Give a recursive definition for the following set of ordered pairs of positive integers ([tex]a|b[/tex] means that a is a factor of b): [tex]S=[/tex]{[tex](a,b)|a \in Z^+, b \in Z^+, a|b[/tex]}

The polynomial function that best fits the graph is f(x) = 130(x+3)(x-2)²(x-5).

The given graph exhibits three x-intercepts at x = -3, 2, and 5, and the y-intercept is positioned at (0, 2). The graph passes through the x-axis linearly at x = -3 and x = 5, indicating that the corresponding factors of the polynomial will be linear. However, at x = 2, the graph bounces off the x-axis at the intercept, implying that the corresponding factor of the polynomial will be quadratic. Therefore, the polynomial function can be expressed as follows:

f(x) = a(x+3)(x-2)²(x-5)

To find the stretch factor 'a,' we can use another point on the graph, such as the y-intercept (0, 2). By plugging in the values, we obtain:

f(0) = a(0+3)(0-2)²(0-5)

-2 = a(0+3)(0-2)²(0-5)

-2 = -60a

a = 130

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Considering the given graph,  we infer that while rolling a dice is random, the median values do exhibit some patterns that can be analyzed and used to make predictions about the expected values.

Looking at the median data from the graph, we can infer that option A is not true, as the median appears to be equally likely to fall between any two numbers from 1 to 6. However, we can also infer that option B is not entirely accurate.

While it is true that rolling a dice is random and each roll is independent, we can observe patterns in the median data.

For example, the median values are more likely to be closer to 3.5, which is the theoretical median value of a fair six-sided dice. This suggests that the more times the dice is rolled, the more likely the median value will approach the expected value.

We can also observe that the spread of the median values tends to decrease as the number of rolls increases, indicating that more rolls lead to more consistent results.

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The graph that shows a proportional relationship between x and y is given as follows:

Graph D.

A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other.

The equation that defines the proportional relationship is given as follows:

y = kx.

In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.

From the equation y = kx we have that it is a linear function with intercept of zero, meaning that the graph D represents the proportional relationship for this problem.

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There are 18 possible combinations of ice cream, topping, and sprinkles.

Probability P(Chocolate, Fudge, Rainbow) = 1/18

There are 18 different possible sundaes that can be made when choosing one flavor of ice cream, one topping, and one color of sprinkles.

To visualize all the possible outcomes, we can use a tree diagram:

                              Ice Cream

                                       |

                          ------------------------------

                      |                |                |

           Chocolate        Vanilla         Strawberry

                       |                |                |

                   --------------   --------------   --------------

                       |              | |              | |              |

 Fudge     Marshmallow   Fudge     Marshmallow   Fudge     Marshmallow

                       |              |                |               |

                     --------------   --------------   --------------

                     |              | |              | |              |

     Rainbow  Chocolate  Rainbow  Vanilla   Rainbow  Strawberry

So there are 18 possible combinations of ice cream, topping, and sprinkles.

To answer part b) which asks for the probability of choosing Chocolate ice cream with Fudge topping and Rainbow sprinkles, we need to know the total number of possible outcomes (which we just calculated as 18) and the number of outcomes that match the specific combination of Chocolate ice cream, Fudge topping, and Rainbow sprinkles. There is only one outcome that matches this combination, so the probability is:

P(Chocolate, Fudge, Rainbow) = 1/18

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1. The difference between the longest and shortest pencil is 4 5/12

2. The total length is 22 3/4 inches

3. The statement is false

4. There are 9 pencils that measure more than 5½ inches and less than 7 2/4 inches

A word problem is a math problem written out as a short story or scenario. This statements are interpreted into mathematical equation or expression.

1. The difference between longest and shortest pencil = 8⅔ - 4¼

= 26/3 - 17/4

= (104-51)/12

= 53/12 = 4 5/12

2. The total length of pencils less than 5 ½ inches = 5×2 + 17/4 × 3

= 10+ 51/4 = 40+51)/4

= 91/4 = 22 3/4 inches

3. The Statement is false because the pencils less than 6 inches is 8 and not upto half of the total pencil

4. There are 9 pencils that measure more than 5½ inches and less than 7 2/4 inches.

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Therefore, 1t5e twelve represents the number 3239 in base ten.

what is system of equations?

A system of equations is a set of two or more equations with the same variables. The solution to a system of equations is a set of values for the variables that satisfy all the equations in the system simultaneously.

For example, consider the following system of two equations:

x + y = 5

2x - y = 3

This is a system of two equations with two variables, x and y. The solution to this system is the values of x and y that make both equations true at the same time. In this case, the solution is x = 2 and y = 3, because when we substitute these values into the equations.

In base twelve, the place values increase by a factor of twelve at each position, starting from the rightmost position. The rightmost position has a place value of 1, the next position to the left has a place value of 12, the next position to the left has a place value of 12^2 = 144, and so on.

To convert the number 1t5e in base twelve to base ten, we need to multiply each digit by its corresponding place value, and then add up the results:

1t5e (base twelve) = 1 * 12^3 + 10 * 12^2 + 5 * 12^1 + 11 * 12^0

= 1 * 1728 + 10 * 144 + 5 * 12 + 11 * 1

= 1728 + 1440 + 60 + 11

= 3239

Therefore, 1t5e twelve represents the number 3239 in base ten.

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The angle measures of w and x are given as follows:

In this problem we have an isosceles triangle, meaning that two of the side lengths, along with two of the angle measures, are congruent.

The congruent side lengths are given as follows:

SR and RQ.

Hence the congruent angle measures are given as follows:

Hence angle w is given as follows:

w = 51º.

The sum of the measures of the internal angles of a triangle is of 180º, hence the measure of angle x is given as follows:

x + 2 x 51 = 180

x = 180 - 102

x = 78º.

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Answer:

120 km²

Step-by-step explanation:

You just need to add all areas, (3×5) + (9×3) + (13×6) = 15 + 27 + 78 = 120

If both Tony and Marcus work on the job and the cost of labor is $48.00 per hour then labor estimate for the job is $576.00.

Marcus: 1 slab / 9 hours = 1/9 slab per hour

Tony: 1 slab / 3 hours = 1/3 slab per hour

The total amount of work they can do in one hour is the sum of their individual rates:

Marcus and Tony: 1/9 + 1/3 = 4/9 slab per hour

So together, Marcus and Tony can lay 4/9 of a slab per hour.

time = work / rate

time = 1 / (4/9) = 2.25 hours

total labor cost = hours worked x cost per hour

The total number of hours worked is the sum of the hours worked by Marcus and Tony:

total hours worked = 9 hours + 3 hours = 12 hours

The cost per hour is $48.00, so the labor estimate for the job is:

total labor cost = 12 hours x $48.00/hour

= $576.00

Therefore, the labor estimate for the job is $576.00.

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Answer: y = -4x + 1. Brainliest?

Step-by-step explanation:

To write a function rule that has a greater rate of change than the given function, we need to find the slope of the given function. We can use the two points (-2, 7) and (2, -5) from the table to calculate the slope as:

slope = (change in y) / (change in x) = (-5 - 7) / (2 - (-2)) = -3

So the slope of the given function is -3. To create a new function rule with a greater rate of change, we can choose a larger slope. Let's choose a slope of -4. We also need to find the y-intercept (b) of the new function, which we can do by plugging in one of the points from the table and solving for b. Let's use the point (0, 1):

y = mx + b

1 = (-4)(0) + b

b = 1

So the function rule with a greater rate of change and passing through the point (0, 1) is:

y = -4x + 1

Answer:

The Correct answer is B

Step-by-step explanation:

The scale factor of figure STUV to figure WXYZ is 3:1. If ST = 39 mm and SV = 51 mm, the length of side WX is 13 mm.

If the scale factor of figure STUV to figure WXYZ is 3:1, it means that every length in figure STUV is three times longer than the corresponding length in figure WXYZ.

To find the length of side WX, we need to first identify the corresponding sides of the two figures. We know that ST is three times longer than W, and SV is three times longer than Y. So, we can set up the following proportion:

ST/WX = SV/YZ

Substituting the given values, we get:

39/WX = 51/YZ

We need to find the value of WX, so we can solve for it by cross-multiplying the proportion:

39 * YZ = 51 * WX

Since we don't know the value of YZ, we need to find it in terms of WX. We can use the scale factor of 3:1 to relate the lengths in the two figures:

ST = 3 * W

SV = 3 * Y

Substituting the first equation, we get:

W = ST/3 = 39/3 = 13 mm

Substituting the second equation, we get:

Y = SV/3 = 51/3 = 17 mm

Now we can substitute these values into the proportion:

39/WX = 51/17

Solving for WX, we get:

WX = (39 * 17) / 51 = 13 mm

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Complete question is:

The scale factor of figure STUV to figure WXYZ is 3:1. If ST = 39 mm and SV = 51 mm, what is the length of side WX?

The volume of the given right cone is approximately 597.9 cubic units.

In this problem, we are going to find the volume of a right cone. A cone is a three-dimensional object that has a circular base and tapers to a point. The term "right" means that the axis of the cone is perpendicular to its base. The formula for the volume of a right cone is V = (1/3)πr²h, where V is the volume, r is the radius of the circular base, and h is the height of the cone.

Now, let's apply this formula to the given cone. We are given that the radius of the circular base is 16 and the height of the cone is 7. So, we can substitute these values into the formula to get:

V = (1/3)π(16)²(7) V = (1/3)π(256)(7) V = (1/3)(1,792π) V ≈ 597.9

We round our answer to the nearest tenth as requested. So, the final answer is V ≈ 597.9.

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The types of systems of linear equations are as follows:

Dependent: The system has infinitely many solutions. The graphs of the equations represent the same lines. Example:

. The system has infinitely many solutions.

Independent: The system has exactly one solution. The graphs of the equations intersect at a single point.

Inconsistent: The system has no solution. The graphs of the equations are parallel lines.

If a 9v battery produces a current of 18 amps then the resistance of the circuit element is 0.5 ohms.

We can use Ohm's law to determine the resistance (R) of a circuit element

Given the voltage (V) and current (I) through it:

R = V / I

In this case, the voltage (V) is 9 volts and the current (I) is 18 amps. Substituting these values into the formula, we get:

R = 9 V / 18 A

Simplifying the expression on the right-hand side, we get:

R = 0.5 Ω

Therefore, the resistance of the circuit element is 0.5 ohms.

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Answer:

x = - 12

Step-by-step explanation:

the central angle subtended by the arc with measure 45° are congruent, that is central angle is 45°

the 3 angles on the diameter then sum to 180° , that is

45 + 65 + x + 82 = 180

x + 192 = 180 ( subtract 192 from both sides )

x = - 12

Okay, here are the steps to solve this problem:

* The recipe calls for 3/4 teaspoon of cinnamon for every 4 cups of granola mix.

* So for 1 cup of granula mix, you need 3/4 / 4 = 3/12 teaspoon of cinnamon.

* For 12 cups of granula mix, you would need 12 * (3/12) = 3 teaspoons of cinnamon.

Therefore, for 12 cups of granola mix you would need 3 teaspoons of cinnamon.

[tex]\textit{since we know that }\triangle FGH \cong \triangle CDE \\\\[-0.35em] ~\dotfill\\\\ HF=EC\implies -3s+44=-3t+50 \\\\\\ HG=ED\implies 6s=t+43\implies \boxed{6s-43=t} \\\\\\ \stackrel{\textit{substituting on the 1st equation}}{-3s+44=-3(6s-43)+50}\implies -3s+44=-18s+129+50 \\\\\\ 15s+44=129+50\implies 15s+44=179\implies 15s=135 \\\\\\ s=\cfrac{135}{15}\implies \boxed{s=9}\hspace{9em}\stackrel{ 6(9)-43 }{\boxed{t=11}}[/tex]

Answer: The answer to your question is C. Brainliest?

Step-by-step explanation:

For the first square, we can multiply both the numerator and denominator by 5 to get an equivalent fraction with a denominator of 60:

2/12 = (2 x 5) / (12 x 5) = 10/60

For the second square, we can multiply both the numerator and denominator by 4 to get an equivalent fraction with a denominator of 60:

2/15 = (2 x 4) / (15 x 4) = 8/60

Now, we can add the two fractions:

10/60 + 8/60 = 18/60

Simplifying this fraction by dividing both numerator and denominator by 6, we get:

18/60 = 3/10

Therefore, the total shaded area in the diagram is 3/10 or 0.3 in decimal form.

The answer is C. 0.3.

The exponent by which base b must be raised to get a positive real number an is the logarithm of a positive real number a with regard to base b, a positive actual number that is not exactly one.

A logarithm is the power to which a number must be raised in order to receive extra values. The simplest approach to express really large numbers is in this way. A number of important features of a logarithm demonstrate the fact that multiplication and division of logarithms can also be used to represent addition and subtraction logarithms.

The exponent by which base b must be raised to get a positive real number an is the logarithm of a positive real number a with regard to base b, a real number that is positive but not equal to one.

i.e., [tex]b^y=a[/tex] ⇔ [tex]log_b[/tex] a = y

In this case, "A" and "B" are two positive real numbers.

Y is an actual number.

Argument occurs inside the log as "a" by the name argument.

It is said that the base, or "b," is at the bottom of the log.

To put it another way, the logarithm provides a solution to the problem of "How many times is a number divided to get the other number?"

How numerous times must three be multiplied, for instance, to yield the number 27?

27 is the outcome of multiplying 3 times by 3.

Consequently, the logarithm is 3.

The logarithm form is written as follows:

[tex]log_3[/tex] (27) = 3 - equation 1

The base 3 logarithm of 27 is therefore 3.

It is also possible to write the above logarithm form as:

3x3x3 = 27

3³ = 27 - equation 2

Equations (1) and (2) are hence equivalent.

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Only first figure of graph have an Euler circuit.

We have to given that;

There are 3 graphs are shown in figure.

Since, A graph has an Euler circuit if and only if the degree of every vertex is even.

Hence, In first graph,

Every vertex have even degree with 2 or 4.

Thus, It shows an Euler circuit.

In second graph,

Some vertex have odd degree with 3.

Hence, It does not shown an Euler circuit.

In third graph,

Some vertex have odd degree with 3.

Hence, It does not shown an Euler circuit.

Thus, Only first figure of graph have an Euler circuit.

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Answer:

2/3 or 67%

Step-by-step explanation:

To find the exact probability for you to reach into the orange balls you'll have to do a data table on which you'll include how many orange balls are by the total amount of balls that are within the urn.

For example:
The urn contains:

* 10 red balls
* 20 yellow balls
* 60 orange balls

Total amount of balls that you have on the urn is 90, you'll get this result by doing a simple addition of the table of content.

Afterwards, we have to find the probability, so you will have to take the amount of orange balls (which is 60) and divide it by 90 (Which is the total amount of balls you have on the urn).

60/90

A quick tip for you to do this on a simplified manner is by dividing the numerator and the denominator by their greatest common divisor (Which in this case is 30) (30x2 = 60) (30x3 = 90)

60/90 = (60 divided 30) / (90 divided 30) = 2/3

To resolve this problem, we get that the probability of selecting an orange ball is 2/3 or approximately 0.67 which we'll simplify to 67%

I hope this helped you

Janeesa needs to drive about 6.9 mph faster than the speed limit to make it on time.

What is the  speed limit

To find out how fast Janeesa needs to drive to make it on time, one can use the formula:

distance = rate x time

In this case, the distance is 247.5 miles, the time is 4 hours, and the rate is what we're trying to find. Rearranging the formula to solve for rate, we get:

rate = distance / time

Plugging in the values we know, we get:

rate = 247.5 / 4 = 61.875

To know how much faster Janeesa needs to drive, one has to subtract the speed limit from the required speed:

Speed Difference = Required Speed - Speed Limit

= 61.875 mph - 55 mph

 = 6.875 mph

Therefore, Janeesa needs to drive approximately 6.9 mph faster than the speed limit to make it on time.

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Answer:

Approximately 15.7 ft

Step-by-step explanation:

We want to find the circumference of the circle

C = pi * diameter

C = pi *5

C = 5pi ft or approximately 15.7 ft