Is SSS disability pension lifetime?

Answer:

The calculated value     t =   2.366 > 2.0301 at 0.05 level of significance

The null hypothesis is rejected

There is a difference between the means      

Step-by-step explanation:

Step(i):-

Given that the first sample size 'n₁' = 22

Given that the mean of the first sample x₁⁻ = 120

Given that the standard deviation of the sample (s₁) = 20

Given that the mean of the second sample x₂⁻ = 100

Given that the standard deviation of the second sample (S₂) = 30

Step(ii):-

T-test statistic

               [tex]t = \frac{x^{-} _{1} -x^{-} _{2} }{\sqrt{S^{2} (\frac{1}{n_{1} }+\frac{1}{n_{2} } ) } }[/tex]

     where

             [tex]S^{2} = \frac{n_{1} S_{1} ^{2}+n_{2} S_{2} ^{2} }{n_{1} +n_{2}-2 }[/tex]

            [tex]S^{2} = \frac{22( 20)^{2}+ 15(30) ^{2} }{22 +15-2 }[/tex]

           S² =  637.1428

           S = √637.1428 = 25.24168  

The standard deviation of the sample 'S' = 25.24168   

Step(iii):-

Null Hypothesis:H₀:

There is no difference between the means

Alternative Hypothesis:H₁:

There is a difference between the means

         T-test statistic

               [tex]t = \frac{x^{-} _{1} -x^{-} _{2} }{\sqrt{S^{2} (\frac{1}{n_{1} }+\frac{1}{n_{2} } ) } }[/tex]

              [tex]t = \frac{ 120 -100 }{\sqrt{637.14 (\frac{1}{22 }+\frac{1}{15 } ) } }[/tex]

             t =   2.366

Degrees of freedom

           γ = n₁+n₂ -2 = 22+15-2 = 35

     t₀.₀₅ = 2.0301

The calculated value     t =   2.366 > 2.0301 at 0.05 level of significance

The null hypothesis is rejected

There is a difference between the means          

The correct test statistic for the test of the hypothesis for the considered situation is 2.2619 approximately.

If the sample sizes < 30, and we want to test the difference between the sample means, then we perform t-test.

Let we have:

Then, the value of t-test statistic is obtained as:

[tex]t = \dfrac{\overline{x}_1 - \overline{x}_2}{\sqrt{\dfrac{s_1^2}{n_1} + \dfrac{s_2^2}{n_2}}}[/tex]

If the level of significance is [tex]\alpha[/tex], then as we have:

the degree of freedom (d.f) = [tex]n_1 + n_2 - 2[/tex],

the critical value of t is found to be [tex]t_{\alpha/2}[/tex] , then if we get:

[tex]|t| < t_{\alpha/2}[/tex] we cannot reject the null hypothesis

and if we get [tex]|t| > t_{\alpha/2}[/tex] , then we may reject the null hypothesis and thus, accept the alternate hypothesis.

For this case, we're specified that:

For sample of stray dogs:

For sample of stray cats:

Thus, the t-test statistic for the difference of mean of these two samples is calculated as:

[tex]t = \dfrac{\overline{x}_1 - \overline{x}_2}{\sqrt{\dfrac{s_1^2}{n_1} + \dfrac{s_2^2}{n_2}}}\\\\t = \dfrac{120-100}{\sqrt{20^2/22 + 30^2/15}} = \dfrac{20}{\sqrt{200/11 + 60}}\\\\\\t \approx 2.2619[/tex]

Thus, the correct test statistic for the test of the hypothesis for the considered situation is 2.2619 approximately.

Learn more about two sample t-test here:

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Answer:

A. triangle, B. quadrilateral, C. triangle, D. quadrilateral, E. quadrilateral, F. triangle, G. triangle, H. quadrilateral, I. triangle, J. triangle

Step-by-step explanation:

triangles have 3 sides, quadrilaterals have 4 sides

Answer:

A-Triangle

B- Quadrilateral

C- Triangle

D- Quadrilateral

E- Quadrilateral

F-Triangle

G-Triangle

H-Quadrilateral

I- Triangle

J-Triangle

Step-by-step explanation:

If it has 3 sides it’s a triangle, if it has 4 it’s a quadrilateral.

Answer:

5 times the sum of 3 and 4, then subtract 4

Answer:

5  times the sum of 3 and 4, then subtract 4

Step-by-step explanation:

Hope this helps

Step-by-step explanation:

2x^2 - 4x - 8 = 0

x^2 - 2x - 8 =0

[tex]x = 2 ( - )(+) \sqrt{2 {}^{2} + 4.1.4 } \div 2.1 \\ x = 2( + )( - ) \sqrt{4 + 16} \div 2 \\ x = 2( - )( + ) \sqrt{20} \div 2 \\ x = 2( - )( + )2 \sqrt{5} \div 2 \\ x = 2(1( - )( + ) \sqrt{5} \div 2 \\ thefore \: x = 1 + \sqrt{5} \: or \: x = 1 - \sqrt{5} [/tex]

Answer:

x^6/2

Step-by-step explanation:

simplify the expression, 4x^4x^3/8x, you make it 4x^7/8x

and it simplifys to 4x^6/8 which then becomes x^6/2

extra note:

a^x * a^y = a^ x+y

(see attachment below)

I hope this helps :)

Answer:

40 m

Step-by-step explanation:

8/12=x/60

x=(8*60)/12

x=40

The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. The height of the building when it cast a shadow of 60 meters is 40 m.

The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. it is given as,

[tex]\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]

where,

θ is the angle,

Perpendicular is the side of the triangle opposite to the angle θ,

The base is the adjacent smaller side of the angle θ.

As it is given that the height of the pole is 8m, while the shadow cast by the pole is 12 m. If we use the ratio of trigonometry then the height of the building can be written as,

[tex]\rm Tan(\theta)= \dfrac{\text{Height of the pole}}{\text{Shadow of the pole}}= \dfrac{\text{Height of the building}}{\text{Shadow of the pole}}[/tex]

[tex]\dfrac{8}{12}= \dfrac{\text{Height of the building}}{\text{60}}\\\\\dfrac{8 \times 60}{12}= {\text{Height of the building}}\\\\\text{Height of the building}=40\ \rm m[/tex]

Hence, the height of the building when it cast a shadow of 60 meters is 40 m.

Learn more about Tangent (Tanθ):

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Answer: look at the picture

Step-by-step explanation: Hope this help :D

answer!

49 cookies were sold!

explaination!

42÷6= 7

42 plus 7 = 49

the amount of cookies sold was 49

(Sorry if it's wrong)

I hope this helps you

Sayi 100A olsun

100A. 0,96=96A

100A-96A=4A

100A da 4A azaldiysa

100 de 4 azalir

Answer:

c

Step-by-step explanation:

(x²-3x+8)-(7x²-2x-1)

x²-3x+8-7x²+2x+1

x²-7x²-3x+2x+8+1

-6x²-x+9

tq

Answer:

241.8 cm squared

Step-by-step explanation:

since this is a 5 sided pyramid, we would just need the triangle area calculating formula:

base X Height divided by 2

and then multiply it by 5

after you get the results, don't forget to add the area of the base too.

Answer:

D. A news organization that is not owned by a corporation.

Step-by-step explanation:

Answer:

do you have a picture or somthing beacuse i dont understand what your asking

Step-by-step explanation:

Answer: prove that two triangles with three congruent, corresponding angles are congruent, you would need to have at least one set of corresponding sides that are also congruent.

Step-by-step explanation:

Answer: +

Step-by-step explanation:

Answer:

the asnwer is 36!

Step-by-step explanation:

Answer:

the area of triangle is

Step-by-step explanation:

A=h{b}  b

2=2·6

2=6

Answer:

20

Step-by-step explanation:

the ratio is 5:3 the you divide the 12 fiction by 3 you get 4 so if the fiction is 4 then you times it by 5 and you get 20

The ratio of fiction books to nonfiction books on the shelf is 5:3, if there are 12 fiction books are on the shelf, then total number of books on the self, 32

A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, while the divisor or number that is dividing is referred to as the consequent.

Given that,

The ratio of nonfiction books to fiction books on a shelf is 5:3

There are 12 fiction books on the shelf

Total number of books on the self  = ?

Suppose, the total number of books  = x

Nonfiction = x - 12

Ratio =   nonfiction/fiction

   5/3     =    x-12/12

   x      =    32

Hence, the total number of books is 32

To know more about Ratio check:

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Answer:

1

Step-by-step explanation:

find common denominator first which is 1/3

Answer:

1. yes     2. no   3. yes

Step-by-step explanation: (put this if you have to show your work)

1.  4*0+2*1.5 (solve with a calculator or by hand)

2 y*5=7*0-5(same as above solve with a calculator or by hand)

3. 1=-2*2+5(same as above solve with a calculator or by hand)

Answer:

first of all,

Step-by-step explanation:

In triangle ABC one side equal  and two sides equal  

Step-by-step explanation:

We are given a prism whose base is square with sides 8 in and height 12 in.

If we take cross section through vertices A, B and C

We will get a cross section as triangle.

In triangle ABC, sides are AB, BC and AC

AB is diagonal of top square whose side 8 in.

AC is face diagonal of front face.

BC is face diagonal of right face.

AC=BC≠AB

Hence, In triangle ABC one side equal  and two side equal  

Hope this helps!!

Answer:

(-2,-3), (0,-3), (-1,1)

Step-by-step explanation:

When reflecting over an axis, the axis you are reflecting over stays the same while the opposite axis becomes its opposite number, like reflect (12, -9) over the y axis, the y (-9) would stay the same but the x (12) would become (-12)

Answer:

Step-by-step explanation:

1) the two members of the expression has 4x in common, so we can rewrite it as: 4x(3x-2)

2) we have to find two numbers that multipied give -36 and that added up give 5

the two number are 9 and -4

we can rewrite the expression as : (x+9)(x-4)

3) we have to solve the associated equation

3x^2+10x+8 = 0

Δ/4 = 25-24 = 1

x1 = (-5+1)/3 = -4/3

x2 = (-5-1)/3 = -2

now we can rewrite the expression as

3(x+4/3)(x+2) = (3x+4)(x+2)

Answer:

1. 12x^2-8x

taking common 4x

4x(x-2)

2. x^2+5x-36

doing middle term factorization

x²+9x-4x-36

x(x+9)-4(x+9)

(x+9)(x-4)

3. 3x^2+10x+8

Doing middle term factorization

3x²+6x+4x+8

3x(x+2)+4(x+2)

(x+2)(3x+4)

Answer: Sparrows generally fly shorter distances than swifts do.

Step-by-step explanation: hope this right!

Answer:

=> Swifts fly in the upper part of the air column as they hunt; swallows pursue insects closer to the ground or water.

=> If the bird is perched on a nest box, power line, or branch, that's a giveaway: Only swallows have the wherewithal to sit upright. Swifts are just stage-five clingers.

=> The swift has a slightly forked tail, not as long as the swallow's.

[tex] \infty \infty [/tex]

Answer:

G

Step-by-step explanation:

Start is at 9 gallons

6 days of water use

9/6 is 1.5

1.5 gallon per day    :)