Equation for line of best fit
correlation positive/negative
r=

Cos u - cos u sin²u simplifies to cos³(u). We can solve it in the following manner.

Starting with the expression Cos u - cos u sin²u, we can factor out cos(u) to get:

Cos u - cos u sin²u = cos(u) (1 - sin²(u))

Using the identity sin²(u) + cos²(u) = 1, we can substitute cos²(u) for 1 - sin²(u):

cos(u) (1 - sin²(u)) = cos(u) cos²(u) = cos³(u)

Therefore, Cos u - cos u sin²u simplifies to cos³(u).

In mathematics, a factor refers to a number, algebraic expression, or function that divides or multiplies with another number, algebraic expression, or function without leaving a remainder. For example, in the expression 12x, 12 is a factor of the expression because it can be divided evenly by 12.

In algebra, factoring is the process of finding the factors of an algebraic expression, which means breaking it down into simpler parts that can be multiplied together to get the original expression. Factoring is an important skill in algebra, as it allows us to simplify and solve equations, identify common factors, and manipulate expressions more easily.

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Answer:

Step-by-step explanation:

6

Answer:

x = 10

Step-by-step explanation:

To solve for x, we need to get x by itself.

Whatever we do to one side, we do it to the other side to keep it balanced.

3x + 15 = 45

     - 15 = -15       (Subtract 15 from both sides)

3x        =   30               (Divide both sides by 3)

3          =    3

x = 10

Answer:

The first quartile ([tex]Q_{1}[/tex]) is defined as the middle number between the smallest number (minimum) and the median of the data set. It is also known as the lower or 25th empirical quartile, as 25% of the data is below this point.

Answer:

The first quartile (Q1) is defined as the middle number between the smallest number (minimum) and the median of the data set. It is also known as the lower or 25th empirical quartile, as 25% of the data is below this point.

Step-by-step explanation:

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: If you add the same number to both sides of an inequality, the inequality remains true. If you subtract the same number from both sides of the inequality, the inequality remains true. If you multiply or divide both sides of an inequality by the same positive number, the inequality remains true.

We can write the quadratic expression 10x^2 + tx + 8 as:

10x^2 + tx + 8 = 10x^2 + (a+b)x + ab

where a and b are constants that we want to determine, and (a+b)x is the middle term in the quadratic expression.

We can factor 10 as 25 and 8 as 22*2, so we have:

10x^2 + tx + 8 = (2x + c)(5x + d)

where c and d are the constants that we need to determine.

Expanding the right-hand side of this equation, we get:

(2x + c)(5x + d) = 10x^2 + (2d+5c)x + cd

Comparing this to the original expression, we see that:

2d + 5c = t

cd = 8

We can use these equations to solve for c and d in terms of t:

c = (t - 2d)/5

d = 8/c

Substituting d in terms of c in the first equation, we get:

2(8/c) + 5c = t

Multiplying through by c, we get a quadratic equation in c:

16 + 5c^2 = tc

We want this equation to have real solutions for c, so the discriminant must be non-negative:

25t^2 - 80 >= 0

Solving this inequality for t, we get:

t <= -8/5 or t >= 8/5

Therefore, the quadratic expression 10x^2 + tx + 8 can be written as the product of two binomials for all values of t less than or equal to -8/5 or greater than or equal to 8/5.

the probability that among the next 8 users from this state who are interviewed, the probability of the first 6 users first took it for psychological problems is 60% is 0.03456.

As per the given information, 60% of the valium users in Massachusetts first took it for psychological problems. Now, we are supposed to find the probability that among the next 8 users from this state who are interviewed, the probability of the first 6 users first took it for psychological problems is: 60%.

What is Valium?

Valium is a prescription medicine that is used to treat the symptoms of anxiety, alcohol withdrawal, and muscle spasm. The use of Valium can lead to addiction, especially if it is not taken as prescribed by the doctor.The probability of the first 6 users first took it for psychological problems is 60%. Hence, the probability that the first user did not take it for psychological problems is: 40%.

Probability of first user did not take Valium for psychological problems = P(A) = 0.40

Probability of first user took Valium for psychological problems = P(B) = 0.60

Now, we are supposed to find the probability that among the next 8 users from this state who are interviewed, the first 6 users first took it for psychological problems is: 60%.Probability of the first 6 users first took it for psychological problems is:

Probability of the next 5 users took it for psychological problems = P(B) × P(B) × P(B) × P(B) × P(B) = (0.60)⁵

Probability of the next 2 users did not take it for psychological problems = P(A) × P(A) = (0.40)²

Thus, the probability that among the next 8 users from this state who are interviewed, the probability of the first 6 users first took it for psychological problems is 60%, is:(0.60)⁵ × (0.40)²= 0.03456 (rounded to five decimal places)

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To find the surface area of the rectangular prism, we need to calculate the area of each of the six sides and then add them together. The area of each of the four walls is the product of the length and height, which gives us:

16 feet × 11 feet = 176 square feet (for the two longest walls)

14 feet × 11 feet = 154 square feet (for the two shorter walls)

The area of the ceiling and floor is the product of the length and width, which gives us:

16 feet × 14 feet = 224 square feet (for the ceiling)

16 feet × 14 feet = 224 square feet (for the floor)

To find the total surface area, we add up the areas of all six sides:

176 + 176 + 154 + 154 + 224 + 224 = 1104 square feet

Therefore, we need at least 1104/100 = 11.04 pints of paint to cover the walls of the room. Rounding up to the nearest whole pint, we need 12 pints of paint.

The rotation that we need to apply to CD is of 270° clockwise.

We want a clockwise rotation that maps CD in E'F'.

Remember that a rotation of 90° will move the figure from one quadrant to the previous one. We can see that E'F' is on the third quadrant. while CD is on the second qudrant, then we need to go from.

Second to first quadrant ---> 90°

First to fourth quadrant ---> 90°

Fourth to third quadrant ---> 90°

Adding these 3 we get.

90° + 90° + 90° = 270°

So we need to applly a rotation of 270° clockwise to CD.

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Answer: Sure, I'd be happy to help you with these questions! Here are the solutions:

To find the area of R, we need to find the points of intersection between the two curves.

Setting y = 3sin(2x) and y = e^x equal to each other, we get:

3sin(2x) = e^x

Taking the natural logarithm of both sides, we get:

ln(3sin(2x)) = x

Now, we can find the x-coordinates of the intersection points by graphing the two curves or using a numerical method, such as a graphing calculator or Newton's method. The intersection points are approximately x = 0.306 and x = 2.313.

To find the area of R, we can integrate the difference between the two curves with respect to x:

A = ∫(e^x - 3sin(2x)) dx from x = 0.306 to x = 2.313

This integral can be evaluated using integration by substitution or a numerical method, such as a calculator or computer software. The area of R is approximately 2.828 square units.

To find the volume of S, we can use the formula for the volume of a solid of revolution:

V = ∫πy^2 dx from x = 0.306 to x = 2.313

Here, y = e^x - 3sin(2x) is the radius of the cross sections of the solid generated by rotating R around the x-axis.

This integral can be evaluated using numerical methods, such as a calculator or computer software. The volume of S is approximately 41.201 cubic units.

To find the volume of Q, we can use the formula for the volume of a solid of revolution around a horizontal line:

V = ∫π(y - 5)^2 dx from x = 0.306 to x = 2.313

Here, y = e^x - 3sin(2x) is the distance from the horizontal line y = 5 to the cross sections of the solid generated by rotating R around the line y = 5.

This integral can be evaluated using numerical methods, such as a calculator or computer software. The volume of Q is approximately 14.503 cubic units.

To find the volume of P, we can use the formula for the volume of a solid with known cross-sectional area:

V = ∫A(x) dx from x = 0.306 to x = 2.313

Here, the cross sections of P are semicircles perpendicular to the x-axis. The radius of each semicircle is given by:

r = (1/2)(e^x - 3sin(2x))

So the area of each semicircle is:

A = (1/2)πr^2 = (1/8)π(e^x - 3sin(2x))^2

Therefore, the volume of P is:

V = ∫(1/8)π(e^x - 3sin(2x))^2 dx from x = 0.306 to x = 2.313

This integral can be evaluated using numerical methods, such as a calculator or computer software. The volume of P is approximately 5.654 cubic units.

I hope this helps! Let me know if you have any further questions.

Step-by-step explanation:

The measures shown, could the figure be a parallelogram: Yes, one pair of opposite sides could measure 10 in., and the other pair could measure 8 in.

A quadrilateral having two sets of parallel sides is referred to as a parallelogram. This indicates that a parallelogram's opposing sides are parallel and congruent (the same length). Moreover, a parallelogram's opposing angles are congruent (have the same measure).

The following are some characteristics of parallelograms:

A parallelogram's opposing sides are parallel and congruent.

A parallelogram's opposing angles are congruent.

The parallelogram's subsequent angles are additional (their sum is 180 degrees).

A parallelogram's diagonals split each other in half (cut each other in half).

For the given quadrilateral to be a parallelogram the opposite sides need to be congruent.

Thus,

10 = x + 2

x = 8

Also,

2x - 3 = x + 5

2x - x = 5 + 3

x = 8

Hence, the measures shown, could the figure be a parallelogram: Yes, one pair of opposite sides could measure 10 in., and the other pair could measure 8 in.

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6.61 is the value of x in the circle.

What does the circle's tangent look like?

A line that only has one point of intersection with a circle is said to be tangent to the circle. Point of contact is the term used to describe the location where the circle and the tangent meet. A straight line that touches a circle at point P is said to be tangent to the circle at P. As the radius connects the circle's centre to point P, the tangent is perpendicular to that radius.

 (39x - 4) = 254

     39x = 254 + 4

      39x =  258

         x = 258/39

         x = 6.61

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Thus, the number of 6-digit numbers that can be formed using the digits 0, 1, 2, 5, 7 and 9 which are divisible by 11 and no digit is repeated is 20.

What is the number of 6 digit numbers that can be formed using the digits 0, 1, 2, 5, 7 and 9 which are divisible by 11 and no digit is repeated?There are 1200 6-digit numbers that can be formed using the digits 0, 1, 2, 5, 7, and 9.Using the formula for a 2-digit number, namely A and B, the number must satisfy A - B = 0,11 or -11.

There is a pattern, therefore, there are 100 numbers that satisfy each. It's because the numbers 0, 1, 2, 5, 7, and 9 are such that the sum of the odd digits minus the sum of the even digits is always either 0, 11, or -11. This is only possible if there is an even number of odd digits or an even number of even digits.

There are 6C3 ways to pick 3 odd digits from {1,5,7,9} and 3C3 ways to pick 3 even digits from {0,2}. By taking the product of these values, we can find the total number of possibilities:[tex]6C3 × 3C3 = 20 × 1 = 20[/tex]

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Answer:

S = [tex]\sqrt{3}[/tex]

H = 2

It's D

Step-by-step explanation:

Considering the attached picture

h = 1 x 2 = 2

s = 1 x [tex]\sqrt{3}[/tex] = [tex]\sqrt{3}[/tex]

To solve the equation × (3 + 8) = 55, we need to simplify the expression inside the parentheses first, which gives us:

× (3 + 8) = × 11

Now we substitute × 11 back into the original equation:

× 11 = 55

To solve for ×, we divide both sides by 11:

× = 5

Therefore, the number that solves the equation × (3 + 8) = 55 is 5.

After 60 minutes in the refrigeration, the can of soda will be approximately 42°F.

What is refrigeration?

We are given the following information:

[tex]T_{a}[/tex] = 35°F (temperature of the refrigerator)

To = 73°F (initial temperature of the can of soda)

T = 58°F (temperature of the can of soda after 10 minutes)

We can use these values to find the decay constant k:

T = [tex]T_{a}[/tex] + (To - [tex]T_{a}[/tex])[tex]e^{-kt}[/tex]

58 = 35 + (73 - 35)[tex]e^{-10k}[/tex]

23 = 38[tex]e^{(-10k)}[/tex]

ln(23/38) = -10k

k ≈ 0.0725 (rounded to the nearest thousandth)

Now we can use this value of k to find the temperature of the can of soda after 60 minutes:

T = [tex]T_{a}[/tex] + (To - [tex]T_{a}[/tex])[tex]e^{-kt}[/tex]

T = 35 + (73 - 35)[tex]e^{(-0.0725*60x^{2} )}[/tex]

T ≈ 42°F (rounded to the nearest degree)

Therefore, after 60 minutes in the refrigerator, the can of soda will be approximately 42°F.

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Answer:

The question seems to be incomplete. It mentions that Mr. Smith keeps track of his students' homework completion and how many boys and girls do not complete their homework. It also mentions that he puts students who don't complete their homework into two categories: first-time offenders and repeat offenders, and uses a table to keep track of the results[1][2]. However, it does not provide enough information to answer a specific question.

If you have a specific question related to this topic, please provide more details so that I can assist you better.

Answer:

A.) w=P/2-l

Step-by-step explanation:

Part A.)

P=2(l+w)

P/2= l+w

P/2-l= w

w=P/2-l

Part B.) In order to get (l+w) by itself, so I could subtract l, I had to divide both sides by two. Then I was able to subtract l from both sides to get just w on the right.

To determine which team typically has the tallest players, we need to compare the measures of center for each team. Since the data sets have outliers, it's better to use the median as a measure of center.

Calculating the median for each team:

Allstars: arrange the heights in order from smallest to largest: 60, 60, 62, 63, 65, 66, 67, 68, 69, 70, 70, 71, 71, 72, 73. The median is the middle value, which is 68 inches.

Champs: arrange the heights in order from smallest to largest: 58, 60, 60, 65, 67, 67, 68, 69, 70, 70, 75. The median is the middle value, which is also 68 inches.

Since both teams have the same median height of 68 inches, we can't say that one team typically has taller players than the other based on this measure alone. Therefore, neither option (C) nor (D) is correct. Instead, we need to choose between options (A) and (B) based on the mean height for each team.

Calculating the mean for each team:

Allstars: add up all the heights and divide by the total number of players: (73+62+60+63+72+65+69+68+71+66+70+67+60+70+71)/15 = 1006/15 ≈ 67.1 inches.

Champs: add up all the heights and divide by the total number of players: (62+69+65+68+60+70+70+58+67+66+75+70+69+67+60)/15 = 996/15 ≈ 66.4 inches.

Thus, the team with the higher mean height is the Allstars, so the correct answer is option (A): "The Allstars, with a mean of about 67.1 inches."

The value of m∠U in the circle is 168 degrees

The tangent of a circle is the line that touches the circle at only one point.

The tangent to a circle is always perpendicular to the radius. Therefore, it forms a right angle.

Therefore, let's use the theorem to find the angle m∠U

Hence,

m∠STU = 90 degrees

m∠UTV = 90 - 84 = 6 degrees

Therefore, the triangle STV is an isosceles triangle. This means the base angle is congruent .

Hence,

m∠SVT = 84 degrees

Therefore,

m∠U = 180 - 6 - 6

m∠U = 180 - 12

m∠U = 168 degrees

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Answer: The material will cost Meghana $95.84 before taxes.

Step-by-step explanation:

a. To find the area of Meghana's kite, we first need to convert the dimensions from feet to yards since the material is sold per square yard:

Length = 18 ft = 6 yards (since 1 yard = 3 feet)

Width = 4 ft = 4/3 yards (since 1 yard = 3 feet)

The area of the kite is the product of its length and width:

Area = Length x Width = 6 x 4/3 = 8 square yards

b. Meghana needs enough material to cover both sides of her kite, so she needs twice the area of the kite:

Area of both sides = 2 x Area of one side = 2 x 8 = 16 square yards

Therefore, Meghana needs 16 square yards of nylon material.

c. The material is sold for $5.99 per square yard, so the total cost of the material before taxes is:

Total cost = Cost per square yard x Number of square yards

Total cost = $5.99 x 16 = $95.84

Therefore, the material will cost Meghana $95.84 before taxes.

The equation of line "g" is y = (-3/4)x + 1. To find the equation of line "g" that goes through the points (-4, 4) and (4, -2), we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.

First, we can find the slope of the line by using the slope formula, which is:

m = (y2 - y1) / (x2 - x1)

Using the coordinates of the two points given, we have:

m = (-2 - 4) / (4 - (-4)) = -6 / 8 = -3 / 4

Next, we can use the slope-intercept form and one of the two points to find the y-intercept, b. Using the point (-4, 4), we have:

4 = (-3/4)(-4) + b

4 = 3 + b

b = 1

Finally, we can substitute the values of m and b into the slope-intercept form to get the equation of line "g":

y = (-3/4)x + 1

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The approximate surface area of the cone is equal to 35 ft²

In Mathematics, the surface area (SA) of a cone can be calculated by using this mathematical expression:

Surface area (SA) of a cone = πr(l + r)

Where:

Note: Radius = diameter/2 = 2/2 = 1 feet.

By substituting the given parameters into the formula for the surface area (SA) of a cone, we have the following;

Surface area (SA) of a cone = 3.14 × (1 + 10)

Surface area (SA) of a cone = 3.14 × (11)

Surface area (SA) of a cone = 34.54 ≈ 35 ft²

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Answer:

Always need to do research to improve your studies

Answer:

$0.03 pretzels cost more than cost of bag of chips.

Step-by-step explanation:

price of 16 snack- size bags of chips = 7.84

Cost of 1 bag of chip = 7.84 /16  = $0.49

Price of 24 snack-size bags of pretzels = 12.48

Cost of 1 snack-size bags of pretzels = 12.48 / 24      = 0.52

$0.03 pretzels cost more than cost of bag of chips.

Answer:

23,381/160 or 146 21/160

Step-by-step explanation:

56 3/4 = 227/4

1 3/8 = 11/8

1 1/5 = 6/5

227/4( 11/8 + 6/5)

227/4(55/40 + 48/40)

227/4( 103/40) = 23,381/160 or 146 21/160