An animal shelter spends $2.35 per day to care for each cat and $5.50 per day to care for eachdog. Pat noticed that the shelter spent $89.50 caring for cats and dogs on Wednesday.
Write an equation to represent the possible numbers of cats and dogs that could have been at the
shelter on Wednesday.
Pat said that there might have been 8 cats and 14 dogs at the shelter on Wednesday. Are Pat’s
numbers possible? Use your equation to justify your answer.
Later, Pat found a record showing that there were a total of 22 cats and dogs at the shelter on
Wednesday. How many cats were at the shelter on Wednesday?
Answers
89.50=2.35c+5.50d
If theres 22 dogs and cats in total you can plug in number less than 22 for c(# of cats) and d(# of dogs).
So we try pats numbers 8 cats and 14 dogs so
89.50=2.35(8)+5.50(14)
89.50=18.8+77
89.50=95.8
So pats numbers were wrong so we try different numbers
So i started pluging in numbers from under 22 so i got c is 10 and d is 12 lets try it with the equation
89.50=2.35(10)+5.50(12)
89.50=23.5+66
89.50=89.50 so it works the answer to how many number of dogs and cats is 12 dogs and 10 cats
Final answer:
The equation representing the costs to care for the animals is 2.35c + 5.5d = $89.50. Pat's proposal of 8 cats and 14 dogs does not match the costs. Upon using additional information of the total number of animals being 22, we can solve the system of equations to find that there were 16 cats and 6 dogs at the shelter on Wednesday.
Explanation:
Let's denote the number of cats as c and the number of dogs as d. We know from the cost of care per day per animal that 2.35c + 5.5d = $89.50. This is the equation representing the possible number of cats and dogs at the shelter in terms of costs. For Pat's numbers, we can substitute c=8 and d=14 into the equation and check if they are possible. That is, substitute and check if 2.35(8) + 5.5(14) equals to 89.5. In this case, it does not since the total here comes to more than $89.50. So, Pat's numbers were not possible.
Regarding the total number of animals, we know that c + d = 22. With this equation, we can solve the system of equations to find out the actual number of cats and dogs at the shelter on Wednesday. Solving these two equations, we will find that 16 cats and 6 dogs were present at the shelter on Wednesday.
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PLEASE HELP ME WITH THESE QUESTIONS
Round 8.043 to the nearest hundredth
In the sample, 72 said "yes."
(a) do the data give good evidence that more than two-thirds (67%) of authors support continuing this system? carry out an appropriate test to help answer this question.
(b) interpret the p-values from your test in the context of the problem.
Answers
Answer:
There is no significant evidence that more than two-thirds (67%) of authors support continuing this system.
Step-by-step explanation:
Let p be the proportion of authors who support continuing the system
Then hypotheses are:
: p=0.67
: p>0.67
To calculate the test statistic:
z= where
- p(s) is the sample proportion of authors who support the publishing system (
≈0.692)
- p is the proportion assumed under null hypothesis. (0.67)
- N is the sample size (104)
Then z= ≈ 0.477
p-value of test statistic is ≈0.317
Assuming a significance level 0.05, since 0.317>0.05 we fail to reject the null hypothesis.
p-value 0.317 is the probability that the sample is drawn from the distribution assumed under null hypothesis, that is where the proportion of authors supporting the new publishing system is at most 0.67
Final answer:
A hypothesis test for a proportion is used to determine whether more than two-thirds of authors support continuing the system. The p-value associated with the test is less than 0.0001, indicating that the data provide good evidence in favor of the alternative hypothesis. Therefore, the majority of authors support continuing the system.
Explanation:
To determine whether the data provides evidence that more than two-thirds (67%) of authors support continuing the system, we can use a hypothesis test for a proportion. We will use a significance level of 0.05.
Let's set up our hypotheses:
- Null hypothesis (H0): p ≤ 0.67 (less than or equal to two-thirds support)
- Alternative hypothesis (Ha): p > 0.67 (more than two-thirds support)
Using the normal approximation to the binomial, we can calculate the test statistic and p-value. With a sample size of 104 and 72 authors in favor, the test statistic is:
z = (72 - 0.67 * 104) / sqrt(0.67 * (1 - 0.67) * 104) ≈ 3.79
The p-value associated with a z-score of 3.79 is less than 0.0001. Since this p-value is less than 0.05, we reject the null hypothesis.
Therefore, the data provide good evidence that more than two-thirds of authors support continuing the system.
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Answers
Step-by-step explanation:
2/3 - 1/4
8/12 - 3/12= 5/12
Sheate5/12poundofturkey.
please seethe attached picture for full solution
hope ithelps
Goodluck on your assignment...
Answers
because f(x+1) where x= -9
-9+1 = -8
Answers
Answer:$ 44.70
Step-by-step explanation: 250/1.3687 = 182.655-150 =32.655 times 1.3687
Answer:
He has 45 USD left.
Step-by-step explanation:
250 USD = 212 Euros. 250 - 212 = 38. 38 euros - about 45 USD, rounded.
Answers
At time 0hrs, there is 30 000.
Since it doubles every 8hrs, at time 8hrs there is 60 000 or 30 000 x 2
In another 8hrs, it will double again, so at time 16hrs, it will be 120 000 or 30 000 x 2 x 2
In another 8hrs, double again, so at time 24hrs, it will be 240 000 or 30 000 x 2 x 2 x 2
This is also 30 000 x 8 as 2x2x2=8. I'll come back to this later.
You add an extra x 2 for each 8 hrs. By the end of the 2nd day, it would be
30 000 x2 x2 x2 x2 x2 x2
This is also
30 000 x8 x8
Every day we add an extra x8
We use powers to specify this.
30 000 x 8^d
So after 4 days
30 000 x 8^4 = 30 000 x8 x8 x8 x8
Note that this is NOT the same as 30 000 x 8 x 4