A class is presented with the following problem.
In a bag of marbles, the ratio of white marbles to red marbles is 2:3 and the ratio of red to black marbles is 6:11. What is the ratio of white to black marbles?
Connor, who likes using fractions, writes 2/3 *6/11 = 4/11 announces, without explanation, that the ratio of white to black marbles is 4:11. Explain why he is right. (Hint: taking the number of black marbles to be the whole unit, what fraction are red, and then what fraction are white?)

The image of point P under a 90-degree counter Clockwise rotation about the origin is (-6, -4).

To find the image of point P = (-4, 6) after a 90-degree counterclockwise rotation about the origin, we can use the following formula:

(x', y') = (xcosθ - ysinθ, xsinθ + ycosθ)

where (x, y) are the coordinates of the original point, θ is the angle of rotation, and (x', y') are the coordinates of the rotated point.

In this case, θ = 90 degrees, so we have:

(x', y') = (-4cos90 - 6sin90, -4sin90 + 6cos90)

        = (-6, -4)

Therefore, the image of point P under a 90-degree counterclockwise rotation about the origin is (-6, -4).

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Answer:

Please provide more details!

To determine the specific type of roots for the given quartic equation, we need to solve it or analyze its discriminant. However, without further calculations, we cannot determine the exact types of roots for f(x) = 3x^4 + 7x^3 + 2x^2 + x + 9.

Answer:   ±1, ±3, ±9, ±[tex]\frac{1}{3}[/tex]  

Step-by-step explanation:

f(x)=3x⁴+7x³+2x²+9

To find all possible roots, you take the last number and all its factors and put it over the first number and all its factors.

Factors of last and first:

9:  1, 3, 9

3: 1, 3

Put all of the factors of 9 divided by all factors of 3 and also make them + and - versions.  Also eliminate any repeats like ± [tex]\frac{1}{1}[/tex]    and   ± [tex]\frac{3}{3}[/tex]

±1, ±3, ±9, ±[tex]\frac{1}{3}[/tex]    

Based on the Tuesday rate, $100 United States dollars is equal to 843.64 French francs.

One hundred US dollars are equivalent to 834.3664 French francs at the exchange rate on Tuesday. Accordingly, you can swap eight hundred forty-three point 64 years old French francs for every one hundred dollars in the United States.

1. From the tables, the Tuesday rate is 0.119 US dollars to 1 French franc.

2. To find the exchange rate, multiply the number of US dollars by the exchange rate: 100 x 0.119 = 11.90.

3. To find the amount in French francs, divide the US dollars by the exchange rate: 11.90 / 0.119 = 843.64 French francs. Based on the Tuesday rate, $100 United States dollars is equal to 843.64 French francs.

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The probability for the dial stops on a red or blue slice is,

P = 7/8.

Since, We know that;

Probability is to measure of the likelihood of an event occurring.

Hence, It is a number between 0 and 1,

Since, The closer the probability is to 1, the more likely the event is to occur.

Hence, Probability can make predictions and decisions in various fields, including finance, statistics, etc.

Since, There are 4 red and 3 blue slices,

Hence, a total of slices,

= 4 + 3

= 7 slices that are either red or blue.

So, The probability of the dial stopping on a red or blue slice,

Probability = ( red or blue slices) / (total of slices)

Probability = 7/8

Therefore, the probability for the dial stops on a red or blue slice is 7/8.

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Complete question is,

A spinner with 8 equally sized slices has 4 red slices, 3 blue slices, and 1 yellow slices. The dial is spun and stops on a slice at random. What is the probability that the dial stops on a red or blue slice?

Write your answer as a fraction in the simplest form.

$6,500 is invested in 11% account.

$6,950 is invested in 14% account.

Let us use x to represent amount invested in the 11% account

Let us use y be represent amount invested in the 14% account.

We can set up system of two equations:

[tex]x + y =[/tex] Total amount invested

0.11x + 0.14y + 450 = Interest earned

Substituting y (Invested - x) into 2nd equation, we get:

0.11x + 0.14(Amount invested - x) + 450 = 255

We solve for x

0.03x + 450 = 255

0.03x = 195

x = 195 / 0.03

x = $6500

As $6,500 is invested in the 11% account. The amount invested in 14% interest account is:

= $6,500 + $450

= $6,950.

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The average team score for the first five basketball games is 46 points.

To find the average team score for the first five basketball games, we simply use Mean.

Mean is the sum of the scores and divide it by the number of games.

Given scores:

Game 1 score = 54

Game 2 score = 60

Game 3 score = 28

Game 4 score = 42

Sum of scores = 54 + 60 + 28 + 42

                        = 184

Number of games = 4 (since we have scores for only four games)

Average team score (Mean) = Sum of scores / Number of games

                                               = 184 / 4

                                               = 46

Therefore, the average team score for the first five basketball games is 46 points.

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Answer:

10

Step-by-step explanation:

1 acre = 43560 ft²

3/4 acre = 3/4 × 43560 ft² = 32670 ft²

The lawn is 32670 ft².

Each bag covers 3500 ft².

number of bags needed = 32670/3500 = 9.33

You need approximately 9 1/3 bags, but since you must buy full bags, you must buy 10 bags.

Answer: 10

The experimental probability that in a group of 4 students, at least one of them has brown eyes, based on the given sample, is 0.898 or 89.8%.

We know that "2", "4", and "8" represent the 30% of students with brown eyes.

Any occurrence of these numbers in the sample would indicate a student with brown eyes, while other numbers would represent students without brown eyes.

Let's examine the sample of 20 random numbers:

3, 7, 1, 6, 4, 2, 0, 9, 8, 5, 2, 7, 6, 8, 4, 3, 1, 2, 0, 4

Out of these 20 numbers, the following represent students with brown eyes: 4, 2, 8, 2, 8, 4, 2, 4.

Total possible combinations of 4 students from the sample = C(20, 4) = 4845 (using the combination formula)

Number of combinations without any student having brown eyes = C(12, 4) = 495 (choosing 4 students from the remaining 12 who don't have brown eyes)

The number of combinations where at least one student has brown eyes = 4845 - 495 = 4350

Experimental probability of at least one student having brown eyes

= 4350 / 4845

= 0.898

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f(x) = 4.1/(42.4x-10(x-2)), x-intercept = -4.878, y-intercept = (0,-2.05), asymptotes: vertical at x=2, horizontal at y=0, and slant at y=4.1/8x.

Given: f(x) = 4.1/(42.4x-10(x-2))

To find the x-intercept, we set f(x) to zero and solve for x:

0 = 4.1/(42.4x-10(x-2))

0 = 4.1/(32.4x+20)

0 = 4.1/4.08(x+4.878)

So, the x-intercept is x = -4.878.

To find the y-intercept, we set x to zero and solve for f(x):

f(0) = 4.1/(42.4(0)-10(0-2))

f(0) = -2.05

So, the y-intercept is (0,-2.05).

To write f(x) in the form f(x) = -1/(ax + b) + q, we can simplify the expression as follows:

f(x) = 4.1/(42.4x-10(x-2))

f(x) = 4.1/(32.4x+20)

f(x) = 4.1/4.08(8x+5)

So, a = 8, b = 5, and q = 4.1/4.08.

To draw the graph of f, we plot the x- and y-intercepts and the vertical asymptote x = 2.

We can find the horizontal asymptote by noting that as x becomes very large or very small, the term 10(x-2) dominates the expression, so f(x) approaches 4.1/-10x. Thus, the horizontal asymptote is y = 0.

To find the equations of the slant asymptotes, we divide the numerator by the denominator using long division:

4.1

8x + 5 | 4.1

- 4.1

0

So, the slant asymptote is y = 4.1/8x.

Therefore, the intercepts of f are x = -4.878 and (0,-2.05), and the equation of f(x) in the form f(x) = -1/(ax + b) + q is f(x) = -1/(8x + 5) + 1.0039.

The graph of f has intercepts with the x-axis at x = -4.878 and the y-axis at (0,-2.05), a vertical asymptote at x = 2, a horizontal asymptote at y = 0, and a slant asymptote at y = 4.1/8x.

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Answer:

the answer is: 258

How?:

Area:

2(wl+hl+hw)

2(9×6 + 5×6 + 5×9) = 258

Answer:

f(- 5) = 10

Step-by-step explanation:

the absolute value function always gives a positive value, that is

| - a | = | a | = a

given

f(x) = 5 + | x |

to find f(- 5) substitute x = - 5 into f)x)

f(- 5) = 5 + | - 5| = 5 + | 5 | = 5 + 5 = 10

Answer:

x=18 or x=6

Step-by-step explanation:

2x=36

x=18

if it was x^2 then

x^2=36

x=6

The probability of a random person on the street having an IQ score of less than 99 is 0.4729.

We have,

We need to standardize the IQ score using the formula:

z = (x - μ) / σ

So,

For x = 99,

z = (99 - 100) / 15

z = -0.067

We can then use a standard normal distribution table or calculator to find the probability of a z-score less than -0.067.

Using a standard normal distribution table, we find that the probability of a z-score less than -0.067 is 0.4729

Therefore,

The probability of a random person on the street having an IQ score of less than 99 is 0.4729.

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Using the concept of exponential decay, the predicted number of people is  233,176,000

To predict the number of gas-powered cars on the road in 10 years, we'll apply the given annual decrease rate of 1.9% to the initial count of 286 million.

First, let's calculate the decrease rate per year:

Decrease rate = 1.9% = 1.9/100 = 0.019

Next, we'll calculate the predicted count after 10 years using the formula for exponential decay:

Predicted count = Initial count * (1 - Decrease rate)^Number of years

Substituting the values:

Predicted count = 286 million * (1 - 0.019)^10

Calculating the value:

Predicted count ≈ 286 million * (0.981)^10

Rounding the answer to the nearest whole number:

Predicted count ≈ 286 million * 0.816

Predicted count ≈ 233,176,000

Therefore, the best prediction for the number of people driving gas-powered cars in 10 years, based on the given information, is approximately 233,176,000.

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a. The concentration of the drug after 8 hours is equal to 24 mg/L.

b. The interval over which the concentration increases is 0 < t < 2. The interval over which the concentration decreases is 2 < t < ∞.

c. The drug is at its maximum concentration when t = 2 hours and the maximum concentration is 64 mg/L.

d. After the drug reaches its maximum concentration, the number of hours that are required for the concentration to decrease to 16 mg/L is 8 hours.

e. After 1 week and 1 month, we can predict that the concentration of the drug kept decreasing after reaching 20 hours.

f. After the drug is taken orally, it took exactly 2 hours to reach a maximum concentration of 64 mg/L.

By critically observing the graph, the time and concentration of the drug after 8 hours is represented by the order pair (8, 24). Therefore, the concentration is equal to 24 mg/L.

Part b.

For any given function, y = f(x), if the output value (range or y-value) is decreasing when the input value is increased, then, the function is generally referred to as a decreasing function.

For any given function, y = f(x), if the output value (range) is increasing when the input value is increased, then, the function is generally referred to as an increasing function.

By critically observing the graph of the given function, we can reasonably infer and logically deduce the following:

Part c.

The vertex (2, 64) of the graph represent the point where the drug is at its maximum concentration, which is time (t) = 2 hours and the maximum concentration is y = 64 mg/L.

Part d.

After the drug reaches its maximum concentration, the number of hours that are required for the concentration to decrease to 16 mg/L can be calculated from the graph as follows;

Number of hours = 10 - 2

Number of hours = 8 hours.

Part e.

After 1 week and 1 month, it can be predicted that the concentration of the drug kept decreasing after reaching 20 hours.

Part f.

After the drug is taken orally, it took exactly 2 hours to reach a maximum concentration of 64 mg/L. Subsequently, the level of the drug in the bloodstream drops after reaching its maximum concentration, reaching approximately 10 mg/L after 12 hours.

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The value of n on the series 5 + 10 + 20 + ... = 5115 is 10

The given sequence is 5, 10, 20, ... is a geometric progression (GP) with

first term a = 5 and

common ratio r = 2

formula for the sum of the first n terms of a GP

Sn = a(rⁿ - 1) / (r - 1)

Substituting the values we have

5115 = 5(2ⁿ - 1) / (2 - 1)

Simplifying and multiplying both sides by 1

1023 = 2ⁿ - 1

2ⁿ = 1024

2ⁿ = 2¹⁰

Equation powers

n = 10

Therefore, the value of n is 10.

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The contrapositive of the statement "If x is a multiple of [tex]10[/tex], it is an even number" is "If [tex]x[/tex] is not a multiple of [tex]10[/tex], then it is not an even number."

To complete the contrapositive of the statement "If [tex]x[/tex] is a multiple of [tex]10[/tex], it is an even number," we need to negate and reverse the original statement.

The original statement can be represented as:

[tex]\[P: \text{If } x \text{ is a multiple of 10, then } x \text{ is an even number.}\][/tex]

The negation of this statement is:

[tex]\[\neg P: \text{If } x \text{ is not an even number, then } x \text{ is not a multiple of 10.}\][/tex]

To form the contrapositive, we reverse the implications:

[tex]\[\text{Contrapositive: If } x \text{ is not a multiple of 10, then } x \text{ is not an even number.}\][/tex]

In symbolic notation, the contrapositive would be:

[tex]\[\text{Contrapositive: } \neg P: \text{If } \neg(x \text{ is a multiple of 10}), \text{ then } \neg(x \text{ is an even number}).\][/tex]

Therefore, the contrapositive of the statement "If x is a multiple of [tex]10[/tex], it is an even number" is "If [tex]x[/tex] is not a multiple of [tex]10[/tex], then it is not an even number."

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The coordinates of the image after the rotation are given as follows:

The five more known rotation rules are given as follows:

The coordinates of the original image are given as follows:

The rotation is a 90º counterclockwise about the origin, hence the rule is given as follows:

(x,y) -> (-y, x).

Meaning that the coordinates of the rotated image are given as follows:

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The evaluation of the value of the arithmetic operation based on the place value of the numbers indicates;

1. The number in the thousands place is; 7

The number is od

2. The difference between the predecessor and successor of the set of integers is; 8 - 6 = 2

Arithmetic operations are operations including, addition, subtraction, division and multiplication.

1. The numbers to be added are; 600, 5800, and 685

The sum of the numbers is; 600 + 5800 + 685 = 7085

Therefore, the place value in the thousands place is 7

The last digit of the number 7085 is 5 indicating that the number is an odd number

2. The predecessor of a number is the number that comes before the number.

The successor of the number is the number that comes after the number

The difference between the predecessor and the successor of a number therefore is; n + 1 - (n - 1) = n + 1 - n + 1 = 2

Example; 8 - 6 = 2

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The graph of the derivative, F', shows that the slope is positive until x = 2 (the right end of the semicircle) and then becomes zero.

Since the graph of F' consists of two line segments and a semicircle, we can determine the values of F using the information provided.

Let's break down the problem into different intervals based on the graph:

Interval (-∞, -5):

Since we don't have specific information about this interval, we cannot determine the exact value of F(-5).

Interval (-5, 0):

In this interval, we have a line segment. Let's assume the equation of the line segment is y = mx + b. We can find the equation of this line segment by using the slope-intercept form of a line and the given point (2, 1).

The slope of the line can be calculated using the difference in y-coordinates divided by the difference in x-coordinates:

m = (1 - F(2)) / (2 - (-5)) = (1 - 1) / 7 = 0/7 = 0

Since the slope is 0, the equation of the line becomes y = b. Plugging in the point (2, 1) into the equation, we get:

1 = b

Therefore, the equation of the line segment for the interval (-5, 0) is y = 1.

Interval (0, ∞):

In this interval, we have a semicircle. The graph of the derivative, F', shows that the slope is positive until x = 2 (the right end of the semicircle) and then becomes zero. This indicates that the original function F is increasing until x = 2 and remains constant afterward.

Since F(2) = 1, we can conclude that F(x) = 1 for x ≥ 2. Therefore, F(-5) cannot be determined based on the given information.

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Answer:

52° is approximately 0.907 radians

Step-by-step explanation:

To find the equivalent radian measure for an angle that measures 52°, we need to convert 52° to radians using the formula:

radians = degrees × π/180

Substituting the value of 52° into the formula, we get:

radians = 52 × π/180

radians ≈ 0.907

Therefore, the equivalent radian measure for an angle that measures 52° is approximately 0.907 radians.

Answer:

so you start with D-6>4

then you add 6 to both sides now you have D>10

the answer is D

The calculated value of the distance covered is 2 km

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

Speeds = 24 km/h and 32 km/h

The time difference is given as

Time = 15 minutes

The distance covered is calculated as

Distance = (Change in speed) * Time

Substitute the known values in the above equation, so, we have the following representation

Distance = (32km/h - 24km/h) * 15 minutes

Evaluate

Distance = 2 km

This means that the distance covered is 2 km

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Answer:

Step-by-step explanation:

To calculate the amount of wrapping paper needed to cover the package, we need to find the area of each face of the trapezoidal prism and add them together.

First, we can find the area of the trapezoidal front and back faces. The formula for the area of a trapezoid is:

Area = (a + b) / 2 * h

where a and b are the lengths of the parallel sides, and h is the height. For the front and back faces, we have:

Front/back area = ((6 + 12) / 2) * 15 = 135 square inches

Next, we can find the area of the top and bottom faces, which are rectangles. The formula for the area of a rectangle is:

Area = length * width

For the top and bottom faces, we have:

Top/bottom area = 4 * 12 = 48 square inches

Finally, we need to find the area of the two slanted faces. These faces are parallelograms, and the formula for the area of a parallelogram is:

Area = base * height

where the base is the distance between the two parallel sides, and the height is the perpendicular distance between the two parallel sides. For the slanted faces, we have:

Slanted face area = 1/2 * (12 + 4) * 10 = 80 square inches

Now we can add up all the areas to get the total amount of wrapping paper needed:

Total area = Front/back area + Top/bottom area + 2 * Slanted face area

Total area = 135 + 48 + 2 * 80

Total area = 343 square inches

Therefore, the minimum amount of wrapping paper needed to cover the package is 343 square inches.

Answer:

The answer is down below

Step-by-step explanation:

1 -6 0 3 6

9 7 + 1 4 7

5 3 2 5 8

= 1+0 -6+3 0+6

9+1 7+4 0+7

5+2 3+5 0+8

= 1 -3 6

10 11 7

7 8 8

Answer:

The blank is "Gross Domestic Product (GDP)."

Answer: 314 mi

Step-by-step explanation:

Area of a circle = (pi) * (radius)^2

Radius is 1/2 the diameter

Radius = 10

10^2 = 100

100*3.14 = 314