A sequence of transformations occurred to create the two similar polygons. Provide a specific set of steps that can be used to create the image from the pre-image with one, two, or three transformations.

A polynomial function of degree n has at most n real zeros and at most n - 1 turning points.

Function is a type of relation, or rule, that maps one input to specific single output.

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.

Linear function is a function whose graph is a straight line

We are given that;

A polynomial function

Now,

Because of the Fundamental Theorem of Algebra states that a polynomial function of degree n has exactly n complex roots (or zeros), some of which may be repeated or non-real. The number of real roots is equal to or less than the number of complex roots.

A turning point is a point where the graph of the polynomial function changes direction from increasing to decreasing or vice versa. The number of turning points is equal to or less than one less than the degree of the polynomial function. This is because each turning point corresponds to a change in the sign of the first derivative of the function, and the first derivative is a polynomial function of degree n - 1.

Therefore, by the function the answer will be n - 1.

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The probability that the essay contains a grammar mistake or a spelling mistake is 11/32

To find the probability that an essay contains a grammar mistake or a spelling mistake, we need to add the probabilities of the essay containing only a grammar mistake, only a spelling mistake, and both a grammar and spelling mistake.

Let's first find the probability of an essay containing only a grammar mistake. From the given information, we know that 1/5 of the mistakes on the essays are grammar mistakes. So, the probability of an essay containing only a grammar mistake is

1/5 - 1/12 = 7/60

The subtraction of 1/12 is necessary because we don't want to count the mistakes that are both grammar and spelling mistakes twice.

Similarly, the probability of an essay containing only a spelling mistake is:

1/8 - 1/12 = 5/96

Again, we subtract 1/12 because we don't want to count the mistakes that are both grammar and spelling mistakes twice.

Finally, the probability of an essay containing both a grammar and spelling mistake is

1/12

Now, we can add these probabilities to find the probability that an essay contains a grammar mistake or a spelling mistake

7/60 + 5/96 + 1/12 = 11/32

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The given question is incomplete, the complete question is:

Based on past experiences, Miss Olenik knows that 1/5 of the mistakes on the essays she grades are grammar mistakes, 1/8 of the mistakes are spelling mistakes, and 1/12 of the mistakes are both grammar and spelling mistakes. If an essay is selected at random, what is the probability that the essay contains a grammar mistake or a spelling mistake?

Answer:

Step-by-step explanation:

A=wl

P=2(l+w)

Width,3

Answer:

Step-by-step explanation:

We can make 3 loaves of bread with 1 2/3 pounds of dough.

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

We have two types of fractions.

Proper fraction and improper fraction.

A proper fraction is a fraction whose numerator is less than the denominator.

An improper fraction is a fraction where the numerator is greater than the denominator.

Example:

1/2, 1/3 is a fraction.

3/6, 99/999 is a fraction.

1/4 is a fraction.

We have,

To find out how many loaves of bread can be made, we need to divide the total amount of dough by the amount of dough needed for each loaf.

The bucket contains 1 2/3 pounds of dough, which we can rewrite as an improper fraction:

1 2/3 = (3 x 1 + 2)/3 = 5/3

So, the bucket contains 5/3 pounds of dough.

Each loaf requires 4/5 of a pound of dough.

To find the number of loaves that can be made, we need to divide the total amount of dough by the amount of dough per loaf:

Number of loaves = Total amount of dough / Amount of dough per loaf

Number of loaves = (5/3) / (4/5)

To divide by a fraction, we can multiply by its reciprocal:

Number of loaves = (5/3) x (5/4)

Number of loaves = 25/12

Since we cannot make a fraction of a loaf, we need to round the result up to the nearest whole number.

Therefore,

We can make 3 loaves of bread with 1 2/3 pounds of dough.

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Answer:66.67%

Step-by-step explanation: At Jefferson High School, there are 250 students who drive to school and 375 students who ride the bus to school. To find the percentage of students who drive to school compared to the number of students who ride the bus to school, we can divide the number of students who drive to school by the number of students who ride the bus to school and multiply by 100%:

(250 / 375) * 100% = (2/3) * 100% = 66.67%

So the number of students who drive to school is 66.67% of the number of students who ride the bus to school. Is there anything else you would like to know?

Received message. At Jefferson High School, there are 250 students who drive to school and 375 students who ride the bus to school. To find the percentage of students who drive to school compared to the number of students who ride the bus to school, we can divide the number of students who drive to school by the number of students who ride the bus to school and multiply by 100%: `(250 / 375) * 100% = (2/3) * 100% = 66.67%` So the number of students who drive to school is **66.67%** of the number of students who ride the bus to school. Is

The explicit rule to represent the arithmetic sequence of seats in the theater is aₙ = 8n + 12

The arithmetic sequence can be represented by the formula:

aₙ = a₁ + (n - 1)d

where an is the nth term of the sequence, a₁ is the first term, n is the position of the term, and d is the common difference between terms.

In this case, we know that the first term (a₁) is 20, and the common difference (d) is 8 (since each row has 8 more seats than the previous row).

Using the formula, we can write the explicit rule for this sequence as

aₙ = 20 + (n - 1)8

or

aₙ = 8n + 12

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The value of x will be equal to 11 unit.

We are given that A||B

There are two angles 5x and 55

Since corresponding means pair wise angles. Like the right corner angles of two triangles etc.

For two similar figures, the pair by pair similar angles of those two similar figures are called corresponding angles which are of same measurement.

Therefore, we know that by the corresponding angles

5x = 55

Solving for x we get;

x = 55/5

x = 11

Hence, the measure of x is 11.

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If the Mean, Median and only Mode of 5 numbers, 15, 12, 14, 19, and x, are all equal, the value of x must be 15.

The mean of a data set refers to the average value, which is obtained as the quotient of the total value divided by the number of items in the data set.

The median is the central (middle) value when the values of the data set are arranged in ascending or descending order.

The mode is the value that occurs most in the data set.

15, 12, 14, 19, and x

The total value = 75 (15 + 12 + 14 + 19 + x), where x = 15

Mean = 15 (75 ÷ 5)

Median = 15 (12, 14, 15, 15, 19)

Mode = 15 (15, 15, occurring more than the other numbers).

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The number of significant figures in the measurement 0.0301 meters is given as follows:

Three.

The rules for significant digits are given as follows:

The number for this problem is given as follows:

0.0301.

Hence the first two digits are not significant, as the zeros are not between significant digits, while the final three digits are significant.

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The solution is , f(x) = tan (x) the function is defined at 0≤x<90 is the domain of the function.

Given the function f(x) = tan (x)

From trigonometry identity, tan (x) = sin(x)/cos(x)

f(x) = sin(x)/cos(x)

Using the quotient rule to find the derivative of the function, we will have;

f'(x) = cos (x)cos (x) - sin (x)[-sin (x)]/ cos²x

f'(x) = cos²x - sin²x/ cos²x

Divide through by cos²x

f'(x) = cos²x/cos²x + sin²x/cos²x / cos²x/cos²x

f'(x) = 1 + sin²x/cos²x / 1

f'(x) = 1 + (sin²x/cos²x)

f'(x) = 1 + tan²x

From trig identity,  1 + tan²x = sec²x

Hence, f'(x) = sec²x

Hence the expression  f'(x)  in terms of the secant function is sec²x

f'(x) = 1/cos²x

For the function to be defined, it means that cos²x ≠ 0

cos²x ≠ 0

cos x ≠ 0

x ≠ cos⁻¹0

x ≠ 90⁰

Hence the value of x must not be equal to 90 for the function to be defined. x can be defined at when x = 0 since cos 0 = 1, the equation will  becomes f'(0) = 1/cos²0 = 1/1 = 1.

Hence the function is defined at 0≤x<90

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complete question:

Consider the function f ( x ) = tan ( x ) , and remember that tan ( x ) = sin ( x ) cos ( x ) . What is the domain of f ? Use the quotient rule to show that one expression for f ′ ( x ) is f ′ ( x ) = cos ( x ) cos ( x ) + sin ( x ) sin ( x ) cos 2 ( x ) . What is the Fundamental Trigonometric Identity? How can this identity be used to find a simpler form for f ′ ( x ) ? Recall that sec ( x ) = 1 cos ( x ) . How can we express f ′ ( x ) in terms of the secant function? For what values of x is f ′ ( x ) defined? How does this set compare to the domain of f ?

The calculated height of the​ brace, h will be 5 ft

From the question, we have the following parameters that can be used in our computation:

Similar triangles

This means that

Ratio = Division or ratio of corresponding sides

So, we have

h : 9 = 10 : 18

So, we have the following representation

h/9 = 10/18

This gives

h = 9 * 10/18

By calculation, we have

height = 5 ft

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The coordinates (4, 3) is not a solution of any equation of straight lines.

We know that the two points equation of the line passing through points (a, b) and (c, d) is:

(y - b)/(x - a) = (b - d)/(a - c)

For Line A:

Line A passes through (-3, 4) and (9, -2) so the equation of the line is,

(y - 4)/(x - (-3)) = (4 - (-2))/(-3 - 9)

(y - 4)/(x + 3) = 6/(-12)

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

2y - 8 = -x - 3

x + 2y = 8 - 3

x + 2y = 5 ............... (i)

For Line B:

Line B passes through (2, 8) and (8, -8) so the equation of the line is,

(y - 8)/(x - 2) = (8 - (-8))/(2 - 8)

(y - 8)/(x - 2) = 16/(-6)

(y - 8)/(x - 2) = -8/3

3y - 24 = 16 - 8x

8x + 3y = 24 + 16

8x +3y = 40 ............................ (ii)

For Line C:

Line C passes through (-3, -4) and (4, 6) so the equation of the line is,

(y - (-4))/(x - (-3)) = (-4 - 6)/(-3 - 4)

(y + 4)/(x + 3) = (-10)/(-7)

(y + 4)/(x +3) = 10/7

7y + 28 = 10x + 30

7y - 10x = 30 - 28

7y - 2x = 2 ................. (iii)

For Line D:

Line D passes through (2, -2) and (5, 6) so the equation of the line is,

(y - (-2))/(x - 2) = (-2 - 6)/(2 - 5)

(y + 2)/(x - 2) = (-8)/(-3)

(y + 2)/(x - 2) = 8/3

3y + 6 = 8x - 16

8x - 3y = 16 - 6

8x - 3y = 10

The given point is (4, 3):

For equation (i): 4 + 2*3 = 4 + 6 = 10 ≠ 5

For equation (ii): 8*4 + 3*3 = 24 + 9 = 33 ≠ 40

For equation (iii): 7*3 - 2*4 = 21 - 8 = 13 ≠ 2

For equation (iv): 8*4 - 3*3 = 32 - 9 = 24 ≠ 10

Hence it does not satisfy either equations or lines.

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Answer:

Step-by-step explanation:

We can use the ratios of similar triangles to solve this problem. Let's call the height of the tree "h". Then, we have two similar right triangles:

Kaylee's triangle: the height is 1.45 meters, the length of the shadow is 34.2 meters, and the angle between the height and the shadow is theta.

Tree's triangle: the height is h meters, the length of the shadow is 39.55 meters, and the angle between the height and the shadow is also theta.

Using these two triangles, we can set up the following proportion:

h / 39.55 = 1.45 / 34.2

Cross-multiplying, we get:

h * 34.2 = 39.55 * 1.45

Simplifying:

h = (39.55 * 1.45) / 34.2

h = 1.68176

So the height of the tree is approximately 1.68 meters (to the nearest hundredth of a meter).

Answer:

A) A pencil.

This means it would be best measured in grams. The answer is the pencil and it would be best measured in grams.

Answer:

Step-by-step explanation:

First calculate total surface area:

l = 6     h = 4   w = 2

2(lw + lh + wh)

2(6·2 + 6 · 4 + 2 · 4)

2 ( 12 + 24 + 8)

2 (44)

88 ft²

Divide the total area by the square feet the spray paint can covers.

88 ft² ÷ 22 ft² = 4 cans of spray paint

The equation for determining the probability of two independent events occurring at the same time is,                       P(A and B) = P(A) * P(B). The probability that at least one of the two independent events occurs is,                                  P(A or B) = 1 - (P(not A) * P(not B)).

The equation for determining the probability of two independent events occurring at the same time is the product of their individual probabilities. For independent events A and B, the equation is:
P(A and B) = P(A) * P(B)

To find the probability that at least one of the two independent events occurs, you can use the complement rule. First, calculate the probability that neither event occurs (i.e., both events don't occur), and then subtract that from 1:
P(A or B) = 1 - P(not A and not B)

Since A and B are independent, the equation for the probability of neither event occurring is:
P(not A and not B) = P(not A) * P(not B)

So the final equation for the probability that at least one of the two independent events occurs is:
P(A or B) = 1 - (P(not A) * P(not B))

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The angles with a common reference angle of 18° in each quadrant will be 18° in the first quadrant, 162° in the second quadrant, 198° in the third quadrant, and 342° in the fourth quadrant.

Given that:

Interval of angle, 0° ≤ θ < 360°

Now we can use the reference angle to find an angle in each quadrant:

For the first quadrant, the angle θ is calculated as,

θ = 162° - 180° = 18°

For the second quadrant, the angle θ is calculated as,

θ = 180° - 18° = 162°

For the third quadrant, the angle θ is calculated as,

θ = 180° + 18° = 198°

For the fourth quadrant, the angle θ is calculated as,

θ  = 360° - 18° = 342°

Therefore, the angles with a common reference angle of 18° in each quadrant are:

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The function represented by the graph in intercept form is:

f(x) = -0.00038(x + 5.8)(x + 5)(x + 2)(x - 1)(x - 4)

We have,

To write the function represented by the graph in intercept form, we need to find the x and y intercepts and write the function as a product of linear factors.

From the graph and the given points, we can see that the function has

4 x-intercepts at -5, -2, 1, and 4.

We can also see that the function has 3 turning points at (-3.8, 95), (-1.4, 35), and (2.5, 40).

To find the y-intercept, we can use the point (-5.8, -160), which the curve emerges from.

This means that the function can be written in the form:

f(x) = a(x + 5.8)(x + 5)(x + 2)(x - 1)(x - 4)

where a is a constant to be determined.

To find the value of a, we can use any of the given points that lie on the curve. Let's use the point (-3.8, 95):

95 = a(-3.8 + 5.8)(-3.8 + 5)(-3.8 + 2)(-3.8 - 1)(-3.8 - 4)

Simplifying and solving for a, we get:

a = -95/((5.8)(3)(0.8)(4.8)(7.8)) ≈ -0.00038

Therefore,

The function represented by the graph in intercept form is:

f(x) = -0.00038(x + 5.8)(x + 5)(x + 2)(x - 1)(x - 4)

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Max purchased 4 lip gloss tubes and 3 nail polish bottles.

Let x be the number of lip gloss tubes purchased by Max and y be the number of nail polish bottles purchased by Max. Then we have:

[tex]x + y = 7[/tex](Max bought a total of 7 items)

[tex]5.32x + 6.89y = 41.95[/tex] (Max spent $41.95 in total)

To solve for x and y, we can use the first equation to express one variable in terms of the other and substitute that expression into the second equation. For example, we can solve for y in terms of x as follows:

[tex]y = 7 - x[/tex]

Substituting this into the second equation, we get:

[tex]5.32x + 6.89(7 - x) = 41.95[/tex]

Simplifying and solving for x, we have:

[tex]5.32x + 48.23 - 6.89x = 41.95\\-1.57x = -6.28\\x = 4[/tex]

So Max purchased 4 lip gloss tubes. Substituting this back into the first equation, we get:

[tex]4 + y = 7\\y = 3[/tex]

Therefore, Max purchased 4 lip gloss tubes and 3 nail polish bottles.

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We can start by using the standard normal distribution to find the z-scores for the two heights:

z1 = (176 - 180) / 4 = -1

z2 = (180 - 180) / 4 = 0

Then, we can use a standard normal distribution table or a calculator to find the area under the curve between these two z-scores. From a table, we find that the area to the left of -1 is 0.1587 and the area to the left of 0 is 0.5. Therefore, the area between -1 and 0 is:

0.5 - 0.1587 = 0.3413

To find the percentage of the population, we can convert this decimal to a percentage by multiplying by 100:

0.3413 x 100 = 34.13%

Therefore, approximately 34.13% of the population would lie between 176cm and 180cm in height.

To find the length of the unknown leg of the triangle, we will need to use the Pythagorean Theorem.

Pythagorean Theorem: a^2 + b^2 = c^2

---a and b are the legs of the triangle

---c is the hypotenuse

a = 2

b = ?

c = 3

2^2 + b^2 = 3^2

4 + b^2 = 9

b^2 = 5

b = 2.236

b (rounded) = 2.2

Answer: 2.2 ft

Hope this helps!

The total actual area of the given logo is:  16.283 ft²

The given composite figure can be divided into a semi circle and a rectangle.

Formula for area of rectangle = length * width

Formula for area of semi circle = ¹/₂πr²

We are told that 1 inch on the printed copy actually represents 8 ft.

Thus:

¹/₂ inch = ¹/₂ * 8 = 4 ft

5/16 in = 5/16 * 8 = 2.5 ft

Thus:

Area of rectangle = 2.5 * 4 = 10 ft²

Area of semi circle = ¹/₂π * 2² = 6.283 ft²

The total actual area = 10 + 6.283 = 16.283 ft²

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Answer:

Step-by-step explanation:

The formula for the volume of a right circular cylinder is:

V = πr²h

where "r" is the radius of the base, "h" is the height, and π is the mathematical constant pi (approximately 3.14).

Substituting the given values, we get:

V = π(5)²(6)

V = 150π cubic inches

Since we are asked to give the volume in cubic inches and not in terms of pi, we can approximate π as 3.14 to get:

V ≈ 150(3.14) ≈ 471

Therefore, the volume of the cylinder is approximately 471 cubic inches, which is closest to option (d) 150.

The piecewise function in the graph is:

f(x) = -1  if x ≤ -5

f(x) = x - 1   if x > 3

First, on the left side we can see a constant function that ends at x = -5, so we can write that first part as:

f(x) = -1  if x ≤ -5

The second part is a line that starts at x = 3 (but does not contain it). It is a linear equation, and we can see the points (3, 2) and (4, 3), so the slope is 1.

y = x + b

To find the value of b, we can replace any of the points there:

2 = 3 + b

2 - 3  =b

-1 = b

Then the piecewise function is:

f(x) = -1  if x ≤ -5

f(x) = x - 1   if x > 3

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Answer:

We assume that A and B are independent events.

P(A) = .6, P(B) = .25

P(A and B) = P(A)P(B) = .6(.25) = .15

P(A or B) = P(A) + P(B) - P(A and B)

= .6 + .25 - .15 = .7

D is correct.

B. The probability of buying bread and cheese is 0.15

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one

Given Data;

The probability that a shopper buys bread, P(A) = 0.6

And, The probability that a shopper buys cheese, P(B) = 0.25

Now, If two events A and B are independent, then the probability that A and B occur is:

P(A∩B) = P(A) x P(B)

Now, Replacing with data:

P(A∩B) = 0.6 x 0.25

P(A∩B)  = 0.15

Thus, The probability of buying bread and cheese is 0.15

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The correct answer is option (B)  [tex]\frac{5}{8}x - 6\frac{1}{2}[/tex]  when  [tex]\frac{5}{8}x +1\frac{1}{3}[/tex] is subtracted from [tex]1\frac{1}{4} x -5\frac{1}{6}[/tex] . Both values are in mixed fraction.

Define mixed fraction ?

A mixed fraction is a mathematical expression that represents a whole number and a fraction together. It is also called a mixed number. In a mixed fraction, the whole number is written first, followed by a space and then the fraction. The fraction represents a part of the whole number, with the numerator (top number) indicating the number of parts and the denominator (bottom number) indicating the total number of parts.

To subtract [tex]\frac{5}{8}x +1\frac{1}{3}[/tex] from [tex]1\frac{1}{4} x -5\frac{1}{6}[/tex] , we can simplify both terms to have a common denominator. The common denominator is 24. Then we have

[tex]1\frac{1}{4}x - 5\frac{1}{6} - \left(\frac{5}{8}x + 1\frac{1}{3}\right)[/tex]

[tex]= \frac{5}{4}\cdot\frac{6}{6}x - \frac{31}{6}\cdot\frac{4}{4} - \frac{15}{24}x - \frac{32}{24}[/tex]

[tex]= \frac{30}{24}x - \frac{124}{24} - \frac{15}{24}x - \frac{32}{24}[/tex]

[tex]= \frac{15}{24}x - \frac{156}{24}[/tex]

[tex]= \frac{5}{8}x - \frac{13}{2}[/tex]

[tex]= \frac{5}{8}x - 6\frac{1}{2}[/tex]

Therefore, the correct answer is option B  [tex]\frac{5}{8}x - 6\frac{1}{2}[/tex] .

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Answer:

842.87 (rounded to 2 dp)

Step-by-step explanation:

Dunno just blag it

If we randomly select a student who works part-time, the probability of that student also driving themselves to school is 1 or 100%.

To find the probability of randomly selecting a student who drives and works part-time, we need to use the formula for conditional probability. This formula states that the probability of event A given event B is equal to the probability of both events A and B occurring together, divided by the probability of event B.

In this case, event A is selecting a student who drives to school, and event B is selecting a student who works part-time. To find the probability of both events occurring together, we need to find the intersection of sets A and B, which is the group of students who both drive and work part-time. According to the Venn diagram, this group has a size of 3.

Therefore, the probability of selecting a student who drives and works part-time is:

P(A|B) = P(A and B) / P(B)

= 3 / 3

= 1

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The key features of the given function include the following:

In Mathematics and Geometry, the vertex form of a quadratic equation is modeled by this formula:

f(x) = a(x - h)² + k

Where:

Based on the information provided about the graph of this quadratic equation, we can reasonably infer and logically deduce that its vertex can be determined as follows:

0 = a(0 + 2)² + 4

0 = 4a + 4

a = -1

f(x) = -(x + 2)² + 4

Vertex, (h, k) = (-2, 4)

Axis of symmetry, Xmax = -2.

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