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3 years ago

How many solutions? y = 5(x – 4) 4x + 12 = -y

Mathematics

1 answer:

kakasveta [241]3 years ago

4 0

Answer:

One solution, x = 8/9

Step-by-step explanation:

One way to solve this is to take one equation and substitute into the other and then solve. So, take y=5(x-4) and put that into the other equation.

4x + 12 = -y

4x + 12 = -(5(x-4)) <--- substitution here

4x + 12 = -5(x-4)

4x + 12 = -5x + 20 <-- simplifying

4x + 5x = 20 - 12

9x = 8

x = 8/9

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2. The prices of several different cereals are given below. Find the mean, median, mode, MAD, and IQR of these values. Which mea

Maru [420]

Mean = $ 4. 72

Median = $ 4. 5

Mode = No mode

MAD = $ 4. 8

IQR = $ 0. 5

Measure of center = $ 4. 5

Measure of variability = $ 2. 50

<h3>How to determine the values</h3>

Given the data;

$3.50, $4.25, $6, $4.75, $5.80, $4

Mean = sum of data/ number of data values

Mean = $\frac{3. 50 + 4. 25 + 6 + 4. 75 + 5. 80 + 4}{6}$

Mean = $ 4. 72

Median is the number in the center when the data is arranged in an ascending order

$3. 50, $4, $4. 25, $4. 75, $5. 80, $6

Median = $\frac{4. 25 + 4. 75}{2}$

Median = $ 4. 5

Mode is the number with the highest repeats.

From the given data, none of the numbers was repeated.

Thus, there is no mode.

MAD, mean absolute deviation = |data value - mean|

MAD = $|(3. 50 - 4. 72) + (4. 25 - 4. 72) + (6 - 4. 72) + (4. 75 - 4. 72) + (5. 80 - 4.72) + (4- 4. 72) |$

MAD = $1. 22 + 0. 47 + 1. 28 + 0. 03 + 1. 08 + 0. 72$

MAD = $ 4. 8

IQR, interquartile range = Quartile 3 - quartile 1

IQR = 4. 75 - 4. 25

IQR = $0. 5

Note that the mean and median are the most common measures of center.

A measure of variability is a single number that is used to describe the spread of a data set

The measure of the center best for the data is the median = $4. 5

Measure of variability = range = highest value - lowest value = $6 - $3. 50 = $2. 50

Learn more about mean here:

brainly.com/question/20118982

#SPJ1

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2 years ago

What are the chances your flight will leave on time? Below are a histogram and summary statistics for the percentage of flights

Jet001 [13]

Answer:

80.0456< $\bar x$ <81.1210

Step-by-step explanation:

-Given the mean, $\bar y=80.5833$ and $s=2.77369$ , the confidence interval can be calculated using the formula:

$\bar x\pm z\times \frac{\sigma}{\sqrt{n}}$

#We substitute our values in the formula to solve for CI:

$=\bar x\pm z\times \frac{\sigma}{\sqrt{n}}\\\\=\bar y\pm z_{0.05}\times \frac{s}{\sqrt{72}}\\\\=80.5833\pm 1.645\times \frac{2.77369}{\sqrt{72}}\\\\=80.5833\pm0.5377\\\\=[80.0456,81.1210]$

Hence, the confidence interval lies between 80.0456 and 81.1210

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