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2 years ago

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Mathematics

2 answers:

Over [174]2 years ago

5 0

Step-by-step explanation:

what was love What was this like? and who do you love

kramer2 years ago

3 0

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The diagram shows a right-angled triangle. a 12 cm 24 cm Find the size of angle x.

Vlada [557]

Given that , Length of Base and Hypotenuse is 12 cm and 24 cm , respectively .

Need To Find : The measure of Angle x .

As We know that ,

Cos ∅ = Base / Hypotenuse

ㅤㅤ By Substituting known Values :

ㅤ⤀Cos x = 12/24

ㅤ⤀Cos x = ½

ㅤ⤀Cos 60⁰ = ½

Therefore,

Value of Angle x is 60⁰

6 0

3 years ago

A sample size must be determined for estimating a population mean given that the confidence level is % and the desired margin o

Sauron [17]

Complete Question

The complete question is shown on the first uploaded image

Answer:

$n =290$

$n =129$

The correct option is D

Step-by-step explanation:

From the question we are told that

The margin of error is $E = 0.23$

The largest value is k = 15

The smallest value is u = 7

From the question we are told the confidence level is 95% , hence the level of significance is

$\alpha = (100 - 95 ) \%$

=> $\alpha = 0.05$

Generally from the normal distribution table the critical value of $\frac{\alpha }{2}$ is

$Z_{\frac{\alpha }{2} } = 1.96$

Generally population standard deviation estimate is mathematically represented as

$\sigma = \frac{Range }{4}$

Here the Range is mathematically represented as

$Range = k - u$

=> $Range = 15 - 7$

=> $Range = 8$

=> $\sigma = \frac{8 }{4}$

=> $\sigma = 2$

Generally the sample size is mathematically represented as

$n = [\frac{Z_{\frac{\alpha }{2} } * \sigma }{E} ] ^2$

=> $n = [1.96 * 2 }{0.23} ] ^2$

=> $n =290$

Generally to obtain a conservatively small sample size the population standard deviation estimate becomes

=> $\sigma = \frac{Range }{6}$

=> $\sigma = \frac{8 }{6}$

=> $\sigma =1.333$

Generally the conservatively small sample size is mathematically evaluated as

$n = [\frac{Z_{\frac{\alpha }{2} } * \sigma }{E} ] ^2$

=> $n = [1.96 * 1.333 }{0.23} ] ^2$

=> $n =129$

6 0

3 years ago

What the answer X/3=3

galina1969 [7]

Answer:

x = 9

Step-by-step explanation:

Isolate the variable. Note the equal sign, what you do to one side, you do to the other. Multiply 3 to both sides.

(x/3)(3) = 3(3)

x = 3(3)

x = 3 * 3

x = 9

x = 9 is your answer.

3 0

3 years ago

The roots of an equation are x=-1 plus or minus I the equation is x^2+ ?

Oxana [17]

Answer:

x^2+2x+2

Step-by-step explanation:

If the roots of the equation are -1\pm i, then by the zero product rule:

$x=-1\pm i \\\\x+1\pm i=0 \\\\(x+1+i)(x+1-i)=0\\\\x^2+x-ix+x+1-i+ix+i+1=0 \\\\x^2+2x+2=0$

You can confirm this with the quadratic equation:

$x=\dfrac{-2\pm\sqrt{4-8}}{2}=\dfrac{-2\pm 4i}{2}=-1\pm i$

Hope this helps!

8 0

3 years ago

The number of airline passengers in 1990 was 466 million. The number of passengers traveling by airplane each year has increased

taurus [48]

Answer:

2010.

Step-by-step explanation:

We have been given an exponential growth formula $P(t)=466\cdot 1.035^t$ , which represents number of passengers traveling by airplane since 1990.

To find the year in which 900 million passengers will travel by airline, we will equate the given formula by 900 and solve for t as:

$900=466\cdot 1.035^t$

$\frac{900}{466}=\frac{466\cdot 1.035^t}{466}$ $1.9313304721030043=1.035^t$

Take natural log of both sides:

$\text{ln}(1.9313304721030043)=\text{ln}(1.035^t)$

Using property $\text{ln}(a^b)=b\cdot \text{ln}(a)$ , we will get:

$\text{ln}(1.9313304721030043)=t\cdot \text{ln}(1.035)$

$0.658209129198=t\cdot 0.034401426717$

$\frac{0.658209129198}{0.034401426717}=\frac{t\cdot 0.034401426717}{0.034401426717}$

$19.1331927775=t\\\\t=19.1331927775$

This means that in the 20th year since 1990, 900 million passengers would travel by airline.

$1990+20=2010$

Therefore, 900 million passengers would travel by airline in 2010.

6 0

3 years ago