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seraphim [82]
2 years ago
9

Al simplificar esta expresion logaritmica, cual es la forma mas simple? ​

Mathematics
1 answer:
Liula [17]2 years ago
6 0

Answer:

La respuesta es

<h2>\frac{1}{2}</h2>

Step-by-step explanation:

<h3>log_{5}( \sqrt{5} )</h3>

Escribe la expresión en forma exponencial con base 5

Eso es

<h3>log_{5}(5)^{ \frac{1}{2} }</h3>

Usando las reglas de los logaritmos que

<h3>log_{ a}( {a})^{x}  = x</h3>

Simplifica la expresión

Tenemos la respuesta final como

<h3>\frac{1}{2}</h3>

Espero que esto te ayude

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Given RT below, if S lies on RT such that the
defon

Answer:

(-2, -3)

Step-by-step explanation:

If a segment having extreme ends as (x_1,y_1) and (x_2,y_2) is divided by a point (x, y) in the ratio of m:n,

x = \frac{mx_2+nx_1}{m+n}

y = \frac{my_2+ny_1}{m+n}

Since, a line RT has extreme ends as R(-5, 3) and T(-1, -5) then a point S(x, y) which divides RT in the ratio of 3 : 1 will be,

x = \frac{3(-1)+1(-5)}{3+1}

  = \frac{-8}{4}

  = -2

y = \frac{3(-5)+1(3)}{3+1}

  = -\frac{12}{4}

  = -3

Therefore, coordinates of the point S will be (-2, -3).

6 0
2 years ago
The heights of students at a college are normally distributed with a mean of 175 cm and a standard deviation of 6 cm. One might
frosja888 [35]

Answer:

25

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 175cm

Standard deviation = 6 cm

Percentage of students below 163 cm

163 = 175 - 2*6

So 163 is two standard deviations below the mean.

By the Empirical rule, 95% of the heights are within 2 standard deviations of the mean. The other 100-95 = 5% are more than 2 standard deviations of the mean. Since the normal distribution is symmetric, 2.5% of them are more than 2 standard deviations below the mean(so below 163cm) and 2.5% are more than two standard deviations above the mean.

2.5% of the students have heights less than 163cm.

Out of 1000

0.025*1000 = 25

25 is the answer

8 0
2 years ago
Read 2 more answers
Exercise 6.12 presents the results of a poll where 48% of 331 Americans who decide to not go to college do so because they canno
tensa zangetsu [6.8K]
<h2>Answer with explanation:</h2>

As per given , we have

\hat{p}=0.48   , n=331

Critical value for 90% Confidence interval : z_{\alpha/2}=1.645

a) Confidence interval :

\hat{p}\pm z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}

0.48\pm (1.645)\sqrt{\dfrac{0.48(1-0.48)}{331}}\\\\\approx 0.48\pm0.02746\\\\=(0.48-0.02746,\ 0.48+0.02746)\\\\=(0.45254,\ 0.50746)

Hence, a 90% confidence interval for the proportion of Americans who decide to not go to college because they cannot a ord it : (0.45254,\ 0.50746)

b) Margin of error : E=1.5%=0.015

Formula for sample size : n=p(1-p)(\dfrac{z_{\alpha/2}}{E})^2

For p =0.48 , we  have

n=0.48(1-0.48)(\dfrac{1.645}{0.015})^2=3001.88373333\approx3002

Hence, the required sample size to survey = 3002

6 0
2 years ago
Brock is training for a Crossfit competition. He began the training completing pull-ups and box jumps origanally, his training p
siniylev [52]

If the adjusted ratio was 2:7, then

2x is the number of pull-ups

and

7x is the number of box jumps.

You can state that since he completed 63 box jumps at the end of his training, then

7x=63,

x=9

and

2x=18.

The total number of exercises performed is 2x+9x=18+63=81.

As at start the ratio was 5:4, then

5y was the number of pull-ups

and

4y was the number of box jumps.

Therefore, 5y+4y=81,

9y=81,

y=9

and 5y=45, 4y=36.

Answer: Initially: 45 pull-ups and 36 box jumps. At the end: 18 pull-ups and 63 box jumps.

8 0
2 years ago
nadia was offered a job for selling ads cor a magazine. She must agree to one of the following paymen options. CHOICE A:$110 for
Fittoniya [83]

Let us say that:

x = is the number of ads that Nadia sold every week

P = payment or amount that she receives every week

 

So the equations we can formulate for choice A and B are:

choice A: P = 110 x

choice B: P = 150 + 85 x

 

The amount that she receives for A must be greater than she receives for choice B, so:

110 x > 150 + 85 x                       (inequality equation)

 

Calculate for x:

110 x – 85 x > 150

25 x > 150

x > 6

 

Therefore Nadia must sell more than 6 ads every week so that Choice A would be the better choice.

6 0
2 years ago
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