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3 years ago

A spinner has 14 equal sectors with different letters for each sector, as shown below:

Mathematics

2 answers:

LuckyWell [14K]3 years ago

8 0

The correct answer would be 1/14

Helen [10]3 years ago

3 0

Answer:

1 over 14

Step-by-step explanation:

The sectors labeled are B, Y, G, C, P, F, O, V, M, A, D, E, H, and R.

Total number of sectors = 14.

When Victoria spins the spinner 18 times, and it stops at the letter B 10 times.

When Victoria spins the spinner the theoretical probability that this time it will stop at the letter B = Favourable outcomes ÷total numner of outcomes.

Favourable outcomes =1 and Total number of outcomes = 14.

Hence Theoritical Probability = 1 over 14.

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3 years ago

Find the equation of the tangent line to the curve (a lemniscate)

olya-2409 [2.1K]

Answer:

$m=\frac{9}{13}$ and $b=\frac{40}{13}$

Step-by-step explanation:

The equation of curve is

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

We need to find the equation of the tangent line to the curve at the point (-3, 1).

Differentiate with respect to x.

$2[2(x^2+y^2)\frac{d}{dx}(x^2+y^2)]=25(2x-2y\frac{dy}{dx})$

$4(x^2+y^2)(2x+2y\frac{dy}{dx})=25(2x-2y\frac{dy}{dx})$

The point of tangency is (-3,1). It means the slope of tangent is $\frac{dy}{dx}_{(-3,1)}$ .

Substitute x=-3 and y=1 in the above equation.

$4((-3)^2+(1)^2)(2(-3)+2(1)\frac{dy}{dx})=25(2(-3)-2(1)\frac{dy}{dx})$

$40(-6+2\frac{dy}{dx})=25(-6-2\frac{dy}{dx})$

$-240+80\frac{dy}{dx})=-150-50\frac{dy}{dx}$

$80\frac{dy}{dx}+50\frac{dy}{dx}=-150+240$

$130\frac{dy}{dx}=90$

Divide both sides by 130.

$\frac{dy}{dx}=\frac{9}{13}$

If a line passes through a points $(x_1,y_1)$ with slope m, then the point slope form of the line is

$y-y_1=m(x-x_1)$

The slope of tangent line is $\frac{9}{13}$ and it passes through the point (-3,1). So, the equation of tangent is

$y-1=\frac{9}{13}(x-(-3))$

$y-1=\frac{9}{13}(x)+\frac{27}{13}$

Add 1 on both sides.

$y=\frac{9}{13}(x)+\frac{27}{13}+1$

$y=\frac{9}{13}(x)+\frac{40}{13}$

Therefore, $m=\frac{9}{13}$ and $b=\frac{40}{13}$ .

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3 years ago

As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $110. What is the minim

alexgriva [62]

110 (goal) - 50 (base pay) = 60 (pay from sales only)

60 (total pay from sales) / 3 (cost per individual sale) = 20 (qty of sales)

7 0

3 years ago

Read 2 more answers

There are 50 chairs in the auditorium. 15 of the chairs are red and the rest are blue. What is the ratio of the number of blue c

navik [9.2K]

Answer: 7:3

Step-by-step explanation:

15 chairs are red

35 are blue

35:15

Simplifies to

7:3

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3 years ago