0= (x-1)^2 -4 and and show explanation please

The formula for the nth term of the series is an = -14n + 68 for n>1 and the nth term an of the series for n > 1 is an = -67.

To find an for n>1, we need to first find the formula for the nth term of the series. We can do this by taking the difference between successive partial sums:
sn - sn-1 = (5n-72n+7) - (5(n-1)-7(2(n-1)+7))
         = 5 - 7(2n-9)
         = -14n + 68
We know that the nth term of the series is given by the difference between the nth partial sum and the (n-1)th partial sum, so we can set this expression equal to an:
an = sn - sn-1
  = -14n + 68
Therefore, the formula for the nth term of the series is an = -14n + 68 for n>1.
To find the nth term an of the series, we need to consider the difference between the (n+1)th and nth partial sums. Using the given formula for the partial sum sn:
s(n+1) = 5(n+1) - 72(n+1) + 7
sn = 5n - 72n + 7
Now, subtract sn from s(n+1):
an = s(n+1) - sn = [5(n+1) - 72(n+1) + 7] - [5n - 72n + 7]
Simplify the expression:
an = 5n + 5 - 72n - 72 + 7 - 5n + 72n - 7
Combine the like terms:
an = 5 - 72
So, the nth term an of the series for n > 1 is an = -67.

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The acceptable conclusions to a hypothesis test are option a, c, d, f.

What is hypothesis test?

Hypothesis Testing is a way of statistical analysis in which a person can  put his assumptions about a population parameter to the test. It usually  used to estimate the relationship between two statistical variables.

By the property of hypothesis test the following can be stated.

⇒The value of the test statistic lies in the non rejection region. Therefore, there is no evidence to suggest that the alternative hypothesis is true.

⇒ The value of the test statistic lies in the rejection region. Therefore, there is evidence to suggest that the null hypothesis is not true.

⇒The value of the test statistic does not lie in the rejection region. Therefore, there is no evidence to suggest that the alternative hypothesis is true.

⇒ The value of the test statistic lies in the rejection region. Therefore, there is evidence to suggest that the alternative hypothesis is true.

Hence the correct options are a, c, d, f.

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Answer:

where is the line?

Step-by-step explanation:

Rewrite the question and I'll do my best to answer it

Let's begin by listing out the information given to us:

Customer A = -$95.00

Customer B = -$75.00

Customer C = -$40.00

Customer D = -$92.00

Observing the figures above, we will observe that the greatest or biggest change is observed with Customer A. The account of Customer A decreased the most decreasing by $95; this was $3 more than Customer

Answer: LOOK below

Step-by-step explanation:

For the human eye to detect an increase in the SNR of an image, the SNR must be increased by a minimum of approximately 20%. Doubling the NEX/NSA in a pulse sequence yields an increase in SNR by 100%.

SNR (Signal-to-Noise Ratio) is a statistical measure that compares the level of a desired signal to the level of background noise. The higher the SNR, the better the image quality. To increase the SNR of an image, various techniques can be used such as increasing the magnetic field strength, optimizing imaging parameters, increasing the number of excitations (NEX), or decreasing the voxel size.

However, for the human eye to detect an increase in the SNR of an image, the SNR must be increased by a minimum of approximately 20%. This is because the human eye is not as sensitive to low levels of noise as it is to high levels of noise. Therefore, a small increase in SNR may not be noticeable to the human eye.Doubling the NEX/NSA in a pulse sequence yields an increase in SNR by 100%.

This is because NEX (Number of Excitations) or NSA (Number of Signal Averages) is directly proportional to the square root of SNR. Therefore, doubling NEX/NSA would increase SNR by a factor of square root of 2 (approximately 1.4) which is equivalent to a 100% increase in SNR.

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Answer:

6 hours

Step-by-step explanation:

so to do this your gonna
50 + 18 = 68$
then you just add 18 till you reach as close as you can get to 160$
68$+18$=86+18=104+18=122+18=140+18=158$
then you count the 18's
there is 6 18's witch means that Luis is can kayak for a max of 6 hours

The maximum number of hours Luis can rent the kayak gven the amount he can spend is 6 hours.

The equation that represents the total amount of money he can spend is:

$160 = $50 + $18h

Where h represents the number of hours

In order to determine the value of h, take the following steps:

Combine similar terms

$160 - $50 = 18h

Add similar terms

$110 = 18h

Divide both sides by 18

h = 6 hours

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Answer:

all 3 options are true : A, B, C

Step-by-step explanation:

warning : it has come to my attention that some testing systems have an incorrect answer stored as right answer for this problem.

they say that A and C are correct.

but I am going to show you that if A and C are correct, then also B must be correct.

therefore, my given answer above is the actual correct answer (no matter what the test systems say).

originally the information about the alignment of the point F in relation to point E was missing.

therefore, I considered both options :

1. F is on the same vertical line as E.

2. F is not on the same vertical line as E.

because of optical reasons (and the - incomplete - expected correct answers of A and C confirm that) I used the 1. assumption for the provided answer :

the vertical line of EF is like a mirror between the left and the right half of the picture.

A is mirrored across the vertical line resulting in B. and vice versa.

the same for C and D.

this leads to the effect that all 3 given congruence relationships are true.

if we consider assumption 2, none of the 3 answer options could be true.

but if the assumptions are true, then all 3 options have to be true.

now, for the "why" :

remember what congruence means :

both shapes, after turning and rotating, can be laid on top of each other, and nothing "sticks out", they are covering each other perfectly.

for that to be possible, both shapes must have the same basic structure (like number of sides and vertices), both shapes must have the same side lengths and also equally sized angles.

so, when EF is a mirror, then each side is an exact copy of the other, just left/right being turned.

therefore, yes absolutely, CAD is congruent with CBD. and ACB is congruent to ADB.

but do you notice something ?

both mentioned triangles on the left side contain the side AC, and both triangles in the right side contain the side BD.

now, if the triangles are congruent, that means that each of the 3 sides must have an equally long corresponding side in the other triangle.

therefore, AC must be equal to BD.

and that means that AC is congruent to BD.

because lines have no other congruent criteria - only the lengths must be identical.

Answer:

the right is the answer :>

Step-by-step explanation:

Answer:

π

Step-by-step explanation:

Irrational numbers cannot be expressed in as the ratio of two numbers

π in decimal form is 3.14159 and it goes on. This can't be expressed in a proper fraction unlike the other three numbers.

Answer:

The answer is x>7

Step-by-step explanation:

Answer:

x > 7

Step-by-step explanation:

Isolate x:

2x - 11 > 3

2x > 14

Divide each side by 2:

x > 7

So, the answer is x > 7

Answer:

Step-by-step explanation:

\(a_n=a_1+d(n-1)\\\\a_{20}=a_1+d(20-1)\\\\36=a_1+4\cdot19\\\\36=a_1+76\\\\a_1=36-76\\\\a_1=-40\)

The solution to the equation is t = log(146)/8, and the approximate value of t is 0.270.

To solve the equation 0.5 *\(10^{8t}\) = 73 for t, we can first simplify the left side of the equation by dividing both sides by 0.5 * 10^8:

\(10^{8t}\) = 146

Next, we can take the logarithm of both sides of the equation using base 10:

\(log(10^{8t}) = log(146)\)

Using the property of logarithms that says \(log(a^{b} ) = b*log(a)\), we can simplify the left side of the equation:

8t * log(10) = log(146)

Since log(10) = 1, we can further simplify the equation:

8t = log(146)

Finally, we can solve for t by dividing both sides by 8:

t = log(146)/8

t = 2.164/8

The approximate the value of t as:

t ≈ 0.27054410

Therefore, the solution to the equation is t = log(146)/8, and the approximate value of t is 0.270.

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The first curve, r = 13cos(θ), and outside the second curve, r = 6cos(θ), is 66.5π square units.

To find the area of the region that lies inside the first curve, r = 13cos(θ), and outside the second curve, r = 6cos(θ), we need to set up the integral and evaluate it.

The curves r = 13cos(θ) and r = 6cos(θ) intersect at certain values of θ. To find these points of intersection, we can set the two equations equal to each other and solve for θ:

13cos(θ) = 6cos(θ)

Dividing both sides by cos(θ):

13 = 6

This equation does not have a valid solution since the left side is always greater than the right side. Therefore, the two curves do not intersect, and we can find the area of the region by evaluating the integral over the desired interval.

The integral for finding the area inside the first curve and outside the second curve is:

A = ∫[a,b] (½r₁² - ½r₂²) dθ

where r₁ = 13cos(θ) and r₂ = 6cos(θ).

Since the curves do not intersect, we can choose any interval for integration. Let's choose the interval [0, 2π] to cover a full revolution.

A = ∫[0, 2π] (½(13cos(θ))² - ½(6cos(θ))²) dθ

Simplifying the integrand:

A = ∫[0, 2π] (½(169cos²(θ)) - ½(36cos²(θ))) dθ

A = ∫[0, 2π] (84.5cos²(θ) - 18cos²(θ)) dθ

A = ∫[0, 2π] (66.5cos²(θ)) dθ

Evaluating the integral:

A = [66.5/2 * (θ + sin(2θ)/2)] [0, 2π]

A = 66.5/2 * (2π + sin(4π)/2 - 0 - sin(0)/2)

Since sin(4π) = sin(0) = 0:

A = 66.5/2 * 2π

A = 66.5π

Therefore, the area of the region that lies inside the first curve, r = 13cos(θ), and outside the second curve, r = 6cos(θ), is 66.5π square units.

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Answer:

d. 32 in.²

Step-by-step explanation:

Bottom face: 6 in. × 0.5 inch

Side faces: 2 × 5 in. × 0.5 in.

Front and back faces: 2 x 6 in. × 4 in. / 2

surface area = 3 in.² + 5 in.² + 24 in.²

surface area = 32 in.²

24 different ways can they line up to receive their championship rings.

What is a permutation mean in math?

What are permutations used for?

Given,

            No. of captains of the football team = 4

So,

         4 ways we can line up  their championship rings = (4,4)

                  4 ×3 ×2 ×1  = 24

Therefore, 24 different ways can they line up to receive their championship rings.

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The ratio of the side length of the square to the brush width is: 1/sqrt(2) : brush width.

The painted area consists of four congruent right triangles, each with legs equal to the side length of the square. Since half the area of the square is painted, the total area of the four triangles is equal to half the area of the square.

Thus, the area of one triangle is equal to one-eighth the area of the square.

The area of a right triangle is given by 1/2(base x height), where in this case, the base and height are both equal to the side length of the square. Therefore, we have:

1/2 x (side length)^2 / 2 = 1/8 x (side length)^2

Simplifying, we get:

(side length)^2 = 4 x (side length)^2 / 8

(side length)^2 = (side length)^2 / 2

Multiplying both sides by 2, we get:

2 x (side length)^2 = (side length)^2

2 = 1 / (side length)^2

Taking the reciprocal of both sides, we get:

(side length)^2 = 1/2

Taking the square root of both sides, we get:

side length = 1/sqrt(2)

The ratio of the side length of the square to the brush width is:

1/sqrt(2) : brush width.

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Answer:

(3, - 1 )

Step-by-step explanation:

Given the 2 equations

2x + 3y = 3 → (1)

x + 6y = - 3 → (2)

Multiplying (1) by - 2 and adding to (2) will eliminate the y- term

- 4x - 6y = - 6 → (3)

Add (2) and (3) term by term eliminating y

- 3x = - 9 ( divide both sides by - 3 )

x = 3

Substitute x = 3 into either of the 2 equations and solve for y

Substituting into (2)

3 + 6y = - 3 ( subtract 3 from both sides )

6y = - 6 ( divide both sides by 6 )

y = - 1

Solution is (3, - 1 )

The volume obtained by rotating region R about the line y = -2 and x = 3 is 0, indicating no difference in volume between the two rotations.

To find the volume of the object obtained by rotating region R about the line y = -2, we can use the method of cylindrical shells.

Rotating about the line y = -2:

The height of each shell is given by the difference between the two functions: f(x) = 3x and g(x) = -2x^2 + 6x + 2. The radius of each shell is the x-coordinate of the point at which the functions intersect.

To find the points of intersection, we set the two functions equal to each other and solve for x:

3x = -2x^2 + 6x + 2

Simplifying and rearranging:

2x^2 - 3x + 2 = 0

Using the quadratic formula, we find two solutions for x:

x = (-(-3) ± √((-3)^2 - 4(2)(2))) / (2(2))

x = (3 ± √(9 - 16)) / 4

x = (3 ± √(-7)) / 4

Since the equation has complex roots, it means there is no intersection point between the two functions within the given range.

Therefore, the volume obtained by rotating region R about the line y = -2 is 0.

Rotating about the line x = 3:

In this case, we need to find the integral of the difference of the two functions squared, from the y-coordinate where the two functions intersect to the highest y-coordinate of the region.

To find the points of intersection, we set the two functions equal to each other and solve for x:

3x = -2x^2 + 6x + 2

Simplifying and rearranging:

2x^2 - 3x + 2 = 0

Using the quadratic formula, we find two solutions for x:

x = (-(-3) ± √((-3)^2 - 4(2)(2))) / (2(2))

x = (3 ± √(9 - 16)) / 4

x = (3 ± √(-7)) / 4

Since the equation has complex roots, it means there is no intersection point between the two functions within the given range.

Therefore, the volume obtained by rotating region R about the line x = 3 is also 0.

In both cases, the volume obtained is 0, so there is no difference in volume between rotating about the line y = -2 and rotating about the line x = 3.

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No, this table does not represent a relation or a function.

Function is an action or process that produces a result. It is a set of instructions that produces an output from one or more inputs. Functions are a key building block in programming and are used to create meaningful results from a given set of data. Functions can be used to simplify complex tasks and make them more efficient. They are also used to organize and structure code, making it easier to read and debug.

A relation is a set of ordered pairs that have an established relationship between them, while a function is a relation where each input is related to only one output. This table does not establish any relationship or link between the X and Y values, so it is not a relation or a function.

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Lucy has $7 less than Kristine and $5 more than Nina together, the three have $35. Lucy has $11.

Let's denote the amount of money that Kristine has as K, the amount of money that Lucy has as L, and the amount of money that Nina has as N.

According to the given information, we can form two equations:

Lucy has $7 less than Kristine: L = K - 7

Lucy has $5 more than Nina: L = N + 5

We also know that the three of them have a total of $35: K + L + N = 35

We can solve this system of equations to find the values of K, L, and N.

Substituting equation 1 into equation 3, we get:

K + (K - 7) + N = 35

2K - 7 + N = 35

Substituting equation 2 into the above equation, we get:

2K - 7 + (L - 5) = 35

2K + L - 12 = 35

Since Lucy has $7 less than Kristine (equation 1), we can substitute K - 7 for L in the above equation:

2K + (K - 7) - 12 = 35

3K - 19 = 35

Adding 19 to both sides:

3K = 54

Dividing both sides by 3:

K = 18

Now we can substitute the value of K into equation 1 to find L:

L = K - 7

L = 18 - 7

L = 11

Finally, we can find the value of N by substituting the values of K and L into equation 3:

K + L + N = 35

18 + 11 + N = 35

N = 35 - 18 - 11

N = 6

Therefore, Lucy has $11.

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Answer:

x+y=10

2.25x+5.50y=42

Extra: 6 hamburgers and 4 drinks

Step-by-step explanation:

x+y=10

2.25x+5.50y=42

x would stand for the drinks and y would stand for the hamburger

I do not know if you want me to solve it or not, but I might as well do so.

To solve it, you could multiply the first equation by 2.25 to get:

2.25x+2.25y=22.5

2.25x+5.50y=42

Now, if you subtract the two systems of equations, you get 3.25y=19.5, where y is equal to 6.

When you plug in 6 for y in the first equation, you should find that x is equal to 4.

In conclusion, Indigo ordered 6 hamburgers and 4 drinks.

Answer:

Poster’s perimeter = 150 in

Step-by-step explanation:

Given:

Width of poster = 2.5 ft = 2.5 × 12 = 30 in

Find:

Poster’s perimeter.

Computation:

Height of poster = [30×6]/4

Height of poster = 45 in

Poster’s perimeter = 2 [Width of poster + Height of poster]

Poster’s perimeter = 2 [30+45]

Poster’s perimeter = 2 [75]

Poster’s perimeter = 150 in

Answer:

It's A

Step-by-step explanation:

DO FOIL

-10d^4+(5+12)d^2s-6s^2=-10d^4+17d^2s-6s^2

Answer:

the first answer: -10a^4 + 17a^2s-6s^2

Step-by-step explanation:

Answer:

7 inches

Step-by-step explanation:

7 inches

bc area of a square is l^2 and square of 7 is 49.

Answer:

\(120-2.614\frac{5}{\sqrt{130}}=118.85\)    

\(120+2.614\frac{5}{\sqrt{130}}=121.15\)    

Step-by-step explanation:

Information given

\(\bar X= 120\) represent the sample mean

\(\mu\) population mean (variable of interest)

s=5 represent the sample standard deviation

n=130 represent the sample size  

For this case we can't set a margin of error just with a % since they not specify 1.13% respect to something for this case we can omit this value

Confidence interval

The confidence interval for the mean is given by the following formula:

\(\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}\)   (1)

The degrees of freedom are given by:

\(df=n-1=130-1=129\)

The Confidence level is 0.99 or 99%, the significance would be \(\alpha=0.01\) and \(\alpha/2 =0.005\), and the critical value would be \(t_{\alpha/2}=2.614\)

And replacing we got:

\(120-2.614\frac{5}{\sqrt{130}}=118.85\)    

\(120+2.614\frac{5}{\sqrt{130}}=121.15\)    

Answer:

A’ (6,-2)

B’ (1,3)

Step-by-step explanation:

Here, we want to give the coordinates after a counterclockwise rotation of 90 degrees

Given a point with coordinates (x,y)

A counterclockwise rotation at 90 degrees to the origin will yield the coordinates (-y,x)

So A (-2,-6) will be A’ (6,-2) while B (3,-1) will be B’ (1,3)