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solmaris [256]
2 years ago
12

Find the value of k when 5^-3 + 5^-4 = 5^k x 5^-4

Mathematics
2 answers:
lubasha [3.4K]2 years ago
8 0

Answer:

Given , 1/2 is a solution of the equation

or, 1/4 - 5/4 = -k/2

or, -k/2 = -1

or k = 2

Step-by-step explanation:

GalinKa [24]2 years ago
4 0

Answer:

k= 6/5 or 1.12

Step-by-step explanation:

You isolate the variable by dividing each side by factors that don't contain the variable. This variable (K) is not a whole number so I gave you the fraction and rounded decimal form. Hope this helps :)

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The manufacturer of hardness testing equipment uses steel-ball indenters to penetrate metal that is being tested, however, the m
masha68 [24]

Answer:

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

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

So on this case the 95% confidence interval would be given by (0.2789;3.055)  

The 95% confidence interval to judge whether the two indeners result in different measurements is?

Yes the confidence interval not contains the value 0 so we can conclude that the values for Diamond are significantly higher than the values for Steel Ball at 5% of significance.

Step-by-step explanation:

We have the following dataset:

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

If we calculate the differences diamond-steel ball we have this datase:

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

The second step is calculate the mean difference  

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

The third step would be calculate the standard deviation for the differences, and we got:

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

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

The confidence interval for the mean is given by the following formula:  

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

In order to calculate the critical value t_{\alpha/2} we need to find first the degrees of freedom, given by:  

df=n-1=9-1=8  

Since the confidence is 0.95 or 95%, the value of \alpha=0.05 and \alpha/2 =0.025, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,9)".And we see that t_{\alpha/2}=2.31.

Now we have everything in order to replace 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  

So on this case the 95% confidence interval would be given by (0.2789;3.055)  

The 95% confidence interval to judge whether the two indeners result in different measurements is?

Yes the confidence interval not contains the value 0 so we can conclude that the values for Diamond are significantly higher than the values for Steel Ball at 5% of significance.

4 0
3 years ago
Help me please<br> 8. Match each angle pair with the corresponding drawing. Choose the best answer!
sdas [7]

Answer:

1. D

2. B

3.  A

4. C

Step-by-step explanation:

1. Vertical angles are a pair of opposite angles formed by the intersection of lines. Choice D has two lines intersecting, and two opposite angles formed by it.

2. Adjacent angles are two angles that have a common vertex and common side but do not overlap. Choice B is two angles with a common vertex and common side, and they don't overlap.

3. Supplementary angles are angles that add up to 180 degrees/make a straight angle. Choice A has two angles that add up to 180 degrees, and the two angles combined make a straight angle/line.

4. Two angles are called complementary angles if they add up to 90 degrees and form a right angle. Choice C has two angles that form a right triangle, meaning it adds up to 90 degrees.

5 0
2 years ago
The lateral surface area is _ square centimeters.
Liula [17]

Answer: 24

Step-by-step explanation:

5 0
3 years ago
I need to solve cy−7=5d+3y for y, any help?
iVinArrow [24]
Given cy - 7 = 5d + 3y, we solve for y as follows:

cy - 3y = 5d + 7

y(c - 3) = 5d + 7

y = (5d + 7) / (c - 3)
8 0
3 years ago
Read 2 more answers
A student's grade for the four quarters are 95, 83, 91, and 85. What does the student need to earn on the final exam to have an
gulaghasi [49]

Answer:

The least score the student can get is 71 to get an overall B average at the end of the year.

Step-by-step explanation:

Let the score she needs to get be = x

We now have to take the mean of all the five subjects <em>(including x)</em> and equate it to the least score she can have to get a B grade.

Let us take the least score the student needs to get a B grade to be 85

Mean of all 5 scores =

\frac{95+83+91+85+x}{5}=85

\frac{354+x}{5} =85

354+x = 425

x = 71

The least score the student can get is 71 to get an overall B average at the end of the year.

3 0
3 years ago
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