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3 years ago

Find the length of the segment that joins the points (-5, 4) and (6,-3).

Mathematics

1 answer:

Helen [10]3 years ago

7 0

Answer:

$\boxed {\boxed {\sf d=\sqrt{170} \ or \ d\approx 13.04}}}$

Step-by-step explanation:

We are asked to find the length of a segment or the distance between the 2 points. The formula for distance is:

$d= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2$

where (x₁ y₁) and (x₂, y₂) are the points. We are given the points ( -5, 4) and (6, -3). If we match the number and the corresponding variable, it is:

x₁= -5
y₁= 4
x₂= 6
y₂ = -3

Substitute the values into the formula.

$d= \sqrt{(6--5)^2+(-3-4)^2$

Solve inside the parentheses.

6--5 (Back to back negative signs become a positive)= 6+5 =11
-3-4= -7

$d= \sqrt{(11)^2+(-7)^2$

Solve the exponents.

(11)²= 11*11= 121
(-7)²= -7*-7= 49

$d= \sqrt {(121)+(49)$

Add.

$d= \sqrt {170}$

$d=13.0384048104$

Even though it's not specified, we could round to the nearest hundredth to make the answer more concise. The 8 in the thousandth place tells us to round the 3 to a 4 in the hundredth place.

13.0384048104

$d\approx 13.04$

The length of the segment is √170 or approximately 13.04.

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In a recent year, the ACT scores for the math portion of the test were normally distributed, with a mean of 21.1 and a standard

Natali5045456 [20]

Answer:

a) $P(X$

And we can find this probability using the normal standard table or excel:

$P(z$

b) $P(19$

And we can find this probability with this difference:

$P(-0.396$

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.

$P(-0.396$

c) $P(X>26)=P(\frac{X-\mu}{\sigma}>\frac{26-\mu}{\sigma})=P(Z>\frac{26-21.1}{5.3})=P(z>0.925)$

And we can find this probability using the complement rule and the normal standard table or excel:

$P(z>0.925)=1- P(Z$

d) We can consider unusual events values above or below 2 deviations from the mean

$Lower = \mu -2*\sigma = 21.1 -2*5.3 =10.5$

A value below 10.5 can be consider as unusual

$Upper = \mu +2*\sigma = 21.1 +2*5.3 =31.7$

A value abovr 31.7 can be consider as unusual

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Part a

Let X the random variable that represent the scores of a population, and for this case we know the distribution for X is given by:

$X \sim N(21.1,5.3)$

Where $\mu=21.1$ and $\sigma=5.3$

We are interested on this probability

$P(X$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(X$

And we can find this probability using the normal standard table or excel:

$P(z$

Part b

$P(19$

And we can find this probability with this difference:

$P(-0.396$

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.

$P(-0.396$

Part c

$P(X>26)=P(\frac{X-\mu}{\sigma}>\frac{26-\mu}{\sigma})=P(Z>\frac{26-21.1}{5.3})=P(z>0.925)$

And we can find this probability using the complement rule and the normal standard table or excel:

$P(z>0.925)=1- P(Z$

Part d

We can consider unusual events values above or below 2 deviations from the mean

$Lower = \mu -2*\sigma = 21.1 -2*5.3 =10.5$

A value below 10.5 can be consider as unusual

$Upper = \mu +2*\sigma = 21.1 +2*5.3 =31.7$

A value abovr 31.7 can be consider as unusual

6 0

3 years ago

You deposit $975.52 in a bank account. Find the balance after 4 years if the account pays 7.25% annual interest compounded quart

sladkih [1.3K]

Answer:

The final ballance will be $1300.37.

Step-by-step explanation:

In this case we have a compounded interest, in order to calculate the final balance we need to use the following formula:

S = P(1 + r/n)^(n*t)

Where S is the final balance, P is the initial investment, r is the rate of interest, t is the time and n is the rate at which it is compounded. Since we have all the values we can directly apply to the formula as follows:

S = 975.52*(1 + 0.0725/4)^(4*4)

S = 975.52*(1.018125)^(16)

S = 975.52*1.333

S = 1300.37

The final ballance will be $1300.37.

4 0

3 years ago

Need help + explanation!! ^_^

Paha777 [63]

780, or C, is correct. Since 9.75 is 1/80th of the actual measurement, we can set up an equation like this:

9.75 = 1/80x

Then multiply each side by 80:

780 = x

The actual building's height is 780 ft.

We can check this answer by plugging in 780 for x in the original equation:

9.75 = 1/80(780)

9.75 = 9.75

Check! ✓

3 0

3 years ago

4x - 30x3 -3x2 what is the answer to this problem

AnnyKZ [126]

Answer

4x-84

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