1. y = 5x − 6 m= _______ b=_________

Using percentages, we know that $515.87 approx is the purchase price at the start.

In mathematics, a percentage is a number or ratio that is expressed as a fraction of 100.

Although "pct," "pct," and occasionally "pc" are also employed as acronyms, the percent symbol "%" has been most usually used to denote it.

A% is a number that has neither dimensions nor a specified unit of measurement.

For example, if you properly completed 75 out of 100 questions on a test, you would have received a 75% grade (75/100).

So, in mathematics, a percentage is a number or ratio that is expressed as a fraction of 100. Let x represent the initial asking price ( in dollars ),

After 10% is deducted, 10% of x less the new selling price, or x - 0.1x, equals 0.9x.

Having reduced the price by 30%,

The final selling price equals 90% less than 90%.

= 0.9x - 0.3 × 0.9x

= 0.9x - 0.27x

= 0.63x

The answer to the query is:

0.63x = 325

x = 325/0.63

x = 515.87

Therefore, using percentages, we know that $515.87 approx is the purchase price at the start.

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Correct question:
A sporting goods store manager was selling a ski set for a certain price. The manager offered the markdowns​ shown, making the​ one-day sale price of the ski set ​$325. Find the original selling price of the ski set. It was marked down 10% and 30%

To find the area under the curve y = 1.5 x^-2.5 from x = 8 to x = t, a) Area ≈ 0.2455 b) Area ≈ 0.0816 c) Area = 3(8)^-1.5 + C

we need to integrate the function with respect to x.

The integral of y = 1.5 x^-2.5 is:

∫ 1.5 x^-2.5 dx = -3x^-1.5 + C

where C is the constant of integration.

To evaluate the definite integral from x = 8 to x = t, we plug in the upper and lower limits of integration and subtract the values:

Area = [-3t^-1.5 + C] - [-3(8)^-1.5 + C]

Simplifying this expression, we get:

Area = -3t^-1.5 + 3(8)^-1.5

Now we can find the area for t = 10 and t = 100:

(a) t = 10:

Area = -3(10)^-1.5 + 3(8)^-1.5

Area ≈ 0.2455

(b) t = 100:

Area = -3(100)^-1.5 + 3(8)^-1.5

Area ≈ 0.0816

To find the total area under the curve for x ≤ 8, we need to integrate the function from 0 to 8:

∫ 1.5 x^-2.5 dx = -3x^-1.5 + C

Area = [-3(8)^-1.5 + C] - [-3(0)^-1.5 + C]

Area = 3(8)^-1.5 + C

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The number of minutes that the housefly had been on the fan during the time it took to travel 19404 π feet will be 162 minutes.

The study of motion without considering the mass and the cause of the motion.

A housefly sits on the outer edge of a rotating circular ceiling fan with a diameter of 6 feet.

The fan rotates constantly at a rate of 20 revolutions per minute.

Then the velocity of the tip of a fan will be

V = 2πrN

V = πdN

V = π · 6 · 20

V = 120 π feet per minutes

The number of minutes that the housefly had been on the fan during the time it took to travel 19404 π feet will be

Time = 19404 π / 120 π

Time = 19404 / 120

Time = 161.7

Time ≈ 162 minutes

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Answer:

11.2square feet

Step-by-step explanation:

Area of a sector = theta/360 * πr²

theta is the central angle = 80degrees

radius r = PC = 4ft

Substitute

Area of the sector = 80/360 * 3.14 * 4²

Area of the sector = 80/360 * 3.14 * 16

Area of the sector = 4,019.2/360

Area of the sector = 11.2ft²

Hence tthe area of the blue sector is 11.2square feet

To find T((5, -4)), we can use the linearity property of linear transformations. First, we can express (5, -4) as a linear combination of the given basis vectors:(5, -4) = 5*(1, 2) + (-6)*(0, 1)

Since T is a linear transformation, we can apply it to each term separately:

T((5, -4)) = T(5*(1, 2) + (-6)*(0, 1))

Using the linearity property of T, we have:

T((5, -4)) = 5*T((1, 2)) + (-6)*T((0, 1))

From the given information, we know that T((1, 2)) = (2, 3) and T((0, 1)) = (1, 4). Substituting these values, we get:

T((5, -4)) = 5*(2, 3) + (-6)*(1, 4)

= (10, 15) + (-6, -24)

= (10 + (-6), 15 + (-24))

= (4, -9)

Therefore, T((5, -4)) is (4, -9). None of the options provided match this result, so the correct answer is not among the given choices.

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Answer:

arc CD = 160°

Step-by-step explanation:

The measures of the arcs on the circle = 360° , then

arc CD = 360 - AC - AD = 360 - 3x - 7x = 360 - 10x

--------------------------------------------------------------------------

The measure of the secant- tangent angle ABC is half the difference of the intercepted arcs, that is

\(\frac{1}{2}\) (7x - 3x) = 40 ( multiply both sides by 2 to clear the fraction )

7x - 3x = 80

4x = 80 ( divide both sides by 4 )

x = 20

Then

CD = 360 - 10x = 360 - 10(20) = 360 - 200 = 160°

Answer:

30-35 minutes

Step-by-step explanation:

The integral ∫cf→ ⋅ dr→, where f→ = xi

To evaluate the integral ∫c(f→ ⋅ dr→), we need to calculate the dot product between the vector field f→ and the differential displacement vector dr→ along the curve defined by c. Let's proceed step by step.

Given:

f→ = xi→ + 4zyj→ + xk→

c is r→ = ti→ + t^2j→ + t^3k→, where 2 ≤ t ≤ 3.

First, we'll express the dot product f→ ⋅ dr→ in terms of t and then integrate with respect to t over the given interval.

f→ ⋅ dr→ = (xi→ + 4zyj→ + xk→) ⋅ (ti→ + t^2j→ + t^3k→)

= (xi→ ⋅ ti→) + (4zyj→ ⋅ t^2j→) + (xk→ ⋅ t^3k→)

= xt + 4z(t^2) + xt^3

= 2xt + 4zt^2 + t^3x

Now, we'll integrate the dot product over the interval [2, 3] with respect to t.

∫cf→ ⋅ dr→ = ∫2t to 3t (2xt + 4zt^2 + t^3x) dt

= ∫2t to 3t 2xt dt + ∫2t to 3t 4zt^2 dt + ∫2t to 3t t^3x dt

Integrating each term separately:

∫2t to 3t 2xt dt = x∫2t to 3t 2t dt

= x[t^2] evaluated from 2t to 3t

= x[(3t)^2 - (2t)^2]

= x(9t^2 - 4t^2)

= 5xt^2

∫2t to 3t 4zt^2 dt = 4z∫2t to 3t t^2 dt

= 4z[(1/3)t^3] evaluated from 2t to 3t

= 4z[(1/3)(3t)^3 - (1/3)(2t)^3]

= 4z[(1/3)(27t^3) - (1/3)(8t^3)]

= 4z(9t^3 - 8t^3)

= 4zt^3

∫2t to 3t t^3x dt = x∫2t to 3t t^3 dt

= x[(1/4)t^4] evaluated from 2t to 3t

= x[(1/4)(3t)^4 - (1/4)(2t)^4]

= x[(1/4)(81t^4) - (1/4)(16t^4)]

= x(65t^4)

Now, we can evaluate the integral:

∫cf→ ⋅ dr→ = 5xt^2 + 4zt^3 + 65t^4

Finally, to express the result in terms of c, we substitute c = r→:

∫cf→ ⋅ dr→ = 5c^2 + 4cz^2 + 65c^4

Therefore, the integral ∫cf→ ⋅ dr→, where f→ = xi

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The combination of  number of ways of groups of 3 customers are  19600 .

What is permutation and combination?

The number of store customer is N = 50

The number of customer that receive a special gift is r = 3

The expression for the number of possible ways to choose 3 customers is

                   = ⁿCr

                   = ⁵⁰C₃

                    = 50 * 49 * 48/3 * 2 * 1

                    = 19600

Thus, the number of ways of groups of 3 customers are  19600.

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Answer:

When numbers become very small or large standard form (or standard index form) is used to make them manageable. In standard form or unit a number is written as:

[a number between 1 and 10] × [ an integer power of 10]

Answer: It is 34$ per one ticket

Step-by-step explanation:

$374 divided by 11 is 34

Answer:

$34 per ticket

Step-by-step explanation:

We were told $374/11tickets.

We are looking for how much per 1 ticket.

Divide to find the per-ticket cost.

Use either 374÷11

374/11 .

374÷11 = 34

This means $34 per ticket.

Answer:

The correct options are;

Heather likely did not make an error writing the equation of the line in her notebook because 0.77 and 1.34 are the slope y-intercept of the equation she recorded

Step-by-step explanation:

Based on the coordinates on the plot, Heather did not make a mistake in writing the line of best fit as the graph plotted with the points in the question  figure as follows;

x,            y

10.6,       9.4

8.2,         8.2

6.4,         7.3

6.6,         5.8

4.4,         5.4

4,            3.4

2.5,         4.4

2.2,         3

0.85,       1.5

Has an equation of he form, y = 0.7885·x + 1.3694.

Answer:

I cant see the picture

Step-by-step explanation:

Split the equation into two separate equations (one with a positive and one with a negative), and then solve both equations.

POSITIVE:

2b - 9 = b - 6

b = 3

NEGATIVE:

2b - 9 = -(b - 6)

2b - 9 = -b + 6

3b = 15

b = 5

Answer: b=3, b=5

Given:

As angle N is 90 degree.

To find the bearing of flight from Elgin to Canton.

Use the sin ratio,

The bearing angle ( clockwise from north ) can be calculated by subtracting the above angle from the west bearing angle of 270 degree.

Answer: 239.37 degree

Answer: Hardwood flooring

Step-by-step explanation:

Given

Rohann renovation of Carpentering cost $875 for \(20\ m^2\)

For hardwood flooring \(17\ m^2\) cost $750

So, cost per square meter for different floors are

\(\Rightarrow \text{Carpentering}=\dfrac{875}{20}\\\\\Rightarrow \text{Carpentering}=\$43.75/m^2\)

\(\Rightarrow \text{Hardwood}=\dfrac{750}{17}\\\\\Rightarrow \text{Hardwood}=\$44.11/m^2\)

Thus, the cost of the Hardwood flooring is more expensive.

The likelihood of striking a 6 on the this unbalanced die is therefore 1, or 100%.

A reasonable transaction result in money, products, or services. 2.: The monetary value of anything. 3.: value, usefulness, or significance in relation to anything else

As the die has only 6 sides, the probability of rolling a 6 is denoted by P(6). Let's use the formula of expected value to find P(6).

The expected value of the die is given by:

E(X) = (1 + 2 + 3 + 4 + 5 + 6)/6 = 21/6 = 3.5

We know that the expected value of the entire die is 4. Therefore, the expected value of the additional bonus for rolling a 6 is:

E(Y) = 4 - E(X) = 4 - 3.5 = 0.5

Since the bonus value can only be obtained by rolling a 6, the probability of getting a 6 is equal to the probability of obtaining the bonus value of 0.5. Hence, we have:

P(6) = P(Y = 0.5) = P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

Since the numbers 1-5 are equally likely to occur, we have:

P(X = 1) = P(X = 2) = P(X = 3) = P(X = 4) = P(X = 5) = 1/5

Therefore,

P(6) = P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = 5/5 = 1

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As per the above given question the reflection of m∠O=112°.

A process of introspection or self-examination is reflection. It entails reflecting critically on one's thoughts, feelings, and experiences in order to comprehend oneself better. Self-awareness and insight can be developed through reflection, which can result in personal development and change.

In a larger sense, reflection also refers to the bouncing back of light, sound, or other waves from a surface and is employed in many disciplines, including arithmetic, computer science, and optics. The capacity of a computer program to review and alter its own structure and behavior at runtime is known as reflection in computer programming.

According to question:

Here are given m∠G=61 m∠f=7

From angle sum property of triangle, we get in ΔGFA

m∠G+m∠F+m∠O=180°

⇒61+7+m∠O=180

⇒68+m∠O=180

Therefore m∠O=180-68=112

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Answer:

20 square feet

Step-by-step explanation:

The length of a rectangular deck is five times it's width if the decks perimeter is 24 feet what is the decks area

Step 1

We find the Length and Width of the deck

Perimeter of a rectangle = 2L + 2W

The length of a rectangular deck is five times it's width

W = Width

L = Length = 5W

P = 24 feet

Perimeter = 2(5W) + 2W

24 = 10W + 2W

24 = 12 W

W = 24/12

W = 2 feet

Solving for L

L = 5W

L = 5 × 2 feet

L = 10 feet

Step 2

We find the area of the deck

Area of the deck(Rectangle) = Length × Width

= 10 feet × 2 feet

= 20 square feet

Answer:

25% increase

Step-by-step explanation:

length is 24 inches after the increase and width is 33 inches (i did length as up and down and width as side to side, that's how I always do it but I might be wrong let me know and I can fix it)

the area before it gets increased it 600

after the increase its 792

and 600 is 75.75% of 792

so it would be 25.25% increase

sorry this was so long hope this helps

Answer:

4891

Step-by-step explanation:

73 can be written as (70 + 3), and 67 can be written as (70 - 3) which means that 73 × 67 is the same as (70 + 3)(70 - 3)

The next step is to use FOIL and expand the brackets:

(70 + 3)(70 - 3) = 4900 + -210 + 210 + -9

This can be simplified to 4891.

Hope this helps!

a) To maximize its net savings, the company should use the new machine for 7 years.  b) The net savings during the first year of use of the machine are $405 (rounded off to the nearest dollar).  c) The net savings over the period determined in part a are $1,833.33 (rounded off to the nearest cent).

Step-by-step explanation: a) To determine for how many years should the company use the new machine to maximize its net savings, we need to find the value of x that maximizes the difference between the savings and the costs.To do this, we need to first calculate the net savings, N(x), which is given by:S'(x) - C'(x) = 175 - x² - (x² + 11x) = -2x² - 11x + 175To find the maximum value of N(x), we need to find the critical values, which are the values of x that make N'(x) = 0:N'(x) = -4x - 11 = 0 ⇒ x = -11/4The critical value x = -11/4 is not a valid solution because x represents the number of years of operation of the machine, which cannot be negative. (i.e., not use it at all).However, this answer does not make sense because the company would not introduce a new machine that it does not intend to use. Therefore, we need to examine the concavity of N(x) to see if there is a local maximum in the feasible interval.

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The correct answer is D. $2.75 / $3.24

To determine how much you should expect to pay for gas in Philadelphia versus Cleveland, we need to compare the transportation expenses in both cities. Based on the given data, the transportation expenses are as follows:

Philadelphia: $117

Cleveland: $106

To calculate the expected gas prices, we need to consider the transportation expenses relative to the national average. The formula to find the expected gas price is:

Expected Gas Price = National Average * (Transportation Expense / National Average)

National Average for gas = $2.59

For Philadelphia:

Expected Gas Price in Philadelphia = $2.59 * ($117 / 92) ≈ $3.30

For Cleveland:

Expected Gas Price in Cleveland = $2.59 * ($106 / 78) ≈ $3.51

Comparing the expected gas prices, we find that:

A. $3.03 / $2.75: This option does not match the expected gas prices in Philadelphia and Cleveland.

B. $1.95 / $2.59: This option does not match the expected gas prices in Philadelphia and Cleveland.

C. $2.34 / $2.75: This option does not match the expected gas prices in Philadelphia and Cleveland.

D. $2.75 / $3.24: This option matches the expected gas prices in Philadelphia and Cleveland.

Therefore, the correct answer is:

D. $2.75 / $3.24

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Answer:

Below

Step-by-step explanation:

4 [x-3] + 2    = y    is not discontinuous anywhere

However    4 / [x-3]  + 2   DOES have a discontinuity at x = 3 because this would cause the denominator to be zero <===NOT allowed !!

Answer:

6 pounds

Step-by-step explanation:

3$ for 2 pounds

9$ has three 3$

9 ÷ 3 = 3

Then multiply it to 2 pounds.

3 x 2 = 6

That's how we get the 6 pounds.

c

Step-by-step explanation: