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2 years ago

Value of x in log5x = 4logx5 is

1 answer:

4 0

Log5 x=4 logx 5
Ln x/ln5=4(ln5 / ln x) logx z=ln x / ln z
least common multiple=ln5 * ln x

ln²x=4ln²5
√(ln² x)=√(4 ln²5)
ln x=2ln 5
x=e^2ln5=25

Answer: x=25.

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Triangle NLM is reflected over the line segment as shown, forming triangle ABC. Which congruency statement is correct? ΔNLM ≅ ΔC

algol13

Given that triangle NLM is reflected over the line segment as shown, forming triangle ABC.

When a point is refrected across a line, the relative distance form the point to the line of refrection is preserved. That is the distance from the point to the line of refrection is equal to the distance of the image to the line of refrection.

Thus, from the figure, it can be seen the point B is of the same distance to the line of refrection as point M, so is point A to point L and point C to point N.

Thus, ΔNLM is similar to ΔCAB

Therefore, the congruency statement that is correct is ΔNLM ≅ ΔCAB

9 0

2 years ago

Read 2 more answers

The batting Wang Xiu Ying uses to fill quilts has a thermal conductivity rate of 0.030.030, point, 03 watts (\text{W})(W)left pa

alexgriva [62]

Answer:

0.0003W/cm°C

Step-by-step explanation:

The question is not properly written. Here is the correct question.

The batting wang xiu ying uses to fill quilts has a thermal conductivity rate of 0.03 watts (W) per meter(m) per degree celsius. what is the batting thermal conductivity when w/cm•c

Given the thermal conductivity in W/m°C to be 0.03W/m°C

We are to rewrite the value in W/cm°C

The difference is the unit. The only thing we need to do is to simply convert the unit (metres) in W/m°C to centimeters (cm)

Since 100cm = 1m, 0.03W/m°C can be expressed as shown below;

= 0.03W/m°C

= 0.03 × W/1m×°C

Note that 1m = 100cm, substituting this conversion into the expression, it will become;

= 0.03 × W/100cm × °C

= 0.03/100 × W/cm°C

= 0.0003W/cm°C

Hence the battling thermal conductivity in W/cm°C is 0.0003W/cm°C

4 0

2 years ago

On average, the number of customers who had items to return for refunds or exchanges at a certain retail store's service desk is

spayn [35]

Answer:

The probability that the service desk will have at least 100 customers with returns or exchanges on a randomly selected day is P=0.78.

Step-by-step explanation:

With the weekly average we can estimate the daily average for customers, assuming 7 days a week:

$M=756/7=108$

We can model this situation with a Poisson distribution, with parameter λ=108. But because the number of events is large, we use the normal aproximation:

$P(\lambda)\approx N(\lambda,\lambda)$

Then we can calculate the z value for x=100:

$z=\frac{x-\mu}{\sigma}=\frac{100-108}{\sqrt{108}}=\frac{-8}{10.4} =-0.77$

Now we calculate the probability of x>100 as:

$P(x>100)=P(z>-0.77)=0.78$

The probability that the service desk will have at least 100 customers with returns or exchanges on a randomly selected day is P=0.78.

5 0

2 years ago

What is the slope of the following 12x - 6y = 30

blagie [28]

Answer:

$slope = m = 2$

6 0

2 years ago

Read 2 more answers

Suppose that a jewelry store tracked the amount of emeralds they sold each week to more accurately estimate how many emeralds to

RUDIKE [14]

Answer:

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

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

And for this case the 95% confidence interval is given by (2.13; 2.37)

We have a point of estimate for the sample mean with this formula:

$\bar X = \frac{Upper+ Lower}{2}= \frac{3.37+2.13}{2}= 2.75$

And for the margin of error we have the following estimation:

$ME= \frac{Upper -Lower}{2}= \frac{3.37-2.13}{2}= 0.62$

Step-by-step explanation:

Previous concepts

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".

$\bar X$ represent the sample mean

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

Solution to the problem

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

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

And for this case the 95% confidence interval is given by (2.13; 2.37)

We have a point of estimate for the sample mean with this formula:

$\bar X = \frac{Upper+ Lower}{2}= \frac{3.37+2.13}{2}= 2.75$

And for the margin of error we have the following estimation:

$ME= \frac{Upper -Lower}{2}= \frac{3.37-2.13}{2}= 0.62$

5 0

2 years ago