How did the function move from the f(x)=|x| to f(x)=|x+2|

Hector needs to find the product of 23 and 97. Which shows a way to Hector could find the product?

zaharov [31]

23 x 97

You didn't provide the options so I chose to show the Array Method:

20 + 3

90 1800 270 = 2070

+ +

7 140 21 = 161

2231

Answer: 2231

3 0

3 years ago

Is there statistically significant evidence that the districts with smaller classes have higher average test scores? The t-sta

Musya8 [376]

Complete Question

The complete question is shown on the first uploaded image

Answer:

The 95% confidence interval is $[670.03 , 673.97 ]$

The test statistics is $t = 7.7$

The p-value is $p-value = 0$

The p-value suggests that the null hypothesis is rejected with a high degree of confidence. Hence there is statistically significant evidence that the districts with smaller classes have higher average test score

Step-by-step explanation:

From the question we are told that

The sample size is n = 408

The sample mean is $\= y = 672.0$

The standard deviation is $s = 20.3$

Given that the confidence level is 95% then the level of significance is

$\alpha = (100 -95 )\% = 0.05$

From the normal distribution table the critical value of $\frac{\alpha }{2} = \frac{0.05 }{2}$ is

$Z_{\frac{\alpha }{2} } = 1.96$

Generally the margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * \frac{s}{\sqrt{n} }$

=> $E = 1.96 * \frac{20.3}{\sqrt{408} }$

=> $E = 1.970$

Generally the 95% confidence interval is mathematically represented as

$\= y -E < \mu < \= y + E$

=> $672.0 -1.970 < \mu < 672.0 +1.970$

=> $670.03 < \mu < 673.97$

=> $[670.03 , 673.97 ]$

From the question we are told that

Class size small large

$Avg.score(\= y)$ $\= y_1 = 683.7$ $\= y_2 = 676.0$

$S_y$ $S_{y_1} =20.2$ $S_{y_2} = 18.6$

sample size $n_1 = 229$ $n_2 = 184$

The null hypothesis is $H_o : \mu_1 - \mu_2 = 0$

The alternative hypothesis is $H_a : \mu_1 - \mu_2 > 0$

Generally the standard error for the difference in mean is mathematically represented as

$SE = \sqrt{\frac{S_{y_1}^2 }{n_1} +\frac{S_{y_2}^2 }{n_2} }$

=> $SE = \sqrt{20.2^2 }{229} +\frac{18.6^2 }{184_2} }$

=> $SE = 1.913$

Generally the test statistics is mathematically represented as

$t = \frac{\= y _1 - \= y_2 }{SE}$

=> $t = \frac{683.7 - 676.0 }{1.913}$

=> $t = 7.7$

Generally the p-value is mathematically represented as

$p-value = P(t > 7.7 )$

From the z-table

$P(t > 7.7 ) = 0$

So

$p-value = 0$

From the values we obtained and calculated we can see that $p-value < \alpha$

This mean that

The p-value suggests that the null hypothesis is rejected with a high degree of confidence. Hence there is statistically significant evidence that the districts with smaller classes have higher average test score

4 0

3 years ago

Hank used 410 stamps. There are 60 stamps in every 3 rolls. How many rolls did Hank use?

Sveta_85 [38]

Answer:

20 rolls

Step-by-step explanation:

there is 20 in each roll 410/20 is 20.8.

7 0

3 years ago

F(-12) if f(x) = 2x + 15

Alenkinab [10]

Answer: $f(-12)=-9$

Step-by-step explanation:

We have the following function:

$f(x)=2x+15$

And we have to evaluate it when $x=-12$ , this means we have to substitute $x$ by $-12$ :

$f(-12)=2(-12)+15$

Solving:

$f(-12)=-24+15$

Finally:

$f(-12)=-9$

8 0

3 years ago

0.1 is 10% of what number?

stiv31 [10]

Let's assign a variable that is the number when multiplied by 10% it is equal to 0.1.

Well let that be x.

Now we want to convert the 10% into a decimal. To convert a percent into a decimal, simply move the % sign two places to the left and make it into a decimal point.

When we say "of" in mathematics what we really mean is to multiply.

0.10 * x = 0.1

That is the equation we need to find the value of x for.

Divide both sides by 0.10

0.10 * x = 0.1

The 0.10 on the left side cancels out.

x = 1

So, the answer to this question is if we multiply 10% by 1 we will get 0.1.

7 0

3 years ago

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