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stiv31 [10]
3 years ago
7

70% of a school budget is spent on teachers, 10% on other staff, and the rest on energy and resources. A Write the ratio of the

amount spent on teachers to other staff to energy and resources in its simplest form. B What fraction of the budget is spent on energy and resources? Write your fraction in its simplest form.
Mathematics
1 answer:
Vesna [10]3 years ago
7 0
A) 70:10:20 = 7:1:2
b) 20/100 = 2/10 = 1/5

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In a certain section of Southern California, the distribution of monthly rent for a one-bedroom apartment has a mean of $2,275 a
KATRIN_1 [288]

Answer:

100% probability of selecting a sample of 65 one-bedroom apartments and finding the mean to be at least $2,095 per month

Step-by-step explanation:

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

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score 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 p-value, 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.

Mean of $2,275 and a standard deviation of $290.

This means that \mu = 2275, \sigma = 290

Sample of 65:

This means that n = 65, s = \frac{290}{\sqrt{65}}

Finding the mean to be at least $2,095 per month

This is 1 subtracted by the p-value of Z when X = 2095. So

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

By the Central Limit Theorem

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

Z = \frac{2095 - 2275}{\frac{290}{\sqrt{65}}}

Z = -5

Z = -5 has a p-value of 0.

1 - 0 = 1

100% probability of selecting a sample of 65 one-bedroom apartments and finding the mean to be at least $2,095 per month

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3 years ago
An electronics shop sells only TVs, phones and tablets. Number sold Select all of the statements below that are true. Number of
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A graph is a way to represent a lot of data in such a visual format. The correct statements are A, B, and D.

<h3>What is a graph?</h3>

A graph is a way to represent a lot of data in such a visual format that it is easy for the user to understand the complete information in one go. Usually, the line of the graph is a function that follows the graph.

The statement that is correct about the given table is,

A.) The largest total number of electronic devices sold was on Wednesday.

B.) The smallest number of TVs sold was on Monday.

D.) On Tuesday, more tablets were sold than any other type of electronic device

hence, the correct statements are A, B, and D.

Learn more about Graph:

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2 years ago
I need help I need to be tutored for middle school I need to be a straight A student ​
Yuri [45]

Answer:

ok

Step-by-step explanation:

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3 years ago
Megan recently invested $2,000 dollars in a fast-growing company. Her financial advisor expects that Megan's investment will gro
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Answer:

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8 0
2 years ago
Help with these precalculus problems, please.
likoan [24]
Yay, easy peasy, nice refresher


53. evaluate for x=infinity
we get 100/(infiniy^2-5) which is basically 100/infinity which is a very small number so about 0



54.
vertical assemtotes, neato
that is where the denomenator equals 0
but wait, simplify first
ok, fraction is simplified (anything factored out would be a hole)
so set the denom to 0 and solve
x^2-5=0
(x-√5)(x+√5)=0
x=-√5 and √5
vertical assemtotes at x=-√5 and x=√5




55. horizontal assemtotes
for the function p(x)/f(x)

if p(x) has lower degree than f(x) then y=0 is the horizontal assemtote

if p(x) has equal degree to f(x) then divide the leading coefients of p(x) and f(x)

if p(x) has greater degree than f(x) then we got slant assemtotes

100/(x^2-5)
100 has lower degree than x^2
y=0 is the horizontal assemtote



56. evalate for x=-5
we get -150/-10=150/10=15
the limit is 15



57. that negative on the right side means that we must approach it from the left
let's see if we can factor out the denomenator
nope
so go and evaluate values like 4, 4.5, 4.9, etc, approaching x=5 from the left
we keep getting smaller and smaller valuse
this make sense because as x approaches 5, we get 30(c)/(c-5) where c is close to 5, and as c appraoches 5 very close, the top part is appraoching 150 but the bottom approaches a very small negative number, and if we do something like 150/-0.00000000001, we get a very negative number
the limit is negative infinity

alternately, you could figure that there is a vertical assemtote at x=5 so we can see that if we aproximaate closer and closer values, we get smaller values. so from what we know about assemtotes, expecially vertical ones, we say that it approaches negative infinity




58.
evalauating we get infintity/inifinty, not helpful
hmmm, is there a horizontal assemtote to help us?
the degree of top is higher so we got a slant assemtote
the only way is to use long division to divide the top by the bottom (see attachment)
we get
\frac{1}{2}x-\frac{1}{4}+\frac{\frac{1}{4}}{2x+1}
the slant assemtote is y=\frac{1}{2}x-\frac{1}{4}
as you can see, as x approaches infinity, y also will approach infinity











ANSWERS:
53. 0
54. VA is x=-√5 and x=√5
55. HA is y=0
56. the limit is 15
57. the limit is -∞
58. the limit is ∞

6 0
3 years ago
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