All categories

3 years ago

What is the value of the fourth term in the geometric sequence

Mathematics

1 answer:

ivanzaharov [21]3 years ago

6 0

Answer:

a(4) = 15/4

Step-by-step explanation:

Here we're told that the first term is a(1) = 30 and that the common factor r = 1/2.

Thus, the geometric sequence formula specific to this case is

a(n) = 30(1/:2)^(n-1).

What is the fourth term? Let n = 4,

a(4) = 30(1/2)^(4-1), or a(4) = 30(1/2)^(3), or a(4) = 30(1/8) = 30/8, or, in reduced form,

a(4) = 15/4.

You might be interested in

The sum of two number is 6. Twice the first number added to three times the second number is 10. Write a system of equations and

seropon [69]

Answer:

4 and 2 are the required numbers which satisfies the given equations

Step-by-step explanation:

Let the two numbers be x and y

According to the first condition

their is is 6

which is

x + y =6 ........................(i)

Now according to second condition

twice the first number i.e. 2x added to three time the second number i.e. 3y is 10

in form of equation it could be written as

2x + 3y = 10 ........................(ii)

Now from first equation we have

x + y =6

subtracting y from both sides

x = 6 - y .....................(iii)

Now putting this value of x in equation (ii)

equation (ii) is

2x + 3y = 10

Putting the value gives

2(6-y)+3y = 10

opening the brackets

12 - 2y + 3y = 10

12 - y = 10

subtracting 12 from both sides

12 - y -12 = 10 -12

it becomes

- y = -2

multiplying both sides by (-1)

it becomes

(-1)(-y) = (-2) * (-1)

y = 2

Now we got the value of y put it in equation iii which is

x = 6 -y

putting the value

x = 6 - 2

x = 4

So the two numbers are x = 4 and y = 2

3 0

3 years ago

Find the sum of the two fractions show your work 3/8 and 1/2

Romashka [77]

Answer: 7/8

Step-by-step explanation: Notice that 1/2 and 3/8 are unlike fractions. Our first when adding unlike fractions is to get a common denominator.

The common denominator of 2 and 8 will be the least common multiple of 2 and 8 which is 8.

To get an 8 in the denominator of 1/2, we multiply the numerator and the denominator by 4 which gives us 4/8.

Notice that 3/8 already has an 8 in the denominator so we leave it how it is.

Now we are adding like fractions.

To add like fractions, or fractions that have the same denominator, simply add the numerators and keep the original denominator.

So here, if we add the numerators we have 4 + 3 which gives us 7 and we put this over our original denominator which is 8 and we have our answer. Also, notice that 7/8 is in lowest terms so it's our final answer.

This means that 3/8 + 1/2 = 7/8

5 0

3 years ago

The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the proba

mart [117]

Answer:

The probablility that there are 8 occurrences in ten minutes is 0.00518 or 0.5%.

Step-by-step explanation:

The distribution that represents the ocurrence of this events is the Poisson distribution.

The probability of having k events in a ten-minute-period can be expressed as:

$P(x=k)=\frac{ \lambda^ke^{-k}}{k!}$

being λ the mean number of occurrences in ten minutes.

The probablility that there are 8 occurrences in ten minutes can be calculated as:

$P(x=k)=\frac{ \lambda^ke^{-k}}{k!}\\\\P(x=8)=\frac{5.3^8e^{-8}}{8!}=\frac{(622596*0.000335463)}{40320}=0.00518$

The probablility that there are 8 occurrences in ten minutes is 0.00518 or 0.5%.

5 0

3 years ago

The maximum depth dmax that a diver can snorkel is set by the density of the water and the fact that human lungs can function ag

postnew [5]

Answer:

17 cm

Step-by-step explanation:

1. Depth in fresh water

p(water) = hρg

d(max) = h = p/(ρg)

Convert atmospheres to pascals

0.056 atm × 101 325 Pa/1 atm = 5670 Pa

h = 5670 Pa/(1000 kg·m⁻³ × 9.806 m·s⁻²) × (1 kg·m⁻¹s⁻²/1 N) = 0.579 m

2. Depth in Dead Sea

d(max) = 5670/(1400 × 9.806) = 0.413 m

3. Difference

Difference = 0.579 – 0.413 = 0.17 m = 17 cm

The difference in d(max) is 17 cm.

5 0

3 years ago

Y= x^3 + 8x^2 +5x<br> work out the coordinates of the two turning points

aliya0001 [1]

Answer:

(-5, 50) and (-1/3, -0.815)

Step-by-step explanation:

The equation is;

y = x³ + 8x² + 5x

Now the turning point will occur at where dy/dx = 0.

Thus;

dy/dx = 3x² + 16x + 5

At dy/dx = 0, we have;

3x² + 16x + 5 = 0

From quadratic formula, we can get;

x = -5 or -⅓

Thus, let's find y at this points.

y = -5³ + 8(-5)² + 5(-5)

y = -125 + 200 - 25

y = 50

Also,at x = -⅓, we have;.

y = (-⅓)³ + 8(-⅓)² + 5(-⅓)

y = -1/27 + 8/9 - 5/3

y = -0.815

Thus,the coordinates of the turning points are;

(-5, 50) and (-1/3, -0.815)

6 0

3 years ago