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3 years ago

Solve the equation by factoring. z2 − 6z − 27 = 0

1 answer:

7 0

The answer is x= 9 and -3

You must fine 2 number that multiply to equal -27 and add to equal -6

(x-9) (x+3)
Then equal the parts of the binomial to zero

x - 9 = 0
x + 3 = 0

You must get x by its self.
When you do so, you'll have the answer as -3 and 9

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February 12, 2009 marked the 200th anniversary of Charles Darwin's birth. To celebrate, Gallup, a national polling organization,

timurjin [86]

Answer:

$Z_{H0}$ = 2.83

Reject H₀

Step-by-step explanation:

Hello!

The objective of the poll is to compare the proportions of people who believe in the theory of evolution. For this, the investigator took a sample of 1018 and divided it into two groups using a criteria their level in college education.

Group 1 (people with some college education)

n₁= 325

x₁= 133

sample proportion ^ρ₁=x₁/n₁ = 133/325 = 0.409

Group 2 (college graduates)

n₂= 228

x₂= 121

sample proportion ^ρ₂=x₂/n₂ = 121/228 = 0.531

pooled proportion ^ρ= 0.459

The statistic test that corresponds to test if the proportions are equal or different is the difference of population proportions and you have to use the normal approximation for the proportions to calculate it.

The hypothesis is:

H₀: ρ₂=ρ₁

H₁: ρ₂≠ρ₁

α: 0.10

Z= (^ρ₂ - ^ρ₁) - (ρ₂ - ρ₁) ≈ N (0;1)

√(^ρ(1 - ^ρ)*(1/n₂+1/n₁)

The critical region is two-tailed, so you have a lower critrical value and an upper critical value:

$Z_{\alpha /2} = Z_{0.05} = -1.64$

$Z_{1-\alpha /2} = Z_{0.95} = 1.64$

If $Z_{H0}$ ≤ -1.64 or if $Z_{H0}$ ≥ 1.64 you reject the null hypothesis.

If -1.64 < $Z_{H0}$ < 1.64, the you do not reject the null hypothesis.

Z= (^ρ₂ - ^ρ₁) - (ρ₂ - ρ₁) = (0.531 - 0.409) - 0 = 2.83

√(^ρ(1 - ^ρ)*(1/n₂+1/n₁) √(0.459(1 - 0.459)*(1/228+1/325)

$Z_{H0}$ = 2.83

Since the calculated Z value is greater than the upper critical value, the decision is to reject the null hypothesis. In other words, there is significative enough evidence to say that there is a difference between the population proportion of people who believe in the evolution theory and graduated from college and the population proportion of people who believe in the evolution theory and have some college education.

I hope it helps!

5 0

3 years ago

Differentiate y=(6x)/(1-cot(x))

My name is Ann [436]

$\bf y=\cfrac{6x}{1-cot(x)}\implies \cfrac{dy}{dx}=\stackrel{quot ient~ru le}{\cfrac{6[1-cot(x)]~-~6x[-csc^2(x)]}{[1-cot(x)]^2}}
\\\\\\
\cfrac{dy}{dx}=\cfrac{6-6cot(x)~+~6xcsc^2(x)}{[1-cot(x)]^2}$

8 0

4 years ago

Question is in the picture

Leviafan [203]

Answer: d,f

$-x\geq 4\\=> x\leq -4$

=> all the values are d and f

Step-by-step explanation:

5 0

3 years ago

Find the 6th term in the sequence

Dimas [21]

Answer:

C.64

Step-by-step explanation:

The first step is to figure out what the sequence is, the first step is 2, 4 the only ways for 2 to get to 4 would be +2 or *2 so we will look at the next step, 4 to 8. The only ways for 4 to get to 8 is +4 or *2, since these both have *2 in common we will check that with all of the terms

2, 4, 8, 16, 32

2 (*2) = 4 (*2) = 8 (*2) = 16 (*2) 32

Since the equation is working we are going to multiply 32 by 2 to get the 6th term

32 (*2) = 64

6 0

3 years ago

Read 2 more answers

Richie spent $120 on 12 rose bushes and 2 gardenias, while Jim spent it $150 on 10 rose bushes and 10 gardenias. What is the cos

Basile [38]

With the given information, we can create several equations:

120 = 12x + 2y
150 = 10x + 10y

With x being the number of rose bushes, and y being the number of gardenias.

To find the values of the variables, we can use two methods: Substitution or Elimination

For this case, let us use elimination. To begin, let's be clear that we are going to be adding these equations together. Therefore, in order to get the value of one variable, we must cancel one of them out - it could be x or y, it doesn't matter which one you decide to cancel out. Let's cancel the x out:

We first need to multiply the equations by numbers that would cause the x's to cancel out - and this can be done as follows:

-10(120 = 12x + 2y)
12(150 = 10x + 10y) => Notice how one of these is negative

Multiply out:

-1200 = -120x - 20y
+ 1800 = 120x + 120y => Add these two equations together
---------------------------------
600 = 100y

Now we can solve for y:

y = 6

With this value of y known, we can then pick an equation from the beginning of the question, and plug y in to solve for x:

120 = 12x + 2y => 120 = 12x + 2(6)

Now we can solve for x:

120 = 12x + 12 => 108 = 12x

x = 9

So now we know that x = 9, and y = 6.

With rose bushes being x, we now know that the cost of 1 rose bush is $9.
With gardenias being y, we now know that the cost of 1 gardenia is $6.

4 0

3 years ago