Identify the direction of rotation that maps triangle BCD to triangle B’C’D’.

The triangle is rotated in a
direction-----

Answer:

Those angles are in opposite either in vertical or horizontal. They are opposite angles

(a) A sound with an intensity of 1 watt per square meter has a decibel level of -120.

(b) A sound with an intensity of 10⁻² watt per square meter has a decibel level of -140.

(c) The number of decibels is not 100 times as great as the intensity, even though the intensity in part (a) is 100 times greater than the intensity in part (b).

Using the relationship of intensity of sound and number of decibels, we can calculated the required number of decibels as follows;

β =10 log(I x 10⁻¹²)

(a) Decibel level: plugging in I = 1 watt per square meter into the equation, we get:

β = 10 log(1 x 10⁻¹²) = 10 log(10⁻¹²) = -120 decibels

(b) Decibel level: plugging in I = 10⁻² watt per square meter into the equation, we get:

β = 10 log(10⁻² x 10⁻¹²) = 10 log(10⁻¹⁴) = -140 decibels

(c) Let's calculate the decibel level for the sound in part (a) using the given formula:

β₁ = 10 log(I₁ x 10⁻¹²) = 10 log(100 x I₂ x 10⁻¹²) = 10 log(I₂ x 10⁻¹⁴) + 20

where;

Using the result from part (b), we can substitute I₂ = 10⁻² watt per square meter and get:

β₁ = -140 + 20 = -120 decibels

Comparing this result to the decibel level for the sound in part (a) (which is also -120 decibels), we see that they are the same.

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The ratio that compares the men to the women who work at the warehouse is 4 : 1.

A ratio is a value that shows the proportional relationship between two quantities.

A ratio indicates how many times one number is contained in another.

For example, in the above task, there is 4x the number of men when compared with the number of women who work at the warehouse.

Men working at the warehouse = 1,200

Women working at the warehouse = 300

Ratio of men to women = 4 : 1 (1,200 : 300)

Thus, the ratio that compares the men to the women who work at the warehouse is 4 : 1.

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Answer: 4:1

i just took a test

Step-by-step explanation:

Answer:

P = 12.50 + 1.25t

Step-by-step explanation:

To find an equation to represent the price of a pizza, we need to first figure out the original price of a pizze.
Since the price is 16.25 dollars, and there are 3 toppings, each of which cost 1.25, the original price would be:

16.25 - 3(1.25) = 12.50

Thus, we can represent the cost of a pizze with toppings as:
P = 12.50 + 1.25t, where P = Price and t = amount of toppings.

Hope this helps!

The distance between these two points is √53 units.

A triangle is a three-sided polygon that consists of three edges and three vertices.

The two points of a triangle are (−3,−6) and (4,−8)

The length along a line or line segment between two points on the line or line segment.

Distance=√(x₂-x₁)²+(y₂-y₁)²

=√(4+3)²+(-8+6)²

=√7²+2²

=√49+4=√53

So the distance between these two points is √53 units

Hence, the distance between these two points is √53 units.

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Answer:

36.2

Step-by-step explanation:

Assuming that the dotted line is a perpendicular bisector, we can say that it splits the side that is 30 units long into 2 sets of 15 units. Then, we can use the pythaogrean theorem to solve (Leg A is 33 and Leg B: 15). a^2+b^2=c^2

33^2+15^2=c^2

1089+225=c^2

1314=c^2

Square root of 1314 = square root of c^2

36.2 aapproximately c

The leading degree of the polynomial is 3. This shows that the polynomial described by the equation is a cubic polynomial

The standard form of a polynomial expression is written as:

\(a_nx^n+ a_{n-1}x^{n-1}+ a_{n-2}x^{n-2}+...\)

A polynomial function has a leading degree that is greater than 2;

Given the polynomial function

\(P(x)=4x^3-31x^3-10058x+158040\)

From the given polynomial, the leading degree of the polynomial is 3. This shows that the polynomial described by the equation is a cubic polynomial

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To rationalize the expression, we have to find common terms between numerators and denominators and then simplify:

To simplify the numerator of the second expression we have to remember that:

Then, the expression would be simplified as:

For the third expression, when factorizing we have to find two numbers that when added equals -3 and when multiplied equals +2, meaning:

Then, the factorization of the numerator of the third expression is:

Finally, to simplify the numerator of the last expression we will use the same factorization as in the third one. And for the denominator we have to use the following:

Answer:

The mean score of 90, and percentile of Bob's score of 80, gives Bob's exam score as approximately 92.5%

The Z-Score of the 80th percentile is 0.8416

The formula for Z-Score is presented as follows;

\(z = \frac{x - \mu}{ \sigma} \)

Where;

\( \sigma = The \: standard \: deviation\)

\( \mu = The \: mean = 90\%\)

x = The given score

Taking the mean as a proportion, we have;

\( \sigma = \sqrt{\frac{\mu \cdot (1-\mu)}{n}}\)

Which gives;

\( \sigma = \sqrt{\frac{0.9 \times (1-0.9)}{100}}= 0.03\)

Therefore, when z = 0.8416, gives;

\(0.8416 = \frac{x - 0.9}{ 0.03} \)

x = 0.8416 × 0.03 + 0.9 ≈ 0.925

Therefore;

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Answer:

-6

Step-by-step explanation:

First, replace x with -2. your equation then looks like:2(-2-3)+4. Then, you multiply 2 by everything in the parenthesis. After you multiply -2 and -3, you are left with -4, -6 +4. You then add everything together, and you get -6.

The solution is Option B.

The area of the triangle is A = 10 units which is one-half the area of a rectangle of length 4 units and width 5 units

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the triangle be represented as ΔABC

Let the coordinates of the triangle ABC be

The coordinate of A = A ( 4 , 6 )

The coordinate of B = B ( 6 , 1 )

The coordinate of C = C ( 2 , 1 )

Now , the base of the triangle B = 4 units

The height of the triangle H = 5 units

And , The area of the triangle = ( 1/2 ) x Length x Base

Substituting the values in the equation , we get

The area of the triangle = ( 1/2 ) x 4 x 5

The area of the triangle = 10 units

Now , one-half the area of a rectangle of length 4 units and width 5 units

Substituting the values in the equation , we get

Area of rectangle = ( 1/2 ) Length x Width

Area of rectangle = ( 1/2 ) 4 x 5

Area of rectangle = 10 units

Hence , the area of triangle is 10 units

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Answer:

want points

Step-by-step explanation:

sorry

For the first set O{(-1, 1,-1), (1, -1, 2), (0, 0, 1)} in R3 and for the second set {(3, -1), (2, 2)} in R2 (I assume you meant R2 instead of R?) they form a basis. We can calculate it in the following manner.

For the first set of vectors, we need to check if they are linearly independent and span the entire space of R3.

First, we can check for linear independence by setting up an equation:
a(-1, 1, -1) + b(1, -1, 2) + c(0, 0, 1) = (0, 0, 0)
Simplifying, we get:
(-a + b) = 0
(a - b) = 0
(-a + 2b + c) = 0
Solving this system of equations, we get a = b = c = 0. Therefore, the vectors are linearly independent.

Next, we need to check if they span the entire space of R3. We can do this by seeing if any vector in R3 can be written as a linear combination of the three given vectors.
Let (x, y, z) be an arbitrary vector in R3. We need to solve for the scalars a, b, and c such that:
a(-1, 1, -1) + b(1, -1, 2) + c(0, 0, 1) = (x, y, z)
Simplifying, we get:
-a + b = x
a - b + 2c = y
-c = z
Solving this system of equations, we get a = (x - z)/2, b = (x + z)/2, and c = -z. Therefore, any vector in R3 can be written as a linear combination of the given vectors.

Since the vectors are linearly independent and span the entire space of R3, they form a basis for R3.

For the second set of vectors, we need to check if they are linearly independent and span the entire space of R1.

First, we can check for linear independence by setting up an equation:
a(3, -1) + b(2, 2) = (0)
Simplifying, we get:
3a + 2b = 0
-1a + 2b = 0
Solving this system of equations, we get a = b = 0. Therefore, the vectors are linearly independent.

Next, we need to check if they span the entire space of R1. We can do this by seeing if any scalar in R1 can be written as a linear combination of the two given vectors.
Let x be an arbitrary scalar in R1. We need to solve for the scalars a and b such that:
a(3, -1) + b(2, 2) = (x)
Simplifying, we get:
3a + 2b = x
-1a + 2b = 0
Solving this system of equations, we get a = (2x)/5 and b = (3x)/10. Therefore, any scalar in R1 can be written as a linear combination of the given vectors.

Since the vectors are linearly independent and span the entire space of R1, they form a basis for R1.

For the third set of vectors, we cannot determine if they form a basis without knowing the dimension of the space they are in.

To determine if a set of vectors forms a basis for a particular space, we must check if the vectors are linearly independent and if they span the space.

For the first set O{(-1, 1,-1), (1, -1, 2), (0, 0, 1)} in R3:
These vectors are linearly independent and span R3, so they form a basis for R3.

For the second set {(3, -1), (2, 2)} in R2 (I assume you meant R2 instead of R?):
These vectors are also linearly independent and span R2, so they form a basis for R2.

For the third set {(2, 1, -2, 3)} in R1:
Since there's only one vector, it cannot span a space with more than one dimension. Therefore, it does not form a basis for R1.

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An equation of the tangent plane to the surface z = 2x^2 + y^2 − 5y at the point (1, 2, -4) is z = 2x - y + 5. The correct option is c.

To find the equation of the tangent plane to the surface z = 2x^2 + y^2 − 5y at the point (1, 2, -4), we need to:

Step 1: Compute the partial derivatives of the surface equation with respect to x and y.
∂z/∂x = 4x
∂z/∂y = 2y - 5

Step 2: Evaluate the partial derivatives at the given point.
At the point (1, 2, -4):
∂z/∂x = 4(1) = 4
∂z/∂y = 2(2) - 5 = -1

Step 3: Use the point-slope form of the tangent plane equation.
The equation of the tangent plane is given by: z - z₀ = ∂z/∂x (x - x₀) + ∂z/∂y (y - y₀)
Here, (x₀, y₀, z₀) = (1, 2, -4)

So, z - (-4) = 4(x - 1) - 1(y - 2)

Simplify the equation:
z + 4 = 4x - 4 - y + 2

Finally, the equation of the tangent plane is:
z = 4x - y + 2

Comparing with the given options, the correct answer is:
c. z = 2x - y + 5

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The model of for the given relationship is,

R(x) = (200 + 50x)*(10 - x), where R(x) is the revenue of one week

This graph has downward parabola, vertex at (3, 2450) intersects X axis at 10 and Y axis at 40.

Hence the Graph Y.

Given that a candlemaker prices one set of scented candles at $10 and sells an average of 200 sets each week.

If he reduces the price by $1 then the sells increases 50 more per week.

When he will reduce $ x then the sells will increase 50x per week.

Now the price of each set of scented candles = (10 - x)

and sells in a week = (200 + 50x)

So if the candlemaker's weekly revenue is R(x) then

R(x) = (200 + 50x)*(10 - x)

R(x) = 2000 + 500x - 200x - 50x²

R(x) = 2000 + 300x - 50x²

If R(x) = y, then

y = 2000 + 300x - 50x²

50(x² - 6x - 40) = - y

50{(x - 3)² - 49} = - y

50(x - 3)² - 2450 = - y

50(x - 3)² = - (y - 2450)

So, the vertex at (3, 2450) and the parabola is downwards.

when intersect X axis then y = 0

x² - 6x - 40 = 0

x² - 10x + 4x - 40 = 0

(x - 10)(x + 4) = 0

x = -4, 10

and where cuts Y axis then x = 0

y = 40

Hence the correct graph is Graph Y.

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The point of diminishing returns is (20.98, 21247.3).

The point of diminishing returns occurs when the marginal cost of producing an extra unit of output exceeds the marginal revenue generated from selling that unit. Mathematically, it is the point at which the derivative of the production function equals zero and the second derivative is negative.

Given the polynomial function N(x) of degree 3, we can find the point of diminishing returns by finding the critical points where the first derivative equals zero and evaluating the second derivative at those points.

The derivative of N(x) is N'(x) = -18x² + 360x + 2250. To find the critical points, we set N'(x) = 0:

0 = -18x² + 360x + 2250

Dividing by -18 simplifies the equation:

0 = x² - 20x - 125

Using the quadratic formula, we find the solutions to the equation:

x₁,₂ = (20 ± √(20² - 4(1)(-125))) / 2(1)

x₁,₂ = 10 ± 5√5

Thus, the two critical points of N(x) are at x = 10 - 5√5 and x = 10 + 5√5.

To determine the point of diminishing returns, we evaluate the second derivative N''(x) = -36x + 360 at these critical points:

N''(10 - 5√5) = -36(10 - 5√5) + 360 ≈ -264.8

N''(10 + 5√5) = -36(10 + 5√5) + 360 ≈ 144.8

From the evaluations, we find that N''(10 + 5√5) is negative while N''(10 - 5√5) is positive. Therefore, the point of diminishing returns corresponds to x = 10 + 5√5.

To find the corresponding y-coordinate (N(10 + 5√5)), we can substitute the value of x into the original function N(x).

Hence, the point of diminishing returns is approximately (20.98, 21247.3).

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The conclusion of the symbolised argument is that N implies (O and P). This can be proven using conditional proof and the eighteen rules of inference, or using the rule of conjunctive simplification.

The symbolic argument's conclusion is that N implies (O and P). This can be demonstrated using conditional proof and the eighteen inference rules.

Proof:

1. N ⊃ O (Premise)

2. N ⊃ P (Premise)

3. N (Assumption)

4. O (1,3 Modus Ponens)

5. P (2,3 Modus Ponens)

6. O•P (4,5 Conjunction)

7. N ⊃ (O•P) (3-6 Conditional Proof)

8. N ⊃ (O•P) (2,7 Disjunctive Syllogism)

This leads us to the conclusion that N implies (O and P).

Without the use of conditional proof, the identical result can be reached. The conjunctive simplification rule can be used to do this.

Proof:

1. N ⊃ O (Premise)

2. N ⊃ P (Premise)

3. N (Assumption)

4. O (1,3 Modus Ponens)

5. P (2,3 Modus Ponens)

6. O•P (4,5 Conjunction)

7. N ⊃ (O•P) (Conjunctive Simplification)

Therefore, we have derived the conclusion that N implies (O and P).

Complete Question:

Use conditional proof and the eighteen rules of inference to derive the conclusions of the following symbolized arguments. Having done so, attempt to derive the conclusions without using conditional proof.

1. N ⊃ O

2. N ⊃ P / N ⊃ (O • P)

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The following correctly refers to the last element in the array of integers called numbers:

numbers[length of numbers-1].

An array is a collection of items, which can be of the same type and stored in contiguous memory. Once an array is created, its size cannot be altered during program execution. The last element in an array of integers called numbers can be referred to using numbers[length of numbers-1]. This is because array indexing starts from zero and the length of an array is the number of elements it contains, but indexing ends at length-1. Therefore, the last element in an array is always at the index length-1.It is important to note that array indexing is an error-prone area of programming, and one should always ensure that indices do not go out of bounds. This can lead to memory access violations and undefined behavior. A good practice is to use loops that start from 0 and end at length-1 when iterating over an array, to ensure that all elements are processed. It is also advisable to use constants or symbolic names to represent array indices, to make the code more readable and easier to maintain.

In summary, an array is a collection of items that can be stored in contiguous memory and cannot be resized during program execution. The last element in an array of integers called numbers can be referred to using numbers[length of numbers-1]. Array indexing is an error-prone area of programming, and one should always ensure that indices do not go out of bounds.

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Answer:

a

Step-by-step explanation:

Answer:

The answer is: A. Hope it helps.

For the given problem:

Let the number = x

Two less than the quotient of a number and 8 is 1/4

so, we can write the following expression:

Now, solve the equation to find (x)

Multiplying by (8) to eliminate the denominators:

Add (6) to both sides:

So, the answer will be the number is 18

so the equation is 1 1/3 ÷ 1 2/5

simpilify it

4/3 ÷ 7/5

since its division, you want to make it multiplication to you switch the fractions around.

you get the equation 3/2 * 5/7

which is 15/14

that converted to a improper fraction is 1 1/14

answer: 1 1/14

Therefore, the area of the region r is 8 square units.

To start, let's graph the two lines and the equation y=x^2+1 in the first quadrant:
As we can see from the graph, the region r is a triangle with a curved bottom. To find the area of this region, we can use integration.
First, we need to find the x-coordinates of the points where the line y=5 intersects with the curve y=x^2+1. To do this, we set the two equations equal to each other:
5 = x^2 + 1
Subtracting 1 from both sides gives us:
4 = x^2
Taking the square root of both sides, we get:
x = ±2
Since we are only interested in the positive x-value (since we are in the first quadrant), we have:
x = 2
Next, we need to set up our integral to find the area of the region r. Since the region is bounded by the lines x=0 and y=5, and the curve y = x^2+1, we can integrate with respect to y, using the limits of integration y=1 and y=5 (since the curve starts at y=1 when x=0).
The area of the region r can be found using the following integral:
A = ∫[1,5] [√y - 1] dy
Integrating, we get:
A = [2/3 y^(3/2) - y] [1,5]
A = [2/3 (5)^(3/2) - 5] - [2/3 (1)^(3/2) - 1]
A = 25/3 - 1/3
A = 8
Therefore, the area of the region r is 8 square units.

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In a case whereby letters in the word bubble are arranged in a row the number of unique arrangements that are there  in the letters is 120.

From the question we were given the word, bubble  which can be recognized as 6! arrangements  however we know that the  3 B’s are interchangeable, from the word which is to be arranged, and we can see that there are 6 letters all together in the word and can be arranged as;

6!/3!

= 720/6

= 120

Hence, we can conclude the arangement here is 120 unique wayas.

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Answer:

A

Step-by-step explanation:

sub each value into x,the value is the minutes,that is, 1,2,3,....and so on to get the answer (gallons of water)

If a red ball is drawn from two urns containing colored balls , then the probability that it came from the first urn is  0.625 or 62.5%   .

Let A = the event that the first urn is chosen, and

B is = the event that a red ball is drawn.

We have to find P(A|B), which means , the probability that the first urn was chosen given that a red ball was drawn.

So , By Bayes' theorem:

we have , P(A|B) = P(B|A) × P(A) / P(B)  ;

Since each urn has an equal probability of being chosen, we have P(A) = P(B) = 1/2 ; and

the probability of drawing a red ball is the same regardless of which urn was chosen.

We need to find P(B|A), the probability of drawing a red ball from the first urn is 50/100 = 0.5   ;

To find P(B), the overall probability of drawing a red ball, we can use the law of total probability:

that is ; P(B) = P(B|A) × P(A) + P(B|A') × P(A')  ;

where A' = event that the second urn was chosen.

Now , we find P(B|A'), which is the probability of drawing a red ball from the second urn is = 30/100 = 0.3    ;

We know that P(A') = 1/2 = 0.5 , because there are only 2 urns.

So , we have : P(A|B) = P(B|A)×P(A) / P(B)  ;

= (0.5×0.5) / (0.5×0.5 + 0.3×0.5)

= 5/8

= 0.625

Therefore, the probability that the red ball came from the first urn is 0.625 or 62.5%   .

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Answer:

It means the area of the square is 17.

Step-by-step explanation:

To find the area of a square you must multiply the length by the width (A=LxW)

to find area of square you would have to multiply squareroot of 17 by squareroot of 17 (because all 4 sides of a square are equal to each other). That would equal squareroot of 289. When you simplify that further, the answer would be 17.

Answer:

then answer it

Step-by-step explanation:

Answer:

4.5 inches long by 2.5 inches wide

Step-by-step explanation:

If the first scale drawing is 1:8, and the second is 1:16, the dimensions are divided into two to get their drawn lengths.

Hope this helps :)

(Brainliest, please? I only need one more to level up)