A restaurant is changing how they make their ice cubes but they want them to be the
same width and height. the original ice cubes were cubes now they will make them
as spheres and they wonder if they will use less water or more water. if the original
ice cube had a side length of 3 cm, and the new sphere ice ball has to have the same
width, what is the volume of the new sphere ice ball?
how much water do they save? (find the volume of both)

The sequence \(an=6ne^{(-5n)}\) is decreasing and bounded.

To determine whether the sequence \(an=6ne^{(-5n)}\)  is increasing, decreasing, or not monotonic and whether it is bounded or not, follow these steps:

1. Analyze the sequence's formula:
[tex]an=6ne^{(-5n)}\) can be rewritten as \(an=6n \frac{1}{e^{(5n)} }\)

2. Examine the factors in the formula:
The first factor, 6n, is increasing as n increases. The second factor, \(\frac{1}{e^{5n} }\), is decreasing as n increases since the exponent in the denominator is increasing, causing the overall value to decrease.

3. Determine the overall trend of the sequence:
The sequence an is a product of an increasing factor and a decreasing factor. To determine the overall trend, we can examine the limit of the sequence as n approaches infinity.

4. Calculate the limit:
As n approaches infinity, the decreasing factor \(\frac{1}{e^{5n} }\) dominates the sequence, causing the limit of the sequence to approach 0. This indicates that the sequence is decreasing.

5. Determine if the sequence is bounded:
Since the sequence is decreasing and approaches 0 as n approaches infinity, it has a lower bound of 0. Additionally, the sequence is positive for all values of n, so it is also upper-bounded. Therefore, the sequence is bounded.

The sequence \(an=6ne^{(-5n)}\) is decreasing and bounded.

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Answer:

r = 3.6 , a = 2

Step-by-step explanation:

given that r is inversely proportional to a then the equation relating them is

r = \(\frac{k}{a}\) ← k is the constant of proportion

to find k use the condition when r = 12 , a = 1.5

12 = \(\frac{k}{1.5}\) ( multiply both sides by 1.5 )

18 = k

r = \(\frac{18}{a}\) ← equation of proportion

when a = 5 , then

r = \(\frac{18}{5}\) = 3.6

when r = 9 , then

9 = \(\frac{18}{a}\) ( multiply both sides by a )

9a = 18 ( divide both sides by 9 )

a = 2

The camp cook made 6 servings of chicken soup

If Number of pots of soup=1\(\frac{1}{2}\)

and one serving of soup equals  \(\frac{1}{4}\) of a pot.

Then the  number of servings of pot of soup= \(\frac{Number of pots of soup}{serving of soup}\)

Therefore the number of servings of pot of soup=   1\(\frac{1}{2}\) ÷\(\frac{1}{4}\)

number of servings of pot of soup(multiplying out ) =

\(\frac{3}{2}\) x \(\frac{4}{1}\)= 6 servings of chicken soup

Therefore, for  1\(\frac{1}{2}\) pots of soup, we will have 6 servings of chicken soup

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Answer:

5 : 7

Step-by-step explanation:

Assuming simplest form means in whole numbers, to find the ratio in simplest form, just multiply both sides by the same value until they are both whole numbers. So 2.5 : 3.5 = 2.5 * 2 : 3.5 * 2 = 5 : 7

Answer:

5:7

Step-by-step explanation:

The simplest form of 2.5 : 3.5 is 5:7 because 2.5 x 2 = 5 and 3.5 x 2 = 7

Answer:

-3.625 < -3.62

Step-by-step explanation:

The correct answer is B

Answer:

0.976 or 97.6%

Step-by-step explanation:

To calculate the frequency of the recessive allele, we need to use the information provided about the frequency of the dominant trait.

Let's assume that the particular dominant trait is determined by a single gene with two alleles: the dominant allele (A) and the recessive allele (a).

Given that 45 out of 1,000 babies are born with the dominant trait, we can infer that the remaining babies (1,000 - 45 = 955) do not have the dominant trait and can be considered as the recessive trait carriers.

The frequency of the recessive allele (q) can be calculated using the Hardy-Weinberg equation:

q = sqrt((Recessive individuals) / (Total individuals))

In this case, the total number of individuals is 1,000, and the number of recessive individuals is 955.

q = sqrt(955 / 1,000)

Using a calculator, we can find the value:

q ≈ 0.976

Therefore, the frequency of the recessive allele is approximately 0.976 or 97.6%.

The surface area of a conical grain storage tank that has a height of 42 meters and a diameter of 24 meters is 1,670.5 square meters.

The surface area of a cone is calculated using the following formula:

Surface area = πr² + πrl, where π is approximately equal to 3.14, r is the radius of the base of the cone, and l is the slant height of the cone.

In this problem, we are given that the height of the cone is 42 meters and the diameter of the base is 24 meters. The radius of the base is half of the diameter, so the radius is 12 meters. The slant height of the cone can be calculated using the Pythagorean theorem.

l² = 12² + 42²

l² = 1764

l = 42.01 meters

The surface area of the cone is then calculated as follows:

Surface area = πr² + πrl

Surface area = 3.14 * 12² + 3.14 * 12 * 42.01

Surface area = 1,670.5 square meters

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Answer:

-12 < 8 < 9 > 0 > -10 < 1

The subshell designated by each set of quantum numbers is as follows:

a) n=3, l=1 -> 3p subshell

b) n=4, l=2 -> 4d subshell

c) n=2, l=0 -> 2s subshell

d) n=5, l=3 -> 5f subshell

In the electron configuration of an atom, each electron is described by a set of four quantum numbers, which includes the principal quantum number (n), the angular momentum quantum number (l), the magnetic quantum number (m), and the spin quantum number (s). The second quantum number (l) determines the shape of the subshell, which in turn influences the energy level and chemical behavior of the atom. The letter designation for each subshell is based on the value of the angular momentum quantum number (l): s (l=0), p (l=1), d (l=2), f (l=3), and so on. Therefore, for a given set of quantum numbers, we can determine the subshell designation by identifying the value of l.

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Answer:

x = 6\(\sqrt{2}\)

Step-by-step explanation:

Using the cosine ratio in the right triangle and the exact value

cos45° = \(\frac{1}{\sqrt{2} }\) , then

cos45° = \(\frac{adjacent}{hypotenuse}\) = \(\frac{6}{x}\) = \(\frac{1}{\sqrt{2} }\) ( cross- multiply )

x = 6\(\sqrt{2}\)

a. To reach the goal of $100,000, they would have to save approximately $4,866.96 each year.

b. To reach the new goal of $140,000, they would have to save approximately $6,813.75 each year.

a. To calculate the amount they need to save each year to reach the goal of $100,000, we can use the future value of an ordinary annuity formula. Given that they earn a 5.0% annual interest rate on their investments, and they start saving on your first birthday, they have a total of 17 years to save before you turn 18. Using the formula, we can solve for the annual savings amount:

PV = (PMT / r) * (1 - (1 + r)^(-n))

Where PV is the present value (which is $0 since they haven't saved anything yet), PMT is the annual savings amount, r is the interest rate per period (5.0% or 0.05), and n is the number of periods (17 years).

Substituting the values into the formula, we can solve for PMT

$100,000 = (PMT / 0.05) * (1 - (1 + 0.05)^(-17))

PMT ≈ $4,866.96 (rounded to the nearest cent)

b. If they decide to save for five years instead of four to have $140,000 saved, the calculation is similar. They now have a total of 16 years to save before you turn 18. Using the same formula and substituting the new values

$140,000 = (PMT / 0.05) * (1 - (1 + 0.05)^(-16))

PMT ≈ $6,813.75 (rounded to the nearest cent)

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The polar equation of the graph shown below include the following: B. r = 4cos5θ.

In Mathematics and Geometry, the relationship between a polar coordinate (r, θ) and a rectangular coordinate (x, y) based on the conversion rules is given by the following polar equations:

a = rcos(θ)    ....equation 1.

b = rsin(θ)     ....equation 2.

Where:

By critically observing the graph of this polar equation, we can logically conclude that it represents a rose and it is symmetric with respect to the polar axis;

-r = -4cos5(π - θ)

-r = -4cos(5π - 5θ)

-r = 4cos(-5θ)

-r = -4cos(5θ)

r = 4cos(5θ)

In conclusion, the graph shown below can be modeled by this polar equation r = 4cos(5θ).

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer: 5¹/₄ cups of dog food

Step-by-step explanation:

There are seven days in a week.

If she feeds the dog 3/4 every day, the amount she feeds Rusty every week is:

= 3/4 * 7

= 21/4

= 5¹/₄ cups of dog food

Answer:

50% chance of harriet picking a blue marbel I hope that this is the answer you wanted

Answer:

80 pennies make 8 dimes

Step-by-step explanation:

10 pennies make a dime

10p=1d

Plug in 8 to each side

(10x8)=(1x8)

p         d

80=8d

The number of books that had no damage or minor damage in the sample is:

722 + 75 = 797

To estimate the number of books in the entire collection that would have no damage or minor damage, we can assume that the proportion of books with no or minor damage in the sample is approximately equal to the proportion of books with no or minor damage in the entire collection.

The proportion of books with no or minor damage in the sample is:

797 / (722 + 75 + 29) = 0.9064

So we can estimate the number of books with no damage or minor damage in the entire collection as:

0.9064 x 70,500 = 63,912.6

Rounding to the nearest whole number, we get:

63,913

Answer:

242

Step-by-step explanation:

   242

4/968   how many times does 4 go into 9?  2 times put the 2 above the 9

 8            4 times 2 equals 8 so you put the 8 below the 9 and subtract

  1 6                   9 minus 8 equals 1 than you drop the 6

  1 6          how many times does 4 go into 16? 4 times. put the  4 above the 6

    0 8        than multiply 4 *4 =16 than 16-16=0 drop the 8

       8          4 goes into 8, 2 times  the 2 goes above the 8. 4*2=8

        0            8-8=0

The dot product associated to sides AB and BC is 0.

In this question we must find the dot product of two vectors associated with two surrounding sides of a triangle. First, we need to find the vectors associated to sides AB and BC:

Side BA

BA = (5, 3) - (0, 0)

BA = (5, 3)

Side BC

BC = (- 3, 5) - (0, 0)

BC = (- 3, 5)

By definition of dot product, the result associated to the two sides of the triangle is:

BA • BC = (5, 3) • (- 3, 5)

BA • BC = (5) · (- 3) + (3) · (5)

BA • BC = - 15 + 15

BA • BC = 0

The dot product associated to sides AB and BC is 0.

The statement is poorly formatted, the correct form is shown below:

If A(x, y) = (5, 3), B(x, y) = (0, 0) and C(x, y) = (- 3, 5) are the vertices of a triangle then the value of the dot product between vectors AB and BC is:

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Answer:

289 feet

Step-by-step explanation:

Good Lucky & Keep Spirit to do that

Answer:

1/10

Step-by-step explanation:

3/5 + (-1/2) =

= 3/5 - 1/2

= 6/10 - 5/10

= 1/10

Answer:

1/10

Step-by-step explanation:

This is right??

Use the calculator

Answer:

You're right...

Step-by-step explanation:

(4-5)-(13-18+2)

(-1)-(-3)

-1+3

2

A regression equation estimates the dependent variable(s). A regression equation is a statistical model that examines the relationship between two variables: one independent variable and one dependent variable.

Regression models are used to predict or explain the value of the dependent variable based on the value of the independent variable. In a regression equation, the dependent variable is the variable being predicted or explained, while the independent variable is the variable being used to make the prediction or explanation. Therefore, a regression equation estimates the dependent variable(s).Objective and constraint functions are terms commonly used in linear programming, which is a different type of statistical modeling. Factors outside the relevant range may be taken into account in some statistical models, but this is not a defining characteristic of regression equations.

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Answer:

\(30\)

Step-by-step explanation:

1. Approach

First, use the Pythagorean theorem to solve for the hypotenuse of the given right triangle. Then find the perimeter by adding up the values of all the sides. The problem then has the lengths of the legs doubled. When the legs undergo a scaling factor, the hypotenuse and perimeter undergo the same scaling factor. Here, the legs are doubled, hence the hypotenuse and the perimeter are also doubled. Finally, subtract the new perimeter from the original perimeter.

2. Find the original hypotenuse

Remember the Pythagorean theorem states;

\(x^{2}+y^{2}=z^{2}\)

Where (a) and (y) are the legs (or the sides adjacent to the right angle), and (z) is the hypotenuse or the side opposite to the right angle.

Substitute in the given value and solve,

\((5)^{2}+(12)^{2}=z^{2}\\\\25 + 144 = z^{2}\\\\169=z^{2}\\\\\sqrt{169}=z\\\\13=z\)

3.Find the perimeter of the original triangle

To find the perimeter of a polygon, one must add up the lengths of all the sides.

\(5 + 12 + 13\\\\= 30\)

4. Find the new perimeter

In a right triangle, when both legs undergo a scaling factor, the hypotenuse also has the same change, and the perimeter also undergoes the same change. In this case, the length of the legs is doubled, therefore, the hypotenuse and the perimeter are also doubled.

New hypotenuse; \(26\)

New perimeter; \(60\)

5. Find the difference

Now all that is left is to subtract the new perimeter from the original perimeter;

(New_perimeter) - (original_perimeter)

= \(60 - 30\)

= \(30\)

Answer:

m∠e = 58

Step-by-step explanation:

180 - supplementary

122 - m∠a

x - m∠e

x + 122 = 180

180 - 122 = x

x = 58

The integral ∫[0 to 1] x² dx evaluates to 1/3.

To evaluate this integral, we can use the power rule for integration. Applying the power rule, we increase the power of x by 1 and divide by the new power. Thus, integrating x² gives us (1/3)x³.

To evaluate the definite integral from x = 0 to x = 1, we substitute the upper limit (1) into the antiderivative and subtract the result when the lower limit (0) is substituted.

Using the Fundamental Theorem of Calculus, the area under the curve is given by the expression A = ∫[0 to 1] f(x) dx. For this case, f(x) = x².

To approximate the area using right endpoints, we can use a Riemann sum. Dividing the interval [0, 1] into subintervals and taking the right endpoint of each subinterval, the Riemann sum can be expressed as lim[n→∞] Σ[i=1 to n] f(xᵢ*)Δx, where f(xᵢ*) is the value of the function at the right endpoint of the i-th subinterval and Δx is the width of each subinterval.

In this specific case, since the function f(x) = x² is an increasing function on the interval [0, 1], the right endpoints of the subintervals will be f(x) values.

Therefore, the area under the curve from x = 0 to x = 1 can be expressed as lim[n→∞] Σ[i=1 to n] (xi*)²Δx, where Δx is the width of each subinterval and xi* represents the right endpoint of each subinterval.

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The correct choice is B. The trinomial 20s^{2}+19s+3 is not factorable.

To determine if a trinomial is factorable, we can look for two binomials that multiply together to give the original trinomial. The binomials would have the form (as+b)(cs+d), where a, b, c, and d are constants.

In this case, we have the trinomial 20s^{2}+19s+3. To factor it, we would need to find values for a, b, c, and d such that (as+b)(cs+d) simplifies to 20s^{2}+19s+3.

We can attempt to factor it by considering all possible combinations of values for a, b, c, and d that satisfy ac=20 and bd=3, and also satisfy ad+bc=19. However, after trying different combinations, we find that there are no such values that satisfy these conditions.

Therefore, the trinomial 20s^{2}+19s+3 is not factorable.

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If z varies with y and inversely with and z = 6 when x = 4 and y = 3, then the value of Proportionality Constant is given by 8.

Proportion is a relation between two mathematical variables. If two variables vary directly that states if one increases another will also decrease and same for decrease.

If two variables are in inverse relation that states that if one variable increases then another decreases and if one variable decreases then another increases.  

Given that, z varies with y and inversely with x. So,

z = k*(y/x), where k is the proportionality constant.

Given that, z = 6 when x = 4 and y = 3. So,

6 = k*(3/4)

k = (6*4)/3

k = 2*4

k = 8

Hence the value of Proportionality Constant is 8.

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The question is incomplete. The complete question will be -

"z varies with y and inversely with x when z=6, x=4, and y=3. Find the value of Proportionality Constant."