Find the unit rate.
48 cupcakes in 6 boxes=cupcakes per box

The experimental probability of selecting a green marble on the next attempt is 1/6 or approximately 0.1667 or 16.67%.

What is probability?

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

The experimental probability of an event happening is calculated by dividing the number of times the event occurs by the total number of trials or attempts.

In this case, Diane has already selected 2 green marbles and 10 other marbles from the bag. So, the total number of marbles left in the bag is 12.

Since there are 2 green marbles left in the bag, the probability of selecting a green marble on the next attempt is:

2 (number of green marbles) / 12 (total number of marbles) = 1/6

So, the experimental probability of selecting a green marble on the next attempt is 1/6 or approximately 0.1667 or 16.67%.

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Given that of the new books the new books the new liberian ordered;

-1/3 are science

-2/5 are biography

Let s, b and f represent the fraction of science, biography and fiction of the new book.

substituting the values of s and b given;

The scale factor is given as follows:

5/3.

The value of x is given as follows:

x = 7.

Two triangles are defined as similar triangles when they share these two features listed as follows:

Equivalent side lengths for this problem are given as follows:

YZ and BC.

Hence the scale factor is given as follows:

10/6 = 5/3.

Then the value of x can be obtained as follows:

(12x - 59)/(2x + 1) = 5/3

Applying cross multiplication, we have that:

3(12x - 59) = 5(2x + 1)

26x = 182

x = 182/26

x = 7.

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The domain of the function is D = (0, +∞), because the range of its inverse function g(x) = b is (0, +∞).

Option D is the correct answer.

We have,

The domain is limited to positive real numbers (x > 0) because the logarithm function is only defined for positive values.

Additionally, since we have a specific base b, the input values (x) must be positive to yield a real result.

As for the range, it depends on the base b.

The range of f(x) = log_b(x) is (-∞, +∞) for any base b > 0 and b ≠ 1.

This means that the function can take any real value as its output.

Therefore,

The domain of the function is D = (0, +∞), because the range of its inverse function g(x) = b is (0, +∞).

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After considering the given data we conclude that the the car was traveling approximately 50 miles per hour when the brakes were applied.

To evaluate the speed of the car when the brakes were applied, we need to calculate the given equation for v (speed) when d (distance) is 235 feet.
The equation given to us is:
\(d = 0.05 v^2 + 2. 2v\)
Staging d = 235 into the equation, we have:
\(235 = 0.05 v^2 + 2. 2v\)
Restructuring the equation, we get a quadratic equation in standard form:
\(0.05 v^2 + 2. 2v - 235 = 0\)
To evaluate this quadratic equation, we can use factoring, completing the square, or the quadratic formula. For the given case, let's use the quadratic formula:
\(V = ( \pm b \sqrt b^2 - 4ac)/(2a)\)
For our quadratic equation, a = 0.05, b = 2.2, and c = -235.
Staging these values into the formula, we can evaluate the two possible speeds (positive and negative):
\(V = (- 2. 2 \pm \sqrt 2.2^2 - 4*0.05 * - 235) / ( 2 * 0.05)\)
Evaluating the expression within the square root:
\(V = ( - 2.2 \pm \sqrt 4.84 + 47)0.1\)
\(V = ( - 2.2 \pm \sqrt 51.85) /0.1\)
Taking the square root:
V ≈ ( - 2.2 ± 7.2)/0.1
Calculating for the positive and negative solutions:
V≈ (- 2.2 + 7.2) ≈ 50
V ≈  (- 2.2 - 7.2) ≈ 90
Since speed cannot be negative in this context, we discard the negative solution.

Hence, the car was traveling approximately 50 miles per hour when the brakes were applied.
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There are 87 possible outcomes that contain at least three heads when a coin is flipped 9 times.

When a coin is flipped nine times, there are 512 possible outcomes, or 29. Using the equation:

P (At least one head) = 1 - 0.5n,

where n is the total number of flips, we can determine the number of outcomes that contain at least three heads.

Therefore, P (At least three heads) = 1 - P (No heads) - P (One head) - P (Two heads)

= 1 - (0.5)⁹ - 9(0.5)⁹ + 36(0.5)⁹

= 0.1718751.

The formula used to calculate the number of possible outcomes that contain at least three heads is C(9,3) + C(9,4) + C(9,5) + C(9,6) + C(9,7) + C(9,8) + C(9,9),

where C(n,r) denotes the variety of options for selecting item(s) r from a set of item(s) n.

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Answer:

p ≥ 5

Scott will buy at least 5 kilograms of candy.

Step-by-step explanation:

Inequalities

The candy Scott buys cost $7 per kilogram.

Let's set p=number of kilograms of candy Scott will buy.

The money spent to buy p kilograms of candy is 7p dollars.

The condition states he will spend at least $35 on candies, thus the following inequality is formed:

7p ≥ 35

Dividing by 7:

p ≥ 35/7

Operating:

p ≥ 5

Scott will buy at least 5 kilograms of candy.

We can see that the coefficients of the expanded expression match the terms of the 5th row of Pascal's triangle.

To evaluate the given expression, we need to use Pascal's triangle to expand the expression (b+c)^4. The coefficients of the expanded expression will be the terms of the 5th row of Pascal's triangle.

Using the formula for the coefficients of the expanded expression, we get:

4(b)(c)^3 + 6(b)^2(c)^2 + 4(b)^3(c) + (b)^4

Comparing this expression to the 5th row of Pascal's triangle, we see that the coefficients are:

1 4 6 4 1

We can rearrange the terms to match the expanded expression:

(b)^4 + 4(b)^3(c) + 6(b)^2(c)^2 + 4(b)(c)^3 + (c)^4

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Calculating this expression, we find that the length of the image of the rectangle is 36 in.

To find the length of the image of the rectangle after dilation, we can use the property of similar triangles. Since the width of the image is known to be 21 in., we can set up a proportion:

(image width) / (original width) = (image length) / (original length)

Substituting the known values, we have:

21 in. / 14 in. = (image length) / 24 in.

Solving for the image length, we get:

(image length) = (21 in. / 14 in.) * 24 in.

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Answer:

The formula for area of a parallelogram is A=bh

x=10.3

Step-by-step explanation:

We don't have the base but we have the height.

the base is x and the height is 5

if the area is 51.5

we should divide the height to find the base.

51.5÷5=10.3

so the base is 10.3

Check if answer is correct:

b=10.3

h=5

a= 51.5

10.3(5)=51.5

a= 51.5cm²

I hope this helps as long as you know the formula it's easy :D

Answer:

$75

Step-by-step explanation:

henry have total money

8/13 x 650= 400

gordon will have remaining = 250

since half of the 650 is $325

so henry will give = 325-250

= $75

Answer:

y = 30

Step-by-step explanation:

y ∝ 1/x

y = k/x     →         y = 60/x

12 = k/5               y = 60/2

60 = k                 y = 30

I hope this helped you :)

Yes ,inclination in between 4in / 15 in < 4in / 18 in

An inclined plane, also known as a ramp, is a flat supporting surface that is tilted at an angle from the vertical direction with one end higher than the other. It can be used to lift or lower a load.

The horizontal line in coordinate geometry is the line perpendicular to the x-axis, and the vertical line is the line perpendicular to the y-axis. Horizontal lines and vertical lines will be parallel to the x-axis and the y-axis, respectively. As a result, lines that share at least one point are perpendicular to one another when they are drawn.

6 feet of horizontal distance for every 1 foot,

ramp shown has a vertical rise of 5 feet.

Therefore

M ≤ 1foot / 6 feet

Converting both to a single units of ( inches )

M ≤ 12 inches / 72 inches

Dividing by 4

M ≤ 4 inches / 18 inches

Where 5 feet = 60 inches

12 inches / 60 inches

= 4 inches / 15 inches

Therefore:

4in / 15 in < 4inch / 18 inch

The condition states the ramp has to be at least 6feet, what this means is it has to be between 0-6 so since it is lesser. Yes it meets the recommendations.

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Yes, inclination in between 4in / 15 in < 4in / 18 in

A flat supporting surface that is inclined at an angle from the vertical direction with one end higher than the other is referred to as an inclined plane or a ramp. A load may be raised or lowered using it.

In coordinate geometry, the horizontal line is the line parallel to the x-axis, while the vertical line is the line parallel to the y-axis. Vertical and horizontal lines will be perpendicular to the x- and y-axes, respectively. As a result, when lines are drawn, they are perpendicular to one another if they share at least one point.

6 feet of horizontal distance for every 1 foot,

ramp shown has a vertical rise of 5 feet.

Therefore

M ≤ 1foot / 6 feet

Converting both to a single units of ( inches )

M ≤ 12 inches / 72 inches

Dividing by 4

M ≤ 4 inches / 18 inches

Where 5 feet = 60 inches

12 inches / 60 inches

= 4 inches / 15 inches

Therefore:

4in / 15 in < 4inch / 18 inch

The condition states the ramp has to be at least 6 feet, what this means is it has to be between 0-6 so since it is lesser. Yes it meets the recommendations.

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After conducting some mathematical operations, we know that the 3 friends will get $28 back in change from a $100 bill.

So, the change they will get back from $100:

The Coaster is $4.50:

4.50 × 3 (friends) = 13.5

13.5 × 2 (Twice) = $27

The Slide $4.00:

4.00 × 3 (friends) = 12

12 × 2 (Twice) = $24

The Drop $3.50:

3.50 × 3 (friends) = 10.5

10.5 × 2 (Twice) = $21

Change:

100 - (27 + 24 + 21)

100 - 72

$28

Therefore, after conducting some mathematical operations, we know that the 3 friends will get $28 back in change from a $100 bill.

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Complete question:
You and three friends are going to Wonderland Water Park. Your group plans to ride each water ride twice. Prices are shown in this table.

How much change will your group get back from a $100 bill?

Wonderland Water Park

The Coaster is $4.50

The Slide $4.00

The Drop$3.50

I assume you mean the mixed number 1 + 7/9.

As an improper fraction, we have

1   7/9 = 1 + 7/9 = 9/9 + 7/9 = (9 + 7)/9 = 16/9

Then the square root of this is

√(1   7/9) = √(16/9) = √(4²/3²) = √((4/3)²) = 4/3

Answer:

Step-by-step explanation:

\(V=\pi r^2h\\r=2\\h=5\\V=20\pi \\\)

wasn't 100% sure what it means by in terms of pi so i left it as is. lmk if i need to fix it.

Answer:

Step-by-step explanation:

2 + 4 > 8

6 > 8

not true

Answer: y = 5x + 26

Step-by-step explanation:

To find the equation of a line that is perpendicular to the given line y = -1/5x + 1 and passes through the point (-5, 1), we need to determine the slope of the perpendicular line. The given line has a slope of -1/5. Perpendicular lines have slopes that are negative reciprocals of each other. So, the slope of the perpendicular line will be the negative reciprocal of -1/5, which is 5/1 or simply 5. Now, we have the slope (m = 5) and a point (-5, 1) that the perpendicular line passes through.

We can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Substituting the values, we get:

y - 1 = 5(x - (-5))

Simplifying further:

y - 1 = 5(x + 5)

Expanding the brackets:

y - 1 = 5x + 25

Rearranging the equation to the slope-intercept form (y = mx + b):

y = 5x + 26

Therefore, the equation of the perpendicular line that passes through the point (-5, 1) is y = 5x + 26.

Answer:

x² + 34x + 104 = 0

x² + 34x = -104

x² + 34x + ((1/2)(34))² = -104 + ((1/2)(34))²

x² + 34x + 17² = -104 + 17²

x² + 34x + 289 = 185

(x + 17)² = 185

x + 17 = +√185

x = -17 + √185

a) (572)8
Step 1:  5 - 101, 7 - 111, and 2 - 010
Step 2: Combine the binary equivalents.
(572)8 = (101 111 010)2

b) (1604)8
Step 1: Convert each digit to its 3-bit binary equivalent.
1 - 001, 6 - 110, 0 - 000, and 4 - 100
Step 2: Combine the binary equivalents.
(1604)8 = (001 110 000 100)2

c) (423)8
Step 1: Convert each digit to its 3-bit binary equivalent.
4 - 100, 2 - 010, and 3 - 011
Step 2: Combine the binary equivalents.
(423)8 = (100 010 011)2

d) (2417)8
Step 1: Convert each digit to its 3-bit binary equivalent.
2 - 010, 4 - 100, 1 - 001, and 7 - 111
Step 2: Combine the binary equivalents.
(2417)8 = (010 100 001 111)2

To convert an octal number to binary, we simply need to replace each octal digit with its 3-bit binary equivalent. Here are the steps for each of the given integers:

a) (572)8
- The octal expansion has three digits: 5, 7, and 2.
- To convert each digit to binary:
  - 5 = 101 in binary (since 5 = 4 + 1 = 2^2 + 2^0)
  - 7 = 111 in binary (since 7 = 4 + 2 + 1 = 2^2 + 2^1 + 2^0)
  - 2 = 010 in binary (since 2 = 2^1)
- So the binary expansion of (572)8 is 101111010.

b) (1604)8
- The octal expansion has four digits: 1, 6, 0, and 4.
- To convert each digit to binary:
  - 1 = 001 in binary (since 1 = 2^0)
  - 6 = 110 in binary (since 6 = 4 + 2 = 2^2 + 2^1)
  - 0 = 000 in binary
  - 4 = 100 in binary (since 4 = 2^2)
- So the binary expansion of (1604)8 is 001101000100.

c) (423)8
- The octal expansion has three digits: 4, 2, and 3.
- To convert each digit to binary:
  - 4 = 100 in binary (since 4 = 2^2)
  - 2 = 010 in binary (since 2 = 2^1)
  - 3 = 011 in binary (since 3 = 2 + 1 = 2^1 + 2^0)
- So the binary expansion of (423)8 is 100010011.

d) (2417)8
- The octal expansion has four digits: 2, 4, 1, and 7.
- To convert each digit to binary:
  - 2 = 010 in binary (since 2 = 2^1)
  - 4 = 100 in binary (since 4 = 2^2)
  - 1 = 001 in binary (since 1 = 2^0)
  - 7 = 111 in binary (since 7 = 4 + 2 + 1 = 2^2 + 2^1 + 2^0)
- So the binary expansion of (2417)8 is 010010001111.


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Answer:

n^2 + 2

Step-by-step explanation:

1st term =1^2 +2 = 3

2nd term = 2^2 + 2 =6

3rd term = 3^2 + 2=11

4th term = 4^2 + 2=18

Answer:

A

Step-by-step explanation:

a. The probability that the student has a shoe size of 8 is 2/23.

b. The probability that the student has a shoe size of 7 or smaller is 7/23.

To calculate the probabilities, we need to know the total number of students and the number of students with each shoe size.

Since the table is not provided, I'll assume you meant "shoe size" instead of "school size" in your question.

I'll also assume that the shoe sizes are whole numbers.

Let's assume the table contains the following information:

Shoe Size:

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

(a) To work out the probability that the student has a shoe size of 8, we need to determine the number of students with a shoe size of 8 and divide it by the total number of students.

Number of students with shoe size 8: 2 (according to the table)

Total number of students: 23

Probability = Number of students with shoe size 8 / Total number of students

Probability = 2 / 23

Therefore, the probability that the student has a shoe size of 8 is 2/23.

(b) To work out the probability that the student has a shoe size of 7 or smaller, we need to determine the number of students with shoe sizes 1 to 7 and divide it by the total number of students.

Number of students with shoe sizes 1 to 7: 7 (according to the table)

Total number of students: 23

Probability = Number of students with shoe sizes 1 to 7 / Total number of students

Probability = 7 / 23

Therefore, the probability that the student has a shoe size of 7 or smaller is 7/23.

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Question : A school has five houses A, B, C, D and E. A class has 23 students, 4 from house A, 8. from house B, 5 from  house C, 2 from house 0 and rest from house E. A single student is selected at random ,to be the class monitor. The probability that the selected student is not from A, Band C is?

The dependent variable must be continuous in order to conduct an ANOVA (Analysis of Variance) test.

Let me briefly explain the key terms and reasoning:
Dependent variable:

This is the outcome variable that you are measuring in an experiment or study.

It depends on the independent variable(s), which are the factors you manipulate or observe to determine their effect on the dependent variable.
Continuous variable:

A continuous variable is a numerical variable that can take on an infinite number of values within a given range. Examples include weight, height, and temperature.
ANOVA:

ANOVA is a statistical method used to compare the means of two or more groups to determine if there are significant differences between them.

It evaluates the effect of one or more independent variables on a continuous dependent variable.
To conduct an ANOVA, the dependent variable must be continuous because the test relies on calculating the variance within and between groups.

The variance is a measure of dispersion or spread of the continuous data.

If the dependent variable were not continuous, it would be difficult to quantify the differences between group means, making it impossible to determine if the independent variable(s) had a significant effect.
ANOVA test, the dependent variable must be continuous, allowing for the calculation of variances and comparison of group means to determine any significant differences based on the effect of the independent variable(s).

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The answers that describe the quadrilateral DEFG area rectangle and parallelogram.

The correct answer choice is option A and B.

A quadrilateral is a parallelogram, which has opposite sides that are congruent and parallel.

Quadrilateral DEFG

if line DE || FG,

line EF // GD,

DF = EG and

diagonals DF and EG are perpendicular,

then, the quadrilateral is a parallelogram

Hence, the quadrilateral DEFG is a rectangle and parallelogram.

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The length of the original piece of fabric, given the proportion cut by Yu Yan and the amount cut in total, is 75 .75 inches

Assume that the original length of fabric was denoted as x, this means that the first cutting by Yu Yan took out :

= 1 / 3 x

The equation would then be :

x - 1 / 3 x - 10 - 5 = 35 + 1 / 2

x - 1 / 3 x - 10 - 5 = 35 . 5

The length of the original fabric is:

2 / 3x  = 35. 5 + 10 + 5

x = 50. 5 ÷ 2 / 3

x = 50. 5 x 3 / 2

x = 75 .75 inches

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This will return `True`, since all the elements in `set1` are also present in `set2`.

True.

The `issubset()` method in Python can be used to determine if a set is a subset of another set. It returns `True` if all the elements of the first set are also present in the second set, and `False` otherwise.

For example, if we have two sets `set1 = {1, 2, 3}` and `set2 = {1, 2, 3, 4, 5}`, we can use the `issubset()` method to check if `set1` is a subset of `set2` as follows:

```

set1.issubset(set2)

```

This will return `True`, since all the elements in `set1` are also present in `set2`.

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a. f'(x) = 40x³

To find the derivative of f(x) = 10x⁴, we apply the power rule.

The power rule states that if f(x) = axⁿ, then f'(x) = naxⁿ⁻¹. Applying this rule, we get f'(x) = 4 * 10x³ = 40x³.

b. : f'(x) = 20 + 90x²

To find the derivative of f(x) = 20x + 30x³, we differentiate each term separately. The derivative of 20x is 20, and the derivative of 30x³ is 90x² (applying the power rule). Adding these derivatives, we get f'(x) = 20 + 90x².

r: f'(x) = (20x - 4x²)(5x - x²) + (10 + 2x²)(-2x + 5)

To find the derivative of f(x) = (10 + 2x²)(5x - x²), we apply the product rule. The product rule states that if f(x) = g(x) * h(x), then f'(x) = g'(x) * h(x) + g(x) * h'(x). Differentiating each term, we get f'(x) = (20x - 4x²)(5x - x²) + (10 + 2x²)(-2x + 5).

d.: f'(x) = 40x

To find the derivative of f(x) = 20x / (x²), we use the quotient rule. The quotient rule states that if f(x) = g(x) / h(x), then f'(x) = (g'(x) * h(x) - g(x) * h'(x)) / (h(x)²). In this case, g(x) = 20x and h(x) = x². After differentiating and simplifying, we obtain f'(x) = 40x.

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In trigonometry, cos B represents the ratio of the adjacent side to the hypotenuse of a right-angled triangle where angle B is one of the acute angles.

The formula for cos B is given as:cos B = adjacent/hypotenuse Now, let's say we have a right-angled triangle ABC where angle B is the acute angle. The side opposite angle B is BC, the side adjacent to angle B is AB and the hypotenuse is AC. To find the value of cos B, we need to know the values of AB and AC. Once we have these values, we can substitute them in the formula for cos B and calculate the value.

To calculate the value of cos B in degrees, we use a calculator or a trigonometric table. If we have the value of cos B in decimal form, we can use the inverse cos function to find the value of B in degrees. For example, if cos B = 0.6, then B = cos-1 (0.6) = 53.13 degrees.To summarize, to find the value of cos B, we need to know the adjacent and hypotenuse sides of a right-angled triangle where angle B is one of the acute angles.

We can then substitute these values in the formula for cos B and calculate the value. If we have the value of cos B in decimal form, we can use a calculator or the inverse cos function to find the value of B in degrees.

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