For each exponential generating function below, give a formula in closed form for the sequence {anin >0} it represents. b. XP 32 1. d. ext

Answer:

4x-3y=6

because it is a way to write in standard form

Answer:

[tex] \frac{4}{5} x + 2y = 6[/tex]

is the correct answer

Step-by-step explanation:

The standard form of a equation is Ax+By=C

Third option satisfy it so option (c)is the correct Answer.

The required point estimate of the population mean and the margin of error are 16 and 4.

The point estimate is the value of a statistic that estimate the value of the parameter.

According to given data in the question:

Given, lower point =12, upper point = 20

we know that

Population mean(x) = 12+20/2 = 16

And formula for margin o error,

x + E = upper point  , x - E = lower point

Then, 16 + E = 20

E = 4

Similarly, 16 - E = 12

E = 4

Hence, population mean and margin of error are 16 and 4 respectively.

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Answer: The last option, [tex]8\sqrt{2}[/tex]

Step-by-step explanation:

       When looking at this triangle, there are two things we can note about it right away. First, it's a right triangle so we can use the Pythagorean theorem. Second, the two legs of the triangle are congruent (as shown by the dash lines) so both of them are equal to 8.

       Using the Pythagorean theorem we will solve.

a² + b² = c²

(8)² + (8)² = c²

64 + 64 = c²

128 = c²

c = [tex]\sqrt{128}[/tex]

c = [tex]\sqrt{64*2}[/tex]

     c = [tex]8\sqrt{2}[/tex]

The critical numbers of the function  x³ - 6x² + 15 is 0 and 4

The given function is x³ - 6x² + 15

To find the critical value first we need to find the derivative, then set the derivative f'(x) to zero

The derivative of  x³ - 6x² + 15 is

3x³⁻¹ - 2(6)x²⁻¹  = 0

3x² - 12x = 0

3x(x - 4) = 0

3x = 0

x = 0

x - 4 = 0

x = 4

so, x = 0 or 4

Therefore, the critical numbers of the function  x³ - 6x² + 15 is 0 and 4

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The required distance of Cori from where he started is 35km.

Distance is a quantitative or qualitative measurement of the distance between two objects or places. Distance can refer to a physical length or an estimation based on other criteria in physics or everyday usage. Because spatial cognition is a rich source of conceptual metaphors in human thought, the term is also used metaphorically to mean a measurement of the amount of difference between two similar objects or a degree of separation. The concept of a metric space is used to codify most such conceptions of distance, both physical and metaphorical.

Given,

Cori races her friend heading south for 9 kilometers, east for 20 kilometers, then south for 6 more kilometers.

The distance of Cori from starting point=9+20+6

=15+20

=35

Hence, the required distance of Cori from where he started is 35km.

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The constant of proportionality of the equation  y = 1 / 4 x is 1 / 4.

Proportional relationships are relationships between two variables where their ratios are equivalent.

A proportional relationship is one in which two quantities vary directly with each other. We say the variable y varies directly as x if:  

y = k x

for some constant k , called the constant of proportionality.

Therefore, let's model the equation to the y = 1 / 4 x .

Therefore, the constant of proportionality is 1 / 4.

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The sentence translated to an equation is given by 8(x+2) = 4.

Let the variable be x which is the unknown number.

Sum of the variable and 2 is represented by (x+2) .

8 times the sum = 8 (x+2)

The sum is equal to 4.

∴  8 (x+2) = 4

Therefore the required equation is  8 (x+2) = 4 .

An equation is regarded as linear when its highest power continuously equals 1. It is also stated as a one-degree equation. A linear equation with one variable typically has the form Ax + B = 0.

In this case, the variables x is a variable while the variable B is a constant. A linear equation with two variables often has the form Ax + By = C. The variables x and y, their respective coefficients A and B, and the constant C are present in this scenario.

In contrast to a linear equation with two variables, x and y, the graph of a linear equation with one variable, x, forms a vertical line that is parallel to the y-axis and vice versa.

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The correct choice regarding the grammar illustrated is A. two thousand people are expected to attend the conference, with 965 coming from outside of the United States.

The grammar of a natural language is the set of structural constraints on the composition of clauses, phrases, and words by speakers or writers. The term can also refer to the study of such constraints, which includes domains such as phonology, morphology, and syntax, which are frequently supplemented by phonetics, semantics, and pragmatics.

There are currently two approaches to grammar study: traditional grammar and theoretical grammar. In this case, it should be noted that the fact that 2000 is written in words make it more logical and better.

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Solving for the unknown variable t in the natural exponent  expression 3e^9t = 100 gave

The given expression is given in natural exponent and is solved as follows

3e^9t = 100

dividing through by 3

3e^9t / 3 = 100 / 3

e^9t = 100/3

take natural logarithm of both sides

In e^9t = In (100/3)

9t = In (100/3)

divide through by 9

9t / 9 = 3.5065578 / 9

t =  0.3896175

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The rectangle-shaped tank is 10 feet by 8 feet by 8 feet is  4800 gallons of water.

Cubic foot holds 7.5 gallons of water

We need to find the amount of gallons of water can a rectangle-shaped tank is 10 feet by 8 feet by 8 feet.

Vol = L*W*H

10 x 8 x 8

640 cubic feet

1 cubic feet hold 7.5 gallons of water

640 cubic feet hold 7.5 x 640 = 4800

Therefore, the amount of gallons of water can a rectangle-shaped tank is 10 feet by 8 feet by 8 feet is  4800 gallons of water.

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In Mexico, 350 dollars would be equivalent to 6769.21 Mexican Pesos.

What is currency conversion?

Currency conversion is the process of exchanging one type of currency for another to facilitate transactions in which the issuer and acquirer use different currencies. Currency conversion usually incurs some additional costs for the customer.

In Mexico, 1 US dollar = 19.34 Mexican Pesos

So In Mexico, $350 = 350 * 19.34

                                 = 6769.21 Mexican Pesos.

Hence, In Mexico, 350 dollars would be equivalent to 6769.21 Mexican Pesos.

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The profit exceeds the cost as y > 1000 + 15x. So, option 1 is correct.

Gaining anything is known as profit. When the Selling price ( SP ) of the product is more than the cost price ( CP ) of the product, we gain profit. Opposite to the profit is loss i.e. losing anything is called loss. When the Selling price ( SP ) of the product is less than the cost price ( CP ) of the product, we get a loss.

Profit can be calculated by the formula,

Profit   =   Selling Price - Cost price

      P   =   SP - CP

Loss can be calculated by the formula,

Loss   =   Cost price - Selling price

    L    =   CP - SP

As per the question,

⇒  When y > 1000 + 15x, then profit exceeds cost:

Therefore, the graph in the 1st option is correct as the profit exceeds the cost.

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The complete question is

The probability that the wheel stops on a white slice, given that the wheel stops on a number less than 9 is 1/2.

We have given that

A spinner with 8 equally size slices numbered 1 to 8 and some slices are white and other gray in colour .

Total possible outcomes = 8 = {1,2,3,4,5,6,7,8}

we have to calculate probability that the wheel stops on a white slice, given that the wheel stops on a number less than 9?

let consider two events

A : wheel stops at white

B: wheel stops on white slice and number less than 9

favourable cases for event A = 4

= { 8,4,2,1}

P( wheel stops at white colour)

= favourable cases/total possible outcomes

= 4/8 = 1/2

favourable cases for event B = 4

= {1,2,4,8}

Probability ( wheel stops white slice with numbered less than 9)= white slice with number less than 9/ total slices numbered less than 9

= 4/8 = 1/2

Hence, the required probability is 1/2.

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Complete question:

spinner has 8 equally sized slices numbered from to 1&8 Some are white and some are grey, as shown below. 1 2 3 4 5 6 7 8 . Answer the following questions Write each answer a fraction. The wheel will be spun and will stop on a slice at random (a) What Is the probabllity that the wheel stops on grey slice, glven that the (b) wheel stops on &n even-numbered slice?

The confidence interval for the mean is (10.7485, 11.6515)

Given Data:

n = 225

×= 11.2

s = 4.1

Note that, Population standard deviation([tex]\alpha[/tex]) is unknown. So we use t distribution.

Our aim is to construct a 90% confidence interval.

c = 0.90

[tex]\alpha[/tex] = 1- c = 1- 0.90 = 0.10

[tex]\alpha[/tex]/2 = 0.10/2 = 0.05

Also, d.f = n - 1 = 225 - 1 = 224

t[tex]\alpha[/tex]/2.d.f- = t[tex]\alpha[/tex]/2.n-1 = t0.05,224 = 1.652

( use t table or t calculator to find this value..)

The margin of error is given by

E = t[tex]\alpha[/tex]/2,d.f. * (s / [tex]\sqrt{n}[/tex])

= 1.652 * (4.1/ √225)

= 0.4515

Now , confidence interval for mean(\mu) is given by:

(× - E ) <  μ< x + E)

(11.2 - 0.4515) < μ < (11.2 + 0.4515)

10.7485 < μ< 11.6515

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The shorted life expectancy to be in top 5% is 52.225

Given that.

Mean = 44

Standard Deviation = 5

a)

Z =36 – 44/5

Z =-8/5

Z =-1.6

P(z<-1.6)=normsdist(-1.6)=0.0548

b)

P(Z > 2) = 0.05

P(Z <=) = 1 -0.05 = 0.95

z=normsinv(0.95)=1.645

shorted life expentancy to be in top 5%=

= 44+1.645*5

Shorted life expentancy to be in top 5% = 52.225

For Minitab use:

Choose Calc > Probability Distributions > Normal.

Select Inverse cumulative probability.

In Mean, enter 44.

In Standard deviation, enter 5.

In Input column, enter Probability=0.95

Hence, The shorted life expectancy to be in top 5% is 52.225.

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Answer:

1640y

Step-by-step explanation:

the reason is y is known as variables constant is number 48y is a monomial that is why it is 26840y

The evaluation of the paths of the ellipse and hyperbola are as follows;

Part A: The vertices are; (0, 36), (0, -4)

Part B: Comet H comes closest to the sun

Part C: The location of the Sun is the location of the x-coordinate of the path of both ellipse

An ellipse is the locus of a point that moves such that the sum of the distances from two points, known as the focal points, is a constant

Part A: The standard form of the equation of a hyperbola is presented as follows;

[tex]\dfrac{(x - h)^2}{a^2} -\dfrac{(y-k)^2}{b^2} =1[/tex]

Where;

(h, ,k) = The center of the ellipse

a = Vertex to center distance

c = The distance from center to foci

The equation of an ellipse is presented as follows  

[tex]\dfrac{(x - h)^2}{a^2} +\dfrac{(y-k)^2}{b^2} =1[/tex]

The vertices of the ellipse are; a + h and k + b

The specified equation is presented as follows;

Comet E = [tex]\dfrac{(y+16)^2}{400} +\dfrac{x^2}{144} =1[/tex]

The vertices for the comet E are;

(0, 20 + 16) = (0, 36) and (0, 16 - 20) = (0, -4)

Part B: Comet H = [tex]\dfrac{(y+13)^2}{144} +\dfrac{x^2}{25} =1[/tex]

The vertex of the comet H = (0, -13 + 12) = (0, -1), and (0, -13 - 12) = (0, -25)

Based on the location of the comet H close to the origin, the comet that comes closest to the Sun is comet H

Part C; The location of the Sun at the origin is the location of the x-coordinate of the center of both comets

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Answer:

[tex]\frac{3} {4}[/tex] cup

Step-by-step explanation:

[tex]\frac{1}{2}[/tex] as a decimal = 0.5

[tex]\frac{3}{4}[/tex] as a decimal = 0.75

The number of choice out of 7 that consumer have are 42.

The term permutation alludes to a numerical computation of the quantity of ways a specific set can be sorted out. Set forth plainly, a change is a word that depicts the quantity of ways things can be requested or organized. With stages, the request for the course of action matters.

Number of choices of side dishes does a customer have,

total dishes(n)=7 , r = 2

ⁿP₂

⁷P₂

7×6 = 42

Thus required number of ways are 42.

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There are 2 rearrangements of abcd in which no two adjacent letters are also adjacent letters in the alphabet.

What is letter arrangements?

A sorting technique that allows the person to arrange alphabets as conditioned according to the question. Then total arrangements are calculated to know the result.

According to the given question:

Using XXXX as stencil for letters arrangement

We can't put B in either of the middle positions, as there would only be the far end at which to put both A and C and we can't put two things in one slot. That is, XBXX would require A and C to both be in the red X in order to avoid putting them next to B...can't do that, so B can't go in the middle.

Similarly, we can't put C in either of the middle positions, as there would only be the far end at which to put both B and D and we can't put two things in one slot.

So, B and C must go on the ends.

BXXC can only be filled in as BDAC.

CXXB can only be filled in as CADB.

Hence there are 2 such arrangements.

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Answer:

loss of $825

Step-by-step explanation:

$275 x 3 =$825

Answer: 825

Step-by-step explanation:

Just times 275 by 3 and you have the answer.

It will take 20 minutes to dissipate the queue that resulted from blockage if

the freeway has the capacity of 4000 vph.

Mean service rate(M) = 4000vph

Mean arrival rate(λ)  = 3000vph

Block time duration of queue (r) = 5min

Time taken to dissipate the queue =  t

t = (M * r)/(M-λ)

Substitute  the given values

t  =  (4000*5)/(4000-3000)

t = 20000/1000

t = 20minutes.

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The real percentage off of pant in the store was 39.99% in the store, which was less than the stated 70% off sign present on the door of store.

The percentage off will be calculated by the formula -

Percentage off = change in cost/original cost × 100

Change in cost = original cost - new cost

Change in cost = 49.99 - 30.

Performing subtraction on Right Hand Side of the equation

Change in cost = 19.99

Keep the values in formula for calculation of percentage off -

Percentage off = 19.99/49.99 × 100

Performing division on Right Hand Side of the equation

Percentage = 0.3999 × 100

Performing multiplication on Right Hand Side of the equation

Percentage = 39.99%

Thus, there was 39.99% off.

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The solution to the system of linear equations is (0,2).

What is equation?

In arithmetic, an equation may be a formula that expresses the equality of 2 expressions, by connecting them with the sign =.

Main body:

2x + 3y = 6 multiplied by 3

-3x + 5y = 10 multiplied by 2

6x + 9y = 18

-6x + 10y = 20

19y = 38

y = 38 / 19

y = 2

2x + 3x2 = 6

2x + 6 = 6

2x = 0

x = 0/2

x = 0

Therefore, The correct answer is (0,2)

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According to the central limit theorem, the given statement is true.

In the given question we have to check the given statement is true or false.

The given statement is:

"Based on the central limit theorem, the sample mean can be used as a good estimator of the population mean, assuming that the sample size, is sufficiently large."

As we know that the average of set of data is known as a sample mean.

Regardless of the distribution of the population, the central limit theorem states that the distribution of sample means approaches a normal distribution as the sample size increases. The Central Limit Theorem is frequently thought to hold for sample sizes equal to or larger than 30.

So according to the central limit theorem, the given statement is true.

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The sixth term of the arithmetic sequence 11, 15, 19, 23, 27, ..... will be 31.

Let a₁ be the first term and d be a common difference.

Then the nth term of the arithmetic sequence is given as,

aₙ = a₁ + (n - 1)d

The arithmetic sequence is given below.

11, 15, 19, 23, 27, .....

The first term is 11. And the common difference between the terms is given as,

d = 15 - 11

d = 4

Then the nth term is given as,

aₙ = 11 + (n - 1) × 4

At n = 6, then the 6th term is given as,

a₆ = 11 + (6 - 1) × 4

a₆ = 11 + 5 × 4

a₆ = 11 + 20

a₆ = 31

The sixth term of the arithmetic sequence 11, 15, 19, 23, 27, ..... will be 31.

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None of these are correct.

m/HZN = m/TZY, so m/YZT = m/HZN demonstrate commutative property

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The simplified form of the expression is, negative five sixths times x plus eight.

What is word problem?

A math word problem is a mathematical question that is stated as one sentence or more and asks students to use their arithmetic skills in a "real-life" situation. Therefore, in order for kids to understand the word problem, they need to be familiar with the terminology that goes along with the mathematical symbols that they are used to.

Given that:   quantity negative two thirds times x minus 6 end quantity minus quantity negative 14 plus one sixth times x end quantity

It can be write in mathematical form as,

[tex](-\frac{2}{3}x-6) - (-14+\frac{1}{6}x)[/tex]

Simplifying the parenthesis,

[tex]= -\frac{2}{3}x-6+14-\frac{1}{6}x\\ = 8 - \frac{15}{18}x\\ = 8 - \frac{5}{6}x\\= -\frac{5}{6}x+8[/tex]

Hence, the simplified form of the expression is, negative five sixths times x plus eight

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The solution set of the inequality |x+2| ≤ 5 is x ∈ [-7,3].

The word inequality means a mathematical expression in which the sides are not equal to each other.

Basically, an inequality compares any two values and shows that one value is less than, greater than, or equal to the value on the other side of the equation.

The modulus function, which is also called the absolute value function gives the magnitude or absolute value of a number irrespective of the number being positive or negative.

Modulus function is denoted as y = |x| or f(x) = |x|, where f: R→ (0,∞) and x ∈ R.

Here, we have an inequality  |x+2| ≤ 5

Solving the modulus , we get

          -5 ≤ x+2 ≤ 5

Subtracting -2 from both sides, we get

      ⇒ -5-2 ≤ x ≤ 5 -2

      ⇒ -7 ≤ x ≤ 3

      ⇒ x ∈ [-7,3]

Therefore, the solution set of the inequality is x ∈ [-7,3].

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NOTE : The question given here is not complete. The complete question is given below.

Question: What is the solution set of the inequality |x+2|≤ 5 ?

The material cost will be $361.1

The tent ha no floor, and it ha a radiu of 3 ft, and a slant height of 5 ft. If canva ell for $23. 00/yd²

Then, radius of base = 3​

Therefore, area of conical tent =πrl

area of conical tent = 3.14 x 3 x 5

area of conical tent = 47.1

If cost of canvas is $23. 00/yd²

1 yard = 3 feet

Then cost of canvas = (47.1/3) x 23.00

cost of canvas = 361.1

Therefore, the material cost will be $361.1

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