A, b and c are integers. They are the length, width and height of a cuboid respectively. It has a volume of 12cm^3, and the top faces has an area of 4 cm^2. If the cuboid is longer than it is width, what are a, b and c?​

The solution to the equation log_6 x + log_6 3 = log_6 (x+1) is x = 1/2.

Explain:

We can reduce the complexity of the left side of the equation by using the logarithmic identity log a + log b = log (ab):

Log6 x plus Log6 3 equals Log6 (3x)

When we add this to the initial equation, we obtain:

Log6 (3x) equals Log6 (x+1).

Because logarithms have the one-to-one property, we can drop the logarithm on both sides to get the following results:

3x = x + 1

When we simplify this equation, we obtain:

2x = 1

x = 1/2

As a result, x = 1/2 is the answer to the equation log 6 x + log 6 3 = log 6 (x+1).

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The probability the math majors are seated together is 0.028 and all seated togeather with their group is 0.0047.

Probability is the probability that something will happen. Whenever the outcome of an event is uncertain, we can speak of the probability, or likelihood, of a particular outcome. Analyzing events according to their probabilities is called statistics.

Probability determines the likelihood of an event occurring.

P(A) = f / N. Odds and probabilities are related, but odds depend on probabilities. Before we can determine the probability that an event will occur, we first need the probability.  

total number of teacher is 10

so number of ways total 10 teacher seat = 10!/(6!*4!)

= 210

and

the number of ways  the math majors are seated together

= 6

probability = 6/210 = 0.028

the number of ways the math majors are seated together and the computer science majors are seated together

= 1

probability = 1/210

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The probability expressed as P(x ≥ 92) in the normal distribution is; C: 0.84

We are given that the normal distribution has;

Population mean: μ = 98

Population standard deviation; σ = 6

Sample mean; x' = 92

Thus, z-score is;

z = (x' - μ)/σ

z = (92 - 98)/6

z = -1

Thus, from z-score tables we have;

P(z ≥ -1) = 0.84

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The range of possible temperatures in Steffi's storage room is between 53°F and 59°F, inclusive.

What is Inequality?

An inequality is a mathematical statement that compares two values, expressing that they are not necessarily equal. It is often represented using one of the following symbols: "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to).

For example, "x > 5" is an inequality that states that the value of x is greater than 5. Similarly, "y ≤ 10" is an inequality that states that the value of y is less than or equal to 10.

Inequalities are commonly used in algebra and other areas of mathematics, as well as in many real-world applications, to express relationships between values that are not necessarily equal.

The inequality |t − 56| ≤ 3 represents all temperatures within 3 degrees of 56°F, including both those above and below 56°F.

We can represent this range graphically as a horizontal line segment centered at 56°F with a length of 6 units (3 units on either side of 56°F).

Thus, the range of possible temperatures in Steffi's storage room is between 53°F and 59°F, inclusive.

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Answer: Frank is going to plant "b" vegetables in one garden and "2b + 1" vegetables in another garden. So, the total number of seeds he is going to plant is b + (2b + 1) = 3b + 1.

Step-by-step explanation:

If the phone is in sale of 30% off, the money April save if she buys the phone on sale is $69.

A sale is a reduction of the basic price of a good or a service. It can occur on any stage in the process of production.

It is given that a phone sells for $230. It is now on sale for 30% off.

Now, Cost price = $230

sale percentage = 30%

so, the sale price = [tex]230 \times 30\%\\[/tex]

or  [tex]230 \times \frac{30}{100}[/tex] = $69

therefore, the money April will save if she buys the phone on sale is $69.

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The percentage increase in her taxes from 2010 to 2011 is 44.30%.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, Sophia paid $3,360,00 in taxes in 2010 and her taxes rose to $4,848,60 in 2011.

So, The amount of tax increase is $(484860 - 336000) = $148860.

Therefore, The percentage increase is,

= (148860/336000)×100%.

= 44.30%.

The net amount change will now be divided by the starting total, and the result will be multiplied by 100% to determine the percentage change.

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Answer:

(x + 7)(x - 3) = 75 square feet.

Step-by-step explanation:

Given that x represents the side length of the mural in Ashwin's classroom, the hallway mural's length is x + 7 feet and its width is x - 3 feet. The area of the hallway mural can be found by multiplying these two binomials, (x + 7)(x - 3), to get x^2 + 4x - 21.

If each side of the classroom mural is 8 feet long, the hallway mural would have sides of 15 feet and 5 feet, so its area would be 75 square feet, which is the answer.

The ratio of the coordinate point on the line is  2 to 7.

The ratio of the coordinate point on the line is calculated as follows;

Let the coordinate points = (xp, yp)

Let the ratio of the line = a:b

xp = x₁  +  (a/(a+b) (x₂ - x₁)

yp = y₁  + (a/a+b) (y₂ - y₁)

-3 = -7 + ( a/a+b)(11 - - 7)

-3 = -7 + (a/a+b)(18)

-3(a + b)  = -7(a+b) + 18a

7(a + b ) - 3(a+b) = 18a

7a + 7b - 3a - 3b = 18a

4b = 14a

4/14 = a/b

2/7 = a/b

2 : 7 = a : b

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Limits function lim p(x) can be calculated if p is a polynomial function by:

To calculate the limits of a polynomial function, p(x), first identify the degree of the polynomial. Then, use the formula Lim p(x) = aₙ xⁿ + aₙ₋₁ xⁿ⁻¹ + ... + a₀, where an is the leading coefficient. For example, if the polynomial is of degree 3, then the formula would be:

Lim p(x) = a₃ x³ + a₂ x² + a₁ x + a₀.

Next, we need to subtitute the variable x with the defined limits. For example, if the defined limit of the function is 2, then the limit function would be:

Lim p(2) =  a₃ (2)³ + a₂ (2)² + a₁ (2) + a₀

Then, we just need to simplify our finding:

Lim p(2) =  8a₃ + 4a₂ + 2a₁ + a₀

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Answer: The equation X + y = -5 represents a straight line in a two-dimensional plane. To determine whether a specific point (X, y) is a solution of the equation, you can substitute the values of X and y into the equation and see if it holds true. If the equation is satisfied, then the point (X, y) is a solution. If the equation is not satisfied, then the point (X, y) is not a solution.

For example, if X = 2 and y = -7, then the equation becomes:

2 + (-7) = -5

-5 = -5

Since the equation holds true, the point (2, -7) is a solution of the equation X + y = -5.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The volume of the three tennis balls combined is approximately 4.88 cubic inches. The volume of the packaging cylinder is approximately 50.33 cubic inches. Thus, the volume of the three tennis balls is about 9.7% of the volume of their packaging cylinder.

To calculate this, we can use the formula for the volume of a sphere (V = 4/3 x π x r3) and the formula for the volume of a cylinder (V = π x r2 x h).

The radius of each tennis ball is half the diameter, or 1.35 inches. So, the volume of each tennis ball is 4/3 x π x (1.35)3 = 4.88 cubic inches.

The radius of the cylinder is the same as the diameter of each tennis ball, or 2.7 inches. The height of the cylinder is 8.1 inches. So, the volume of the cylinder is π x (2.7)2 x 8.1 = 50.33 cubic inches.

The volume of the three tennis balls is 4.88 x 3 = 14.64 cubic inches. The volume of the packaging cylinder is 50.33 cubic inches. Thus, the volume of the three tennis balls is 14.64 ÷ 50.33 = 0.097 = 9.7% of the volume of their packaging cylinder.

Answer:

Reflection across the x-axis followed by dilation by a scale factor of with the center of dilation at the origin

Step-by-step explanation:

Rectangle EFGD has vertices at points E(-6,8), F(0,8), G(0,1) and D(-6,1).

1 transformation - reflection across the x-axis with the rule

So, the image rectangle E''F''G''D'' has vertices with coordinates

2 transformation - dilation by a scale factor of with the center of dilation at the origin. This transformation has the rule

Thus,

These are exactly vertices of rectangle E'F'G'D'.

1. The function for this problem is defined as follows: y = 2x + 3.

2. The numeric value of the function at x = 2 is given as follows: y = 7.

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

We define a function as follows:

y = 2x + 3.

At x = 2, the numeric value is found replacing the lone instance of x by 2, hence:

y = 2(2) + 3

y = 7.

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The number of hours that the prices of the two stocks be the​ same will be 4 hours.

In other words, the collection of all feasible values for the parameters that satisfy the specified mathematical equation is the convenient storage of the bunch of equations.

Let 'x' be the number of hours and 'y' be the price of stocks. Then the equations are written as,

y = 13.52 + 0.05x           ...1

y = 14.27 - 0.14x             ...2

From equations 1 and 2, then we have

13.52 + 0.05x = 14.27 - 0.14x

0.14x + 0.05x = 14.27 - 13.52

0.19x = 0.75

x = 3.947 ≈ 4 hours

The number of hours that the prices of the two stocks be the​ same will be 4 hours.

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Exponential growth is a pattern of data that shows a rapid increase over time, while exponential decay is a pattern of data that shows a rapid decrease over time.

An rise in the resultant quantity for a given quantity is referred to as exponential growth, and a decrease in the resultant quantity for a given quantity is referred to as exponential decay.

The fundamental distinction between the two is that in an exponential decay relationship, the output values rise quickly as the input value rises, whereas in an exponential growth relationship, the output rises noticeably faster as the input value rises.

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Answer: 1067/10000 is a fraction in simplest form. where, 0.1067 is a decimal, 10.67% is a percentage.

Step-by-step explanation:

Answer:

100

Step-by-step explanation:

I hate that I have to use 20 characterz

the boat will coast for a distance of 400 ln(2) ft, which is approximately 277.3 ft.

To find how far the boat will coast, we need to use the concept of differential equations. The equation that describes the velocity of the boat at any time "t" after its motor quits is given by:

dv/dt = -k*v

where "v" is the velocity of the boat at time "t", "k" is the proportionality constant, and the negative sign indicates that the velocity is decreasing with time.

We can solve this differential equation to obtain the velocity of the boat as a function of time:

v(t) = v(0) * e^(-k*t)

where "v(0)" is the initial velocity of the boat (40 ft/sec).

Using the given information, we can set up two equations:

v(10) = 20 (velocity after 10 sec)

v(0) = 40 (initial velocity)

Plugging these values into the equation, we get:

20 = 40 * e^(-10k)

Solving for "k", we get:

k = ln(2)/10

Now, we can integrate the velocity equation to find the distance the boat travels during the coasting period:

d = [tex]\int\limits^{\infty}_{10} {v(t)} \, dt[/tex]

Plugging in the values, we get:

d = (40/k) * [e^(-k*10) - 0] = 400 ln(2) ft

To explain the solution, we used the concept of differential equations to model the motion of the boat as it coasts after its motor quits. We used the given information to solve for the proportionality constant "k", which allowed us to find the velocity of the boat at any time.

Finally, we integrated the velocity equation to find the distance the boat travels during the coasting period. The key to this problem was using the concept of differential equations to model the motion of the boat and setting up the appropriate equations to solve for the unknowns.

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Complete question is:

Suppose that a motorboat is moving at 40 ft/sec when its motor suddenly quits, and then 10 sec later the boat has slowed to 20 ft/sec. Assume, that the resistance it encounters while coasting is proportional to its velocity. How far will the boat coast in all?

Answer:

Step-by-step explanation:

The perimeter of one square which combined with other to form a rectangle of 288 cm² is 12 cm.

The area of rectangle is given by the formula -

Area = length × width

Now we know that all the sides of square are same. Also, the identical squares have been kept side by side. So, let us represent one dimension of square with b. Thus, length of rectangle will be (b + b)

Length of rectangle = 2b

Width of rectangle will be b. Now, finding the value of b first.

288 = 2b×b

Performing multiplication

2b² = 288

b² = 288/2

Performing division

b² = 144

b = ✓144

Taking square root

b = 12 cm

The perimeter of one square = 2(length + width)

Perimeter of one square = 2 ( 12 + 12)

Perimeter = 2 × 24

Performing multiplication

Perimeter = 48 cm

Thus, perimeter of one square is 48 cm.

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Answer:

The down payment that Jordan made on the house was $300,000 x 10% = $30,000. So, he financed $300,000 - $30,000 = $270,000.

where

M = monthly payment

P = loan amount ($270,000)

r = monthly interest rate (3% / 12 months = 0.003)

n = number of payments (30 years x 12 months/year = 360)

This comes out to a monthly payment of approximately $1,173.38.

To simplify

The loan amount is- $270,000

Her monthly payment will be- $1,173.38

The amount of interest she will pay is- $8,100

At a price of $10 per square foot, it will cost $1920 to carpet the 12 by 16-foot space.

The rectangle's area in square meters The area's width and length should be measured in feet. To calculate area, multiply your length by your width. Use our length converter to convert your measures if they aren't already in feet.

Area is length times breadth, or 12 feet by 16 feet, or 192 square feet. The cost of the carpet is $10 per square foot. By dividing the square footage of the room by the price per square foot, we can get the overall cost to carpet it.

Total cost is equal to Area. Cost per square foot is $1920 or 192 square feet (around 18 m2) times $10 per square foot.

Therefore, at a price of $10 per square foot, it will cost $1920 to carpet the 12 by 16-foot space.

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As the university is sending out questionnaires, the data collection method the university is using is a survey

The term "survey" describes the method of gathering data on a certain subject generally by employing questionnaires. In order to understand more about a certain topic, a survey is a method of data collection that involves asking a sample of respondents a number of questions. In the given case, the university is using a survey as a tool for gathering data. 

Here, the institution is distributing a survey to undergraduate students to learn more about their study habits and what they believe to be the most effective method of studying. In order to efficiently gather data from a large number of participants quickly and effectively, surveys are frequently employed in research investigations.

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