a group of seven people are attending the movies together. (a) two of the seven insist on sitting side-by-side. in how many ways can the seven be seated together in a row? (b) two of the people do not like each other and do not want to sit side-by-side. now how many ways can the seven be seated together in a row?

Answer:

2,700 years

Explanation:

We were given the following details:

Half-life of carbon-14, T = 5600 years

78% of carbon-14 is left. This indicates that the amount of carbon-14 left is 78% of the initial amount:

We will calculate the time since when the tree died as shown below:

Therefore, the tree died 2,700 years ago

Since the training set consists of 40 observations, you would need to fill in the counts for each category based on the actual classifications made by the model using the 0.5 cutoff value.

To construct the confusion matrix for a 40-observation training set, we need to use a cutoff value of 0.5 to classify each profile observation as either interested or not interested. The confusion matrix is a tool that shows the performance of a classification model.

Let's denote the four possible outcomes as follows:
- True Positive (TP): The model correctly classified an observation as interested.
- True Negative (TN): The model correctly classified an observation as not interested.
- False Positive (FP): The model incorrectly classified an observation as interested when it was actually not interested.
- False Negative (FN): The model incorrectly classified an observation as not interested when it was actually interested.

Since we have a cutoff value of 0.5, any observation with a prediction score above or equal to 0.5 will be classified as interested, while any observation with a prediction score below 0.5 will be classified as not interested.

Based on this information, we can construct the confusion matrix:

                   Predicted Interested   Predicted Not Interested
Actually Interested       TP                           FN
Actually Not Interested    FP                           TN

Note that the values TP, TN, FP, and FN are counts of observations falling into each category.

In your case, since the training set consists of 40 observations, you would need to fill in the counts for each category based on the actual classifications made by the model using the 0.5 cutoff value.

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Your question is not complete so there are two answers:

The measure of one angle is 13 times the measure of the other angle.

Answer:

Step-by-step explanation:

Two angles of a linear pair create a straight angle therefore they add to 180°

x°     - the other angle

(13x)°  - one angle

x + 13x = 180

   14x = 180

  ÷14      ÷14

   x ≈ 12.86

13x = 13•12.86 = 167.14

Checking:  12.96+167.14 = 180

The measure of one angle is 13 more than the measure of the other angle.

Answer:

Step-by-step explanation:

Two angles of a linear pair create a straight angle therefore they add to 180°

x°     - the other angle

(x+13)°  - one angle

x + x + 13 = 180

       -13        -13

    2x  =  167

    ÷14      ÷14

     x ≈ 83.5

x+13 = 83.5 + 13 = 96.5

Checking:  83.5+96.5 = 180

Since 11.25 feet is the exact answer, we can be quite certain that our answer is correct because it is extremely close to that figure.

Something is referred to as "lengthy" when it is measured end to end. In other terms, the bigger dimension is the larger of the third or upper two dimensions of a geometric object. The length and width of a rectangle serve as an example.

If each person has 1 7/8 feet of counter space and there are 6 people, then the total counter space required is:

Total length of counter = 6 × 1 7/8 feet

Total length of counter = 6 × 1.875 feet

Total length of counter = 11.25 feet

Therefore, the length of the counter is 11.25 feet.

To check if this answer is reasonable, we can use estimation. If we round 1 7/8 feet to 2 feet, then each person would need 2 feet of counter space, and 6 people would need a total of:

6 x 2 feet = 12 feet

This is very close to the actual answer of 11.25 feet, so we can be reasonably confident that our answer is correct.

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v₁ = [[-1], [-2], [-2]] and v₂ = [[-4], [8], [-6]] are the vectors that satisfy the given conditions.

To write vector y as the sum of a vector v₁ in W and a vector v₂ orthogonal to W, we need to find the orthogonal projection of y onto the subspace W spanned by u₁ and u₂.

y = [[-5], [6], [-8]]

u₁ = [[1], [2], [2]]

u₂ = [[6], [2], [-5]]

To find v₁, we'll use the formula for the orthogonal projection

v₁ = ((y · u₁) / (u₁ · u₁)) × u₁

where "·" represents the dot product.

Calculating the dot products

y · u₁ = (-5 × 1) + (6 × 2) + (-8 × 2) = -5 + 12 - 16 = -9

u₁ · u₁ = (1 × 1) + (2 × 2) + (2 × 2) = 1 + 4 + 4 = 9

Substituting the values

v₁ = ((-9) / 9) × [[1], [2], [2]] = [[-1], [-2], [-2]]

Now, to find v₂, we'll subtract v₁ from y

v₂ = y - v₁ = [[-5], [6], [-8]] - [[-1], [-2], [-2]] = [[-4], [8], [-6]]

Therefore, we can write y as the sum of v₁ and v₂

y = v₁ + v₂ = [[-1], [-2], [-2]] + [[-4], [8], [-6]] = [[-5], [6], [-8]]

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Answer:

y = x^2 - 4.

Step-by-step explanation:

This graph is the reslt of translating y = x^2 down by 4 nits

If there is 5 pts per question.

20-5=15 20 ?'s and 5 pts per ?

15x5=75 the 5 is pts per ?

75+8=81 The 8 is the bonus

so his score is 81...

sorry if it's wrong

Answer:

Cumulative Frequency:

The sum of all the frequencies for all classes is equal to the number of elements in the given data and that summation is termed as the cumulative frequency which defines the number of entries of that statistical data.

The sum of relative frequencies is also equal to one, since the sum of all fractional parts must equal the whole.

Step-by-step explanation:

To solve the equation |x-3|=9, we consider two cases: (x-3) = 9 and -(x-3) = 9. In the first case, we find that x = 12. In the second case, x = -6. To check our answers, we substitute them back into the original equation, and they satisfy the equation. Therefore, the solutions to the equation are x = 12 and x = -6.

To solve the equation |x-3|=9, we need to consider two cases:

Case 1: (x-3) = 9
In this case, we add 3 to both sides to isolate x:
x = 9 + 3 = 12

Case 2: -(x-3) = 9
Here, we start by multiplying both sides by -1 to get rid of the negative sign:
x - 3 = -9
Then, we add 3 to both sides:
x = -9 + 3 = -6

So, the two solutions to the equation |x-3|=9 are x = 12 and x = -6.


The equation |x-3|=9 means that the absolute value of (x-3) is equal to 9. The absolute value of a number is its distance from zero on a number line, so it is always non-negative.

In Case 1, we consider the scenario where the expression (x-3) inside the absolute value bars is positive. By setting (x-3) equal to 9, we find one solution: x = 12.

In Case 2, we consider the scenario where (x-3) is negative. By negating the expression and setting it equal to 9, we find the other solution: x = -6.

To check our answers, we substitute x = 12 and x = -6 back into the original equation. For both cases, we find that |x-3| is indeed equal to 9. Therefore, our solutions are correct.

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Answer:

100/x+6=20/x-6

100x-600=20x+120

80x=720

x=9 miles an hour as the rowing teams' rate in still water

Answer:

Step-by-step explanation

To make the problem easier, we are gonna have to change the denominator into 16

8*2=16 after we times 8 with 2 we now have to do the same 7

So this would show 7*2=14

Now it would be 6 14/16 - 6 15/16

All we have to do now is minus 14 with 15 which equals -1.

Now for the whole numbers, you can just minus the 6’s with eachother 6-6=0. Taking the denominator, we now have -1/16.

Hope this is the answer you are looking for.

Answer:

0.043

Step-by-step explanation:

Divide by 100.

4.3 / 100 = 0.043

Best of Luck!

The correct option is B. The length of arc AB of the circle C rounded to the nearest tenth is 15.7cm.

We shall use the formula:

arc length = (arc angle/360) × 2 × 22/7 × radius

where arc angle is measured in degrees and radius is the distance from the center of the circle to the point on the circle where the arc begins.

If BC = 10cm and is the radius, with the arc angle m ∠ACB = 90° then the arc length AB is derived as follows:

(90°/360°) × 2 × 22/7 × 10cm

90°/360° can be reduced to 1/4

1/4 × 2 × 22/7 × 10cm

By simplifying further, we have;

1 × 11/7 × 10cm

110cm/7

15.71cm

Therefore, the circle C have the arc length AB equal to 15.7cm rounded up to the nearest tenth.

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Answer:

147?

Step-by-step explanation:

Kami will have $1,413.60 in the account after 4 years.

(1) Depositing $550 at 3% interest for one year generated a $16.50 profit for Abe.

(2) Jessi returned a $1,500 loan with a quarterly 3% rate and paid $1,511.25 in total.

(3) After keeping a deposit worth $418 at 2% for a year, Heath made an $8.36 profit. In 5.5 years, his account balance grew to $463.98.

(4) By depositing $825.50 at 4%, Pablo saw a $33.02 profit within a year.

(5) Kami put down $1,140 earning a $68.40 annual yield thanks to the 6% interest rate. Four years later, her account balance reached $1,413.60.

Interest = 1,140 * 0.06 * 4 = $273.60

Now, add the interest to the principal:

Total Amount = Principal + Interest = 1,140 + 273.60 = $1,413.60

Kami will have $1,413.60 in the account after 4 years.

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Answer:

79

Step-by-step explanation:

Order of operations GERMDAS

Grouping: no grouping

Exponents: 9²=81 so 6÷3+81-4

Radicals: no radicals

Multiplication: no multiplication

Division: 6÷3=2 so 2+81-4

Addition: 2+81=83 so 83-4

Subtraction: 83-4=79

Answer:

79

Step-by-step explanation:

6/3+9^2-4             9^2= 81           6/3+81-4                  6/3 = 2                  2+81-4= 79

Answer:

Canoe Rental Service Fee ($Y) = $20 + $30*Per Hour($x)

Answer:4.76

Step-by-step explanation:

tan 0= opposite side/adjacent side

tan x = 1/12

x =tan-1 (1/12)

~~ 4.76 degrees

The angle of inclination x of this ramp is 4.76 degrees.

'A right-angled triangle is a triangle, that has one of its interior angles equal to 90 degrees or any one angle is a right angle.'

According to the given problem,

Perpendicular = 1 inch

Base = 12 inches

Angle of inclination = x

We know,

tan (x) = \(\frac{Perpendicular}{Base}\)

⇒ tan(x) = \(\frac{1}{12}\)

⇒ x = \(tan^{-1} \frac{1}{12}\)

⇒ x = 4.76 degrees.

Hence, we can conclude, the angle of inclination is 4.76 degrees.

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Answer:

(x-3)(x+4)(x-6) =A

Step-by-step explanation:

f(3)=27-45-54+72=0

f(6)=0

so (x-3)(x+4)(x-6)

Answer:

a=-14

Step-by-step explanation:

10+2a=-18

subtract 10 from 10 and -18

2a = -28

then devid by 2 from 2 and -28

a=-14

The distance between the hotel and the victim is approximately 3.57 ft.

To determine the distance between the hotel and the victim, we can use the concept of trigonometry. Let's denote the distance between the hotel and the victim as 'd.'

We know the height of the hotel balcony, which is 428 ft, and the angle of elevation from the shooter to the victim, which is 57 degrees.

Using the tangent function (tan), we can set up the following equation:

tan(57 degrees) = height of the victim / distance between the hotel and the victim

tan(57 degrees) = 5.5 ft / d

To find 'd,' we can rearrange the equation:

d = 5.5 ft / tan(57 degrees)

Using a calculator, we can evaluate this expression:

d ≈ 5.5 ft / tan(57 degrees) ≈ 5.5 ft / 1.5407 ≈ 3.57 ft

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Answer:

5

Step-by-step explanation:

2x+10+3x-6=29

5x+4=29

5x=25

x=5

Answer:

B

Step-by-step explanation:

I dont know how to show my work...

Answer: Choice A (20 yards)

Step-by-step explanation:

Bobby's football team received four five-yard penalties in the first quarter, which means they lost 4 x 5 = 20 yards in total.

The team started at the 45-yard line, which means they had 45 yards to go until the goal line.

The team ended at the 25-yard line, which means they had progressed 45 - 25 = 20 yards down the field.

However, they lost 20 yards due to penalties, so their actual progress down the field was 20 - 20 = 0 yards.

Therefore, the change in their progression down the field as a result of these penalties is -20 yards (choice A).

Let's solve for x by factoring this quadratic equation.

We first need to determine which two numbers multiply to -28 (c) but add to 3 (b).

The two numbers that multiply to -28 and add to 3 are 7 and -4.

Therefore, we can factor this equation like so:

Now, we can set this equation to 0 and solve for x.

If we look at each factor individually, we can determine the values of x:

Subtract 7 from both sides of the equation.

Now, let's look at the other factor:

Add 3 to both sides of the equation.

The solution of x^2 + 3x - 28 is x = -7, x = 4.

An example of an equation is 4.5 x = 13.2 because it shows that two expressions are equal.

We can say that an expression is a random combination of numbers, variables, functions, etc.

For example, 3x - 2 is an expression.

While on the other hand, an equation means that two different expressions are connected to each other by an equal sign in between, For example, 3x - 2 = 5 + x is an equation.

Based on the above examples, we can say that:

An example of an equation is 4.5 x = 13.2 because it shows that two expressions are equal.

Therefore, An example of an equation is 4.5 x = 13.2 because it shows that two expressions are equal.

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The largest integers of the numbers is 406.

The sum of five consecutive positive integers is 2020.

Therefore,

let

the first positive integer = x

Hence,

x + x + 1 + x + 2 + x + 3 + x + 4 = 2020

5x + 10 = 2020

5x = 2020 - 10

5x = 2010

x = 2010 / 5

x = 402

largest integer = 402 + 4 = 406

Therefore, the largest integers of the numbers is 406.

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Answer:

t = 4

Step-by-step explanation:

In step two, instead of multiplying by -6 on both sides, you need to divide by -6 to isolate t.

-6t = -24

÷-6    ÷-6

t = 4

When you multiply by -6 on both sides, the equation would be 36t = 144, which is not what we want. The opposite of multiplication is division, and in order to get the answer, you divide by the number multiplied.