Determine which ordered pair in the form (x, y) is a solution of the given equation.

a 120 degree sector of a circle has an area of 67 square centimeters. to the nearest centimeter, what is the diameter of the cir

Vitek1552 [10]

Answer:

16 cm

Step-by-step explanation:

We have to first find the radius of the circle.

The area of a sector is given as:

$A = \frac{\alpha }{360} * \pi r^2$

where α = central angle of the sector = 120°

r = radius of the circle

Therefore:

$67 = \frac{120}{360} * \pi r^2\\\\\pi r^2 = \frac{360 * 67}{120}\\ \\r^2 = \frac{360 * 67}{120 * \pi}\\\\r^2 = 63.98\\\\r = \sqrt{63.98} = 8.0 cm$

The diameter of a circle is twice its radius, therefore:

D = 2 * 8 = 16 cm

The diameter of the circle is 16 cm

8 0

3 years ago

Juan has 2 liters of juice he drinks 0.21 each day for how many days will the juice last

inna [77]

You can do a quick division to figure this out:

2 L / (0.21 L/day) = 9.5 days

5 0

3 years ago

Joe has 10 marbles. Ken has fewer marbles than Joe. Which inequality represents the

Colt1911 [192]

Answer:

m<10

Step-by-step explanation:

Inequality is used to show comparison between two values. It helps to determine which is

• Greater than (>),

• Less than (<),

• Equal to(=),

• Not equal to,

• Greater than or equal to,

• Less than or equal to.

• Greater than is used when one value is more than the other.

• Less than is used when a value is less or smaller than another value.

• Equal to is used when both values are the same.

• Not Equal to is used when both values are not the same

Let Ken marbles= m

Remember that Ken's marbles is fewer than Joe's, that is less than Joe's marbles.

The inequality will be

m<10

8 0

3 years ago

You have a coin that is not weighted evenly and therefore is not a fair coin. Assume the true probability of getting heads when

Alexandra [31]

Answer:

$X \sim Binom(n=157, p=0.52)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

And we want this probability:

$P(X$

And we can use the following Excel code to find the exact answer:

"=BINOM.DIST(75,157,0.52,TRUE)"

And we got 0.1633

The other way to solve the problem is using the normal approximation

We need to check the conditions in order to use the normal approximation.

$np=157*0.52=81.64 \geq 10$

$n(1-p)=157*(1-0.52)=75.36 \geq 10$

So we see that we satisfy the conditions and then we can apply the approximation.

If we appply the approximation the new mean and standard deviation are:

$E(X)=np=157*0.52=81.64$

$\sigma=\sqrt{np(1-p)}=\sqrt{157*0.52(1-0.52)}=6.26$

We want this probability:

$P(X$

And using the continuity correction we have this:

$P(X$

We can use the z score given by this formula $Z=\frac{x-\mu}{\sigma}$ .

$P(X< 76.5)=P(\frac{X-\mu}{\sigma}< \frac{76.5-81.64}{6.26})=P(Z < -0.821)=0.206$

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=157, p=0.52)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

And we want this probability:

$P(X$

And we can use the following Excel code to find the exact answer:

"=BINOM.DIST(75,157,0.52,TRUE)"

And we got 0.1633

The other way to solve the problem is using the normal approximation

We need to check the conditions in order to use the normal approximation.

$np=157*0.52=81.64 \geq 10$

$n(1-p)=157*(1-0.52)=75.36 \geq 10$

So we see that we satisfy the conditions and then we can apply the approximation.

If we appply the approximation the new mean and standard deviation are:

$E(X)=np=157*0.52=81.64$

$\sigma=\sqrt{np(1-p)}=\sqrt{157*0.52(1-0.52)}=6.26$

We want this probability:

$P(X$

And using the continuity correction we have this:

$P(X$

We can use the z score given by this formula $Z=\frac{x-\mu}{\sigma}$ .

$P(X< 76.5)=P(\frac{X-\mu}{\sigma}< \frac{76.5-81.64}{6.26})=P(Z < -0.821)=0.206$

4 0

4 years ago

The length of a rectangular piece of cardboard is 2 cm greater than its width. If the length and the width were each decreased b

Vladimir [108]

9514 1404 393

Answer:

13 cm wide; 15 cm long

Step-by-step explanation:

Let w represent the original width. Then the original length is (w+2) and the original area is w(w+2). After the decrease, the width is (w-1) and the length is (w+1). The decreased area is (w-1)(w+1). The difference between these areas is 27, so we have ...

w(w+2) -(w-1)(w+1) = 27

w^2 +2w -(w^2 -1) = 27

2w +1 = 27

w = (27-1)/2 = 13

The original piece of cardboard was 13 cm wide and 15 cm long.

8 0

3 years ago