The first term of a geometric sequence is 5 and the sixth term is 160.
What is the common ratio?

Two two numbers whose difference is 88 and whose product is a minimum are -44 and 44.

Let the numbers be x and y where x is larger value and y is smaller number.

According to ques,

x - y =88

and we need to make product of numbers i.e 'xy' minimum.

So we can take x = 88 + y ------(2)

substituting value of x in xy, we get

(88 + y) (y) = y² + 88y ------(1) to make it minimum we need to equate its derivative equal to zero.

derivative of  (1) is 2y + 88

Equating it to zero, we get

2y + 88 = 0

subtracting 88 from both sides, we get

2y = -88

Dividing 2 from both sides, we get

y = -44 ------(3)

Substituting value of y from (3) in (2), we get

x = 88 - 44

x = 44

So, we get value of x as 44 and y as -44 to get their product as minimum.

Learn more about word problem here:

https://brainly.com/question/1553954

#SPJ4

Answer:

20090089$

Step-by-step explanation:

Answer: $359

Step-by-step explanation:

I got the same problem on DeltaMath- You use the formula A = P ( 1 + r/n ) ^nt

P = 4700

R = 0.055

T = 12

N = 4

You plug it in to get 9052.7283 and then subtract 8693.386 to get 359.3423 which rounds to 359

The example of rational function is option(1) which is f(x)=3x²+1 over x-1

What is Rational Function ?

Hence, the example of rational function is option(1) which is f(x)=3x²+1 over x-1.

To read more about Rational Function

https://brainly.com/question/1851758

#SPJ1

The large figurine old for $12 each, and the mall figurine old for $8 each. The amount of money he received from the ale of the large figurine wa equal to the 42

Let x represent the number of large figurines that Kami sold.

Let y represent the number of small figurines that Kami sold.

This month kami sold 70 figurines in 2 sizes. This means that

x + y = 70 - - - - - - - - - - 1

The large figurines sold for $12 each and the small figurines sold for $8 each. The amount of money he received from the sales of the large figurines was equal to the amount of money he received from the sales of the small figurines. This means that

12x = 8y

y = 12x/8

y = 1.5x

Substituting y = 1.5x into equation 1, it becomes

x + 1.5x = 70

2.5x = 70

x = 70/2.5 = 28

y = 1.5x = 1.5 × 28 = 42

learn more about of amount here

https://brainly.com/question/14520535

#SPJ4

The point (25,125) means that the monthly home heating bill was $5 for an average monthly temperature of 1°F.

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

Point (25, 125)

This point can be expressed as

(x, y) = (25, 125)

The average monthly temperature bill is then calculated using the following equation

Average monthly temperature bill = y/x

Substitute the known values in the above equation, so, we have the following representation

Average monthly temperature bill = 125/25

Evaluate

Average monthly temperature bill = 5

Hence, the average monthly temperature = 5

Read more about slope at

https://brainly.com/question/3493733

#SPJ1

The following, find 2 solutions and 2 non solutions is [tex]x=\frac{30-5 y}{2}[/tex]

What is non solutions?

Ideal solutions are those that follow Raoult's law throughout the whole concentration range. A solution is said to as a non-ideal solution if it violates Raoult's law.

[tex]$$2 x+5 y=30$$[/tex]

[tex]Move $5 y$ to the right side[/tex]

[tex]$$2 x=30-5 y$$[/tex]

[tex]Divide both sides by 2[/tex]

[tex]$$\frac{2 x}{2}=\frac{30}{2}-\frac{5 y}{2}$$Simplify$$x=\frac{30-5 y}{2}$$[/tex]

Non solutions, in the plural, refer to anything that falls short of offering a fix for a problem. These batteries also lose their charge, rendering them useless for solving the more significant issue of storing and utilizing renewable energy.

To learn more about non solutions visit

https://brainly.com/question/3184550

#SPJ1

The resistance of wire to the nearest hundredth of one mile of the wire with mentioned details is 2.59 ohm.

Firstly we will convert length of wire to feet. As per the known information, 1 mile is 5280 feet. Moreover, as known resistance and length are directly proportional to each other.

Resistance 1/Resistance 2 = length 1/length 2

0.65/Resistance 2 = 1325/5280

Rewriting the equation according to length 2

Resistance 2 = (0.65×5280)/1325

Performing multiplication on Right Hand Side of the equation

Resistance 2 = 3432/1325

Performing division on Right Hand Side of the equation

Resistance 2 = 2.59 ohm

The resistance of wire is 2.59 ohm.

Learn more about resistance -

https://brainly.com/question/17563681

#SPJ4

a^45d^9

To find the fifteenth term of the binomial expansion of (a³+d)24, we can use the binomial theorem, which states that the expansion of (a+b)n is given by the sum of the terms in the following formula:

(a+b)^n = a^n + na^(n-1)b + (n(n-1))/2a^(n-2)*b^2 + ... + b^n

Answer: 1,961,256a³⁰d¹⁴

Step-by-step explanation:

[tex]\displaystyle\\(x+y)^n \ is\ the\ binomial\ expansion \\\\The\ k\ term =C_n^{k-1}x^{n-k+1}y^{k-1}\\\\ n - the\ power \ of\ the \ binomial\\\\k - number\ of\ the\ term \ of\ the\ binomial[/tex]

                                        [tex](a^3+d)^{24}[/tex]

[tex]The \ fifteenth\ term=C^{15-1}_ {24}(a^3)^{24-15+1}d^{15-1}\\\\The \ fifteenth\ term=C^{14}_{24}(a^3)^{10}d^{14}\\\\The \ fifteenth\ term=\frac{24!}{(24-14)!14!} a^{30}d^{14}\\\\The \ fifteenth\ term=\frac{24!}{10!14!}a^{30}d^{14} \\\\The \ fifteenth\ term=1,961,256 a^{30}d^{14}[/tex]

C. The slope of the graph is 1/3

Slope = (y2 - y1) ÷ ( x2- x1)

y2= 5, y1=2, x2=9, x1=0

y2-y1 = 5-2 = 3

x2-x1 = 9-0 = 9

Slope = 3/9 = 1/3

The value of x is 27 in the given figure.

An angle is formed when two straight lines or rays meet at a common endpoint.

We need to find the value of x.

The given two angles are (4x+7) and 5(x-4).

The two angles are opposite angles so the two angles are equal.

Let us equate 4(x+7) and 5(x-4).

4x+7=5(x-4).

Apply distributive property on RHS

4x+7=5x-20

4x-5x=-20-7

-x=-27

Multiply both sides by minus

x=27.

Hence, the value of x is 27.

To learn more on Angles click:

https://brainly.com/question/28451077

#SPJ1

The coefficient x⁵ in expansion of (2x - 1)⁶ is; -192

We are given the expression;

(2x - 1)⁶

Using Pascals triangle, the coefficient of the terms here are;

1      6     15     20     15     6     1

The general formula for binomial expansion is;

(x + y)ⁿ = ⁿC₀xⁿy⁰ + ⁿC₁xⁿ⁻¹y¹ + ⁿC₂xⁿ⁻²y²+......+ ⁿCₙx⁰yⁿ

Thus, we can find the expansion of (2x - 1)⁶ as;

1[(2x)⁶ * (-1)⁰] + 6[(2x)⁵ * (-1)¹] + 15[(2x)⁴ * (-1)²] + 20[(2x)³ * (-1)³] + [15(2x)² * (-1)⁴] + [6(2x)¹ * (-1)⁵] + [1(2x)⁰ * (-1)⁶]

= 64x⁶ - 192x⁵ + 240x⁴ - 160x³ + 60x² - 12x + 1

The coefficient we are looking for is -192

Read more about Binomial expansion at; https://brainly.com/question/13602562

#SPJ1

-480 ÷ 8 = -60

2x = -120

-20 × 3 = -60

(2 × 3) × (-5 × 2) = -60

Answer:

option c

Step-by-step explanation:

c. 9 billion people

Answer:

B. 9 Billion people

Step-by-step explanation:

189.55

...

.............

...

The product of the given numbers is, [tex]-7\frac{7}{16}[/tex].

What is product?

One of the four fundamental arithmetic operations, along with addition, subtraction, and division, is multiplication. A product is the output of a multiplication operation.

The outcome of multiplying two or more numbers together in mathematics is called the product. With the help of examples, learn more about the product of fractions and decimals.

Given:

2 and one-eighth times negative 7 times five tenths.

We have to determine the product.

[tex]2\frac{1}{8} (-7)(\frac{5}{10} )[/tex]

Convert improper fraction into a fraction

[tex]2\frac{1}{8} = \frac{(2)(8)+1}{8} = \frac{17}{8}[/tex]

⇒

[tex](\frac{17}{8} )(-7)(\frac{1}{2}) \\-\frac{119}{16} \\-7\frac{7}{16}[/tex]

Hence, the product of the given numbers is, [tex]-7\frac{7}{16}[/tex].

To know more about product, click on the link

https://brainly.com/question/13934852

#SPJ1

Answer:

-1 /3

Step-by-step explanation:

To get from one point to the next, go DOWN1 and OVER3.

DOWN1 and OVER3 is the slope -1/3

From B to C it looks like DOWN2 and OVER6. That is -2/6. But that can be reduced to -1/3. So its the same.



A triangle has three angles that measure 16˚, 38˚ and 126˚ will lead to

There are an infinite number of triangles produced when no side is specified.

The three angles produce an unlimited number of distinct triangles if side lengths are not provided.

The option that offered just angles—namely, angles of 16˚, 38˚ and 126˚—and no sides—meets the requirement for the production of an infinite number of triangle sides.

When there are options have sides or a side is provided, but not in accordance with that, to form an infinite number of triangles.

This condition forms infinite number of triangles

Learn more about Infinite number of triangles at:

https://brainly.com/question/29637739

#SPJ1

Answer:

C) Infinite (More than one)

Step-by-step explanation:

Answer:

Step-by-step explanation:

The given sequence is an arithmetic sequence with a common difference of 4. The 77th term of the sequence is the 77th term of the arithmetic sequence, which is given by the formula:

a_n = a_1 + (n - 1) * d

where a_n is the nth term of the sequence, a_1 is the first term of the sequence, and d is the common difference. Substituting the values for a_1, n, and d into this formula, we get:

a_77 = -8 + (77 - 1) * 4

= -8 + 76 * 4

= -8 + 304

= 296

Therefore, the 77th term of the sequence is 296.

The unit rate of the graph that represents the proportional relationship is $12.5, which is below $13 per week. Therefore, Louis made the correct statement.

The graph of a proportional relationship is typically a straight line that runs through the point of origin (0, 0).

The slope of the graph gives the unit rate, which is calculated as m = y/x.

Given the graph that shows the proportional relationship between the number of weeks and the amount spent on coffee, we can use one point on the line, (4, 50) to find the unit rate, which will given us how much is spent per week.

Therefore:

Slope/unit rate or amount spent per week = y/x = 50/4 = $12.5.

Based on this, we can state that Louis is correct by saying Janie has not met her goal, because $12.5 per week is below the target of $13 each week.

Learn more about the proportional graph on:

https://brainly.com/question/23318486

#SPJ1

Answer: $892.44

Step-by-step explanation:

Take 27 times 18.66 = $503.82

Then take 34 times 11.43 = $388.62

Then add them to find total

503.82 + 388.62 = $892.44

The owner only owe $892.44

Let x is average for rest of seven test. Then average for remaining test is x= 2.27

The middle number, which is obtained by dividing the sum of all the numbers by the variety of numbers, is the average value in a set of numbers. To calculate the average of a set of data, add up all the values and divide the result by the total number of values.

The middle point of the set of values is the mean. It represents the mean of the data set's values. In statistics, the centre number, also known as the mean, is referred to as the average.

We want the TOTAL average to equal 94

4/9 of the 5 scores have an average of 178

Let x = average of the 5 remaining test, which is worth 5/9 of the total average.

We get: 94 = (4/9)(178) + (5/59)(x)

94=712/9+59x/9

846=712+59x

846-712=59x

134=59x

134/59=x

Solve: x = 2.27

To learn more about average value visit the link:

https://brainly.com/question/130657

#SPJ4

A 95% confidence interval with a 4% margin of error suggests that your statistic will be 95% of the time within 4 percentage points of the true population value.

A survey, may reveal that the 98% confidence interval is between 4.88 and 5.26. So, if the poll is repeated using the same methods, the true population parameter (parameter vs. statistic) will fall 98% of the time within the interval estimates (i.e. between 4.88 and 5.26).

The formal definition, on the other hand, includes a little more information. The margin of error in a confidence interval is defined as the range of values below and above the sample statistic. The confidence interval is a tool for demonstrating the level of uncertainty associated with a certain statistic (i.e. from a poll or survey).

In 2012, a Gallup poll (incorrectly) predicted that Romney would win the election, with Romney polling at 49% and Obama polling at 48%. The declared level of confidence was 95%, with a margin of error of 2. We can conclude that the results were computed to be 95% accurate within 2 percentage points.

To learn more about confidence interval visit:

https://brainly.com/question/24131141

#SPJ4

The anticipated total number of heads produced by this method is 1/2n=N when fair coin is tossed n times, and the results are tallied by counting the heads.

Given that,

A fair coin is tossed n times, and the results are tallied by counting the heads. The coin is then thrown a further n times.

We have to calculate the anticipated total number of heads produced by this method.

We know that,

Either head or tail will appear when a coin is tossed.

The sample space of a random experiment is the collection of all feasible results. Therefore, if your random experiment involves flipping a coin, the sample space is "Head, Tail," or more tersely, "H, T."

So,

1/2n=N

Therefore, the anticipated total number of heads produced by this method is 1/2n=N when fair coin is tossed n times, and the results are tallied by counting the heads.

To learn more about number visit: https://brainly.com/question/17429689

#SPJ4

The equation used to represent the situation:

Cost per pound = Total Cost of Turkey / Number of Pounds

A formula known as an equation uses the equals sign to express how two expressions are equal. The meanings of the word equation and its translations into other languages might vary slightly; Finding the values of the variables that cause the equality to be true is the first step in solving an equation with variables.

Quantity = 19 pounds

Total Cost = $25.65

Now to calculate the cost of Turkey per pound, we can use the following equation:

Cost of Turkey per pound = Total Cost / Quantity of Pounds

Cost per pound = 25.65 / 19

Therefore, the cost of turkey per pound = $1.35

To know more about Equation, refer to this link:

https://brainly.com/question/12788590

#SPJ4

Answer:

Step-by-step explanation:

The best bank depends on the amount that Gerard will deposit. He can open an account with My bank and receive $100, or he can open with New bank and deposit lets say $5000 and he would receive an additional $250 because of the 5% bonus. It depends on the amount that Gerard is putting into the bank account when he opens it.

Answer:

(1,-6)

Step-by-step explanation:

Ordered pairs are (x,y)

The vertex of the quadratic formula is its lowest point if opening up, and its highest point if opening down

This one opens up so it is the lowest point

The x value of the vertex is x=1

the Y value of the vertex is y=-6

The statement which is true for the inequality will be equal to 9 > -5, so 9 is located to the right of -5 on a horizontal number line.

A straight line of numbers is shown visually as a number line. This line is employed to compare integers on an endless line that extends on both sides, either horizontally or vertically, at equal intervals.

As per the given inequalities given in the question,

1.

-10 > -15, so -10 is located to the left of -15 on a horizontal number line.

The statement is wrong because -10 is located on the right side of -15

2.

8 > -13, so 8 is located to the left of -13 on a horizontal number line.

The statement is wrong because 8 is located on the right side of -13.

3.

9 > -5, so 9 is located to the right of -5 on a horizontal number line.

This statement is true, that 9 is located to the right of -5.

4.

-6 < 1, so -6 is located below 1 on a vertical number line.

This statement is true, that -6 is located to the below of -5.

5.

-14 > 7, so -14 is located below 7 on a vertical number line.

This statement is false.

6.

11 < -13, so 11 is located to the right of -13 on a horizontal number line.

This statement is also false.

To know more about number line:

https://brainly.com/question/13425491

#SPJ1

The orientation factor in a chemical reaction relates the frequency factor to the collision factor and depends on the extent of complexity of the reactants in a reaction.

Does the orientation factor depend on temperature?

The direction of the collision between the chlorine atoms and the ozone determines the pace of reaction; if the direction is incorrect, no reaction takes place. The right orientation will allow for response. The direction of collisions is independent of temperature.

According to the Collision Theory, molecules must collide with sufficient activation energy to break and re-form existing bonds, as well as with favorable spatial orientation, in order for a chemical reaction to occur.

To learn more about  Collision Theory visit:https://brainly.com/question/14566831

#SPJ4