5200 at 4% for 3 years ??

The rate of the first bus is 15 mph. The solution involves using the formula distance = rate x time for both buses and setting them equal to each other to solve for the unknown rate of the first bus.

Let's assume that the first bus is traveling at a rate of x miles per hour.

We know that the second bus is traveling at a rate of 35 miles per hour.

When they meet, they will have traveled a total distance of 350 miles.

Using the formula distance = rate x time, we can set up the following equation

x(7) + 35(7) = 350

Simplifying this equation

7x + 245 = 350

7x = 105

x = 15

Therefore, the rate of the first bus is 15 miles per hour.

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Answer:

There are 1.295 or 1.29 moles

Step-by-step explanation:

1 mole = 6.022 × 10^23 molecules

So, number of moles present in 5.7 × 10^23 molecules of water = (5.7 × 10^23) / 6.022 × 10^23 = 0.946 moles

Hope, this helps.

Answer:The equation 4x +2(x-5) = 3(2x-4) don't have any solution.Step-by-step explanation: Equations with one solution If a linear equation has a variable term alone on one side and a constant term alone on the other side, it has one solution.  And I hope this helps you!!

Answer:

She found 19 pennies and 21 dimes

Step-by-step explanation:

Let the number of dimes present be d and the number of pennies present be p

From the question, the total of both is 40

Mathematically;

p + d = 40 •••••••(i)

While a penny worths 1 cent, a dime is worth 10 cents

Total penny amount would be 1 * p = p cents

While total dime amount would be 10 * d = 10d cents

Before we add both to give the total amount, let’s convert this total amount to cents and that would be 2.29 * 100 = 229 cents

So mathematically;

p + 10d = 229 •••••••(ii)

So let’s solve both equations simultaneously

From i) p = 40 - d

let’s put this into equation ii

40 - d + 10d = 229

40 + 9d = 229

9d = 229-40

9d = 189

d = 189/9

d = 21

Recall;

P = 40-d

P = 40-21

P = 19

A group contains n men and n women. 2n! number of ways are there to arrange these people in a row if the men and women alternate. Arrangement is known as permutation.

A permutation of a set in mathematics is, broadly speaking, the rearrangement of its elements if the set already has an ordered structure into a sequence or linear order. The act or procedure of altering the linear order of an ordered set is referred to as a "permutation."

When the order of the arrangements counts, a permutation is a mathematical technique that establishes the total number of alternative arrangements in a collection. Choosing only a few items from a collection of options in a specific sequence is a common task in arithmetic problems.

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The appropriate family of distributions to approximate the probability of rolling a 6 on a fair die is the discrete uniform distribution, which assumes equal probabilities for each outcome. In this case, the probability of rolling a 6 would be approximately 1/6 based on the assumption of fairness.

For the problem of approximating the probability of rolling a 6 on a fair die, an appropriate family of distributions to consider is the discrete uniform distribution.

The discrete uniform distribution is commonly used to model situations where each outcome has an equal probability of occurring. In the case of rolling a fair die, the die has six equally likely outcomes (numbers 1 to 6).

Each outcome has a probability of 1/6 of occurring, making the discrete uniform distribution a suitable choice.

By assuming a discrete uniform distribution, we can assign equal probabilities to each outcome (1/6 for rolling a 6) and approximate the probability of rolling a 6 based on the assumption of fairness.

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Answer:

96cm

Step-by-step explanation:

A=1/2bxh (Area=BasexHeight) is the formula to find it.

A=1/2x192

A=96

The total conversion cost for given the following data direct materials, $352,700; direct labor, $198,300; factory overhead, $177,600 is $375,900.

Conversion costs refer to the expenses incurred during the transformation process of raw materials into finished goods. The conversion costs consist of two main components: direct labor and factory overhead.

In this case, the direct materials cost is $352,700, and the direct labor cost is $198,300. The factory overhead cost is $177,600. To compute the conversion cost, we need to add the direct labor and factory overhead costs.

Conversion costs = Direct labor cost + Factory overhead cost

= $198,300 + $177,600

= $375,900

The conversion cost is an essential metric for manufacturers as it helps them to determine the total expenses incurred during the production process. By knowing the conversion cost, manufacturers can make informed decisions about pricing, production processes, and profitability.

Additionally, it enables manufacturers to compare their expenses with those of their competitors and identify areas where they can reduce costs to improve efficiency and increase profits.

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When the curve splits into two parts, the relationship between a and c is that a must be non-zero (otherwise, the curve would be a straight line), and c must be non-zero and have the opposite sign of a (otherwise, the curve would not change direction at the inflection point).

The given curve is:

\(y = ax^3 + bx^2 + cx + d\)

We can investigate the variety of shapes that this curve may have by examining its first and second derivatives.

First derivative:

\(y' = 3ax^2 + 2bx + c\)

Second derivative:

y'' = 6ax + 2b

From the second derivative, we can see that the sign of y'' determines whether the curve is concave up (y'' > 0) or concave down (y'' < 0).

When y'' = 0, the curve changes concavity at that point. So, we need to find the values of x for which y'' = 0:

6ax + 2b = 0

x = -b/3a

This gives us the x-coordinate of the inflection point.

When y'' > 0, the curve is concave up, and when y'' < 0, the curve is concave down.

Now, let's consider what happens when the curve splits into two parts. This can occur when the curve has an inflection point, which is the point where the concavity changes.

At the inflection point, the curve changes from concave up to concave down, or vice versa. Therefore, the inflection point is where the curve changes direction.

If we assume that the curve is continuous and smooth, then at the inflection point, the first derivative is also continuous and the curve is differentiable. This means that the first derivative exists on both sides of the inflection point.

Now, let's consider the relationship between a and c when the curve splits into two parts.

At the inflection point, y'' = 0, so we can substitute the value of x = -b/3a into the expression for y'' and get:

y'' = 6ax + 2b

y'' = 6a(-b/3a) + 2b

y'' = -2b

So, when the curve splits into two parts, the second derivative must be zero at the inflection point, and therefore, b must be zero.

Substituting b = 0 into the expression for the first derivative, we get:

\(y' = 3ax^2 + c\)

Now, we can see that c determines the slope of the tangent line at the inflection point. If c is positive, then the slope of the tangent line is positive, and if c is negative, then the slope of the tangent line is negative.

Therefore, when the curve splits into two parts, the relationship between a and c is that a must be non-zero (otherwise, the curve would be a straight line), and c must be non-zero and have the opposite sign of a (otherwise, the curve would not change direction at the inflection point).

In summary, the curve y = ax^3 + bx^2 + cx + d may have a variety of shapes, depending on the values of a, b, c, and d. When the curve splits into two parts, b must be zero, and a and c must have opposite signs

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Answer:

5/3 or 1 2/3

Step-by-step explanation:

5/4 divided by 3/4

Answer:

20/12 = 5/3

Step-by-step explanation:

Keep, change, flip

−12ma=−1, for a To solve for a, we need to isolate a on one side of the equation. To do this, we can divide both sides by −12m

−12ma=−1(−1)−12ma

=112am=−112a

=−1/12m

Therefore, a = −1/12m.

2x+k=1, for x.

To solve for x, we need to isolate x on one side of the equation. To do this, we can subtract k from both sides of the equation:2x+k−k=1−k2x=1−k.

Dividing both sides by 2:

2x/2=(1−k)/2

2x=1/2−k/2

x=(1/2−k/2)/2,

which simplifies to

x=1/4−k/4.

a=−1/12m

x=1/4−k/4

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Answer:

3 mph

Step-by-step explanation:

For Igor     6 mi/hr  * 2 hr = 12 miles   total distance

for Sally   12 miles / 4hrs = 3 mph

Answer:

x = 11

Step-by-step explanation:

Theorem:

The measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles.

Angle ABC is an exterior angle of the triangle.

Angles D and C are its remote interior angles.

m<ABC = m<D + m<C

12x - 2 = 57 + 7x - 4

Combine like terms on the right side.

12x - 2 = 7x + 53

Subtract 7x from both sides.

5x - 2 = 53

Add 2 to both sides.

5x = 55

Divide both sides by 5.

x = 11

Answer: x = 11

Answer:

According to exterior angle property, one of the exterior angles of a triangle is equal to the sum of the opposite 2 interior angles.

Thus,

12x-2= 57+7x-4

= 12x = 57-4+7x

= 12x = 53+7x

= 53= 7x-12x

= 53=-5x

= 53÷-5=x

= x= 10.6

Thus x= 10.6

The probability that the four s's are adjacent and the three a's are adjacent is 1/18

The total number of possible permutations of the letters in "sassafras" is 9!/(4!3!2!) = 1260, where 4! and 3! account for the permutations of the four s's and three a's, respectively, and 2! accounts for the permutations of the two remaining letters (f and r).

To calculate the number of permutations where the four s's are adjacent and the three a's are adjacent, we can consider them as a single block of seven letters: (ssssaaa). This block can be arranged in 7!/(4!3!) = 35 ways. The remaining two letters (f and r) can be placed in the remaining two positions in 2! ways.

Therefore, the number of permutations that satisfy the given conditions is 35 x 2! = 70.

The probability of selecting a permutation that satisfies both conditions is then 70/1260 = 1/18.

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Answer:

Option A that is best describes the given scenario is option A that is “LaTricia is not correct. The word product does mean to multiply, but 12 should be the product and 3 should be one of the factors.”

Step-by-step explanation:

Given that LaTricia wrote a sentence as an equation.  Given sentence is “Twelve is the product of three and a number”

Expression written by LaTricia =

Lets first concentrate on sentence and we will create our expression based on sentence and check it against the expression created by LaTricia.  Let the number represented by variable w.

So product of 3 and the number will be represented by

And as Twelve is the product of three and a number

That is three is one of the factor and result product is 12. Hence option A that is best describes the given scenario is option A that is “LaTricia is not correct. The word product does mean to multiply, but 12 should be the product and 3 should be one of the factors.”

Answer:

The smallest integer is 11.

Step-by-step explanation:

Let the first integer be x.

Then the second will be (x + 1) and the third will be (x + 2).

The sum is 36. Hence:

\(x+(x+1)+(x+2)=36\)

Solve for x:

\(3x+3=36\)

So:

\(3x=33\)

Hence:

\(x=11\)

Our sequence is 11, 12, 13.

So, the smallest integer is 11.

Answer:

Maya is hiking down at a speed of 100 feet per hour.

Step-by-step explanation:

Given that Maya is hiking down a mountain, and after one hours she is at 500 feet elevation while after three hours she is at 300 feet elevation, to determine the speed at which Maya is hiking down the following calculation must be performed:

3-1 = 2

500-300 = 200

200/2 = 100

Thus, Maya is hiking down at a speed of 100 feet per hour.

The simplified expression is 20\(\sqrt{6}\) - 30\(\sqrt{3}\) + 12 - 9\(\sqrt{2}\)  for the given irrational fraction.

To simplify the expression (5√6 + 3)(4 - 3√2), we can use the distributive property of multiplication over addition/subtraction. Let's break it down step by step:

(5\(\sqrt{6}\)+ 3)(4 - 3\(\sqrt{2}\) )

Using the distributive property, we multiply each term in the first set of parentheses by each term in the second set of parentheses:

5\(\sqrt{6}\) * 4 + 5\(\sqrt{6}\)  * (-3\(\sqrt{2}\) ) + 3 * 4 + 3 * (-3\(\sqrt{2}\) )

Simplifying each multiplication term:

20\(\sqrt{6}\)  - 15\(\sqrt{12}\)  + 12 - 9\(\sqrt{2}\)

Now, let's simplify the square root terms.

\(\sqrt{6}\)  can't be simplified any further because 6 doesn't have any perfect square factors other than 1.

\(\sqrt{12}\)  can be simplified as follows:

\(\sqrt{12}\) = √(4 * 3) =\(\sqrt{4}\)* \(\sqrt{3}\) = 2\(\sqrt{3}\)

Replacing \(\sqrt{12}\)  with 2\(\sqrt{3}\) :

20\(\sqrt{6}\) - 15(2\(\sqrt{3}\)) + 12 - 9\(\sqrt{2}\)

Distributing the multiplication:

20\(\sqrt{6}\) - 30\(\sqrt{3}\) + 12 - 9\(\sqrt{2}\)

Finally, combining like terms:

(20\(\sqrt{6}\)- 30\(\sqrt{3}\)) + (12 - 9\(\sqrt{2}\) )

The simplified expression is:

20\(\sqrt{6}\) - 30\(\sqrt{3}\) + 12 - 9\(\sqrt{2}\)

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The correct question is given below-

(5√6 + 3)(4 - 3√2), Simplify your answer as much as possible.

Answer: 4x+6/x^2

Step-by-step explanation:

The volume generated by rotating the region bounded by the curves y = x and x = 4y about the axis x = 17 can be found using the method of cylindrical shells.

To start, let's consider a vertical strip in the region, parallel to the y-axis, with a width dy. As we rotate this strip around the axis x = 17, it creates a cylindrical shell. The radius of each shell is given by the distance between the axis of rotation (x = 17) and the curve y = x or y = x/4, depending on the region. The height of each shell is given by the difference between the curves y = x and y = x/4.

We can express the radius as r = 17 - y and the height as h = x - x/4 = 3x/4. The circumference of each cylindrical shell is given by 2πr, and the volume of each shell is given by 2πrhdy. Integrating the volumes of all the shells over the appropriate range of y will give us the total volume.

By setting up and evaluating the integral, we can find the volume generated by rotating the region about the axis x = 17 using the method of cylindrical shells.

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Answer:

2/7

Step-by-step explanation:

14/2=7. 4/2=2 .2/7 is the answer

Answer:

2/7

Step-by-step explanation:

Divide by 2

4 divided by 2 is 2

14 divided by 2 is 7

So 2/7 is the simplest form

Hope this helps :)

Answer:

Step-by-step explanation:

All you do is multiply 75 x .25 = 18.75

Subtract 75 - 18.75 = $56.25

Answer:

get from (4,1) to (2,9) go up 8 and over 2 left (-2) - (4 - 2, 1 + 8), do this again (2 - 2, 9+8) and end up at (0,17) which is the y how do you change 7x+3y=3 into slope intercept form.

:D thanks :D

Answer:

Step-by-step explanation:

Rational numbers;

Numbers which can be written in the form of \(\frac{p}{q}\) or repeating decimal numbers are the rational numbers.

Examples : 1, 2, \(\frac{2}{3}\)

Irrational numbers:

Numbers which can't be written in he form of a fraction or non repeating decimal numbers are the Irrational number.

Example: \(\sqrt{8},\pi,\sqrt{\frac{8}{21} }\)

From the given numbers,

Rational numbers:  \(\frac{11}{3}\), 6.25, 0.01045, \(\sqrt{\frac{16}{81} }\), 0.424242....

Irrational numbers:  \(\sqrt{48}, \sqrt{\frac{3}{16} }\)

The formula to find the distance between a point and a line is

Graphically

So, in this case, you have

Then

The absolute value is the distance between a number and zero. The distance between -10 and 0 is 10.

Therefore, the distance between the point of the line is 10 units.

Answer:

E

Step-by-step explanation:

Answer:

33.3333333

Step-by-step explanation:

Adding 2 to the x side of the equation y = x to become y = x + 2 lead to transformation 2 units up

Adding 2 to the y side of the equation will result to translation 2 units down

multiplying the equation by x will make the equation not to be a linear equation

Translation 2 units up means the line will move 2 units upward and this is caused by adding two to the x.

While adding the 2 to the y will result to to subtracting 2 to the x and that is translation 2 units down.

This is shown mathematically as y = x

y + 2 = x

y + 2 - 2 = x - 2

y = x - 2

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Answer:

D

Step-by-step explanation:

using the rule of logarithms

\(log_{b}\) x = n ⇒ x = \(b^{n}\) , then

\(log_{2}\) x = 4.3 ⇒ x = \(2^{4.3}\) ≈ 19.70 ( to 2 dec. places )