Give your answer to the nearest tenth.

Answer Choices:

44


44.5


45


45.5

The answer  is that the quadratic function is the one that models the situation.

The function that models the situation is a quadratic function in the form of ax² + bx + c.

In this scenario, the engineer is designing a flashlight with a parabolic mirror. A parabolic mirror has a shape that can be represented by a quadratic function. Quadratic functions are typically in the form of f(x) = ax² + bx + c, where a, b, and c are constants.

The explanation for this is that a parabolic mirror reflects light in a way that the reflected rays converge at the focus, which is the vertex of the parabola. This means that the distance between the reflector and the light source should be the same as the distance between the reflector and the focus. The shape of the parabolic mirror is defined by a quadratic function, which is y = ax²

The variable y represents the height of the mirror at a given point, x represents the distance from the vertex, and a is a constant that determines the steepness of the curve. Therefore, the engineer can use this equation to design the parabolic mirror that will maximize the output of the flashlight.
.

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Answer:

Step-by-step explanation:

The Probability of Landing a heads is (1/2)

Now, to find the probability of landing it five times in a row, it is

1/2 x 1/2 x 1/2 x 1/2 x 1/2

( 1/2 is multiplied to the number of times to get a head )

The final answer will be,

Probability of landing heads 5 times in a row = 1/32

Based on the amount predicted to be spent, the hypotheses Null Hypothesis = $1,007.24 and Alternate Hypothesis ≠ $1,007.24

The null hypothesis, or H0, in statistics science is the exact reverse of what the researcher wants to investigate. Generally, unless there is compelling proof to the contrary, the null hypothesis is taken to be correct. Another theory that will demonstrate the area one wants to investigate and be reflected by H1 must be developed.

The forecast is confirmed by the null hypothesis, which in this instance is that the typical consumer will indeed spend $1,007.24. According to the Alternate Hypothesis, the predicted occurrence won't occur, so in this instance, the shopper wouldn't spend $1,007.24. In conclusion, the variant contradicts the null hypothesis and supports it.

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Answer:

19 11/16

Step-by-step explanation:

Convert to decimal form.

5 1/4 = 5.25

3 3/4 = 3.75

Multiply

5.25 x 3.75 = 19.6875

(If you are working out the problem on paper notice how the answer has 4 decimal places. This is because each factor has 2 decimal places so the final answer would have a total of 4.)

Convert back to a fraction

Take the 0.6875 and put it over it's place value which is the ten thousandths place.

\(\frac{6875}{10000}\)

Simplify

Find the GCF and divide it into both the numerator and the denominator.

\(\frac{6875/ 625}{10000/625}\)  = \(\frac{11}{16}\)

The original answer was 19.6875 so we also have to put 19 back into the answer.

So the answer is \(19\frac{11}{16}\)

The y-intercept of the given line defined by the given equation as in the task content is; -6.

It follows from the task content that the y-intercept of the line defined by the given equation as in the task content is to be determined.

Since the given equation is; y = 1/3x - 6.

Therefore, since the y-intercept is the value of y when, x = 0;

y = 1/3(0) - 6

y = 0 - 6

y = -6.

On this note, the required y-intercept of the line is; -6.

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The solutions to the equation are x= -9 and x = 6

From the information given, we have that;

|x2 + 9x| = 6x + 54

To solve the quadratic equation, collect the like terms, we have;

x² + 9x - 6x = 54

subtract the terms

x² + 3x = 54

Put in standard form

x² + 3x - 54 = 0

Find the pair factors of -54 that add up to give 3 and substitute the values

x² + 9x - 6x - 54 = 0

group in pairs

(x² + 9x) - (6x - 54) = 0

factorize the expressions

x(x + 9) - 6(x + 9) = 0

Then, we have;

x- 6 = 0

x = 6

x + 9 = 0

x = -9

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0.7 as a fraction:

6.63324958071 is the mean of 2 and

Answer:

2 sqrt(11)

Step-by-step explanation:

To find the geometric mean of two numbers, take the square root

sqrt( 2*22)

sqrt(44)

sqrt(4*11)

2 sqrt(11)

Answer:

\(\Huge \boxed{\mathrm{61.22 \ m}}\)

Step-by-step explanation:

A stone is thrown downward straightly with the velocity of 20 m/s and it reaches the ground at the velocity of 40 m/s. What will be the height of building? (Question)

The initial velocity ⇒ 20 m/s

The final velocity ⇒ 40 m/s

We can apply a formula to solve for the height of the building.

\((V_f)2 - (V_i)^2 =2gh\)

\(V_f = \sf final \ velocity \ (m/s)\)

\(V_i = \sf initial \ velocity \ (m /s)\)

\(g = \sf acceleration \ due \ to \ gravity \ (m/s^2 )\)

\(h = \sf height \ (m)\)

Plugging in the values.

Acceleration due to gravity is 9.8 m/s².

\((40)^2 - (20)^2 =2(9.8)h\)

Solve for \(h\).

\(1600 - 400 =19.6h\)

\(1200 =19.6h\)

\(\displaystyle h=\frac{1200}{19.6}\)

\(h= 61.22449\)

The height of the building is 61.22 meters.

Answer: you don't need to know anything about the jazz CD's

Isabel is incorrect because the point of intersection between line B and parabola A that can be determined is the y-intercept of the equations, not the vertex.  This can be obtained using finding y intercept of both parabolas and vertex of parabola A.

Parabola A, (x + 3)² = y = x² + 6x + 9

Parabola B, y = mx + 9

x=0, y = 9

y coordinate of parabola A is (0,9)

⇒The vertex coordinate,

(-b/2a , -(b²-4ac)/4a) = (-3,0)          

x=0, y = 9  

y coordinate of parabola B is (0,9)    

Isabel claims one solution to the system of two equations must always be the vertex of parabola A which is wrong.  

Hence Isabel is incorrect because the point of intersection between line B and parabola A that can be determined is the y-intercept of the equations, not the vertex.

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Disclaimer: The question was given incomplete on the portal. Here is the complete question.

Question: Parabola A can be represented using the equation (x + 3)2 = y, while line B can be represented using the equation y = mx + 9. Isabel claims one solution to the system of two equations must always be the vertex of parabola A. Which best describes the reasonableness of her claim?

Answer:

D

Step-by-step explanation:

The last option in the picture

Answer:

let the two numbers = x and y

according to the statement : x-y=4

x+y=22

by elimination method: 2x=26

x=13

so... y = 13-4=9

Answer:

The two numbers (x and y) are 13 and 9 respectively. 13 minus 9 is 4 and 13 plus 9 is 22.

Step-by-step explanation:

Let the two numbers be x and y.

The difference between x and y (x - y) = 4. (eqn 1)

Their sum (x + y) = 22. (eqn 2)

From eqn 1, we can get that x = 4 + y

Substituting x as (4 + y) in eqn 2 gives the following:

(4+y) + y = 22

4 + 2y = 22

and 2y = 22 - 4

2y = 18

dividing both sides by 2 gives y = 9.

Substituting y as 9 in eqn 1 gives

x - 9 = 4

x = 4 + 9

x = 13

A cylindrical object is 3.13 cm in diameter and 8.94 cm long and weighs 60.0 g. The density of the cylindrical object is 0.849 g/cm^3.

To calculate the density, we first need to find the volume of the cylindrical object. The volume of a cylinder can be calculated using the formula V = πr^2h, where r is the radius (half of the diameter) and h is the height (length) of the cylinder.

Given that the diameter is 3.13 cm, the radius is half of that, which is 3.13/2 = 1.565 cm. The length of the cylinder is 8.94 cm.

Using the values obtained, we can calculate the volume: V = π * (1.565 cm)^2 * 8.94 cm = 70.672 cm^3.

The density is calculated by dividing the weight (mass) of the object by its volume. In this case, the weight is given as 60.0 g. Therefore, the density is: Density = 60.0 g / 70.672 cm^3 = 0.849 g/cm^3.

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Answer: B or 52

Step-by-step explanation: I will explain later

Answer:

Answer is 1/5 which is exactly 0.2

Step-by-step explanation:

5x + 1 = 2

5x = 2 - 1

5x = 1

x = 1/5

x = 0.2

Answer:

There is no such set of two numbers that multiply to get 0 and add to get 7. Since any number multiplied by 0 is 0, it is impossible for two numbers to multiply to 0 and add to 7 as adding two numbers that multiply to 0 will always result in zero.

Answer:

Step-by-step explanation:

the numbers are 0 and 7 itself.

Multiply : 0*7 = 0

Add       : 0+7 = 7

Answer:

Step-by-step explanation:

A geometric sequence is generated by multiplying the first term in the sequence, , several times by a fixed scalar . and so on, down to ..Using the result above, the sequences you're interested in are

31)  

33)

We can rewrite these results to make them slightly cleaner.

The correct option is d) mathematical

What is a technical system model?

A mathematical model is a set of equations or algorithms that represent technical aspects of a system. These equations or algorithms are used to predict or simulate system behavior and performance. Mathematical models are often used in engineering, science, economics, and other fields where complex systems need to be analyzed and optimized. For example, a mathematical model could be used to analyze how a communication network would perform with different levels of traffic or to predict how a chemical reaction would proceed under various conditions. Mathematical models are often represented graphically to provide a clear visualization of the complex relationships between variables within a system. Overall, mathematical models are an essential tool for designing, optimizing, and managing complex systems.

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The velocity of the boat when it reaches the buoy is approximately 17.32 m/s. This is found using the equation v² = u² + 2as, where u is the initial velocity, a is the acceleration, and s is the displacement.

To solve this problem, we can use the equations of motion. The initial velocity of the boat, u, is 30 m/s, the acceleration, a, is -3.0 m/s² (negative because the boat is slowing down), and the displacement, s, is 100 m. We need to find the final velocity, v, when the boat reaches the buoy.

We can use the equation: v² = u² + 2as

Substituting the given values, we have:

v² = (30 m/s)² + 2(-3.0 m/s²)(100 m)

v² = 900 m²/s² - 600 m²/s²

v² = 300 m²/s²

Taking the square root of both sides, we find:

v = √300 m/s

v ≈ 17.32 m/s

Therefore, the velocity of the boat when it reaches the buoy is approximately 17.32 m/s.

The problem provides the initial velocity, acceleration, and displacement of the boat. By applying the equation v² = u² + 2as, we can find the final velocity of the boat. This equation is derived from the kinematic equations of motion. The equation relates the initial velocity (u), final velocity (v), acceleration (a), and displacement (s) of an object moving with uniform acceleration.

In this case, the boat is decelerating with a constant acceleration of -3.0 m/s². By substituting the given values into the equation and solving for v, we find that the velocity of the boat when it reaches the buoy is approximately 17.32 m/s.

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The difference between the numbers ABCD and DCBB is 10000

From the information given, we have that:

We can say that:

B + D = 10

A = 3

B = 4

C = 5

D = 6

Now,

ABCD = 3456

DCBB = 6544

Difference between the numbers ABCD and DCBB = 3456 + 6544 = 10, 000

Thus, the difference between the numbers ABCD and DCBB is 10000

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Answer:

2,000 steps.

Step-by-step explanation:

In this case, you have 3 B's, 2 A's and 3 C's, so the total amount of cases are 3+3+2=8. If only one of these cases was an A, then the probability would be 1/8, but you have 2 A's, so the probability is 2/8. This in percentage is found by 100*2/8=25%

Answer:  the answer is -7/5

Answer:

The answer is C

Step-by-step explanation:

The given system of simultaneous equation when solved gives a solution of

The simultaneous equation may be solved using several methods however we will solve using the elimination method

The given equation

-2x - 9y = -25  

-4x - 9y = -23

subtract both equations

2x + 0 = -2

x = -1

plugging x = -1 into -2x - 9y = -25

-2 * -1 - 9y = -25

2 - 9y = -25

-9y = -25 - 2

-9y = -27

y = -3

the solution is x = -1 and y = - 3

5x - 3y = 16  

5x + 4y = 2 rearranging gives 4y + 5x = 2 re

subtract both equations

0 - 7y = 14

y = -2

plugging y = -2 into 5x + 4y = 2

5x + 4 * -2 = 2

5x - 8 = 2

5x = 2 + 8

5x = 10

x = 2

The solution of the equation is x = 2 and y = -2

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Answer: a+b=b+a is a clear example of commutative property.

Step-by-step explanation: The commutative property applies to addition and multiplication. The property states that terms can “commute,” or move locations, and the result will not be affected. This is expressed as a+b=b+a for addition, and a×b=b×a for multiplication. The commutative property does not apply to subtraction or division.

Answer:

52.5

Step-by-step explanation:

=24.5/7

=3.5

Then

3.5*15

=52.5 ans#