TV Value
You have just bought a new Sony 55" 3D television set for $1,900. The value of the television set decreases by $225 per year. How long before the television set is worth half of its original value?
Round your answer to the nearest tenth as needed.

It will take
years for the television set to be worth half of its original value.

x - intercept of line A = (1 , 0)

x - intercept of line B = (-4, 0)

A line is a one-dimensional figure, which has length but no width. A line is made of a set of points which is extended in opposite directions infinitely.

A line with no curve is called straight line.

Given,

Equation of line A

y = 6x - 6

for x - intercept y = 0

0 = 6x - 6

6x = 6

x = 6/6

x = 1

x - intercept = (1 , 0)

Given table of values on line B

x   y

-4  0

-2  -1

0   -2

By the table, when y = 0, x = -4

x- intercept of line B = (-4 , 0)

Hence, (1, 0) is x - intercept of line A.

(-4 , 0) is x - intercept of line B.

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The sample space lists all possible outcomes of rolling a number cube twice, where W represents a roll with a value of 6 or higher, and L represents a roll with a value of 5 or lower.

What is probability ?

Probability can be defined as ratio of number of favourable outcomes and total number of outcomes.

The answer to Question 3 is List 2, which gives the sample space for pulling 2 marbles from the bag with replacement.

The answer to Question 4 is two ninths. Since there are three cards with one D each, the probability of selecting a D on the first draw is 1/3. Since the cards are replaced, the probability of selecting a D on the second draw is also 1/3. Therefore, the probability of selecting D and D in that order is (1/3) * (1/3) = 1/9. However, since the order of selection does not matter, we must also consider the probability of selecting D and D in the reverse order, which is also 1/9. Therefore, the total probability is 1/9 + 1/9 = 2/9.

The answer to Question 5 is four thirty sixths or one ninth. The only ways to get a sum of 5 are by rolling a 1 and a 4, a 2 and a 3, or a 3 and a 2. Each of these outcomes has a probability of 1/6 * 1/6 = 1/36, so the total probability is 3 * 1/36 = 1/12 = 4/36.

The answer to Question 6 is Rolling a number cube twice.  For example, WW represents rolling a 6 or higher on both rolls, and LL represents rolling a 5 or lower on both rolls.

Therefore, The sample space lists all possible outcomes of rolling a number cube twice, where W represents a roll with a value of 6 or higher, and L represents a roll with a value of 5 or lower.

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Answer:

Step-by-step explanation:

list 4

Answer:

19

Step-by-step explanation:

111111111

+

1111111111

count how many 1ns are there.

ans is 19

Answer:

See Screenshot

Step-by-step explanation:

Answer: X would equal 134

Step-by-step explanation: You add 25 and 21 together and then subtract that from 180 then that number would be your answer.

Answer:2.2%

Step-by-step explanation: I took the test

Based on the definition of a right angle, the value of x is: B. 40.

A right angle is an angle that measures exactly 90 degrees, or one quarter of a full circle. The symbol used to represent a right angle is a small square placed in the corner where the two lines or rays meet

Therefore, if two parts of a right angle measures 10 degrees and 2x respectively, we would have:

2x + 10 = 90

Subtract 10 from both sides:

2x = 90 - 10

2x = 80

2x/2 = 80/2

x = 40

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Answer: The correct answer is 4988.

Step-by-step explanation: 4007+981 = 4988 Add the one to the eight then add the 8 to the tens place and add the 9 to the hundreds place.

THIS IS THE CORRECT ANSWER.

The event with the highest probability is "reaching into a bag full of 50 strawberry chews and 10 cherry chews without looking and pulling out a strawberry chew", with a probability of 5/6 or approximately 0.83. Option D

To determine which event is most likely to occur, we need to compare the probabilities of each event happening.

Rolling a multiple of 4 on an eight-sided die:

There are 8 possible outcomes when rolling an eight-sided die, and 2 of them are multiples of 4 (4 and 8). So, the probability of rolling a multiple of 4 is 2/8, or 1/4.

Spinning a spinner and landing on pink:

There are 4 possible outcomes when spinning the spinner, and only one of them is pink. So, the probability of landing on pink is 1/4.

Winning a raffle that sold a total of 100 tickets, if you buy 53 tickets:

The total number of possible outcomes is the total number of tickets sold, which is 100. The number of favorable outcomes is the number of tickets the person bought, which is 53. So, the probability of winning the raffle is 53/100.

Reaching into a bag full of 50 strawberry chews and 10 cherry chews without looking and pulling out a strawberry chew:

The total number of possible outcomes is the total number of candies in the bag, which is 50 + 10 = 60.

The number of favorable outcomes is the number of strawberry chews in the bag, which is 50. So, the probability of pulling out a strawberry chew is 50/60, which simplifies to 5/6.

Comparing the probabilities, we can see that the event with the highest probability is "reaching into a bag full of 50 strawberry chews and 10 cherry chews without looking and pulling out a strawberry chew", with a probability of 5/6 or approximately 0.83. Therefore, this event is the most likely to occur.

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Answer:

First choice

Step-by-step explanation:

Answer:

Th answer is the FIRST CHOICE(A).

Have a GOOD DAY!

Answer:

New value =

56 - Percentage decrease =

56 - (14% × 56) =

56 - 14% × 56 =

(1 - 14%) × 56 =

(100% - 14%) × 56 =

86% × 56 =

86 ÷ 100 × 56 =

86 × 56 ÷ 100 =

4,816 ÷ 100 =

48.16

56 decreased by 14% = 48.16

Absolute change (actual difference):

48.16 - 56 = - 7.84

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Answer:

r≈0.56m

Step-by-step explanation:

C=2πr

r=C

2π=3.5

2·π≈0.55704m

To find the scale factor of the dilation, we can compare the corresponding dimensions of the original and the enlarged card.

The original card has a length of 3 1/2 inches and is being enlarged to a length of 5 1/4 inches. So the scale factor for the length is:

5 1/4 inches / 3 1/2 inches = 3/2

Similarly, the original card has a width of 2 inches and is being enlarged to a width of 3 inches. So the scale factor for the width is:

3 inches / 2 inches = 3/2

Therefore, the scale factor of the dilation is 3/2 or 1.5.

The derivative of composite functions are listed below:

Case A

Subcase i: y' = 4 · (x³ + 8 · x² - x + 3) · (3 · x² + 16 · x - 1)

Subcase ii: y' = (2 · x - 7)² · [(2 · x + 4) · (2 · x - 7) + 6 · (x² + 4 · x - 2)]

Case B

Subcase i: y' = 5 · (2 · x - 1 / x²) · [(2 · x - 1 / x²) + 2 · x · (2 - 2 / x³)]

Subcase ii: y' = [- (x² + 3 · x - 1) - (2 - x) · (2 · x + 3)] / (x² + 3 · x - 1)²

Chain rule is powerful resource to find the derivative of a composite function, that is, a function of the form:

f ° u (x) = f[u(x)]

And chain rule is now defined:

df[u(x)] / dx = (df / du) · (du / dx)

There are three cases requiring chain rule, now we proceed to determine the derivative for each expression:

Case A

Subcase i

y = (x³ + 8 · x² - x + 3)⁴

y' = 4 · (x³ + 8 · x² - x + 3) · (3 · x² + 16 · x - 1)

Subcase ii

y = (x² + 4 · x - 2) · (2 · x - 7)³

y' = (2 · x + 4) · (2 · x - 7)³ + 6 · (x² + 4 · x - 2) · (2 · x - 7)²

y' = (2 · x - 7)² · [(2 · x + 4) · (2 · x - 7) + 6 · (x² + 4 · x - 2)]

Case B

Subcase i

y = 5 · x · (2 · x - 1 / x²)²

y' = 5 · [(2 · x - 1 / x²)² + 2 · x · (2 · x - 1 / x²) · (2 - 2 / x³)]

y' = 5 · (2 · x - 1 / x²) · [(2 · x - 1 / x²) + 2 · x · (2 - 2 / x³)]

Subcase ii

y = (2 - x) / (x² + 3 · x - 1)

y' = [- (x² + 3 · x - 1) - (2 - x) · (2 · x + 3)] / (x² + 3 · x - 1)²

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The probability that a random sample of 150 bowlers will have an average score greater than 165 is 0

Probability is a branch of mathematics that deals with the study of random events or outcomes. It is used to measure the likelihood or chance of an event occurring, ranging from impossible (0 probability) to certain (1 probability).

The basic concept of probability involves determining the ratio of the number of favorable outcomes to the total number of possible outcomes. This ratio is expressed as a fraction, decimal, or percentage.

For example, if you toss a fair coin, there are two possible outcomes: heads or tails. The probability of getting heads is 1/2 or 0.5 or 50%, and the probability of getting tails is also 1/2 or 0.5 or 50%.

To give the probability that a random sample of 150 bowlers will have an average score greater than 165

P( [tex]\bar X[/tex]> 165) = P(z > (165 - 157)/(12/√(150)))

= P(z > 8.16)

= 0 [since from z table]

= 0

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no

it doesn't start at (0,0)

Answer:

Step-by-step explanation:

The equation of a line in slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept. The slope of a line is a measure of how steep the line is, and it is defined as the change in y divided by the change in x between any two points on the line. In other words, if we choose two points (x1, y1) and (x2, y2) on the line, then the slope of the line is:

m = (y2 - y1) / (x2 - x1)

The y-intercept of a line is the point where the line crosses the y-axis. In other words, it is the value of y when x = 0. To find the y-intercept of a line given in slope-intercept form, we simply look at the constant term (the term with no x) in the equation.

In the given equation, y = -6x - 7, we can see that the coefficient of x is -6, which means that the slope of the line is -6. This tells us that as we move along the line from left to right, the y-value will decrease by 6 units for every 1 unit that the x-value increases. In other words, the line is sloping downwards from left to right.

To find the y-intercept of the line, we look at the constant term, which is -7. This tells us that when x = 0, y is equal to -7. So the y-intercept is the point (0, -7), which means that the line crosses the y-axis at the point (0, -7).

To summarize, the slope of the line y = -6x - 7 is -6, which means that the line is sloping downwards from left to right. The y-intercept of the line is (0, -7), which means that the line crosses the y-axis at the point (0, -7).

Answer:

B. 5

Step-by-step explanation:

The expression "4 to the power of 5" can be written as 4^5. Here, 4 is the base, and 5 is the exponent. So the exponent in the expression 4 to the power of 5 is option B, 5.

The volume of the sand pit is V = 694.6 feet²

The volume of the rectangle is given by the product of the length of the rectangle and the width of the rectangle and the height of the rectangle

Volume of Rectangle = Length x Width x Height

Volume of Rectangle = Area of Rectangle x Height

Given data ,

Let the volume of the rectangle be represented as V

Now , the length of the sand pit = 30.2 feet

The width of the sand pit = 9.2 feet

The depth of the sand pit = 30 inches = 2.5 feet

Now , the volume of the rectangular pit = L x W x H

On simplifying the equation , we get

The volume of the rectangular pit V = 30.2 x 9.2 x 2.5

The volume of the rectangular pit V = 694.6 feet²

Hence , the volume of the rectangular sand pit is 694.6 feet²

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The Average rate of change is defined as

r{average} = Δy/Δx = (y₂ - y₁/x₂ - x₁).

The rate at which one quantity changes per unit change with the other quantity is called unit rate.

Given is the average rate of change.

Average rate of change is defined as the change in the value of a quantity over the interval change in the other quantity.

Mathematically -

r{average} = Δy/Δx = (y₂ - y₁/x₂ - x₁)

Therefore, the Average rate of change is defined as

r{average} = Δy/Δx = (y₂ - y₁/x₂ - x₁).

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Answer:

what basic business principle does the author of your reading material state that automakers igno red in recent years leading to the need for an industry bailout

Therefore , the solution of the given problem of ordered pair comes out to be system of equations is the ordered pair (-4, 1).

Two independent variables that are grouped in a fashion that suggests a particular order are known as "ordered pairs." The 1 and 2 parts each indicate one of an order pair's y-coordinates. The ordered pair is shown in close parenthesis in the example that follows.

Here,

We can solve this system of equations by substitution or elimination.

Here's how to do it using the substitution method:

From the first equation, we know that y = x + 5. We can substitute this expression for y in the second equation to get:

$x - 5y = -9

$x - 5(x + 5) = -9

$x - 5x - 25 = -9

Simplifying the equation, we get:

$-4x = 16$

$x = -4$

Now that we know the value of x, we can substitute it back into the first equation to find y:

y = x + 5 = -4 + 5 = 1$

Therefore, the solution to the system of equations is the ordered pair (-4, 1).

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The statement 3/4> 13/16 is false and the statement 6/7> 5/8is true.

Least Common Multiple is the meaning of the acronym LCM. The smallest number that both numbers can divide by is known as the least common multiple (LCM) of two numbers. It can also be computed for two or more different numbers. There are numerous ways to calculate the LCM of a given collection of numbers. Using the prime factorization of each number and then calculating the product of the highest powers of the common prime factors yields the LCM of two integers in a short amount of time.

The first statement is:

3/4 > 13/16

Take the LCM:

12/16 > 13> 16

Comparing the numerator we see that, 12 > 13 is false. Hence, the statement is false.

The second statement is:

6/7 > 5/8

Take the LCM:

48/56 > 35/56

Comparing the numerator we see that, 48 > 35 is True.

Hence, the statement is True.

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The solution is,

y = 2(x+1)^2+6

The vertex (−1,6)

Equation of axis of symmetry is x = -1

minimum at (-1,6)

y = -(x-1)^2/2 -4

The vertex (1,-4)

Equation of axis of symmetry is x = 1

maximum at (1,-4)

A graph can be defined as a pictorial representation or a diagram that represents data or values.

here, we have,

y = 2(x+1)^2+6

The vertex (−1,6)

Equation of axis of symmetry is x = -1

minimum at (-1,6)

y = -(x-1)^2/2 -4

The vertex (1,-4)

Equation of axis of symmetry is x = 1

maximum at (1,-4)

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Answer:

14

Step-by-step explanation:

To find the value of (f-g)(2), we first need to compute the function (f-g), which is defined as the difference between f(x) and g(x), and then evaluate it at x=2.

So, (f-g)(x) = f(x) - g(x)

Substituting the given functions, we get:

(f-g)(x) = (3x^2 + 1) - (1-x)

(f-g)(x) = 3x^2 + x

Now, to find (f-g)(2), we substitute x=2 into the expression we just obtained:

(f-g)(2) = 3(2)^2 + 2

(f-g)(2) = 3(4) + 2

(f-g)(2) = 12 + 2

(f-g)(2) = 14

Therefore, the value of (f-g)(2) is [14.]

It cost to build a fence around a square field which is 240 feet on each side $2040.

What is a square?

A square is a regular quadrilateral in Euclidean geometry, which means that it has four equal sides and four equal angles. It can also be explained as a rectangle with two adjacent sides that are of equal length.

Given that fencing is sold in 8-foot sections at $15 per section and the fence posts cost $4 each.

The length of each side is 240 feet.

The perimeter of the square field is 4×240 = 960 feet.

The number of sections that need to fence the field is 960/8 = 120.

The number of posts that need to fence the field is 120.

The cost of 120 Fencing sections is 120×$15 = $1800.

The cost of 120 posts is 120 × 4 = $240.

The total cost of the  fence around a square field  is  $1800 + $240 = $2040

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The cumulative frequency graph indicates that the percentage of the vehicles that go over the 30 mph speed limit is about 62.6% which more than the allowable 20%, therefore, a speed camera will have to be installed.

The cumulative frequency is the sum of the frequency up to an interval. The cumulative frequency indicates the total number of observations located above or below a value.

The cumulative frequency graph indicates the value of the sum of the number of vehicles travelling at a particular speed, therefore;

The cumulative frequency of cars traveling at 20 mph = 13

Cumulative frequency of cars traveling at 10 mph = 8

The cumulative frequency if the cars travelling at 30 mph = 50

Cumulative frequency of the cars travelling at 40 mph = 59

The cumulative frequency of the cars traveling at 50 mph = 60

Number of cars that go over the 30 mph speed limit = 59 + 60 = 119

Percentage of the cars that go over the 30 mph is therefore;

The percentage of cars that go over the 30 mph speed limit is 62.6% which is more than the 20%, therefore;

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Answer: one

Step-by-step explanation:

Using Pythagoras' Theorem, we found the length of Road C and the respective time taken to travel along each road.

What is meant by Pythagoras' theorem?

The Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse. In essence, Pythagoras' theorem is used to determine a triangle's angle and length of an unknown side. This theorem allows us to obtain the hypotenuse, perpendicular, and base formulas.

The given figure is a right triangle.

The length of road A = 16.01 km

The length of road B = 10 km

a) The length of road C can be found using Pythagoras' theorem.

From figure,

A² = B² + C²

16.01 ² = 10² + C²

C² = 156.32

C = 12.5 km

b) Speed of bike = 19.5 km/h

   Length of road C = 12.5 km

Time = Length/speed = 12.5/19.5 = 0.64 hours

 Length of road B =10 km

Time = Length/speed = 10/19.5 = 0.51 hours

c) Length of road A = 16.01

Time taken = Length/speed = 16.01/19.5 = 0.82 hours.

Therefore using Pythagoras' Theorem, we found the length of Road C and the respective time taken to travel along each road.

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The term B. One Optimal Solution best describes the system of inequalities 2x + y < 15, 3x + y < 12, f(x, y) = 2x + 2y.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given, Two inequalities 2x + y < 15 and 3x + y < 12.

has one optimal solution as if we subtract these two inequalities, 'y' will get canceled and we can have the value of 'x' from that we can determine 'y' also.

Q. Which term best describes the solution of the situation represented by the system of inequalities? 2x + y < 15, 3x + y < 12, f(x,y) = 2x+2y

A. alternate optimal solutions

B. One Optimal Solution

C. Unbounded

D. Infeasible

True, false, true, true, false and true are the answers of statements a to f respectively.

A matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns.

(a) A linear transformation [tex]T:R^n\rightarrow R^m[/tex] is completely determined by the effect on the columns of the n x n identity matrix is true from the fact that the columns of any n x n matrix A completely determine the linear transformation T defined by T(x) = Ax for any vector x in Rⁿ.

(b) False. There exist linear transformations from Rⁿ to Rⁿ that are not matrix transformations.

(c) True. The range of the matrix transformation H Ax is the set of all possible linear combinations of the columns of A.

(d) True. A linear transformation  [tex]T:R^n\rightarrow R^m[/tex]  is one-to-one if and only if T(x) = T(y) implies x = y for any vectors x and y in Rⁿ.

(e) False. The matrix transformation x → Ax is one-to-one if and only if the equation Ax = 0 has only the trivial solution (i.e., x = 0).

(f) True. The matrix transformation x → Ax is one-to-one if and only if the kernel of the linear transformation T(x) = Ax is trivial, which is equivalent to the columns of A being linearly independent.

Hence, true, false, true, true, false and true are the answers of statements a to f respectively.

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