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2 years ago

What is the difference between independent choices and dependent choices in a problem?

1 answer:

7 0

A dependent variable is a variable whose variations depend on another variable—usually the independent variable. An Independent variable is a variable whose variations do not depend on another variable but the researcher experimenting.

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Write in exponential notation of 4x1000+9x100+0x10+7x1

Llana [10]

Answer

4000

900

Step-by-step explanation:

Not so sure about the answer though

5 0

2 years ago

Read 2 more answers

A satellite cable company charges an installation fee of $50 plus an additional $35.95 per month for service.

wolverine [178]

My answer would be 85.95

3 0

2 years ago

What is the volume of the composite figure? Explain your work. A complete answer should include how you broke up the figure, whi

Sphinxa [80]

Answer:

$15,000\:\mathrm{mm^3}$

Step-by-step explanation:

The composite figure consists of a square prism and a trapezoidal prism. By adding the volume of each, we obtain the volume of the composite figure.

The volume of the square prism is given by $V=s^2\cdot h$ , where $s$ is the base length and $h$ is the height. Substituting given values, we have: $V=14^2\cdot 30=196\cdot 30=5,880\:\mathrm{mm^3}$

The volume of a trapezoidal prism is given by $V=\frac{b_1+b_2}{2}\cdot l\cdot h$ , where $b_1$ and $b_2$ are bases of the trapezoid, $l$ is the length of the height of the trapezoid and $h$ is the height. This may look very confusing, but to break it down, we're finding the area of the trapezoid (base) and multiplying it by the height. The area of a trapezoid is given by the average of the bases ( $\frac{b_1+b_2}{2}$ ) multiplied by the trapezoid's height ( $l$ ).

Substituting given values, we get:

$V=\frac{14+24}{2}\cdot (30-14)\cdot 30,\\V=19\cdot 16\cdot 30=9,120\:\mathrm{mm^3}}$

Therefore, the total volume of the composite figure is $5,880+9,120=\boxed{15,000\:\mathrm{mm^3}}$ (ah, perfect)

Alternatively, we can break the figure into a larger square prism and a triangular prism to verify the same answer:

$V=30^2\cdot 14+\frac{1}{2}\cdot10\cdot 16\cdot 30=\boxed{15,000\:\mathrm{mm^3}}\checkmark$

8 0

2 years ago

HELP, Prove: (cos(x))/(sin(x)tan(x))=cot^2x

Mice21 [21]

Answer:

Steps shown below

Step-by-step explanation:

We will simplify this using definitions and identities. Let's start.

$\frac{cos(x)}{sin(x)tan(x)}$

Using $tanx=\frac{sinx}{cosx}$ , we have:

$\frac{cos(x)}{sin(x)\frac{sin(x)}{cos(x)}}\\=\frac{cos^2(x)}{sin^2(x)}$

Using $cot(x)=\frac{cos(x)}{sin(x)}$ , we have:

$\frac{cos^2(x)}{sin^2(x)}\\=cot^2(x)$

Hence, proved.

7 0

2 years ago

Read 2 more answers

Given an equilateral triangle that has an area of 1959 cm2. What is the length of its sides?

Nina [5.8K]

Equilateral
equi means equal
lateral means sides

all sides are equal
triangle has 3 sides

perimiter=side1+side2+side3
side1=side2=side3

area=1/2 times base times height
base=side
draw a line down the middle of te tiangle so you get 2 right triangles side by side
1/2base is one leg
base is hypotonuse
height is unknown
equilateral means that it is a 30-60-90 triangle with hypotonuse equal to 2x, height=x√3, bottom is x
1/2 times base times height=1959
1/2 times x times x√3=1959
multiply both sides by 2
(x^2)√3=3918
divide both sides by √3
x^2=3918/√3
square root both sides
x=47.5611
side=hypotonuse=2x
2x=2*47.5611
side=95.12222

legnth of each side is $2\sqrt{ \frac{3918}{ \sqrt{3} } }$ cm or about 95.12222 cm

7 0

2 years ago