Justin picked out 300 dollars worth of clothing (regularly priced) at Mary's Department Store. As part of a
promotion, he will flip a fair coin at the cash register. If the coin lands on heads, he will get 40% off of his entire
purchase. If the coin lands on tails, he will have to pay the regular price.

Answer:

the interest earned will be $106.38.

The probability that the third largest observation in the sample is less than 0.7 is  0.2401 =  24.01%.

The sample size n = 5,

Therefore the order statistics will be represented as X₁, X₂, X₃, X₄, and X₅.

Probability that X₃ is less than 0.7:

Since X₃ is the third largest observation =  (X₁ and X₂) < 0.7.

The probability that X₃ is less than 0.7 is (0.7)² = 0.49.

.

The probability that both X₁ and X₂ are less than or equal to 0.7 is (0.7)² = 0.49 because in a continuous uniform distribution, the probability of any single observation being less than 0.7 is 0.7 - 0 = 0.7.

We then get the product of both cases:

Probability = 0.49 * 0.49 = 0.2401

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Answer:

From the given options, option D is the only choice that contains (w-5).

Step-by-step explanation:

Given the expression

\(w^2-w-20\)

Breaking the expression into groups

\(=\left(w^2+4w\right)+\left(-5w-20\right)\)

Factor out 'w' form w²+4w = w(w+4)

Factor out 'w' from -5w-20= -5(w+4)

so

\(=w\left(w+4\right)-5\left(w+4\right)\)

Factor out common term: w+4

\(=\left(w+4\right)\left(w-5\right)\)

Thus, the factors are: (w+4) and (w-5)

Therefore, from the given options, option D is the only choice that contains (w-5).

Answer:

Quantitative data

Step-by-step explanation:

When we measure something, then we can quantify them. By also making a count, we are trying to quantify a particular entity.

Now in this case, we know that age is something we can quantify or measure. By nothing the difference between the year of birth and the present year, we can simply give the number of years or simply how

old a person is.

This clearly show that we have measured the count of that entity. This makes age an example of quantitative data

categorical data Step-by-step explanation:

Answer:

87/103

Step-by-step explanation:

6(2/9)

4(2/3)

18/54

8/12

=18/54

=8/12

u divided all

Let the number should be duvided be X

Given number = 6 2/9

⇛ (6×9+2)/9

⇛ (54+2)/9

⇛ 56/9

On dividing 56/9 by X then the result

= (56/9)/X

= 56/9X

According to the given problem

The result = 4 2/3 = 14/3

⇛ 56/9X = 14/3

⇛ 9X×14 = 56×3

⇛ 9X = 56×3/14

⇛ 9X = 4×3

⇛9X = 12

⇛X = 12/9

=⇛X = 4/3 or 1 1/3

Answer↓

The required number is 4/3 or 1 1/3

Check↓

On dividing 6 2/9 by 1 1/3

⇛ 6 2/9 ÷ 1 1/3

⇛ (56/9)÷(4/3)

⇛ (56/9)×(3/4)

⇛ (56×3)/(9×4)

⇛ 14/3

⇛4 2/3

Verified.

Answer:

9a-2=7

Step-by-step explanation:

4a+ 5a-2=5+3-1

To simplify each side, combine like terms.

4a+5a = 9a

5+3-1 = 7

The equation becomes:

9a-2=7

Answer:

9.3275

Step-by-step explanation:

Answer:

The percent  decrease is 12.20%

Step-by-step explanation:

$10.25 - $9 / $10.25 * 100% = 12.19512195121951 = 12.20%

Answer:yes

The value of x is (-∞, -5) ∪ (1, ∞).

Given is a polynomial, \(x^4+2x^3-12x^2+14x-5 > 0\),

Solving for x,

Factors =

\(x^4+2x^3-12x^2+14x-5\\ \\= \quad \left(x-1\right)^3\left(x+5\right)\)

Therefore,

\(\left(x-1\right)^3\left(x+5\right) > 0\)

\(x < -5\quad \mathrm{or}\quad \:x > 1\)

Hence the value of x is (-∞, -5) ∪ (1, ∞).

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Answer:

We can start by using the second equation to eliminate x:

2x + 5y - 2z = 3

2x = -5y + 2z + 3

x = (-5/2)y + z + 3/2

Now we can substitute this expression for x into the first and third equations:

x + y + z = 4

(-5/2)y + z + 3/2 + y + z = 4

(-5/2)y + 2z = 5/2

x + 7y - 7z = 5

(-5/2)y + z + 3/2 + 7y - 7z = 5

(9/2)y - 6z = 7/2

Now we have a system of two equations with two variables, (-5/2)y + 2z = 5/2 and (9/2)y - 6z = 7/2. We can use any method to solve for y and z, such as substitution or elimination. However, we will find that the system is inconsistent, meaning there is no solution that satisfies both equations.

Multiplying the first equation by 9 and the second equation by 5 and adding them, we get:

(-45/2)y + 18z = 45/2

(45/2)y - 30z = 35/2

Adding these two equations, we get:

-12z = 40/2

-12z = 20

z = -5/3

Substituting z = -5/3 into (-5/2)y + 2z = 5/2, we get:

(-5/2)y + 2(-5/3) = 5/2

(-5/2)y - 10/3 = 5/2

(-5/2)y = 25/6

y = -5/12

Substituting y = -5/12 and z = -5/3 into any of the original equations, we get:

x + y + z = 4

x - 5/12 - 5/3 = 4

x = 29/12

Therefore, the solution is (x, y, z) = (29/12, -5/12, -5/3). However, if we substitute these values into any of the original equations, we will find that it does not satisfy the equation. For example:

2x + 5y - 2z = 3

2(29/12) + 5(-5/12) - 2(-5/3) = 3

29/6 - 5/2 + 5/3 ≠ 3

Since there is no solution that satisfies all three equations, the system is inconsistent.

Step-by-step explanation:

Answer:

See below for proof.

Step-by-step explanation:

A system of equations is not consistent when there is no solution or no set of values that satisfies all the equations simultaneously. In other words, the equations are contradictory or incompatible with each other.

Given system of equations:

\(\begin{cases}x+y+z = 4\\2x+5y-2z =3\\x+7y-7z =5\end{cases}\)

Rearrange the first equation to isolate x:

\(x=4-y-z\)

Substitute this into the second equation to eliminate the term in x:

\(\begin{aligned}2x+5y-2z&=3\\2(4-y-z)+5y-2z&=3\\8-2y-2z+5y-2z&=3\\-2y-2z+5y-2z&=-5\\5y-2y-2z-2z&=-5\\3y-4z&=-5\end{aligned}\)

Subtract the first equation from the third equation to eliminate x:

\(\begin{array}{cccrcrcl}&x&+&7y&-&7z&=&5\\\vphantom{\dfrac12}-&(x&+&y&+&z&=&4)\\\cline{2-8}\vphantom{\dfrac12}&&&6y&-&8z&=&1\end{aligned}\)

Now we have two equations in terms of the variables y and z:

\(\begin{cases}3y-4z=-5\\6y-8z=1\end{cases}\)

Multiply the first equation by 2 so that the coefficients of the variables of both equations are the same:

\(\begin{cases}6y-8z=-10\\6y-8z=1\end{cases}\)

Comparing the two equations, we can see that the coefficients of the y and z variables are the same, but the numbers they equate to is different. This means that there is no way to add or subtract the equations to eliminate one of the variables.

For example, if we subtract the second equation from the first equation we get:

\(\begin{array}{crcrcl}&6y&-&8z&=&-10\\\vphantom{\dfrac12}-&(6y&-&8z&=&\:\:\;\;\:1)\\\cline{2-6}\vphantom{\dfrac12}&&&0&=&-11\end{aligned}\)

Zero does not equal negative 11.

Since we cannot eliminate the variable y or z, we cannot find a unique solution that satisfies all three equations simultaneously. Therefore, the system of equations is inconsistent.

The equation of the exponential regression is y = 17100\(e^{-0.194x}\) and the value of a car after 12 years is $1667

It is a model that explains processes that experiences growth at a double rate. It is used for situations where the growth begins slowly but rapidly speeds up without bounds or where the decay starts rapidly but slows down to get to zero.

Given that, the given table shows the value of a car over time that was purchased for 14100 dollars, where x is years and y is the value of the car in dollars.

We need to find the exponential regression equation for this set of data,

We know that,

The exponential regression equation is : y = A₀eᵃˣ

Where A₀ is the coefficient of exponential regression and a is the constant.

For x = 0, the value of y will be $17100.

Therefore,

17100 = A₀e⁰

A₀ = 17100

Therefore, the equation will be =

y = 17100eᵃˣ

Find for a,

For x = 1, the value of y will be $14090.

14090 = 17100eᵃ

eᵃ = 14090/17100

Taking ln both sides, then we have,

a lne = -0.194

a = -0.194

Therefore, the exponential regression equation for this set of data is :

y = 17100\(e^{-0.194x}\)

Finding the value of the car, after 12 years =

y = 17100\(e^{-0.194(12)\)

y = 1667

Hence, the equation of the exponential regression is y = 17100\(e^{-0.194x}\) and the value of a car after 12 years is $1667

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Step-by-step explanation:

distance = 90 km

time = 3 hours 15 min

= 3+ 15/60 hours

= 3+ 1/4 hours

= 13/4 hours

speed = distance/ time

= 90/ (13/4)

= 90 * 4 /13

= 27.69 km/ hr

Answer:

\(\Huge \boxed{\boxed{ x = 1}}\)

Step-by-step explanation:

Isolate the variable on one side of the equation before trying to solve it. It means that you should only have constants (numbers) on the other side of the equal sign and the variable alone on the one side.

To do this, you can add, subtract, multiply, divide, or use any other operation to both sides of the equation as long as you do the same thing on both sides.

Your final step depends on the equation and how you've simplified it. In general, you want to figure out how you arrived at the final equation by working backwards from it. You'll isolate the variable in the last action you took.

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

Step1: Subtract \(\bold{2x}\) from both sides

Step 2: Subtract 3 from both sides

Step 3: Divide both sides of the equation by 6

So the solution to the equation \(\bold{8x + 3 = 2x + 9}\) is \(\bold{x = 1}\).

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

the height of a binary tree is the number of edges in the longest path from the root to a leaf.The best-case height of a binary tree with seven nodes is 3.

A binary tree is a type of tree structure consisting of nodes that are connected by edges. The number of edges in the longest path from a binary tree's root to a leaf determines the tree's height.In the best-case scenario, the binary tree is perfectly balanced and each node has exactly two children. With seven nodes, the best-case height is three because each node has two children and three edges connect the root node to the leaves. This means that the longest path from the root to a leaf is three edges, resulting in a height of three.

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1a. The percentage total return is -19.56%

1b. The dividend yield is 2.42%.

1c. The capital gains yield is -21.98%.

2a. The arithmetic average annual return on large-company stocks in nominal terms is 14.5%.

2b. The arithmetic average annual return on large-company stocks in real terms is 9.67%.

3a. The real return on long-term government bonds is 3.195%

3b. The real return on long-term corporate bonds is 3.291%

In Financial accounting, the percentage total return (P) can be calculated by using this formula;

P = [(Ending price - Initial price) + Dividend] ÷ Initial price

P = [(71 - 91) + 2.20] ÷ 91

P = -0.1956 or -19.56%

1b. For the dividend yield, we have:

Dividend yield = Dividend ÷ Initial price

Dividend yield = 2.20 ÷ 91

Dividend yield = 0.0242 or 2.42%

1c. For capital gains yield, we have:

Capital gains yield = (Ending price - Initial price) ÷ Initial price

Capital gains yield = (71 - 91) ÷ 91

Capital gains yield = -0.2198 or -21.98%.

Part 2.

a. The arithmetic average of annual return on large-company stocks in nominal terms is equal to 14.5%.

b. For arithmetic average annual return in real terms, we have:

(1 + 0.145) = (1 + r)(1 + 0.044)

r = (1.145/1.044) - 1

r = 9.67%

Part 3.

a. For real return on the long-term government bonds, we would apply Fisher equation:

(1 + i) = (1 + r)(1 + h)

Where:

(1 + 0.066) = (1 + r)(1 + 0.033)

1 + r = 1.066/1.033

r = 3.195%

b. For real return on long-term corporate bonds:

(1 + 0.067) = (1 + r)(1 + 0.033)

1 + r = 1.067/1.033

r = 3.291%

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Answer:

C

The lines will intersect once because this systems has one solution

Step-by-step explanation:

Start by putting everything into slope intercept form (AKA y=mx+b

2x-4y=3

2x-3=4y

y= .5x-.75

And the other one

7y-5x=8

-5x-8= -7y

y=(5x+8)/7

Because their slopes are different there's an intersection

Because their y intercepts are different there's only 1 solution

So, the given triangle is a scalene right triangle.

what is triangle ?

With three consecutive sides and three angles, a triangle is an enclosed plane shape. It is one of the fundamental geometric shapes and is frequently used in physics, maths, and engineering. A triangle's total angles are always 180 degrees. Triangles come in a variety of shapes, such as equilateral triangles, which have three equal sides and angles, isosceles triangles, which have two equal sides and angles, and scalene isosceles (all sides and angles are different).

To determine the type of triangle based on the given side lengths, we can use the following rules:

If all three sides are equal, it's an equilateral triangle.

If two sides are equal, it's an isosceles triangle.

If all three sides are different, it's a scalene triangle.

We can also use the Pythagorean theorem to determine if the triangle is a right triangle. According to this theorem, in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side.

Let's check the sides of the given triangle using these rules:

The three sides are different, so it's a scalene triangle.

To check if it's a right triangle, we can find the longest side (53) and see if it satisfies the Pythagorean theorem with the other two sides. Using a calculator, we find that \(28^2 + 45^2 = 784 + 2025 = 2809\), and \(53^2 = 2809.\)Therefore, the triangle is a right triangle.

So, the given triangle is a scalene right triangle.

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Answer:

96 and 270

Step-by-step explanation:

12×8=96

90

×13

180

+90

270

4 yr. = 12 ft

=> 4.4 yr. = 48 ft

48 - 12 = 36 ft

Answer: 36

Answer:

B 4.05^3

Step-by-step explanation:

Just mulityply

The odds against Jenny winning a headset are 88.89% or 8 out of 9, and the odds in favor of Jenny winning a headset are 11.11% or 1 out of 9.

Since Jenny won a charity raffle, and her prize will be randomly selected from the 9 prizes shown below, and the prizes include 7 rings, 1 camera, and 1 headset, to find the odds against Jenny winning a headset, and find the odds in favor of Jenny winning a headset, the following calculations must be performed:

· 1 headset out of 9 total prizes

· 1/9 = headset

· 1/9 x 100 = 11.11%

· 100 - 11.11 = 88.89%

Therefore, the odds against Jenny winning a headset are 88.89% or 8 out of 9, and the odds in favor of Jenny winning a headset are 11.11% or 1 out of 9.

Rounded to the nearest hundredth, the value of y at \(x = 7\) is approximately \(12.78\), according to the concept of linear regression line.

To find the linear regression line for the given data, we can use statistical software or a calculator. The equation of the linear regression line is of the form \(y = mx + b\), where m represents the slope and b represents the y-intercept.

Using the provided data, the linear regression line equation is:

\(\[ y = 1.3642x + 3.2324 \]\)

To find the value of \(y\) at \(x = 7\), we substitute \(x = 7\) into the equation:

\(\[ y = 1.3642(7) + 3.2324 \]\)

Simplifying the equation, we get:

\(\[ y = 9.5494 + 3.2324 \]\[ y = 12.7818 \]\)

In conclusion, the linear regression analysis allows us to determine the relationship between the variables x and y in the given data set. By finding the equation of the linear regression line, we can estimate the value of y for any given x. In this case, the linear regression line equation is \(y = 1.3642x + 3.2324\). By substituting \(x = 7\) into the equation, we find that the estimated value of y is approximately \(12.78\). This analysis provides a useful tool for predicting and understanding the relationship between variables, allowing us to make informed decisions and interpretations based on the data.

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The transformation is a translation (x + 7, y + 4) plus a dilation of scale factor 2.

We know that Circle 1 is centered at (-3,-2) and has a radius of 2 centimeters, and Circle 2 is centered at (4,2) and has a radius of 4 centimeters.

The radius of circle 2 is twice the radius of circle 1, then we need to have a dilation of scale factor 2.

Now let's apply a translation of (a, b) units such that:

(-3 + a, -2 + b) = (4, 2)

(a, b) = (4 + 3, 2 + 2)

(a, b) = (7, 4)

Then we have the translation (x + 7, y + 4) plus a dilation of scale factor 2.

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In the given graph, it is visible that Sia is swinging from a chandelier. The horizontal distance between Sia and the wall, in meters, is modeled by D(t) where t is the time in seconds. The function is graphed below, along with one segment highlighted.

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Answer:

A bat

Step-by-step explanation:

Answer:

The bat flies faster by 7 feet

Step-by-step explanation:

first, you need to find some common ground. 84 and 4 can both be divided by two 84/2=42 so now we know that:

-The bat flies 42 feet in two seconds

-The dove flies 35 feet in two seconds

So we know that the bad flies faster because the number is greater, but by how much?

To find this just subtract 35 from 42 to get 7.

So to summarize

The bat flies faster by 7 feet

Answer:

x = 6

Step-by-step explanation:

From the diagram AB = BC

4x-9 = 15

Add to both sides

4x-9+9 = 15 + 9

4x = 24

Divide both sides by 4

4x/4 = 24/4

x = 6

Hence the value of x is 6

Answer:

32.6°F.

Step-by-step explanation:

The initial temperature of the water was 33.2°F. After several minutes, the temperature of the water changed by -0.6°F. So, the new temperature of the water is

33.2 + (-0.6)  

=  

(30 + 3) + [0.2 + (-0.6)]

=  

33 + (-0.4)

=  

33 – 0.4

=  

32.6°F.

copied the answer from Edmentum