Which statement best describes a sequence? a.All sequences have a common difference. b.A sequence is always infinite. c.A sequence is an ordered list. d.A sequence is always arithmetic or geometric.

Answer:

a = 4

Step-by-step explanation:

(15)(16)/ a = (3)(4)(5)

15 * 16 = 240

240/ a = (3)(4)(5)

240/a = 60

240/60 = a

a = 4

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Answer:18.5

Step-by-step explanation:

10+8=18

18*5=90

90/4

22.5-4=18.5

Answer:

12 days

Step-by-step explanation:

The answer of the problem is the LCM of 3 and 4=12. Hence the answer is 12 days

On 12 March she will swim and cycle on the same day if Amira starts an exercise program on the 3rd of March.

It is defined as the common number of two integers, which is the lowest number that is a multiple of two or more numbers. The full name of LCM is the least common multiple.

We have:

Amira starts an exercise program on the 3rd of March.

She will swim every 3 days and cycle every 4 days.

Total days =3 + 4 = 7 days = 1 week

The day she swims and cycles on the same day = LCM of 3 and 4

= 3, 6, 9, 12, 15

= 4, 8, 12, 16

= 12

Thus, on 12 March she will swim and cycle on the same day if Amira starts an exercise program on the 3rd of March.

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Answer:

Step-by-step explanation:

I'm having difficulty reading your input:  25, y, + 18, 25.  Please clarify your meaning.

5x3 – 6x2 is a polynomial expression with two terms.

The term  is a ratio.  False.   See above.

The entire expression is a difference.  True.

There are four terms.  False.   See above.

Two statements B and C are true for the expression 5x3 – 6x2 25y+ 18

A. The term is a ratio. False

B. There are three terms.terms. True

C. The entire expression is a difference. True

D. There are four terms. False

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Answer:  3.79 litres

Step-by-step explanation:

1 litre is equivalent to about ‭1.05668821‬ American quarts.

4 quarts would therefore be;

= 4/‭1.05668821‬

= 3.78541178

= 3.79 litres

Answer:

Option C - Reject H0. We have convincing evidence that the mean salary offer for accounting graduates of this university is higher than the national average of $48,722.

Step-by-step explanation:

First of all let's define the hypothesis;

Null hypothesis;H0; μ = $48,722

Alternative hypothesis;Ha; μ > $48,722

Now, let's find the test statistic for the z-score. Formula is;

z = (x' - μ)/(σ/√n)

We are given;

x' = 48,722

μ = 49,870

σ = 3900

n = 50

Thus;

z = (49870- 48722)/(3900/√50)

z = 2.08

So from online p-value calculator as attached, using z = 2.08 and α = 0.05 ,we have p = 0.037526

This p-value of 0.037526 is less than the significance value of 0.05,thus, we reject the claim that that the mean salary offer for accounting graduates of this university is higher than the national average of $48,722

Answer:

Dilation changes (x,y) values not the grid or coordinate plane. Basically, dilating a graph or a coordinate grid means the original coordinates you may have had will be changed with the dilation.  For example, a triangle plotted had its original area of 26 dilated to an area of 58.

Answer:

(a^3/b^7)^2 = (a^6/b^14)

Answer:

0.14

Step-by-step explanation:

The z score is a score used in statistics to determine by how many standard deviations ti the raw score above or below the mean. If the raw score is above the mean then the z score is positive while If the raw score is below the mean then the z score is negative, It is given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

From the normal distribution table, The area under the curve shaded is 1 to 2 = P(1 < z < 2) = P(z < 2) - P(z < 1) = 0.9772 - 0.8413 = 0.1359 ≈ 0.14

The area under the curve shaded is 1 to 2 is 0.14

Probabilities are used to determine the chances of an event

The shaded region represents the probability of the z-scores

The shaded region 1 to 2 is represented as:

P(1 < z < 2) =

Using the probability of z-score, we have the formula

P(1 < z < 2) = P(z < 2) - P(z < 1)

From the given standard normal table:

P(z < 2) = 0.9772

P(z < 1) = 0.8413

So, we have:

P(1 < z < 2) = 0.9772 - 0.8413

P(1 < z < 2) = 0.1359

Approximate

P(1 < z < 2) = 0.14

Hence, the area under the curve shaded is 1 to 2 is 0.14

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Answer:

Please do it by your shelf because if we measure it and send you may not be able to do by online .So, please do it by by yourself using your scale .

Answer:

∠ H ≈ 23°

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan H = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{FG}{HG}[/tex] = [tex]\frac{5}{12}[/tex] , thus

∠ H = [tex]tan^{-1}[/tex] ( [tex]\frac{5}{12}[/tex] ) ≈ 23° ( to the nearest degree )

Answer:

  x = 1.00995066776

  x = 2.52925492433

Step-by-step explanation:

This sort of equation is best solved using a graphing calculator. For that purpose, I like to rewrite the equation as a function whose zeros we're seeking. Here, that becomes ...

  [tex]f(x)=\log{(x)}-\log{(x-1)}^2-2\log{(x-1)}[/tex]

The attached graph shows zeros at

  x = 1.00995066776 and 2.52925492433

_____

Comment on the equation

Note that we have taken the middle term to be the square of the log, rather than the log of a square. For the latter interpretation, see mberisso's answer at https://brainly.com/question/17210068

Comment on the answer refinement

We have used Newton's method iteration to refine the solutions to this equation. The solution near 1.00995 requires the initial guess be very close for that method to work properly. Fortunately, the 1.01 value shown on the graph is sufficient for the purpose.

Answer:

The volume of this cone is V = 50 (~50.27)

(I'm assuming that 'his' is height?)

Answer: 50

Step-by-step explanation:

Answer:

x=(n+12)π, y=mπ∴x=n+12π, y=mπ and z = rπ where n∈I, m∈I, r∈I

Step-by-step explanation:

∴ LHS ≤ 2 and RHS ≥ 2

So, sin2 x = 1, cos2 y = 1 and sec2 z = 1

∴x=(n+12)π, y=mπ∴x=n+12π, y=mπ and z = rπ where n∈I, m∈I, r∈I

Answer:

137, 280 feet

Step-by-step explanation:

There are 5,280 feet in a mile.

26 * 5,280 = 137,280

There are 137, 280 feet in 26 miles.

There are 137,280 feet in 26 miles.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

We know that there are 5,280 feet in a mile.

So, the solution would be;

26 x 5,280 = 137,280

Thus, There are 137,280 feet in 26 miles.

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Answer:

x=-3 and x=4

Step-by-step explanation:

Since x=-2 is a zero of the function, we can find the other two factors by dividing f(x) by (x+2) using long division to obtain the other two roots. The quadratic obtained is x^2-x-12. Now factorising this quadratic will result in (x-4)(x+3)=0, x=-3 and 4 are the other rrots

The factorization of the function f(x) = x³ + x² - 14x - 24​ will be (x + 2), (x + 3), and (x - 4).

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

The function is given below.

f(x) = x³ + x² - 14x - 24​

Factorize the function, then we have

f(x) = x³ + x² - 14x - 24​

f(x) = x³ + x² - 14x - 24

f(x) = x³ + 2x² - x² - 2x - 12x - 24

f(x) = x²(x + 2) - x(x + 2) - 12(x + 2)

f(x) = (x + 2)(x² - x - 12)

f(x) =(x + 2)(x² - 4x + 3x - 12)

f(x) = (x + 2)[x(x - 4) + 3(x - 4)]

f(x) = (x + 2)(x + 3)(x - 4)

The factorization of the function f(x) = x³ + x² - 14x - 24​ will be (x + 2), (x + 3), and (x - 4).

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Answer:

w = [tex]\frac{ku}{d^{2} }[/tex]

Step-by-step explanation:

An equation that expresses the given relationship is ud²=1.

Given that, w varies directly with u and inversely with the square of d.

We need to write an equation that expresses the following relationship.

Direct variation is a linear function defined by an equation of the form y = kx when x is not equal to zero. Inverse variation is a nonlinear function defined by an equation of the form xy = k when x is not equal to zero and k is a nonzero real number constant.

Now, w∝u⇒w=ku

and w∝1/d²⇒w=k/d²

⇒wd²=k

⇒w=wd²u

⇒ud²=1

Therefore, an equation that expresses the given relationship is ud²=1.

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Let y be a solution to the given differential equation,

[tex]y' = xy[/tex]

where

[tex]\displaystyle y = \sum_{n=0}^\infty c_n x^n \\\\ y' = \sum_{n=0}^\infty nc_nx^{n-1} = \sum_{n=1}^\infty nc_nx^{n-1} = \sum_{n=0}^\infty (n+1)c_{n+1}x^n[/tex]

Substituting these series into the DE gives

[tex]\displaystyle \sum_{n=0}^\infty (n+1)c_{n+1}x^n = x\sum_{n=0}^\infty c_nx^n \\\\ \sum_{n=0}^\infty (n+1)c_{n+1}x^n = \sum_{n=0}^\infty c_nx^{n+1} \\\\ \sum_{n=0}^\infty (n+1)c_{n+1}x^n = \sum_{n=1}^\infty c_{n-1}x^n \\\\ c_1 + \sum_{n=1}^\infty (n+1)c_{n+1}x^n = \sum_{n=1}^\infty c_{n-1}x^n \\\\ c_1 + \sum_{n=1}^\infty \bigg((n+1)c_{n+1}-c_{n-1}\bigg)x^n = 0[/tex]

Then the coefficients [tex]c_n[/tex] in the series solution are governed by the recurrence,

[tex]\begin{cases}c_0 = c_0 \\ c_1 = 0 \\ (n+1)c_{n+1}-c_{n-1} = 0&\text{for }n\ge1\end{cases}[/tex]

We have

[tex](n+1)c_{n+1}-c_{n-1} = 0 \implies nc_n - c_{n-2} = 0 \implies c_n = \dfrac{c_{n-2}}n[/tex]

so it follows that [tex]c_1=c_3=c_5=\cdots = 0[/tex], while

[tex]c_0 = \dfrac{c_0}1 = \dfrac{c_0}{2^0\times0!} \\\\ c_2 = \dfrac{c_0}2 = \dfrac{c_0}{2^1\times1!}\\\\ c_4 = \dfrac{c_2}4 = \dfrac{c_0}{2\times4} = \dfrac{c_0}{2^2\times2!}\\\\ c_6 = \dfrac{c_4}6 = \dfrac{c_0}{2\times4\times6} = \dfrac{c_0}{2^3\times3!}[/tex]

and so on, with the general n-th coefficient being

[tex]c_n = \begin{cases}0&\text{if }n\text{ is odd} \\ \dfrac{c_0}{2^{n/2}\left(\frac n2\right)!} &\text{if }n\text{ is even}\end{cases}[/tex]

Then the power series solution is

[tex]\displaystyle y(x) = c_0 \sum_{n=0}^\infty \frac{x^n}{2^{n/2}\left(\frac n2\right)!} = c_0 \sum_{n=0}^\infty \frac1{\left(\frac n2\right)!} \left(\frac x{\sqrt2}\right)^n[/tex]

but this doesn't tell the whole story because it doesn't capture the odd-index-is-zero case.

More concisely: let n = 2k for integers k ≥ 0. Then

[tex]\displaystyle y(x) = c_0 \sum_{k=0}^\infty \frac{x^{2k}}{2^k k!} = c_0 \sum_{k=0}^\infty \frac1{k!} \left(\frac{x^2}2\right)^k[/tex]

and as a bonus, it's easier to get an exact solution for this DE,

[tex]y(x) = c_0e^{x^2/2}[/tex]

[tex] \begin{array}{l} 2^x = 3^y = 12^z \\ 2^x = 3^y = 2^{2z} \cdot 3^z \\ \Rightarrow 3 = 2^{\frac{x}{y}} \\ \Rightarrow 2^x = 2^{2z} \cdot 2^{\frac{xz}{y}} \\ \Rightarrow x = 2z + \frac{xz}{y} \\ \Rightarrow xy = 2zy + xz \\ \Rightarrow 2zy = xy - xz \\ \text{Dividing both sides by }xyz,\text{ we get:} \\ \dfrac{2}{x} = \dfrac{1}{z} - \dfrac{1}{y} \end{array} [/tex]

Answer:

opt 4

Step-by-step explanation:

when x=0, 0+3y= -3, so y=-1    (0,-1) is solution

         when x=3 , 21+3y=-3,  3y= -3-21= -24

                                                    y= -8                  (3,-8) is also solution

Answer:

86.28 ft²

Step-by-step explanation:

The figure given consists of a rectangle and a semicircle.

The area of the figure = area of rectangle + area of semicircle

Area of rectangle = [tex] l*w [/tex]

Where,

l = 10 ft

w = 8 ft

[tex] area = l*w = 10*8 = 80 ft^2 [/tex]

Area of semicircle:

Area of semicircle = ½ of area of a circle = ½(πr²)

Where,

π = 3.14

r = ½ of 8 = 4 ft

Area of semi-circle = ½(3.14*4) = 6.28 ft²

Area of the figure = area of rectangle + area of semi-circle = 80 + 6.28 = 86.28 ft² (nearest hundredth)

Answer:

the area of the figrue is 105.12

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

Integers are always whole numbers

negative, 0, positive:: whole numbers

Answer:

100000

Step-by-step explanation:

Answer:

-5-9i

Step-by-step explanation:

-1-8i-4-i

-1-4-8i-i

-5-9i

Answer:

fourth option

Step-by-step explanation:

Common difference is given by difference of two consecutive term

d = nth term - (n-1)th term

______________________________________

for all the  series lets take second term as nth term

and first term as (n-1)th term

_________________________________________

for first series

n th term = -3 1/2 = -3.5

(n-1)th term = -5

therefore

d= -3.5 -(-5) = -3.5 +5 = 1.5

______________________________________

for second series

n th term = 4 1/2 = 4.5

(n-1)th term = 2 1/2 = 2.5

therefore

d= 4.5 -(2.5) =2

_________________________

for third series

n th term = 3

(n-1)th term =1.5

therefore

d= 3 - 1.5 = 1.5

__________________________________

for fourth series

n th term = -1.5

(n-1)th term = -4

therefore

d= -1.5 -(-4) = -1.5 + 4 = 2.5 = 2 1/2

___________________________________

Thus, based on above solution option four has common difference of 2 1/2

Answer:

243

Step-by-step explanation:

The general term for this arithmetic sequence is:

a(n) = -2 + 5(n - 1).

Then a(50) = -2 + 5(49) =   243

Answer:

Below

Step-by-step explanation:

● (3.5× 10^8) × (4×10^(-12))

● (3.5×4) × (10^8 × 10^(-12) )

● 14 × 10^ (-12+8)

● 14 × 10^(-4)

● 14/10^4

Answer:

work is shown and pictured