Which equation can be used to solve for the measure of

angle ABC?

[Not drawn to scale)

O tan(x) = 36

O tan(x) =

O since) –

sin(x) = 10. 3

The required six algebraic equations to relate the given different pairs of angles are in the solution part.

The supplementary angles are defined as when pairing of angles addition to 180° then they are called supplementary angles.

Given: AD, BE and FC intersect at point P.

AD⊥FC.

According to the given figure, the required equations would be as:

m∠APB = m∠EPD  (vertical angles)

m∠FPD = m∠APC  (right angles are congruent)

m∠EPC + m∠EPF = 180 degrees (linear pair)

m∠BPC = m∠EPD (vertical angles)

m∠APB + m∠BPC = 90 degrees (complementary angles)

m∠FPB + m∠BPC = 180 degrees (linear pair)

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Answer: Apples: $2      Mangos: $1.50

Step-by-step explanation:

8m+3a = 183m+5a=14.5

Multiply the first equation by 5 and multiply the second equation by 340m+15a=909m+15a=43.5

Subtract the equations

31m=46.5m=46.5/31m=1.5

Substitute to find the price of apples

8(1.5)+3a=1812+3a=183a=18-123a=6a=2

Apples cost $2.00 each mangoes cost $1.50 each

The smallest and the largest area of the window will be 9.8 and 11.1 sq. metres respectively.

This problem is based on the area of rectangle .

Here, since the height and the width of the window are distinct, so the window can be assumed to be of rectangular shape.

Now, the area of a rectangle is given by = l x b where l and b are respectively the height and the width of the window respectively.

The area would be smallest when both the height and width are least i.e. 140 cm and 70 cm .

So, smallest area = lxb = 140 x 70 = 9800 sq. cm = 9.8 sq. m.

Similarly the largest area would be when both the height and the width are maximum i.e. largest area = lxb = 150x 74 = 11,100 sq cm. =11.1 sq metres.

Therefore, the smallest and the largest area of the window will be 9.8 and 11.1 sq. metres respectively.

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The smallest and the largest area of the window will be 9.8 and 11.1 sq. metres respectively.

This problem is based on the area of a rectangle.

Here, since the height and the width of the window are distinct, so the window can be assumed to be of rectangular shape.

Now, the area of a rectangle is given by = l x b where l and b are respectively the height and the width of the window respectively.

The area would be smallest when both the height and width are least i.e. 140 cm and 70 cm .

So, smallest area = lxb = 140 x 70 = 9800 sq. cm = 9.8 sq. m.

Similarly, the largest area would be when both the height and the width are maximum i.e. largest area = lxb = 150x 74 = 11,100 sq cm. =11.1 sq metres.

Therefore, the smallest and the largest area of the window will be 9.8 and 11.1 sq. metres respectively.

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Using the given fractions, we can see that for the stew they use (27/10) pints and for the rice (18/10) pints.

We know that the carton has a volume of:

(4 + 1/2) pints of chicken stock.

He uses 3/5 of the carton to make a stew, so he uses:

(3/5)*(4 + 1/2) pints = (12/5 + 3/10) pints

                               = (27/10) pints.

And the rest, (2/5) of the carton, is used to make rice, then:

(2/5)*(4 + 1/2) pints  = (8/5 + 2/10) pints = (18/10) pints.

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The value of the variable that makes the equation true -1/10

An equation is a mathematical statement that shows the equality of two or more things. that is An equation is a mathematical statement that shows that two mathematical expressions are equal

The given equation is 1=-10c

To make the statement true, we have to determine the value of the variable c

this is done by making the variable c the subject of the relation

Now, 1/-10 = -10c/-10

Therefore c = -1/10 makes the equation true

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Answer:102+31-180 = 47

so x = 47

Step-by-step explanation:

this is very simple

The matrix is now in row echelon form. The inverse is the right side of the augmented matrix: [tex]$$\begin{bmatrix}1 & 1 & 0 \\2 & 1 & 3 \\0 & 1 & 2\end{bmatrix}$$[/tex]

We will use the algorithm for finding the inverse of a matrix by row reducing.

Step 1: Augment the matrix with the identity matrix.

[tex]$$\begin{bmatrix}1 & 1 & 0 & | & 1 & 0 & 0\\2 & 1 & 3 & | & 0 & 1 & 0\\0 & 1 & 2 & | & 0 & 0 & 1\end{bmatrix}$$[/tex]

Step 2: Use row operations to transform the matrix into the identity matrix.

1. Multiply the first row by [tex]$\frac{1}{2}$[/tex] to get:

[tex]$$\begin{bmatrix}\frac{1}{2} & \frac{1}{2} & 0 & | & \frac{1}{2} & 0 & 0\\2 & 1 & 3 & | & 0 & 1 & 0\\0 & 1 & 2 & | & 0 & 0 & 1\end{bmatrix}$$[/tex]

2. Subtract two times the first row from the second row to get:

[tex]$$\begin{bmatrix}\frac{1}{2} & \frac{1}{2} & 0 & | & \frac{1}{2} & 0 & 0\\0 & 0 & 3 & | & -1 & 1 & 0\\0 & 1 & 2 & | & 0 & 0 & 1\end{bmatrix}$$[/tex]

3. Subtract the first row from the third row to get:

[tex]$$\begin{bmatrix}\frac{1}{2} & \frac{1}{2} & 0 & | & \frac{1}{2} & 0 & 0\\0 & 0 & 3 & | & -1 & 1 & 0\\0 & 0 & 2 & | & -\frac{1}{2} & 0 & 1\end{bmatrix}$$[/tex]

4. Multiply the third row by [tex]$\frac{1}{2}$[/tex] to get:

[tex]$$\begin{bmatrix}\frac{1}{2} & \frac{1}{2} & 0 & | & \frac{1}{2} & 0 & 0\\0 & 0 & 3 & | & -1 & 1 & 0\\0 & 0 & 1 & | & -\frac{1}{4} & 0 & \frac{1}{2}\end{bmatrix}$$[/tex]

5. Subtract [tex]$\frac{3}{2}$[/tex]times the second row from the third row to get:

[tex]$$\begin{bmatrix}\frac{1}{2} & \frac{1}{2} & 0 & | & \frac{1}{2} & 0 & 0\\0 & 0 & 3 & | & -1 & 1 & 0\\0 & 0 & 0 & | & \frac{7}{4} & -1 & \frac{1}{2}\end{bmatrix}$$[/tex]

Step 3: The matrix is now in row echelon form. The inverse is the right side of the augmented matrix:

[tex]$$\begin{bmatrix}1 & 0 & 0\\-1 & 1 & 0\\\frac{7}{4} & -1 & \frac{1}{2}\end{bmatrix}$$[/tex]

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All the given statements does not make sense by the definition of dot product.

(a) (dot product)(a): The dot product is a mathematical operation and doesn't take any arguments or values, so this expression doesn't make sense as written.

(b) u\bullet(v\bulletw): The dot product is associative, meaning that u\bullet(v\bulletw) = (u\bullet v)\bullet w. However, the expression itself is not well defined, since the inner expression v\bullet w doesn't specify what values v and w represent.

(c) (u\bullet v) + w: The dot product is an scalar product, meaning it results in a scalar value, and adding a scalar to a vector does not make sense mathematically.

(d) k\bullet(u+v): The dot product is between two vectors, and the expression k\bullet(u+v) implies that the dot product is between a scalar (k) and a vector (u+v). This does not make mathematical sense, as the dot product is only defined between two vectors of the same dimension.

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Answer:

15 CDs

Step-by-step explanation:

The total percentage of the CDs is 100% because it basically means all the CDs. Therefore, the percentages of types need to add up to 100%. If 30% are country and 40% are pop, 100 - 30 - 40 = 30% are other.

30% is equivalent to 30/100 or 0.3 when written as a decimal. You would then multiply this by the number of CDs to get the number of other CDs:

[tex]50 * 0.3 = 15[/tex]

Therefore, 15 CDs are other types of music

Answer:

y = -2

Step-by-step explanation:

The equation is y = mx + b

But this line has no slope, but it has a y-intercept at (0,-2), so the equation is

y = -2

y = k asymptotically stable critical point because f'(k) < 0 and f'(0) > 0. So y = 0 is an an asymptotically unstable critical point.

The Gompetz equation is dy/dt = ry In(K/y).

In order to find critical points equate dy/dt equal to zero

dy/dt = 0

ry In(k/y) = 0

Here, k and r are constants

y In(k/y) = 0

y = 0

In (k/y) = 0

Eliminating In

k/y = e^0

k/y = 1

Multiply by y on both side, we get

k = y

y = 0 and y = k

The critical points are 0 and k

Since zero is a critical point

dy/dt = f(y)

dy/dt = ry In(k/y)

Differentiation on both side

f'(y) = ry In(k/y) - ry × y/k × k/[tex]y^2[/tex]

f'(y) = r In(k/y) - r

f'(k) = r In(k/k) - r

f'(x) = -r < 0

So that, y = k asymptotically stable critical point because f'(k) < 0

f'(0) > 0

That means y=0 is asymptotically unstable critical point.

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the value of x=2 and y =5, for the given trapezoid.

What is trapezoid?

A trapezoid, commonly referred to as a trapezium, is a quadrilateral or polygon with four sides. It has a set of parallel opposite sides as well as a set of non-parallel sides. The bases and legs of the trapezoid are referred to as parallel and non-parallel sides, respectively. A trapezoid is a four-sided closed 2D figure with a perimeter and an area. The bases of the trapezoid are two of the shape's sides that are parallel to one another. The legs or lateral sides of a trapezoid are its non-parallel sides. The altitude is the shortest distance between any two parallel sides.

Given, HM =5x-3

BM = x+5

So 5x-3 = x+5

4x = 8

x = 2.

and (4y - 3) =(2y+3)+(10x+1) /2

8y-6 =  2y+3 + 10x+1

6y = 10+20

y =5

Hence the value of x=2 and y =5, for the given trapezoid.

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The polynomial -3x^3 + 2 has only one turning point.

A turning point is a point on a curve where the curve changes direction, either from going up to going down or vice versa. In other words, it is a point where the first derivative of the curve changes sign.

For the polynomial -3x^3 + 2, the first derivative is given by:

d/dx (-3x^3 + 2) = -9x^2

Since the first derivative is a monotonically decreasing function (that is, its slope is always negative), the polynomial -3x^3 + 2 has only one turning point.

Slope of first derivative

d²(-3x^3 + 2)/dx² = -18x

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Answer:

x-6y=-24

Step-by-step explanation:

do it

Answer:

Step-by-step explanation:

The slope-intercept form of a linear equation is given by y = mx + b, where m is the slope and b is the y-intercept.

To find the slope and y-intercept of the equation 2x - 6y = 24, you can first isolate y by adding 6y to both sides and then dividing both sides by -6. This gives you: y = (-1/3)x + 4

So, the slope is -1/3 and the y-intercept is 4.

The celestial coordinates of the given point are (0.92868, 0.36983, 0.04921).

The right ascension and declination of a particular point in the sky can be used to calculate its corresponding celestial coordinates. Right ascension (RA) is measured in hours, minutes and seconds, while declination (Dec) is measured in degrees, minutes and seconds.

The RA of the given point is 15 h 06 m 53.62 s. This can be converted to degrees by multiplying by 15. The result is 225.1045 degrees. The Dec of the given point is 62° 20' 10.0" which can be converted to radians by multiplying by pi/180. The result is 1.08269 radians.

The celestial coordinates can then be calculated using the formula:

sin(RA)cos(Dec) = sin(225.1045)*cos(1.08269) = 0.92868

cos(RA)cos(Dec) = cos(225.1045)*cos(1.08269) = 0.36983

sin(Dec) = sin(1.08269) = 0.04921

Therefore the celestial coordinates of the given point are (0.92868, 0.36983, 0.04921).

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Vector a2 is in the subspace spanned by vectors a1, a2, and a3 if it can be written as a linear combination of these vectors.

What is vector ?

A vector is a quantity or phenomenon that has two independent properties: magnitude and direction. The term also denotes the mathematical or geometrical representation of such a quantity. Examples of vectors in nature are velocity, momentum, force, electromagnetic fields and weight.

Let W be a subspace of a vector space V and let a1, a2, and a3 be vectors in V. The vector a2 is in the subspace W if and only if it can be written as a linear combination of the vectors a1, a2, and a3. That is, there exist scalars c1, c2, and c3 such that:

a2 = c1 * a1 + c2 * a2 + c3 * a3

This equation can be written in matrix form as:

[a2] = [a1 a2 a3] * [c1; c2; c3]

where [a2] is the column vector representation of a2, [a1 a2 a3] is the matrix with a1, a2, and a3 as columns, and [c1; c2; c3] is the column vector of scalars c1, c2, and c3.

Vector a2 is in the subspace spanned by vectors a1, a2, and a3 if it can be written as a linear combination of these vectors.

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There are 23,311,945,600 possible ways to deal the cards to the four players and choose one card to be turned face-up in the middle.

We can calculate the number of ways to deal the cards to the four players and then multiply by the number of ways to choose which card is turned face-up in the middle.

First, there are 24 choose 5 ways to deal the first hand, since each player receives 5 cards. Then, there are 19 choose 5 ways to deal the second hand, since there are now 19 cards left. Similarly, there are 14 choose 5 ways to deal the third hand and 9 choose 5 ways to deal the fourth hand.

So, the number of ways to deal the cards to the four players is:

24 choose 5 * 19 choose 5 * 14 choose 5 * 9 choose 5 = (24! / (5! * 19!)) * (19! / (5! * 14!)) * (14! / (5! * 9!)) * (9! / (5! * 4!))

Now, we need to multiply this result by 4, since there are 4 possible cards to turn face-up in the middle. So, the final answer is:

4 * 24 choose 5 * 19 choose 5 * 14 choose 5 * 9 choose 5 = 4 * (24! / (5! * 19!)) * (19! / (5! * 14!)) * (14! / (5! * 9!)) * (9! / (5! * 4!)) = 4 * 5,827,986,400 = 23,311,945,600.

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A. KP = ST is given

B. Given as PR = TV is known

C. KP + PR = ST + TV using the addition property.

D. Segment addition in KP + PR = KR

E. ST + TV = SV

F. Segment addition has obtained this answer

G. KR = SV by substitution property

The solution has been obtained by using the concept of mathematical reasoning.

What is mathematical reasoning?

In mathematics, reasoning entails making logical deductions from data or presumptions.

A. For this, we are stated a reason that it is given.

So, the statement is KP = ST.

B. We are given the statement as PR = TV

The reason is that it is given.

C. For this, we are stated a reason that it is obtained by addition property.

So, the statement is KP + PR = ST + TV.

D. We are given the statement as KP + PR = KR

The reason is that it is obtained by segment addition.

E. ST + TV = SV is the statement

F. The reason for the statement is that it is obtained by segment addition.

G. For this, we are stated a reason that it is obtained by substitution property.

So, the statement is KR = SV.

Hence, the statements and their respective reasons have been arranged.

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The length of side DB can be expressed as [tex]\sqrt{ (15x - 55)(3x - 28).}[/tex]

To solve this, we can use the Pythagorean theorem:

[tex]DB^2 = AE^2 + EC^2[/tex]

Substituting the values of AE and EC:

[tex]DB^2 = (6x - 55)^2 + (3x - 16)^2[/tex]

[tex]DB^2 = 36x^2 - 720x + 3025 + 9x^2 - 96x + 256[/tex]

[tex]DB^2 = 45x^2 - 816x + 3281[/tex]

[tex]DB =[/tex] [tex]\sqrt{ (15x - 55)(3x - 28).}[/tex]

Key points:

The Pythagorean theorem states:

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The complete question is:

In a quadrilateral ABCD, the length of sides AB and CD are equal and measure x units. If AE = 6x - 55 and EC = 3x - 16, find the length of side DB.

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The midpoint Riemann sum approximation of ∫64x3 1−−−−−√ⅆx using 4 subintervals of equal width is 9980

The midpoint Riemann sum approximation of ∫64x3 1−−−−−√ⅆx using 4 subintervals of equal width is calculated by summing the area of each subinterval under the midpoint of the interval.

The formula for the midpoint Riemann sum is given by:

Sum = (width of interval) * (height of midpoint)

For this problem, since the width of each interval is 16/4 = 4, the midpoint Riemann sum is calculated by:

Sum = 4 * (1 + (16/4)^3 + (32/4)^3 + (48/4)^3)

Substituting the values for each midpoint, we get the following equation:

Sum = 4 * (1 + 4^3 + 8^3 + 12^3)

This simplifies to:

Sum = 4 * (1 + 64 + 512 + 1728)

Therefore, the midpoint Riemann sum approximation of ∫64x3 1−−−−−√ⅆx using 4 subintervals of equal width is:

Sum = 4 * (2495)

Sum = 9980

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The expression x 2a-b=3(x a)-2(2a-b) has the result x = 2a / (2a + 3).

An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is the expression. A number, a variable, or a combination of numbers, variables, and operation symbols constitutes an expression. An equation consists of two expressions joined by an equal sign. Example of a word: the sum of 8 and 3. Example of a word: The sum of 8 and 3 equals 11. 8 + 3 is an expression.

Here,

To solve for x, we can simplify the equation first:

x * 2a - b = 3(x + a) - 2(2a - b)

Expanding the right side:

x * 2a - b = 3x + 3a - 2 * 2a + 2b

Combining like terms:

x * 2a - b = 3x + 3a - 4a + 2b

x * 2a - b = 3x - a + 2b

Now, we can isolate x on one side of the equation:

x * 2a - 3x = a - b + 2b

x * 2a - 3x = a + b

Multiplying both sides by -1:

-x * 2a + 3x = -a - b

Adding 2a to both sides:

x * 2a + 3x + 2a = -a - b + 2a

Combining like terms:

x * 2a + 3x + 2a = -a + 2a

x * 2a + 3x + 2a = 2a

Finally, collecting all x terms on one side:

x * (2a + 3) = 2a

Dividing both sides by (2a + 3):

x = 2a / (2a + 3)

The value of x for the expression x 2a-b=3(x a)-2(2a-b) is x = 2a / (2a + 3).

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Answer is 1/104. Probability is a branch of mathematics that deals with numerical descriptions of the probability of an event occurring or the probability that a statement is true.

What is the probability that both the second and third cards are the same suit?

Probability that the first card is a club = 1/4. (There are 13 club cards in the deck, and 13/52 = 1/4). Probability that the second card is a 3 = 1/13. (There are four 3 cards in the deck, and 4/52 = 1/13). Probability that the third card is red = 1/2. (There are 26 red cards in the deck, and 26/52 = 1/2). The probability of an event is a number between 0 and 1, where 0 represents approximately an impossibility and 1 represents a certainty. The higher the probability of an event, the more likely the event will occur. A simple example is mining a fair (impartial) coin. Since the coin is fair, both outcomes ("heads" and "tails") are equally likely; the probability of heads is equal to the probability of heads; and since no other outcome is possible, the probability of "heads" or "heads" is 1/2 (which can also be written as 0.5 or 50%).

Probability that the first card is a club, the second card is a 3, and the third card is red = 1/4 * 1/13 * 1/2

= 1/104

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About 68% of the data in a typical normal curve is within one of the mean's standard deviation. Accordingly, 68% of the data should fall between -1 and 1 if the data's mean was 0 and its standard deviation was 1.

A theoretical continous probability distribution known as the "standard normal curve" depicts a bell-shaped, symmetrical curve. The normal distribution or the Gaussian distribution are other names for it. The standard normal curve, which serves as a benchmark for other normal distributions, has a means of 0 and a variance of 1. For simpler analysis and comparison, data sets can frequently be translated into the normal form standards. The distributions of many real-world events, including IQ scores, length, weight, and heart rate, to mention a few, is described by the curve, which is significant in statistics. Among other uses, the normalised curve is employed in statistical inference, quality control, and hypothesis testing.

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Team B will need to sell at least 192 candies to avoid losing money.

When an algebraic equation is graphed, it always results in a straight line since each term in a linear equation has an exponent of 1. For this reason, it is referred to as a "linear equation."

There are both one-variable and two-variable linear equations.

Given total amount to be raised by each team is $100,

Team B wants to sell cotton candy,

rent of candy machine = $25

total cost to be earned for team B = $100 + $25 = $125

let the number of candies sold be x

cost used in candy sticks = $0.10 per stick

cost used in x candy sticks = $0.10x

the selling price of each candy = $0.75

the selling price of x  each candy  = $0.75x

total gain = $0.75x - $0.10x

total gain = $0.65x

minimum candies to be sold for no loss

$0.65x = $125

x = 125/0.65

x = 192.30

x = 192

Hence for no loss, at least 192 candies are to be sold.

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Answer:

5(y+7)

Step-by-step explanation:

Answer:

5(y + 7)

Step-by-step explanation:

Answer:

Step-by-step explanation:

2/3 - 5/9 = 1/

9

≅ 0.1111111

Answer: 1/9

Step-by-step explanation:

The best surface tolerance and finish would be gotten if all inside vertical corners had a fillet radius of (b) > 0.125 inches.

The choice of fillet radius is an important factor in determining the surface tolerance and finish of a machined part. A fillet radius is a rounded corner between two flat surfaces. A fillet radius that is too small can result in a rough surface, while a fillet radius that is too large can weaken the part.

In this scenario, a 1/4 inch diameter mill is being used, so the best surface tolerance and finish would be achieved if the fillet radius is greater than 0.125 inch, but less than 0.25 inch. This will ensure that the part is not weakened and the surface is smooth. The exact value of the fillet radius will depend on the specific requirements of the machining process.

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Complete Question:

If you must use a 1/4 inch diameter mill, then the best surface tolerance and finish would be gotten if all inside vertical corners had a fillet radius with the minimum requirement of:

(a) < 0.25 inch

(b) > 0.125 inch

(c) > 0.25 inch

(d) = 0.25 inch

(e) = 0.125 inch

(f) < 0.125 inch

The probability that Kyle will pass all 15 tests if he does not study for them is approximately 0.0017.

This is because the probability of passing each individual test without studying is 0.45, and the probability of passing all tests without studying is equal to 0.45 multiplied by itself 15 times, which is 0.0017. This means that the odds of Kyle passing all 15 tests without studying are very slim.

Even if he has a good understanding of the material and has been able to recall the information without studying, it is very unlikely that he will be able to do so for all 15 tests. It is therefore recommended that Kyle studies for his tests in order to increase his chances of passing them.

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If he p-value is used for hypothesis testing , then the Null Hypothesis is rejected if (a) p-value ≤ α .

In a hypothesis testing, the p-value represents the probability of observing a test statistic as extreme or more extreme than the one observed, provided that the null hypothesis is True.

The significance level, represented by "α" , is a pre-determined threshold which determines the level of evidence required to reject the null hypothesis.

If the p-value is less than or equal to α, this indicates that the observed test statistic is sufficiently unlikely to occur under the null hypothesis, and therefore the null hypothesis is rejected.

Therefore , the Null hypothesis is rejected if (a) p-value ≤ α .

The given question is incomplete , the complete question is

When the p-value is used for hypothesis testing, the null hypothesis is rejected if

(a) p-value ≤ α

(b) α < p-value

(c) p-value ≥ α

(d) p-value = 1 - α

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The correct answer is a) p-value ≤ α. In hypothesis testing, the null hypothesis is typically assumed to be true initially. The p-value is used to determine the probability of observing a test statistic as extreme or more extreme than the one obtained from the data, assuming that the null hypothesis is true.

The significance level (α) is chosen beforehand and represents the maximum acceptable probability of rejecting the null hypothesis when it is actually true.

If the p-value is less than or equal to the significance level (p-value ≤ α), then the result is considered statistically significant and the null hypothesis is rejected. This implies that the observed effect is unlikely to have occurred by chance alone and that the alternative hypothesis is more likely to be true.

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Answer:

Perimeter 18.42

Area 20.13

Step-by-step explanation:

Perimeter:

This is the distance around the figure.

The distance around the triangle is 9.

The distance around the 1/2 circle

c= 2[tex]\pi[/tex]r

c [2(3.14)(3)]/2

c = 9.42

9.42 + 9 = 18.42

Area:

triangle

a = 1/2(bh)

a - 1/2 (3)(4)

a = 6

circle

a = 1/2([tex]\pi r^{2}[/tex])

a = 1/2(3.14)(9)

a = 14.13

6 + 14.13 = 20.13