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2 years ago

X^2+16x+48=0 it says to solve each quadratic equation by factoring.

Mathematics

2 answers:

mote1985 [20]2 years ago

8 0

Answer:

x = -4 and x = -12

Step-by-step explanation:

x^2 + 16x + 48 = 0 is to be factored.

Note that 48 is the product of 4 and 12 and that the sum of 4 and 12 is 16.

Therefore,

x^2 + 16x + 48 = 0 in factored form is:

(x + 4)(x + 12) = 0, so that x + 4 = 0 → x = -4, and

x + 12 = 0 → x = -12

12345 [234]2 years ago

3 0

Answer:

(x + 4) (x + 12)

Step-by-step explanation:

to factor x² + 16x + 48 = 0, you need to find 2 numbers that when multiplied together give you 48 and when added together give you 16

you can list the factors of 48 and see what adds up together to give you 16, but here is a hint:

the numbers probably end in a 2, 4, 0, 6, 5, or 1, as a pair of these numbers added together give us 6. i looked at a factor chart and saw that 12 and 4 that when added together, give us 16 and when multiplied, give us 48

in factored form it looks like the following:

(x + 4) (x + 12)

this would be the answer in factored form

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How do u solve -18-6k=6 (1+3k)

Anarel [89]

Let's solve your equation step-by-step.−18−6k=6(1+3k)

Step 1: Simplify both sides of the equation.
−18−6k=6(1+3k)
Simplify: (Show steps)−6k−18=18k+6

Step 2: Subtract 18k from both sides.−6k−18−18k=18k+6−18k−24k−18=6

Step 3: Add 18 to both sides.−24k−18+18=6+18−24k=24

Step 4: Divide both sides by -24.−24k−24=24−24k=−1

Answer:k=−1

5 0

2 years ago

Read 2 more answers

6.In a sample of 131 women with cosmetic dermatitis from using eye shadow, 12 were diagnosed with a nickel allergy. In a sample

aivan3 [116]

Answer:

a) $0.0916 - 1.96\sqrt{\frac{0.0916(1-0.0916)}{131}}=0.0422$

$0.0916 + 1.96\sqrt{\frac{0.0916(1-0.0916)}{131}}=0.1410$

So then we can conclude that the true proportion of women with cosmetic dermatitis from using eye shadow at 95% of confidence is between (0.0422 and 0.1410)

b) $\hat p = \frac{25}{250}= 0.1$

$0.1 - 1.96\sqrt{\frac{0.1(1-0.1)}{250}}=0.0628$

$0.1 + 1.96\sqrt{\frac{0.1(1-0.1)}{250}}=0.1372$

So then we can conclude that the true proportion of women with cosmetic dermatitis from using mascara at 95% of confidence is between (0.0628 and 0.1372)

c) For this case we see that both confidence intervals contains the value of 0.12 so then we can't conclude that only one group is referenced at the significance level of 0.05 used.

Step-by-step explanation:

Part a

The estimated proportion of women with cosmetic dermatitis from using eye shadow is given by:

$\hat p =\frac{12}{131}= 0.0916$

The confidence interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96$

The confidence interval for the proportion is given by the following formula:

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

Replacing we got:

$0.0916 - 1.96\sqrt{\frac{0.0916(1-0.0916)}{131}}=0.0422$

$0.0916 + 1.96\sqrt{\frac{0.0916(1-0.0916)}{131}}=0.1410$

So then we can conclude that the true proportion of women with cosmetic dermatitis from using eye shadow at 95% of confidence is between (0.0422 and 0.1410)

Part b: A 95% confidence interval for the women with cosmetic dermatitis from using mascara

$\hat p = \frac{25}{250}= 0.1$

$0.1 - 1.96\sqrt{\frac{0.1(1-0.1)}{250}}=0.0628$

$0.1 + 1.96\sqrt{\frac{0.1(1-0.1)}{250}}=0.1372$

So then we can conclude that the true proportion of women with cosmetic dermatitis from using mascara at 95% of confidence is between (0.0628 and 0.1372)

Part c: Suppose you are informed that the true proportion with a nickel allergy for one of the two groups (eye shadow or mascara) is .12. Can you determine which group is referenced? Explain.

For this case we see that both confidence intervals contains the value of 0.12 so then we can't conclude that only one group is referenced at the significance level of 0.05 used.

7 0

2 years ago

A sociologist wants to determine if the life expectancy of people in africa is less than the life expectancy of people in asia.

Colt1911 [192]

Answer:

The sample statistics are attached.

First, we need to determine the hypothesis.

The null hypothesis should be: $H_{o} : u_{africa} \geq u_{asia}$ .

The alternative hypothesis should be: $H_{a}: u_{africa}$

The next step is about calculating the t statistics based on the samples. This t test will give the probability value or p-value, which determines if there's enough to reject the null hypothesis. The formula we need to use to find the t-value is: $t=\frac{x_{1}-x_{2} }{\sqrt{\frac{s_{1} ^{2} }{n_{1} } +\frac{s_{2} ^{2} }{n_{2} } } }$

Replacing all the values into the formula, we have:

$t=\frac{52.4-58.1}{\sqrt{\frac{(7.4)^{2} }{45}+\frac{(8.8)^{2} }{35} } } \\t=\frac{-5.7}{\sqrt{1.2+2.2} } =\frac{-5.7}{1.8} =-3.2$

Therefore, the t-value is -3.2.

Now, we using a level of significance of 0.01, and a degree of freedom (df) of 34, we use the t-table to find the p-value for this results. (df = N -1; in this case, we take the smaller sample, which is 35, giving us 34 of df).

Therefore, according to the table attached, the p-value is less than 0.01, which is less than our level of significance. This result means that the null hypothesis is rejected. In other words, there's enough evidence to say that the life expectancy of people in Africa is less than the life of expectancy of people in Asia.

3 0

2 years ago

Z to the power of 2 =1

stiv31 [10]

That would be written as:

$z^{2} = 1$

And the step-by-step equation would be:

$z^{2} = 1$ → we take the 2 to the right side of the equation and do the IO*

$z = \sqrt{1}$ →we solve for $\sqrt{1}$

$z = 1$ → final answer

*Ps - IO is not an existing term and stands for inverse operation. In this case, because when we take to 2 to the right side of the equation (the 2 is a power) it'll have to turn into a square root (because exponents and roots are inverse operations)

Hope it helped,

BioTeacher101

3 0

2 years ago

Rachel has 30 pounds of a mixture of candy that sells for $1.00/lb. If lollipops sell for $0.95/lb and caramel candies sell for

Butoxors [25]

20 pounds of lollipops. 20 x .95 = 19, 10 x 1.1 = 11. sorry i'm awful at explaining math.

8 0

2 years ago

Read 2 more answers