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3 years ago

An isosceles right-angled triangle is shown.

Mathematics

1 answer:

Bad White [126]3 years ago

6 0

Answer:

$\boxed{x=4}$

Step-by-step explanation:

Area of triangle = 0.5 × Base × Height

→ Substitute in the values

200 = 0.5 × 5x × 5x

→ Simplify

200 = 12.5x²

→ Divide both sides by 12.5

16 = x²

→ Square root both sides

4 = x ∴ x = 4

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What is the product? (x+3)(2x - 1) 2x²-3 2x²+66 O 2x²+5x-3 2x²+6x-3

Bess [88]

It’s 2x^2 + 5x - 3.

5 0

2 years ago

Suppose X, Y, and Z are random variables with the joint density function f(x, y, z) = Ce−(0.5x + 0.2y + 0.1z) if x ≥ 0, y ≥ 0, z

kompoz [17]

$f_{X,Y,Z}(x,y,z)=\begin{cases}Ce^{-(0.5x+0.2y+0.1z)}&\text{for }x\ge0,y\ge0,z\ge0\\0&\text{otherwise}\end{cases}$

is a proper joint density function if, over its support, $f$ is non-negative and the integral of $f$ is 1. The first condition is easily met as long as $C\ge0$ . To meet the second condition, we require

$\displaystyle\int_0^\infty\int_0^\infty\int_0^\infty f_{X,Y,Z}(x,y,z)\,\mathrm dx\,\mathrm dy\,\mathrm dz=100C=1\implies \boxed{C=0.01}$

b. Find the marginal joint density of $X$ and $Y$ by integrating the joint density with respect to $z$ :

$f_{X,Y}(x,y)=\displaystyle\int_0^\infty f_{X,Y,Z}(x,y,z)\,\mathrm dz=0.01e^{-(0.5x+0.2y)}\int_0^\infty e^{-0.1z}\,\mathrm dz$

$\implies f_{X,Y}(x,y)=\begin{cases}0.1e^{-(0.5x+0.2y)}&\text{for }x\ge0,y\ge0\\0&\text{otherwise}\end{cases}$

Then

$\displaystyle P(X\le1.375,Y\le1.5)=\int_0^{1.5}\int_0^{1.375}f_{X,Y}(x,y)\,\mathrm dx\,\mathrm dy$

$\approx\boxed{0.12886}$

c. This probability can be found by simply integrating the joint density:

$\displaystyle P(X\le1.375,Y\le1.5,Z\le1)=\int_0^1\int_0^{1.5}\int_0^{1.375}f_{X,Y,Z}(x,y,z)\,\mathrm dx\,\mathrm dy\,\mathrm dz$

$\approx\boxed{0.012262}$

7 0

3 years ago

There are 7052 boys and adults at carnival.

Basile [38]

Answer:

There are 6,296 children at the carnival

Step-by-step explanation:

The number of each group of people can be expressed as;

Number of boys (b)+number of adults (a)=7,052

b+a=7,052....equation 1

Number of girls (g)=Number of adults (a)-756

g=a-756....equation 2

But Number of girls (g)=number of boys (b)

Replacing the value of b in equation 1 with that of g in equation 2;

(a-756)+a=7,052

a+a=7,052+756

2 a=7,808

a=7,808/2

a=3,904

Replace the value of a in equation 2 with 3,904

g=3,904-756

g=3,148

But since g=b

g=b=3,148

b=3,148

Total number of children=Total number of boys (b)+total number of girls (g)

Total number of children=b+g

where;

b=3,148

g=3,148

replacing;

Total number of children=(3,148+3,148)=6,296

There are 6,296 children at the carnival

6 0

3 years ago

Sydney read 50 pages in 40 minutes. She reads at a constant rate.How many pages can Sydney read per minute?

7nadin3 [17]

Here we are given how much work is done in a fix time interval

then they ask to find the rate of doing the work .

in such problem we can find the rate of doing a work by using the formula :

amount of work done

--------------------------------------------------- = work done in unit time

Time taken to do that amount of work

In 40 minutes number of pages she reads = 50

In 1 minutes number of pages she would be reading = 50 /40

= 5/4 page

Answer 5/4 page .

3 0

3 years ago

Joe's Plumbing and Mark's Plumbing have different ways of charging their customers. The function defined by J(t)=45t represents

puteri [66]

Answer:

Joe's Plumbing charges more per hour ($45) than Mark's Plumbing (S40)

Step-by-step explanation:

Let

t ------> the number of hours

J(t) ---->the total amount in dollars that Joe's Plumbing charges

M(t) ---->the total amount in dollars that Mark's Plumbing charges

we know that

The linear equation in slope form is equal to

$f(x)=mx+b$

where

m is the slope or rate of the linear equation

b is the y-intercept (initial value)

In this problem we have

Joe's Plumbing

$J(t)=45t$

The slope or rate is equal to

$m=\$45\ per\ hour$

$b=\$0$

Mark's Plumbing

$M(t)=40t+25$

The slope or rate is equal to

$m=\$40\ per\ hour$

$b=\$25$

therefore

Joe's Plumbing charges more per hour ($45) than Mark's Plumbing (S40)

4 0

3 years ago