Find the partial sum S₁7 for the arithmetic sequence with a = 3, d = 2. S17 = ________

The image of the given arbitrary quadratic polynomial is T([tex]ax^2 + bx + c[/tex]) = [tex](-2a + 2c)x^2 + (-2b + a)x + (-2a + b + 7c)[/tex].

To find the image of the arbitrary quadratic polynomial [tex]ax^2 + bx + c[/tex] under the linear transformation T, we can express the polynomial in terms of the standard basis of P3, which is {[tex]1, x, x^2[/tex]}.

The polynomial [tex]ax^2 + bx + c[/tex] can be written as a linear combination of the basis vectors:

[tex]ax^2 + bx + c = a(x^2) + b(x) + c(1)[/tex]

Since we know the values of T(1), T(x), and T([tex]x^2[/tex]), we can substitute them into the expression:

[tex]T(ax^2 + bx + c) = aT(x^2) + bT(x) + cT(1)[/tex]

Substituting the given values:

[tex]T(ax^2 + bx + c) = a(-2x^2 + x - 2) + b(-2x + 1) + c(2x^2 + 7)[/tex]

Simplifying the expression:[tex]T(ax^2 + bx + c) = (-2ax^2 + ax - 2a) + (-2bx + b) + (2cx^2 + 7c)[/tex]

Combining like terms:

[tex]T(ax^2 + bx + c) = (-2a + 2c)x^2 + (-2b + a)x + (-2a + b + 7c)[/tex]

Therefore, the image of the arbitrary quadratic polynomial [tex]ax^2 + bx + c[/tex] under the linear transformation T is [tex](-2a + 2c)x^2 + (-2b + a)x + (-2a + b + 7c)[/tex].

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Answer:

im guessing 32.5$ but i honestly dont know lol

Step-by-step explanation:

Answer:

The third one down

Step-by-step explanation:

Answer:

0.004 km; 400 cm; 4000 mm

Step-by-step explanation:

1 km = 1000 m

1 = (1 km)/(1000 m)

4 m * (1 km)/(1000 m) = 4/1000 km = 0.004 km

1 m = 100 cm

1 = (100 cm)/(1 m)

4 m * (100 cm)/(1 m) = 400 cm

1 m = 1000 mm

1 = (1000 mm)/(1 m)

4 m * (1000 mm)/(1 m) = 4000 mm

Answer: 0.004 km; 400 cm; 4000 mm

Answer:

c

Step-by-step explanation:

Answer:

value = 8

Step-by-step explanation:

when a paired-samples t test is used by this researcher we will write out the hypothesis as follows

H0: μd ≤ 8  ( null )

Ha: μd >  8 ( alternate )

Given the above Hypothesis

If a paired-sample T test is used by the researcher  the value that would be at the center of the comparison will be 8

Answer:A

Step-by-step explanation:

the y-intercept is when x-axis is 0 and that means that hours of jogging is 0 and the y-axis is 1 minunte

Answer:

The first option.

Step-by-step explanation:

The y-intercept is where the line crosses through the y-axis, which, in this case, would be at point (0, 1). The labeling on the left side shows what each number on the y-axis represents, and it would be minutes stretching when not jogging.

hope this helped! :)

The conclusion F ⸧ (E ⸧ G) is valid

To construct a formal proof of validity for each of the given arguments, we will use logical inference rules.

⁓ A

Conclusion: A ⸧ B

⁓ A (Premise)

A ⸧ ⁓ A (Conjunction, from 1)

A (Simplification, from 2)

B (Modus ponens, from 3)

Therefore, the conclusion A ⸧ B is valid.

C

Conclusion: D ⸧ C

C (Premise)

D ⸧ C (Implication, from 1)

Therefore, the conclusion D ⸧ C is valid.

E ⸧ (F ⸧ G)

Conclusion: F ⸧ (E ⸧ G)

E ⸧ (F ⸧ G) (Premise)

F ⸧ G (Simplification, from 1)

G ⸧ F (Commutation, from 2)

E ⸧ G (Simplification, from 1)

E ⸧ F (Transposition, from 4)

F ⸧ (E ⸧ G) (Implication, from 5)

Therefore, the conclusion F ⸧ (E ⸧ G) is valid.

In all three arguments, we have successfully constructed formal proofs of validity using logical inference rules, demonstrating that the conclusions are logically valid based on the given premises.

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Answer:

16. Right isosceles

17. D

Step-by-step explanation:

The triangle has a right angle this makes it a right trangle. Also all parallelograms are not squares, all rectangles aren't squares and all parallelograms aren't rhombuses.

16. right isosceles

17. C: all rectangles are squares

Answer:

The answer is B.

Step-by-step explanation:

Answer:

B.

1.09x + 1.59y + 1.59z

I hope this helps

Answer:

The equation (sin(x) + cos(x))(tan(x) + cot(x)) = sec(x)csc(x) is not solvable because the two sides are not equal.

Answer:

3.8

Step-by-step

Got it wrong so you could get it right

Answer:

the first one.

Step-by-step explanation:

Answer:

C : 89%

Step-by-step explanation:

If they sold 235 scoops of marshmallow ice cream and in total of all day they sold a total of 265 scoops of ice cream. 265 - 235 = 30

My answer is C : 89%

Answer:

The image below explains read for the steps Your Welcome :)

Answer:

400,000

Step-by-step explanation:

Calculate the doubling time period-

Doubling time period(t)=

doubling time period(t)= 2

Calculate the new population using the doubling time formula below where t is the number of doubling periods:

Population = Initial Population * [tex]2^{t}[/tex]

Population = 100000 * [tex]2^{2}[/tex]

Population = 100000 * 4

Answer:

12*18

Step-by-step explanation:

18*12 is the same as 12*18 and they both equal 216

The value of the chi-square statistic for this independence test is approximately 82.23.

To calculate the expected values for the independence test, we need to determine the expected number of individuals in each category if age and voting behavior were independent. We can calculate the expected values using the formula:

Expected value = (Row total * Column total) / Total number of observations

Let's calculate the expected values for each category:

Age Voted?         Under 30    30 - 50    Over 50    Total

Yes                       35                  64               25               124

No                        56                  19                 1                 76

Total                     91                  83               26               200

Expected value for "Yes" under "Under 30" category:

Expected value = (91 * 124) / 200 = 56.57 (approximately 57)

Expected value for "No" under "Under 30" category:

Expected value = (91 * 76) / 200 = 34.82 (approximately 35)

Similarly, calculate the expected values for the other categories:

Expected values for "Yes" in the "30 - 50" and "Over 50" categories:

30 - 50: 83 * 124 / 200 ≈ 51.77 (approximately 52)

Over 50: 26 * 124 / 200 ≈ 16.12 (approximately 16)

Expected values for "No" in the "30 - 50" and "Over 50" categories:

30 - 50: 83 * 76 / 200 ≈ 31.63 (approximately 32)

Over 50: 26 * 76 / 200 ≈ 9.88 (approximately 10)

The expected table for the independence test is as follows:

Age Voted?         Under 30    30 - 50    Over 50      Total

Yes                       57                  52               16               124

No                        35                  32               10                76

Total                     91                  83               26               200

To find the chi-square statistic for this independence test, we use the formula:

χ² = Σ [(Observed value - Expected value)² / Expected value]

Now, let's calculate the chi-square statistic by summing the values for each category:

χ² = [(35 - 57)² / 57] + [(64 - 52)² / 52] + [(25 - 16)² / 16] + [(56 - 35)² / 35] + [(19 - 32)² / 32] + [(1 - 10)² / 10]

χ² = 23.09 + 2.46 + 5.06 + 40.69 + 4.53 + 6.4

χ² ≈ 82.23

Therefore, the value of the chi-square statistic for this independence test is approximately 82.23.

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To estimate the unknown parameter λ using maximum likelihood, given X₁ = 3, X₂ = 4, X₃ = 5, we need to find the value of λ that maximizes the likelihood function based on the observed data. The likelihood function represents the probability of observing the given data for different values of λ.

The likelihood function L(λ) is defined as the product of the probability density function evaluated at each observed data point. In this case, we have L(λ) = f(3) * f(4) * f(5), where f(x) is the given probability density function.
Substituting the values into the likelihood function, we have L(λ) = ((λ - 1)/3^λ) * ((λ - 1)/4^λ) * ((λ - 1)/5^λ).
To find the maximum likelihood estimate of λ, we need to maximize the likelihood function. Taking the natural logarithm of the likelihood function (ln L(λ)), we can simplify the problem to finding the value of λ that maximizes ln L(λ).
Taking the derivative of ln L(λ) with respect to λ and setting it to zero, we can solve for the maximum likelihood estimate of λ.
By solving the equation, we can obtain the estimate for λ based on the observed data X₁ = 3, X₂ = 4, X₃ = 5.

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Answer:

[tex] \: x = 10[/tex]

Step-by-step explanation:

prefer the attachment

according to the question

[tex] \displaystyle \: \frac{6}{17.5-x} = \frac{8 + 6}{17.5} [/tex]

simplify addition:

[tex] \displaystyle \: \frac{6}{17.5-x} = \frac{14}{17.5 } [/tex]

simplify fraction;

[tex] \displaystyle \: \frac{6}{17.5 - x} = 0.8[/tex]

cross multiplication:

[tex]\displaystyle 6 = 14 - 0.8x[/tex]

cancel 14 from both sides:

[tex] \displaystyle - 8= - 0.8x[/tex]

divide both sides by -0.8:

[tex] \therefore \: x = 10[/tex]

Answer:

-4x - 16y

Step-by-step explanation:

Given:

-4(3x - 2x + 4y)

Required:

Simplify

Solution:

To simplify, apply the distributive property by multiplying every term that is inside the brackets by -4

Thus:

-4*3x -4*-2x -4*+4y

-12x + 8x - 16y

Add like terms

-4x - 16y

One possible values of the integers is: a = 8020k, b = -10025k, and c = 401k where k is an arbitrary integer.

To find integers s, t, u, v such that 1485s + 952t = 690u + 539v, we can use the Extended Euclidean Algorithm. First, we compute the greatest common divisor of 1485 and 952:

gcd(1485, 952) = gcd(952, 533) = gcd(533, 419) = gcd(419, 114) = gcd(114, 91) = gcd(91, 23) = 23

Using the algorithm, we can write 23 as a linear combination of 1485 and 952:

23 = (-17) * 1485 + (27) * 952

Multiplying both sides by (30), we get:

690 = (-510) * 1485 + (810) * 952

and

539 = (357) * 1485 + (-567) * 952

Therefore,

s = -510u + 357v

t = 810u -567v

where u and v are arbitrary integers.

For the second part of the question, we need to find integers a, b, c, d such that:

211a + 307b +401c +503d =0

One possible way is:

a = -262

b = -169

c = 122

d = 97

To check that this, we substitute these values into the equation:

211(-262) +307(-169) +401(122) +503(97) = -55682 -52083 +51122 +50691 =0

Therefore, this is a valid solution.

Finally, for the third part of the question, we need to find integers a, b, c such that:

690a +539b=401c

Using the Extended Euclidean Algorithm, we can write:

gcd(690, 539) = gcd(539, 151) = gcd(151, 86) = gcd(86, 65) = gcd(65, 21) = gcd(21, 2) = 1

and

1 = (20) * 690 + (-25) * 539

Multiplying both sides by 401, we get:

401 = (8020) * 690 + (-10025) * 539

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Answer

5/36 ([tex]\frac{5}{36}[/tex])

Answer:

22/35

Step-by-step explanation:

27/9 = 3

3 × 11/5 ×2/21

=22/35

Answer:

A for ever I  P=25

b. 5.76

Step-by-step explanation:

Answer:

Answer:

68%

Step-by-step explanation:

The percentage of males in the town who have systolic blood pressure between 98 and 112 is 68%.

It is also called the Gaussian Distribution. It is the most important continuous probability distribution. The curve looks like a bell, so it is also called a bell curve.

For males in a certain town, the systolic blood pressure is normally distributed with a mean of 105 and a standard deviation of 7.

68 percent of the data is within one standard deviation of the mean, i.e. between μ - σ and μ + σ.

μ - σ = 105 - 7 = 98

μ + σ = 105 + 7 = 112

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To evaluate the triple integral ∫∫∫ xyzdv using cylindrical coordinates, we need to express the integral in terms of the cylindrical coordinates (ρ, φ, z).

The given solid E lies under the paraboloid z = 4 - z² - y². In cylindrical coordinates, this paraboloid equation becomes z = 4 - ρ² - y².

To set up the triple integral, we need to determine the limits of integration for each variable.

Since the solid lies in the first octant, the limits of integration are as follows:

ρ: from 0 to some value ρ₁

φ: from 0 to π/2

z: from 0 to the upper limit of the paraboloid, which is given by the equation z = 4 - ρ² - y².

Now we can set up the triple integral:

∫∫∫ xyzdv = ∫₀^(π/2) ∫₀^ρ₁ ∫₀^(4-ρ²-y²) (ρcosφ)(ρsinφ)z dz dρ dφ

Simplifying the integrand and integrating, we can evaluate the triple integral to obtain the final result.

Note: The specific value of ρ₁ and the complexity of the integration depend on the precise shape of the solid E, which is not provided in the given information. Therefore, the final evaluation of the integral requires additional information about the solid E.

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Answer:

(√3·x - 1)(√3·x + 1)(4x - 3)

Step-by-step explanation:

Note that the last two coefficients are -4 and +3, and the associated factor is (4x - 3).

The first two terms are

12x^3 - 9x^2, which become 3x(4x^2 - 3x) through factoring and then 3x^2(4x - 3).  

Therefore, 12x3 – 9x2 – 4x + 3 can be rewritten as:

                   (4x - 3)(3x^2 - 1).  

It's possible to factor 3x^2 - 1, even though 3 is not a perfect square.  Write 3x^2 - 1 as (√3·x - 1)(√3·x + 1)    

Then 12x3 – 9x2 – 4x + 3 = (√3·x - 1)(√3·x + 1)(4x - 3)

Answer:

( 3 x2 –  1 )( 1  ⇒ 4x –  3 )

Step-by-step explanation:

I did it lol