A cell phone tower services an area of 1,256

A and B have certain number of mangoes. A says to B, " If you give me 10 of your mangoes, I will have twice as many as left with

Stella [2.4K]

Answer:

A had 22 mangoes, B had 26 mangoes

Step-by-step explanation:

We can write the following system:

A + 10 = 2(B - 10) -- Equation 1

3(A - 10) = B + 10 -- Equation 2

A + 10 = 2B - 20 → A = 2B - 30 -- Equation 3 (Simplify Equation 1)

3(2B - 30 - 10) = B + 10 -- Equation 4 (Substitute 3 into 2)

3(2B - 40) = B + 10

6B - 120 = B + 10

5B = 130

B = 26 -- (Solve for B in Equation 4)

A = 2 * 26 - 30 = 22 -- (Substitute B = 26 into Equation 3)

7 0

2 years ago

In math class, Sam correctly multiplied 3.625×10-8 by 500, then reported his product in scientific notation.

Minchanka [31]

<h3><u>Question:</u></h3>

In math class, Sam correctly multiplied 3.625×10-8 by 500, then reported his product in scientific notation. What was the exponent in Sam’s product? A -16 B -10 C -7 D -5

<h3><u>Answer:</u></h3>

OPTION D

The exponent in Sam’s product is -5

<h3><u>Solution:</u></h3>

Given that,

In math class, Sam correctly multiplied $3.625 \times 10^{-8}$ by 500, then reported his product in scientific notation.

<em><u>To find: exponent in Sam’s product</u></em>

Let us first multiply 500 with $3.625 \times 10^{-8}$

$3.625 \times 10^{-8} \times 500 = 1812.5 \times 10^{-8}$

Then Sam has reported this answer in scientific notation

Lets understand what is scientific notation of any number.

Scientific notation is a way of representing number between 1 and 10 incluing 1 and excluding 10 multiplied by appropriate power of 10.

Let us rewrite the Sam's answer in scientific notation

<em><u>The format for writing a number in scientific notation is:</u></em>

(first digit of the number) followed by (the decimal point) and then (all the rest of the digits of the number), times (10 to an appropriate power).

In $1812.5 \times 10^{-8}$ , we move the decimal 3 times to left side

Since the decimal is moved left side, we multiply by $10^3$

$1812.5 \times 10^{-8} = 1.8125 \times 10^3 \times 10^{-8} \\\\1812.5 \times 10^{-8} = 1.8125 \times 10^{-5}$

Exponent is a quantity representing the power to which a given number or expression is to be raised

So in $1.8125 \times 10^{-5}$ exponent is -5

5 0

2 years ago

3.52 A coin is tossed twice. Let Z denote the number of heads on the first toss and W the total number of heads on the 2 tosses.

Rufina [12.5K]

Answer:

a) The joint probability distribution

P(0,0) = 0.36, P(1,0) = 0.24, P(2,0) = 0, P(0,1) = 0, P(1,1) = 0.24, P(2,1)= 0.16

b) P( W = 0 ) = 0.36, P(W = 1 ) = 0.48, P(W = 2 ) = 0.16

c) P ( z = 0 ) = 0.6

P ( z = 1 ) = 0.4

Step-by-step explanation:

Number of head on first toss = Z

Total Number of heads on 2 tosses = W

% of head occurring = 40%

% of tail occurring = 60%

P ( head ) = 2/5 , P( tail ) = 3/5

<u>a) Determine the joint probability distribution of W and Z </u>

P( W =0 |Z = 0 ) = 0.6 P( W = 0 | Z = 1 ) = 0

P( W = 1 | Z = 0 ) = 0.4 P( W = 1 | Z = 1 ) = 0.6

P( W = 1 | Z = 0 ) = 0 P( W = 2 | Z = 1 ) = 0.4

The joint probability distribution

P(0,0) = 0.36, P(1,0) = 0.24, P(2,0) = 0, P(0,1) = 0, P(1,1) = 0.24, P(2,1)= 0.16

<u>B) Marginal distribution of W</u>

P( W = 0 ) = 0.36, P(W = 1 ) = 0.48, P(W = 2 ) = 0.16

<u>C) Marginal distribution of Z ( pmf of Z )</u>

P ( z = 0 ) = 0.6

P ( z = 1 ) = 0.4

8 0

2 years ago

Nevaeh has $560 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax. She buys

AnnyKZ [126]

Answer:

The number of outfits she purchase with the left money = 3

Step-by-step explanation:

The exact question is as follows :

Given - Nevaeh has $560 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax. She buys a new bicycle for $383.32. She buys 4 bicycle reflectors for $9.09 each and a pair of bike gloves for $21.07. She plans to spend some or all of the money she has left to buy new biking outfits for $39.75 each.

To find - Write and solve an inequality which can be used to determine x where x, the number of outfits Nevaeh can purchase while staying within her budget.

Proof -

Given that,

Total money Nevaeh have = $ 560

She spent money on bicycle = $ 383.32

She spend money on 1 reflector = $ 9.09

As she buy 4 bicycle reflector, So

Total money spent on bicycle reflector = $ 4×9.09 = $ 36.36

She spend money on a pair of bike gloves = $ 21.07

So,

Total money she spend on the items = $ 383.32 + 36.36 + 21.07

= $ 440.75

⇒Total money she spend on the items = $ 440.75

So,

Total money Left = $ 560 - $ 440.75 = $ 119.25

Now,

She plans to spend some or all of the money she has left to buy new biking outfits for $ 39.75 each.

Let us assume ,

The number of outfits she purchase with the left money = x

AS,

each outfit cost = $ 39.75

So, x outfits cost = $ 39.75 x

Now,

$ 39.75 x = $ 119.25 (because total money left = $ 119.25)

⇒ x = $\frac{119.25}{39.75}$ = 3

∴ we get

The number of outfits she purchase with the left money = x = 3

6 0

1 year ago

What is the error due to using linear interpolation to estimate the value of sinxsin⁡x at x = \pi/3? your answer should have at

Serhud [2]

<h3>Answer:</h3>

using y = x, the error is about 0.1812
using y = (x -π/4 +1)/√2, the error is about 0.02620

<h3>Step-by-step explanation:</h3>

The actual value of sin(π/3) is (√3)/2 ≈ 0.86602540.

If the sine function is approximated by y=x (no error at x = 0), then the error at x=π/3 is ...

... x -sin(x) @ x=π/3

... π/3 -(√3)/2 ≈ 0.18117215 ≈ 0.1812

You know right away this is a bad approximation, because the approximate value is π/3 ≈ 1.04719755, a value greater than 1. The range of the sine function is [-1, 1] so there will be no values greater than 1.

___

If the sine function is approximated by y=(x+1-π/4)/√2 (no error at x=π/4), then the error at x=π/3 is ...

... (x+1-π/4)/√2 -sin(x) @ x=π/3

... (π/12 +1)/√2 -(√3)/2 ≈ 0.026201500 ≈ 0.02620

6 0

2 years ago