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3 years ago

What's the explicit formula for the sequence :")

Mathematics

1 answer:

zzz [600]3 years ago

7 0

Hello from MrBillDoesMath!

Answer:

a(n) = 12 - 3(n-1) , n = 1,2,3.,,

Discussion:

The terms are 12, 9, 6, 3 so we are apparently subtracting 3 from each succeeding term. . Hence

a(n) = 12 - 3(n-1) , n = 1,2,3.,,

Thank you,

MrB

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Which of the following is not a postulate of Euclidean geometry?

Readme [11.4K]

It’s C, All equilateral triangles have interior angles equal to 60 degrees

8 0

3 years ago

Suppose Carla has $7000 to invest. Which investment yields the greater return over 4 years: 7% compounded quarterly or 6.85% com

tatiyna

Answer:

The correct answer is B. The rate of 7% compounded quarterly is better.

Step-by-step explanation:

In the case of investment at 7% compounded quarterly, the final result after 4 years of investment arises from the following calculation:

X = 7000 x (1 + 0.7 / 3) 4x3

X = 9,232.16

Therefore, after 4 years of investment, the amount in the account would be $ 9,232.16.

In turn, in the case of the investment at 6.85% compounded monthly, the final result after the same investment period arises from the following calculation:

X = 7000 x (1 + 0.685 / 12) 4x12

X = 9,199.33

Thus, in this case, the amount in the account after 4 years of investment would be $ 9,199.33.

8 0

3 years ago

What fractions are equivalent to 2/3

just olya [345]

4/6
10/15
6/9
8/12
Hope these help you!!! =')

4 0

3 years ago

Read 2 more answers

Consider the following data on x = rainfall volume (m^3) and y = runoff volume (m^3) for a particular location.

nydimaria [60]

Answer:

Step-by-step explanation:

From the given information:

x y xy x² y²

4 4 16 16 16

12 10 120 144 100

14 13 182 196 169

20 15 300 400 225

23 15 345 529 225

30 25 750 900 625

40 27 1080 1600 729

48 44 2112 2304 1936

55 38 2090 3025 1444

67 46 3082 4489 2116

72 53 3816 5184 2809

85 71 6035 7225 5041

96 82 7872 9216 6724

112 99 11088 12544 9801

127 101 12827 16129 10201

$\sum _{xi} = 805$ $\sum_{yi} = 643$ $\sum_{x_iy_I}= 51715$ $\sum_{x_i^2}= 63901$ $\sum_{y_i^2} = 42161$

The least-square regression equation is: $\hat y = b_o+b_1 x$

$b_1 = \dfrac{n \sum xy - ( \sum _x) ( \sum_y)}{n \sum x^2 - ( \sum x)^2}$

$b_1 = \dfrac{15(51715) - (803) (643)}{15(63901)-(805)^2}$

$b_1 = \dfrac{775725-516329}{958515-648025}$

$b_1 = \dfrac{259396}{310490}$

b₁ = 0.835440

∴ Slope term, b₁ = 0.835

$SS_{XX} = \sum x^2 - \dfrac{(\sum x)^2}{n}= 63901 - \dfrac{(805)^2}{15}=20699.33$

$SS_{yy} = \sum y^2 - \dfrac{(\sum y)^2}{n }= 42161 - \dfrac{(643)^2}{15}= 14597.73$

$SS_{xy} = \sum xy - \dfrac{(\sum x) (\sum y)}{n}= 51715 - \dfrac{(803)(643)}{15}= 17293.067$

$SST = SS_{yy}= 14597.73$

$SSR = \dfrac{SS_{xy}^2}{SS_{xx}}= \dfrac{17293.067^2}{20699.33}=14447.34$

SSE = SST - SSR = 14597.73 - 14447.34 = 150.39

The hypothesis test for the significance of $\beta_1$ is:

$H_o: \beta_1 = 0 \\ \\ H_1: \beta_1 \ne 0$

Significance level ∝ = 1 - 0.95 = 0.05

The sample slope $b_1$ = 0.835440

$Test \ statistic = t_{observed} = \dfrac{b_1-0}{\sqrt{\dfrac{SSE}{(n-2)SS_{xx}}}}$

$t_{o} = \dfrac{0.835440-0}{\sqrt{\dfrac{150.39}{(15-2)20699.33}}}$

$t_{o} = \dfrac{0.835440}{\sqrt{\dfrac{150.39}{269091.29}}}$

$t_o = 35.339$

Degree of freedom df = n - 2

df = 15 -2

df = 13

Using the Excel formula to determine the P_value.

$P-value = P(t, \Big|35.339 \Big|)$

P-value = 2 × t.dist(35.339,13,1)

P-value = 0.0000

P-value = 0

Critical value: $t_{critical} = t_{\alpha/2,df} = t_{0.05/2,13}= 2.160$

Rejection region: To reject $H_o$ ; if $\Big | t_o \Big | > t_c$

Decision: Since $\Big | t_o \Big | > t_c$ ; we reject $H_o$

Conclusion: There is enough evidence to conclude that the linear relationship between x & y

Thus; we reject $H_o$ & there is a useful linear relationship between x & y.

The 95% C.I for slope is given by the equation:

$=b_1 \pm t_{(\alpha/2,n-2)} \sqrt{\dfrac{SSE}{n-2}}\sqrt{\dfrac{1}{SS_{xx}} }$

$=0.835440 \pm 2.160 \sqrt{\dfrac{150.39}{15-2}}\sqrt{\dfrac{1}{20699.33} }$

= 0.835440 ± 2.160 (3.40124)(0.006951)

= 0.835440 ± 0.0511

= (0.835440 - 0.0511, 0.835440 + 0.0511)

= (0.78434, 0.88654)

= (0.784, 0.887) to three decimal places.

∴ 95% C.I of slope = $\mathbf{( 0.784 < \beta_1 < 0.887) \ to \ 3 \ d.p}$

6 0

3 years ago

Jimmy is a carpenter. The graph shows the number of chairs that he assembles and the amount of time it takes him.

alexdok [17]

Answer:

36 chairs assembled

Step-by-step explanation:

I don't think that the equation you gave, c = h, is accurate based on the graph. Based off the graph, I will make a different equation.

c = 8h

c = (8)(4.5)

c = 36

5 0

3 years ago

Read 2 more answers