Prove that in , (0.5,1] is a relatively open set of [0,1], although it is not itself an open set.

Answer:

The system has no solution.

Step-by-step explanation:

In order for the system to have a solution, both graphs must have an intercept to each others. We see in the picture that both graphs are parallel and do not have any interceptions which we don't know the solution to the system.

That means if graphs are parallel and have no interceptions, there are no solutions. The system of equations are for finding the interceptions of both graphs. But of course! Parallel lines do not intercept.

If you have any questions, feel free to ask.

Answer:

x= 12.942

Law of sines :)

Answer:

i got a orange

Step-by-step explanation:

Answer:

4186.67 cubic mm=V

Step-by-step explanation:

The volume of a sphere can be found using the equation, [tex]\frac{4}{3} \pi r^{3}[/tex]. It gives us the diameter but we need the radius. To find the radius just divde the diameter by 2, so the radius of the sphere is 10mm.

[tex]\frac{4}{3} (3.14) (10^{3})[/tex]=V

[tex]\frac{4}{3} (3.14) (1000)[/tex]=V

[tex]\frac{4}{3}[/tex](3140)=V

4186.67 cubic mm=V

Answer:

a). -8    b). 4/19

Step-by-step explanation:

F(x)= x²+9x       g(x)=1/x.

g(-1) = 1/ - 1

= -1

f(-1) = x²+9x

= -1² + 9(-1)

= 1 - 9

= -8

G(f(1/2))

f(1/2) = x²+9x

= 1/2² + 9(1/2)

= 1/4 + 9/2

= 19/4

g (19/4) = 1/x

= 1/19/4

= 4/19

Answer:

1). -8    2). 4/19

Step-by-step explanation:

F(x)= x²+9x       g(x)=1/x.

g(-1) = 1/ - 1

= -1

f(-1) = x²+9x

= -1² + 9(-1)

= 1 - 9

= -8

G(f(1/2))

f(1/2) = x²+9x

= 1/2² + 9(1/2)

= 1/4 + 9/2

= 19/4

g (19/4) = 1/x

= 1/19/4

= 4/19

Answer:

I think the answer would be A or B, the best would be B.

Step-by-step explanation:

K so since it is monthly, it would not be all positive data. So you are left with A or B. Integers are numbers that are positive and negative so since the data can be a range of positive and negative numbers, that is why the data set of all integers (b) is the best choice.

Your welcome :D

Answer:

(5.871 `; 6.127)

Step-by-step explanation:

Given :

Mean = 6

Standard deviation. σ = 0.5

Samplr size, n = 100

Zcritical at 99% confidence = 2.58

The confidence interval :

Mean ± margin of error

Margin of Error = Zcritical * σ / sqrt(n)

Margin of Error = 2.58 * 0.5/sqrt(100) = 0.129

Confidence interval :

Lower boundary = 6.00 - 0.129 = 5.871

Upper boundary = 6.00 + 0.129 = 6.129

(5.871 `; 6.127)

Answer:

0.03259..

Step-by-step explanation:

The coordinates of the midpoint of the line segment GH with endpoints G(-3, 2) and H(3, -2) are (0, 0). The correct option is (C).

To determine the coordinates of the midpoint of the line segment GH with endpoints G(-3, 2) and H(3, -2), we can use the midpoint formula.

The midpoint formula states that the coordinates of the midpoint (M) are given by the average of the x-coordinates and the average of the y-coordinates of the endpoints.

Midpoint (M) = ((x1 + x2) / 2, (y1 + y2) / 2)

For GH, plugging in the coordinates, we have:

Midpoint (M) = ((-3 + 3) / 2, (2 + -2) / 2)

Midpoint (M) = (0, 0)

Therefore, the coordinates of the midpoint of GH are (0, 0), which corresponds to option c. (0, 0).

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To find the change-of-coordinates matrix from basis B to the standard basis, we need to express the standard basis vectors as linear combinations of the vectors in B. Then, to write t^2 as a linear combination of the polynomials in B, we can use the change-of-coordinates matrix to transform t^2 into the coordinates with respect to B.

To find the change-of-coordinates matrix from basis B to the standard basis, we express the standard basis vectors as linear combinations of the vectors in B. Let's denote the standard basis vectors as e1, e2, and e3. We can write:

e1 = 1(1 - 7t^2) + 0(-6 + t + 43t^2) + 0(1 + 6t)

e2 = 0(1 - 7t^2) + 1(-6 + t + 43t^2) + 0(1 + 6t)

e3 = 0(1 - 7t^2) + 0(-6 + t + 43t^2) + 1(1 + 6t)

The coefficients in these equations give us the entries of the change-of-coordinates matrix.

To write t^2 as a linear combination of the polynomials in B, we can use the change-of-coordinates matrix. Let [t^2]_B represent the coordinates of t^2 with respect to B. Then, [t^2]_B = C[t^2]_std, where C is the change-of-coordinates matrix. We can solve this equation to find [t^2]_B.

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Answer:220

Step-by-step explanation:

LET X BE THE LENGTH OF RECTANGLE AND FOR UPPER PORTION OF DIA GRAM BASE OF RIGHT ANGLE TRIANGLE SO X=20

LET Y BE WIDTH OF RECTANGLE SO Y=8

LET P BE THE PERPENDICULAR OF THE RIGHT TRIANGLE SO P=6

THEN

AREA OF RECTANGLE=LENGTH*WIDTH

SO AREA OF RECTANGLE BECOMES=(20)(8)=160

AND AREA OF RIGHT ANGLE TRIANGLE BECOMES=1/2(BASE*(PERPENDICULAR)

SO =1/2(20)(6)=60

SO THE TOTAL AREA OF THE DIAGRAM=AREA OF RIGHT ANGLE TRIANGLE+AREA OF RECTANGLE=160+60=220

The expression x^3 - 2x^2 - 8x + 16 can be factored as (x - 2)(x^2 - 8).

To factor the given expression x^3 - 2x^2 - 8x + 16, we can look for common factors or factor it using grouping. In this case, we can observe that the expression can be factored by grouping.

First, we can factor out a common factor of (x - 2) from the first two terms:

x^3 - 2x^2 - 8x + 16 = (x - 2)(x^2 - 8x - 8)

Now, we can further factor the quadratic expression (x^2 - 8x - 8) by factoring out a common factor of 8:

(x^2 - 8x - 8) = (x - 2)(x - 8)

Therefore, the complete factorization of the expression x^3 - 2x^2 - 8x + 16 is:

(x - 2)(x - 2)(x - 8) which can also be written as (x - 2)(x^2 - 8).

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The values of a and b are dependent on the equation. For example, in the equation a = 2y and b = 3, then a = 6 and b = 3. However, in the equation a = 2y and b = -3, then a = -6 and b = -3.

In the given options, the values of a and b are stated as a = 2y and b = –3. This means that the value of a is equal to twice the value of y (a = 2y), and the value of b is equal to -3. The other options do not match these conditions. It is important to note that without further context or information about the variable y, we cannot determine a specific value for a or b. The values provided only establish the relationship between a, b, and y as described in the option a = 2y and b = –3.

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The area of the circle is 452.16 cm², and the circumference is 75.36 cm.

To determine the area and circumference of a circle with a radius of 12 cm, we can use the formulas:

Area = π * r²

Circumference = 2 * π * r

The radius (r) is 12 cm, we can substitute this value into the formulas to find the area and circumference.

Area = π * (12 cm)²

      = π * 144 cm²

      ≈ 3.14 * 144 cm²

      ≈ 452.16 cm²

The area of the circle is approximately 452.16 square centimeters.

Circumference = 2 * π * 12 cm

                   = 2 * 3.14 * 12 cm

                   ≈ 75.36 cm

The circumference of the circle is approximately 75.36 centimeters.

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Answer:

40 cm²

Step-by-step explanation:

A = 1/2bh

A = 1/2 (8) (10)

A = (4) (10)

A = 40

Answer:

Step-by-step explanation:

The measure of central tendency that is usually the preferred number by researchers for describing a group of scores is the mean.

The measure of central tendency that is usually the preferred number by researchers for describing a group of scores is the mean. The mean provides the average score for a given set of data. It is calculated by summing up all the scores and dividing by the total number of scores. While other measures of central tendency, such as the median and mode, are also useful, the mean provides the most comprehensive picture of the data.


10. To calculate the standard deviation for the following data: 115, 125, 145, 150, 115, 125, you can use the following formula:

σ = √[(Σ(x - μ)²) / N]

Where:
σ = standard deviation
Σ = sum of
x = each score
μ = mean of all the scores
N = total number of scores

To find the standard deviation, first find the mean of the scores:

115 + 125 + 145 + 150 + 115 + 125 = 775
Total number of scores = 6
Mean = 775 / 6 = 129.17

Now, subtract the mean from each score, square the result, and add up all the squared differences:

(115 - 129.17)² + (125 - 129.17)² + (145 - 129.17)² + (150 - 129.17)² + (115 - 129.17)² + (125 - 129.17)² = 4666.79

Then, divide the sum of squared differences by the total number of scores and take the square root:

σ = √(4666.79 / 6) = 17.20


Mean = (115 + 125 + 145 + 150 + 115 + 125) / 6 = 129.17

Standard Deviation = √[ {(115 - 129.17)² + (125 - 129.17)² + (145 - 129.17)² + (150 - 129.17)² + (115 - 129.17)² + (125 - 129.17)² } / 6 ]

= √[4666.79 / 6]

= 17.20

Therefore, the standard deviation of the given data is 17.20.

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Answer:

x = 3/2

Step-by-step explanation:

Simplify this equation by dividing all three terms by 1/4:

2x - 1 = 2, or

2x  = 3

Then x = 3/2

Answer:

7. -4/5

8. 1

9. 0

10. 3/4

11. undefined/nonlinear

12. -9/4

13. parallel

Answer:

The integer that represents the change in temperature is 17.

Step-by-step explanation:

Answer:

I am not sure rdbugs h h on grh g ih fv vy f byv7iplovh v v6c78

Answer:

1 is C

2 is B

3 is C

Step-by-step explanation:

Answer:

give em brainliest because i have no idea

Step-by-step explanation:

a) The cumulative distribution function for X is F(x) = 1 – exp(-x²)

is = 1 – exp(-x²)

b) P(X ≤ 2) = 0.865

c) Generate a uniformly distributed random number u between 0 and 1.

a) We have given a probability density function f(x) = 2x exp(-x²), x ≥ 0

To find the cumulative distribution function (CDF), we integrate the probability density function (PDF) from negative infinity to x as follows;

∫f(x)dx = ∫2x exp(-x²)dx

Using u =

-x², du/dx = -2x

dx = -du/2∫2x exp(-x²)dx

= -∫exp(u)du

= -exp(u) + C

= -exp(-x²) + C

We know that, F(x) = ∫f(x)dx.

From the above calculation, the CDF of X is given by;

F(x) = 1 – exp(-x²)

b)

We are to calculate P(X ≤ 2)

We know that F(2) = 1 – exp(-2²)

= 0.865

Therefore, P(X ≤ 2) = 0.865

c)

The inversion method is a way of generating random values of a random variable X using the inverse of the cumulative distribution function of X, denoted as F⁻¹(u),

where u is a uniformly distributed random number between 0 and 1.

The steps for generating a random value of X using the inversion method are:

Generate a uniformly distributed random number u between 0 and 1.

Find the inverse of the cumulative distribution function, F⁻¹(u).

This gives us the value of X.

d)

R command for one random value of X by using the inversion method```{r}

# setting seed to be 100 sets. seed(100)

# defining the inverse CDFF_inv = function(u) q norm(u, lower.tail=FALSE)

# generating a random value of Uu = run if(1)

# calculating the corresponding value of Xx = F_inv(u)```

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The degree of the extension [K: F] ≤ p.

Suppose K = F_p(t) has transcendence degree n over F_p.

Then K is an algebraic extension of F_p(t^p).

(a) We need to find a polynomial of degree p in F[x] for which t is a root.

In F_p, we have t^p - t ≡ 0 (mod p).

So, we can write t^p ≡ t (mod p).

Since F_p[t] is a polynomial ring over F_p, we have t^p - t ∈ F_p[t] is an irreducible polynomial.

Hence the degree of the extension [K: F] ≤ p.

Suppose K = F_p(t) has transcendence degree n over F_p.

Then K is an algebraic extension of F_p(t^p).

The minimal polynomial of t over F_p(t^p) is x^p - t^p. Thus, [K: F_p(t^p)] ≤ p.

Since K/F_p is an algebraic extension, we have [K: F_p] = [K: F_p(t^p)][F_p(t^p): F_p].

Thus, [K: F_p] ≤ p².

Therefore, [K: F] ≤ p².

(b) We need to show that the automorphism δ of K defined by δ (t) = t + 1 fixes F.

Let f(x) be the polynomial obtained in part (a). Since f(t) = 0, we have f(t + 1) = 0. This implies δ (t) = t + 1 is a root of f(x) also.

Hence, f(x) is divisible by x - (t + 1). We can writef(x) = (x - (t + 1))g(x)for some g(x) ∈ K[x].

Since [K: F] ≤ p², we have deg(g) ≤ p.

Substituting x = t into the above equation yields 0 = f(t) = (t - (t + 1))g(t) = -g(t).

Therefore, f(x) = (x - (t + 1))g(x) = (x - t - 1)(a_{p-1}x^{p-1} + a_{p-2}x^{p-2} + ··· + a_1 x + a_0)where a_{p-1}, a_{p-2}, ..., a_1, a_0 ∈ F_p are uniquely determined.

(c) To show that K is a Galois extension of F and determine the Galois group Gal(K/F), we need to check that K is a splitting field over F.

That is, we need to show that every element of F_p(t^p) has a root in K.Since K = F_p(t)(t^p - t) = F_p(t)(w), it suffices to show that w has a root in K.

Note that w = t^p - t = t(t^{p-1} - 1).

Since t is a root of f(x) = x^p - x ∈ F_p[t], we have t^p - t = 0 in K. Thus, w = 0 in K.

Therefore, K is a splitting field over F_p(t^p).Since [K : F_p(t^p)] ≤ p, the extension K/F_p(t^p) is separable.

Therefore, the extension K/F_p is also separable. Hence, K/F_p is a Galois extension. The degree of the extension is [K: F_p] = p².

The Galois group is isomorphic to a subgroup of S_p. Since F_p is a finite field of p elements, it contains a subfield isomorphic to Z_p. This subfield is fixed by any automorphism of K that fixes F_p.

Since F_p(t^p) is generated by F_p and t^p, any automorphism of K that fixes F_p(t^p) is uniquely determined by its effect on t.

Since there are p choices for δ(t), the Galois group has order p. It follows that the Galois group is isomorphic to Z_p.

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Answer: B

Step-by-step explanation:

I know I’m late :(

Answer:

Area of the circle = 572.3 square ft.

Step-by-step explanation:

Area of a circle is given by the formula,

Area of a circle = πr²

Here 'r' = Radius of the circle

Diameter of circle given in the picture = 27 ft

Radius of the circle = [tex]\frac{27}{2}[/tex]

                                = 13.5 ft

Area of the circle = π(13.5)²

                             = 3.14(13.5)²

                             = 572.265

                             ≈ 572.3 square ft

Answer:

630 in^3

Step-by-step explanation:

6 x 6 x 14 = 504

(0.5 x 3 x 6) x 14 = 126

504 + 126 = 630

Answer:

15.5769230769

Step-by-step explanation:

8×13 = 104

1620÷104 = 15.5769230769

The equation that represents the sentence "28 is the quotient of a number and 4" is 28 = n/4.

In the given sentence, "28 is the quotient of a number and 4," we can break down the sentence into mathematical terms. The term "quotient" refers to the result of division, and "a number" can be represented by the variable "n." The divisor is 4.

1) Define the variable.

Let's assign the variable "n" to represent "a number."

2) Write the equation.

Since the sentence states that "28 is the quotient of a number and 4," we can write this as an equation: 28 = n/4.

The equation 28 = n/4 represents the fact that the number 28 is the result of dividing "a number" (n) by 4. The left side of the equation represents 28, and the right side represents "a number" divided by 4.

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Answer:

the first one

Step-by-step explanation:

the first one