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2 years ago

15

two rulers and one pencil cost £2.40 five rulers and one pencil cost £5.10 work out the cost of a ruler and the cost of a pencil

.

1 answer:

Thepotemich [5.8K]2 years ago

3 0

Answer:

Ruler: £0.90

Pencil: £0.60

Step-by-step explanation:

Ruler = x

Pencil = y

2x + y = 2.4

5x + y = 5.1

3x = 2.7

x = 0.9

y = 0.6

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Below is the five-number summary for 144 hikers who recently completed the John Muir Trail (JMT). The variable is the amount of

bearhunter [10]

Answer:

The IQR is given by:

$IQR = Q_3 -Q_1 = 28-18= 10$

If we want to find any possible outliers we can use the following formulas for the limits:

$Lower= Q_1 - 1.5 IQR$

$Upper= Q_3 + 1.5 IQR$

And if we find the lower limt we got:

$Lower= Q_1 - 1.5 IQR= 18-1.5*10 = 3$

$Upper= Q_3 + 1.5 IQR= 28+1.5*10= 43$

So then the left boundary for this case would be 3 days

Step-by-step explanation:

For this case we have the following 5 number summary from the data of 144 values:

Minimum: 9 days

Q1: 18 days

Median: 21 days

Q3: 28 days

Maximum: 56 days

The IQR is given by:

$IQR = Q_3 -Q_1 = 28-18= 10$

If we want to find any possible outliers we can use the following formulas for the limits:

$Lower= Q_1 - 1.5 IQR$

$Upper= Q_3 + 1.5 IQR$

And if we find the lower limt we got:

$Lower= Q_1 - 1.5 IQR= 18-1.5*10 = 3$

$Upper= Q_3 + 1.5 IQR= 28+1.5*10= 43$

So then the left boundary for this case would be 3 days

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2 years ago

Find the cube roots of 8(cos 216° + i sin 216°).

Tomtit [17]

$z^3=8(\cos216^\circ+i\sin216^\circ)$
$z^3=2^3(\cos(6^3)^\circ+i\sin(6^3)^\circ)$
$\implies z=8^{1/3}\left(\cos\left(\dfrac{216+360k}3\right)^\circ+i\sin\left(\dfrac{216+360k}3\right)^\circ\right)$

where $k=0,1,2$ . So the third roots are

$z=\begin{cases}2(\cos72^\circ+i\sin72^\circ)\\2(\cos192^\circ+i\sin192^\circ)\\2(\cos312^\circ+i\sin312^\circ)\end{cases}$

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2 years ago

Ann's car can travel 228 miles on 6 gallons of gas. a. Write an equation to represent the distance, y, in miles Ann's car can tr

Murrr4er [49]

Answer:

288 gallons ÷ 6 miles = 48 miles per gallon

48 miles per gallon • 7 miles = 366 miles

Step-by-step explanation:

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2 years ago

Sierra is selling bracelets to raise money for the Language Club at school. Each bracelet with yellow beads sells for $5. Each b

matrenka [14]

Answer:

Correct answer is:

$5y+6r=660\\y=2r+8$

Step-by-step explanation:

Given that Number of bracelets with yellow beads is represented by $y$

Each bracelet with yellow beads is sold for $5.

Total money raised by bracelets with yellow beads = Number of bracelets sold $\times$ Money raised by sale of one such bracelet = $5y$

Also Given that Number of bracelets with Orange beads is represented by $r$

Each bracelet with orange beads is sold for $6.

Total money raised by bracelets with orange beads = Number of bracelets sold $\times$ Money raised by sale of one such bracelet = $6r$

Given that total money raised by sale of both type of bracelets is $660.

so, the first equation becomes:

$5y+6r=660 ....... (1)$

It is also given that "<em>The number of bracelets with yellow beads that Sierra sold is 8 more than twice the number of bracelets with orange beads</em>"

$\Rightarrow r =2r+8 ...... (2)$

So, by equation (1) and (2), the system of equations is:

$5y+6r=660\\y=2r+8$

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2 years ago

Which of the following is a true statement for 0 degrees less than theta less than 90 degrees?

Grace [21]

Answer:

c

Step-by-step explanation:

See the graph for an example using the specific angles $\theta=60^\circ , \,\, \180^\circ-\theta=120^\circ$

See how the red segments are equal in length but going in opposite directions?

$\tan{60^\circ}=\sqrt{3} \\ \tan{120^\circ=-\sqrt{3}$

a. This can't be correct: it says $\tan{\theta}$ is equal to its opposite. That is never true in Quadrant I where all tangent values are positive.

b. Not true in Quad. I. Consider $\tan{60^\circ}, \,\, \tan{30^\circ}$ .

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2 years ago