Tama spent 25% of his money. Which fraction represents this percentage?

Answer:

c=(0,-9)

Step-by-step explanation:

A function g is said to be even if \(g(x) = g(-x)\).

The statements about the function that are true, are:

\(g(1) = 1\)

\(g(-1) = 1\)

\(g(0) = 0\)

From the question, we have the following points:

\((x_1,y_1) = (-2.3,5)\)

\((x_2,y_2) = (0,0)\)

\((x_3,y_3) = (2.3,5)\)

We can assume that the function is an even function because the function satisfies the condition of an even function at:

\(g(-2.3) = g(2.3) = 5\)

\((x_2,y_2) = (0,0)\) means that:

\(g(0) = 0\)

From the list of options:

\(g(1)= -1\)

\(g(0) = 0\)

\(g(4) = -2\)

\(g(1) = 1\)

\(g(-1) = 1\)

The true options are:

\(g(1) = 1\)

\(g(-1) = 1\)

\(g(0) = 0\)

They are true because:

\(g(0) = 0\) represents point \((x_2,y_2) = (0,0)\)

\(g(1) = 1\) and \(g(-1) = 1\) satisfy the condition of an even function \(g(1) = g(-1) = 1\)

See attachment for the graph of the function.

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Answer:

(-2)

Step-by-step explanation:

We have to find the determinant of the given matrix,

\(A=\begin{bmatrix}(a-1) & (a^2-a+1)\\ (a+1) & (a^2+a+1)\end{bmatrix}\)

det A = (a - 1)(a² + a + 1) - (a + 1)(a² - a + 1)

         = a(a² + a + 1) - 1(a²+ a + 1) - a(a² - a + 1) - 1(a² - a + 1)

         = a³ + a² + a - a² - a - 1 - a³ + a² - a - a² + a - 1

         = (a³ - a³) + (-a² + a² - a² - a²) - 1 - 1

         = -2

Therefore, determinant of the given matrix is (-2).

The domain of a function is defined as the set of input values a function can take.

In the case of our function, the domain is all the values contained in the ellipse on the left.

These values are

which is our domain. The answer we got matches choice B; therefore, choice B is the correct answer.

If these conditions are met, the sampling distribution of x will be approximately normally distributed. This is helpful in statistical analyses, as it allows us to make inferences about the population mean using the properties of the normal distribution.

The sampling distribution of x (the sample mean) will be approximately normally distributed if certain conditions are met. These conditions are based on the Central Limit Theorem (CLT), which states that:

1. The sample size (n) is large enough, typically n > 30. This ensures that the sampling distribution of x becomes more normally distributed as the sample size increases.
2. The population from which the sample is drawn is either normally distributed or the sample size is large enough to compensate for non-normality.

The sampling distribution of x overbarx (the sample mean) will be approximately normally distributed if certain conditions are met. These conditions include:
1. The population distribution must be normal or approximately normal.
2. The sample size should be large (typically n > 30).
3. The samples should be randomly selected from the population.

If these conditions are met, the sampling distribution of x will be approximately normally distributed. This is helpful in statistical analyses, as it allows us to make inferences about the population mean using the properties of the normal distribution.

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The exponential decay model for this situation is P(t) = 200,000 * (1 - 0.03)^t

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

We need to Write the percent as a fraction in simplest form

16.24%

So, we can rewrite it as;

16.24 / 100

16 and 24/100 or 16 6/25

So the percent as a fraction is 16 6/25

We are given that;

Population in 1992=200000

Time=6years

Rate=3%

To write an exponential decay model to represent this situation, we can use the formula:

P(t) = P * (1 - r)ᵗ

where P(t) is the population after t years, P is the initial population, r is the annual rate of decline as a decimal, and t is the number of years. In this case, the initial population P is 200,000, the annual rate of decline r is 0.03 (since the population declines by 3% each year), and t is the number of years from 1992, so t = 0 corresponds to 1992 and t = 6 corresponds to 1998.

P(t) = 200,000 * (1 - 0.03)^t

where t is the number of years from 1992 to 1998.

Therefore, by the given percent answer will be P(t) = 200,000 x (1 - 0.03)^t

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The cost to border the outside of the mural using 1-centimeter square tiles is 600 dollars.

The area of Rectangle is length times of width.

We have been given that a rectangular mural has a length of 90 centimeters and a width of 30 centimeters less than its length.

Length = 90 cm

Width = 90 - 30 = 60 cm

The formula to calculate the perimeter of a rectangle,

Perimeter = 2(length + breadth)

Perimeter = 2(90 + 60)

Perimeter = 2(150)

Perimeter = 300

Therefore, the cost to border the outside of the mural using 1-centimeter square tiles costs $2 each.

= 300 x 2

= 600 dollar

Hence, the cost to border the outside of the mural using 1-centimeter square tiles is 600 dollars.

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Answer: x=8

Step-by-step explanation:

3(x+4) = 36

3x+12= 36

3x-12= -12

3x = 24

— —

3 3

X=8

Answer:2.0 m/s,south

Step-by-step explanation:

Firslty, we need to find the function, whcih we can do by substituting one into the other:

Now, for the domain we have more complicated approach.

We first have to find the domain for both f(x) and g(x).

The domain of f(x) is all real number, because it is a quadratic polynomial.

The domain of g(x) is all the real numbers except the x values that makes the square root interior negative, so all real numbers so that:

Now, the domain of the composite function f(g(x)) is the set of all the values of x in the domain of g(x) such that the corresponding g(x) is in the domain of f(x).

Since the domain of f(x) is all real numbers and g(x) is a real number function, all the values of g(x) will be in the domain of f(x), so we just need to check the values of x that are in the domain of g(x).

The domain of g(x), as we saw, is:

And any value of x will give a g(x) that will be in the domain of f(x) so, the domain of f(g(x)) is:

So, the correct alternative is:

Isaac need to invest $ 36720.

Given,

Isaac is going to invest in an account paying an interest rate of 6.3% compounded monthly.

and,  the value of the account to reach $57,000 in 7 years.

To find the how much would Isaac need to invest.

Now, According to the question:
Let x be the invest in an account.

Based on the given conditions,

formulate:

x . \((\)1 + 6.3%/ 12\()^7^.^1^2\) = 57000

Solve the equation

x . (1 + 0.063/12\()^7^.^1^2\) = 57000

Convert decimals to integers

x . (1 + 63/12000\()^7^.^1^2\) = 57000

Reduce the fraction

x . (1 + 21/4000\()^7^.^1^2\) = 57000

x . (\(\frac{4000+21}{4000})^8^4\) = 57000

Calculate the sum or difference

x . (4021 / 4000\()^8^4\) = 57000

x = \(\frac{57000}{(\frac{4021}{4000})^8^4 }\)

Simplify using exponent rule with same exponent :

\((ab)^n = a^n . b^n\)

x = \(\frac{57000 . 4000^8^4}{4021^8^4}\)

Solve the above equation, we get

x = 36720

Hence, Isaac need to invest $ 36720

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Answer:

B. 2.618 units

Step-by-step explanation:

the arc length = (5π/6) / 2π × 2×3.14×1

= 5/12 × 6.28

= 31.4/ 12

= 2.618 units

The arc length is = 2.618 units

Arc measure is a degree measurement, equal to the central angle that forms the intercepted arc. Arc length is a fraction of the circumference of the circle.

Given : r=1, \(\theta\)= 5π/6

Now, arc length

= \(\theta\)/ 2π * 2πr

= (5π/6) / 2π × 2×3.14×1

= 5/12 × 6.28

= 31.4/ 12

= 2.618 units

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H0: p1 ≥ p2 (Null hypothesis: Proportion of ADHD-diagnosed students in School A is equal to or greater than in School B)

Null Hypothesis: The proportion of students diagnosed with ADHD in School A is equal to or greater than the proportion of students diagnosed with ADHD in School B.

Symbolically, the null hypothesis can be stated as:

H0: p1 ≥ p2

Where:

H0: Null Hypothesis

p1: Proportion of students diagnosed with ADHD in School A

p2: Proportion of students diagnosed with ADHD in School B

In other words, the null hypothesis assumes that there is no significant difference or that School A may have an equal or higher proportion of students diagnosed with ADHD compared to School B.

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Answer:

-6

Step-by-step explanation:

9=5(3)+[?] means that [?] = -6

Answer:

y = 5x - 6

Step-by-step explanation:

Slope of the parallel lines are same

So, m= 5

(3,9)

Equation: y - y1 = m(x -x1)

y - 9 = 5(x - 3)

y - 9 = 5x - 3*5

y -9 = 5x -15          {add 9 to both sides}

y - 9 + 9 = 5x - 15 + 9

y = 5x - 6

The hypotheses for the test are H₀: σ₁² = σ₂² and H₁: σ₁² ≠ σ₂². This is a two-tailed test to assess if there is a difference in the standard deviations of sound levels between the areas designated as "casualty doors" and operating theaters. The claim being investigated is whether or not there is a difference in the standard deviations.

The hypotheses for the test are:

H₀: σ₁² = σ₂² (There is no difference in the standard deviations of the sound levels between the areas designated as "casualty doors" and operating theaters.)

H₁: σ₁² ≠ σ₂² (There is a difference in the standard deviations of the sound levels between the areas designated as "casualty doors" and operating theaters.)

This hypothesis test is a two-tailed test because the alternative hypothesis is not specifying a direction of difference.

To substantiate the claim that there is a difference in the standard deviations, we will conduct a two-sample F-test at a significance level of 0.10, comparing the variances of the two groups.

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The chords, inscribed angles, and central angles in the figure has been identified below.

A chord is a line segment that has both endpoints that lies on the circumference of a circle.

An inscribed angle can be defined as an angle that is formed by two chords in a circle, and having its vertex on the circumference of the circle.

A central angle is an angle that has its vertex at the center of the circle and it is formed by two radii of the circle.

1. The chords in the circle are: DE and EF

Inscribed angle is: angle DEF

Central angle are: angle DCF

2. The chords in the circle are: RS, ST, and SU

Inscribed angle are: angles STR, SRT, SRT, and RSU

Central angle are: angles TCU, SCT, SCR, and RCU

3. The chords in the circle are: DG and EF

Inscribed angle are: angles DGF and GEF

Central angle is: none

4. The chord in the circle is: AE

Inscribed angles are: none

Central angle is: angles DCE, ACB, BCE, and BCD

5. m<DGE = 1/2(84)

m<DGE = 42°

6. m<EFD = 1/2(84)

m<EFD = 42°

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Steffensen's method is a modified form of the fixed point iteration method that can provide faster convergence for some functions. If you specifically want to use Steffensen's method, please let me know, and I'll provide a modified subroutine accordingly.

To determine an interval [a, b] on which fixed point iteration will converge, we need to analyze the behavior of the given function in that interval. Since you haven't provided the function or equation in your question, I'll assume you have the equation and can substitute it into the following explanations.

To find a suitable interval [a, b] for convergence, you can follow these steps:

Choose an initial guess value of p0 for the fixed point.

Compute the function value f(p0) at the initial guess.

Compute the derivative f'(p0) at the initial guess.

Check if the absolute value of the derivative |f'(p0)| is less than 1 in the interval [a, b]. If it is, then the fixed point iteration will converge in that interval.

If |f'(p0)| < 1, expand the interval around p0 until you find an interval [a, b] where |f'(p0)| < 1 for all values in [a, b].

Once you have determined a suitable interval for convergence, you can proceed with the fixed point iteration to find a fixed point accurate within 10^(-5). The fixed point iteration method involves repeatedly applying a function transformation until convergence is achieved. The iteration formula is typically of the form:

p(i+1) = g(p(i))

where p(i) is the current approximation and g(p) is a function that transforms p.

Here's an example implementation of a MATLAB subroutine that uses the fixed point iteration method:

Matlab

Copy code

function [p, flag] = fixed-point iteration(fun, p0, tol, max)

   % Inputs:

   %   - fun: The function to find the fixed point of.

   %   - p0: The initial guess for the fixed point.

   %   - tol: The tolerance for convergence.

   %   maxt: The maximum number of iterations allowed.

   % Outputs:

   %   - p: The approximation of the fixed point.

   %   - flag: A flag indicating the convergence status (1: converged, 0: not converged).

   p = p0;

   flag = 0;

   for i = 1:maxIt

       p_prev = p;

       p = fun(p_prev);

       if abs(p - p_prev) < tol

           flag = 1;

           break;

       end

   end

   if flag == 0

       fprintf('Fixed point iteration did not converge within the maximum number of iterations.\n');

   end

end

You can use this subroutine by providing the appropriate function handle fun, initial guess p0, tolerance tol, and a maximum number of iterations max. It will return the approximation of the fixed point p and a convergence flag.

Please note that Steffensen's method is a modified form of the fixed point iteration method that can provide faster convergence for some functions. If you specifically want to use Steffensen's method, please let me know, and I'll provide a modified subroutine accordingly.

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Answer: D. The quadratic function has two distinct real zeros.

There are no complex roots as a quadratic's roots are maxed out at 2. The fundamental theorem of algebra says that if you have an nth degree polynomial, then the max number of real roots is n.

This quadratic's roots are distinct because the two x intercepts are in different places. Each x intercept is a root.

The gradient of the curve at point A to 1 is 0.4. The slope of tangent is equivalent to the slope of the curve.

The tangent line to a curve at a point in geometry is the straight line that best approximates (or "clings to") the curve at that point. As the second point approaches the first, it may be considered the limiting position of straight lines passing through the given point and a nearby point of the curve.

The tangent cuts the curve at A.

The coordinate of A is (8,3). The tangent passes through the point (1,0.2).

The slope of the points (x₁, y₁) and (x₂, y₂) is [(y₂ - y₁)/(x₂ - x₁)

The slope of the tangent is (0.2-3)/(1-8) = 0.4.

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Answer:

Option 2

Step-by-step explanation:

Given :

\(\frac{xy^{-6} }{x^{-4}y^{2} }\)

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

Applied Rule :

\(\frac{x^{a} }{x^{b} } = x^{a-b}\)

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

Solving :

⇒ To remove negative exponents, bring to the opposite side (e.g. if in the denominator, bring to the numerator)

⇒ \(\frac{x(x^{4}) }{y^{2}(y^{6}) }\)

Answer:

Option (2).

Step-by-step explanation:

This question is incomplete; here is the complete question and find the figure attached.

In the diagram of a circle O, what is the measure of ∠ABC?

27°

54°

108°

120°

m(minor arc \(\widehat {AC}\)) = 126°

m(major arc \(\widehat {AC}\)) = 234°

By the intersecting tangents theorem,

If the two tangents of a circle intersect each other outside the circle, measure of angle formed between them is half the difference of the measures of the intercepted arcs.

m∠ABC = \(\frac{1}{2}[m(\text {major arc{AC})}-m(\text{minor arc} {AC})]\)

             = \(\frac{1}{2}(234-126)\)

             = 54°

Therefore, Option (2) will be the answer.

Answer:

B.

Step-by-step explanation:

h = 11.9 cm

cos = adjacent/ hypotenuse

therefore:

cos(24) = h/ 13

rearrange:

h = 13cos(24)

put into calculator:

h = 11.8760...

rounded to one decimal point:

h = 11.9cm

The matrix A of T

a. \(A = [ 0 -1 ]\)

b. \(A = [ 0 -1 ]\)

c. \(A = [ 1/sqrt(2) 1/sqrt(2) ]\)

d. \(A = [ -1/sqrt(2) 1/sqrt(2) ]\)

To find the matrix A of the reflection transformation T in the line \(y = -x\), we can use Theorem 2.6.2 as follows:

Let e1 = [1 0] and e2 = [0 1] be the standard basis vectors of R2. Then, the images of these basis vectors under T are:

\(T(e1) = [-1 0]\) and \(T(e2) = [0 -1]\)

The matrix A of T with respect to the standard basis is:

\(A = [T(e1) T(e2)] = [ -1 0 ]\)

\([ 0 -1 ]\)

To find the matrix A of the transformation \(T(x) = -x\) for each x in R2, we can use Theorem 2.6.2 as follows:

Let e1 = [1 0] and e2 = [0 1] be the standard basis vectors of R2. Then, the images of these basis vectors under T are:

\(T(e1) = [-1 0]\) and \(T(e2) = [0 -1]\)

The matrix A of T with respect to the standard basis is:

\(A = [T(e1) T(e2)] = [ -1 0 ]\)

\([ 0 -1 ]\)

To find the matrix A, we can use Theorem 2.6.2 as follows:

Let e1 = [1 0] and e2 = [0 1] be the standard basis vectors of R2. Then, the images of these basis vectors under T are:

\(T(e1) = [1 1] / sqrt(2)\)  and \(T(e2) = [-1 1] / sqrt(2)\)

The matrix A of T with respect to the standard basis is:

\(A = [T(e1) T(e2)] = [ 1/sqrt(2) -1/sqrt(2) ]\)

\([ 1/sqrt(2) 1/sqrt(2) ]\)

d. To find the matrix A, we can use Theorem 2.6.2 as follows:

Let e1 = [1 0] and e2 = [0 1] be the standard basis vectors of R2. Then, the images of these basis vectors under T are:

\(T(e1) = [1 -1] / sqrt(2)\) and \(T(e2) = [1 1] / sqrt(2)\)

The matrix A of T with respect to the standard basis is:

\(A = [T(e1) T(e2)] = [ 1/sqrt(2) 1/sqrt(2) ]\)

\([ -1/sqrt(2) 1/sqrt(2) ]\)

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Answer:

Kindly check explanation and attached picture

Step-by-step explanation:

Given the data on the number of pages read by each of 20 students last summer :

163, 170, 171, 173, 175, 205, 220, 220, 220, 253, 267, 281, 305, 305, 305, 355, 371, 388, 402, 431

Using an online histogram plotter, the plotted histogram can be found in the picture attached.

With frequency on the y-axis and class on the x - axis.

Class 160 - 220 has the highest frequency of 6 students while 400 - 460 has the least with 2

Answer:

The average rate of change of a function over an interval is found by taking the difference between the function's values at the endpoints of the interval and dividing by the length of the interval. In this case, we have:

f(1) = -3(1)^3 + 7(1) = -3 + 7 = 4

f(3) = -3(3)^3 + 7(3) = -27 + 21 = -6

The average rate of change over the interval from x=1 to x=3 is therefore (-6 - 4) / (3 - 1) = -10 / 2 = -5.

To label your answer, you could write something like: "The average rate of change of the whale's movement over the interval from x=1 to x=3 seconds is -5 meters/second."

Step-by-step explanation:

Given: 3x - 6 + 4b+ 5 + 7 -2x

x - 6 + 4b + 12

x +6 + 4b

In scientific notation, a number is written as the base number times ten raised to a power. The base number, known as the significand, is also referred to as the mantissa.

The term mantissa is used for the fractional part of a common logarithm as well.

The mantissa is the fractional part of a logarithm. In the context of scientific notation, the mantissa refers to the base number, which is multiplied by 10 raised to a certain power to represent a number.

In other words, the mantissa is the significant digits of a number, excluding the leading and trailing zeros, expressed as a decimal fraction between 1 and 10. For example, in the number 3.24 x 10^5, the mantissa is 3.24.

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Answer:

13/20 of a mile

Step-by-step explanation:

2/5 x 4 = 8/20

1/4 x 5 = 5/20

8/20 + 5/20 = 13/20

Answer:

Step-by-step explanation:

To find the time of the commercial plane ride from Vancouver to Regina, we can follow these steps:

Step 1: Determine the speed of the commercial airplane.

Since the jet plane travels two times the speed of the commercial airplane, we can let the speed of the commercial airplane be 'x' km/h. Therefore, the speed of the jet plane would be 2x km/h.

Step 2: Calculate the time taken by the jet plane.

Using the formula Time = Distance / Speed, we can calculate the time taken by the jet plane.

The distance between Vancouver and Regina is 1,730 km, and the speed of the jet plane is 2x km/h. Therefore, the time taken by the jet plane is:

Time _ jet = 1730 km / (2x km/h) = 865 / x hours.

Step 3: Calculate the time taken by the commercial airplane.

According to the problem, the commercial airplane takes 140 minutes longer than the jet plane. We need to convert this additional time to hours.

140 minutes = 140/60 = 2.33 hours.

The time taken by the commercial airplane would be the time taken by the jet plane plus the additional 2.33 hours:

Time _ commercial = Time _ jet + 2.33 hours = (865 / x) hours + 2.33 hours.

Step 4: Solve for the time of the commercial plane ride.

Now, we need to find the value of 'x' that satisfies the given conditions. Since we know that the distance between Vancouver and Regina is 1,730 km, we can set up the following equation:

(865 / x) hours + 2.33 hours = Time _ commercial.

By substituting the known values, we have:

(865 / x) hours + 2.33 hours = Time _ commercial.

Solving this equation will give us the value of 'x' and, subsequently, the time of the commercial plane ride from Vancouver to Regina.

Answer:

the third one

Step-by-step explanation:

Answer:

Option 3 is the correct answer

Step-by-step explanation:

The surface area of a prism is the area of the full net.

The area of the full net is the sum of the areas of each part

For the given net, there are three rectangles, and two triangles.

The area for rectangles and triangles are given by the following formulas:

\(A_{rectangle}=base*height\)

\(A_{triangle}=\frac{1}{2}*base*height\)

It is important to recognize that due to the fact that the 3-D shape is a prism, the two triangles are congruent, and have exactly the same dimensions and area.

Looking at the options:

Option 1 has three products added together.  This would be the base time height of each of the three rectangles.  It does not include the area for either of the triangles.

Option 2 does have an extra term in front with 3 numbers multiplied together.  It most closely resembles 2 times the product of the base and height of the triangle, but recall the area for a triangle is one-half of the base times height (this may make more sense when looking at option 3).  This over-calculates the area of the triangle, and then doubles that over-calculated area (to match the second triangle)

Option 3 has an extra term in front with the number 2 times a parenthesis with 3 terms.  These three terms represent the "one-half" from the formula for the area of a triangle, and the base and height of the triangle.  The 2 in front of the parentheses represents that there are two of those triangles, both with that area.  This correctly calculates the area of the net, and thus, the surface area of the triangular prism.

Option 4 has an extra term in front, similar to option 3 which calculates the area of one triangle correctly, but fails to account for the area of the second triangle.

Option 3 is the correct answer.

The coordinate rule for reflecting a point across the y-axis is (x, y)→(-x, y).

While graphing trapezoid WXYZ and its image after a reflection across the y-axis in the coordinate plane,

the coordinates of W are (-1, 3), those of X are (-1, -4), those of Y are (-5, -4), and those of Z are (-3, 1).

The following are the graphs of trapezoid WXYZ and its image after a reflection across the y-axis:

Part A Graph trapezoid WXYZ and its image after a reflection across the y-axis.

Part B Determine the coordinate rule for reflecting a point across the y-axis.

In general, to reflect a point (x, y) across the y-axis, one simply negates the x-coordinate, resulting in the point (-x, y).

Therefore, the coordinate rule for reflecting a point across the y-axis is (x, y)→(-x, y).

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