Gravel is being dumped from a conveyor belt at a rate of 40 ft3/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 11 ft high? (Round your answer to two decimal places.)

Answer:

(x-4)^2 + (y-4)^2 = 49

Step-by-step explanation:

The equation of a circle is given by

(x-h)^2 + (y-k)^2 = r^2  where ( h,k) is the center and r is the radius

(x-4)^2 + (y-4)^2 = 7^2

(x-4)^2 + (y-4)^2 = 49

Answer:

C

Step-by-step explanation:

it is not my percentage, it is not constant, it is increasing over time

Answer:

I) 0.386 = 38.6% probability that exactly one six occurs.

II) 0.518 = 51.8% probability that at least one six occurs.

Step-by-step explanation:

For each throw, there are only two possible outcomes. Either it is a six, or it is not. The probability of a six being rolled is independent of other throws, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Thrown four times

This means that [tex]n = 4[/tex]

Probability of rolling a six:

Six sides, one of which is 6. So

[tex]p = \frac{1}{6} = 0.1667[/tex]

i) exactly one six occurs

This is [tex]P(X = 1)[/tex]. So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 1) = C_{4,1}.(0.1667)^{1}.(0.8333)^{3} = 0.386[/tex]

0.386 = 38.6% probability that exactly one six occurs.

ii) at least one six occurs​

This is:

[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]

So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{4,0}.(0.1667)^{0}.(0.8333)^{4} = 0.482[/tex]

[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.482 = 0.518[/tex]

0.518 = 51.8% probability that at least one six occurs.

Answer:

r = 22.9 in.

Step-by-step explanation:

Central angle in radians, ∅ = π/4

Length of arc, S = 18 in.

radius (r) = ?

Length of arc, C = r∅

Plug in the values and find r

18 = r*π/4

18 = (πr)/4

Multiply both sides by 4

4*18 = πr

72 = πr

Divide both sides by π

72/π = r

r = 22.9183118

r = 22.9 in. (Nearest tenth)

Answer:

4 liters

Step-by-step explanation:

8/2 8 divided by 2 is 4 how do I know this, because if its per apple juice then we have to find out what can get me per apple juice, you just basically had to divde it by its own number

Answer:

x=-6

Step-by-step explanation:

1. Move the variable to the left-hand side and change its sign

3x-4-2x=-10

2. Collect like terms

x=-10+4

-10+4= -6

Answer:

The player made one two-point shot and 13 free throws.

Step-by-step explanation:

We can write a system of equations to model the situation.

Let t represent the number of two-point shots and let f represent the number of free throws made.

Since she scored a total of 14 times, the sum of two-pointers and free throws must equal 14. Hence:

[tex]t+f=14[/tex]

And since she scored a total of 15 points and each two-pointers is worth two points and every free throw is worth one:

[tex]2t+f=15[/tex]

Solve the system. We can use elimination. From the first equation, multiply both sides by negative one:

[tex]-t-f=-14[/tex]

We can add this to the second equation:

[tex](2t+f)+(-t-f)=(15)+(-14)[/tex]

Simplify:

[tex]t=1[/tex]

So, the player made only one two-point shot.

Using the first equation again, substitute one for t and solve for f:

[tex](1)+f=14\Rightarrow f=13[/tex]

Therefore, the player made one two-point shot and 13 free throws.

Answer:

Dependent and independent variables are variables in mathematical modeling, statistical modeling and experimental sciences. Dependent variables are studied under the supposition or demand that they depend, by some law or rule, on the values of other variables.

Step-by-step explanation:

Answer:

3.7821 (SDF)

Step-by-step explanation:

Take the number by 378 21 and place it in the right forms/place marks. Such as ones and tens place ect. Then there is your answer.

Answer:

11 hours

Step-by-step explanation:

9514 1404 393

Answer:

  False

Step-by-step explanation:

"Always" and "never" statements are generally false--especially when they relate to something like a topic of conversation. Even in the context of math and physics, we find exceptions to most "rules."

Step-by-step explanation:

-6 + 4a = 18

4a= 24

a=6

!!!!!!!!!!!!

Answer:

OC) 6

Step-by-step explanation:

Transpose -6 to the other side

-6 + 4a = 18

4a = 18+6

4a = 24

a = 6

Answer:

The angle is in the third quadrant

Answer:

3 is exactly halfway between 2.5 and 3.5​.

Step-by-step explanation:

The first number is 2.5

The second number is 3.5

We need to find the number that is exactly halfway between 2.5 and 3.5​. It can be calculated as follows :

[tex]n=\dfrac{2.5+3.5}{2}\\\\n=\dfrac{6}{2}\\\\n=3[/tex]

Hence, 3 is exactly halfway between 2.5 and 3.5​.

Answer:

if following simple addition/multiplication, the answer should be 12 cartons of vanilla.

Answer:

3/10 quarts.

Step-by-step explanation:

Set the denominators equal to one another.

4/5 = 8/10 (multiplied by a factor of 2)

1/2 = 5/10 (multiplied by a factor of 5)

Subtract the 5/10 from the 8/10

3/10 qt

Answer:

PUT THEM IN ORDER SO I CAN UNDERSTAND oh 56.86

Answer:

Ŷ = 1.3082X + 3.3436

Step-by-step explanation:

Given the data :

X : 11, 12, 4, 6, 13, 14, 8, 10, 7, 5, 9

Y : 18.69, 19.17, 6.13, 11.37, 19.31, 19.31, 15.28, 17.88, 13.49, 8.91, 16.75

Using technology, the data above gave the resulting linear regression model :

Ŷ = 1.3082X + 3.3436

Slope of model = 1.3082

Intercept = 3.3436

Scatter plot is attached below :

Answer:

what next five shapes in the pattern

Answer:

I can make one up for you

Square , Circle ,  Square , Prism ,  Sphere , Cone , Semi-Circle , Square , Circle,

What are the next 5 shapes ?

Step-by-step explanation:

Answer:

The solution set to the absolute value is:

[tex]S = \{x \in \mathbb{R}| x \ge 0\}[/tex] or [tex]S = [0, +\infty)[/tex]

Negative real numbers are not included in the solution set, as for [tex]x < 0[/tex], [tex]|x| = - x[/tex].

Step-by-step explanation:

From Mathematics, we know that absolute values are defined by the following characteristics:

1) For [tex]x \ge 0[/tex], [tex]|x| = x[/tex]

2) For [tex]x < 0[/tex], [tex]|x| = - x[/tex]

Then, if [tex]|x| = x[/tex], then the solution set to the absolute value is:

[tex]S = \{x \in \mathbb{R}| x \ge 0\}[/tex] or [tex]S = [0, +\infty)[/tex]

Negative real numbers are not included in the solution set, as for [tex]x < 0[/tex], [tex]|x| = - x[/tex].

Step-by-step explanation:

The power reducing formulas are given by the following:

[tex]\sin^2 x = \dfrac{1- \cos2x}{2}[/tex]

[tex]\cos^2 x = \dfrac{1+ \cos2x}{2}[/tex]

We can then write the given expression as

[tex]\sin^25x \cos^25x[/tex]

[tex]= \left(\dfrac{1- \cos 2(5x)}{2} \right) \left(\dfrac{1+ \cos 2(5x)}{2} \right)[/tex]

[tex]= \dfrac{1}{4}(1- \cos 10x)(1+ \cos 10x)[/tex]

[tex]= \dfrac{1}{4}(1- \cos^2 10x)[/tex]

[tex]= \dfrac{1}{4} \left(\dfrac{1- \cos 20x}{2} \right)[/tex]

or

[tex]\sin^25x \cos^25x= \dfrac{1}{8}(1- \cos 20x)[/tex]

Answer:

(x , y ) = (39/22 , -2/11 )

.............

Answer:

-2,3 3,-7

Step-by-step explanation:

took test :)

9514 1404 393

Answer:

  ∠A ≈ 72°

Step-by-step explanation:

Fill in the given numbers and do the arithmetic.

  cos A = (2.9² +2.5² -3.2²)/(2(2.9)(2.5)) = 4.42/14.5

The inverse cosine function is used to find the angle, given its cosine.

  A = arccos(4.42/14.5)

  ∠A ≈ 72°

Answer:

6

Step-by-step explanation:

In a circle equation, the radius can be found by taking the square root of the r² value.

In this equation, the r² value is 36.

Take the square root:

√36

= 6

So, the radius is 6.

Answer:

3x−6x+11−(10x−4x+6)

=5x10−10x7+3x5

         x10

=5x5−10x2+3

      x5

Step-by-step explanation:

i hope this helps and i hope you understand this, sorry if you dont understand

Answer:

4

Step-by-step explanation:

2+2=4