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3 years ago

Is a square a rectangle and a rhombus? explain (pls answer asap)

Mathematics

1 answer:

Nesterboy [21]3 years ago

4 0

Answer:

Step-by-step explanation:

A square is a square. I don't even know how this is a question-

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Find out the number of combinations and the number of permutations for 8 objects taken 6 at a time. Express your answer in exact

umka2103 [35]

Solution:

The permutation formula is expressed as

$\begin{gathered} P^n_r=\frac{n!}{(n-r)!} \\ \end{gathered}$

The combination formula is expressed as

$\begin{gathered} C^n_r=\frac{n!}{(n-r)!r!} \\ \\ \end{gathered}$

where

$\begin{gathered} n\Rightarrow total\text{ number of objects} \\ r\Rightarrow number\text{ of object selected} \end{gathered}$

Given that 6 objects are taken at a time from 8, this implies that

$\begin{gathered} n=8 \\ r=6 \end{gathered}$

Thus,

Number of permuations:

$\begin{gathered} P^8_6=\frac{8!}{(8-6)!} \\ =\frac{8!}{2!}=\frac{8\times7\times6\times5\times4\times3\times2!}{2!} \\ 2!\text{ cancel out, thus we have} \\ \begin{equation*} 8\times7\times6\times5\times4\times3 \end{equation*} \\ \Rightarrow P_6^8=20160 \end{gathered}$

Number of combinations:

$\begin{gathered} C^8_6=\frac{8!}{(8-6)!6!} \\ =\frac{8!}{2!\times6!}=\frac{8\times7\times6!}{6!\times2\times1} \\ 6!\text{ cancel out, thus we have} \\ \frac{8\times7}{2} \\ \Rightarrow C_6^8=28 \end{gathered}$

Hence, there are 28 combinations and 20160 permutations.

7 0

1 year ago

A lottery offers two options for the prize. Option A: $1000 a week for life. Option B: $600 000 in one lump sum. Which option wo

Anna71 [15]

Option B
Because you would not make as much money

5 0

3 years ago

Use substitution to solve the system. -5x + 3y = 19 x = 3y - 11

telo118 [61]

Answer:

x = -2

y = 3

Step-by-step explanation:

-5x + 3y = 19

x = 3y - 11

-5x + 3y = 19

-5(3y - 11) + 3y = 19

-15y + 55 + 3y = 19

-15y + 3y + 55 = 19

-12y + 55 = 19

-12y = 19 - 55

-12y = -36

y = -36/-12

y = 3

x = 3y - 11

x = 3(3) - 11

x = 9 - 11

x = -2

5 0

3 years ago

At the Foremost State Bank the average savings account balance in 2012 was $1900. A random sample of 45 savings account balanes

lakkis [162]

Answer:

The calculated |t| = |-26.517|=26.517 > 2.326 at 0.01 level of significance

Null hypothesis is rejected at 0.01 level of significance

There is difference between mean savings account balance in 2013 is different from the mean savings account balance in 2012

Step-by-step explanation:

Step(i):-

Mean of the Population = 1900

Given random sample size 'n' = 45

Mean of the sample x⁻ = 1000

Standard deviation of the sample = 225

Null Hypothesis:-

There is no difference between mean savings account balance in 2013 is different from the mean savings account balance in 2012.

Alternative Hypothesis :-

There is difference between mean savings account balance in 2013 is different from the mean savings account balance in 2012

Step(ii):-

Test statistic

$t = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }$

$t = \frac{1000-1900 }{\frac{225}{\sqrt{45} } }$

t = -900 /33.54 = -26.517

|t| = |-26.517|=26.517

Degrees of freedom

γ = n-1 = 45-1 =44

t₍₀.₀₁ , ₄₄₎ = 2.326

The calculated |t| = |-26.517|=26.517 > 2.326 at 0.01 level of significance

Null hypothesis is rejected at 0.01 level of significance

There is difference between mean savings account balance in 2013 is different from the mean savings account balance in 2012

4 0

3 years ago

What is the product of 1/3 and 4/7?

Travka [436]

Answer:

4/21

Step-by-step explanation:

Multiply 1 and 4. Then multiply 3 and 7. So 1x4=4, and 3x7=21. Therefore, the answer is 4/21. In multiplying fractions, you just multiply straight across (: (Hope this helps)

7 0

2 years ago

Read 2 more answers