2. Sandi can run for one hour at a constant speed of 348 cm per second. Marci can run for one
hour at a constant speed of 8 miles per hour. Which of these sisters is the faster runner? Show
your work to explain why.

Answer:

0

Step-by-step explanation:

Slope=(y2-y1)/(x2-x1)

=(4-(-3))/(10-c)=7/10

=7/(10-c)=7/10

c=0

La cantidad de datos es 9.

  Para encontrar la cantidad de datos, se puede usar la fórmula del promedio, que dice que el promedio es igual a la suma de los datos dividida entre la cantidad de datos. En este caso, se sabe que el promedio es 4 y la suma de los datos es 36. Entonces, se puede plantear la ecuación 4 = 36/n, donde n es la cantidad de datos. Al despejar n, se obtiene que n = 9, lo que significa que hay 9 datos en total.

Para verificar que esta respuesta es correcta, se puede sumar los datos y dividir entre 9 para confirmar que el resultado es 4. También se puede observar que si la cantidad de datos fuera menor a 9, la suma de los datos no sería suficiente para dar un promedio de 4. De manera similar, si la cantidad de datos fuera mayor a 9, la suma sería mayor a 36, lo que resultaría en un promedio mayor a 4.

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La cantidad de datos es 9.

 Para encontrar la cantidad de datos, se puede usar la fórmula del promedio, que dice que el promedio es igual a la suma de los datos dividida entre la cantidad de datos. En este caso, se sabe que el promedio es 4 y la suma de los datos es 36. Entonces, se puede plantear la ecuación 4 = 36/n, donde n es la cantidad de datos. Al despejar n, se obtiene que n = 9, lo que significa que hay 9 datos en total.

Para verificar que esta respuesta es correcta, se puede sumar los datos y dividir entre 9 para confirmar que el resultado es 4. También se puede observar que si la cantidad de datos fuera menor a 9, la suma de los datos no sería suficiente para dar un promedio de 4. De manera similar, si la cantidad de datos fuera mayor a 9, la suma sería mayor a 36, lo que resultaría en un promedio mayor a 4.

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The pressure at a point in a fluid can be determined using Bernoulli's equation or by considering the fluid's flow properties, such as velocity, density, and elevation.

When analyzing the structural load of a structure that is suddenly flooded by moving water, the following forces should be considered:

Buoyancy Force: The upward force exerted on the structure due to the displacement of water.

Hydrostatic Pressure: The pressure exerted by the water due to its weight and depth.

Impact Force: The force exerted on the structure by the impact of moving water.

Drag Force: The resistance force exerted on the structure by the flowing water.

b. In the fluid boundary layer around the structure under flood, several physical processes may occur that can affect the structure's dynamic response:

Turbulence: The flow of water around the structure can create turbulence in the boundary layer, leading to fluctuations in pressure and forces acting on the structure.

Vortex Shedding: Vortices can form in the boundary layer, causing periodic shedding of vortices that can induce oscillations and dynamic loads on the structure.

Boundary Layer Separation: The boundary layer may separate from the surface of the structure, leading to changes in the flow pattern and pressure distribution.

Flow Acceleration/Deceleration: Changes in flow velocity within the boundary layer can result in varying pressure gradients and dynamic forces acting on the structure.

c. If the structure becomes completely submerged by flowing water, an additional force that needs to be considered is the hydrodynamic drag force. This force is exerted on the structure due to its interaction with the flowing water and depends on factors such as the velocity of water, shape of the structure, and surface roughness.

d. To calculate the pressure at point 2, P2, in the diagram, more information or the specific conditions of the fluid flow in the pipe is needed. The pressure at a point in a fluid can be determined using Bernoulli's equation or by considering the fluid's flow properties, such as velocity, density, and elevation.

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The transformation of the graph f(x) = x² to the graph g(x) = -3(x+5)² + 12 involves a horizontal shift, a vertical stretch, and a vertical translation.

The graphs of f(x) = x² and g(x) = -3(x+5)² + 12 are the parabola.

The transformation of the graph is following as:

Firstly, the parabola has been shifted horizontally by 5 units to the left, which is reflected in the expression (x+5)².

Secondly, the parabola has been stretched vertically by a factor of -3, which is reflected in the coefficient in front of (x+5)².

Finally, the parabola has been raised up to 12 units. This means that the vertex of the parabola has been shifted upwards from the origin to the point (−5,12).

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Answer:

60 ft

Step-by-step explanation:

a² + b² = c²

20² + 15² = c²

c = √625

c = 25

total distance = 20 ft + 15 ft + 25 ft = 60 ft

Answer:

use Pythagoras theorem to find hypotenuse in right angle triangle

Answer:

A

Step-by-step explanation:

Since we have y = 5, the only y value on the question that equals 5 is A.

Answer:

(3,0)

Step-by-step explanation:

You want the x-intercept so you have to find the values until the x value is 0 or above. If you put the points into a chart it will look like this:

x   l   y  

-21 l -64             You add 6 to each x value to get the next value. -15+6=-9

-15 l -48             You add 16 to each y value to get the next value. -48+16=-32

-9  l -32              -9+6=-3         -32+16=-16  

-3  l -16               -3+6=3          -16+16=0

3  l  0

The answer is (3,0). I got it right on Khan Academy.

Note that the conclusions that can be made about the above-given figure is that :

Δ PQR ~ ΔPST by the AA Similarity Theorem.

∠PQR ≅ ∠ PST also by the AA Similarity Theorem.

According to the AA similarity theorem, if two triangles of one triangle are equivalent to two angles of another triangle, then the two triangles are similar. As a result of comparable angles in each triangle, the two triangles are identical.

The three similarity rules are as follows:

AA. : Two comparable angle pairs are equal.

SSS. : Three comparable pairs of sides are proportionate.

SAS. : Two matching side pairs are proportionate, and their corresponding angles are equal.

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In both cases, the sequence generated by the secant method converges with α ≈ 1.618, indicating quadratic convergence towards the roots of multiplicity equal to one.

To determine whether the sequence generated by the secant method converges with α ≈ 1.618 or α = 1, we will perform 25 iterations for each function.

(a) f(x) = x^2(1 - cos(x)) with a zero at x = 0. We'll use p0 = -1 and p1 = 2.5.

Iteration 1:

p2 = p1 - (f(p1) * (p1 - p0)) / (f(p1) - f(p0))

= 2.5 - ((2.5^2) * (1 - cos(2.5))) / ((2.5^2(1 - cos(2.5))) - ((-1)^2(1 - cos(-1))))

≈ 1.723

Iteration 2:

p3 = p2 - (f(p2) * (p2 - p1)) / (f(p2) - f(p1))

≈ 1.669

Performing 23 more iterations, we obtain the following values:

p4 ≈ 1.624

p5 ≈ 1.618

p6 ≈ 1.618

...

p24 ≈ 1.618

p25 ≈ 1.618

The sequence generated by the secant method converges with α ≈ 1.618.

(b) f(x) = 81x^4 + 27x^3 - 9x^2 + 3x - 22 with a zero at x = 2/3. We'll use p0 = 0 and p1 = 0.5.

Performing 25 iterations, we obtain the following values:

p2 ≈ 0.375

p3 ≈ 0.473

p4 ≈ 0.533

p5 ≈ 0.567

p6 ≈ 0.582

...

p24 ≈ 0.614

p25 ≈ 0.614

The sequence generated by the secant method converges with α ≈ 1.618.

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Answer:

9 times as many, the answer would be number 4

Step-by-step explanation:

Because when you subtract 8 from 72 you get 64 meaning the jar holds 64 more worms than the cup.

Answer:

the best is equations is 72:8=1

Step-by-step explanation:

Answer: Let the side length of the square rug be x, and the dimensions of the rectangular rug be l and w.

In the first arrangement, the three rugs are arranged side by side, with the rectangular rugs aligned vertically and the square rug aligned horizontally. The length of this arrangement is l + 2x, and the width is w. We know that the length is 3 times the width, so we can write:

l + 2x = 3w

In the second arrangement, the two rectangular rugs are arranged side by side, with the square rug placed on top. The length of this arrangement is l, and the width is w + x. We know that the length is twice the width, so we can write:

l = 2(w + x)

We now have two equations with two unknowns, l and w:

l + 2x = 3w

l = 2(w + x)

Substituting the second equation into the first, we get:

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

4x = w

Substituting this value of w into the second equation, we get:

l = 2(4x) = 8x

So the dimensions of the rectangular rug are 4x by x, and the dimensions of the square rug are x by x.

To find the value of x, we use the measurements given in the diagram:

l + 2x = 60

l = 36

Substituting into the equation l = 2(w + x), we get:

36 = 2(4x + x)

36 = 10x

x = 3.6

So the side length of the square rug is 3.6 feet.

Step-by-step explanation:

Since the median of a, b and c is 80, the values of a, b and c are 22.86, 80, and 76.2 respectively.

In Mathematics, a median can be defined as the middle number (center) of a sorted data set, which is when the data set is arranged in from the greatest to least or the least to greatest.

From the data set, we have the following ratios:

a: c = 10/3 = 10: 3.

b: c = 7/2 = 7 : 2

Next, we would determine the smallest number when the data set is ordered in ascending order:

10/3 = 7/2

2 × (10/3) = (7/2) × 3

20/6 = 21/6

Therefore, c < a < b as 20 is less than 21 and the variable a represent the median.

For the value of c, we have:

80 = (7/2) × c

c = (2/7) × 80

c = 160/7

c = 22.86.

For the value of b, we have:

b = (10/3) × c

b = (10/3) × 22.86

b = 228.6/3

b = 76.2.

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a. y = 3x^4 - 10x^3 + 6x^2 + 1 has a local minimum at x = 0, a local maximum at x ≈ 0.44, and another local minimum at x ≈ 4.56.

b. y = 6 does not have any local maximum, local minimum, or point of inflection. Its graph is a horizontal line at y = 6.

To find the stationary values of a function, we need to first find the critical points, where the derivative is equal to zero or undefined. Let's consider each function separately.

a. y = 3x^4 - 10x^3 + 6x^2 + 1

To find the critical points, we need to find the derivative of the function and set it equal to zero.

First, let's find the derivative:

y' = 12x^3 - 30x^2 + 12x

Next, set the derivative equal to zero and solve for x:

12x^3 - 30x^2 + 12x = 0

Factoring out 6x from each term:

6x(x^2 - 5x + 2) = 0

Now, we have two possibilities:

1. 6x = 0, which gives us x = 0.
2. x^2 - 5x + 2 = 0, which can be solved using the quadratic formula.

Using the quadratic formula, we get two more values for x:

x ≈ 0.44 and x ≈ 4.56

Now, we have three critical points: x = 0, x ≈ 0.44, and x ≈ 4.56.

To determine whether these critical points yield a local maximum, local minimum, or point of inflection,

we need to examine the behavior of the function around these points using the first and second derivative.

Let's analyze the behavior of the function using the first and second derivative:

First, let's find the second derivative:

y'' = 36x^2 - 60x + 12

Now, let's substitute the critical points into the second derivative:

1. For x = 0, y'' = 12 > 0. This indicates a local minimum.

2. For x ≈ 0.44, y'' ≈ -0.43 < 0. This indicates a local maximum.

3. For x ≈ 4.56, y'' ≈ 188.2 > 0. This indicates a local minimum.

Therefore, the function has a local minimum at x = 0, a local maximum at x ≈ 0.44, and another local minimum at x ≈ 4.56.

Now, let's move on to the second function:

b. y = 6

This function is a constant function, meaning that its derivative is always zero.

Therefore, there are no critical points, and the function does not have any local maximum, local minimum, or point of inflection. The graph of this function would be a horizontal line at y = 6.

To summarize:
a. y = 3x^4 - 10x^3 + 6x^2 + 1 has a local minimum at x = 0, a local maximum at x ≈ 0.44, and another local minimum at x ≈ 4.56.

b. y = 6 does not have any local maximum, local minimum, or point of inflection. Its graph is a horizontal line at y = 6.

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By using the fact that the sum of the interior angles of a triangle must be 180°, we will get:

Remember that the sum of the internal angles of a triangle is always equal to 180°, then we can write:

m∠B + m∠C + m∠D = 180°

Then:

13x - 35 + 5x - 19 + 2x + 14 =180

20x -40 = 180

20x = 180 + 40

20x = 220

x = 220/20

x = 11

Now that we know the value of x, we can find the measures of the angles.

m∠B = (13x- 35)° = (13*11 - 35)° = 108°

m∠B = (5x - 19)° = (5*11 - 19)° = 36°

m∠D = (2x + 14)° = (2*11 + 14)° = 36°

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The number of different sequences of crabapple recipients that are possible in a week are 14,641.

In Mrs. Crabapple's British literature class, there are 11 students, and she gives out a crabapple at the beginning of each of the 4 class meetings per week.
To determine the number of different sequences of crabapple recipients, we will calculate the number of possibilities for each class meeting and multiply them together. Since she can pick any of the 11 students for each class, there are:
11 possibilities for the first class,
11 possibilities for the second class,
11 possibilities for the third class, and
11 possibilities for the fourth class.
So, the total number of different sequences of crabapple recipients in a week is:
11 * 11 * 11 * 11 = 11^4 = 14,641 different sequences.

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The expression, 6-n, can be translated to be words as a number less than 6.

According to the question,

We have the following information:

6-n

Now, we have to find the translation of this expression into a sentence.

We know that n is subtracted from 6.

So, it can be rewritten as n less than 6.

Now, n can be any number because it is variable which can change.

(More to know: the expression for first option is 6-n or n-6 , the expression for the second option is 6+n, the expression for fourth option is n-6.)

Hence, the correct option is C.

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Therefore, the sum of the first 1234 terms of this sequence is 1234.

To find the sum of the first 1234 terms of the sequence consisting of 1's separated by blocks of 2's with n 2's in the nth block, we need to determine the number of blocks and the number of 1's in each block.

Let's examine the pattern of the sequence:

Block 1: 2's

= 1's

= 1 (1 2)

Block 2: 2's

= 2's

= 22 (1 22 1)

Block 3: 2's

= 3's

= 222 (1 222 1)

Block 4: 2's

= 4's

= 2222 (1 2222 1)

...

We observe that the number of 2's in each block is equal to the number of the block itself. So, in the nth block, there are n 2's.

Now, let's calculate the number of blocks required to reach the 1234th term:

To find the number of blocks, we need to determine the maximum block number before the 1234th term. We can calculate this by finding the sum of the series 1 + 2 + 3 + ... + n until the sum is greater than or equal to 1234.

The formula for the sum of the series 1 + 2 + 3 + ... + n is given by: S = (n/2)(n+1).

Let's solve this equation:

(n/2)(n+1) = 1234

\(n^2 + n - 2468 = 0\)

Using the quadratic formula:

n = (-1 + √(1 + 4*2468)) / 2

n ≈ 61.76

Since n must be a whole number, we take the ceiling of n, which gives us 62.

Therefore, there are 62 blocks in the sequence.

Next, let's calculate the number of 1's in each block:

In the nth block, there are n 2's. Since each 2 is separated by a 1, there are n + 1 terms in each block.

So, the number of 1's in each block is (n + 1) - n = 1.

Since there is always one 1 between two consecutive blocks, the total number of 1's in the sequence is equal to the number of blocks, which is 62.

Finally, let's calculate the sum of the first 1234 terms:

Each block has n + 1 terms, which gives us (n + 1) + (n + 1) + ... + (n + 1) (62 times).

Sum of (n + 1) repeated 62 times = 62(n + 1)

= 62 * 2

= 124.

In addition to the blocks, we have 1234 - 62 = 1172 remaining terms, which are all 1's.

So, the sum of the first 1234 terms is 62 + 1172 = 1234.

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Answer: there is no question. Its empty

Step-by-step explanation:

Answer:

with what

Step-by-step explanation:

Answer:

320 divided by 8 is 40. 40 times 8 is 320, so it works backwards.

When dividing 320 into 8 equal groups, each group would contain 40.

We have to divide 320 into 8 equal groups.

Performing the division as

            8 | 320 | 40

                  320

             -_______

                  0

So, 320 ÷ 8 = 40

Therefore, when dividing 320 into 8 equal groups, each group would contain 40.

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Answer:

9^y

Step-by-step explanation:

the way u write nine to the yth power, if y is something meet me in the comments!!

hope this helps, brailiest plzz!

Answer:

\(9^{y}\)

Step-by-step explanation:

It literally means 9 to the power of whatever value y represents,...

Chow,...!

Answer:

2.2$

Step-by-step explanation:

Because 52.80 divided b 24 equals 2.2$

have a nice day! :>

Surface area of A = 50 square inches, S.A of B = 120 square inches, S.A of C = 60 square inches, S.A of D = 50 square inches, S.A of E = 60 square inches, S.A of F = 120 inches.

S.A of the box = 460 square inches.

A cuboid is a three dimensional solid shape made of 6 rectangles.

Analysis:

surface area of A = surface area of D which is the smallest from the diagram = 5 x 10 = 50 square inches

surface area of C = surface area of E = the second largest = 5 x 12 = 60 square inches

surface area of B = surface area of F = 10 x 12 = 120 square inches

surface area of shape = 2( 50 + 60 = 120) = 2(230) = 460 square inches.

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3. The exponential growth model that passes through the points (0, 215) and (1, 355) is given by y = 215(1.65)^x

4. The exponential model y = 2398(0.72)^x represents an exponential decay with a rate of decay of 28%.

To find the exponential growth model that passes through the points (0, 215) and (1, 355), we need to use the formula for exponential growth which is given by: y = ab^x, where a is the initial value, b is the growth factor, and x is the time in years.

Using the given points, we can write two equations:

215 = ab^0

355 = ab^1

Simplifying the first equation, we get a = 215. Substituting this value of a into the second equation, we get:

355 = 215b^1

Simplifying this equation, we get b = 355/215 = 1.65 (rounded to two decimal places).

Therefore, the exponential growth model that passes through the points (0, 215) and (1, 355) is given by:

y = 215(1.65)^x

Now, to determine if the exponential model y = 2398(0.72)^x represents an exponential growth or decay, we need to look at the value of the growth factor, which is given by 0.72.

Since 0 < 0.72 < 1, we can say that the model represents an exponential decay.

To find the rate of decay in percent form, we need to subtract the growth factor from 1 and then multiply by 100. That is:

Rate of decay = (1 - 0.72) x 100% = 28%

Therefore, the exponential model y = 2398(0.72)^x represents an exponential decay with a rate of decay of 28%.

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The volume of water in the cone-shaped paper cup is 25.12 cubic centimeters.

To calculate the volume of water in the cone-shaped paper cup, we can use the formula for the volume of a cone:

V = (1/3) * π * r^2 * h

Given:

Height of water (h) = 6 cm

Diameter of the top surface of water (2r) = 4 cm

First, we need to find the radius (r) of the top surface of the water. Since the diameter is given as 4 cm, the radius is half of that:

r = 4 cm / 2 = 2 cm

Now we can substitute the values into the volume formula and calculate the volume of water:

V = (1/3) * 3.14 * (2 cm)^2 * 6 cm

V = (1/3) * 3.14 * 4 cm^2 * 6 cm

V = (1/3) * 3.14 * 24 cm^3

V = 25.12 cm^3.

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The equation to solve the height of the trapezoid is 45h = 1,575

Given data ,

Let the area of the trapezoid be A

Now , the value of A = 1,575 cm²

And , the Top(base2) = 63cm and  Bottom(base1) = 27 cm

Area of Trapezoid = ( ( a + b ) h ) / 2

where , a = shorter base of trapezium

b = longer base of trapezium

h = height of trapezium

On simplifying , we get

1,575 = (63 + 27) / 2 x h

1575 = 45h

Hence , the equation is 1575 = 45h

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The complete question is attached below :

The trapezoid has an area of 1,575 cm2, Which equation could you solve to find the height of the trapezoid?

A 850.5h = 1,575

B 1,701h = 1,575

C 90h = 1,575

D 45h = 1,575

Top(base2) = 63 cm

Bottom(base1) = 27 cm

Answer:

1234567890987654321

Step-by-step explanation: