The sum of the first three terms of a geometric sequence of positive integers is equal to seven times the first term, and the sum of the first four terms is 45. What is the first term of the sequence

The probability of randomly selecting the chair and the ranking member is 1/105 or approximately 0.0095.

There are 15 members of the Senate Committee on Homeland Security and Governmental Affairs, two of whom are selected to serve as the committee chair and ranking member. Each member is equally likely to be chosen for either of these positions.

To begin, we must first determine the total number of ways two members can be selected from a committee of 15. This is calculated using the combination formula:

nCr = (n!)/((r!)(n-r)!)where n = 15 and r = 2.

Thus,

nC2 = (15!)/((2!)(15-2)!)

nC2 = (15x14)/(2x1)nC2

= 105

Now we must determine the probability of selecting one member to be the committee chair and the other to be the ranking member.

This is calculated as follows: P = 1/105 or approximately 0.0095. Hence, the probability of randomly selecting the chair and ranking member is 1/105 or approximately 0.0095.

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Answer:

\(y = \frac{1}{2}e^x -\frac{1}{2} e^{2-x}\)

Step-by-step explanation:

Given

\(y=c_1e^x +c_2e^{-x\)

\(y(1) = 0\)

\(y'(1) =e\)

Required

The solution

Differentiate \(y=c_1e^x +c_2e^{-x\)

\(y' = c_1e^x - c_2e^{-x}\)

Next, we solve for c1 and c2

\(y(1) = 0\) implies that; x = 1 and y = 0

So, we have:

\(y=c_1e^x +c_2e^{-x\)

\(0 = c_1 * e^1 + c_2 * e^{-1}\)

\(0 = c_1 e + \frac{1}{e}c_2\) --- (1)

\(y'(1) =e\) implies that: x = 1 and y' = e

So, we have:

\(y' = c_1e^x - c_2e^{-x}\)

\(e = c_1 * e^1 - c_2 * e^{-1}\)

\(e = c_1 e - \frac{1}{e}c_2\) --- (2)

Add (1) and (2)

\(0 + e = c_1e + c_1e + \frac{1}{e}c_2 - \frac{1}{e}c_2\)

\(e = 2c_1e\)

Divide both sided by e

\(1 = 2c_1\)

Divide both sides by 2

\(c_1 = \frac{1}{2}\)

Substitute \(c_1 = \frac{1}{2}\) in \(0 = c_1 e + \frac{1}{e}c_2\)

\(0 = \frac{1}{2} e+ \frac{1}{e}c_2\)

Rewrite as:

\(\frac{1}{e}c_2 = -\frac{1}{2} e\)

Multiply both sides by e

\(c_2 = -\frac{1}{2} e^2\)

So, we have:

\(y=c_1e^x +c_2e^{-x\)

\(y = \frac{1}{2}e^x -\frac{1}{2} e^2 * e^{-x}\)

\(y = \frac{1}{2}e^x -\frac{1}{2} e^{2-x}\)

Answer:

\(\frac{1}{2} (2\frac{3}{4})(\frac{7}{8})\)

Step-by-step explanation:

Area of a triangle = 1/2bh

Answer:

first guy is correct!

Step-by-step explanation:

Answer:

x = 4√5 ≈ 8.94 (2 d.p.)

y = 8√5 ≈ 17.89 (2 d.p.)

Step-by-step explanation:

To find the values of x and y, use the Geometric Mean Theorem (Leg Rule).

The altitude drawn from the vertex of the right angle perpendicular to the hypotenuse separates the hypotenuse into two segments. The ratio of the hypotenuse to one leg is equal to the ratio of the same leg and the segment directly opposite the leg.

\(\boxed{\sf \dfrac{Hypotenuse}{Leg\:1}=\dfrac{Leg\:1}{Segment\;1}}\quad \sf and \quad \boxed{\sf \dfrac{Hypotenuse}{Leg\:2}=\dfrac{Leg\:2}{Segment\;2}}\)

From inspection of the given right triangle RST:

Substitute the values into the formulas:

\(\boxed{\dfrac{20}{y}=\dfrac{y}{16}}\quad \sf and \quad \boxed{\dfrac{20}{x}=\dfrac{x}{4}}\)

Solve the equation for x:

\(\implies \dfrac{20}{x}=\dfrac{x}{4}\)

\(\implies 4x \cdot \dfrac{20}{x}=4x \cdot \dfrac{x}{4}\)

\(\implies 80=x^2\)

\(\implies \sqrt{x^2}=\sqrt{80}\)

\(\implies x=\sqrt{80}\)

\(\implies x=\sqrt{4^2\cdot 5}\)

\(\implies x=\sqrt{4^2}\sqrt{5}\)

\(\implies x=4\sqrt{5}\)

Solve the equation for y:

\(\implies \dfrac{20}{y}=\dfrac{y}{16}\)

\(\implies 16y \cdot \dfrac{20}{y}=16y \cdot \dfrac{y}{16}\)

\(\implies 320=y^2\)

\(\implies \sqrt{y^2}=\sqrt{320}\)

\(\implies y=\sqrt{320}\)

\(\implies y=\sqrt{8^2\cdot 5}\)

\(\implies y=\sqrt{8^2}\sqrt{5}\)

\(\implies y=8\sqrt{5}\)

(a) Player Column's best response is given by:

BR_Column(p) = { L if p < 1/2, R if p > 1/2 (indifferent if p = 1/2)

(b) Where both players are indifferent between their available strategies.

(c)  The normal form representation of the game is above.

(d) No player can gain an advantage by deviating from this strategy.

This equilibrium results in an expected payoff of 0 for each player.

(a) To derive the best response functions, we need to find the strategies that maximize the payoffs for each player given the mixed strategy of the other player.

Player Row's best response function:

If Player Column chooses L with probability q, Player Row's expected payoff for choosing U is 0q + 2(1-q) = 2 - 2q.

If Player Column chooses R with probability 1-q, Player Row's expected payoff for choosing U is 0*(1-q) + 1*q = q.

Therefore, Player Row's best response is given by:

BR_Row(q) = { U if q < 1/3, D if q > 1/3 (indifferent if q = 1/3)

Player Column's best response function:

If Player Row chooses U with probability p, Player Column's expected payoff for choosing L is 0p + 2(1-p) = 2 - 2p.

If Player Row chooses D with probability 1-p, Player Column's expected payoff for choosing L is 0*(1-p) + (-1)*p = -p.

Therefore, Player Column's best response is given by:

BR_Column(p) = { L if p < 1/2, R if p > 1/2 (indifferent if p = 1/2)

Plotting the best response functions on a graph with p on the horizontal axis and q on the vertical axis will result in two line segments: BR_Row(q) is horizontal at U for q < 1/3 and horizontal at D for q > 1/3, while BR_Column(p) is vertical at L for p < 1/2 and vertical at R for p > 1/2.

The two segments intersect at the point (p, q) = (1/2, 1/3).

(b) To find the Nash equilibria, we look for the points where the best response functions intersect. In this case, the only Nash equilibrium is at (p, q) = (1/2, 1/3), where both players are indifferent between their available strategies.

Now let's move on to the rock-paper-scissors-lizard game:

(c) The normal form representation of the game can be written as follows:

    R    P    S    L

------------------------

R | 0,0 -1,1 1,-1 1,-1

P | 1,-1 0,0 -1,1 1,-1

S | -1,1 1,-1 0,0 -1,1

L | -1,1 -1,1 1,-1 0,0

(d) To find the Nash equilibria, we look for any strategy profiles where no player can unilaterally deviate to improve their payoff.

In this game, there are no pure strategy Nash equilibria since each strategy can be countered by another strategy with a higher payoff.

However, there is a mixed strategy Nash equilibrium where each player chooses their actions with equal probabilities: r = p = s = l = 1/4.

In this case, no player can gain an advantage by deviating from this strategy.

This equilibrium results in an expected payoff of 0 for each player.

In summary, the rock-paper-scissors-lizard game has a unique mixed strategy Nash equilibrium where each player randomly chooses their actions with equal probabilities.

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Answer:

Volume left in the cylinder if all the cone is made full:

\(\bold{345.72 \ ml }\)

Step-by-step explanation:

Given

Radius of cylinder = 5 cm

Height of cylinder = 14 cm

Radius of cone = 6 cm

Height of cone = 20 cm

To find:

Liquid remaining in the cylinder if cone is made full from cylinder's liquid.

Solution:

We need to find the volumes of both the containers and find their difference.

Volume of cylinder is given by:

\(V_{cyl} = \pi r^2h\)

We have r = 5 cm and

h = 14 cm

\(V_{cyl} = \dfrac{22}{7} \times 5^2\times 14 = 1100 cm^3\)

Volume of a cone is given by:

\(V_{cone} = \dfrac{1}{3}\pi r^2h = \dfrac{1}{3}\times \dfrac{22}{7} \times 6^2 \times 20 = \dfrac{1}{3}\times \dfrac{22}{7} \times 36 \times 20 = 754.28 cm^3\)

Volume left in the cylinder if all the cone is made full:

\(1100-754.28 =345.72 cm^3\ OR\ \bold{345.72 \ ml }\)

Dewey believed that the pair of binoculars found near the Clutter's house was a clue worth pursuing early in the investigation.

In Truman Capote's "In Cold Blood," Dewey, the lead investigator, believed that the binoculars found near the Clutter's house were a significant clue that could lead to identifying the killers. The binoculars were found by a neighbor, who had seen a car parked on the side of the road near the Clutter's house the night of the murder. Dewey believed that the killers may have used the binoculars to survey the Clutter's home before committing the crime.

In "In Cold Blood," Truman Capote chronicles the brutal murders of the Clutter family in their home in Holcomb, Kansas. Dewey, the lead investigator, was tasked with solving the crime and bringing the killers to justice. Early in the investigation, Dewey believed that the pair of binoculars found near the Clutter's house was a clue worth pursuing. The binoculars were discovered by a neighbor who had seen a car parked on the side of the road near the Clutter's house the night of the murder. The neighbor thought it was suspicious and went to investigate. Upon searching the area, he found a pair of binoculars lying on the ground near the car. Dewey believed that the killers may have used the binoculars to survey the Clutter's home before committing the crime.

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Answer:

 13 Vehicles Sold

Step-by-step explanation:

20% of 65 is equal to 13 :)

Answer:

Step-by-step explanation:

Lets divide it into parts.

I divided it into parts, now, we have to multiply these numbers.

20x7=140

9x6=54

Now, we have to add these numbers

140+54=194

So hence, your answer is 194m²

Thanks!

MiniMeteorologist

Answer:

Step-by-step explanation:

Area of rectangle I = length * width

                                = 7 * 14

                                = 98 m²

Rectangle II:

length = 9 + 7 = 16 m

Width = 6 m

Area of rectangle II = 16 *6

                                = 96 m²

Area of composite shape = area of rectangle I + area of rectangle II

                                           = 98 + 96

                                           = 194 m²

MACARONI AND AN POT THATS AN WAAAAAPP

Answer:

1800 grams

Step-by-step explanation:

1.8 × 1000 = 1800

To convert kg to g you have to multiply the mass value by 1000

hope it helps!

the electric field at a distance (r) from the center of the cylinder is approximately 0.0203 N/C, with a radial direction.

To solve this problem, let's analyze the given information step by step:

Radius of the cylinder: r = 2.00 cm = 0.02 m

Volume charge density: ρ = 18.0 μC/m²3

Now, let's find the electric field (E) at a distance (r) from the center of the cylinder using Gauss's law for a cylindrical symmetry.

Gauss's law states that the electric flux (Φ) through a closed surface is equal to the enclosed charge divided by the permittivity of free space (ε₀).

For an infinitely long cylinder, the electric field outside the cylinder will have a radial direction and a magnitude given by:

E = (ρ × r) / (2 × ε₀)

where ε₀ is the permittivity of free space, approximately equal to 8.854 × 10²-12 C²2/(N·m²2).

Substituting the given values, we can calculate the electric field:

E = (18.0 μC/m²3 × 0.02 m) / (2 × 8.854 × 10²-12 C²2/(N·m²2))

E ≈ 0.0203 N/C

Therefore, the electric field at a distance (r) from the center of the cylinder is approximately 0.0203 N/C, with a radial direction.

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It will take them 2 hours to do the whole task if they work together.

If one person can do a task in 3 hours and another person can do the same task in 6 hours, then we can calculate their individual rates of work as follows:

The first person can do 1/3 of the task per hour (since it takes them 3 hours to do the whole task).

The second person can do 1/6 of the task per hour (since it takes them 6 hours to do the whole task).

When they work together, their rates of work will add up, so their combined rate of work is:

1/3 + 1/6 = 1/2

This means that working together, they can do 1/2 of the task per hour. To find out how long it will take them to do the whole task, we can use the formula:

time = work ÷ rate of work

Since the whole task is 1 unit of work, and their combined rate of work is 1/2 units per hour, we can plug in these values to get:

time = 1 ÷ (1/2) = 2 hours

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Answer:

m<2 = 52 degrees

Step-by-step explanation:

Exterior angle theorem

m<4 = m<2 + m<1

73 = x + 21

x = 52 degrees.

Mr. Jericho needs to teach his students how to make change. Vygotsky would recommend that he set up a pretend shop and have all of the students act as cashiers in it.

One of the four methods of teaching is the interactive or participative method of teaching. In this method, students are taught certain stuff with the use of hands-on techniques. These include acting out whatever is being taught so that students have a better view of whatever is happening around them.

This method is quite useful and this is exactly what Vygotsky suggested for the students in the class in the very first place.

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Answer:

Can you put slashes (/) in between because it’s hard for me to see what the fractions are

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

Answer:

He paid $33 dollars for the shoes

Step-by-step explanation:

The expected count of women who ranked the dark-skinned model as the most beautiful is 100.

Since there are three models, we would expect 100/3 = 33.33% of the women to have ranked each model as the most beautiful if there were no relationship between skin color and beauty judgements. Thus, we can calculate the expected count of women who ranked the dark-skinned model as the most beautiful as follows:

Expected count = 300 * 33.33% = 100

Therefore, we can expect that 100 women out of the 300 sampled would have ranked the dark-skinned model as the most beautiful if there were no relationship between skin color and beauty judgements. The observed count of 55 women who ranked the dark-skinned model as the most beautiful is higher than the expected count, which suggests that there may be a relationship between skin color and beauty judgements. However, further statistical tests would be needed to confirm this.

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.253 as a fraction would be

253/100

In question 27, the price elasticity of supply for shampoo is given as 20, and the price of shampoo increases by 0.7%. The expected change in the quantity of shampoo supplied can be determined using the concept of price elasticity of supply. However, the specific percentage change in quantity supplied is not provided, so a precise answer cannot be given based on the given information.

In question 20, an inferior good in which the income effect dominates the substitution effect is referred to as a Giffen good. It is not classified as a normal good, luxury good, mass-produced good, or favored good.

In question 30, the cross elasticity of demand measures the responsiveness of the quantity demanded of a particular good to changes in the prices of its substitutes and complements. The correct answer is that the cross elasticity of demand measures the responsiveness to changes in both substitutes and complements.

In question 27, without the specific percentage change in quantity supplied, we cannot determine the exact outcome based on the given information. The price elasticity of supply of 20 suggests that the quantity supplied is highly responsive to changes in price, but the specific percentage change in quantity supplied cannot be calculated without additional data.

In question 28, the relationship between pasta being a Giffen good and other characteristics is not specified. While pasta being a Giffen good indicates that the quantity demanded increases as the price increases, it does not imply whether pasta is a normal good, luxury good, or how price changes affect quantity demanded.

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The number of days in which Meena would be able to complete the work alone is 24 days.

In order to determine the number of days in which Meena would be able to complete the work alone, we would have to assign variables to the amount of time taken by Mala, Meena, and Vinay, and then translate the word problem into an algebraic equation as follows;

Note: Combined work rate = 1/x + 1/y + 1/z

Based on the information provided, we have the following equations that models the work rate by each person;

1/(x + y) = 10 ⇒ 1/10 = x + y    ........equation 1.

1/(y + z) = 12 ⇒ 1/12 = y + z    ........equation 2.

1/(x + z) = 15 ⇒ 1/15 = x + z    ........equation 3.

x + y + y + z + x + z = 1/10 + 1/12 + 1/15

2(x + y + z) = 15/60

2(x + y + z) = 1/4

x + y + z = 1/8

From equation 2, we have:

x + (y + z) = 1/8

x + 1/12 = 1/8

x = 1/8 - 1/12

x = 1/24

x = 24 days.

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The geometric series that has been provided is of divergence, since r>5.

The series is given as /10 + 3/2 + 15/2 + 75/2 + 325/2 +.....

The common ratio is

3/2 ÷ 3/10

= 3/2 ×10/3

= 5

Then,

15/2 ÷ 3/2

= 15/2 × 2/3

= 5

Thus, the common ratio is greater than 5. Therefore, the series is divergence.

Hence, the given geometric series is divergence, since r>5.

A series is considered to be convergent if the partial sums tend to a particular value, also known as a limit. In contrast, a divergent series is one whose partial sums do not approach a limit. Typically, the Divergent series either reach, reach, or don't reach a particular number.

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Answer:

44h

Step-by-step explanation:

money earned per extra hour worked=100+25/100×10.80=13.50

amount earned if working for 38 hours=10.80×38=410.40

remaining money=491.40-410.40=81

number of extra hours worked=81÷13.50=6

total hours worked=38+6=44h

Answer: Its going to be answer B. or 36 blocks.

Step-by-step explanation:

40-36 = 4 they're were 4 blocks on the left and 40 on the right.

To balance the scale, you must remove nine blocks from the right side.

The area of arithmetic operations encompasses the study of numbers and their operations, which are essential to all other branches of mathematics. These systems use the four operations of addition, subtraction, multiplication, and division as their foundation.

It is given that, One blue x-block, 20 green blocks, and 40 green blocks make up the scale's left and right sides, respectively.

If one blue x-block and three green blocks were all that was left on the left side of the scale after a student bumped into it and knocked several blocks off.

The number of blocks you need to remove from the right side to make the scale balance is obtained as,

=40 - 4

=36

Thus, for the scale to be balanced, nine blocks must be removed from the right side.

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Answer:

Step-by-step explanation:

t a pet store, Ms. Pike paid $34.75 for 5 dog bowls and 7 bones. Mr. Moore paid $20.50 for 3 dog bowls and 4 bones. Determine the cost of one dog bowl(x) and one bone(y).

Answer:

-2/3<t

Step-by-step explanation:

You can treat the inequality like an equal sign.

The first step is to add 10 to both sides,

2>-3t

Then we need to divide both sides by -3 to isolate the t. The only difference between an equals sign and an inequality when solving is when dividing by a negative number. When you divide by a negative, you flip the sign around.

-2/3>t →-2/3<t

Answer:

0 ≤ t ≤ 18

Step-by-step explanation:

The cost of renting the boat without any discount is $8 per hour. However, Leila has a discount coupon for $3 off, so the effective cost per hour would be $8 - $3 = $5.

Let's assume Leila rents the boat for t hours. The total cost of renting the boat for t hours would be $5 multiplied by t, which is 5t.

According to the problem, Leila wants to spend at most $93. Therefore, we can set up the following inequality:

5t ≤ 93

This inequality represents the condition that the total cost of renting the boat (5t) should be less than or equal to $93.

Simplifying the inequality:

5t ≤ 93

Dividing both sides by 5 (since the coefficient of t is 5):

t ≤ 93/5

t ≤ 18.6

Since we cannot rent the boat for a fraction of an hour, we can round down the decimal value to the nearest whole number:

t ≤ 18

0 ≤ t ≤ 18

Answer: 0≤t≤12

Step-by-step explanation:

(I’m not sure if it’s 5 dollars off per hour, or total, but here’s what I did!)

If Leila has a $3 coupon, than she can spend +$3 because when you get a coupon, you can spend more, so 93+3 is equal to 96, now we just divide by 8 (because a boat costs $8 per hour) and we get 96/8=12.

Then, in inequality form it’s t≤12, because she can rent the boat for at most 12 hours, you could also do 0≤t≤12, because you can’t rent it for a negative amount of time, but either works.