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3 years ago

HELPPPP ME PLEASE

1 answer:

3 0

The best fit curve for #1 is D. The easiest way to check these is by pluggin in to the equation and seeing if they come close. By doing just the first ordered pair along, it is apparent that only D will work.

With x = 1 input

A) -36

B) 24.2

C) 17.5

D) 11.58

#2 is also D. We can tell this because multiplying any of these options always results in a middle term between them. For instance, if you multiply out C, you will not only get x^4 and x^4, but you will also get terms such as 4x^2y^2 in the middle.

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Two catalysts may be used in a batch chemical process. Twelve batches were prepared using catalyst 1, resulting in an average yi

aalyn [17]

Answer:

a) $t=\frac{(91-85)-(0)}{2.490\sqrt{\frac{1}{12}}+\frac{1}{15}}=6.222$

$df=12+15-2=25$

$p_v =P(t_{25}>6.222) =8.26x10^{-7}$

So with the p value obtained and using the significance level given $\alpha=0.01$ we have $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis.

b) $(91-85) -2.79 *2.490 \sqrt{\frac{1}{12} +\frac{1}{15}} =3.309$

$(91-85) +2.79 *2.490 \sqrt{\frac{1}{12} +\frac{1}{15}} =8.691$

Step-by-step explanation:

Notation and hypothesis

When we have two independent samples from two normal distributions with equal variances we are assuming that

$\sigma^2_1 =\sigma^2_2 =\sigma^2$

And the statistic is given by this formula:

$t=\frac{(\bar X_1 -\bar X_2)-(\mu_{1}-\mu_2)}{S_p\sqrt{\frac{1}{n_1}}+\frac{1}{n_2}}$

Where t follows a t distribution with $n_1+n_2 -2$ degrees of freedom and the pooled variance $S^2_p$ is given by this formula:

$\S^2_p =\frac{(n_1-1)S^2_1 +(n_2 -1)S^2_2}{n_1 +n_2 -2}$

This last one is an unbiased estimator of the common variance $\sigma^2$

Part a

The system of hypothesis on this case are:

Null hypothesis: $\mu_2 \leq \mu_1$

Alternative hypothesis: $\mu_2 > \mu_1$

Or equivalently:

Null hypothesis: $\mu_2 - \mu_1 \leq 0$

Alternative hypothesis: $\mu_2 -\mu_1 > 0$

Our notation on this case :

$n_1 =12$ represent the sample size for group 1

$n_2 =15$ represent the sample size for group 2

$\bar X_1 =85$ represent the sample mean for the group 1

$\bar X_2 =91$ represent the sample mean for the group 2

$s_1=3$ represent the sample standard deviation for group 1

$s_2=2$ represent the sample standard deviation for group 2

First we can begin finding the pooled variance:

$\S^2_p =\frac{(12-1)(3)^2 +(15 -1)(2)^2}{12 +15 -2}=6.2$

And the deviation would be just the square root of the variance:

$S_p=2.490$

Calculate the statistic

And now we can calculate the statistic:

$t=\frac{(91-85)-(0)}{2.490\sqrt{\frac{1}{12}}+\frac{1}{15}}=6.222$

Now we can calculate the degrees of freedom given by:

$df=12+15-2=25$

Calculate the p value

And now we can calculate the p value using the altenative hypothesis:

$p_v =P(t_{25}>6.222) =8.26x10^{-7}$

Conclusion

So with the p value obtained and using the significance level given $\alpha=0.01$ we have $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis.

Part b

For this case the confidence interval is given by:

$(\bar X_1 -\bar X_2) \pm t_{\alpha/2} S_p \sqrt{\frac{1}{n_1} +\frac{1}{n_2}}$

For the 99% of confidence we have $\alpha=1-0.99 = 0.01$ and $\alpha/2 =0.005$ and the critical value with 25 degrees of freedom on the t distribution is $t_{\alpha/2}= 2.79$

And replacing we got:

$(91-85) -2.79 *2.490 \sqrt{\frac{1}{12} +\frac{1}{15}} =3.309$

$(91-85) +2.79 *2.490 \sqrt{\frac{1}{12} +\frac{1}{15}} =8.691$

7 0

2 years ago

If B = { p : p is a factor of 12 } list the elements of this set and find n ( B )

anastassius [24]

Answer:

B={1,2,3,4,6and12}

n (B) =6

Step-by-step explanation:

<h3>Greetings !</h3>

Factor, in mathematics, a number or algebraic expression that divides another number or expression evenly—i.e., with no remainder. For example, 3 and 6 are factors of 12 because 12 ÷ 3 = 4 exactly and 12 ÷ 6 = 2 exactly. The other factors of 12 are 1, 2, 4, and 12.

Hope it helps!

3 0

1 year ago

(5x^4 - 3x^3 + 6x) - ( 3x^3 + 11x^2 - 8x)

sergeinik [125]

(5x⁴ - 3x³ + 6x) - (3x³ + 11x² - 8x)

Expand the second bracket by multiplying throughout by -1
5x⁴ - 3x³ + 6x - 3x³ - 11x² + 8x

Group like terms and simplify
5x⁴ - 3x³ - 3x³ - 11x² + 6x + 8x

5x⁴ - 6x³ - 11x² + 14x

3 0

2 years ago

A computer can sort x objects in t seconds, as modeled by the function

r-ruslan [8.4K]

Answer:

36 objects

Step-by-step explanation:

You want the value of x when t=9, so you're solving ...

9 = 0.007x^2 +0.003x

9 = 0.007(x^2 + 3/7x)

From here, we observe that an approximation is probably sufficient.

9/0.007 = x(x +3/7) . . . . . the expression on the right is nearly x^2

x ≈ 3/√.007 ≈ 35.9 ≈ 36

We can check:

.007(36)(36 3/7) = 9.18

.007(35)(35 3/7) = 8.68

To keep the computer busy for 9 seconds, it needs to sort 36 objects.

6 0

3 years ago

6th grade math help me, please:))

Leokris [45]

Answer:

40 percent

Step-by-step explanation:

(10/25 ) x 100 = (2/5) x100 = (0.4) x 100 = 40% of the roses was given away.

7 0

2 years ago

Read 2 more answers