Adrian kept an eye on the basketball game score by looking online every 10 minutes. Over the course of 2 hours, 4 times Adrian’s favorite team was ahead by 3 points, and 4 times Adrian’s favorite team was behind by 4 points. All other times, the two teams were tied.
What is the average score of Adrian’s favorite team relative to its opponent using the observations Adrian made during the game?

\(\boldsymbol{\sf{3(x-4) > 5x +2 }}\)

Use the distributive property to multiply 3 by x−4.

\(\boldsymbol{\sf{3x-12 > 5x+2 }}\)

Subtract 5x on both sides.

\(\boldsymbol{\sf{3x-12-5x > 2 } }\)

Combine 3x and −5x to get −2x.

\(\boldsymbol{\sf{-2x-12 > 2 }}\)

Add 12 to both sides.

\(\boldsymbol{\sf{-2x > 2+12 \ \longmapsto \ \ [Add \ 2 +12]}}\)

\(\boldsymbol{\sf{-2x > 14}}\)

Divide both sides by −2. Since −2 is < 0, the inequality direction is changed.

\(\boldsymbol{\sf{x < \dfrac{14}{-2} \ \ \longmapsto \ \ \ [Split]}}\)

\(\boxed{\boldsymbol{\sf{x < -7 }}}\)

So in the inequality 3(x-4)>5x +2, the value of x is -7.

ヘ( ^o^)ノ＼(^_^ )If you want to learn more about mathematics, I share this link to complement your learning:

Answer:

Step-by-step explanation:

The value of measurement of the closest to the height of the mountain cliff in feet is,

⇒ Mountain Height = 360 feet

Given that;

When Donetle stands at point R, he is 1000 feet from point S at the base of a cliff.

And, When he looks up at an angle of 20 degrees, he sees a friend at the top of the mountain cliff at point T

Hence, By graph we get;

⇒ tan 20° = Mountain Height / 1000

⇒ 0.36 = Mountain Height / 1000

⇒ 0.36 × 1000 = Mountain Height

⇒ Mountain Height = 360 feet

Thus, The value of measurement of the closest to the height of the mountain cliff in feet is,

⇒ Mountain Height = 360 feet

Learn more about the multiplication visit:

https://brainly.com/question/10873737

#SPJ2

If a series an is defined by the equations a1 = 2 an+1 = 3 + cos(n) / √n · an, then  Σan is absolutely convergent. Therefore, the answer is: a) absolutely convergent.

To determine whether Σan is absolutely convergent, conditionally convergent, or divergent, we need to analyze the behavior of the series as n approaches infinity.

First, let's look at the absolute value of the terms in the series:

|an| = |2 × (3 + cos(n) / √n · an-1)|
    = |6 + 2cos(n) / √n · an-1|

Next, we can use the Comparison Test by comparing the series to a known convergent or divergent series. Let's compare the series to the p-series:

∑1/n^p

where p = 3/2. This series is known to converge by the p-test.

Now, we can rewrite the absolute value of an in terms of the p-series:

|an| = |6 + 2cos(n) / √n · an-1|
     ≤ |6 + 2 / √n · an-1|          (since cos(n) ≤ 1)
     ≤ 6 + 2 / √n · |an-1|           (using the triangle inequality)

Therefore, we have:

|an| ≤ 6 + 2 / √n · |an-1|

If we take the limit of both sides as n approaches infinity, we get:

lim n→∞ (6 + 2 / √n · |an-1|) / |an-1|
= lim n→∞ (6 / |an-1|) + (2 / (√n · |an-1|))
= 6 / lim n→∞ |an-1| + 0

Since lim n→∞ |an-1| exists (as an is a well-defined series), we can conclude that the limit is a finite number. Therefore, by the Comparison Test, Σ|an| converges.

Finally, we can use the Ratio Test to determine whether Σan converges absolutely or conditionally:

lim n→∞ |an+1 / an|
= lim n→∞ |(3 + cos(n+1) / √(n+1) · an) / an|
= lim n→∞ |(3 + cos(n+1)) / (√(n+1) · an)|

Using L'Hopital's Rule, we can show that the limit of the cosine term is 0, and the limit of the denominator is infinity. Therefore, the limit of the ratio is 0.

Since the limit of the ratio is less than 1, we can conclude that Σan converges absolutely.

Therefore, the answer is: a) absolutely convergent.

More on convergent: https://brainly.com/question/31064900

#SPJ11

A few properties of a parallelogram.

1) Opposite sides are always equal.

2) Opposite angles are always equal.

3) The sum of all the angles is 360.

In part 2, we are given the angles. Therefore, we can apply the 2nd property.

11x = 55

5y = z (lets say the unknown is z).

Now, 11x = 55

x = 55/11

x = 5

Now, we have to angles of 55 degrees but we don't know about y and z. Therefore, we have to apply the third property.

55 + 55 + 5y + z = 360

110 + 5y + z = 360

5y + z = 360 -110

5y + z = 250. (i)

According to property 2, 5y = z. Hence, put the value of 5y in the equation (i), we get

5y + z = 250

z + z = 250

2z = 250

z = 250/2

z = 125

From the value of z, we can find the value of y using z = 5y

125 = 5y

5y = 125

y = 125/5

y = 25

Hence, x = 5 and y = 25

The solution to the linear programming problem is:

Maximum value of z = 120

x₁ = 0, x₂ = 6

To solve the given linear programming problem using the graphical method, we first need to plot the feasible region determined by the constraints and then identify the optimal solution.

The constraints are:

x₁ + x₂ ≥ 12

x₁ + x₂ ≤ 6

x₁, x₂ ≥ 0

Let's plot these constraints on a graph:

The line x₁ + x₂ = 12:

Plotting this line on the graph, we find that it passes through the points (12, 0) and (0, 12). Shade the region above this line.

The line x₁ + x₂ = 6:

Plotting this line on the graph, we find that it passes through the points (6, 0) and (0, 6). Shade the region below this line.

The x-axis (x₁ ≥ 0) and y-axis (x₂ ≥ 0):

Shade the region in the first quadrant of the graph.

The feasible region is the overlapping shaded region determined by all the constraints.

Next, we need to find the corner points of the feasible region by finding the intersection points of the lines. In this case, the corner points are (6, 0), (4, 2), (0, 6), and (0, 0).

Now, we evaluate the objective function z = 15x₁ + 20x₂ at each corner point:

For (6, 0): z = 15(6) + 20(0) = 90

For (4, 2): z = 15(4) + 20(2) = 100

For (0, 6): z = 15(0) + 20(6) = 120

For (0, 0): z = 15(0) + 20(0) = 0

From the evaluations, we can see that the maximum value of z is 120, which occurs at the corner point (0, 6).

Know more about linear programming problem here:

https://brainly.com/question/29405467

#SPJ11

Answer:

Step-by-step explanation:

The slopes of both those lines are the same so there is no solution. Use slope triangles to find out the slope. They are both 1/4.

A. No solution

y = 1/4x+5

x - 4y = 4

You can simplify the second equation into y = 1/4x - 1

Since these equations both have the same slope, they are parallel. When two lines are parallel, they have no solutions.

a. The value corresponding to surviving the year is $0, and the value corresponding to not surviving the year is -$90,000.

b. The expected value for the 33-year-old male purchasing the policy is -$579.06.

c. Yes, the insurance company can expect to make a profit from many such policies because the expected profit per 33-year-old male insured for 1 year is $408.06.

a. The monetary value corresponding to surviving the year is $0 because the individual would not receive any payout from the insurance policy if he survives. The monetary value corresponding to not surviving the year is -$90,000 because in the event of the individual's death, the policy pays out a death benefit of $90,000.

b. To calculate the expected value for the 33-year-old male purchasing the policy, we need to multiply the probability of each event by its corresponding monetary value and sum them up. The probability of surviving the year is 0.9988, and the value corresponding to surviving is $0. The probability of not surviving the year is (1 - 0.9988) = 0.0012, and the value corresponding to not surviving is -$90,000.

Expected value = (Probability of surviving * Value of surviving) + (Probability of not surviving * Value of not surviving)

Expected value = (0.9988 * $0) + (0.0012 * -$90,000)

Expected value = -$108 + -$471.06

Expected value = -$579.06 (rounded to the nearest cent)

c. The insurance company can expect to make a profit from many such policies because the expected value for the 33-year-old male purchasing the policy is negative (-$579.06). This means, on average, the insurance company would pay out $579.06 more in claims than it collects in premiums for each 33-year-old male insured for 1 year. Therefore, the insurance company expects to make an average profit of $579.06 on every 33-year-old male it insures for 1 year.

For more questions like Company click the link below:

https://brainly.com/question/30532251

#SPJ11

Answer:

$98000

Step-by-step explanation:

Starting annual salary: $53,000

10 x 4500 = 45,000

His salary after 10 years would be 98000.

Answer: The distributive property states that multiplying the sum of two or more addends by a number yields the same outcome as multiplying each addend separately by the number and combining the resulting products.

Answer:

The Distributive property is used when you have to multiply the given number by the sum of the two numbers.

Step-by-step explanation:

nvm

guess im wrong

...........

Answer:

0

Step-by-step explanation:

The equation is g(x) = 3x. The y-intercept occurs where x = 0, so to find the y-intercept, plug in a zero for x. g(x) = 3(0) = 0.

Answer:

0 is the answer

Step-by-step explanation:

plz give me the brainlyest

Order from largest to smallest: 2.5 mL, 250μL, 0.025 mL, 2.5μL

Order from largest to smallest: 100μL, 0.015 mL, 250μL, 0.01 mL

To convert from μL to mL, divide by 1,000. Therefore, 1μL is equal to 0.001 mL or 1,000 μL is equal to 1 mL.To convert μL to mL, divide by 1,000. Thus, 2.5 mL is equal to 2,500 μL.To convert from μL to mL, divide by 1,000. Hence, 100μL is equal to 0.1 mL.To convert from μL to mL, divide by 1,000. Therefore, 250μL is equal to 0.25 mL.To convert from mL to μL, multiply by 1,000. So, 0.08 mL is equal to 80 μL.To convert from mL to μL, multiply by 1,000. Thus, 0.025 mL is equal to 25 μL.To convert from μL to mL, divide by 1,000. Hence, 2.5μL is equal to 0.0025 mL.To convert from mL to μL, multiply by 1,000. So, 0.01 mL is equal to 10 μL.To convert from mL to μL, multiply by 1,000. Thus, 0.015 mL is equal to 15 μL.

a. The volumes in order from largest to smallest are: 2.5 mL, 250μL, 0.025 mL, 2.5μL. This is determined by comparing the numerical values, with larger volumes being placed before smaller volumes.

b. The volumes in order from largest to smallest are: 100μL, 0.015 mL, 250μL, 0.01 mL. Again, this is determined by comparing the numerical values, with larger volumes placed before smaller volumes.

a. Setting the micropipette within its designated range is important to ensure accurate and precise volume measurements. Each micropipette has a specific volume range it can handle effectively, and using it within that range ensures reliable results.b. Using a micropipette with the appropriate tip is crucial for accurate volume transfer. Micropipette tips are designed to fit specific micropipette models, ensuring a secure and proper seal. Using the correct tip prevents leaks or inaccuracies in volume measurements.c. Holding a loaded micropipette in a vertical position helps prevent any air bubbles from being introduced into the sample or the pipette tip. This ensures accurate volume delivery and avoids any potential errors or contamination.d. Releasing the micropipette plunger slowly is necessary to ensure.

Learn more about divide here:

https://brainly.com/question/15381501

#SPJ11

Answer:

Are u a door, because u left me on open..

Step-by-step explanation:

Step-by-step explanation:

\( { ({3}^{3} )}^{4} \)

\( = {3}^{3 \times 4} \)

\( = {3}^{12} \)

\(or \)

\( = 531441\)

Answer:

a = 2 - 3b

        2

Step-by-step explanation:

3(a + b) = a + 2   expand

3a + 3b = a + 2

3a - a = 2 - 3b

2a = 2 - 3b

a = 2 - 3b

        2

The alternate hypothesis, also known as the alternative hypothesis, is a statement that contradicts or challenges the null hypothesis. It is a fundamental component of hypothesis testing in statistics and scientific research.

The alternate hypothesis represents the researcher's belief or expectation that there is a significant relationship, difference, or effect between variables being studied.

In hypothesis testing, the null hypothesis assumes that there is no significant relationship or difference between variables, while the alternate hypothesis proposes otherwise. The alternate hypothesis is typically the hypothesis of interest, as it represents the researcher's hypothesis that there is a meaningful effect or relationship to be discovered.

The alternate hypothesis is designed to be tested against the null hypothesis using statistical methods. The goal is to gather evidence and evaluate whether the data provide enough support to reject the null hypothesis in favor of the alternate hypothesis. If the evidence is statistically significant, meaning that it is highly unlikely to have occurred by chance, then the null hypothesis is rejected, and the alternate hypothesis is accepted.

The alternate hypothesis plays a crucial role in hypothesis testing, as it guides the research and provides a specific direction for investigation. It represents the researcher's expectation or hypothesis about the relationship between variables, and the statistical analysis aims to either support or refute this hypothesis based on the collected data.

Learn more about hypothesis here:

https://brainly.com/question/30899146

#SPJ11

Answer:

See explanation below.

Step-by-step explanation:

1. (-1, -1) and (2, -2)

  m = -2+1 / 2+1

  m = -1/3

2. (-1, -4) and (0, -1)

  m = -1+4 / 0+1

  m = 3/1

  m = 3

3. (-4, 0) and (-2, -3)

  m = -3-0 / -2+4

  m = -3/2

4. (2, 0) and (0, -3)

  m = -3-0 / 0-2

  m = -3/-2

  m = 3/2

5. (-1, 2) and (-4, -3)

  m = -3-2 / -4+1

  m = -5/-3

  m = 5/3

6. (4, 3) and (1, -4)

  m = -4-3 / 1-4

  m = -7/-3

  m = 7/3

Answer:

845

Step-by-step explanation:

50*25= 1250

2mins 15seconds= 135 seconds

135*3= 405

1250-405 = 845

Applying one of the properties of a parallelogram, the value of x is 10°, then 6x=60° and 12x=120°.

There are different quadrilaterals, for example square, rectangle, rhombus, trapezoid, and parallelogram.  Each type is defined accordingly to its length of sides and angles. For example, a parallelogram presents some properties that are presented below.

The figure of the exercise shows two adjacent angles. From the property: the adjacent angles are supplementary, you have:

6x+12x=180

18x=180

x=10°

Therefore, 6x= 6*10=60° and 12x=12*10=120°.

Read more about the parallelogram here:

brainly.com/question/20526916

#SPJ1

Answer:

106⁰

Step-by-step explanation:

As in cyclic quadrilateral sum of opposite angles is equal to 180⁰

Answer:

11m+5n

Step-by-step explanation:

you just add the m and or n with the numbers

Answer:

z = -1

Step-by-step explanation:

You must first start out by adding 19 to both sides to isolate the variable z, which results in:

2z = -2

Now, you can just divide by two on both sides to get z completely on its own, which gives you:

z = -1

Hope this helped somewhat! :D

The simplification of rational expressions can be achieved by using the Greatest Common Factor (GCF).

Take the common terms in the numerator and denominator and remove them from the expression to make it simpler.

The simplification of rational expressions can be achieved by using the Greatest Common Factor (GCF).Similar to fractions with variables in the denominators, rational expressions appear like them (and often numerators too).

For instance, the expression x 2 x + 3 is a rational expression: x squared, divided by x, plus 3, end fraction.

1)2m^2-4m)/2(m-2)

=[2m(m-2m)]/2(m-2)

= 2m/2

=m

2)m^2-2m+1/m-1

= (m-1)^2/(m-1)

=(m-1)(m-1)/(m-1)

=(m-1)

3)m^2-3m+2/m^2-m

=m^2-m-2m+2/m(m-1)

=m(m-1)-2(m-1)/m(m-1)

= (m-1)(m-2)/m(m-1)

=(m-2)/m

To learn more about rational expression refer

https://brainly.com/question/10242441

#SPJ1

Answer:

0.4987

Step-by-step explanation:

What we must do is calculate the z value for each value and thus find what percentage each represents and the subtraction would be the percentage between those two values.

We have that z is equal to:

z = (x - m) / (sd)

x is the value to evaluate, m the mean, sd the standard deviation

So for 80 we have:

z = (80 - 80) / (3)

z = 0

and this value represents 0.5

for 89 we have:

z = (89 - 80) / (3)

z = 3

and this value represents 0.9987

we subtract:

0.9987 - 0.5 = 0.4987

Which means that it represents 49.87%

a) Laplace transform :

1) 2s/(s² + 4)²

2)  1/s-2 + 2/(s-2)² + 4

b) Inverse laplace transform :

1)  \(e^{-3t}\)(1 + 2t)

2)  1/2(\(e^{3t} + e^{-3t}\))

Given,

Functions.

a)

1)

f(t) = tsintcost

L(tsintcost) = L(tsin2t/2)

= 1/2 L(tsin2t)

= 2s/(s² + 4)²

2)

f(t) =  \(e^{2t}\)  (sint + cost)²

L( \(e^{2t}\) (sint + cost)² ) = L( \(e^{2t}\) +  \(e^{2t}\)  sin2t)

= L( \(e^{2t}\) ) + L ( \(e^{2t}\) sin2t)

= 1/s-2 + 2/(s-2)² + 4

b)

1)

f(s) = s+5/s² + 6s + 9

f(s) = s+ 5 /(s+3)²

Take partial fraction,

= 1/s+3 + 2/(s+3)²

Take inverse of the f(s),

\(L^{-1}\) (f(s)) = \(L^{-1}\)( 1/s+3 + 2/(s+3)²)

f(t) = \(e^{-3t}\)(1 + 2t)

2)

f(s) = s/s² - 9

f(s) = s/(s+3)(s-3)

Taking partial fraction ,

f(s) = 1/2/s+3 + 1/2 /s-3

Taking inverse laplace of f(s),

\(L^{-1}\) (f(s))  =  \(L^{-1}\) ( 1/2/s+3 + 1/2 /s-3)

f(t) =  1/2(\(e^{3t} + e^{-3t}\))

Know more about laplace transform,

https://brainly.com/question/30759963

#SPJ4

The process is capable of producing outputs within the specification limits is true.

There are a number of potential reasons for why the process is not meeting the target value. One possibility is that the target value is too ambitious and is not realistic given the current process capability. Another possibility is that there is some inherent variability in the process that is not being accounted for. It is also possible that there are some external factors that are affecting the process, such as changes in the raw materials or the environment.

The design engineers have established an upper specification limit of 22 and a lower specification limit of 18. This means that they are confident that the process is capable of producing outputs within these limits. However, the fact that the process is consistently averaging 19.8 with a standard deviation of 0.5 suggests that there is some room for improvement.

One potential way to improve the process is to focus on reducing the inherent variability. This can be done by identifying and addressing the sources of variability in the process. Another potential way to improve the process is to reduce the target value. This may be necessary if the current target value is not realistic given the process capability.

It is also important to monitor the process over time to ensure that it is remaining within the specification limits. This will help to identify any potential issues that may arise and allow for corrective action to be taken if necessary.

Learn more about standard deviation at : https://brainly.com/question/16555520

#SPJ4

A.The process is in statistical control.

B.The process is capable of producing outputs within the specification limits.

C.The process is capable of producing outputs within the tolerance limits.

D.The process is capable of producing outputs within the control limits.

E.The process is capable of producing outputs that are normally distributed. The process is capable of producing outputs within the specification limits

which statement concerning this process is true?

Answer:

The range for the third side is 11 in. to 40 in.

Step-by-step explanation:

The third side of a triangle must satisfy the triangle inequality theorem, which states that the sum of the lengths of any two sides must be greater than the length of the third side. In this case, the two sides have lengths of 22 in. and 17 in., so the third side must have a length between 11 in. (the smaller of the two given lengths) and 40 in. (the sum of the two given lengths).

Theorem 3.7: [Insert specific theorem statement here]

Proof:
Column 1: Statements
1. [State the given or known information]
2. [State any definitions or previously proven theorems that are applicable]
3. [State any logical or algebraic manipulation steps]

Column 2: Reasons
1. Given
2. Definition of [insert term or concept]
3. [Justify each step using a valid reason, such as the transitive property, substitution property, or a previously proven theorem]

Please note that this is a general template, and the specific steps and reasons will vary depending on the theorem you are working on. Make sure to include all the necessary information and justifications to support your proof. If you provide me with the specific Theorem 3.7 you are referring to, I can help you create a more tailored proof.

Learn more about Algebraic manipulation:

https://brainly.com/question/30549736

#SPJ11