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3 years ago

Log7 5 + log7 x = log7 60

1 answer:

5 0

Use your rules of logs. First the sum of two logs with same base is the product of the parts. Log7 (5x) = log7 60. Now since both sides have same log and base the parts are equal. 5x = 60. Divide by 5 to get a result of x = 12

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Zoltan read 15 pages of his book in 6 minutes. At this rate, how many pages can he read in 10 minutes?

9966 [12]

Answer:

25 pages in 10 minutes.

5 0

3 years ago

A group of 59 randomly selected students have a mean score of 29.5 with a standard

algol [13]

Answer:

$29.5-1.671\frac{5.2}{\sqrt{59}}=28.37$

$29.5+1.671\frac{5.2}{\sqrt{59}}=30.63$

And we can conclude that the true mean for the scores are given by this interval (28.37; 30.63) at 90% of confidence

Step-by-step explanation:

Information given

$\bar X = 29.5$ represent the sample mean

$\mu$ population mean

s= 5.2 represent the sample standard deviation

n=59 represent the sample size

Confidence interval

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

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

The degrees of freedom are given by:

$df=n-1=59-1=58$

The Confidence interval is 0.90 or 90%, the significance is $\alpha=0.1$ and $\alpha/2 =0.05$ , and the critical value is $t_{\alpha/2}=1.671$

Now we have everything in order to replace into formula (1):

$29.5-1.671\frac{5.2}{\sqrt{59}}=28.37$

$29.5+1.671\frac{5.2}{\sqrt{59}}=30.63$

And we can conclude that the true mean for the scores are given by this interval (28.37; 30.63) at 90% of confidence

8 0

2 years ago

XY bisects DF at point E. If DE=2y and EF=8y-3, find the value of DF

nirvana33 [79]

Answer:

Step-by-step explanation:

If XY bisects DF at point E, then DE = EF.

Given DE = 2y and EF = 8y-3

2y = 8y-3

subtract 8y from both sides

2y-8y = 8y-8y-3

-6y = -3

y = 3/6

y = 1/2

y = 0.5

DF = DE+EF

DF= 2y+8y-3

DF = 10y - 3

DF = 10(0.5)-3

DF = 5-3

DF = 2

7 0

3 years ago

Paul and jose are trying to measure the height of a tree. paul is standing 19m from the foot of the tree and measures the angle

Nina [5.8K]

The firts thig we are going to do is create tow triangles using the angles of elevation of Paul and Jose. Since the problem is not giving us their height we'll assume that the horizontal line of sight of both of them coincide with the base of the tree.
We know that Paul is 19m from the base of the tree and its elevation angle to the top of the tree is 59°. We also know that the elevation angle of Jose and the top of the tree is 43°, but we don't know the distance between Paul of Jose, so lets label that distance as $x$ .
Now we can build a right triangle between Paul and the tree and another one between Jose and the tree as shown in the figure. Lets use cosine to find h in Paul's trianlge:
$cos(59)= \frac{19}{h}$
$h= \frac{19}{cos(59)}$
$h=36.9$
Now we can use the law of sines to find the distance $x$ between Paul and Jose:
$\frac{sin(43)}{36.9} = \frac{sin(16)}{x}$
$x= \frac{36.9sin(16)}{sin(43)}$
$x=14.9$

Now that we know the distance between Paul and Jose, the only thing left is add that distance to the distance from Paul and the base of the tree:
$19m+14.9=33.9m$

We can conclude that Jose is 33.9m from the base of the tree.

3 0

3 years ago

110 decreased by 70%

Bess [88]

110x0.7= 77
110-77= 33
so 33 is your answer

7 0

2 years ago