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miss Akunina [59]
2 years ago
5

The graph of the piecewise function f(x) is shown.

Mathematics
1 answer:
NeTakaya2 years ago
4 0

Answer:

{f(x) | -∞ < f(x) ≤ 4 }

Step-by-step explanation:

The range is made up of the y values.  Remember f(x) = y

In this graph the least value of y is -∞ and the greatest value of y is 4

So, the range is {f(x) | -∞ < f(x) ≤ 4 } which is the 2nd choice

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Is -1 part of the set of whole numbers
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No.  The whole numbers are the natural numbers (counting numbers, 1, 2, 3...), but starting with zero instead of one.   -1 is an integer but not a whole number.

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When eight times an unknown number is decreased by 208 the result is four times the unknown number.
Naddika [18.5K]
I think

This is your typical algebra question where you are looking for an unknown value given some information. The information can be set up as:
8 - x = 4*(x +3)

Distribute the 4:
8 - x = 4x + 12

Rearrange to get variables on one side:
8 - 12 = 4x + x

Simplifiy:
-4 = 5x

Isolate the variable:
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6 0
3 years ago
Question a) Compare the Variability of Expenditure of Families in Two Towns given as follows: Number of families Expenditure (Ru
Karolina [17]

Answer:

Kindly check explanation

Step-by-step explanation:

Given the data:

Number of families __________Expenditure

______midpoint (x) ____Town A __Town B

21-30 __25.5____________3 _______2

31-40 __35.5____________61 ______14

41-50 __45.5___________132 _____ 20

51-60 __55.5__________ 153 ______27

61-70 __65.5__________ 140 ______ 28

71-80 __75.5___________ 51 _______ 7

81-90 __85.5___________ 2 _______ 2

The variability is the variance and standard deviation :

The variance (s):

√Σ(x - m)²/Σf(x)

Town A:

m = Σ(X * f(x)) / Σf ; Σf = 542

Σ x * f(x) = (25.5*3) + (35.5*61) + (45.5*132) + (55.5*153) + (65.5*140) + (75.5*51) + (85.5*2)

= 29931 / 542

= 55. 22

Σf(x - m)² / Σf - 1 = [3(25.5-55.22)^2 + 61(35.5-55.22)^2 + 132(45.5-55.22)^2 + 153(55.5-55.22)^2 + 140(65.5-55.22)^2 + 51(75.5-55.22)^2 + 2(85.5-55.22)^2] / 541

= 76458. 4928 / 541

Variance = 141.32808

Standard deviation = √variance

Standard deviation = √141.32808

Standard deviation = 11.89

TOWN B:

m = Σ(X * f(x)) / Σf ; Σf = 100

Σ x * f(x) = (25.5*2) + (35.5*14) + (45.5*20) + (55.5*27) + (65.5*28) + (75.5*7) + (85.5*2)

= 5490 / 100

= 54.90

Variance :

Σf(x - m)² / Σf - 1 = [2(25.5-54.90)^2 + 14(35.5-54.90)^2 + 20(45.5-54.90)^2 + 27(55.5-54.90)^2 + 28(65.5-54.90)^2 + 7(75.5-54.90)^2 + 2(85.5-54.90)^2] / 99

= 16764 / 99

= 169.33

Standard deviation = √variance

Standard deviation = √169.3333

Standard deviation = 13.013

From the result above, Town A has lesser variability than Town B due to the slightly lower variance and standard deviation values.

8 0
3 years ago
Determine the point estimate of the population proportion, the margin of error
ahrayia [7]

Answer:

\hat p=0.645\\\\ME=0.233\\\\x=645 \ individuals

Step-by-step explanation:

-Given the boundaries as 0.412 and 0.878

-\hat p is the point estimate for the population proportion and is calculated as follows:

\hat p=\frac{Upper \ Bound+Lower \ Bound}{2}\\\\=\frac{0.878+0.412}{2}\\\\=0.645\\\\

#The margin of error, ME can be calculated for the confidence intervals using the formula:

ME=\frac{Upper \ Bound-Lower \ Bound}{2}\\\\=\frac{0.878-0.412}{2}\\\\=0.233

#The number of individuals in the sample is the product of the point estimate and population size:

\hat p=\frac{x}{n}\\\\x=\hat pn\\\\=0.645\times 1000\\\\=645

Hence, there are 645 individuals in the sample.

8 0
2 years ago
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