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kolezko [41]
3 years ago
15

Linda's income, in thousands of dollars, is given by the function f(x) = 40x + 10, where x is the number of years. Her expenses,

in thousands of dollars, each year is given by the function g(x) = 25x + 5.
Which function best describes the amount she is able to put into savings, h, each year, in thousands of dollars?

h(x) = 65x + 15
h(x) = (40x + 10)(25x + 5)
h(x) = -15x - 5
h(x) = 15x + 5
Mathematics
2 answers:
Pani-rosa [81]3 years ago
7 0

the correct answer for plato is h(x) = 15x + 5.

SashulF [63]3 years ago
4 0
<span>The function best describes the amount she is able to put into savings, h, each year, in thousands of dollars is </span><span>h(x) = 15x + 5.</span>
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Please help! <br><br><br><br> _________
gavmur [86]

Answer:

Step-by-step explanation:

A and D = 20

C and B = 160

160 +160 +20 +20 =360

6 0
3 years ago
The composite scores of individual students on the ACT college entrance examination in 2009 followed a normal distribution with
Mumz [18]

Answer:

35.57% probability that a single student randomly chosen from all those taking the test scores 23 or higher.

0.41% probability that a simple random sample of 50 students chosen from all those taking the test has an average score of 23 or higher.

The lower the standard deviation, the higher the z-score, which means that the higher the pvalue of X = 23, which means there is a lower probability of scoring above 23. By the Central Limit Theorem, as the sample size increases, the standard deviation decreases, which means that Z increases.

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 normally distributed samples are solved using 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.

In this problem, we have that:

\mu = 21.1, \sigma = 5.1

What is the probability that a single student randomly chosen from all those taking the test scores 23 or higher?

This is the pvalue of Z when X = 23.

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

Z = \frac{23 - 21.1}{5.1}

Z = 0.37

Z = 0.37 has a pvalue of 0.6443

1 - 0.6443 = 0.3557

35.57% probability that a single student randomly chosen from all those taking the test scores 23 or higher.

What is the probability that a simple random sample of 50 students chosen from all those taking the test has an average score of 23 or higher?

Now we use the central limit theorem, so n = 50, s = \frac{5.1}{\sqrt{50}} = 0.72

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

Z = \frac{23 - 21.1}{0.72}

Z = 2.64

Z = 2.64 has a pvalue of 0.9959

1 - 0.9959 = 0.0041

0.41% probability that a simple random sample of 50 students chosen from all those taking the test has an average score of 23 or higher.

Why is it more likely that a single student would score this high instead of the sample of students?

The lower the standard deviation, the higher the z-score, which means that the higher the pvalue of X = 23, which means there is a lower probability of scoring above 23. By the Central Limit Theorem, as the sample size increases, the standard deviation decreases, which means that Z increases.

5 0
3 years ago
What is the equation of a line , in a slope -intercept form , that passes through (5,-3) and has a slope of 2/3? A. y-3= 2/3(x+5
zmey [24]
Ur asking for slope intercept form, but ur answer choices are in point slope form....so I am gonna find the answer in point slope form.

y - y1 = m(x - x1)
slope(m) = 2/3
(5,-3)....x1 = 5 and y1 = -3
now we sub...but pay very close attention to ur signs
y - (-3) = 2/3(x - 5) = 
y + 3 = 2/3(x - 5) <=== ur answer in point slope form


8 0
3 years ago
Determine if x+3 is a factor of -3x^3+6x^2+6x+9. How do u know
krek1111 [17]
By the factor theorem, if x + 3 is a factor of f(x) = -3x^3 + 6x^2 + 6x + 9, then f(-3) = 0
f(-3) = -3(-3)^3 + 6(-3)^2 + 6(-3) + 9 = -3(-27) + 6(9) - 18 + 9 = 81 + 54 - 9 = 126.

Therefore, x + 3 is not a factor of the given function
6 0
3 years ago
What is the vertex of f(x)=x^2+6x+1 <br><br> Write your answer as an ordered pair without spaces
netineya [11]

Answer:

3

Step-by-step explanation:

5 0
2 years ago
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