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zheka24 [161]
3 years ago
11

What is the sum of the first five terms of a geometric series with a1 =20 and r =1/4?

Mathematics
1 answer:
drek231 [11]3 years ago
5 0
The sum of the first n terms in a geometric sequence given the first term (a1) and the common ratio (r) is calculated through the equation,

                            <span>Sn </span>= (<span><span><span>a1</span>(1−<span>r^n</span>) / (</span><span>1−r)

Substituting the known terms,
                           Sn = (20)(1 - (1/4)^4)) / (1 - 1/4)
                           Sn = 26.5625

Thus, the sum of the first four terms is 26.5625. </span></span>
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Fill in the missing value to make the equations true.
Furkat [3]

Answer:

a) 7/4 b) 5 c) 2

Step-by-step explanation:

Logrithmic Rule for a and b

Let a, M, N be positive real numbers.

a)  

logaM - logaN = loga(M/N)

log9(7) - log9(4) = log9 (7/4)

b)

logaM + logaN = logaMN

log2 (x) + log2(9) = log2(45)

x9=45

(x9)/9 = 45/9

x = 5

c)

Change of base formula.

logb​(x)=logd​(b)/logd​(x)​

x log6(5) = log6(25) divide each term by log6(5)

x log6(5) / log6(5) = log6(25) / log6(5)   Cancel common factor log6(5)

x = log6(25) / log6(5)

x = log6(5^2) / log6(5)

Expand log6(5^2) by moving 2 outside the logarithm.

x = 2log6(5) / log6(5) cancel the like term log6(5)

x = 2

7 0
3 years ago
If a wheelchair-marathon racer moving at 13.1 miles per hour expends energy at a rate of 645 calories per hour, how much energy
Anna71 [15]

Answer:

1290 calories

Step-by-step explanation:

Given: The racer moves at 13.1 miles per hour expends energy at a rate of 645 calories per hour.

To find: Energy in calories, required to complete a marathon race 26.2 miles at this pace.

Solution: We have,

The racer moves at 13.1 miles per hour.

The racer expends energy at a rate of 645 calories per hour.

So, energy expended while moving 13.1 miles =645 calories.

Now, energy expended while moving 1 mile =\frac{645}{13.1} calories.

So, energy expended while moving 26.2 miles =\frac{645}{13.1}\times 26.2=645\times 2=1290 calories.

Hence, 1290 calories of energy is required to complete a marathon race 26.2 miles at this pace.

6 0
3 years ago
The giant outlier is Palm Beach county. We can see that it lies well beyond the range of votes this regression model would predi
notka56 [123]

Answer:

Hello your has some missing information attached below is the missing information

answer : 2355.62

Step-by-step explanation:

<u>Calculating the residual for Palm Beach county</u>

Given that total votes = 430772

and The regression equation = 56.115131 + 0.0023197 * Total Votes

The predicted Buchanan = 56.115131 + 0.0023197 * 430772 = 1055.377

while the Actual Votes Buchannan = 3411

Residual for Palm Beach county = Actual votes Buchannan - Predicted

                                                      = 3411 - 1055.377 = 2355.62

Note :

b0: 56.1132

b1: 0.0023

R2: 0.4593

The statistic that tests H0: ß1= 0: 7.43

5 0
3 years ago
a rule that assigns each value of the independent variable to exactly one value of the dependent variable?
e-lub [12.9K]

Answer:

Answer:- Function

please mark me as brainliest

3 0
2 years ago
What is the answer to this?
ch4aika [34]

Answer:

39

Step-by-step explanation:

41+x=80

x=39

5 0
3 years ago
Read 2 more answers
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