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3 years ago

Which exponential function is represented by the values in the table?

Mathematics

2 answers:

inn [45]3 years ago

8 0

Answer: Its C.

Step-by-step explanation: Edge2020

svlad2 [7]3 years ago

7 0

Here we use the equation

$y = a(b)^x$

Taking points (0,4), (1,2)

Substituting the point (0,4) , we will get

$4 = a(b)^0
\\
4 = a(1) \\
a =4$

Substituting (1,2) we will get

$2 = 4 (b)^1
\\
2/4 = b
\\
b = 1/2$

So we have

$a = 4, b = 1/2$

Therefore , required equation is

$y = 4(1/2)^x$

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3 years ago

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The roots of 2x^2-3x=4 are a and b. Find the simplest quadratic equation which has roots 1/a and 1/b

Tju [1.3M]

Find the roots

solve
we use hmm, completing the suare
2(x²-1.5x)=4
divide both sides by 2
x²-1.5x=2
take 1/2 of linear coeiftn and square it
-1.5/2=-0.75, (-0.75)²=0.5625
add that to both sides
x²-1.5x+0.5625=2+0.5625
factor perfect squaer trinomial
(x-0.75)²=2.5625
square root both sides, remember to take positive and negative square roots
x-0.75=+/-√2.5625
add 0.75 to both sides
x=0.75+/-√2.5625

the roots are x=0.75+√2.5625 and x=0.75-√2.5625

1/a and 1/b
1/(0.75+√2.5625) and 1/(0.75-√2.5625)

if the roots of a quadratic equation are r1 and r2 then it factors to
(x-r1)(x-r2)
so then we can factor our equation to be
$(x-\frac{1}{0.75+\sqrt{2.5625}})(x-\frac{1}{0.75-\sqrt{2.5625}})$

if we were to try and expand it, we would get
x²+0.75x-0.5
that's the simpliest equation with roots 1/a and 1/b where a and b are he roots of 2x²-3x=4

x²+0.75x-0.5 is answer

8 0

3 years ago

In a survey, the planning value for the population proportion is . How large a sample should be taken to provide a confidence in

tatuchka [14]

Answer:

n=350

Step-by-step explanation:

Notation and definitions

$n$ random sample taken (variable of interest)

$\hat p=0.35$ estimated proportion (value assumed)

$p$ true population proportion

Confidence =0.95 or 95% (value assumed)

Me=0.05 (value assumed)

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by: