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3 years ago

the first term in a geometric series is 64 and the common ratio is 0.75. Find the sum of the first 4 terms in a series.

Mathematics

1 answer:

Rufina [12.5K]3 years ago

6 0

u0 = 64 with u(n+1) = un *0.75

u3 = 64 *0.75^3 = 27

sum is : 64 * ( 0.75^4 -1) / 0.75-1 = 175

manual proof : 64 + 48+36+27 = 175

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Solve the system using elimination y=-3x+6 y=x^2-4

ElenaW [278]

Mutiply first equation by -1 and add to 2nd

-y=3x-6
y=x^2-4 +
0=x^2+3x-10
factor like any equation
what 2 numbers multiply to -10 and add to 3
-2 and 5
0=(x-2)(x+5)
set to zero
x-2=0
x=2

x+5=0
x=-5
solve for y in each case

for x=2
y=2^2-4
y=4-4
y=0
(2,0) is a point

for x=-5
y=(-5)^2-4
y=25-4
y=21
(-5,21) is another

the solutions are
(2,0) and
(-5,21)

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3 years ago

D = {x|x is a whole number} E = {x|x is a perfect square between 1 and 9} F = {x|x is an even number greater than or equal to 2

ser-zykov [4K]

E = {x|x is a perfect square between 1 and 9} = {1,4
F = {x|x is an even number greater than or equal to 2 and less than 9}
D = {x|x is a whole number}

answer
D ∩ (E ∩ F) = 4

4 0

4 years ago

Solve for x. Enter the solutions from least to greatest. 4x^2 + 40x + 84 = 0

crimeas [40]

Answer:

x= -3 , -7

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Genetic Defects Data indicate that a particular genetic defect occurs in of every children. The records of a medical clinic show

Dovator [93]

Complete Question

The complete question is shown on the first uploaded image

Answer:

The probability that there exist 60 or more defected children is $P(x \ge 60)=0.0901$

Looking at the value for this probability we see that it is not so small to the point that the observation of this kind would be a rare occurrence

Step-by-step explanation:

From the question we are told that

in every 1000 children a particular genetic defect occurs to 1

The number of sample selected is $n= 50,000$

The probability of observing the defect is mathematically evaluated as

$p = \frac{1}{1000}$

$= 0.001$

The probability of not observing the defect is mathematically evaluated as

$q = 1-p$

$= 1-0.001$

$= 0.999$

The mean of this probability is mathematically represented as

$\mu = np$

Substituting values

$\mu = 50000*0.001$

$= 50$

The standard deviation of this probability is mathematically represented as

$\sigma = \sqrt{npq}$

Substituting values

$= \sqrt{50000 * 0.001 * 0.999}$

$= \sqrt{49.95}$

$= 7.07$

the probability of detecting $x \ge60$ defects can be represented in as normal distribution like

$P(x \ge 60)$

in standardizing the normal distribution the normal area used to approximate $P(x \ge 60)$ is the right of 59.5 instead of 60 because x= 60 is part of the observation

The z -score is obtained mathematically as

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

$= \frac{59.5 - 50 }{7.07}$

$=1.34$

The area to the left of z = 1.35 on the standardized normal distribution curve is 0.9099 obtained from the z-table shown z value to the left of the standardized normal curve

Note: We are looking for the area to the right i.e 60 or more

The total area under the curve is 1

$P(x \ge 60) \approx P(z > 1.34)$

$= 1-P(z \le 1.34)$

$=1-0.9099$

$=0.0901$

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3 years ago

Determine the period of each function. Show Work plzzz

suter [353]

For determining the period of a function, you pick two recognizable tops of the graph and calculate the time difference between them. In this situation the period is 5-1=4, by picking the first two tops

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2 years ago