5. A solid with volume 8 cubic units is dilated by a scale factor of k. Find the volume of the image for each given value of k. (Lesson 5-6)

a. k = 1/2
b. k = 0.6
c. k = 1
d. k = 1.5

Check the picture below.

[tex]\cos(\theta )=\cfrac{\stackrel{adjacent}{3}}{\underset{hypotenuse}{3.4}}\implies \theta =\cos^{-1}\left( \cfrac{3}{3.4} \right)\implies \theta \approx 2807^o[/tex]

Make sure your calculator is in Degree mode.

In this scenario, the population would be all the chickens in the county, and it would be very difficult for Krista to survey every single chicken in the county.

A possible representative sample for Krista's claim could be to randomly select a certain number of chicken farms in the county and then record how many eggs their chickens laid on a given day.

The number of farms selected and the number of chickens counted would depend on the size of the county and the resources available to Krista.

However, it is important to note that even a random sample may not perfectly represent the entire population, and there could be other factors that affect egg production, such as the age and breed of the chickens or the quality of their feed.

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x-coordinate of the other point on the line that has a y value of -12 is 0

The slope of a line in mathematics serves as a gauge for how steep it is. It is described as the proportion of the y-coordinate change to the x-coordinate change between any two locations on a line. A line's slope can be either positive, negative, zero, or undefinable.

Given

vertex=(8,6)

intercept=-12

To find:  x-coordinate of the other point that has a y value of -12

Equation of line

y=mx+c

Putting the values, we get

6=8m-12

m=18/8

m=9/4

Now, finding the x coordinate

y=mx+c

-12=9/4x-12

x=0

Hence,  x-coordinate of the other point that has a y value of -12 is 0.

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Answer:

67.466%

Step-by-step explanation:

No. of people aged below 14 years old= 60,094

No. of people aged between 15 and 64 years old= 212,468

No. of people aged above 65 years old= 42,362

Age Dependency Ratio= No. of people aged between 15 and 64 years old

                                          /Total People

                                       = [tex]\frac{212,468}{60,094+212,468+42,362}[/tex] × 100

                                       = [tex]\frac{212,468}{314,924}[/tex] × 100

                                       = 67.466%

∴ the Age Dependency Ratio is 67.466%.

the probability of guessing the correct answers to both questions is 1/9, or approximately 0.111.

What is probability?

By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.

Since there are three possible choices for each question, the probability of guessing the correct answer to one question is 1/3. Since each question is independent of the other, the probability of guessing the correct answer to both questions is the product of the individual probabilities:

P(guessing both answers correctly) = P(guessing first answer correctly) * P(guessing second answer correctly)

P(guessing both answers correctly) = (1/3) * (1/3)

P(guessing both answers correctly) = 1/9

Therefore, the probability of guessing the correct answers to both questions is 1/9, or approximately 0.111.

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Answer:

The expression 5/(9x+1) is already simplified. It cannot be further simplified or "solved" because it is not an equation, it is just an expression.

Step-by-step explanation:

Based on the above, the the midpoint of AB is M = (2, 1).

To find the midpoint of AB, we need to average the x-coordinates and the y-coordinates of A and B separately. That is:

Midpoint = ((x-coordinate of A + x-coordinate of B) / 2, (y-coordinate of A + y-coordinate of B) / 2) simply say:

M = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)

So, for A = (10, -1) and B = (-6, 3), we have:

Midpoint = ((10 + (-6)) / 2, (-1 + 3) / 2)

Midpoint = (2, 1)

Therefore, the midpoint of AB is M = (2, 1). This means that if we drew a line segment from A to B and marked the point exactly halfway between them, that point would be at the coordinates (2, 1).

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The remaining credit after 50 minutes of calls is[tex]$19.68[/tex].To calculate the remaining credit after 50 minutes of calls, the linear function is substituted with the given value of 50 for TCT.RC = -0.14 × 50 + 33.68 RC = 19.68

The linear function representing the credit remaining on a phone card (in dollars) with respect to the total calling time (in minutes) is given by:Remaining Credit (RC) = m × Total Calling Time (TCT) + c where m is the gradient and c is the intercept.To solve for the linear function, two points are needed. The two points are:(24, 21.88) and (38, 20.6)Substituting the values into the linear function, the gradient (m) is calculated to be -0.14 and the intercept (c) is calculated to be 33.68.Therefore, the linear function representing the credit remaining on a phone card (in dollars) with respect to the total calling time (in minutes) is:RC = -0.14 × TCT + 33.68.To calculate the remaining credit after 50 minutes of calls, the linear function is substituted with the given value of 50 for TCT.RC = -0.14 × 50 + 33.68 RC = 19.68.Therefore, the remaining credit after 50 minutes of calls is [tex]$19.68.[/tex]

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To find the length of the diagonal fence that stretches from one corner to the opposite corner of a rectangle, we can use the Pythagorean theorem, which states that the square of the length of the diagonal (hypotenuse) is equal to the sum of the squares of the lengths of the two other sides (legs) of the rectangle.

In this case, the rectangle has dimensions 24 meters by 45 meters. Therefore, the length of the diagonal fence is:

Diagonal fence = √(24^2 + 45^2) meters

Simplifying the equation, we get:

Diagonal fence = √(576 + 2025) meters

Diagonal fence = √2601 meters

Diagonal fence = 51 meters

So Steve will need 51 meters of fencing to stretch diagonally from one corner to the opposite corner of his backyard.

Answer:

arc length ≈ 29.32 mm

Step-by-step explanation:

arc length is calculated as

arc = circumference of circle × fraction of circle

      = 2πr × [tex]\frac{80}{360}[/tex]

     = 2π × 21 × [tex]\frac{8}{36}[/tex]

    = 42π × [tex]\frac{2}{9}[/tex]

   = [tex]\frac{42\pi (2)}{9}[/tex]

   ≈ 29.32 mm ( to the nearest hundredth )

The section of the bar labeled x must be less than 117 for the inequality to be true.

so x < 117.

We can find the solution with linear inequalities with one unknown.

x + 9 < 126

Group all constants on the RHS of the equation

so we need to subtract the 9 from both sides of the equation.

x + 9 - 9 < 126 -9

x < 117

We can also plot the solution on a coordinate plane for this we have coordinates like (-∞, 117)

The bar graph of the inequality is shown in below here dotted line represents 126.

As in inequality show < the sign, which means the box is drawn on the left of the 126.

The bar represents x + 9. Label the bar diagram.

The section of the bar labeled x must be less than 117 for the inequality to be true.

so x < 117.

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Although the statements are not clearly written, the proof that ΔABC ≅EFG is:


AC = EG - Given

BA = FE - Given

BC = FG - Given

∠ABC = ∠EFG - Given

∠BAC = ∠FEG - Given

∠BCA = ∠FGE - Given

Thus, ΔABC ≅EFG  on the bases of the S-S-S Angle postulate or the A-A-A congruence postulate.

The S-S-S Angle Postulate and the A-A-A Congruence Postulate are both mathematical principles used to prove that two triangles are congruent (having the same size and shape).

The S-S-S Angle Postulate states that if two triangles have three sides that are congruent to the corresponding sides of another triangle, then the triangles are congruent.

The A-A-A Congruence Postulate, on the other hand, states that if two triangles have three angles that are congruent to the corresponding angles of another triangle, then the triangles are congruent.

Both of these postulates are fundamental to the study of geometry and are used to prove a wide range of geometric theorems and relationships.

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Answer:

(-6, 4/3, 7)

Step-by-step explanation:

To solve the system of equations, we can use elimination or substitution. Here, we will use elimination:

First, we can eliminate z by adding the first and third equations:

x - 3y - 5z = 7

6x + 5y - 6z = 85

7x + 2y = 92

Next, we can use the second equation to eliminate z from the second equation:

6y + z = 27

-6z from both sides:

6y = -6z + 27

Divide both sides by 6:

y = -z/6 + 9/2

Now, we can substitute y = -z/6 + 9/2 into the equation 7x + 2y = 92:

7x + 2(-z/6 + 9/2) = 92

7x - z/3 + 9 = 92

7x - z/3 = 83

Multiplying both sides by 3 to eliminate the fraction:

21x - z = 249

We now have two equations:

7x + 2y = 92

21x - z = 249

To eliminate x, we can multiply the first equation by 3 and subtract it from the second equation:

21x - z = 249

- (3 * (7x + 2y = 92))

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

-13x - 6z = -215

Solving this equation for z, we get:

-13x - 6z = -215

6z = 13x + 215

z = (13/6)x + 35 + 1/3

Now we can substitute this value of z into one of the equations to solve for y. Let's use the second equation:

6y + z = 27

6y + [(13/6)x + 35 + 1/3] = 27

6y + (13/6)x + 35 + 1/3 - 27 = 0

6y + (13/6)x + 8 + 1/3 = 0

6y + (13/6)x = -25/3

y = (-13/36)x - (25/18)

Finally, we can substitute these values for x, y, and z into one of the original equations to check our work. Let's use the first equation:

x - 3y - 5z = 7

x - 3[(-13/36)x - (25/18)] - 5[(13/6)x + 35 + 1/3] = 7

x + (13/12)x + (25/6) - (65/6)x - 175 - (5/3) = 7

-51x/12 - 215/6 = 7

-17x/4 - 35/2 = 7

-17x/4 = 21/2

x = -6

Substituting this value of x into the expressions we found for y and z, we get:

y = (-13/36)x - (25/18) = (13/6) - (25/18) = 4/3

z = (13/6)x + 35 + 1/3 = -(13/6)*6 + 35 + 1/3 = 7

In the triangle , the value of SB is 9.

What is triangle?

A triangle is a form of polygon with three sides; the intersection of the two longest sides is known as the triangle's vertex. There is an angle created between two sides. One of the crucial elements of geometry is this.

Certain fundamental ideas, including the Pythagorean theorem and trigonometry, rely on the characteristics of triangles. The angles and sides of a triangle determine its kind.

Here in the given triangle  TC=18 , CU = 6 and SU=12 .

Let us take SB as x. Then,

BU = SU - SB = 12-x.

Now using triangle proportionality theorem then,

=> [tex]\frac{TC}{CU}=\frac{SB}{BU}[/tex]

=> [tex]\frac{18}{6}=\frac{x}{12-x}[/tex]

=> 3 = [tex]\frac{x}{12-x}[/tex]

=> 36-3x=x

=> 36 = x+3x = 4x

=> x = 36/4 = 9

Hence the value of SB is 9.

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The total number of ways five of them to sit in a row of chairs under the given condition is equal to 152 ways.

Use the principle of inclusion-exclusion to solve this problem.

Let us first consider the case where Alice sits next to Bob or Carla.

Now, treat Alice, Bob, and Carla as a block, which can be arranged in 3! = 6 ways.

Within this block, Alice can sit in two different positions,

And Bob and Carla can sit in the remaining two positions.

There are 6 x 2 = 12 ways for Alice to sit next to Bob or Carla.

Now,

Let us consider the case where Derek sits next to Eric.

Treat Derek and Eric as a block,

which can be arranged in 2! = 2 ways.

Within this block,

Derek can sit in two different positions,

And Eric can sit in the remaining position.

There are 2 x 2 = 4 ways for Derek to sit next to Eric.

However,

Double-counted the case where Alice sits next to Bob or Carla AND Derek sits next to Eric.

Treat Alice, Bob, Carla, Derek, and Eric as two blocks,

which can be arranged in 2! x 3! = 12 ways.

Within each block,

There are 2 ways to arrange the people.

There are 12 x 2 x 2 = 48 ways for both conditions to be satisfied.

Using the principle of inclusion-exclusion,

The total number of ways for the five of them to sit in a row of chairs under these conditions.

Total

= total number of ways - number of ways Alice sits next to Bob or Carla - number of ways Derek sits next to Eric + number of ways both conditions are satisfied

= 5! - 12 - 4 + 48

= 152

Therefore, there are 152 ways for the five of them to sit in a row of chairs under these conditions.

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The smallest number that has 1, 2, 3, 4, 5 as factors is 60. This number is called the LCM (Least Common Multiple) of the given numbers.

The smallest number that has 1, 2, 3, 4, 5 as factors is 60. This number is called the LCM (Least Common Multiple) of the given numbers.The least common multiple (LCM) of two numbers is the smallest number that is a multiple of both of these numbers. We can find the LCM of more than two numbers by following the below procedure:Firstly, find the LCM of two numbers.

This will be the smallest number that is a multiple of both these numbers. Then, find the LCM of this number and the third number. This will be the smallest number that is a multiple of all the three numbers. Repeat the same process for other numbers until we have found the LCM of all the given numbers.

Here, the given numbers are 1, 2, 3, 4, and 5.LCM of 1 and 2 is 2.LCM of 2 and 3 is 6.LCM of 6 and 4 is 12.LCM of 12 and 5 is 60.

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Answer: C 48

Step-by-step explanation:

There is 36 apples. 7 pears to 9 apples. 36 divided by 9 is 4.

4 times 7 is 28.

7 pears to 12 oranges.

28 pears divided by 7 pears is 4.

4 times 12 oranges is 48

Answer:

y = 3x + 11

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 3, 2 ) and (x₂, y₂ ) = (- 2, 5 )

m = [tex]\frac{5-2}{-2-(-3)}[/tex] = [tex]\frac{3}{-2+3}[/tex] = [tex]\frac{3}{1}[/tex] = 3 , then

y = 3x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (- 2, 5 )

5 = 3(- 2) + c = - 6 + c ( add 6 to both sides )

11 = c

y = 3x + 11 ← equation of line

Yes, the figure shown in the xy-coordinate plane is a parallelogram because side OP is parallel to side TS and side OT is parallel to side PS

In order for any quadrilateral to be considered a parallelogram, two pairs of its parallel sides must be equal (congruent). Therefore, we would determine the slope of each side by using this mathematical equation:

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

For side OP, the slope is given by:

Slope (m) = (b - 0)/(a - 0)

Slope (m) = b/a.

For side TS, the slope is given by:

Slope (m) = (0 - )/(c - (a + c))

Slope (m) = -b/-a = b/a

Therefore, side OP is parallel to side TS.

For side OT, the slope is given by:

Slope (m) = (0 - 0)/(c - 0)

Slope (m) = 0.

For side PS, the slope is given by:

Slope (m) = (b - b)/((a + c) - c)

Slope (m) = 0

In conclusion, the figure shown above is a parallelogram because side OT is parallel to side PS and side OP is parallel to side TS.

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Answer:

Here is an ad campaign to promote Ray and Kelsey's roller coaster

Step-by-step explanation:

(Opening shot of the roller coaster with screaming riders)

Voiceover: "Get ready for the ride of your life!"

(Cut to Ray and Kelsey, standing in front of the roller coaster)

Ray: "Hey, I'm Ray, and this is Kelsey. We're the creators of the most thrilling roller coaster in town."

Kelsey: "Our coaster is packed with twists, turns, and loops that will leave you screaming for more!"

Ray: "Come on down to the amusement park and experience the thrill for yourself."

Kelsey: "Our coaster is perfect for adrenaline junkies who love a good rush!"

(Cut back to the roller coaster with more screaming riders)

Voiceover: "Don't miss out on the ride of a lifetime. Come ride Ray and Kelsey's roller coaster today!"

(Optional closing shot of the roller coaster with a tagline: "Are you brave enough?")

If preparing an interview or report, here is a script.

Interviewer: "So, Ray and Kelsey, tell us about your new roller coaster."

Ray: "Well, it's the most thrilling coaster in town. We wanted to create a ride that would really get people's hearts racing."

Kelsey: "Our coaster has twists, turns, and loops that will leave riders screaming for more. It's perfect for anyone who loves a good adrenaline rush."

Interviewer: "What inspired you to create this coaster?"

Ray: "We both love roller coasters, and we wanted to create something that would be just as exciting as our favorite rides."

Kelsey: "We spent months designing and testing the coaster to make sure it was the best it could be."

Interviewer: "What can riders expect when they ride your coaster?"

Ray: "They can expect a thrilling ride that will leave them breathless."

Kelsey: "Our coaster is perfect for anyone who loves a good rush. We can't wait for everyone to experience it for themselves."

The probability of having 3 earthquakes in the same year that all measure 6.0 or more is approximately 0.1106 or 11.06%.

What is probability?

Probability is a measure of the likelihood or chance that an event will occur. It is usually expressed as a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain.

Assuming that the number of earthquakes measuring 6.0 or more on the Richter scale in a year follows a Poisson distribution with a mean of 0.93 (i.e., an average of 0.93 such earthquakes per year over the past 100 years), we can use the Poisson probability formula to find the probability of having exactly 3 such earthquakes in a year:

[tex]P(X = 3) = (e^{(-0.93)} * 0.93^3) / 3![/tex]

where X is the number of earthquakes measuring 6.0 or more on the Richter scale in a year.

Plugging in the values, we get:

[tex]P(X = 3) = (e^{(-0.93)} * 0.93^3) / 3! = 0.1106[/tex]

Therefore, the probability of having 3 earthquakes in the same year that all measure 6.0 or more on the Richter scale, given that there have been 93 such earthquakes in the past 100 years, is approximately 0.1106 or 11.06%.

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Answer: area = 60 yd^2

Step-by-step explanation: I am not sure if this is correct but this is what I got as my answer.

Based on Kamila's description, the dot plot that matches her description is Dot plot 1.

The presence of an outlier and the right-skewed distribution can be inferred from the high frequency of data points on the left side of the plot and the single data point that is much larger than the others on the right side.

What is frequency of dot plot?

The frequency in a dot plot refers to the number of dots or data points that appear in a particular bin or category. In a dot plot, each dot typically represents one data point, and the frequency of the dot is the number of data points that have that value. For example, if a dot plot shows the heights of students in a class, with bins for each inch, then the frequency of a particular bin would be the number of students whose height falls within that bin. The frequency can be represented by the number of dots in that bin or by a numerical value.

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Answer:

nails weight 50 lbs by knowing the weight u can find the mss

Answer:

$1.46

Step-by-step explanation:

a bottle of pineapple juice at store A is [tex]\frac{2.40}{5}=0.48[/tex]

a bottle of pineapple juice at store B is [tex]\frac{29.10}{15}=1.94[/tex]

the difference:

$1.94 - $0.48 = $1.46

A two-tailed test is considered to be more powerful than a one-tailed test. Therefore, Option D (a two-tailed test) is the correct answer.

The one-tailed test and the two-tailed test are two sorts of hypothesis tests. The number of tails, as the name implies, is the fundamental distinction between the two sorts of hypothesis tests. The tails are the areas under the probability distribution curve that are beyond the critical values or the cut-off points.

The one-tailed test is one of the types of hypothesis testing in which an alternative hypothesis is generated in a specific direction. In comparison to two-tailed tests, they are simpler to conduct. The one-tailed test is less likely to reject the null hypothesis since it only tests one of the tails. On the other hand, the two-tailed test tests both tails of the distribution, making it more powerful since it is more inclusive than the one-tailed test.

The two-tailed test is more effective since it tests for discrepancies on both sides of the distribution, whereas the one-tailed test only tests for discrepancies on one side of the distribution.

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Step-by-step explanation:

Not true....is they are perpendicular  the slopes have the relation

  m   and    - 1/m    where m is the slope

slope 2 has a perpendicular slope = - 1/2

The expression that means the same as “a number plus 14” is “14 more than a number”.

In mathematical terms, when we say “a number plus 14”, we are essentially talking about adding 14 to an unknown number.

The word “plus” is used to indicate the operation of addition.
Similarly, when we say “14 more than a number”, we are also talking about the same operation of addition. Here, we are adding 14 to an unknown number.

However,

The words used to describe the operation are different.
Both expressions essentially convey the same mathematical idea, which is adding 14 to an unknown quantity. Depending on the context and the problem at hand, either expression can be used interchangeably.
It is important to note that in mathematics, expressions can be written in different forms while still conveying the same meaning.

This flexibility in writing expressions allows for more efficient and effective communication in problem-solving.

The expression that means the same as "a number plus 14" can be written in algebraic form as x + 14, where x represents any number.

In this expression, the variable x can be replaced by any number, and when we add 14 to that number, we get the result of "a number plus 14".

For example,

If we substitute x with 7, we get 7 + 14 = 21, which means "a number plus 14" is equal to 21.

The algebraic expression x + 14 means the same as "a number plus 14".

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Answer:

Step-by-step explanation

x = 159.6

If you find an error in my solution, tell me and I will immediately re-solve!