There is a bag filled with 5 blue and 6 red marbles.

Someeee one?????????????????

Ad libitum [116K]

Answer:

Option B) $a_{n} = 2\cdot 4^{n-1}$

Step-by-step explanation:

The given geometric sequence is

2, 8, 32, 128,....

The general form of a geometric sequence is given by

$a_{n} = a_{1}\cdot r^{n-1}$

Where n is the nth term that we want to find out.

a₁ is the first term in the geometric sequence that is 2

r is the common ratio and can found by simply dividing any two consecutive numbers in the sequence,

$r=\frac{8}{2} = 4$

You can try other consecutive numbers too, you will get the same common ratio

$r=\frac{32}{8} = 4$

$r=\frac{128}{32} = 4$

So the common ratio is 4 in this case.

Substitute the value of a₁ and r into the above general equation

$a_{n} = 2\cdot 4^{n-1}$

This is the general form of the given geometric sequence.

Therefore, the correct option is B

Note: Don't multiply the first term and common ratio otherwise you wont get correct results.

Verification:

$a_{n} = 2\cdot 4^{n-1}$

Lets find out the 2nd term

Substitute n = 2

$a_{2} = 2\cdot 4^{2-1} = 2\cdot 4^{1} = 2\cdot 4 = 8$

Lets find out the 3rd term

Substitute n = 3

$a_{3} = 2\cdot 4^{3-1} = 2\cdot 4^{2} = 2\cdot 16 = 32$

Lets find out the 4th term

Substitute n = 4

$a_{4} = 2\cdot 4^{4-1} = 2\cdot 4^{3} = 2\cdot 64 = 128$

Lets find out the 5th term

Substitute n = 5

$a_{5} = 2\cdot 4^{5-1} = 2\cdot 4^{4} = 2\cdot 256 = 512$

Hence, we are getting correct results!

6 0

3 years ago

Solve the equation and check the solution.

777dan777 [17]

Answer:

a = 4

Step-by-step explanation:

Here, we want to write and solve the given equation

a - 2.5 = 1.5

a = 2.5 + 1.5

a = 4

To check, we simply substitute a = 4

That would be;

4-2.5 = 1.5

This is correct

7 0

2 years ago

Read 2 more answers

A girl is walking 10 miles every 3 hrs whats her average speed ♥

Nookie1986 [14]

We want to find miles per hour.
Speed is distance over time.
So take 10 miles (distance) / 3 hours (time)
This is the same as 10/3.
10/3 = 3 and 1/3
Therefore, the girl is going 3 and 1/3 miles per hour.

6 0

2 years ago

Someone please help me with this one quick

astraxan [27]

The length of AC is 16 km.

Solution:

Given data:

AB = c = 14 km, ∠A = 30° and ∠B = 89°

AC = b = ?

Let us first find angle C:

Sum of all angles in a triangle = 180°

m∠A+ m∠B + m∠C = 180°

30° + 89° + m∠C = 180°

119° + m∠C = 180°

Subtract 119° from both sides, we get

m∠C = 61°

To find the length of AC:

Using sine formula:

$$\frac{b}{\sin B } =\frac{c}{\sin C}$

Substitute the given values in the formula.

$$\frac{b}{\sin 89^\circ } =\frac{14}{\sin 61^\circ }$

Multiply by sin 89° on both sides.

$$\sin 89^\circ \times \frac{b}{\sin 89^\circ } =\frac{14}{\sin 61^\circ } \times \sin 89^\circ$

$$b=\frac{14}{0.8746 } \times0.9998$

$b=16$

The length of AC is 16 km.

4 0

2 years ago

A bottling company uses a filling machine to fill cans with an energy drink. The cans are supposed to contain 250 ml. The machin

sveta [45]

Answer:

a) Mean 250 ml, standard deviation 1.2247 ml.

b) 74.14% probability that the volume of a single randomly chosen can differs from the target value by 1 ml or more.

c) 41.22% probability that the sample mean volume of a random sample of 6 cans differs from the target value by 1 ml or more

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question:

$\mu = 250, \sigma = 3$

a) Assume that the process mean is exactly equal to the target value, that is μ=250. What will be the mean and standard deviation of the sampling distribution of the sample mean x?

By the Central Limit Theorem, the mean is 250 ml and the standard deviation is $s = \frac{3}{\sqrt{6}} = 1.2247$ ml.

b) What is the probability that the volume of a single randomly chosen can differs from the target value by 1 ml or more?

Greater than 250 + 1 = 251 or lesser than 250 - 1 = 249.

Since the normal distribution is symmetric, these probabilities are the same, so we can find one of them and multiply by 2.

Lesser than 249:

pvalue of Z when X = 249.

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{249 - 250}{3}$

$Z = -0.33$

$Z = -0.33$ has a pvalue of 0.3707

0.3707*0.2 = 0.7414

74.14% probability that the volume of a single randomly chosen can differs from the target value by 1 ml or more.

c) What is the probability that the sample mean volume of a random sample of 6 cans differs from the target value by 1 ml or more?

Since more than 1 can, we use the Central Limit Theorem.

The probability follows the same logic as b.

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{249 - 250}{1.2247}$

$Z = -0.82$

$Z = -0.82$ has a pvalue of 0.2061

2*0.2061 = 0.4122

41.22% probability that the sample mean volume of a random sample of 6 cans differs from the target value by 1 ml or more

5 0

3 years ago