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Over [174]
3 years ago
8

Need help with this ASAP

Mathematics
1 answer:
bagirrra123 [75]3 years ago
3 0

a) The diagram shows that 16% of the students plays only the piano, 13% of the students plays only the violin, and 5% of the students plays both instruments.

So, the percentage of students playing the piano is 21%, because you can choose a students who plays only the piano (16%) or a student who plays both instruments (5%)

b) We can't answer this question without knowing the number of students in the school. In fact, we only know that 5% of the students plays both instrument. This means that, if the total number of students is x, the number of students who play both instruments is

\dfrac{5x}{100}=\dfrac{x}{20}

And it is impossible to evaluate this quantity without knowing the value for x.

c) Since the probability of N is 21% (see point a), the probability of not N will be 100-21 = 79

d) By the same logic, the probability of V is 13+5=18 percent. So, we have

P(N\cup V) = P(N)+P(V)-P(N\cap V) = 0.21+0.18-0.05=0.34

e) We have

P(\lnot N \cap \lnot V) = P(\lnot(N\cup V))

And we just computed the probability of N\cup V to be 0.34. So, we have

P(\lnot(N\cup V))=1-0.34=0.66

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The radius of a circle is 20 cm. Find its area in terms of π π.
natulia [17]

Answer:

A = 400\pi cm^2

Step-by-step explanation:

Area of a circle is:

A = πr²

We are given a radius of 20 cm.

A = πr²

A = π(20)²

A = π400

<em>A = 400πcm²</em>

Hope this helps.

4 0
3 years ago
A rectangular plot of farmland will be bounded on one side by a river and on the other three sides by a single-strand electric f
likoan [24]

Step-by-step explanation:

Let x be the length and y be the width of the rectangular plot.

The plot is bounded on one side by a river and on the other three sides by a single-strand electric fence. It means,

x+2y = 1500

x = 1500 - 2y ....(1)

We know that the area of a rectangular plot is given by :

A = xy ....(2)

Put the value of x from equation (1) in (2)

A=(1500-2y)y\\\\A=1500y-2y^2 .....(3)

For largest area, differentiate above area equation wrt y.

\dfrac{dA}{dy}=\dfrac{d}{dy}(1500y-2y^2)\\\\=1500-4y\\\\\text{Put}\ \dfrac{dA}{dy}=0\\\\1500-4y=0\\\\y=\dfrac{1500}{4}\\\\=375

Put the value of y in equation (1).

x = 1500-2(375)

= 750 m

Put the value of y in equation (3).

A =1500(375)-2(375)^2\\A=281250\ m^2

Hence, the largest area is 281250 m² and its dimensions are 750 m and 375 m.

3 0
3 years ago
HELP PLZZ I WILL REWARD IF ANSWERS RIGHT
pentagon [3]
I know you have 1 and 3 right but I'm sorry about not knowing the rest.
8 0
3 years ago
Find the remaining trigonometric ratios of θ if csc(θ) = -6 and cos(θ) is positive
VikaD [51]
Now, the cosecant of θ is -6, or namely -6/1.

however, the cosecant is really the hypotenuse/opposite, but the hypotenuse is never negative, since is just a distance unit from the center of the circle, so in the fraction -6/1, the negative must be the 1, or 6/-1 then.

we know the cosine is positive, and we know the opposite side is -1, or negative, the only happens in the IV quadrant, so θ is in the IV quadrant, now

\bf csc(\theta)=-6\implies csc(\theta)=\cfrac{\stackrel{hypotenuse}{6}}{\stackrel{opposite}{-1}}\impliedby \textit{let's find the \underline{adjacent side}}&#10;\\\\\\&#10;\textit{using the pythagorean theorem}\\\\&#10;c^2=a^2+b^2\implies \pm\sqrt{c^2-b^2}=a&#10;\qquad &#10;\begin{cases}&#10;c=hypotenuse\\&#10;a=adjacent\\&#10;b=opposite\\&#10;\end{cases}&#10;\\\\\\&#10;\pm\sqrt{6^2-(-1)^2}=a\implies \pm\sqrt{35}=a\implies \stackrel{IV~quadrant}{+\sqrt{35}=a}

recall that 

\bf sin(\theta)=\cfrac{opposite}{hypotenuse}&#10;\qquad\qquad &#10;cos(\theta)=\cfrac{adjacent}{hypotenuse}&#10;\\\\\\&#10;% tangent&#10;tan(\theta)=\cfrac{opposite}{adjacent}&#10;\qquad \qquad &#10;% cotangent&#10;cot(\theta)=\cfrac{adjacent}{opposite}&#10;\\\\\\&#10;% cosecant&#10;csc(\theta)=\cfrac{hypotenuse}{opposite}&#10;\qquad \qquad &#10;% secant&#10;sec(\theta)=\cfrac{hypotenuse}{adjacent}

therefore, let's just plug that on the remaining ones,

\bf sin(\theta)=\cfrac{-1}{6}&#10;\qquad\qquad &#10;cos(\theta)=\cfrac{\sqrt{35}}{6}&#10;\\\\\\&#10;% tangent&#10;tan(\theta)=\cfrac{-1}{\sqrt{35}}&#10;\qquad \qquad &#10;% cotangent&#10;cot(\theta)=\cfrac{\sqrt{35}}{1}&#10;\\\\\\&#10;sec(\theta)=\cfrac{6}{\sqrt{35}}

now, let's rationalize the denominator on tangent and secant,

\bf tan(\theta)=\cfrac{-1}{\sqrt{35}}\implies \cfrac{-1}{\sqrt{35}}\cdot \cfrac{\sqrt{35}}{\sqrt{35}}\implies \cfrac{-\sqrt{35}}{(\sqrt{35})^2}\implies -\cfrac{\sqrt{35}}{35}&#10;\\\\\\&#10;sec(\theta)=\cfrac{6}{\sqrt{35}}\implies \cfrac{6}{\sqrt{35}}\cdot \cfrac{\sqrt{35}}{\sqrt{35}}\implies \cfrac{6\sqrt{35}}{(\sqrt{35})^2}\implies \cfrac{6\sqrt{35}}{35}
3 0
4 years ago
-5+4=3x-9 <br> My teacher told me it was negative three.. can someone help?
Alexxx [7]

Answer:

x = 8/3

Step-by-step explanation:

(When solving for a variable, always do the opposite of PEMDAS)

-5 + 4 = 3x - 9

-1 = 3x - 9

8 = 3x

8/3 = x

4 0
3 years ago
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