Sand falls from an overhead bin and accumulates in a conical pile with a radius that is always three times its height. Suppose the height of the pile increases at a rate of 3 cm/s when the pile is 14 cm high. At what rate is the sand leaving the bin at that instant? Let V and h be the volume and height of the cone, respectively. Write an equation that relates V and h and does not include the radius of the cone. (Type an exact answer, using π as needed.) Differentiate both sides of the equation with respect to t. dV/dt = (______) dh/dt The sand is leaving the bin at a rate of _________ (Type an exact answer, using π as needed.)

Answer: 32

Step-by-step explanation:

From the question, we are informed that one carton of milk contains 128 ounces and that Sara's son drinks 4 ounces with every meal.

The number of 4-ounce servings that will be in a carton of milk will be:

= 128 / 4

= 32

Answer:

minimum=31

maximum=74

median=52

first quartile=¼×9=2.25. =47

third quartile=¾×9=6.75 =70

explanation

hi use the example above to workout.

No, the plan will not work because tan B = 8/5; B ≈ 58°

There are three primary trigonometric ratios for a right angle triangle and they are:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

To get angle B, we will make use of trigonometric ratios to get:

tan B = 8/5

tan B = 1.6

B = tan⁻¹1.6

B = 58°

From the ramp, we can see that the angle is greater than what Gael wants to build and as such we can say it will not work.

Read more about trigonometric ratios at: https://brainly.com/question/13276558

#SPJ1

Answer:

C

Step-by-step explanation:

negative four raised to the sixth power divided by negative four raised to the fourth power

because  negative four raised to the fourth power divided by negative four raised to the second power = negative four raised to the second power

negative four raised to the sixth power divided by negative four raised to the fourth power also = negative four raised to the second power

The answer is A: negative four raised to the second power divided by negative four raised to the fourth power. This is obtained by applying the rules of exponents, specifically, when dividing with the same base, subtract the exponents.

This question pertains to exponents division rules. According to the rule of Power of a Power in exponents, when you divide expressions with the same base, you subtract the exponents. So if you have negative four raised to the fourth power (-4⁴) and you want to divide it by negative four raised to the second power (-4²), you subtract 2 from 4 to get an exponent of 2. This results in a negative four raised to the second power (-4²). So, the correct option from the given choices in your question is A: negative four raised to the second power divided by negative four raised to the fourth power.

Learn more about Exponents here:

https://brainly.com/question/5497425

#SPJ2

(a) For p(x) = c(ſ)^x, x = 1, 2, 3, ..., the value of the constant c, such that p(x) satisfies the condition of being a probability mass function (pmf) of one random variable X is : (ſ - 1)/ſ.

(b) For p(x) = cm, x = 1, 2, 3, 4, 5, 6, and zero elsewhere, the value of the constant c, such that p(x) satisfies the condition of being a probability mass function (pmf) of one random variable X is :  1/21.

(a) For p(x) = c(ſ)^x, x = 1, 2, 3, ..., and zero elsewhere, we need to ensure that the sum of all probabilities equals 1. Since the function is defined for positive integers, we can use the geometric series formula:

Σ(c(ſ)^x) = 1, where x ranges from 1 to infinity.

c * (ſ/(ſ - 1)) = 1 (geometric series formula)

To find c, we simply rearrange the equation:

c = (ſ - 1)/ſ

So for this pmf, the constant c is (ſ - 1)/ſ.

(b) For p(x) = cm, x = 1, 2, 3, 4, 5, 6, and zero elsewhere, we again need the sum of all probabilities to equal 1:

Σ(cm) = 1, where x ranges from 1 to 6.

c * (1 + 2 + 3 + 4 + 5 + 6) = 1

c * 21 = 1

To find c, we rearrange the equation:

c = 1/21

So for this pmf, the constant c is 1/21.

To learn more about probability mass function visit : https://brainly.com/question/30765833

#SPJ11

Answer:

-85 is rational and an integer, though an integer is the most specific

Step-by-step explanation:

Whole numbers do not include negative numbers

:]

SOLUTION:

Step 1:

In this question, we are given the following:

A pancake recipe asks for one and one-half times as much milk as flour.

If three and one-half cups of milk are used, what quantity of flour would then be needed, according to the recipe?

Step 2:

The details of the solution are as follows:

The pancakes require 1.5 cups of milk and 1 cup of flour or a ratio of 1.5:1 or a fraction of

(1.5) / (1)

If you have 3.5 cups of milk you need x cups of flour

Set up a ratio of 1.5 / 1 = 3.5 / x

(1.5 divided by 1 equals 3.5 divided by x)

Cross multiply one numerator by the other denominator, and then the other way.

1.5x = 3.5

divide both sides by 1.5

x = 35/15 = 2 1/3 cups

CONCLUSION:

The quantity of flour that would be needed, according to the recipe =

Answer:

3*3*44.14$

That's the answer

Use a calculator

Yes, the implications of leaving farm fields unused for the economy's PPF diagram can be seen in the output of agricultural products.

The PPF diagram shows the maximum output of two products that an economy can produce at a given time, and it is shaped like a curve. When farm fields are left unused, the amount of agricultural products that can be produced is decreased, resulting in a shift in the PPF curve inwards. This means that the economy has to sacrifice other goods to maintain the same level of production of agricultural products, leading to an opportunity cost. Thus, leaving farm fields unused has implications for the economy's PPF diagram, as it reduces the output of agricultural products, resulting in a shift in the PPF curve inwards.

Learn more about maximum output here:

https://brainly.com/question/30149485

#SPJ4

Answer:

1. 7+62+5+4

2. 18+62+5

3.15+4+1

4.5 families

6. three

Step-by-step explanation:

Answer:

Inequality would be the answer

The expected value of E(X+6) is 34 and the variance of Var(5X) is 450.

Given that the expected value of X is E(X) = 28 and variance of X is Var(X) = 18.

We have to find the expected value of E(X+6) and variance of Var(5X).

Expected value of E(X+6)E(X+6) = E(X) + E(6)

By linearity of expected values, we have

E(X+6) = E(X) + E(6)

= 28 + 6 = 34.

Therefore, the expected value of E(X+6) is 34.

Variance of Var(5X)Var(5X) = Var(X)*5²

By linearity of variance, we have

Var(5X) = Var(X)*5²

= 18*25

= 450.

Therefore, the variance of Var(5X) is 450.

Thus, the expected value of E(X+6) is 34 and the variance of Var(5X) is 450. Hence, the correct option is 34,450.

The expected value of E(X+6) is 34 and the variance of Var(5X) is 450.

To know more about variance visit:

brainly.com/question/14116780

#SPJ11

Answer:

f(x) is the blue graph, g(x) is the red graph.

x^2 - 3x + 17 - (2x^2 - 3x + 1) = 16 - x^2

16 - x^2 = 0 when x = -4, 4

So the area between these two graphs is (using the TI-83 graphing calculator):

fnInt (16 - x^2, x, -4, 4) = 85 1/3

Answer:

D(300

Step-by-step explanation:

It in edu 2021

Answer:

The equation of the line of best fit is y=(1)(12)x using the exponential regression.

The proper conclusion is as follows:Option E is the correct conclusion. We are 90% confident that the difference in proportions between Toyota and Subaru car owners who are satisfied with their drive systems is between -0.278 and -0.116.

What is a confidence interval estimate?

Confidence intervals are statistical tools used to make inferences about population parameters based on sample statistics. A confidence interval is a range of values that has a high probability of containing an unknown parameter. The width of a confidence interval is determined by the level of confidence and the variability of the data.Random SamplingIn random sampling, every item in the population has an equal chance of being selected as part of the sample. As a result, random sampling should produce a representative sample, which is important in drawing valid conclusions. However, it is not always feasible or cost-effective to conduct a complete enumeration or census. Instead, a sample of the population is usually taken.

For more questions on drive systems

https://brainly.com/question/11017131

#SPJ11

The number of possible distinguished arrangements of the 8 coins will be 630.

We have Gold= 4             Silver= 4  coins.

So the number of ways of arranging 8 coins where four are similar and other four are similar is

8! /4!*4! = 70.

Now let's take cases with

U = head up

D = head down

Therefore, total number of ways will be 70*9 = 630.

For more questions related to arrangement of coins

https://brainly.com/question/17110818

#SPJ4

Answer:

495

Step-by-step explanation:

there are three 10-year periods in 30 years so multiply 55 · 3(3), which is 495

The tourist had $1200.91 in US dollars when he left the country.

The American tourist exchanged 80% of $8175 to local currency, which is:

0.8 x $8175 = $6540

To calculate how much local currency the tourist received for $6540, we can use the buying rate of Kshs.83.25 per US dollar:

Amount in local currency = $6540 x Kshs.83.25 per US dollar = Kshs.544335

After spending Kshs.443,595, the tourist had Kshs.544,335 - Kshs.443,595 = Kshs.100,740 left.

To calculate how much US dollars the tourist can buy with Kshs.100,740, we can use the selling rate of Kshs.84.05 per US dollar:

Amount in US dollars = Kshs.100,740 / Kshs.84.05 per US dollar = $1200.91

Therefore, the tourist had $1200.91 in US dollars when he left the country.

Learn more about currency exchange here:

https://brainly.com/question/17185506

#SPJ1

The possible solutions of the inequality expression given as 20y < -5 + 18y are (c) y < -5/2, y < -2.5 and (d) -2.5 > y

From the question, we have the following parameters that can be used in our computation:

20y < -5 + 18y.

To start with, we need to collect the like terms of both sides

Using the above as a guide, we have the following:

20y -18y < -5

Next, we need to evaluate the like terms of both sides

Using the above as a guide, we have the following:

2y < -5

Lastly, we divide both sides by 2

y < -5/2

Express as decimal

y < -2.5

Switch the positions

-2.5 > y

Hence, the solutions are y < -5/2, y < -2.5 and -2.5 > y

Read more about inequality at

https://brainly.com/question/25275758

#SPJ1

Answer:

7 dollars and 25 cents

Step-by-step explanation:

there is 8 quarts in 2 gallons then divide 58 dollars by 8 and you get 7 dollars 25 cents

Division is one of the four fundamental arithmetic operations. The price per quart is $7.25 per quart.

The division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.

Given that A 2-gallon bucket of paint costs $58.00. Therefore, the price per gallon is,

Price per gallon = $58/2

Since a gallon is equal to 4 quarts. Therefore, the price per quart is,

Price per quart  = $58/(4×2) = $7.25 per quart

Learn more about Division:

https://brainly.com/question/369266

#SPJ2

Answer:

No

Step-by-step explanation:

x=(b-5)/c≠(5-b)/c

supposedly

b=6

c=1

x=6-5/1=1

x=5-6/1= -1

1≠ -1

Answer:

No

Step-by-step explanation:

x = b - 5 / L equal to - (5 - b) / L

Answer:

Step-by-step explanation:

Answer:

3400

Step-by-step explanation:

60 * 70 = 4200

70 - 10 - 20 = 40

20 * 40 = 800

4200 - 800 = 3400

Answer:

3,400

Step-by-step explanation:

I did 70 times 60 which gave me 4,200 then with the 10 and 20 I subtracted it to 70 and did 20 times 40 that gave me 800 then subtracted that by 4200 then it gave me 3,400.

The value for x is 7π/6 and 11π/6.

sin2xsecx+2cosx=0

(2sinxcosx)(1/cosx)+2cosx=0

sinxcosx/cosx+2cosx=0

So,

2sinx+2cosx=0

2(sinx+cosx)=0

(2(sinx+cosx))²=0

4(sin²x+cos²x+2sinxcosx)=0

hence,

(sin²x+cos²x+2sinxcosx)/4=0/4

sin2x+cos2x+2sinxcosx=0

1+sin2x=0

sinx=−1/2

=7π/6 and 11π/6

Know more about trigonometry at:

https://brainly.com/question/20519838

#SPJ4

Hypothesis: If two angles are congruent.

Conclusion: Then they have the same measure.

The hypothesis states that if two angles are congruent, which means they are identical in shape and size, then the conclusion is that they have the same measure. In other words, when two angles are congruent, their measures are equal.

Angles are typically measured in degrees or radians. When we say that two angles are congruent, it implies that the measures of those angles are the same. This can be understood through the transitive property of congruence, which states that if two angles are congruent to a third angle, then they are congruent to each other.

For example, if angle A is congruent to angle B, and angle B is congruent to angle C, then it follows that angle A is congruent to angle C. This implies that the measures of angle A and angle C are equal, as congruent angles have the same measure.

In conclusion, the hypothesis that if two angles are congruent implies that they have the same measure is valid and supported by the principles of congruence and the transitive property.

For more information about hypothesis and conclusion, refer:

brainly.com/question/28564896

#SPJ11

Answer:

4 out of 14

Step-by-step explanation:

there is only 4 door bells and 14 bells in total

Answer:

Step-by-step explanation:

1. a = 3, b = 4

 3^2 + 4^2 = c^2

  9 + 16 = c^2

   25 = c^2

square root both sides

    5  = c

2. 5^2 + 12^2 = c^2       a = 5, b = 12

    25 + 144 = c^2

    169 = c^2

  square root both sides

    13 = c

3. 6^2 + 8^2 = c^2    a = 6, b = 8

    36 + 64 = c^2

   100 = c^2

Square root both sides

  10 = c

You have the following expression:

In order to express the previous number as an expression with the imaginary unit, you consider the following:

where the square root of -1 is the imaginary unit i by definition. Thus, by replacing you obtain:

Hence, the given expression in terms of the imaginary unit is :