9. You have been saving your money to buy a new pair of shoes. Three different
stores are having a sale on them. Which store has the best deal? Order from
lowest price (top) to highest price (bottom).
A. Original Price $150 - Take $20 off. Then Take 10% off.
B. Sale Price $115
C. Original Price $160 - Take 10% off. Then take 20 $ off.

Answer:

V  =  339 in³

Step-by-step explanation:

The formula for the volume of a sphere of radius r is V = (4/3)πr³

Here the diameter is 18 m, so the radius must be 9 m, and the volume of the sphere is

V = (4/3)(3.14)(9 m)², or

V  =  339 in³

The distribution of intelligence test scores in the general population forms a bell-shaped pattern is known as a normal distribution.

Normal distribution, also known as Gaussian distribution, is a continuous probability distribution used in statistics. The normal distribution has a bell-shaped curve that is symmetrical about the mean (average).The normal distribution has some important properties, including that its mean, median, and mode are equal.

Furthermore, the total area under the curve is 1. A normally distributed population is one in which the majority of the data is clustered around the mean, with fewer data points further from the mean. It is a common distribution for a variety of natural phenomena, and many statistical analyses depend on it.

The normal distribution plays a critical role in statistical hypothesis testing and other statistical analyses because of its properties, and it has numerous applications in science, engineering, and finance.

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The rate increases by a factor of 9 when the concentration is tripled.

It is given to us that the rate law is -

\(R=k(NO_{2} )^{2}\) ----- (1)

We have to find out the change in the rate if the concentration is tripled.

When the concentration is tripled, we can rewrite the equation (1) as -

\(R_{new} =k(3*NO_{2} )^{2}\\= > R_{new} =9*k(NO_{2} )^{2}\\= > R_{new} =9R\)[From equation (1)]

Thus, we see that the rate increases by a factor of 9 when the concentration is tripled.

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We want to answer different things by using the linear relation that relates the length of the two pieces of ribbon.

A) 15 ft

B) -1

C) It means that a unit increase in x causes a unit decrease in y.

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

here, we have,

A) First we want to see how long is the ribbon.

Notice that:

x = second piece length

y = first piece length.

You can see that when x = 0ft (so we don't cut anything) we have y = 15ft, thus the length of the ribbon is 15ft (we also can see that when y = 0ft, x is equal to 15ft).

B) We want to get the slope.

Notice that the line passes through the points (0, 15) and (15, 0), so the slope is:

a= 0-15/15-0

 = -1

C) The slope of -1 implies that each unit increase in x causes a unit decrease in y.

This makes sense because if the second ribbon is cut 1 ft longer, this means that the first ribbon becomes 1 ft shorter.

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The value of the actual width of the building is 2400000 m

From the question, we have the following parameters that can be used in our computation:

Width of the offcie = 30 mm

Scale = 1 : 80,000

using the above as a guide, we have the following:

Actual = Scale * Width of the offce

when the given values are substituted in the above equation, we have the following equation

Actual = 80000 * 30 m

Evaluate

Actual = 2400000 m

Hence the actual width of the building is 2400000 m

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Answer:

A. the answer is supplementary

The given data is,

→ the ratio of cups of water to cups of milk in a recipe is 1 to 5

Now we have to,

→ find three ratios equivalent to the ratio

Then the ratios will be,

→ 1 (×2) : 5 (×2)

= 2 : 10

→ 1 (×3) : 5 (×3)

= 3 : 15

→ 1 (×4) : 5 (×4)

= 4 : 20

Thus, 2 : 10, 3 : 15 & 4 : 20 are the ratios.

Answer:

decreased by 50%

Step-by-step explanation:

\(\frac{x}{y}\)

100% - 60% = 40% = 0.4

100% - 20% = 80% = 0.8

\(\frac{0.4x}{0.8y}\) = \(\frac{x}{2y}\) = 0.5 × \(\frac{x}{y}\) ⇒ the original fraction is decreased by 50%

Answer:

p - p(.60)

Step-by-step explanation:

to find 60% of p you turn 60% into a decimal, which is .60, next you multiply .60 by p which will give you 60% off of p,

finally you take the total which is p and subtract off the discount which is .60p, thus p-p(.60)

also... another way to solve this is that if you are getting 60% off that means you are paying 40% of the price, thus you could just multiply p(.40) to get the amount the person would actually pay

We are required to determine the inverse Laplace transform using convolution method for the function

F(s) = S² (S²+2).Step-by-step solution The inverse Laplace transform of a function F(s) can be found by breaking it into partial fractions and using the known inverse Laplace transforms.

However, in case of complex roots, it is difficult to use partial fractions. In such cases, convolution method can be used. The steps to determine the inverse Laplace transform using convolution method are as follows: Step 1: Write the function in partial fraction form. In this case, we have:S²/(S²+2) = A - A/(S²+2)S²+2/(S²+2)

= A/(S-i√2) + A/(S+i√2)

Step 2: Take the inverse Laplace transform of both sides:

S²(t) = L^-1{A - A/(S²+2)} = Aδ(t) - A/√2L^-1{1/(S²+2)}S²+2(t)

= L^-1{A/(S-i√2) + A/(S+i√2)}

= A/√2 e^(i√2t) + A/√2 e^(-i√2t)L^-1{S²+2}Step 3: Use convolution theorem

S(t) = L^-1{F(s)}

= L^-1{S²/(S²+2)}

= L^-1{A - A/(S²+2)} * L^-1{1/(S²+2)}

= [Aδ(t) - A/√2L^-1{1/(S²+2)}] * [A/√2 e^(i√2t) + A/√2 e^(-i√2t)]S(t)

= A/√2 δ(t) + A/√2 e^(i√2t) - A/√2 e^(-i√2t)S(t)

= A/√2 [δ(t) + e^(i√2t) - e^(-i√2t)]Answer: The inverse Laplace transform of F(s) = S² (S²+2) is given as

S(t) = A/√2 [δ(t) + e^(i√2t) - e^(-i√2t)].

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Answer:

We factor the number 16 into prime numbers to get their factors.

We do the same with any given number. Only if it has the same factor as 16 that numberwill be divisible by 16

Both numbers proposed (144&256) are divisible by 16

Step-by-step explanation:

To prove it we need to factor the number 16 to get their expression in prime numbers:

16     2

 8    2

 4    2

 2    2

 1

16 is equal to \(2^{4}\)

We have to factor a number and if their factor include \(2^{4}\) or a higher power

then, they are divisible by 16

144        2

 72       2

 36       2

 18        2

   9       3

   3       3

   1

144 is queal to:  \(2^4 . 3^2\) as it does have \(2^4\) It is divisible by 16

256         2

128          2

  64        2

  32        2

   16        2

    8        2

    4        2

    2        2

    1

256 is equal to \(2^8\) This contains \(2^4\) as \(2^8 = 2^4 . 2^4\)

therefore it is divisible by 16

Answer:

1 cm = 100 m

Explanation:

The conversion factor to go from cm to m is

1 cm = 0.01 m or

1 m = 100 cm

Additionally, the conversion factor from km to m and from dm to m is:

1 km = 1000 m

1 dm = 0.01 m or 1 m = 10 dm

Therefore, the incorrect conversion factor is:

1 cm = 100 m

Because 1 cm is smaller than 1 m

Answer:

x = 3/4

y = 2.5

Step-by-step explanation:

No there is just one.

Equate the ys

-2/3 x + 3 = 2/3 x + 2                        Add 2/3 x to both sides

3 = 2/3 x + 2/3x + 2                          Combine

3 = 4/3 x + 2                                     Subtract 2

3-2 = 4/3 x                                        Multiply by 3

1 * 3 = 4x                                          Divide by 4

3/4 = x

====================

y = 2/3 x + 2

y = 2/3 * 3/4 + 2

y = 6/12 + 2

y = 1/2 + 2

y = 2 1/2

y = 2.5

The height of the building is approximately 102.86 meters.

Given that from a certain distance, the angle of elevation to the top of a building is 17 degrees. At a point 50 meters closer to the building, the angle of elevation is 31 degrees. To find the height of the building.In the given figure, AB is a building and C and D are two different points at a certain distance from the building. So that, angle BCA = 17° and angle BDA = 31°.We have to find the height of the building AB.

Now, let's find the distance between the building and point C and D. Let, BC = x50 meters closer to the building, so BD = x + 50 metersWe know, tangent of an angle = Perpendicular / BaseFor the angle 17°, we have to find AC, so;tan(17°) = AB / ACAB = AC tan(17°) ---(1)For the angle 31°, we have to find AD, so;tan(31°) = AB / ADAB = AD tan(31°) ---(2)Now, find the difference between (1) and (2).AC tan(17°) - AD tan(31°) = 0AC / AD = tan(31°) / tan(17°) [Divide both sides by AD tan(17°)]AC / (AD + 50) = tan(31°) / tan(17°) ----(3)We know the value of (AC + AD) is the actual distance between the building and the point.

So,(AC + AD) = x + (x + 50) = 2x + 50 metersNow we can use the value of AC / (AD + 50) in equation (3) and solve for AB.AB = AC tan(17°) = (2x + 50) tan(17°) tan(31°) / (tan(31°) - tan(17°))Substitute the value of AB from equation (1), so;AC tan(17°) = (2x + 50) tan(17°) tan(31°) / (tan(31°) - tan(17°))AC = (2x + 50) tan(31°) / (tan(31°) - tan(17°))Now, let's use the value of AC in equation (1),AB = AC tan(17°) = (2x + 50) tan(17°) tan(31°) / (tan(31°) - tan(17°)) = 102.86 meters (approx.)So, the height of the building is AB = 102.86 meters (approx.)

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In the inequality 3x + 1 ≤ 4 at x = {1, 0, -1, -2, -3} all the values are satisfied therefore, the graph matches with this inequality.

What is Linear Inequality?

A linear inequality is a mathematical inequality that incorporates a linear function. A linear inequality contains one of the inequality symbols. It displays data that is not equal in graph form.

Solution:

To find the answer we need to put the values of x in options

3x + 1 ≤ 4

Putting x = {1, 0, -1, -2, -3}

At x =  1

3*1 + 1 ≤ 4

At x = 0

3*0 + 1 ≤ 4

At x = -1

3*-1 + 1 ≤ 4

At x = -2

3 * -2 + 1 ≤ 4

At x = -3

3*-3 + 1 ≤ 4

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The number of emergency kits that Neil packed in total for the 150 bottles is gotten as; k = 50 kits.

We are told that Neil puts 3 water bottles into each emergency kit packed.

Now, let the number of emergency kits be k.

Thus;

3k = 150

Division property of equality, we have;

3k/3 = 150/3

k = 50

Thus, the number of emergency kits that Neil packed is gotten as k = 50 kits.

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If 22 inches of wire costs 88 cents then at the same rate, 16 inches of wire will cost 64 cents.

To determine the cost of 16 inches of wire at the same rate as 22 inches, we can set up a proportion using the given information. We have that 22 inches of wire costs 88 cents. We can set up the proportion:

22 inches / 88 cents = 16 inches / x cents

By cross-multiplying, we get:

22 inches * x cents = 16 inches * 88 cents

Simplifying, we have:

22x = 1408

Dividing both sides by 22, we find:

x = 64

Therefore, 16 inches of wire will cost 64 cents at the same rate as 22 inches. The cost is directly proportional to the length of the wire, so we can use this proportion to calculate the cost of different lengths.

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The evidence does not strongly support the claim that women with above-average looks earn significantly more than women with average looks.

To understand the findings, we need to discuss a few key concepts. First, let's clarify the null hypothesis (H0) and the alternative hypothesis (H1). In this case, the null hypothesis states that there is no relationship between physical appearance and income (β2 = 0), while the alternative hypothesis suggests that there is a relationship (β2 ≠ 0).

In this scenario, the one-sided p-value of 0.272 means that there is a 27.2% chance of observing a relationship between physical appearance and income as strong or stronger than what was found in the study, purely by chance, if there is actually no relationship (β2 = 0). Since this p-value is relatively high (greater than the commonly used threshold of 0.05), it implies weak evidence against the null hypothesis.

Therefore, based on the given information, the evidence does not provide sufficient statistical support to reject the null hypothesis that there is no relationship between physical appearance and income (H0: β2 = 0).

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The probability of having a 5-card hand that is a flush or royal flush is 0.00196

Probability: Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.

Flush, straight flush, and royal flush probabilities are calculated as follows: 5148/2598960≅0.00198

A flush's likelihood (while eliminating straight and royal flushes) is 5108/2598960, ≅0.00196.

Finding the fraction with the number of ways to have a flush as the numerator and the number of possible five-card hands as the denominator will allow us to determine the likelihood.

Combinations will be used to find each of these numbers (we don't care about the draw order; only about what shows up in our hand). Combinations' general formula is Cn,k=n!/(k)!(n-k)! with k=picks and n=population

Let's first determine the denominator by selecting 5 cards at random from a deck of 52 cards: C52,5=52!/(5)!(525)!

=52!/(5!)(47!)

Let's assess it!

52×51×50^10×49×48^2×47!/5×4×3×2×47!=52×51×10×49×2=2,598,960

Let's now determine the numerator.

In order to examine each hand with five cards of the same suit, we will compute all hands that feature a flush (including straight flushes, royal flushes, and flushes) (with a suit having 13 cards in total). We can say that we understand this by:

C13,5

Remember that there are 4 suites in which this might occur, but we only want 1, so multiply by C4,1. Putting it all together, we obtain:

C4,1×C13,5=4!/(1!)(4−1)!×13!/(5!)(13−5)!=4!13!/3!5!8!

Let's assess this.

4!×13×12×11×10×9^3×8!/3×2×5×4!×8!=13×12×11×3=5148

(Remember that we just calculated all hands, including straight flushes and royal flushes, that have a flush component to them!

The probability of getting a hand with a flush is:

5148/2598960≅.00198

We may exclude straight and royal flush possibilities from the 5148 flush hands by excluding those hands (which are hands with 5 consecutive value cards in the same suit, such as 3, 4, 5, 6, and 7 of hearts). Since there are four suits and 10 potential ways to get a straight (A-5, 2-6, 3-7,..., 10-A), we can subtract 4 from 5148 to get 5108 hands, which gives us the result 5108/2598960=0.00196.

The probability of having a 5-card hand that is a flush or royal flush is 0.00196

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As a result οf answering the given questiοn, we may state that Therefοre, x = 2 is the sοlutiοn tο the equatiοn.

An equatiοn in mathematics is a statement that states the equality οf twο expressiοns. An equatiοn is made up οf twο sides separated by an equals sign (=). Fοr example, the equatiοn "2x + 3 = 9" argues that the expressiοn "2x + 3" is equal tο the value "9". The purpοse οf equatiοn sοlving is tο determine the value οr values οf the variable(s) that make the equatiοn true. Simple οr cοmplex equatiοns, linear οr nοnlinear, and invοlving οne οr mοre variables are all pοssible. Fοr example, the quadratic equatiοn "x² + 2x - 3 = 0" invοlves the variable x raised tο the secοnd pοwer. Equatiοns are utilised in many areas οf mathematics, such as algebra, calculus, and geοmetry.

The answer -

x = 2

√(x+3) - √(x-1)=2

√(x+3) = 2+ √(x-1)

(x+3)=(2+√(x-1))²

(x+3)=4+4√(x-1)+(x-1)

(x+3)-(x-1)=4(x-1)+4

4 = 4√(x-1)

√(x-1)=1

x -1 = 1x = 2

Therefore, x = 2 is the solution to the equation.

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Answer:

Divide a percent by 100 and remove the percent sign to convert from a percent to a decimal. The shortcut way to convert from a percentage to a decimal is by removing the percent sign and moving the decimal point 2 places to the left.

Step-by-step explanation:

5.25% = .0525

Kono Dio Da

Answer:

Divide a percent by 100 and remove the percent sign to convert from a percent to a decimal.

Step-by-step explanation:

Answer:

D. n= 0 or n= 4/5

Step-by-step explanation:

Factor and set each factor equal to zero.

n

=

0

,

4

5

Isolate the variable by dividing each side by factors that don't contain the variable.

Exact Form:

n

=

0

,

4

5

Decimal Form:

n

=

0

,

0.8

Answer:

3.25

Step-by-step explanation:

The loan option with the lowest total value is the one with simple interest, which amounts to $57,247.50. Therefore, the small business owner would be better off choosing the loan with Simple interest, as it results in a lower overall cost compared to the other options.

Part A: To calculate the total value of the loan with simple interest, we use the formula: Total Value = Principal + (Principal * Rate * Time).

Here, the Principal (P) is $50,000, the Rate (R) is 4.35% or 0.0435, and the Time (T) is 3 years and 4 months, which is equivalent to 3.33 years.

Plugging the values into the formula, we have:

Total Value = $50,000 + ($50,000 * 0.0435 * 3.33)

Total Value ≈ $50,000 + $7247.5

Total Value ≈ $57,247.50

Part B: To calculate the total value of the loan with quarterly compounded interest, we use the formula: Total Value = Principal * (1 + (Rate / n))^(n * Time).

Here, n represents the number of compounding periods per year, which is 4 (quarterly compounding).

Plugging the values into the formula, we have:

Total Value = $50,000 * (1 + (0.0435 / 4))^(4 * 3.33)

Total Value ≈ $50,000 * (1.010875)^13.32

Total Value ≈ $50,000 * 1.156977

Total Value ≈ $57,848.85

Part C: To calculate the total value of the loan with continuously compounded interest, we use the formula: Total Value = Principal * e^(Rate * Time).

Here, e represents the mathematical constant approximately equal to 2.71828.

Plugging the values into the formula, we have:

Total Value = $50,000 * e^(0.0435 * 3.33)

Total Value ≈ $50,000 * e^(0.145005)

Total Value ≈ $50,000 * 1.15514

Total Value ≈ $57,757.00

Part D: Comparing the total values of the loans, we find that:

- The total value with simple interest is $57,247.50.

- The total value with quarterly compounded interest is $57,848.85.

- The total value with continuously compounded interest is $57,757.00.

Based on these calculations, the loan option with the lowest total value is the one with simple interest, which amounts to $57,247.50. Therefore, the small business owner would be better off choosing the loan with simple interest, as it results in a lower overall cost compared to the other options.

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Answer:

-Scalene

- Isosceles

-Perpendicular lines

Answer:

mn(5mn² + 9) ;

2mn(1 - 1/2mn²)

Step-by-step explanation:

Given:

5m²n³ +9mn

(8mn - 4m²n³ ÷ 4)​

5m²n³ + 9mn

mn(5mn² + 9)

(8mn - 4m²n³ ÷ 4)​

8mn/ 4 - 4m²n³ / 4

2mn - m²n³

2mn(1 - 1/2mn²)

Answer: x = 3

Step-by-step explanation:

I guess that the equation is:

(45 - 3x)^1/2 = x - 9

so let's solve it for x.

first, we can square both sides:

(45 - 3x) = (x - 9)^2 = x^2 - 18x + 81

now we can write this as a quadratic equation:

x^2 - 18x + 81 - 45 + 3x = 0

x^2 -15x + 36 = 0

now we can use the Bhaskara's equation to find the solutions for that equation:

where for a equation a*x^2 + b*x + c = 0

the solutions are:

\(x = \frac{-b +- \sqrt[2]{b^2 -4ac} }{2a}\)

here a = 1, b = -15 and c = 36

\(x = \frac{15 +- \sqrt[2]{15^2 -4*36} }{2} = \frac{15+- 9}{2}\)

then the solutions are:

x = (15 + 9)/2 = 24/2 = 12

x = (15 - 9)/2 = 6/2 = 3

where 12 is the solution for the positive (45 - 3x)^1/2 and x = 3 is the extraneous solution (because it works for the negative  (45 - 3x)^1/2)

Answer:

3

Step-by-step explanation: