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SVEN [57.7K]
3 years ago
10

Roberto wants to raise money for new equipment by selling T-shirts. He pays $5.00 for each T-shirt and needs to raise $450. If 7

5 students order T-Shirts, by what percent must roberto markup the T-shirts to raise $450?
Mathematics
1 answer:
zvonat [6]3 years ago
6 0

Answer: Mark up percent = 20%

Step-by-step explanation:

Given: Cost price of each T-shirt = $5.00

Amount required = $450

Total students = 75

Market price for each T-shirt to raise the required amount = (Amount required ) ÷ 75

= $450 ÷ 75

= $ 6

Mark up percent = \dfrac{\text{Market price - Cost price}}{\text{Cost price}}\times100

=\dfrac{6-5}{5}\times100\\\\=20\%

Hence, Mark up percent = 20%

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The value of
marusya05 [52]

\large\underline{\sf{Solution-}}

We have to find out the value of the fraction.

<u>Let us assume that:</u>

\sf \longmapsto x =2 +   \dfrac{1}{2 +  \dfrac{1}{2 +  \dfrac{1}{2 + ... \infty} } }

<u>We can also write it as:</u>

\sf \longmapsto x =2 + \dfrac{1}{x}

\sf \longmapsto x =\dfrac{2x + 1}{x}

\sf \longmapsto  {x}^{2}  =2x + 1

\sf \longmapsto {x}^{2}  - 2x - 1 = 0

<u>Comparing </u>the given <u>equation</u> with <u>ax² + bx + c = 0,</u> we get:

\sf \longmapsto\begin{cases} \sf a =1 \\ \sf b =  - 2 \\ \sf c =  - 1 \end{cases}

<u>By quadratic formula:</u>

\sf \longmapsto x =  \dfrac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a}

\sf \longmapsto x =  \dfrac{2 \pm \sqrt{ {( - 2)}^{2} - 4(1)( - 1)} }{2 \times 1}

\sf \longmapsto x =  \dfrac{2 \pm \sqrt{4 + 4} }{2 \times 1}

\sf \longmapsto x =  \dfrac{2 \pm \sqrt{8} }{2}

\sf \longmapsto x =  \dfrac{2 \pm2 \sqrt{2} }{2}

\sf \longmapsto x = 1 \pm\sqrt{2}

\sf \longmapsto x = \begin{cases} \sf 1  + \sqrt{2} \\ \sf 1 -  \sqrt{2}  \end{cases}

<u>But </u><u>"</u><u>x"</u><u> cannot be negative. Therefore:</u>

\sf :\implies x = 1 + \sqrt{2}

So, the value of the fraction is 1 + √2.

4 0
2 years ago
Write an equation for the line that passes through the point (5, -4) and is parallel to the line y =
wel
Answer:
y = 2x - 14

5 0
3 years ago
Find an equation of the tangent line to the curve 2(x2+y2)2=25(x2−y2) (a lemniscate) at the point (−3,1). An equation of the tan
valina [46]

2(x^2+y^2)^2=25(x^2-y^2)

Let y=y(x), so that differentiating both sides wrt x gives

4(x^2+y^2)\left(2x+2y\dfrac{\mathrm dy}{\mathrm dx}\right)=25\left(2x-2y\dfrac{\mathrm dy}{\mathrm dx}\right)

If x=-3 and y=1, the above reduces to

40\left(-6+2\dfrac{\mathrm dy}{\mathrm dx}\right)=25\left(-6-2\dfrac{\mathrm dy}{\mathrm dx}\right)\implies\dfrac{\mathrm dy}{\mathrm dx}=\dfrac9{13}

This is the slope of the tangent line, which has equation

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3 years ago
I Need help wit this.
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Z varies directly as x2. If z = 16 when x = 2, find z when x = 5.<br> ...<br> Z=
PtichkaEL [24]

Answer:

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Step-by-step explanation:

it is a bit unclear to me, what that problem description means.

if I understand it correctly, than z is directly depending on x².

so, z = 16 for x = 2. x² = 4

I pondered a little bit, as there are several possibilities to connect 16 with 4 as a driving factor (e.g. 2⁴ = 16, 4×4 = 16, 12 + 4 = 16).

I decided to go with the simplest interpretation with the usual meaning of "varies" (multiplication) : 4×x²

that would mean

z = 4×x² = 4×5² = 4×25 = 100

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3 years ago
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