A 4-foot tall child walks directly away from a 12-foot tall lamppost at 2 mph. How quickly is the length of her shadow increasing when she is 6 feet away from the lamppost (rounded to the nearest tenth of a foot per second)

Answer: Option B is the correct answer.

Step-by-step explanation:

Let x represent the number of pennies.

Out of 40 coins, 16 are dimes. This means that the number of coins remaining is

40 - 16 = 24

Half of the remaining coins are quarters. This means that the number of quarters is

1/2 × 24 = 12 quarters

the rest are pennies and nickels. This means that the total number of

pennies and nickels is 12

There are 2 nickels for every penny. This means that the number if nickels is 2x. Therefore,

2x + x = 12

3x = 12

x = 12/3 = 4

there are 4 pennies

Answer:

The answer is B.) 4

Step-by-step explanation:

I took a quiz and according to that its correct

Answer:

e. Pie Chart

Step-by-step explanation:

In a student survey, students are asked about their favorite movie and so, the favorite movies can be divided into different categories but can't be meaningfully represented in numerical form. Thus, the favorite movie is a qualitative variable. For the qualitative type of variable pie chart is most suitable chart.

Histogram, IQR, box plot and steam plot are created for quantitative type of data.

Thus, the data would be best displayed by using Pie chart.

The domain for n is  [tex]-\infty<n<\infty[/tex]

Explanation:

The arithmetic sequence is    

To determine the domain of the sequence, let us consider  [tex]a_n[/tex] as  [tex]f(n)[/tex]  

Thus, the sequence becomes,  [tex]f(n)=4-4(n-1)[/tex]  

The domain of the function is the set of all x-values for which the function is real and well defined.

Since, the function has no domain constraints or undefined points. Therefore, the domain of the function is

Thus, the domain of the arithmetic sequence  [tex]a_n=4-4(n-1)[/tex] is  [tex]-\infty<n<\infty[/tex]

Answer:

17160

Step-by-step explanation:

1×2×3×4×5×6×7×8×9×10×11×12×13 / 1×2×3×4×5×6×7×8×9

10×11×12×13=17160

Answer: The salesperson would take home $1088.01 for the day

Step-by-step explanation:

Let x represent the salesperson's total sales per day.

A salesperson earns $99 per day, plus a 9% sales commission. This means that in a day in which the salesperson makes a total sales of x dollars, the total amount that he would earn is

99 + 0.09x

Therefore, the function that expresses her earnings as a function of sales is

99 + 0.09x

if the total sales were $999, then the amount that the salesperson would take home for the day is

99 + 0.99 × 999

= $1088.01

Answer:

With Processor Monitor Tool Technician B should be able to determine what changes were made during installation

Step-by-step explanation:

Technician B, can you a utility software tool called Processor Monitor to check track of system logs.

Process Monitor is an advanced monitoring tool for Windows that shows real-time file system, Registry and process/thread activity. It features include, an extensive list of enhancements including rich and non-destructive filtering, comprehensive event properties such session IDs and user names, reliable process information, full thread stacks with integrated symbol support for each operation, simultaneous logging to a file, and much more.

Its uniquely powerful features will make Process Monitor a core utility in your system troubleshooting and malware hunting toolkit.

With Processor Monitor Tool Technician B should be able to determine what changes were made during installation.

Technician B can use the Event Viewer to determine the changes made to folder permissions during software installation.

Technician B can use the Event Viewer to determine the changes made to folder permissions during software installation. Here's how:

Using the Event Viewer, Technician B can effectively track the changes that were made and troubleshoot the permissions errors experienced by users.

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Answer:

The answer to your question is letter B or C they have the same response.

Step-by-step explanation:

From the graph we get the center and the radius

- The center is the point shown in the graph and its coordinates are (1, -4).

- The length of the radius is 3 units, from the center we count horizontally the number of squares (3)

Substitution

                    (x - 1)² + (y + 4)² = 3²

or                 (x - 1)² + (y + 4)² = 9

Answer:

t = 460.52 min

Step-by-step explanation:

Here is the complete question

Consider a tank used in certain hydrodynamic experiments. After one experiment the tank contains 200 liters of a dye solution with a concentration of 1 g/liter. To prepare for the next experiment, the tank is to be rinsed with fresh water flowing in at a rate of 2 liters/min, the well-stirred solution flowing out at the same rate.Find the time that will elapse before the concentration of dye in the tank reaches 1% of its original value.

Solution

Let Q(t) represent the amount of dye at any time t. Q' represent the net rate of change of amount of dye in the tank. Q' = inflow - outflow.

inflow = 0 (since the incoming water contains no dye)

outflow = concentration × rate of water inflow

Concentration = Quantity/volume = Q/200

outflow = concentration × rate of water inflow = Q/200 g/liter × 2 liters/min = Q/100 g/min.

So, Q' = inflow - outflow = 0 - Q/100

Q' = -Q/100 This is our differential equation. We solve it as follows

Q'/Q = -1/100

∫Q'/Q = ∫-1/100

㏑Q  = -t/100 + c

[tex]Q(t) = e^{(-t/100 + c)} = e^{(-t/100)}e^{c} = Ae^{(-t/100)}\\Q(t) = Ae^{(-t/100)}[/tex]

when t = 0, Q = 200 L × 1 g/L = 200 g

[tex]Q(0) = 200 = Ae^{(-0/100)} = Ae^{(0)} = A\\A = 200.\\So, Q(t) = 200e^{(-t/100)}[/tex]

We are to find t when Q = 1% of its original value. 1% of 200 g = 0.01 × 200 = 2

[tex]2 = 200e^{(-t/100)}\\\frac{2}{200} = e^{(-t/100)}[/tex]

㏑0.01 = -t/100

t = -100㏑0.01

t = 460.52 min

Answer:

The work done is 5.084 J

Step-by-step explanation:

From Hooke's law of elasticity,

F = ke

F/e = k

F1/e1 = F2/e2

F2 = F1e2/e1

F1 = 10 lbf, e2 = 6 in, e1 = 4 in

F2 = 10×6/4 = 15 lbf

Work done (W) = 1/2F2e2

F2 = 15 lbf = 15×4.4482 = 66.723 N

e2 = 6 in = 6×0.0254 = 0.1524 m

W = 1/2×66.723×0.1524 = 5.084 J

x = 37.5 (or) [tex]\frac{75}{2}[/tex]

Solution:

Given [tex]\triangle A B C \sim \triangle D B E[/tex].

Let us take BE = x and BC = 25 + x.

To determine the value of x:

If two triangles are similar then the corresponding angles are congruent and the corresponding sides are in proportion.

[tex]$\frac{AC}{DE}=\frac{B C}{B E}[/tex]

[tex]$\frac{50}{30} =\frac{25+x}{x}[/tex]

Do cross multiplication, we get

[tex]50x=30(25+x)[/tex]

[tex]50x=750+30x[/tex]

Subtract 30x from both sides of the equation.

[tex]20 x=750[/tex]

Divide by 20 on both sides of the equation, we get

x = 37.5 (or) [tex]\frac{75}{2}[/tex]

Hence the value of x is 37.5 or [tex]\frac{75}{2}[/tex].

Answer:

Maximum number of 3x3x2 bricks = 23.

Step-by-step explanation:

The volume of the box = 13 x 8 x 4 = 416 cubic unit

The volume of the brick with the dimensions = 18 cubic unit

Now as per the question, we want to fill an empty box with 416 cubic unit with the help of bricks which are 18 cubic unit each.

The maximum number of bricks required to fill the box = Volume of the box ÷ Volume of one brick.

→ The number of bricks required to fill the box = 416 ÷ 18 = 23.11

But, number of bricks can never be in fraction so it means a maximum of 23 bricks can accommodate in the given box. We will not choose 24 or more than 24 bricks because these much bricks will go out of the dimensions.

Note: Volume of a cuboid = length x breadth x height (l x b x h).

To solve the problem, you divide each dimension of the box by the corresponding dimension of the brick, rounding down to the nearest whole number to get the number of bricks that can fit in each direction. You then multiply these together to get the total. In this case, a maximum of 16 bricks can fit.

The problem at hand requires spatial reasoning and division. The challenge is to determine how many 'bricks' (which we'll engage as 3x3x2 units) can fit into a larger 'box' (which is 13x8x4 units). This can be determined by individually dividing the dimensions of the box by the dimensions of the brick.

For instance, considering the length, we divide 13 by 3 to get approximately 4.33. Considering that we can't fractionate a brick, we can place only 4 bricks along the length. Using the same approach, we divide 8 by 3 for the width to get approximately 2.67, and we can place 2 bricks here. It's the same for the height; 4 divided by 2 is 2. Therefore, we can place 2 bricks along the height.

To get the total number of bricks that can fit in the box, multiply the numbers together: 4 (length) x 2 (width) x 2 (height), giving a result of 16 bricks. Hence, a maximum of 16 bricks of size 3x3x2 can fit into a box of size 13x8x4 without going out of the box or overlapping.

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Duku is 9 meters below the surface of the water, calculated by adding Duku's 5 meters above Kojo's position to Kojo's 14 meters below the surface.

The question asks about Duku's position relative to the surface of the water given Kojo is 14 meters below the surface and Duku is 5 meters above Kojo. To find Duku's position, subtract 5 meters (Duku's position above Kojo) from -14 meters (Kojo's position below the surface). Therefore, Duku's position relative to the surface of the water is -14 meters + 5 meters = -9 meters. This means Duku is 9 meters below the surface of the water.

Yo sup??

This question can be solved by applying trigonometric ratios

let angle U be x, then

tanx=4/7

x=29.7

Hope this helps

(3x³ - 17x² + 15x - 25)/(x - 5) =

= (3x³ - 15x² - 2x² + 0x + 5x - 25)/(x - 5)

= [3x²(x - 5) - 2x(x - 5) + 5(x - 5)]/(x - 5)

= (3x² - 2x + 5)(x - 5)/(x - 5)

= 3x² - 2x + 5

(5x³ + 18x² + 7x - 6)/(x + 3) =

= (5x³ + 5x² + 13x² + 13x - 6x - 6³)/(x + 3)

= [5x²(x + 1) + 13x(x + 1) - 6(x + 1)]/(x + 3)

= (x + 1)(5x² + 13x - 6)/(x + 3)

= (x + 1)(5x² + 15x - 2x - 6)/(x + 3)

= (x + 1)[5x(x + 3) - 2(x + 3)]/(x + 3)

= (x + 1)(5x - 2)(x + 3)/(x + 3)

= (x + 1)(5x - 2)

(4x³ + 8x² - 9x - 18)/(x + 2) =

= [4x²(x + 2) - 9(x + 2)]/(x + 2)

= (4x² - 9)(x + 2)/(x + 2)

= (4x² - 9)

= (2x - 3)(2x + 3)

(9x³ - 16x - 18x² + 32)/(x - 2) =

= [x(9x² - 16) - 2(9x² - 16)]/(x - 2)

= (9x² - 16)(x - 2)/(x - 2)

= 9x² - 16

= (3x - 4)(3x + 4)

(- x³ + 75x - 250)/(x + 10) =

= ( - x³ + 5x² - 5x² + 25x + 50x - 250)/(x + 10)

= [ - x²(x -5) - 5x(x - 5) + 50(x - 5)]/(x + 10)

= - (x - 5)(x² + 10x - 5x - 50)/(x + 10)

= - (x - 5)[x(x + 10) - 5(x + 10)]/(x + 10)

= - (x - 5)(x - 5)(x + 10)/(x + 10)

= - (x - 5)²

(3x³ - 16x² - 72)/(x - 6) =

= (3x³ - 18x² + 2x² - 72)/(x - 6)

= [3x²(x - 6) + 2(x² - 36)]/(x - 6)

= [3x²(x - 6) + 2(x - 6)(x + 6)]/(x - 6)

= [3x² + 2(x + 6)](x - 6)/(x - 6)

= 3x² + 2x + 12

Answer:

Segment [tex]EB[/tex] is parallel to segment [tex]FC[/tex].

Segment  [tex]CD[/tex] is skew to segment  [tex]AB[/tex].

Step-by-step explanation:

For this exercise it is necessary to know the following definitions:

1. Coplanar lines are defined as those lines that lie in the same plane.

2. Non-Coplanar lines  are defined as those lines that does not lie in the same plane.

3. Parallel lines  are defined as Coplanar lines that never intersect each other.

4. Skew lines are defined as Non-Coplanar lines that never intersect each other.

Knowing those definitions, you can solve the exercise.

You need to analize the figure given in the exercise.

Based on the explanation given above,  you can conclude that the segment [tex]EB[/tex] is parallel to the segment [tex]FC[/tex], because they are in the same plane and they never intersect each other.

You can also identify in the figure that the segment [tex]AB[/tex] and the segment [tex]CD[/tex] are not in the same plane and they never intersect each other.

Therefore, you can determine that the segment  [tex]CD[/tex] is skew to the segment  [tex]AB[/tex].

Answer:

ARITHMETIC SENTENCE

Step-by-step explanation:

Final answer:

Naledi's altitude sequence is an arithmetic sequence because it increases by a constant amount each hour.

Explanation:

Naledi's altitude at the beginning of the nth hour of her climb can be described by the function g(n), where g(n) is the altitude at that hour. Since she starts at 40 meters above sea level and increases her altitude by 10 meters every hour, the sequence representing her altitude over time is an arithmetic sequence. This is because each term in the sequence increases by a constant value, which is the definition of an arithmetic sequence.

The general formula for the nth term of an arithmetic sequence is aₙ = a₁ + (n - 1)d, where a₁ is the first term and d is the common difference between terms. In Naledi's case, a₁ is 40 meters (her initial altitude), and d is 10 meters (the constant increase each hour).

Answer:

The slope is = -1/4

Step-by-step explanation:

We are looking for the slope of the line CD. You are given the coordinates for each point as follows:

A(0,-1)     B(5,3)    C(2,3)   D(6,2)

To find the slope of a straight line, you use the formula:

slope (m) = (y2 - y1)/(x2 - x1)

In other words the slope is the "rise over run":

Remember: the coordinates of a point are (x;y). Choose one of the points to be point 1 and the other to be point 2. I would suggest that you follow the order they have given you ie. CD:

So if our points are C (2; 3) and D (6, 2) we can say point C is point 1 and point D is point 2. Plug into the formula:  

slope (m) = (y2-y1)/(x2-x1)

y1  = 3

y2 = 2

x1  = 2

x2 = 6

∴ m = (2-3)/(6-2)

      = -1/4

Answer:  Parameter

Step-by-step explanation:

A parameter is defined as :

A statistic is defined as :

Given : Mark had competed in the​ 100-meters event a total of 328 times.

Here ,  Population of interest =  Number of times Mark competed in the​ 100-meters event =328

His average time for these 328 races was 15 seconds.

Since this average is calculated from the entire population, therefore , 15 is representing a parameter .

Hence, the correct answer is : "Parameter"

Answer:

(x+3)

Step-by-step explanation:

Volume = Base area × height

Base area = x²+5x+6

= x²+2x+3x+6

= x(x+2)+3(x+2)

= (x+2)(x+3)

Since the length is the longer side, length = (x+3)

Dimensions of the box are:

(x+2)×(x+3)×(x+4)

Answer:

The value of the [tex]13^{th}[/tex] term is ≈ 1.

Step-by-step explanation:

A geometric sequence is a series of numbers where each term is computed by multiplying the previous term by a constant, r also known as the common ratio.

The formula to compute the [tex]n^{th}[/tex] term of a GP is: [tex]a_{n}=a_{1}\times r^{n-1}[/tex]

Here, a₁ is the first term.

It is provided that a₄ = 19625 and a₉ = 95.

Determine the value of a₁ and r as follows:

[tex]\frac{a_{4}}{a_{9}}=\frac{a_{1}r^{4-1}}{a_{1}r^{9-1}} \\\frac{19625}{95}= \frac{r^{3}}{r^{8}}r^{5}=\frac{95}{19625}\\ r=(\frac{95}{19625})^{1/5}\\=0.344[/tex]

The common ratio is, r = 0.344.

The value of a₁ is:

[tex]a_{4}=19625\\a_{1}\times(0.344)^{3}=19625\\a_{1}=\frac{19625}{0.040707584} \\=482096.898\\\approx482097[/tex]

The first term is, a₁ = 482097.

13th term of this geometric sequence is:

[tex]a_{13}=a_{1}\times r^{13-1}\\=482097\times (0.344)^{12}\\=1.3234\\\approx1[/tex]

Thus, the [tex]13^{th}[/tex] term is approximately equal to 1.

Line perpendicular to m is y =–4.

Distance from P to m is 5 units.

Solution:

Line m contains points (1, 1) and (5, 1).

Slope passing through two points formula:

[tex]$\text{slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]

        [tex]$=\frac{1-1}{5-1}[/tex]

Slope = 0

Slope of the line perpendicular to the line m:

[tex]$\text{Slope}=\frac{-1}{\text{slope}}=0[/tex]

Equation of a line passing through one point and slope formula:

[tex]y-y_1=m(x-x_1)[/tex]

Here, m = 0 and P(2, –4)

[tex]$\Rightarrow y-(-4)=0(x-2)[/tex]

[tex]$\Rightarrow y+4=0[/tex]

[tex]$\Rightarrow y=-4[/tex]

⇒ y = –4

Equation of a line perpendicular to m and passing through P is y = –4.

Option C is the correct graph. Because it only has slope 0 and P(2, –4).

Point of intersection where line m and P meets is (2, 1).

Let us find the distance between the line m in the point (2, 1) and P(2, –4).

Distance formula:

[tex]\text {Distance}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

              [tex]=\sqrt{(2-2)^2+(-4-1)^2}[/tex]

              [tex]=\sqrt{25}[/tex]

              = 5

Distance = 5 units

Hence line perpendicular to m is y =–4.

Distance from P to m is 5 units.

Answer:

The percentage of lemonade in the recipe is 25%.

Step-by-step explanation:

Given:

A recipe for lemonade punch calls for 6 cups of lemonade for every 24 cups of punch.

Now, to find [tex]x[/tex], the percentage of lemonade in the recipe.

In the recipe 6 cups of lemonade for every 24 cups of punch.

The percentage of lemonade = Cups of lemonade / cups of punch.

So, the equation to get the percentage:

[tex]x=\frac{6}{24} \times 100[/tex]

[tex]x=0.25\times 100[/tex]

[tex]x=25\%.[/tex]

Therefore, the percentage of lemonade in the recipe is 25%.

Answer:

263,606.9

Step-by-step explanation:

In 2004 the population in Morganton, Georgia, was 43,000.

(0, 43000)

The population in Morganton doubled by 2010

In 6 years the population is doubled (86000)

(6,86000)

[tex]A= a(b)^t[/tex]

Use (0,43000) in the above equation

[tex]A= a(b)^t\\43000= a(b)^0\\a=43000[/tex]

Now plug in (6,86000)

[tex]A= a(b)^t\\A= 43000(b)^t\\86000=43000(b)^6\\2=b^6\\b=\sqrt[6]{2} \\b=1.12[/tex]

[tex]A=43000(1.12)^t[/tex]

Now find out A when t=16 (2020)

[tex]A=43000(1.12)^t\\A=43000(1.12)^{16}\\A=263606.9[/tex]

If the growth rate from 2004 to 2010 continues, the expected population in Morganton, Georgia in 2020 would be around 172,000 as the population is doubling every 6 years.

The population of Morganton, Georgia in 2004 was 43,000 and it doubled by 2010 to 86,000. This shows a constant growth rate in which the population size doubles every 6 years. If this rate of growth remains consistent, the population of Morganton is expected to double again by 2020. Therefore, by 2020, the population of Morganton, Georgia could be around 172,000 people.

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Answer: she can only make 6 completed barrettes

Step-by-step explanation:

Samantha makes hair barrettes from ribbon. The total length of ribbon that she has is 3 1/4 feet. Converting 3 1/4 feet to improper fraction, it becomes 13/4 feet.

She uses 1/2 feet of ribbon to make each barrette. This means that the number of completed barrettes that Samantha can make with the ribbon she has would be

(13/4)/(1/2) = 13/4 × 2/1

= 6 1/2 barrettes

The complete barrette must be whole number.

Therefore, she can only make 6 completed barrettes

Answer:

6

Step-by-step explanation:

The exact circumference of the circle is [tex]7 \frac{49}{150} k m[/tex]

The approximate circumference of the circle is [tex]7.33 k m[/tex]

Explanation:

The diameter of the circle is [tex]2 \frac{1}{3} \mathrm{km}[/tex]

Now, we shall find the circumference of the circle.

The formula to determine the circumference of the circle is given by

[tex]C=\pi d[/tex]

Where C is the circumference , [tex]\pi[/tex] is 3.14 and [tex]d=2 \frac{1}{3} \mathrm[/tex] is the diameter of the circle.

The exact circumference of the circle is given by

[tex]\begin{aligned}C &=\pi d \\&=(3.14)\left(2 \frac{1}{3}\right) \\&=(3.14)\left(\frac{7}{3}\right) \\&=\frac{21.98}{3}\end{aligned}[/tex]

Multiply both numerator and denominator by 100, we get,

[tex]C=\frac{2198}{300} \\C=\frac{1099}{150}[/tex]

Converting [tex]\frac{1099}{150}[/tex] into mixed fraction, we get,

[tex]C=7 \frac{49}{150}[/tex]

Thus, the exact circumference of the circle is [tex]7 \frac{49}{150} k m[/tex]

The approximate value of the circumference can be determined by dividing the value [tex]\frac{1099}{150}[/tex]

[tex]C=\frac{1099}{150}=7.327[/tex]

[tex]C=7.33km[/tex]

Thus, the approximate circumference of the circle is [tex]7.33 k m[/tex]

Answer:

3/2

Step-by-step explanation:

(7/2)/(3/7) = 3/2 or 1.5 pieces

Answer:

The answer to your question is 8 pieces

Step-by-step explanation:

Data

rope = 7/2

length of a piece = 3/7

Process

1.- Divide 7/2 by 3/7

                 [tex]\frac{7}{2} / \frac{3}{7} = \frac{49}{6}[/tex]

2.- Divide 49 by 6 to get the pieces that can be made out of the rope

                         49 / 6 = 8 1/6

3.- Conclusion. We can get 8 pieces of the rope and there will be a remainder of 1/6.

Answer:

c

Step-by-step explanation:

in the question there is a confusion about " schedule shown" , either it is missing or by schedule shown it mean looking to the choices given

so if it is missing then sorry, but if it mean choices then the only possible answer is option C i.e. 12 hours because she works daily and missing only one day thus possible answer is 12 i.e. 6*2=12

hope it may help you

Answer:D

Step-by-step explanation:

Hope this helps

Answer:

The response does not seem reasonable.

Step-by-step explanation:

The current price of shorts is a sum of the original price plus profit. In this case, a simple formula is given:

Profit = Selling price  - Buying price

Therefore, the selling price can be anything less than $ 41.

Expressing the information in a linear equation gives x ≤ 41

where x is the buying price of the shorts.

To determine if David's answer that the original price of the shorts was $41 seems reasonable, we can use an equation to represent the situation. By solving the equation, we find that the original price of the shorts is $21.98, not $41.

To determine if David's answer that the original price of the shorts was $41 seems reasonable, we can use an equation to represent the situation. Let's assume the original price of the shorts is x dollars.

If the total cost of the T-shirt and shorts, including tax, is $22.45 as given, we can write the equation: x + 1.47 = 22.45.

Simplifying the equation, we subtract 1.47 from both sides: x = 21.98.

Therefore, the original price of the shorts would be $21.98, not $41. Hence, David's answer does not seem reasonable.

Answer:

-∞<x<∞

Step-by-step explanation:

Answer:

First option

Step-by-step explanation:

There's no value of x which makes the function undefined .

So x can take any real value

i.e. -infinity < x < +infinity

Answer:

a=128 feet   b=256 feet

Step-by-step explanation:

hope i got it

Answer:

A.) 128FT

B.) A=256

Step-by-step explanation:

A.)

16 x 4 = 64FT

62 x 2 = 128FT

So, 2 Laps Would Equal Up To 128FT.

B.)

Find the length of one of the sides (as each side is the same length) and then multiply this by itself to find the area.