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3 years ago

Help me with these 3 and explain too thank you :))

Mathematics

1 answer:

xz_007 [3.2K]3 years ago

5 0

Answer:

1) 25

2) 2

3) f(g(1)) = 42

Step-by-step explanation:

1) Given that f(x) = 4x^2 + 9

If x = -2

f(-2) = 4(-2)^2 + 9

f(-2) = 4(4) + 9

f(-2) = 16 + 9

f(-2) = 25

2) Given that f(x) = 4x - 6

y = 4x - 6

Replace y with x

x = 4y - 6

MAke y the subject of the forfmula

4y = x+ 6

y = (x+6)/4

SInce x = 2

f^(-1)(2) = (2+6)/4

f^(-1)(2) = 8/4 = 2

3) If f(x) = 6x and g(x) = x+6

f(g(x)) = f(x+6)

f(x+6) = 6(x+6)

Since x = 1

f(g(1)) = 6(1+6)

f(g(1)) = 6(7)

f(g(1)) = 42

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What is another way to write the equation 3(1.25)+3(2.00)=9.75

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Answer:

3.75+6=9.75

Step-by-step explanation:

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2 years ago

You have been assigned to determine whether more people prefer Coke or Pepsi. Assume that roughly half the population prefers Co

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Answer:

$n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11$

And rounded up we have that n=1068

Step-by-step explanation:

For this case we have the following info given:

$ME=0.03$ the margin of error desired

$Conf= 0.95$ the level of confidence given

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

the critical value for 95% of confidence is $z=1.96$

We can use as estimator for the population of interest $\hat p=0.5$ . And on this case we have that $ME =\pm 0.03$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

And replacing into equation (b) the values from part a we got:

$n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11$

And rounded up we have that n=1068

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3 years ago

During a snowstorm, 4 -1/2 inches of snow fell in 1 -1/3 hours. The same amount of snow fell each hour.

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4 1/2 inches of snow

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3 years ago

Approximate <img src="https://tex.z-dn.net/?f=-8%20%2B%5Csqrt%7B20%7D" id="TexFormula1" title="-8 +\sqrt{20}" alt="-8 +\sqrt{20}

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The value of the radical expression -8 + √20 when expanded and solved is -3.6, based on the given parameters

<h3>What are equivalent expressions?</h3>

Equivalent expressions are different expressions that have equal values when evaluated and compared

<h3>How to approximate the radical expression?</h3>

The expression is given as:

-8 + √20

The above expression is a radical expression

So, we start by doing the following

Express 20 as 5 * 4

-8 + √20 = -8 + √(5 * 4)

Split the radical expression √(5 * 4)

-8 + √20 = -8 + √5 * √4

Evaluate the square root of 4 i.e. √4 = 2

-8 + √20 = -8 + √5 * 2

This gives

-8 + √20 = -8 + 2√5

Evaluate the square root of 5

-8 + √20 = -8 + 2 * 2.2

Evaluate the product of 2 and 2.2

-8 + √20 = -8 + 4.4

Evaluate the difference

-8 + √20 = -3.6

Based on the given parameters, the value of the radical expression -8 + √20 when expanded and solved is -3.6

So, the complete equation is:

-8 + √20 = -3.6