x | 2 9 16 23
y | 4 8 16 32
is the relationship linear, exponential, or neither?​

The given matrix is non linear matrix combination of a and b matrix.

a - b = [tex]\left[\begin{array}{ccc}-8&1\\0&4\\\end{array}\right][/tex] ≠ [tex]\left[\begin{array}{ccc}-19&4\\3&16\\\end{array}\right][/tex]

An equation in which the maximum degree of a term is 2 or more than two is called a nonlinear equation.

Matrix, a set of numbers arranged in rows and columns so as to form a rectangular array. The numbers are called the elements, or entries, of the matrix. Matrices have wide applications in engineering, physics, economics, and statistics as well as in various branches of mathematics.

Given that,

a = [tex]\left[\begin{array}{ccc}-3&2\\1&4\\\end{array}\right][/tex]

b = [tex]\left[\begin{array}{ccc}5&1\\0&-2\\\end{array}\right][/tex]

The given matrix is a linear combination of a and b

a - b = [tex]\left[\begin{array}{ccc}-3&2\\1&4\\\end{array}\right] - \left[\begin{array}{ccc}5&1\\0&-2\\\end{array}\right][/tex] ≠ [tex]\left[\begin{array}{ccc}-19&4\\3&16\\\end{array}\right][/tex]

a - b = [tex]\left[\begin{array}{ccc}-3-5&2-1\\1-1&4-0\\\end{array}\right][/tex] ≠ [tex]\left[\begin{array}{ccc}-19&4\\3&16\\\end{array}\right][/tex]

a - b = [tex]\left[\begin{array}{ccc}-8&1\\0&4\\\end{array}\right][/tex] ≠ [tex]\left[\begin{array}{ccc}-19&4\\3&16\\\end{array}\right][/tex]

Therefore,

The given matrix is non linear matrix combination of a and b matrix.

a - b = [tex]\left[\begin{array}{ccc}-8&1\\0&4\\\end{array}\right][/tex] ≠ [tex]\left[\begin{array}{ccc}-19&4\\3&16\\\end{array}\right][/tex]

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The inverse of the cube root function used to act for the situation in model is f⁻¹(x) = √x³ - 4

Inverse of the cube root function f(x)

f(x) = ∛ (x + 4) ²

To find the inverse function, let f(x) = y

So, y = ∛ (x + 4) ²

Taking the cube of both sides, we have

y³ = [∛ (x + 4) ²] ³

y³ = (x + 4) ²

Taking square root of both sides, we have

√y³ = √ (x + 4) ²

√y³ = (x + 4)

Subtracting 4 from both sides, we have

√y³ - 4 = x + 4 - 4

√y³ - 4 = x

change y with x, we have

√x³ - 4 = y

Replacing y with f⁻¹(x), we have

f⁻¹(x) = √x³ - 4

So, the inverse of the cube root function used to represent the situation in model is f⁻¹(x) = √x³ - 4

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[tex]$\int_{-2}^{4} f(x)dx$[/tex] with the substitution [tex]$u = x^2$[/tex] . The new limits of integration are 0 and 8.

The substitution [tex]$u = x^2$[/tex] implies that [tex]$du = 2x dx$[/tex], so when [tex]x = -2$, $u = (-2)^2 = 4$[/tex]. Similarly, when [tex]x = 4$, $u = 4^2 = 16$[/tex]. Thus, the new limits of integration are 0 and 8.

To determine the new limits of integration, we must first find the values of u for the original limits of integration. Since we have [tex]$u = x^2$[/tex], when x = -2, we have [tex]$u = (-2)^2 = 4$[/tex]. Similarly, when x = 4, we have [tex]u = 4^2 = 16$.[/tex]Therefore, the new limits of integration are 0 and 8.

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The meaning of the slope and of the intercept of the linear function are given as follows:

The slope is negative -3/2, and the y-intercept is 9. The candle starts at a height of 9 inches and decreases 3/2 of an inch every hour.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The two points for the function in this problem are given as follows:

(0,9) and (2,6).

When x = 0, y = 9, hence the intercept b is given as follows:

b = 9.

Meaning that the initial value of the problem is of 9.

The slope is given as the change in y divided by the change in x, hence:

m = (6 - 9)/(2 - 0)

m = -3/2.

Meaning that the rate of change is a decrease of 3/2 units for each unit of the input.

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-2.25 is larger when it compares to -3, because when you order negative numbers, the larger the number after the negative sign, the smaller the number actually is. This means -2.25 > -3

What is negative numbers?

On a number line, numbers always move from right to left and grow (become "more positive") in that direction. The numbers to the right are bigger than the numbers to the left, while the numbers to the left are smaller. Numbers with a minus sign before them are considered negative numbers. They could be fractions, decimals, or integers. Negative numbers include, for instance, -4, -15, -4/5, and -0.5. A negative number in mathematics represents the reverse. A negative number is one that is less than zero in the real number system. Negative numbers are frequently used to indicate how great a loss or a shortage is.

-2.5>-3 because the bigger a negative number is like -15,-18, etc the smaller it’s value actually gets so -2.5 is greater because it is closer to 0 on a number line.

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Answer:

B

Step-by-step explanation:

B..................

Based on the random sample results, the prediction statements for the entire machine of 200 gumballs is completed below;

Total gumballs in the gumball machine= 200 gumballs

Result from the random sample= 25 gumballs

From the random sample selected:

10 gumballs are red

8 gumballs are blue

5 gumballs are green

2 gumballs are white

There are 10 red gumballs in the machine.

There are 3 more green gumballs than white gumballs in the machine.

= Green gumballs - red gumballs

= 5 - 2

= 3 gumballs

There are 13 gumballs that are either blue or green in the machine.

= Blue gumballs + green gumballs

= 8 + 5

= 13 gumballs

Ultimately, the prediction statement is completed using 10, 3 and 13 respectively.

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If Six Republicans and six Democrats orally cast their vote in the U.S. Senate , if they are alternate Republican, Democrat, Republican, Democrat, and so on, and if a Republican must always be the first to vote then the number of ways in which they can vote is 518400 ways .

the number of Republicans for voting is = 6 ;

the number of Democrats for voting is = 6 ;

so , total number of voters is = 12 ,

they have to vote alternately starting with a Republicans .

the first republican has to choose from = ⁶C₁ = 6 ;

the second republicans has to choose from the remaining 5 republicans , = ⁵C₁ = 5 ;

Similarly following the pattern ,

we get ;

Total chances of required way of casting votes ;

= 6×6×5×5×4×4×3×3×2×2×1×1

= (1×2×3×4×5×6)²

= (6!)² = (720)² = 518400 ways .

Therefore , the number of ways of voting is 518400 ways .

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The product of the expression (-4) x (-4) x (-4) x y x y is -64y²

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given that, an expression, (-4) x (-4) x (-4) x y x y

We need to find its product,

(-4) x (-4) x (-4) x y x y

= -4³ × y²

= -64 × y²

= -64y²

Hence, the product of the expression (-4) x (-4) x (-4) x y x y is -64y²

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The subset of consisting of vectors of the form is indeed a subspace.

A subspace is a special type of set within a vector space that has the same properties as the larger vector space.

In order to determine if a subset of a vector space is a subspace, we must check if it satisfies certain conditions.

The first condition is that the subset must contain the zero vector.

The second condition is that the subset must be closed under addition.

The third condition is that the subset must be closed under scalar multiplication.

Now, let's apply these conditions to the subset of consisting of vectors of the form . It is clear that the zero vector satisfies this condition, as.

The subset is also closed under addition, as adding two vectors of the form and will result in a vector of the form.

Finally, the subset is closed under scalar multiplication, as multiplying a vector of the form by a scalar will result in a vector of the form .

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Each malleable piece of wire he can produce has a length of 2 metres.

Prime factorization

26 = 2 × 13

20 = 2² × 5

HCF = 2

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Answer:

After 17,190 years, the amount of carbon-14 left would be approximately 5 mg.

The half-life of carbon-14 is 5,730 years, which means that every 5,730 years, half of the remaining carbon-14 decays. To calculate the amount of carbon-14 remaining after 17,190 years, we can use the formula:

A = A0 * (1/2)^(t/T)

where:

A0 is the initial amount (80 mg)

t is the time elapsed (17,190 years)

T is the half-life (5,730 years)

A = 80 * (1/2)^(17,190/5,730)

A = 80 * (1/2)^3

A = 80 * (1/8)

A = 10 mg * 1/2

A = 5 mg

Answer:

1320

MDAS Method

Answer:

Your answer is 1320

Step-by-step explanation:

hope this is what you were looking for

The lengths 6, 8 and 15 cannot represent the sides of the triangle. The solution has been obtained by using the triangle inequality theorem.

What is the triangle inequality theorem?

The triangle inequality theorem outlines the relationships between a triangle's three sides. According to this theorem, the lengths of any triangle's two shorter sides add up to be longer than the triangle's third side. In other terms, this theorem states that the shortest path between any two places is always a straight line.

We are given the lengths to be 6, 8 and 15.

Using the triangle inequality theorem,

⇒ 6 + 15 > 8

⇒ 21 > 8

Also,

⇒ 8 + 15 > 6

⇒ 23 > 8

Also,

⇒ 6 + 8 > 15

But,

⇒ 14 < 15

Hence, the lengths 6, 8 and 15 cannot represent the sides of the triangle.

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The integral is equal to zero, since the divergence of a constant vector is always zero.

The integral ∫ (∇ × a® ).® is equal to zero. This is due to the fact that the curl of a constant vector is always zero. The vector a® is given to be eˆ eˆ eˆ, therefore it is a constant vector. Since the divergence of a constant vector is always zero, the integral is equal to zero.

To further illustrate this point, we can expand the integral in terms of its components. ∇ × a® is equal to 0 as it is the curl of a constant vector. Similarly, a® .® is equal to 0 since the inner product of two constant vectors is always zero. Therefore, the integral is equal to 0.

The surface defined by the paraboloid is not used in this calculation, as the surface does not affect the value of the integral. The surface is used to define the range of the integral, but not to calculate the value of the integral itself.

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Answer:

24.12 feet.

Step-by-step explanation:

The formula to find the diameter of a circle from its circumference is:

diameter = circumference / π

Plugging in the given values:

diameter = 75.36 feet / π

diameter = 75.36 / 3.14

diameter ≈ 24.12 feet

So, the diameter of the circular garden is approximately 24.12 feet.

It is found that 22 miles in 20 minutes is LESS

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

We have to compare the two rates:

=> 22 miles in 20 minutes

=> 38 miles in 30 minutes

Let's simplify each rate by finding the speed, which is distance divided by time.

That is:

Speed = distance/time

For the first one:

s = 22/20 = 1.1 milesl/min

For the second one:

s = 38/30 = 1.27 milesl/min

Since 1.1 is less than 1.27, so, 22 miles in 20 minutes is less than 38 miles in 30 minutes.

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The complete question is;

Is 22 miles in 20 minutes greater than, equal to or less than 38 miles in 30 minutes?

Answer:

a) $2125

b) $2000

Step-by-step explanation:

In this problem, we are asked to solve for the manufacturing price of different printers if the printer company sells their printers at a price that makes them 25% profit, assuming there are no extra expenses.

We can solve this type of problem by manipulating ratios, like for example:

manufacturing price : sale price

           100                  :       125

This ratio represents the the sale price being 25% more than the manufacturing price.

a) We can equate the above ratio to the ratio of the manufacturing price (in this problem, $1700) to the sale price of the printer (represented by x).

100 : 125 = 1700 : x

This can be solved for x when the ratios are represented as fractions.

[tex]\dfrac{100}{125} = \dfrac{1700}{x}[/tex]

↓ simplify the fraction on the left side

[tex]\dfrac{4}{5} = \dfrac{1700}{x}[/tex]

↓ cross multiply

[tex]4x = 1700 \cdot 5[/tex]

↓ divide both sides by 4

[tex]x=\$ \, 2125[/tex]

So, the price that the customer would pay for a printer that the company bought for $1700 is $2125.

b) We can solve in the same way that we did for section a.

However, this time, the variable (y) represents the manufacturing price, NOT the sale price.

100 : 125 = y : 2500

↓ rewrite with fractions

[tex]\dfrac{100}{125} = \dfrac{y}{2500}[/tex]

↓ simplify the fraction on the left side

[tex]\dfrac{4}{5} = \dfrac{y}{2500}[/tex]

↓ cross multiply

[tex]5y = 2500 \cdot 4[/tex]

↓ divide both sides by 5

[tex]y = \$ \, 2000[/tex]

So, the price that the company would pay for a printer that a customer buys for $2500 is $2000.

7/3 t^(3/2) + C This equation represents the volume of water in the tank as a function of time t.

The equation r(t) = 7t √ represents the rate at which water is flowing into the tank, measured in cubic feet per hour, at time t after 9:00am. The expression 7t √ means that the rate of flow increases over time, starting at 0 cubic feet per hour at t = 0 and increasing as t increases.

To find the volume of water in the tank at a specific time t after 9:00am, we can integrate the rate of flow over the time interval from 9:00am to t. The volume of water in the tank at time t can be expressed as:

V(t) = ∫ r(t) dt from 9:00am to t

= ∫ 7t √ dt from 0 to t

= 7/3 t^(3/2) + C

where C is an arbitrary constant of integration. This equation represents the volume of water in the tank as a function of time t.

Therefore, 7/3 t^(3/2) + C This equation represents the volume of water in the tank as a function of time t.

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We are 90% confident that the true proportion of times the die would land on the number 1 is between 0.438 and 0.602. Since this includes 0.5, the die appears to be fair.

The correct option is C.

The Probability in mathematics is the possibility of an event in time. In simple words, how many times that incident is happening in any given time interval.

Given:

While playing a game of chance,

Tarik rolled a regular six-sided die 100 times and noticed that it landed on the number 1 exactly 52 times.

The probability P is = 52/100 = 0.52.

The lower limit = P - z√(P(1 - P)/n

The lower limit = 0.52 - 1.645√(0.52 x 0.48)/100

The lower limit ≈ 0.438.

The upper limit = P + z√(P(1 - P)/n

The upper limit = 0.52 + 1.645√(0.52 x 0.48)/100

The upper limit ≈ 0.602.

Therefore, the die would land on the number 1 is between 0.438 and 0.602.

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Answer:

Step-by-step explanation:

The given exponential function will grow at 6.1%

Given,

y =

To find,

identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.

Solution,

We have,

y =

The equation represents exponential growth because the growth factor is greater than 1.

The general form equation is:

y(x)= a(1-r)^x such that r is the growth percent.

==> 1+r = 1.061

==> r = 0.061 = 6.1%

The mean difference in game scores over the six games is 12

The mean difference, or difference in means, measures the absolute difference between the mean value in two different groups.

Given the points by which a basketball team either won or lost 6 games.

- Won by 7 points = +7

- Lost by 10 points = -10

- Won by 8 points = +8

- Won by 11 points = +11

- Lost by 2 points = -2

- Won by 10 points = +10

Thus;

Mean difference of the 6 games is;

= (+7 - 10 + 8 + 11 - 2 + 10)/6

= 24/6

= 12

Hence, the mean difference in game scores over the six games is 12

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Total mortgage brokerage fees is $1,596.75. Thus, option c is correct.

These factors include the total amount you're borrowing from a bank, the interest rate for the loan, and the amount of time you have to pay back your mortgage in full. For your mortgage calc, you'll use the following equation: M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1].

Calculate H = P*J, this is your current monthly interest.

Calculate C = M - H, this is your monthly payment minus your monthly interest, so it is the amount of principal you pay for the month.

Calculate Q = P - C, this is the new balance of your principal of your loan.

P = the payment.

L = the loan value.

c = the period interest rate, which consits of dividing the APR as a decimal by the frequency of payments. ...

n = the total number of payments in the life of the loan (for monthly loan payments this is the loan term in years times twelve)

With given data:

123,500 x 1.05% =$1,296.75 percentage of the fee.

Total mortgage brokerage fees

$1,296.75 + $300 =$1,596.75

Thus, Total mortgage brokerage fees is $1,596.75. Thus, option c is correct.

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The number of games cole can play $12.5 to enter and $1.5 to play each game  by subtracting and dividing with $35 is 15 games.

The total money cole have is $35

To enter an amusement parks it costs around $12.5

so, remaining money by subtracting = 35-12.5 = $22.5

so, by dividing the remaining money with $1.5 paid per each game gives how many games does cole can play.The number of games cole can play $12.5 to enter and $1.5 to play each game  by subtracting and dividing with $35 is 15 games. By dividing the remaining money with $1.5 paid per each game gives how many games does cole can play. Total number of games does cole can play is 22.5/1.5 = 14 games.

Therefore , the number of games cole can play are 14 games exactly.

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When u, v are nonzero vectors, then span{u, v} contains the line through u and the origin, as well as the line through v and the origin, this statement is false.

The span of two nonzero vectors, u and v, is the set of all linear combinations of u and v. This can be a line, a plane, or even the entire space, depending on the vectors u and v. In general, the span of two nonzero vectors does not contain the line through each vector and the origin, unless the two vectors are collinear (i.e. they lie on the same line).

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The length of Q'R' is 5 * 5 = 25.

The steps to find the measure of Q'R' are:

So, the measure of Q'R' is 25.

This method is applicable for finding the length or width of a dilated figure when the original length or width and the scale factor are given. The formula to find the length (or width) of a dilated figure is: length (or width) of dilated figure = scale factor * length (or width) of original figure. The formula for finding the length or width of a dilated figure is a basic concept in geometry and is widely used in solving related problems.

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Answer:

$400

Step-by-step explanation:

25% = 0.25

320 times 0.25 = $80

$320 + $80 = $400

So, the Johnsons set aside $400 in their budget for food for the party.

Answer: 40.75

Step-by-step explanation:

The x-intercept of the composition is x = -1/2.

Remember that a linear function can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If a liear function passes through two points (x₁, y₁) and (x₂, y₂), then the  slope is:

a = (y₂ - y₁)/(x₂ - x₁)

For g(x) we can use (-1, 2) and (1, 6), the slope is:

a = (6 - 2)/(1 + 1) = 2

Then the function is something like:

g(x)=  2x + b

To find the value of b, we use again the point (1, 6)

g(1) = 6 = 2*1 + b

      6 - 2 = b

         4 = b

So:

g(x) = 2x + 4

Now the same for h(x), we can use the points (-1, -1) and (1, 7), we will get:

a = (7 + 1)/(1 + 1) = 4

h(x) = 4x + b

Using the point (1, 7)

h(1) = 7 = 4*1 + b

        7 - 4 = b

        3 = b

h(x) = 4x + 3

The composition is:

g( h(x)) = 2*h(x) + 4

           = 2*(4x + 3) + 4

            = 8x + 10

The x-intercept is the value of x such that:

0 = 8x + 4

-4 = 8x

-4/8 = x

-1/2 = x

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