A bag contains red and yellow cubes in the ratio of 3:4. What is the probability that a red cube is picked at random from the bag?

1.

If x > 5, then the absolute value on |x+3| isn't actually doing anything.  

|x+3| = x+3 (without the absolute value) since x+3 is positive for x > 5.

2.

If x > 2, then the absolute value on |x+3| again isn't actually doing anything.  

|x+3| = x+3 (without the absolute value) since x+3 is positive for x > 2.

You'd have to be dealing with x-values less than -3 for the absolute value to impact the calculation.  Only for x < -3 would "x+3" not be positive and only then does the absolute value change the result.

Fourth month in business, George's new store will have a profit of $4500. The option "The new store will have a profit of $4500 after its fourth month in business" is the correct response.

To determine the meaning of (r - c)(4) for George's new store, we need to evaluate the expression (r - c) at x = 4.

Given that r(x) represents the store's revenue and c(x) represents the store's expenses, (r - c)(4) represents the difference between the revenue and expenses of the store after four months.

Substituting x = 4 into the expressions for revenue and expenses, we get:

r(4) = (4)^2 + 6(4) + 10 = 16 + 24 + 10 = 50

c(4) = (4)^2 - 4(4) + 5 = 16 - 16 + 5 = 5

Thus, (r - c)(4) = r(4) - c(4) = 50 - 5 = 45.

Therefore, (r - c)(4) means that after its fourth month in business, George's new store will have a profit of $4500 (since r(x) and c(x) are measured in hundreds of dollars).

The option "The new store will have a profit of $4500 after its fourth month in business" is the correct response.

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The linear equation is solved and slope is m = (24 - b) / 3 = 8

Given data ,

a)

To write a linear function that models the relationship between the cost, c, of octopus and the weight, w, in pounds, we need to determine the equation of a line in slope-intercept form, y = mx + b, where y represents the cost of octopus (c) and x represents the weight in pounds (w).

We are given that three pounds of octopus costs $24. This gives us a point on the line, which is (3, 24). Using this point, we can find the slope (m) of the line.

Let's use the slope formula:

m = (y2 - y1) / (x2 - x1)

Taking (3, 24) as our first point, and choosing another arbitrary point on the line, let's say (0, b), we can substitute the coordinates into the slope formula:

m = (24 - b) / (3 - 0)

Since the slope is constant for the linear function, we can set this expression equal to m:

m = (24 - b) / 3

Now, we have the slope (m) in terms of b. To find the value of b, we can substitute the coordinates of the known point (3, 24) into the slope-intercept form:

24 = m * 3 + b

Substituting the expression for m:

24 = [(24 - b) / 3] * 3 + b

Simplifying:

24 = 24 - b + b

24 = 24

Since the equation is true for any value of b, we can choose any value for b. Let's choose b = 0 for simplicity.

Plugging in the values of m = (24 - b) / 3 and b = 0, we have:

m = (24 - 0) / 3

m = 24 / 3

m = 8

Therefore, the slope of the linear function is 8

b)

The meaning of the slope in this context is that for each additional pound of octopus purchased, the cost increases by $8. This means that the cost of octopus is increasing at a constant rate of $8 per pound. The positive slope indicates that as the weight of the octopus increases, the cost also increases.

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The number in the mathematical statemnent is 1 1/2

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

The sum of a number, 1/6 of that number, 2 1/2 that number, and 7 is 12 1/2

Represent the number with x

So, we have the following equation

x + x/6 + 5x/2 + 7 = 12 1/2

So, we have

x + x/6 + 5x/2 = 5 1/2

Multiply through by 6

This gives

6x + x + 15x = 33

Evaluate the like terms

22x = 33

Divide through by 22

So, we have

x = 33/22

This gives

x = 1 1/2

Hence, the number is 1 1/2

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The value of the number is 1.5

First, we have that;

Let the number be x

From the information given, we have that;

The sum of a number, 1/6 of that number, 2 1/2 that number, and 7 is 12 1/2. Find the number

This is represented as;

x + 1/6x + 5/2x + 7 = 25/2

find the LCM, we get;

42x + 7x + 105x + 294  /42 = 25/2

collect the like terms, we have;

154x + 294/42 = 25/2

cross multiply the values, we have;

(154x + 294) = 25 × 21

154x = 231

Divide both sides by the coefficient

x = 1. 5

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Answer:

f(x) = x^2

f'(x) = 2x, so f'(1.8) = 2(1.8) = 3.6

B is the correct answer.

The value of the function , f'(1.8) = 3.6. option B

A function can simply be defined as an expression, a law or a rule that is used to represent the relationship between two variables in an equation.

These variables are listed as;

From the information given, we have that;

The function , f(x) is represented as x²

This is written as;

f(x) = x²

Find the derivative of the function, we get;

f'(x) = 2x

Now, substitute the value of x as 1.8 in the function, we have that;

f'(1.8) = 2(1.8)

expand the bracket, we have that;

f'(1.8) = 3.6

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To find the length of an arc intercepted by a central angle in a circle, we need to use the formula:

Arc Length = (Angle in radians) * (Radius)

In this case, the circle has a diameter of 9 meters, which means the radius is half of the diameter, so the radius is 4.5 meters.

The central angle measures radians, which we need to convert to radians. To convert a fraction to radians, we divide the numerator by the denominator and multiply by π (pi).

Radians = (7/18) * π

Now we can calculate the length of the arc:

Arc Length = (7/18) * π * 4.5

Simplifying this expression, we can calculate the approximate length of the arc.

It's important to note that the length of the arc is proportional to the measure of the central angle and the radius of the circle. The larger the central angle or the radius, the longer the arc.

In this case, the length of the arc will be determined by the specific value of the central angle in radians and the radius of the circle.

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Monomials are algebraic expressions that consist of a single term, whereas binomials consist of two terms.A binomial is an algebraic expression that consists of two terms.

Monomials are algebraic expressions that consist of a single term, whereas binomials consist of two terms.A binomial is an algebraic expression that consists of two terms. These terms can be added or subtracted, and they may contain variables, constants, and exponents. Binomials are commonly used in algebra to represent equations, formulas, and functions.

Monomials:
- 9x²
- 7x
- ln x
- -3x³
- 2x
- x
- x³
- √x
- 18x14x
- √x
- 7x-1
- 1
- Sin (x)
- x³
- e*
- √x +y
- 3-x
Binomials:
- 18x14x + 14
- (x + 4)²
- - 3n+2y + 2x + 1
- x³-5
Here are the monomials and binomials from the given algebraic expressions:
Monomials:
- ln x
- x
- x³
- √x
- 1
- Sin(x)
- e*
- 3-x
Binomials:
- +9x²+7x-35
- -3x³ + 2x
- 18x¹⁴x + 14
- 7x-1
- x³-5
- (x + 4)²
- -3n+2y + 2x + 1
- √x + y

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Answer:

266.9cm

Step-by-step explanation:

there's no explanation.

Answer:

52.334

Step-by-step explanation:

3.14[phi] x 5 cm =15.70 x 10 [height] = 157.0 x 1/3 = 52.334

cone = phi x d x height x1/3

this is the volume btw

The coordinates of A′ for the dilation with a scale factor of 1.5 and center at the origin are (3, 6).

To find the coordinates of A′, we need to apply the dilation formula:
A′ = (1.5)(A - O) + O
Where O is the center of dilation, which in this case is the origin (0, 0).
Substituting the values we have:
A′ = (1.5)(2, 4 - 0, 0) + (0, 0)
A′ = (3, 6) + (0, 0)
A′ = (3, 6)
Therefore, the coordinates of A′ for the dilation with scale factor 1.5 and center at the origin are (3, 6).
To find the coordinates of A' for the dilation with a scale factor of 1.5 and center at the origin, follow these steps:
1. Identify the given point A(2, 4) and the scale factor 1.5.
2. The center of dilation is at the origin (0, 0).
3. Multiply the x-coordinate of point A by the scale factor: 2 * 1.5 = 3.
4. Multiply the y-coordinate of point A by the scale factor: 4 * 1.5 = 6.
5. The coordinates of A' after dilation are (3, 6).
So, the coordinates of A′ for the dilation with a scale factor of 1.5 and center at the origin are (3, 6).

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The length FE in the circle is 6 units

The arc AE has a measure of 64 degrees

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

The circle

Given that the lengths from the center to either chords are equal

This means that

FE = 6 units

For the other circle, we have

BC = 58 degrees

AB = ED

The arc AE is calculated as

AE = 180 - BC - ED

Where

AB = ED = BC = 58 degrees

So, we have

AE = 180 - 58 - 58

Evaluate

AE = 64

Hence, the arc AE is 64 degrees

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The coordinates of the triangle after transformation are:

L′(1, −5), M′(1, 0), N′(2, −5)

There are different methods of transformation such as:

Translation

Rotation

Reflection

Dilation

Now, a rotation of 180 degrees counterclockwise about the origin is equivalent to the coordinate transformation given as (x, y) → ( −x, −y) . Meanwhile, a rotation of 270 degrees counterclockwise about the origin is equivalent to the coordinate transformation (x, y) → ( y, -x) .

Applying the rule for rotation of 180 degrees counterclockwise to the coordinates L(−1, 5), M(−1, 0), N(−2, 5) gives us:

L'(1, -5), M'(1, 0), N'(2, -5)

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The measures of angles 8 and 9 are given as follows:

m < 8 = m < 9 = 28.5º.

To obtain the angle measures, first we must consider that the sum of the measures of the internal angles of a triangle is of 180º.

Considering this, looking at the top triangle, we find the measure of angle 7 as follows:

m < 7 + 58 + 65 = 180

m < 7 = 180 - (58 + 65)

m < 7 = 57.

By the exterior angle theorem, an angle is supplementary with it's exterior angle, hence the measure of angle 6 is obtained as follows:

m < 6 = 180 - 57

m < 6 = 123º.

Triangle XWZ is an isosceles triangle, hence the measures of angles 8 and 9 are obtained as follows:

m < 8 + m < 9 + 123 = 180

m < 8 = m < 9 = (180 - 123)/2

m < 8 = m < 9 = 28.5º.

(isosceles triangle, these two angles have the same measure).

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The maximum area of the patio is, 450 feet²

Now, Lets remove the brackets from the function's expression

A(x) = -2x² + 60x

So we got the quadratic function and we have to find the x that corresponds to function's maximum. Let it be X max

As we know ,

X (max) = (X₁ + X₂)/2 ,

where X₁ and X₂ are the roots of the function A(x)

Lets find X₁ and X₂

x (60 - 2x) = 0

Hence, x₁ = 0  

And, 60 - 2X₂=0

x₂ = 30

So, X max= (0 + 30)/2 = 15

So A max= A(15) = 15 (60-2 x 15) = 15 (60 - 30) = 15 x 30 = 450 feet²

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The values of the points on the graph of the concentration of the drug in the bloodstream, indicates;

1 a. 24 mg/L

b. Increases; [0, 2]

Decreasing; [2, 20

c. The drug is at the maximum concentration at t = 2 hours

The maximum concentration is 64 mg/L

d. 8 hours

e. The concentration after 1 week is minute

The concentration after 1 month is more reduced than the concentration after 1 week.

f. The concentration of the drug for the first 20 hours increases in the first 2 hours, then decreases and approaches the x-axis as the x-value increases.

A graph is a visual display of the ordered pair of a function on the coordinate plane.

1. The graph in the question specifies the concentration of the drug in the bloodstream after t hours in mg/L

a. The graph indicates that the concentration after 8 hours is 24 mg/L

b. The interval over which the concentration increases is; [0, 2)

The interval over which the concentration decreases is; (2, 20]

c. The graph indicates that the drug is at its maximum concentration when the time t = 2 hours

The maximum concentration, based on the peak of the graph is 64 mg/L

d. The concentration of the drug is 16 mg/L at t = 10 hours, therefore, the time it takes the concentration to decrease to 16 mg/L from the peak therefore is; 10 hours - 2 hours = 8 hours

e. The shape of the graph indicates that the concentration of the drug in the bloodstream continuously decreases after the first two hours, therefore, the concentration after a week will be approximately 0

The concentration after 1 month will trace amounts

f. The concentration of the drug in the bloodstream over the first 20 hours indicates that concentration increases within the first 2 hours, and decreases rapidly in the next 8 hours, such that after 20 hours, the concentration in the blood is less than 4 mg/L

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Answer:

The range of the function is all real numbers less than or equal to 9.

Step-by-step explanation:

Find the domain by finding where the function is defined. The range is the set of values that correspond with the domain.

have a great day and thx for your inquiry :)

The perimeter of the figure is 9k² + 13k - 8

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

The figure

The perimeter of the figure is the sum of the side lengths

Using the above as a guide, we have the following:

Perimeter = -k + k² - 2 + 2k² + 5k + 2 + k² - 2 - k + 5k² + 10k - 6

When the expression is evaluated, we have

Perimeter = 9k² + 13k - 8

Hence, the perimeter of the figure is 9k² + 13k - 8

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The value of f (2) for the function is,

⇒ f (2) = undefined

We have to given that;

The function is defined as;

⇒ f (x) = { x³ + 18x² + 99x + 162  ; x ≤ - 3

          = { (3x - 6) / (x³ - 7x + 6)  ; - 3 < x ≤ 2

          = { √(x² - 4)  ; x > 2

Hence, We can see that;

At x = 2;

Function is defined as;

⇒ f (x) =  (3x - 6) / (x³ - 7x + 6)

Plug x = 2;

⇒ f (2) = (3 × 2 - 6) / (2³ - 7×2 + 6)

⇒ f (2) = (6 - 6) / (8 - 14 + 6)

⇒ f (2) = 0 / 0

⇒ f (2) = undefined

Thus, The value of f (2) for the function is,

⇒ f (2) = undefined

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Answer:

Therefore, the mass of the trolley (T) and the mass of the watermelons (W) cannot be determined uniquely based on the given information. We can only express their relationship using Equation (3): 3T + W = 33.

Step-by-step explanation:

Let's assign variables to the masses involved to solve the problem systematically.

Let's say:

Mass of the trolley = T kg

Mass of the mangoes = M kg

Mass of the watermelons = W kg

According to the given information:

The total mass of the trolley and mangoes is 11 kg:

T + M = 11 -- Equation (1)

The mass of the watermelons is three times the mass of the mangoes:

W = 3M -- Equation (2)

Now, we can use these equations to find the values of T, M, and W.

From Equation (2), we can express M in terms of W:

M = W / 3

Substitute this value of M into Equation (1):

T + W / 3 = 11

Multiply through by 3 to eliminate the fraction:

3T + W = 33 -- Equation (3)

Now, we have a system of two equations (Equation 2 and Equation 3) with two unknowns (T and W). We can solve this system to find the values.

Since we don't have a specific value for any variable, we can express the solution in terms of the variables.

Therefore, the mass of the trolley (T) and the mass of the watermelons (W) cannot be determined uniquely based on the given information. We can only express their relationship using Equation (3): 3T + W = 33.

Answer:

(1600 + (3200π)/3) mm²

Step-by-step explanation:

1 cm = 10mm. (1cm)² = (10²)mm = 100mm²

area of rectangle = 2 X 8 = 16cm² = 1600mm²

radius of circle = 8cm.

area of full circle would be = π r² = π (8)² = 64π cm²

360° in full circle

area of triangular sector = (60/360) X (64π) = (32π)/3 cm² = (3200π)/3 mm²

total area = (1600 + (3200π)/3) mm²

To find the measures of angles T and S, we can use the fact that the sum of the angles in a triangle is always 180 degrees.

m∠R + m∠S + m∠T = 180°

We know that m∠R = 29°, and we can use the Law of Cosines to find the measure of angle S:

cos(m∠S) = (6^2 + 3^2 - x^2) / (2 * 6 * 3) = 0.9167

m∠S = cos^-1(0.9167) = 23.6°

Now we can use the fact that the sum of the angles in a triangle is 180 degrees to find the measure of angle T:

m∠T = 180° - m∠R - m∠S = 180° - 29° - 23.6° = 127.4°

Therefore, m∠T is 127.4° and m∠S is 23.6°.

mm  m mm Answer:

Step-by-step explanation:

mnnmnmn

The probability of choosing a red golf ball as a fraction would be = 1/10.

To calculate the probability of choosing a red ball at random, the formula that should be used is given below.

That is;

Probability = possible outcome/sample space

Total number of yellow balls= 8

Total number of red ball= 3

Total number of orange balls = 5

Total number of green balls = 6

Total number of pink balls = 8

possible outcome = 3 balls(red)

Sample space = 8+3+5+6+8= 30 balls

Then probability= 3/30 = 1/10

Therefore, when a ball is selected at random the probability that Zane would pick a red ball out of all the golf coloured balls would be= 1/10.

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Mrs. Golden will not have any Fractional pieces of silver paper left over as the area of the bulletin board is exactly divisible by the area of each silver paper square.

To cover Mrs. Golden's bulletin board, we need to calculate the total area of the board and then divide it by the area of each silver paper square to get the total number of squares required.

The area of the bulletin board can be calculated by multiplying its length and width:

Area of bulletin board = 6.5 ft x 4 ft = 26 sq. ft.

Since the silver paper comes in 1 ft squares, the area of each square is 1 sq. ft.

Therefore, the total number of silver paper squares required to cover the bulletin board can be calculated by dividing the area of the bulletin board by the area of each square:

Total number of squares required = Area of bulletin board / Area of each square

= 26 sq. ft / 1 sq. ft

= 26 squares

So, Mrs. Golden will need 26 silver paper squares to cover her bulletin board.

As the area of the bulletin board is not exactly divisible by the area of each silver paper square, there will be some fractional pieces of silver paper left over. The leftover fractional area will be equal to the remainder obtained when the area of the bulletin board is divided by the area of each square. In this case, the remainder is 0 sq. ft since the area of the bulletin board is exactly divisible by the area of each square.

Therefore, Mrs. Golden will not have any fractional pieces of silver paper left over as the area of the bulletin board is exactly divisible by the area of each silver paper square.

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Answer:

The given function h has a domain of -3 ≤ x ≤ 11 and a range of 1 ≤ h(x) ≤ 25, and we also know that h(8) = 19 and h(-2) = 2.

Since we know the range of h(x) is 1 ≤ h(x) ≤ 25, statement B cannot be true because it suggests a value of h(x) outside of this range.

Statement A suggests that h(8) = 21, which is outside the given range for h(x). Therefore, statement A cannot be true.

Statement C suggests that h(2) = 16, but we do not have any information about the value of h(x) at x = 2. Therefore, statement C may or may not be true.

Statement D suggests that h(13) = 18, but 13 is outside the domain of h(x). Therefore, statement D cannot be true.

Thus, the only statement that could be true for h is B. However, we cannot be certain that statement B is true without more information about the function h.

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Step-by-step explanation:

The area of the given parallelogram is 12 yd².

Given that a parallelogram of base 2 yds and height 6 yds,

We need to find the area of the parallelogram,

A parallelogram is a quadrilateral in which the opposite sides are parallel and equal. Parallelograms are classified into three main types: square, rectangle, and rhombus, and each of them has its own unique properties.

A parallelogram is a special kind of quadrilateral that is formed by parallel lines. The angle between the adjacent sides of a parallelogram may vary but the opposite sides need to be parallel for it to be a parallelogram. A quadrilateral will be a parallelogram if its opposite sides are parallel and congruent.

So, the area of a parallelogram = base × height

so the area of the given parallelogram = 6 × 2 = 12 yd²

Hence the area of the given parallelogram is 12 yd².

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