in a race in which 9 contestants are entered in how many ways can first second and third place be awarded

Answer: b=18.1 and c=14.3

Step-by-step explanation:o solve for the lengths of the sides b and c in triangle ABC, we can use the law of sines, which relates the lengths of the sides of a triangle to the sines of the angles opposite those sides. Specifically, the law of sines states that:

a/sin(A) = b/sin(B) = c/sin(C)

where A, B, and C are the angles of the triangle opposite sides a, b, and c, respectively.

Given that a = 17, B = 70°, and C = 48°, we can write:

b/sin(70°) = 17/sin(A)

c/sin(48°) = 17/sin(A)

To solve for b and c, we need to find sin(A). We can do this by using the fact that the angles of a triangle sum to 180°:

A + B + C = 180°

A = 180° - B - C

A = 180° - 70° - 48°

A = 62°

Now we can substitute sin(A) = sin(62°) into the equations above and solve for b and c:

Answer: 1/6 = cos(8π)/6 + i*sin(8π)/6

Step-by-step explanation: In the context of complex numbers, the division of 1 by 6 can be accomplished by employing a straightforward procedure that involves dividing both the real and imaginary components by 6.

The mathematical expression 1/6 may be represented in academic prose via the complex number format (cos(8π)/6 + i*sin(8π)/6).

Answer:

V = 62.8 m[tex]^{3}[/tex]

Step-by-step explanation:

V = pi × (radius)[tex]^{2}[/tex] × height

V = [tex]\pi[/tex] × [tex]r^{2}[/tex] × h

V = (3.14 × [[tex]2^{2}[/tex]]) × 5

V = (3.14 × 4) × 5

V = 12.56 × 5

V = 62.8 m[tex]^{3}[/tex]

If circle with center N with m∠MNP=124 ∘ and MN=13,  the area of sector MNP is approximately equal to 194.86 square units.

To find the area of a sector of a circle, we need to use the formula:

Area of sector = (central angle/360°) x πr²

Where r is the radius of the circle.

In this problem, we know that the central angle m∠MNP is 124° and MN, which is also the radius of the circle, is 13. So we can substitute these values into the formula:

Area of sector = (124/360) x π(13)²

Area of sector ≈ 194.86

Therefore, the area of sector MNP is approximately equal to 194.86 square units.

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Answer:

To find the missing side of a right triangle given an angle and a side, you can use trigonometric functions. In this case, we have the angle opposite the missing side, so we can use the sine function.

The sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse. Therefore, we can set up the following equation:

sin(34°) = opposite / 12

To solve for the opposite side, we can multiply both sides by 12:

opposite = 12 * sin(34°) ≈ 6.60

Therefore, the missing side of the triangle is approximately 6.60 units long.

Step-by-step explanation:

The value of the expression 9 squared will be 81.

In Mathematics, it is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information.

In this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.

The value will be:

= 9²

= 9 × 9.

= 81

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Answer:

192pie

Step-by-step explanation:

To find the area of a circle, it is pie (3.14) times r². The radius is 24, so it is 24² times pie. The area is 576 pie. Now to find the area of the shaded, you would do 1/3 times the area. 1/3 of 576 is 192. The answer is 192pie

A graph of quadrilateral M'N'O'P' after a vertical translation is shown below.

In Mathematics and Geometry, the translation of a graph downward simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image.

By translating the pre-image of quadrilateral MNOP vertically downward 4 units, the coordinates of quadrilateral M'N'O'P' include the following:

(x, y)                               →                  (x, y - 4)

M (-2, 5)                        →                  (-2, 5 - 4) = M' (-2, 1).

N (-3, 2)                        →                  (-3, 2 - 4) = N' (-3, -2).

O (-5, 2)                        →                  (-5, 2 - 4) = O' (-5, -2).

P (-6, 5)                        →                  (-6, 5 - 4) = P' (-6, 1).

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The missing exponent of the expression is determined as 4.

The value of the missing exponent is calculated as follows;

The given function is;

81/256 = (3/4)ˣ

To determine the value of the missing exponent, we will apply the power law of indicial equation as follows;

From base of the exponential function, we will determine the value of x;

3⁴/4⁴ = (3/4)x

(3/4)⁴ = (3/4)ˣ

4 = x

Thus, the missing value of the exponential function is determined by applying rules of exponent.

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The complete question is below:

Find the missing exponent 81/256 =  (3/4)ˣ

Answer: 0.8958

Step-by-step explanation:

Answer:

  128

Step-by-step explanation:

You want a prediction for x=2 when the given data is modeled by an exponential model.

A graphing calculator's exponential regression function models this data with the formula ...

  y = 135.7 · 0.9711^x

  y = 137.7 · 0.9711^2 ≈ 127.94 . . . . when x=2

This model gives a value for variable 2 of approximately 128 when variable 1 = 2.

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1. When people find themselves in an unfamiliar environment, it is common to feel vulnerable, lonely, and uncertain.

2. Globalization can change the mix of customers and products for an organization by creating new markets and opportunities for growth.

3. You can improve your GQ by practicing mindfulness and meditation

Businesses may need to concentrate on creating new goods and services that appeal to a global market as well as modifying their business models to satisfy the needs of clients in various regions of the world if they want to be leaders in the organization's future state.

In order for them to be more adaptable and receptive to changes in the global marketplace, they might also need to invest in technology and tactics.

Globalization can significantly impact an organization's mix of customers and products. The organization must adapt to this by investing in research and development to create new products.

By applying mindfulness, the GQ can be adequately raised for the organization.

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Answer:

[tex]\sqrt{2}[/tex]

Step-by-step explanation:

When t = 0, the velocity is:

[tex]\begin{aligned}\vec{v}(t)&=3^t \vec{i}+e^{6t} \vec{j}\\\\t=0 \implies \vec{v}(0)&=3^0 \vec{i}+e^{(6 \cdot 0)} \vec{j}\\ &=1 \vec{i}+1 \vec{j} \end{aligned}[/tex]

Speed is the magnitude of the velocity of the object.

[tex]\boxed{\text{A vector $\binom{x}{y}$ has magnitude $\sqrt{x^2+y^2}$}}[/tex]

Therefore, the particle's speed at time t = 0 is:

[tex]\begin{aligned}\implies |v|&=\sqrt{1^2+1^2}\\&=\sqrt{1+1}\\&=\sqrt{2}\end{aligned}[/tex]

As per the given details, the equation in Ax + By = C form is -5x + y = -25, where A = -5, B = 1, and C = -25.

To rewrite the equation y+5=5(x-4) in Ax+By=C form, we need to simplify and rearrange the equation to isolate y on one side:

y + 5 = 5(x - 4)

y + 5 = 5x - 20 (Distribute 5 on the right side)

y = 5x - 20 - 5 (Subtract 5 from both sides)

y = 5x - 25

Now the equation is in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. To rewrite it in Ax + By = C form, we need to rearrange the terms to get the x and y terms on the left side and a constant on the right side:

y = 5x - 25

-5x + y = -25

So the equation in Ax + By = C form is -5x + y = -25, where A = -5, B = 1, and C = -25.

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A relation represents a function when each input value is mapped to a single output value.

On a graph, a function is represented if the graph contains no vertical aligned points, that is, if there are no values of x at which we could trace a vertical line that would cross the graph of the function more than once.

Tracing a vertical line for any x > -3, the vertical line would cross the graph at two points, meaning that the relation is not a function.

As for the domain and the range, we have that:

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The confidence interval using the 95 percent level of significance is given as CI = (0.57, 0.63)

Solve for the sample proportion

= 602/1000 = 0.602

z* is the critical value from the standard normal distribution at the 95% confidence level = (1.96)

n =  sample size (1000)

CI = 0.602 ± 1.96√((0.602(1-0.602))/1000)

CI = 0.602 ± 0.032

0.602 - 0.032 , 0.602 + 0.032

CI = (0.57, 0.63)

Hence the confidence interval using the 95 percent level of significance is given as CI = (0.57, 0.63)

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Answer:

n=-4

Step-by-step explanation:

5(3n+4n+3) = -125

First, combine like terms:

5(7n+3) = -125

Then, distribute the 5:

35n+15 = -125

Then, get n by itself:

35n= -140

Then, divide by 35 to get n by itself:

n = -140/35

Simplify

n = -4

The period of the function in the graph is 2π

Period represents the distance across horizontally located between successive duplicates of an equivalent outline within a graphed function.

In other words, we can say that period is the distance to complete an oscillation where this distance is counted in time. Hence period is measured is seconds

In the graph, the period can be calculated using the points

These points shows a complete oscillation.

Using from 2π to 0

= 2π - 0

= 2π

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Answer:

[tex]8n=32[/tex]

Step-by-step explanation:

Muriel's algebraic expression for the phrase "the product of a number and 8" would be 8n, where n represents the number. When n = 4, the value of 8n would be 8 times 4, which is 32. Therefore, the correct expression and value is 8n = 32 when n = 4.

Answer:

8n=32

Step-by-step explanation:

got it right on homework

Answer:

[tex]3 \frac{3}{4} \times 4 \frac{1}{2} \times 5 = \frac{15}{4} \times \frac{9}{2} \times 5 = \frac{675}{8} = 84\frac{3}{8} [/tex]

The volume is 84 3/8 cubic meters = 84.375 cubic meters.

since i don't see the graph ill go with... B The slope of the line is 24, which means that the swimmer must complete 24 laps in the race.

-24/6 = -4

Step-by-step explanation:

The slope of the line can be found using the formula:

slope = (change in y) / (change in x)

In this case, we can use the two given points on the line: (0, 24) and (6, 0).

Change in y = 0 - 24 = -24

Change in x = 6 - 0 = 6

Therefore, slope = -24/6 = -4

This means that for every minute that passes, the swimmer completes four laps. The swimmer's pace is steady and consistent throughout the race, gradually decreasing the number of laps remaining until they finish at 0 after six minutes.

Answer:

The slope of the line represents the rate of change in the number of laps remaining per unit of time (in this case, per minute). In other words, it tells us how quickly the swimmer is completing laps.

Since the slope of the line is -4, this means that the swimmer is completing 4 laps every minute. This could be interpreted as the swimmer's pace or speed in the race. The negative sign indicates that the number of laps remaining is decreasing over time, which is expected as the swimmer completes more and more laps.

It's worth noting that the slope is constant throughout the race, meaning that the swimmer is maintaining a consistent pace. This information could be useful for the swimmer and their coach in terms of planning and pacing the race.

The amount of money that Nora would need to invest is $25913.

In Mathematics and Financial accounting, compound interest can be calculated by using the following mathematical equation (formula):

[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]

Where:

By substituting the given parameters into the formula for compound interest, we have the following;

[tex]72,000 = P(1 + \frac{0.064}{365})^{365 \times 16}\\\\72,000 = P(1 + 1.75 \times 10^{-4})^{5,840}\\\\72,000 = P(1.000175)^{5,840}[/tex]

P = 72,000/2.77849825425152

Principal, P = $25913.28 ≈ $25913

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Answer:

To solve this problem, we can use trigonometry. Let's call the length of the shadow "s" and the height of the tree "h". Since the tree is leaning, we can't just use the height of the tree directly as one leg of a right triangle. Instead, let's draw a diagram of the situation and see if we can find a way to use trigonometry.

             |\

             | \

             |  \ h

             |20\

             |   \

             |    \

     ________|____\

            s

In this diagram, the angle between the ground and the sunlight is 68 degrees, and the angle between the tree and the ground is 70 degrees (since the tree is leaning 20 degrees off vertical). We can use the tangent function to relate these angles to the lengths of the sides of the triangle:

tan(68) = h / s

tan(70) = h / (s + 125)

We can solve for "h" in terms of "s" using the second equation:

h = (s + 125) * tan(70)

Then we can substitute this expression for "h" into the first equation and solve for "s":

tan(68) = [(s + 125) * tan(70)] / s

s * tan(68) = (s + 125) * tan(70)

s * tan(68) = s * tan(70) + 125 * tan(70)

s = 125 * tan(70) / [tan(68) - tan(70)]

s ≈ 318.8 ft

Therefore , the shadow will be approximately 318.8 feet long.

Step-by-step explanation:

Answer: 20

Step-by-step explanation:

because Juanita has a aquarium that is 5 feet LONG, 4 feet WIDE, and 2 feet DEEP, in part b it asks what if the water is 1 foot DEEP so what they're trying to say is what if you replace the original 2 feet DEEP with 1 foot DEEP?

so it would be length x width x depth

5x4x1=20

so the volume is 20ft^3

The half-life of this radioactive element is approximately 2 years.

We have,

The decay of a radioactive element follows an exponential decay model of the form:

[tex]N = N_0 e^{-kt}[/tex]

where:

N0 is the initial concentration of the radioactive element

N is the concentration after time t

k is the decay constant

We are given that the element has decayed to 1/32 of its original concentration, which means that its current concentration is 1/32 times its initial concentration:

N/N0 = 1/32

Taking the natural logarithm of both sides and rearranging, we get:

ln(N/N0) = ln(1/32) = -3.465

Now we can use the formula for half-life, which relates the decay constant to the half-life t1/2:

t1/2 = ln(2) / k

We can solve for the decay constant k by using the information that the element has decayed to 1/32 of its original concentration in 10 years:

ln(N/N0) = -kt

-3.465 = -k x 10

k = 0.3465

Substituting this value of k into the formula for half-life, we get:

t1/2 = ln(2) / k = ln(2) / 0.3465 = 2.0 x 10^0 years = 2 years.

Therefore,

The half-life of this radioactive element is approximately 2 years.

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Answer:

c 57

Step-by-step explanation:

Answer:

second one

the y intercept is 8, the slope is -6/8, reduced -3/4

Step-by-step explanation:

equation if a line in slope intercept form is y=mx+

An exponential model for the number of SMS messages sent annually for years before 2012 is [tex]y = 12421e^{0.2325x}[/tex].

In this scenario, the year would be plotted on the x-axis (x-coordinate) of the scatter plot while the SMS messages would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.

On the Microsoft Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an exponential equation for the line of best fit (trend line) on the scatter plot.

From the scatter plot (see attachment) which models the relationship between the year and SMS messages, an exponential equation for the line of best fit is given by

[tex]y = 12421e^{0.2325x}[/tex]

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The volume of the bottle is 56.52 cubic inches, and the density is 22.12 g/in³.

The volume of a cylinder is expressed as;

V = π × r² × h

Where r is radius of the circular base, h is height and π is constant pi ( π = 3.14 ).

Density is expressed mathematically as;

p = m / v

Where m is mass and v is volume.

Given that:

Diameter = 3 in

Radius r = diameter/2 = 3/2 = 1.5 in

Height h = 8 in

Mass m = 1250 g

Find the volume:

V = π × r² × h

V = 3.14 × (1.5 in )² × 8in

V = 56.52 in³

Find the density:

p = m / v

p = 1250g / 56.52 in³

p = 22.12 g/in³

Therefore, the density is 22.12 g/in³.

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