MATHEMATICS COLLEGE

Find the midpoint of the segment with the endpoints: (-2, 6) and (-3, 7)

Answers

Answer 1

Answer:

Answer:

The midpoint is ( -2.5, 6.5)

Step-by-step explanation:

To find the x coordinate of the midpoint, add the x coordinates of the endpoints and divide by 2

(-2+-3)/2 = -5/2 = -2.5

To find the y coordinate of the midpoint, add the y coordinates of the endpoints and divide by 2

(6+7)/2 = 13/2 = 6.5

The midpoint is ( -2.5, 6.5)

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A local BBQ restaurants offers 2 side dishes with a lunch plate. There are 7 side dishes. How many choices of side dishes does a customer have

Answers

Step-by-step explanation:

This is a question that bothers combination. Combination has to do with selection.

When selecting r objects out of a pool of n objects, the number of ways this can be done is:

nCr = n!/(n-r)!r!

If a local BBQ restaurants offers 2 side dishes with a lunch plate, and there are 7 side dishes, the number of choices that the customer have is expressed as:

7C2 = 7!/(7-2)!2!

7C2 = 7!/(5)!2!

7C2 = 7*6*5!/5! * 2

7C2 = 7*6/2

7C2 = 42/2

7C2 = 21 choices

Hence the customer has 21 choices of side dishes to make

Simplify the expression- 3 - 5/6 / 5/2

Answers

Answer:

10/3

Step-by-step explanation:

-3-5/6/5/2=-10/3

decimal 0.33333 reaccuring

Answer:

Step-by-step explanation:

A smoothie recipe calls for 3 cups of soy milk, 2 frozen bananas and, 1 tablespoon of chocolate syrup. Write a sentence that uses a ratio to describe this recipe.

Answers

Answer:

3:2:1

Step-by-step explanation:

Dmitri wants to cover the top and sides of this box with glass tiles that are 1 cm square. How many tiles will he need? Dmitri will need [Blank] glass tiles. The dimentions are...26 , 15, 8.

Answers

The number of tiles needed to cover the surface area of the box excluding the bottom is: 1,046 tiles.

What is the Surface Area of a Box?

The surface area of a box is the area surrounding all its faces. A box has 6 rectangular faces. Therefore, the total surface area of the box equals the sum of all 6 rectangular faces.

What is the Surface Area of a Box?

SA = 2(lw + lh + hw), where:

l = length
w = width
h = height of the box

The image attached below shows the box Dmitri wants to cover. Since the bottom of the box would be excluded, therefore:

The surface area to be covered = surface area of the box - area of the bottom rectangular face

The surface area to be covered = 2(lw + lh + hw) - (l)(w)

l = 26

w = 15

h = 8

Substitute

The surface area to be covered = 2(l×w + lh + hw) - (l)(w) = 2·(15·26+8·26+8·15) - (26)(15) =

The surface area to be covered = 1436 - 390 = 1,046 cm

Area of one tile = 1 cm square

Number of tiles needed = 1,046/1

Number of tiles needed = 1,046 tiles.

Learn more about Surface Area of a Box on:

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The operator of a pumping station has observed that demand for water during early afternoon hours has an approximately exponential distribution with mean 100 cfs (cubic feet per second). (a) Find the probability that the demand will exceed 190 cfs during the early afternoon on a randomly selected day. (Round your answer to four decimal places.)

Answers

Answer:

The probability that the demand will exceed 190 cfs during the early afternoon on a randomly selected day is $P(Y>190)=\frac{1}{e^{(19)/(10)}}\approx 0.1496$

Step-by-step explanation:

Let Y be the water demand in the early afternoon.

If the random variable Y has density function f (y) and a < b, then the probability that Y falls in the interval [a, b] is

$P(a\leq Y \leq b)=\int\limits^a_b {f(y)} \, dy$

A random variable Y is said to have an exponential distribution with parameter $\beta > 0$ if and only if the density function of Y is

$f(y)=\left \{ {{(1)/(\beta)e^{-(y)/(\beta) }, \quad{0\:\leq \:y \:\leq \:\infty} } \atop {0}, \quad elsewhere} \right.$

If Y is an exponential random variable with parameter β, then

mean = β

To find the probability that the demand will exceed 190 cfs during the early afternoon on a randomly selected day, you must:

We are given the mean = β = 100 cubic feet per second

$P(Y>190)=\int\limits^(\infty)_(190) {(1)/(100)e^(-y/100) } \, dy$

Compute the indefinite integral $\int (1)/(100)e^{-(y)/(100)}dy$

$(1)/(100)\cdot \int \:e^{-(y)/(100)}dy\n\n\mathrm{Apply\:u \:substitution}\:u=-(y)/(100)\n\n(1)/(100)\cdot \int \:-100e^udu\n\n(1)/(100)\left(-100\cdot \int \:e^udu\right)\n\n(1)/(100)\left(-100e^u\right)\n\n\mathrm{Substitute\:back}\:u=-(y)/(100)\n\n(1)/(100)\left(-100e^{-(y)/(100)}\right)\n\n-e^{-(y)/(100)}$

Compute the boundaries

$\int _(190)^(\infty \:)(1)/(100)e^{-(y)/(100)}dy=0-\left(-\frac{1}{e^{(19)/(10)}}\right)$

$\int _(190)^(\infty \:)(1)/(100)e^{-(y)/(100)}dy=\frac{1}{e^{(19)/(10)}}\approx 0.1496$

The probability that the demand will exceed 190 cfs during the early afternoon on a randomly selected day is $P(Y>190)=\frac{1}{e^{(19)/(10)}}\approx 0.1496$

An train station has determined that the relationship between the number of passengers on a train and the total weight of luggage stored in the baggage compartment can be estimated by the least squares regression equation y=103+30x. Predict the weight of luggage for a flight with 86 passengers.

Answers

Answer:

2683

Step-by-step explanation:

Using the linear regression equation that predict the relationship between the weight of the luggage and the total number of passenger y = 103 + 30x, we can plug in the number of passenger x = 86 to predict the weight of the luggage on a flight:

y = 103 + 30*86 = 2683

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