rachel collects vintage dolls. she pays $22 for large ones and $16 for small ones. she spends $120 on 6 dolls. write and solve a system of equations to show how many large dolls and how many small dolls rachel purchased

Answer:

Step-by-step explanation:

Since AB is parallel to DE, we know that:

(ABC + BCD) = (CDE + EDC)

Substituting the given values, we get:

800 + BCD = 280 + EDC

Simplifying, we get:

BCD = EDC - 520

We also know that:

(BCD + CDE + DCE) = 180

Substituting BCD = EDC - 520 and CDE = 280, we get:

(EDC - 520 + 280 + DCE) = 180

Simplifying, we get:

EDC + DCE - 240 = 0

EDC + DCE = 240

Now we can solve for DCE in terms of BCD:

DCE = 240 - EDC

DCE = 240 - (BCD + 520)

DCE = 760 - BCD

Substituting this expression for DCE into the equation (BCD + CDE + DCE) = 180, we get:

BCD + 280 + (760 - BCD) = 180

Simplifying, we get:

1040 - BCD = 180

BCD = 860

Therefore, (DCB) = 180 - (BCD + CDE) = 180 - (860 + 280) = -960. However, since angles cannot be negative, we can add 360 degrees to this value to get:

(DCB) = -960 + 360 = -600

Therefore, (DCB) = -600 degrees.

Answer:

m = 1/2

Step-by-step explanation:

We Know

The slope of a line is the rise/run

Pick 2 points (0,1) (2,2)

We see the y increase by 1, and the x increase by 2, so the slope of the line is

m = 1/2

The manager will need to pay $244.95 to purchase the silverware, including sales tax.

What is decimal?

Decimals are numbers that have two parts: a whole number part and a fractional part separated by a decimal point.

According to the given information:

If the silverware costs $230 and the sales tax is 6.5%, we need to calculate the amount of tax that will be added to the cost of the silverware:

Tax = 6.5% of $230 = 0.065 x $230 = $14.95

So the total cost of the silverware including tax is:

$230 + $14.95 = $244.95

Therefore, the manager will need to pay $244.95 to purchase the silverware, including sales tax.

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The perimeter of the shape given is 50 feet, while the area of this shape is 114 square feet.

Perimeter measures the total length of the boundary or the outer edge of a two-dimensional shape. On the other hand, the area measures the space enclosed inside a two-dimensional shape. The area of a shape is determined by multiplying its length by its width

Based on this, let's calculate the perimeter:

7 feet + 6 feet + 4 feet + 6 feet + 9 feet + 9 feet + 2 feet + 7 feet =  50 feet

Now, let's calculate the area by dividing the shape in three:

First rectangle:

3 feet x 7 feet = 21 square feet

Second rectangle:

5 feet x 3 feet = 15 square feet

Third rectangle

9 feet x 9 feet =  81 square feet

Total: 21 + 12 + 81 = 114 square feet

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Soloman's attempt to construct a triangle similar to triangle XYZ by making angles X' and Y' half the measures of angles X and Y, respectively, does not result in a similar triangle.

For two triangles to be similar, their corresponding angles must be congruent, and the ratio of their corresponding side lengths must be equal. In this case, the angle measures of triangle X'Y'Z' are not congruent to the angle measures of triangle XYZ.

Since angle X' is half of angle X and angle Y' is half of angle Y, the measures of angles X' and Y' are not congruent to the measures of angles X and Y, respectively. Therefore, the triangles are not similar.

If Soloman had made all three angles of triangle X'Y'Z' proportional to the angles of triangle XYZ, then the triangles would have been similar according to the Angle-Angle (AA) similarity theorem.

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Particular solution is: f(x) = (0.25/24) x⁹ - 6553.3333 x + 2

We need to integrate it twice. Integrating once gives us:

f'(x) = (0.25/3) x⁸ + C1

where C1 is the constant of integration. Using the initial condition f'(4) = 8, we can solve for C1:

8 = (0.25/3) 4⁸ + C1
C1 = 8 - (0.25/3) 4⁸
C1 = -6553.3333

Integrating again gives us:

f(x) = (0.25/24) x⁹ + C1 x + C2

where C2 is another constant of integration. Using the initial condition f(0) = 2, we can solve for C2:

2 = (0.25/24) 0⁹ + C1 0 + C2
C2 = 2

So the particular solution is:

f(x) = (0.25/24) x⁹ - 6553.3333 x + 2

Note that we did not need to use the second initial condition, f'(4) = 8, to find the particular solution. This is because it was already used to find the constant of integration C1.

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Answer: 6

Step-by-step explanation:

So, he wears the shirt 10 out of 20 days.

10 days is half of 20 days.

This means he wears the shirt approximately half of the time, by the logic of 10/20 days.

So, now we apply this to 12 days.

What's half of 12? 6.

This means that he most likely wears the green shirt on 6 out of the 12 days.

Answer:

Step-by-step explanation:

The gold vein is at (-3,9) and the farthest gold dust strike is at (33,9). The distance between the two points is 36 miles.

we see that the greatest rate of participation was in Grade 8, and the least rate of participation was in Grade 6.

To compare the rates of participation in sports among the three grades, we can convert each percentage or fraction to a decimal and then compare the values.

Grade 6: 0.872

Grade 7: 0.87 (87% converted to decimal)

Grade 8: 0.875 (7/8 converted to decimal)

Therefore, we see that the greatest rate of participation was in Grade 8, and the least rate of participation was in Grade 6.

Answer:

Grade 8 had the greatest rate of participation.

Grade 6 had the least rate of participation.

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The derivative of the function at s=0 is approximately 258.

The derivative of the function[tex]r=[5(e4s-e-45)]/e45[/tex]is:

[tex]r' = 5[(4e4s + 45e-45)e45 - e45(4e4s - e-45)(e45)]/e902[/tex]

Plugging in s=0, we get:

[tex]r' = 5[(4 + 45)e45 - (4 - 1)(e45)]/e902[/tex]

[tex]r' = 5[49e45 - 3e45]/e902[/tex]

[tex]r' = 5(46e45)/e902[/tex]

r' ≈ 258

Therefore, the derivative of the function at s=0 is approximately 258.

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Answer: y= |x-1| -1

Step-by-step explanation:

Explanation:

This is an absolute value function.

The parent function looks like: y=|x|   When transformations take place, we use this function to describe those transformations:

y = a|x-h|+k  

where (h, k) is your new vertex

"a" is your stretch

and a - would be placed in the front if there was a reflection

Solution:

Your equation has a new vertex at (1, -1)

There is no stretch and no reflection

Plug into equation:

y= |x-1| -1

The median weight of the black bass caught by the fisherman is 10.5 pounds.

To find the median, we need to arrange the weights in order from smallest to largest: {6, 7, 8, 12, 13, 14}. Since there are an even number of weights, the median is the average of the two middle values, which are 8 and 12. Therefore, the median weight is (8+12)/2 = 10.5 pounds.

The median is a measure of central tendency that represents the middle value in a dataset. It is less sensitive to extreme values than the mean and is useful for describing the typical value in a skewed distribution.

In this case, the median weight of 10.5 pounds indicates that half of the black bass caught by the fisherman weighed less than 10.5 pounds, and half weighed more than 10.5 pounds.

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Answer:

x's will eliminate because they have opposite coefficients

Step-by-step explanation:

Because the x's have opposite coefficients, they will eliminate when the given system of linear equations (2-var) are summed up

Answer:

x's will eliminate because they have opposite coefficients.

Step-by-step explanation:

Why the other choices are incorrect:

y's will eliminate because they have opposite coefficients - not true, they don't have opposite coefficients.

x's will eliminate because you always have to solve for x first - you can solve for y too.

y's will eliminate because why not - isn't a good explanation.

The magnitude of vector v is 4 and the direction is 125 degrees.

Given that vector u has a magnitude of 2 and a direction of 55 degrees, we can determine the magnitude and direction of vector v.

To find the magnitude of vector v, we can use the equation:

|v| = |-2u|

Since u has a magnitude of 2, we can substitute it into the equation:

|v| = |-2 * 2|

|v| = |-4|

|v| = 4

The magnitude of vector v is 4.

To find the direction of vector v, we can note that multiplying a vector by -1 (in this case, multiplying u by -2) reverses its direction. So the direction of v is the exact opposite of the direction of u.

Since the direction of u is 55 degrees, the direction of v is 55 degrees in the opposite direction. In the interval of 0 degrees ≤ θ < 360 degrees, the direction of v can be expressed as:

θ = 180 - 55

θ = 125 degrees

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The measure of each labeled angles in the rhombus are  ∠1 = 49°, ∠2 = 90°, ∠3 = 49° and ∠4 = 41°

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

The rhombus

By corresponding angles, we have

∠3 = 49°

∠1 = 49°

The diagonals of a rhombus bisect each other at right angles

So, we have

∠2 = 90°

Ths sum fo angles in a triangle is 180

So, we have

∠4 = 180 - 90 - 49°

Evaluate

∠4 = 41°

Hence, the measure of the angles in the rhombus are  ∠1 = 49°, ∠2 = 90°, ∠3 = 49° and ∠4 = 41°

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Answer:

B

Step-by-step explanation:

15 pounds and 5 pounds per day so to figure out how many days you do division. The equation is 15÷5=3 so the answer is 3 days.

The set builder form of the sets are

1) { | = ², where is a positive integer between 1 and 9}

2) { | = 5ⁿ, where n is a non-negative integer less than or equal to 5}

3) { | = 3, where is a positive integer between 1 and 6}

In set-builder notation, we use the curly brackets {} to enclose the elements of a set, and a rule or condition to define the elements that belong to the set.

Let's look at each of the sets given and express them in set-builder form:

{1, 4, 9,……..81}

This set contains the perfect squares of the numbers 1 to 9. To express it in set-builder notation, we can use the following rule:

{ | = ², where is a positive integer between 1 and 9}

{1, 5, 25, 125, 625, 3125}

This set contains the powers of 5, starting from 5⁰=1 up to 5⁵=3125. To express it in set-builder notation, we can use the following rule:

{ | = 5ⁿ, where n is a non-negative integer less than or equal to 5}

{3, 6, 9, 12, 15, 18}

This set contains the multiples of 3, from 3 to 18. To express it in set-builder notation, we can use the following rule:

{ | = 3, where is a positive integer between 1 and 6}

In this rule, we multiply 3 by the positive integers 1 to 6 to obtain the elements of the set.

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Complete Question:

Express the following sets in set-builder form.

1. {1, 4, 9,……..81}

2. {1, 5, 25, 125, 625, 3125}

3. {3, 6, 9, 12, 15, 18}

Hi there! Your question involves Ms. Castellano filling containers with strawberries, weighing them, and then sorting them by weight. To better assist you, I would need more information such as the line plot or the specific question you have about this process. Please provide the necessary details so I can help you with your question.

Based on the information you provided, it seems that Ms. Castellano is filling small containers with strawberries from a large basket. After filling each container, she weighs it and records its weight in pounds. She then sorts the containers by weight.

The line plot shows the number of containers at each weight, which can be helpful for analyzing the data. It sounds like Ms. Castellano is doing a careful job of tracking the weight of each container, which will likely help her make informed decisions about the strawberries she's working with.

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To optimize the given function e - 222 - 4xy - 2y^2 subject to the constraint 0x^2 - 4xy + ly^2 = 10, we'll first set up the Lagrange function L(x, y, λ) as follows:

Langrange- L(x, y, λ) = e - 222 - 4xy - 2y^2 + λ(0x^2 - 4xy + ly^2 - 10)
Now, we'll get the partial derivatives of L with respect to x, y, and λ and set them equal to zero:
Step:1. ∂L/∂x = -4y - λ(-4y) = 0
Step:2. ∂L/∂y = -4x - 4y - 2λy = 0
Step:3. ∂L/∂λ = 0x^2 - 4xy + ly^2 - 10 = 0
These three equations represent the system of equations we need to solve to find the critical points. To reiterate, the equations are:
1. -4y + 4yλ = 0
2. -4x - 4y - 2λy = 0
3. -4xy + ly^2 - 10 = 0

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Based on the graph, it appears that F(x) is a downward-facing parabola that has been shifted horizontally and vertically.

The vertex of the parabola is located at the point (3,-3), so the equation must include (x - 3) and (y + 3). Additionally, since the graph is narrower than the graph of G(x) = x^2, there must be a coefficient that is greater than 1 in front of the squared term.

Looking at the answer choices, we can eliminate options B and D because they have positive coefficients in front of the squared term, which would result in an upward-facing parabola. Option C has a negative coefficient in front of the squared term, which would result in a wider parabola than the graph shown.

Therefore, the correct answer is A, F(x) = 3(x-3)^2 - 3.

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The height of a 16-year-old boy in the 96th percentile is approximately 73.8 inches. Rounded to the nearest inch, the answer is 74 inches.

To find the z-score associated with the 96th percentile, we need to use the standard normal distribution, which has a mean of 0 and a standard deviation of 1. We can convert the given distribution to a standard normal distribution by using the formula:

z = (x - μ) / σ

where z is the z-score, x is the value we want to convert, μ is the mean of the distribution, and σ is the standard deviation of the distribution.

In this case, we want to find the z-score associated with the 96th percentile. The 96th percentile is the value below which 96% of the observations fall. We can find this value by using a standard normal table or a calculator. Using a calculator, we get:

invNorm(0.96) ≈ 1.75

This means that the z-score associated with the 96th percentile is 1.75.

To find the height of a 16-year-old boy in the 96th percentile, we can use the formula:

x = μ + z * σ

where x is the value we want to find, μ is the mean of the distribution, σ is the standard deviation of the distribution, and z is the z-score we just found.

In this case, we have:

x = 68.3 + 1.75 * 2.9 ≈ 73.8

Thus, 74 inches is the conclusion.

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Hunter has 32 different possible outcomes if he rolls a pyramid-shaped die with four sides, spins a spinner with four equal-sized sections, and flips a coin.

There are different methods to approach this problem, but one possible way is to use the multiplication principle of counting, which states that if there are m ways to perform one task and n ways to perform another task, then there are m x n ways to perform both tasks in sequence.

In this case, Hunter has three tasks: rolling the die, spinning the spinner, and flipping the coin.

For the first task, rolling the die, there are four possible outcomes.

For the second task, spinning the spinner, there are four possible outcomes as well.

For the third task, flipping the coin, there are two possible outcomes.

Using the multiplication principle, the total number of possible outcomes is:

4 x 4 x 2 = 32

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The magnitude of the force of the car against the hill is approximately 13690 pounds.

a. To find the magnitude of the force required to keep the car from sliding down the hill, we need to calculate the force component perpendicular to the hill (the normal force) and the force component parallel to the hill (the force of friction). The force of friction must be equal and opposite to the component of the weight of the car parallel to the hill to keep the car from sliding.

First, we need to calculate the weight of the car in Newtons:

3100 pounds = 1406.13 kg

Weight = mg = 1406.13 kg * 9.81 m/s^2 = 13791.68 N

The force component perpendicular to the hill is equal to the weight of the car multiplied by the cosine of the angle of inclination:

F_perpendicular = Weight * cos(5.6°) = 13791.68 N * cos(5.6°) = 13689.55 N

The force component parallel to the hill is equal to the weight of the car multiplied by the sine of the angle of inclination:

F_parallel = Weight * sin(5.6°) = 13791.68 N * sin(5.6°) = 1275.02 N

The force of friction is equal to the force parallel to the hill, so:

F_friction = F_parallel = 1275.02 N

Therefore, the magnitude of the force required to keep the car from sliding down the hill is equal to the force component perpendicular to the hill plus the force of friction:

F_required = F_perpendicular + F_friction = 13689.55 N + 1275.02 N = 14964.57 N

Rounded to the nearest whole number, the magnitude of the force required to keep the car from sliding down the hill is approximately 14965 pounds.

b. To find the magnitude of the force of the car against the hill, we just need to calculate the force component perpendicular to the hill (the normal force):

F_normal = F_perpendicular = 13689.55 N

Rounded to the nearest whole number, the magnitude of the force of the car against the hill is approximately 13690 pounds.

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Ramiro is correct that if all corresponding angles are equal then the triangle is said to be similar.

Triangles are said to be similar if any of the following is true:

1. All or any two of the corresponding angles are equal

2. All the corresponding sides are proportional to each other

3. One of the corresponding angles is equal and the adjoining corresponding sides are proportional.

Triangles are said to be congruent if any of the following is true:

1. All of the corresponding sides are equal

2. Two of the angles are equal and so is one of the corresponding sides of the triangle.

3. One of the corresponding angles is equal and the adjoining corresponding sides are also equal.

4. In a right-angled triangle, either the base or height and the hypotenuse are equal.

Since in the question, the criteria for the similar triangles is fulfilled then Ramiro is correct.

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If the scatter plot shows no discernible relationship between the variables and the points appear randomly scattered, then the r-value of 0.01 is accurate. However, if there is a visible relationship, the value of r may need to be recalculated or checked for errors in data input or analysis.

To find whether a correlation coefficient of r = 0.01 is an accurate value for the data based on the scatter plot, it's essential to consider the following factors:

1. Visual inspection of the scatter plot: Observe the overall pattern of data points in the scatter plot. If the points seem randomly scattered with no discernible pattern, then a correlation coefficient close to 0, such as r = 0.01, would be accurate. However, if there is a clear linear or non-linear relationship between the variables, the value of r = 0.01 may not be accurate.

2. Strength of the relationship: The correlation coefficient r ranges from -1 to 1, where -1 represents a strong negative relationship, 0 represents no relationship, and 1 represents a strong positive relationship. An r-value of 0.01 indicates a very weak or no relationship between the variables. Confirm that this is consistent with the scatter plot pattern.

To determine if the r-value of 0.01 is accurate for the data, carefully examine the scatter plot and consider these factors. If the scatter plot shows no discernible relationship between the variables and the points appear randomly scattered, then the r-value of 0.01 is accurate. However, if there is a visible relationship, the value of r may need to be recalculated or checked for errors in data input or analysis.

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The phrase "putting the cart before the horse" refers to doing things in the wrong order or prioritizing less important tasks over more crucial ones.

In the context of the puzzle time question, the answer is: You should never put the cart before the horse, as it is essential to follow the proper sequence of actions to achieve the desired outcome effectively.

In the context of the puzzle time question, the phrase "putting the cart before the horse" implies that it is crucial to follow the proper sequence of actions or steps to solve the puzzle correctly.

By prioritizing less important tasks or skipping essential steps, the desired outcome may not be achieved, and the solution may be flawed.

To effectively solve the puzzle, it is essential to understand and follow the rules, guidelines, and necessary steps in the correct order. This ensures that each action builds upon the previous one and leads to a coherent solution.

By doing so, you avoid the mistake of putting the cart (less important tasks) before the horse (more crucial steps), leading to a successful and accurate solution.

In summary, the phrase "putting the cart before the horse" emphasizes the importance of following the correct sequence of actions or steps in any given task, including solving puzzles. It serves as a reminder to prioritize tasks appropriately to achieve the desired outcome effectively.

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The price of the medium pizza without the coupon is approximately $14.74.

To find the original price of the pizza without the coupon, we can use the following formula:

Original Price = Discounted Price / (1 - Discount Percentage)

In this case, the discounted price is $10.32 and the discount percentage is 30% or 0.3. Plugging the values into the formula:

Original Price = $10.32 / (1 - 0.3)

Original Price = $10.32 / 0.7

Original Price ≈ $14.74

So, the price of the medium pizza without the coupon is approximately $14.74.

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The median for the number of pencils can be found by locating the middle value on the dot plot, which appears to be 3 pencils.

The dot plot displays the number of pencils each boy has at his desk in class. By locating the middle value of the data on the dot plot, the median number of pencils can be determined to be 3.

This indicates that half of the boys have 3 pencils or fewer, while the other half have 4 pencils or more.

The dot plot provides a visual representation of the distribution of the data and allows for easy identification of the median value.

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The coupon rate is about 8.716%

To find the coupon rate of a bond, we need to use the formula for the present value of a bond's cash flows.

The present value formula for a bond is:

PV = C * (1 - (1 + r)^(-n)) / r + F * (1 + r)^(-n)

Where:

PV = Present value of the bond (given as $1,011.38)

C = Coupon payment

r = Yield to maturity (given as 9.19% or 0.0919)

n = Number of periods (6 years, so n = 12)

We know that the face value (F) of the bond is $1,000.

Using the given information, we can rewrite the formula as:

$1,011.38 = C * (1 - (1 + 0.0919)^(-12)) / 0.0919 + $1,000 * (1 + 0.0919)^(-12)

Now we can solve for C, the coupon payment:

$1,011.38 = C * (1 - 1.0919^(-12)) / 0.0919 + $1,000 * 1.0919^(-12)

To find the coupon rate, we need to divide the coupon payment (C) by the face value ($1,000):

Coupon Rate = (C / $1,000) * 100%

Now we can solve for C and calculate the coupon rate:

$1,011.38 = C * (1 - 1.0919^(-12)) / 0.0919 + $1,000 * 1.0919^(-12)

$1,011.38 - $1,000 * 1.0919^(-12) = C * (1 - 1.0919^(-12)) / 0.0919

(C * (1 - 1.0919^(-12)) / 0.0919) = $1,011.38 - $1,000 * 1.0919^(-12)

C * (1 - 1.0919^(-12)) = ($1,011.38 - $1,000 * 1.0919^(-12)) * 0.0919

C = (($1,011.38 - $1,000 * 1.0919^(-12)) * 0.0919) / (1 - 1.0919^(-12))

Once we calculate C, we can find the coupon rate:

Coupon Rate = (C / $1,000) * 100%

Therefore, the coupon rate is 2 × $43.58 / $1000 = 8.716% (rounded to three decimal places).

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