Quels sont les deux nombres dont la somme est 2095 et la différence 699

Please help right away.

Travka [436]

$\sum\limits_{k=1}^{\infty}420\left(\dfrac{1}{6}\right)^{k-1}$

The infinite geometric series is converges if |r| < 1.

We have r=1/6 < 1, therefore our infinite geometric series is converges.

The sum S of an infinite geometric series with |r| < 1 is given by the formula :

$S=\dfrac{a_1}{1-r}$

We have:

$a_1=420\left(\dfrac{1}{6}\right)^{1-1}=420\left(\dfrac{1}{6}\right)^0=420\\\\r=\dfrac{1}{6}$

substitute:

$S=\dfrac{420}{1-\frac{1}{6}}=\dfrac{420}{\frac{5}{6}}=420\cdot\dfrac{6}{5}=84\cdot6=504$

Answer: d. Converges, 504.

8 0

2 years ago

Find the amount in an account if 7,650 is invested at 9.15 percent compounded quarterly for 8 years and 6 months

storchak [24]

We have been given that in an account an amount of 7,650 is invested at 9.15 percent compounded quarterly for 8 years and 6 months.

We will use compound interest formula to find our answer.

$A=Pcdot(1+\frac{r}{n}) ^{nT}$ ,

Where, P= principle amount, A= amount after T years, n= period of compounding and r = interest rate (decimal).

Let us substitute our given values in our formula.

$A=7650(1+\frac{0.0915}{4} )^{(8.5\times4)}$

$A=7650(1+0.022875)^{34}$

$A=7650(1.022875)^{34}$

$A=7650\cdot 2.15758136398$

$A=16505.4974$

Therefore, after 8 years and 6 months our amount will be 16505.497.

7 0

2 years ago

((Recall: 1 oz = 28.4 g. and 1 kg. = 1,000 g.) 100 oz ~ kg.

swat32

Since 1 oz is equal to 28.4 g and 1 kg is equal to 1000 g that means that 3521.12 kg are equal to 100 oz

4 0

2 years ago

Henry has collected data to find that the typing speeds for the students in a typing class has a normal distribution. What is th

Mekhanik [1.2K]

Answer: 0.8413

Step-by-step explanation:

Given : Henry has collected data to find that the typing speeds for the students in a typing class has a normal distribution.

Mean : $\mu=47$

Standard deviation : $\sigma= 4$

Let x be the random variable that represents the typing speeds for the students.

The z-score :-

$z=\dfrac{x-\mu}{\sigma}$

For x= 51

$z=\dfrac{51-47}{4}=1$

Using the standard normal distribution table ,the probability that a randomly selected student has a typing speed of less than 51 words per minute :-

$P(x$

Hence, the probability that a randomly selected student has a typing speed of less than 51 words per minute = 0.8413

8 0

2 years ago

Two birds sit at the top of two different trees. The distance between the first bed and a birdwatcher on the ground is 34 feet t

stira [4]

Answer:

Step-by-step explanation:

The given triangle is a right angle triangle.

The distance between the first bed and the bird watcher on the ground represents the opposite side of the right angle triangle.

The distance between the birdwatcher and the second bird is 47 feet. This represents the hypotenuse of the right angle triangle. To determine the angle of depression, x degrees, we would apply the Sine trigonometric ratio which is expressed as

Sin θ = opposite side/hypotenuse

Sin x = 34/47 = 0.723

x = Sin^-1(0.723)

x = 46.3 degrees to the nearest tenth.

5 0

2 years ago

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