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3 years ago

Double bubble/ triple 100 points !!!!!!

Mathematics

2 answers:

viktelen [127]3 years ago

4 0

Answer:

Diagonal < Diameter

Step-by-step explanation:

The square will fit inside without touching if the diagonal length is less than the diameter

Diagonal = sqrt(7² + 7²)

7sqrt(2)

Diameter = 11

7sqrt(2) < 11

Because

(7sqrt(2))² < 11²

98 < 121

balu736 [363]3 years ago

3 0

Answer:

see below

Step-by-step explanation:

We need to find the diameter of the square

We can find this using the Pythagorean theorem

a^2+b^2 = c^2 where the legs are 7 and 7 and the diameter is c

7^2 +7^2 = c^2

49+49 = c^2

98 = c^2

Taking the square root of each side

sqrt(98) = sqrt(c^2)

9.899494937 = c

Since 9.9 is less than 11 which is the diameter of the circle it will never touch the circle.

Since the longest part of the square is less than the diameter of the circle, the square will fit inside the circle without touching

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The volume of a cube can be found using the equation V = s³, where V is the volume and s is the measure of one side of the cube.

Harrizon [31]

$V=s^3\\\\s^3=729\ in^3\\\\s=\sqrt[3]{729\ in^3}\\\\ s=\sqrt[3]{729} \ in$
Answer

$s=\sqrt[3]{9^3}\ in\\\\s=9\ in$

6 0

2 years ago

Read 2 more answers

Given that D(x) = 2x, select all of the following that are true statements

Keith_Richards [23]

Answer:

D(x) is a function

D(x) is a direct variation

D(x) is a rule for the set of points (5.10). (6, 12) and (-2,-4)

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $y/x=k$ or $y=kx$

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

In this problem

$D(x)=2x$

D(x) is a direct variation (linear function)

The variable x is the independent variable or input value

The variable D(x) is the dependent variable or output value

Verify each statement

case 1) D(x) is a function

The statement is true

see the explanation

case 2) x is the dependent variable

The statement is false

The variable x is the independent variable or input value

case 3) D(x) is a direct variation

The statement is true

see the explanation

case 4) D(x) is a rule for the set of points (5.10). (6, 12) and (-2,-4)

The statement is true

Because

For x=5

substitute in the linear equation

$D(x)=2(5)=10$ ---> is ok

For x=6

substitute in the linear equation

$D(x)=2(6)=12$ ---> is ok

For x=-2

substitute in the linear equation

$D(x)=2(-2)=-4$ ---> is ok

6 0

3 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

2 years ago

Write an equation in slope-intercept form for the line that has the given slope and

NARA [144]

Answer:

y = - x + 5 should be the answer. Hope this helps!

Step-by-step explanation:

8 0

2 years ago

1. The number of rabbits on an island is increasing exponentially.

Zina [86]

Answer:

There are approximately 114 rabbits in the year 10

Step-by-step explanation:

Exponential Growth

The natural growth of some magnitudes can be modeled by the equation:

$P=P_o(1+r)^t$

Where P is the actual amount of the magnitude, Po is its initial amount, r is the growth rate and t is the time.

We are given two measurements of the population of rabbits on an island.

In year 1, there are 50 rabbits. This is the point (1,50)

In year 5, there are 72 rabbits. This is the point (5,72)

Substituting in the general model, we have:

$50=P_o(1+r)^1$

$50=P_o(1+r)\qquad\qquad[1]$

$72=P_o(1+r)^5\qquad\qquad[2]$

Dividing [2] by [1]:

$\displaystyle \frac{72}{50}=(1+r)^{5-1}=(1+r)^{4}$

Solving for r:

$\displaystyle r=\sqrt[4]{\frac{72}{50}}-1$

Calculating:

r=0.095445

From [1], solve for Po:

$\displaystyle P_o=\frac{72}{(1+r)^5}$

$\displaystyle P_o=\frac{72}{(1.095445)^5}$

$P_o=45.64355$

The model can be written now as:

$P=45.64355(1.095445)^t$

In year t=10, the population of rabbits is:

$P=45.64355(1.095445)^{10}$

P = 113.6

$P\approx 114$

There are approximately 114 rabbits in the year 10

5 0

2 years ago