Find the distance between M(-2,3) and N (8,2)

The unit square is usually some standard unit, like a square meter, a square foot, or a square inch. So, if you are trying to find the area of a sheet of paper that is 9 inches by 11 inches, and the unit square you want is the square inch, then there are 9 X 11 = 99 square inches in that sheet of paper.
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3 0

3 years ago

N(t) = 100,000e−(t − 10)2/8

mafiozo [28]

The approximation of the slope of the graph at t = 10 days using this secant lines are 11750 and -11750, respectively.

<h3>How to determine the slope of the secant lines?</h3>

(a) t = 10 days and a day earlier

This means that:

t = 10 and t = 9

The function is given as:

$N(t) = 100000e^{\frac{-(t - 10)^2}{8}}$

Calculate N(10)

$N(10) = 100000e^{\frac{-(10 - 10)^2}{8}}$

Evaluate

N(10) = 100000

Next, calculate N(9)

$N(9) = 100000e^{\frac{-(9 - 10)^2}{8}}$

Evaluate

N(9) = 88249.6902585

The slope is then calculated using"

$m = \frac{N(10) - N(9)}{10 - 9}$

This gives

$m = \frac{100000 - 88249.6902585}{10 - 9}$

Evaluate

m = 11750.3097415

Approximate

m = 11750

(b) t = 10 days and a day later

This means that:

t = 10 and t = 100

The function is given as:

$N(t) = 100000e^{\frac{-(t - 10)^2}{8}}$

In (a), we have:

N(10) = 100000

Next, calculate N(11)

$N(9) = 100000e^{\frac{-(11 - 10)^2}{8}}$

Evaluate

N(11) = 88249.6902585

The slope is then calculated using:

$m = \frac{N(11) - N(10)}{11 - 10}$

This gives

$m = \frac{88249.6902585 - 100000}{11 - 10}$

Evaluate

m = -11750.3097415

Approximate

m = -11750

Hence, the approximation of the slope of the graph at t = 10 days using this secant lines are 11750 and -11750, respectively.

Read more about secant lines at:

brainly.com/question/14438198

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7 0

2 years ago

A bagel shop wants to estimate their daily demand for their popular poppy seed bagel. The shop owner determined that the daily d

forsale [732]

Answer:

Probability that the number of poppy seed bagels sold on a particular day exceeds 400 is 0.0475.

Step-by-step explanation:

We are given that the shop owner determined that the daily demand follows the normal probability model with mean 300 bagels and standard deviation 60.

Let X = daily demand of poppy seed bagels

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

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

where, $\mu$ = mean bagels = 300

$\sigma$ = standard deviation = 60

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

Now, Probability that the number of poppy seed bagels sold on a particular day exceeds 400 is given by = P(X > 400)

P(X > 400) = P( $\frac{ X-\mu}{\sigma}} }$ > $\frac{ 400-300}{60}} }$ ) = P(Z > 1.67) = 1 - P(Z $\leq$ 1.67)

= 1 - 0.95254 = 0.0475

So, in the z table the P(Z $\leq$ x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 1.67 in the z table which has an area of 0.95254.

Hence, the probability that the number of poppy seed bagels sold on a particular day exceeds 400 is 0.0475.

3 0

3 years ago