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4 years ago

(2^(5x-4))/16=4. Find x

Mathematics

2 answers:

Brilliant_brown [7]4 years ago

7 0

2^(5x-4)/2^4=2^2
2^(5x-8)=2^2
5x-8=2
5x=10
x=2

Masja [62]4 years ago

3 0

Answer:

x = 2

Step-by-step explanation:

(2^(5x-4))/16=4 can be rewritten as

2^(5x - 4)

-------------- = 2^2

2^4

Using properties of logs, this simplifies to:

2^(5x - 4 - 4) = 2^2

Cancelling out the base 2, we get:

5x - 8 = 2

Then 5x = 10 and x = 2.

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3 years ago

Erica has six boxes of buttons. Each box holds 28 buttons. Explain how Erica can use place value and regrouping to find how many

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3 years ago

You have a standard deck of 52 playing cards (13 of each suit). You draw a hand of the top 17 of them. Spades are one of the fou

Vadim26 [7]

Answer:

The expected value of the number of spades are = 4.25

Step-by-step explanation:

As per the question,

W know that in a standard deck of 52 playing card, there are 4 suits, and each suit have 13 playing card.

Since, we know that

$Probability\ of\ a \ event\ = \frac{Number\ of\ Favorable\ Outcomes}{Total\ Number\ of\ Possible\ Outcomes}$

Therefore,

Probability of any random card being a spade is

$=\ \frac{13}{52}$

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So the expected number of spades we draw are

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7 0

4 years ago

The percent, X , of shrinkage o n drying for a certain type of plastic clay has an average shrinkage percentage :, where paramet

never [62]

Answer:

a) $t=\frac{18.4-17.5}{\frac{2.2}{\sqrt{45}}}=2.744$

The degrees of freedom are given by:

$df=n-1=45-1=44$

The critical value for this case is $t_{\alpha}=1.68$ since the calculated value is higher than the critical we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 18.4

b) $p_v =P(t_{(44)}>2.744)=0.0044$

Step-by-step explanation:

Information given

$\bar X=18.4$ represent the sample mean

$s=2.2$ represent the sample standard deviation

$n=45$ sample size

$\mu_o =17.5$ represent the value to verify

$\alpha=0.05$ represent the significance level

t would represent the statistic

$p_v$ represent the p value

Part a

We want to test if the true mean is higher than 17.5, the system of hypothesis would be:

Null hypothesis: $\mu \leq 17.5$

Alternative hypothesis: $\mu > 17.5$

The statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

And replacing we got:

$t=\frac{18.4-17.5}{\frac{2.2}{\sqrt{45}}}=2.744$

The degrees of freedom are given by:

$df=n-1=45-1=44$

Part b

The p value would be given by:

$p_v =P(t_{(44)}>2.744)=0.0044$

5 0

4 years ago

A ship traveled for a total of 72 miles over the course of 6 hours. Heading south, the ship traveled at an average speed of 13 m

Alexxx [7]

Recall your d = rt, distance = rate * time

the rate going south is 13, the rate going east is 10

it took a total amount of 6hours and 72miles for the whole travel

so.. if going say hmmm South, it covered a distance of "d", then going East it covered a distance of the slack from 72 and "d", it covered "72 - d" miles

so, if going South it took "t" hours, then going East it took the slack from 6 and "t", or "6 - t" hours

thus $\bf \begin{array}{lccclll}
&distance&rate&time\\
&-----&-----&-----\\
South&d&13&t\\
East&72-d&10&6-t
\end{array}
\\\\\\
\begin{cases}
\boxed{d}=13t\\
72-d=10(6-t)\\
----------\\
72-\boxed{13t}=10(6-t)
\end{cases}$

solve for "t"

so, it travelled East for 6-t hours

3 0

4 years ago