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3 years ago

Solve the inequality $-4x > -24.$ Give your answer in interval notation.

Mathematics

1 answer:

notka56 [123]3 years ago

7 0

Answer:

(negative infinity, 6)

Step-by-step explanation:

To get this:

1. -4x > 24

Divide by -4

2. x < 6

When you divide by a negative you have to flip the inequality. Therefore, any number that is less than 6 is the answer.

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Compound interest is different from simple interest because you earn money on previous

Nataliya [291]

Answer:

Simple interest is calculated based only on the principal balance, whereas compound interest is calculated based on the principal balance and the accumulated interest from the previous periods. This means compound interest will make the amount owed grow at a much faster rate than simple interest.

Hope this helps!!!

Step-by-step explanation:

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3 years ago

simon is making wreaths to sell .he has 60 bows, 36 silk roses and 48 silk carnation .he wantsto put the same numbers of items o

myrzilka [38]

We must assume that he must put a whole number of objects in each wreath so we must find the greatest common factor

60=2 time 2 times 3 times 5
36=2 times 2 times 3 times 3
48=2 times 2 times 2 times 2 times 3

the factors are 2 times 2 times 3 or 12
there can be 12 wreath max
we total them up and divide by 12
60+36+48=144
144/12=12
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8 0

3 years ago

Plzzzz help me with this 20 points

nydimaria [60]

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6 0

3 years ago

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3 + x, when the value of x is 15

lora16 [44]

Answer:

The answer is 18

Step-by-step explanation:

If you add 15 to 3 then you get 18

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3 years ago

Read 2 more answers

The table showing the stock price changes for a sample of 12 companies on a day is contained in the Excel file below.

AfilCa [17]

Answer:

(a) The sample variance for the daily price change is 0.2501.

(b) The sample standard deviation for the daily price change is 0.5001.

Step-by-step explanation:

Let the random variable X denote the stock price changes for a sample of 12 companies on a day.

The data provided is:

X = {0.82 , 1.44 , -0.07 , 0.41 , 0.21 , 1.33 , 0.97 , 0.30 , 0.14 , 0.12 , 0.42 , 0.15}

(a)

The formula to compute the sample variance for the daily price change is:

$s^{2}=\frac{1}{n-1}\sum\limits^{12}_{i=1}{(X_{i}-\bar X)^{2}}$

The sample mean is computed using the formula:

$\bar X=\frac{1}{n}\sum\limits^{12}_{i=1}{X_{i}}$

Consider the Excel output attached below.

In Excel the formula to compute the sample mean and sample variance are:

$\bar X$ =AVERAGE(A2:A13)

$s^{2}$ =VAR.S(A2:A13)

Thus, the sample variance for the daily price change is 0.2501.

(b)

The formula to compute the sample standard deviation for the daily price change is:

$s=\sqrt{\frac{1}{n-1}\sum\limits^{12}_{i=1}{(X_{i}-\bar X)^{2}}}$

Consider the Excel output attached below.

In Excel the formula to compute the sample standard deviation is:

$s$ =STDEV.S(A2:A13)

Thus, the sample standard deviation for the daily price change is 0.5001.

(c)

The (1 - α)% confidence interval for population variance is:

$CI=[\frac{(n-1)s^{2}}{\chi^{2}_{\alpha/2} } \leq \sigma^{2}\leq \frac{(n-1)s^{2}}{\chi^{2}_{1-\alpha/2} } ]$

Compute the critical value of Chi-square for α = 0.05 and (n - 1) = (12 - 1) = 11 degrees of freedom as follows:

$\chi^{2}_{\alpha/2, (n-1)}=\chi^{2}_{0.05/2,11}=21.920$

$\chi^{2}_{1-\alpha/2, (n-1)}=\chi^{2}_{(1-0.05/2),11}=\chi^{2}_{0.975,11}=3.816$

*Use a Chi-square table.

Compute the 95% confidence interval estimates of the population variance as follows:

$CI=[\frac{(n-1)s^{2}}{\chi^{2}_{\alpha/2} } \leq \sigma^{2}\leq \frac{(n-1)s^{2}}{\chi^{2}_{1-\alpha/2} } ]$

$=[\frac{(12-1)\times 0.2501}{21.920 } \leq \sigma^{2}\leq \frac{(12-1)\times 0.2501}{3.816} ]$

$=[0.125506\leq \sigma^{2}\leq 0.720938]\\\approx [0.1255, 0.7210]$

Thus, the 95% confidence interval estimates of the population variance is (0.1255, 0.7210).

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4 years ago