Find each function value.

A construction crew built 514 miles of road in 412 days. What is the unit rate in miles per day? Write your answer as a fraction

geniusboy [140]

Answer:

$R=\dfrac{257}{206}\ \text{miles/day}$

Step-by-step explanation:

Given that,

Distance, d = 514 miles

Time, t = 412 days

We need to find the unit rate in miles per day. Its rate is given calculated by dividing distance and time as follows :

$R=\dfrac{514\ \text{miles}}{412\ \text{days}}\\\\R=\dfrac{257}{206}\ \text{miles/day}$

So, the unit rate is $\dfrac{257}{206}\ \text{miles/day}$ .

5 0

3 years ago

I need help plzzzzzzz

Gre4nikov [31]

6) C, 7) B, 8) B, a spring scale is one tool that can be used to measure force. Explain that a spring scale measures force in units called newtons.

5 0

3 years ago

Bt= 8500 *(8/27)^t/3After a special medicine is introduced into a Petri dish full of bacteria, the number of bacteria remaining

ozzi

Answer:

Every 1.71 seconds, the bacteria loses $\frac{1}{2}$

Step-by-step explanation:

Given

$B(t) = 8500 * (\frac{8}{27})^\frac{t}{3}\\$

Required [Missing from the question]

Every __ seconds, the bacteria loses $\frac{1}{2}$

First, we model the function from t/3 to t.

$B(t) = 8500 * (\frac{8}{27})^\frac{t}{3}\\$

Apply law of indices

$B(t) = 8500 * (\frac{8^\frac{1}{3}}{27^\frac{1}{3}})^t$

Evaluate each exponent

$B(t) = 8500 * (\frac{2}{3})^t$ --- This gives the number of bacteria at time t

At time 0, we have:

$B(0) = 8500 * (\frac{2}{3})^0$

$B(0) = 8500 * 1$

$B(0) = 8500$

Let r be the time 1/2 disappears.

When 1/2 disappears, we have:

$B(r) = \frac{B(0)}{2}$

$B(r) = \frac{8500}{2}$

$B(r) = 4250$

So, we have:

$B(t) = 8500 * (\frac{2}{3})^t$

Substitute r for t

$B(r) = 8500 * (\frac{2}{3})^r$

Substitute $B(r) = 4250$

$4250 = 8500 * (\frac{2}{3})^r$

Divide both sides by 8500

$\frac{4250}{8500} = (\frac{2}{3})^r$

$\frac{1}{2} = (\frac{2}{3})^r$

Take log of both sides

$log(\frac{1}{2}) = log (\frac{2}{3})^r$

Apply law of logarithm

$log(\frac{1}{2}) = r\ log (\frac{2}{3})$

Make r the subject

$r = log(\frac{1}{2}) / log (\frac{2}{3})$

$r = \frac{-0.3010}{-0.1761}$

$r = 1.71$

<em>Hence, it reduces by 1/2 after every 1.71 seconds</em>

6 0

3 years ago

On a recent day, 8 euros were worth $11 and 32 euros were worth $44. Enter an equation of the form y = kx to show the relationsh

navik [9.2K]

Answer:

On a recent day, 8 euros were worth $11 and 40 euros were worth $55. Enter an equation of the form y = kx to show the relationship between the number of euros and the value in dollars. First solve k which is the slope so k = ( 55- 11) / ( 40 -8) = 1.375

Y= 1.375x

Step-by-step explanation:

4 0

4 years ago

In relation to a computer what do the letters cpu stand for

photoshop1234 [79]

CPU means Central Processing Unit

7 0

3 years ago

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