when solving an oblique triangle given three sides, use the ---select--- form of the law of cosines to solve for an angle.

Step-by-step explanation:

let's first sort the data points from low to high :

42, 68, 70, 72, 74, 75, 79, 80, 82, 83, 84, 85, 86, 87, 91, 92, 94, 95, 97, 98

67.

the mean score is the sum of all data points divided by the number of data points :

1634/20 = 81.7

=> BC is correct

68.

the median is the number in the sorted list, what half of the data points are lower, and the other half higher.

in case of an even number of data points, it is the mean value of the 2 central data points.

in our case these are 83 and 84. the mean value between these two numbers is 83.5.

=> BE is correct

69.

the mode is the most frequent number among the data points.

but all scores appear only once.

so, some say, the mode is the set of all data points.

or, others say, there is no mode (like your teacher, apparently)..

=> ABC is correct.

70.

mean absolute deviation (MAD) of a data set is the average distance between each data value and the mean.

so, now we are creating a new data set : the individual distances of the original data points to their mean value :

39.7, 13.7, 11.7, 9.7, 7.7, 6.7, 2.7, 1.7, 0.3, 1.3, 2.3, 3.3, 4.3, 5.3, 9.3, 10.3, 12.3, 13.3, 15.3, 16.3

the man value for these is the MAD of the original data points :

187.2/20 = 9.36

=> B is correct

71.

the range is the difference between the highest and lowest values in a set of numbers.

so, in our case that is

98 - 42 = 56

=> AD is correct

72.

quartiles are the values that divide a list of numbers into quarters (4 equally long parts).

we have here 20 numbers, so all Qs are between 2 numbers.

Q1 is between the 5th and the 6th number (and again, the mean value between these two numbers is the result) :

Q1 = (74 + 75)/2 = 74.5

=> AE is correct

73.

as above, just for Q3 it is between the 15th and 16th number :

Q3 = (91 + 92)/2 = 91.5

=> DE is correct

74.

the interquartile range (IQR) contains the second and third quartiles, or the middle half of your data set.

while the range gives you the spread of the whole data set, the interquartile range gives you the range of the middle half of a data set - so, between Q1 and Q3 :

91.5 - 74.5 = 17

=> E is correct

75.

outliers are extreme values that differ from most other data points in a dataset (much lower or higher than the others).

outliers are therefore values at the extreme ends of a dataset.

often we see at least some of them right away, like 42 in our set.

but are there any others ?

there are some guidelines like building an upper and lower "fence" (or limit), and any value beyond these limits are great candidates for being outliers.

upper fence = Q3 + 1.5 × IQR = 91.5 + 1.5×17 = 117

we have no values higher than 117.

lower fence = Q1 - 1.5 × IQR = 74.5 - 1.5×17 = 49

we have one value (as expected) lower than that (42), which makes this a confirmed outlier.

=> AB is correct.

The scale factor that takes triangle C to triangle D is 3/10.

Scale factor is a number by which the size a geometrical figure or shape can be changed with respect to its original size.

To find the scale factor that takes triangle C to triangle D, we use the formula below

Formula:

Where:

From the diagram in the question,

Given:

Substitute these values into equation 1

Hence, the scale factor is 3/10.

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From the given expression we have come to find that a²- b when a=8 and b=7 is equal to 57.

In mathematics, an expression is a combination of numbers, variables, and mathematical operations that can be evaluated to produce a value. Expressions can be as simple as a single number or variable, or they can be complex combinations of multiple terms and operations.

For example, "3 + 5" is an expression that consists of the two numbers 3 and 5, combined by the mathematical operation of addition. This expression can be evaluated to produce the value 8.

To evaluate the expression a² - b when a=8 and b=7, we simply substitute the values of a and b into the expression and simplify:

a²  - b = 8² - 7 (substitute a=8 and b=7)

= 64 - 7 (simplify)

= 57 (final answer)

Therefore, a²  - b when a=8 and b=7 is equal to 57.

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To calculate the probability of selecting a boy or a red-haired person as a homeroom representative to student council, we need to find the probability of each event and then use the formula P(A or B) = P(A) + P(B) - P(A and B).

There are 31 students in total (16 girls + 15 boys). The probability of selecting a boy is 15/31.

There are 5 red-haired students (3 girls + 2 boys). The probability of selecting a red-haired person is 5/31.

However, we need to account for the overlap between boys and red-haired students. There are 2 red-haired boys, so the probability of selecting a red-haired boy is 2/31.

Now we can use the formula: P(boy or red-haired) = P(boy) + P(red-haired) - P(boy and red-haired) = (15/31) + (5/31) - (2/31) = 18/31.

So, the probability of selecting a boy or a red-haired person as a homeroom representative to student council is 18/31.

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To estimate the difference 10 1/9 - 5 14/15, we can round both numbers to the nearest whole number and it gives (c) 4

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

10 1/9 - 5 14/15

Using the above as a guide, we have the following:

The estimated difference is: 10 - 6

Evaluate

The estimated difference is: 4

Therefore, the Estimated  difference is 5

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The x-intercepts with multiciplity greater than 1 is x = 0

The number of distinct intercepts is 3 and the number of zeros is 4

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

f(x) = x²(x + 2)(x - 7)

The x-intercepts with multiciplity greater than 1 is the factor that has a power greater than 1

So, we have

x² = 0

This gives

x = 0

The number of distinct intercepts is the number of factors i.e. 3

The number of zeros is the sum of powers

i.e. Zeros = 2 + 1 + 1

Zeros = 4

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Answer:

12 bowls

Step-by-step explanation:

If marry had nine pounds of salad, and each salad bowl holds 3/4 pounds each, then the equation is 9 divided by 3/4, which equals twelve.

The statement that is equivalent to each other would be =

2×(4+2)-6 = 14÷(3.5×2)+4. That is option A.

An equivalent equation is the type of equation that appears different but has the same answer when simplified or solved.

The first part;

=2×(4+2)-6

= 2×(6)-6

= 12-6 = 6

The second part;

= 14÷(3.5×2)+4

= 14÷7+4

= 2+4

= 6

Therefore, 2×(4+2)-6 = 14÷(3.5×2)+4. is a true statement.

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Answer:

48 ounces

Step-by-step explanation:

12*4= 48

The triangle with side lengths 11, 12, and 13 is not a right triangle

We can use the Pythagorean theorem to determine whether the given triangle is a right triangle.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

That is, for a right triangle with sides of lengths a, b, and c (where c is the hypotenuse), we have:

a^2 + b^2 = c^2

Let's apply this to the given triangle with side lengths 11, 12, and 13. We need to check whether 13 is the hypotenuse (the longest side) and whether 11 and 12 are the other two sides:

11^2 + 12^2 = 121 + 144 = 265

13^2 = 169

Since 169 is not equal to 265, we can see that the Pythagorean theorem does not hold for this triangle. Therefore, the given triangle is not a right triangle.

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An expression that has any value other than 0 is considered true by an if statement. The answer to this statement is True.

The idea of truth values in mathematics is connected to the validity of a statement or proposition. A statement can either be true or untrue; there is no other option. When dealing with Boolean values, however, a different technique is employed in programming. In this context, any value other than 0 is deemed true.

This implies that when used in an if statement, a value that is negative, decimal, or a non-zero integer will be assessed as true. This is due to the statement's focus on the presence of a value rather than its truth or falsity.

Therefore, the statement that says that an expression that has any value other than 0 is considered true by an if statement is True.

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True. In programming, an expression that has any value other than 0 is considered true by an if statement. The value of an expression can be a number, a string, a boolean, or any other data type.

If the value is not 0, then it is considered true, and the if statement will execute the code block associated with it. If the value is 0, then it is considered false, and the if statement will skip the code block associated with it.

In an if statement, an expression with any value other than 0 is considered true. If the expression's value is 0, the if statement evaluates it as false. This means the code block associated with the true condition will execute when the expression's value is not 0, and the code block associated with the false condition will execute when the expression's value is 0.

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The probability that a randomly selected can in the box is dented or contains vegetables is 19/20.

To solve the problem, we need to use the formula for the probability of the union of two events:

P(A or B) = P(A) + P(B) - P(A and B)

where A and B are two events.

In this case, we want to find the probability that a randomly selected can is dented or contains vegetables. Let's call these events D and V, respectively.

We are given that there are 20 cans in total, 12 of which contain vegetables, and 5 of which are dented, with 2 of the dented cans containing vegetables. This information allows us to calculate the probabilities of the individual events

P(D) = 5/20 = 1/4

P(V) = 12/20 = 3/5

P(D and V) = 2/20 = 1/10

To find the probability of the union of these events, we plug these values into the formula

P(D or V) = P(D) + P(V) - P(D and V)

= 1/4 + 3/5 - 1/10

= 19/20

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Plugging in the values given into the expression, and simplifying, we would have our answer as: B.  [tex]\frac{9}{25}[/tex]

Given that, a = 5 and k = -2, substitute the values into the expression given and simplify:

[tex](\frac{3^2(5^{-2})}{3(5^{-1})} )^{-2}[/tex]

Simplify:

[tex](\frac{9 * \frac{1}{25} }{3* \frac{1}{5} } )^{-2}[/tex]

[tex](\frac{\frac{9}{25} }{\frac{3}{5} } )^{-2}\\\\(\frac{9}{25} * \frac{5}{3} } )^{-2}\\\\(\frac{3}{5} )^{-2}\\\\ = \frac{9}{25}[/tex]

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In this case, both triangles have a side length of 5 units and a side length of 7 units, and they share an angle of 117 degrees. Therefore, they satisfy the ASA criterion, and we can conclude that they are congruent.

Congruent is a mathematical term used to describe two figures or shapes that have the same size and shape. In other words, two figures are congruent if they have exactly the same dimensions and the same angles. When two figures are congruent, they can be superimposed on each other without any overlap or gap between them. Congruent figures are often denoted by the symbol ≅. For example, if two triangles have the same size and shape, we can write them as ∆ABC ≅ ∆DEF, which means that triangle ABC is congruent to triangle DEF. Congruent figures play an important role in geometry and other branches of mathematics.

Yes, the two triangles are congruent.

In Euclidean geometry, if two angles and a side of one triangle are equal to two angles and a side of another triangle, then the two triangles are congruent. This is known as the angle-side-angle (ASA) congruence criterion.

In this case, both triangles have a side length of 5 units and a side length of 7 units, and they share an angle of 117 degrees. Therefore, they satisfy the ASA criterion, and we can conclude that they are congruent.

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the fraction that rounds to 5 is option B, 5 1/2.

What is a fraction?

If the numerator is bigger, it is referred to as an improper fraction and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder.

Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.

To round a fraction to 5, we need to find the fraction that is closest to 5. Therefore, we need to look at the fractional parts of each option and find which one is closest to 1/2.

A. 5 2/3 = 17/3, which is closer to 6 than to 5.

B. 5 1/2 = 11/2, which is exactly halfway between 5 and 6, so it rounds to 5.

C. 5 9/20 = 259/20, which is closer to 6 than to 5.

D. 4 9/20 = 209/50, which is closer to 4 than to 5.

Therefore, the fraction that rounds to 5 is option B, 5 1/2.

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If Alice has $50 and spends 4/5 of her money, she spends $40.

A fraction is a mathematical expression that represents a part of a whole or a ratio between two quantities. Fractions are commonly represented using two numbers separated by a horizontal line, where the top number is called the numerator and the bottom number is called the denominator.

Alice spends 4/5 of her money, which is equivalent to 0.8 of her money.

To find out how much Alice spends, we can multiply her total money ($50) by 0.8

= $50 x 0.8

Multiply the numbers

= $40

Therefore, Alice spends $40.

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I have solved the question in general, as the given question is incomplete.

The complete question is:

Alice has $50 and spends 4/5 of her money. How much does Alice spend?

The chance that you will both win the raffle and win $500 is 0.0025, or 0.25%.

To find the chance of both winning the raffle and correctly guessing the organizer's favorite season, you need to multiply the probabilities of these two independent events.

Step 1: Determine the probability of winning the raffle.
The probability of winning the raffle is given as 0.01.

Step 2: Determine the probability of correctly guessing the favorite season.
The probability of correctly guessing the favorite season is given as 0.25.

Step 3: Multiply the probabilities of the two independent events.
To find the probability of both events happening, you multiply their probabilities: 0.01 (winning the raffle) * 0.25 (correctly guessing the favorite season).

0.01 * 0.25 = 0.0025

So, the chance that you will both win the raffle and win $500 is 0.0025, or 0.25%.

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The probability of both winning the raffle and correctly guessing the organizer's favorite season to win the $500 prize is 0.0025 or 0.25%.

To find the probability of both winning the raffle and guessing the organizer's favorite season correctly, you'll need to multiply the individual probabilities of each event.

Probability of winning the raffle: 0.01 (given in the question)
Probability of guessing the organizer's favorite season: 0.25 (given in the question)
Now, multiply these probabilities together:
0.01 * 0.25 = 0.0025.

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A. We can see here that triangles ABX and DCX are similar because using the Angle-Angle Similarity:

B. Length XD = 12.5cm.

Similar triangles are triangles that have the same shape but not necessarily the same size. In other words, corresponding angles of similar triangles are equal, and corresponding sides are in proportion.

More formally, two triangles ABC and DEF are similar if and only if:

The length of XD:

CD/AB = XD/AX

10/4 = XD/5

XD = 50/4 = 12.5cm.

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The average speed of the current is 1 mile per hour.

To construct a rational equation that can be solved for the speed of the current, we can use the relationship t = d/r, where t is the time taken, d is the distance traveled, and r is the speed. We can set up two equations using this relationship, one for the upstream journey and one for the downstream journey:

Upstream journey: t = 4/(10-c)

Downstream journey: t = 6/(10+c)

Here, c represents the speed of the current. We use 10-c for the upstream journey because the current is going against the boat's direction, effectively reducing the boat's speed. Conversely, we use 10+c for the downstream journey because the current is aiding the boat's direction, effectively increasing the boat's speed.

Now, we can set these two equations equal to each other and solve for c:

4/(10-c) = 6/(10+c)

Multiplying both sides by (10-c)(10+c), we get:

4(10+c) = 6(10-c)

Simplifying and solving for c, we get:

c = 1

This means that when the boat is traveling with the current, its effective speed is 11 miles per hour, and when it's traveling upstream, its effective speed is 9 miles per hour.

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The statement "Some twins are sisters. All twins are siblings. Therefore, some siblings are sisters" is true.

Usually an illustration of a substantial deductive contention in which the conclusion takes coherently from the premises.

The primary introduction states that a few twins are sisters, which suggests that they are female twins. The moment preface states that all twins are kin, which implies that they are related by blood.

In this manner, on the off chance that a few twins are sisters and all twins are kin, it consistently takes after that a few kin are sisters.

It is imperative to note that the conclusion isn't essentially genuine for all kin, as a few kin may be brothers or mixed-gender twins. Be that as it may, the contention is still consistently substantial since the conclusion takes after coherently from the premises 

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To form a suitable quadratic equation using the values from the table given in the question also  considering the event of forming a equation that represents f(x) is Option A.
In order to find the equation that is  represented by f(x), we have to implement the standard form of a quadratic function
f(x) = ax² + bx + c
here a, b and c = constants.
We can utilize the given table of values to evaluate these constants.

Now, we have to  place each x value into f(x) to get the concerning y value. Then we can utilize these points to create three equations with three undetermined (a, b and c).
Evaluating these equations will give us the values of a, b and c.

Now, the table of values given in the question is

f(-2) = 48 = 4a - 4b + c
f(-1) = 50 = a - b + c
f(0) = 48 = c
f(1) = 42 = a + b + c
f(2) = 32 = 4a + 4b + c
f(3) = 18 = 9a + 3b + c
f(4) = 0 = 16a + 4b + c


Calculating these equations

a = -2
b = -4
c = 48

Hence, the equation that represents f(x) is f(x) = -2x² - 4x + 48.

The correct option for the given question after considering the given conditions is Option A.

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The complete question is
The table of values forms a quadratic function f(x). X f(x)−2 48
f(−1) = 50
f(0) = 48
f(1) = 42
f(2) = 32
f(3) = 18
f(4) = 0

What is the equation that represents f(x)?
a) f(x) = –2x² – 4x + 48
b) f(x) = 2x² + 4x – 48
c) f(x) = x² + 2x – 24
d) f(x) = –x² – 2x + 24

Answer: 12 inches is one foot

Step-by-step explanation: hope that this is what you were asking ;)

The terms arranged in order from smallest to biggest are: (-2)³, -√25, √11, 10, and 4² after comparing the values of the final numbers.

We shall first simplify the numbers to get their final values and then compare to which is smaller as follows:

4² = 4 × 4 = 16

-√25 = -5

10 = 10

√11 = 3.3166

(-2)³ = -2 × -2 × -2 = -8

In conclusion, we have by comparing the final values of the numbers the terms arranged from smallest to the biggest as: (-2)³, -√25, √11, 10, and 4².

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Exponential smoothing uses a weighted average of past time-series values to forecast the value of the time series in the next period.

Exponential smoothing is a forecasting method that assigns exponentially decreasing weights to past observations. The weights decrease exponentially as the observations get older, giving more weight to recent observations and less weight to older observations.

The formula for exponential smoothing is as follows:

F(t+1) = α * Y(t) + (1-α) * F(t)

where F(t+1) is the forecasted value for the next period, Y(t) is the actual value for the current period, F(t) is the forecasted value for the current period, and α is the smoothing parameter (0 < α < 1) that determines the weight given to the current observation.

Exponential smoothing is simple and easy to use, and it can provide accurate forecasts when the time series is relatively stable and does not have a trend or seasonality. However, it may not perform well when the time series has a trend or seasonality, in which case other methods such as moving average, weighted moving average, or regression may be more appropriate.

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Complete Question:

What uses a weighted average of past time-series values to forecast the value of the time series in the next period?

a. moving average

b. exponential smoothing

c. weighted moving average

d. regression

Answer: The area is 182 ft².

Step-by-step explanation:

We will use this formula for the area of a parallelogram:

     ➜ See attached for why this formula works.

     A = BH

We will substitute known values and solve by multiplying.

     A = BH

     A = (13 ft)(14 ft)

     A = 182 ft²

Answer: 2

Step-by-step explanation: Mode is the most frequent number

The solution to the system of inequalities is given by the image presented at the end of the answer.

One point on the solution set is given as follows:

(-9,3).

A system of inequalities is a set of two or more inequalities involving one or more variables. In a system of inequalities, the solution is a set of values for the variables that satisfy all of the given inequalities simultaneously.

The solution is the shaded region on the graph given by the image presented at the end of the answer.

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The tape diagram for the equation can be given using rectangular boxes. The unknown value of x is a. 7, b. 7.

A tape diagram, often referred to as a strip diagram, is a visual representational tool in mathematics used to compare or illustrate numerical relationships. It consists of a rectangle or a segment of a line that has been divided into equal portions, each of which represents a specific amount. The magnitude of the quantity being measured is indicated by the length or area of the parts.

In order to help students understand the information offered and to visualise the relationships between the values involved, tape diagrams are frequently utilised in problem-solving scenarios.

Given that,

a.x+9=16

x = 16 - 9

x = 7

b.4•x=28

x = 7

Hence, the unknown value of x is a. 7, b. 7.

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The results of the balls in Phillip's bag are:

The mean = 8.

The median = 7.

The mode = blue

The range = 12

The mean (or the average) is the sum of all the values divided by the total number of values. Let's calculate the mean for the given data:

Total number of balls = 8 + 3 + 6 + 3 + 13 + 15 = 48

Mean = (8 + 3 + 6 + 3 + 13 + 15) / 6 = 48 / 6 = 8

Mean = 8.

The median is the middle value when a set of values is arranged in ascending or descending order.

Let's arrange the given data in ascending:

3, 3, 6, 8, 13, 15

As the total number of values is even, the median will be the average of the two middle values, which are 6 and 8.

Median = (6 + 8) / 2 = 7

The median = 7.

The mode is the value that appears most frequently in a set of values. Let's find the mode of the given data:

Red balls: 8

Green balls: 3

Yellow balls: 6

Orange balls: 3

Black balls: 13

Blue balls: 15

Blue balls have the highest frequency (i.e., 15) among all the colors.

The range is the difference between the highest and lowest values in a set of values. Let's find the range of the given data:

Highest value = 15 (blue balls)

Lowest value = 3 (green balls and orange balls)

Range = Highest value - Lowest value = 15 - 3 = 12

Range = 12.

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