What ratio is equivalent to the ratio 18:24

Which expression is equivalent to (10x)^-3?

Inessa [12570]

(10x)^(-3)
= 1/[(10x)^3]
= 1/[10^3 * x^3]
= 1/(1000x^3)

The final result is 1/(1000x^3), and none of the given choices seem correct. (Option C would be correct if it used round brackets.)

Hope this helps~

4 0

12 days ago

Read 2 more answers

The manufacturer of hardness testing equipment uses steel-ball indenters to penetrate metal that is being tested, however, the m

Inessa [12570]

Answer:

$1.667-2.31\frac{1.803}{\sqrt{9}}=0.2789$

$1.667+2.31\frac{1.803}{\sqrt{9}}=3.055$

Based on the analysis, the 95% confidence interval is specified as (0.2789;3.055)

The question regarding the 95% confidence interval's ability to ascertain potential differences in measurements between the two indenters is as follows:

Indeed, the confidence interval does not include the value 0, thus indicating that the Diamond values significantly exceed those of the Steel Ball at a 5% significance level.

Step-by-step explanation:

Here is the dataset in consideration:

specimen 1 2 3 4 5 6 7 8 9

Steel Ball 51 57 61 70 68 54 65 51 53

Diamond 53 55 63 74 69 56 68 51 56

By calculating the differences between diamond and steel ball measurements, we create the dataset:

d: 2, -2, 2, 4, 1, 2, 3, 0, 3

In the next step, we compute the mean difference

$\bar d= \frac{\sum_{i=1}^n d_i}{n}=1.667$

Following that, we determine the standard deviation of the differences, arriving at:

$s_d =\frac{\sum_{i=1}^n (d_i -\bar d)^2}{n-1} =1.803$

A confidence interval refers to "a range of values that’s likely to encompass a population value with a certain level of confidence. It is typically expressed as a percentage indicating where a population mean falls within an upper and lower limit."

The margin of error represents the extent to which values diverge above and below the sample statistic in a confidence interval.

Normal distribution, is described as a "probability distribution that is symmetric about the mean, illustrating that data points close to the mean occur more frequently than those further away."

The confidence interval for the mean is derived using the following formula:

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

To calculate the critical value $t_{\alpha/2}$ , we first determine the degrees of freedom using:

$df=n-1=9-1=8$

Given a confidence level of 0.95 or 95%, the appropriate critical value can be found using Excel, a calculator, or a table. The Excel command would be: "=-T.INV(0.025,9)". Therefore, we observe that $t_{\alpha/2}=2.31$ .

Finally, we can substitute all our findings into formula (1):

$1.667-2.31\frac{1.803}{\sqrt{9}}=0.2789$

$1.667+2.31\frac{1.803}{\sqrt{9}}=3.055$

In this case, the 95% confidence interval is calculated as (0.2789;3.055)

In determining if the two indenters yield distinct measurements, we find that the confidence interval does not enclose zero, allowing us to conclude that Diamond readings greatly surpass Steel Ball readings at the 5% significance level.

4 0

14 days ago

I helped 3.6 customer per half hour yesterday. so i helped _____ customers in 7.5 hour yesterday

lawyer [12517]

Customers served in 0.5 hours : 3.6 versus x customers served in 7.5 hours

-------------------- = --------------------

0.5 hours 7.5 hours

Applying cross multiplication:

3.6 multiplied by 7.5 equals x times 0.5

Dividing both sides by 0.5:

x = (3.6 * 7.5) / 0.5

x = 54

So, you assisted 54 customers in 7.5 hours.

7 0

1 month ago

A company director investigated whether there is a difference in the mean number of overtime hours worked each week by employees

PIT_PIT [12445]

C. No, because at least one of the sample sizes exceeds 10 percent of the population.

0 0

27 days ago

Angelica is working with function machines. She has the two machines at shown at the right. She wants to put them in order so th

Leona [12618]

To achieve the desired output, first use the machine with the function y = x^2 - 6, followed by the machine that computes y = sqrt(x-5). This way, when you input 6, the output from the first machine is calculated as x = 6, yielding y = 6^2 - 6, resulting in 30 as the input for the second machine. The second machine then processes this to provide the final output of sqrt(30 - 5), which equals sqrt(25) = 5. Alternatively, to obtain a negative final output, you should first utilize the machine with the function y = sqrt(x-5). Assuming you start with the value x = 9, the first machine computes this to sqrt(9-5), which is sqrt(4) = 2. Then, the second machine converts y to 2^2 - 6, leading to a result of 4 - 6 = -2.

3 0

1 month ago