the question is in the photo :)

Answer: Explicit Rule: a_n=30,000 • 2^n-1

Recursive Rule: a_n = 2a_n-1; a_1 = 30,000

Step-by-step explanation: the explicit rule for a geometric sequence is a_n = a_1 • r^n-1 and the recursive rule is a_n= r • a_n -1.
a_1 is the first term of the sequence, which is this case is 30,000. R is the common ration, which is 2 since it doubles each time. Substitute those numbers into the formulas and that’s what you’ll get. Hope this helps. God bless you!!!

Answer:

1/6

Step-by-step explanation:

hope this helps!!

Answer:

1/6

Step-by-step explanation:

1/2 ÷ 3 → 1/2 ÷ 3/1     *Let's write both as fractions to make things easier

1/2 ÷ 3/1  → 1/2 · 1/3    *Change the division sign into multiplication and turn      3/1 into its reciprocal which is 1/3 (aka just change the numerator into denominator and denominator into numerator)

1/2 · 1/3 = 1/6   *Multiply straight across! So, 1 · 1 = 1 (numerator) over 2 · 3 = 6 (denominator)

Answer:

$3.30

Step-by-step explanation:

Shirt price * city sales tax = sales tax amount on shirt. $39.95 * 0.0825 = $3.30

Answer:

Right scalene

Step-by-step explanation:

Answer:

1 pound for $3.75

if you divide $15.63 by 4, you would get 3.9075, which is more than $3.75

Step-by-step explanation:

Statements are False: 1. interchanging rows changes determinant. 2. determinant zero not implies specific rows. 3. determinant not product of diagonal entries. 4. determinant is scalar not matrix.

What is matrix ?

A matrix is a rectangular array of numbers or other mathematical objects, typically arranged in rows and columns. Matrices are often denoted using capital letters, such as A, B, and C. Each element of a matrix is identified by its row and column indices,

1) False, If two row interchanges are made in succession, the determinant of the new matrix is the negative of the determinant of the original matrix.

2) False, If the determinant of a matrix is zero, it does not necessarily mean that two rows or two columns are the same or a row or column is zero, it only means that the matrix is singular, i.e. non-invertible and it also can mean that the matrix is linearly dependent.

3) False, The determinant of a matrix is not always equal to the product of the diagonal entries, it is a scalar value calculated through a specific method called matrix expansion which is based on the entries of the matrix and it depends on the size of the matrix.

4) False, The determinant of a matrix is a scalar value, it cannot be equal to another matrix.

Statements are False: 1. interchanging rows changes determinant. 2. determinant zero not implies specific rows. 3. determinant not product of diagonal entries. 4. determinant is scalar not matrix.

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Answer:

I belive the answer is 3.

Step-by-step explanation:

35-2x4^2

35-2x16

35-32

3

Answer:

\(1225-140x^4+4x^8\)

Step-by-step explanation:

(35-2x^4)^2 is a form of \((a-b)^2=a^2+b^2-2ab\)

Applying this formula, we get 1225+4x^8-140x^4

Answer:

b)

x= 5

Step-by-step explanation:

4x = 20

:4

x=5

Based on the calculations, the sum of the areas of the rectangles is equal to: A. 0.25 square unit.

Mathematically, the area of a rectangle can be calculated by using this formula;

A = LW

Where:

By critically observing the figure (see attachment), we can logically deduce the following information:

Width of rectangle A = 2 units

Width of rectangle B = 2 units.

Width of rectangle C = 4 units.

Next, we would determine the length and area of each of the rectangle.

The length of the first rectangle is given by:

Length of rectangle, y = 3^-x

Length of rectangle, y(0) = 3⁻⁰ = 1 units.

Length of rectangle, y = 3^-x

Length of rectangle, y(2) = 3⁻² = 0.11 unit.

Area of first rectangle = 2(0.11)

Area of first rectangle = 0.22 square unit.

For the second rectangle, we have:

Length of second rectangle, y = 3^-x

Length of second rectangle, y(4) = 3⁻⁴ = 0.012 unit.

Area of second rectangle = 2(0.012)

Area of second rectangle = 0.025 square unit.

For the third rectangle, we have:

Length of third rectangle, y = 3^-x

Length of third rectangle, y(8) = 3⁻⁸ = 0.00015 unit.

Area of third rectangle = 4(0.00015)

Area of third rectangle = 0.0006 square unit.

Now, we can calculate the sum of the areas of the rectangles:

Total area = 0.22 square unit + 0.025 square unit + 0.0006 square unit.

Total area = 0.246 ≈ 0.25 square unit.

Total area of rectangle = 0.25 square unit.

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Complete Question:

Figure 3 shows the graph of y = 3^−x and three inscribed rectangles. What is the sum of the areas of the rectangles?

[a] 0.25

[b] 0.50

[c] 2.45

[d] 6.26

[e] 12.68

As per the remainder that the greatest possible value of 17

The term remainder in math defined as if a number is not completely divisible by another number  then we are left with a value once the division is done

Here we have if x is a positive integer, then r is the remainder when x is divided by 4 and r is the remainder when x is divided by 9.

As we all know that the remainder is always smaller than the divisor.

Here we have also know that it will be 0 if the dividend is evenly divisible or a positive integer less than the divisor.

So, when we divided by 4 then the largest remainder will be 3 and then here we have to  divided by 9, then the largest remainder will be written as

=> r² + R = 32 + 8

=> 9 + 8 = 17

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To solve the triangle using the Law of Sines, we can use the following formula:

\(\(\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}\)\(\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}\)\)

Given that \(\(\angle A = 38^\circ\), \(\angle C = 73^\circ\), and \(b = 19\),\) we can substitute these values into the formula and solve for the remaining sides \(\(a\) and \(c\).\)

\(\(\frac{a}{\sin(38^\circ)} = \frac{19}{\sin(B)}\) (1)\)

\(\(\frac{c}{\sin(73^\circ)} = \frac{19}{\sin(B)}\) (2)\)

From equation (1), we can solve for \(\(\sin(B)\):\)

\(\(\sin(B) = \frac{19}{a} \cdot \sin(38^\circ)\)\)

Substituting this value into equation (2), we can solve for \(\(c\):\)

\(\(\frac{c}{\sin(73^\circ)} = \frac{19}{\frac{19}{a} \cdot \sin(38^\circ)}\)\)

Simplifying, we get:

\(\(c = a \cdot \frac{\sin(73^\circ)}{\sin(38^\circ)}\)\)

Now we have expressions for both \(\(a\) and \(c\).\)

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The x and y values of the intersections are:

For t = u: (x, y) = (5 - (4/2u^2), -4/u^3 + 4u + 1)

For t = -u: (x, y) = (5 - (4/2u^2), -4/u^3 - 4u + 1).

To find the t-values at which the curve given by the parametric equations x = 5 - (4/2t^2) and y = -4/t^3 + 4t + 1 intersects itself, we need to find the values of t for which the x-coordinates and y-coordinates are the same.

Setting the x-coordinates equal to each other:

5 - (4/2t^2) = 5 - (4/2u^2),

- (4/2t^2) = - (4/2u^2).

-1/t^2 = -1/u^2.

u^2 = t^2.

u = ±t.

Now, let's set the y-coordinates equal to each other:

-4/t^3 + 4t + 1 = -4/u^3 + 4u + 1.

-4/t^3 = -4/u^3.

t^3 = u^3.

t = ±u.

Therefore, the t-values at which the curve intersects itself are t = ±u.

To find the corresponding x and y values of the intersection, we can substitute these t-values back into the parametric equations:

For t = u:

x = 5 - (4/2t^2) = 5 - (4/2u^2)

y = -4/t^3 + 4t + 1 = -4/u^3 + 4u + 1.

For t = -u:

x = 5 - (4/2t^2) = 5 - (4/2(-u)^2) = 5 - (4/2u^2)

y = -4/t^3 + 4t + 1 = -4/(-u)^3 + 4(-u) + 1 = -4/u^3 - 4u + 1.

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Answer:   506.8 (1dp)

Step-by-step explanation:

400 x 1.07^3.5 = 506.8  

i think this is the answer

the noun press itself is already a noun. though the word can also be expressed as a verb, (for example: he pressed his face against the glass) it can also be a noun (for example: the incident was not reported to the press).

hope this helps. :)

have a great day! stay safe, happy, and healthy!

Answer:

A=29.12ft^2

Step-by-step explanation:

first, find the area of the triangle and semicircle separately, then add them together to find the total area of the figure:

area of a triangle: 1/2bh

1/2(6)(8)=24ft^2

area of a circle: πr^2

(**we're using 3.14 instead of pi, and it's a semicircle)

1/2(3.14)(4)^2

1/2(3.14)(16)

1/2(50.24)

25.12ft^2

total area of the figure:

24+25.12=29.12ft^2

Answer: 49.12 ft²

Step-by-step explanation:

This figure is composed of

First, find the area of the half-circle.

The area of a full circle is π · r², but since it's only half a circle, we divide that by half, resulting in (π · r²)/2

Therefore, the area of the half-circle is:

(3.14 · 4²)/2 = (3.14 · 16)/2 = 50.24/2 = 25.12 ft²

Second, find the area of the right triangle.

The area of a triangle = ½bh.

Therefore, the area of the triangle is:

½ · 6 · 8 = ½ · 48 = 24 ft²

Add the two areas together:

24 + 25.12 = 49.12 ft²

Answer: They are parallel and congruent.

Step-by-step explanation:

The translation (x, y)= (x+1, y-4) will translate the entire figure 1 unit right and 4 units down thus the distance AA' = BB" so both will be parallel as well as congruent.

Transformation is rearranging a graph by a given rule it could be either increment of coordinate or decrement or reflection.

If we reflect any graph about y = x then the coordinate will interchange it that (x,y) → (y,x).

As per the given translation rule,

(x, y)= (x+1, y-4)

Suppose a random triangle as shown below,

The translation according to the given rule has been translated.

Since the entire figure shifts thus the AA' = BB" and AA' || BB".

Hence "The translation (x, y)= (x+1, y-4) will translate the entire figure 1 unit right and 4 units down thus the distance AA' = BB" so both will be parallel as well as congruent".

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Answer:

I count 10 triangles.....

Answer:

3

Step-by-step explanation:

t think it's the because everything else is 4 sided

The probability that the dart lands inside the triangle is \(\frac{1}{4}\).

we know that

Probability = \(\frac{Favourable outcomes}{total outcomes}\)

Probability = \(\frac{162}{648} = \frac{1}{4}\)

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Answer:

25%.

Step-by-step explanation:

Answer:

\(\sf \boxed{\sf y = -x^2-x +2 }\)

Step-by-step explanation:

A graph of the quadratic function is given to us and by using the Zeroes , we need to write the function . From the graph , we can sew that , it cuts the x axis on (-2,0) and (1,0) .

Hence , x = -2 and 1 are the zeroes of the function .

In general if we have \(\alpha\) and \(\beta\) as the zeroes of the function , then the quadratic function is given by ,

\(\sf\longrightarrow\gray{ f(x) = (x -\alpha )(x-\beta) }\)

Here the zeroes are -2 and 1 , on substituting the respective values in the formula , we have ,

\(\sf\longrightarrow f(x) = \{ x -(-2)\} ( x -1) \)

Simplify inside the curly brackets ,

\(\sf\longrightarrow f(x) = ( x +2)(x-1) \)

Multiply the two terms ,

\(\sf\longrightarrow f(x) = x ( x -1)+2(x-1) \)

Simplify the brackets ,

\(\sf\longrightarrow f(x) = x^2-x +2x -2 \)

Add the constants and the variables ,

\(\sf\longrightarrow f(x) = x^2+x -2 \)

When the constant of the function is (-1),

\(\sf\longrightarrow\boxed{\blue{\sf y = -x^2-x+2}} \)

Hence the equation of the function is y = -x² -x + 2 .

Answer:

the answer is " y=-3x^2-3x+6"

Step-by-step explanation:

i just took the test

Answer:79y

Step-by-step explanation:

h*6vhvytvt/88ugu

Answer:

Step-by-step explanation:

2(3 + x) = 18 / : 2

3 + x = 9

x = 9 - 3

x = 6

Answer:

x = 6

Step-by-step explanation:

2(3 + x) = 18 ( divide both sides by 2 )

3 + x = 9 ( subtract 3 from both sides )

x = 6

Adjust the parameters as needed, such as the step size (h) and the final x-value (xn), and run the code to obtain the solution for y(x).

The resulting plot will show the solution curve.

To solve the given set of differential equations using the Runge-Kutta method in MATLAB, we need to convert the second-order differential equations into a system of first-order differential equations.

Let's define new variables:

y = y(x)

z = dz/dx

Now, we have the following system of first-order differential equations:

dy/dx = z (1)

dz/dx = -k/(2y) (2)

To apply the Runge-Kutta method, we need to discretize the domain of x. Let's assume a step size h for the discretization. We'll start at x = 0 and proceed until x = infinite.

The general formula for the fourth-order Runge-Kutta method is as follows:

k₁ = h f(xn, yn, zn)

k₂ = h f(xn + h/2, yn + k₁/2, zn + l₁/2)

k₃ = h f(xn + h/2, yn + k₂/2, zn + l₂/2)

k₄ = h f(xn + h, yn + k₃, zn + l₃)

yn+1 = yn + (k₁ + 2k₂ + 2k₃ + k₄)/6

zn+1 = zn + (l₁ + 2l₂ + 2l₃ + l₄)/6

where f(x, y, z) represents the right-hand side of equations (1) and (2).

We can now write the MATLAB code to solve the differential equations using the Runge-Kutta method:

function [x, y, z] = rungeKuttaMethod()

   % Parameters

   k = 1;              % Constant k

   h = 0.01;           % Step size

   x0 = 0;             % Initial x

   xn = 10;            % Final x (adjust as needed)

   n = (xn - x0) / h;  % Number of steps

   % Initialize arrays

   x = zeros(1, n+1);

   y = zeros(1, n+1);

   z = zeros(1, n+1);

   % Initial conditions

   x(1) = x0;

   y(1) = 0;

   z(1) = 0;

   % Runge-Kutta method

   for i = 1:n

       k1 = h * f(x(i), y(i), z(i));

       l1 = h * g(x(i), y(i));

       k2 = h * f(x(i) + h/2, y(i) + k1/2, z(i) + l1/2);

       l2 = h * g(x(i) + h/2, y(i) + k1/2);

       k3 = h * f(x(i) + h/2, y(i) + k2/2, z(i) + l2/2);

       l3 = h * g(x(i) + h/2, y(i) + k2/2);

       k4 = h * f(x(i) + h, y(i) + k3, z(i) + l3);

       l4 = h * g(x(i) + h, y(i) + k3);

       y(i+1) = y(i) + (k1 + 2*k2 + 2*k3 + k4) / 6;

       z(i+1) = z(i) + (l1 + 2*l2 + 2*l3 + l4) / 6;

       x(i+1) = x(i) + h;

   end

   % Plotting

   plot(x, y);

   xlabel('x');

   ylabel('y');

   title('Solution y(x)');

end

function dydx = f(x, y, z)

   dydx = z;

end

function dzdx = g(x, y)

   dzdx = -k / (2*y);

end

% Call the function to solve the differential equations

[x, y, z] = rungeKuttaMethod();

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13

Explanation:

Given: 52 divided by 4​

There should be an equal to sign in order to perform an inverse operation.

Let the answer we get after dividing 52 by 4 = x

52/4 = x

52 divided by 4​ becomes:

52 = 4x

x is multiplied by 4. The inverse operation of multiplication is division.

So, we will divide 4 on both sides of the equation:

52/4 = 4x/4

13 = x

x = 13

The answer is 13

Answer: five hundred thirty seven thousand six hundred ninety nine

Step-by-step explanation:

The correct answer to the given question is "b. Individual Matching."Individual matching is a type of matching that selects the controls based on specific characteristics, one at a time, which matches with the cases of the population.

Explanation: In the case-control study, we compare the histories of two groups, cases and controls, in search of factors that may contribute to the disease's development.  This type of matching is useful in a case-control study where a small sample is chosen, and the investigators are interested in the individual risk factors. The odds ratio examining the association between the exposure (marijuana use) and the disease (lung cancer) in the study is b. 1.56.

Here is the calculation: Odds ratio = (33/167) / (33/367) = 0.1975 / 0.0899 = 2.20 (corrected)Or, Odds ratio = ad/bc = (33 * 367) / (33 * 167) = 6,711 / 5,511 = 1.2171Logarithm of odds ratio = ln (OR) = ln (1.2171) = 0.1956Standard error = sqrt (1/a + 1/b + 1/c + 1/d) = sqrt (1/33 + 1/134 + 1/33 + 1/267) = 0.3421Lower limit of the 95% confidence interval (CI) = ln (OR) - 1.96 x SE = -0.8726Upper limit of the 95% CI = ln (OR) + 1.96 x SE = 1.2638Therefore, the odds ratio examining the association between the exposure (marijuana use) and the disease (lung cancer) in the study is 1.56, as the confidence interval does not include the value 1.0.

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Nine hundred Fifty-Six and three hundreths

900 + 50 + 6 + 3/100

956.03

900+ 50+ 6+ .03

The mean is calculated by summing up all the values in the distribution and dividing it by the total number of values, while the median is the middle value when the data is arranged in ascending or descending order.

Another difference is that the mean is affected by outliers, meaning that extreme values can greatly influence its value. On the other hand, the median is not affected by outliers, as it only depends on the position of the middle value.

Therefore, to summarize, the mean is influenced by all values in the distribution and is affected by outliers, while the median is only influenced by the middle value and is not affected by outliers.

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