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3 years ago

The diameter of a circle is 6 in. Find its area to the nearest tenth.

Mathematics

1 answer:

Marrrta [24]3 years ago

8 0

Answer and Step-by-step explanation:

The area formula for a Circle is:

A = $\pi r^2$

Diameter is equal to the radius times 2.

So, divide the diameter to get the radius.

6 divided by 2 equals 3.

Now, plug it into the formula.

$A = \pi (3)^{2}$

A = $9\pi$

Plug this into your calculator by multiplying 9 by pi.

We get the answer to be 28.3 when rounded to the nearest tenth.

#teamtrees #PAW (Plant And Water)

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Derive the equation of the parabola with a focus at (_5, 5) and a directrix of y = -1.

mars1129 [50]

Answer: Option D is correct.

Step-by-step explanation:

Since we have given that

focus = (-5,5)

and a directrix y= -1

Since, equation of parabola in this case will be

$(x-h)^2=4.a(y-k)$

Now, here

$y=k-a=-1\\\\\text { focus =(h,k+a)}\\\\\text{So,} k+a=5\\\\\text{ by solving these two equation , we get }\\\\a=3\text{ and } k=2$

So equation will be

$(x+5)^2=4\times 3(y-2)\\\\(x+5)^2=12(y-3)\\\\y=\frac{1}{12}(x+5)^2+2$

So, option D is correct .

4 0

3 years ago

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Which is smaller half of 36 or one seventh of 42

lyudmila [28]

1/7 of 42 is smaller. 47/7= 6 < 18 = 36/2

4 0

3 years ago

5 friend's are having a tennis tournament.Each friend will play the other 4 friend once. How many matches will be played

Paraphin [41]

The handshake problem!
Each of the five will play against 4 others, but since A vs B can be considered the same game as B vs A, so there are 5*4/2=10 matches.

3 0

3 years ago

Kind of confused on this question, please help

Wittaler [7]

Answer:

4th option

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = $\frac{3}{5}$ x - 6 ← is in slope- intercept form

with slope m = $\frac{3}{5}$

Given a line with slope m then the slope of a line perpendicular to it is

$m_{perpendicular}$ = - $\frac{1}{m}$ = - $\frac{1}{\frac{3}{5} }$ = - $\frac{5}{3}$

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Here m = - $\frac{5}{3}$ and (a, b ) = (- 2, 5 ) , then

y - 5 = - $\frac{5}{3}$ (x - (- 2) ) , that is

y - 5 = - $\frac{5}{3}$ (x + 2)

8 0

3 years ago

Of all the soft drink consumers in a particular sales region, 30% prefer Brand A and 70% prefer Brand

victus00 [196]

Answer:

Option D -0.67

Step-by-step explanation:

Given : Preference of Brand A =30% ⇒ $P(A)=\frac{30}{100}=0.3$

Preference of Brand B =70% ⇒ $P(B)=\frac{70}{100}=0.7$

Prefer Brand A and are Female = 20% ⇒ $P(A/F)=\frac{20}{100}=0.2$

Prefer Brand B and are Female = 40% ⇒ $P(B/F)=\frac{40}{100}=0.4$

To find : Selected consumer is female, given that the person prefers Brand A $P(F/A)$

Solution : Using Bayes' theorem, which state that

$P(A/B)=\frac{P(B/A)P(A)}{P(B)}$

where, P(A) and P(B) are probabilities of observing A and B.

P(B/A)= is a conditional probability where event B occur and A is true

P(A/B)= also a conditional probability where event A occur and B is true.

Now, applying Bayes' theorem,

$P(F/A)=\frac{P(A/F)P(A)}{P(B)P(B/F)+P(A)P(A/F)}$

$P(F/A)=\frac{(0.2)(0.3)}{(0.7)(0.4)+(0.3)(0.2)}$

$P(F/A)=\frac{0.6}{0.28+0.6}$

$P(F/A)=\frac{0.6}{0.88}$

$P(F/A)=0.68$

Therefore, Option D is correct probability that a randomly selected consumer is female, given that the person prefers Brand A -0.67

3 0

3 years ago

Read 2 more answers