What is a formula for the nth term of the given sequence?
Select Explicit Formula for Sequence

Answer:

A

Step-by-step explanation:

We can factor 625x^4 - 81 by recognizing it as the difference of two squares:

625x^4 - 81 = (25x^2)^2 - 9^2

This can be further simplified using the formula for the difference of squares, which states that:

a^2 - b^2 = (a + b)(a - b)

In this case, a = 25x^2 and b = 9, so we have:

(25x^2 + 9)(25x^2 - 9)

We can then use the difference of squares formula again to factor 25x^2 - 9:

25x^2 - 9 = (5x)^2 - 3^2 = (5x + 3)(5x - 3)

Substituting this into our original expression, we get:

625x^4 - 81 = (25x^2 + 9)(25x^2 - 9) = (25x^2 + 9)(5x + 3)(5x - 3)

Therefore, the fully factored form of 625x^4 - 81 is (25x^2 + 9)(5x + 3)(5x - 3). Answer: (A) (5x - 3)(5x - 3)(25x² + 9)

The equations to have infinite solutions and no solutions are 3x + 5 = 3x + 5 and 3x + 5 = 3x + 6

Infinite many solutions

From the question, we have:

[ ] x + 2x + (-4 + 9) = [] x+ []

This gives

[ ] x + 2x + 5 = [] x+ []

For an equation to have infinite many solutions, both sides must be equal

So, we have

[1] x + 2x + 5 = [3] x+ [5]

Evaluate

3x + 5 = 3x + 5

No solution

Here, we have:

[ ] x + 2x + (-4 + 9) = [] x+ []

This gives

[ ] x + 2x + 5 = [] x+ []

For an equation to have no solutions, both sides must be unequal

So, we have

[1] x + 2x + 5 = [3] x+ [6]

Evaluate

3x + 5 = 3x + 6

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Answer:

61

Step-by-step explanation:

triangles add up to 180

56+63 is 119

180-119 to find the missing angle is 61

hope this helped

The shoe sizes that will only have one dot are 5 1/2, 7, 8 and 10 1/2

From the question, we have the following parameters that can be used in our computation:

The record of shoe sizes

From the data values, we have the following shoe sizes that appear once

5 1/2, 7, 8 and 10 1/2

These are the data values that will have only one dot  if the data is recorded on a line plot

Hence, the shoe sizes that will only have one dot are 5 1/2, 7, 8 and 10 1/2

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Answer:

B , C and F

Step-by-step explanation:

Answer: 260(0.962)^8

Step-by-step explanation:

Pretty simple. We have a base of 260, which all of the answers include. Then for a decay rate of 3.8, we reduce to percentage form ( 0.038 ) and subtract that from 1 ( or 100 in standard form ). Then we get 0.962. We choose the second option because it includes both these terms and 8 ( which I'm assuming is an exponent )

Answer:

x=0, y=6

x=4, y=0

x=8, y=-6

Step-by-step explanation:

6x + 4y = 24

6(0) + 4y = 24

y = 6

So x=0, y=6

y=0

6x+4y=24

6x+4(0)=24

6x=24

x=4

When x=4, y=0

x=8

6x+4y=24

6(8) + 4y = 24

48 + 4y = 24

4y = 24-48

4y = -24

y = -24/4

y = -6

When x = 8, y = -6

Answer:

18 more sessions

Step-by-step explanation:

Her goal is to practice 800 minutes.

She already did 175 minutes.

That means she has 800 - 175 = 625 minutes remaining, and she says that she will only practice in 35 minute sessions.

To determine the number of sessions she has left, just divide 625 by 35.

[tex]\frac{625}{35}[/tex]

= 17.85714

However, you can't have a portion of a session, as she only does 35 mins every session. Therfore, she must do 18 more sessions.

~~~Harsha~~~

[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$3000\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=years\dotfill &7 \end{cases} \\\\\\ A = 3000e^{0.04\cdot 7} \implies \boxed{A \approx 3969.39} \\\\[-0.35em] ~\dotfill[/tex]

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$2800\\ r=rate\to 5.2\%\to \frac{5.2}{100}\dotfill &0.052\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &7 \end{cases}[/tex]

[tex]A = 2800\left(1+\frac{0.052}{4}\right)^{4\cdot 7}\implies A=2800(1.013)^{28} \implies \boxed{A \approx 4019.97} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\Large \begin{array}{llll} 4019.97 ~~ > ~~ 3969.39 \end{array}}~\hfill[/tex]

The required equation of the function with the given characteristics is y = (2/9)|x| whose height will be compressed to 2/9 of the original height.

As per the question, the absolute value function y = |x| looks like a "V" shape with its vertex at the origin and opening upward.

To shrink it vertically by a factor of 2/9, we need to multiply the function by this factor.

Thus, the equation of the function with the given characteristics is:

y = (2/9)|x|

The resulting graph will still have a "V" shape, but its height will be compressed to 2/9 of the original height.

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The number of ways to choose the letters is given as follows:

First we must decide which formula to use, depending if the order matters, as follows:

The number of possible permutations of x elements from a set of n elements is given by:

[tex]P(n,x) = \frac{n!}{(n-x)!}[/tex]

Hence, if the order matters, the number of ways is given as follows:

P(3,2) = 3!/(3 - 2)! = 6.

The combination formula is given as follows:

[tex]C(n,x) = \frac{n!}x!{(n-x)!}[/tex]

Hence, if the order does not matter, the number of ways is given as follows:

C(3,2) = 3!/(2! x 1!) = 3.

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There are no intersecting points.

The given equations are

y = (2x)² - 6x+5   ....(i)

2y + x =4 ....(ii)

Since we know that,

Degree of equation (i)  = 2

Therefore,

equation (i) is a quadratic equation.,

And equation (ii) has degree 1,

So it is a equation of line,

To find the intersection,

First of we have to plot both graphs,

Then find the coordinate of the intersection of the given line and curve.

After plotting graph,

We can see that,

The given curve and line are not intersecting,

Therefore,

There are no intersecting points.

Hence we can not find the required equation of line.

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The solution of the expression, [tex](\frac{2}{3} )^{-4}[/tex] is 81 / 16.

An algebraic expression is an expression which is made up of variables and constants, along with algebraic operations such as multiplication, subtraction, addition etc.

Therefore, lets solve the expression as follows:

[tex](\frac{2}{3} )^{-4}[/tex]

Using exponential laws,

b⁻¹ = 1 / b

Let's apply the law to the expression as follows:

[tex](\frac{2}{3} )^{-4} = \frac{1}{(\frac{2}{3})^{4} }[/tex]

Therefore,

1 ÷ (2  / 3)⁴ = 1 × (3 / 2)⁴ = 3⁴ / 2⁴

Finally,

3⁴ / 2⁴ = 81 / 16

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Answer:

1×1=1

2×2=4

3×3=9

4×4=16

An equation that represents the cost of green squash at the local farmers market include the following: C = 1.50p.

In Mathematics and Geometry, a proportional relationship is a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical equation:

c = kp

Where:

Next, we would determine the constant of proportionality (k) by using the various data points from table D as follows:

Constant of proportionality, k = c/p

Constant of proportionality, k = 15/10

Constant of proportionality, k = $1.5 per pounds.

Therefore, the required linear equation is given by;

c = kp

c = 1.50p

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

-3993

Step-by-step explanation:

Answer:

8 more red counters

Step-by-step explanation:

It would make it 9:3, which, when simplified, is 3:1.

The correct test statistic for this hypothesis test is t = -2.88, not z = -2.65 or z = 2.65.

To perform a hypothesis test, we start by stating the alternative hypotheses:

H0: μ = 62 (the population temperature is 62 degrees F)

Ha: μ < 62 (the population  temperature is less than 62 degrees F)

X is the sample temperature, μ is the population temperature, s is the sample standard deviation, and n is the sample size.

Plugging in the values, we get:

t = (59 - 62) / (6.21 / √(30)) = -2.88

Finally, we compare the test statistic to the critical value from the t-distribution with n - 1 f and an alpha level of 0.05. Since the alternative hypothesis is one-tailed (μ < 62), we use a one-tailed test and look up the critical value for a t-distribution with 29 f and an alpha level of 0.05. The critical value is -1.699.

Since the test statistic of -2.88 is smaller than the critical value of -1.699, we reject the null hypothesis and conclude that there is convincing evidence at the alpha = 0.05 level that the  temperature in fall and winter months in southwest is less than 62 degrees F.

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The value of function for x = 6 is f(6) = 2.1

Given that f(x) = [tex]18 / [ 6 + 5^{e-0.1x ][/tex]

We have to find the value of this function at x = 6.

f(6) =

  [tex]18 / [ 6 + 5^{e-0.1 * 6} ] \\ \\ = 18 / [ 6 + 5^{e-0.6} ][/tex]

≈  2.1

Therefore, f(6) = 2.1

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Answer:

2.1

Step-by-step explanation:

The equation subject to p is P = (n - 7/2)/q.

To solve for p, we need to isolate it on one side of the equation.

Starting with:

Pq+7/2=n

Subtract 7/2 from both sides:

Pq = n - 7/2

Divide both sides by q:

P = (n - 7/2) / q

Therefore, the solution for p is:

P = (n - 7/2) / q

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The equation that represents a proportional relationship

[tex]\[Y = \frac{1}{2}x\][/tex]

In a proportional relationship, the dependent variable (Y) is directly proportional to the independent variable (x). This means that as x increases or decreases, Y changes in a consistent ratio or fraction. In this equation, the ratio or fraction is [tex]\(\frac{1}{2}\)[/tex], indicating that for every unit increase in x, Y increases by [tex]\(\frac{1}{2}\)[/tex] units.

Let's break down the equation:

[tex]\(Y\)[/tex] represents the dependent variable, and it varies linearly with respect to the independent variable [tex]\(x\).[/tex]

The equation states that the value of Y is equal to [tex]\(\frac{1}{2}\)[/tex] times the value of [tex]\(x\).[/tex]

For example, if we have [tex]\(x = 4\)[/tex], we can substitute it into the equation to find the corresponding value of Y:

[tex]\[Y = \frac{1}{2}(4) = 2\][/tex]

So, when [tex]\(x\)[/tex] is 4, [tex]\(Y\)[/tex] is 2. This satisfies the proportional relationship because the ratio [tex]\(\frac{Y}{x}\)[/tex] remains constant at [tex]\(\frac{1}{2}\).[/tex]

Similarly, if we have [tex]\(x = -6\)[/tex], we can substitute it into the equation:

[tex]\[Y = \frac{1}{2}(-6) = -3\][/tex]

Therefore, when [tex]\(x\)[/tex] is -6, [tex]\(Y\)[/tex] is -3. Again, the ratio [tex]\(\frac{Y}{x}\)[/tex] remains constant at [tex]\(\frac{1}{2}\)[/tex].

Hence, the equation [tex]\(Y = \frac{1}{2}x\)[/tex] represents a proportional relationship where Y is directly proportional to x with a constant ratio of [tex]\(\frac{1}{2}\)[/tex].

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Answer:

62.25

Step-by-step explanation:

Rectangle Area Formula: A=l•w

7.5•5=37.5

=hbb/2=7.5·4.2/2=15.75

=hbb/2=7.5·2.4/2=

Add all three =62.25

The values of the probabilities are P(5) = 1/8 and P(Number > 2) = 75%

From the question, we have the following parameters that can be used in our computation:

The spinner

There are 8 sections on the spinner

So, we have

Section = 8

One of the sections is 5

So, we have

P(5) = 1/8

There are 6 sections greater than 2

So, we have

P(Number > 2) = 6/8

Evaluate

P(Number > 2) = 75%

Hence, the probabilities are 1/8 and 75%

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The required length is 11 units for the given triangle.

The sine rule defines the side length ratios of triangles to their opposing angles. This proportion is true for all three sides and opposing angles.

a/sinA = b/sinB = c/sinC

The triangle is given in the question, as follows:

In ΔABC, ∠A=120°, ∠B=37°, and c = 5 units

Here, ∠C= 180° - 120° - 37° = 23.

We have to determine the length of a.

As per the sine rule, the required solution would be as:

a/sin∠A = c/sin∠C

Substitute the known values and we get

a/sin 120° = 5/sin 23°

a = (18/sin 1240°) × sin 23°

k ≈ 11

Thus, the length of c is 11 units.

Hence, the number that belongs in the green box is 11.

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