the length of a rectangle is 3 in longer than its width. if the perimeter of the rectangle is 50 in, find its length and widths​

Answers

Answer 1

First, re-read the problem until you understand it and can put it into your own words.  I re-wrote it like this:  "Find the area of a rectangle by first finding the length (L) and the width (W)."   [note that I added "find L and W," but that is how I'm going to solve the problem;  I could also have said that we will need the formulas, P=2L+2W and A=LW, but you knew that already, right?).

Translate the problem:

 "The length of a rectangle is 3 ft longer than its width"      means

         L                             =    3             +         W                 (eq1)

 "the perimeter of the rectangle is 30 ft"     means

            P                                = 50                      (eq2)

So, now the math is easy, just find L and W so we can compute the area:

     P = 50 = 2L + 2W                         (eq3; from eq2 and the formula for P)

          50 = 2(3+W)  +  2W              (use eq1 to substitute for L)

          50 = 6 + 2W   + 2W              (distribute)

           50 = 6 + 4W                       (collect terms)

            44 = 4W                        (subtract 6 from both sides)

            11 ft = W                        (divide both sides by 4)

Use the easiest equation (either eq1 or else eq3) to find L:

          L = 3 + W        (eq1)

          L = 3 + 11

         L = 14 ft

What is the area (A)?

          A = L*W

          A = (14 ft) x (11 ft)

          A = 154 sq ft


Related Questions

Which of the following are the first four nonzero terms of the Maclaurin series for the function g defined by g (x) = (1+x)e-* ? A 1 + 2x + 3x2 + x3 + ... B 1+ 2x + 3 x2 + x3 + ... с 1-222 + x3 – 124 + ... D 1 - 3x2 + 3x3 – 6:24 + ...

Answers

Let x₁ and x₂ be two independent random variabIes, each with a mean of 10 and a variance of 5.y has a mean of 203 and a variance of 85.

What is function ?

A function, in mathematics, is a reIationship between a set of possibIe inputs and an equaIIy IikeIy set of outputs, where each input is associated to exactIy one outcome. Functions are commonIy represented as equations or graphs, and they are used to modeI many reaI-worId processes in domains such as physics, engineering, and economics.

Function types incIude Iinear, quadratic, trigonometric, and exponentiaI functions, among others. CaIcuIus, a fieId of mathematics that investigates how quantities change over time or space, heaviIy reIies on functions.

given

The foIIowing is the MacIaurin series for the function g(x) = (1+x)e(-x):

g(x) = ∑[n=0 to ∞] ((-1)ⁿ*xⁿ) / n!

We may simpIify and pIug in the first few vaIues of n to determine the first four nonzero terms of this series:

n = 0: ((-1)⁰*x⁰) / 0! = 1

n = 1: ((-1)¹*x¹) / 1! = -x

n = 2: ((-1)²*x²) / 2! = x²/2

n = 3: ((-1)³*x³) / 3! = -x³/6

The MacIaurin series for g(x) therefore has the foIIowing first four nonzero terms:

1 - x + x²/2 - x³/6

Let x₁ and x₂ be two independent random variabIes, each with a mean of 10 and a variance of 5.  y has a mean of 203 and a variance of 85.

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NEED HELP DUE TODAY!!!! GIVE GOOD ANSWERS PLEASE!!!!
2. How do the sizes of the circles compare?





3. Are triangles ABC and DEF similar? Explain your reasoning.

4. How can you use the coordinates of A to find the coordinates of D?

Answers

When the radius of circle 2 is twice the radius of circle 1, the size of circle 2 is larger than circle 1.

What is triangle?

In geometry, a triangle is a polygon with three sides and three angles. The sum of the angles in a triangle is always 180 degrees. Triangles are one of the most basic and fundamental shapes in geometry and are used in many mathematical and real-world applications, such as in architecture, engineering, and physics. There are different types of triangles based on the length of their sides and the measures of their angles, such as equilateral triangles, isosceles triangles, scalene triangles, acute triangles, obtuse triangles, and right triangles.

Here,

2. This is because the circumference and area of a circle are directly proportional to the radius.

3. To determine if triangles ABC and DEF are similar, we need to check if their corresponding angles are congruent and if their corresponding sides are in proportion. From the diagram, we can see that angle A is congruent to angle D, angle B is congruent to angle E, and angle C is congruent to angle F. This satisfies the angle-angle (AA) similarity criterion. Additionally, we can use the side-side-side (SSS) similarity criterion to determine if the corresponding sides are in proportion. From the diagram, we can see that side AB is parallel to side DE, side AC is parallel to side DF, and side BC is parallel to side EF. Therefore, we can conclude that triangles ABC and DEF are similar.

4. To find the coordinates of D using the coordinates of A, we need to determine the translation from A to D. From the diagram, we can see that A is translated two units to the right and three units down to get to D. Therefore, we can find the coordinates of D by adding two to the x-coordinate of A and subtracting three from the y-coordinate of A. If the coordinates of A are (x1, y1), then the coordinates of D would be (x1 + 2, y1 - 3).

A= (-0.87,0.5)

D=(-0.87 + 2, 0.5 - 3)

D=(1.13,-2.5)

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Use the unique factorization theorem to write the following integers in standard factored form. (a) 756 2^2.3^3.7. (b) 819 3^2.7.11 (c) 9,075 3^2.5^2.7

Answers

The factorizations of these integers above represent their factorizations into their respective prime numbers.

(a) 756 = 2^2.3^3.7, (b) 819 = 3^2.7.11, (c) 9,075 = 3^2.5^2.7The unique factorization theorem refers to an essential theorem in standard algebraic theory that characterizes the unique factorization properties of integers. Standard factored form, on the other hand, refers to an expression in which an integer is factored into its standard, irreducible components.In view of this, the three provided integers, 756, 819, and 9,075 can be factored as follows:756 = 2^2.3^3.7 (in standard factored form)819 = 3^2.7.11 (in standard factored form)9,075 = 3^2.5^2.7 (in standard factored form)Note that the factorizations of these integers above represent their factorizations into their respective prime numbers.

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if you flipped a fair coin 40 times, what is the heoretical proportion of heads? in other words, what percent do you expect to come up heads> based on your confidence interval, do yuou think thje copi used was fair? wy or why not

Answers

A fair coin is flipped 40 times. The probability of getting a head when the coin is tossed is 0.5. If the same coin is flipped 40 times, the probability will remain 0.5. That is, there are equal chances of getting heads and tails when a fair coin is flipped.

Based on the confidence interval, if the actual proportion of heads falls within the range of the confidence interval, it can be said that the coin used was fair. If the actual proportion is outside the confidence interval, it may be an indication that the coin was not fair.

The level of confidence is typically 95% or 99%. If a confidence interval is constructed for the proportion of heads based on a sample of 40 flips and the interval includes the expected proportion of 50%, it can be said that the coin used was fair. If the interval does not include 50%, there is evidence that the coin may not be fair.

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Thabang save money by putting coins in a money box. The money box has 600 coins that consist of 20 cents and 50 cents
So calculate how many 50 cents pieces are in the container if there are 220 pieces of 20 cents

Answers

The number of 50 cents in the container is 380 fifty cents

How to find the number of 50 cents in the container?

Since Thabang save money by putting coins in a money box. The money box has 600 coins that consist of 20 cents and 50 cents

To calculate how many 50 cents pieces are in the container if there are 220 pieces of 20 cents, we proceed as follows.

Let

x = number of 20 cents and y = number of 50 cents

Since the total number of cents in the container is 600, we have that

x + y = 600

So, making y subject of the formula, we have that

y = 600 - x

Since x = 220

y = 600 - 220

= 380

So, there are 380 fifty cents

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What is the value of x? X = X-38° O X X-33°​

Answers

Answer:

Step-by-step explanation:

Un número tiene 8 divisores. Además, cada uno de la mitad y la tercera parte de él tienen cuatro divisores. Si la suma de todos los divisores del número es 216, obtén tal número

Answers

The number we are looking for is N = 2 × 2^3 × 3^2 = 72.

Let's first recall some properties of the number of divisors of an integer. If we factorize an integer n as a product of prime powers, say

n = p_1^a_1 × p_2^a_2 × ... × p_k^a_k

then the number of divisors of n is given by

d(n) = (a_1 + 1) × (a_2 + 1) × ... × (a_k + 1).

Using this fact, we can deduce some information about the number we are looking for. Let's call it N. We know that N has 8 divisors, so it must be of the form

N = p_1^2 × p_2^2, or N = p_1^7,

where p_1 and p_2 are distinct prime numbers.

Now, we are told that each of N/2 and N/3 has four divisors. We can use the same fact about the number of divisors to conclude that

N/2 = q_1^3 × q_2, or N/2 = q_1^1 × q_2^3,

and

N/3 = r_1^3 × r_2, or N/3 = r_1^1 × r_2^3,

where q_1, q_2, r_1, and r_2 are distinct prime numbers.

To simplify the notation, let's introduce the variables a, b, c, d, e, and f, defined by

p_1 = q_1^a × q_2^b,

p_2 = r_1^c × r_2^d,

N/2 = q_1^e × q_2^f,

N/3 = r_1^g × r_2^h.

Using the information we have so far, we can write down equations for a, b, c, d, e, f, g, and h in terms of unknown exponents:

a + 1 × (b + 1) = e + 1 × (f + 1) = 4,

c + 1 × (d + 1) = g + 1 × (h + 1) = 4,

2a × 2b = ef,

2c × 2d = gh.

We can solve this system of equations by trial and error. For example, we can start by trying all possible values of a and b such that 2a × 2b = 4. This gives us two possibilities: a = 0, b = 2, or a = 1, b = 1. Using the first possibility, we get e = 3, f = 1, which leads to N/2 = q_1^3 × q_2, and hence N = 2 × q_1^3 × q_2^2. Substituting this into the equation for the sum of divisors, we get

(1 + q_1 + q_1^2 + q_1^3) × (1 + q_2 + q_2^2) = 216.

We can solve this equation by trial and error as well, or by observing that 216 = 2^3 × 3^3, and hence the two factors on the left-hand side must be equal to 2^3 and 3^3, respectively. This gives us the unique solution q_1 = 2 and q_2 = 3, and hence N = 2 × 2^3 × 3^2 = 72.

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A company finds that if it charges x dollars for a cell phone, it can expect to sell 1,000−2x phones. The company uses the function r defined by r(x)=x⋅(1,000−2x) to model the expected revenue, in dollars, from selling cell phones at x dollars each. At what price should the company sell their phones to get the maximum revenue? x i tercept

Answers

The company should sell their phones for $250 each to get the maximum revenue.

What do you mean by maximum revenue?

Maximum revenue refers to the highest possible amount of income that can be generated from a particular product or service. In the context of the given problem, it means finding the price at which the company can sell its cell phones to earn the highest amount of revenue.

Finding the price at which the company should sell their phones to get the maximum revenue:

We need to find the vertex of the parabolic function [tex]r(x)=x(1,000-2x)[/tex], which represents the revenue as a function of the selling price.

To find the vertex of the function r(x), we need to first rewrite it in standard form by expanding the product:

[tex]r(x) = 1000x - 2x^2[/tex]

Now we can see that the function is a quadratic polynomial in standard form, with [tex]a=-2, b=1000[/tex], and [tex]c=0[/tex]. To find the x-coordinate of the vertex, we can use the formula:

[tex]x = -b / (2a)[/tex]

Substituting the values of a and b, we get:

[tex]x = -1000 / (2\times(-2)) = 250[/tex]

Therefore, the company should sell their phones for $250 each to get the maximum revenue. To find the maximum revenue, we can substitute this value of x into the function r(x):

[tex]r(250) = 250\times(1000-2\times250) = $125,000[/tex]

So the maximum revenue the company can expect to earn is $125,000 if they sell their phones for $250 each.



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a teacher monitored the number of people texting during class each day and calculated the corresponding probability distribution. what type of probability distribution did the teacher use?

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The given probability distribution "a teacher monitored the number of people texting during class each day and calculated the corresponding probability distribution." is a type of discrete probability distribution.

What is the Probability distribution?

The probability distribution is used to describe the probability of each outcome in a series of possible outcomes. It is a mathematical representation of the outcomes of an experiment.

The teacher likely used a discrete probability distribution to calculate the probability of a certain number of people texting during class each day.

A discrete probability distribution is used to analyze data where the outcome is counted in whole numbers, such as the number of people texting in a given class period.

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James has 27 metres of red wire and 12 metres
of black wire. He needs to cut both wires into
smaller pieces so that all of the smaller pieces are
the same length and there is no wire left over. The
length of each piece must be a whole number of
metres.
What is the longest he can make each smaller
piece of wire? Give your answer in metres (m).

Answers

Answer:

3m

Step-by-step explanation:

red wire = 27

black wire= 12

so, we take HCF (highest common factor)

which would be 3 so all the wires would be cut into 3m long.

I hope it helps.

Answer:2m

Step-by-step explanation:

as the factors of 12 are:1, 2, 3, 4, 6 and 12

and the factors of 26 are:1, 2, 13 and 26

so if you are talking meters 2 would be the longest

i hope you get this right x

Please help I will give brainliest

Answers

The point that partitions segment AB in a 1:4 ratio is (-1/2, -1).

What is Segment?

In geometry, a segment is a part of a line that has two endpoints. It can be thought of as a portion of a straight line that is bounded by two distinct points, called endpoints. A segment has a length, which is the distance between its endpoints. It is usually denoted by a line segment between its two endpoints, such as AB, where A and B are the endpoints. A segment is different from a line, which extends infinitely in both directions, while a segment has a finite length between its two endpoints.

To find the point that partitions segment AB in a 1:4 ratio, we need to use the midpoint formula to find the coordinates of the point that is one-fourth of the distance from point A to point B. The midpoint formula is:

((x1 + x2)/2, (y1 + y2)/2)

where (x1, y1) and (x2, y2) are the coordinates of the two endpoints of the segment.

So, let's first find the coordinates of the midpoint of segment AB:

Midpoint = ((-3 + 7)/2, (2 - 10)/2)

= (2, -4)

Now, to find the point that partitions segment AB in a 1:4 ratio, we need to find the coordinates of a point that is one-fourth of the distance from point A to the midpoint. We can use the midpoint formula again, this time using point A and the midpoint:

((x1 + x2)/2, (y1 + y2)/2) = ((-3 + 2)/2, (2 - 4)/2)

= (-1/2, -1)

So, the point that partitions segment AB in a 1:4 ratio is (-1/2, -1).

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Can 3 feet, 3 feet and 7 feet create a triangle explain why or why not

Answers

The given lengths of 3 feet, 3 feet, and 7 feet cannot form a triangle because they do not satisfy the Triangle Inequality Theorem, which is the sum of the lengths of any two sides is greater than the length of the third side.

To form a triangle, the sum of the lengths of any two sides of the triangle must be greater than the length of the third side. This is known as the Triangle Inequality Theorem.

Let's apply this theorem to the given lengths of 3 feet, 3 feet, and 7 feet:

The sum of the first two sides is 3 + 3 = 6 feet, which is less than the length of the third side of 7 feet. So, the first two sides cannot form a triangle.

The sum of the first and third sides is 3 + 7 = 10 feet, which is greater than the length of the second side of 3 feet. However, the sum of the second and third sides is 3 + 7 = 10 feet, which is also greater than the length of the first side of 3 feet.

Therefore, neither of the two combinations of sides satisfy the Triangle Inequality Theorem, and so it is impossible to form a triangle with sides of 3 feet, 3 feet, and 7 feet.

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Imagine that 3 committee members arrive late. The other 5 memebers have already shaken hands. How many handshakes will there be when the 3 late members arrive?

Answers

There will be a total of 28 handshakes when the 3 late members arrive.

What is sum of n positive integers?

The first n-1 positive integers are added together using the formula n(n-1)/2, where n is the total number of terms being added together.

The number of combinations or arrangements of a given collection of items may be determined using this formula, which can be obtained using the process of mathematical induction. It is often used in combinatorics and discrete mathematics. For instance, the formula was used to determine how many times a group of individuals shook hands in the scenario above. It might also be used to determine the number of pathways in a network of nodes or vertices or the number of ways to choose a portion of an object set from a bigger set in other settings.

Given that, 3 members arrive late, and 5 members are already present.

The total members are 5 + 3 = 8.

Now, using the sum of positive integer formula:

n(n-1)/2

We can determine the number of handshakes.

8(8-1)/2 = 28

Hence, there will be a total of 28 handshakes when the 3 late members arrive.

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Translate Into a equation!
The sum of 7 times a number and 6 is 3

Answers

Step-by-step explanation:

x is the number.

the equation is

7x + 6 = 3

I NEED HELP ON THIS ASAP!! IT's DUE TODAY, I'LL GIVE BRAINLIEST!

Answers

Answer:

Let's start by defining our variables:

Let x be the number of mahogany boards sold.Let y be the number of black walnut boards sold.

Now, let's write the system of inequalities to represent the constraints:

The company has 260 boards of mahogany, so x ≤ 260.

The company has 320 boards of black walnut, so y ≤ 320.

The company expects to sell at most 380 boards, so x + y ≤ 380.

We cannot sell a negative number of boards, so x ≥ 0 and y ≥ 0.

Graphically, these constraints represent a feasible region in the first quadrant of the xy-plane bounded by the lines x = 260, y = 320, and x + y = 380, as well as the x and y axes.

To maximize profit, we need to write a function that represents the objective. The profit for selling one board of mahogany is $20, and the profit for selling one board of black walnut is $6. Therefore, the total profit P can be calculated as:

P = 20x + 6y

To maximize P, we need to find the values of x and y that satisfy the constraints and make P as large as possible. This is an optimization problem that can be solved using linear programming techniques.

The solution to this problem can be found by graphing the feasible region and identifying the corner point that maximizes the objective function P. However, since we cannot draw a graph here, we will use a table of values to find the maximum profit.

Let's consider the corner points of the feasible region:

Corner point (0, 0):

P = 20(0) + 6(0) = 0

Corner point (260, 0):

P = 20(260) + 6(0) = 5200

Corner point (0, 320):

P = 20(0) + 6(320) = 1920

Corner point (100, 280):

P = 20(100) + 6(280) = 3160

Corner point (200, 180):

P = 20(200) + 6(180) = 5520

Corner point (380, 0):

P = 20(380) + 6(0) = 7600

The maximum profit is $7600, which occurs when the company sells 380 boards of wood, all of which are mahogany.

rotate M(-3,5) to 270 degrees

Answers

Answer:

Clockwise it would be (3,-5)

Step-by-step explanation:

Counterclockwise it would be (-3,-5)


hope this helps!

solve for x and graph the solution on the number line below

Answers

We can graph this solution on the number line by placing a point at 7.6.

What is graph ?

Graphs are visual representations of data or information. They are used to show relationships between different pieces of data and display numerical data in a more meaningful way. Graphs are made up of individual elements called nodes which are connected by edges. Nodes represent individual data points or pieces of information. Edges represent the relationship between two nodes and can represent either a physical or a logical link. Graphs can be used to represent many different types of data or information, such as social networks, transportation networks, and even biological relationships. Graphs are a powerful tool for understanding complex data sets, making them an essential tool for data analysis.

80∠ 10x + 4 = 20

80 10x + 4 = 20

80 - 4 = 10x

76 = 10x

7.6 = x

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We can graph this solution on the number line by placing a point at 7.6.

What is graph ?

Graphs are visual representations of data or information. They are used to show relationships between different pieces of data and display numerical data in a more meaningful way. Graphs are made up of individual elements called nodes which are connected by edges. Nodes represent individual data points or pieces of information. Edges represent the relationship between two nodes and can represent either a physical or a logical link. Graphs can be used to represent many different types of data or information, such as social networks, transportation networks, and even biological relationships. Graphs are a powerful tool for understanding complex data sets, making them an essential tool for data analysis.

80∠ 10x + 4 = 20
80 10x + 4 = 20
80 - 4 = 10x
76 = 10x
7.6 = x

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CONNAIS TU LES LIMITES ?

Answers

Answer:

yes

Step-by-step explanation:

please ive been on this question for a week

Answers

The times by 43 which equals 67
X=67cm

Binomial Problem:A jury has 12 jurors. A vote of at least 10 out of 12 for "guilty" is necessary for a defendant to be convicted of a crime. Assume that each juror acts independently of the others and that the probability that any one juror makes the correct decision on a defendant is .80. If the defendeant is guitly, what is the probability that the jury makes the correct decision?

Answers

The probability that the jury makes the correct decision is approximately 0.7063.

To solve this problem, we need to find the probability that the jury makes the correct decision if the defendant is guilty. Let's break down the problem into smaller steps.

We know that the probability of a single juror making the correct decision is 0.80. If the defendant is guilty, then the probability of a juror making the correct decision is still 0.80. Therefore, the probability that a single juror makes the correct decision if the defendant is guilty is 0.80.

We can use the binomial distribution formula to determine the probability of at least 10 out of 12 jurors making the correct decision. The formula is:

P(X ≥ k) = 1 - Σ(i=0 to k-1) [n!/(i!(n-i)!) x [tex]p^i \times (1-p)^{(n-i)}[/tex] ]

where:

P(X ≥ k) is the probability of at least k successes

n is the total number of trials (in this case, 12 jurors)

p is the probability of success in a single trial (in this case, 0.80)

k is the number of successes we want to find the probability of (in this case, 10)

Plugging in the values, we get:

P(X ≥ 10) = 1 - Σ(i=0 to 9) [12!/(i!(12-i)!) x [tex]0.80^i \times (1-0.80)^{(12-i)}[/tex]]

Using a calculator or software, we can calculate this to be approximately 0.7063.

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Need help with b, please show work

Answers

Step-by-step explanation:

remember, the sum of all angles in a triangle is always 180°.

the law of sine :

a/sin(A) = b/sin(B) = c/sin(C)

with a, b, c being the sides, and A, B, C being the three corresponding opposite angles.

so, the angle at Q is

180 = 48 + 48 + angle Q = 96 + angle Q

84° = angle Q

5mm/sin(48) = PR/sin(84)

PR = 5×sin(84)/sin(48) = 6.691306064... mm

The length of PR is approximately 10.33 mm.

what is isosceles triangle ?

An isosceles triangle is a triangle with at least two sides that have equal length, and thus two corresponding angles that are also equal in measure. The third side and angle of an isosceles triangle may or may not be of different length or measure. The two sides that are equal in length are called the legs, and the third side is called the base. The angle opposite the base is called the vertex angle, while the angles adjacent to the legs are called the base angles. In an isosceles triangle, the two base angles are equal in measure.

Since the sum of the angles in a triangle is 180 degrees, we can find the measure of angle PQR as follows:

PQR = 180 - QPR - QRP

PQR = 180 - 48 - 48

PQR = 84 degrees

Since angles QRP and QPR have the same measure, we know that sides OP and OR have equal length (they are opposite those angles). Therefore, triangle POR is an isosceles triangle.

To find the length of PR, we can use the Law of Cosines:

PR^2 = OP^2 + OR^2 - 2(OP)(OR)cos(POR)

Since OP and OR are equal in length, we can simplify this equation to:

PR^2 = 2(OP^2) - 2(OP^2)cos(POR)

We know that POR is 180 - PQR = 96 degrees. We also know that OP = OR, and that QP = 5 mm. Using the Law of Cosines, we can find the length of OP:

OP^2 = QP^2 + OR^2 - 2(QP)(OR)cos(QPR)

OP^2 = 5^2 + OR^2 - 2(5)(OR)cos(48)

OP^2 = OR^2 - 5ORcos(48) + 25

Since OP = OR, we can substitute OP for OR in the above equation:

OP^2 = OP^2 - 5OPcos(48) + 25

5OPcos(48) = 25

OP = 25/(5cos(48))

OP ≈ 6.25 mm

Now we can substitute this value into the equation we derived earlier to find PR:

PR^2 = 2(OP^2) - 2(OP^2)cos(POR)

PR^2 = 2(6.25^2) - 2(6.25^2)cos(96)

PR ≈ 10.33 mm

Therefore, the length of PR is approximately 10.33 mm.  

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Please help it is due tomorrow

Answers

Answer: 30

Step-by-step explanation: So what you do is,

1) Add the 25 to the 8

2) Find the sum

3) Subtract 3 from the sum

4) Done!

I hope this helps!

Best,

Abigail H

8th Grade

1) Add the 25 to the 8
2) Find the sum
3) Subtract 3 from the sum
4) Done!
I hope this helps!
Best,

ratings services measure television audiences. the measurement of the percentage of all households with televisions that are tuned into the same show at the same time is called

Answers

Therefore , the solution of the given problem of percentage comes out to be were tuned in to a specific program or show at a given moment.

What is percentage?

A number or figure stated as a fraction of 100 is referred to as "a%" in statistics. The versions that begin with "pct," "pct," and "pc" are also uncommon. The common way to indicate it is with the numeral "%," though. Furthermore, there are no indicators and a flat ratio of every single thing to the total number. Percentages are basically integers because they frequently add up to 100.

Here,

The TV ratings, also known as the TV audience share, are a measurement of the proportion of all television-owning households that are watching the same program at the same moment.

Networks and marketers use it as a gauge of a TV show's popularity to decide how successful a program will be and how much to charge for advertising during it.

Companies like Nielsen, which use a sample of homes with televisions to estimate the audience size for a given program or show, are usually in charge of gathering the TV ratings.

TV ratings are expressed as a proportion of all households with televisions that were tuned in to a specific program or show at a given moment.

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a random variable x has the following probability distribution. values of x -1 0 1 probability 0.3 0.4 0.3 (a) calculate the mean of x.

Answers

The mean (also called the arithmetic mean or average) is a measure of central tendency that represents the typical or average value of a set of data. The mean is calculated by summing up all the values in the data set and dividing by the number of values.

The mean of x is calculated by the following formula:

mean of x = ∑(x * P(x))

Where, ∑ = Summation operator

            x = Value of random variable  

            P(x) = Probability of the corresponding value of x.

Let's calculate the mean of x using the formula provided above.

mean of x = (-1 × 0.3) + (0 × 0.4) + (1 × 0.3)

                = -0.3 + 0 + 0.3  

                = 0

Therefore, the mean of x is 0.

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you are dealt one card from a standard 52-card deck. playing cards find the probability of being dealt a three and an ace. the probability of being dealt a three and an ace is . (type an integer or a fraction.)

Answers

The probability of getting an ace and a three is (4/52) × (3/51) = 12/2652 which simplifies to 1/221.

There are 4 aces and 4 threes in a deck of 52 standard cards.

The probability of getting an ace on your first draw is 4/52.

Once you have the ace, there are 51 cards left in the deck, 3 of which are threes.

Therefore, the probability of drawing a three is 3/51.

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Consider the function f (x, y) = xy - 7y - 49x + 343 on the region on or above y = x^2 and on or below y = 50. Find the absolute minimum value: -7 Find the points at which the absolute minimum value is attained. List your answer sas points in the form (a, b). (0, 50) Find the absolute maximum value: 343 Find the points at which the absolute maximum value is attained. List your answers as points in the form (a, b) (0, 0).

Answers

The absolute maximum value is attained: (0, 0)

The given function is, f(x, y) = xy - 7y - 49x + 343The region is on or above y = x^2 and on or below y = 50. To find the absolute minimum and absolute maximum value of the function, f(x, y), first we will find the critical points of the function.f(x, y) = xy - 7y - 49x + 343 ⇒ ∂f/∂x = y - 49 = 0 ⇒ y = 49 ⇒ ∂f/∂y = x - 7 = 0 ⇒ x = 7Thus, the critical point is (7, 49).Next, we will check for the boundary points. The boundary of the region is y = x^2 and y = 50. The points of intersection are:x^2 = 50 ⇒ x = ±√50 (not in the region)x = ±1.58 ⇒ y = x^2 = 2.50 (not in the region)Also, x = 0 ⇒ y = 0, and x = 0 ⇒ y = 50Thus, the critical points are (7, 49) and (0, 0).f(7, 49) = 7(49) - 7(49) - 49(7) + 343 = -7f(0, 0) = 0 - 7(0) - 49(0) + 343 = 343f(0, 50) = 0 - 7(50) - 49(0) + 343 = -357f(±1.58, 2.50) = ±1.58(2.50) - 7(2.50) - 49(±1.58) + 343 = ∓36.97The absolute minimum value is -7. The points at which the absolute minimum value is attained are (7, 49) and (0, 50).The absolute maximum value is 343. The point at which the absolute maximum value is attained is (0, 0).Hence, the required points are as follows:Points at which the absolute minimum value is attained: (7, 49) and (0, 50)Points at which the absolute maximum value is attained: (0, 0)

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Each section of the graphic organizer contains a vocabulary term or the possible
solution type for the system shown. Use the list below to complete the graphic
organizer. Some terms may be used more than once.
slope y-intercept linear equations
infinitely many solutions no solution one solution
System of
y= 3x+ 2
y= - 4x+ 2
Different
y= 2x+ 7
y= 2x- 4
Same
y= 6x+ 3
y= - x- 4
Number of solutions:
y= 4x+ 3
y= 4x- 1
Different
y= 3x+ 6
y= 3x+ 6
Same
y= 4x+ 3
y= 4x- 1
Number of solutions:
y= 3x+ 6
y= 3x+ 6
Number of solutions:

Answers

For the first equation with y = 3x + 2 and y = -4x + 2, the lines have the same slope, but a different y-intercept. This means that the lines are parallel and they will never intersect. Therefore, the system of equations has no solution.

For the second equation with y = 2x + 7 and y = 2x - 4, the lines have the same slope and the same y-intercept. This means that the lines are coincident and they will intersect at one point. Therefore, the system of equations has one solution.

For the third equation with y = 6x + 3 and y = -x - 4, the lines have a different slope and a different y-intercept. This means that the lines are not parallel and they will intersect at one point. Therefore, the system of equations has one solution.

For the fourth equation with y = 4x + 3 and y = 4x - 1, the lines have the same slope and the same y-intercept. This means that the lines are coincident and they will intersect at one point. Therefore, the system of equations has one solution.

For the fifth equation with y = 3x + 6 and y = 3x + 6, the lines have the same slope and the same y-intercept. This means that the lines are coincident and they will intersect at one point. Therefore, the system of equations

One characteristic of all exponential functions is that they change by

Answers

One characteristic of all exponential functions is that they change by a constant factor at each step, which means that they exhibit exponential growth or decay.

The constant factor by which an exponential function changes is called the base, which is usually denoted by the symbol "b". If b is greater than 1, the function exhibits exponential growth, and if b is between 0 and 1, the function exhibits exponential decay.

For example, the function f(x) = 2^x is an exponential function with a base of 2. At each step, the function increases by a factor of 2. For instance, f(0) = 1, f(1) = 2, f(2) = 4, f(3) = 8, and so on.

On the other hand, the function g(x) = (1/2)^x is an exponential function with a base of 1/2. At each step, the function decreases by a factor of 1/2. For instance, g(0) = 1, g(1) = 1/2, g(2) = 1/4, g(3) = 1/8, and so on.

Therefore, exponential functions exhibit a characteristic change by a constant factor at each step, which leads to either exponential growth or decay.

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Find the value of x.
22
39
X

Answers

The value of x in the right triangle when calculated is approximately 13.8 units

Calculating the value of x in the triangle

Given the right-angled triangle

The side length x can be calculated using the following sine ratio

So, we have

sin(39) = x/22

To find x, we can use the fact that sin(39 degrees) = x/22 and solve for x.

First, we can use a calculator to find the value of sin(39 degrees), which is approximately 0.6293.

Then, we can set up the equation:

0.6293 = x/22

To solve for x, we can multiply both sides by 22:

0.6293 * 22 = x

13.8446 = x

Rewrite as

x = 13.8446

Approximate the value of x

x = 13.8

Therefore, x is approximately 13.8 in the triangle

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using the net below find the area of the triangular prism
10 cm
7 cm
6 cm
4 cm
4 cm
10 cm
6 cm
4 cm

Answers

Answer:51

Step-by-step explanation:

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