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stiv31 [10]
2 years ago
12

Evaluate, and round your answer to the nearest hundredth.

Mathematics
1 answer:
VashaNatasha [74]2 years ago
7 0

Answer:

  (d)  -1.83

Step-by-step explanation:

The explicit expression for the sum is ...

  S = (-11/5)×(1 -(-1/5)^10)/(1 -(-1/5)) = -2.2(1 -1.024×10^-7)/1.2

  S = -1.8333331456

The sum is approximately -1.83.

_____

<em>Additional comment</em>

For a sum of a sequence with multiplier 'a' and common ratio r, we find ...

  \displaystyle S=\sum_{n=1}^{10}ar^n=ar+ar^2+ar^3+\dots+ar^{10}\\\\rS=ar^2+ar^3+\dots+ar^{10}+ar^{11}\\\\S-rS=ar+(ar^2-ar^2)+(ar^3-ar^3)+\dots+(ar^{10}-ar^{10})-ar^{11}\\\\S=\dfrac{ar-ar^{11}}{1-r}=ar\dfrac{1-r^{10}}{1-r}

__

A calculator or spreadsheet can also find the sum for you.

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On one side of the balance scale, Henry placed a 6-gram weight. On the other side of the scale, he placed a ballet slipper.
olchik [2.2K]

Answer:

  • <u><em>A. 6,000 miligrams</em></u>

Explanation:

A <em>balance scale</em> is balanced when the weights on both sides are equal. Then, since the image shows that both sides are equal, the weight of the <em>6-gram weight</em>, placed by Henry on one side of the balance scale is equal to the weight of the <em>ballet slipper </em>placed on the other side.

  • Weight of the balance slipper = weight of the 6-gram weight
  • Weight of the balance slipper = 6 grams

<u>Conversion of units: </u>

  • 6 grams × 1,000miligrams/1gram = 6,000 miligrams

  • Weight of the balance slipper = 6,000 miligrams

That is the option A.

7 0
3 years ago
Use distributive property to calculate the following.
sattari [20]

Answer:

Step-by-step explanation:

1. 2x + y

2. 48 +  60 = 108

3. 840 - 210 = 630

4 0
2 years ago
SUPER EASY What is 4a + 5 × S simplified
Elodia [21]

Answer:

4a + 5S

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Find the exact value of the following expression (without using a calculator): tan(Sin^-1 x/2)
Sati [7]

Answer:

tan(Sin^-1 x/2)=  \frac{x/2}{\sqrt{1-x^{2}/4 } }

Step-by-step explanation:

Let sin^-1 x/2= θ

then sinθ= x/2

on the basis of unit circle, we have a triangle with hypotenuse of length 1,   one side of length x/2 and opposite angle of θ.

          tan(Sin^-1 x/2) = tanθ

           tanθ= sinθ/cosθ

as per trigonometric identities cosθ= √(1-sin^2θ)

           tanθ= sinθ/ √(1-sin^2θ)

substituting the value sinθ=x/2 in the above equation

             tanθ= \frac{x/2}{\sqrt{1-x^{2}/4 } }

now substituting the value sin^-1 x/2= θ in above equation

             tan(sin^-1 x/2) =  \frac{x/2}{\sqrt{1-x^{2}/4 } }

!

3 0
3 years ago
A = 2√3 ft.;c = 4 ft.<br> A = 8√3 sq. ft.<br> True<br> False
Vladimir79 [104]

False . The equation a= 2√3 ft.;c = 4 ft is: A= 2√3 ft².

<h3>Area of the triangle</h3>

Given:

a = 2√3 ft,

c = 4 ft,


Lengths of the sides of a right triangle = a and b

Hypotenuse= c

Hence:

<h3>Using Pythagorean theorem</h3>

c²=a²+b²

4²=(2√3)²+b²

16=12+b²

4=b²

b=2

Area of triangle

A=1/2×a×b

A=1/2×2√3×2

A=4√3÷2

A=2√3 sq.ft

The Area of the triangle is 2√3 ft².

Learn more about Area of the triangle here:

brainly.com/question/4441121

#SPJ1

8 0
2 years ago
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