Mia climbs 5/8 of the height of the rock wall. Lee climbs 4/5 of Mia's distance. What fraction of the wall does climb? Show work

Use inductive reasoning to predict the most probable next number in each list.

PolarNik [594]

Answer:

93

Step-by-step explanation:

First differences increase by 4 each time. The given numbers are a quadratic sequence that can be described by 2n² -2n +9. The 7th term would be 93.

_____

First differences are ...

13-9 = 4, 21-13 = 8, 33-21 = 12, 49-33 = 16, 69-49 = 20

Second differences are ...

8-4 = 4, 12-8 = 4, 16-12 = 4, 20-16 = 4

When second differences are constant, the sequence can be represented by a second-degree polynomial function. The leading coefficient is half the value of the second differences.

3 0

3 years ago

Simplify: (6x-4) (9x-2)

Vinil7 [7]

Step-by-step explanation:

Hey, there!!

While simplifying the algebraic expression, you must be very careful about the signs.

Here,

(6x-4) (9x-2)

Multiply 2nd expression by 1st expression,

= 6x ( 9x - 2) -4 ( 9x - 2)

$= (54 {x}^{2} - 12x) - (36x - 8)$

Opening brackets,

$= 54 {x}^{2} - 12x - 36x + 8$

Simplifying them we get,

$= 54 {x}^{2} - 48x + 8$

Therefore, the answer is 54x^2 - 48x +8.

Hope it helps..

5 0

3 years ago

Use function notation to write a recursive formula to represent the sequence: 4, 8, 12, …

kogti [31]

Answer:

f(1) = 4
f(n) = f(n - 1) + 4

Step-by-step explanation:

Given the sequence:

4, 8, 12, …

The first term is 4 and common difference is 4

Recursive formula:

f(1) = 4
f(n) = f(n - 1) + 4

7 0

3 years ago

What is an angle that is complementary to _1?

makvit [3.9K]

Answer:

Angle 2

Step-by-step explanation:

Because if you add angle 2 to angle 1 it's gonna be 90 degree which is complementary. So angle 2 is complementary to angle 1

8 0

3 years ago

Question 5. We have 5-year statistics of average amount of wheat crop (tons) harvested from 1 km2 per year, the results are as f

tino4ka555 [31]

Answer:

a) $t=\frac{524.6-550}{\frac{27.682}{\sqrt{5}}}=-2.052$

$p_v =P(t_{(4)}$

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis.

We can say that at 5% of significance the true mean is not significantly different from 550.

b) The 95% confidence interval would be given (490.184;559.016).

We are confident at 95% that the true mean is between (490.184;559.016).

Step-by-step explanation:

Part a

Data given and notation

560, 525, 496, 543, 499

The mean and sample deviation can be calculated from the following formulas:

$\bar X =\frac{\sum_{i=1}^n x_i}{n}$

$s=\sqrt{\frac{\sum_{i=1}^n (x_i -\bar X)}{n-1}}$

$\bar X=524.6$ represent the sample mean

$s=27.682$ represent the sample standard deviation

$n=5$ sample size

$\mu_o =550$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the population mean is equal to 550, the system of hypothesis are:

Null hypothesis: $\mu = 550$

Alternative hypothesis: $\mu \neq 550$

Since we don't know the population deviation, is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{524.6-550}{\frac{27.682}{\sqrt{5}}}=-2.052$

P-value

We need to calculate the degrees of freedom first given by:

$df=n-1=5-1=4$

Since is a one-side left tailed test the p value would given by:

$p_v =P(t_{(4)}$

Conclusion

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis.

We can say that at 5% of significance the true mean is not significantly different from 550.

Part b

The confidence interval for a proportion is given by this formula

$\bar X \pm t_{\alpha/2} \frac{s}{\sqrt{n}}$

The degrees of freedom are 4 from part a

For the 95% confidence interval the value of $\alpha=1-0.95=0.05$ and $\alpha/2=0.025$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$t_{\alpha/2}=2.78$

And replacing into the confidence interval formula we got:

$524.6 - 2.78 \frac{27.682}{\sqrt{5}}=490.184$

$524.6 + 2.78 \frac{27.682}{\sqrt{5}}=559.016$

And the 95% confidence interval would be given (490.184;559.016).

We are confident at 95% that the true mean is between (490.184;559.016).

4 0

4 years ago