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2 years ago

The first five terms of a pattern are shown.

Mathematics

1 answer:

Andrej [43]2 years ago

6 0

Answer:

Step-by-step explanation:

There is a common ratio between consecutive term in the sequence, that is

$\frac{3}{10}$ ÷ $\frac{3}{100}$ = 3 ÷ $\frac{3}{10}$ = 30 ÷ 3 = 300 ÷ 30 = 10

This indicates the sequence is geometric with n th term

$a_{n}$ = a $(r)^{n-1}$

where a is the first term and r the common ratio

Here a = $\frac{3}{100}$ and r = 10 , thus

$a_{n}$ = $\frac{3}{100}$ $(10)^{n-1}$

= $\frac{3}{10^{2} }$ × $10^{n-1}$

= 3 × $10^{-2}$ × $10^{n-1}$

= 3 × $10^{n-3}$

Thus

$a_{n}$ = 3 $(10)^{n-3}$ → C

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A certain plant runs three shifts per day. Of all the items produced by the plant, 50% of them are produced on the first shift,

Snezhnost [94]

Answer:

0.2941 = 29.41% probability that it was manufactured during the first shift.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Defective

Event B: Manufactured during the first shift.

Probability of a defective item:

1% of 50%(first shift)

2% of 30%(second shift)

3% of 20%(third shift).

$P(A) = 0.01*0.5 + 0.02*0.3 + 0.03*0.2 = 0.017$

Probability of a defective item being produced on the first shift:

1% of 50%. So

$P(A \cap B) = 0.01*0.5 = 0.005$

What is the probability that it was manufactured during the first shift?

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.005}{0.017} = 0.2941$

0.2941 = 29.41% probability that it was manufactured during the first shift.

6 0

2 years ago

A = πηγ2<br> What do you divide by?

defon

Answer:

76.20+q; 76.60Es

Step-by-step explanation:

5 0

2 years ago

Every weekday, Mr. Jones bikes from his home to his job. Sometimes he rides along two roads, the long route that is shown by the

notka56 [123]

Answer:

(A)6 kilometers

Step-by-step explanation:

First, we determine the value of a using Pythagoras Theorem.

$Hypotenuse^2=Opposite^2+Adjacent^2\\17^2=a^2+15^2\\a^2=17^2-15^2\\a^2=289-225\\a^2=64\\a^2=8^2\\a=8$ km$

Therefore:

Distance along the long route = 8 + 15 =23 km

Distance along the shortcut =17 km

Difference =23-17 =6km

Therefore, Mr. Jones bikes 6km less when he takes the shortcut instead of the long route.

5 0

2 years ago

Read 2 more answers

Please help

Zolol [24]

Given:

The function is

$r(x)=0.05(x^2+1)(x-6)$

where, function r gives the instantaneous growth rate of a fruit fly population x days after the start of an experiment.

To find:

Number of complex and real zeros.

Time intervals for which the population increased and population deceased.

Solution:

We have,

$r(x)=0.05(x^2+1)(x-6)$

$r(x)=0.05(x^3+x-6x^2-6)$

Here, degree of function x is 3. It means, the given function has 3 zeros.

From the given graph it is clear that, the graph of function r(x) intersect x-axis at once.

So, the given function r(x) has only one real root and other two real roots are complex.

Therefore, function r has 2 complex zeros and one real zero.

Before x=6, the graph of r(x) is below the x-axis and after that the graph of r(x) is above the x-axis.

Negative values of r(x) represents the decrease in population and positive value of r(x) represents the increase in population.

Therefore, based on instantaneous growth rate, the population decreased between 0 and 6 hours and the population increased after 6 hours.

3 0

2 years ago

⚠️I MARK BRAINLIST PIC INCLUDED ⚠️What is the initial value of the sequence?

densk [106]

Answer:

Step-by-step explanation:

8 0

2 years ago