me and my sister went shopping. I spent $120 on 3 pairs of jeans and 6 Blouses. my sister spent $90 on 2 pairs of jeans and 5 Blouses. what was the cost of 1 pair of jeans and the cost of 1 blouse? use different methods to solve.
​

The final polynomial equation after synthetic division is \(x^5-3x^4-81x+243\)

We need to solve;

Put the solution in the appropriate spot on the grid after using synthetic division to divide the following polynomial. Respond with descending powers of x.

The polynomial equation given is;

\(\left(x^4-81\right)\left(x-3\right)\)

By using synthetic division;

⇒ \(x^4x+x^4\left(-3\right)-81x-81\left(-3\right)\)

    \(x^5-3x^4-81x+243\)

→ The required final equation in descending powers of x is \(x^5-3x^4-81x+243\) .

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The blacksmith is rather selfish, while the king's groom shows great concern for others. The blacksmith is responsible and dedicated while the king's groom is confused and unreliable.

Who is known as the blacksmith?

Blacksmiths, also known as smiths, are artisans who create iron things via hot and cold forging on an anvil. Farriers were the term used to describe blacksmiths who specialized in creating horseshoes.

Did Benjamin Franklin lack a nail when he wrote?

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Answer:

If they are not parallel they will cross.

The angle types that are still congruent are the angles that are the same size.

Step-by-step explanation:

Parallel lines never cross but non parallel lines cross.

Answer:

vertical ?

Step-by-step explanation:

sorry if wrong :')

Because b > 1, the correct response in this situation would be: "1.022 is the growth factor for the GDP since 1950, and the GDP increases by a factor of 1.022 every year."

In this instance, we're assuming that we can use the following function to simulate the US GDP, or gross domestic product, in dollars:

\(GDP = 11(1.0220)^{t}\)

We can also see that the exponential model formula given by: governs this formula.

\(GDP = 11(1.0220)^{t\)

Where a denotes the starting sum, b the model's growth/decay rate, and t is the number of years since 1950.

The value of b in this instance is provided by:

b = 1.022

And when we calculated r as the growth rate, we obtained:

1.022 = 1 + r

r = 1.022 - 1

r = 0.022

Because b > 1, the correct response in this situation would be: "1.022 is the growth factor for the GDP since 1950, and the GDP increases by a factor of 1.022 every year."

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Answer:

18p

Step-by-step explanation:

6x3=18

add the p

18p

Answer:

18p

Step-by-step explanation:

you can simply multiply the numbers and add p to the end

The decrease in diameter of the bar due to the applied load is -0.005434905d and the final diameter of the bar is 1.005434905d.

A compressive load of 80,000 lb is applied to a bar with a circular section of 0.75 in diameter and a length of 10 in.

if the modulus of elasticity of the bar material is 10,000 ksi and the Poisson's ratio is 0.3.

We have to determine the decrease in diameter of the bar due to the applied load.

Let d be the initial diameter of the bar and ∆d be the decrease in diameter of the bar due to the applied load, then the final diameter of the bar is d - ∆d.

Length of the bar, L = 10 in

Cross-sectional area of the bar, A = πd²/4 = π(0.75)²/4 = 0.4418 in²

Stress produced by the applied load,σ = P/A

= 80,000/0.4418

= 181163.5 psi

Young's modulus of elasticity, E = 10,000 ksi

Poisson's ratio, ν = 0.3

The longitudinal strain produced in the bar, ɛ = σ/E

= 181163.5/10,000,000

= 0.01811635

The lateral strain produced in the bar, υ = νɛ

= 0.3 × 0.01811635

= 0.005434905'

The decrease in diameter of the bar due to the applied load, ∆d/d = -υ

= -0.005434905∆d

= -0.005434905d

The final diameter of the bar,

d - ∆d = d + 0.005434905d

= 1.005434905d

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To find out how much the Guilderian trader must pay for the same 50 flop barrel of pickles, we need to calculate the cost per gulp and then multiply it by the number of gulps in the barrel.

Given that the Guilderian trader initially exchanged 25 gulps for the 50 flop barrel of pickles, we can determine the cost per gulp by dividing the total cost (50 flops) by the number of gulps (25).  Cost per gulp = 50 flops / 25 gulps = 2 flops/gulp . Since the gulp depreciates to 0.5 flops per gulp, the Guilderian trader must pay 0.5 flops per gulp for the same barrel of pickles.

Therefore, the Guilderian trader must pay 0.5 flops/gulp * 25 gulps = 12.5 flops for the 50 flop barrel of pickles. For the Florish trader, we need to calculate the cost per flop and then multiply it by the number of flops in the crate.

Given that the Florish trader initially exchanged 40 flops for the 20 gulp crate of apples, we can determine the cost per flop by dividing the total cost (40 flops) by the number of flops (20).

Cost per flop = 40 flops / 20 flops

= 2 flops/flop .

Therefore, the Florish trader must pay 2 flops per flop for the same crate of apples.

The Guilderian trader must pay 12.5 flops for the same 50 flop barrel of pickles, and the Florish trader must pay 2 flops for the same 20 gulp crate of apples.

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Answer:

y= 3x + 7                                                                                                            Step-by-step explanation:

y= -1/3x+3 (so, gradient of this line is -1/3).

formula: gradient of line one x gradient of line two= -1 (applies for 2 perpendicular lines only).

So, m1 x -1/3= -1

m1= (\(\frac{-1}{\frac{-1} {3} }\))

m1= 3 (gradient of perp line)

y=mx+c

4= 3 x -1 + c

7=c

therefore, y=3x+7 (eqn of the line perp to y=-1/3x+3)

The natural breaks, quantile, and equal interval classification schemes are methods used to categorize data for the purpose of creating thematic maps. Each scheme has its own approach and considerations: Natural Breaks, Quantile, Equal Interval.

Natural Breaks (Jenks): This classification scheme aims to identify natural groupings or breakpoints in the data. It seeks to minimize the variance within each group while maximizing the variance between groups. Natural breaks are determined by analyzing the distribution of the data and identifying points where significant gaps or changes occur. This method is useful for data that exhibits distinct clusters or patterns.

Quantile (Equal Count): The quantile classification scheme divides the data into equal-sized classes based on the number of data values. It ensures that an equal number of observations fall into each class. This approach is beneficial when the goal is to have an equal representation of data points in each category. Quantiles are useful for data that is evenly distributed and when maintaining an equal sample size in each class is important.

Equal Interval: In the equal interval classification scheme, the range of the data is divided into equal intervals, and data values are assigned to the corresponding interval. This method is straightforward and creates classes of equal width. It is useful when the range of values is important to represent accurately. However, it may not account for data distribution or variations in density.

In summary, the natural breaks scheme focuses on identifying natural groupings, the quantile scheme ensures an equal representation of data in each class, and the equal interval scheme creates classes of equal width based on the range of values. The choice of classification scheme depends on the nature of the data and the desired representation in the thematic map.

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Answer:

12.4

Step-by-step explanation:

Answer: 1. 54, 2. 48

Step-by-step explanation: To find the area of a trapezoid you add the top base and the bottom base then divide them by two, and multiply them by the height.For #1. 8+10/2= 9 then 9x6=54 For #2. 4+12/2=8 then 8 x 6=48.

Answer:

Figure it out using this: Area= 1/2(Base 1 + Base 2) x Height

Bases are the tops and bottoms of the trapezoids

Step-by-step explanation:

Answer:

There are 208 male students in the eight grade.

Step-by-step explanation:

320 students all together - 35% female students= 208 male students

The average speed must you maintain in the remaining distance in order to have an overall average speed of 33.6 mph is 50.39 mph.

We have to find the average speed must you maintain in the remaining distance in order to have an overall average speed of 33.6 mph.

Let the speed be x.

The total average we want = 33.6 mph

The distance from your home to town = 90 miles

Time = Distance/Speed

Time = 90/33.6

At 45 miles (half way), you find you have averaged only 25.2 mph. So

Time first leg = 45/25.2

Time second leg= 45/x

Now the average speed;

45/25.2 + 45/x = 90/33.6

Subtract 45/25.2 on both side, we get

45/x = 90/33.6 - 45/25.2

After solving the ratio, we get

45/x = 0.893

Multiply by x on both side, we get

0.893x = 45

Divide by 0.893 on both side, we get

x = 45/0.893

x = 50.39 mph

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The complete question is:

On a drive from your home to town, you wish to average 33.6 mph. The distance from your home to town is 90 miles. However, at 45 miles (half way), you find you have averaged only 25.2 mph. What average speed must you maintain in the remaining distance in order to have an overall average speed of 33.6 mph?

Answer:

7200 word in 1 hour

Step-by-step explanation:

360/3 to get how many words she can read in a minute which is 120.

Then times it by 60 (60 mins in an hour) to get the total amout of words she reads in an hour. 120 x 60 = 7200 words.

The total number of people with flyers after 3 days of copying and distributing them is 343, which can be calculated using the formula P = 7^n, where P is the total number of people with flyers and n is the number of times the flyers are copied and distributed.

The formula for this problem is P = 7^n where P is the total number of people with flyers and n is the number of times the flyers are copied and distributed.

In this problem, n = 3 as the flyers were distributed on three separate days.

Therefore, P = 7^3 = 343

The calculation can be shown as follows:

1st day: 7 people receive the flyer

2nd day: 7 x 7 = 49 people receive the flyer

3rd day: 49 x 7 = 343 people receive the flyer

Therefore, the total number of people with flyers after 3 days is 343.

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1a)The values of l range from 0 to (n-1), so for n = 3, l can have the values 0, 1, and 2.

b) The values of m can be -2, -1, 0, +1, and +2

c) There are a total of 9 orbitals

The qualities and traits of quantum systems, like the electrons in atoms, are described by a set of numbers known as quantum numbers. They offer knowledge on the system's energy, angular momentum, orientation, and spin, among other characteristics.

Using the formula, number of electrons = \(n^2\)

Number of electrons =\(3^2 = 9\)

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Types of quadrilaterals are parallelograms, rectangles, squares, rhombi, trapezoids, kites, and isosceles trapezoid.

A polygon having four sides and four angles are called a quadrilateral. Quadrilaterals come in a wide variety of forms, each with its own set of qualities and attributes.

Some of the most typical varieties are listed below:

Parallelogram - A quadrilateral has opposing sides that are equally long and parallel.

Rectangle - A parallelogram with all angles at 90 degrees is referred to as a rectangle.

Square - A rectangle with equally long sides.

Rhombus - A parallelogram with equal-length sides is referred to as a rhombus.

Trapezoid - A quadrilateral with just one set of diagonally opposed sides is called a trapezoid.

Kite - A quadrilateral has two sets of adjacent sides that are of equal length or a kite.

Isosceles trapezoid - An isosceles trapezoid is one with equally long non-parallel sides.

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The expected value of the continuous random variable V is 5. The expected value of V is 5, indicating that, on average, we expect the value of V to be around 5.

To calculate the expected value of a continuous random variable V with a given probability density function (PDF), we integrate the product of V and the PDF over its entire range.

The PDF of V is defined as:

f(v) = 6/24 = 0.25 for 3 ≤ v ≤ 7, and 0 otherwise.

The expected value of V, denoted as E(V), can be calculated as:

E(V) = ∫v * f(v) dv

To find the expected value, we integrate v * f(v) over the range where the PDF is non-zero, which is 3 to 7.

E(V) = ∫v * (0.25) dv, with the limits of integration from 3 to 7.

E(V) = (0.25) * ∫v dv, with the limits of integration from 3 to 7.

E(V) = (0.25) * [(v^2) / 2] evaluated from 3 to 7.

E(V) = (0.25) * [(7^2 / 2) - (3^2 / 2)].

E(V) = (0.25) * [(49 / 2) - (9 / 2)].

E(V) = (0.25) * (40 / 2).

E(V) = (0.25) * 20.

E(V) = 5.

Therefore, the expected value of the continuous random variable V is 5.

The expected value represents the average value or mean of the random variable V. It is the weighted average of all possible values of V, with each value weighted by its corresponding probability. In this case, the expected value of V is 5, indicating that, on average, we expect the value of V to be around 5.

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Answer:

Hamish's earning = $20

Harry's earning = $26

Step-by-step explanation:

Given the following :

Let Harry's earning per hour = x

Let Hamish earning per hour = y

Harry earns a dollar more than more than 5/4 the amount hamish earns per hour;

Therefore,

x = 5/4y + 1

x - 5/4y = 1 - - - - (1)

the amount Harry earns per hour is $2 less than 7/5 the amount Hamish earns per hour

x = 7/5y - 2 - - - - (2)

Substituting (2) into (1)

7/5y - 2 - 5/4y = 1

7/5y - 5/4y = 1 + 2

7/5y - 5/4y = 3

Taking the L. C. M

(28y - 25y) / 20 = 3

28y - 25y = 60

3y = 60

y = 20

Substitute y = 20 into (1)

x - 5/4(20) = 1

x - 100/4 = 1

x - 25 = 1

x = 1 + 25

x = 26

y = Hamish's earning = $20

x = Harry's earning = $26

To run this code, you need a C compiler installed on your machine. You can copy the code into a file with a ".c" extension (e.g., "logarithm.c"), compile it, and then execute the compiled program. Make sure to capture a screenshot of both the code and the output screen.

Here's the C programming code to calculate the logarithm base 10 of a decimal number:

```c

#include <stdio.h>

#include <math.h>

int main() {

   double number, result;

       printf("Enter a number: ");

   scanf("%lf", &number);

       result = log10(number);

       printf("Logarithm base 10 of %.3lf: %.4lf\n", number, result);

       return 0;

}

```

To run this code, you need a C compiler installed on your machine. You can copy the code into a file with a ".c" extension (e.g., "logarithm.c"), compile it, and then execute the compiled program. Make sure to capture a screenshot of both the code and the output screen.

Please note that I am unable to directly receive or view any files you upload. If you have any questions or need further assistance while running the code, feel free to ask.

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Answer:

m = \(\frac{1}{8}\)

Step-by-step explanation:

Slope Formula is...

m= rise / run      or    \(\frac{y_2 - y_1}{x_2 - x_1}\)

Two Coordinate Points / Ordered Pair: (16,2) and (32,4)

Your rise is...

4 - 2

Your run is...

32 - 16

Together the fraction reads...

(4 - 2) / (32 - 16)

Then do the subtracting to get....

2 / 16 ( 2 over 16)

Don't forget to simplify...

*2 can go into 2 and 16

Making the equation....

1 / 8 (one over 8)

So your m (slope) is ...  \(\frac{1}{8}\)

(a) The parametric equations that model the path of the rocket are x = 30t and y = 30√3t.

(b) The rectangular equation that models the path of the rocket is t = 6.928 seconds.

(c) 207.84 feet the rocket is in flight, and 359.97 feet the horizontal distance covered.

What is the angle?

An angle is a figure in Euclidean geometry created by two rays, called the sides of the angle, that share a common termination, called the vertex of the angle. Angles created by two rays are also known as plane angles because they lie in the plane in which the rays are located.

Here, we have

Given: A rocket is launched from the ground with a velocity of 60 feet per second at an angle of 60° with respect to the ground.

(a) We have to determine the parametric equations that model the path of the rocket.

Velocity = 60ft/sec

θ = 60°

Distance = speed × time

d = 60t

dₓ is the displacement in x- the direction

dₓ = vcosθ

dₓ = 60tcos60°

dₓ = 60t×1/2

dₓ = 30t

x = 30t

\(d_{y}\) is the displacement in y- the direction

\(d_{y}\)  = vsinθ

\(d_{y}\)  = 60tsin60°

\(d_{y}\)  = 60t×√3/2

\(d_{y}\)  = 30t√3

y = 30√3t

Hence, the parametric equations that model the path of the rocket are x = 30t and y = 30√3t.

(b) We have to determine the rectangular equation that models the path of the rocket.

v = u + at

a = acceleration

v = final velocity

Here,

a = gcos30° but in opposite direction.

So,

a = -gcos30°

a = -10×√3/2

a = -5√3

Now, we put the value of a in v = u + at and we get

v = u + at

0 = 60 -5√3t

t = 6.928seconds

Hence, the rectangular equation that models the path of the rocket is t = 6.928 seconds.

(c) We have to determine how long the rocket is in flight and the horizontal distance covered.

x = 30t = 30(6.928) = 207.84feet

y = 30√3t = 30√3(6.928) = 359.97feet

Hence, 207.84 feet the rocket is in flight, and 359.97 feet the horizontal distance covered.

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The size of a television screen that is 21.6 inches wide and 16.2 inches high is approximately 27 inches (measured diagonally).

What is the Pythagorean theorem?

It's a relation in Euclidean geometry among the three sides of a right triangle. In it, the square of the hypotenuse is equal to the sum of the squares of the other 2 sides.

The size of a television screen can be found by using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, the length of the diagonal of the screen is the hypotenuse, the width is 21.6 inches, and the height is 16.2 inches. We can use the theorem to find the length of the diagonal:

diagonal²= width² + height²

diagonal² = 21.6² + 16.2²

diagonal² = 467.76 + 262.44

diagonal² = 730.2

diagonal = √730.2

diagonal ≈ 27 inches

Hence, the size of a television screen that is 21.6 inches wide and 16.2 inches high is approximately 27 inches (measured diagonally).

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SOLUTION

We want to simplify

This becomes

Hence the answer is 24x, the last option

Answer:

Dispensed

Step-by-step explanation:

Answer:

y= -4x+4

Step-by-step explanation:

y=mx+b

where x=-1, y=8, and m=-4

8=(-4)(-1)+b

8=4+b

4=b

Thus, y= -4x+4

Answer:

0.593,0.55,0.5,0.19

Step-by-step explanation:

The probability that the remaining bill is a $2 bill is approximately 0.2857 or 28.57%.

To solve this problem, we can use conditional probability. Let's denote the events as follows:

A: The wallet initially contains a $2 bill.

B: The wallet initially contains a $20 bill.

C: The bill drawn from the wallet is a $2 bill.

We want to find the probability of Provenience is the horizontal and vertical position of an artifact within the matrix.  A occurring given that event C has occurred, P(A|C).

To begin, let's analyze the given information:

- The wallet either contains a $2 bill or a $20 bill, with equal likelihood. So, P(A) = P(B) = 0.5.

- If the wallet initially contains a $2 bill (event A), the probability of drawing a $2 bill (event C) is 2/3, since there are two $2 bills and one $20 bill in the wallet.

- If the wallet initially contains a $20 bill (event B), the probability of drawing a $2 bill (event C) is 1/2, as there is only one $2 bill left in the wallet.

Now, let's calculate the probability using Bayes' theorem:

P(A|C) = (P(C|A) * P(A)) / P(C)

P(C|A) = 2/3 (probability of drawing a $2 bill given that the wallet initially contains a $2 bill)

P(C) = P(C|A) * P(A) + P(C|B) * P(B) (total probability of drawing a $2 bill)

P(C|B) = 1/2 (probability of drawing a $2 bill given that the wallet initially contains a $20 bill)

P(C) = (2/3 * 0.5) + (1/2 * 0.5) = 1/3 + 1/4 = 7/12

P(A|C) = (2/3 * 0.5) / (7/12)

      = 4/6 / 7/12

      = (4/6) * (12/7)

      = 2/7

Therefore, the chances that the remaining bill in the wallet is a $2 bill, given that a $2 bill was drawn, is 2/7 or approximately 0.2857 (or 28.57%).

So, the probability that the remaining bill is a $2 bill is approximately 0.2857 or 28.57%.

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The polynomial that passes through the points is y = x⁴ + 2x³ + 3x² - x + 1

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

(-3, 58), (-2, 15), (1, 6), (2, 43), (5, 946)

Given that there are 5 points

This means that the degree of the polynomial is 4

And it can be represented as

y = ax⁴ + bx³ + cx² + dx + e

Using the points, we have

a(-3)⁴ + b(-3)³ + c(-3)² + d(-3) + e = 58

a(-2)⁴ + b(-2)³ + c(-2)² + d(-2) + e = 15

a(1)⁴ + b(1)³ + c(1)² + d(1) + e = 6

a(2)⁴ + b(2)³ + c(2)² + d(2) + e = 43

a(5)⁴ + b(5)³ + c(5)² + d(5) + e = 946

So, we have

81a - 27b + 9c - 3d + e = 58

16a - 8b + 4c - 2d + e = 15

a + b + c + d + e = 6

16a + 8b + 4c + 2d + e = 43

625a + 125b + 25c + 5d + e = 946

When evaluated, we have

a = 1 and b = 2 and c = 3 and d = -1 and e = 1

So, we have

y = x⁴ + 2x³ + 3x² - x + 1

Hence, the polynomial is y = x⁴ + 2x³ + 3x² - x + 1

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Answer:

yall smart

Step-by-step explanation: