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2 years ago

The endpoints of CD are C(3,−5) and D(7, 9). The coordinates of the midpoint M of CD are?

Mathematics

1 answer:

Nutka1998 [239]2 years ago

3 0

Answer:

M(5,2)

Step-by-step explanation:

We use the midpoint rule:

$( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} )$

We just have to find the arithmetic mean of the x and y-coordinates.

The endpoints of CD are given as C(3,−5) and D(7, 9).

We substitute these values to get:

$( \frac{7 + 3}{2}, \frac{9 + - 5}{2} )$

$( \frac{10}{2}, \frac{4}{2} )$

$(5, 2)$

Therefore the coordinates of the midpoint M of CD are (5,2)

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Maria records random speeds from three different Internet providers in the table. Provider Download Speed (megabits per second)

Igoryamba

Answer:

Able Cable

Step-by-step explanation:

Mean Value of Samples

It's central tendency statistics measure that gives one representative value out of a complete dataset. It can be computed as the sum of the values by the number of values:

$\displaystyle \bar x=\frac{\sum x_i}{n}$

We need to evaluate the mean value of the three internet providers mentioned in the question.

For CityNet:

$\displaystyle \bar x_1=\frac{3.6+3.7+3.7+3.6+3.9}{5}=3.7$

For Able Cable:

$\displaystyle \bar x_2=\frac{3.9+3.9+4.1+4.0+4.1}{5}=4.0$

And for Tel-N-Net:

$\displaystyle \bar x_3=\frac{3.9+3.7+4.0+3.6+3.8}{5}=3.8$

We can conclude Able Cable offers the fastest mean downloading internet speed

7 0

2 years ago

An certain brand of upright freezer is available in three different rated capacities: 16 ft3, 18 ft3, and 20 ft3. Let X = the ra

ruslelena [56]

Answer:

$E(X)=16\cdot 0.3+18\cdot 0.1+20\cdot 0.6=18.6$

$E(X^2)=16^2\cdot 0.3+18^2\cdot 0.1+20^2\cdot 0.6=349.2$

$V(X) = E(X^2)-[E(X)]^2=349.2-(18.6)^2=3.24$

The expected price paid by the next customer to buy a freezer is $466

Step-by-step explanation:

From the information given we know the probability mass function (pmf) of random variable X.

$\left|\begin{array}{c|ccc}x&16&18&20\\p(x)&0.3&0.1&0.6\end{array}\right|$

Point a:

The Expected value or the mean value of X with set of possible values D, denoted by E(X) or μ is

$E(X) = $\sum_{x\in D} x\cdot p(x)$

Therefore

$E(X)=16\cdot 0.3+18\cdot 0.1+20\cdot 0.6=18.6$

If the random variable X has a set of possible values D and a probability mass function, then the expected value of any function h(X), denoted by E[h(X)] is computed by

$E[h(X)] = $\sum_{D} h(x)\cdot p(x)$

So $h(X) = X^2$ and

$E[h(X)] = $\sum_{D} h(x)\cdot p(x)\\E[X^2]=$\sum_{D}x^2\cdot p(x)\\ E(X^2)=16^2\cdot 0.3+18^2\cdot 0.1+20^2\cdot 0.6\\E(X^2)=349.2$

The variance of X, denoted by V(X), is

$V(X) = $\sum_{D}E[(X-\mu)^2]=E(X^2)-[E(X)]^2$

Therefore

$V(X) = E(X^2)-[E(X)]^2\\V(X)=349.2-(18.6)^2\\V(X)=3.24$

Point b:

We know that the price of a freezer having capacity X is 60X − 650, to find the expected price paid by the next customer to buy a freezer you need to:

From the rules of expected value this proposition is true:

$E(aX+b)=a\cdot E(x)+b$

We have a = 60, b = -650, and E(X) = 18.6. Therefore

The expected price paid by the next customer is

$60\cdot E(X)-650=60\cdot 18.6-650=466$

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2 years ago

In strategy games, in addition to the common 6-sided dice, dice having 4, 8, 12, or 20 sides are also used. determine the nu

Dovator [93]

There are 1010 possibilities for the 1010 sided die and 66 possibilities for the 66 sided die. Please mark Brainliest!!!

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2 years ago

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Mel slides down waterslide A, and Victor slides down waterslide B. After 2 seconds, Mel was 50 feet in the air, and after 5 seco

antiseptic1488 [7]

Mel moves 50-35=15 feet in 5-2=3 seconds. Descent rate=15/3=5 ft/sec.
Victor moves 60-50=10 feet in 4-1=3 seconds. Descent rate=10/3=3⅓ ft/sec. Mel is faster at 5 ft/sec.

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2 years ago

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For which values of k does the system of linear equations have zero, one, or an infinite number of solutions? [Note: not all thr

anastassius [24]

Answer:

For k = 36, there is 0 solutions

For other values of k, there is 1

We never got infinite solutions on the system.

Step-by-step explanation:

We have 2 unknowns and 2 equations:

E1 8x1 + x2 = 18

E2 k*22 x1 + 9 x2 = 18

If we multiply the E1 by 9 we obtain

E3 72 x1 + 9x2 = 162

if we substract E3 with E2 we obtain

(72- 2k) x1 = 144

Thus,

x1 = 144/ (72-2k)

That is, if 72-2k = 0, otherwise there is no solution. And 72-2k = 0 when k = 72/2 = 36.

If k is not 36, then

x1 = 144/(72-2k) and we can replace this value to obtain x2 by using E1

x2 = 18-8x1 = 18- 8 * (144/72-2k)

Which is a specific number that depends only on k. Thus,

for k = 36, there is 0 solutions

for other values of k, there is unique solution.

4 0

2 years ago