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2 years ago

How to solve 2(-3x + 4) = 5x + 2

Mathematics

1 answer:

ryzh [129]2 years ago

8 0

Answer:

x = 6/11

Step-by-step explanation:

2(-3x + 4 ) = 5x + 2

-6x + 8 = 5x + 2

- 2 - 2

-6x + 6 = 5x

+6x +6x

6 = 11x

/11 /11

6/11 = x

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CosA.cosecA=cotA can you please help me with this

chubhunter [2.5K]

CscA = 1/sinA

CosACscA = cosA × 1/sinA = cosA/SinA = cotA

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3 years ago

If we wanted to create a new 90% confidence interval from a different sample for the proportion of those with a two on one date

slava [35]

Answer: 271

Step-by-step explanation:

The formula we use to find the sample size is given by :-

$n=p(1-p)(\dfrac{z_{\alpha/2}}{E})^2$

, where $z_{\alpha/2}$ is the two-tailed z-value for significance level of $(\alpha)$

p = prior estimation of the proportion

E = Margin of error.

If prior estimation of the proportion is unknown, then we take p= 0.5 , the formula becomes

$n=0.5(1-0.5)(\dfrac{z_{\alpha/2}}{E})^2$

$n=0.25(\dfrac{z_{\alpha/2}}{E})^2$

Given : Margin of error : E= 0.05

Confidence level = 90%

Significance level $\alpha=1-0.90=0.10$

Using z-value table , Two-tailed z-value for significance level of $0.10$

$z_{\alpha/2}=1.645$

Then, the required sample size would be :

$n=0.25(\dfrac{1.645}{0.05})^2$

Simplify,

$n=270.6025\approx271$

Hence, the required minimum sample size =271

3 0

3 years ago

Which of the following is equal to (3^-3)(3^7)? a. 3^4 b. 3^-4 c. 3^-10 d. 3^10

balu736 [363]

a. 3^4 which is equal to (3^-3)(3^7)

5 0

3 years ago

The second term in a geometric series is 10, and the seventh term is 10,240. Find the sum of the first six terms.

just olya [345]

Answer:

The sum of the first 6 terms is 3,412.5.

Step-by-step explanation:

The second term of the geometric series is given by:

$a_{2}=a_{1}*r$

Where a1 is the first term and r is the common ratio. The seventh term can be written as a function of the second term as follows:

$a_{7}=a_{1}*r^{6} \\a_{7}=a_{2}*r^{5} \\10,240 = 10*r^{5}\\r=\sqrt[5]{1024} \\r = 4$

The sum of "n" terms of a geometric series is given by:

$a_{1} = \frac{10}{4} = 2.5\\S_{n}=a_{1}(\frac{r^{n}-1 }{r-1})\\S_{6}=2.5(\frac{4^{6}-1 }{4-1})\\S_{6}=3,412.5$

The sum of the first 6 terms is 3,412.5.

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2 years ago

Following three questions refer to the information below. A coal-fired power plant produces and sells 10,000 MW electricity whil

natita [175]

Answer: Heat rejected=150000MW

Heat rate= 2.5

Step-by-step explanation:

Thermal efficiency is defined as work out divided by heat in.

Therefore

thermal efficiency = 40/100= 100000 MW/Heat in

Heat in = 250000MW

For a closed system undergoing a cycle the change in internal energy is zero. Therefore the work out of the system is equal to the net heat transfer of the system. Therefore

Work out= heat in - heat out

Therefore heat out = heat in - work out

Heat out = 250000 MW - 100000MW = 150000 MW which is the amount of heat rejected

The heat rate is defined as the inverse of the thermal efficiency expressed in kJ/kWh.Therefore

Heat rate = 1/thermal efficiency

Heat rate = 1/0.4 = 2.5 kJ/kWh

4 0

2 years ago