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Allushta [10]
3 years ago
8

If log 5 = p and log 2=q then log 200 can be written in terms of p and q as?

Mathematics
1 answer:
Andrei [34K]3 years ago
8 0
<h3>Answer:  2p + 3q</h3>

Work Shown:

log(200) = log(2^3*5^2)

log(200) = log(2^3) + log(5^2)

log(200) = 3*log(2) + 2*log(5)

log(200) = 3*q + 2*p

log(200) = 2p + 3q

The log rules I used were

log(A*B) = log(A)+log(B)

log(A^B) = B*log(A)

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In tests of a computer component, it is found that the mean time between failures is 937 hours. A modification is made which is
VladimirAG [237]

Answer:

Null hypothesis is \mathbf {H_o: \mu > 937}

Alternative hypothesis is \mathbf {H_a: \mu < 937}

Test Statistics z = 2.65

CONCLUSION:

Since test statistics is greater than  critical value; we reject the null hypothesis. Thus, there is sufficient evidence to support the claim that the modified components have a longer mean time between failures.

P- value = 0.004025

Step-by-step explanation:

Given that:

Mean \overline x = 960 hours

Sample size n = 36

Mean population \mu = 937

Standard deviation \sigma = 52

Given that the mean  time between failures is 937 hours. The objective is to determine if the mean time between failures is greater than 937 hours

Null hypothesis is \mathbf {H_o: \mu > 937}

Alternative hypothesis is \mathbf {H_a: \mu < 937}

Degree of freedom = n-1

Degree of freedom = 36-1

Degree of freedom = 35

The level of significance ∝ = 0.01

SInce the degree of freedom is 35 and the level of significance ∝ = 0.01;

from t-table t(0.99,35), the critical value = 2.438

The test statistics is :

Z = \dfrac{\overline x - \mu }{\dfrac{\sigma}{\sqrt{n}}}

Z = \dfrac{960-937 }{\dfrac{52}{\sqrt{36}}}

Z = \dfrac{23}{8.66}

Z = 2.65

The decision rule is to reject null hypothesis   if  test statistics is greater than  critical value.

CONCLUSION:

Since test statistics is greater than  critical value; we reject the null hypothesis. Thus, there is sufficient evidence to support the claim that the modified components have a longer mean time between failures.

The P-value can be calculated as follows:

find P(z < - 2.65) from normal distribution tables

= 1 - P (z ≤ 2.65)

= 1 - 0.995975     (using the Excel Function: =NORMDIST(z))

= 0.004025

6 0
3 years ago
9 + |-78| - (-22)<br><br> Answer truthfully please.
GuDViN [60]

Answer:

109

Step-by-step explanation:

9 + |-78| - (-22)

Apply the absolute value which states |-x| = x.

9 + 78 - (-22)

Apply the rule that states x - (-y) = x + y.

9 + 78 + 22

Add 9 and 78.

87 + 22

Add 87 and 22.

109.

4 0
2 years ago
What is 5/6 - 1/5 =​
Daniel [21]

5/6 - 1/5 = 19/30 = 0.633

Hope this helped you! Please mark brainliest if this helped you at all and have a wonderful rest of your day!

4 0
3 years ago
Read 2 more answers
Write the equation in slope intercept form of the line that passes through the point (1,-3) and a slope of -2
Alborosie

Answer:y=-2x-1


Step-by-step explanation:

(1,-3) and a slope of -2

Use Formula

Y= mx +b to find b. By using the slope and point given .

M is slope

Y is -3

X Is 1



Y=mx+b


-3= -2(1)+b


-3= -2+b


-3+2=b


-1=b


Now create the equation by inputting the slope they gave you which is -2 and answer we solved for b which is -1 .


Y= -2x-1

4 0
3 years ago
(x+3)²(65)=x(6)<br>Solve using quadric formula​
Angelina_Jolie [31]

Step 1: Simplify both sides of the equation.

  • 65x²+390x+585=6x

Step 2: Subtract 6x from both sides.

  • 65x²+390x+585−6x=6x−6x
  • 65x²+384x+585=0

For this equation: a=65, b=384, c=585

  • 65x²+384x+585=0

Step 3: Use quadratic formula with a=65, b=384, c=585

  • x=−b±√b2−4ac/2a
  • x=−(384)±√(384)2−4(65)(585)/
  • 2(65)
  • x=−384±√−4644/130

Therefore, There are no real solutions.

6 0
3 years ago
Read 2 more answers
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