40 points!! The first term of an arithmetic sequence is -12. The common difference of the sequence is 7. What is the sum of the first 30 terms of the sequence?

Answer:

5

Step-by-step explanation:

a+b=-1

x+y+z=2

7a+7b+6z+6x+6y=7(a+b)+6(z+x+y)=7(-1)+6(2)=-7+12=5

Answer:7980 ways

Step-by-step explanation:

When select predident:21 ways

When select secretary: 20 ways

When select treasurer: 19 ways

It is permutation

N permutation r=NPR

20permutation3=21×20×19= 7980 ways

Answer:

7980 ways

Step-by-step explanation:

Pretty simple.

we are finding variation.

Variation = N factorial/ (N-P)factorial/

N = the total number of elements we have available

P = the number of elements out of n we need to select

N = 21

P = 3

Variation = 21 factorial/(21-3)factorial = 21 factorial/ 18 factorial

Variation = 21x20x19x 18factorial/ 18 factorial

Variation = 21x20x19 = 7980 possible ways of selecting 3 positions out of a board of 21 members.

is it clear?

Answer:

The estimated number of deer in this population will be 147.

Step-by-step explanation:

Let we assume

Total number of deer = x

If we presume that this sample ratio is typical for the entire herd

Then,

The ratio of total number of the deer and initially collected, tagged and released deer will be equal to the ratio of later captured 55 deer and 9 tagged deer.

So

[tex]\frac{x}{24}=\frac{55}{9}[/tex]

[tex]x=\frac{55}{9}\times24[/tex]

[tex]x=146.66[/tex]

Hence the estimate number of deer = 147

Answer:

Tommy earned $250 altogether.

Step-by-step explanation:

Let the total earning of Tommy be 'x' dollars.

Given:

Money spent on entertainment = $80

From the circle shown below:

Percent spent on clothes = 19%

Percent spent on food = 25%

Percent spent on other things = 14%

Percent of savings = 10%

Addition of all percents = 100%

⇒ 19% + 25% + 10% + 14% + % Entertainment = 100%

⇒ 68% + % Entertainment = 100%

⇒ % Entertainment = 100% - 68% = 32%

Therefore, as per question:

[tex]32\%\ of\ x=\$80\\\\0.32x=80\\\\x=\frac{80}{0.32}\\\\x=\$250\\[/tex]

Hence, Tommy earned $250 altogether.

(a) The equation [tex]2h^{2} +7h+4=0[/tex] has two irrational solutions.

(b) The equation [tex]m^{2} =-40m-400[/tex] has one rational solution.

(c) The equation [tex]14r^{2} =5-7r[/tex] has two irrational solutions.

(d) The equation [tex]7w^{2} -w=-9[/tex] has two imaginary solutions.

(e) The equation [tex]3f-9f^{2} =6[/tex] has two imaginary solutions.

Explanation:

(a) Solving the equation [tex]2h^{2} +7h+4=0[/tex] , we get the solutions,

[tex]h=\frac{-7+\sqrt{17}}{4}[/tex] and [tex]h=\frac{-7-\sqrt{17}}{4}[/tex]

Thus, [tex]h=-0.719223[/tex] and [tex]h=-2.78077[/tex]

Hence, the equation [tex]2h^{2} +7h+4=0[/tex] has two irrational solutions.

(b) Solving the equation [tex]m^{2} =-40m-400[/tex] , we get the solution,

[tex]m=-20[/tex]

Hence, the equation [tex]m^{2} =-40m-400[/tex] has one rational solution.

(c) Solving the equation [tex]14r^{2} =5-7r[/tex] , we get the solutions,

[tex]r=\frac{-7+\sqrt{329}}{28}[/tex] and [tex]r=\frac{-7-\sqrt{329}}{28}[/tex]

Thus, [tex]r=-0.39779[/tex] and [tex]r=-0.89779[/tex]

Hence, the equation [tex]14r^{2} =5-7r[/tex] has two irrational solutions.

(d) Solving the equation [tex]7w^{2} -w=-9[/tex] , we get the solutions,

[tex]w=\frac{1}{14}+i \frac{\sqrt{251}}{14}[/tex] and [tex]w=\frac{1}{14}-i \frac{\sqrt{251}}{14}[/tex]

Hence, the equation [tex]7w^{2} -w=-9[/tex] has two imaginary solutions.

(e)  Solving the equation [tex]3f-9f^{2} =6[/tex] , we get the solutions,

[tex]f=\frac{1}{6}-i \frac{\sqrt{23}}{6}[/tex] and [tex]f=\frac{1}{6}+i \frac{\sqrt{23}}{6}[/tex]

Hence, the equation [tex]3f-9f^{2} =6[/tex] has two imaginary solutions.

Answer:

Step-by-step explanation:

total number of marbles=3+6+5+4+2=20

favorable events=3+4=7

P=(7/20)^{100}

Answer:

Step-by-step explanation:

sin = opposite / hypotenuse

sin x = 36 / 45

sin x = 4/5

the least common number for 36 and 45 is 9

36/9=4

45/9=5

Answer:

sin X = 4/5

Step-by-step explanation:

Hey common, I quite simple. When ever you get a question of this magnitude always remember SohCahToa.

SOH = opposite / hypotenuse

CAH = Adjacent / Hypotenuse

TOA = Opposite / Adjacent

From the question:

Sin X = Opposite / Hypotenuse.

(The opposite of angle X is 36°) over (Hypotenuse - the longest side = 45)

sin X = 36/ 45

Divide through by 3

sin X = 12/15

Divide through by 3 Again

Sin X = 4/5

Hope that makes it simple for you

Which definition for a ligament did you think was better? Explain. 1- A ligament is made up of tissue that forms a band. 2- A ligament is a band of tough tissue connecting bones or holding organs in place.

A ligament is a band of tough tissue connecting bones or holding organs in place is the better definition.

Option B

Ligament is a type of connective tissue which develops from the mesoderm. Its actually a tough band containing mostly collagen tissue. Ligament joins two bones which forms a joint.

Ligament is formed of collagen fibres which run parallel to each other and this forms a band. It's very tough and this is why, it can hold bones together.

Ligaments that hold organs are actually pseudo ligaments which are actually folds of peritonium that holds the organs in place.

A biconditional form of the statement about a ligament could be: 'An anatomical structure is a ligament if and only if it is a band of tough tissue connecting bones or holding organs in place.' It defines what a ligament is and the conditions under which we can define a structure as a ligament.

The statement, a 'ligament is a band of tough tissue connecting bones or holding organs in place,' can be written in biconditional form as: 'An anatomical structure is a ligament if and only if it is a band of tough tissue connecting bones or holding organs in place.'

This biconditional statement provides a precise definition and condition as to when we can consider a structure as a ligament. Conversely, it also states that if a structure carries out the functions mentioned, it must be a ligament.

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Answer:

maximum height =7.347m

Step-by-step explanation:

maximum height = (U²sin²θ)/2g

where θ = 90° as the ball is thrown straight up.

sin90°=1 , so our formula reduces to;

H= U²/2g

U=12m/s  , g=9.8m/s²

H= 12²/(2*9.8)

H=7.347m

Answer:H=7.339m

Step-by-step explanation:

The formula to find maximum height is :

H= v^2/(2× g)

V means speed=12 m/s

g means acceleration due gravity (constant)= 9.81m/s^2

Apply the formula

H=(12^2)/(2×9.81)

H=144/19.62

H=7.339m

Answer: 64 ft

Step-by-step explanation:

We are given the following equation that models the baseball's parabolic path:

[tex]s=16t^{2}+V_{o}t[/tex] (1)

Where:

[tex]s[/tex] is the ball maximum height

[tex]t[/tex] is the time

[tex]V_{o}=64 ft/s[/tex] is the initial height

With this information the equation is rewritten as:

[tex]s=16t^{2}+(64)t[/tex] (2)

Now, we have to find [tex]t[/tex], and this will be posible with the following formula:

[tex]V=V_{o}-gt[/tex] (3)

Where:

[tex]V=0 ft/s[/tex] is the final velocity of the ball at the point where its height is the maximum

[tex]g=32 ft/s^{2}[/tex] is the acceleration due gravity

Isolating [tex]t[/tex]:

[tex]t=\frac{V_{o}}{g}[/tex] (4)

[tex]t=\frac{64 ft/s}{32 ft/s^{2}}[/tex] (5)

[tex]t=2 s[/tex] (6)

Substituting (6) in (2):

[tex]s=16 ft/s^{2}(2 s)^{2}+(64 ft/s)(2 s)[/tex] (7)

Finally:

[tex]s=64 ft[/tex]

Answer:

Step-by-step explanation:

The kinetic energy for a given mass and velocity is ...

  KE = (1/2)mv^2 . . . . . m is mass

At its initial speed, the kinetic energy of the car is ...

  KEi = (1/2)(810 kg)(23.6 m/s)^2 ≈ 2.256×10^5 J . . . . . m is meters

At its final speed, the kinetic energy of the car is ...

  KEf = (1/2)(810 kg)(47.2 m/s)^2 ≈ 9.023×10^5 J

The ratio of final to initial kinetic energy is ...

  (9.023×10^5)/(2.256×10^5) = 4

4 times as much work must be done to stop the car.

_____

You know this without computing the kinetic energy. KE is proportional to the square of speed, so when the speed doubles, the KE is multiplied by 2^2 = 4.

Answer:

5

Step-by-step explanation:

Final answer:

The volume of an oblique pyramid with a square base of edge length 2 cm and a vertical height of 3.75 cm is 5 cm³.

Explanation:

To calculate the volume of an oblique pyramid with a square base, you can use the formula for the volume of a regular pyramid since the oblique nature of the pyramid does not affect the calculation of the volume. The volume formula is Volume = (1/3) times base area times height.

Here, the base edge length is 2 centimeters, so the area of the square base (base area) is Area = side times side = 2 cm times 2 cm = 4 cm². The vertical height of the pyramid is given as 3.75 centimeters. Now we can plug these values into the volume formula:

Volume = (1/3) times base area times height
Volume = (1/3) times 4 cm² times 3.75 cm
Volume = (1/3) times 15 cm³
Volume = 5 cm³

Therefore, the volume of the oblique pyramid is 5 cubic centimeters (cm³).

Answer: Rita's paddling speed in still water is 2.5 miles pet hour and the speed of the river's current is 0.5 miles per hour.

Step-by-step explanation:

Let x represent Rita's paddling speed in still water.

Let y represent the speed of the river's current.

On a canoe trip, Rita paddled upstream (against the current) at an average speed of 2 miles per hour relative to the riverbank. This means that

x - y = 2 - - - - - - - - - - - - -1

On the return trip downstream (with the current) . Her average speed was 3 miles per hour. This means that

x + y = 3 - - - - - - - - - - - - -2

Adding equation 1 and equation 2, it becomes

2x = 5

x = 5/2 = 2.5 miles per hour.

Substituting x = 2.5 into equation 1, it becomes

2.5 - y = 2

y = 2.5 - 2 = 0.5 miles per hour

Answer:

per hour relative to the riverbank. On the return trip downstream (with the current) . Her average speed was 3 miles per hour. Find Rita's paddling

Step-by-step explanation:

Missing portion of the question:

Question has missing the images for both type of tents hence the lengths were also missing which is attached in the picture.

Answer:

Tunnel Tent requires less nylon as its area (214.80ft²) is less than the area of Pup tent (247.40ft²)

Step-by-step explanation:

Pup Tent:

Area for Pup Tent: (Perimeter)(Height) + 2 (Area of front triangular side)

Perimeter=sum of all sides = 8+8+8=24

Height = 8

Area of Triangle = (1/2) length * height

length=8

height can be calculated by Pythagorean Theorem:

hyp²=base²+perp²

height = perp=4√3

So,

Area of Triangle = (1/2) length * height

=27.7

Hence,

Area for Pup Tent: (Perimeter)(Height) + 2 (Area of front triangular side)

=(24)(8)+(2)(27.7)

=247.40m²

Tunnel Tent:

Area of tunnel tent = πrh + πr² + 2rh

π=constant=3.14

r=radius=4

h=height=8

Area of tunnel tent = πrh + πr² + 2rh

=(3.14)(4)(8)+(3.14)(4)²+2(4)(8)

=214.80m²

In Physics, accuracy and precision are terms used to discuss the validity of measurements. Accuracy refers to how close a measured value is to its true value, while precision discusses the consistency or reproducibility of measurements. Good precision can reduce errors but does not necessarily improve accuracy.

In the field of Physics, accuracy and precision are used to discuss the reliability of measurements taken during experiments. Accuracy refers to how closely the measured value of a quantity corresponds to its 'true' value. For example, if we aim to measure a length of 10 meters, an accurate measurement would be as close to 10 meters as possible.

On the other hand, precision represents the degree of similarity, or reproducibility, between repeated measurements. If we measure the same length of 10 meters multiple times and get results like 9.9m, 10.1m, 10.0m, 9.9m, the measurements would be considered precise because they are closely clustered together, even if they are not necessarily 'accurate' (exact 10m).

It's important to understand that better precision does not always ensure better accuracy. The more measurements you make and the better the precision, the smaller the error will be, but accuracy requires measurements to be close to the actual value.

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There were 20 people in the room, as each person kissed every other person once, resulting in [tex]\( \frac{20 \times 19}{2} = 190 \)[/tex] kisses.

Let's denote n as the number of people in the room. In this scenario, each person kisses every other person once, resulting in a total of [tex]\( \frac{n(n-1)}{2} \)[/tex] kisses.

Given that there were 190 kisses, we can set up the equation:

[tex]\[ \frac{n(n-1)}{2} = 190 \][/tex]

To solve for n, we multiply both sides of the equation by 2 to get rid of the fraction:

[tex]\[ n(n-1) = 380 \][/tex]

Expanding the left side:

[tex]\[ n^2 - n = 380 \][/tex]

Rearranging the equation into a quadratic form:

[tex]\[ n^2 - n - 380 = 0 \][/tex]

Now, we can solve this quadratic equation. One way is by factoring, if possible. If not, we can use the quadratic formula:

[tex]\[ n = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} \][/tex]

where [tex]\( a = 1 \), \( b = -1 \), and \( c = -380 \).[/tex]

Plugging in the values:

[tex]\[ n = \frac{{-(-1) \pm \sqrt{{(-1)^2 - 4(1)(-380)}}}}{{2(1)}} \]\[ n = \frac{{1 \pm \sqrt{{1 + 1520}}}}{2} \]\[ n = \frac{{1 \pm \sqrt{{1521}}}}{2} \]\[ n = \frac{{1 \pm 39}}{{2}} \]\[ n = \frac{{1 + 39}}{{2}} \quad \text{or} \quad n = \frac{{1 - 39}}{{2}} \]\[ n = \frac{{40}}{{2}} \quad \text{or} \quad n = \frac{{-38}}{{2}} \]\[ n = 20 \quad \text{or} \quad n = -19 \][/tex]

Since the number of people cannot be negative, we discard n = -19.

Therefore, there were [tex]\( \boxed{20} \)[/tex] people in the room.

The value of the constants b and c in the given polynomial, p(x) = x² + bx + c are b = 2, and c = -24.

Given a polynomial:

p(x) = x² + bx + c

It is also given that:

[tex]\lim_{x \to 4} \frac{p(x)}{x-4} =10[/tex]

Since the denominator is x - 4 when the limit sets to 4, the denominator will have 0 there.

But, this can't be possible.

So, the expression inside the limit is given below:

[tex]\lim_{x \to 4}\frac{(x+a)(x-4)}{x-4}=10[/tex]

When the limit tends to 10, the expression becomes:

4 + a = 10

a = 6

So, the expression inside the limit becomes:

p(x) = (x + 6)(x - 4)

      = x² + 6x - 4x - 24

      = x² + 2x - 24

So, x² + bx + c = x² + 2x - 24

Comparing the coefficients of the polynomial expression:

b = 2

c = -24

Hence, the constants are b = 2, and c = -24.

Learn more about Polynomials here :

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The constants b and c in the polynomial satisfy the equation 4b + c = 24. There are infinitely many pairs of (b, c) that can satisfy this equation, therefore they are not unique.

In this question, we are dealing with limits and polynomials. We are given that p(x) = x2 + bx + c and lim x→4 [p(x)/(x-4)] = 10.

Substituting p(x) into the equation, we get lim x→4 [(x2 + bx + c) / (x - 4)] = 10.

Using the rule lim x→a [f(x)] = f(a), we find that 42 + 4b + c = 40. This simplifies to 16 + 4b + c = 40, and further to 4b + c = 24.

So, the constants b and c must satisfy this equation. Therefore, they are not unique as there are infinitely many pairs of (b, c) that can satisfy this equation. For example, if b = 5, then c = 4. If b = 6, then c = 0. And so on.

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Answer:

The answer to your question is letter D

Step-by-step explanation:

To demonstrate if the data are measurements of the sides of a right triangle use the pythagorean theorem.

                         c² = a² + b²

A. 25, 23, 7       25² = 23² + 7²

                        625 = 529 + 49

                        625 ≠ 578            These values are not of a right triangle

B. 9, 6,3             9² = 6² + 3²

                       81 = 36 + 9

                        81 ≠ 45                These values are not of a right triangle

c. 18, 15, 4         18² = 15² + 4²

                        324 = 225 + 16

                        324 ≠  241             These values are not of a right triangle

D. none of the above                     This is the right answer

Answer:

The answer is D. none of the above

Step-by-step explanation:

The length of the sides of a right triangle will be related according to the formula a^2 + b^2 = c^2, A,B,C will not work with this formula.

Hope this helps :)

Answer:

Option D = Use a histogram with class width equal to 10

Step-by-step explanation:

A histogram will be better to represent the data. A histogram is a graphical representation of a frequency distribution, where you have rectangular bars placed side by side. the vertical axis represent the frequency while the horizontal axis represent the variable being represented which is the length of time worked by the employees.

One of the advantages of the histogram is that it has no gaps between the bars and it is mostly used for grouped data. This explains why the best representation ad the best option is to use the HISTOGRAM.

Final answer:

Option D, a histogram with class width equal to 10, would likely be the best representation for the data set of the length of time worked by employees, as it would facilitate easy viewing of data distribution and patterns.

Explanation:

The question asks for a better way to represent a data set of the length of time worked by employees at a local Honda plant. The provided options include a time plot, split stems, a pie chart, and a histogram with a class width of 10. Looking at the options:

In conclusion, option D, which suggests using a histogram with a class width equal to 10, would likely be the best graphical representation for this data set.

Answer:

The standard deviation is 9.34

Step-by-step explanation:

First we need to find mean of the sample:

[tex]m=(23.9+15.3+40.2+30.3+12+22.8)/6=24.08[/tex]

Standard deviation will be like below:

[tex]d=\sqrt{(x-m^2)/6}=9.34[/tex]

Answer:

  8/3

Step-by-step explanation:

The range of possible lengths for the third side is 16±9, or 7 to 25. For lengths of 7 and 25, the area of the triangle will be zero, so the ratio of altitudes will be infinite (actually, undefined, as division by 0 is involved).

For positive triangle area and integer side lengths, the range of side lengths can be from 8 to 24. For any given triangle, the ratio of maximum altitude to minimum altitude will be the same as the ratio of the maximum side length to the minimum side length.

For the triangles under consideration, the shortest side length we can have is 8. For that 8-9-16 triangle, the ratio of the maximum to minimum side lengths is 16/8 = 2.

The longest side length we can have is 24. For that 9-16-24 triangle, the ratio of maximum to minimum side lengths is 24/9 = 8/3 = 2 2/3. This is more than 2, so 8/3 is the largest possible ratio of any two altitudes.

_____

More explanation

The area of a triangle is given by the formula ...

  A = (1/2)bh

Then the altitude for a given base (b) is ...

  h = 2A/b

That is, the altitude is inversely proportional to the base length for a triangle of a given area. Once you choose the three sides of the triangle, the area is fixed, so the ratio of altitudes is the inverse of the ratio of base lengths. The ratio of maximum altitude to minimum altitude is the ratio of the inverse of the minimum base length to the inverse of the maximum base length, which is to say it is the same as the ratio of maximum to minimum base lengths.

Answer:

8/3

Step-by-step explanation:

Answer:

A prison administration wants to know whether the prisoners think the guards treat them fairly. The explanation, of each component could be used to produce biased and unbiased results, is as follow  

A) Component 2:

B) Component 4:

Bias in research on prisoner-guard dynamics can result from the involvement of researchers and the phrasing of questions. To ensure unbiased results, neutral interactions and carefully worded questions are vital.

Biased Research Components in Prisoner-Guard Dynamics

In research, it is crucial to mitigate factors that can lead to bias. Two such components in the study of prisoner-guard dynamics are researcher involvement and the phrasing of measurements and questions. If the researcher has direct contact with participants, they can unknowingly influence responses based on their body language, tone, or preconceived notions.

To produce unbiased results, researchers should maintain a neutral demeanor and minimize unnecessary interaction. The exact nature of measurements and questions can also introduce bias. Leading or emotional language in survey questions can skew results towards a specific answer. To avoid this, questions must be neutrally worded and designed to reflect the respondent's true perspective without influence.

Answer:The following states how confident are you? So Quadratic Functions are simple functions listen to this example Multiplying (x+4) and (x−1) together (called Expanding) gets x2 + 3x − 4 :

expand vs factor quadratic

So (x+4) and (x−1) are factors of x2 + 3x − 4

Just to be sure, let us check:

Step-by-step explanation:

Yes, (x+4) and (x−1) are definitely factors of x2 + 3x − 4

Answer:

y = (x + 7) (x + 6) (x − 3)

Step-by-step explanation:

Using rational root theorem, possible rational roots are:

±1, ±2, ±3, ±6, ±7, ±9, ±14, ±18, ±21, ±42, ±63, ±126

Using trial and error, we find that +3 is one of the roots.

There are 3 ways to continue from here: continue using trial and error to look for other rational roots; use long division to factor; or use grouping.

Using grouping:

y = x³ + 10x² + 3x − 126

y = x³ + 10x² − 39x + 42x − 126

y = x (x² + 10x − 39) + 42 (x − 3)

y = x (x + 13) (x − 3) + 42 (x − 3)

y = (x (x + 13) + 42) (x − 3)

y = (x² + 13x + 42) (x − 3)

y = (x + 7) (x + 6) (x − 3)

Answer:

Step-by-step explanation:

variance = 48,326.5, standard deviation = 219.8

Answer: variance = 48,326.5, standard deviation = 219.8

Step-by-step explanation: I completed the quiz, and option A. variance = 48,326.5, standard deviation = 219.8 was the correct answer!

Answer:

There are 198 children at the circus show.

Step-by-step explanation:

Let the total number of spectators be 'x'.

Given:

Number of men = [tex]\frac{1}{4}[/tex] of the total number

Number of women = [tex]\frac{2}{5}[/tex] of the remaining number.

Also, number of women = 132

Number of men = [tex]\frac{1}{4}\ of\ x=\frac{x}{4}[/tex]

Now, spectators remaining = Total number - Number of men

Spectators remaining = [tex]x-\frac{x}{4}=\frac{4x-x}{4}=\frac{3x}{4}[/tex]

Now, number of women = [tex]\frac{2}{5}\times \frac{3x}{4}=\frac{6x}{20}[/tex]

Now, as per question:

Number of women = 132. Therefore,

[tex]\frac{6x}{20}=132[/tex]

[tex]6x=132\times 20[/tex]

[tex]x=\frac{2640}{6}=440[/tex]

Therefore, the total number of spectators = 440

Also, number of men = [tex]\frac{x}{4}=\frac{440}{4}=110[/tex]

Now, total number of spectators is the sum of the number of men, women and children.

Let the number of children be 'c'.

Total number = Men + Women + Children

[tex]440=110+132+c\\440=242+c\\c=440-242=198[/tex]

Therefore, there are 198 children at the circus show.

Answer:

The correct option would be 'B. 4034'.

Step-by-step explanation:

If a population grows continuously

Then the final population is

[tex]P=P_{0}e^{rt}[/tex]

Where,

[tex]P_{0}[/tex] = Initial population

t = Number of period

r = rate of increasing per period

We have

[tex]P_{0}[/tex] = 10

r = 200%= 2  [tex](\because 1\%=\frac{1}{100})[/tex]

t = 3 years

Hence, the population of rabbits, after 3 years is,

[tex]P=10e^{2\times 3}[/tex]

[tex]P=10e^6[/tex]

[tex]P\approx 4034[/tex]

Therefore, option B is correct.

The number of rabbits after 3 years is B. 4034.

To calculate the number of rabbits after 3 years, we need to apply the continuous growth formula:

New Value = Initial Value x (1 + Growth Rate)^Time

Given that the initial value is 10 and the growth rate is 200%, we can plug in the values to find

Thus, P = 10e6

= 4034

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Answer:

Therefore the Distance across the Pond is

[tex]x=391\ ft[/tex]

Step-by-step explanation:

Given:

Triangle are Similar

AB = 90 ft

AC = 170 ft

BD = 207 ft

DE = x

To Find:

x = ?

Solution:

In Δ ABC and Δ DBE

∠A ≅ ∠D …………..{ measure of each angle is 90° given }  

∠ABC ≅ ∠DBE ……….....{Vertical Angle Theorem}  

Δ ABC ~ Δ DBE ….{Angle-Angle Similarity test}  

If two triangles are similar then their sides are in proportion.  

[tex]\dfrac{AB}{DB} =\dfrac{AC}{DE} \textrm{corresponding sides of similar triangles are in proportion}\\[/tex]  

Substituting the values we get

[tex]\dfrac{90}{207} =\dfrac{170}{x}\\\\x=23\times 17=391\ ft[/tex]

Therefore the Distance across the Pond is

[tex]x=391\ ft[/tex]

The calculated distance across the pond is 391 feet

How to determine the distance across the pond?

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

The figure

Also, we have that

The figures are similar triangles

Using the proportional equation of similar triangles, we have

x/207 = 170/90

This gives

x = 207 * 170/90

Evaluate

x = 391

Hence, the distance across the pond is 391 feet

To find the number of different committees, we can use combinations. For part a, subtract the committees with the 2 men from the total number. For part b, use the same method with the women. For part c, subtract the committees with both the man and woman from the total number.

To find the number of different committees that are possible, we can use combinations. In this case, we want to choose 3 men from a group of 6 and 3 women from a group of 8. The number of combinations can be calculated using the formula:

C(n, r) = n! / (r! * (n - r)!)

a. If 2 of the men refuse to serve together, we need to subtract the number of committees with these 2 men from the total number of committees. The number of committees with the 2 men can be calculated by choosing 1 man from the remaining 4, and then choosing 2 men from the remaining 3. So the number of committees without the 2 men is C(6, 3) * C(8, 3), and the number of committees with the 2 men is C(4, 1) * C(3, 2). The total number of committees is the difference between these two values.

b. If 2 of the women refuse to serve together, we use the same method as in part a, but with the women instead of the men.

c. If 1 man and 1 woman refuse to serve together, we can subtract the number of committees with both of them from the total number of committees. The number of committees with both of them can be calculated by choosing 2 women from the remaining 6 and choosing 2 men from the remaining 5. The total number of committees is the difference between C(6, 3) * C(8, 3) and C(6, 2) * C(5, 2).

A. Jose would be 30 feet east of the mailbox after 5 seconds.

B. A formula that expresses Jose's distance from the mailbox is,

D = 10 + 6t

C. As time increases, his distance from the mailbox increases proportionally.

Given that;

Jose is standing 10 feet east of a mailbox when he begins walking directly east of the mailbox at a constant speed of 6 feet per second.

A. In 5 seconds,

Jose would have travelled a distance equal to his speed multiplied by the time.

Since he is walking directly east, the distance travelled would be;

6 feet/second × 5 seconds = 30 feet.

Therefore, Jose would be 30 feet east of the mailbox after 5 seconds.

B. To express Jose's distance from the mailbox (D) in terms of the number of seconds (t) since he started walking, use the formula:

D = 10 + 6t

The initial distance from the mailbox which is 10 feet is added to the distance he walks 6 feet/second × t seconds to get the total distance.

C. Yes, Jose's distance from the mailbox is proportional to the time elapsed since he started walking away from the mailbox.

This is evident from the formula D = 10 + 6t

Where the coefficient of t (6) represents the constant rate at which his distance increases with time.

As time increases, his distance from the mailbox increases proportionally.

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Jose is 40 feet from the mailbox after 5 seconds. His distance from the mailbox can be expressed by the formula D=10+6t. His distance from the mailbox is proportional to the time elapsed since he started walking away from the mailbox.

A. Since Jose is moving at a speed of 6 feet per second, after 5 seconds, he would have walked 5*6=30 feet. He initially starts 10 feet east of the mailbox, so his total distance from the mailbox 5 seconds later is 10+30=40 feet.

B. The formula that expresses Jose's distance from the mailbox in terms of the number of seconds t since he started walking is D = 10 + 6t, where D is the distance and t is the time in seconds. In this formula, 10 represents his initial distance from the mailbox, and 6t represents how far he walks.

C. Yes, as Jose walks away from the mailbox, his distance from the mailbox is proportional to the time elapsed since he started walking away from the mailbox. This can be seen from the formula D=10+6t, which is in the form y=mx+b, indicating a linear relationship in which the dependent variable (distance) is proportional to the independent variable (time). The coefficient of t, which is 6, is the constant of proportionality.

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