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valentinak56 [21]

2 years ago

7

Haruka hiked several kilometers in the morning. She hiked only 6 kilometers in the afternoon, which was 25%, percent less than s

he had hiked in the morning. How many kilometers did Haruka hike in all?

1 answer:

Semenov [28]2 years ago

4 0

Answer:

14 km

Step-by-step explanation:

6 km in the afternoon

x km in the morning

6= x- 25%

6= 0.75x

x= 6/0.75

x= 8 km

total 6+8= 14 km

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T varies inversely as the square root of u.<br>t = 3 when u = 4.<br>Find t when u = 49.

RoseWind [281]

Answer:

t = $\frac{6}{7}$

Step-by-step explanation:

Given that t varies inversely as the square root of u then the equation relating them is

t = $\frac{k}{\sqrt{u} }$ ← k is the constant of variation

To find k use the condition t = 3 when u = 4, thus

k = t $\sqrt{u}$ = 3 × $\sqrt{4}$ = 3 × 2 = 6

t = $\frac{6}{\sqrt{u} }$ ← equation of variation

When u = 49, then

t = $\frac{6}{\sqrt{49} }$ = $\frac{6}{7}$

6 0

2 years ago

A boat tour guide expects his tour to travel at a rate of x mph on the first leg of the trip. On the return route, the boat trav

Georgia [21]

<em><u>The intervals included in solution are:</u></em>

$\frac{1}{x} + \frac{1}{x}-10\ge \frac{2}{24}\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:0$

<em><u>Solution:</u></em>

Given that,

A boat tour guide expects his tour to travel at a rate of x mph on the first leg of the trip

On the return route, the boat travels against the current, decreasing the boat's rate by 10 mph

The group needs to travel an average of at least 24 mph

<em><u>Given inequality is:</u></em>

$\frac{1}{x} + \frac{1}{x} - 10\geq \frac{2}{24}$

<em><u>We have to solve the inequality</u></em>

$\frac{1}{x} + \frac{1}{x} - 10\geq \frac{2}{24}\\\\\frac{2}{x} - 10\geq \frac{2}{24}$

$\mathrm{Subtract\:}\frac{2}{24}\mathrm{\:from\:both\:sides}\\\\\frac{2}{x}-10-\frac{2}{24}\ge \frac{2}{24}-\frac{2}{24}\\\\Simplify\\\\\frac{2}{x}-10-\frac{2}{24}\ge \:0$

$\frac{2}{x}-\frac{10}{1}-\frac{2}{24} \geq 0\\\\\frac{ 2 \times 24}{x \times 24} -\frac{10 \times 24}{1 \times 24} - \frac{2 \times x }{24 \times x}\geq 0\\\\\frac{48}{24x}-\frac{240x}{24x}-\frac{2x}{24x}\geq 0\\\\Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions\\\\\frac{48-240x-2x}{24x}\geq 0\\\\Add\:similar\:elements\\\\\frac{48-242x}{24x}\ge \:0$

$\mathrm{Multiply\:both\:sides\:by\:}24\\\\\frac{24\left(48-242x\right)}{24x}\ge \:0\cdot \:24\\\\Simplify\\\\\frac{48-242x}{x}\ge \:0\\\\Factor\ common\ terms\\\\\frac{-2\left(121x-24\right)}{x}\ge \:0\\\\\mathrm{Multiply\:both\:sides\:by\:}-1\mathrm{\:\left(reverse\:the\:inequality\right)}$

When we multiply or divide both sides by negative number, then we must flip the inequality sign

$\frac{\left(-2\left(121x-24\right)\right)\left(-1\right)}{x}\le \:0\cdot \left(-1\right)\\\\\frac{2\left(121x-24\right)}{x}\le \:0\\\\\mathrm{Divide\:both\:sides\:by\:}2\\\\\frac{\frac{2\left(121x-24\right)}{x}}{2}\le \frac{0}{2}\\\\Simplify\\\\\frac{121x-24}{x}\le \:0$

$\mathrm{Find\:the\:signs\:of\:the\:factors\:of\:}\frac{121x-24}{x}\\$

This is attached as figure below

From the attached table,

$\mathrm{Identify\:the\:intervals\:that\:satisfy\:the\:required\:condition:}\:\le \:\:0\\\\0$

<em><u>Therefore, solution set is given as</u></em>:

$\frac{1}{x} + \frac{1}{x}-10\ge \frac{2}{24}\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:0$

8 0

2 years ago

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Sienna is solving the quadratic equation by completing the square. 3x2 + 9x – 4 = 0 3x2 + 9x = 4 A(x2 + 3x) = 4 What is the valu

bogdanovich [222]

Answer:

I am going to show you the first steps to complete squares for the given equation: 1) Starting equation: 3x^2 + 9x -4 = 0 2) Add 4 to both sides => 3x^2 + 9x - 4 + 4 = 4 => 3x^2 + 9x = 4 3) Extract common factor 3 in the left side => 3 (x^2 + 3x). Now, compare with a(x^2 + 3x) and you get a = 3. Answer: a = 3.

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1 year ago

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A group of 10 students participate in chess club, karate club, or neither.

Afina-wow [57]

Total number of students = 10

As we have to find

P(A/B) = Probability( A when B has happend)

P(A/B)= P(A intersection B)/P(B)

According to given figure only yolanda and Rob are in both club

Therefore,P(A intersection B) $=\frac{2}{10}$

Number of student in karate club =6

P(B) $= \frac{6}{10}$

P(A/B) $= \frac{2}{10}\div{\frac{6}{10}$

Converting division into multiplication by reciprocating the term after division

P(A/B) $= \frac{2}{10}\times{\frac{10}{6}$

On solving we get ,

P(A/B) $= \frac{2}{6}$

P(A/B) $=\frac{1}{3}$

P(A/B) $=0.33$

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2 years ago

John deposited $2860 in a bank that pays 9% interest, compounded monthly. Find the amount he will have at the end of 3 years.

Verdich [7]

All you got to do first is:

Change the 9% to decimal, which is .9
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$2860 x .9 x3 is $7,722

Hope this helps! (Hope im right)

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2 years ago