a spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.3 cm/min. at what rate is the volume of the snowball decreasing when the radius is 15 cm. (note the answer is a positive number).

Answer:

9.42 or 3pi

Step-by-step explanation:

equation of a circle is 2*pi*r

2r is d which is 3 so the answer would be 3pi which equals about 9.42

The height, in inches, of the entertainment center is 32 inches while other dimensions are 16 inches.

The volume of the unit will be the product of length, depth and height. Now the depth will be 2x. Based on this, performing the calculation to find the value of x.

Volume = length × depth × height

8192 = x × x × 2x

Performing multiplication on Right Hand Side of the equation

8192 = 2x³

Rewriting the equation according to x

x³ = 8192/2

Performing division on Right Hand Side of the equation

x³ = 4096

Taking cube root on Right Hand Side of the equation

x = \( \sqrt[3]{4096} \)

x = 16 inches

Height = 2×16

Performing multiplication on Right Hand Side of the equation

Height = 32 inches

Thus, length and depth are 16 inches and height is 32 inches.

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Answer:

18x

Step-by-step explanation:

-It is the same as 3x^-2 • 6x^3.

-Multiply the constants (in this case 3 and 6 =18)

-Add the exponents (-2+3=1)

-Your answer is 18x

The outcomes of each trial are independent events because the selection of a month does not affect the probability of selecting a particular day within that month.

to determine whether the given outcomes are dependent or independent events.

In this scenario, you have two trials:

1. Selecting a month at random.
2. Selecting a day of that month at random.

These outcomes are considered independent events because the outcome of the first trial (selecting a month) does not influence or affect the outcome of the second trial (selecting a day). Each trial is independent and can occur without any reliance on the outcome of the other trial.

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Based on the function shown on the graph, the statement that is true is: D. The candle started at 9 mm and shrinks 5 mm every 4 minutes.

A function is a relationship between input and output values.

On a graph, the average rate of change represents the unit rate, while the point where the line intercepts the y-axis is the initial value or starting value.

Therefore:

The starting value = 9 mm (the candle length when it started burning).

In conclusion, based on the function shown on the graph, the statement that is true is: D. The candle started at 9 mm and shrinks 5 mm every 4 minutes.

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False. The expected cell frequency in statistical analysis, specifically in the context of contingency tables and chi-square tests, is not based on the researcher's opinion. Instead, it is determined through mathematical calculations and statistical assumptions.

In contingency tables, the expected cell frequency refers to the expected number of observations that would fall into a particular cell if the null hypothesis of independence is true (i.e., if there is no relationship between the variables being studied). The expected cell frequency is calculated based on the marginal totals (row totals and column totals) and the overall sample size.

The expected cell frequency is computed using statistical formulas and is not influenced by the researcher's opinion or subjective judgment. It is a crucial component in determining whether the observed frequencies in the cells significantly deviate from what would be expected under the null hypothesis.

By comparing the observed cell frequencies with the expected cell frequencies, statistical tests like the chi-square test can assess the association or independence between categorical variables in a data set.

Thus, the statement "the expected cell frequency is based on the researcher's opinion" is false. The expected cell frequency is derived through statistical calculations and is not subject to the researcher's subjective input.

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Since q1 and q2 are integers, their difference (q1 - q2) is also an integer. Therefore, the difference between a and b is divisible by 6.

Using the pigeonhole principle, we can show that in any group of 7 integers, there is at least 2 whose difference is divisible by 6.

When an integer is divided by 6, the possible remainders (r) are from the set {0, 1, 2, 3, 4, 5}. There are 6 possible remainders. Now, consider a group of 7 integers. According to the pigeonhole principle, since there are 7 integers and only 6 possible remainders, at least two of these integers must have the same remainder when divided by 6.

Let these two integers be a and b, with a > b, and both having the same remainder r when divided by 6. So, we can write a = 6q1 + r and b = 6q2 + r.

Now, let's find the difference: a - b = (6q1 + r) - (6q2 + r) = 6q1 - 6q2 = 6(q1 - q2).

Since q1 and q2 are integers, their difference (q1 - q2) is also an integer. Therefore, the difference between a and b is divisible by 6.

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Answer:

Step-by-step explanation:

387828

The solution set of the system of equations y = -x + 1 and y = x² + 5x + 6 includes the ordered pairs (-1, 2) and (-5, 6).

To find the ordered pair that is in the solution set of the system of equations y = -x + 1 and y = x² + 5x + 6, we need to solve the equations simultaneously.
First, let's set the two equations equal to each other:
-x + 1 = x² + 5x + 6
Rearranging the equation, we have:
x² + 6x + 5 = 0
Next, we can factor the quadratic equation:
(x + 1)(x + 5) = 0
Setting each factor equal to zero, we find two possible values for x:
x + 1 = 0

-->  x = -1
x + 5 = 0  

-->  x = -5
Now that we have the possible values for x, we can substitute them back into either of the original equations to find the corresponding y-values.
For x = -1:
y = -(-1) + 1

= 2
So, the ordered pair (-1, 2) is in the solution set.
For x = -5:
y = -(-5) + 1

= 6
In conclusion, The ordered pair (-5, 6) is also in the solution set.

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The 22-volume (area) of the parallelepiped defined by the vectors \(\(\vec{v_1} = [1, 3, 3, -3]\)\) and \(\(\vec{v_2} = [0, 2, 1, -3]\)\) in \(\(\mathbb{R}^4\)\) is 7.

The 22-volume of a parallelepiped in \(\(\mathbb{R}^4\)\) is calculated using the scalar triple product. Let \(\(\vec{v_1}\) and \(\vec{v_2}\)\) be two vectors defining the parallelepiped. The 22-volume (area) of the parallelepiped is given by the magnitude of the scalar triple product of \(\(\vec{v_1}\), \(\vec{v_2}\)\), and their cross product \(\(\vec{n}\)\) (normal vector to the parallelepiped), divided by the magnitude of \(\(\vec{n}\)\).

To calculate the scalar triple product, we find the cross product of \(\(\vec{v_1}\) and \(\vec{v_2}\)\):

\(\(\vec{n} = \vec{v_1} \times \vec{v_2}\).\)

Next, we calculate the scalar triple product:

\(\(V = |\vec{v_1} \cdot \vec{v_2} \times \vec{n}| / |\vec{n}|\).\)

In this case, the cross product \(\(\vec{n}\) of \(\vec{v_1}\) and \(\vec{v_2}\)\) is [-7, 3, -2, -2]. The scalar triple product is \(\(V = |(-1) \cdot (-2) \cdot (-2) \cdot (-2)| / |(-7, 3, -2, -2)| = 7\)\).

Therefore, the 22-volume (area) of the parallelepiped is 7.

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The required position of the -2.25 lies above the -2.25 on the vertical number line.

Given that,
If -2.5 < -2.25, how are the positions of the two numbers related on the vertical number line is to be determined.

A number line is defined as the number marked on the line calibrated into an equal number of units. For example -1, 0, 1, and so on.

Here,
Since -2.5 is 0.25 lower than -2.25, and also the -2.25 is greater than -2.5.
So on the vertical number line, -2.25 lies 0.25 units above the number -2.5.

Thus, the required position of the -2.25 lies above the -2.25 on the vertical number line.

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Answer:

On the vertical number line, -2.5 is located below -2.25.

Step-by-step explanation:

edmentum answer. have a good day

Answer:

Una relación lineal es de la forma:

y = a*x + b.

donde a es la pendiente y b es la ordenada al origen.

en este caso, y es el precio de la camioneta, x es el numero de años que pasaron, a es la razon de depreciación de la camioneta y b es el precio inicial de la camioneta, b = $42,000.

Sabemos que después de 5 años, el precio de la camioneta es 21,000, entonces podemos resolver:

$21,000 = a*5 + $42,000

a*5 = $21,000 - $42,000 = -$21,000

a = -$21,000/5 = -$4,200

Esto significa que el precio decae $4,200 por año

El valor de depreciación de la camioneta es de $4200 por año.

Dado que Juana compró una camioneta 4x4 a $42 000; y además, sabe que la camioneta se depreciará (bajará su precio) en forma lineal durante 6 años, para determinar, si al quinto año la camioneta tendrá un valor de $21 000, cuál es el valor de la depreciación de la camioneta, se debe realizar el siguiente cálculo:

Por lo tanto, el valor de depreciación de la camioneta es de $4200 por año.

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The probability of renting exactly three apartments in a week is approximately 0.2018 or 20.18%.

If the average number of units rented per week is 2.3 and the distribution is Poisson, then the parameter lambda is also equal to 2.3.

The probability of renting exactly three apartments in a week is given by the Poisson probability function:

\(P(X = 3) = (e^(-lambda) * lambda^x) / x!\)

Substituting the values, we get:

\(P(X = 3) = (e^(-2.3) * 2.3^3) / 3!\)

P(X = 3) = (0.09963 * 12.167) / 6

P(X = 3) = 0.2018

Therefore, the probability of renting exactly three apartments in a week is approximately 0.2018 or 20.18%.

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Emerson actually hit the ball 32% of times at bat.

Since in Game 1, Emerson struck out 30 times in 90 times at bat; in Game 2, he struck out 40 times in 120 times at bat; and in Game 3, Emerson struck out 42 times in 140 times at bat; To determine what percentage of times at bat did Emerson actually hit the ball, the following calculation must be performed:

(30 + 40 + 42) / (90 + 120 + 140) = X

112/350 = X

0.32 = X

Therefore, Emerson actually hit the ball 32% of times at bat.

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Answer:

g(f(x)) = 6x - 14

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define

g(x) = 3x + 1

f(x) = 2x - 5

Step 2: Find

The form of listing an ingredient as "3 pounds of mushrooms, diced" is known as a weighted measure. In this form of listing, the weight of the ingredient is given along with a description of how it should be prepared or processed.

Weighted measures are often used in recipes to ensure consistency in the amount of ingredients used, especially when ingredients are prepared differently or come in different forms.

By including the weight of the ingredient along with a description of how it should be prepared or processed, the recipe ensures that the same amount of ingredient is used regardless of how it is prepared or processed. This can be particularly important in baking, where precise measurements are crucial to the success of the recipe.

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The probability that this team will win both of their next two games is 16%

The probability of Allie's hockey team winning both of their next two games can be calculated by multiplying the probability of winning each individual game.

Since the team has a 40% chance of winning each game, the probability of winning both games is:

0.40 * 0.40 = 0.16

Therefore, the probability of Allie's team winning both of their next two games is 0.16, or 16%.

To express this answer as a percent, simply multiply by 100:

0.16 * 100 = 16%

So the final answer is 16%.

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The probability of getting one head and the rest tails when flipping 5 fair coins is 0.156 or 15.6% to three decimal place accuracy.

To calculate the probability that one coin shows heads and the rest show tails, we need to use the formula:

P = (number of ways to get one head and four tails) / (total number of possible outcomes)

The total number of possible outcomes when flipping 5 coins is 2^5 = 32 (since each coin can either show heads or tails).

To calculate the number of ways to get one head and four tails, we can use the combination formula:

C(5,1) = 5

This means that there are 5 ways to choose which coin will show heads. Once we have chosen that coin, the other 4 coins must show tails. Since each coin has a 50/50 chance of showing heads or tails, the probability of this occurring is:

P = 5/32

Rounding to three decimal places, the probability is:

P = 0.156

Therefore, the probability of getting one head and four tails when flipping 5 fair coins randomly is 0.156 or 15.6%.

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Answer:

8.12

Step-by-step explanation:

we first multiply 8 by 12 and we will get 96 as our answer

Answer:

4

Step-by-step explanation:

Let x be the number of shirts that Rachel can buy, and y be the number of pants she can buy. Then the cost equation would be:

Cost = 25x + 20y

Since Rachel has a total budget of $200, we can write:

25x + 20y ≤ 200

To find the maximum number of shirts that Rachel can buy if she buys 5 pants, we can substitute y = 5 into the inequality and solve for x:

25x + 20(5) ≤ 200

25x ≤ 100

x ≤ 4

Therefore, Rachel can buy a maximum of 4 shirts if she buys 5 pants.

Answer:

The answer is 2

Step-by-step explanation:

5x² = 20

x² = 4

x = 2

Answer:

A. The rate of change of the table is equal to the rate of change of the graph.

Answer:

C: 1/2

Step-by-step explanation:

\(\quad \huge \quad \quad \boxed{ \tt \:Answer }\)

\(\qquad \tt \rightarrow \: C. \cfrac{1}{2}\)

____________________________________

\( \large \tt Solution \: : \)

\( \textsf{Slope of line - } \)

\(\qquad \tt \rightarrow \: m = \cfrac{rise}{run} \)

\(\qquad \tt \rightarrow \: m = \cfrac{0 - ( - 4)}{8 - 0} \)

\(\qquad \tt \rightarrow \: m = \cfrac{ 4}{8 } \)

\(\qquad \tt \rightarrow \: m = \cfrac{ 1}{2} \)

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For a linear demand curve given as q = a - bp when the monopolist operates in the inelastic region of the demand curve, it can increase total revenue, r(q) raising price.

A linear demand curve is a straight line that depicts the relationship between a product's or service's demand and its price. Everyone understands that sales are proportional to price: the higher the price, the fewer items you can expect to sell.

When the price of a good or service changes, its quantity remains constant. Inelastic demand means that when the price of a good or service rises, consumers' purchasing habits remain relatively unchanged, and when the price falls, consumers' purchasing habits also remain relatively unchanged.

Demand inelasticity means that demand remains constant despite changes in economic factors. Products and services with many alternatives typically have elastic demand, whereas products and services with few alternatives are typically inelastic.

When the monopolist operates in the inelastic region of the demand curve, r(q) raising price, for a linear demand curve given as q = a - bp.

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We can conclude that the measure of length AB is 23.46 ft and the measure of length BC is 9 ft.

Sine formula is used to calculate the sine angle of a right-angled triangle which is the ratio of the opposite side and the hypotenuse.

Given is that a 40-ft-wide house has a roof with a 6-12 pitch (the roof

rises 6 ft for a run of 12 ft). The owner plans a 14-ft-wide addition that will

have a 3-12 pitch to its roof.

We can write the measure of length AB as -

AB = 6 + √(9 + 296)

AB = 6 + 17.46

AB = 23.46 ft

We can write the measure of length BC as -

BC = 6 + 1/4 x 12

BC = 6 + 3

BC = 9 ft

Therefore, we can conclude that the measure of length AB is 23.46 ft and the measure of length BC is 9 ft.

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Answer:

a. 651

Step-by-step explanation:

To solve the problem, you can start by finding out how many students bike or walk to school by multiplying the total number of students by the percentage that bike or walk:

1860 x 0.45 = 837

Next, you can subtract the number of students who drive to school to find out how many students travel by bus:

1860 - 837 - 372 = 651

Therefore, the answer is 651, so the option (a) is correct.

Answer:

a. 651

Step-by-step explanation:

We first need to find the number of students that bike or walk.

We can do this by plugging the numbers into this equation:

\(\frac{is}{of} = \frac{percent}{100}\)

We know that the percent is 45, and we know the total amount of students, 1860, so we are solving for is.

\(\frac{x}{1860} = \frac{45}{100}\)  where x = is.

To solve this, we cross multiply:

1860(45) = 100x

83,700 = 100x

837 = x

Now we know that 837 students bike or walk, and 372 drive.

We can calculate how many students travel by bus by subtracting these numbers from the total number of students, 1860.

1860 - 837 - 372 = 651

Therefore, 651 students travel to school by bus.

The given number is 515.

It is asked to round off the number to nearest hundred.

This means that the resultant number will have zeroes in its unit and tens place.

Now consider that the tenth digit of the given number is 1, which less quite less than 5, so the digit 1 will be dropped and replaced by zero so that the place value of 5 remains entact.

Thus, the resulting number will be 500.

Alternative Explanation:

Just observe that the near hundred numbers to 515 are 500 and 600.

But 515 lies nearer to 500, so rounding off 515 to nearest hundred will yield 500.

The factored form of 9a² - b² - 4c² + 4bc is

(3a + b - 2c) (3a - b + 2c)

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

9a² - b² - 4c² + 4bc

9a² - (b² + 4c² - 4bc)

Now,

(b² + 4c² - 4bc)

This can be written as,

= (b² - 4bc + 4c²)

= (b - 2c)²

Now,

9a² - (b - 2c)²

(3a)² - (b - 2c)²

This is in the form of a² - b².

a² - b² = (a + b) (a - b)

So,

(3a + b - 2c) (3a - b + 2c)

Thus,

(3a + b - 2c) (3a - b + 2c) is the factored form.

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The probability of having, at most, 9 girls, is 0.9515

The probability that a random baby is a girl is:

p = 0.5

And the probability that a random baby is a boy is:

q = 0.5

Then the probability that, at most, 9 out of 11 babys are girls, is given by:

1 - p(10) - p(11)

Where P(10) is the probability that 10 of the babies are girls and p(11) is the probability that the 11 babies are girls.

p(10) = C(11, 10)*(0.5)^10*(0.5)^1 = C(11, 9)*(0.5)^11

Where C(11, 10) is the combinations of 10 elements that we can make with a set of 11 elements, such that:

C(11, 10)=  11!/(11 - 10)!*10! = 11

Replacing that, we get:

P = 11*(0.5)^11 = 0.0054

p(11) = C(11, 11)*0.5^11 = 1*0.5^11 = 0.0005

Then the probability is:

P = 1 - 0.0054 - 0.0005 = 0.9515

The probability of having, at most, 9 girls, is 0.9515

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The cost for 1.42 kg of this cheese will be $ 31.44 .

The process of translating measurements of a given quantity between different units, frequently using multiplicative conversion factors that change the value of the measured quantity without changing its effects, is known as unit conversion. The specific circumstances and the desired result dictate the conversion process. This may be governed by a regulation, contract, set of technical requirements, or other publicly available standards.

In its simplest form, the unitary procedure is used to determine the value of a single unit from a given multiple.

How to calculate the value of one pen, for example, if 40 cost Rs. 400. To finish it, using the unitary method. Additionally, after the value of a single unit has been established, we can multiply that value by the quantity of additional units required to establish the value of the additional units. This is typically how the concepts of ratio and proportion are used. The unitary method entails calculating the value of a single unit before calculating the value of the required number of units.

Given that 0.429 kg of cheese cost $9.50

As a result, the price of 1 kg of cheese is $9.50/0.429, which is $ 22.14.

As a result, 1.42 kg of cheese will cost you $22.14 * 1.42 = $31.44.

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