Your friend has a bag of yellow and purple candy. He wants to use them to play a game with you.

Purple is worth 2 points and yellow is worth three points. Pick 9 candies from the bag

Create a system of equations where the combination of the candies gives you a total of 22 points. Make sure you label and define your variables.

Answer:

[tex]\frac{10n}{1-30n}:\frac{m}{10(1+3m)}[/tex]

Step-by-step explanation:

Solve for 'm' and 'n':

'm' = [tex]\frac{10n}{1-30n}[/tex]

'n' = [tex]\frac{m}{10(1+3m)}[/tex]

Ratio: [tex]\frac{10n}{1-30n}:\frac{m}{10(1+3m)}[/tex]

The value of x and y will be

a) x= 48  y= 72

b) x= 10   y= 3

c) x= 18  y= 3

What is triangle proportionality theorem ?

Triangle Proportionality Theorem Statement

If a line is drawn parallel to any one side of a triangle so that it intersects the other two sides in two distinct points, then the other two sides of the triangle are divided in the same ratio.

DA/BD = EC/BE

How we can calculate the value of x and y from the figure ?

The value of x and y can be calculated as

a ) x/4 + 5 =x/2-7                  y/3-6=66-2/3y

   x/4- x/2 = -7-5                   y/3+ 2y/3= 66 + 6  

   x-2x/4=-12                          3y/3= 72

    x= 48                                   y=72

b) x/5 +3 = 4x-35                   2y + 1 = 5y-8

  x/5 - 4x = -35-3                    2y-5y= -8-1

 x-20x/5 = -38                        -3y=-9

 -1 9x/5 = -38                            y=3

    x= 10

c) x/3 + 2= 2x/3-4                    5y=7y/3+8

   x/3-2x/3= -4-2                      5y-7y/3=8

  -x/3 = -6                                  15y-7y=8x3

   x= 18                                           y=3

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If John pours the partially filled bucket into an empty one, he would still have 29 full buckets and a bucket with 2/3 of its capacity filled.

In order to arrive at a solution, it is necessary to commence by reducing the fraction 1/1.5 into a more basic form.

Thus, we do this below:

1 ÷ 1.5 = 1 ÷ (3/2) = 1 × (2/3) = 2/3

So, John has 29 full buckets and another bucket that is 2/3 full.

If he pours the partially filled bucket into an empty one, he would still have 29 full buckets and a bucket with 2/3 of its capacity filled.

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John has 29 full buckets of water and another bucket that is 1/1.5 full. How many full buckets of water would he have if he pours the partially filled bucket into an empty one?

If the value of a certain collectible card in dollars from January 2020 to May 2021 can be modeled by the function V(m)=250m² – 3,500m + 18,000, the value of the card was declining over the period 0 < m < 7.

To determine when the value of the collectible card was declining, we need to look for when the first derivative of the function is negative. If the first derivative of the function is negative over a certain period, then the function is decreasing over that period. The first derivative of the function V(m) is:

V'(m) = 500m - 3,500

To find when the value of the card was declining, we need to solve the inequality V'(m) < 0. Solving for m, we get:

500m - 3,500 < 0

500m < 3,500

m < 7

Therefore, the value of the card was declining over the period 0 < m < 7. This corresponds to the months from January 2020 to July 2020. During this period, the first derivative of the function V(m) is negative, which means the value of the card was decreasing.

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By looking at the y-values of the points, we can see that the first four terms are.

2, -2, -6, -10

We know that the x-value of each of the points is the index of the term, so:

x = 1 is the first term

x = 2 is the second term.

And so on.

The y-value will be the actual value of the term.

Here we can see 4 points graphed, these are:

(1, 2), (2, -2), (3, -6), (4, -10)

Then the values of the first four terms of the sequence are:

2, -2, -6, -10

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The expanded form of log y^10 is either 10 log y or 10 ln y

Assuming that the base of the logarithm is not specified, we can use the change of base formula to expand the logarithm:

log y^10 = log (y^10) / log (base)

Since the base is not specified, we can use any base we like. For example, we can use base 10 or base e (natural logarithm).

Using base 10:

log y^10 = log (y^10) / log 10

= 10 log y / 1

= 10 log y

Using natural logarithm:

log y^10 = log (y^10) / log e

= 10 log y / 1

= 10 ln y

Therefore, the expanded form of log y^10 is either 10 log y or 10 ln y, depending on the base used.

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Answer:

Set your calculator to degree mode.

Please sketch the figure to confirm my answer.

tan(18°) = h/510

h = 510tan(18°) = 165.7 feet

Answer:

Construction Model Stats

User

Consider the time taken to completion time (in months) for the construction of a particular model of homes: 4.1 3.2 2.8 2.6 3.7 3.1 9.4 2.5 3.5 3.8 Find the mean, median mode, first quartile and third quartile. Find the outlier?

ChatGPT

To find the mean, we add up all the values and divide by the number of values:

Mean = (4.1 + 3.2 + 2.8 + 2.6 + 3.7 + 3.1 + 9.4 + 2.5 + 3.5 + 3.8) / 10

Mean = 36.7 / 10

Mean = 3.67

To find the median, we need to put the values in order:

2.5, 2.6, 2.8, 3.1, 3.2, 3.5, 3.7, 3.8, 4.1, 9.4

The middle number is the median, which is 3.35 in this case.

To find the mode, we look for the value that appears most often. In this case, there is no mode as no value appears more than once.

To find the first quartile (Q1), we need to find the value that separates the bottom 25% of the data from the top 75%. We can do this by finding the median of the lower half of the data:

2.5, 2.6, 2.8, 3.1, 3.2

The median of this lower half is 2.8, so Q1 = 2.8.

To find the third quartile (Q3), we need to find the value that separates the bottom 75% of the data from the top 25%. We can do this by finding the median of the upper half of the data:

3.7, 3.8, 4.1, 9.4

The median of this upper half is 3.95, so Q3 = 3.95.

To find the outlier, we can use the rule that any value more than 1.5 times the interquartile range (IQR) away from the nearest quartile is considered an outlier. The IQR is the difference between Q3 and Q1:

IQR = Q3 - Q1

IQR = 3.95 - 2.8

IQR = 1.15

1.5 times the IQR is 1.5 * 1.15 = 1.725.

The only value that is more than 1.725 away from either Q1 or Q3 is 9.4. Therefore, 9.4 is the outlier in this data set.

We can use trigonometry to solve this problem. Let h be the height of the building, and let d be the distance from the base of the building to the point where the angle of elevation is measured. Then we have:

tan(18 degrees) = h / d

Solving for h, we get:

h = d * tan(18 degrees)

Substituting d = 510 feet and using a calculator to evaluate the tangent of 18 degrees, we get:

h = 510 feet * tan(18 degrees)

h ≈ 157.3 feet

Rounding this to the nearest whole number, we get that the height of the building is approximately 157 feet.

Answer: 6/1

Step-by-step explanation: 2/1 x 3/1 = 6/1

Step-by-step explanation:

[tex] \frac{ {x}^{2} + 3x - 10 }{x + 5} \\ = \frac{(x + 5)(x - 2)}{(x + 5)} \\ = (x - 2)[/tex]

Answer: 116.985 mm2

Step-by-step explanation:

Dice game for a particular child’s game are numbered 1-10. Then, the  likelihood of rolling a single one and ending up with an even number is 1/20.

The probability of rolling a single one is 1/10, since there is only one die face with the number one out of ten possible outcomes.

The probability of rolling an even number is 5/10, since half of the die faces are even numbers (2, 4, 6, 8, 10) out of ten possible outcomes.

To find the likelihood of both events happening together, we need to multiply their individual probabilities;

P(rolling a single one and ending up with an even number) = P(rolling a single one) x P(ending up with an even number)

= (1/10) x (5/10)

= 1/20

Therefore, the likelihood of rolling a single one and ending up with an even number is 1/20.

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Answer:

Step-by-step explanation:

m = n + 1 + x/p

First, we can start by subtracting (n+1) from both sides:

m - (n+1) = x/p

Then, we can multiply both sides by p to isolate x:

p(m - (n+1)) = x

So the final answer is:

x = p(m - (n+1))

In this case, the cube root is = 0

We can use the rule Sarrus to evaluate the determinant

1 w w²

w w² 1

w² 1 w

Starting with the first column, we can wrte out the terms for the diagonal products and

then sum the terms for the products of the diagonal elements that wrap around

(1 x w² x  w) +(w x 1 x w²) + (w² x w x w)    - (w ² x w x 1) - (w x w² x w) - (1 x w x w ²)

Simplifying each term:

w³ +   w³ + w³ -   w³ -w³   - w³

We can see that all the terms cancel   out, leaving us with a determinant of 0. So it is clear that

|1 w w²|

|w w² 1 |

|w² 1 w | = 0

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Full Question:

Although part of your question is missing, you might be referring to this full question:

Evaluate the determinant 1 w w2 , w w2 1, w2 1 w. where w is a cube root of unity.

Answer:

3 x 195 = 585 minutes

Step-by-step explanation:

In one week, Alejandro attends a 45-minute lesson and practices for (6 x 25) = 150 minutes (assuming a 7-day week). So, the total number of minutes that Alejandro spends on his guitar in one week is:

45 + 150 = 195 minutes

In 3 weeks, the total number of minutes that Alejandro spends on his guitar is:

3 x 195 = 585 minutes

Therefore, Alejandro spends 585 minutes on his guitar in 3 weeks, including attending a 45-minute lesson once a week and practicing for 25 minutes on the remaining days of the week.

Answer: The mean absolute deviation is approximately is 11.43.

The probability is P = 0.51, and the odds are 15 to 14.

If all the ties have the same probability of being randomly choosen, then the probability of randomly selecting a tie that goes well with the sports coat is equal to the quotient between the number of ties that goes well with the sports coat (15) and the total number of ties.

The probability will be:

P = 15/29 = 0.51

And the odds are the number of good ties to the number of the other ones, there are 15 good ones and 14 bad ones, so the odds are 15 to 14.

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The volume of the rectangular prism is given as follows:

V = 0.9375 cubic inches.

The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, according to the equation presented as follows:

Volume = length x width x height.

The dimensions for this problem are given as follows:

Hence the volume is given as follows:

V = 1 x 1.25 x 0.75

V = 0.9375 cubic inches.

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The conic section that is formed when a right, circular cone is intersected by a plane that is parallel to the base of the cone is a circle

The summary statement from the question is given as

A plane parallel to the base of a circular cone that intersects the cone.

By definition, a circle is the cross-section that is parallel to the base of a cone

This means that when a cone is cut through the base, the resulting shape is a circle

So, the conic section that is formed when a right, circular cone is intersected by a plane that is parallel to the base of the cone is a circle

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The contradicting statement is

B. I and III

The contradictory statement is that of I and III since the sum of angles in a triangle is always 180 degrees.

Given that

I. triangle ABC is a right triangle. say angle C = 90 degrees and

angle B = 103 degrees,

So the sum of the angles in the triangle would be:

= angle B + m angle C

= 103 + 91

= 194

This is against the law of angles of a triangle

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The value of measure of ∠A would be,

⇒ ∠ A = 38.68 degree

We have to given that;

In triangle ABC,

AB=32, AC= 22, and BC= 20

Hence, We can formulate;

⇒ sin A = BC / AB

⇒ sin A = 20 / 32

⇒ sin A = 0.625

⇒ A = 38.68 degree

Thus, The value of measure of ∠A would be,

⇒ ∠ A = 38.68 degree

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Answer:

A line that is perpendicular to another is one that has a slope that is the multiplicative reciprocal of the original funtion's slope and it also has the opposite sign in front. Considering a slope with a value of [tex]\dfrac{1}{7}[/tex], the reciprocal multiplicative is 7, because is a number that equals 1 if multiplied by the original value. Then, we change the sign for it, making it -7.

Thus, correct answer is a. -7.

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Answer:

The weight that does not round to 2.46 pounds is C 2.454 pounds.

Step-by-step explanation:

Based on the given information, the weights of the four similar packs of tomatoes are as follows:

Malcolm rounds the weights to the nearest hundredth pound. To round to the nearest hundredth pound, we look at the digit in the hundredths place. If it is 5 or greater, we round up the digit in the tenths place. If it is less than 5, we leave the digit in the tenths place as it is. Therefore, we can obtain the rounded weights as follows:

From the above rounded weights, we see that Pack C rounds to 2.45 pounds and does not round to 2.46 pounds. Therefore, the weight that does not round to 2.46 pounds is C 2.454 pounds.

The population of Greensville 10 years from now will be approximately 13,184.

To find the population of Greensville 10 years from now, we need to use the formula for compound interest:

A = P(1 + r)ᵗ

Where A is the future value, P is the present value, r is the annual interest rate as a decimal, and t is the number of years.

In this case, the present value (P) is 8,000, the annual interest rate (r) is 5.6% or 0.056 as a decimal, and the time (t) is 10 years. Plugging these values into the formula, we get:

A = 8,000(1 + 0.056)¹⁰

A = 8,000(1.648)

A = 13,184

This calculation assumes that the population growth rate remains constant at 5.6% per year.

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Answer:

a quotient is the result obtained by dividing one quantity by another.

The only expression that is not equivalent to the given fraction expression is: D (2 x 1/3) + (4 x 1/3)

The correct procedure that we will use to multiply fractions is:

- find a common denominator

- multiply the numerators

- multiply the denominators

- Simplify if necessary.

- Add the numerators and add the denominators

Looking at the options and comparing with the given fraction multiplication problem 2/3 * 4, we see that only option D is not equivalent to it because:

(2 x 1/3) + (4 x 1/3) = 6/3 = 2

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Complete question is:

Which expression is NOT equivalent to 2/3 x 4

A (2x4) /3

B 1/3 x (2x4)

C (4 x 1/3) x 2

D (2 x 1/3) + (4 x 1/3)

Answer:

C Exponential

Step-by-step explanation:

3x^2 -- its using an exponent

Answer: each package weighs 3.25lb 

Step-by-step explanation:

looking at the weight of each package (3lb 4oz), we can convert the 4oz to pounds by dividing by 16oz/lb; 4/16 = 0.25lb 

The area of the shaded region is given as follows:

298.3 units².

The area of a circle of radius r is given by the multiplication of π and the radius squared, as follows:

A = πr²

The larger circle has a radius of 7 + 5 = 12 units, hence it's area is given as follows:

A = 3.14 x 12²

A = 452.16 units².

The smaller circle has a radius of 7 units, hence it's area is given as follows:

A = 3.14 x 7²

A = 153.86 units².

Hence the area of the shaded region is given as follows:

452.16 - 153.86 = 298.3 units².

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Since MO is parallel to PR, then angle MNQ and angle RQN are alternate interior angles and are congruent. Therefore, angle MNQ = angle RQN = 115 degrees.

When a line that intersects two parallel lines, also known as a transversal, creates an intersection with a pair of other lines, it forms what is referred to as alternate interior angles.

From the diagram we can see that RQN and MQN are similar angles from the diagram

Hence we have that RQN=115 = MNQ

Therefore MNQ = 115 degrees

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The shortest path from vertex A to vertex L in the given diagram is ABDGJLKFI, with a total length of 89.

We can find the length of the shortest path from vertex A to vertex L by calculating the sum of the shortest paths from A to C to F to I to L.

Using Dijkstra's algorithm, we can find the shortest path from A to C, then from C to F, then from F to I, and finally from I to L.

The shortest path from A to C is AB + BC = 3 + 16 = 19. The shortest path from C to F is CF = 25. The shortest path from F to I is FI = 21. The shortest path from I to L is IL = 24.

Therefore, the length of the shortest path from A to L is 19 + 25 + 21 + 24 = 89.

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