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Phoenix [80]
3 years ago
11

Laura left Dunkin Donuts at 1 PM traveling 30 mph. Two hours later her friend Jen left the same Dunkin Donuts and started after

her on the same route traveling 45 mph. At what time will Jen catch up to Laura?
Mathematics
1 answer:
Wewaii [24]3 years ago
5 0

Answer:

It took Jen 4 hours to catch up with Laura

Step-by-step explanation:

Gaining speed 45-30= 15 mph

Laura's head start 30×2=60 miles

Time for Jen to catch up 60÷15= 4 hours

In other words

30(t+2)= 45t

30t+60= 45t

60=45t-30t

60= 15t

t=4 hours

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So I know the answer for 8 is 2.24, but I'm not sure how to get that!!
Furkat [3]
Multiply 15 and 24 then divide that answer by 11.2.
8 0
3 years ago
Joe can cut and split a cord of firewood in 3 fewer hours than Dwight can. When they work​ together, it takes them 2 hours. How
aalyn [17]

Answer:

Dwight will take 6 hours to finish the job alone and Joe will take 3 hours to finish the job alone.

Step-by-step explanation:

Let us assume the time taken by Dwight to split a cord of firewood  = K hrs

So, the per hour rate of Dwight  = (\frac{1}{K})

As, Joe uses 3 LESS hours then Dwight.

So, the time taken by Joe to split a cord of firewood  = (K- 3) hrs

So, the per hour rate of Joe  = (\frac{1}{K-3})

Now, when both of them wok together, it takes them 2 hours.

So, the per hour rate of BOTH of them  = (\frac{1}{2})

⇒ Per hour rate of ( Dwight  + Joe)  =(\frac{1}{2} )

\implies (\frac{1}{K}) +  (\frac{1}{K-3}) = (\frac{1}{2})

Now, solving for the value of K , we get:

(\frac{1}{K}) +  (\frac{1}{K-3}) = (\frac{1}{2})\\\implies  \frac{(K-3) + K}{K (K-3)}  = (\frac{1}{2})\\\implies 2(2K -3) = K^2 - 3K\\\implies k^2 - 3K -4K +6 = 0\\\implies K^2 - 7K  + 6=  0\\\implies K^2 - 6K - K  + 6=  0\\\implies K(K-6) -1(K - 6)=  0\\\implies (K-6)(K-1) = 0

Implies either K = 6 Or K = 1

But if K = 1, (K-3)  = 1- 3  = -2 hours would be A CONTRADICTION.

⇒ K  = 6 hours

Hence, Dwight will take 6 hours to finish the job alone and Joe will take (k-3) = (6-3) = 3 hours to finish the job alone.

8 0
3 years ago
Identify the factors of the function y = 6x2 – 9x
Sindrei [870]

Answer:

3x(2x - 3)

Step-by-step explanation:

Given

y = 6x² - 9x ← factor out 3x from each term

  = 3x(2x - 3)

6 0
3 years ago
In an examination of purchasing patterns of shoppers, a sample of 16 shoppers revealed that they spent, on average, $54 per hour
Lesechka [4]

Answer:

54-1.64\frac{21}{\sqrt{16}}=45.39    

54 +1.64\frac{21}{\sqrt{16}}=62.61    

So on this case the 90% confidence interval would be given by (45.39;62.61)    

Step-by-step explanation:

Previous concepts

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".

\bar X=54 represent the sample mean  

\mu population mean (variable of interest)

\sigma=21 represent the sample standard deviation

n=16 represent the sample size  

Solution to the problem

The confidence interval for the mean is given by the following formula:

\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}   (1)

Since the Confidence is 0.90 or 90%, the value of \alpha=1-0.9=0.1 and \alpha/2 =0.05, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.05,0,1)".And we see that z_{\alpha/2}=1.64

Now we have everything in order to replace into formula (1):

54-1.64\frac{21}{\sqrt{16}}=45.39    

54 +1.64\frac{21}{\sqrt{16}}=62.61    

So on this case the 90% confidence interval would be given by (45.39;62.61)    

4 0
3 years ago
How do u solve this<br> Yes
Elodia [21]

Answer:

yes

Step-by-step explanation:

3 0
3 years ago
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