x(5x2 - x)
Maaad confused

If OT is the bisector of angle PTR, then PT=RT and ST=TQ, proved.

Since OT is the bisector of angle PTR, we have:

∠PTO = ∠RTO (by definition of angle bisector)

Since O is the centre of the circle, we have:

PO = RO, and

TO = TO (common side)

Therefore, by the triangle congruence criterion ASA (angle-side-angle), we have:

△PTO ≅ △RTO

Hence, we get:

PT = RT (by corresponding parts of congruent triangles)

Now, let us consider the angles of the quadrilateral PQTS:

∠PTQ + ∠STP + ∠TSR + ∠QRS = 360°

Since PT = RT, we have:

∠PTQ = ∠RTS

Also, since OT is the bisector of ∠PTR, we have:

∠STP = ∠STR

Therefore, the above equation becomes:

∠RTS + ∠STR + ∠TSR + ∠QRS = 360°

2∠RTS + 2∠TSR = 360° (since ∠STP = ∠STR)

∠RTS + ∠TSR = 180°

But, ∠RTS = ∠PTQ and ∠TSR = ∠QRS (by vertical angles)

Therefore, we have:

∠PTQ + ∠QRS = 180°

Thus, ST is a diameter of the circle (by the converse of Thales' theorem), and hence:

ST = 2 × radius

Also, since OT is the perpendicular bisector of PT and RT, we have:

OP = OR

Therefore, we get:

TQ = TP, and

TS = TR

Hence, ST = TQ + TS = TP + TR = 2 × PT

Therefore, we have:

TQ = PT, and

ST = 2 × PT

Substituting the value of ST in terms of PT, we get:

TQ = ST/2 = PT

Hence, we have proved that ST = TQ.

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The given statement "The median of a quantitative data set is always one of the individual data values" is false.

When a given data set is arranged in ascending order the observation which at the between of the data is the median of that data set. It is a value in the set whose left and right both have the same number of observations.

The given statement is not true, this is because the median is the mid-value of any data set.

Hence, the given statement "The median of a quantitative data set is always one of the individual data values" is false.

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Answer:

\(A\approx 110.02 \text{ cm}^2\)

\(P \approx 53.31 \text{ cm}\)

Step-by-step explanation:

To find the area of a triangle, we need two dimensions: its base and height.

\(A_\triangle = \dfrac{1}{2}bh\)

To find the base of this triangle, we can apply the trigonometric ratio cosine to the right triangle that is half of larger triangle.

\(\cos(x) = \dfrac{\text{adjacent}}{\text{hypotenuse}}\)

↓ plugging in the given values

\(\cos(39\°) = \dfrac{\dfrac{1}{2}b}{15}\)

↓ multiplying both sides by 15

\(15\cos(39\°) = \dfrac{1}{2}b\)

↓ multiplying both sides by 2

\(30\cos(39\°) = b\)

↓ evaluating using a calculator

\(b\approx 23.31 \text{ cm}\)

To find the height of the triangle, we can apply the Pythagorean Theorem to the right triangle that is half of the larger triangle, now that we know what the base is.

\(a^2 + b^2 = c^2\)

↓ plugging in the relevant values

\(a^2 + \left(\dfrac{1}2\cdot 23.31\right)^2 = 15^2\)

↓ isolating a²

\(a^2 = 225 - 135.89\)

\(a^2 = 89.11\)

↓ taking the square root of both sides

\(a \approx 9.44\)

\(h \approx 9.44\)

Finally, we can find the area of the triangle.

\(A=\dfrac{1}{2}bh\)

\(A=\dfrac{1}2 \cdot 23.31 \cdot 9.44\)

\(\boxed{A\approx 110.02 \text{ cm}^2}\)

We can find the perimeter by adding the lengths of each side.

\(P \approx 15 + 15 + 23.31\)

\(\boxed{P \approx53.31 \text{ cm} }\)

1 gallon of gas for William= 37.76 ÷ 16= 2.36 $

1 gallon of gas for Regina= 14.64 ÷ 6= 2.44 $

so william got a better deal per gallon.

Inferential statistics involves using sample data to make inferences, predictions, or generalizations about a larger population, providing valuable insights and conclusions based on statistical analysis.

The term "inferential statistics" is associated with the task of making inferences or drawing conclusions about a population based on sample data.

In other words, it involves using sample data to make generalizations or predictions about a larger population.

Inferential statistics is concerned with analyzing and interpreting data in a way that allows us to make inferences about the population from which the data is collected.

It goes beyond simply describing the sample and aims to make broader statements or predictions about the population as a whole.

This branch of statistics utilizes various techniques and methodologies to draw conclusions from the sample data, such as hypothesis testing, confidence intervals, and regression analysis.

These techniques involve making assumptions about the underlying population and using statistical tools to estimate parameters, test hypotheses, or predict outcomes.

The goal of inferential statistics is to provide insights into the larger population based on a representative sample.

It allows researchers and analysts to generalize their findings beyond the specific sample and make informed decisions or predictions about the population as a whole.

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Answer:

5.75 miles

Step-by-step explanation:

Answer:

(h, k). (2,0)

All five brothers have a total of $100 combined.

Let's assume Peter's total amount of money is P dollars. We are given that 25% of Peter's money is equal to $5,

so we can set up the equation:

0.25P = 5

To solve for P,

we divide both sides of the equation by 0.25:

P = 5 / 0.25 = 20

Now that we know Peter has $20,

we can find out how much money all five brothers have combined. Since Peter and his four brothers combined their money, the total amount would be:

Total = Peter's money + 4 brothers' money

Total = $20 + 4 x (Peter's money)

Total = $20 + 4 x $20

Total = $20 + $80

Total = $100

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Answer:

ok im telling people to help u because i dont know that xd

Step-by-step explanation:

Answer:

Subtraction property of equality

Step-by-step explanation:

You subtracted c from both sides of the equation to preserve equality

The step 1 is explained by subtraction property of equality.

The correct option is A.

The standard form of Quadratic Equation is

ax² + bx + c = 0

Also, we must remove c from the right side and move it to the left side in order to derive the quadratic formula from the quadratic equation.

And to do that, we must subtract c from both sides, which is

-c = ax² + bx

Then, we have used subtraction property here.

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Answer:

234

Step-by-step explanation:

The consecutive terms of the sequence have a common difference d

d = 17 - 10 = 24 - 17 = 7

This indicates the sequence is arithmetic with n th term

\(a_{n}\) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 10 and d = 7 , thus

\(a_{33}\) = 10 + (32 × 7) = 10 + 224 = 234

An approximate of 4 gaps will be there in one hour that are longer than 6 seconds at the flow rate of 1800 vph.

The flow rate is given to be 1800 vph.

This means that 1800 vehicles pass through the lane every hour.

To determine the number of gaps that are longer than 6 seconds, we need to calculate the time it takes for one vehicle to pass and then subtract it from 60 minutes.

Assuming that the vehicle length is negligible, the gap between two consecutive vehicles is equal to the time taken by one vehicle to pass by completely plus the time taken by the following vehicle to reach the starting position of the preceding vehicle.

Let's say, for example, that the time it takes for one vehicle to pass is 2 seconds.

The gap between two consecutive vehicles would then be 2 + 2 = 4 seconds, meaning that there would be 60/4 = 15 gaps in one minute, or 900 gaps in one hour.  

If we assume that the time it takes for one vehicle to pass is 2 seconds, the total time taken for a vehicle to cover the distance would be 1/1800*60*60= 2 sec.

Hence, 60/2 = 30 vehicles would pass through the lane in one minute.1800 vehicles/60 minutes = 30 vehicles/min

Now, we know that the gap between two consecutive vehicles is 2 seconds, so we can calculate the number of vehicles that pass through the lane in one minute.

30 vehicles/min x 2 sec/vehicle = 60 seconds/min

We can see that there are 60 seconds in a minute.

Thus, the total time taken for a vehicle to pass is 60/1800 = 0.033 minutes.

So, the total number of gaps that are longer than 6 seconds would be:

Number of minutes in an hour = 60.

Number of vehicles that pass through the lane in an hour = 1800.

Time taken for one vehicle to pass = 0.033 minutes.

Therefore, number of gaps = 60 - (1800 x 0.033) / 6 = 4 gaps.

An approximate of 4 gaps will be there in one hour that are longer than 6 seconds.

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Answer:

The cotangent of x is defined to be the cosine of x divided by the sine of x: cot x = cos x sin x . The secant of x is 1 divided by the cosine of x: sec x = 1 cos x , and the cosecant of x is defined to be 1 divided by the sine of x: csc x = 1 sin x . = tan 5π 4

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Step-by-step explanation:

The dimension of the rectangle is 40 inches by 64 inches. Then the area of the rectangle is 2,560 square inches.

Assume L is the length and W is the width. Then the area is given as,

A = L × W

And the perimeter is given as,

P = 2(L + W)

A rectangle has a width-to-height ratio of 8:5. The perimeter of the rectangle is 208 inches. Then the equations are given as,

208 = 2(W + H)

H + W = 104                ...1

H / W = 8 / 5              ....2

From equations 1 and 2, then we have

(8/5)W + W = 104

(13/5)W = 104

W = 40 inches

Then the height is given as,

H = (8/5) x 40

H = 64 inches

Then the area of the rectangle is given as,

A = 40 x 64

A = 2,560 square inches

The dimension of the rectangle is 40 inches by 64 inches. Then the area of the rectangle is 2,560 square inches.

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The expression be written as 4 × -3 = -12, which can be simplified to -3 × 4 = -12. Therefore, the answer for M4 = -12 is -3.

M4 = -12 is an algebraic expression that is asking us to solve for the value of M. To solve, we can start by rewriting the expression as 4 × -3 = -12. This can be simplified to -3 × 4 = -12.Now, it is easier to see that the value of M is -3. This is because when we multiply -3 by 4, we get -12. Since -12 is the same value as the original equation, M must be equal to -3.To summarize, M4 = -12 is an algebraic expression that can be simplified to -3 × 4 = -12. Solving for M, we end up with M = -3. This is because when we multiply -3 by 4, we get -12, which is the same value as the original equation.

M4 = -12

4 × -3 = -12

-3 × 4 = -12

M = -3

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Answer:

Divide

Step-by-step explanation:

When you see something say "how many times larger than __ is __" You will Divide

(e.g. how many times larger is 6 than 3? divide 6 by 3 and you'll find out that 6 is 2 times as large as 3)

Hope this helps!

Times= multiplication

How many times larger means how many times that numner can get multiplied by the smaller number.

Hope it helped! :)

Here, the Laplace transform of f(t) being f(s), the Laplace transform is a technique used to convert a time-domain function, f(t), into a complex frequency-domain function, f(s). The response you're looking for would be the definition of the Laplace transform for positive s values and f(s) otherwise.

The Laplace transform is defined as:
F(s) = L{f(t)} = ∫(e^(-st) * f(t)) dt, from 0 to infinity,
where F(s) is the Laplace transform of f(t), s is a complex variable, and t is the time variable.
For all positive s values, the Laplace transform will exist if the integral converges. Otherwise, the Laplace transform does not exist, and you would use f(s) as given.
In summary, the Laplace transform of f(t) is F(s) for all positive s values when the integral converges, and f(s) otherwise.

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The volume of the candle is approximately 94 cubic inches.

A circular cylinder is a three-dimensional solid object made up of two parallel and congruent circular bases and a curving surface connecting the bases.

The volume of a right circular cylinder is given by the formula:

V = πr²h

Where

Substituting the given values into the formula, we get:

V = 3.14 x 2² x 7.5

V = 3.14 x 4 x 7.5

V = 94.2

Rounding to the nearest cubic inch, we get:

V ≈ 94 cubic inches

Therefore, the volume of the candle is approximately 94 cubic inches.

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The solution to the inequality are the region in the shaded area and the graph is attached

From the question, we have the following parameters that can be used in our computation:

y ≥3(0.8)^x

y ≥ x² - 5

Represent properly

y ≥ 3(0.8)^x

y ≥ x² - 5

Next, we make a plot of the system to determine the solution

The shaded area in the plot represent the solution to the inequality

In this case, one of the coordinates in the shaded area has a coordinate of (0, 5)

None of the options represent the shaded area (see attachment)

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Answer:

3

Step-by-step explanation:

Because Johns friends both got 3 and 5 so he needs a number higher to win i.e 6, 7, 8 so the answer is three.

Second  Option is correct.  

There will be  3 desired outcomes John should use in his probability calculation.

Probability is the measure of the likelihood of occurrence of an event.

An outcome is a possible result of an experimental or trial.

\(P(A) = \frac{number of favorable outcomes }{Total number of outcomes}\)

where,

P(A) is the probability of an event.

According to the given question

we have

sample space = {1,2,3,4,5,6,7,8}

Total number of outcomes = 8

Jhon needs to spin a number higher than both friends in order to win the game

⇒ the numbers must be greater than 5

⇒ the numbers will be 6, 7, 8

therefore,

the total number of favorable outcomes =3.

Hence. there are 3 desired outcomes should John use in his probability calculation.

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Answer:

It is d

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Because the graph intercepts 2 times the x axis

Answer:

A

Step-by-step explanation:

A is a parabola, which is non linear. A linear function will be a straight line that goes infinitely both ways.

Answer:

Step-by-step explanation:

Let m = slope

m = (-14 - 1)/(7 - (-3))

m = (-15)/(7 + 3)

m = -15/10

m = -3/2

Done.

Step-by-step explanation:

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Answer:

Step-by-step explanation:

1)

2)

Correct choice is D

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We can calculate supplementary angles by subtracting the given one angle from 180 degrees. To find the other angle, use the following formula: ∠x = 180° – ∠y or ∠y = 180° – ∠x where ∠x or ∠y is the given angle.

The supplementary of 97° is (180°-97°)=83°

An unnormalized relation refers to a table in a relational database that contains more than one row. This means that there are duplicate rows in the table, which violates the rules of normalization.

Normalization is a process in database design that aims to eliminate data redundancy and ensure data integrity. It involves breaking down a database into multiple tables and defining relationships between them. By doing so, we can efficiently store and retrieve data while minimizing inconsistencies.

In an unnormalized relation, duplicate rows can lead to various problems. For example, it can result in data inconsistencies, as updating one instance of a row may not reflect changes in other duplicate rows. Additionally, it can cause unnecessary storage and maintenance overhead.

To normalize an unnormalized relation, we need to identify the functional dependencies in the table and create separate tables for related data. This helps organize the data and reduces redundancy.

In summary, an unnormalized relation is a table in a relational database that has duplicate rows. It is important to normalize such relations to ensure data integrity and efficiency.

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