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Phoenix [80]
3 years ago
5

Help ASAP

Mathematics
1 answer:
max2010maxim [7]3 years ago
3 0

Answer:

Step-by-step explanation:

The formula for determining the sum of n terms, Sn of a geometric sequence is expressed as

Sn = (ar^n - 1)/(r - 1)

Where

n represents the number of term in the sequence.

a represents the first term in the sequence.

r represents the common ratio.

1) 2 – 4 + 8 – 16 + ...

a = 2

r = - 4/2 = - 2

n = 6

Since r is negative, we would use

Sn = a(1 - r^n)/(1 - r)

Therefore, the sum of the first 6 terms, S6 is

S6 = 2(1 - (- 2^6))/(1 - - 2)

S6 = 2(1 - 64)/3 = (2 × - 63)/3

S6 = - 42

2) -2, 6, -18, 54

a = - 2

n = 4

r = 6/- 2 = - 3

S4 = - 2(1 - (- 3^4))/(1 - - 3)

S6 = - 2(1 - 81)/4 = (- 2 × - 80)/4

S6 = 40

3) 1, 2, 4, 8, 16, 32, 64, 128, 256

r = 2/1 = 2

n = 9

a = 1

Sn = (ar^n - 1)/(r - 1)

S9 = (1 × 2^9 - 1)/(2 - 1)

S9 = 512 - 1

S9 = 511

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8_murik_8 [283]

Answer:

Step-by-step explanation:

h(t) = -16t² + 14400

0= -16t² + 14400

(1/-16)×-14400=-16t²(1/-16)

900=t²

\sqrt{900} =\sqrt{t^{2}}

30=t

7 0
2 years ago
HELP PLEASE, WILL MARK BRANLIEST!!!
zhannawk [14.2K]

Answer:

144

Step-by-step explanation:

angle A + angle B = 180 (supplementary angle)

A = 4B

4b+b=180

5b=180

Divide 5 on both sides to get b=36

180-36= measure of angle A

180-36=144

4 0
3 years ago
B
Tom [10]

Answer:

(a) 320 cm²

(b) 75 cm³

Step-by-step explanation:

The scale factor from A to B is 8/4 = 2.

The scale factor of the areas is 2² = 4.

The scale factor of the volumes is 2³ = 8.

(a)

80 cm² * 4 = 320 cm²

(b)

600 cm / 8 = 75 cm³

8 0
2 years ago
After a college football team once again lost a game to their archrival, the alumni association conducted a survey to see if alu
valentina_108 [34]

Answer:

P-value for this hypothesis test is 0.00175.

Step-by-step explanation:

We are given that the alumni association conducted a survey to see if alumni were in favor of firing the coach.

A simple random sample of 100 alumni from the population of all living alumni was taken. Sixty-four of the alumni in the sample were in favor of firing the coach.

<u><em>Let p = proportion of all living alumni who favored firing the coach</em></u>

SO, Null Hypothesis, H_0 : p = 0.50   {means that the majority of alumni are not in favor of firing the coach}

Alternate Hypothesis, H_A : p > 0.50   {means that the majority of alumni are in favor of firing the coach}

The test statistics that will be used here is <u>One-sample z proportion</u> <u>statistics</u>;

                                  T.S.  = \frac{\hat p-p}{{\sqrt{\frac{\hat p(1-\hat p)}{n} } } } }  ~ N(0,1)

where, \hat p  = sample proportion of the alumni in the sample who were in favor of firing the coach = \frac{64}{100} = 0.64

            n = sample of alumni = 100

So, <em><u>test statistics</u></em>  =  \frac{0.64-0.50}{{\sqrt{\frac{0.64(1-0.64)}{100} } } } }

                               =  2.92

<u>Now, P-value of the hypothesis test is given by ;</u>

         P-value = P(Z > 2.92) = 1 - P(Z \leq 2.92)

                                             = 1 - 0.99825 = 0.00175

Therefore, the P-value for this hypothesis test is 0.00175.

4 0
3 years ago
. Use the vectors v = -i +2j and w= -3i + 4j to find 5v + 8w.
Anarel [89]
  • 5v+8w

put values

  • 5(-i+2j)+8(-3i+4j)

Do like you do algebraic addition

  • -5i+10j-24i+32j
  • -5i-24i+10j+32j
  • -29i+42j

Option A

5 0
2 years ago
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