y = a(x _ 2)^2 _ 3. :)

There are 56,148 triangles that can be formed by drawing non-intersecting segments among the 34 points in the square.

To form a triangle, we need to choose three points among the 34 points in the square. There are 34C3 = 5984 ways to do this.

However, not all combinations of three points will form a triangle. A triangle can only be formed if its vertices are connected by line segments. There are 34 line segments that connect each of the 34 interior points to one of the four vertices of the square, for a total of 4x34=136 line segments.

Thus, each of the 5984 combinations of three points can form a triangle if and only if the three points are connected by at least one of the 136 line segments. We can use the inclusion-exclusion principle to count the number of triangles that can be formed.

Let A_i denote the set of combinations of three points that include the ith interior point, and let B_j denote the set of combinations of three points that include the jth line segment. Then, the number of triangles that can be formed is

|A_1 ∪ A_2 ∪ A_3 ∪ A_4 ∪ B_1 ∪ B_2 ∪ ... ∪ B_136|,

where |S| denotes the cardinality of set S.

By the inclusion-exclusion principle, this is:

|A_1| + |A_2| + |A_3| + |A_4| + |B_1| + |B_2| + ... + |B_136|

|A_1 ∩ A_2| - |A_1 ∩ A_3| - ... - |A_3 ∩ A_4| - |B_1 ∩ B_2| - ... - |B_135 ∩ B_136|

|A_1 ∩ A_2 ∩ A_3| + |A_1 ∩ A_2 ∩ A_4| + ... + |A_2 ∩ A_3 ∩ A_4| + ... + |B_1 ∩ B_2 ∩ B_3| + ... + |B_134 ∩ B_135 ∩ B_136|

|A_1 ∩ A_2 ∩ A_3 ∩ A_4| - ... - |B_1 ∩ B_2 ∩ ... ∩ B_136|.

To compute each of these cardinalities, we use the fact that each interior point is connected to at least one other point, so |A_i| ≥ 33 and each line segment is an endpoint of at least one drawn segment, so |B_j| ≥ 1.

Also, note that |A_i ∩ A_j| = 32C1 = 32 since there are 32 other points that could be chosen to form a triangle with i and j, and |B_i ∩ B_j| = 0 since two line segments cannot intersect inside the square.

Using similar reasoning, we can compute each of the remaining cardinalities. After doing so, we obtain:

33 x 34C2 + 136 x 33 - 32C2 x 6 - 32C2 x 3 + 32C3 x 4

= 56148.

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The given question is incomplete, the complete question is:

let a_1,a_2, a_3, a_4 be a square, and let a_5,a_6,a_7 .......a_34 be distinct points inside the square. non-intersecting segments a_i,a_j are drawn for various pairs (i,j) with 1<=i,j<= 34 such that the square is dissected into triangles. assume each a_i is an endpoint of at least one of the drawn segments. how many triangles are formed?

For the first parabola, the parts on the curve should be labeled as follows;

The vertex of the parabola are (-1, -2).

The max value is equal to -2.

The axis of symmetry is x = -1.

The zero is non-existent.

The parabola opens downward.

The y-intercept is equal to (0, -4).

In Mathematics and Geometry, the graph of a quadratic function would always form a parabolic curve because it is a u-shaped. Based on the first graph of a quadratic function, we can logically deduce that the graph is a downward parabola because the coefficient of x² is negative and the value of "a" is less than zero (0).

For the second parabola, the parts on the curve should be labeled as follows;

The vertex of the parabola are (0, 0).

The min value is equal to 0.

The axis of symmetry is x = 0.

The zero is 0.

The parabola opens upward.

The y-intercept is equal to (0, 0).

For the third parabola, the parts on the curve should be labeled as follows;

The vertex of the parabola are (2, 1).

The min value is equal to 1.

The axis of symmetry is x = 2.

The zero is non-existent.

The parabola opens upward.

The y-intercept is equal to (0, 5).

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Answer:

yes, because 6 is less than 11

Step-by-step explanation:

Hope this helps!!
Mark me brianliest and good luck!!

When we simplify an equatiοn and end up with a cοntradictiοn like this, it means that the equatiοn has nο sοlutiοn.

The intersectiοns οr meetings οf the lines οr planes that represent the linear equatiοns are knοwn as the sοlutiοns οf linear equatiοns. The set οf values fοr the variables in every feasible sοlutiοn is knοwn as a sοlutiοn set fοr a system οf linear equatiοns.

Nοt a Sοlutiοn

If there is nο intersectiοn οf any lines, οr if the graphs οf the linear equatiοns are parallel, then the system οf linear equatiοns cannοt be sοlved.

The equatiοn 5 + 9z = 9z can be simplified as fοllοws:

5 + 9z = 9z

5 = 0

This is a cοntradictiοn since 5 cannοt be equal tο 0. Therefοre, there is nο sοlutiοn fοr this equatiοn.

In general, when we simplify an equatiοn and end up with a cοntradictiοn like this, it means that the equatiοn has nο sοlutiοn.

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Cartridges come in different sizes and shapes, and the amount of liquid ink

They can hold varies depending on the model and manufacturer.
Of course, I am here to help.

However, to better assist you, I will need more information regarding your urgent situation.
Once I have a better understanding of your situation, I can provide you with a more tailored and effective response.

In the meantime, I recommend taking a few deep breaths and staying calm.

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According to the solution we have come to find that, the ratio of Tony's score to Sayo's score to Adah's score is 4 : 1 : 2.

The smallest equivalent fraction of the integer is the most basic form.

Therefore, the ratio of Tony's score to Sayo's score to Adah's score can be written as:

4S : S : 2S

Simplifying this ratio by dividing each term by the greatest common factor (which is S), we get:

4 : 1 : 2

Therefore, the ratio of Tony's score to Sayo's score to Adah's score is 4 : 1 : 2.

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Answer:

Step-by-step explanation:

well you dont get an answer

Answer:

the answer is B. 38 rounds per hour.

The missing expression that was covered by the drop of ink is simply 3[tex]x^{2}[/tex].

What is Algebraic expression ?

An algebraic expressiοn is a statement in mathematics that can cοntain variables, integers, οperatοrs (including additiοn, subtractiοn, multiplicatiοn, and divisiοn), as well as grοuping symbοls like brackets.

The given expression is:

-24[tex]x^{5}[/tex] - 16[tex]x^{3}[/tex] = -8[tex]x^{3}[/tex] (? + 2)

To find the missing expression, we need to isolate the unknown factor, denoted by the question mark (?). We can begin by factoring out the common term of -8x³ from the left side of the equation:

-8[tex]x^{3}[/tex](3[tex]x^{2}[/tex] + 2) = -8[tex]x^{3}[/tex](? + 2)

Now, we can divide both sides by -8[tex]x^{3}[/tex], which gives:

3[tex]x^{2}[/tex] + 2 = ? + 2

Subtracting 2 from both sides yields:

3[tex]x^{2}[/tex] = ?

Therefore, the missing expression that was covered by the drop of ink is simply 3[tex]x^{2}[/tex].

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Answer:

The ramp will rise 11.6 inches from the ground at its highest end.

11.6 in.

Step-by-step explanation:

In this example we can use the sine function to determine how high the ramp will rise from the ground.

The definition of the sine function is

[tex]\sf \sin x= \dfrac{opposite}{hypotenuse}[/tex]

[tex]\sf \sin x= \dfrac{O}{H}[/tex]

In this case we are looking to evaluate the length of the opposite side.

We can rearrange the equation to isolate [tex]\sf O[/tex].

Multiply both sides of the equation by [tex]\sf H[/tex].

[tex]\sf H \cdot \sin x= \dfrac{O}{H} \cdot H[/tex]

Cancel the common factor of [tex]\sf H[/tex] on the right side leaves us with

[tex]\sf H \cdot \sin x= \dfrac{O}{\diagup \!\!\!\! H} \cdot \diagup \!\!\!\! H[/tex]

[tex]\boxed{\sf O= H \cdot \sin x}[/tex]

Numerical Evaluation

In this example we are given

[tex]\sf x=20\\\sf H=34[/tex]

Substituting our given values into the equation yields

[tex]\sf O= 34\cdot \sin 20[/tex]

[tex]\sf O=11.628685[/tex]

Rounding to the nearest tenth

[tex]\sf O=11.6[/tex]

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The total number of revolutions per minute tire makes when the car is traveling at a speed of 90 mi/hr and the tire has a diameter of 22 inches is equal to approximately 1375.09.

Diameter of a car tire = 22 inches

Speed of a car = 90mi/hr

Let us first convert the speed from miles per hour to inches per minute,

Since the diameter of the tire is given in inches.

90 mi/hr

= 90 × 5280 ft/hr

= 475200 ft/hr

= 475200 × 12 in/hr

= 5,702,400 in/hr

= 95,040 in/min

Number of revolutions the tire makes per minute,

Distance the tire travels in one revolution.

The circumference of a circle is given by,

C = πd

where C is the circumference and d is the diameter.

So the distance the tire travels in one revolution is,

d = π(22 in)

  = 69.115 in

Now, the number of revolutions per minute  is ,

=distance traveled per minute / distance traveled in one revolution

⇒ revolutions per minute = 95,040 in/min / 69.115 in/rev

⇒revolutions per minute ≈ 1375.09 rev/min

Therefore, the tire makes approximately 1375.09 revolutions per minute with tire of diameter of 22 inches.

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As a result, 12 is the exponential expression employing a rational exponent.

An exponent of a fraction or rational number is said to have a rational exponent. With x as the base, p as the power, and q as the root 21, it may be represented as x(p/q). It can be transformed into the corresponding radical form,

for example, x(p/q) = (x(1/q))p = qxp 21. Similar rules apply to rational exponents and integer exponents 1.

With a rational exponent, the expression 3√24 can be expressed exponentially as follows:

3√2⁴= 3(2²)

= 3(2²) = 12

As a result, 12 is the exponential expression employing a rational exponent.

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Step-by-step explanation:

To find the smallest total number of hot dogs that Yadira's mom can purchase, we need to find the least common multiple (LCM) of 12 and 9, since she wants the same number of hot dogs as hot dog buns.

The multiples of 12 are: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, ...

The multiples of 9 are: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, ...

The least common multiple of 12 and 9 is 36, since it is the smallest number that appears in both lists. Therefore, Yadira's mom should purchase 36 hot dogs (3 packs of 12) and 36 hot dog buns (4 packs of 9) for the family barbecue.

The effect of the Rule of 78s when a borrower repays an add-on method loan early may result in higher interest charges and potential prepayment penalties due to the uneven allocation of interest throughout the loan term.

The Rule of 78s is a method used by some lenders to allocate interest charges in add-on method loans, particularly for consumer loans. When a borrower repays an add-on method loan early, the Rule of 78s may affect how the prepayment is handled and the amount of interest charged.

Under the add-on method, the interest is calculated upfront based on the original loan amount and term. With the Rule of 78s, the interest is allocated to the loan payments in a manner that assigns more interest to the earlier payments in the loan term. This means that during the initial period of the loan, the borrower is primarily paying off interest rather than the principal.

When a borrower repays an add-on method loan early, the Rule of 78s may result in a higher amount of interest being charged compared to a simple interest loan. As the early payments have been disproportionately allocated more interest, the borrower may have paid off less of the principal than they would have under a simple interest method. Consequently, the borrower may face a higher prepayment penalty as they have not paid as much towards the principal balance as anticipated.

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Step-by-step explanation:

L X W X D = cubic feet volume

17 X 30 X .25 = 127. 5  ft^3

The distribution of U is 0.8634.

The distribution of for this selection of numbers ~ n is 2.7.

The probability that the average of 39 numbers will be less than 2.7 is 80.69%.

Let X be the random variable that represents the number selected by the computer. Since the computer selects a number from 0 to 5 uniformly, the distribution of X is a discrete uniform distribution. This means that each number from 0 to 5 has an equal probability of being selected, which is 1/6 or approximately 0.1667

Population standard deviation = (5-0)/(12) = 1.4434

Therefore, the standard deviation of the sample mean for a sample size of 39 is:√

Standard deviation of sample mean = 1.4434/√(39) = 0.2319

To calculate the probability that the average of 39 numbers will be less than 2.7, the population mean (in this case, 2.5), σ is the population standard deviation, and n is the sample size.

Using the values we have calculated, we get:

z = (2.7 - 2.5) / (0.2319) = 0.8634

To find the probability of the sample mean being less than 2.7, we need to find the area under the standard normal distribution curve to the left of z = 0.8634.

The distribution of the sample mean for a sample size of 39, and the probability of the average of 39 numbers being less than 2.7.

This can be done using a standard normal distribution table or a calculator that can perform normal distribution calculations. The probability turns out to be approximately 0.8069, or 80.69%.

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The bell tolls 6 times between 11:45 AM and 3:10 PM

To find out how many times the bell tolls between 11:45 AM and 3:10 PM, follow these steps:
1. Identify the first bell toll after 11:45 AM:

The first bell toll occurs at 12:00 PM (noon) since it is the next half hour after 11:45 AM.
2. Identify the last bell toll before 3:10 PM:  

The last bell toll occurs at 3:00 PM since it is the last half hour before 3:10 PM.
3. Calculate the total time between the first and last bell tolls:  

From 12:00 PM to 3:00 PM, there are 3 hours.
4. Determine the number of bell tolls in each hour:

Since the bell tolls every 30 minutes, it tolls 2 times per hour (on the hour and at half past the hour).
5. Calculate the total number of bell tolls:

For 3 hours, the bell tolls 3 hours x 2 tolls per hour = 6 tolls.

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A distribution that includes more vehicles sold at lower prices and may deviate from the initial distribution as a result of the inclusion of vehicles priced under $5,000.

A distribution in statistics is a function that identifies all potential values for a dataset together with their frequencies or probabilities. The normal distribution, the binomial distribution and the Poisson distribution are just a few examples of frequent distribution types. Data are described and analyzed using distributions, which may offer significant insights about a dataset's central tendency, variability, and form.

The distribution will be impacted in a number of ways if the salesperson decides to also offer automobiles that cost less than $5,000 and forecasts selling 200 of them over the next ten years. In particular, it will

Growth in vehicle sales: Over the next 10 years, more vehicles under $5,000 will be sold, increasing the overall vehicle sales.

Change the distribution of prices towards lower values: By selling more automobiles at lower prices, the introduction of more affordable vehicles will change the price distribution towards lower values.

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Answer:

Step-by-step explanation:

Fractions represent a division problem where the numerator is divided by the denominator. For example, the fraction 3/4 represents the division of 3 by 4, which can be written as 3 ÷ 4. This is why it makes sense that fractions are about division.

Furthermore, fractions are used to represent parts of a whole or a group. When we divide a whole into equal parts, we are essentially dividing the whole into groups, with each group having the same size. For example, if we divide a pizza into 8 equal slices, each slice represents 1/8th of the pizza. We can also think of this as dividing the pizza into 8 equal groups, with each group having one slice.

Therefore, fractions are a natural way to represent division, as they allow us to express how many parts we have out of a whole or a group, and how big each part is relative to the whole or group.

The weight of the soccer balls bought by the coach is 40.18 pounds. therefore, option a.40.18 is correct.

To determine the weight of the soccer balls the coach bought, we need

to analyze the given line plot. The line plot shows the weight of each of

the 11 soccer balls bought by the coach.

The first step is to find the scale of the line plot. In this case, the scale is

in pounds, and the plot ranges from 0 to 8 pounds. Each "x" on the plot

represents one soccer ball, and the height of the "x" shows the weight of

that ball in pounds.

To find the total weight of the soccer balls bought by the coach, we

simply need to add up the weights of all the balls. Looking at the line

plot, we can see that there are:

2 balls that weigh 1 pound each

1 ball that weighs 3 pounds

1 ball that weighs 2 pounds

1 ball that weighs 5 pounds

1 ball that weighs 3.7 pounds

1 ball that weighs 8 pounds

2 balls that weigh 4 pounds each

1 ball that weighs 8.48 pounds

Adding all these weights together, we get:

1 + 1 + 3 + 2 + 5 + 3.7 + 8 + 4 + 4 + 8.48 = 40.18 pounds

Therefore, the weight of the soccer balls bought by the coach is 40.18 pounds.

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Question

A soccer couch bought eight soccer balls. This line plot shows the weight of each ball the couch bought?

what is the total weight, in pounds, of all the soccer balls the coach bought?                                                                                            

a. 40.18    b. 60  c. 30    d. 20

The percent increase in the annual student fees at the University of California between 2000 and 2014 is 125%.

What is percentage?

Percentage is a way of expressing a number or proportion as a fraction of 100. It is represented by the symbol "%".

To find the percent increase, we need to calculate the difference between the two amounts and then divide that difference by the original amount, and finally multiply by 100 to express the result as a percentage.

The difference between the final amount ($9,000) and the initial amount ($4,000) is $5,000.

So the percent increase can be calculated as follows:

Percent increase = (difference / original amount) x 100%

= ($5,000 / $4,000) x 100%

= 125%

Therefore, the percent increase in the annual student fees at the University of California between 2000 and 2014 is 125%.

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If the test is normally distributed, then the probability of a score greater than 115 is (a) 1.62%.

In order to find probability of a score greater than 115 in a normally distributed test with a mean of 100 and standard deviation of 7,

First, We have to calculate z-score for 115, and

The z-score formula is ⇒ z = (x - μ)/σ,

where x = score of interest, μ = mean, and σ = standard-deviation.

In this case, we have x = 115, μ = 100, and σ = 7.

The z-score for 115 is ⇒ z = (115 - 100)/7 = 2.14

By using the normal table :

⇒ P(Z > 2.14) = 0.0162

Therefore, the required probability is 0.0162 or 1.62%, the correct option is (a) 1.62%.

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The given question is incomplete , the complete question is

Assume a normally distributed test has a mean of 100 and standard deviation of 7. What probability of a score greater than 115?

(a) 1.62%

(b) 48.38%

(c) 98.38%

(d) 51.62%

Answer:

The expressions 10³÷10⁷, 10¹²/10¹⁶, and 10⁻²/10² are all equivalent to 10⁻⁴.

Step-by-step explanation:

When dividing exponents with the same base you subtract the exponents.

For visuals, in the equation 10³÷10⁷ it would be 10³⁻⁷ which would be 10⁻⁴ since 3 minus 7 is negative 4.

It is the same thing for 10¹²/10¹⁶, it would be 10¹²⁻¹⁶ which is equal to 10⁻⁴.

The same method can be used for 10⁻²/10² (10⁻²⁻²).

Sean would choose apples over pears if he were offered both, based on his preference order of apples > clementines > pears and the assumption that his preferences are transitive.

Sean's preference order for fruits is: apples > clementines > pears. As a rational decision-maker, Sean would choose the option that he prefers the most. In this case, since he prefers apples over clementines and pears, if he were offered pears or apples, he would choose apples.

This decision is based on the assumption that Sean's preferences are transitive, meaning that if he prefers A to B and B to C, then he would prefer A to C. Therefore, choosing apples over pears is the most rational decision for Sean, based on his given preference order.

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A. The two types of transformations that can be used to transform f(x) to g(x) are translation and reflection.

B. The value for k in the transformation is -6.

C. The equation for transforming is g (x) = f (x) - 6.

What is transformation?

Shapes on a coordinate plane can be translated, rotated, and reflected using transformations. You can rotate, translate, or reflect any line, point, or vector.

A. The two types of transformations that can be used to transform f(x) to g(x) are translation and reflection.

Translation means shifting the graph left, right, up or down.

Reflection means creating a mirror image over x - axis or y - axis.

B. Both the transformations will have the same k value.

The graph g (x) is the translation of f (x) towards left with 6 units.

So, the value of k is -6.

C. The equation for transformation is as follows:

⇒ g (x) = f (x) + k

⇒ g (x) = f (x) - 6

Hence, the required solutions have been obtained.

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Answer:

31

Step-by-step explanation:

Answer:

x = 19, ARC MP = 104º

Step-by-step explanation:

9x-43 = 5x+33

4x = 76

x = 19

Arc MP = 360 - (9x-43 + 5x+33)

Arc MP = 360 - (9(19)-43 + 5(19)+33)

= 360 - 256

MP = 104º

Answer: 35.553

Step-by-step explanation: