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garri49 [273]
3 years ago
13

A cat and dog shelter houses 23 animals that are 5 more cats than dogs y. Write and solve a system of linear equations to find t

he number of cats and dogs in the shelter.
SOMEONE PLZ HELP!!
Mathematics
1 answer:
dybincka [34]3 years ago
5 0

Answer:

There would be 14 cats and 9 dogs

Step-by-step explanation:

In order to find the amount of cats and dogs, we need to set up the system of equations. To do so, start by setting cats as x and dogs as y. Now we can write the first equation to show the total number of animals.

cats + dogs = 23

x + y = 23

Now we can write a second one that shows the difference in the number of cats and dogs.

cats - dogs = 5

x - y = 5

Now we can add the two equations together to solve for x.

x + y = 23

x - y = 5

2x = 28

x = 14

Now that we have the number of cats, we can find the number of dogs by using either equation.

x + y = 23

14 + y = 23

y = 9

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Can someone please help me with this?
podryga [215]

9514 1404 393

Answer:

  x = 3

Step-by-step explanation:

Tangents to a circle from the same point are the same length.

  43 -2x = 12x +1

  42 = 14x . . . . . . . add 2x-1

  3 = x  . . . . . . . divide by 14

4 0
3 years ago
a) A large hotel in Miami has 900 rooms (all rooms are equivalent). During Christmas, the hotel is usually fully booked. However
Olegator [25]

Answer:

14.69% probability that this happens

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use 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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \mu = p and standard deviation s = \sqrt{\frac{p(1-p)}{n}}

1000 people were given assurance of a room.

This means that n = 1000

Let us assume that each customer cancels their reservation with a probability of 0.1.

So 0.9 probability that they still keep their booking, which means that p = 0.9

Probability more than 900 still keeps their booking:

n = 1000, p = 0.9

So

\mu = 0.9, s = \sqrt{\frac{0.9*0.1}{1000}} = 0.0095

901/1000 = 0.91

So this is 1 subtracted by the pvalue of Z when X = 0.91.

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

By the Central Limit Theorem

Z = \frac{0.91 - 0.9}{0.0095}

Z = 1.05

Z = 1.05 has a pvalue of 0.8531

1 - 0.8531 = 0.1469

14.69% probability that this happens

3 0
2 years ago
Hii I need help with these questions tyy!
9966 [12]

Answer:

(7x+2)(3x-1); (5x+4)^2 or (5x+4)(5x+4);

Step-by-step explanation:

formula to find area is L* W = A ; meaning length multiplied by width equals to the area.

21.

using the formula to find area...

l*w=a

(7x+2)(3x-1) would be your answer

btw, don't put the "=a" at the end, since it's an expression :))

22.

since the problem states that it's a square, you can just say either...

(5x+4)^2 or (5x+4)(5x+4) not sure which one your teacher accepts

4 0
2 years ago
Read 2 more answers
Laura invests $2500 in one account and $1500 in an account paying 2 % higher interest. At the end of one year she had earned $11
Crank

Answer:

$2500 - 2%

$1500 - 4%

Step-by-step explanation:

Say the interest for the $2500 is x, so the interest for the $1500 is x+0.02.

As an equation, they would look like this:

2500x+1500(x+0.02)=110

Now solve

2500+1500x+30=110

4000x=80

x=0.02

That means the interest for the $2500 is 0.02, or 2%, and the interest for the $1500 is 0.04, or 4%.

6 0
3 years ago
The interquartile range of a data set is 10 units. What does this represent?
Zepler [3.9K]
The interquartile range is from Q1 to Q3 and to get this you have to subtract Q2 by Q3. The 10 units represent that only 10 units are fit in the given range.
7 0
3 years ago
Read 2 more answers
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