Draw the image of triangle △ABC under a dilation whose center is P and scale factor is 3

The average rate of change of the function, [tex]f(x) = 10\sqrt[3]{x}-5[/tex] over the interval of x=8 to x=64 is calculated as: 0.357.

The average rate at which one quantity changes in relation to another's change is referred to as the average rate of change function.

A method that determines the amount of change in one item divided by the corresponding amount of change in another is known as an average rate of change function.

The average rate of change = f(b) - f(a) / b - a.

Given the following:

The function is: [tex]f(x) = 10\sqrt[3]{x}-5[/tex]

Interval is: x = 8 to x = 64

Therefore:

a = 8

b = 64

f(a) = f(8) =

[tex]f(x) = 10\sqrt[3]{8}-5\\\\f(x)=10*(2)-5\\\\f(x)=20-5\\\\f(x)=15[/tex]

f(a) = f(8) = 15

f(b) = f(10)

[tex]f(x) = 10\sqrt[3]{64}-5\\\\f(x)=10*(4)-5\\\\f(x)=40-5\\\\f(x)=35[/tex]

f(b) = f(64) = 35

Therefore:

Average rate of change =

[tex]=\frac{f(b)-f(a)}{b-a}\\\\=\frac{35-15}{64-8} \\\\=\frac{20}{56} \\\\=0.357[/tex]

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Using the Venn diagram to determine the roster form of set (A-C)'  =  { 1, 2, 5, 6, 7, 9, 10, 11, 12, 13, 14 }.

The difference of the sets A and C in this order is the set of elements which belong to A but not to C.

A - C = elements in set A but not in set C

A - C = { 3, 4 , 8 }

The A minus C complements include the following;

(A - C)' = { 1, 2, 5, 6, 7, 9, 10, 11, 12, 13, 14 }

Thus, using the Venn diagram to determine the roster form of set (A-C)' depends on the number of elements in the universal set.

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The number of outcomes in the complement of the given event is 61.

The complement of the event "choosing a nonfictional book from the bookcase" is "choosing a fictional book from the bookcase. "Number of outcomes in complement = Total number of books - Number of nonfictional books

The number of outcomes in the complement is equal to the total number of books in the bookcase minus the number of nonfictional books in the bookcase:

Number of results in complement = Number of nonfiction books - Overall number of books = 216 - 155 = 61

Therefore, there are 61 outcomes in the complement of the given event.

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If Cecily purchases a box of 100 paper clips. She puts 37 /100 of the paper clips in a jar on her desk and puts another 6 /10 in her drawer at home. The number  of the paper clips that are in Cecily's jar  is: 43.

Here is a grid to show the number of paper clips that Cecily has in her jar and drawer:

JAR | DRAWER

|

37 | 60

|

100 | 100

The fraction that the grid represents is :

37/100 + 6/100 = 43/100.

Therefore, Cecily has 43 out of 100 paper clips in her jar and drawer.

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(a) p ∨ r: "x≥7 or 12>x.", (b) r ∧ p: "12>x and x>7." and (c) r ∧ (q ∨ p) : "12>x and (x=7 or x>7),

" which simplifies to "12>x." The second part, (p ∨ q) ∧ r ∨ (p ∼ q) ∧ r ∨ (p ∧ q) ∧ r ∼ (p ∨ q), is always true when r is true, so it is equivalent to r. Thus, the entire statement is equivalent to "12>x and (x=7 or x>7)."

(a) p ∨ r: This statement is a logical disjunction, also known as an "or" statement. It is true if either the left side (p) is true or the right side (r) is true, or both. The statement "x>7" is equivalent to "x≥7 or x=7", so the statement p ∨ r can be read as "x≥7 or 12>x."

(b) r ∧ p: This statement is a logical conjunction, also known as an "and" statement. It is true only if both the left side (r) and the right side (p) are true. The statement "12>x" is equivalent to "x<12", so the statement r can be read as "x<12." Combining this with the statement p (x>7) gives "12>x>7."

(c) r ∧ (q ∨ p): This statement is a conjunction of r and a logical disjunction (q ∨ p). As we saw in part (a), p is equivalent to "x≥7 or x=7", so the statement (q ∨ p) can be read as "x=7 or x≥7". Combining this with the statement r (12>x) gives "12>x and (x=7 or x>7)", which can be simplified to "12>x."

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Two equivalent expressions for the model include the following:

4 + 6x.

2(2 + 3x).

Assuming a third row of tiles identical to the ones above is added to the model, the two expressions becomes;

6 + 9x.

3(2 + 3x).

In Mathematics, an expression is sometimes referred to as an equation and it can be defined as a mathematical equation which is typically used for illustrating the relationship that exist between two (2) or more variables and numerical quantities (number).

Based on the information provided about the algebra tile model, we can logically deduce the following:

Positive signs (+) = 4

Negative signs (-) = 6

Expression = 4 + 6x

By factoring, we have:

4 + 6x = 2(2 + 3x).

By adding a third row of tiles identical to the ones above, we have the following expression:

Positive signs (+) = 6

Negative signs (-) = 9

Expression = 4 + 6x + 2 + 3x = 6 + 9x

By factoring, we have:

6 + 9x = 3(2 + 3x).

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Answer:

Attached. Hope this helps

Anοther system οf linear equatiοns with the same number οf sοlutiοns is 12x + 51y = 156

24x + 102y = 312

A linear equatiοn is a mathematical equatiοn that describes a straight line in a twο-dimensiοnal space. It is an equatiοn that has οnly οne independent variable and οne οr mοre cοefficients that represent the slοpe and intercept οf the line.

The general fοrm οf a linear equatiοn is: y = mx + b

Where: y is the dependent variable x is the independent variable

m is the slοpe οf the  is the y-intercept

Accοrding tο the questiοn:

Tο determine whether this system οf equatiοns has οne sοlutiοn, nο sοlutiοns, οr infinitely many sοlutiοns, we can use variοus methοds such as substitutiοn οr eliminatiοn. Here, we'll use the eliminatiοn methοd:12x + 51y = 156-8x - 34y = -104

Tο eliminate οne οf the variables, we need tο find a cοmmοn multiple οf the cοefficients οf x οr y in bοth equatiοns. In this case, the cοmmοn multiple is 17, because 51 and -34 have 17 as a cοmmοn factοr:12x + 51y = 156 (multiply by 2)-16x - 68y = -208 (multiply by 2)

Nοw, we can add the twο equatiοns tο eliminate

y:12x + 51y = 156-16x - 68y = -208---------------4x - 17y = -52

We can sοlve fοr y in terms οf x:-4x - 17y = -5217y = -4x + 52y = (-4/17)x + 52/17This is the equatiοn οf a line in slοpe-intercept fοrm, with slοpe -4/17 and y-intercept 52/17.

We can alsο write anοther system οf equatiοns with the same number οf sοlutiοns that uses the first equatiοn οnly by multiplying bοth sides οf the equatiοn by a cοnstant

12x + 51y = 156

24x + 102y = 312

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Answer:3 1/2

[tex]\frac{3}{2} times\frac{7}{3} =\frac{21}{6} =3\frac{3}{6} = 3\frac{1}{2}\\[/tex]

The side length of the square that will give the closest approximation to the area of the circle described is e. s = π/4 inches

The region encircled by a circle with a radius r is known as r2 in geometry. Here, the Greek letter stands for the constant proportion of a circle's circumference to its diameter, which is roughly equivalent to 3.14159.

The area of a circle with a diameter of 1 inch is given by the formula πr^2, where r is the radius of the circle. The radius of the given circle is 1/2 inch, so its area is approximately π * (1/2)^2 = π/4 square inches.

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The first line that should be removed is the print statement. The code should not display the result right away, as this will prevent it from counting the number of prime numbers in the list.

The second line of code that should be removed is the second statement, which checks to see if the index is equal to 0. This line of code is unnecessary, as the prime numbers are already tested in the if statement before it.

In order for the program to work as intended, the code should only include the if statement that checks to see if the number is a prime number, the for loop that iterates through the list and increments the counter for each prime number found, and the print statement that displays the result at the end. This will ensure that the program counts the number of prime numbers in the list and displays the result correctly.

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Answer:

I can lead you with this equation: 1.41x + 29 = Cost

I think it will be easy from here on for you.

Step-by-step explanation:

I would assume its 4

The proposition is false, and there exist nonnegative integers x that cannot be expressed as the sum of at most two squares and a cube of nonnegative integers.

This proposition is false. A counterexample is x = 7.

Assume for the sake of contradiction that there exist nonnegative integers a, b, and c such that x = a² + b² + c³. Since a² and b² are always nonnegative, we must have c³ ≤ 7. The only possible values for c are 0, 1, and 2, since 3³ = 27 > 7.

For c = 0, we have x = a² + b², which is the sum of two squares, and is a well-known result.

For c = 1, we have x = a² + b² + 1. However, it is a known result that a sum of two squares cannot be equal to a number of the form [tex]4^{k}[/tex](8m + 7) for some nonnegative integers k and m. Since 7 is of the form 4(8×0 + 7), it cannot be expressed as a sum of two squares, and therefore, x cannot be expressed as the sum of at most two squares and a cube of nonnegative integers.

For c = 2, we have x = a² + b + 8. Similarly, it can be shown that a sum of two squares cannot be equal to a number of the form [tex]4^{k}[/tex](8m + 7) for some nonnegative integers k and m. Since 8 is of the form 4(8×1 + 0), it cannot be expressed as a sum of two squares, and therefore, x cannot be expressed as the sum of at most two squares and a cube of nonnegative integers.

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Answer:

4/5

Step-by-step explanation:

Because 1/5 is winning chance.

and the rest percentage will be losing

Conjectures are unsubstantiated claims. A theorem is created when someone proves a conjecture. In logic types that deal with conjunctions, the rule of simplification is a valid argument. The rule of inference that states that ∀xP(x) is true given the premise that P(c) is true for all elements c in the domain is known as universal generalization.

The Conjecture Rule

Conjectures are unsubstantiated claims. A theorem is created when someone proves a conjecture.

We seek to understand a conjecture on three levels: we want to know what it means, we want to know why we think the claim is true, and we want to know how it fits into a larger set of ideas.

Rule for Simplification

In logic types that deal with conjunctions, the rule of simplification is a valid argument.

This includes propositional and predicate logic, as well as natural deduction.

(1) Proof Rule: If we can reach a conclusion ϕ∧ψ, we can infer ϕ.

(2): If we can reach a conclusion ϕ∧ψ, we can infer ψ.

Rule of Universal Generalization

The rule of inference that states that ∀xP(x) is true given the premise that P(c) is true for all elements c in the domain is known as universal generalization. When we show that ∀xP(x) is true by taking an arbitrary element c from the domain and showing that P(c) is true, we are using universal generalization. The element c that we choose must be arbitrary and not a specific domain element.

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The complete question is:

Write about the conjecture rule, simplification rule, universal generalization rule.

Answer:

(1, -6)

Step-by-step explanation:

3x + y = -3

y = -3x - 3

The estimated difference of 3 1/2 and 1 1/3 is 2 1/6.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, Are two fractions 3 1/2 and 1 1/3.

Now, The difference between 3 1/2 and 1 1/3 would be,

1/2 - 1/3 is 1/6 and 3 - 1 is 2,

So, The estimated 3 1/2 -1 1/3 is 2 1/6.

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The ratio will be equal to 13:15 for the students who attended the games.

The ratio actually compares the data of two numbers. It identifies that the one data is how many times the other data.

Melanie randomly selected 15 seventh-grade students and asked them how many soccer games they had attended this school year. Each student's number of games attended is listed below 3. 2 , 6, 4, 7, 0, 4, 5, 0, 1, 2, 3, 2, 1, 4

Here, the number of students who did not attendgames=2   [since there are 2 0s]

The total number of students = 15

Number of students attending games= 15-2=13

The ratio will be equal to 13: 15

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The complete question is given below.

Melanie asked 15 random seventh-grade students how many soccer games they attended this school year. The number of games attended by each student is listed below. 2, 3, 6, 4, 7, 0, 4, 5, 0, 1, 2, 3, 2, 1, 4 What is the ratio of the total number of surveyed students who attended soccer games to the total number of students surveyed?

The distance between the two planes after 10 minutes is 10 miles.

We can use the Pythagorean Theorem to find the distance between the two planes. According to the theorem, the distance between two points in a plane is given by the equation:

d = √( (x2 - x1)^2 + (y2 - y1)^2 )

where (x1, y1) and (x2, y2) are the coordinates of the two points.

The first plane is flying due north, so its position after 10 minutes will be (0, 10). The second plane is flying due east, so its position after 10 minutes will be (10, 0).

We can plug these coordinates into the equation to find the distance between the two planes:

d = √( (10 - 0)^2 + (10 - 0)^2 )

d = √( 100 )

d = 10

So the distance between the two planes after 10 minutes is 10 miles

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Answer: this doesnt seem complete, like what are we supposed to explain with that

Step-by-step explanation:

The values of the expressions are  7x - 5y = -1, 12z + 2y² = 6 and 2xy + 8z = 4

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

x = 2, y = 3 and z = -1

Substitute the known values in the given equations, so, we have the following representation

7x - 5y = 7 * 2 - 5 * 3

7x - 5y = -1

12z + 2y² = 12 * -1 + 2 * 3²

12z + 2y² = 6

2xy + 8z = 2 * 2 * 3 + 8 * -1

2xy + 8z = 4

Hence, the expressions have their values to be -1, 6 and 4

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Complete question

Consider the following expressions:

7x-5y=

12z+2y²=

2xy+8z=

Determine the values when x = 2, y = 3 and z = -1

The correct inequality is,

⇒ 7 + 10b ≥ 22

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Translate the sentence into an inequality,

''Seven increased by the product of a number and 10 is at least 22.''

Now,

Let an unknown variable = b

Hence, We can formulate;

⇒ 7 + b × 10 ≥ 22

⇒ 7 + 10b ≥ 22

Therefore, The correct inequality is,

⇒ 7 + 10b ≥ 22

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(a) Bar A: A, Bar B: O, Bar C: F

(b) One interesting feature of the graphical display is the clear difference in the percentage of individuals who are considered unfit between adolescents and adults.

(a) Bar A: Adolescents

Bar B: Overall (both adolescents and adults)

Bar C: Adult Males vs. Adult Females

(b) The percentage of unfit individuals is much higher in adolescents (33.9%) than in adults (14%). Additionally, within the adult group, the percentage of unfit individuals is higher in females (16.2%) than in males (11.2%). Another interesting feature is that there is no significant difference in the percentage of unfit individuals between male and female adolescents.

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According to the given information the answer is JK thus has a 10-unit length.

The measurement or size of a thing end to end is referred to as its length. In other words, it is the larger of an object's elevated two or three geometric dimensions. For instance, a rectangle's dimensions are determined by its length and width.

We must determine the separation among points J and K in order to get the length of JK. The distance formula is as follows:

d = √((x2 - x1)² + (y2 - y1)²)

Where (x1, y1) = (-5, 6) is the coordinate of J and (x2, y2) = (5, 6) is the coordinate of K.

Plugging in the values, we get:

d = √(5 - (-5))² + (6 - 6)²)

= √(10² + 0²)

= √100

= 10

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Answer:

Step-by-step explanation:

-3 1/3 goes to between -3 and -4

9/2=4 1/2 between 4 and 5

[tex]\sqrt{15}[/tex] between 3 and 4

16/5=3 1/5 between 3 and 4

\sqrt{15} between 2 and 3

The measure of angle 2 from the diagram is equivalent to 111 degrees

An angle is defined as the point where two lines meet. From the diagram shown the measure of <1 and <2 lies on the same straight line.

Since the sum of angles on a straight line is 180 degrees, hence;

<1 + < 2 = 180

Substitute the given angle

69 + <2 = 180

<2 = 180 - 69

<2 = 111 degrees

Hence the measure of <2 from the given diagram is 111 degrees.

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Answer:

To find the answer, we need to subtract the amount of bags Ben used from the amount he bought:

6 and 3/5 - 4 and 1/5

To subtract fractions, we need to have a common denominator. The smallest common denominator for 5 and 20 is 20, so we'll convert both fractions:

6 and 3/5 = 6 * 5/5 + 3/5 = 30/5 + 3/5 = 33/5

4 and 1/5 = 4 * 20/20 + 1/5 = 80/20 + 1/5 = 81/20

Now we can subtract:

33/5 - 81/20

We need to convert the mixed number to an improper fraction and find a common denominator:

33/5 - 81/20 = 132/20 - 81/20

Now we can subtract:

132/20 - 81/20 = 51/20

So Ben has 51/20 bags of rocks left. This can be simplified to 2 and 11/20 bags.

Answer:

2 2/5

Step-by-step explanation:

6 3/5 - 4 1/5 = 2 2/5

Answer: look at the images for the answer ( the first image is for #1 and the second image is for #2 )

Step-by-step explanation: