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3 years ago

Graph the first six terms of a sequence where a, = 4 and r = 2.

Mathematics

1 answer:

Ahat [919]3 years ago

5 0

The first six terms are {4,8,16,32,64,128}

Further explanation:

The given sequence will be a geometric sequence as common ratio is given.

So,

Common ratio = r = 2

First term = a = 4

The next terms will be obtained by multiplying each term with 2.

$a_1 = 4\\a_2 = 4*2 = 8\\a_3 = 8*2 = 16\\a_4 = 16*2 = 32\\a_5 = 32*2 = 64\\a_6 = 64*2 = 128\\So\ the\ first\ 6\ terms\ are \{4,8,16,32,64,128\}$

For graph, the placement number of terms will be taken along x-axis and the terms will be along y-axis.

The graph is attached herewith.

Keywords: Geometric sequence, Common ratio

Learn more about geometric sequence at:

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A bag contain 5 red marbles,4 green marbles and 1 blue marble. A marble is chosen at random from the bag and not replaced; then

jarptica [38.1K]

Answer:

$\frac{2}{15}$

Step-by-step explanation:

GIVEN: A bag contain $5$ red marbles, $4$ green marbles and $1$ blue marble. A marble is chosen at random from the bag and not replaced, then a second marble is chose.

TO FIND: What is the probability both marbles are green.

SOLUTION:

Total marbles in bag $=10$

total number of green marbles $=4$

Probability that first marble will be green $P(A)=\frac{\text{total green marbles}}{\text{total marbles}}$

$=\frac{4}{10}=\frac{2}{5}$

Probability that second marble will be green $P(B)=\frac{\text{total green marble in bag}}{\text{total marble in bag}}$

$\frac{3}{9}=\frac{1}{3}$

As both events are disjoint

probability both marbles are green $=P(A)\times P(B)$

$=\frac{2}{5}\times\frac{1}{3}=\frac{2}{15}$

Hence the probability both marbles are green is $\frac{2}{15}$

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3 years ago

The Law and Order detectives enter a house at 11:30 am and found a man on the floor murdered. They take his body temperature fin

taurus [48]

Answer:

Time of murder = 10:39 am

Step-by-step explanation:

Let the equation of exponential function representing the final temperature of the body after time 't' is,

f(t) = $a(e)^{nt}$

Here, a = Initial temperature

n = Constant for the change in temperature

t = Duration

At 11:30 am temperature of the body was 91.8°F.

91.8 = $98.6(e)^{nt}$ --------(1)

Time to reach the body to the morgue = 12:30 pm

Duration to reach = 12:30 p.m. - 11:30 a.m.

= 1 hour

Therefore, equation will be,

84.4 = $91.8(e)^{n\times 1}$

eⁿ = $\frac{84.4}{91.8}$

ln(eⁿ) = ln(0.9194)

n = -0.08403

From equation (1),

91.8 = $98.6(e)^{-0.08403t}$

$(e)^{0.08403t}=\frac{98.6}{91.8}$

$ln[(e)^{0.08403t}]=ln[\frac{98.6}{91.8}]$

0.08403t = 0.07146

t = 0.85 hours

t ≈ 51 minutes

Therefore, murder was done 51 minutes before the detectives arrival.

Time of murder = 11:30 - 00:51

= 10:90 - 00:51

= 10:39 am

7 0

3 years ago

On an exam you get two points for every question answered correctly, zero points for each question left blank and lose one-half

Paraphin [41]

Using multiplication, the total score on the exam if you answered 13 questions correctly, leave 7 questions blank and answer 5 questions incorrectly is 39 point.

According to the question,

For each correct question, you get 2 points, and there are 22 correct questions, so multiply 22 by 2

22 * 2 = 44 points.

For each question left blank, you get 0 points, and there are 7 questions left blank, so multiply 7 by 0

7 * 0 = 0 points

For each incorrect question, you get -1 point, and there are 5 incorrect questions, so multiply 5 by -1

5 * (-1) = -5 points.

The total number of score = 22*2 + 7*0 + 5*(-1) = 44 + 0 - 5 = 39 points.

Hence, using multiplication, the total score on the exam if you answered 13 questions correctly, leave 7 questions blank and answer 5 questions incorrectly is 39 point.

Learn more about multiplication here

brainly.com/question/2865130

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2 years ago

A right triangle has a leg of 12 cm and a hypotenuse of 16 cm what is the length of the other leg

Oksi-84 [34.3K]

The length of the other leg is 12 cm

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3 years ago

Really need this todayyyyyy

Bond [772]