10 cm 10 cm 30 cm. 14.1 cm

What is the explicit formula for the sequence? -7,-4,-1,2,5

Archy [21]

an =a1+d(n-1)

a1=-7

d= -4--7=-4+7=3

an =-7+3(n-1)

or

an = -7+ 3n-3

an=-10+3n

5 0

3 years ago

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The population of Jalicia City was 24,000 people

notsponge [240]

When using a calculator I got: 26996.736

However since it's people you should round to: 26997.

3 0

2 years ago

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A simple random sample of 28 Lego sets is obtained and the number of pieces in each set was counted.The sample has a standard de

Karo-lina-s [1.5K]

Answer:

Step-by-step explanation:

Given that:

A simple random sample n = 28

sample standard deviation S = 12.65

standard deviation $\sigma$ = 11.53

Level of significance ∝ = 0.05

The objective is to test the claim that the number of pieces in a set has a standard deviation different from 11.53.

The null hypothesis and the alternative hypothesis can be computed as follows:

Null hypothesis:

$H_0: \sigma^2 = \sigma_0^2$

Alternative hypothesis:

$H_1: \sigma^2 \neq \sigma_0^2$

The test statistics can be determined by using the following formula in order to test if the claim is statistically significant or not.

$X_0^2 = \dfrac{(n-1)S^2}{\sigma_0^2}$

$X_0^2 = \dfrac{(28-1)(12.65)^2}{(11.53)^2}$

$X_0^2 = \dfrac{(27)(160.0225)}{132.9409}$

$X_0^2 = \dfrac{4320.6075}{132.9409}$

$X_0^2 = 32.5002125$

$X^2_{1- \alpha/2 , df} = X^2_{1- 0.05/2 , n-1}$

$X^2_{1- \alpha/2 , df} = X^2_{1- 0.025 , 28-1}$

From the chi-square probabilities table at 0.975 and degree of freedom 27;

$X^2_{0.975 , 27}$ = 14.573

$X^2_{\alpha/2 , df} = X^2_{ 0.05/2 , n-1}$

$X^2_{\alpha/2 , df} = X^2_{0.025 , 28-1}$

From the chi-square probabilities table at 0.975 and degree of freedom 27;

$X^2_{0.025 , 27}=$ 43.195

Decision Rule: To reject the null hypothesis if $X^2_0 \ > \ X^2_{\alpha/2 , df} \ \ \ or \ \ \ X^2_0 \ < \ X^2_{1- \alpha/2 , df}$ ; otherwise , do not reject the null hypothesis:

The rejection region is $X^2_0 \ > 43.195 \ \ \ or \ \ \ X^2_0 \ < \ 14.573$

Conclusion:

We fail to reject the null hypothesis since test statistic value 32.5002125 lies between 14.573 and 43.195.

6 0

3 years ago

–x(7x – 8) simplify and answer 70points and not solving for x

EastWind [94]

The answer should be $7x^{2} -8x$ :)

7 0

2 years ago

Determine the center and radius of the following circle equation:<br> x^2 + y^2 + 12x + 16y + 19 = 0

Oksanka [162]

Answer:

radius: 9

center: (-6, -8)

Step-by-step explanation:

First, you may wan to rearrange the equation so it is easier to sole, like:

x^2 + 12x + y^2 + 16y + 19 =0

Next, we need to complete the square. x^2 + 12x is the start of the square of x + 6, which ends in 36, and y^2 + 16y is the start of the square of x + 8, which ends in 64. We can start to write in the squares like:

x^2 + 12x + 36 - 36 + y^2 + 16y + 64 - 64 + 19 = 0

(36 & 64 are subtracted so the equation stays the same)

You can factor getting:

(x + 6)^2 - 36 + (y + 8)^2 - 64 + 19 = 0

You can combine the constants to get -36 - 64 + 19 = -81 and we can add 81 to both sides to get:

(x + 6)^2 + (y + 8)^2 = 81

The standard form of a circle equation is:

(x - h)^2 + (y - k)^2 = r^2

where (h, k) is the center and r is the radius.

In this case, by substituting, we get the center is (-6, -8) and the radius is 9.

6 0

2 years ago

10 cm 10 cm 30 cm. 14.1 cm​

10 cm 10 cm 30 cm. 14.1 cm