the function determine the intervals of the continuity

The LCM of A = 3² × 5⁴ × 7 and B = 3⁴ × 5³ × 7 × 11 is 3898125 using Prime factorization.

Given are two numbers which are showed in the prime factorized form.

A = 3² × 5⁴ × 7

B = 3⁴ × 5³ × 7 × 11

Prime factorization is the factorization of a number in terms of prime numbers.

In order to find the LCM of these two numbers, we have to first match the common primes and write down vertically when possible and then bring down the primes in each column.

A = 3² ×         5³ × 5 × 7

B = 3² × 3² × 5³ ×       7 × 11

Bring down the primes in each column.

LCM = 3² × 3² × 5³ × 5 × 7 × 11

        = 3898125

Hence the LCM is 3898125.

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a. The marginal profit function Py is Py = -30x + 47y - 915 and

b. Change in profit if price increase by 1 cent is 831 cents.

To find the marginal profit functions Px and Py, we need to find the partial derivatives of the profit function P(x, y) with respect to x and y, respectively.

Given:

P(x, y) = (x - 40)(55 - 4x + 5y) + (y - 45)(70 + 5x - 7y)

a. Marginal profit function Px:

To find Px, we differentiate P(x, y) with respect to x while treating y as a constant:

Px = ∂P/∂x = (∂/∂x) [(x - 40)(55 - 4x + 5y) + (y - 45)(70 + 5x - 7y)]

Expanding the terms and simplifying:

Px = (55 - 4x + 5y) + (x - 40)(-4) + (70 + 5x - 7y)(5)

Simplifying further:

Px = 55 - 4x + 5y - 4x + 40 + 350 + 5x - 7y

Combining like terms:

Px = 355 - 3x - 2y

b. Marginal profit function Py:

Similarly, to find Py, we differentiate P(x, y) with respect to y while treating x as a constant:

Py = ∂P/∂y = (∂/∂y) [(x - 40)(55 - 4x + 5y) + (y - 45)(70 + 5x - 7y)]

Expanding the terms and simplifying:

Py = (x - 40)(5) + (70 + 5x - 7y)(-7) + (y - 45)(5)

Simplifying further:

Py = 5x - 200 - 7y - 490 - 35x + 49y + 5y - 225

Combining like terms:

Py = -30x + 47y - 915

This is the profit function Py.

b. Estimating the daily change in profit:

To estimate the daily change in profit, we need to evaluate Px and Py at the given prices and calculate the change in profit when the prices are increased as specified.

Given initial prices:

First brand price (x) = 70 cents

Second brand price (y) = 73 cents

To estimate the change in profit, we substitute the initial prices into Px and Py and calculate the results:

Px(70, 73) = 355 - 3(70) - 2(73)

          = 355 - 210 - 146

          = -1

Py(70, 73) = -30(70) + 47(73) - 915

          = -2100 + 3431 - 915

          = 416

The daily change in profit can be estimated by multiplying the changes in price (1 cent for the first brand and 2 cents for the second brand) with the respective marginal profit functions:

Change in profit = ΔP ≈ Px(70, 73) * 1 + Py(70, 73) * 2

               ≈ -1 * 1 + 416 * 2

               ≈ -1 + 832

               ≈ 831 cents

Therefore, the estimated daily change in profit when the salesperson increases the price of the first label by 1 cent and the price of the second label by 2 cents is 831 cents.

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Answer:

76°

Step-by-step explanation:

starting fromX ,the line coming from the north pole and ending at the line coming from Y while moving in clockwise direction is the bearing of Y from X

= 180-104=76°

The probability that the selected number is even is 7/15.

The probability that the selected number is a multiple of 4 is 1/5.

The probability that the selected number is a prime number is 2/5.

Based on the information illustrated, the following can be deduced:

Even numbers = 2, 4, 6, 8, 10, 12, 14.

Multiple of 4 = 4, 8 and 12.

Prime numbers = 2, 3, 5, 7, 11, and 13.

Therefore, the probability that the selected number is even will be:

= 7/15.

The probability that the selected number is a multiple of 4 is:

= 3/15 = 1/5.

The probability that the selected number is a prime number is:

= 6 / 15

= 2/5.

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Answer:

C AND D

Step-by-step explanation:

JUST PRESS C AND D AND ITS RIGHT LOL

The equation that represents the situation will be 0.10d + 0.25 = 5 and 10d + 25q = 500. Then the correct options are C and D.

The act of converting a specified statement into an expression or equation is known as a sentence-to-equation transformation.

A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.

Noah has a coin jar containing dimes (d) and quarters (q) worth a total of $5.00.

The equation that represents the situation will be given as,

0.10d + 0.25 = 5

10d + 25q = 500

The equation that represents the situation will be 0.10d + 0.25 = 5 and 10d + 25q = 500. Then the correct options are C and D.

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Answer:

$0.64 per cup

Step-by-step explanation:

There are 16 cups in 1 gallon, so the number of cups in 2 gallons is:

1 gallon: 16 cups

2 gallon = 2 x 1 gallon = 2 x 16 cups = 32 cups

So we need to find the price of each cup:

1 cup = ($20.48 / 32 cups) = $0.64 per cup.

Answer:

21 cases

Step-by-step explanation:

red cases=2x.    white cases=x

2x+x=81

3x=81

x=21 cases

Answer: -10

Step-by-step explanation:

:)

The given options, the only value greater than 1 is 1.003. Therefore 0.886, which is less than 1 and makes the inequality true.

The given number sentence is 5.3 × > 5.3, where we need to find the scaling factor that makes the inequality true. To do this, we can divide both sides of the inequality by 5.3. This gives us:

5.3 × x > 5.3 ÷ 5.3 × k

We need to find the value of k that makes the inequality true. Simplifying the right-hand side of the equation, we get:

5.3 ÷ 5.3 × k = k × 1 = k

Substituting this into our equation, we get:

5.3 × x > k

We know that 5.3 × 1 = 5.3, which means that k must be greater than 1 to satisfy the inequality. Among the given options, the only value greater than 1 is 1.003. However, this value would make the inequality too large, so it is not the correct answer.

The correct answer is therefore 0.886, which is less than 1 and makes the inequality true.

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Answer:

I got

10% of 70 is 7

Answer:

First one is 70

Second one is 24

Step-by-step explanation:

First one :7*100=700

700÷10=70

The second one :6*100=600

600÷25=24

Answer:

-3x + 6

Step-by-step explanation:

-3(x - 2) to find the equivalent of this expression, we need to multiply inside the parenthesis with -3 (with both x and -2)

-3(x - 2 = -3x + 6 (two negative expressions multiplied results in positive)

All variables must be greater than or equal to 0, indicating that no shipping is allowed if the cost is negative.

The network representation of the Herman Company distribution system is as follows:

Plants (P1, P2, P3) -> Warehouses (W1, W2) -> Customers (C1, C2, C3, C4).

A linear programming model of the problem can be formulated as:

Minimize Z = 2x14 + 3x15 + 4x24 + 5x25 + 6x34 + 7x35 + 8x46 + 9x47 + 10x48 + 11x49 + 12x56 + 13x57 + 14x58 + 15x59

Subject to:

x14 + x15 ≤ 2

x24 + x25 ≤ 3

x34 + x35 ≤ 4

x46 + x47 + x48 + x49 ≤ 5

x14 + x24 + x34 ≤ 6

x15 + x25 + x35 ≤ 7

x46 + x56 + x66 ≤ 8

x47 + x57 + x67 ≤ 9

x48 + x58 + x68 ≤ 10

x49 + x59 + x69 ≤ 11

All variables ≥ 0

The objective of this problem is to minimize the total shipping cost from plants to warehouses and warehouses to customers. The constraints represent the limited capacities of each plant, warehouse and customer and the maximum number of units that can be shipped from each plant to each warehouse or each warehouse to each customer. All variables must be greater than or equal to 0, indicating that no shipping is allowed if the cost is negative.

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The equation of the line with a slope of -1 that passes through (0, 4) is: A. y = -x + 4.

The equation of a line can be written in the slope-intercept form, as y = mx + b or in the point-slope form, as y - b = m(x - a).

Given the following:

A point (a, b) = (0, 4).

Slope (m) = -1.

Substitute m = -1, a = 0, and b = 4 into y - b = m(x - a):

y - 4 = -1(x - 0)

Rewrite the equation in slope-intercept form:

y - 4 = -x + 0

y = -x + 4

The answer is: A. y = -x + 4.

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Answer: 5 yards

Step-by-step explanation:

1. Look at the vertical parts of the drawing from right to left

2. Notice that the longest vertical part is 11 yards

3. Notice that the other labels vertical part is 6 yards

4. Notice that the third vertical part, the one with the ? is 11 yds - 6 yds since the two shorter vertical parts would make a line as long as the longest vertical part of they were put together. Since this is the case the missing part is 11 yds-6 yds = 5 yds.

Solution :

solve by considering data :

The perimeter of a rectangular pool is 56 meters. If the length of the pool is 16 meters, then find its width.

Here the perimeter and the length of the rectangular pool are given. We have to find the width of the pool.

The perimeter P of a rectangle is given by the formula, P=2l+2w, where l is the length and w is the width of the rectangle.

Given that, the perimeter is 56 meters and the length is 16 meters. So, substitute these values into the formula.

56=2(16)+2w

Simplify.

56=32+2w

Subtract 32 from both sides.

24=2w

Divide each side by 2 .

12=w

Therefore, the width of the rectangular pool is 12 meters.

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Answer:

Step-by-step explanation:

To solve for r, you need to first find the values of x that make y equal to 24. These values of x are called the roots of the polynomial equation y = (x+3)(x-2)(x-r).

To find the roots of the equation, you can use the quadratic formula:

x = (-b +/- sqrt(b^2 - 4ac)) / (2a)

where a, b, and c are the coefficients of the quadratic equation y = ax^2 + bx + c.

In this case, the coefficients are:

a = 1

b = -3

c = -24

Substituting these values into the quadratic formula, we get:

x = (3 +/- sqrt(9 - 96)) / 2

= (3 +/- sqrt(-87)) / 2

Since sqrt(-87) is not a real number, there are no real roots for this equation. Therefore, the value of r cannot be determined.

Answer:

The graph below shows the answer to

2x - 3y < 12

Also shown as

-3y < -2x + 12

Step-by-step explanation:

You can rearrange the inequality by subtracting 2x from both sides to isolate the y.

You now have -3y < 12 -2x

which can be put into the standard linear equation form of

-3y < -2x + 12

Then you divide both sides by -3 to get singular value of y, which is something like

-3/-3y < -2/-3x + 12/-3

which is

y > 2/3x -4

Note: I switched direction of the inequality because you are dividing both sides by a negative value.

Answer:

7

Step-by-step explanation:

subtracting a negative is the same as just adding the number, so five minus negative seven is just five plus seven

the best approximation of the area of the circle with a diameter of 17 meters is approximately 226.99m².

Why it is and what is diameter?

The diameter of the circle is 17 meters, which means the radius is half of the diameter, or 8.5 meters.

The formula for the area of a circle is:

A = πr²2

where A is the area and r is the radius.

Substituting the value of the radius into the formula, we get:

A = 3.14 x 8.5²2

A = 3.14 x 72.25

A ≈ 226.99

Therefore, the best approximation of the area of the circle with a diameter of 17 meters is approximately 226.99 m².

In geometry, the diameter of a circle is a line segment that passes through the center of the circle and has its endpoints on the circle. It is the longest chord (a line segment connecting any two points on a circle) of the circle, and it divides the circle into two equal halves, also known as hemispheres.

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The length of the mid-segment of the trapezoid is 66.5.

To find the midsegment of a trapezoid, you need to calculate the lengths of the bases and divide this by 2. Note that the midsegment is to be in between the line that runs from M to N.

The sides are parallel as shown in the double and single lines. So, to obtain the length of the midsegment, we would add 76 ad 57 and divide the result by 2.

So:

76 + 57 = 133/2

= 66.5

Thus, the length of the midsegment of the given trapezoid is 66.5 cm.

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Answer:

\( \frac{9x { }^{2 } - 63x}{ 3x} \\ = \frac{3x(3x - 21)}{3x} \\ = 3x - 21 \)

hope it helps:)

Answer:3x-21

Step-by-step explanation:

\(\frac{9x^{2} - 63x }{3x}\) ⇒ \(\frac{3x * (3x - 21) }{3x}\) ⇒ cancel out 3x ⇒ 3x - 21

Answer:

My answer would be; the performer displays rapid initial improvement followed by a decline in the rate of improvement.

Step-by-step explanation:

Usually a learning curve means that struggles are occurring after time of understanding and if we were creating a linear graph of this learning curve, it would be decreasing.

I don't know how to represent it on a nomberline

I

Answer:

b

Step-by-step explanation:

\( {x}^{ - \frac{5}{3} } = = = > \\ \frac{1}{x} ^{ \frac{5}{3} } \)

So the root is 3 and the power is 5

finally your answer

\( \frac{1}{ \sqrt[3]{ {x}^{5} } } \)

Answer:

1/9 rise 1 run 9

Step-by-step explanation:

if you graph the y coordinate as 3 and find the x value, x value should be 0. Point (0,3) and (-9,2) and do rise over run

Answer:

C. Yes, no two ordered pairs in this list has a repeat of the domain element.

Step-by-step explanation:

An equation that produces a set of ordered pairs defines a function, but it needs to be a proper function!

A function is a set of ordered pairs in which no two different ordered pairs have the same x -coordinate. Which means that answer C is correct.

Answer:

C. Yes, no two ordered pairs in this list has a repeat of the domain element.

Step-by-step explanation:

ODY 2022

1. There are two performance obligations in a contract to buy a pair of SunBoots from Clarks Inc: Delivery of Sunboots and Discount Coupon.

2. The journal entry to record the revenue for the sale of 1,000 pairs of SunBoots when Clarks cannot estimate the standalone selling price of a pair of SunBoots sold without a coupon is as follows:

Debit Cash $70,000

Credit Sales Revenue $65,800

Credit Deferred Revenue from Discount Coupon $4,200

(To record the sale of 1,000 pairs of SunBoots, including the discount coupon.)

Performance obligations refer to distinct goods and services agreed to be provided in a contract between the two parties.

Performance obligations arise because each separate goods or services benefit the customer distinctly from others.

In accounting for the revenue or costs, efforts should be geared toward recognizing the activity as soon as they bestow or transfer economic benefits to the buyer.

Selling price per pair = $70

Discount coupon = 30%

Estimated percentage of customers who will utilize the coupon = 20%

The number of SunBoots sold = 1,000

Cash $70,000 Sales Revenue $65,800 Deferred Revenue from Discount Coupon $4,200 ($70,000 x 30% x 20%)

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The measure of ∠1 is 41°, ∠2 is 27° and ∠3 is 63°.

Same-side exterior angles are two external angles to the parallel lines that are on the same side of the transverse line. According to the theorem, same-side exterior angles are supplementary, which means they add up to 180 degrees.

⇒∠1 + ∠2 + 22°+90° =180°

⇒∠1 + ∠2 = 180° - 112° = 68°

⇒∠1 + ∠2 = 68°

Similarly,

⇒∠3 =180°-117°=63°

⇒63°+ 90°+∠2 = 180°

⇒153°+∠2 = 180°

⇒∠2 =180°-153° =27°

⇒∠1 = 68°-27°= 41°       (since ∠1 + ∠2 = 68°)

Hence, the measure of ∠1 is 41°, ∠2 is 27° and ∠3 is 63°.

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