change 6 1/3 to a percent

a. You 97 or more should be scored to get an A grade. b You should score less than 67 to lose B grade.

The arithmetic mean is defined as the ratio of the sum of observations to the total number of observations. It can be referred to as the average of a specific set of data or the arithmetic mean.

The formula for the mean of a given set of data is as follows:

Mean = Sum of Observations/Total number of observations

a) Average of the three examinations should be greater than or equal to 90 to get an A grade

Let x represent the grade in the third exam

So, (82+91+x)/3=90

⇒ x= 270 - (82+91) = 270 - 173 = 97

Thus, 97 or more should be scored to get an A grade.

b) Let x represent the grade in the third exam

Then;

(x+82+91)/3 = 80

⇒ x = 240 - 173 = 67

Thus, you should score less than 67 to lose B grade.

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The question seems incomplete, the complete question would be as:

On two​ examinations, you have grades of 81 and 92. There is an optional final​ examination, which counts as one grade. You decide to take the final in order to get a course grade of​ A, meaning a final average of at least 90. a. What must you get on the final to earn an A in the​ course?

Part B: By taking the​ final, if you do​ poorly, you might risk the B that you have in the course based on the first two exam grades. If your final average is less than​ 80, you will lose your B in the course. Describe the grades on the final that will cause this to happen.

We can use the complement rule to solve this problem, which states that the probability of an event happening is equal to 1 minus the probability of the event not happening.

The event we're trying to find the probability of is "at least 2 of the candies have a caramel center." The complement event is "fewer than 2 of the candies have a caramel center."

To find the probability of the complement event, we need to find the probability that exactly 0 candies have a caramel center, plus the probability that exactly 1 candy has a caramel center.

The probability that exactly 0 candies have a caramel center is (2/5)^0 * (3/5)^3 = (3/5)^3

The probability that exactly 1 candy has a caramel center is 3 * (2/5) * (3/5)^2 = (18/125)

The probability of the complement event is (3/5)^3 + (18/125)

Therefore, the probability of at least 2 of the candies having a caramel center is 1 - (3/5)^3 - (18/125)

I hope this helps :)

An inequality which models the scenario correctly is 4x + 7y ≤ 55.

In order to write an inequality that represents or models this scenario, we would assign variables to the number of green bows and number of yellow bows respectively, and then translate the word problem into algebraic equation as follows:

Since Inda is purchasing hair bows, and she has a total of $55 to spend with Green bows costing $4 each, and yellow bows costing $7 each, an inequality that represents this situation can be written as follows;

4x + 7y ≤ 55.

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The receiver should be positioned 3.0625 inches from the vertex.

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

Given that:

A certain parabolic microphone has a reflector dish with a diameter of 14 inches and a depth of 4 inches.

Here, we have;

Diameter = 14 inches

Depth = 4 inches

So, Radius = 14 / 2 = 7 inches

Hence, The coordinate is, (x, y) → (7, 4)

So, By the equation of parabola we get;

⇒ y = 1/4c × x²

⇒ 4 = 1/4c × 7²

⇒ 4 × 4c = 49

⇒ 16c = 49

⇒ c = 49/16

⇒ c = 3.0625 inches

Thus, The receiver should be positioned 3.0625 inches from the vertex.

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The speed of the larger pulley is 20 radian

An equation consists of numbers and variables linked together by mathematical operations to form an expression.

The speed of two connected pulleys given their diameters is given as:

d₁n₁ = d₂n₂

Where d₁, d₂ are their diameters and n₁, n₂ are their speeds

A belt connects a pulley of 2-inch radius with a pulley of 5-inch radius. If the smaller pulley turns through 50 radians, hence:

d₁ = 2 in, n₁ = 50 rad, d₂ = 5 in:

d₁n₁ = d₂n₂

2(50) = 5(n₂)

n₂ = 20 rads

The larger pulley turn with 20 radian

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the equation of the true by converting the numbers is 362.

What is Tenths?

The place value of the digit that follows the decimal is tenths. It denotes the digit's 1/10th position. The denominator and numerator are the two components of a fraction. Therefore, if a fraction has 10 as the denominator, we can represent it as a decimal number with a digit in the tenths place. The place value of the digits that come after a decimal point is defined in mathematics as tenths and hundredths. When we count from right to left, the place values of the digits in a number are ones, tens, hundreds, and thousands.

x*100+y*10+z*1

=3*100+6*10+2*1

=362.

Hence the equation of the true by converting the numbers is 362.

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The value of each variable in the parallelogram:

u = 63° and g = 60°.

A special form of quadrilateral called a parallelogram has both pairs of its opposite sides parallel and equal.

Given:

The shape is a parallelogram.

That means, the opposite sides are parallel and equal.

u=66°

3v°

u=66°=3v°

3v - u =66

u = 66 -  3v

u = 66-3v

u=63v

And opposite angles of a parallelogram are also equal.

v=63 -3

v = 60°

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Given the roots of a quadratic equation, we can find the equation by using the fact that the product of the roots equals to the constant term (c) divided by the coefficient of the quadratic term (a) and the sum of the roots equals to the opposite of the coefficient of the linear term (b) divided by the coefficient of the quadratic term (a).

The general form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants, and x is the variable.

Given that the roots of the equation are -6 and 1, we can find the equation as follows:

The product of the roots is -6 * 1 = -6

The sum of the roots is -6 + 1 = -5

We know that:

c / a = product of roots and

-b / a = sum of roots

So we can form the equation as:

ax^2 + bx + c = 0

ax^2 + (-5)x + (-6) = 0

So the quadratic equation whose roots are -6 and 1 is

ax^2 - 5x - 6 = 0

We can also verify that the roots of this equation are -6 and 1 by factoring or using the quadratic formula.

Answer:

Try It 1

Option C: 14

Try It 2
Option B: 6

Step-by-step explanation:

Definition GCF

The greatest common factor (GCF or GCD or HCF) of a set of whole numbers is the largest positive integer that divides evenly into all numbers with zero remainder

Try It 1:
GCF of 14 and 28 is 14

This is the largest number that can divide both 14 and 28 evenly

So, Option C

Try It 2:

This problem is nothing but asking to find the GCF of 12, 24 and 30

The smallest number is 12

But 30 cannot be divided evenly by 12

Take 12/2 = 6

Yes, all 3 numbers can be divided evenly by 6

So the correct answer is 6 packs and is Option B

The usual approach to solving bigger problems of this type is to find the factors of each of the numbers and then proceed to find the number which is common to all and the highest value is taken which divides each number evenly

For 12, 24, 30:

The factors of 12 are: 1, 2, 3, 4, 6, 12

The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24

The factors of 30 are: 1, 2, 3, 5, 6, 10, 15, 30

As you can see 6 is common to all three numbers; so it is the GCF of 12, 24 and 30

The constant of proportionality for the relationship between x and y is defined as,

⇒ y = kx

Where, k is constant of proportionality.

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

We know that;

If y is directly proportion to x, then we can defined as;

⇒ y = kx

Where, k is constant of proportionality.

Hence, The constant of proportionality for the relationship between x and y is defined as,

⇒ y = kx

Where, k is constant of proportionality.

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The constant of proportionality in the box to match the table will be 2/3. Then the last option is correct.

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.

The table is given below.

x      y

0     0

3      2

6      4

9      6

The variable 'y' is directly proportional to the variable 'x'. Then we have

y ∝ x

y = k x

At (9, 6), the value of the constant 'k' is given as,

6 = 9k

k = 6 / 9

k = 2/3

The proportionality is given as,

y = (2/3) x

The constant of proportionality in the box to match the table will be 2/3. Then the last option is correct.

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Answer:

options d is the correct answer of this

The number of years it will take the national debt of Bovinia to exceed -- that is, be greater than -- the national debt of Porcini is x > 8.75 years

let

Number of years = x

Bovinia:

2 + 0.65x

Porcini:

5.5 + 0.25x

Number of years national debt of Bovinia exceed the national debt of Porcini;

2 + 0.65x > 5.5 + 0.25x

0.65x - 0.25x > 5.5 - 2

0.4x > 3.5

divide both sides by 0.4

x > 3.5/0.4

x > 8.75

In conclusion, the number of years it will take Bovinia debt to exceed Porcini debt is x > 8.75 years.

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Answer:

6/8 is equivalent to 3/

Answer:

[tex]\textrm{In terms of f(x),}\\\\f(x) = \dfrac{(x-3)^2}{16} + 1\\\\[/tex]

Unable to match any of the answer choices provided. There has to be a mistake in the typing of the answer choice equations

Step-by-step explanation:

The equation of a vertical upward parabola given vertex (h, k) and focus(f, k) is :

(x-h)² = 4a(y-k)

a is the vertical distance between the y-coordinate of the focus and the y-coordinate of the vertex

The given parameters are vertex = (h, k) with h = 3, k = 1

Focus is (f, k) with f = 3, k = 5
(y-coordinate of a vertical parabola's vertex = y-coordinate of its focus)

a = 5- 1 = 4

Apply the equation:

[tex](x-h)^2 = 4a(y-k)\\\\(x - 3)^2= 4\cdot4(y - 1)\\\\(x - 3)^2= 16(y - 1)\\\\(x - 3)^2= 16y - 16\\\\[/tex]

Switch sides and add 16 to both sides:

[tex]16y = (x-3)^2 + 16\\\\\\\textrm{Divide throughout by 16:}\\\\y = \dfrac{(x-3)^2}{16} + 1\\\\[/tex]

[tex]\textrm{In terms of f(x),}\\\\f(x) = \dfrac{(x-3)^2}{16} + 1\\\\[/tex]

Answer:

2) If you spent a total of $1,200, you had the phone for 20 months.

Step-by-step explanation:

From the equation, the cost of the phone is 400 and the monthly data plan costs $30 per month

For 20 months, you would have paid:
30 x20 + 400 = 600 + 400 = $1000

and not $1200

So statement 2 is false

We can write the piecewise function as -

          {f(x) = x + 1 ,   x ∈ (- ∞, 1)}

f(x) →  {f(x) = 5 ,        x ∈ (1, 4)}

          {f(x) = x - 1 ,   x ∈ [5, ∞)}

In mathematics, a piecewise-defined function (also called a piecewise function, a hybrid function, or definition by cases) is a function defined by multiple sub-functions, where each sub-function applies to a different interval in the domain.

A piecewise function is continuous on a given interval in its domain if the following conditions are met:

For a piecewise function to be differentiable on a given interval in its domain, the following conditions have to fulfilled in addition to those for continuity above:

Give is a piecewise function in the graph.

We can write the piecewise function as follows.

For the interval (- ∞, 1) →

The line passes through the point -

(- 1, 0) and (0, 1)

We can write slope of the line -

{m} = (1 - 0)/(0 + 1) = 1

{m} = 1

and

{c} = 1

So, we can write f(x) as -

f(x) = x + 1

For the interval (1, 4) →

f(x) = 5

For the interval [5, ∞) →

The line passes through the point -

(4, 3) and (5, 4)

We can write slope of the line -

{m} = (4 - 3)/(5 - 4) = 1/1

{m} = 1

and

For the point (5, 4), we can write -

4 = 1 x 5 + c

c = 4 - 5

{c} = - 1

So, we can write f(x) as -

f(x) = x - 1

Combining all the parts, we can write piecewise function as -

          {f(x) = x + 1 ,   x ∈ (- ∞, 1)}

f(x) →   {f(x) = 5 ,        x ∈ (1, 4)}

          {f(x) = x - 1 ,   x ∈ [5, ∞)}

Therefore, we can write the piecewise function as -

          {f(x) = x + 1 ,   x ∈ (- ∞, 1)}

f(x) →  {f(x) = 5 ,        x ∈ (1, 4)}

          {f(x) = x - 1 ,   x ∈ [5, ∞)}

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GCF of 22 and 32:

=

2 .

They are not alike in anyway

Answer:

x ≥ - 6

Step-by-step explanation:

- 4x ≤ 24

Step 1 : Multiply - 1 on both sides

4x ≥ - 24

Step 2 : Divide 4 on both sides

4x/4 ≥ - 24/4

x ≥ - 6

The final simplified answer is x ≥ - 6

Answer:

x ≥ -6

Step-by-step explanation:

Divide each term in -4x ≤ 24 by −4 and simplify

Answer:

Step-by-step explanation:

You want the perimeter and area of a composite figure that has an isosceles triangle atop a semicircle of diameter 12 mm. The triangle's height is 9 mm.

The length of the semicircle is half the circumference of the circle with the same diameter:

  C = 1/2πd . . . . circumference of semicircle

  C = 1/2π(12 mm) = 6π mm ≈ 18.85 mm

When the two straight sides are added, the perimeter is found to be ...

  P = (2×10.82 +18.85) mm ≈ 40.48 mm

The perimeter of the figure is about 40.48 mm.

The area is the sum of the areas of the triangle and the semicircle:

  A = 1/2bh +1/2πr²

  A = 1/2(12 mm)(9 mm) +1/2π(6 mm)² = 1/2(108 mm² +36π mm²)

  A = (54 +18π) mm² ≈ 110.55 mm²

The area of the figure is about 110.55 mm².

The measure of ∠D is equal to 120°.

In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

Given is a parallelogram as shown in the image attached.

We can write -

{8x}° + {4x}° + ∠B = 180°

∠B = 180° - {8x}° - {4x}°

∠B = 180 - 40 - 20

∠B = 120°.

∠B = ∠D = 120°      [Opposite angles of a ||gm are equal}

Therefore, the measure of ∠D is equal to 120°.

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The height (in inches) of a visitor able to ride is h ≥ 52.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

A visitor must be taller than 52 inches.

let h be the height (in inches) of a visitor able to ride.

So, h must be greater than or equal to 52.

Then, the mathematical expression as

h ≥ 52.

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The correct option is A)The sum of the angle measures of trapezoid PQRS is 180° less than the sum of the angle measures of trapezoid P'Q'R'S'.

What  is rotation about origin?

The term "rotation" refers to an object moving in a circle around its centre. The centre point can be rotated at an angle to create various shapes. The rotation group of a particular space is the collective name for all rotations that revolve around a fixed point and form a structure. With respect to three-dimensional shapes, we can turn or rotate the elements about an endless number of fictitious axes.

Since, By the definition of rotation about origin, When a figure is rotate 180° about the origin then we get a congruent figure to that figure.

Thus, when PQRS is rotated 180° about the origin to form trapezoid P'Q'R'S'. Then trapezoid P'Q'R'S' is congruent to trapezoid PQRS.

By the definition of congruence,

The corresponding sides and angle of trapezoid P'Q'R'S' are congruent to that of trapezoid PQRS.

=> ∠P' ≅ ∠P, ∠Q' ≅ ∠Q, ∠R' ≅ ∠R and  ∠S' ≅ ∠S

Option D) is correct.

=>P'Q'R'S' is a trapezoid ⇒ Sum of the angle measures of trapezoid P'Q'R'S' is also 180°

Option A) is incorrect.

=>Since, trapezoid P'Q'R'S' is congruent to trapezoid PQRS.

Option B) is incorrect.

We know that if two shapes are congruent then their area must be equal.

⇒ Area of trapezoid P'Q'R'S' = Area of trapezoid PQRS

Thus, Option C) is also incorrect.

Hence the correct option is A)The sum of the angle measures of trapezoid PQRS is 180° less than the sum of the angle measures of trapezoid P'Q'R'S'.

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The following two-column proof can be used to demonstrate the congruency of triangles MNO and XYZ:

Two figures are said to be "congruent" if they can be perfectly positioned over each other. When stacked on top of each other, both bread slices are the same size and shape. Things that are exactly the same size and shape are said to be congruent.

Given: Line segment OZ bisects line segment MN and line segment XZ, and MNO is reflected across line OZ to form XYZ.

Prove: Triangles MNO and XYZ are congruent.

Statements | Reasons

OZ bisects MN, OZ bisects XZ | Given

Angle MOZ = Angle XOZ, Angle NOZ = Angle YOZ | Definition of angle bisector

∠MOZ = ∠XOZ, ∠NOZ = ∠YOZ | Using Corresponding angles postulate

∠MON = ∠XOY, ∠NOZ = ∠YOZ | Using definition of angle bisector

m∠MON = m∠XOY, m∠NOZ = m∠YOZ | Using Angle addition postulate

MN = XZ, MO = XO, NO = YO | Using Segment addition postulate

MNO ≅ XYZ | Using SAS congruence theorem

Therefore, we can conclude that the triangles MNO and XYZ are congruent.

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Answer:

B. $52.50

Step-by-step explanation:

Just multiply the initial value by 1.05...

Answer:

Step-by-step explanation:

The function is described as f(x) = 1/2x, while the inverse is defined as f-1(x) = 2x.

The inverse function "undoes" the original function given a function. To get the inverse of a function, we must first swap the x and y variables before solving for y.

We may obtain the inverse function of f(x) = 1/2x by exchanging x and y: y = 1/2x.

then calculate x: x = 2y

As a result, the inverse function f-1(x) = 2x.

We may now employ these functions to solve issues by undoing the original function with the inverse function.

The function is defined as f(x) = 1/2x, and the inverse as f-1(x) = 2x.

The inverse function of a function "undoes" the original function. To get the inverse of a function, swap the x and y variables before solving for y.

By exchanging x and y, we may derive the inverse function of f(x) = 1/2x: y = 1/2x.

then compute x: x = 2y

The inverse function f-1(x) Equals 2x as a result.

By redoing the original function with the inverse function, we may now use these functions to solve problems.

Answer:

1,2,2 then -4,-2, -2 and for the last one is x

Step-by-step explanation:

engenuity

The prove that triangle ABC is congruent to triangle CDA as shown is done using the SSS congruence theorem.

The given figure is a square hence all the sides are equal as rightly given.

Considering that the figure is a square means that

AB = BC = CD = DA

Using the reflexive property theorem  side AC is shared by the two triangles. Because of this the 3 sides of the triangle are equal to t=each other

This completes the side side side sss congruence theorem

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Roster notation is a straightforward way to represent a set in mathematical form. Within the curly brackets, the components (or members) of a set are listed in a row in the roster form.

A set's roster method is fairly straightforward and consists of of a list of the set's components encircled by curly brackets. It is easier to construct sets with large or even infinite cardinalities using set-builder notation because it specifies the constituents of the set rather than just listing them. I'll start with the roster technique for my response, followed by the set-builder approach.

A. S = 15 (-15, -5, -3, -1, 1, 3, 5) = x (Z) | 15 (x (Z)

By using the set-builder notation, I am creating a set of all integers where x is a factor of 15 and 15/x is an integer.

b. S = {0} = {x ∈ R | 8x = 0}

c. S = {-2, 2} = {x ∈ Z | 2x^2 = 8}

The complete quesyion is,

Write the following sets using roster method and set builder notation.

A.     Write the following sets using roster method and set builder notation.

a.        Set of all factors of 15

b.       Set of all solution of the equation 8x=0

c.        Set of all integer’s solution of 2x^2 = 8

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Answer:

x=35

Step-by-step explanation:

3x+16=5x-54

-2x=-70

x=35

Answer:

35

Step-by-step explanation:

the given two unknown angles are co-interior angles and for the lines to be parallel, they must be equal . So on equating them , we have ,

5x - 54 = 3x + 16

5x - 3x = 54 + 16

2x = 70

x = 70/2 = 35 [ required answer]

and we are done!

-Rishabh