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BartSMP [9]
2 years ago
9

(1)Explain the three different ways of writing a ratio. Provide an example.

Mathematics
1 answer:
PolarNik [594]2 years ago
8 0

Answer:

1. Three ways to write Ratios are : in form of fraction, in form of decimals. Consecutively, they can also be written in form of percentage.

2. Divide the numerator by the denominator. The resulting decimal number is the unit rate.

3. A ratio table is a structured list of equivalent (equal value) ratios that helps us understand the relationship between the ratios and the numbers. Rates, like your heartbeat, are a special kind of ratio, where the two compared numbers have different units.

    Ex: Ben 1 glass of milk for every 2 cookies that he eats. We can use this ratio to begin a ratio table. If Ben drinks 2  glasses of milk, then he eats 4 cookies.

          Glasses of milk     Cookies

                        1                     2

                        2                    4

Notice that both of the ratios in the ratio table are equivalent

      1/2=2/4

If Ben drinks 4 glasses of milk, then he eats 8 cookies.

             Glasses of milk     Cookies

                        1                      2

                        2                     4

                        4                     8

Notice that all of the ratios in the ratio table are equivalent:

1/2=2/4=4/8

4. Write 32% as  32 /100

Since, finding the fraction of a number is same as multiplying the fraction with the number, we have

32 /100  of 150 =  32 /100  × 150

Therefore, the answer is 48

If you are using a calculator, simply enter 32÷100×150 which will give you 48 as the answer.

5. A ratio is a comparison of two numbers or measurements. The numbers or measurements being compared are sometimes called the terms of the ratio. A rate is a special ratio in which the two terms are in different units.

Step-by-step explanation:

Hope that helps :)

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Given a population with a mean of muμequals=100100 and a variance of sigma squaredσ2equals=3636​, the central limit theorem appl
lakkis [162]

Answer:

a) \bar X \sim N(100,\frac{6}{\sqrt{25}}=1.2)

\mu_{\bar X}=100 \sigma^2_{\bar X}=1

b) P(\bar X >101)=1-P(\bar X

c) P(\bar X

Step-by-step explanation:

Previous concepts

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".  

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".  

The complement rule is a theorem that provides a connection between the probability of an event and the probability of the complement of the event. Lat A the event of interest and A' the complement. The rule is defined by: P(A)+P(A') =1

Let X the random variable that represent the variable of interest on this case, and for this case we know the distribution for X is given by:  

X \sim N(\mu=100,\sigma=6)  

And let \bar X represent the sample mean, by the central limit theorem, the distribution for the sample mean is given by:  

\bar X \sim N(\mu,\frac{\sigma}{\sqrt{n}})  

a. What are the mean and variance of the sampling distribution for the sample​ means?

\bar X \sim N(100,\frac{6}{\sqrt{25}}=1.2)

\mu_{\bar X}=100 \sigma^2_{\bar X}=1.2^2=1.44

b. What is the probability that x overbarxgreater than>101

First we can to find the z score for the value of 101. And in order to do this we need to apply the formula for the z score given by:  

z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}  

If we apply this formula to our probability we got this:  

z=\frac{101-100}{\frac{6}{\sqrt{25}}}=0.833  

And we want to find this probability:

P(\bar X >101)=1-P(\bar X

On this last step we use the complement rule.  

c. What is the probability that x bar 98less than

First we can to find the z score for the value of 98.

z=\frac{98-100}{\frac{6}{\sqrt{25}}}=-1.67  

And we want to find this probability:

P(\bar X

5 0
3 years ago
Pls help. First answer marked as brainliest
Misha Larkins [42]
-2; 3-5= -2 or -5 - (-3)

-1; 4-5 or -5 - (-4) = -1

-5; -6 - (-1)= 1-6= -5

5 0
2 years ago
If PR = 5x – 3 and QS = 3x – 5 and QS == PR, what are the length of the<br> diagonals?
OleMash [197]

Answer:

Step-by-step explanation:

5x - 3 = 2(3x - 5)

5x - 3 = 6x - 10

6x - 5x = 10 - 3

x = 7

QS = 3(7) - 5 = 16 units

PR = 5 × 7 - 3 = 32 units

8 0
2 years ago
A low calorie dinner has 480 calories in an 9 ounce serving. What is the unit rate in simplest form? 9/48 160/3 48/9 3/160
LenaWriter [7]

Answer:Hi, the correct answer is \frac{160}{3}.

Step-by-step explanation:

 As you are being asked for rate and the importat value is the number of calories consumed. We need to simplify the fraction \frac{480 calories}{9 ounce} . Then we simplify.

Note that 480 is divisible by 3 and 9 as well. 480/3 = 160 and 9/3 = 3. Therefore, 480/9 = 160/3.

8 0
3 years ago
What is the value of x? 6x - 2x = 16
agasfer [191]

6x - 2x = 16

4x = 16    |divide both sides by 4

<h3>x = 4</h3>
5 0
3 years ago
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