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2 years ago

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The difference between number 20 and its opposite is what percentage of 200? (if you do not remember: opposite of 15 is −15; opp

osite of −7 is 7.) Answer:

2 answers:

True [87]2 years ago

8 0

20%

This is because 20 and it's opposite -20 is 40. (20 - -20 = 40). Then 40 is 20% of 200.

Fed [463]2 years ago

4 0

Answer:

20%

Step-by-step explanation:

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One fourth of all telephones at the office have built in speaker phones. One -half the phones with the built-in speaker phones h

Helga [31]

Answer:

$\frac{1}{8}$ of the phones in office has both a speaker phone and a conference-call capability

Step-by-step explanation:

Since total number of phones in the office is not given, the answer will be "in that terms".

let it be x

So built in speaker phones is (1/4)x

Hence conference call phones would be (1/2)(1/4x) = (1/8)x

Hence "1/8th of the phones in office has both a speaker phone and a conference-call capability"

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1 year ago

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A toy airplane climbs 30 vertical feet while traveling 50 feet horizontally. A toy helicopter climbs 20 feet while traveling 40

Amiraneli [1.4K]

Answer:

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Step-by-step explanation:

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1 year ago

Sadie simplified the expression StartRoot 54 a Superscript 7 b cubed EndRoot, where a greater-than-or-equal-to 0, as shown colon

Nadusha1986 [10]

Answer:

Sadie's error is " she made error in step 2 $=\sqrt{3^2\times 6\times a^2\times a^5\times b^2\times b}$ where $a\geqslant 0$ "

Because she made error in splitting the powers to simplify the square root

<h3>Therefore the correct answer for Sadie's expression is $3ab\sqrt{6ab}$ where $a\geqslant 0$ </h3>

Step-by-step explanation:

Given that " Sadie simplified the expression StartRoot 54 a Superscript 7 b cubed EndRoot, where a greater-than-or-equal-to 0, "

It can be written as $\sqrt{54a^7b^3}$ where $a\geqslant 0$

The given expression is $\sqrt{54a^7b^3}$ where $a\geqslant 0$

To find Sadie's error and explain the correct answer :

Sadie's steps are

$\sqrt{54a^7b^3}$ where $a\geqslant 0$

$=\sqrt{3^2\times 6\times a^2\times a^5\times b^2\times b}$

$=3ab\sqrt{6a^5b}$

<h3> $\sqrt{54a^7b^3}=3ab\sqrt{6a^5b}$ where $a\geqslant 0$ </h3><h3><u>Now corrected steps are</u></h3>

$\sqrt{54a^7b^3}$ where $a≥0$

$=\sqrt{(9\times 6)(a^{6+1})(b^{2+1})$

$=\sqrt{(3^2\times 6)(a^6.a^1)(b^2.b^1)$ (by using the identity $a^{m+n}=a^m.a^n$

$=\sqrt{3^2\times 6\times ((a^3)^2.a)(b^2.b)$ (by using the identity $a^{mn}=(a^m)^n$ )

$=3ab\sqrt{6ab}$

Therefore $\sqrt{54a^7b^3}=3ab\sqrt{6ab}$ where $a\geqslant 0$

<h3>The correct answer is $3ab\sqrt{6ab}$ where $a\geqslant 0$ </h3>

Sadie's error is " she made error in step 2 $=\sqrt{3^2\times 6\times a^2\times a^5\times b^2\times b}$ " where $a\geqslant 0$

Because she made error in splitting the powers to simplify the square root

<h3>Therefore the correct answer for Sadie's expression is $3ab\sqrt{6ab}$ where $a\geqslant 0$ </h3>

5 0

1 year ago

Read 2 more answers

Barbara drives between Miami, Florida, and West Palm Beach, Florida. She drives 50 mi in clear weather and then encounters a thu

NeX [460]

Distance traveled in clear weather = 50 miles

Distance traveled in thunderstorm = 15 miles

Let speed in clear weather = x

⇒ Speed in thunderstorm = x-20

Total time taken for trip = 1.5 hours

We need to determine average speed in clear weather (i.e. x) and average speed in the thunderstorm (i.e. x-20 ).

Total time taken for trip = Time taken in clear weather + Time taken in thunderstorm

⇒ Total time taken for trip = $\frac{Distance covered in clear weather}{Speed in clear weather}$ + $\frac{Distance covered in thunderstorm}{Speed in thunderstorm}$

⇒ 1.5 = $\frac{50}{x}$ + $\frac{15}{x-20}$

⇒ 1.5 = $\frac{50(x-20)+15(x)}{(x)(x-20)}$

⇒ 15*x*(x-20) = 10*[50*(x-20)+15*x]

⇒ 15x² - 300x = 500x - 10,000 + 150x

⇒ 15x² - 300x = 650x - 10,000

⇒ 15x² - 950x + 10,000 = 0

⇒ 3x² - 190x + 2,000 = 0

The above equation is in the format of ax² + bx + c = 0

To determine the roots of the equation, we will first determine 'D'

D = b² - 4ac

⇒ D = (-190)² - 4*3*2,000

⇒ D = 36,100 - 24,000

⇒ D = 12,100

Now using the D to determine the two roots of the equation

Roots are: x₁ = $\frac{-b+\sqrt{D}}{2a}$ ; x₂ = $\frac{-b-\sqrt{D}}{2a}$

⇒ x₁ = $\frac{-(-190)+\sqrt{12,100}}{2*3}$ and x₂ = $\frac{-(-190)-\sqrt{12,100}}{2*3}$

⇒ x₁ = $\frac{190+110}{6}$ and x₂ = $\frac{190-110}{6}$

⇒ x₁ = $\frac{300}{6}$ and x₂ = $\frac{80}{6}$

⇒ x₁ = 50 and x₂ = 13.33

So speed in clear weather can be 50 mph or 13.33 mph. However, we know that in thunderstorm was 20 mph less than speed in clear weather.

If speed in clear weather is 13.33 mph then speed in thunderstorm would be negative, which is not possible since speed can't be negative.

Hence, the speed in clear weather would be 50 mph, and in thunderstorm would be 20 mph less, i.e. 30 mph.

7 0

2 years ago

The accompanying data are lengths (inches) of bears. Find the percentile corresponding to 65.5 in.

Jlenok [28]

Complete question is missing, so i have attached it.

Answer:

Percentile is 74th percentile

Step-by-step explanation:

All the lengths given are;

Bear Lengths 36.5 37.5 39.5 40.5 41.5 42.5 43.0 46.0 46.5 46.5 48.5 48.5 48.5 49.5 51.5 52.5 53.0 53.0 54.5 56.8 57.5 58.5 58.5 58.5 59.0 60.5 60.5 61.0 61.0 61.5 62.0 62.5 63.5 63.5 63.5 64.0 64.0 64.5 64.5 65.5 66.5 67.0 67.5 69.0 69.5 70.5 72.0 72.5 72.5 72.5 72.5 73.0 76.0 77.5

The number of lengths (inches) of bears given are 54 in number.

We are looking for the percentile corresponding to 65.5 in.

Looking at the lengths given, since they are already arranged from smallest to highest, let's locate the position of 65.5 in.

The position of 65.5 in is the 40th among 54 lengths given.

If the percentile is P, then;

P% x 54 = 40

P = (40 × 100)/54

P ≈ 74

3 0

1 year ago