-1.58(6.02) Find The product Please explain

The angle bisector of ∠PQR is Ray QE. If m∠PQE = 2n°,   m∠PQR= 4n°

Given :

The angle bisector of ∠PQR is Ray QE

\(m<PQE = 2n\)

QE bisects angle PQR. When any ray bisects an angle then it divides the angle equally.

so , m∠PQE= m∠EQR

m<EQR=2n

\(m<PQR= m<PQE+ m<EQR\\m<PQR= 2n+2n \\m<PQR= 4n\)

The measure of angle   m∠PQR= 4n°

Option C is  correct.

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5

First order equations include linear equations. In the coordinate system, the linear equations are defined for lines. A linear equation in one variable is one in which there is a homogeneous variable of degree 1 (i.e., only one variable). Multiple variables may be present in a linear equation. Linear equations in two variables, for example, are used when a linear equation contains two variables. Examples of linear equations include 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, and 3x - y + z = 3.

Total books borrowed = 8+4 = 12

No. of non - fiction books = 7

No. of fiction books = 12 -7

                                    = 5

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We can use Coulomb's law to calculate the magnitude of the electric field at a distance r away from a point charge Q:

E = k * Q / r^2

where k is Coulomb's constant, Q is the charge of the point charge, and r is the distance from the point charge.

In this problem, we have a point charge Q of -10 nC located at (1.2 cm, 0 cm), and we want to find the x-component of the electric field at a distance r = 5.3 cm away at position (-4.1 cm, 0 cm).

To find the x-component of the electric field, we need to use the cosine of the angle between the electric field vector and the x-axis, which is cos(180°) = -1.

So, the x-component of the electric field at position (-4.1 cm, 0 cm) is:

E_x = - E * cos(180°) = - (k * Q / r^2) * (-1)

where k = 9 x 10^9 N*m^2/C^2 is Coulomb's constant.

Substituting the given values, we get:

E_x = - (9 x 10^9 N*m^2/C^2) * (-10 x 10^-9 C) / (0.053 m)^2

E_x ≈ -30,566.04 N/C

Rounding this to two significant figures and including the appropriate units, we get:

The x-component of the electric field is about -3.1 x 10^4 N/C (to the left).

D. No, because these vectors form the columns of a 3x3 matrix that is not invertible.

By the invertible matrix theorem, the following statements are equivalent: A is a singular matrix, the columns of A form a linearly independent set, and the columns of A span R³.

To check if the set is a basis for R³, we can form a matrix with the given vectors as its columns and then check if the matrix is invertible. In this case, we have:

-1 0 7

-4 -7 -5

7 -2 -2

We can see that the determinant of this matrix is 0, which means that it is not invertible and therefore the set of vectors is linearly dependent. Therefore, the set is not a basis for R³.

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Answer:

79.44 ft²

Step-by-step explanation:

Area (wall)

If g satisfies the functional equation 9(x + y) = g(x)g(y) for all x, y ∈ ℝ, then g is continuous at all x ∈ ℝ if and only if it is continuous at a point x₀ ∈ ℝ.

To show that the function g is continuous at all x ∈ ℝ if and only if it is continuous at a point x₀ ∈ ℝ, we can use the fact that g satisfies the functional equation 9(x + y) = g(x)g(y) for all x, y ∈ ℝ.

a) If g is continuous at all x ∈ ℝ, then it is continuous at any particular point x₀ ∈ ℝ since continuity at a point is a local property. This means that for any ε > 0, there exists a δ > 0 such that |g(x) - g(x₀)| < ε whenever |x - x₀| < δ.

d) Now, let's consider the behavior of g(1). If g(1) > 1, then for any positive x, we can choose y = 1 such that x + y > 1, and from the functional equation, we have g(x) = g(x)g(1), which implies g(x) > 1. Therefore, g is strictly increasing.

If g(1) = 1, then for any x, we can choose y = 1 such that x + y > 1, and from the functional equation, we have g(x) = g(x)g(1) = g(x), which means g(x) remains constant.

If g(1) < 1, then for any positive x, we can choose y = 1 such that x + y > 1, and from the functional equation, we have g(x) = g(x)g(1), which implies g(x) < 1. Therefore, g is strictly decreasing.

Note that this analysis holds even without assuming that g is differentiable at x₀.

In conclusion, if g satisfies the functional equation 9(x + y) = g(x)g(y) for all x, y ∈ ℝ, then g is continuous at all x ∈ ℝ if and only if it is continuous at a point x₀ ∈ ℝ. Furthermore, the behavior of g can be determined based on the value of g(1): if g(1) > 1, g is strictly increasing; if g(1) = 1, g is constant; and if g(1) < 1, g is strictly decreasing.

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Answer:

Top graph only

Step-by-step explanation:

A function links two set in a way that for each element from the origin set (called domain) you get one and only one element of the target set (co-domain, or range). In layman terms, once you pick your x, you get a single y. In term of graphing it it means that a vertical line of equation  touches the function either zero times (c is outside the domain, or only once (if c is in the domain. If you try it on the various functions there are intervals where you are touching the graphs twice. Or even infinite times as it happens in the last one.

The fracture toughness for this solid is 1843.89 Y MPa√mm.  The plain strain fracture toughness value (K_ICc) is 2534.54 MPa√mm. For a valid fracture toughness test, the minimum required thickness would be 16.5 mm.

a) The fracture toughness (K_IC) of a solid is a measure of its resistance to crack propagation. It can be calculated using the formula:

K_IC = Yσ√(πa)

Where K_IC is the fracture toughness, Y is the geometric factor (typically ranging from 1 to 1.6), σ is the applied stress, and a is the crack length.

In this case, the crack diameter (2a) is given as 22 mm, so the crack length (a) is 11 mm. The stress (σ) for catastrophic fracture is 600 MPa.

Substituting the values into the formula, we get:

K_IC = Yσ√(πa) = Y * 600 MPa * √(π * 11 mm) ≈ 1843.89 Y MPa√mm

b) According to the ASTM E399 standard, the critical stress intensity factor (K_IC) should be compared to the material's plane strain fracture toughness (K_ICc). If K_IC is higher than K_ICc, it is considered an acceptable value.

The plane strain fracture toughness (K_ICc) can be calculated using the formula:

K_ICc = Tys√(πc)

Where Tys is the yield strength and c is the half-crack length.

The given Tys value is 1342 MPa. Since the crack length (c) is half the crack diameter (11 mm), c is equal to 5.5 mm.

Substituting the values into the formula, we get:

K_ICc = Tys√(πc) = 1342 MPa * √(π * 5.5 mm) ≈ 2534.54 MPa√mm

Comparing the calculated K_IC with K_ICc, we can determine if the fracture toughness value is acceptable.

c) To perform a valid fracture toughness test, the material should be in a state of plane strain, meaning that the crack should be sufficiently deep compared to the thickness of the specimen. The ASTM E399 standard recommends a minimum thickness of 1.5 times the crack length.

In this case, the crack length (a) is 11 mm. Therefore, the minimum required thickness would be:

Minimum thickness = 1.5 * a = 1.5 * 11 mm = 16.5 mm

In summary, the fracture toughness of the solid is approximately 1843.89 Y MPa√mm. To determine if it is acceptable according to ASTM E399, it should be compared to the plane strain fracture toughness value (K_ICc) of approximately 2534.54 MPa√mm. Lastly, for a valid fracture toughness test, the minimum required thickness would be 16.5 mm.

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Answer:

Step-by-step explanation:

To calculate the length of the training track running around the field, we need to add the lengths of the two semicircles and the rectangle. The rectangle has a length of 84m and a width of 50m, so its perimeter is 2(84m + 50m) = 268m. The semicircles have a diameter of 50m, so their radius is 25m. The perimeter of each semicircle is half of the circumference of a full circle with a radius of 25m, which is 2 x 3.14 x 25m = 157m. The total length of the training track is therefore 268m + 2 x 157m = 582m.

Answer:

6 inches

Step-by-step explanation:

1 inch = 2.54 cm.

 1 cm = 1/2.54 inches.

14 cm = 14/2.54

14 cm, when rounded to nearest inch, results in around 6 inches.

Answer:

x2=45/50

Step-by-step explanation:

z=71. the box of 15 is 75

The constant 5 represents the flat fee of $5, while the term 0.75x represents a cost of $0.75 per minute for use of the services for x minutes. Therefore, option D is the correct answer.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

The given expression is 5+0.75x.

In the given expression, 5 is constant term and 0.75x is another term.

In the term 0.75x, 0.75 is the coefficient of x

In the expression 5+0.75x, 5 is fixed price and 0.75 is price for second or minute or hour or year and x can be number seconds or minutes or hours or years.

Therefore, option D is the correct answer.

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Answer:

8

Step-by-step explanation:

\(x^2-2x \\x=4\\(4)^2-2(4)\\16-8\\8\)

Answer:

\(7\frac{5}{9}\)

Step-by-step explanation:

Hi there!

We are given this expression:

34÷(14-5)×2

And we want to evaluate it

We'll be using the order of operations

Depending on the country you're in, the acronym can be different, but in the US, the typical acronym used for the order of operations is PEMDAS, or Parentheses, Exponents, Multiplication, Division, Addition, Subtraction

The order of operations states that we should start with any expressions in parentheses

In this case, it's (14-5), which is equal to 9

The expression now becomes

34÷9×2

There are no exponents, so let's skip that

Now this is where it gets tricky:

Based on the acronym alone, we should be doing 9*2 next, however, we should always work left to right, even if in a case like this, we'll be doing division instead of multiplication

Divide 34 by 9

\(\frac{34}{9}\)×2

Now multiply \(\frac{34}{9}\) by 2

\(\frac{68}{9}\)

(as a mixed fraction, it's 7\(\frac{5}{9}\))

Hope this helps!

How to do the displaying of data:-

Form a table.

Make a top section with a the name of the species.

And below the names write how many were found dead.

(FYI, I told you how to make the table, I'm 2 lazy to make it and send the pic.)

You're welcome!

The coin is flipped at least 52 times in order to obtain a 99% confidence interval of width of at most . 18 for the probability of flipping a head.

Hence, Option F is correct answer.

In a sample with a number n of people surveyed with a probability of a success of π , and a confidence level of (1-α), we have the following confidence interval of proportions.

\(\pi\) ± z\(\sqrt{\frac{\pi \p(1-\pi )}{n} }\)

z is the z-score that has a pvalue of \(1-\frac{\alpha }{2}\)

Since, the coin is fair, so \(\pi =0.5\).

The margin of error is:

\(M=z\sqrt{(\frac{\pi (1-\pi )}{n} )}\)

99% confidence level:

So \(\alpha =0.01\) ,z is the value of Z that has a p value of 1-\(\frac{0.01}{2}\)=0.995,

so Z= 2.575

We have to flip the coin in order to obtain a 99% confidence interval of width of at most 18 for the probability of flipping a head at least n times.

n is found when M=0.18 .

So

M=\(z\sqrt{\frac{\pi (1-\pi )}{n} }\)

\(0.18=2.575\sqrt{\frac{0.5*0.5}{n} }\)

\(0.18\sqrt{n} =2.575*0.5\)

\(\sqrt{n}=\frac{2.575*0.5}{0.18}\)

\(\sqrt{n} ^{2} =(\frac{2.575*0.5}{0.18} )^{2}\)

n = 51.16

Thus, we have to flip the coin at least 52 times.

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Answer:

300,000

Step-by-step explanation:

423 x 764 = 323,172

Therefore, analytics is a critical tool for businesses and organizations looking to gain a competitive advantage and improve their operations.

Analytics is often described as the study of historical data to extract insights and make informed decisions. It involves the collection, processing, and analysis of data to discover patterns, identify trends, and gain insights into business operations. By examining data sets, analytics can help businesses identify areas of improvement, optimize performance, and increase efficiency. Analytics tools and techniques can be used across many different fields, including finance, marketing, healthcare, and sports. In finance, analytics can be used to analyze market trends and predict future outcomes. In marketing, analytics can help businesses identify customer behavior patterns and optimize marketing campaigns. In healthcare, analytics can help identify patterns in patient data and improve healthcare outcomes. In sports, analytics can be used to analyze player performance and predict game outcomes.

Therefore, analytics is a critical tool for businesses and organizations looking to gain a competitive advantage and improve their operations.

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Answer:

Midpoint (-1 , 1)

Step-by-step explanation:

Formula: (midpoint)

Let the point A(x , y) be the midpoint of CD.

\(x=\frac{x_c+x_D}{2} =\frac{-3+1}{2} =\frac{-2}{2} =-1\)

\(y=\frac{x_C + y_D}{2} =\frac{4+(-2)}{2} =\frac{2}{2} =1\)

Then

A(-1 , 1)

Answer: (-1;1)

Step-by-step explanation:

x =(-3+1)/2

Y=(4-2)/2

The statement that is false of quadrilaterals is C. Adjacent angles in a parallelogram are complementary.

In the tapestry of geometrical relationships, adjacent angles within a parallelogram are not bestowed with the nature of complementarity. Rather, they exhibit a distinct quality known as supplementary.

Unlike the enchanting dance of complementary angles, which combine to form a sum of 90 degrees, adjacent angles in a parallelogram intertwine their measures to yield a sum of 180 degrees. The allure of the parallelogram resides in the congruence of its opposite angles, not the complementarity of its adjacent angles.

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Answer:

m - 4m = 2m

-4 = 2m -m

- 2 = m

Answer:

m = -4

Step-by-step explanation:

Add 4 to both sides of the equation

Simplify

Add the numbers

= 2 + 4

Subtract 2 from both sides of the equation

=2+4

−2=2+4−2

Simplify

Divide both sides of the equation by the same term

Simplify

Answer:

$16.00

Step-by-step explanation:

It is given that a $20.00 pair of jeans is discounted 20%. We need to find the final price of the jeans. Therefore, the final price of the jeans is $16.00.

how to set it up

20-4=16

Answer: To find the value of the car after 8 years, we can use the given information to create a linear equation in the form:

y - y1 = m(x - x1)

Where:

y is the value of the car after 8 years (what we want to find)

y1 is the value of the car after a given time (either 3 or 5 years)

x is the given time (either 3 or 5 years)

x1 is the starting time (when the car was purchased)

m is the rate of decrease (slope of the line)

We can use the two given data points to find the slope of the line:

m = (y2 - y1) / (x2 - x1)

m = (11,000 - 15,000) / (5 - 3)

m = -2,000 per year

Now, we can use one of the data points to solve for the y-intercept of the line:

y - y1 = m(x - x1)

y - 15,000 = (-2,000)(3 - x1)

y - 15,000 = (-2,000)(3 - x1)

y - 15,000 = (-6,000 + 2,000x1)

y = 2,000x1 - 6,000 + 15,000

y = 2,000x1 + 9,000

So the linear equation that represents the value of the car after x years is:

y - 15,000 = (-2,000)(x - 3)

Simplifying this equation gives:

y - 15,000 = -2,000x + 6,000

Now, we can use x = 8 to find the value of y:

y - 15,000 = -2,000(8) + 6,000

y - 15,000 = -2,000

y = $13,000

Therefore, the value of the car after 8 years will be $13,000.

So the completed expression is:

y - 15,000 = -2,000(x - 3)

The value of the car after 8 years will be $13,000.

Step-by-step explanation:

The experimental probability that Kyle's next toss will be a hit is 11/18 or approximately 0.61.

The experimental probability of Kyle's next toss being a hit can be calculated by dividing the number of hits by the total number of tosses. In this case, the total number of tosses is the sum of hits and misses, which is 22 + 14 = 36. Therefore, the experimental probability of Kyle's next toss being a hit is 11/18 or approximately 0.61.
To find the experimental probability of Kyle's next toss being a hit, you need to consider the number of hits and total tosses so far.
Hits: 22
Misses: 14
Total tosses: 22 hits + 14 misses = 36 tosses
Now, calculate the experimental probability by dividing the number of hits by the total number of tosses:
Experimental probability = Hits / Total tosses = 22 / 36
Simplify the fraction:
Experimental probability = 11/18
So, the experimental probability that Kyle's next toss will be a hit is 11/18.

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Answer:

11/18

Step-by-step explanation:

The maximum height of the projectile is 56.53 meters.

The height of a projectile at time t is represented by the function h (t)= −4.9 t² +18t + 40, where h(t) is the height in meters and t is the time in seconds.

This is a quadratic function of the form h(t) = at² + bt + c, where a = -4.9, b = 18, and c = 40.

To find the maximum height of the projectile, we need to find the vertex of the parabolic graph of the function h(t).

The vertex of the parabola is at the point (t, h(t)) where t = -b/2a. Substituting the values of a and b, we get t = -18/(2(-4.9)) = 1.8367 seconds.

To find the maximum height, we need to substitute t = 1.8367 seconds into the function h(t). h(1.8367) = -4.9(1.8367)^2 + 18(1.8367) + 40 = 56.53 meters.

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If two events are collectively exhaustive, then the probability that both occur at the same time is 1.00 (Option c)

Probability is a quantification of how likely an event is to occur. Typically, probabilities are defined as the chances that a specific outcome will occur out of a given selection of outcomes. A probability is expressed mostly in decimal form, taking values between 0 and 1. Probabilities cannot exceed this particular range of values.

Firstly, To clarify : You are confusing mutually exclusive and jointly collectively exhaustive.

The former describes condition which cannot both (or all) obtain. and so exclude one another.

i.e., "not - (both A and not - A)"

The latter describes conditions, one of which must obtain, and so exhaust the field of possibilities. i.e., "either A or not - A"

I presume you intend to refer to the latter.

Second, to answer your question: If two events - are jointly exhaustive, their probabilities must by definition sum to 1.

It is thus certain, not merely probable, that one or the other will obtain.

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Answer:

y=3x

Step-by-step explanation:

Number of plates Aaliyah makes=x

Amount of clay she uses (in pounds)= y.

There is a proportional relationship between x and y: y=mx

To make 2 plates, Aaliyah uses 6 pounds of clay.

Therefore:

Substituting the given values into the proportional relationship y=mx, we obtain:

6=2m

Divide both sides by 2

m=3

Therefore, the equation for the relationship between x and y is:

y=3x, where 3 is our constant of proportionality.