I NEED HELP ASAP!!!!!!!

Calculate the rate of change for the following data:

Licemer1 [7]

Given:

The table of values.

To find:

The rate of change.

Solution:

From the given table it is clear that the rate of change is constant and function passes through two points (-1,5) and (2,-4). So, the rate of change is

$m=\dfrac{y_2-y_1}{x_2-x_1}$

$m=\dfrac{-4-5}{2-(-1)}$

$m=\dfrac{-9}{2+1}$

$m=\dfrac{-9}{3}$

$m=-3$

So, the rate of change is -3.

Therefore, the correct option is C.

6 0

3 years ago

Mr. Walker gave his class the function f(x) = (x + 3)(x + 5). Four students made a claim about the function. Each student’s clai

Oksana_A [137]

Answer:

stephen

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

What is 0.0 1 2 3 4 5 6 7 9 0 1 as a simple number

Aleksandr [31]

Answer:

its 0.01

Step-by-step explanation:

because you only need to round it up if there is an option

5 0

3 years ago

The following data lists the ages of a random selection of actresses when they won an award in the category of Best Actress, al

Valentin [98]

Answer:

a) $p_v =P(t_{(9)}$

The p value is higher than the significance level given 0.01, so then we can conclude that we FAIL to reject the null hypothesis. And we can say that the true difference for Best Actresses is not significantly lower than the mean for Best Actors at 1% of significance.

b) The 99% confidence interval would be given by (-21.469;2.069)

c) We got the same conclusion as part a, sicne the confidence interval contains the value 0, we FAIL to reject the null hypothesis that the difference between the two

Step-by-step explanation:

Part a

Let put some notation

x=actor's age , y = actress's age

x: 58 41 36 36 34 33 48 37 37 43

y: 26 27 34 26 35 29 23 42 30 34

The system of hypothesis for this case are:

Null hypothesis: $\mu_y- \mu_x \geq 0$

Alternative hypothesis: $\mu_y -\mu_x$

The first step is calculate the difference $d_i=y_i-x_i$ and we obtain this:

d: -32, -14, -2, -10, 1, -4, -25, 5, -7, -9

The second step is calculate the mean difference

$\bar d= \frac{\sum_{i=1}^n d_i}{n}= -9.7$

The third step would be calculate the standard deviation for the differences, and we got:

$s_d =\frac{\sum_{i=1}^n (d_i -\bar d)^2}{n-1} =11.451$

The 4 step is calculate the statistic given by :

$t=\frac{\bar d -0}{\frac{s_d}{\sqrt{n}}}=\frac{-9.7 -0}{\frac{11.451}{\sqrt{10}}}=-2.679$

The next step is calculate the degrees of freedom given by:

$df=n-1=10-1=9$

Now we can calculate the p value, since we have a left tailed test the p value is given by:

$p_v =P(t_{(9)}$

The p value is higher than the significance level given 0.01, so then we can conclude that we FAIL to reject the null hypothesis. And we can say that the true difference for Best Actresses is not significantly lower than the mean for Best Actors at 1% of significance.

Part b

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The confidence interval for the mean is given by the following formula:

$\bar d \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

Since the Confidence is 0.99 or 99%, the value of $\alpha=0.01$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,9)".And we see that $t_{\alpha/2}=3.25$

Now we have everything in order to replace into formula (1):

$-9.7-3.25\frac{11.451}{\sqrt{10}}=-21.469$

$-9.7+3.25\frac{11.451}{\sqrt{10}}=2.069$

So on this case the 99% confidence interval would be given by (-21.469;2.069)

Part c

We got the same conclusion as part a, sicne the confidence interval contains the value 0, we FAIL to reject the null hypothesis that the difference between the two means is 0.

8 0

3 years ago

6. The base of a triangular field is three times its height. If the cost of cultivating the field

dedylja [7]

Answer:

base = 519.62, height = 173.21 m

Step-by-step explanation:

Let the base and height of the triangle be represented by b and h respectively.

Thus,

b = 3h

Area of a triangle = $\frac{1}{2}$ x base x height

For the given triangle,

area = $\frac{1}{2}$ x b x 3h

= $\frac{3}{2}$ bh

Area of the triangle = $\frac{3}{2}$ bh

To determine the number of hectares,

36 per hectare = 486

hectare = $\frac{486}{36}$

= 13.5

numbers of hectares = 13.5

Area of the hectares = number of hectares x 10 000 m²

= 13.5 x 10 000

= 135000

Total area of the hectares = 135 000 m²

So that,

area of the hectares = area of the triangle

area of the triangle = $\frac{3}{2}$ bh

135 000 = $\frac{3}{2}$ bh

270000 = 3bh

bh = $\frac{270000}{3}$

= 90000

bh = 90000

But, b = 3h

3h x h = 90000

3 $h^{2}$ = 90000

$h^{2}$ = $\frac{90000}{3}$

= 30000

h = $\sqrt{30000}$

= 173.2051

h = 173.21 m

So that,

b = 3 x 173.2051

= 519.6153

b = 519.62

Therefore, the base of the triangle is 519.62 m, while the height is 173.21 m.

7 0

3 years ago