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mixer [17]
3 years ago
8

Income tax returns show that the mean income of self-employed persons in a particular year was £15,000, with a standard deviatio

n of £975. A random sample of 169 returns from people in the clothing industry gave a mean income of £14,500. Did this indicate that income from self-employment in the clothing industry was significantly different?
Mathematics
1 answer:
DochEvi [55]3 years ago
6 0

Answer:

Yes, There is significant difference.

Step-by-step explanation:

Null Hypothesis , H0 : Mean income = 15000

Alternate Hypothesis , H1 : Mean income  ≠  15000

t = (x - u) / ( s / √n)

x = sample mean = 14500 here, u = population mean = 15000 here ,             s = standard deviation =  975 here  , n = sample size

t = (14500 - 15000) / (975 / √169)

-500 / 75 = - 6.66

As  calculated t value in absolute terms is > 1.96 , ie tabulated value at 95% significance level (two sided). So we reject the null hypothesis in favor of alternate hypothesis. Hence, we state that 'Mean Income ≠  15000'

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The length of a rectangular field is 24 meters this is 3 meters less than twice the width find the width
stepladder [879]

Answer:

The width is 5 meters

Step-by-step explanation:

The rectangular field is 24 meaning adding just one width and length of the rectangle would be 12.

x = width

2x - 3 + x = 12

3x - 3 = 12

3x - 3 + 3 = 12 + 3

3x = 15

x = 5

5 0
3 years ago
Which set is a function?
Sonja [21]
B, short explanation remember the sets are set up like (x,y) in a set there should be no matching x points so if it matches it's not a function :)

long explanation: these are (x,y) sets {(0,3), (3,0), (0,4), (4,0)} the first choice shows that there are two X solutions <span>if they are equal to 0 (0,3) (0,4) so this cant be a function.

second choice</span><span> {(0,2), (2,0), (4,6), (6,4)} does not have two X solutions so this is a function
third choice</span>{(2,6), (3,6), (4,6), (2,0)} has two X solutions if x is equal to 2
and the last choice <span>{(6,2), (2,0), (4,6), (6,4)} has two X solutions if x is equal to 6
hope i helped! if i did please give me brainlest :)
</span>
8 0
3 years ago
PLEASE HELP
zmey [24]

Law of cosines :

The law of cosines establishes:

c ^ 2 = a ^ 2 + b ^ 2 - 2*a*b*cosC.

general guidelines:

The law of cosines is used to find the missing parts of an oblique triangle (not rectangle) when either the two-sided measurements and the included angle measure are known (SAS) or the lengths of the three sides (SSS) are known.


Law of the sines:


In ΔABC is an oblique triangle with sides a, b, and c, then:

\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}

The law of the sines is the relation between the sides and angles of triangles not rectangles (obliques). It simply states that the ratio of the length of one side of a triangle to the sine of the angle opposite to that side is equal for all sides and angles in a given triangle.

General guidelines:

To use the law of the sines you need to know either two angles and one side of the triangle (AAS or ASA) or two sides and an opposite angle of one of them (SSA).


The ambiguous case :


If two sides and an angle opposite one of them is given, three possibilities may occur.


(1) The triangle does not exist.


(2) Two different triangles exist.


(3) Exactly a triangle exists.


If we are given two sides and an included angle of a triangle or if we are given 3 sides of a triangle, we can not use the law of the sines because we can not establish any proportion where sufficient information is known. In these two cases we must use the law of cosines

3 0
3 years ago
One number is twelve greater than another number. Twice the larger plus five times the smaller is 38. Find both numbers.
SSSSS [86.1K]

Answer:

I need points because i have a question

Step-by-step explanation:

And i need major help hope u understand also thanks

8 0
3 years ago
Jasper's lawn is 3/4 of an acre in size. The fertilizer bag states that 5 1/2 bags are required for 1 acre. How many bags does J
Nady [450]

Answer: 4\dfrac{1}{8}\ \text{bags}

Step-by-step explanation:

Given

Jasper lawn is three-fourth of an acre

1 acre of land requires 5\frac{1}{2} bags

convert mixed numeral to fraction

\Rightarrow 5\dfrac{1}{2}=\dfrac{11}{2}

\therefore 1\ \text{acre}\equiv\dfrac{11}{2}\ \text{bags}\\\\\Rightarrow \dfrac{3}{4}\ \text{acre}\equiv \dfrac{11}{2}\times \dfrac{3}{4}=\dfrac{33}{8}\ \text{bags}

\Rightarrow \dfrac{33}{8}\ \text{bags}=4\dfrac{1}{8}\ \text{bags}

8 0
2 years ago
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