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3 years ago

Evaluate 5x2−9 when x=−2

Mathematics

1 answer:

Elena-2011 [213]3 years ago

3 0

answer: 11

explanation: just plug in -2 for x. the new problem becomes 5(-2)^2 - 9. Negative two squared is 4. 5 times 4 is 20. 20 minus 9 is 11.

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Consider the following data to determine whether there is a significant difference between the values of Group 1 and Group 2. Le

cestrela7 [59]

Using the t-distribution, it is found that since the p-value of the test is 0.72 > 0.05, there is not significant difference between the values of each group.

At the null hypothesis, we test if the groups have the same values, that is, the subtraction of their means is 0:

$H_0: \mu_2 - \mu_1 = 0$

At the alternative hypothesis, we test if the groups have different values, that is, the subtraction of their means is different of 0:

$H_1: \mu_2 - \mu_1 \neq 0$

First, we have to find the mean and the standard deviation for both samples, hence, using a calculator:

$\mu_1 = 18.75, \sigma_1 = 6.2507, \mu_2 = 19.75, \sigma_2 = 4.2678$

The standard errors are:

$s_1 = \frac{\sigma_1}{\sqrt{n_1}} = \frac{6.2507}{\sqrt{8}} = 2.21$

$s_2 = \frac{\sigma_2}{\sqrt{n_2}} = \frac{4.2678}{\sqrt{8}} = 1.5089$

For the distribution of differences, we have that:

$\overline{x} = \mu_2 - \mu_1 = 19.75 - 18.75 = 1$

$s = \sqrt{s_1^2 + s_2^2} = \sqrt{2.21^2 + 1.5089^2} = 2.676$

We have the standard deviation for the samples, hence, the t-distribution is used. The test statistic is given by:

$t = \frac{\overline{x} - \mu}{s}$

In which $\mu$ is the value tested at the null hypothesis, which is 0 for this problem. Hence, the value of the test statistic is:

$t = \frac{\overline{x} - \mu}{s}$

$t = \frac{1 - 0}{2.676}$

$t = 0.37$

To find the p-value, we have a two-tailed test, as we test if the means are different from a value, with t = 0.37 and 8 + 8 - 2 = 14 df.

Using a t-distribution calculator, this p-value is of 0.72.

Since the p-value of the test is 0.72 > 0.05, there is not significant difference between the values of each group.

A similar problem is given at brainly.com/question/15682365

3 0

3 years ago

Regal theater in Tikahtnu sold 548 tickets to Moana on Sunday. A adult’s ticket was $6.50 while a child’s ticket was $3.50. In t

irga5000 [103]

Regal theater sold 321 adult tickets and 227 children tickets.

Step-by-step explanation:

Given,

Cost of each adult ticket = $6.50

Cost of each child's ticket = $3.50

Total tickets sold = 548

Total worth of sold tickets = $2881

Let,

x represent the number of adult tickets sold

y represent the number of child tickets sold

According to given statement;

x+y=548 Eqn 1

6.50x+3.50y=2881 Eqn 2

Multiplying Eqn 1 by 6.50

$6.50(x+y=548)\\6.50x+6.50y=3562\ \ \ Eqn\ 3$

Subtracting Eqn 2 from Eqn 3

$(6.50x+6.50y)-(6.50x-3.50y)=3562-2881\\6.50x+6.50y-6.50x-3.50y=681\\3y=681$

Dividing both sides by 3

$\frac{3y}{3}=\frac{681}{3}\\y=227$

Putting y=227 in Eqn 1

$x+227=548\\x=548-227\\x=321$

Regal theater sold 321 adult tickets and 227 children tickets.

Keywords: linear equation, elimination method

Learn more about elimination method at:

#LearnwithBrainly

6 0

3 years ago

6. Which question cannot be answered by the solut

valentinak56 [21]

Answer:

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

For what value of the variable will the expression 8b-27 -11

raketka [301]

Answer: 8b - 38

Step-by-step explanation:

8 0

3 years ago

Solve 13^x+2=5 having a bit of trouble

-Dominant- [34]

Solve: $13^{x} + 2 = 5$

Start by isolating the x-variable as much as you can:
$13^{x} = 5 - 2 = 3$
$13^{x} = 3$

Now, if we take the log with base 13 of both sides, then the left hand side will cancel out really easily. This is based on the concept of inverse operations. For example, when we take the square of a square root, we get our initial value. This is because the two operations are inverses of each other, and basically undoes each other.

Logarithms and exponentials are the inverse operations of each other. If we want to extrapolate the power of an exponential, we take the logarithmic function of it, and vice versa.

In this case, we are saying what power of '13' will produce us with 13ˣ, and the only answer will be x itself.

$log_{13}(13^{x}) = log_{13}(3)$
$x = log_{13}(3)$

3 0

4 years ago