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3 years ago

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Test the claim that the proportion of men who own cats is smaller than 70% at the 0.05 significance level. The null and alternat

ive hypothesis would be:

1 answer:

Ghella [55]3 years ago

3 0

Answer:

the null hypothesis would be: p = 70%/0.7

The alternative hypothesis would be: p < 0.7

Step-by-step explanation:

The null hypothesis is most of the time always the default statement while the alternative hypothesis is tested against the null and is its opposite.

In this case study the null hypothesis would be: the proportion of men who own cats is 70%: p = 0.7

The alternative hypothesis would be: the proportion of men who own cats is smaller than 70% : p < 0.7

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Choose a method (factoring. square root property, completing the square, and the quadratic formula) to solve each of the followi

Natasha_Volkova [10]

Answer:

Part A) $x=(+/-)\frac{3\sqrt{3}}{2}$

Part B) $x=2.5$ and $x=-0.5$

Part C) $x=-1$ and $x=3$

Part D) $x=\frac{9+\sqrt{193}}{8}$ and $x=\frac{9-\sqrt{193}}{8}$

Step-by-step explanation:

Part A) we have

$4x^{2}-27=0$

we know that

The <u><em>square root property</em></u> states that if we have an equation with a perfect square on one side and a number on the other side, then we can take the square root of both sides and add a plus or minus sign to the side with the number and solve the equation.

isolate the term that contains the squared variable

$4x^{2}=27$

$x^{2} =\frac{27}{4}$

take the square root of both sides

$x=(+/-)\frac{\sqrt{27}}{2}$

simplify

$x=(+/-)\frac{3\sqrt{3}}{2}$

Part B) we have

$4x^{2}-8x-5=0$

Using the quadratic equation

The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$ is

$x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$4x^{2}-8x-5=0$

so

$a=4\\b=-8\\c=-5$

substitute in the formula

$x=\frac{-(-8)(+/-)\sqrt{-8^{2}-4(4)(-5)}} {2(4)}$

$x=\frac{8(+/-)\sqrt{144}}{8}$

$x=\frac{8(+/-)12}{8}$

$x=\frac{8(+)12}{8}=2.5$

$x=\frac{8(-)12}{8}=-0.5$

Part C) we have

$4x^{2}-8x-12=0$

Using Factoring

Simplify the expression first

Divide by 4 both sides

$x^{2}-2x-3=0$

Find two numbers a and b such that

a+b=-2

ab=-3

Solve the system by graphing

The solution is a=1, b=-3

see the attached figure

so

$4x^{2}-8x-12=4(x-1)(x+3)$

The solutions are

$x=1, x=-3$

Part D) we have

$4x^{2}-9x-7=0$

Solve by completing the square

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$4x^{2}-9x=7$

Factor the leading coefficient

$4(x^{2}-\frac{9}{4}x)=7$

Complete the square. Remember to balance the equation by adding the same constants to each side

$4(x^{2}-\frac{9}{4}x+\frac{81}{64})=7+\frac{81}{16}$

$4(x^{2}-\frac{9}{4}x+\frac{81}{64})=\frac{193}{16}$

Rewrite as perfect squares

$4(x-\frac{9}{8})^{2}=\frac{193}{16}$

$(x-\frac{9}{8})^{2}=\frac{193}{64}$

take square root both sides

$(x-\frac{9}{8})=(+/-)\frac{\sqrt{193}}{8}$

$x=\frac{9+\sqrt{193}}{8}$

$x=\frac{9-\sqrt{193}}{8}$

7 0

3 years ago