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Nostrana [21]
2 years ago
10

If S_6=922.32 and r = 4/5, what is the value of a₁?

Mathematics
1 answer:
il63 [147K]2 years ago
3 0

Answer:

  a₁ = 250

Step-by-step explanation:

Use the given values in the formula for the sum of a geometric series, and solve for the unknown.

__

  S₆ = a₁×(1 -r⁶)/(1 -r) . . . . sum of 6 terms of a geometric series

  922.32 = a₁×(1 -(4/5)⁶)/(1 -4/5) = a₁×5×(1 -4096/15625) = a₁×11529/3125

  922.32×3125/11529 = a₁ = 250 . . . . divide by the coefficient of a₁

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Which description best compares the graphs given by the equations:
nexus9112 [7]

x - 5y = -5, -5x - 25y = 25

First, you'll need to get the x variable by itself.

x - 5y = -5<u>
</u><u>    +5    +5</u><u>
</u>       x = 0
So x is plotted on the 0.

For the second part of the first equation, you'll be looking for what the y variable represents.

x - 5y = -5
<u>-x           -x</u><u>
</u>     <u>-5y</u> = <u>-5</u><u>
</u><u>       5      5</u><u>
</u>        y = 1
So y is plotted on the 1 on the vertical line above the 0.

For the first part of the second equation, you'll do the same thing as in the first equation.

-5x - 25y = 25
<u>        +25   +25</u><u>
</u>          <u>-5x</u> = <u>50</u><u>
</u>            5      5
            x = 10
So the x for this equation is plotted on 10 on the horizontal line.

For the second part of the second equation, you will do the same thing as in the first equation.

-5x - 25y = 25
<u>+5               +5</u><u>
</u>       <u>-25y</u> = <u>30</u><u>
</u>        25      25
           y = 1.2
So the y for the second half of the second question is plotted on 1.2 on the vertical line.

<h2>Answer: B) Perpendicular</h2>

Perpendicular means the lines may or may not be of equal length and they will not be perfectly in line with each other.

Parallel means the lines may or may not be of equal length but will be perfectly in line with each other.

Intersecting means the lines may or may not be of equal length but will touch each other.

6 0
2 years ago
A greenhouse is offering a sale on tulip bulbs because they have inadvertently mixed pink bulbs with red bulbs. If​ 40% of the b
True [87]

Answer:

The probabilty of having at least one pink bulb if 4 bulbs are purchased is 13%.

Step-by-step explanation:

The proportion of pink bulbs is p=0.4.

If X is the amount of pink bulbs in a group of 4 bulbs, we can model this as a binomial distribution problem.

The probability that at least one of the bulbs is pink is P(X≥1)

P(X\geq 1)=1-P(X=0)=1-(\binom{4}{0}p^0(1-p)^4)\\\\P(X\geq 1)=(1-p)^4=0.6^4=0.1296

The probabilty of having at least one pink bulb if 4 bulbs are purchased is 13%.

6 0
3 years ago
What is the product of -11 x 7
zepelin [54]

Answer:

-77

Step-by-step explanation:

Multiply 11 x 7 first which gives you 77. And since the Negative sign is before 11, which means the product negative always, it will be -77!

hope this helped!

7 0
3 years ago
Read 2 more answers
What is the slope of the line given by the equation below? y - 9 = 15(x - 5)
Elina [12.6K]
Y - 9 = 15x - 75

y = 15x - 75 + 9

y = 15x - 66              y = mx + c,   slope = m

m = slope = 15
7 0
3 years ago
There are 4 cards in the box with the numbers 2, 5, 6, and 8. Two cards are drawn one after the other. The second card drawn is
malfutka [58]

It is given that there are 4 cards with numbers 2, 5, 6, and 8.

1) It is required to list all the numbers available when two cards are drawn one after the other and the second card is placed at the right of the first card drawn.

To do this, find the sample space of the draw which are:

25,26,28,52,56,58,62,65,68,82,85,86

Hence, the required numbers.

2) Recall that probability is the ratio:

Probability=\frac{\text{ number of favorable outcomes}}{\text{ total number of possible outcomes}}

From the numbers listed, notice that the total number of possible outcomes is 12.

Since event A is "obtained number is even", notice that the number of even numbers in the listed numbers is 9 (26,28,52,56,58,62,68,82,86).

Hence, the number of favorable outcomes is 9.

Substituting into the probability ratio gives the required probability:

P(A)=\frac{9}{12}=\frac{3}{4}

Check the number of numbers that are a multiple of 5, notice that they are 3 (25,65,85).

Hence, the required probability of event B is:

P(B)=\frac{3}{12}=\frac{1}{4}

The number of multiple of 3 in the listed numbers is 0 since there is no number that is a multiple of 3.

Hence, the required probability of event C is:

P(C)=\frac{0}{12}=0

Answers:

1) {25,26,28,52,56,58,62,65,68,82,85,86}

2) P(A) = 3/4

P(B) = 1/4

P(C)= 0

7 0
1 year ago
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