At a sale this week, a sofa is being sold for $272. This is a 36% discount from the original price. What is the original price?

Answer: A:171

Step-by-step explanation:

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

\(7x-5y=-6\implies -5y=-7x-6\implies y=\cfrac{-7x-6}{-5} \\\\\\ y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{7}{5}}x+\cfrac{6}{5}\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\)

so we're really looking for the equation of a line whose slope is 7/5 and it passes through (-4 , -5)

\((\stackrel{x_1}{-4}~,~\stackrel{y_1}{-5})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{7}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-5)}=\stackrel{m}{ \cfrac{7}{5}}(x-\stackrel{x_1}{(-4)}) \implies y +5 = \cfrac{7}{5} ( x +4) \\\\\\ y+5=\cfrac{7}{5}x+\cfrac{28}{5}\implies y=\cfrac{7}{5}x+\cfrac{28}{5}-5\implies {\Large \begin{array}{llll} y=\cfrac{7}{5}x+\cfrac{3}{5} \end{array}}\)

By using the arithmatic operations we can say that the sticker price of the small pickup with the given options is $36,050.

What are arithmetic equations?

Arithmetic equations are mathematical expressions that involve arithmetic operations such as addition, subtraction, multiplication, and division. Arithmetic equations typically have a left-hand side and a right-hand side, separated by an equal sign (=).

To determine the sticker price of the small pickup with the given base price and options, we need to add up the prices of the options and the base price, and then add the destination charge.

Base price = \($31,100\)

Stereo/SiriusXM radio/navigation system = \($1,445\)

Power sunroof = \($850\)

Security package = \($640\)

Aluminum wheels = \($545\)

Tubular side steps = \($525\)

Heated front seats = \($250\)

Trailer tow group = \($525\)

Pearlcoat paint = \($225\)

All-terrain tires = \($100\)

Destination charge = \($645\)

Sticker price = Base price + Options + Destination charge

Sticker price = \(31,100 + $1,445 + $850 + $640 + $545 + $525 + $250 + $525 + $225 + $100 + $645\)

Sticker price = \($36,050\)

Therefore, the sticker price of the small pickup with the given options is $36,050.

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Answer: x=4 y=14 z=4

Step-by-step explanation:

On edge it is that

The required exponent on x is 4, the exponent on y is 14, and the exponent on z is 4.

Using math and algebraic principles, simplification entails removing pointless variables, factors, or operations from an expression. Getting an expression that is simpler to use, manipulate, or solve is the aim. For example, simplifying an algebraic expression might involve combining like terms, factoring, or using the distributive property.

Here,
To simplify the given expression, we need to use the rules of exponents:

= [(x²y³)⁻¹ / (x⁻²y²z)²]²

= [(1 / x²y³) / (x⁻⁴y⁴z²)]²

= [(1 / x²y³) * (x⁴ / y⁴z²]²

= x⁴ / y¹⁴z⁴

Therefore, the exponent on x is 4, the exponent on y is 14, and the exponent on z is 4.

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Answer:

45 in

Step-by-step explanation:

Given 2 similar figures with ratio of radii = a : b , then

ratio of volumes = a³ : b³

Here ratio of volumes = 8 : 27 , then

ratio of radii = \(\sqrt[3]{8}\) : \(\sqrt[3]{27}\) = 2 : 3

let r be the radius of the larger sphere then by proportion

\(\frac{2}{30}\) = \(\frac{3}{r}\) ( cross- multiply )

2r = 90 ( divide both sides by 2 )

r = 45

The radius of the larger sphere is 45 in

According to the information we can infer that Dora's conclusion may be incorrect because the information provided only states that the number of people who spent time reading falls within specific ranges (0-2 hours, 2-4 hours, and 2-10 hours), but it does not give a specific count for those who spent at least 4 hours. Therefore, Dora's assumption that "most people spent at least 4 hours a week reading" is not supported by the given data.

The range of the time spent reading cannot be determined from the information provided because the ranges are overlapping. For example, a person who spent exactly 2 hours reading could fall into both the first range (0-2 hours) and the second range (2-4 hours). Without more specific data or non-overlapping ranges, it is not possible to determine the exact range of time spent reading.

To estimate the mean time spent reading by Dora's friends, we can calculate the midpoint of each range and use it as an approximate value. The midpoint for the first range (0-2 hours) is 1 hour, for the second range (2-4 hours) is 3 hours, and for the third range (2-10 hours) is 6 hours. We can then calculate the estimated mean by taking the weighted average of these midpoints using the respective number of people as weights.

Estimated mean = [(4 * 1) + (5 * 3) + (11 * 6)] / (4 + 5 + 11) = 4.53 hours (approximately)

So, an estimate of the mean time spent reading by Dora's friends is approximately 4.53 hours.

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A demand that is completely inelastic is one in which a change in price has no impact on the quantity demanded. The demand curve in this situation is vertical, and there is no demand elasticity.

A demand curve in economics is a graph showing the relationship between the price of a specific good (the y-axis) and the amount of that good that is desired at that price (the x-axis). Demand curves can be applied to both the price-quantity relationship for a single consumer (an individual demand curve) and for all consumers in a specific market.

Demand curves are typically thought to slope downward, as the adjacent image illustrates. This is due to the law of demand, which states that for the majority of goods, the quantity demanded decreases as the price increases. This law does not apply in some peculiar circumstances. These include Veblen goods, Giffen goods, and speculative bubbles, in which consumers are drawn to a commodity if its price increases.

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The percentage of the original area of wetlands currently left in the United States is approximately 50%. So, the correct

option is 50% (option 3).

Percentages are a way of expressing a proportion or a fraction as a part of 100. It is denoted by the symbol "%".

According to the United States Environmental Protection Agency (EPA), it is estimated that about 50% of the original

wetlands in the contiguous United States have been lost since the 1600s due to human activities such as agriculture,

development, and urbanization. Therefore, the correct answer to the question is 50%.

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The percentage of the original area of wetlands currently left in the United States is approximately 50%.

Wetlands are regions of land where the soil is continually or intermittently soaked with water. Wetlands have a particular hydrology, soil, and vegetation mix that results in specialised ecosystems that offer a variety of ecological functions.

There are many different types of habitats where wetlands can be found, such as coastal locations, interior regions, and high-altitude mountain regions. They come in a variety of shapes, such as marshes, swamps, bogs, fens, and estuaries, and can be freshwater, brackish, or saline.

Wetlands are significant for several reasons. For species, such as migrating birds, amphibians, and fish, they offer crucial habitats. They also aid in removing contaminants from water, lessen the effects of flooding, and give people access to recreational activities. Wetlands are crucial for carbon sequestration as well.
Based on the information provided, the question is asking for the approximate percentage of the original area of wetlands currently left in the United States. The answer is approximately 50%.

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Answer: 2.2 mph

Step-by-step explanation:

there's 60 minutes in an hour so you multiply the 1.1 miles to get how many miles they would walk in an hour.

Answer:

1 per minute

Step-by-step explanation:

9 min = 9 petunias

11 min = 11 petunias

so on and so forth

If you failed to pay the minimum payment by the due date and are now being charged the penalty APR of 28.99%, your monthly interest charge on a balance of $1800 would be approximately $518.82. This is calculated as follows:

However, it is important to note that this calculation is an estimate and the actual amount of interest you would owe in one month could be different, depending on factors such as the number of days in the billing period and the daily interest rate. It is also worth noting that you were charged $6.31 in interest for purchases, which is separate from the interest charged on your unpaid balance.

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7 / 4/5 = 8.75 or 8 3/4

3 1/2 / 3/4 = 4 2/3

---

hope it helps

Answer:

(4,4)

Step-by-step explanation:

The solution set of the system of equations can be found by setting the two equations equal to each other and solving for x.

x^2 - 6x + 12 = 2x - 4

x^2 - 8x + 16 = 0

(x - 4)^2 = 0

x = 4

Since both equations in the system are equal to y, we can substitute x = 4 into either equation to find the corresponding value of y.

y = 2x - 4 = 2(4) - 4 = 4

Therefore, the solution of this system of equations is (4, 4).

Therefore, the correct answer is (4, 4).

The proof that the equation is correct if a + b + C = 0 is

Given a + b + c = 0, we want to prove that:

[1 / (b² + c² - a²)] + [1 / (c² + a² - b²)] + [1 / (a² + b² - c²)] = 1

Now, let's substitute these expressions for a, b, and c into the terms of the expression we want to prove:

1 / (b² + c² - a²) = 1 / (b² + c² - (-(b + c))²)

1 / (c² + a² - b²) = 1 / (c² + a² - (-(a + c))²)

1 / (a² + b² - c²) = 1 / (a² + b² - (-(a + b))²)

Now, let's add these terms together:

[1 / (-2bc)] + [1 / (-2ac)] + [1 / (-2ab)] = (-2ab - 2ac - 2bc) / [(-2ab)(-2ac)(-2bc)]

We can simplify the numerator by factoring out -2:

-2(ab + ac + bc) / [(-2ab)(-2ac)(-2bc)]

Recall that a = -(b + c), b = -(a + c), and c = -(a + b). We can substitute these expressions back in:

[(-(b + c) + c - (b + c))(-a - a - c)] / [(-(b + c)(-a - c)(-a - b))]

Simplifying:

[(-b)(-2a)] / [(bc)(ac)(ab)]

The -2a cancels out:

1 / (bc) + 1 / (ac) + 1 / (ab) = 1

So, we have proved that:

[1 / (b² + c² - a²)] + [1 / (c² + a² - b²)] + [1 / (a² + b² - c²)] = 1

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If a pollster wishes to estimate the number of left-handed scientists. The sample that is needed in order to be 95% confident that the sample proportion will not differ from the true proportion by more than 4% is: 176.71.

Using this formula to find the sample

n =Z²π (1-π) ÷ e²

Where:

n =sample size =?

Z =  Z -score for 95% confidence level =1.960

π = Population proportion = 0.08

e = Margin of error = 0.04

Let plug in the formula

n = 1.96² × 0.08 × (1 - 0.08) ÷ 0.04²

n =  3.8416× 0.08 × 0.92 ÷ 0.0016

n = 176.71

Therefore the sample is 176.71.

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Answer:

12/16

That’s one

Answer:

  A.  x ≈ 25/16

Step-by-step explanation:

You want the solution to 5^(-x) +7 = 2x +4 using 3 iterations of successive approximation.

There are many methods of successive approximation. We presume from the answer choices that you want to use the bisection method. Here, it can start with the interval [1, 2], bounded by the integers either side of the x-coordinate of the point where the curves intersect.

The bisection method has you evaluate the function at the midpoint of the interval. The midpoint of the interval will replace the endpoint whose function value has the same sign, thus reducing the interval width by half.

The attached table shows the intervals containing the solution to the equation are reduced after 3 iterations to ...

  [1, 2] ⇒ [3/2, 2] ⇒ [3/2, 7/4] ⇒ [3/2, 13/8]

The midpoint of this last interval is (12/8 +13/8)/2 = 25/16. This is our approximation of the solution.

  x ≈ 25/16

__

Additional comment

We find it convenient to rewrite the equation to the form f(x) = 0. Then we are looking for the x-intercept of the function f(x). For the function we have chosen, the function value is positive at the left end of the interval, and negative at the right end. Thus, we can choose which interval bound to replace based on the sign of the function value. This simplifies the mental effort required.

If you do the arithmetic using separate functions for the left- and right-sides of the equation, then you need to compare those values and choose the interval end to change based on that comparison. We find that to be extra work.

The bisection method, on average, adds about 1/3 of a decimal place to the precision of the solution with each iteration. Other iteration methods can converge much more quickly. For example, Newton's method iteration can get a 6 decimal place answer in two iterations starting from x ≈ 1.5.

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Answer:

The stated solution is correct (lengths of 16 feet and 8 feet).

Based on the way the variable is defined, the equation should be x + 2x = 24.

The way the variable is defined, and because x=16, the longer piece of rope would be 32 feet, which is not possible.

Step-by-step explanation:

Answer: a, b & d !

Step-by-step explanation:

Answer:

.40x < 15

x < 37.5 copies

The maximum number of copies is 37.

37 × $.40 = $14.80

The length of g 1029.8 in the given  ΔFGH.

What is Trigonometric Functions?

Trigonometry uses six fundamental trigonometric operations. Trigonometric ratios describe these operations. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions. The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities. Using trigonometric formulas, the sine, cosine, tangent, secant, and cotangent values are calculated for the perpendicular side, hypotenuse, and base of a right triangle.

The Law of Sines (or Sine Rule) is very useful for solving triangles:

\(\frac{a}{sinA} = \frac{b}{sinB} + \frac{c}{sinC}\)

840 / sin(38) = g /sin(49)

g = (840 / sin(38) ) *sin(49)

g= (840/0.615) *0.754 = 1029.8

Hence, the length of g 1029.8 in the given  ΔFGH.

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(a) List all hotels: π(hotelNo, hotelName, city)(Hotel)

(b) List all single rooms with a price below £20 per night: σ(type = 'single' ∧ price < 20)(Room)

(c) List the names and cities of all guests: π(guestName, city)(Guest ⨝ Booking)

(d) List the price and type of all rooms at the Grosvenor Hotel: π(price, type)(Room ⨝ hotelNo = hotelNo(π(hotelNo)(Hotel), 'Grosvenor Hotel'))

(e) List all guests currently staying at the Grosvenor Hotel: π(guestNo, guestName, guestAddress)(Guest ⨝ Booking ⨝ roomNo = roomNo(π(hotelNo)(Hotel), 'Grosvenor Hotel'))

(f) List the details of all rooms at the Grosvenor Hotel, including the name of the guest staying in the room, if the room is occupied: π(roomNo, hotelNo, type, price, guestName)(Room ⨝ Booking ⨝ Guest ⨝ hotelNo = hotelNo(π(hotelNo)(Hotel), 'Grosvenor Hotel'))

(g) List the guest details (guestNo, guestName, and guestAddress) of all guests who have ever stayed at the Grosvenor Hotel: π(guestNo, guestName, guestAddress)(Guest ⨝ Booking ⨝ roomNo = roomNo(π(hotelNo)(Hotel), 'Grosvenor Hotel'))

(a) List all hotels:

π(hotelNo, hotelName, city)(Hotel)

(b) List all single rooms with a price below £20 per night:

σ(type = 'single' ∧ price < 20)(Room)

(c) List the names and cities of all guests:

π(guestName, city)(Guest ⨝ Booking)

(d) List the price and type of all rooms at the Grosvenor Hotel:

π(price, type)(Room ⨝ hotelNo = hotelNo(π(hotelNo)(Hotel), 'Grosvenor Hotel'))

(e) List all guests currently staying at the Grosvenor Hotel:

π(guestNo, guestName, guestAddress)(Guest ⨝ Booking ⨝ roomNo = roomNo(π(hotelNo)(Hotel), 'Grosvenor Hotel'))

(f) List the details of all rooms at the Grosvenor Hotel, including the name of the guest staying in the room, if the room is occupied:

π(roomNo, hotelNo, type, price, guestName)(Room ⨝ Booking ⨝ Guest ⨝ hotelNo = hotelNo(π(hotelNo)(Hotel), 'Grosvenor Hotel'))

(g) List the guest details (guestNo, guestName, and guestAddress) of all guests who have ever stayed at the Grosvenor Hotel:

π(guestNo, guestName, guestAddress)(Guest ⨝ Booking ⨝ roomNo = roomNo(π(hotelNo)(Hotel), 'Grosvenor Hotel'))

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Answer:

Step-by-step explanation:

One solution if they intersect (which is the case), and zero if they are parallel and apart, and infinite if they are parallel and coincident, two lines piled on top of each other.

The 99% confidence interval for the true mean length of the manufactured bolt is (2.9177, 3.0823)

Here, we need to construct a 99% confidence interval for population mean (μ) is given by

μ = x + Zα/2 * σ/√n   or    μ = x - Zα/2 * σ/√n

where, μ = population mean

x = sample mean

  = 3 inches

σ = population standard deviation

  = 0.3 inches

Zα/2= z score for a two tailed test at level of significance α = 2.576( for a 99% confidence level)

So, the upper limit would be,

μ = 3 + 1.645 * (0.3/√36)

μ = 3 + 1.646 * (0.3/6)

μ = 3.0823

And the lower limit would be,

μ = 3 - 1.645 * (0.3/√36)

μ = 3 - 1.646 * (0.3/6)

μ = 2.9177

Hence, the 99% confidence interval is (2.9177, 3.0823)

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To solve this system, first multiply the first equation by 2 to get 8x+6y=-4.

An equation is a mathematical statement that expresses two values or ideas as equal. It consists of two parts: an expression and an equals sign. The expression on the left side of the equals sign is compared to the expression on the right side of the equals sign. An equation may be used to describe relationships between physical, chemical, and mathematical quantities.

Then add the two equations to get 14x=-8. Therefore,

x=-8/14 and substituting x=-8/14

into the first equation yields y=3/2.

Thus, the solution to the system is x=-8/14 and y=3/2.

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Discount amount = price x discount percentage as a decimal:

Discount amount = 62.00 x 0.15 = 9.30

Discount = $9.30

Answer:

$52.70

Step-by-step explanation:

Answer:

Step-by-step explanation:

45

Step-by-step explanation:

3x+x=180

4x=180

x=45

Hope this helps hit the crown :D

Answer:

Step-by-step explanation:

25 feet for 8 mins

300/25=12

8*12=96

The line will move to 300 feet in 96 mins

Answer:

Step-by-step explanation:

Yes you can multiply 5 and 2x. As you said 5×2x is 10x

So you can go forward from there...3x + 10x = 26. Next, combine like terms, that means adding the 3x and the 10x together to get 13x. Here is where you could NOT add, IF one was an x term and one was a plain number, couldn't happen. But they are both x's in this case so you get 13x =26 and divide by 13 on both sides of the equation and get x = 2 for your final answer.

Hey there!

3x + 5 * 2x = 26

3x + 5(2)x = 26

3x + 10x = 26

COMBINE the LIKE TERMS

(3x + 10x) = 26

13x = 26

DIVIDE 13 to BOTH SIDES

13x/13 = 26/13

CANCEL out: 13/13 because it gives you 1

KEEP: 26/13 because it helps solve for the x-value

NEW EQUATION: x = 26/13

SIMPLIFY IT!

x = 2

Therefore, your answer is: x = 2 and yes!

SIDE NOTE:

TRY TO MAKE IT TRUE

3(2) + 5(2)(2)

= 6 + 10(2)

= 6 + 20

= 26

Therefore, your statement would be true if that’s the case!

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

i dont get this why is it crossed out

Step-by-step explanation: