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3 years ago

14

Jim bought a fishing rod for $42. This price was 70% of the original price. What was the original price?

1 answer:

Dmitry [639]3 years ago

5 0

Answer:

54.6

Step-by-step explanation:

42 = 70%

100% - 70% = .30%

42 x 1.3 = 54.6

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Find the 12th term of the geometric sequence 5, -25, 125, ...5,−25,125,...

katovenus [111]

Answer:

$a_{12}=-244140625$

Step-by-step explanation:

Considering the geometric sequence

$5,-25,\:125,\:...$

$a_1=5$

As the common ratio ' $r$ ' between consecutive terms is constant.

$\mathrm{Compute\:the\:ratios\:of\:all\:the\:adjacent\:terms}:\quad \:r=\frac{a_{n+1}}{a_n}$

$r=\frac{-25}{5}=-5$

$r=\frac{125}{-25}=-5$

The general term of a geometric sequence is given by the formula:

$a_n=a_1\cdot \:r^{n-1}$

where $a_1$ is the initial term and $r$ the common ratio.

Putting $n = 12$ , $r = -5$ and $a_1=5$ in the general term of a geometric sequence to determine the 12th term of the sequence.

$a_n=a_1\cdot \:r^{n-1}$

$a_n=5\left(-5\right)^{n-1}$

$a_{12}=5\left(-5\right)^{12-1}$

$=5\left(-5^{11}\right)$

$\mathrm{Remove\:parentheses}:\quad \left(-a\right)=-a$

$=-5\cdot \:5^{11}$

$\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^{b+c}$

$=-5^{1+11}$ ∵ $5\cdot \:5^{11}=\:5^{1+11}$

$=-244140625$

Therefore,

$a_{12}=-244140625$

6 0

3 years ago

I didnt mean to click on the 31.50 but what is the answer ?

Genrish500 [490]

Answer:

D. $67.50

Step-by-step explanation:

A ticket costs $5.25, a drink costs $2.00, and a popcorn costs 4.00. Each person in the group buys all of these. So we know that each person is paying:

4.00 + 2.00 + 5.25 = 11.25

Since there are 6 people in the group we can multiply that by 6:

11.25 * 6 = 67.50

4 0

2 years ago

Read 2 more answers

Rewrite using exponential notation \root(6)((4\pi )^(3))

Nezavi [6.7K]

$~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] ~\dotfill\\\\ \sqrt[6]{(4\pi )^3}\implies (4\pi )^{\frac{3}{6}}\implies (4\pi )^{\frac{1}{2}}$

5 0

2 years ago

Help please……..??.?.?.?.?.?

aleksklad [387]

9514 1404 393

Answer:

c) 16,500 m³

d) 277,088 mm³

a) V = LWH

b) V = πr²h

Step-by-step explanation:

The relevant volume formulas are ...

rectangular pyramid: V = 1/3LWH
cylinder: V = πr²h
rectangular prism: V = LWH

__

13c. The pyramid formula above tells us the volume is ...

V = 1/3(60 m)(15 m)(55 m) = 16,500 m³

__

13d. The cylinder formula above tells us the volume is ...

V = π(35 mm)²(72 mm) ≈ 277,088 mm³ ≈ 277 mL

__

14a. The shape appears to be a rectangular prism, so its volume is given by the formula ...

V = LWH . . . . . where L, W, H represent the length, width, and height

__

14b. The volume of a cylinder is given by the formula ...

V = πr²h . . . . . where r, h represent the radius and height (length)

7 0

3 years ago

An eagle perched 40 ft up in a tree looks down at a 35 degree angle(angle of depression) and spots a vole. How far is the vole f

maria [59]

Answer:

$X=49ft$

Step-by-step explanation:

From the question we are told that:

Height of Eagle $h=40ft$

Angle of depression $\theta=35\textdegree$

Generally the trigonometry equation for diagonal X is mathematically given by

$Cos\theta \textdegree=\frac{Adjacent}{Hypotenuse} }$

$Cos\theta \textdegree=\frac{h}{X} }$

$X=\frac{40}{Cos 35 } }$

$X=48.83ft$

$X=49ft$

3 0

3 years ago