Each free throw in a game of basketball is worth 1 point and each field goal is worth 2 points. George's team scores a total of 16 points. They make a free throws and y field goals.

The evaluation of the function gives:

f(-4) = 1, f(1) = 2, f(2) = 6, f(5) = 29/3

A function is an expression that shows the relationship between the independent variable and the dependent variable.  A function is usually denoted by letters such as f, g, etc.

The evaluation is as follow:

For f(-4):

since x = -4. This means x ≤ -4. Thus, we use the function |2x + 7|. That is:

f(-4) = |2*(-4) + 7|

f(-4) = |-8 + 7|

f(-4) = | -1 |

f(-4) = 1

For f(1):

x = 1. Thus, -4< x ≤ 1. Use 1 + x²

f(1) = 1 + x²

f(1) = 1 + 1²

f(1) = 2

For f(2):

x = 2. Thus, 1< x < 3. Use the value 6

f(2) = 6

For f(5):

x = 5. Thus, x ≥ 3. Use (1/3)x + 8.

f(5) = (1/3)*5 + 8

f(5) = 29/3

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Evaluating the function at various values of x over different intervals,

f(-4) = 1, f(1) = 2, f(2) = 6, f(5) = 29/3

To evaluate the function f(x) at various values of x, we need to use the definition of the function for each interval of x.

For x ≤ -4:

f(x) = |2x + 7|

f(-4) = |2(-4) + 7| = |-1| = 1

For -4 < x ≤ 1:

f(x) = 1 + x²

f(1) = 1 + 1² = 2

For 1 < x < 3:

f(x) = 6

f(2) = 6

For x ≥ 3:

f(x) = (1/3)x + 8

f(5) lies in the interval x ≥ 3, so we use the definition of f(x) for this interval:

f(5) = (1/3)(5) + 8 = 29/3

Therefore,

f(-4) = 1

f(1) = 2

f(2) = 6

f(5) = 29/3

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Answer:

Step-by-step explanation:

If you substitute x = 7, then the reasoning is correct, but if you think that x = 7 should turn out at the end (answer), then this is not correct, because it turns out [tex]\frac{19}{3}[/tex]

In order to obtain a 96.5% confidence interval of width of at most 0.16 for the probability of flipping a head in a coin flipping experiment, the coin needs to be flipped 533 times.

How to calculate the number of times we have to flip a coin?

We can use the formula:

n = ((Z_α/2) / E)²

Where, n is the number of times we need to flip a coin,

Z_α/2 is the Z-score at the α/2 level of significance for the normal distribution, and E is the desired margin of error or the maximum allowable deviation from the population proportion.

In this problem, the margin of error is 0.16, and the confidence level is 96.5%.

The α value is 1 - 0.965 = 0.035.

We need to find the Z-score corresponding to α/2 = 0.0175 using a standard normal distribution table.

Z_0.0175 = -1.96n = ((-1.96) / 0.16)²n ≈ 533

Therefore, the coin needs to be flipped 533 times to obtain a 96.5% confidence interval of width of at most 0.16 for the probability of flipping a head.

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Answer:

Step-by-step explanation:

two circles: 2(πr²)

1 rectangle:Lw

3.14(7)(7)

3.14(49)

2(153.86)=307.72

307.72(14)

4308.08

We can use a proportion to estimate the number of students who could be expected to bring their lunch:

9 out of 15 students brought their lunch from home.

Let x be the number of students in the school who bring their lunch from home.

So we can set up the proportion:

9/15 = x/500

We can solve for x by cross-multiplying:

9 * 500 = 15x

x = (9 * 500) / 15

x = 300

Therefore, we can expect that 300 out of 500 students in the school bring their lunch from home.

An equation that shoes the total amount paid y if they played x number of games is y = 2x + 5

In mathematics, an equation is-a-statement that shows the equality between two-expressions. An equation typically has one or more unknowns that need to be solved for in order to satisfy the equality.

Here, y = total amount paid

x = number of games

Each game costs $2

So total cost of all games played = $2x

But to enter the game they need to rent shoes $5.

So, total amount paid = $5 + $2x

Thus, An equation that shoes the total amount paid y if they played x number of games is y = 2x + 5

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It takes 1,95,000 seconds longer for light from the sun to reach Pluto as to reach Earth.

It is given to us that light from the sun takes 5×10² seconds to reach Earth and it takes 2×10⁴ seconds to reach Pluto.

We need to find the difference in the time it takes for the light to reach Pluto from the sun than it takes to reach the earth

First, lets convert the time it takes for the light to reach Pluto from the sun:

2×10⁴ seconds to reach Pluto

= 2 x 100000 = 200000 seconds

now lets convert the time it takes for the light to reach earth from the sun:

5×10² seconds to reach Earth

= 5 x 1000 = 5000 seconds

therefore the difference = time taken to reach Pluto - time taken to reach Earth

= 2,00,000 - 5,000 = 1,95,000

Therefore, it takes 1,95,000 seconds longer for light from the sun to reach Pluto as to reach Earth.

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Answer: I'm not sure what birdhouse you're talking about, but I'll tell you the average amount of wood that would be needed to build a birdhouse.

Many cavity-nesting birds will add their own nest material, but the woodpeckers, waterfowl and owls prefer nest boxes with 2-3 inches of dry sawdust or woodchips in the bottom.

Answer:

-720

Step-by-step explanation:

Simplify the two negatives with positive:

120 * 6 * -1

Multiply 6 and -1 with -6:

120 * -6

= -720

A(n) asymptote is a line that a graphed curve gets closer to but never touches as the value of a variable gets extremely small or extremely large. Asymptotes can be horizontal, vertical, or slanted, and they are often used to describe the behavior of functions or graphs as they approach certain limits or values.

Answer:

A(n) asymptote is a line that a graphed curve gets closer to but never touches as the value of a variable gets extremely small or extremely large. Asymptotes can be horizontal, vertical, or slanted, and they are often used to describe the behavior of functions or graphs as they approach certain limits or values.

answer = (3x - 5) (3x + 3).

simplified = 3(x + 1) (3x - 5).

Answer:

72 i think

Step-by-step explanation:

i think your supposed to multiply 9 and 8 because count the sides on the shaded part ir

ts 8

Terry and Ricky traveled 35% of the total distance on the first day of their canoe trip.

Terry and Ricky went on a 60-mile canoe trip with their class, and on the first day, they traveled 21 miles. To find the percent of the total distance they traveled on the first day, follow these steps:
Divide the distance traveled on the first day (21 miles) by the total distance of the trip (60 miles).
Multiply the result by 100 to convert it into a percentage.
Step-by-step explanation:
Divide 21 miles by 60 miles:
  21 / 60 = 0.35
Convert the result into a percentage by multiplying by 100:
  0.35 x 100 = 35%

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On solving the provided question we can say that Therefore, the percent decrease in video games sales in consoles is approximately 10.43%.

Percentage is a way of expressing a number as a fraction of 100. It is often denoted using the percent symbol (%). For example, if a student scores 80 out of 100 in a test, the percentage score is calculated as (80/100) x 100, which is equal to 80%. This means the student scored 80% of the total marks available in the test. Percentages are commonly used to express rates of change, proportions, and percentages of a whole, and they are used in many fields, such as finance, science, and statistics.

$1,150 million - $1,030 million = $120 million

$120 million ÷ $1,150 million = 0.1043

0.1043 x 100% = 10.43%

Therefore, the percent decrease in video games sales in consoles is approximately 10.43%.

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In the scenario where a nutritionist selected a random sample of adults and asked them about their eating and exercise habits, the data show that people who eat organic fruits and vegetables are more likely to exercise regularly than those who do not eat organic fruits and vegetables, this scenario describes an observational study.

What is an observational study?Observational study, also known as non-experimental research, is a type of research design where researchers observe the behavior of a particular group of individuals without influencing it in any way. A researcher is not allowed to interfere with or manipulate any variables.

He just observes the environment and the behavior of the individuals under study. This is why observational studies are sometimes also referred to as naturalistic observations.

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The tour guide should row towards the point on the coast closest to point Q, which is the point of perpendicular intersection between the coast and the line passing through points Q and the initial position of the tour guide.

To reach point Q in the least time, the tour guide should row towards the point on the coast that is closest to point Q. Let's call this point P.

We can use the Pythagorean theorem to find the distance from point P to point Q

distance PQ = sqrt((3 miles)^2 + (1 mile)^2) = sqrt(10) miles

Now, let's consider two scenarios

Scenario 1: The tour guide rows directly towards point Q.

The distance the tour guide needs to row is 2 miles + sqrt(10) miles. This will take the tour guide

time = (2 miles + sqrt(10) miles) / (3 miles/hour) = (2/3) + (1/3)*sqrt(10) hours

Scenario 2: The tour guide rows towards point P, then walks the rest of the way to point Q.

The distance the tour guide needs to row is 2 miles - x miles, where x is the distance from point P to the nearest point on the coast. By similar triangles, we know that

x / 3 miles = 1 mile / sqrt(10) miles

Solving for x, we get

x = 3/sqrt(10) miles

So the distance the tour guide needs to row is

2 miles - 3/sqrt(10) miles = 2 - (3/sqrt(10)) miles

The distance the tour guide needs to walk is

sqrt(10) miles - 1 mile = sqrt(10) - 1 miles

The time it takes the tour guide to row and walk is:

time = (2 - (3/sqrt(10))) / (3 miles/hour) + (sqrt(10) - 1) / (3 miles/hour)

Simplifying this expression, we get

time = (2/3) - (1/3)*sqrt(10) + (sqrt(10)/3) - (1/3) = (1/3) + (1/3)*sqrt(10) hours

Comparing the two scenarios, we see that scenario 2 takes less time, so the tour guide should row towards point P in order to reach point Q in the least time.

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We can use trigonometry to solve this problem. Let the length of the rope be x. Then, we can draw a right triangle where the height of the tree is the opposite side, the length of the rope is the hypotenuse, and the angle of elevation is 60 degrees. The adjacent side can be found using the trigonometric function cosine:

cos 60° = adjacent / hypotenuse

1/2 = adjacent / x

Multiplying both sides by x, we get:

x/2 = adjacent

To find the length of the hypotenuse, we can use the Pythagorean theorem:

hypotenuse^2 = adjacent^2 + opposite^2

Substituting in the values we know, we get:

x^2 = (x/2)^2 + (9√5)^2

Simplifying the right side, we get:

x^2 = x^2/4 + 405

Multiplying both sides by 4, we get:

4x^2 = x^2 + 1620

Subtracting x^2 from both sides, we get:

3x^2 = 1620

Dividing both sides by 3, we get:

x^2 = 540

Taking the square root of both sides, we get:

x = √540 = 6√60

Therefore, the length of the rope that Rachel needs to hang the piñata is 6√60 feet. Rounded to the nearest tenth, this is approximately 74.1 feet.

Answer:

  43.4 ft

Step-by-step explanation:

You want to know the length of rope needed to hang a piñata from the top of a tree that is 9√5 feet tall, if the rope makes an angle of 60° with the ground.

The hypotenuse of the triangle can be found by considering the sine of the 60° angle. The sine of the angle is given by ...

  Sin = Opposite/Hypotenuse

Then the hypotenuse of the triangle can be found from ...

  sin(60°) = tree height / hypotenuse

  hypotenuse = tree height/sin(60°) = 9√5/sin(60°)

We presume the length of rope Rachel wants is the total of the lengths from the anchor point to the tree top and back to the ground. That will be ...

  9√5 + 9√5/sin(60°) = 9√5·(1 +1/sin(60°)) ≈ 43.4 . . . . feet

Rachel needs about 43.4 feet of rope to hang the piñata.

After answering the presented question, we can conclude that r is the equation distance from the origin and is the angle measured anticlockwise from a reference direction.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "[tex]2x + 3 = 9[/tex]" asserts that the phrase "[tex]2x + 3[/tex]" equals the value "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "[tex]x2 + 2x - 3 = 0[/tex]." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.

We may use two alternative reference points or coordinate systems to find the end of the hiking trail. As an example:

Using a Cartesian coordinate system: Assume the origin is the trailhead and the x-y axis is standard. If the trail's end is 5 units to the right and 7 units up from the trailhead, we may write it as (5, 7).

Using a polar coordinate system: Assume that the origin is defined as the centre of a circular trail and that we use polar coordinates (r,), where r is the distance from the origin and is the angle measured anticlockwise from a reference direction

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the answer is that Sophia, Lexi, and Jason collected a total of 162 bananas.

In this problem, we are given that Sophia picked 18 bananas. We are also told that Lexi picked 6 more bananas than Sophia, so Lexi picked 18+6=24 bananas. Additionally, we are told that Jason picked 5 times as many bananas as Lexi, so we need to multiply Jason picked 5*24=120 bananas.

To find the total number of bananas picked by all three people, we need to add up the number of bananas picked by Sophia, Lexi, and Jason. So, we add 18 + 24 + 120 = 162 bananas.

Therefore, the answer is that Sophia, Lexi, and Jason collected a total of 162 bananas.

It's important to understand the relationships between the numbers given in the problem in order to solve it. Sophia is the starting point, with 18 bananas, and Lexi is picking 6 more bananas than her. Jason's number is more complex, being 5 times Lexi's amount. By breaking down each piece of information and understanding how they relate to each other, we can easily find the total number of bananas collected by all three.

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Answer: 1. -8, 2. 12, 3.-4 , 4.-7 , 5.3 , 6.15 , 7. 1, 8. 12, 9. -15, 10.318 ,

Step-by-step explanation:

The probability of getting P(sum > 9) when a cube is rolled twice is 6/36.

Mathematical study of random occurrences and their results is the subject of probability theory. It entails analysing and quantifying risk, chance, and uncertainty. For modelling and studying complex systems and events in disciplines like physics, engineering, economics, and finance, probability theory offers a framework. Concepts like random variables, probability distributions, expected values, variance, and covariance are all part of the theory. In many aspects of daily life, including forecasting weather patterns, data analysis for scientific study, and calculating the likelihood of certain outcomes in games of chance, probability theory is applied.

The total number of outcomes for a 6 sided cube rolled twice is 6 x 6 = 36.

For a sum greater than 9 the possibilities are:

(4, 6), (5, 5), (5, 6), (6, 4), (6, 5), (6, 6) = 6 possibilities.

Thus,

P(sum > 9) = 6 / 36.

Hence, the probability of getting P(sum > 9) when a cube is rolled twice is 6/36.

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The required solution of the linear programming problem for the given objective function and subject to constraints are,

Linear programming problem is Maximize 15x1 + 2x2

Subject to:

7x1 + x2 < 23

3x1 - x2 < 5

x1, x2 > 0

Objective function value for rounding up fraction 1/2 solution is 53

Objective function value for rounding up all fraction solution is 23.

Optimal objective function value 53 is lower than optimal value 95.5.

Optimal objective function value is always less than or equal to the LP's optimal objective function value as ILP problem is a more constrained version.

To solve the problem as an LP,

we can ignore the integer constraints

And solve the problem as a continuous linear program.

The problem can be written as,

Maximize 15x1 + 2x2

Subject to:

7x1 + x2 < 23

3x1 - x2 < 5

x1, x2 > 0

Rounding up fractions greater than or equal to 1/2,

The following feasible solution is,

x1 = 3, x2 = 4

The objective function value for this solution is 53.

However, this is not the optimal integer solution since both x1 and x2 are not integers.

Rounding down all fractions, we get the following feasible solution,

x1 = 1, x2 = 4

The objective function value for this solution is 23, which is less than the LP's optimal objective function value of 95.5.

This is not the optimal integer solution either.

Optimal objective function value for the ILP is lower than that for the optimal LP, solve the ILP problem.

In any one constraints

When x1 = 0 ⇒ x2 = 23

x2 = 0 ⇒ x1 = 3.3

Optimal value is ,

15(3.3) + 2(23)

= 49.5 + 46

= 95.5

Optimal objective function value is lower than optimal value.

The optimal objective function value for the ILP problem is always less than or equal to the corresponding LP's optimal objective function value .

Because the ILP problem is a more constrained version of the linear programming problem.

The ILP problem restricts the variables to be integers, which reduces the feasible region and makes the problem more difficult to solve.

The optimal objective function values for the LP and ILP problems are equal.

If the LP problem has an optimal solution that satisfies the integer constraints.

In general, the optimal objective function value of the MILP problem can be better or worse than that of the LP or ILP problem.

It depends on the specific problem instance.

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The above question is incomplete, the complete question is :

Given the following all-integer linear program:

Max 15x1 + 2x2

s. t.

7x1 + x2 < 23

3x1 - x2 < 5

x1, x2 > 0 and integer

a. solve the problem as an lp, ignoring the integer constraints.

b. what solution is obtained by rounding up fractions greater than or equal to 1/2? is this the optimal integer solution?

c. what solution is obtained by rounding down all fractions? is this the optimal integer solution? explain.

d. show that the optimal objective function value for the ilp (integer linear programming) is lower than that for the optimal lp.

e. why is the optimal objective function value for the ilp problem always less than or equal to the corresponding lp's optimal objective function value? when would they be equal? comment on the optimal objective function of the milp (mixed-integer linear programming) compared to the corresponding lp and ilp.

Let x be pounds of hamburger and y be pounds of hot dogs.

The equation is: 8x + 6y ≤ 75.

An equation is a mathematical statement that uses the equal sign (=) to show that two expressions are equal. Equations can include variables, which are symbols that represent unknown or changing values. Solving an equation means finding the value of the variable that makes the equation true. Equations are commonly used in many areas of mathematics, science, and engineering, as well as in everyday life.

Let x be the pounds of hamburger purchased and y be the pounds of hot dogs purchased.

The cost of hamburger at $8 per pound would be 8x dollars.

The cost of hot dogs at $6 per pound would be 6y dollars.

The total cost of the purchases should not exceed $75, so we can write:

8x + 6y ≤ 75

This is the equation that represents Breanna's situation, where x represents the pounds of hamburger purchased and y represents the pounds of hot dogs purchased, and the total cost of the purchases should not exceed $75.

Therefore, Let x be pounds of hamburger and y be pounds of hot dogs.

The equation is: 8x + 6y ≤ 75.

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Answer:

the GCF is 5y and the factored form is 5y(2y^4 + 6y^2 - 3).

Step-by-step explanation:

The greatest common factor (GCF) of the terms 10y^5, 30y^3, and -15y is 5y.

To factor out the GCF, we can divide each term by 5y:

10y^5 / (5y) = 2y^4

30y^3 / (5y) = 6y^2

-15y / (5y) = -3

So we have:

10y^5 + 30y^3 - 15y = 5y(2y^4 + 6y^2 - 3)

Therefore, the GCF is 5y and the factored form is 5y(2y^4 + 6y^2 - 3).

Answer: GCF=5

Factored form= 5y(2y^4+6y^2-3

Step-by-step explanation:

The output of g(x) when x is -2 is 1/3.

How to find output?

To find the output of g(x) when x is -2, we simply substitute -2 into the formula for g(x):

g(-2) = 3⁻²/²

Simplifying the exponent, we get:

g(-2) = 3⁻¹

Now, we need to evaluate 3⁻¹. Recall that any number raised to a negative exponent can be written as its reciprocal raised to the corresponding positive exponent. That is:

a⁻ⁿ = 1/(aⁿ)

In our case, a is 3 and n is 1, so we have:

3⁻¹= 1/(3¹) = 1/3

Therefore, the output of g(x) when x is -2 is 1/3.

Note that 1/3 is already in its simplest form, so we do not need to simplify it any further. We also do not need to round it to two decimal places since it is a fraction.

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Answer:no

Step-by-step explanation:

for example Exponents are numbers that have been multiplied by themselves. For instance, 3 · 3 · 3 · 3 could be written as the exponent 34

For the given linear equation, the solution is (3,3) i.e. B.

What is a linear equation, exactly?

A linear equation is a mathematical equation in which the highest power of the variable(s) is one. In other words, it is an equation of the form:

y = mx + b

where y and x are variables, m is the slope or gradient of the line, and b is the y-intercept (the point at which the line intersects the y-axis). The slope represents the rate of change of the line, or how steep it is, and the y-intercept represents the value of y when x is zero.

Now,

We can solve this problem by plugging in the x and y values of each ordered pair and seeing if they make the equation true.

Let's start with option A, which is (2,4):

-3x+5y = 2x+3y (original equation)

-3(2) + 5(4) = 2(2) + 3(4) (substituting x=2 and y=4)

-6 + 20 = 4 + 12

14 = 16

The left side of the equation is not equal to the right side, so (2,4) is not a solution.

Now let's move on to option B, which is (3,3):

-3x+5y = 2x+3y (original equation)

-3(3) + 5(3) = 2(3) + 3(3) (substituting x=3 and y=3)

-9 + 15 = 6

6 = 6

The left side of the equation is equal to the right side, so (3,3) is a solution.

Therefore, the answer is option B, which is "Only (3,3)".

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For x-intercept, [tex]y=0[/tex]

[tex]\implies b-x=0[/tex]

[tex]\implies b=6[/tex]

For vertical intercept [tex]y\rightarrow \pm \infty[/tex]

[tex]\implies cx+d=0[/tex]

[tex]\implies-3x+d=0[/tex]

[tex]\implies d=3c[/tex]

Now, [tex]y=\dfrac{6-x}{cx+3c}[/tex]

[tex]\implies x(xy+1)=6-3cy[/tex]

[tex]\implies x=\dfrac{6-3xy}{cy+1}[/tex]

At horizontal asymptote, [tex]x\rightarrow\pm\infty\implies cy+1=0[/tex]

[tex]\implies c(-1)+1=0[/tex]

[tex]\implies c=1[/tex]

[tex]\implies d=3[/tex].