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shutvik [7]
3 years ago
8

an arithmetic series has first term 160 and common difference d . the sum of the first 25 terms of the series 3500 . find the co

mmon difference d.
Mathematics
1 answer:
mina [271]3 years ago
6 0

Answer:

d = - \frac{5}{3}

Step-by-step explanation:

The sum to n terms of an arithmetic series is

S_n} = \frac{n}{2} [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

Here a₁ = 160, n = 25 and S_{25} = 3500 , thus

\frac{25}{2} [ (2 × 160) + 24d ] = 3500, that is

12.5(320 + 24d) = 3500 ( divide both sides by 12.5 )

320 + 24d = 280 ( subtract 320 from both sides )

24d = - 40 ( divide both sides by 24 )

d = - \frac{40}{24}  = - \frac{5}{3}

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3 years ago
A set of computer science exam scores are normally distributed with a mean of 71.33 point, and a standard deviation of 3 points.
Bess [88]

Answer: 0.86 of the exam scores are between 68 and 77.99 points

Step-by-step explanation:

Since the set of computer science exam scores are normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = computer science exam scores .

µ = mean score

σ = standard deviation

From the information given,

µ = 71.33 points

σ = 3 points

We want to find the proportion of the exam scores are between 68 and 77.99 points. It is expressed as

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For x = 68,

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Looking at the normal distribution table, the probability corresponding to the z score is 0.13

For x = 68,

z = (77.99 - 71.33)/3 = 2.22

Looking at the normal distribution table, the probability corresponding to the z score is 0.99

P(68 ≤ x ≤ 77.99) = 0.99 - 0.13 = 0.86

5 0
3 years ago
Mrs. JOHNSON paid $40.68 for 3kg of shrimp. What’s the cost of 1 kilogram of shrimp?
Goshia [24]

Answer:

It is 13.56

Step-by-step explanation:

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Read 2 more answers
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Ahat [919]

Answer:

-29 and -24

Step-by-step explanation:

-24 = (-29) = -53

-29-(-24) = -5

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3 years ago
Write the equation in slope-intercept form of the line that has a slope of 6 and contains the point (1, 1).
valentinak56 [21]

Answer: y=6x-5

Step-by-step explanation:

Since we know the slope, we can plug it into the slope-intercept equation. We can plug in the given point to find the y-intercept.

y=6x+b

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Now that we know the y-intercept, we can complete the equation.

y=6x-5

5 0
3 years ago
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