The following expression gives an approximate value of the total average credit card debt in a u.s. household (in dollars) t years after 1995. 410t+5690 Use this expression to predict what the total average credit card debt was or will be in the year 1998. answer: in the year 1998, the total average credit card debt for a u.s. household will be (or was) ______dollars.

Answer:

k=8 is not part of the solution set

Step-by-step explanation:

5(8) < 39

40 < 39

If you plug in 8 for K it makes the inequality incorrect. 40 is not less than 39.

The kernel of A is {(0,0,1,0)^T} and  the basis is {(1,0,2,4)^T, (0,1,0,-3)^T}.

The kernel of a matrix A is the set of all vectors x such that Ax = 0, where 0 is the zero vector.

To find a basis for the kernel of A, we can row reduce the augmented matrix [A | 0] to reduced row echelon form using Gaussian elimination.

The row reduced echelon form of the matrix A is

1 0 2 4

0 1 0 -3

0 0 0 0

0 0 0 0

Write out the elements in the second column

0 1 0 0

Reverse the elements

0 0 1 0

So, the basis for the kernel of A is {(0,0,1,0)^T}.

The image of a matrix A is the set of all linear combinations of the columns of A.

So, the basis for the image of A is {(1,0,2,4)^T, (0,1,0,-3)^T}.

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Answer:

each bar costs $3.

Step-by-step explanation:

The inequality that describes the problem is:

3x > 18

This inequality states that the total cost of the soap bars, represented by 3x, is greater than Colleen's budget of $18. The variable x represents the number of bars of soap Colleen bought. So, if x represents the number of bars of soap Colleen bought, 3x represents the total cost of those bars, since each bar costs $3.

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There does not exist a constant C > 0 such that p∞(v) ≤ Cp1(v) for all vectors v in V. Therefore, p1-norm < p2-norm < p∞-norm implies there is no c such that p∞-norm < c p1-norm.

Given two norms, p and q, on a vector space V, we say that p is less than q, written p ≤ q, if there exists a constant C > 0 such that for all vectors v in V,

p(v) ≤ Cq(v)

Now, let's consider the three norms:

   The 1-norm: p1(v) = ∑|v_i|

   The 2-norm: p2(v) = √(∑v_i^2)

   The infinity-norm: p∞(v) = max{|v_i|}

We are given that p1(v) ≤ p2(v) for all vectors v in V and that p2(v) ≤ p∞(v) for all vectors v in V. We want to show that there does not exist a constant C > 0 such that p∞(v) ≤ Cp1(v) for all vectors v in V.

Suppose for the sake of contradiction that such a constant C does exist. Then, for any non-zero vector v in V,

p∞(v) ≤ Cp1(v)

max{|v_i|} ≤ C ∑|v_i|

Since v is non-zero, there exists an index i such that |v_i| > 0. We can divide both sides of the inequality by |v_i| to get:

1 ≤ C ∑|v_j| / |v_i|

Now, since p1(v) ≤ p2(v) for all vectors v in V, we have:

p1(v) = ∑|v_j| ≤ √(∑v_j^2) = p2(v)

So, we can substitute this into the inequality above to get:

1 ≤ C √(∑v_j^2) / |v_i| = Cp2(v) / |v_i|

Finally, since p2(v) ≤ p∞(v) for all vectors v in V, we have:

p2(v) / |v_i| ≤ p∞(v) / |v_i| = 1

So, we have reached a contradiction:

1 ≤ Cp2(v) / |v_i| ≤ C

This contradicts the assumption that C > 0, so there does not exist a constant C > 0 such that p∞(v) ≤ Cp1(v) for all vectors v in V. Therefore, p1-norm < p2-norm < p∞-norm implies there is no c such that p∞-norm < c p1-norm.

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The probability that a randomly selected student takes both computer science and statistics courses is 26%.

Let's call the event that a student takes a computer science course "C" and the event that a student takes a statistics course "S". We want to find the probability that a student takes both C and S, which can be written as P(C ∩ S).

The probability that a student takes at least one of these two courses can be written as P(C ∪ S), which is equal to 63%. This means that 63% of the students take either computer science or statistics, or both.

To find the probability that a student takes both courses, we can use the formula for the intersection of two events:

P(C ∩ S) = P(C | S) × P(S)

where P(C | S) is the probability that a student takes a computer science course given that they also take a statistics course. To find this value, we can use the formula:

P(C | S) = P(C ∩ S) ÷ P(S)

Substituting this into the first equation, we get:

P(C ∩ S) = P(C ∩ S) ÷ P(S) × P(S)

P(C ∩ S) = P(C ∩ S) × P(S)

We know that P(S) = 48% and we can use the formula for the union of two events to find P(C ∪ S):

P(C ∪ S) = P(C) + P(S) - P(C ∩ S)

Substituting in the values we know:

63% = 41% + 48% - P(C ∩ S)

P(C ∩ S) = 41% + 48% - 63% = 26%

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Answer:

A

Step-by-step explanation:

In a systems of equations we have to set up two equations which relate to each other and in this case we're setting up two linear equations, so let's take a look at the question.

Let's first make an equation from: "A monster pizza, m, has 7 fewer slices than twice the number on a large pizza, l" That means if we subtracted  twice the large pizza from monster pizza, we would get 7 slices. [tex]2l-m=7[/tex] and if we multiply by -1 on both sides: [tex]m-2l=-7[/tex]

Now let's use the second piece of information given: "the difference between the number of slices on a monster pizza and the number of slices on a large pizza is 4 slices" this means if we take away 4 slices from the monster pizza we get the same amount of slices on a large pizza: [tex]m-4=l[/tex] and rearranging we get: [tex]m-l=4[/tex] making A the correct option

Answer:

it's 3gc brought video gloves

Triangle AHIJ is theree-sided polygon where the measure of angle JHI is (3x + 28) degrees.

Answer:

7 + [x/(3x9)]

Step-by-step explanation:

The value of the unknown number x is given as follows:

x = -65.

The number is unknown, hence the variable is given as follows:

x.

-1/5 of the number is given as follows:

-1/5x = -x/5.

The difference of -1/5 of a number and 1 is given as follows:

-x/5 - 1.

The difference has a result of 12, hence:

-x/5 - 1 = 12.

Then the variable x is obtained as follows:

-x/5 = 13

x = -13 x 5

x = -65.

The problem asks for the value of the unknown number.

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Check the picture below.

now, doing a prime factoring on both the denominators, notice, the repeated factors get used only once in the LCD calculation, so the red "3" only goes once in the LCD and then the others, so the LCD for both of those is 3*3*2*2 = 36.

"L" in LCD stands for Least, so that's the smallest, however we can have a CD that's no small and is simply a multiple of the LCD, let's check who isn't an LCD or CD

[tex]\begin{array}{rllll} 108=3\cdot 36 & \bigotimes\\\\ 72=2\cdot 36& \bigotimes\\\\ 36=1\cdot 36&\bigotimes\\\\ 24&\textit{\LARGE \checkmark} \end{array}[/tex]

Answer:

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

Evaluate expressions using respective points on graphs :

Answer:

8

Step-by-step explanation:

Let's call the first of the three consecutive even integers x.

Since the integers are consecutive and even, we know that the next integer will be x+2, and the next one will be x+4.

We can use this information to set up an equation:

x + (x+2) + (x+4) = 30

Simplifying this equation, we get:

3x + 6 = 30

Subtracting 6 from both sides:

3x = 24

Dividing by 3:

x = 8

So the first of the three consecutive even integers is 8

If sample variance were to be computed by dividing SS by n, then the average value of the sample variances from all the possible random samples would consistently underestimate the population variance.

The sample variance is an estimate of the population variance, and it is calculated by dividing the sum of squared deviations (SS) by the sample size minus one (n - 1).

The reason for dividing by n-1 instead of n is due to the fact that the sample variance is an estimate of the population variance and not the exact value. When computing the sample variance, we use the sample data to make an estimate of the population variance. By dividing by n-1 instead of n, we adjust for the fact that the sample is a subset of the population and introduce a small amount of bias into the estimate to correct for this lack of representation.

This correction is known as the Bessel's correction and it makes the sample variance a more accurate estimate of the population variance by adjusting for the variability inherent in sampling. As a result, when sample variance is computed using the Bessel's correction (dividing by n-1), the average value of the sample variances from all possible random samples will consistently underestimate the population variance.

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The equation of g(x) is g(x) = 2*x^(1/2)

Explanation:

The original function f(x) is defined as f(x) = x^(1/2) which is the square root of x. When the function is stretched horizontally by a factor of 2, the x term becomes 2x. So the new function g(x) is defined as g(x) = 2*x^(1/2)

7. The statement regarding the set is false.

8. The statement regarding the set is correct.

In problem 7, we are given the subsets of a set, and then the statement is that the subset {a,e} is contained into the set S.

The subset {a,e} is not one element of the set S, which are a, ... {e, empty}, hence the statement is false.

In problem 8, we are given the union operation, which has the result given by the elements that belong to at least one of the sets.

The empty set belongs to set T, hence it belongs to the union of sets S and T, and thus the statement is correct.

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The science of statistics focuses on creating and researching strategies for gathering, analysing, interpreting, and presenting empirical data.

Data is frequently presented in graphs, tables, and charts that analyse the data and aid in problem- and decision-solving. Calculating the sample size and population, determining the mean, mode, and median, as well as the standard deviation and variance, are some of the most crucial statistical calculations. Data, which can take the form of words or numbers, are the actual values of the variable.

Statistics is a technique for interpreting, analysing, and summarising data in mathematics. In light of these characteristics, the various statistical types are divided into: Statistics that are descriptive and inferential.

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If the line segment joining the points A (x1, y1) and B(x2, y2) is divided by a point P in the ratio 1 : k internally, then the coordinates of the point P are P[(1x₂ + kx₁)/(1 + k)],  [(1y₂ + ky₁)/(1 + k)].

In this scenario, we would use line ratio to determine the coordinates of the point P on the directed line segment that partitions the segment into a ratio of 1 to k.

In Mathematics, line ratio can be used to determine the coordinates of the point P and this is modeled by this mathematical expression:

P(x, y) = [(mx₂ + nx₁)/(m + n)],  [(my₂ + ny₁)/(m + n)]

Substituting the given parameters into the line ratio formula, we have the following;

P(x, y) = [(1x₂ + kx₁)/(1 + k)],  [(1y₂ + ky₁)/(1 + k)]

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The possibilities of the combinations that are there for rearranging the pages in the right order are 100 !.

The probability of getting the story in the right order is 1 / 100 !.

There are 100 pages in the history text which means that when they are randomly mixed, each page could take a different position out of the 100 and so lead to a new combination.

The possibilities of combinations is therefore:

= n !

= 100 !

The probability that the story is in the right order will happen with only a single combination which means the probability is:

= Number of correct orders / Number of combinations

= 1 / 100 !

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The equivalent ratios for the given cost to toss the ring are found as:

For the stated question:

The cost to toss 34 rings = $17.

Part a: ___ to $1.

$17 ---> 34 toss

$1 ---> 34/17 toss

$1 ---> 2 toss

Part b:

34 toss   ---> $17

20 toss ---> $17*20 / 34

20 toss ---> $10

Thus, the equivalent ratios for the given cost to toss the ring are found as:

2 toss --->  $1

20 toss ---> $10

Thus, the graph is plotted for the points on the coordinate axes.

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The complete question is attached:

By using elimination method, the solution of the system of equations are x = - 8, y = 9.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The system of equations are,

⇒ 5x + 4y = - 4

⇒ 4x + 4y = 4

Now, We can solve by using elimination method as;

The system of equations are,

⇒ 5x + 4y = - 4  .. (i)

⇒ 4x + 4y = 4

⇒ x + y = 1 .. (ii)

Multiply by 5 in (ii) and subtract from (i);

⇒ 5x + 4y - 5x - 5y = - 4 - 5

⇒ - y = - 9

⇒ y = 9

And, From (ii);

⇒ x + y = 1

⇒ x + 9 = 1

⇒ x = 1 - 9

⇒ x = - 8

Thus, The solution of the system of equations are x = - 8, y = 9.

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According to the representation of the linear model, the balloon's height is zero feet after 15 seconds.

Depending on the context, the word "linear model" in statistics might signify many things.

The phrase is frequently used interchangeably with a linear regression model since it most frequently relates to regression models.

The phrase has a different connotation when applied to time series analysis.

In each instance, "linear" refers to a subclass of models for which the complexity of the underlying statistical theory can be greatly reduced.

The linear model shows that the water balloon is launched from a height of 40 feet above.

The linear model shows that the water balloon is launched from a height of 40 feet above.

Now, the balloon rises to a height of 70 feet before falling back to the ground as a result of gravity.

After about ten seconds, the balloon lands on the surface and makes a splash.

The balloon will therefore stay on the ground for a while longer.

As a result, the balloon's height at time 15 seconds is always 0 feet, according to the linear model.

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Answer:

Y- intercept is (0,-5), not (0,5), but everything is right! Nice job

Step-by-step explanation:

Finding slope and Y-intercept

Slope being (y2-y1)/(x2-x1) of any two points

I'll do (6,7) and (9,13), so

(13-7)/(9-6) = 6/3 = 2.

Slope = 3

For Y-Intercept

That's where X = 0. On this graph, X = 0, where Y= -5, making the Y-intercept -5

Slope intercept form is y = mx + b

Plugging everything together, we get K(X) = 3x - 5

Answer:

1/7

Step-by-step explanation:

All parts are equal to one therefore raisons are just 1 out of 7 other slices on the pie chart

To determine what part of the premium trail mix is composed of raisins, refer to the given pie chart. The portion represented by 'raisins' indicates the amount of raisins in the mix. Raisins slice is 1/7, so 14.28% of premium blend is composed of raisins.

To find out what part of the premium blend trail mix is composed of raisins, you need to look at the pie chart. The pie chart should be separated into multiple sections, with each section representing a different ingredient in the trail mix. The section labeled as raisins would represent the part of the premium blend that is composed of raisins.

For example, if the 'raisins' slice is 1/4, 25%, or 90 degrees of the pie chart, this means that 1/4, 25%, or a proportional quantity of the trail mix is composed of raisins. This is because a pie chart is a circle, and a full circle is 100% or 360 degrees - so 1/4, 25%, or 90 degrees all represent the same quantity in this context.

Remember to always check the labels and any information provided in the pie chart. It provides a visual representation of data and can help you understand the proportions of different components in a mixture.

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Answer:

coordinates r the: (-2, -4.50)

Step-by-step explanation:

option b is the ans

The number of years it will take the population of the city to reach 1million is 14.1 years

Exponential function, in mathematics, a relation of the form y = ax, with the independent variable x ranging over the entire real number line as the exponent of a positive number a.

1000000 = 10⁶

10⁶ = P(t)

10⁶ = 244115e0.1t

10⁶/244115 = 0.1t

e0.1t = 4.096

ln0.1t = ln 4.096

0.1t = 1.41

t = 1.41/0.1

t = 14.1 years

therefore the years it will take the city to be populated with 1million is 14.1 years

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