem. Remember that OJ is a perpendicular bisector.

FO^2 = FJ^2 + OJ^2
FO = sqrt(5) + sqrt(2)
FJ = 1/2 [(sqrt(5) + sqrt(2)] \
OJ = ??

[Sqrt(5) + sqrt(2)]^2 = [1/2(sqrt(5) + sqrt(2) ] ^2 + OJ^2
5 + 2 + 2*sqrt(10) = [1/4 (5 + 2 + 2*sqrt(10) + OJ^2
7 + 2sqrt(10) = 1/4 (7 + 2sqrt(10)) + OJ^2 Multiply through by 4
28 + 8* sqrt(10) = 7 + 2sqrt(10) + 4 OJ^2 Subtract 7 + 2sqrt From both sides
21 + 6 sqrt(10) = 4OJ^2 Divide both sides by 4
21/4 + 6/4* sqrt(10) = OJ^2
21/4 + 3/2 * sqrt(10) = OJ^2 Take the square root of both sides.
sqrt OJ^2 = sqrt(21/4 + 3/2 sqrt(10) )
OJ = sqrt(21/4 + 3/2 sqrt(10) )

Step three
find h
h = 2 * OJ
h = 2* sqrt(21/4 + 3/2 sqrt(10) ) <<<<<< answer.

7 0

3 years ago

Of the 200 packages of bagels sold 15 of them are sesame seed bagels what percent of the bagel packages sold are sesame seed bag

Shalnov [3]

15 = x% from 200
<span>15 = </span><span> * 200</span>
15 = 2x / ÷ 2 (both sides)
<u>x = 7.5 [percent]</u>

6 0

3 years ago

Read 2 more answers

A pharmaceutical company receives large shipments of ibuprofen tablets and uses an acceptance sampling plan. This plan randomly

Keith_Richards [23]

Answer:

0.7208 = 72.08% probability that this whole shipment will be accepted.

Step-by-step explanation:

For each tablet, there are only two possible outcomes. Either it meets the required specifications, or it does not. The probability of a tablet meeting the required specifications is independent of any other tablet, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

4% rate of defects

This means that $p = 0.04$

26 tablets

This means that $n = 26$

What is the probability that this whole shipment will be accepted?

Probability that at most one tablet does not meet the specifications, which is:

$P(X \leq 1) = P(X = 0) + P(X = 1)$

Thus

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{26,0}.(0.04)^{0}.(0.96)^{26} = 0.3460$

$P(X = 1) = C_{26,1}.(0.04)^{1}.(0.96)^{25} = 0.3748$

Then

$P(X \leq 1) = P(X = 0) + P(X = 1) = 0.3460 + 0.3748 = 0.7208$

0.7208 = 72.08% probability that this whole shipment will be accepted.

3 0

3 years ago

What is the solution for the system of equations x+y=2 and x-y=4

dmitriy555 [2]

X+y=2 (label equation one)
x-y=4 (label equation two)

y=-x+2 (equation one rearranged, label this equation equation three)

sub 3 into 2
x-(-x+2)=4
x+x-2=4
2x-2=4
2x=6
x=3
sub x=3 into equation one

3+y=2
y=-1

therefore x=3 and y=-1

5 0

3 years ago

H=2.9L+78.1<br> About how tall would the male have been if the length of the humerus measured 39 cm?

dalvyx [7]

Answer:H=191.2

Step-by-step explanation:

H=2.9(39)+78.1

H=113.1+78.1

H=191.2 cm

3 0

4 years ago