consider the expression 3 * 2 ^ 2 < 16 5 andalso 100 / 10 * 2 > 15 - 3. which operation is performed first?

The ordered pair of C'' after the sequence of transformation is (-14, -5)

Here we have know that  ABC can be plotted at A (-14, 14), B (-8, 11) & C (-14, 5).

Here we all know that the y-axis reflection rule is written as,

=> (x, y) → (-x, y)

And the value of x coordinate flips in sign from positive to negative, or vice versa. Then the value of y coordinate stays the same.

Then the point is look like C(-14,5) will then reflect based on the following rule,

=> (x, y) → (x, y)

The transformed coordinates are look like,

=> (-14,5) ((-14),5)

=> (-14,5)→ (14,5)

Therefore, here we have point C' located at (14,5) after applying the y-axis reflection rule on point C.

Now, the next operation to do is is the 180 degree rotation.

And this can be clockwise or counterclockwise.

Then the rotation rule is written as

=> (x, y) → (-x,y)

Now, for this time both coordinates flip in sign.

Here we have know that this rule only works if the center of rotation is the origin.

Now, let us apply that rotation rule to C' to find where C" is located.

Then the rule can be written as,  (x, y) → (-x,y)

=> (14,5)→ (-14, -5)

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The formula for sin and cos are opposite side/hypotenuse and adjacent side/hypotenuse respectively.  

Sin and Cos formulae are based on the sides of the right-angled triangle. Along with the tan function, the fundamental trigonometric functions in trigonometry are sin and cos. In contrast to the cosine of an angle, which corresponds to the ratio of the adjacent side to the hypotenuse, the sine of an angle is the ratio of the opposing side to the hypotenuse.

Sine of an angle θ = opposite side/hypotenuse

Cosine of an angle θ = adjacent side/hypotenuse

The figure given in the attachment is a right angled triangle which shows opposite side, adjacent side and hypotenuse side with an angle θ which is specified.

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Answer: Rational

This is because the number is in the form P/Q where P and Q are integers

We have P = -13 and Q = 12.

You can think of "rational" as in "ratio" which is very closely tied to fractions. Any rational number is a fraction of two integers. The denominator can never be zero.

Answer:

Rational

Step-by-step explanation:

A rational number is any integer, fraction, terminating decimal, or repeating decimal.

Decimal form: − 1.08 3

3 repeats itself, so it's rational.

Answer: 57.8

Step-by-step explanation:48.7 seconds + 49.3 seconds.= 57.8

Answer:

Step-by-step explanation:

Answer: 7 classes enrolled in

Step-by-step explanation:

200+40n=480

40n = 280

n = 7

Explanation:

We have 5 slices shaded out of 8 total. Therefore, we have 5/8 = 0.625 = 62.5% of this figure is shaded.

Answer:

62.5%

Step-by-step explanation:

Answer:

£68

Step-by-step explanation:

Width of one tile = 20cm

Calculate how many tiles you need to fit the width of the wall:

width of wall ÷ width of tile = 300 ÷ 20 = 15 tiles wide

Height of one tile = 25cm

Calculate how many tiles you need to fit the height of the wall:

height of wall ÷ height of tile = 250 ÷ 25 = 10 tiles high

Therefore, total tiles needed = 15 x 10 = 150 tiles

If there are 20 tiles in each box,  

total tiles ÷ 20 = 150 ÷ 20 = 7.5 boxes

So we need to round this UP to 8 boxes (else we won't have enough tiles)

Therefore, 8 boxes of tiles at £8.50 per box:

Total cost = 8 x 8.50 = £68

The basic formula to find the scale factor of a dilated figure is: Scale factor = Dimension of the new shape ÷ Dimension of the original shape.The dilation o a triangle with a scale factor of 2 3 represents a contraction.

The scale factor is defined as the proportion of the new image's size to that of the previous image. A fixed location in the plane serves as the centre of dilatation. The scale factor and the centre of dilation are used to determine the dilation transformation.

Finding the dilation's centre point is the first step in determining the scale factor. Next, we measure the distances between the centre point and various points on the preimage and the image. According to Math Bits Notebook, the scale factor is equal to the ratio of these distances.

Since each angle is congruent, every segment is proportional, the slope of every segment is preserved, and the perimeter of the preimage and image have the same scale factor, we may use dilation scale factors to compress or enlarge a figure to the size we desire.

Dilate a triangle with a scale factor

Assume that the coordinate plane's centre of dilation is at (0, 0) at the origin. Every coordinate point of the original triangle is multiplied by the scale factor 2/3 if the scale factor is 2/3. multiplying by half after a scale factor of two.

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Answer:

k = - 8

Step-by-step explanation:

given that (x - a) is a factor of f(x) , then f(a) = 0

given

(x - 1) is a factor of f(x) then f(1) = 0 , that is

3(1)³ + 5(1) + k = 0

3(1) + 5 + k = 0

3 + 5 + k = 0

8 + k = 0 ( subtract 8 from both sides )

k = - 8

Answer:

Step-by-step explanation:

you first take A15 and square it. Then you take B20 and square it also. Then you add them together and that is your answer. the hypotenuse of a triangle.

Answer: Side length C will be 25

Step-by-step explanation:

C^2 = A^2+B^2

15^2+20^2=C^2
225+400=625

Take square root of 625 to get side C

The volume in gallons of the water cooler is 183.49 gallons

We know that the volume of a cylinder of radius R and height H is.

V = pi*R²*H

Where pi = 3.14

Here we know that the diameter is 2.5 ft, then the radius is:

R = 2.5ft/2 = 1.25ft

And the height is 5ft

So the volume is:

V = 3.14*(1.25ft)²*5ft = 24.53125 ft³

And we know that

1ft³ =  7.48 gallons

Then we can do a change of units to get:

24.53125*7.48 gal = 183.49 gal

That is the correct option.

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The original equation and the orthogonal equation are the same, we can conclude that the family of conics with the same focus x^2/a^2+C + y^2/b^2+C = 1 is its own orthogonal family of curves.

To show that the family of conics with the same focus x^2/a^2+C + y^2/b^2+C = 1 is its own orthogonal family of curves, we need to take the derivative of the equation and set it equal to -1/b^2, the slope of the orthogonal line.

First, we take the derivative of the equation with respect to x:

2x/a^2 = -2y/b^2 * dy/dx

Simplifying, we get:

dy/dx = -b^2*x/a^2*y

Now, we set this equal to -1/b^2:

-b^2*x/a^2*y = -1/b^2

Cross-multiplying and simplifying, we get:

x/a^2*y = 1/b^2

Finally, we can rearrange this equation to get:

y = b^2*x/a^2

This equation represents the orthogonal family of curves to the original family of conics. Since the original equation and the orthogonal equation are the same, we can conclude that the family of conics with the same focus x^2/a^2+C + y^2/b^2+C = 1 is its own orthogonal family of curves.

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The probability that both digits in a New York State daily lottery game are different is 0.9, or 9 out of 10.

To find the probability that both digits in a New York State daily lottery game are different, we need to first calculate the total number of possible outcomes. Since there are 10 digits (0-9) that can be selected for each of the two digits in the sequence, there are a total of 10 x 10 = 100 possible outcomes.

Now, we need to determine the number of outcomes where both digits are different. There are 10 possible choices for the first digit and only 9 possible choices for the second digit, since we cannot choose the same digit as the first. Therefore, there are a total of 10 x 9 = 90 outcomes where both digits are different.

The probability of both digits being different is equal to the number of outcomes where both digits are different divided by the total number of possible outcomes. Thus, the probability is 90/100, which simplifies to 9/10, or 0.9.

In summary, the probability that both digits in a New York State daily lottery game are different is 0.9, or 9 out of 10. This means that there is a high likelihood that both digits selected will be different.

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Step-by-step explanation:

Statements

1.RS tangent to circle A and circle B at point R and point S

2.AR is perpendicular to RS, BS is perpendicular to RS

3.AR is parallel to BS

Reasons

1.Given

2.Radius are perpendicular to tangent

3. 2 lines perpendicular to the same line are parallel to each other

Walking is not safe on the path whenever rabbits have been seen in the area, and berries are ripe along the path. This is formalized by using the →(if-then) and ∧(logical and) operators.

Given information and corresponding atomic propositions:

We need to formalize the given statements in terms of atomic propositions r, b, and w, which are defined as follows:

r: Rabbits have been seen in the area.

b: Berries are ripe along the path.

w: Walking on the path is safe.

Now, let us formalize each of the given statements in terms of these atomic propositions:

a) Berries are ripe along the path, but rabbits have not been seen in the area.

b: Rabbits have not been seen in the area, and walking on the path is safe, but berries are ripe along the path.

c: If berries are ripe along the path, then walking is safe if and only if rabbits have not been seen in the area.

d: It is not safe to walk along the path, but rabbits have not been seen in the area, and the berries along the path are ripe.

e) For walking on the path to be safe, it is necessary but not sufficient that berries not be ripe along the path and for rabbits not to have been seen in the area.

Walking is not safe on the path whenever rabbits have been seen in the area, and berries are ripe along the path.

The formalizations in terms of atomic propositions are:

a) b ∧ ¬r.b) ¬r ∧ w ∧

b.c) (b → w) ∧ (¬r → w).

d) ¬w ∧ ¬r ∧

b.e) (¬r ∧ ¬b) → w.b ∧

Berries are ripe along the path, but rabbits have not been seen in the area.

This is formalized by using the ∧(logical and) operator.

(¬r ∧ ¬b) → w: It means For walking on the path to be safe, it is necessary but not sufficient that berries not be ripe along the path and for rabbits not to have been seen in the area.

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Answer:

l = 40 m

Step-by-step explanation:

The formula for area of a rectangle is

A = lw, where

Step 1:  Since we're given the area and width, we plug in these two values for A and w and to solve for l (length):

360 = 9l

Step 2:  Divide both sides by 9 to solve for l

(360 = 9l) / 9

40 m = l

Optional Step 3:  We can check our answers by checking that the product of 40 and 9 is 360

40 * 9 = 360

360 = 360

Answer: 56.9

Step-by-step explanation:

Let the original number be denoted by x.

We are informed that when the number is increased by 5.5%, the result is 60. This can be represented by:

x + (5.5% of x) = 60

x + (0.055 × x) = 60

x + 0.055x = 60

1.055x = 60

x = 60/1.055

x = 56.9

The original number is 56.9

Answer:

Concept:

Mean is just another name for average. To find the mean of a data set, add all the values together and divide by the number of values in the set. The result is your mean!

The values are given below as

The image below shows how to calculate the mean

By substituting values, we will have

Hence,

The mean = 10

To calculate the variance, we will use the formula below

Hence

The variance = 21

To calculate the standard deviation,

Hence,

The standard deviation is = 4.58

The magnitude of the projection of f1 onto the line of action of f2 is 5.55.

The magnitude of the projection of f1 onto the line of action of f2 can be calculated using the dot product of the two vectors. The dot product is given by the formula:

f1 • f2 = |f1| |f2| cos θ

Where f1 • f2 is the dot product of f1 and f2, |f1| and |f2| are the magnitudes of f1 and f2 respectively, and θ is the angle between the two vectors.

To find the magnitude of the projection, we need to find the dot product of f1 and f2 and divide it by the magnitude of f2. The magnitude of the projection is given by:

Magnitude of the projection = (f1 • f2) / |f2|

Let's calculate it step by step:

Step 1: Calculate the dot product of f1 and f2:
f1 • f2 = (3.8 * 9.3) + (6.3 * 3.0) = 35.34 + 18.9 = 54.24

Step 2: Calculate the magnitude of f2:
|f2| = √(9.3^2 + 3.0^2) = √(86.49 + 9) = √95.49 = 9.772

Step 3: Calculate the magnitude of the projection:
Magnitude of the projection = (f1 • f2) / |f2| = 54.24 / 9.772 = 5.55

Therefore, the magnitude of the projection of f1 onto the line of action of f2 is 5.55.

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No, this is not a function because it does not have any equal values.

The cross-sections perpendicular to the x-axis in this particular case are rectangles of height 10. The base of this solid is the region that is bounded by the graphs of y = 3x, y = 6 and x = 0. The graphs of these three lines will form a triangle with base equal to 2, height equal to 6, and area of 6 square units.

The cross-sections perpendicular to the x-axis in this particular case are rectangles of height 10. The base of this solid is the region that is bounded by the graphs of y = 3x, y = 6 and x = 0. The graphs of these three lines will form a triangle with base equal to 2, height equal to 6, and area of 6 square units. The height of the solid in this case will be 10 as that's what the rectangle of height 10 represents. The cross-sections of the solid are perpendicular to the x-axis, which means that they are perpendicular to the base of the solid as well. This means that the cross-sectional area will be the product of the height and the width of the cross-section. The width of the cross-section in this case is equal to 2x, and since the cross-section is a rectangle, the perimeter of the rectangle is equal to 2(width + height) = 2(2x + 10) = 4x + 20. Since the question asks about the cross-sectional perimeter, we can conclude that the answer to the question is b. rectangles of perimeter 20.

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The volumes of solids in the question can be calculated by using integrals with the base area and the height or width of the rectangular cross-sections. For rectangles of constant height, we find the width from the difference between the two functions and multiply it by the height. For cross-sections of a constant perimeter, the calculation is a bit more complex.

The subject of this question is the calculation of the volume of a solid. This solid is defined by the bounded region by the graphs of \(y = 3x, y = 6\), and x = 0, meaning its base is a triangle. The cross-sections perpendicular to the x-axis are rectangles of either height 10 or perimeter 20. To calculate the volume, we need to find the area of each cross-section and integrate over the range from x=0 to where y=6 intersects with y=3x (which is at x=2).

For rectangles with constant height, the width varies thus we use the equations of the boundary lines. The width of the rectangle is the difference between the two functions at a specific x, or 6 - 3x. Multiply this by the height of 10 to get the cross-sectional area. Then, we integrate the area over the x-range of the base, which is [0,2]. As for rectangles of constant perimeter, this requires more steps and could rather be achieved by setting up and solving a system of equations using x and y.

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\(\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{"y" varies inversely with }x^2}{y = \cfrac{k}{x^2}}\hspace{5em}\textit{we also know that} \begin{cases} x=10\\ y=1 \end{cases} \\\\\\ 1=\cfrac{k}{10}\implies 10 = k\hspace{9em}\boxed{y=\cfrac{10}{x^2}} \\\\\\ \textit{when x = 5, what's "y"?}\qquad y=\cfrac{10}{5^2}\implies y=\cfrac{10}{25}\implies y=\cfrac{2}{5}\)

Answer:

Either b or c

Step-by-step explanation:

Answer:

no solution

no solution

Step-by-step explanation:

To solve radical equations, you need to isolate the square root and square both sides. Then at the end, you must check solutions for extraneous solutions.

10.

\( \sqrt{5x - 10} + 6 = 4 \)

\( \sqrt{5x - 10} = -2 \)

A square root is always a non-negative number. Since the square root on the left equals -2, there is no real solution.

11.

\( \sqrt{2x^2 + 8x - 4} + 6 = 5 \)

\( \sqrt{2x^2 + 8x - 4} = -1 \)

A square root is always a non-negative number. Since the square root on the left equals -2, there is no real solution.

At the 0.1 level of significance, the conclusion we come up with is to reject the null hypothesis.

we are given that a random sample of 150 people was taken. 98 of the people in the sample favored the candidate, were it to determine whether or not the proportion of the population in favor of candidate a is significantly more than 57%.So we need to find the test statistic, which is 1.98  determined from the z score, here the rejection region is the number more than 1.28, and 1.98 is greater than 1.28, so it is better to simply reject the null hypothesis.

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Answer: −

7p^4 + 2p^3 + 10p^2

Step-by-step explanation:

Answer:

did you use google.if not use it it is good to use.

Answer:

Step-by-step explanation:

1. -10+18+6=8+6=14

2. -1+84=83

3. -2×(−6)2 +7=12×2+7=24+7=31

4. 50-(−6)2 +(−8)=50+12-8=62-8=54

5. (-2+2)× (−3)3=0× (−3)3=0

6. 30+8-42=38-42=-4

7. -9-2-1=-12

8. -32+6+6=-20

9. -10×3÷5+9=-30÷5+9=-6+9=3

10. -24÷ 8 + 33=-3+33=30