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2 years ago

This is 15 points for whoever answers.

Mathematics

1 answer:

zalisa [80]2 years ago

7 0

Answer:

Y = 40

Step-by-step explanation:

First, find the slope-intercept of the table

Slope-intercept form: y = mx + b

$m=\frac{y_2-y_1}{x_2-x_1}$

(3, 1) and (6,2)

$m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{2-1}{6-3}\\\\m=\frac{1}{3}$

$y=mx+b$

$y=\frac{1}{3}x+b$

Find b using (6,2):

$y=\frac{1}{3}x+b\\\\2=\frac{1}{3}(6)+b\\\\2=\frac{6}{3}+b\\\\2=2+b\\\\-2\ -2\\\\0=b$

$y=\frac{1}{3}x+b== > y=\frac{1}{3}x+0== > y=\frac{1}{3}x$

$y=\frac{1}{3}x$

What will be the value of Y when X = 120?

Substitute 120 for x into $y=\frac{1}{3}x$

$y=\frac{1}{3}x\\\\y=\frac{1}{3}(120)\\\\y=\frac{120}{3}\\\\y=40$

(120, 40)

Therefore, when X = 120, Y = 40

Hope this helps!

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A rumor spreads through a small town. Let y(t) be the fraction of the population that has heard the rumor at time t and assume t

sladkih [1.3K]

Answer:

The answer is shown below

Step-by-step explanation:

Let y(t) be the fraction of the population that has heard the rumor at time t and assume that the rate at which the rumor spreads is proportional to the product of the fraction y of the population that has heard the rumor and the fraction 1−y that has not yet heard the rumor.

$\frac{dy}{dt}\ \alpha\ y(1-y)$

$\frac{dy}{dt}=ky(1-y)$

where k is the constant of proportionality, dy/dt = rate at which the rumor spreads

$\frac{dy}{dt}=ky(1-y)\\\frac{dy}{y(1-y)}=kdt\\\int\limits {\frac{dy}{y(1-y)}} \, =\int\limit {kdt}\\\int\limits {\frac{dy}{y}} +\int\limits {\frac{dy}{1-y}} =\int\limit {kdt}\\\\ln(y)-ln(1-y)=kt+c\\ln(\frac{y}{1-y}) =kt+c\\taking \ exponential \ of\ both \ sides\\\frac{y}{1-y} =e^{kt+c}\\\frac{y}{1-y} =e^{kt}e^c\\let\ A=e^c\\\frac{y}{1-y} =Ae^{kt}\\y=(1-y)Ae^{kt}\\y=\frac{Ae^{kt}}{1+Ae^{kt}} \\at \ t=0,y=10\%\\0.1=\frac{Ae^{k*0}}{1+Ae^{k*0}} \\0.1=\frac{A}{1+A} \\A=\frac{1}{9} \\$

$y=\frac{\frac{1}{9} e^{kt}}{1+\frac{1}{9} e^{kt}}\\y=\frac{1}{1+9e^{-kt}}$

At t = 2, y = 40% = 0.4

c) At y = 75% = 0.75

$y=\frac{1}{1+9e^{-0.8959t}}\\0.75=\frac{1}{1+9e^{-0.8959t}}\\t=3.68\ days$

5 0

3 years ago

Two large and 1 small pumps can fill a swimming pool in 4 hours. One large and 3 small pumps can also fill the same swimming poo

sergey [27]

Answer:

It would take you 5/3 hours, or 1 hour and 40 minutes.

Hope I helped! ☺

7 0

2 years ago

In the proportion 2:3 = 16:24 ,the product of the two middle values is __.

klio [65]

Answer:

48 and 48

Step-by-step explanation:

product means multiplication

two middle values are 3 and 16

3*16 = 48

two outside values are 2 and 24

2*24 = 48

4 0

3 years ago

Find the H.C.F of 48,60 and 96. please no links . please step by step explanation

krek1111 [17]

Answer:

Do you mean GCF?

Step-by-step explanation:

48, 60, and 96 all have a GCF of 12

12 x 4 = 48

12 x 5 = 60

12 x 8 = 96

6 0

3 years ago

A videotape store has an average weekly gross of $1,158 with a standard deviation of $120. Let x be the store's gross during a r

statuscvo [17]

Answer:

The number of standard deviations from $1,158 to $1,360 is 1.68.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value 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. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 1158, \sigma = 120$

The number of standard deviations from $1,158 to $1,360 is:

This is Z when X = 1360. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{1360 - 1158}{120}$

$Z = 1.68$

The number of standard deviations from $1,158 to $1,360 is 1.68.

3 0

3 years ago