T.J. is hosting a dinner party. T.J. greets the first guest and they shake hands. The second guest arrives and shakes hands with T.J. and the first guest. The third guest arrives and shakes hands with T.J., the first guest, and the second guest. This pattern continues. How many handshakes have taken place after the ninth guest arrives?

Answer:

16th term = 39.

Step-by-step explanation:

Plug 16 into the formula -6 + 3(n - 1):

A(16) = -6 + 3(16-1)

= - 6 + 3*15

= -6 + 45

= 39.

Answer:

Step-by-step explanation:

Answer: 918km^2

Step-by-step explanation:

[tex]area(a): 1700km^2\\percentage(p): 5.75 = \frac{5.75}{100}=0.0575\\years(y): 8[/tex]

Let x be the new dimension of the area;

[tex]x=a-(a*p*y)[/tex]

[tex]x=(1700km^2)-(1700km^2*0.0575*8)\\x=1700km^2-782km^2\\x=918km^2[/tex]

Answer:

60

Step-by-step explanation:

Answer:

I'd say 2/3

Step-by-step explanation:

I play a lot of Monopoly

Answer:

1 in 216

Step-by-step explanation:

the chance of rolling doubles once is 1/6 if you go through all possible outcomes, and six to the power of 3 (the amount of consecutive doubles desired) is 216

Answer:

3/2

Step-by-step explanation:

First, you find the mean (((4 + 5 + 6 + 1)/4) = 4)

Find the absolute difference between each data value and the mean: 0, 1, 2, 3

Add the differences (in the previous step) and divide by number of terms: (0+1+2+3)/4 = 6/4 = 3/2

Answer:

1,3,10

Step-by-step explanation:

I got it wright on the test.

Answer:

1

3

10

Step-by-step explanation:

edu 2020

Answer:

your expression is (10x+15)+11x

Step-by-step explanation:

let the missing number be X

(10x+15)+11x

Answer:

125000 square feet

Step-by-step explanation:

Since there are only three sides of the rectangle, the perimeter of the fence is:

Let x and y be the sides of the rectangle, we are left with:

2 * x + y = 1000

solving for and:

y = 1000 - 2 * x

The area of the corral is:

A = x * y

replacing

A = x * (1000 - 2*x)

A = 1000 * x - 2*x^2

to find the maximum for the parabolic function A = 1000 * x - 2*x^2

The function has a maximum since the quotient before x ^ 2 is negative: -2 <0

Amax = c - b^2 /4*a

where a = -2, b = 1000, c = 0

A max = 0 - 1000^2/(4 * (- 2))

A max = 125000 ft^2

The maximum possible area of the pen is 125000 square feet.

Final answer:

125,000 square feet,

Explanation:

Let us denote the length of the rectangular area parallel to the creek as L and the width of the area as W. Given that the total amount of fencing available is 1000 feet, we can express the perimeter that Jake can fence as 2W + L = 1000 feet, since the creek forms one of the longer sides of the rectangle, and no fencing is required there.

The area A of the rectangle is given by the product of its length and width, i.e., A = L × W. Our goal is to maximize A. From the perimeter equation 2W + L = 1000, we can express L as L = 1000 - 2W.

Substituting this into the area formula, we get A = W * (1000 - 2W). This is a quadratic function and can be written as

A = -2W^2 + 1000W, which is a parabola opening downwards. The maximum value of this function can be found by completing the square or by using the vertex form of a parabola.

The vertex of the parabola, which gives the maximum area, occurs at W = -b/(2a), with 'a' being the coefficient of

W^2 (-2 in this case) and 'b' the coefficient of W (1000 in this case). Plugging these values in, we find that

W = -1000 / (2 * -2) = 250.

Therefore, the width that gives the maximum area is 250 feet. Substituting W back into the perimeter formula, we get

L = 1000 - 2*250 = 500 feet.

So, the dimensions for the maximum area are 500 feet by 250 feet, and the maximum area is A = 500 * 250 = 125,000 square feet.

Answer:

D

Step-by-step explanation:  

Hope this Helps :D

Answer:

D

Step-by-step explanation:

Answer:

27

Step-by-step explanation:

StartRoot 27 EndRoot cm

Answer:

9 fruit baskets.

Step-by-step explanation:

Given:

Steve sold 36 fruit baskets for a school fundraiser.

Evie sold 25% of the number of baskets that Steve sold.

Question asked:

How many fruit baskets did Evie sell?

Solution:

As given that Evie sold 25% of the number of baskets that Steve sold.

Number of baskets sold by Evie = 25% of 36

                                                      [tex]=\frac{25}{100}\times36\\\\ =\frac{900}{100}\\ \\=9[/tex]

Thus, 9 fruit baskets sold by Evie.

Answer:

D on e2020

Step-by-step explanation:

got it right

Answer:

D. (StartFraction 7 Over 2 EndFraction) squared

Step-by-step explanation:

Answer:

The area of the corral is 2976 ft²

Step-by-step explanation:

Here, we have the perimeter of the rectangle given as 220 ft

Therefore, since in a rectangle, we have 2 sides of the four sides equal, that is;

Perimeter = 2×One side + 2×Other side

or Perimeter = 2×X + 2×Y

Here perimeter = 220 ft = 2×X + 2×Y

As one of the sides is 48 ft, we have;

220 ft = 2 × 48 + 2×Y

Therefore, 2×Y = 220 ft - 2×48 ft = 124 ft

∴ Y = 124 ft ÷ 2 = 62 ft

The area of the corral = Area of rectangle = Length × Width = 62 ft × 48 ft

Area of the corral = 2976 ft².

Answer:

lower quartile: 163  upper quartile: 184

Step-by-step explanation:

1. put the numbers in order from least to greatest. 97, 163, 169, 175, 184, 199

2. find the median. 172

3. find the median of the first 3 numbers to get your Q1. 163

4. find the median of the last 3 numbers to get your Q3. 184

Answer:

The correct answer is must have a positive slope.

Step-by-step explanation:

The coefficient of determination varies between -1 to 1. It shows the how strong is the relationship between two variables.

Coefficient closer to -1 indicate negative relationship and that y decreases with increase in x and the regression equation has a negative slope.

Coefficient closer to 1 indicate positive relationship and that y increases with increase in x and the regression equation has a positive slope.

Coefficient closer to 0 indicate that there is no possible relationship between the variables under consideration. It is not possible to construct a particular regression equation.

Answer:

The value of k is 0.448.

Step-by-step explanation:

Given the exponential growth function is

[tex]A=23e^{kt}[/tex]

A= The population of the country

k= growth rate.

The population of the country increased by 10 million in 13 years after 1982.

Then the population is =(23+13)million = 36 million.

Here,

A= 36 million, t= 13

[tex]A=23e^{kt}[/tex]

[tex]\Rightarrow 36=23e^{13k}[/tex]

[tex]\Rightarrow e^{13k}=\frac{36}{23}[/tex]

Taking ln function both sides

[tex]\Rightarrow ln|e^{13k}|=ln|\frac{36}{23}|[/tex]

[tex]\Rightarrow {13k}=ln|\frac{36}{23}|[/tex]

[tex]\Rightarrow {k}=\frac{ln|\frac{36}{23}|}{13}[/tex]

[tex]\Rightarrow k=0.448[/tex]

The value of k is 0.448.

The mean of the normal monthly precipitation for August in these 20 U.S. cities is obtained by adding all precipitation values and dividing by the total number of values, which gives a mean of 3.09 inches.

To find the mean of the data, we sum all the values and then divide by the number of values. After adding all the given 20 precipitation values, the total sum comes out to be 61.8 inches. So the mean of the data will be 61.8/20 = 3.09 inches. Therefore, the mean normal monthly precipitation for August in these 20 U.S. cities is 3.09 inches.

https://brainly.com/question/23562402

#SPJ3

Answer: Your sister is not correct. You can determine how far the overhang should extend by dividing 8 by [tex]tan(70\°)[/tex]

Step-by-step explanation:

The complete exercise is attached.

Observe the picture attached. You can identify that the angle A and the angle B are congruent (which means that they have equal measure).

Let be "CB" is the length in feet that the overhang should be in order to keep the Sun out when it is at its highest point in the sky.

You need to use the following Trigonometric Identity:

[tex]tan\alpha =\frac{opposite}{adjacent}[/tex]

You can notice that, in this case:

[tex]\alpha =70\°\\\\opposite=8\ ft\\\\adjacent=CB[/tex]

Knowing these values you can substitute them into  [tex]tan\alpha =\frac{opposite}{adjacent}[/tex] and then solve for "CB" in orde to find its value.

You get:

[tex]tan(70\°)=\frac{8}{CB}\\\\CB*tan(70\°)=8\\\\CB=\frac{8}{tan(70\°)}\\\\CB=2.91[/tex]

Therefore, your sisteter is not correct.

Answer:

Your sister is not correct. You can determine how far the overhang should extend by dividing 8.

Step-by-step explanation:

You can determine how far the overhang should extend by dividing

Observe the picture attached. You can identify that the angle A and the angle B are congruent (which means that they have equal measure).

Let be "CB" is the length in feet that the overhang should be in order to keep the Sun out when it is at its highest point in the sky.

You need to use the following Trigonometric Identity:

You can notice that, in this case:

Knowing these values you can substitute them into   and then solve for "CB" in orde to find its value.

Therefore, your sisteter is not correct.

The ball hits the ground at t=0 or t=3 seconds. The maximum height of the ball is 9 feet. The ball reaches its highest point at t=1.5 seconds.

To find out how long after the kick the ball hits the ground, we need to solve the equation h=-4t^2+12t  for t when h=0. We can set the equation to zero and solve for t by factoring or using the quadratic formula. In this case, you can factor out a t from the equation and solve for t to find that t=0 or t=3.

To find out how high the soccer ball gets, we need to find the maximum height of the ball. The maximum height occurs at the vertex of the parabolic equation. The formula for finding the x-coordinate of the vertex is x = -b/2a. In this case, a = -4 and b = 12, so the x-coordinate of the vertex is x = -12/(2*-4) = 1.5. Substituting this value into the equation, we can find the maximum height by solving for h, which is h = -4*(1.5)^2 + 12*(1.5) = 9 feet.

The soccer ball hits its highest point at the x-coordinate of the vertex. In this case, the highest point occurs at t = 1.5 seconds.

https://brainly.com/question/29545516

#SPJ12

A=Player A runs; B=Player B runs=A-16

A+B=242 Substitute for B.

A+A-16=242 Add 16 to each side.

2A=258 Divide each side by 2.

A=129 ANSWER 1: Player A batted in 129 runs.

B=A-16=129-16=113 ANSWER 2: Player B batted in 113 runs

CHECK:

A+B=242

129+113=242

242=242

Final answer:

Player A batted in 118 runs and Player B batted in 104 runs during the 2008 regular season. We found this by setting up two equations based on the given information and solving for the variables representing the number of runs batted in by each player.

Explanation:

To solve this problem, let's use two variables, A for the number of runs batted in by Player A, and B for the number of runs batted in by Player B. We know that Player A led the league, and Player B had 14 fewer runs batted in, so we can write the following equation:

B = A - 14

We also know that together they brought in 222 runs, so we can write another equation:

A + B = 222

Substituting the first equation into the second gives us:

A + (A - 14) = 222

Simplifying this equation, we get:

2A - 14 = 222

2A = 236

A = 118

Using the value of A, we can find B:

B = 118 - 14

B = 104

Therefore, Player A batted in 118 runs and Player B batted in 104 runs during the 2008 regular season.

Answer:

20%

Step-by-step explanation:

14/70x100=20%

Answer:

10x^3+16

Step-by-step explanation:

Answer:

add the third choice, "the average rate of change for the function is 1"

Step-by-step explanation:

Answer:

36 is the answer........

Answer:

36

Step-by-step explanation:

You can use the bus stop method on this

540 how many 15 goes in it =36

Answer:

A) 330 cd/sq. M per m

Step-by-step explanation:

To find the average rate at which the light intensity decreases as Caleb goes from a depth of 5m to a depth of 14m inside the cave, we need to calculate the change in light intensity and divide it by the change in depth.

To find the average rate at which the light intensity decreases as Caleb goes from a depth of 5m to a depth of 14m, we need to calculate the change in light intensity and divide it by the change in depth.

Let's denote the initial light intensity at 5m as I1 and the final light intensity at 14m as I2. Using the graph, we can estimate the values of I1 and I2.

Then, the average rate of decrease in light intensity is given by:

Average rate = (I2 - I1) / (14m - 5m)

https://brainly.com/question/33537305

#SPJ3

Answer:

B: 50% chance

Step-by-step explanation:

50/50 chance of happening is an equal chance

Answer:

no its B

Step-by-step explanation:

Because you have a 50 50 % chance

Answer:

3 m + 4  n = $24.25

9 m +   n = $37.00  are the required set of equations.

The cost of 1 cold drink  = $3.75

The cost of 1 pop corn bag  = $3.25

Step-by-step explanation:

Let us assume the cost of 1 drink = $ m

And the cost of 1 bag of popcorn = $ n

Now, Brianna buys 3 drinks + 4 bag popcorn  for  $24.25

⇒ Cost of 3 drinks +  4 bag popcorn =  $ 24.25

or, 3 ( Cost of 1 drink) + 4 ( Cost of i bag popcorn)  = $ 24.25

⇒ 3 m + 4  n = $24.25  ...  (1)

Also, Chloe buys 9 drinks + 1 bag popcorn  for  $37.00

⇒ Cost of 9 drinks +  1 bag popcorn =  $37.00

or, 9 ( Cost of 1 drink) + 1 ( Cost of 1 bag popcorn)  = $37.00

⇒ 9 m +   n = $37.00 ...  (2)

Now, solving equation (1) and (2) ,we get:

3 m + 4  n = $24.25

9 m +   n = $37.00   ⇒ n  = 37 -  9 m

Substitute the value of n in the equation (1),we get:

3 m + 4  n = $24.25  ⇒ 3  m + 4 ( 37 - 9 m ) = 24.25

or, 3 m + 148 - 36 m = 24.25

or, -33 m = -123.75

or, m = 123.75/33 =  3.75, or m = 3.75

Now, n = 37 - 9 m = 37  - 9(3.75)  =  3.25, or n = 3.25

Hence the cost of 1 cold drink =  m = $3.75

And the cost of 1 pop corn bag  =  n  = $3.25

Read more on Brainly.com - https://brainly.com/question/14072592#readmore

Step-by-step explanation:

Answer: Given:

(r, θ) is equivalent to (x, y) = (7, 5).

By definition,

r = √(7² + 5²) = 8.6023

θ = tan⁻¹ (7/5) = 0.9505 rad

Therefore

2r = 17.2047

θ + π/2 = 0.9505 + π/2 = 2.5213

In rectangular coordinates,

x = 2r cos(θ + π/2) = 17.2047*cos(2.5213) = -14

y = 2r sin(θ + π/2) = 17.2047*sin(2.5213) = 10

Answer: (-14, 10)

The rectangular coordinates of the polar coordinates (2√2, -π/12) are (-14,10).

The polar coordinate system is a two-dimensional coordinate system in mathematics in which points are defined by an angle and a distance from a central point known as the pole (equivalent to the origin in the more familiar Cartesian coordinate system).

We know polar coordinates are in the form (r, θ).

Also, (r, θ) = (x, y) = (7, 5).

So, r = √(7² + 5²)

r = 8.6023

and, θ = tan⁻¹ (7/5)

θ = 0.9505 rad

Now, 2r = 17.2047

and, θ + π/2 = 0.9505 + π/2 = 2.5213

Thus, the rectangular coordinates are

x = 2r cos(θ + π/2)

x = 17.2047 . cos(2.5213)

x = -14

and, y = 2r sin(θ + π/2)

y = 17.2047 . sin(2.5213)

y = 10

Learn more about polar coordinate here:

https://brainly.com/question/11657509

#SPJ3

Answer:

The sum of the first 6 terms of the series is 504.

Step-by-step explanation:

Given that,

Common ratio in a geometric series is, r = 0.5

First term of the series, a = 256

We need to find the sum of the first 6 terms in the series. If a and r area the first term and common ratio of a series, then the series becomes:

[tex]a,ar^1,ar^2,ar^3......[/tex]

The sum of n terms of a GP is given by :

[tex]S_n=\dfrac{a(1-r^n)}{1-r}[/tex]

Here, n = 6

[tex]S_n=\dfrac{256\times (1-(0.5)^6)}{1-0.5}\\\\S_n=504[/tex]

So, the sum of the first 6 terms of the series is 504.

Final answer:

To solve the equation by factoring, we factor out common terms from both sides of the equation and set each factor equal to zero. We consider the factors separately and solve for θ to find the solutions.

Explanation:

To solve the given equation, we need to factorize the trigonometric terms. Let's start by factoring out the common factor of sin(θ) cot(θ) from the left side of the equation:

csc(θ) cot(θ) − sin(θ) tan(θ) = cos(θ)

sin(θ) cot(θ)(csc(θ) − tan(θ)) = cos(θ)

Now we have a product of two factors equal to zero, so we can set each factor equal to zero and solve for θ:

sin(θ) cot(θ) = 0

csc(θ) − tan(θ) = cos(θ)

To find the solutions for sin(θ) cot(θ) = 0, we can consider the factors separately:

sin(θ) = 0 or cot(θ) = 0

For sin(θ) = 0, the solutions are θ = kπ, where k is an integer.

For cot(θ) = 0, we can rewrite it as cos(θ)/sin(θ) = 0, which means cos(θ) = 0 and sin(θ) ≠ 0. The solutions for cos(θ) = 0 are θ = (2k + 1)π/2, where k is an integer.

Now let's solve csc(θ) − tan(θ) = cos(θ):

csc(θ) − (sin(θ)/cos(θ)) = cos(θ)

(1/sin(θ)) − (sin(θ)/cos(θ)) = cos(θ)

Using a common denominator, we can combine the fractions:

(cos(θ) − sin(θ))/sin(θ) = cos(θ)

Now we have a fraction equal to a constant. This can only be true if the numerator is zero:

cos(θ) − sin(θ) = 0

Using the identity cos(θ) − sin(θ) = −√2 sin(θ + π/4), we can rewrite the equation as:

−√2 sin(θ + π/4) = 0

Solving for sin(θ + π/4) = 0, we get θ + π/4 = kπ, where k is an integer.

Therefore, the solutions to the equation csc(θ) cot(θ) − sin(θ) tan(θ) = cos(θ) are:

θ = kπ (for sin(θ) cot(θ) = 0)

θ = (2k + 1)π/2 (for csc(θ) − tan(θ) = cos(θ))