Sand is being dumped from a conveyor belt and forms a conical pile. Assuming that the height of this cone is always exactly 3 times the size of the radius of its base, and that thesand is added at the rate of 10 m^3/min, how fast is the height increasing when the pile is15 m high?

425 is the smallest sample size required when the percentage of pupils in the population who LOVE statistics.

Given that,

We have to find the smallest sample size required to determine the percentage of pupils in the population who LOVE statistics. With 99% confidence, the estimate should be within 5% of the true proportion. Assume that past research pegged that percentage at 20%.

p =  0.20

1 - p =  0.80

Margin of error = E = 0.05

At 99% confidence level

α= 1 - 99%  

α = 1 - 0.99 =0.01

α/2 = 0.005

Zα/2 = Z0.005 = 2.576

Sample size = n = (Zα / 2 / E )2 × p × (1 - p)

= (2.576 / 0.05)2 × 0.20 × 0.80

= 424.68

Sample size = n = 425

Therefore, 425 is the smallest sample size required when the percentage of pupils in the population who LOVE statistics.

To learn more about size visit: https://brainly.com/question/18587054

#SPJ4

The form of association that would be found in the variables would be:

As the number of hours spent playing a video game increases, the player is likely to reach higher levels within the game. So positive association.

The number of letters in a person's name and the last digit of their phone number are likely to be unrelated and randomly distributed. There is no association.

As the temperature of the drink decreases, the number of ice cubes in the drink is likely to increase, and vice versa. This is therefore negative association.

Find out more on negative association at https://brainly.com/question/29264211

#SPJ1

Answer:

Skateboarder B will have traveled 1,680 feet farther.

Step-by-step

Possible reasoning: There are 240 seconds in 4 minutes

Answer:

10/10

Step-by-step explanation:

For the given figure,   x = 23°  and      y = 129°

Parallel lines:

                        Parallel lines are lines that always stay the same distance apart and never meet.

Transversal line :

                             A transversal is a line that crosses two or more other lines.

given,

     ∠TLN = (3x - 18)°

    ∠MZQ = (5x + 14)°

    ∠NLM = y°

Now,

         ∠MZP + ∠MZQ = 180°  (Linear Pair)

        ∠MZP  = 180° - ∠MZQ  ...........(I)

again,

          ∠NLM + ∠TLN  =180°  ...........(II)      (Linear Pair)

  As,         ∠TLN = ∠MZP  (Corresponding Angle)

             (3x - 18)° =  180° - ∠MZQ  

           (3x - 18)° = 180° - (5x + 14)°

         3x + 5x  = 180° - 14° + 18°

           8x = 184°

           x = 184 / 8

          x = 23°

      From (II),

      ∠NLM + ∠TLN  =180°

    y° + 3x - 18° = 180°

 y = 180 - 3x + 18

     = 180 - 3* 23 + 18

      = 180 - 69 +18

     y = 129°

For the given figure,

                                     x = 23°  and      y = 129°

To learn more about Parallel line visit:

https://brainly.com/question/17432060

#SPJ9

the third one, you have written not clearly

bwhwhsbsh hsbsvs bw wjw wjw whe

By the formula d = rt, we obtain that the speed of John is 46 miles per hour.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, John drove 138 miles in 3 hours.

The speed of John can be obtained by dividing the total distance covered by the amount of time.

Also given, The formula to find John's rate of speed is, d = rt.

Therefore,

138 = 3r.

r = 138/3.

r = 46 miles per hour.

learn more about the unitary method here :

https://brainly.com/question/28276953

#SPJ1

The remainder is 5 + c, which means that the expression P(x) = \(5x^4 + 7x^3 - 2x^2 - 3x + c\) divided by (x + 1) results in a quotient of\(5x^3 + 2x^2 - 4x + 4\) and a remainder of 5 + c.

To divide the polynomial P(x) = \(5x^4 + 7x^3 - 2x^2 - 3x + c\) by the binomial (x + 1), we can use polynomial long division.

Let's set up the long division:

    \(5x^3 + 2x^2 - 4x + 4\)

_______________________

x + 1 | \(5x^4 + 7x^3 - 2x^2 - 3x + c\)

We start by dividing the highest degree term of the dividend (5x^4) by the divisor (x + 1), which gives us 5x^3. We then multiply this quotient by the divisor (x + 1) and subtract it from the dividend:

              \(5x^3(x + 1)\)

     _______________________

x + 1 | \(5x^4 + 7x^3 - 2x^2 - 3x + c\)

- (\(5x^3 + 5x^2)\)

This leaves us with a new polynomial:\(2x^3 - 7x^2 - 3x + c\). We repeat the process by dividing the highest degree term of this polynomial (2x^3) by the divisor (x + 1), resulting in 2x^2. We then multiply this quotient by the divisor and subtract it from the polynomial:

              \(5x^3(x + 1) + 2x^2(x + 1)\)

     _______________________

x + 1 | \(5x^4 + 7x^3 - 2x^2 - 3x + c\)

-\((5x^3 + 5x^2)\)

_______________________

\(2x^2 - 3x + c\)

We continue this process until we reach the constant term, resulting in the remainder of the division.

At this point, we have:

               \(5x^3(x + 1) + 2x^2(x + 1)\)

     _______________________

x + 1 | \(5x^4 + 7x^3 - 2x^2 - 3x + c\)

- \((5x^3 + 5x^2)\)

_______________________

\(2x^2 - 3x + c\)

-\((2x^2 + 2x)\)

_______________________

- 5x + c

- (-5x - 5)

_______________________

5 + c

For more such questions on remainder visit:

https://brainly.com/question/29347810

#SPJ8

Answer:

0.25  decimal

1/4  decimal

Step-by-step explanation:

Answer:

The first one is d) fluid ounces

The second one I think is c) meters

the third one I think is d) 2kg

Step-by-step explanation:

Answer:

To increase, use 1.3

to decrease, use .7

Step-by-step explanation

Answer:

The total price of the refrigerator is $798.75.

Step-by-step explanation:

6.5% of $750 is $48.75

So, $750 plus $48.75 equals $798.75.

The equation of the sphere with center coordinates  (4, −12, 8) and radius 10 is x² -8x + y² + 24y + z² -16z + 124 =0 .

And different plane equations are :

Intersection with xy-plane : ( x - 4 )² + ( y + 12 )² = 6²

Intersection with yz plane :( y + 12 )² + ( z - 8 )² = (√84)²

Intersection with zx plane :( x - 4 )² +  ( z - 8 )² = -44

Equation of the sphere with center coordinates (4, −12, 8) and radius 'r' = 10 is :

( x - 4 )² + ( y + 12 )² + ( z - 8 )² = 10²

⇒ x² -8x + y² + 24y + z² -16z + 224 = 100

⇒x² -8x + y² + 24y + z² -16z + 124 =0

Intersection with xy-plane

z = 0

( x - 4 )² + ( y + 12 )² + ( 0 - 8 )² = 10²

⇒( x - 4 )² + ( y + 12 )² = 6²

Circle with center ( 4,-12) and radius 6.

Intersection with yz-plane

x = 0

( 0 - 4 )² + ( y + 12 )² + ( z - 8 )² = 10²

⇒( y + 12 )² + ( z - 8 )² = (√84)²

Circle with center ( -12, 8) and radius √84.

Intersection with zx-plane

y = 0

( x - 4 )² + ( 0 + 12 )² + ( z - 8 )² = 10²

⇒( x - 4 )² +  ( z - 8 )² = -44

Not possible as radius cannot be negative.

Therefore, the equation of the sphere with the given center and radius is equal to x² -8x + y² + 24y + z² -16z + 124 =0 and equation of the intersection of different planes are:

xy-plane : ( x - 4 )² + ( y + 12 )² = 6²

yz plane :( y + 12 )² + ( z - 8 )² = (√84)²

zx plane :( x - 4 )² +  ( z - 8 )² = -44

Learn more about sphere here

brainly.com/question/12390313

#SPJ4

9514 1404 393

Answer:

  f(x) = -0.8x^3 +0.2x

Step-by-step explanation:

For root 'a', one of the factors will be (x-a). For the three given roots, the factored form of the polynomial can be written ...

  f(x) = c(x -(-1/2))(x-0)(x -1/2) = cx(x^2 -1/4)

Then for x=-2, the value is ...

  f(-2) = c(-2)((-2)^2 -1/4) = -7.5c

  f(-2) = 6 = -7.5c

  c = -6/7.5 = -0.8

Then the polynomial can be written as ...

  f(x) = -0.8x^3 +0.2x

The volume of water that Keith's kitchen kettle holds when it is full is 1800 ml.

Assume that Keith's kitchen kettle has a "x" ml capacity when it is full.

The kettle is initially 80% full, which means it holds 0.8x ml of water, according to the problem.

20% of the water is poured out, leaving 80% of the original amount of water in the kettle, which is:

0.8x * 0.8 = 0.64x ml

We are informed that the 1152 ml of water that is left equates to:

0.64x = 1152

By multiplying both sides by 0.64, we obtain:

x = 1800

Consequently, Keith's cooking kettle has an 1800 ml capacity when it is full.

To know more similar question visit:

https://brainly.com/question/79178

#SPJ1

The fish tank has a total volume of 288 inch³. As a result, Jessica's new fish tank has a capacity of 288 inch³ for water.

The volume of a rectangular prism can be calculated using the formula:

V = l x b x h..........(i)

where,

V ⇒ Volume

l  ⇒ length

b ⇒ width

h ⇒ height

From the question, we are given the values,

l = 8 inches

b = 4 inches

h = 9 inches

Putting these values in equation (i), we get,

V = 8 x 4 x 9

⇒ V = 288 in³

Therefore, the fish tank has a total volume of 288 inch³. As a result, Jessica's new fish tank has a capacity of 288 inch³ for water.

Learn more about the volume of rectangular prism on:

https://brainly.com/question/24284033

Answer:

B. (2,1)

Step-by-step explanation:

Substitute the first value from the parentheses for x, and the second value for y in the equation.

Calculate.

If the answer is true, the point is a solution on the line.

3(2) -5(1) = 1

6 –5 = 1

1 = 1. True. point B is a solution on the line.

D* for example:

3(2) -5(3) = 1

6 - 15 = 1

–9 = 1 False. This is not a solution on the line.

You get the idea. The others are also false.

▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓\(\pmb{\qquad{\qquad{\underline{\green{\underline{\sf{Photosynthesis}}}}}}}\)

Photosynthesis is the process by which green plants take in carbon dioxide and water, in the presence of chlorophyll by using sunlight to make their own food. Oxygen is released as a by product.

Chemical Reaction for PHOTOSYNTHESIS:

\(\sf 12H_2O + 6CO_2 \underset{chlorophyll}{\xrightarrow{Sunlight}} C_6H_{12}O_6 + 6H_2O + 6O_2 \uparrow\)▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓

The given expression represents the present value of a series of future cash flows discounted at a rate of 6.5% per year.

Each term in the expression represents a cash flow at a specific time in the future, and the denominator in each term represents the discount factor, which reflects the time value of money.

The first term, $250,000 / (1+0.065)^1, represents a cash flow of $250,000 that will be received in one year.

To determine its present value, we divide it by the discount factor (1+0.065)^1, which reflects the fact that the money will be received one year from now and is, therefore, less valuable than money received today.

Similarly, the second term, $37,500 / (1+0.065)², represents a cash flow of $37,500 that will be received in two years.

To determine its present value, we divide it by the discount factor (1+0.065)²,

which reflects the fact that the money will be received two years from now and is, therefore, less valuable than money received today.

This process is repeated for each term in the expression, representing cash flows that will be received in three, four, five, and six years, respectively.

The sum of these present values represents the total present value of the cash flows or the amount that they are worth today if they are discounted at a rate of 6.5% per year.

Learn more about Simplification here:

https://brainly.com/question/28996879

#SPJ1

Given:

A function

and value of g(x) at x.

To find:

Maximum value of both functions.

Explanation:

For criticle points find f'(x) = 0 and f''(x)>0. Then value will be maximum.

Solution:

Now, first derivative is

Now, put f'(x)=0 and criticle point will be 0.

Now,

As second derivative of function is negetive at x=0. So, we will get maximum at x=0

So, At x=0

So, maximum value of f(x) is 9 and maximum value of g(x) is 11.

Hence, this is the maximum values of f(x) and g(x).

Answer:

1.  

Vert. asymptote: x = {-3, 2}

Horiz. asymptote: y = 0

x-int: None

Question 3.

a. There is no hole

b. Vert. asymptote: x = {-2, 2}

c. f(x) = 0: x = {0, -1/2}

d. The graph has no hole at (-2, 4)

Question 4.

a. Vert. asymptote: x = {-2, 2}

b. f(x) = 0: x = {0, -1/2}

c. Horizontal asymptote: y = 2

d. The graph has no hole

I'm a bit confused.  Some of the things stated in the question aren't true like how there are holes in places where there aren't.

Answer:

Step-by-step explanation:

Do you still need help?

Answer:

\(\frac{187}{112}\)

Step-by-step explanation:

Just add them all up in the calculator and divide by the number of numbers, which in this case is 4

Step-by-step explanation:

follow the steps in the attached

Traveling from Earth to Mars is approximately 9.249626 x 10^7 km farther than traveling from Earth to the moon.

Earth to Mars is compared to traveling from Earth to the moon, we need to calculate the difference between the distances.

The distance from Earth to the moon is approximately 3.74 x 10^5 km.

The distance from Earth to Mars is approximately 9.25 x 10^7 km.

To find the difference, we subtract the distance to the moon from the distance to Mars:

9.25 x 10^7 km - 3.74 x 10^5 km

To subtract these numbers, we need to make sure the exponents are the same. We can rewrite the distance to the moon in scientific notation with the same exponent as the distance to Mars:

3.74 x 10^5 km = 0.374 x 10^6 km (since 0.374 = 3.74 x 10^5 / 10^6)

Now we can perform the subtraction:

9.25 x 10^7 km - 0.374 x 10^6 km = 9.25 x 10^7 km - 0.374 x 10^6 km

To subtract, we subtract the coefficients and keep the same exponent:

9.25 x 10^7 km - 0.374 x 10^6 km = 9.25 x 10^7 - 0.374 x 10^6 km

Simplifying the subtraction:

9.25 x 10^7 - 0.374 x 10^6 km = 9.249626 x 10^7 km

Therefore, traveling from Earth to Mars is approximately 9.249626 x 10^7 km farther than traveling from Earth to the moon.

Scientific notation is a convenient way to express very large or very small numbers. It consists of a coefficient (a number between 1 and 10) multiplied by a power of 10 (exponent). It allows us to write and manipulate such numbers in a compact and standardized form.

To know more about Traveling .

https://brainly.com/question/21219866

#SPJ11

Answer: 20 weeks

Step-by-step explanation:

340 - 40 = 300

15 (w)

300 / 15 = 20

15 (20) = 300

The null hypothesis is \(\mu = 39.09\)  

The symbol \(\mu\) is the Greek letter mu

The alternate hypothesis is \(\mu \ne 39.09\) telling us we have a two-tailed test here. The "not equal" is directly tied to the keyword "different" given in the instructions. In other words, mu being different from 39.09 directly leads to \(\mu \ne 39.09\)

So either mu is 39.09 or it's not 39.09

You can use H0 and H1 to represent the null and alternate hypotheses respectively.  

----------------------

Summary:

The two hypotheses are

H0: \(\mu = 39.09\)

H1: \(\mu \ne 39.09\)

This is a two tailed test.

Answer:

Step-by-step explanation:

Therefore, at least 49 street lights can be installed along one side of the street with equal distance between the lights.

An equation is a mathematical statement that shows that two expressions are equal. It consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), separated by an equals sign (=). The equals sign indicates that the two expressions are equal, and the goal of solving the equation is to find the value of x that makes this statement true. Equations can be solved using various algebraic techniques, such as simplifying and rearranging the expressions, applying operations to both sides of the equation, and factoring or expanding expressions. Solving an equation involves finding the values of the variables that make the equation true.

Here,

The distance between point A and B is AB, and the distance between point B and C is BC. Let's assume that the distance between each street light is "d".

Since there must be a street light at points A, B, and C, there will be a total of two gaps between these three street lights, which are AB and BC. Thus, the number of street lights required is equal to the sum of the lengths of AB and BC, divided by the distance "d" between the street lights, plus 1 for the street light at point B.

So, the total number of street lights required is

Number of street lights = (AB + BC) / d + 1

We know that AB = 1170 m and BC = 1625 m, and the distance between each street light should be equal. Therefore, we need to find the greatest common factor (GCF) of 1170 and 1625 to determine the distance between each street light.

1170 = 2 x 3 x 3 x 5 x 13

1625 = 5 x 5 x 13

The GCF of 1170 and 1625 is 65, which means the distance between each street light should be 65 meters.

Now we can calculate the total number of street lights required:

Number of street lights = (1170 + 1625) / 65 + 1

= 49

To know more about equation,

https://brainly.com/question/28243079

#SPJ9

Answer:

61

Step-by-step explanation:

add 42 the 19 because of reverse operation