please help me
Can the measure of an exterior angle of a triangle ever exceed 180°? Explain your reasoning.​

Therefore, the rate of change of the radius of the cone with respect to time when the water is 8 meters deep is twice the rate of change of the water level with respect to time at that point.

A.) To find the rate of change of water level with respect to time, we can use the concept of similar triangles. Let h be the height of the water in the tank. The radius of the cone at height h can be expressed as r = (h/10) * 20, where 20 is half the diameter of the base.

The volume of a cone can be calculated as V = (1/3) * π * r^2 * h. Taking the derivative with respect to time, we get:

dV/dt = (1/3) * π * (2r * dr/dt * h + r^2 * dh/dt)

Since the water is flowing into the tank at a rate of 50 m^3/min, we have dV/dt = 50. Substituting the expression for r, we get:

50 = (1/3) * π * (2 * ((h/10) * 20) * dr/dt * h + ((h/10) * 20)^2 * dh/dt)

Simplifying, we have:

50 = (1/3) * π * (4 * h * (h/10) * dr/dt + (h/10)^2 * 20^2 * dh/dt)

B.) At t = 0, the tank is empty, so the water level is h = 0. As water flows into the tank at a constant rate, the water level increases linearly with time. Therefore, the water level, h, as a function of time, t, can be expressed as:

h(t) = (50/600) * t

C.) To find the rate of change of the radius of the cone with respect to time when the water is 8 meters deep, we can differentiate the expression for the radius with respect to time. The radius of the cone at height h can be expressed as r = (h/10) * 20.

Taking the derivative with respect to time, we have:

dr/dt = (1/10) * 20 * dh/dt

Substituting the given depth h = 8 into the equation, we get:

dr/dt = (1/10) * 20 * dh/dt = 2 * dh/dt

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Correlational statistics quantify the strength of a relationship between variables but do not provide information about causality because they cannot assess the temporal sequence of variables.

Correlational statistics, such as correlation coefficients, measure the degree of association between variables.

They indicate the strength and direction of the relationship but do not establish a cause-and-effect relationship. This limitation arises because correlational analysis does not allow for determining the temporal sequence of variables, which refers to the order in which the variables occur or change.

Without knowledge of the temporal sequence, we cannot ascertain whether one variable causes the other or if they are both influenced by an external factor. To establish causality, additional research methods such as experimental designs or longitudinal studies are necessary, where variables can be manipulated or observed over time, respectively.

Thus, correlational statistics serve as valuable tools for understanding associations but do not provide insights into causation.

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The options that serves the purpose will be :

To establish speaker credibility .

To grab the audience's attention .

Given,

Purpose of introduction of speech .

Purpose of introduction of speech :

1) Making their audience members interested in the speech topic .

2 ) Gain the interest of the audience .

3) To tell about the topic of speech .

4) To establish the credibility of speaker .

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The length of line segment AB in the triangle using the midsegment theorem is 64.

The Midsegment Theorem states that "the segment joining the midpoints of two sides of a triangle is parallel to and half the length of the third side."

From the diagram:

Midsegment = 3x + 5

Third side = 7x + 1

First, we solve for x, using the midsegment theorem:

( 3x + 5 ) = 1/2 × ( 7x + 1 )

Multiply both sides by 2:

2( 3x + 5 ) = ( 7x + 1 )

6x + 10 = 7x + 1

Collect and add like terms:

7x - 6x = 10 - 1

x = 10 - 1

x = 9

Now, we solve for line AB:

Line AB = 7x + 1

Plug in x = 9

Line AB = 7(9) + 1

Line AB = 63 + 1

Line AB = 64

Therefore, the line segment AB is 64.

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Answer:

1.1 : C - x^2 + x - 2

1.2 : A - 4a^2 - 6b^2 + 12

Step-by-step explanation:

When we have the expression p(x) - q(x), we can substitute those functions in:

(x^2 + 2x - 5) - (x - 3)

We can distribute:

x^2 + 2x - 5 - x + 3

and then combine like terms(2x & -x, -5 & 3)

x^2 + x - 2

This is the same as C.

We can start by distributing:

a^2 - 2b^2 + 3 - 4b^2 + 5 + 3a^2 + 4

Now, we can combine all the a^2 terms(a^2 & 3a^2):

4a^2 - 2b^2 + 3 - 4b^2 + 5 + 4

Then, we can combine the b^2 terms(-2b^2 & -4b^2):

4a^2 - 6b^2 + 3 + 4 + 5

and lastly, all the constants:

4a^2 - 6b^2 + 12

This aligns with option A

Answer:

11520000000

Step-by-step explanation:

11520000000

Hypothesis testing is a powerful statistical tool that enables us to determine whether the collected data is consistent with what is stated in the null hypothesis.

Hypothesis testing is a statistical method that allows us to determine whether the collected data is consistent with what is stated in the null hypothesis. The null hypothesis is a statement that assumes there is no significant difference between two groups or two variables being compared.

In contrast, the alternative hypothesis is the opposite of the null hypothesis, and it assumes that there is a significant difference between the two groups or variables being compared.

To test a hypothesis, we start by formulating the null hypothesis and the alternative hypothesis. Then, we collect data that is relevant to the hypothesis being tested. Next, we use statistical tests to analyze the data and calculate the probability of obtaining the observed results under the null hypothesis.

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A direct relationship between two variables is reflected in a "POSITIVE" correlation coefficient.

Correlation is a statistical technique for measuring and describing the relationship between two variables.

The variables move in the same direction when they have a positive correlation. In other words, as one variable increases, so does the other, and conversely, as one variable decreases, so does the other.

Typically, the two variables are simply observed rather than manipulated. Two scores from the same individuals are required for the correlation.

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Answer:

17.5 hours

I hope this helps and you can give a brainliest!

Step-by-step explanation:

Given: time spent per day follows the arithmetic sequence 1,1.5,2... (for 7 terms) with first term 1 and common difference 0.5 (in hours)

Concept used: the total study time is the partial sum S7of the given arithmetic series.

Calculation: As the number of terms is small, it can be calculated by hand.

S7 = 1+1.5+2+2.5+3+3.5+4

S7= 17.5 hours

Conclusion: Total time spent after one week is 17.5 hours

Answer:

17 and 1/2 hours.

Step-by-step explanation:

this is an arithmetic series  with common difference 0.5 hours.

Number of hours after 7 days

= (n/2)[2a + (n -1)d]

= (7/2)(2*1 + (7-1)0.5)

= 3.5 * 5

= 17.5 hours

The general solution for the given differential equation is:
y(x) = c1 *\(e^{(-7/3 * x)}\) + c2 * x * \(e^{(-7/3 * x)}\)

To find the general solution to the given differential equation, 9(d²/dx²) + 42(dy/dx) + 49y = 0, first note that this is a second-order linear homogeneous differential equation with constant coefficients. The general solution can be expressed as where c1 and c2 are arbitrary constants, and r1 and r2 are the roots of the characteristic equation.

The characteristic equation for this differential equation is given by:

9r² + 42r + 49 = 0

This quadratic equation can be factored as:

(3r + 7)(3r + 7) = 0

As the quadratic has a double root, r = -7/3.

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The vector-valued function at each given value of t  is :

a) i

b)  1/√2i+9/√2j

c)−cos(θ)i+9sin(θ)j

d)  −2sin(π/6+△t/2)sin(△t/2)i+18cos(π/6+△t/2)sin(△t/2)j

The given problem is related to trigonometric Ratios of Angle, where there are six trigonometric ratios sine, cosine, tangent, cotangent, cosecant, and secant. Since it is given that a  vector valued function:

r(t)= cos(t)i + 9 sin(t)j

r(t)=cos(t)i+9sin(t)j

so ,  r(0)=  cos(0)i+9sin(0)j = i ( sine cos0 =1 and sin0 =0)

r(π/4) =  cos(0)i+4sin(0)j = cos(π/4)i+9sin(π/4)j

           = 1/√2i+9/√2j

r(θ−π)= cos(θ−π)i+9sin(θ−π)j= −cos(θ)i+9sin(θ)j

(π/6+△t)−r(π/6)= cos(π/6+△t)i+9sin(π/6+△t)j−cos(π/6)i−9sin(π/6)j

=  cos(π/6+△t)i−cos(π/6)i+9sin(π/6+△t)j−9sin(π/6)j

= −2sin(π/6+△t/2)sin(△t/2)i+18cos(π/6+△t/2)sin(△t/2)j

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Evaluate (If possible) the vector-valued function at each given value of t. (If an answer does not exist, enter DNE.)

r(t)=cos(t)i+9sin(t)jr(t)

a)r(0)=?

b)r(π/4)=?

c)r(θ−π)=?

d)r(π/6+△t)−r(π/6)=?

3j+1≥10

Subtract 1 from both sides.

3j ≥ 9

Then divide both sides by 3.

j ≥ 3

Answer:

T=x/78

height/78=76

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Answer:

travel 2 hour stop 1 hour then again for 2 hours

Step-by-step explanation:

Answer:

It travels for 1 hour, then stops for 1 hour, and finally travels again for 3 hours.

The correct statement regarding the solution to the system of equations is given as follows:

A. There are no solutions.

The system of equations for this problem is defined as follows:

Multiplying the first equation by 3, we have that:

1.5x - y = 5.

Substituting the second equation into the first, the solution for y is obtained as follows:

3/2(2y/3 + 10) - y = 5.

y + 15 - y = 5

0y = -10

y = -10/0.

Division by zero is not possible, hence the system of equations has zero solutions.

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Answer:

1/2

Step-by-step explanation:

The multiples of 2 in between 1 and 10: 2, 4, 6, 8, 10

5 out of 10 are multiples of 2

5/10 = 1/2

The frequently used strategic approach to setting a company apart from rivals and achieving a sustainable competitive advantage which is not included among the options is: simply trying to mimic the successful strategies of rivals.An effective strategy is needed for companies to achieve their goals, which includes setting themselves apart from their rivals and achieving a competitive edge. There are different strategic approaches that companies use in order to achieve this.

Some of the strategic approaches are;Outcompeting rivals on the basis of such differentiating features as higher quality, wider product selection, added performance, better service, or more attractive styling.Focusing on a narrow market niche and winning a competitive edge by doing a better job than rivals of satisfying the needs and tastes of buyers comprising the niche.Aiming for a cost-based competitive advantage.

However, one of the strategic approaches to setting a company apart from rivals and achieving a sustainable competitive advantage that is not frequently used is simply trying to mimic the successful strategies of rivals.Therefore, option B is the correct answer to the question.Meanwhile, a company's strategy evolves over time due to some basic reasons which include:the need to respond to the actions and competitive moves of rival firms,the proactive efforts of company managers to improve the company's financial performance and secure a competitive advantage,an ongoing need to abandon those strategy features that are no longer working well.

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Answer:

Step-by-step explanation:

8x + 4 = 28

8x = 28 - 4

8x = 24

x = 24 / 8

x = 3

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Radioactive particles 2000  the sample have 80 years from today.

We have the information:

There is 2000 radioactive particles in a sample.

and,  your grandmother measured 4000 radioactive particles in it 80 years ago.

We have to find the samples of radioactive particles present it in 80 years from today.

By the definition of Half line,  The half line of the item is 80 years.

=> 80 years from now, means that another half life is achieved means, 2000 will reduced to half on decay.

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The value of p is -4 in the linear equation in one variable 4 - 3p = -5p - 24 the answer is -14.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

The linear equation in one variable is:

4 - 3p = -5p - 24

After solving:

5p - 3p = -24 - 4

2p = -28

p = -28/2

p = -14

Thus, the value of p is -4 in the linear equation in one variable 4 - 3p = -5p - 24 the answer is -14.

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Answer: \(a=\sqrt{60}\)

Step-by-step explanation:

To solve for a, we want to use Pythagorean Theorem as provided int eh problem. a and 2 are the legs while 8 is the hypotenuse.

\(a^2+2^2=8^2\)           [exponent]

\(a^2+4=64\)            [subtract both sides by 4]

\(a^2=60\)                  [square root both sides]

\(a=\sqrt{60}\)

Now we know that \(a=\sqrt{60}\).

Question 1.3.101:  The value of y = x²

Question 1.3.102:  The value of the expression x(t) = 2e³Pt² - 3t.


To solve this equation, we must use the power rule for exponents. In this equation, y is being raised to the power of x, which means we must raise both sides of the equation to the power of x. We then have: 2x²y = yx, which simplifies to 2xy = y. By dividing both sides by y, we have x² = 1. Therefore, y = x².



To solve this equation, we must use the method of separation of variables. This method involves separating the two different types of variables (in this case x and t) on opposite sides of the equation.

On one side of the equation, we have all of the terms containing x, and on the other side, all of the terms containing t.

By doing this, we can integrate both sides of the equation. We then have: ∫ (x - 3)dx = ∫ (3Pt² - 3)dt. Solving this integration, we have x - 3Pt² + c = 3t + c, where c is a constant of integration.

The initial value of x at time t = 0 is x(0) = 2. We can use this to solve for c, which gives us c = -2. Finally, substituting this value of c back into our equation gives us the answer x(t) = 2e³Pt² - 3t.

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Answer:

X=8.7 (1dp)

Step-by-step explanation:

X=8.7

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Its true that perpendicular bisectors also exist for the height from an isosceles triangle's vertex angle to its base.

Given that,

We have to find perpendicular bisectors also exist for the height from an isosceles triangle's vertex angle to its base.

We know that

Let us take a triangle ABC and draw an altitude CD

Being an isosceles triangle

In ΔACD and ΔCDB

CD=CD (common )

CA=CB ( equal opposite sides)

∠ A=∠ B (the angle between the opposing sides is also equal)

Triangle ACD and triangle CDB are congruent

So , AD=DB by CPCT

So, its true

Therefore, Its true that perpendicular bisectors also exist for the height from an isosceles triangle's vertex angle to its base.

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To check which point satisfies the inequality 2x + y > 10, we substitute each value of x and y in the equation.

A. 2(2) + 3 > 10

    7 > 10

  This is incorrect. So the point does not satisfy the expression.

B. 2(3) + 2 > 10

    8 > 10

    This is also incorrect.

C. 2(4) + 3 >10

     11 > 10

     This is correct since 11 is greater than 10. So point (4,3) satisfies the inequality.

D. 2(3) + 4 > 10

    10 > 10

 This is also incorrect.

What is inequality?

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Answer:

k=5

Step-by-step explanation:

The graph of g(x) is raised by 5 units so k is 5

Answer:

Step-by-step explanation:

As we see the two expressions are equal in value

Answer:

log3 1/3 = logb 1/b

(Both expressions are equal)

Step-by-step explanation:

Now we have to,

→ find the expression with greater value.

Then the greatest value is,

→ log3 1/3 = logb 1/b

→ log3 3^(-1) = logb b^(-1)

→ -1 = -1

→ [ LHS = RHS ]

Hence, both have same value.