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3 years ago

494 divided by 14 is

Mathematics

2 answers:

miv72 [106K]3 years ago

6 0

Answer:

35.28571429

or rounded to the hundreths is 35.29

Step-by-step explanation:

nordsb [41]3 years ago

3 0

Answer:

35.2857142857

Step-by-step explanation:

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What is an equation of the line that passes through the points (2, -2) and (8, 4)?

WITCHER [35]

Answer:

HAVE YOU WATCHED OCTOPUS GAME

Step-by-step explanation:

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3 years ago

Find the quotient of -88,11

nata0808 [166]

The answer is 11....................

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3 years ago

Find the linear approximation of the function g(x) = 3 1 + x at a = 0. g(x) ≈ Correct: Your answer is correct. Use it to approxi

EleoNora [17]

Answer:

$3.296x+3$

2.835

3.330

Step-by-step explanation:

$g(x) = 3^{1+x}$

Let the linear approximation be L(x) at a = 0. This is given by

$L(x) = g(a) + g'(a)(x-a)$

$g'(x)$ is the derivative of $g(x)$ . To find this, we use the form

If $f(x) = a^x$ , then $f'(x) =a^x\ln a$

By doing this and applying chain rule for the power (which is a function of x), we have

$g'(x) = 3^{1+x}\ln 3$

Then

$g'(0) = 3^{1+0}\ln 3 = 3.296$

Also $g(0) = 3^{1+0} = 3$

Hence $L(x) = 3+(x-0)\times3.296 = 3.296x + 3$

For $3^{0.95}$ , $1+x = 0.95$ and $x=-0.05$

Using this in $L(x)$ ,

$3^{0.95} = 3.296(-0.05) + 3 = 2.835$

For $3^{1.1}$ , $1+x = 1.1$ and $x=0.1$

Using this in $L(x)$ ,

$3^{1.1} = 3.296(0.1) + 3 = 3.330$

7 0

4 years ago

Suppose a certain capsule is manufactured so that the dosage of the active ingredient follows the distribution Y ~ N(μ = 10 mg,

lianna [129]

Answer:

(a) Probability that Y falls into the dangerous region is 0.0013.

(b) Probability that the mean Y-bar falls into the dangerous region is 0.00001.

Step-by-step explanation:

We are given that a certain capsule is manufactured so that the dosage of the active ingredient follows the distribution Y ~ N(μ = 10 mg, σ = 1 mg).

A dosage of 13 mg is considered dangerous.

Let Y = dosage of the active ingredient

The z-score probability distribution for normal distribution is given by;

Z = $\frac{ Y-\mu}{\sigma} } }$ ~ N(0,1)

where, $\mu$ = population mean = 10 mg

$\sigma$ = standard deviation = 1 mg

(a) Probability that Y falls into the dangerous region is given by = P(Y $\geq$ 13 mg)

P(Y $\geq$ 13 mg) = P( $\frac{ Y-\mu}{\sigma} } }$ $\geq$ $\frac{ 13-10}{1} } }$ ) = P(Z $\geq$ 3) = 1 - P(Z < 3)

= 1 - 0.9987 = 0.0013

The above probability is calculated by looking at the value of x = 3 in the z table which has an area of 0.9987.

(b) We are given that a dosage of 13 mg is considered dangerous. And we sample 49 capsules at random.

Let $\bar Y$ = sample mean dosage

The z-score probability distribution for sample mean is given by;

Z = $\frac{\bar Y-\mu}{\frac{\sigma}{\sqrt{n} } } } }$ ~ N(0,1)

where, $\mu$ = population mean = 10 mg

$\sigma$ = standard deviation = 1 mg

n = sample of capsules = 49

So, Probability that the mean Y-bar falls into the dangerous region is given by = P( $\bar Y$ $\geq$ 13 mg)

P(Y $\geq$ 13 mg) = P( $\frac{\bar Y-\mu}{\frac{\sigma}{\sqrt{n} } } } }$ $\geq$ $\frac{13-10}{\frac{1}{\sqrt{49} } } } }$ ) = P(Z $\geq$ 21) = 1 - P(Z < 21)

= 0.00001

6 0

3 years ago

Dorothy put $470 into a savings account for one year. The rate of interest on the account was 5.5%. Find the interest earned on

Rama09 [41]

Answer:

D. $25.85

Step-by-step explanation:

470 x 5.5% = 25.85

6 0

3 years ago