Question 6(Multiple Choice Worth 2 points)
(Two-Column Tables MC)

The table below shows the ratios of black to white keys on pianos of various sizes.


Black A 18 45 72
White 13 B 65 C


Determine which table has the correct values for A, B, and C.

None of the available possibilities is an equivalent expression.

Supplemental methods add up to 180 degrees, just like all other options.

    If two expressions function the same way while having different looks, they are said to be comparable. Two identical algebraic expressions have the same value when the same value(s) for the variable are entered (s).

  No one in the available possibilities satisfies the requirement of a comparable expression.

2x - 15 + 3x + 15 = 180

2x - 10 + 3x = 180

5x - 10  = 180

5x - 10 + 10 = 180 +10

add the numbers

5x = 190

5x /5 = 190 5

x = 38

As a result, none of the possibilities shown are identical expressions.

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Answer:

B) 0.9, 0.45, -0.77, -0.95

Explanation:

The correlation coefficient is a statistical measure that indicates the strength of the relationship between two variables. The value usually ranges from -1 to 1 where:

• 1 indicates a strong positive relationship.

• -1 indicates a strong negative relationship.

• A result of 0 indicates no relationship at all.

Therefore, the given correlation coefficients classified from the strongest to the weakest is:

The correct choice is B.

Answer:

if LJK is 28, then by using the triangle sum theorem, JLK is 62. because the triangles are congruent,( angle+side+hypotneus/HL), JLK is congruent to JLM, so you add them together and get 62+62=124 = MLK. I'm pretty sure thats the right answer, might want to go over that.

The best line and parabola fitting to the given points can be found by minimizing the sum of squared differences between the actual and predicted y-values using least squares approximation.

1. Best Line Fitting:

- Set up the equation for the sum of squared differences: S(a, b) = Σ[i=1 to 6] (yi - (a + bxi))^2.

- Differentiate S(a, b) with respect to a and b, and set the derivatives to zero.

- Solve the resulting equations to find the values of a and b that minimize the sum of squared differences.

- The resulting line equation, y = a + bx, represents the best line fitting to the given points.

2. Best Parabola Fitting:

- Set up the equation for the sum of squared differences: S(c, d, e) = Σ[i=1 to 6] (yi - (c + dxi + exi^2))^2.

- Differentiate S(c, d, e) with respect to c, d, and e, and set the derivatives to zero.

- Solve the resulting equations to find the values of c, d, and e that minimize the sum of squared differences.

- The resulting parabola equation, y = c + dx + ex^2, represents the best parabola fitting to the given points.

By following these steps, you can determine the best line and parabola fit to the provided points using the least squares approximation method.

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Answer:

1 significant figure: 50,000 2 significant figures: 52,000 3 significant figures: 51,800

Step-by-step explanation:

FIrst, a significant figure is basically a non-zero digit (at least in your case). Basically, the 1 significant figure in your case would be to the nearest 10 thousand, which would be 50,000. Now, for 2 significant figures. This would be the nearest thousand, 52,000. Finally, 3 significant figures is to the nearest hundred, aka 51,800. Note: If you find a problem like this again 0 in between two digits that aren't 0 is a significant digit, aka the 0 in 51809. Hope this helped!

The probability that the sum of the rolls is divisible by 6 is 1/1296, which is approximately 0.00077 or 0.077%.

To find the probability that the sum of the rolls is divisible by 6, we need to determine the favorable outcomes and the total number of possible outcomes.

First, let's identify the favorable outcomes. In this case, the sum of the rolls can be divisible by 6 if the sum is either 6 or 12.

1. For the sum of 6:
  - One possible outcome is rolling a 6 on the first roll and rolling a 1 on the remaining four rolls.
  - Another possible outcome is rolling a 5 on the first roll and rolling a 2 on the remaining four rolls.
  - We can also have rolling a 4 on the first roll and rolling a 3 on the remaining four rolls.
  - Similarly, rolling a 3 on the first roll and rolling a 4 on the remaining four rolls.
  - Finally, rolling a 2 on the first roll and rolling a 5 on the remaining four rolls.
  - This gives us a total of 5 favorable outcomes.

2. For the sum of 12:
  - One possible outcome is rolling a 6 on all five rolls.
  - This gives us a total of 1 favorable outcome.

Now let's determine the total number of possible outcomes. Since we are rolling a fair 6-sided die 5 times, the total number of possible outcomes is 6^5 (since each roll has 6 possible outcomes).

Therefore, the probability that the sum of the rolls is divisible by 6 is:

(total number of favorable outcomes) / (total number of possible outcomes)
= (5 + 1) / (6^5)
= 6 / 7776
= 1 / 1296

So, the probability that the sum of the rolls is divisible by 6 is 1/1296, which is approximately 0.00077 or 0.077%.

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Answer:

the answer is either x= 4 , or it is   9\(x^{2} \\\) - \(x\) - 10

Step-by-step explanation:

Sorry dude, I'm confused a little bit on what to do, but i think one of these is right.

lmk if you get it right, and which one you used

As per the given confidence interval, the value of P is lees than significant.

Confidence interval:

In statistics, a range around a measurement that conveys how precise the measurement is referred as confidence interval.

Given,

A precision instrument is guaranteed to read accurately to within 2 units. a sample of four instrument readings on the same object yielded the measurements 353, 351, 351, and 355. find a 90% confidence interval for the population variance.

Here we need to find the assumptions of the given situation,

From the given question we have identified the following,

Reading of instruments = 353, 351, 351, and 355.

Confidence interval = 90% = 0.09

Number of units = 2.

Based on these details, the standard deviation of this temple is 0.7.

So, the Z score is the same as the sample mean minus the population mean divided by the standard error, which is 2.857.

Therefore, P value was less than significant.

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Answer:

f(5)=3(5)+2 = 17

Step-by-step explanation:

The given proof that all horses are the same color is a fallacy of circular reasoning or proof by induction.                                

   Here’s why: There is a fallacy in the statement given in the proposition P(k) is true, so that all the horses in any set of k horses are the same color. The fallacy is that it assumes the truth of the proposition to be proven by circular reasoning. By saying that all horses in any set of k horses are the same color, it means that all horses in a set of 1 horse, which is the basis step, are the same color. But this is false because a horse, as a solitary individual, can be of any color.                                

So, the statement, "all horses in any set of k horses are the same color" assumes the conclusion to be proven. This flaw invalidates the entire proof by induction. Therefore, the "proof" that all horses are the same color is wrong.

What is induction?                                                                                                                                                                                                             Induction is the process of establishing a general statement or principle by looking at examples or instances. It involves a specific observation or case that leads to a general conclusion. It is useful in mathematical proofs, scientific inquiry, and problem-solving.
The issue with this "proof" that all horses are the same color lies in the inductive step. To clarify, let's go through the proof by induction process:

1. Basis Step: P(1) is true since there is only one horse, and it must be the same color as itself.
2. Inductive Step: Assume P(k) is true for some arbitrary k (all k horses have the same color).

Now, proof consider a set of k + 1 horses. You claimed that the first k horses have the same color and the last k horses have the same color. However, this argument fails when k = 1. In this case, you would have a set of 2 horses (k+1), and there is no overlap between the first horse and the second horse, so you cannot conclude that they have the same color based on the induction assumption.

Thus, the inductive step does not hold for all cases, and the proof that all horses are the same color is incorrect.

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Answer:

The segment that connects the midpoints of the legs of a trapezoid is called the median of the trapezoid.

Step-by-step explanation:

Answer:

$10.83

Step-by-step explanation:

Answer:2,2

Step-by-step explanation:

The mistake Simeone made was that he didn't separate it into two inequalities properly.

The correct solution should be: 308/177 < y < 18.

To solve the compound inequality, 18 < - 3y + 72 < 1/3(168y - 92), first separate it into two inequalities.

First part:

18 < - 3y + 72

18 - 72 < -3y

-54 < -3y

18 > y or y < 18

Second part:

- 3y + 72 < 1/3(168y - 92)

3(-3y + 72) < 168y - 92

-9y + 216 < 168y - 92

-9y - 168y < -216 - 92

-177y < -308

y > 308/177 or 308/177 < y

Joining both together, we will have the solution as:

308/177 < y < 18

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From the  X coordinate is -0.45 centimeter and Y coordinate is -2.0 cm of the center of mass for the uniform plate.

According to the Question:

Since the plate is uniform, we can divide it into three rectangles, each with a mass proportional to its area and with its barycenter at its geometric center. We will refer to the large piece of 35cm x 10cm; it occupies 63.6% of the total surface and its barycenter is at

(x₁, y₁) = (−5.0cm,−2.5cm).

Now,

The top 20cm× 5cm piece has 18.2 % of the total area; its center of mass is at (x₂, y₂) = (10cm,12.5cm).  

Now,

The bottom 10cm× 10cm piece (section 3) also has 18.2 % of the total area; its center of mass is at (x₃, y₃)​ = (5cm,−15cm).

(a) The x coordinate of the center of mass for the plate is

   \(X_{com} = (0.636)X_1 + (0.182)X_2 + (0.182)X_3\)

            = -0.45 cm

(b) The y coordinate of the center of mass for the plate is

    \(Y_{com} = (0.636)Y_1 + (0.182)Y_2 + (0.182)Y_3\)

             = -2.0 cm.

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To determine if the average commute time in your county differs from the national average of 40 minutes, you will need to conduct a hypothesis test. The appropriate test to use in this case is a one-sample t-test.

The one-sample t-test is used to compare the mean of a single sample to a known population mean when the standard deviation of the population is unknown.

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The shaded area is 52.5 cm².

What is an area of a rectangle?

The area a rectangle occupies is the space it takes up inside the limitations of its four sides. The dimensions of a rectangle determine its area. In essence, the area of a rectangle is equal to the sum of its length and breadth.

Here, we have

We are given a rectangle and we have to find the area of the shaded region

Let us first find the area of the rectangle

The length and width of the rectangle from the figure are 17 cm and 5 cm

Hence the area is the product of two

A = 17*5

A = 85 cm²

Now let us find the area of the triangles

The measurements of the base and height of the large triangle are 5 cm and 11 cm respectively

Hence the area of that triangle becomes

T1 = 0.5× 11×5

T1 = 27.5cm²

Now the measure of the base and height of the smaller triangle is 2cm and 5cm respectively

Hence the area becomes

T2 = 0.5×5×2

T2 = 5cm²

Now we subtract these 2 areas from the area of a rectangle to find the area of the shaded region

We get,

Area of the shaded region  = 85 - 27.5 -5

Area of the shaded region = 52.5 cm².

Hence, the shaded area is 52.5 cm².

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The correct answer is option b.24.

The given options are Meat: beef, chicken, pork vegetables: baked beans, corn, potatoes, tomatoesDessert: brownies, chocolate cake, chocolate pudding, ice creamThe order of food items is not important, so we need to find the number of combinations we can form by selecting one type of meat, two types of vegetables, and one dessert from the given options.

In selecting the meat, we have three choices, i.e. beef, chicken, and pork. We need to choose one of these three types. So, the number of ways to choose meat is 3. In selecting the vegetables, we have four choices, i.e. baked beans, corn, potatoes, and tomatoes. We need to choose two of these four types.

So, the number of ways to choose two vegetables is,4C2 = 6 (We can select any two vegetables out of four, and the order of vegetables does not matter)In selecting the dessert, we have four choices, i.e. brownies, chocolate cake, chocolate pudding, ice cream. We need to choose one of these four types. So, the number of ways to choose the dessert is 4. So, by the rule of multiplication, we can select a meal in 3 × 6 × 4= 72ways.

However, as the order of food items is not important, we need to divide the total number of combinations by the number of ways to arrange the selected items, i.e. 2! (since we have selected two types of vegetables), and 1! (for meat and dessert). So, the total number of possible meals that Tyler can choose is,72/2! = 36/2 = 18 meals (arranging 2 items from 4),18 × 4! = 18 × 24 = 432 total possible arrangements.

Hence the answer is option b.24.

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Answer:

D. 104º

Step-by-step explanation:

So the inside of a triangle is equal to 180º and we already know two of the angles.

D = 47º

C = 57º

47 + 57 = 104

To solve angles A and B, we know that a straight line is 180º and we can figure out the angle of B because now all we have to do is subtract 104 from 180.

180 - 104 = 76, B = 76º

Because we know that a straight line is 180º and we already have the measure of angle B, all we have to do now is subtract 76 from 180.

180 - 76 = 104º

Answer:

Equilateral triangle

Step-by-step explanation:

Equalateral triangles has 3 60 degre angles, and 3 congruent sides

Answer:

there are 6 faces

Step-by-step explanation:

there are 4 faces around and 1 on to and 1 on the bottom

Given:

Tyler wants to increase the number of each type of exercise by 20% by the end of the month.

Current number of pushups = 25

Total more squats and pushups than he does now = 13

To find:

The equation to show how many squats, x, Tyler does now.

Solution:

Let x be the number of squats Tyler does now.

Each type of exercise increased by 20% by the end of the month.

Current number pushups = 25

Increased number of pushups is 20% of 25.

\(\dfrac{20}{100}\times 25=5\)

Increased number of squats is 20% of x.

\(\dfrac{20}{100}\times x=\dfrac{x}{5}\)

If Tyler meets his goal, he will do a total of 13 more squats and pushups than he does now.

\(\dfrac{20}{100}\times 25+\dfrac{20}{100}\times x=13\)

\(5+\dfrac{x}{5}=13\)

\(\dfrac{25+x}{5}=13\)

Multiply both sides by 5.

\(25+x=65\)

Subtract 25 from both sides.

\(x=65-25\)

\(x=40\)

Therefore, required equation is \(\dfrac{20}{100}\times 25+\dfrac{20}{100}\times x=13\) and the number of current squats is 40.

When a vertical line intersects the graph of a function more than once, it indicates that for that output there is more than one input, which means the function is not a relation.  (option b).

In mathematics, functions are an essential concept used to describe relationships between sets of numbers. A function is a set of ordered pairs, where each input corresponds to exactly one output.

Conversely, if every vertical line intersects the graph at most once, then the graph represents a function. This is because there is only one output for each input, satisfying the definition of a function.

It's important to note that not all relations are functions. A relation is a set of ordered pairs, while a function is a relation where each input corresponds to exactly one output.

Therefore, if a vertical line intersects a graph more than once, it indicates that there is more than one output for that particular input, and the relationship is not a function.

Hence the option (b) is correct.

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Answer: Check explanations

Step-by-step explanation: When lines are parallel, then there are infinite solutions (the answer), if they are intersecting there is only 1 solution, which is the point where the lines intersect, and if they aren't intersecting or parallel, then No solutions.

The probability distribution of the number of hours per day people are able to relax is constructed, and probabilities of relaxing more than 4 hours, between 2 to 6 hours, and not relaxing at all are 0.283, 0.767 and 0.068 respectively. The mean and standard deviation are 3.326 hours and 1.950 hours (approx.) respectively.

The probability distribution of X is:

X Frequency Probability

0 114                    0.068

1 156                    0.093

2 336                    0.201

3 251                     0.150

4 316                      0.189

5 231                     0.138

6 149                    0.089

7 33                    0.020

8 60                    0.036

      1676                     1.000

The probability that a person relaxes more than 4 hours per day is:

P(X > 4) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8)

= 0.138 + 0.089 + 0.020 + 0.036

= 0.283

The probability that a person relaxes from 2 to 6 hours per day is:

P(2 ≤ X ≤ 6) = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)

= 0.201 + 0.150 + 0.189 + 0.138 + 0.089

= 0.767

The probability that a person does not relax at all is:

P(X = 0) = 0.068

The mean Mx is:

Mx = Σ(X * P(X))

= 00.068 + 10.093 + 20.201 + 30.150 + 40.189 + 50.138 + 60.089 + 70.020 + 8*0.036

= 3.326 hours

The standard deviation Ox is:

Ox = sqrt[Σ(X^2 * P(X)) - Mx^2]

= sqrt[(0^20.068)+(1^20.093)+(2^20.201)+(3^20.150)+(4^20.189)+(5^20.138)+(6^20.089)+(7^20.020)+(8^2*0.036) - 3.326^2]

= 1.950 hours (approx.)

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Using the conceptual Formula, the sum of the squares is option (C) 422

To compute the standard deviation using the conceptual (deviation score) formula, we need to follow these steps:

Calculate the mean of the scores:

mean = (40 + 25 + 15 + 19 + 16) / 5 = 23

Calculate the deviation score for each score:

deviation score = score - mean

The deviation scores for each score are:

40 - 23 = 17

25 - 23 = 2

15 - 23 = -8

19 - 23 = -4

16 - 23 = -7

Square each deviation score:

17^2 = 289

2^2 = 4

(-8)^2 = 64

(-4)^2 = 16

(-7)^2 = 49

Calculate the sum of the squared deviation scores:

Sum of squares = 289 + 4 + 64 + 16 + 49 = 422

Therefore, the correct option is (C) 422

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Answer:

6 cookies

____________________

Christine has 2 MORE than Matt.

2 + 2 = 4(Christine)

4 + 2 = 6(total)

Answer:

O q= 52

Step-by-step explanation: