Determine if each of the following sets is a subspace of {\mathbb P}_{n}, for an appropriate value of n. Type "yes" or "no" for each answer.
Let W_{1} be the set of all polynomials of the form p(t)= at^{2}, where a is in {R}.
Let W_{2} be the set of all polynomials of the form p(t)= t^{2} + a, where a is in {R}.
Let W_{3} be the set of all polynomials of the form p(t)= at^{2} + at, where a is in {R}

Answer:

3/22

Step-by-step explanation:

There's a very neat trick for this kind of problem.

First, choose a letter to represent the number.

n = 0.1363636...

Observe that there is a 2-digit block that repeats ("36"), but that block does not repeat immediately to the right of the decimal point.  Do two muliplications, one to put the decimal point in front of the repeating block, the other to put the decimal point after the block.

    10n =    1.363636...

1000n = 136.363636...

Here comes the cool part:  subtract the first equation from the second.

990 n = 135  See? The repeating decimal parts, all lined up as they are, subtract to zeros.

Finally, n = 135/990 = 15/110 = 3/22

Answer: B. The reflection preserves the side lengths and angles of the triangle. The dilation preserves angles but not side lengths.

Step-by-step explanation:

Reflections are congruency transformations, but dilations are similarity transformations.

Answer:

46

Step-by-step explanation:

9514 1404 393

Answer:

  C

Step-by-step explanation:

Solve for y to find the inverse:

  x = f(y)

  x = y/3 -2

  x +2 = y/3

  y = 3(x +2)

  f⁻¹(x) = 3(x +2) . . . . the inverse function

Answer:

3-2.5/3+4/3

3-0.833+4/3

3+1.33-0.833

4.33-0.833

3.500

To determine if the new fertilizer is effective, the farmer can use hypothesis testing, specifically a one-sample t-test. This test compares the mean yield of the corn crop using the new fertilizer to the historical mean yield of the corn crop using the old fertilizer.

1. Formulate hypotheses: Set up a null hypothesis (H0) stating that the fertilizer has no effect on yield, and an alternative hypothesis (H1) stating that the fertilizer increases yield.

2. Collect data: The farmer should divide his field into two sections - one with the new fertilizer and one without. He should then measure the corn yield from each section.

3. Determine the test statistic: Calculate the mean yield for each section and find the difference between them.

4. Set a significance level: Choose an acceptable level of Type I error (commonly 5%, represented as α = 0.05).

5. Calculate p-value: Using the appropriate statistical test (e.g., t-test or ANOVA), determine the probability of observing the calculated test statistic or a more extreme value, assuming the null hypothesis is true.

6. Compare p-value to α: If the p-value is less than α, reject the null hypothesis in favor of the alternative hypothesis, indicating that the fertilizer was effective in increasing corn crop yield.

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Answer:

no

Step-by-step explanation:

Answer:

rational number

Answer:

Step-by-step explanation:I don’t know u nerdy boy

To value a four-year coupon bond, we need to calculate the present value of its future cash flows, which include both the periodic coupon payments and the final face value payment. The discount factor is used to discount these cash flows back to their present values.

A. To calculate the price or value of the bond, we first need to determine the present value of the coupon payments. The bond has a face value of $1,000 and a coupon rate of 5%, which means it pays an annual coupon of $50 (5% of $1,000). Assuming annual coupon payments, we discount each coupon payment using the appropriate discount factor for the corresponding year. For example, if the discount factor for year one is 0.95, the present value of the first coupon payment would be $50 * 0.95 = $47.50. We repeat this calculation for each coupon payment and also discount the final face value payment. Finally, we sum up all the present values to obtain the price or value of the bond.

B. The yield to maturity (YTM) of the bond represents the rate of return an investor would earn if they hold the bond until maturity. It is the discount rate that equates the present value of the bond's cash flows to its current market price. To find the YTM, we need to iterate different interest rates until we find the rate that makes the present value of the bond's cash flows equal to its market price. This process involves solving a non-linear equation and can be done using numerical methods or financial calculators/software.

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The equation \(y = -10x + 4\) describes a linear relationship between x and y, with a y-intercept of 4 and a negative slope of -10.

The equation \(y = -10x + 4\) represents a linear function in slope-intercept form, where the coefficient of x is -10 and the y-intercept is 4.

The y-intercept is the value of y when x is 0, which in this case is 4.

It means that the graph of this equation will intersect the y-axis at the point (0, 4).

The slope of -10 indicates that for every unit increase in x, y will decrease by 10 units.

This negative slope means that the line will slope downwards from left to right on a coordinate plane.

By analyzing the equation, we can determine that the line is relatively steep due to the magnitude of the slope.

It indicates a rapid change in y with respect to x.

The equation \(y = -10x + 4\) describes a linear relationship between x and y, with a y-intercept of 4 and a negative slope of -10.

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Answer:

y = 4x + 5

Step-by-step explanation:

The equation of a straight line line is;

y = mx + b

where m is the slope and b is the y-intercept

We start by calculating the slope value by using the slope equation

m = (y2-y1)/(x2-x1)

m = (9+ 7)/(1+ 3) = 16/4 = 4

So we have the equation as;

y = 4x + b

to get the value of b, we substitute the coordinates of any of the two points

let us use (1,9)

9 = 4(1) + b

b = 9-4

b = 5

so, we have the equation of the line as;

y = 4x + 5

Considering the distance between the two points and the scale, the distance between the two homes is of 2,953 miles.

Suppose that we have two points, \((x_1,y_1)\) and \((x_2,y_2)\). The distance between them is given by:

\(D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

In this problem, the points are:

(116, 27) and (33,51).

Hence the distance between them is:

\(D = \sqrt{(116 - 33)^2+(27 - 51)^2}\)

D = 86.4.

Each unit represents 55 kilometers, hence the distance in km is:

D = 86.4 x 55 = 4752 km.

Each km represents 0.621371 miles, hence the distance in miles is:

4752 x 0.621371 = 2,953 miles.

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Answer:

its 2 it is a medium of exchange

Answer:

B

Step-by-step explanation:

It a medium of exchange

The height of the triangle is 1 cm.

What is area?

The amοunt οf space οccupied by a flat (2-D) surface οr an οbject's shape is knοwn as its area.

A planar figure's area is the area that its perimeter enclοses. The quantity οf unit squares that cοmpletely encircle the surface οf a clοsed figure is its area. Square measurements fοr area include cm2 and m2. A shape's area can οnly be measured in twο dimensiοns.

The space fοund within a clοsed shape's perimeter οr limit is referred tο as the "area." Such a shape's geοmetry cοnsists οf at least three sides that are cοnnected tο οne anοther tο fοrm a bοundary. The "area" fοrmula is used tο express such a space symbοlically in mathematics.

Here base length = 24 cm , area of triangle a=12cm²

Now using area of triangle formula A = \(\frac{bh}{2}\) square unit.

=> 12 = \(\frac{24\times h}{2}\)

=> 24 = 24*h

=> h = 1 cm

Hence the height of the triangle is 1 cm.

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Part A:

If a quadratic has only one x-intercept, then that is where the vertex lies. being that the vertex is the highest or lowest point in the quadratic. To sketch, it will open downwards with a single x-cept

Part B:

The graph will be above the x-axis. And having the vertex being at (0,1) as it says its the minimum value. All the minimum means is that its the lowest value of this given parabola.

Part C:

Plot the points of the y-intercept and z-intercepts. Then plot the maximum value is. Connect the dots.

Answer: she must sell 6 large photos and 6 small photos

Step-by-step explanation: and how I knew that is I multiplied 6 40 times and that gives you 240 and if you multiply 6 ten times that gives you 60 so 240 plus 60 is $300

Every convergent sequence in a metric space is Cauchy, which emphasizes the importance of completeness in various results and applications in mathematics.

Every convergent sequence in metric space is Cauchy.To prove: Show that every convergent sequence in metric space is Cauchy.Proof:Let {a_n} be a convergent sequence in a metric space (X, d).

Therefore, there exists an element 'a' in X such that for any ε > 0, there exists an N ∈ ℕ such that for all n ≥ N,d(a_n, a) < ε.It needs to be shown that {a_n} is a Cauchy sequence.

For this, consider any ε > 0, then there exists an N such that for all n ≥ N,d(a_n, a) < ε/2. Now for any m, n ≥ N, by the triangle inequality,d(a_n, a_m) ≤ d(a_n, a) + d(a_m, a) < ε/2 + ε/2 = ε.

It shows that for any ε > 0, there exists an N such that for all m, n ≥ N,d(a_n, a_m) < ε. Therefore, {a_n} is a Cauchy sequence. Hence, proved.

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The simplified polynomial function representing the volume of the metal tray is V(x) = x³ - 3x² + 2x.

To model this problem with mathematics, let x represent the side length of each square.

a. Write expressions for the length, width, and height of the metal tray:
- Length: Since two squares are cut from each side, the length would be x - 2.
- Width: One square is cut from each side for the width, so the expression would be x - 1.
- Height: The height is equal to the side length of the squares removed, which is x.

b. Write and simplify a polynomial function V to represent the volume of the tray:
The volume of a rectangular tray can be calculated by multiplying its length, width, and height. In this case, the polynomial function for the volume V can be written as:
V(x)= Length x Width x Height
V(x) = (x - 2)(x - 1)(x)

Now, let's simplify the expression:

First, multiply the first two expressions:
(x - 2)(x - 1) = x² - 3x + 2

Now, multiply this result by the third expression (x):
V(x) = x(x² - 3x + 2) = x³ - 3x² + 2x

So, the simplified polynomial function representing the volume of the metal tray is V(x) = x³ - 3x² + 2x.

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Answer:

x=5

Step-by-step explanation:

set the first equation to 18. Then add 12 to both sides. Then divide by 6 by both sides. final answer is 5. Hope that helps!

The general solution of the equation (x+1)(1+y²) = 0 can be obtained by solving for y in terms of x. The solutions are y = ±sqrt(-1) and y = ±sqrt(-x-1), where sqrt denotes the square root.

Therefore, the general solution is y = ±sqrt(-x-1), where y can take on any real value and x is a real number.

To find the general solution of the equation (x+1)(1+y²) = 0, we can solve for y in terms of x. First, we set each factor equal to zero:

x + 1 = 0 and 1 + y² = 0.

Solving x + 1 = 0 gives x = -1. Substituting this into the second equation, we have 1 + y² = 0. Rearranging, we get y² = -1. Taking the square root of both sides, we obtain y = ±sqrt(-1).

However, it is important to note that the square root of a negative number is not a real number, so y = ±sqrt(-1) does not have real solutions. Therefore, we need to consider the case when 1 + y² = 0.

Solving 1 + y² = 0 gives y² = -1. Again, taking the square root of both sides, we obtain y = ±sqrt(-1) = ±i, where i is the imaginary unit.

Combining the solutions, we have y = ±sqrt(-x-1) or y = ±i. However, since we are looking for the general solution, we consider only the real solutions y = ±sqrt(-x-1), where y can take on any real value and x is a real number.

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The solution to the system of equations y = 1.5x - 4 and y = -x  is (1.6,-1.6)

The equations are given as: y = 1.5x - 4 & y = -x

The system of linear equations is the set of two or more linear equations involving the same variables. Here, linear equations can be defined as the equations of the first order, i.e., the highest power of the variable is 1. Linear equations can have one variable, two variables, or three variables. Thus, we can write linear equations with n number of variables

Substitute y = -x in the first equation

-x = 1.5x - 4

Collect like terms

-1.5x - x = -4

Any set of values of x1, x2, x2,…xn which simultaneously satisfies the system of linear equations given above is called a solution of the system. If the system of equations has one or more solutions, the equations are called consistent. Also, if the system of equations does not admit any solution, then the equations are called inconsistent.

This gives

-2.5x = -4

Divide both sides by -2.5

x = 1.6

Substitute x = 1.6 in y = -x

y = -1.6

Hence, the solution to the system of equations is (1.6,-1.6).

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Answer:

Percentage increase every year is 9%

Explanation:

If we have a function of the form

then a* 100% is the percent increase.

Now, the function

can be rewritten as

meaning a = 0.09; therefore, the percent increase is

which is our answer!

Answer:

2.48 seconds

Step-by-step explanation:

The given function is

\(y=-60t^2+4t+380\)

When \(y=0\) the ball will be at the ground

\(0=-60t^2+4t+380\)

\(\Rightarrow t=\dfrac{-4\pm \sqrt{4^2-4\left(-60\right)\times 380}}{2\left(-60\right)}\)

\(\Rightarrow t=-2.48,2.55\)

So, the time taken by the rock to hit the ground is \(2.48\ \text{seconds}\).

When there is a multiplication between a term with parenthesis and another term we apply the distributive property:

It says that the parenthesis indicates that the term outside will multiply each of the terms inside it.

For the first parethesis:

- 3(2x + 4) = (-3) · 2x + (-3) · 4

since

(-3) · 2x = -6x

(-3) · 4 = -12

then

- 3(2x + 4) = (-3) · 2x + (-3) · 4

- 3(2x + 4) = -6 x - 12

For the second

– (2x + 4) ​= – 1 (2x + 4)

= ​(-1) · 2x + (-1) · 4

=-2x -4

We can see in this case that both parenthesis are the same, then it is the common factor of - 3(2x + 4) and – (2x + 4) ​,

We can factor it by separating it of each term and letting the remaining terms inside a parenthesis

- 3(2x + 4) – (2x + 4) ​= (2x + 4) ( -3 -1)

= (2x + 4) ( -4)

= -4 (2x + 4)

Answer:

Area: 120m²

Flowers: 600kg

Step-by-step explanation:

we can use Heron's formula to solve for the area.

Heron's formula:

Area of triangle = \(\sqrt{ s(s-a)(s-b)(s-c)}\)

s = 1/2 (a+b+c)

s = 1/2 (10 +24+26)

s = 30

Area of triangle

\(=\sqrt{30(30-10)(30-24)(30-26)} \\=120m^{2}\)

Since every 1 m² of area can grow 5kg of flowers,

the yield of flowers will be:

120 x 5

=600kg

Step-by-step explanation:

you don't know Pythagoras ?

c² = a² + b²

c is the Hypotenuse (the side opposite of the 90° angle), a and b are the legs.

please remember this for life !

so, in our case :

c² = 6² + 4² = 36 + 16 = 52

c = sqrt(52) = sqrt(4×13) = 2×sqrt(13) =

= 7.211102551... ≈ 7.2 miles

Answer:

10%

Step-by-step explanation:

The multiples of 2 are 2,4,6,8,10, and so on

The multiples of 5 are 5, 10, 15, 20 , 25, and so on

It is evident that the only one that matches up between 1-10 is 10.

There are 10 options, and our chances are random. There is only 1 option for it to be a multiple of both 2 and 5. Therefore, the probability is 1/10, or 10%

Answer:

\((x-1)^2 + (y+4)^2 = 100\\\\\)

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

Work Shown:

\((x-h)^2 + (y-k)^2 = r^2\\\\(x-1)^2 + (y-(-4))^2 = 10^2\\\\(x-1)^2 + (y+4)^2 = 100\\\\\)

You could expand terms out and simplify, but I think it's more handy to leave it in this form so you can easily spot the center and radius from a glance.

The solution is, (x - 1)² + (y + 4)² = 100 , is the equation of a circle that is centered at (1,-4) with a radius of 10.

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. The perimeter around the circle is known as the circumference.

here, we have,

we know that,

the standard form of a circle equation is

(x - h)² + (y - k)² = r²

where (h, k) is the center of the circle, and r is the radius.

to get r² we simply use the given radius,

here, r = 10

so, we get,

r² = 100

now, circle that is centered at (1,-4)

so, we have,

(x - 1)² + (y + 4)² = 10²

we get, equation in standard form is therefore

(x - 1)² + (y + 4)² = 100

Hence, The solution is, (x - 1)² + (y + 4)² = 100 , is the equation of a circle that is centered at (1,-4) with a radius of 10.

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A right angled triangle with height = 7, base = 11, by using the Pythagorean theorem, we can calculate the hypotenuse is approximately 13. Therefore, the missing side, x = 13.

In a right angled triangle, using the Pythagorean theorem: sum of the squares of the base and height is equal to the square of the hypotenuse, we can find the hypotenuse x.

\(x^2 = 7^2 + 11^2\)

\(x^2 = 49 + 121\)

\(x^2 = 170\)

Taking the square root of both sides, we get:

x ≈ 13.0384

Rounding this to the nearest tenth, we get:

x ≈ 13.0

Therefore, the length of x is approximately 13.0 units (rounded to the nearest tenth).

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