What is the range of the numbers below? 26, 37, 15, 21, 3, 42,53

The angle of sinθ between the horizontal vector (1, 0) and the slant vector (15/17, -8/17) is sin⁻¹(8/17), which is approximately 29.11 degrees.

To find the angle of sinθ between a horizontal vector and a slant vector, we can use the dot product formula:

a · b = |a| |b| cos(θ)

where a and b are vectors, |a| and |b| are their magnitudes, and theta is the angle between them.

In this case, the horizontal vector is (1, 0) and the slant vector is (15/17, -8/17).

The magnitude of the horizontal vector is 1, and the magnitude of the slant vector is:

|b| = sqrt((15/17)² + (-8/17)²) = sqrt(225/289 + 64/289) = sqrt(289/289) = 1

The dot product of the two vectors is:

a · b = (1)(15/17) + (0)(-8/17) = 15/17

So we have:

15/17 = (1)(1) cos(θ)

cos(θ) = 15/17

To find sin(θ), we can use the trigonometric identity:

sin²(θ) + cos²(θ) = 1

sin²(θ) = 1 - cos²(θ) = 1 - (15/17)² = 64/289

Taking the square root of both sides, we get:

sin(theta) = sqrt(64/289) = 8/17

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List of possible integral roots = 1, -1, 2, -2, 3, -3, 6, -6

List of corresponding remainders = 0, -16, -4, 0, 0, 96, 600, 1764

Check out the table below for a more organized way to represent the answer. The x values are the possible roots while the P(x) values are the corresponding remainders.

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Explanation:

We'll use the rational root theorem. This says that the factors of the last term divide over the factors of the first coefficient to get the list of all possible rational roots.

We'll be dividing factors of 6 over factors of 1. We'll do the plus and minus version of each. Since we're dividing over +1 or -1, this means that we're basically just looking at the plus minus of the factors of 6.

Those factors are: 1, -1, 2, -2, 3, -3, 6, -6

This is the list of possible integral roots.

Basically we list 1,2,3,6 with the negative versions of each value thrown in as well.

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From there, you plug each value into the P(x) function

If we plugged in x = 1, then,

P(x) = x^4 - 3x^3 - 3x^2 + 11x - 6

P(1) = (1)^4 - 3(1)^3 - 3(1)^2 + 11(1) - 6

P(1) = 1 - 3 - 3 + 11 - 6

P(1) = 0

This shows that x = 1 is a root, since we get a remainder 0. Do the same for the other possible rational roots listed above. You should find (through trial and error) that x = -2 and x = 3 are the other two roots.

The least common denominator needed to solve the equation is given as follows:

D. x(x - 3).

The equation in this problem is given as follows:

1/x + 2/(x - 3) = 5.

The denominators of each expression are given as follows:

x and x - 3 are not factors of each other, hence we multiply them and the least common denominator needed to solve the equation is given as follows:

D. x(x - 3).

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Answer:

This is my best solution for your question

The perimeter of the rectangle whose dimensions are (x + 5) and (y - 1) is, P = 2x + 2y + 8The correct option from the given choices is A.What is a rectangular perimeter?The whole distance that a rectangle borders, or its sides, the cover is known as its perimeter. Given that a rectangle has four sides, the perimeter of the rectangle will be equal to the total of its four sides.Given:A shape is a rectangle.And P is the perimeter of that rectangle.And the dimensions of the rectangle are (x + 5) and (y - 1).So, the perimeter of the rectangle,= 2 [(x + 5) + (y - 1)]= 2 [ x + y + 4]= 2x + 2y + 8Therefore, the perimeter of the shape is P = 2x + 2y + 8.

If the certain truck traveled 7,605 miles in 15 days. The average number of miles traveled per day will be 507.

It is defined as the single number that represents the mean value for the given set of data or the closed value for each entry given in the set of data.

It is given that, a certain truck traveled 7,605 miles in 15 days.

The average number of miles traveled per day is obtained by dividing the total distance traveled by the total time taken as,

Suppose the average number of miles traveled per day is x,

x=76015 / 15

x=507 miles per day.

Thus, if the certain truck traveled 7,605 miles in 15 days. The average number of miles traveled per day will be 507.

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Answer:

39 / 3 = 13

Step-by-step explanation:

first find out how many times 39 goes into 3 by writing the multiplication facts of 3.

3x1=3             3x8=24

3x2=6            3x9=27

3x3=9            3x10=30

3x4=12           3x11=33

3x5=15           3x12=36

3x6=18           3x13=39

3x7=21           3x14=42

You use 3x13 because 3x13 equals to 39 and that is our dividend.

The answer is 13

Answer:

First one is:

1 + 8 + 64 + 512 + 4096

Second one is:

73

Answer:

First one is:

1 + 8 + 64 + 512 + 4096

Second one is:

73

Step-by-step explanation:

Answer:

n ≤ 1 or n ≥ 7

Step-by-step explanation:

solve each part separately

86n + 13 ≤ 99 ( subtract 13 from both sides )

86n ≤ 86 ( divide both sides by 86 )

n ≤ 1

n + 90 ≥ 97 ( subtract 90 from both sides )

n ≥ 7

solution is n ≤ 1 or n ≥ 7

Answer:

$62.50

Step-by-step explanation: 250 divided by 4 equals $62.10

Answer:

If you round it the 30. If not round 29.7

Step-by-step explanation:

Branliest plz :)

Answer:

80m2 wtfffffffffffffffffffff

Answer:

"2a − 6".

Step-by-step explanation:

The correct expression is "2a − 6".

This is a way to verify:

Let's say Adrianna sold 36 magazines. Now, substitute in that for a in the expression and calculate:

\(2a-6=\\ \\2(36)-6=\\ \\72-6=\\ \\66\)

Now, is 66 six less than the double of 36? The answer is yes, therefore, the expression is correct.

Answer: 2a - 6

Step-by-step explanation:

Took the test

To solve this problem, we need to convert all the measurements to a consistent unit. Let's convert the height to inches since the height of the bounce is given in inches.

64 ft = 64 * 12 inches = 768 inches

Now, we can set up an equation to represent the height of each bounce. Let's use "b" to represent the number of bounces, and "h" to represent the height of each bounce in inches.

The height of each bounce is three-fourths (3/4) the height of the previous bounce. So, we can write the equation as:

h = (3/4) * h_previous

where h_previous is the height of the previous bounce.

We know that the initial height of the ball is 768 inches, and we want to find the number of bounces when the height of the bounce is less than 9 inches. We can set up an inequality to represent this situation:

h < 9

Substituting the expression for h from the equation above, we get:

(3/4) * h_previous < 9

Now, we can start with the initial height of 768 inches and keep applying the equation for each bounce until the height of the bounce is less than 9 inches.

1st bounce:

h = (3/4) * 768 = 576 inches

2nd bounce:

h = (3/4) * 576 = 432 inches

3rd bounce:

h = (3/4) * 432 = 324 inches

4th bounce:

h = (3/4) * 324 = 243 inches

5th bounce:

h = (3/4) * 243 = 182.25 inches

6th bounce:

h = (3/4) * 182.25 = 136.6875 inches

7th bounce:

h = (3/4) * 136.6875 = 102.515625 inches

8th bounce:

h = (3/4) * 102.515625 = 76.88671875 inches

9th bounce:

h = (3/4) * 76.88671875 = 57.6650390625 inches

10th bounce:

h = (3/4) * 57.6650390625 = 43.248779296875 inches

So, the ball will bounce up to a height less than 9 inches after 10 bounces.

Answer:

Step-by-step explanation:

Let's get inverse of g(x) and compare it with f(x):

g'(x) and f(x) are different so the answer is No

The 95% confidence interval for the effectiveness of the blood-pressure drug is given as follows:

\(22.6 < \mu < 24.4\)

The mean, the standard deviation and the sample size for this problem, which are the three parameters, are given as follows:

\(\overline{x} = 23.5, \sigma = 12.2, n = 775\)

Looking at the z-table, the critical value for a 95% confidence interval is given as follows:

z = 1.96.

The lower bound of the interval is then given as follows:

\(23.5 - 1.96 \times \frac{12.2}{\sqrt{775}} = 22.6\)

The upper bound of the interval is then given as follows:

\(23.5 + 1.96 \times \frac{12.2}{\sqrt{775}} = 24.4\)

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Answer:

2x^3+17x^2+10x−50

Step-by-step explanation:

Hence, He had to pay $ 18.11 for the tip on a restaurant bill.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.

Josiah ate dinner at a restaurant and his bill was $15.75,

He wanted to leave  15% tip,

Then He had to pay,

=15.75+15 % of 15.75

=15.75 + 0.15*15.75

=18.11

Hence, He had to pay $ 18.11 for tip on the restaurant bill.

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Answer: The correct answer would be D

Step-by-step explanation:

I’m just guessing ;)

Answer:

8 should be multiplied in the parenthesis

Step-by-step explanation:

8(9 + x) = 192

72 + 8x = 192

8x = 120

x = 4

Javier made the mistake while expanding the brackets.

Order of operation means simplify the function , expression etc. in given manner.  

To expand a single bracket multiply each term inside the bracket by the term outside the bracket.

8 (9+x) = 192

8*9 + 8*x = 192

72 + 8x = 192

Now, rearranging the above expression

8x = 192 - 72

8x = 120

x = 120/ 8

x = 5

Hence, Javier made the mistake while expanding the brackets.

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\(\\ \sf\longmapsto 10x=\dfrac{1}{0.001}\)

\(\\ \sf\longmapsto 10x=\dfrac{1}{\dfrac{1}{1000}}\)

\(\\ \sf\longmapsto 10x=1000\)

\(\\ \sf\longmapsto x=\dfrac{1000}{10}\)

\(\\ \sf\longmapsto x=100\)

Around 0.000125 or 0.0125% of the time, the song will be played exactly six out of seven days.

Every day represents a trial in this binomial probability issue, and there are only two potential results:

either the music is played (a success), or it is not (failure). We're looking for the likelihood that exactly 6 out of 7 trials will be successful.

The likelihood of success (performing the song) is 1/6, while the likelihood of failure (not playing the song) is 1 - 1/6 = 5/6, on any given day.

We can use the binomial probability formula to find the probability of exactly 6 successes in 7 trials:

P(6 successes) = (7 choose 6) * (1/6)⁶ * (5/6)¹

where (7 choose 6) is the number of ways to choose 6 days out of 7 to play the song, and is calculated as:

(7 choose 6) = 7! / (6! * 1!) = 7

Plugging in the values, we get:

P(6 successes) = 7 * (1/6)⁶ * (5/6)¹

P(6 successes) ≈0.00012502

Therefore, the probability that the song will be played on exactly 6 days out of 7 is approximately 0.000125 or 0.0125%.

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Answer: Should be 275%

Step-by-step explanation:

Answer:

The roots are -2 and 4

Step-by-step explanation:

Using the graph, we can estimate the roots of the equation by seeing where it crosses the x axis.

It appears to cross the x axis at -2 and 4.

The roots are -2 and 4

The relation that can not be supported by the evidence in the image is option B

Corresponding angles are those that are located on the same side of the transversal and in identical relative positions to the parallel lines. Angles that correspond to one another have the same measure.

Alternate interior angles are those that are located on the transverse and within the area between the parallel lines, respectively. Congruent alternate interior angles exist.

Alternate external angles are those that are outside of the space between the parallel lines and on the opposing sides of the transversal. Congruent external angles exist between the two.

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Answer: To calculate the amount of canvas needed for one tent, we need to calculate the total surface area of the tent. The tent consists of two parts: the cylindrical lower part and the conical upper part.

The surface area of the cylindrical part can be calculated as follows:

The base area of the cylinder = π × r² = π × 2.8² ≈ 24.61 m²

The lateral area of the cylinder = 2 × π × r × h = 2 × π × 2.8 × 3.5 ≈ 54.99 m²

So, the total surface area of the cylindrical part is the sum of the base area and lateral area, which is:

Total surface area of cylindrical part = 24.61 + 54.99 ≈ 79.60 m²

The surface area of the conical part can be calculated as follows:

The slant height of the cone = √(r² + h²) = √(2.8² + 2.1²) ≈ 3.44 m

The lateral area of the cone = π × r × slant height = π × 2.8 × 3.44 ≈ 24.12 m²

So, the total surface area of the conical part is the sum of the base area and lateral area, which is:

Total surface area of conical part = 24.61 + 24.12 ≈ 48.73 m²

Therefore, the total surface area of one tent is:

Total surface area of one tent = 79.60 + 48.73 ≈ 128.33 m²

To make 1500 tents, the total amount of canvas required is:

Total amount of canvas required = 1500 × 128.33 ≈ 192,495 m²

The cost of the canvas is given as Rs 120 per m². Therefore, the total cost of the canvas required to make the tents is:

Total cost of canvas = 192,495 × 120 ≈ Rs 23,099,400

As 50 schools have decided to share the expenditure equally, the amount shared by each school will be:

Amount shared by each school = Total cost of canvas / 50

Amount shared by each school = 23,099,400 / 50

Amount shared by each school ≈ Rs 461,988

Therefore, each school will have to contribute approximately Rs 461,988 to set up the tents.

Step-by-step explanation:

The solution set includes all real numbers less than -5, and all real numbers greater than 1, but does not include -5 or 1 themselves.

Option D is the correct answer.

We have,

We need to isolate the absolute value |x + 2| on one side of the inequality.

We subtract 7 from both sides.

|x + 2| > 3

Next, we can split this inequality into two separate inequalities, one for when the expression inside the absolute value is positive, and one for when it is negative:

x + 2 > 3

or

- (x + 2) > 3

Solving for x in the first inequality.

x > 1

Solving for x in the second inequality.

-x - 2 > 3

Adding 2 to both sides and multiplying by -1.

x < -5

So the solution set for the inequality |x + 2| + 7 > 10 is the set of all x-values that satisfy either x > 1 or x < -5.

Using interval notation.

(-∞, -5) U (1, ∞)

Thus,

The solution set includes all real numbers less than -5, and all real numbers greater than 1, but does not include -5 or 1 themselves.

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Answer: -18

Step-by-step explanation: