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erastova [34]
2 years ago
15

The linear function m=55-8.5b represents the amount m (in dollars) of money that you have after buying b books. Find the domain

of the function. Is the domain discrete of continuous? Explain.
Mathematics
1 answer:
Amiraneli [1.4K]2 years ago
8 0

Answer:

The domain is (-∞ , ∞)

The domain is continuous

Step-by-step explanation:

Here, we want to identify the domain of the linear function

The domain in this case can be represented by the set of all real numbers.

When we talk of the domain of a function, we are simply referring to the the range of values between the smallest value on the x-axis and the largest number on the x-axis

Hence, mathematically, we are simply considering the smallest value of b up to the largest value of b in this case. Where b simply represents the number of books

Thus, the domain here will be (-∞ , ∞)

On if the domain is discrete or continuous, we can see that the domain is continuous.

The domain is continuous simply because, the domain we have contains all the values and not some in the set of real numbers. If it had contain only some, then it would have been discrete. But since it contains all, it is continuous

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Kendal bought x boxes of cookies to bring to a party. Each box contains 12 cookies. She decides to keep two boxes for herself. S
Georgia [21]

Answer:

Step-by-step explanation:

Total number of boxes of cookies that Kendal bought to bring to the party is x.

Each box contains 12 cookies. This means that total number of cookies in x boxes would be

12 × x = 12x

She decides to keep two boxes for herself. This means that the total number of cookies that she kept for herself would be

12 × 2 = 24 cookies

She brings 60 cookies to the party.

The equation that can be used to find the number of boxes, x, Kendal bought would be

12x = 24 + 60

12x = 84

x = 84/12 = 7 boxes

6 0
2 years ago
Given a normal distribution with u = 75 and o = 40, if you select a sample of n = 16, a) what is the probability that the sample
Volgvan

Answer:

a) 0.0228

b) 94.6

Step-by-step explanation:

The formula for calculating a z-score when you are given a random.number of samples is z = (x-μ)/σ/√n

where x is the raw score

μ is the population mean

σ is the population standard deviation

n = random number of samples

Given a normal distribution with u = 75 and o = 40, if you select a sample of n = 16,

a) what is the probability that the sample mean is above 95? (4 d.p.) b)

= x = 95

Hence:

z = 95 - 75/40/√16

= 20/40/4

= 20/10

= 2

Probability value from Z-Table:

P(x<95) = 0.97725

P(x>95) = 1 - P(x<95) = 0.02275

The probability that the sample mean is above 95 to 4 decimal places = 0.0228

b) What is the value, of which there is 97.5% chance that a sample mean is less than that value?

97.5% chance = z score for the confidence interval = 1.96

Hence:

z = (x-μ)/σ/√n

1.96 = x - 75/40/√16

1.96 = x - 75/ 40/4

1.96 = x - 75/10

Cross Multiply

1.96 × 10 = x - 75

19.6 = x - 75

x = 19.6 + 75

x = 94.6

The value, of which there is 97.5% chance that a sample mean is less than that value is 94.6

5 0
2 years ago
What is the domain of validity for csctheta =start fraction 1 over sine theta end fraction? (1 point) all real numbers all real
dem82 [27]
We know the following relationship:

csc(\theta)=\frac{1}{sin(\theta)}

The domain of a function are the inputs of the function, that is, a function f is a relation that assigns to each element x in the set A exactly one element in the set B. The set A is the domain (or set of inputs) of the function and the set B contains the range (or set of outputs).Then applying this concept to our function csc(\theta) we can write its domain as follows:

1. D<span>omain of validity for csc(\theta):
</span>
D: \{\theta \in R/ sin(\theta) \neq 0 \} \\ In words: All \ \theta \ that \ are \ real \ values \ except \ those \ that \ makes \ sin(\theta)=0 
 
When:

sin(\theta)=0?

when:

\theta=..., -2\pi,-\pi,0,\pi,\2pi,3pi,...,k\pi

where k is an integer either positive or negative. That is:

sin(k\theta)=0 \ for \ k=...,-2,-1,0,1,2,3,...

To match this with the choices above, the answer is:

<span>"All real numbers except multiples of \pi"

</span>
2. which identity is not used in the proof of the identity 1+cot^{2}(\theta)=csc^{2}(\theta):

This identity can proved as follows:

sin^2{\theta}+cos^{2}(\theta)=1 \ Dividing \ by \ sin^{2}(\theta) \\ \\ \therefore \frac{sin^2{\theta}}{sin^{2}(\theta)}+\frac{cos^{2}(\theta)}{sin^{2}(\theta)}=\frac{1}{sin^{2}(\theta)} \\ \\ \therefore 1+cot^{2}(\theta)=csc^{2}(\theta)

The identity that is not used is as established in the statement above:

<span>"1 +cos squared theta over sin squared theta= csc2theta"

Written in mathematical language as follows:

</span>\frac{1+cos^{2}(\theta)}{sin^{2}(\theta)}=csc^{2}(\theta)<span>


</span>
4 0
2 years ago
Read 2 more answers
Perry, maria, and lorna are painting rooms in a college dormitory. working alone, perry can paint a standard room in 3 hours, ma
Leviafan [203]

Answer:Perry and Lorna take the maximum time and Maria and Lorna take the minimum time when they work together.

Explanation: Since, according to the question- Perry takes time when he works alone = 3 hours

Similarly, Maria takes = 2 hours, While Lorna takes= 2 hours 30 minutes or 2.5 hours.

since, there are three people thus their are three possibility to choose any two of them.

1- when Perry and Maria work together then time taken by them is \frac{1}{1/2+1/3}=\frac{1}{5/6}= 6/5= 1 hour 12 minutes.

2- when Maria and Lorna work together then time taken by them is \frac{1}{1/2 + 1/2.5}= 10/9= 1 hours 1/9 minutes ≈ 1 hours 7 min

3- when Perry and Lorna work together then time taken= \frac{1}{1/3+1/2.5}= 15/11= 1 hour 4/11 minutes≈ 1 hours 21 minutes

From the above explanation, it has been proved that when we talk about 2 members team then Perry and Lorna take the maximum time. While Maria and Lorna take the minimum time when they work together.


3 0
2 years ago
Read 2 more answers
A bacteria sample can be modeled by the function f(x) - 350(1.20) which gives the number of bacteria in the sample at the end of
marissa [1.9K]

Answer: A) The initial number of bacteria is 350.

Step-by-step explanation:

Exponential growth equation: f(x)=A(1+r)^x , where A=Initial value, r= growth rate.          (i)

Given: A bacteria sample can be modeled by the function f(x) = 350(1.20)which gives the number of bacteria in the sample at the end of x days.

Here, f(x)=350(1+0.20)

Compare this equation to  (i) , we get A = 350 and r= 0.20 = 20% (growth rate)

So, the  best interpretation of one of the values in this function are:

A) The initial number of bacteria is 350.

3 0
2 years ago
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