The base diameter and the height of a cone are both equal to
x units.
Which expression represents the volume of the cone, in
cubic units?

pix2
2pix3
1/3pix2
1/12pix3

Answer:

Step-by-step explanation:

To solve this problem, we need to find the number which express the whole park.

Notice that the park is divided in two sections, one occupies 5/8 of the total, and the other occupies 2/7 of the total. So, the sum would be

[tex]\frac{5}{8}+\frac{2}{7}=\frac{35+16}{56} =\frac{51}{56}[/tex]

Now we have the total space there, we need to divide 5/8 by 51/56, so

[tex]\frac{5}{8} \div \frac{51}{56}=\frac{5}{8} \times \frac{56}{51}=\frac{280}{408} \approx 0.69[/tex]

Therefore, the rink occupies 69% of the whole park, approximately, which is equivalent to 280/408.

Answer:

Step-by-step explanation:

cos X(tanX+cotX) =cscX​

cos X(sinx/cosx +cosx/sinx) =cscx

cos X (sin²+cos²/cossin)=cscx

cosx(1/cossin)=cscx

cross out cosines

1/sinx=cscx

Answer:

Suppose a population of rodents satisfies the differential equation dP 2 kP dt = . Initially there are P (0 2 ) = rodents, and their number is increasing at the rate of 1 dP dt = rodent per month when there are P = 10 rodents.  

How long will it take for this population to grow to a hundred rodents? To a thousand rodents?

Step-by-step explanation:

Use the initial condition when dp/dt = 1, p = 10 to get k;

[tex]\frac{dp}{dt} =kp^2\\\\1=k(10)^2\\\\k=\frac{1}{100}[/tex]

Seperate the differential equation and solve for the constant C.

[tex]\frac{dp}{p^2}=kdt\\\\-\frac{1}{p}=kt+C\\\\\frac{1}{p}=-kt+C\\\\p=-\frac{1}{kt+C} \\\\2=-\frac{1}{0+C}\\\\-\frac{1}{2}=C\\\\p(t)=-\frac{1}{\frac{t}{100}-\frac{1}{2} }\\\\p(t)=-\frac{1}{\frac{2t-100}{200} }\\\\-\frac{200}{2t-100}[/tex]

You have 100 rodents when:

[tex]100=-\frac{200}{2t-100} \\\\2t-100=-\frac{200}{100} \\\\2t=98\\\\t=49\ months[/tex]

You have 1000 rodents when:

[tex]1000=-\frac{200}{2t-100} \\\\2t-100=-\frac{200}{1000} \\\\2t=99.8\\\\t=49.9\ months[/tex]

Step-by-step explanation:

x and x+2 are the numbers

x(x+2)=143

x²+2x-143=0

x²+13x-11x-143=0

x(x+13)- 11(x+13)=0

(x+13). (x-11)=0

x+13=0. x=-13

x-11=0. x=11

Answer: D.

Step-by-step explanation:

You want to cube each term in the parentheses. When you take an exponent to an exponent, you just multiply them. You get (27m^-12). In order to get rid of that negative exponent, you should put a one over the m term and make -12, +12:

[tex](\frac{27}{m^12} )(3m^5)[/tex]

Multiply the numerators to get:

[tex]81m^5[/tex]

You now have:

[tex]\frac{81m^5}{m^12}[/tex]

When you divide exponents, you subtract them. 5 - 12 = -7

You have m^-7 which is the same as 1/m^7. Finally, mulitply that by the 81 we left out to get the answer of D.

The expression equivalent to the given expression (3m⁻⁴)³(3m⁵) is 81/m⁷. So, option D is correct.

Exponentiation is a mathematical operation that involves two numbers, the base b, and the exponent or power n, and is pronounced as "b raised to the power of n." It is written as bⁿ and is pronounced as "b raised to the power of n."

When n is a positive integer, bⁿ = b × b × b ×...× b

and b⁻ⁿ = 1/bⁿ

If n = 0, then b⁰ = 1.

Here, (3m⁻⁴)³(3m⁵) = (3³)(m⁻⁴)³(3m⁵) = (27m⁻¹²)(3m⁵) = 81m⁵⁻¹² = 81/m⁷

Therefore, the expression equivalent to the given expression (3m⁻⁴)³(3m⁵) is 81/m⁷. So, option D is correct.

Learn more about exponentiation here -

https://brainly.com/question/14513824

#SPJ2

Answer:

B. Isosceles triangle

Answer: obtuse and isosceles <3

Step-by-step explanation:

Answer:

y-intercept decreased by 3-1= 2 points

Step-by-step explanation:

y=-9x+ 3 ⇒ y-intercept= 3

y=-9x + 1 ⇒ y-intercept= 1

y-intercept decreased by 3-1= 2 points = the line shifted down by 2 points

Answer:

Hello!

Answer: y-intercept decreased by 2 points because 3-1=2

I hope I was of help.  If not, please let me know!  Thanks!

Step-by-step explanation:

Answer:

360360

Step-by-step explanation:

We have the following information:

Number of ways of choosing 5 car models from 15 different models = 15C5

Number of arranging above 5 models = 5!

Therefore, the total number of displayong 5 models would be:

15C5 * 5!

nCr = n! / (r! * (n-r)!)

we replace:

 15! / (5! * (15-5)!) * 5! = 15! / 10! = 360360

So there are a total of 360 360 ways to display the 5 car models.

Answer:  360,360

Step-by-step explanation:

Answer:

work is shown and pictured

[tex]answer \\ g(x) = |x - 2| + 1 \\ here \: f(x) = |x| \\ if \: we \: want \: to \: shift \: this \: function \: 2 \: \\ unit \: right \: then \: make \: transformation \\ \: of \: x \: by \: (x - 2) \\ and \: if \: we \: want \: to \: make \: function \: \\ goes \: up \: with \: 1 \: unit \: then \: transformation \\ is \: f(x) \: by \: f(x) + 1 \\ now \\ g(x) = |x - 2| + 1 \\ hope \: it \: helps[/tex]

Answer:

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

(-1, -9) is a vertex or minimum.

(-4, 0) is an x-intercept / zero of the function / solution

(2, 0) is also an x-intercept / zero of the function / solution

The parabola has a minimum.

Answer:

629

Step-by-step explanation:

l x w

25x14

4x7

12x18

5x7

629

Answer:

a

Step-by-step explanation:

because as absolute value gets smaller the line gets steeper

r

Answer:

5 hours and 40 minutes would be class

Step-by-step explanation:

We know that the total time is 7 hours, which in minutes would be:

7 * 60 = 420

420 minutes would be class, now, we subtract the other times that are not to be in class and it would be:

420 - 30 - 50 = 340

So we could say that in class it takes 340 minutes, and if we spend hours it would be:

340/60 = 5.67 hours or also 5 hours and 40 minutes would be class.

Answer:

28.45.

Step-by-step explanation:

5 x 5.69

Answer:

Step-by-step explanation: its 24

1,2,5

Step-by-step explanation:

Answer:

2044

Step-by-step explanation:

just follow the story

a person uses a

hanger (2)

to pop a

ball  (0)

then flies

two kites (44)

Answer:

1). 2044

Step-by-step explanation:

The story includes: a hanger, a ball, and two kites (in that order)

From the information given, a hanger is 2, a ball is 0, and a kite is 4.

So it would be 2044.

Answer:

b) False

Explanation:

It is not needed to keep 50/50 split.

Answer:

Savannah

Step-by-step explanation:

Emery has solved it incorrectly;

x = 100

Answer: 896

Step-by-step explanation:

Let's use a rule of three here.

[tex]\frac{576}{x}=\frac{18}{28}[/tex]

Solve for x;

[tex]x=\frac{576*28}{18}[/tex]

[tex]x=896[/tex]

Answer:

multiples of 12

Step-by-step explanation: when looking at the GCF, the answer is 12

Answer: 0.0965

Step-by-step explanation:

This would happen if:

First toss: Here we must have any number that is not 6.

the options are 1, 2, 3, 4, 5 so the probablity is p1 = 5/6

The same happens for the second toss, p2 = 5/6

and for the third one: p3 = 5/6

for the fourth toss, person B must roll a 6, so the probability here is p4 = 1/6

Now, the joint probability is equal to the product of the probabilities for each toss, this is:

P = p1*p2*p3*p4 = (5/6)^3*(1/6) = 0.0965

Answer:

A)1/18

B)1/6

C)13/18

Step-by-step explanation:

THIS IS THE COMPLETE QUESTION BELOW,

The chess clubs of two schools consist of, respectively, 8 and 9 players. Four members from each club are randomly chosen to participate in a contest between the two schools. The chosen players from one team are then randomly paired with those from the other team, and each pairing plays a game of chess. Suppose that Rebecca and her sister Elise are on the chess clubs at different schools. What is the probability that (a) Rebecca and Elise will be paired? (b) Rebecca and Elise will be chosen to represent their schools but will not play each other? (c) either Rebecca or Elise will be chosen to represent her school?

CHECK THE ATTACHMENT'S FOR STEP BY STEP EXPLANATION

9514 1404 393

Answer:

  £2272.54

Step-by-step explanation:

An equation for the value is ...

  v = £2300(0.998^t)

Then for t=6, the value is ...

  v = £2272.54

_____

Additional comment

The growth factor (0.998) is (1 - decay rate) = (1 -0.002).

Answer:

the answer is 2272.54

Step-by-step explanation:

:))

Answer:

They got £84 altogether.

Step-by-step explanation:

We can see that Richard get's 6 parts and Stephen gets 1 part. We can subtract these two to get 5 parts. We know that five parts equals £60, so we can divide by 5 to get 1 part equals £12. We are looking for the amount they got altogether, which is equal to 7 parts, 6 parts + 1 part. We multiply £12 by 7, leaving us with £84, which is our answer.

Step-by-step explanation:

p = x / n

p = 550 / 1083

p = 0.5078

Answer:

51.56% probability that the mean weight of the sample of cows would differ from the population mean by greater than 11lbs if 49 cows are sampled at random from the herd

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

[tex]\mu = 3181, \sigma = 119, n = 49, s = \frac{119}{\sqrt{49}} = 17[/tex]

What is the probability that the mean weight of the sample of cows would differ from the population mean by greater than 11lbs if 49 cows are sampled at random from the herd

Lower than 3181 - 11 = 3170 lbs or greater than 3181 + 11 = 3192 lbs. Since the normal distribution is symmetric, these probabilities are equal. So i will find one of them, and multiply by 2.

Probability of mean weight lower than 3170 lbs:

This is 1 subtracted by the pvalue of Z when X = 3170. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{3170 - 3181}{17}[/tex]

[tex]Z = -0.65[/tex]

[tex]Z = -0.65[/tex] has a pvalue of 0.2578

2*0.2578 = 0.5156

51.56% probability that the mean weight of the sample of cows would differ from the population mean by greater than 11lbs if 49 cows are sampled at random from the herd

Answer:

it's b 59° because it's at the side