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d1i1m1o1n [39]
3 years ago
5

Tanya runs a catering business. Based on her records, her weekly profit can be approximated by the function LaTeX: f\left(x\righ

t)=2x^2-44x-150 f ( x ) = 2 x 2 − 44 x − 150 , where LaTeX: x x is the number of meals she caters. If LaTeX: f(x) f ( x ) is negative, it means that the business has lost money. What is the number of meals that Tanya needs to cater in order to break-even?
Mathematics
1 answer:
Shtirlitz [24]3 years ago
4 0

The function

2x^2-44x-150

is a parabola concave up, whose solutions are

2x^2-44x-150=0 \iff x^2-22x-75=0

from here, you can use the quadratic formula

x_{1,2} = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}

to find that the solutions of the parabola are -3,\ 25

So, the parabola is positive if x (which wouldn't make sense in our case) or x

So, if Tanya caters 25 meals she breaks even, and starting with the 26th meal she will begin to profit.

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If line q bisects EG at point T, and if ET= 1/3 x and TG= x-2, then find EG
kvasek [131]

Answer:

EG = 2 units

Step-by-step explanation:

Given that line q bisects EG at T , then

ET = TG  ( substitute values )

\frac{1}{3} x = x - 2 ( multiply through by 3 to clear the fraction )

x = 3x - 6 ( subtract x from both sides )

0 = 2x - 6 ( add 6 to both sides )

6 = 2x ( divide both sides by 2 )

3 = x

Then

ET = \frac{1}{3} x = \frac{1}{3} × 3 = 1

TG = x - 2 = 3 - 2 = 1

Thus

EG = ET + TG = 1 + 1 = 2 units

8 0
2 years ago
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In the rhombus m<1=160. What are m<2 and <3? The diagram is not drawn to scale.
xxMikexx [17]
Since a rhomubs is a 4 sided quadrilateral when parallel lines intersect within we solve for the triangles that are the result of the intersecting lines m<2=10, m<3=10
8 0
3 years ago
A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 421 gram setting. It is
Anastaziya [24]

Answer:

The p-value is approximately 0.0508

Step-by-step explanation:

The given parameters are;

The expected mass of banana chips bag filled by the machine, μ = 421 gams

The number of bags in the sample of bags filled by the machine, n = 26 bags

The mean mass of the bags in the sample, \overline x = 413 grams

The standard deviation of the mass in the bags, s = 24 grams

The level of significance, α = 0.02

The null hypothesis, H₀; μ = 421 grams

The alternative hypothesis, Hₐ; μ < 421 grams

The test statistic is given as follows;

t=\dfrac{\bar{x}-\mu }{\dfrac{s}{\sqrt{n}}}

We get;

t=\dfrac{413-421 }{\dfrac{24}{\sqrt{26}}} \approx -1.6996731712

The t-value = -1.6996731712

The degrees of freedom df = n - 1 = 26 - 1 = 25

From an online source, we get the critical-t =  2.166587

The p-value is obtained using an online source as p(t ≤  -1.6996731712) = 0.0508

From the p-value table, we get

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3 0
2 years ago
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Inessa [10]

Answer:

$2,660

Step-by-step explanation:

9.5% of 1300 is 123.5

So to figure out what the rent would cost in 11 years, we just have to multiply 123.5 by 11.

123.5 × 11 = 1358.5

We can then add that number to 1300.

1358.5 + 1300 = $2658.5

Then we round.

Your final answer would be:

$2,660

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