Write 245.499 in word form.

The speed of the second pedestrian is 5 kilometers per hour.

Let's say that the speed of the second pedestrian is S.

We know that the other pedestrian walks at a speed of 4km/h, and they (together) travel a distance of 27km in 3 hours, then we can write the linear equation:

(4km/h + S)*3h = 27km

It says that both pedestrians work, together, a total of 27km in 3 hours.

Now we can solve that linear equation for S, to do this, we need to isolate S in the left side of the equation.

4km/h + S = 27km/3h = 9 km/h

S = 9km/h - 4km/h = 5km/h

The speed of the second pedestrian is 5 kilometers per hour.

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The equation of tangent plane to the given parametric surface \(r(u,v) = u.cos(v)i + u.sin(v)j + vk\) is \(\frac{\sqrt3}{2}x - \frac{5}{2}y + 5z = \frac{5\pi}{3}\) .

The given parametric surface is

\(r(u,v) = u.cos(v)i + u.sin(v)j + vk\)

The tangent vectors are

⇒ \(r_u = \frac{dx}{du} i+ \frac{dy}{du}j + \frac{dz}{du}k\)

⇒ \(r_u =\) \(r(u,v) = cos(v)i + sin(v)j + 0k\)

⇒ \(r_v = \frac{dx}{dv} i+ \frac{dy}{dv} j+ \frac{dz}{dv} k\)

⇒ \(r_v =\)  \(r(u,v) = -u.sin(v)i + u.cos(v)j + 1k\)

The normal vector to the tangent plane is

\(r_u r_v = \left[\begin{array}{ccc}i&j&k\\cos(v)&sin(v)&0\\-usin(v)&ucos(v)&1\end{array}\right]\)

⇒ \(r_u r_v =\) \(sin(v)i - cos(v)j + u.k\)

When u = 5, v = \(\frac{\pi }{3}\), the normal vector becomes

⇒  \(sin(\frac{\pi}{3})i - cos( \frac{\pi}{3})j + k\)

⇒ \(\frac{\sqrt{3} }{2}i - \frac{1}{2} j + k\)

The point on the surface corresponding to the u = 5 & v= \(\frac{\pi}{3}\) is

\(r(5, \frac{\pi}{3}) = (5)cos(\frac{\pi}{3})i + (5)sin(\frac{\pi}{3})j + (\frac{\pi}{3})k\\r(5, \frac{\pi}{3}) = \frac{5}{2}i + \frac{5\sqrt3}{2}j + \frac{\pi}{3}k\)

If a is the position vector of a point on the plane & n is a vector normal to the plane, then the equation of the plane is

⇒ (r - a).n = 0

⇒ \((x - \frac{5}{2}) . ( \frac{5\sqrt3}{2}) + (y - \frac{5\sqrt3}{2}).(- \frac{5}{2}) + (z - \frac{\pi}{3}).(5) = 0\)

⇒  \(\frac{\sqrt3}{2}x - \frac{5}{2}y + 5z = \frac{5\pi}{3}\)

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Answer: x = -3

Step-by-step explanation:

2 x 2 + x - 1 = 0

4 + x - 1 = 0

3 + x = 0

x = -3

Answer:

X=-3

Step-by-step explanation:

See steps below:)

We want to see how long it will take for Lin and Noah to run 1 mile. We will see that:

So we know that:

The time in which they run a single mile is given by the quotient between the time and the distance.

For Lin we have:

\(T = \frac{2/5 }{2 + 3/4} h/mi = \frac{2/5}{11/4} h/mi = \frac{2*4}{5*11} h/mi = \frac{8}{55} h/mi\)

So Lin runs a mile in (8/55) hours

For Noah we have:

\(T = \frac{4/3}{8 + 2/3} h/mi = \frac{4/3}{26/3} h/mi = \frac{4}{26} mi/h = \frac{2}{13} h/mi\)

Noah runs 1 mile in (2/13) hours.

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We can express the number 98 in exponential form as 10 raised to the power of 2. This means that by multiplying the base, which is 10, by itself twice, we obtain the value of 98.

To express 98 in exponential form, we need to determine the base and exponent that can represent the number 98.

Exponential form represents a number as a base raised to an exponent. Let's find the base and exponent for 98:

We can express 98 as 10 raised to a certain power since the base 10 is commonly used in exponential notation.

To find the exponent, we need to determine how many times we can divide 98 by 10 until we reach 1. This will give us the power to which 10 needs to be raised.

98 ÷ 10 = 9.8

Since 9.8 is still greater than 1, we need to continue dividing by 10.

9.8 ÷ 10 = 0.98

Now, we have reached a value less than 1, so we stop dividing.

From these calculations, we can see that 98 can be expressed as 10 raised to the power of 1 plus the number of times we divided by 10:

98 =\(10^1\) + 2

Therefore, we can write 98 in exponential form as:

98 = \(10^3\)

In summary, 98 can be expressed in exponential form as 10^2. The base is 10, and the exponent is 2, indicating that we multiply 10 by itself two times to obtain 98.

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The final counts are:

Given a survey of 240 students, 35% of students were interested in athletics, which is equal to 84 students.

3/5 of students were interested in academic clubs, which is equal to 144 students.

26 students were interested in both athletics and academic clubs.

Using this information, we can fill in the remaining cells of a table to show the number of students in each category.

The final counts are:

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Answer:

1000π

Step-by-step explanation:

π(r^2*h/3)=volume of cone

π(10√3^2*10/3)

10√3 is from using 30 60 90 Triangle to find AO

The line of reflection is the vertical line passing through (-5, 6), (-9, 6), (-9, 3), and (-7, 1).

A line of reflection is a line that acts as a mirror, reflecting a figure across it. Each point on the original figure is reflected over the line and the resulting image is the same size and shape as the original, but appears to be "flipped" or "mirrored" across the line of reflection. The line of reflection is the perpendicular bisector of the segment connecting each point on the original figure to its corresponding point on the reflected image.

In the given question,

To determine the line of reflection, we need to find the perpendicular bisector of each line segment between the point and its image.

First, we find the midpoint of the line segment between A and A': (A + A')/2 = (-3 + (-5))/2, (3 + 3)/2 = (-4, 3)

The perpendicular bisector of the line segment AA' is a vertical line passing through (-4, 3).

Similarly, we find the midpoints and perpendicular bisectors of the line segments BB', CC', DD', and EE'.

The perpendicular bisectors of the line segments BB', CC', DD', and EE' are also vertical lines passing through (-5, 6), (-9, 6), (-9, 3), and (-7, 1), respectively.

Therefore, the line of reflection is the vertical line passing through (-5, 6), (-9, 6), (-9, 3), and (-7, 1).

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Answer:

  $1741.44

Step-by-step explanation:

The discounted amount is 100% -10% = 90% of the original. The amount of the discount is 10% of the original, or 1/9 of the discounted amount:

  10% = 90% × 1/9

The discount was ...

  $15,673/9 = 1,741.44

_____

Check

The original is the sum of the discounted amount and the discount:

  original price = $15,673.00 +1,741.44 = $17, 414.44

10% of that value is 1,741.44, as shown above.

Answer:

65.4°

Step-by-step explanation:

According to question

The equation is

Cos(x)=5/12

x=acos(5/12)

x=65.4°

Considering the definition of an equation and the way to solve it, the girls will both pay the same if they buy six pairs of pants and one sweater.

An equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values appear.

The solution of a equation means determining the value that satisfies it. In this way, by changing the unknown to the solution, the equality must be true.

To solve an equation, keep in mind:

Being "x" the number of pairs of pants, you know that:

The equation in this case is:

17.95x + 24 = 18.95x + 18

Solving:

24 -18= 18.95x - 17-95x

6= x

Finally, this means that Kelsey and Jeana pay the same if they buy six pairs of pants and one sweater.

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Answer:

737 cooks are required to prepare a meal for 737 people in 5 hours

Step-by-step explanation:

According to the given information, 10 cooks can prepare a meal for 536 people working for 8 hours each.

Let's calculate the total work done by the 10 cooks in 8 hours.

Total work done = Number of cooks * Hours worked

Total work done = 10 * 8 = 80

Now, let's calculate the work done by one cook in one hour.

Work done by one cook in one hour = Total work done / (Number of cooks * Hours worked)

Work done by one cook in one hour = 80 / (10 * 8) = 1

Therefore, one cook can prepare food for 1 person in 1 hour.

Now, let's calculate the number of cooks required to prepare a meal for 737 people in 5 hours.

Total work required = Number of people * Hours required

Total work required = 737 * 5 = 3685

Number of cooks required = Total work required / (Hours worked * Work done by one cook)

Number of cooks required = 3685 / (5 * 1) = 737

Therefore, 737 cooks are required to prepare a meal for 737 people in 5 hours.

Answer:

B. 46.

Step-by-step explanation:

First we set up the equation A(n)=-172 and substitute the given equation for A(n), giving us -172=8+(n-1)(-4). Simplifying, we get -180=(-4n+12), or -4n=-192, or n=48. However, n represents the number of terms in the sequence, and since the sequence starts with n=1, we need to subtract 1 from our answer to get the term number corresponding to A(n)=-172. Therefore, the answer is B) 46.

Answer:

It is "The y-intercept is one space higher."

Step-by-step explanation:

Assuming your original equation is 6(9)^X, the + 1 at the end is moving the entire function up since all y values that are the output are 1 higher. This means the point on the y-axis will be one higher, leading us to the answer.

The statement that is not true about mean is A) Mean is the most commonly used average, as average is unique for every data set.

Mean is the average of a given data set it can be arithmetic mean or it can be geometric mean depending upon how a data is distributed.

We know that mean(arithmatic) is the sum of scores divided by the number of scores.

Mean also measures the deviation of each score as we take the the difference of the data sets from the mean and square it to obtain standard deviation.

It can also be thought of as a point where deviation sum to zero makes sense but mean is not the most frequently used average as there is nothing like most frequently used average as every data set has an unique average.

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Answer: 149 cartridges will be sold at 20 dollars per cartridge.

Step-by-step explanation:

Given: The projected sales volume of a video game cartridge is given by the function \(s(p)=\dfrac{3000}{2p+a}\), where s is the number of cartridges sold, in thousands; p is the price per cartridge, in dollars; and a is a constant.

Put s(p)=100000, p= 10, we get

\(100000=\dfrac{3000}{2(10)+a}\\\\\Rightarrow\ 100=\dfrac{3}{20+a}\\\\\Rightarrow\ 100(20+a)=3\\\\\Rightarrow\ 2000+100a=3\\\\\Rightarrow\ 100a=-1997\\\\\Rightarrow\ a=-19.97\)

i.e. \(s(p)=\dfrac{3000}{2p-19.97}\)

Put p=20, we get

\(s(20)=\dfrac{3000}{2(20)-19.97}\\\\=\dfrac{3000}{40-19.97}\\\\=\dfrac{3000}{20.03}\approx149\)

Hence, 149 cartridges will be sold at 20 dollars per cartridge.

The ball is in the air for approximately 2.8 + √7 seconds, which rounds to 5.2 seconds when rounded to one decimal place.To write the equation in vertex form, we need to complete the square.

The given equation is h = -4.9t² + 27.44t + 0.584. We can rewrite it as:

h = -4.9(t² - 5.6t) + 0.584

Now, we want to complete the square inside the parentheses. To do this, we need to add and subtract the square of half the coefficient of t. In this case, the coefficient is -5.6, so we have:

h = -4.9(t² - 5.6t + (5.6/2)² - (5.6/2)²) + 0.584

Simplifying, we get:

h = -4.9((t - 2.8)² - 2.8²) + 0.584

Expanding further:

h = -4.9(t - 2.8)² + 4.9(2.8)² + 0.584

Thus, the equation in vertex form is: h = -4.9(t - 2.8)² + 34.328

b) The ball's height when it was hit can be found by evaluating the equation at t = 0:

h = -4.9(0 - 2.8)² + 34.328

h = -4.9(-2.8)² + 4.328

h = -4.9(7.84) + 34.328

h ≈ 0.784 meters

To find the time at which the ball reaches its maximum height, we can use the fact that the maximum height occurs at the vertex of the parabolic equation. The vertex of a parabola in the form h = a(t - h₀)² + k is given by (h₀, k). Comparing this to our equation, we can see that the vertex occurs at t = 2.8 and h = 34.328. Therefore, the ball reaches its maximum height at 2.8 seconds, and the maximum height is 34.328 meters.

The total time the ball is in the air can be determined by finding the time it takes for the ball to reach the ground. When the ball hits the ground, its height is 0. To find this time, we can set the equation equal to 0 and solve for t:

0 = -4.9(t - 2.8)² + 34.328

4.9(t - 2.8)² = 34.328

(t - 2.8)² ≈ 7

t - 2.8 ≈ ±√7

t ≈ 2.8 ± √7

Since time cannot be negative in this context, we can ignore the negative value.

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Answer:

6 friends can share the pizza

Step-by-step explanation:

1 1/2 ÷ 1/4 =6

Answer:

Divide 1 1/2 by 1/4. Note that 1 1/2 = 1 2/4 = 6/4. So now we divide 6/4 by 1/4, obtaining 6.

6 friends can enjoy an equal share.

The ratio of the given 240 kg to 6 kg will be 40:1.

What is Ratio?

Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorise ratios. Part to whole ratio is one, and part to part ratio is the other. The part-to-part ratio shows the relationship between two separate entities or groupings. Mathematicians use the term "ratio" to compare two or more numbers. It serves as a comparison tool to show how big or tiny an amount is in relation to another. Two quantities are compared using division in a ratio. In this case, the dividend is referred to as the "antecedent" and the divisor as the "consequent."

the ratio 240 kg to 6 kg.

It will be simple 240/6 :: 40 :1

Hence the ratio of the given data will be 40:1

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The quadratic function f(x) =\(3(x+3)^2 - 7\) has a minimum at x = -1, and the minimum value is 5.

To determine whether the quadratic function f(x) =\(3(x+3)^2 - 7\)has a minimum or maximum, we can examine the coefficient of the x^2 term, which is positive (3 in this case).

When the coefficient of the x^2 term is positive, the parabola opens upward, indicating that the function has a minimum value. The vertex of the parabola represents the minimum point.

Now let's find the coordinates of the vertex, which will give us the minimum value of the function.

The general form of a quadratic function is f(x) =\(ax^2 + bx + c\), where the vertex can be found using the formula:

x = -b / (2a)

In our case, a = 3 and b = 3*2 = 6 (from (x+3)^2).

Substituting the values into the formula, we have:

x = -6 / (2 * 3)

x = -6 / 6

x = -1

To find the y-coordinate of the vertex, we substitute the x-value (-1) into the function:

\(f(-1) = 3((-1)+3)^2 - 7\)

\(f(-1) = 3(2)^2 - 7\)

f(-1) = 3(4) - 7

f(-1) = 12 - 7

f(-1) = 5

The graph of this function will have a downward-opening parabola, and the vertex will be the lowest point on the curve.

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Answer:

YZ is located at Y (0, 1) and Z (-2, 1) and is one-third the size of Y'Z'.

Step-by-step explanation:

Since Y'Z' was dilated from the origin at a scale factor of 3, you can divide its X and Y coordinates by 3 to find the coordinates of YZ.

The statement fourth "segment YZ is located at Y (0, 1) and Z (−2, 1) and is one-third the size of segment Y prime Z prime" is correct.

The transformation dilation is used to resize an item. Dilation is a technique for making items appear larger or smaller. The image created by this transformation is identical to the original shape.

The question is incomplete.

The complete question is:

Segment Y prime Z prime has endpoints located at Y'(0, 3) and Z'(−6, 3). segment YZ was dilated at a scale factor of 3 from the origin. Which statement describes the pre-image?

As we know, in the dilation image of the two-dimensional figure can be larger or smaller depending on the dilation factor.

We have:
segment Y prime Z prime has endpoints located at Y'(0, 3) and Z'(−6, 3).

After dilation:

Y (0, 1) and Z (−2, 1)

Thus, the statement fourth "segment YZ is located at Y (0, 1) and Z (−2, 1) and is one-third the size of segment Y prime Z prime" is correct.

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Answer:

In order: 18, 24, 48

Step-by-step explanation:

Let the number on the three evenings be a, b, and c, in order.

a + b + c = 90

a = b - 6

c = 2b

b - 6 + b + 2b = 90

4b - 6 = 90

4b = 96

b = 24

a = b - 6 = 24 - 6 = 18

c = 2b = 2(24) = 48

In order: 18, 24, 48

Answer:

8(3+4p)

Step-by-step explanation:

8 goes into 24 and 32, so it can be factored out:

\(24+32p=8(3+4p)\)

Answer:

8(3 + 4p)

Step-by-step explanation:

Factor 24 + 32p

First, factor out the GCF. In this case, the GCF is 8, and we have

8(3 + 4p)

We can't factor anymore so the answer is 8(3 + 4p)

Answer:

O The cost of the hamburger will increase by $1.40 per topping.

Step-by-step explanation:

Answer:

The cost of the hamburger will increase by $1.40 per topping

Step-by-step explanation:

Given equation:

y = 1.90 + 1.40x

where

The slope-intercept form of a linear equation is y = mx + b (where m is the slope and b is the y-intercept).

Rearranging the given equation to this form:  y = 1.40x + 1.90

Therefore, 1.40 is the slope and 1.90 is the y-intercept.

The slope is the rate of change.  This is the amount by which y will change with respect to changes in x.  The slope is positive, so as x increases, y will increase.  

Therefore, the cost of the hamburger will increase by $1.40 per topping.

You have a pentagon. In order to determine the value of x for the given expression, of the measure of the angles, take into account that the sum of the interior angles of a pentagon is 540°.

Then, by using the given expressions you have:

(98) + (149 - x) + (2x + 4) + (114) + (128) = 540

To solve for x, proceed as follow:

(98) + (149 - x) + (2x + 4) + (114) + (128) = 540 eliminate parenthesis

98 + 149 - x + 2x + 4 + 114 + 128 = 540 simplify like terms left side

493 + x = 540 subtract 493 both sides

x = 540 - 493

x = 47

Hence, the value of x is x = 47

To find the surface area of square OABC, we calculate the side length using the coordinates of point B, resulting in 25/16 units.

To find the surface area of square OABC, we need to determine the length of one side of the square. Since point B lies on the line with the equation y = -4x + 5, we can use this information to find the coordinates of point B and then calculate the distance between points O and B to determine the side length.

First, we need to find the x-coordinate of point B. Since we know the equation of the line y = -4x + 5, we can substitute y = 0 (since point B lies on the x-axis) and solve for x:

0 = -4x + 5

4x = 5

x = 5/4

Therefore, the x-coordinate of point B is 5/4.

Next, we substitute this x-coordinate back into the equation y = -4x + 5 to find the y-coordinate of point B:

y = -4(5/4) + 5

y = -5 + 5

y = 0

So, the coordinates of point B are (5/4, 0).

Now, we can calculate the distance between points O and B using the distance formula:

Distance = \(\sqrt{[(x2 - x1)^2 + (y2 - y1)^2]}\)

        = \(\sqrt{[(0 - 0)^2 + (5/4 - 0)^2]}\)

        = \(\sqrt{[(5/4)^2]}\)

        =\(\sqrt{ [25/16]}\)

        = 5/4

Since OABC is a square, all sides are equal in length. Therefore, the side length of square OABC is 5/4.

To find the surface area of the square, we use the formula:

Surface Area = \(Side Length^2\)

            =\((5/4)^2\)

            = 25/16

Therefore, the surface area of square OABC is 25/16 square units.

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Answer:

y-10

Step-by-step explanation:

Answer:

B and D

Step-by-step explanation:

This is because for B you do 8x9x1 which is basically 8x9 which is 72. Then, for D you do 12x3x2. Do 3x2 first and you get 6. Then, do 6x12 which is also 72. So the correct answers that will give you the volume of 72 units cube is B and D. Hope this helps!

Answer:

2x^2 - 6x

Step-by-step explanation:

2x(x-3)

= 2x^2 - 6x