The area of the base of a cube is 36 inches squared. What is the volume of the cube?
A. 6 inches cubed
B.216 inches cubed
C. 1296 inches cubed
D.18 inches cubed

Answer:

angle XYW = -20x + 155

Step-by-step explanation:

angle XYZ = 150

angle WYZ = 20x - 5

angle XYW = y

angle XYZ = 20x - 5 + y

150 = 20x - 5 + y

150 + 5 = 20x + y

y = -20x + 155

So angle XYW = -20x + 155

(a) lim (х, у) — (0, 0) cos(xy) – 1, this limit does not exist.

(b) The limit of x^(y^(x/y)) as (x, y) approaches (0, 0) is 1.

(c) The limit of (x² + y + 2) as (x, y) approaches (0, 0) is 2.

a) The limit of (exy - 1)/(cos(xy) - 1) as (x, y) approaches (0, 0) does not exist. The reason is that when (x, y) approaches (0, 0), the expression becomes indeterminate form 0/0.

Applying L'Hôpital's rule, we differentiate the numerator and denominator with respect to xy. The derivative of exy is exy, and the derivative of cos(xy) is -sin(xy)xy. Evaluating the limit again, we get (1 - 1)/(0 - 0) = 0/0, which is still an indeterminate form. Therefore, the limit does not exist.

(b) The limit of x^(y^(x/y)) as (x, y) approaches (0, 0) exists and equals 1. To show this, we take the natural logarithm of the expression to simplify it. Let z = x/y, so x = zy. Then the expression becomes ln(x^(y^(x/y))) = ln((zy)^(y^z)) = y^z ln(zy). Now, as (x, y) approaches (0, 0), z approaches 0.

Applying the limit properties and the continuity of the natural logarithm and exponential functions, we find that ln(zy) approaches ln(0) = -∞. Multiplying by y^z, we have y^z ln(zy) approaches 0 * -∞ = 0. Finally, taking the exponential of both sides, we obtain e^(y^z ln(zy)), which simplifies to e^0 = 1. Therefore, the limit of x^(y^(x/y)) as (x, y) approaches (0, 0) is 1.

(c) The limit of (x^2 + y + 2) as (x, y) approaches (0, 0) exists and equals 2. Since the limit is a sum of continuous functions, we can evaluate it by substituting the values of x and y directly into the expression.

Plugging in x = 0 and y = 0, we get (0² + 0 + 2) = 2. Therefore, the limit of (x² + y + 2) as (x, y) approaches (0, 0) is 2.

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Answer:

x=9/7

Step-by-step explanation:

14x+3=21

14x=21-3

14x=18

14x/14=18/14

x=9/7

14(9/7)+3=21

2*9+3=21

18+3=21

21=21

if you have any question about this you can ask me

Answer:

B. 5 1/3

Step-by-step explanation:

5 4/12=5 1/3

Of the two ratios, the ratio that is a rate is 260 miles/8 gallons

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

260 miles/8 gallons

260 miles/8 miles

As a general rule

Rates are used to compare quantities of different measurements

Hence, the ratios that is a rate is 260 miles/8 gallons

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The temperature of an apple pie during the time it spends in the oven shows the continuous relationship.

In mathematics, a continuous function is a function that does not have discontinuities that means any unexpected changes in value. A function is continuous if we can ensure arbitrarily small changes by restricting enough minor changes in its input.

A function f(x) is said to be a continuous function in calculus at a point x = a if the curve of the function does NOT break at the point x = a.

A continuous function, on the other hand, is a function that can take on any number within a certain interval. For example, if at one point, a continuous function is 1 and 2 at another point, then this continuous function will definitely be 1.5 at yet another point.

Therefore, option C and E are the correct answers.

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The company has to pay $1,462. 50 within 10 days.

A business will set aside funds known as "provisions" to pay for certain expected future costs or other financial effects. By making a provision, the bank incurs a loss and, as a result, lowers its capital by the amount of money it won't be able to recover from the client.

The phrase "2/10 net 30" indicates that the buyers get a 2% discount on trade credit if the due amount is paid within 10 days. The rules for 2/10 net 30 state that after those 10 days, the whole invoice amount is due within 30 days without the 2% reduction.

Then, this 2.5% is written as 0.025. First, we have to find a discount. The discount rate multiplied by the listed price equals the discount.

Here, the discount rate is 0.025 and the listed price is $1,500. Then,

($1,500 x 0.025) = $37.50

So, $37.50 is the discount amount. Subtracting this value from the listed price yields the payment within 10 days as ($1,500 - $37.50) = $1,462.50.

The fourth option is the correct one.

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Answer:

a

Step-by-step explanation:

Answer:

it would be the 2nd option

{(2,1) (1, 0) (0,1)}

Step-by-step explanation:

Among the given options, the correct statement is: C. Var (X + Y) = Var (X) + Var (Y).

This statement is known as the addition rule for variance and holds true for all random variables X and Y, regardless of their specific distributions.

To understand why this statement is true, let's briefly discuss the concept of variance. Variance measures the dispersion or spread of a random variable's values around its expected value (mean). Mathematically, variance is defined as the average of the squared deviations of the random variable from its mean.

Now, let's prove statement C:

Var (X + Y) = E[(X + Y - E[X + Y])^2] (definition of variance)

= E[(X + Y - E[X] - E[Y])^2] (linearity of expectation)

Expanding the square term:

mathematica

Copy code

       = E[(X - E[X])^2 + 2(X - E[X])(Y - E[Y]) + (Y - E[Y])^2]

By linearity of expectation, we can split this expression into three parts:

scss

Copy code

       = E[(X - E[X])^2] + 2E[(X - E[X])(Y - E[Y])] + E[(Y - E[Y])^2]

       = Var(X) + 2Cov(X, Y) + Var(Y)     (definition of variance and covariance)

Note that Cov(X, Y) represents the covariance between X and Y, which measures the extent to which X and Y vary together. However, the given options do not mention anything about the covariance between X and Y, so we cannot determine its value.

Therefore, statement C is correct because it expresses the addition rule for variance, which states that the variance of the sum of two random variables is equal to the sum of their individual variances.

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To find the largest area you can enclose with a single-strand electric fence and m units of wire at your disposal, you need to optimize the dimensions of the rectangular plot.

Let's denote the length of the rectangular plot as L and the width as W. The perimeter of the plot can be calculated as P = L + 2W.

Since one side of the plot is already bounded by the river, we have L + W = m. Rearranging this equation, we get L = m - W.

To find the largest area, we need to maximize the function A = L * W. Substituting the value of L, we have A = (m - W) * W.

Expanding the equation, we have A = mW - W^2.

To find the maximum value of A, we take the derivative of A with respect to W and set it equal to zero: dA/dW = 0.

Differentiating, we get m - 2W = 0. Solving for W, we have W = m/2.

Substituting this value back into the equation for L, we have L = m/2.

Therefore, the dimensions of the largest area are L = m/2 and W = m/2.

To find the area, we substitute these values into the equation for A: A = (m/2) * (m/2) = m^2/4.

In conclusion, the largest area that can be enclosed is m^2/4, with dimensions L = m/2 and W = m/2.

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Answer:

25.157

Step-by-step explanation:

28-2.843=25.157

The approximate probability that fewer than 71 seeds germinate is 0.0082, or 0.82%.

The probability that a seed germinates is 87%, which means the probability that a seed does not germinate is 13%.

To approximate the probability that fewer than 71 seeds germinate, we can use the normal approximation to the binomial distribution since the sample size is large (90 seeds) and the probability of success is not too close to 0 or 1 (0.87).

First, we calculate mean and standard deviation of this binomial distribution:

Mean = n * p = 90 * 0.87 = 78.3
Standard deviation =\(\sqrt{(n * p * (1 - p))}  = \sqrt{(90 * 0.87 * 0.13)}\) = 3.25

Now, we can standardize the random variable X (number of seeds that germinate) using the formula:

Z = (X - mean) / sd

For X = 70.5 (the midpoint of the interval "fewer than 71 seeds germinate"), we get:

Z = (70.5 - 78.3) / 3.25 = -2.40

Using a standard normal table or calculator, we find probability that Z value is less than -2.40, which equals to nearly 0.0082.

Therefore, the approximate probability that fewer than 71 seeds germinate is 0.0082, or 0.82%.

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Taylor polynomials of degree 2 and 3 centered at x = 0 for the function f(x) = 16tan(x) are:

P2(x) = 16x + 8x^2

P3(x) = 16x + 8x^2

To find the Taylor polynomials centered at x = 0 for the function f(x) = 16tan(x), we can use the Taylor series expansion for the tangent function and truncate it to the desired degree.

The Taylor series expansion for tangent function is:

tan(x) = x + (1/3)x^3 + (2/15)x^5 + (17/315)x^7 + ...

Using this expansion, we can find the Taylor polynomials of degree 2 and 3 centered at x = 0:

Degree 2 Taylor polynomial:

P2(x) = f(0) + f'(0)(x - 0) + (1/2!)f''(0)(x - 0)^2

= 16tan(0) + 16sec^2(0)(x - 0) + (1/2!)16sec^2(0)(x - 0)^2

= 0 + 16x + 8x^2

Degree 3 Taylor polynomial:

P3(x) = P2(x) + (1/3!)f'''(0)(x - 0)^3

= 0 + 16x + 8x^2 + (1/3!)(48sec^2(0)tan(0))(x - 0)^3

= 16x + 8x^2

Therefore, the Taylor polynomials of degree 2 and 3 centered at x = 0 for the function f(x) = 16tan(x) are:

P2(x) = 16x + 8x^2

P3(x) = 16x + 8x^2

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Answer:

It looks like you would need 8 1/5 cups of sugar to make all 48 cookies.

Step-by-step explanation:

Well, half a dozen is 6 so I did 48 divied by 6 which is 8.

Answer:

49.65$

Step-by-step explanation:

(20.40 x 2) + 8.85 = 49.65 $

Answer:

Step-by-step explanation:

The probability P(Z>1.28) represents the area under the standard normal distribution curve to the right of the z-score 1.28.

Using a standard normal distribution table or a calculator, we find that the area to the right of 1.28 is approximately 0.1003.

Therefore, the answer is closest to option (b) 0.10. there is a 10% chance of obtaining a value above 1.28 in a standard normal distribution.

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Jimmy can use Hypothesis test for goodness of fit to test whether or not the shuffle feature is working correctly

Chi-Squared Test can also be used to compare the observed frequencies of each each music genre in the 100 songs that he listened to with the expected frequencies which will be based on how the music genres are distributed in his library

The Shuffle feature is working correctly and the frequencies which are observed  in 100 songs are not different from the frequencies which are to be expected that will be the null hypothesis for this test

The Shuffle feature is not working correctly and the frequencies which are observed in 100 songs are somewhat different from the expected frequencies

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If the p-value is less than or equal to the selected significance level, the null hypothesis is rejected; otherwise, it is not. In other words, if p, reject\(H_{0}\); if p>, do not reject \(H_{0}\).

In null hypothesis testing, this criterion, also known as (alpha), is frequently set to 05. If there is less than a 5% chance that the null hypothesis would be accepted and a result as spectacular as the effects that result would occur, the null hypothesis is rejected. When this happens, the result is said to be statistically significant.

The null hypothesis would be rejected if a statistical test was conducted with a threshold of relevance = 0.1, 0.05, & 0.01.

If the P value is smaller than alpha, the preset level of statistical significance, the alternative hypothesis is considered instead of the null hypothesis.

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Answer:

1453/23328

Step-by-step explanation:

Since we are going to have at least three 5's to obtain a number divisible by 125, the number of ways we can combine exactly three 5's is ⁶C₃. The number of ways we can combine the remaining dice without containing a five is 5³, since there are 3 remaining dice. So, for exactly three 5's , we have ⁶C₃ × 5³. Similarly, for exactly four 5's, we have ⁶C₄ × 5² (5² since there are two dice left). Also, for exactly five 5's, we have ⁶C₅ × 5¹ (5¹ since there are one die left). Finally, for exactly six 5's, we have ⁶C₆ × 5⁰(5⁰ since there are no dice left without a five).

So, for at least three 5's, we have ⁶C₃ × 5³ + ⁶C₄ × 5² + ⁶C₅ × 5¹ + ⁶C₆ × 5⁰

= 20 × 125 + 15 × 25 + 6 × 5 + 1 × 1

= 2500 + 375 + 30 + 1

= 2906 ways

The total number of ways of combining the six dice is 6⁶

So, the probability of obtaining a product divisible by 6 is thus P = 2906/6⁶ = 2906/46656

= 1453/23328

Using the binomial distribution, it is found that there is a 0.0536 = 5.36% probability that the product is divisible by 125.

The product will be divisible by 125 in two outcomes:

For each dice, there are only two possible outcomes, either the result is 5, or it is not. The results of the dices are independent, hence, the binomial distribution is used to solve this question.

Binomial probability distribution

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are:

In this problem:

The probability that the product is divisible by 125 is:

\(p = P(X = 3) + P(X = 6)\)

Hence:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 3) = C_{6,3}.(0.1667)^{3}.(0.8333)^{3} = 0.0536\)

\(P(X = 6) = C_{6,6}.(0.1667)^{6}.(0.8333)^{0} \approx 0\)

Then:

\(p = P(X = 3) + P(X = 6) = 0.0536 + 0 = 0.0536\)

0.0536 = 5.36% probability that the product is divisible by 125.

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Answer:

Step-by-step explanation:

3(\sqrt(25)-10)+5  = -10

It's B 3(√25 -10)+5

Answer:

D

Step-by-step explanation:

it is because the brackets at B makes sense when you calculate individually

If queen bee has a colony of 2000 drones and 18000 worker bees, One-sixth (1/6) of the worker bees in the queen bee's colony are drones.

The total number of bees in the queen bee's colony is the sum of drones and worker bees. Therefore, we can calculate the total number of bees as follows:

Total number of bees = number of drones + number of worker bees

Total number of bees = 2000 + 18000

Total number of bees = 20000

Out of the total number of worker bees (18000), 6000 are foragers. Therefore, the number of worker bees that are not foragers is:

Number of worker bees that are not foragers = 18000 - 6000

Number of worker bees that are not foragers = 12000

Now we can find the part of worker bees that are drones by dividing the number of drones by the total number of bees that are not foragers:

Part of worker bees that are drones = number of drones / number of worker bees that are not foragers

Part of worker bees that are drones = 2000 / 12000

Part of worker bees that are drones = 1/6

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9.27  rounded to 2 decimal places is 9.27

The important thing to remember is that you should round 9.270 to two digits or places after the decimal point. As a result, we wish to do rid of the final digit in 9.270. We utilize the following Two Decimal Places Rules to find the answer by removing the final digit in 9.270:

Rule #1 for two decimal places: If the final digit in 9.27 is less than 5, it should be removed.

Two Decimal Places Rule #2: If the second-to-last digit in 9.27 is less than 9 and the previous digit is 5 or greater, the last digit must be removed and one added to the second-to-last digit.

Three Decimal Places Rule #3: If the final digit in a number, such as 9.27, is five or more, the second to last digit is nine, and the third to last digit is less than nine, the last digit is eliminated, the second to last digit is changed to zero, and the third to last digit is increased by one.

Fourth Rule of Two Decimal Places: Add 1 to the value on the left side of the decimal point and change the right side of the decimal point to 00 if the final digit in 9.270 is 5 or more, the next-to-last digit is 9, and the next-to-last digit is 9.

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In accordance with the definition of a system of linear equations, Arianys contains 15 pennies and 6 nickels, respectively.

The groups of linear equations with the same unknowns for which a common solution is required are known as degrees of systems of linear equations.

A system of equations is solved by determining the value of each unknown until the system's equations are all satisfied.

A set of linear equations must be provided in this scenario, keeping in mind that "x" is the total number of pennies that Arianys possesses.

Arianys has "y" nickels in his possession.

Given,

Arianys has pennies and nickels worth $0.45.

She has a combined total of 21 pennies and nickels.

The equations are written as follows:

x + y = 21

0.01x + 0.05y = 0.45

There are several ways to solve a system of equations, but it is decided to use the graphical method, which involves displaying the graphs connected to the system's equations in order to determine its solution. The location where the two graphs converge is the system's solution since its coordinates fulfil both equations.

The intersection point between the two equations in this example is determined to be (x,y)=(15,6) by graphing the system of equations (see attached image). As a result, Arianys has 15 pennies and 6 nickels.

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Answer:

483000

Step-by-step explanation:

To write a linear expression in standard form, rearrange the terms in alphabetical order.

Answer:

48300000

We can write the above number as

4.83 x 10000000

=4.83 x 10 ^7

Answer:

A Square plus B square equals

Step-by-step explanation:

T

Answer: 3 quarts and 14 ounces

Step-by-step explanation:

1 gallon = 4 quarts = 128 ounces,

1 quart = 2 pints,

1 pint = 16 ounces.

Therefore:

5 gallons - ( 4 gallons 1 pint 2 ounces ) =

= 5 * 128 - ( 4 * 128 + 1 * 16 + 2 ) = 640 ounces - 530 ounces = 110 ounces

110 ounces = 3 * 32 + 14

Answer:

52

Complementary Angles:

Two angles that add up to 90.

Answer:

Please check the explanation.

Step-by-step explanation:

Given the statement:

''Twice the difference of a number and 2 is added to 6 and the result is 4 more than 3 times the number''.

Let us break down the statement into an algebraic expression.

First Portion:

Let the number be: n

The difference of a number n and 2: n -2

Twice the difference of a number n and 2: 2(n-2)

Twice the difference of a number and 2 is added to 6 = 2(n-2) + 6

Second Portion:

3 times the number n:  3n

4 more than 3 times the number: 3n + 4

Combine the First portion and Second Portion:

Twice the difference of a number and 2 is added to 6 and the result is 4 more than 3 times the number:

2(n - 2) + 6 = 3n + 4

Therefore, the required algebraic expression is:

BONUS SOLUTION to determine the number n

Let us solve the expression

2(n - 2) + 6 = 3n + 4

2n - 4 + 6 = 3n + 4

flip the equation

3n + 4 = 2n - 4 + 6

3n + 4 = 2n + 2

3n - 2n = 2 - 4

n = -2

Thus, the value of n = -2