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3 years ago

Factor x^2+7x+10=0 plz

Mathematics

1 answer:

Musya8 [376]3 years ago

6 0

Given:

$x^2+7x+10=0$

Since the quadratic equation is equal to 0, we need to solve for x. Let's factor. Since a ≠ 1, we can easily solve. We need to find out what factors of 10 add up to 7. I know that 5*2 = 10 and 5+2 = 7. This fits out problem perfectly. Now that we have that, we can simplify it into two binomials:

$(x+2)(x+5)$

Now, if it was not equal to zero, we would be done. However, we are not done. We need to set both terms equal to 0 to solve for x.

$x+2=0$

To isolate x, subtract 2 from both sides to cancel the +2 on the left.

$x=-2$

Let's do the other one:

$x+5=0$

Same thing, subtract 5 from both sides to isolate x.

$x=-5$

So, in conclusion, your solutions are:

$x=-2$

$x=-5$

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You flip a fair coin until you see three tails in a row. What is the average number of headsthat you’ll see until gettingTTT?

Verdich [7]

Answer:

Step-by-step explanation:

From the given information:

suppose, Y is the number of times a coin is being flipped.

If the coin is flipped for the first time and we get H, then we have:

TTT = $\dfrac{1}{2}(Y+1)$

Afterward, if we get H, then we waste two times plus the probability of this event $\dfrac{1}{4}$ .

Therefore, we have : $\dfrac{1}{4}(Y+2)$

Afterward, if we get H, then we waste three times plus the probability of this event $\dfrac{1}{8}$ .

Therefore, we have : $\dfrac{1}{8}(Y+3)$

If we got T at the third time, then;

T = $\dfrac{1}{8}(3)$

Thus, average number of headsthat you’ll see until gettingTTT can be expressed as:

$= \dfrac{1}{2}(Y+1)+ \dfrac{1}{4}(Y+2)+ \dfrac{1}{8}(Y+3)+ \dfrac{1}{8}(3)$

= 14

7 0

3 years ago

The amount of time that a customer spends waiting at an airport check-in counter is a random variable with mean 8.2 minutes and

masya89 [10]

Answer:

a) There is a 100% probability that the (sample) average time waiting in line for these customers is less than 10 minutes.

b) There is a 100% probability that the (sample) average time waiting in line for these customers is between 5 and 10 minutes.

c) There is a 0% probability that the (sample) average time waiting in line for these customers is less than 6 minutes.

d) Because there are less observations, it would be less accurate.

e) Because there are moreobservations, it would be more accurate.

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $\frac{\sigma}{\sqrt{n}}$

Problems of normally distributed samples can be 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.

In this problem, we have that:

The amount of time that a customer spends waiting at an airport check-in counter is a random variable with mean 8.2 minutes and standard deviation 1.5 minutes. This means that $\mu = 8.2, \sigma = 1.5$ .

Suppose that a random sample of n = 49 customers is observed

This means that $s = \frac{1.5}{\sqrt{49}} = 0.21$ .

(a) Less than 10 minutes.

This probability is the pvalue of Z when $X = 10$ . So:

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

$Z = \frac{10 - 8.2}{0.21}$

$Z = 8.57$

$Z = 8.57$ has a pvalue of 1.

This means that there is a 100% probability that the (sample) average time waiting in line for these customers is less than 10 minutes.

(b) Between 5 and 10 minutes.

This probability is the pvalue of Z when X = 10 subtracted by the pvalue of Z when X = 5.

From a), we have that the zscore of X = 10 has a pvalue of 1.

For X = 5.

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

$Z = \frac{5 - 8.2}{0.21}$

$Z = -15.24$

$Z = -15.24$ has a pvalue of 0.

Subtracting, we have that there is a 100% probability that the (sample) average time waiting in line for these customers is between 5 and 10 minutes.

(c) Less than 6 minutes.

This probability is the pvalue of Z when X = 6. So:

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

$Z = \frac{6 - 8.2}{0.21}$

$Z = -10.48$

$Z = -10.48$ has a pvalue of 0.

This means that there is a 0% probability that the (sample) average time waiting in line for these customers is less than 6 minutes.

(d) If you only had two observations instead of 49 observations, would you believe that your answers to parts (a), (b), and (c), are more accurate or less accurate? Why?

The less observations there are, the less acurrate our results are.

So, because there are less observations, it would be less accurate.

(e) If you had 1,000 observations instead of 49 observations, would you believe that your answers to parts (a), (b), and (c), are more accurate or less accurate? Why?

The more observations there are, the more acurrate our results are.

So, because there are moreobservations, it would be more accurate.

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3 years ago

If y varies directly as x, and y is 16 when x is 4, when y= 24 what is the value of x?

sergejj [24]

Answer:

x = 6 possibly

Step-by-step explanation:

I am just an algebra student, but if I am correct I would appreciate a crown.

16/4 is 4, so i assumed that was the geometric pattern, so i divided 24 by 4 and got 6.

Hoped this helped.

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4 years ago

Which function has a range of all real numbers greater than or equal to -4

shtirl [24]

Answer:

The domain is all real numbers, and the range is all real numbers f(x) such that f(x) ≤ 4. You can check that the vertex is indeed at (1, 4). Since a quadratic function has two mirror image halves, the line of reflection has to be in the middle of two points with the same y value.

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3 years ago

Josie is training for a race the ratio of the number of minutes she wants to the number of miles she wants is 2043 she plans to

guajiro [1.7K]

Answer:

Josie takes 0.93 minutes to run 2 miles.

Step-by-step explanation:

We are given the following in the question:

Ratio:

Number of minutes: Number of miles = 20:43

Josie wants to run 2 miles. We have to find the number of minutes she need to run to maintain the ration.

Let x be the number of minutes Josie run.

This can be done in the following manner:

$\dfrac{20}{43} = \dfrac{x}{2}\\\\\Rightarrow x = \dfrac{20}{43}\times 2\\\\\Rightarrow x = 0.93$

Thus, Josie takes 0.93 minutes to run 2 miles.

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3 years ago