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3 years ago

14

For the expression, use a property to write an equivalent expression, tell which property you used. Please help, and thank you :

)

1 answer:

raketka [301]3 years ago

4 0

What about if you use the distributive property? You could do 1(x+13) because the 1 would distribute to the x and the 13 making it x+13. Hope that is helpful.

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What is the vertex of the graph of y = x^2 + 4x?

Sidana [21]

The answer is (-2,-4)

7 0

3 years ago

---- PLEASE HELP <3 .. with steps :( <3

Zielflug [23.3K]

1) 6, 18, 54

2) 5/3, 14/9, 41/27

3) 1.5, 2.5, 2.5

Step-by-step explanation:

1)

The function that we have in this problem is

$g(x)=3x$

We want to find the first 3 iterations.

The initial value is:

x = 2

To find the value of the 1st iteration, we just substitute this value into the expression of the function, and we get:

$g_1(x)=3x=3\cdot 2 = 6$

The to find the value of the 2nd iteration, we just substitute this value into the expression of the function, and we get:

$g_2(x)=3\cdot g_1(x)=3\cdot 6 = 18$

Finally, the 3rd iteraction is given by:

$g_3(x)=3g_2(x)=3\cdot 18=54$

2)

Here in this problem the function that we have to use is

$g(x)=\frac{1}{3}x+1$

The initial value is

$x=2$

So the first iteration is given by

$g_1(x)=\frac{1}{3}\cdot 2 + 1 = \frac{5}{3}$

To find the 2nd iteration, we substitute this value into g(x) again:

$g_2(x)=\frac{1}{3}g_1+1=\frac{1}{3}\cdot \frac{5}{3}+1=\frac{5}{9}+1=\frac{14}{9}$

Finally, to find the 3rd iteration, we substitute this value into g(x) again:

$g_3(x)=\frac{1}{3}\cdot \frac{14}{9}+1=\frac{14}{27}+1=\frac{41}{27}$

3)

The function in this problem is

$g(x)=-|x-2|+3$

The initial value is

x = 0.5

So, the first iteration is:

$g_1(x)=-1|0.5-2|+3=-1|-1.5|+3=-1\cdot 1.5 +3=-1.5+3=1.5$

The second iteration is given by

$g_2(x)=-|g_1-2|+3=-|1.5-2|+3=--0.5+3=2.5$

Finally, the 3rd iteration is

$g_3(x)=-|g_2-2|+3=-|2.5-2|+3=-0.5+3=2.5$

5 0

3 years ago

X^4-28x^2=0 solve algebraically

Paha777 [63]

$x^4 - 28x^2 = 0$

$x^2(x^2 - 28) = 0$

$x^2 = 0 \ \ or \ \ (x^2 - 28) = 0$

$x = 0 \ \ or \ \ x^2 = 28$

$x = 0 \ \ or \ \ x = \pm \sqrt{28}$

$x = 0 \ \ or \ \ x = \pm2 \sqrt{7}$

---------------------------------------------------
Answer : x = 0 or 2√7 or -2√7
---------------------------------------------------

8 0

3 years ago

Rockwell hardness of pins of a certain type is known to have a mean value of 50 and a standard deviation of 1.8. (Round your ans

Alenkinab [10]

Answer:

a) 0.011 = 1.1% probability that the sample mean hardness for a random sample of 17 pins is at least 51

b) 0.0001 = 0.1% probability that the sample mean hardness for a random sample of 45 pins is at least 51

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

$\mu = 50, \sigma = 1.8$

(a) If the distribution is normal, what is the probability that the sample mean hardness for a random sample of 17 pins is at least 51?

Here $n = 17, s = \frac{1.8}{\sqrt{17}} = 0.4366$

This probability is 1 subtracted by the pvalue of Z when X = 51. So

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{51 - 50}{0.4366}$

$Z = 2.29$

$Z = 2.29$ has a pvalue of 0.9890

1 - 0.989 = 0.011

0.011 = 1.1% probability that the sample mean hardness for a random sample of 17 pins is at least 51

(b) What is the (approximate) probability that the sample mean hardness for a random sample of 45 pins is at least 51?

Here $n = 17, s = \frac{1.8}{\sqrt{45}} = 0.2683$

$Z = \frac{X - \mu}{s}$

$Z = \frac{51 - 50}{0.0.2683}$

$Z = 3.73$

$Z = 3.73$ has a pvalue of 0.9999

1 - 0.9999 = 0.0001

0.0001 = 0.1% probability that the sample mean hardness for a random sample of 45 pins is at least 51

8 0

4 years ago

1. A Square shaped wooden plate has a diagonal length of 30cm. Can you find the Perimeter of plate ?

DerKrebs [107]

Answer:

84.85cm

Step-by-step explanation:

Let the sides of the square be x

The perimeter of the square = 4x

Get x using the pythagoras theorem

x^2 + x^2 = 30^2

2x^2 = 900

x^2 = 450

x = 21.21cm

Perimeter of the plate = 4(21.21)

Perimeter of the plate = 84.85cm

6 0

3 years ago