You find a great deal on a computer that has been marked down by 45% to be $715. What was the original
price of the computer?

[tex]A =\left[\begin{array}{ccc}3&0\\-2&1\\\end{array}\right][/tex] , [tex]B =\left[\begin{array}{ccc}-2&0\\2&0\\\end{array}\right][/tex] so that A,B are non-invertible matrices and  A+B is invertible.

An invertible matrix is a matrix in given square matrix A of order n × n is called invertible if there exists another n × n square matrix B such that, AB = BA = Iₙ, where Iₙ is an identity matrix of order n × n.

A non-invertible matrix is a matrix that does not have an inverse, i.e. non-invertible matrices do not satisfy the requisite condition to be invertible.

We have to find non-invertible matrices A,B such that A+B is invertible

so, A =[tex]\left[\begin{array}{ccc}3&0\\-2&1\\\end{array}\right][/tex]

and B =[tex]\left[\begin{array}{ccc}-2&0\\2&0\\\end{array}\right][/tex]

AB = [tex]\left[\begin{array}{ccc}-6&0\\6&0\\\end{array}\right][/tex]  

Therefore A and B matrix are non- invertible

A + B = [tex]\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right][/tex]

A square matrix in which every element except the principal diagonal elements is zero is called a Diagonal Matrix.

so, A,B neither is a diagonal matrix and A,B are not scalar multiples of each other.

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Step-by-step explanation:

To find the greatest common factor (GCF) of the expression (8 + 12), we need to first simplify the expression by finding the sum, which is 20. Therefore, the GCF of (8 + 12) is simply the GCF of 20, which is 20.

To rewrite the expression as a multiple of a sum of two whole numbers with no common factor, we can factor out the GCF of 4 from both 8 and 12, giving us:

(8 + 12) = 4(2 + 3)

The expression (8 + 12) is thus a multiple of the sum of the whole numbers 2 and 3, which have no common factor.

Jack may not be obligated to pay Sam the $100 reward because he revoked the offer before Sam found the wallet.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.

We are given that;

The amount of reward= $100

Now,

An offer can be revoked at any time before acceptance, and the revocation must be communicated to the offeree. In this case, Jack placed a second ad in the same newspaper revoking his offer before Sam found the wallet. Therefore, Sam did not accept the offer before it was revoked.

Additionally, Sam may not have provided consideration for the reward. Consideration is something of value given in exchange for a promise. In this case, Sam found the wallet before the reward was offered, so he did not provide consideration for the reward when he returned the wallet.

since the offer was revoked before acceptance and Sam did not provide consideration for the reward,

Therefore, by unitary method Jack may not be obligated to pay Sam the $100.

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It would be 20 because of the numbers

The square root of 7 is approximately 2.65 when rounded to the nearest hundredth.

By the face of the pyramid that lies in a base of the prism and the face of the pyramid, h2 = 108°

Let B and C be the vertices adjacent to A on the same base as A, and let D be the last vertex of the triangular pyramid. Then angle CAB = 120. Let x be the foot of the altitude from A to line BC. Then since triangle ABX is a 30-60-90 triangle, AX=6. Since the dihedral angle between triangle ABC  and triangle BCD is 60 degree, triangle AXD is a 30-60-90 triangle and 

[tex]AD = 6 \sqrt{3} = h[/tex]

Therefore,

[tex] {h}^{2} = 108[/tex]

A triangular prism is a three-sided prism that has three faces joining the corresponding sides of its triangular base, translated copy, and polyhedron construction. If the sides of a right triangular prism are not rectangular, the prism is oblique. Having square sides and equilateral bases, a uniform triangular prism is a right triangle.

It is, in essence, a polyhedron with three faces, all of whose surface normals are in the same plane (which need not be parallel to the base planes), and two of whose faces are parallel. It is a parallelogram that has these three faces. The same triangle can be seen in all cross-sections that are perpendicular to the base faces.

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i. The assumptions required to use Theorem 7.4 are that the daily downtimes are independent and identically distributed with a mean of 4 hours and a standard deviation of .8 hour.

ii. The approximate probability that the average daily downtime for a period of 30 days is between 1 and 5 hours is about 0.998.

b. The approximate probability that the total downtime for a period of 30 days is less than 115 hours is about 0.03.

a) i) The assumptions that must be true to use the result of Theorem 7.4 (Central Limit Theorem) are:

The daily downtime observations must be independent.

The number of daily downtime observations, n = 30, must be large enough such that the normal approximation is valid. A general guideline is n >= 30, but for this specific case, n = 30 is sufficient.

The individual daily downtime observations must have the same mean and standard deviation, with mean μ = 4 hours and standard deviation σ = 0.8 hours.

ii) Under these assumptions, we can use the Central Limit Theorem to approximate the distribution of the average daily downtime as normal with mean μ = 4 hours and standard deviation σ/√n = 0.8/√30 = 0.17 hours.

Using a standard normal table or calculator, we can find that the approximate probability that the average daily downtime for a period of 30 days is between 1 and 5 hours is:

P(1 < μ_bar < 5) = P( (1-4)/0.17 < Z < (5-4)/0.17 ) = P(-23.53 < Z < 2.94) = 0.998

So, the answer is approximately 0.998 or 99.8%.

b) Under the same assumptions, the total downtime for a period of 30 days is a sum of 30 independent daily downtime observations, and we can use the central limit theorem to approximate its distribution as normal with mean 30*4 = 120 hours and standard deviation 0.8 * sqrt(30) = 2.7 hours.

Using a standard normal table or calculator, we can find that the approximate probability that the total downtime for a period of 30 days is less than 115 hours is:

P(X < 115) = P((115-120)/2.7 < Z) = P(-1.85 < Z) = 0.03

So, the answer is approximately 0.03 or 3%.

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One possible set of positive integers that satisfies the given condition is the set of powers of 2, i.e., {2, 4, 8, 16, 32, ...}.

To see why this set works, note that any two distinct powers of 2 have a different binary representation, differing in at least one bit. This means that their sum will have one more "1" bit in its binary representation than either of the two numbers being added.

Since any prime number greater than 2 is odd, it follows that the sum of any two distinct powers of 2 will have an even number of distinct prime factors, namely the powers of 2 that appear in its binary representation.

First, let's note that every positive integer can be uniquely expressed as a product of prime powers, e.g., 36 = 2^2 * 3^2. The prime factors of an integer are the primes that appear in its prime factorization, e.g., the prime factors of 36 are 2 and 3.

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The range of the given data is 15, the sum is 110, variance is 37.

The sample variance is a value that measures the variability of values in the data set and how much the observed values deviate from the value of the mean or central value of the data set.

X=[23,17,15,30,25]

(a)

The value of the range is the difference between the maximum value and minimum value:

range=30-15=15

(b)

Sum(x)= 23+17+15+30+25=110

the sum of x2 = [tex]23^2+17^2+15^2+30^2+25^2=2568[/tex]

(c)

from part (b)

[tex]s^2=\sum x_i-nX^2]/[n-1]\\\\=[2568-5(22)^2][5-1]\\\\=37[/tex]

(d)

Using the definition of the variance, first we calculate the mean,

u=110/5=22

u=22

[tex]v^2=\frac{1}{n-1}\sum (x_i-u)^2\\\\=148/4\\=29.6\\s=6.083.[/tex]

e)

The value of population variance is v =5.44

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The linear equation is y = $25 + $10*w, and its graph is on the image at the end.

Here we know that he started with $25 He adds $10 to the cookie jar each week. Then we can model this with a linear equation:

y = $25 + $10*w

Where w is the number of weeks.

Now we want to graph this, to do so, we just need to find two points on the line.

if w = 0

y = $25 + $10*0 = $25

if w = 6

y = $25 + $10*6 = $85

So we need to graph the points (0, 25) and (6, 85) and connect them witha  line.

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Mean absolute deviation of the data is 1.

The mean absolute deviation of a dataset is the average distance between each data point and the mean. It gives us an idea about the variability in a dataset.

Given, In bar chart

Number of artists n = 4

Number of albums for Lil Shane x₁ = 7

Number of albums for Ben Raises x₂ = 9

Number of albums for Nicky x₃ = 6

Number of albums for Underdog x₄ = 6

Mean of the number of albums

μ = (7 + 9 + 6 + 6)/4 = 28/4 = 7

|μ - x₁| = |7 - 7| = 0

|μ - x₂| = |7 - 9| = |-2| = 2

|μ - x₃| = |7 - 6| = 1

|μ - x₄| = |7 - 6| = 1

Mean absolute deviation = ∑|x - μ|/n

= (0 + 2 + 1 + 1)/4

= 1

Hence, 1 is the mean absolute deviation (MAD) of the data in the bar chart.

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Answer:

D

Step-by-step explanation:

The notation is not what I am used to, but I think that I understand.  To go from the large figure to the smaller figure.  You need to dilate your figure by 1/3 .  The length of the big figure is 6 and 1/3 of that is a length of 2.  The width of the big figure is 3.  !/3 of that is 1 and that is what I see on the smaller figure.

Assuming the center of the dilation is point J.  If you move the shrunken figure 2 to the left and 5 down, it would fit right on top of the smaller figure.

The correct translation rule is given as -

(D_1/3 . T_<-2,-5> ) JKLM.

Translation is defined as the movement of graphical image over the two

dimensional plane. In genera, we can write the translation as -

(x, y) → (x ± k, y ± a)

here, we have,

Given is the composition of transformations that maps JKLM to PQRS.

Firstly →

The image is first translated according to the rule -

(x, y) → (x - 2, y - 5).

Secondly -

The image is then dilated by the scale factor -

{K} = 1/3.

Therefore, the correct translation rule is given as -

(D_1/3 . T_<-2,-5> ) JKLM.

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(a) Glen Cove's current population is 5,000.

In order to determine Glen Cove's current population, we must calculate P(0) because P(t) provides the population (in thousands) for t years in the future. In other words,

P(0) = (35(0)2 + 125(0) + 200) / (02 + 4(0) + 40)

      = 200 / 40

      = 5.

Since P(t) yields the population in thousands, Glen Cove's current population is 5,000.

(b) The population in the long run (as t approaches infinity) is 35,000.

As t approaches infinity, we must discover the limit of P(t) in order to determine the population over the long term. To do this, we can divide the function's numerator and denominator by t2, which results in the formula: P(t) = (35 + 125/t + 200/t2) / (1 + 4/t + 40/t2).

The terms 125/t and 200/t2 get smaller and smaller as t increases, so we can ignore them in the numerator. We can therefore disregard the terms 4/t and 40/t2 because they also degenerate in the denominator to lower and smaller values. Thus, we are left with:

P(t) ≈ 35/1 \s = 35

Since P(t) represents the population in thousands, the population in the long run (as t approaches infinity) is 35,000.

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The point-slope form of data contained in this table is y - 15 = 8.3(x - 7.2).

The slope-intercept form of data contained in this table is y = 8.3x - 10.

In Mathematics, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

At data point (7.2, 15), a linear equation in standard form for this line can be calculated by using the point-slope form as follows:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 15 = (35 - 15)/(4.8 - 7.2)(x - 7.2)

y - 15 = 8.3(x - 7.2)

y - 15 = 8.3x - 25

y = 8.3x - 10

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Brandon have a total of $32 originally

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

When he spends $24, he has 3/4 of the original amount left

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

24 = Original * 3/4

Make "Original" the subject of the formula

So, we have the following representation

Original = 24/(3/4)

Evaluate the expression

Original = 32

Hence, the amount is $32

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Answer:

Below

Step-by-step explanation:

You have ONE equation and TWO unknowns, so there is infinite solutions for a and c......you cannot solve for a specific a and c unless you have another equation relating the two or a definition of one of them.

 You can Solve for a

  20a + 15 c = 340

     20 a = 340-15c

        a = ( 340 -15c) / 20 = 17 - 3/4 c

Similarly:

   20 a + 15 c = 340

  15c = 340 - 20 a

c = (340-20a)/15

Answer: It is D.

Step-by-step explanation:

Answer: 63

63-15=48

Step-by-step explanation:

Answer: The store paid $84 to purchase the skateboard

Step-by-step explanation:

If the selling price of the skateboard is $147 and the markup is 75%, we can find the cost of the skateboard by working backwards from the selling price.

Let's start by calculating the original cost of the skateboard before the markup was applied. We can do this by dividing the selling price by 1 plus the markup percentage as a decimal:

original cost = selling price / (1 + markup percentage)

Converting the markup percentage to a decimal:

markup percentage = 75% = 0.75

original cost = 147 / (1 + 0.75)

original cost = 147 / 1.75

original cost = 84

For x ≤ -1, the function is given by f(x) = 4x + 1. This is a linear function with a slope of 4 and y-intercept of 1. The graph of this part of the function is a straight line passing through (0, 1) with a steep slope, extending towards negative x-values.

In mathematics, a function is a rule that associates each element in one set (called the domain) to a unique element in another set (called the range). Functions are one of the most important concepts in mathematics and have a wide range of applications in various fields.

A function is usually denoted by a letter, such as f(x), where x is an element in the domain and f(x) is the corresponding element in the range. The domain of a function is the set of all possible values of x for which the function is defined, and the range is the set of all possible values of f(x).

To graph the piecewise function f(x), we will graph each part of the function separately.

For -1 < x < 2, the function is given by f(x) = -2x - 3. This is also a linear function with a slope of -2 and y-intercept of -3. The graph of this part of the function is a straight line passing through (-1, 1) with a gentle slope, extending towards positive x-values until it reaches x=2.

For x ≥ 2, the function is given by f(x) = 5. This is a horizontal line at y=5, which is a constant function. The graph of this part of the function is a horizontal line at y=5 starting from x=2.

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Answer:

Step-by-step explanation:

if we simplify both of them,

5/10=1/2

and

6/12=1/2

then it means they are equal

The sustainable growth rate is calculated by subtracting the payout ratio from the ROE.

The sustainable growth rate is calculated by subtracting the payout ratio from the ROE. To calculate the sustainable growth rate for Gold Corp., we must first calculate the retention ratio. The retention ratio is calculated by subtracting the payout ratio from 100%. In this case, the retention ratio would be 100% - 20% = 80%. The sustainable growth rate is then calculated by multiplying the retention ratio by the ROE. In this case, the equation would be 80% * 12% = 9.6%. The sustainable growth rate for Gold Corp. is 9.6%, which can be rounded to 9.6%.

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The actual dimensions of the rectangular garden are 17.5 cm by 12.5 cm

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

Scale: 1.6 cm = 2 cm

A scale is the ratio of the size of the drawing to the size of the actual object.

Given that the dimension is

14 cm by 10 cm

Using the above as a guide, we have the following equation

Actual = 14 * 2/1.6 cm by 10 * 2/1.6 cm

Evaluate

So, we have the following representation

Actual = 17.5 cm by 12.5 cm

Hence, the actual is 17.5 cm by 12.5 cm

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The required line is y = -(3/2)x - 6 which is perpendicular and shifted down 8 units.

Perpendicular lines are two lines that cross one other and create a 90-degree angle. Two lines are perpendicular if the product of their slopes is -1.

The slope-intercept form of a line is y = (2/3)x + 2.

To find the slope of the perpendicular line, we simply need to negate the reciprocal of the original line's slope.

The slope of the original line is 2/3. The slope of the perpendicular line is therefore -3/2.

To shift the line down 8 units, we simply need to subtract 8 from the y-intercept.

The slope-intercept form of the line perpendicular to y = (2/3)x + 2 and shifted down 8 units is:

y = -(3/2)x + 2 - 8 = -(3/2)x - 6

So the line that is perpendicular and shifted down 8 units is y = -(3/2)x - 6.

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The probability that a randomly selected person will have a z-score less than 2.00 is about 97.72%. (option closest: 0.9750)

To utilize the experimental rule, we want to know the z-score comparing to a given likelihood. The z-score addresses the quantity of standard deviations an information point is from the mean.

Utilizing the mean and standard deviation given, we can switch the crude score of somebody's pay over completely to a z-score utilizing the recipe:

z = (x - μ)/σ

z = (64,000 - 64,000) / 12,000 = 0

where x is the crude score (family pay), μ is the mean, and σ is the standard deviation.

To find the likelihood that somebody chose indiscriminately will have a z-score under 2.00, we can utilize a standard typical dispersion table or number cruncher to track down the region under the bend to one side of 2.00. This relates to the likelihood of a haphazardly chosen individual having a pay under 2 standard deviations over the mean.

The exact decide states that for an ordinary dissemination with a symmetric recurrence conveyance, around 68% of the information falls inside one standard deviation of the mean, around 95% falls inside two standard deviations of the mean, and around 99.7% falls inside three standard deviations of the mean.

Since we are searching for the likelihood of a z-score under 2.00, which is inside two standard deviations of the mean, we can utilize the experimental decide and gauge that the likelihood is around 95%.

Nonetheless, on the off chance that we need a more exact response, we can utilize a standard typical dissemination table or mini-computer to track down the region under the bend to one side of 2.00. The region under the standard typical dispersion bend to one side of 2.00 is 0.9772, which relates to a likelihood of 0.9772 or 97.72%. Accordingly, the right response is roughly 0.9772 or 97.72%.

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The amount to be paid by Bo is 0.82B

A percent of a number is the 100th part of it.

Given that, the board game costs B dollars. Price is reduced by 18%.  we need to calculate the final bill.

Cost of game = B dollars

Discount = 18% = 0.18

Discount amount = 0.18B

Final cost = B-0.18B

Amount to pay = 0.82B

Hence, the amount to be paid by Bo is 0.82B

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The complete question is:-

Bo is buying a board game which usually costs B dollars. The game is on sale, and the price has been reduced by 18% There are different ways of thinking about how to calculate Bo's final bill. Match the expressions to their meanings.

Answers:

B ' (6, 4)

C ' (2, 3)

D ' (3, -1)

E ' (7, 0)

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

Explanation:

The y-axis reflection rule is:

[tex](\text{x},\text{y})\to (-\text{x},\text{y})[/tex]

The x coordinate flips from positive to negative, or vice versa. The y coordinate stays the same.

So for example, the point B(-6,4) moves to B ' (6, 4).

You can use a graphing tool like GeoGebra to confirm the answers are correct.

Answer:

B , 0.75 grams/cm3

Step-by-step explanation:

Crispin's mass measurement (202 grams) has three significant figures, but his volume measurement (270 cm3) only has two significant figures. So when one of these factors is divided by the other, the factor with the lowest number of significant figures takes precedence. This means that the density calculation can only have two significant figures.

The density of an object is its mass divided by its volume:

So, 202 grams ÷ 270 cm3 = 0.75 grams/cm3

(I also did this on study island and the other person made me get it wrong so i got the answer)