Find the exact value of sin(x + y), given sin(x) = Negative one-half, cos(y) = Negative one-third, x is an angle in quadrant III, and y is an angle in quadrant II.

StartFraction 2 minus StartRoot 5 EndRoot Over 6 EndFraction

StartFraction 1 minus 2 StartRoot 6 EndRoot Over 6 EndFraction

StartFraction 6 minus StartRoot 5 EndRoot Over 6 EndFraction

StartFraction StartRoot 3 EndRoot minus StartRoot 5 EndRoot Over 6 EndFraction

Answer:

We get that x > -5

Step-by-step explanation:

1. Split up the inequality into two parts

We think of it as a > b > c and know that it is the same as a > b and b > c.

Apply this to the compound inequality

3x + 2 > 2x-3 and 2x - 3 > x - 12

2. Start solving 3x + 2 > 2x-3

Subtract 2x from both sides

x + 2 >-3

Subtract 2 from both sides

x > -5

3. Start solving 2x - 3 > x - 12

Subtract x from both sides

x - 3 > -12

Add 3 to both sides

x > -9

4. Finish

Now we have to think how we started with 3x + 2 > 2x-3 and 2x - 3 > x - 12

Since it is an and we need to identify the interval in which it is true on both inequalities which is when the x overlap. In this case is from x > -5.

The mean and approximate standard deviation of the difference in the total weight of lobster john traps in a day are 2 pounds and 8.32 pounds respectively. Hence, option d is the right answer.

Since the weight of lobsters produced by each trap is independent of the other, we can find the mean and standard deviation of the difference in the total weight of lobsters trapped in a day by subtracting the mean and standard deviation of the west bay trap from the mean and standard deviation of the east bay trap.

Mean = 12 pounds (east bay) - 10 pounds (west bay) = 2 pounds

Standard deviation = √(7^2 + 4.5^2) = √69.25 ≈ 8.32 pounds

So, the mean and approximate standard deviation of the difference in the total weight of lobsters trapped in a day is -

Mean = 2 pounds

Standard deviation = 8.32 pounds

Therefore, the answer is (d) Mean=2; Standard deviation= 8.32.

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The complete question is -

John maintains two separate lines of lobster traps in Penobscot bay. the east bay trap produces a mean of 12 pounds of lobsters per day with a standard deviation of 7 pounds. the west bay trap produces a mean of 10 pounds of lobsters a day with a standard deviation of 4.5 pounds. the weight of lobsters produced by each trap is independent of the other. which of the following are the mean and approximate standard deviation of the difference in the total weight of lobsters john traps in a day?

(a) Mean=11; Standard deviation=2.50

(b) Mean=2; Standard deviation=2.50

(c) Mean=2; Standard deviation= 5.36

(d) Mean=2; Standard deviation =8.32

(e) Mean=2; Standard deviation=11.50

It is possible for Angela to have spent 80 minutes playing soccer if she plays for a total of exactly 125 minutes and plays soccer for 45 minutes longer than she plays golf because 80+45 adds up to 125.

A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.

Angela plays soccer and golf for a total of 125 minutes every day. She plays soccer for 45 minutes longer than she plays golf.

Part A:  A pair of linear equations to show the relationship between the number of minutes Angela plays soccer (x) and the number of minutes she plays golf (y) every day.

x = y + 45

Part B: A pair of linear equations to show how much Angela spends playing golf every day.

125 - 45 = 80,

80/2 = 40

Part C: Yes, it is possible for Angela to have spent 80 minutes playing soccer if she plays for a total of exactly 125 minutes and plays soccer for 45 minutes longer than she plays golf because 80+45 adds up to 125.

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The values of each type of energy the object has:

Kinetic energy is 67.5J and Gravitational Potential Energy is 435 J.

KE: Mass= 15 kg Velocity = 3 m/s Velocity2= 9 m²/s²

KE = ½ (15) (9) = 67.5 J

GPE: Mass= 15 kg Gravity (g)=9.8 m/s² Height = 2.5 m

GPE= (15) (9.8) (2.5) = 367.5 J

KE+GPE= 67.5 + 367.5 = 435 J

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The inequality equation is 8.498 > 8.478

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be represented as A

Now , the value of A is

Let the first number be represented as = p

Let the second number be represented as = q

Now , the value of p = 8.498

The value of q = 8.478

And , the hundredths value in the number 8.498 is greater than the hundredths value in the number 8.478

So , the value of p is greater than q

Therefore , 8.498 > 8.478

Hence , the inequality is 8.498 > 8.478

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Answer:

raised 53%

Step-by-step explanation:

goal = $8,000

raised = $4,200

$4,200/$8,000 = 0.525 = about 53%

As per the given subset, the set T and U are not closed under multiplication.

In math the term subset is defined through the example set A is a subset of another set B if all elements of the set A are elements of the set B.

Here let us consider that S be a subset of R that is closed under multiplication

Here we have also consider that  T and U be disjoint subsets of S whose union is S.

Here we have given that the product of any three elements of T is in T and that the product of any three elements of U is in U, now we have to show that at least one of the two subsets T, U is closed under multiplication.

Here we have to start out with the assumption that neither T nor U is closed under multiplication and use proof by contradiction to prove that at least one of T or U must be closed under multiplication.

Here let us write this as,

=> t1,t2,t3∈T1,2,3 and 

=> u1,u2,u3∈U1,2,3∈,

While it is given by the problem that, then  T and U are disjoint subsets of S and therefore, 

=> T∩U = ∅.

At this time we have take that

=> t3 = u1⋅u2

=> 3 = 1⋅2 and 

=> u3=t1⋅t2

=> 3=1⋅2.

While we looking these statements are valid because T and U are not closed under multiplication, where as the product of u1⋅u21⋅2 must not be in the set U and the product of t1⋅t21⋅2 must not be in set T.

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The answer would be x^-10, since the question asks you to rewrite it with a single variable.

I hope this helps!  o(〃＾▽＾〃)o

Answer:

This is nonsense, if GP = 16 and GH = 12 then HP = 4 (16 - 12 = 4). FP is looking basically the same size as HP, so FP = 4, not 2.

Step-by-step explanation:

These are all lies, your teacher is a liar and EF must be around 12 too.

Answer:

30

Step-by-step explanation:

It will take 4 months to pay off the debt for Farah.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that Farrah borrowed $155 from her brother. She has already paid back $15. She plans to pay back $35 each month until the debt is paid off.

The expression can be written as:-

35x + 15 = 155

35x = 155 - 15

35x = 140

x = 140 / 35

x = 4 months

Hence, the number of months will be 4.

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The length of each equal piece is 17/6 feet, the mixed fraction is 2 5/6.

There is a fraction, containing numerator(upper value) and denominator(lower value).

When the numerator is less than the denominator, the fraction is called proper fraction, otherwise it is called improper fraction.

A proper fraction is also called fraction which is less than 1.

And an improper fraction is ≥ 1

A mixed fraction contains a sum of whole number and a proper fraction.

Given;

The board is 10 feet long

First he has to cut off 1 1/2 feet from one end of the board

Now, after the first cut remaining board will be;

=10-1 1/2=17/2

After cutting it in 3 equal pieces

=17/2/3

=17/6

=2 5/6

Therefore, the answer in mixed fraction will be 2 5/6

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The circumference of a circle whose radius is 21 feet, is 132 feet, thus the first option is the correct one.

We know that for a circle of radius R, the circumference is given by:

C = 2*π*R

Where π = 22/7

And here we know that the radius is 21 feet, then we can replace that in the formula above and we will get:

C = 2*(22/7)*21 feet = 132 feet

The circumference of that triangle is 132 feet, thus, the correct option is the first one.

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Answer:

Step-by-step explanation:

Answer:

1.91 lb

Step-by-step explanation:

1 3/4 cups of pecans per pie = 1.75 cups.

For 5 pies, 5 × 1.75 cups = 8.75 cups are needed.

1 cup = 99 g

8.75 cup × (99 g) / (1 cup) = 866.25 g

Exact conversion: 453.59237 g = 1 lb

866.25 g × (1 lb)/(453.59237 g) = 1.91 lb

Answer: 1.91 lb

There are 56 students as freshmen. The correct answer would be an option (A).

The percentage is defined as a ratio expressed as a fraction of 100.

A bar graph with the first bar labeled Jaguars, divided into freshmen from 0 to 40 percent and sophomores from 40 to 100 percent.

This can be determined by multiplying the percentage of freshmen who selected Jaguars (40%) by the total number of students surveyed (140).

⇒ 40% × 140 = 56

So there are 56 students as freshmen.

Hence, the correct answer would be option (A).

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Answer:

∠ QPT = 59°

Step-by-step explanation:

• the opposite sides are parallel

then

∠ SPT = ∠ QRT ( alternate angles ), that is

16x - 17 = 10x + 1 ( subtract 10x from both sides )

6x - 17 = 1 ( add 17 to both sides )

6x = 18 ( divide both sides by 6 )

x = 3

then

∠ SPT = 16x - 17 = 16(3) - 17 = 48 - 17 = 31°

• the vertices of a rectangle are right

∠ QPS = 90° , so

∠ QPT = 90° - ∠ SPT = 90° - 31° = 59°

The algebraic expression which represents the total cost of buying watermelons and tomatoes as described is; C = 0.68w + 3.25t.

The cost of buying a watermelon that weighs 18.5 pounds and 5 pounds of tomatoes is; $28.83.

It follows from the task content that the cost of buying Tomatoes are $3.25 / lb and Watermelon is $0.68 / lb.

Hence, the algebraic expression which represents the cost of buying a watermelon that weighs, w pounds and tomatoes that weigh t pounds is;

C = 0.68w + 3.25t.

Hence, if the watermelon bought weighs 18.5 pounds and tomatoes weigh 5 pounds,

C = 0.68 (18.5) + 3.25 (5)

C = 12.58 + 16.25

C = $28.83.

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we can conclude that option (A) , (B) and (C) are true.

We know that in a triangle,

• Sum of any to sides is greater than the third side.

• Difference between any two sides is smaller than the third side.

So, in ∆EFG, we have,

• EF + FG > EG

• FG + EG> EF

• EF + EG > FG

and,

• EF - FG <EG or FG - EF <EG

• FG - EG < EF or EG - FG < EF

• EF - EG <FG or EG - EF < FG

From options now we get,

A) EF + FG > EG is true

B)EG + FG > EF is true

C) EG - FG < EF is true

D) EF - FG > EG is false

E) EG + EF < FG is false

Therefore, we can conclude that option () , () and () are true.

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We can conclude that option (A) , (B) and (C) are true.

We know that in a triangle,

• Sum of any to sides is greater than the third side.

• Difference between any two sides is smaller than the third side.

So, in ∆EFG, we have,

• EF + FG > EG

• FG + EG> EF

• EF + EG > FG

and,

• EF - FG <EG or FG - EF <EG

• FG - EG < EF or EG - FG < EF

• EF - EG <FG or EG - EF < FG

From options now we get,

A) EF + FG > EG is true

B)EG + FG > EF is true

C) EG - FG < EF is true

D) EF - FG > EG is false

E) EG + EF < FG is false

Therefore, we can conclude option (A) , (B) and (C) are true.

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Answer:

  6√2

Step-by-step explanation:

You want one side of a square whose half-diagonal has length 6.

If X is the center point of the square where the diagonals cross at right angles, triangle EXG is an isosceles right triangle with leg length 6. The hypotenuse of an isosceles right triangle is √2 times the leg length, so ...

  EG = 6√2

__

Additional comment

If you like, you can use the Pythagorean theorem to prove that.

  EG² + EX² +GX² = 6² +6² = 72

  EG = √72 = √(36·2) = 6√2

A square is a rhombus, so the diagonals cross at right angles. A square is a rectangle, so the diagonals are the same length. A square is a parallelogram, so the diagonals bisect each other.

Answer:

  G(u+t, s)

Step-by-step explanation:

Given coordinates E(-1, 0), F(0, s), and H(u, 0) of parallelogram EFGH, you want the coordinates of point G.

Segment FG is a horizontal line. Its length will be the same length as horizontal line EH. Since the lines are horizontal, the length is the difference of x-coordinates.

Point H is (u -(-t)) = u+t units to the right of point E. The x-coordinate of point G will be the same number of units to the right of point F.

The x-coordinate of G is 0 +(u+t) = u+t, the length of EH added to the x-coordinate of F.

The y-coordinates of any point on a horizontal line are the same. The y-coordinate of point F is 's'. Point G lies on that same horizontal line, so has the same y-coordinate.

The coordinates of point G are (u+t, s).

__

Additional comment

The midpoints of the diagonals are the same. This means ...

  (E+G)/2 = (F+H)/2

  E+G = F+H . . . . . . multiply by 2

  G = F +H -E . . . . . subtract E

Using the given coordinates:

  G = (0, s) +(u, 0) -(-t, 0) = (0+u+t, s+0+0) = (u+t, s) . . . . as above

All of your "parallelogram" problems are worked the same way. The fourth point has coordinates that are the sum of the coordinates of the end points of the known diagonal, less the known point on the unknown diagonal.

If you work the problem any of several other ways, you get the same answer.

Point E is (u -(-t)) = (u +(-t)) units away from point H. Point G will be located the same amount of units to the right of point F in terms of its x-coordinate.  G(u+t, s)

You need to know the coordinates of point G in the parallelogram EFGH given the coordinates E(-1, 0), F(0, s), and H(u, 0).

FG is a horizontal segment. It will have a length equal to that of a horizontal line, EH. The length is determined by the difference in x-coordinates because the lines are horizontal.

The length of EH multiplied by the x-coordinate of F yields the x-coordinate of G, which is 0 +(u+t) = u+t.

Horizontal line

In a horizontal line, all points have the same y-coordinates. Point F has the y-coordinate of's'. Point G's y-coordinate is the same because it is located on the same horizontal line.

The coordinates of point G are (u+t, s).

__

Additional comment

The midpoints of the diagonals are the same. This means ...

 (E+G)/2 = (F+H)/2

 E+G = F+H . . . . . . Multiply by 2

 G = F +H -E. . . . . Subtract E

Using the given coordinates:

G = (0, s) +(u, 0) (u, 0) (-t, 0) = (u+t, s) + (u+t, s) + (u+t, s) . . . . As mentioned earlier

Your “parallelogram” issues are all solved in the same manner. The fourth point's coordinates are equal to the sum of the coordinates of the known diagonal's end points, minus the known diagonal's known point.

The solution is the same regardless of how you approach the issue.

Vertical line

Any point on a horizontal line has the same y-coordinates. Point F's y-coordinate is's'. Point G has the same y-coordinate since it is located on the same horizontal line.

Point G's coordinates are (u+t, s).

Further commentary

The diagonals' midpoints are identical. This implies...

(E+G)/2 = (F+H)/2

E+G = F+H, multiply by 2, and so on.

G = F + H -E.... Remove E.

Using the coordinates provided:

G = (0, s) +(u, 0) (u, 0) (-t, 0) = (u+t, s) + (u+t, s) + (u+t, s) . . . . as mentioned earlier

Therefore, Your “parallelogram” issues are all solved in the same manner. The fourth point's coordinates are equal to the sum of the coordinates of the known diagonal's end points, minus the known diagonal's known point.

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All of the following are possible steps of scientific investigation except for

C. assumption of conclusions without prior experimentation or observation

All of the following are possible steps of scientific investigation except for.

A. the development of one or more working hypotheses or models to explain facts

B. development of observations and experiments to test the hypotheses

C. assumption of conclusions without prior experimentation or observation

D. the collection of scientific facts through observation and measurement

All of the following are possible steps of scientific investigation except for

C. assumption of conclusions without prior experimentation or observation

At the core of biology and other sciences lies a problem-solving approach called the scientific method. The scientific method has five basic steps, plus one feedback step:

Make an observation.

Ask a question.

Form a hypothesis, or testable explanation.

Make a prediction based on the hypothesis.

Test the prediction.

Iterate: use the results to make new hypotheses or predictions.

The scientific method is used in all sciences—including chemistry, physics, geology, and psychology. The scientists in these fields ask different questions and perform different tests. However, they use the same core approach to find answers that are logical and supported by evidence.

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The formula for determining the strength of a negative association between two variables is Pearson's Correlation coefficient (r).

This coefficient measures the degree of linear relationship between two variables and ranges from -1 to +1. If two variables have a negative association, the correlation coefficient will be negative.

For example, let's say we are looking at the relationship between daily consumption of donuts (dd) and daily temperature (tt). To calculate the Pearson's Correlation coefficient, we would first calculate the covariance of the two variables using the following formula:

Cov(dd,tt) =  (∑ (dd - dd_mean) * (tt - tt_mean)) / n

Next, we would calculate the standard deviation of both variables using the following formula:

Stdev_dd = √(∑ (dd - dd_mean)^2/n)

Stdev_tt = √(∑ (tt - tt_mean)^2/n)

Finally, we would calculate the Pearson's Correlation coefficient using the following formula:

r = Cov(dd,tt) / (Stdev_dd * Stdev_tt)

If r is close to -1, then this indicates a strong negative association between dd and tt.

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Answer:

3,2 °C

Step-by-step explanation:

40,2 °C - 37 °C = 3,2 °C

The expression 18-x represents the length of the candle that has been burned. As x increases (representing more inches being burned), 18-x decreases (representing less inches remaining).

b) x represents the inches burned from the candle, y represents the inches of candle remaining, 18 represents the initial height of the candle before it is lit, and 18-x represents the length of the candle that has been burned.

c) y = 18 - x (The height of the candle remaining is 18 inches minus the inches that have been burned, represented by x)

d) It is not possible to write the formula in part (c) without using a constant quantity. Constant quantities, such as the initial height of the candle (18 inches), help to define the relationship between the two varying quantities (x and y) and provide a starting point for the calculation.

Without the constant quantity, it would not be clear what the relationship is between x and y.

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Both f(x) and g(x) have one x-intercept at x = -1/3.

Theorem A states that for a cubic function of the form f(x) = x^3 + x + b, with b > 1, the function f has exactly one x-intercept. Using Theorem B, we can conclude that for any nonzero real number k, the function g(x) = kf(x) = kx^3 + kx + bk also has exactly one x-intercept.

For example, if f(x) = x^3 + x + 5 and k = 2, then g(x) = 2x^3 + 2x + 10. Both f(x) and g(x) have exactly one x-intercept. This can be shown by solving the quadratic equation formed by setting f(x) = 0 or g(x) = 0. Doing this yields x = -1/3. Therefore, both f(x) and g(x) have one x-intercept at x = -1/3.4

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Answer: We know that:

x + y = 12 (because he can work at most 12 hours in total)

7x + 10y ≥ 90 (because he must earn no less than $90)

We can graph these inequalities on the coordinate plane.

The equation x + y = 12 represents a line with a slope of -1 and y-intercept of 12. This is the line that separates the region where he works more hours babysitting and the region where he works more hours clearing tables.

The inequality 7x + 10y ≥ 90 represents the region where he earns more than $90.

You can find the solution by finding the intersection of the line and the shaded region. The solution will be a point that lies on both the line and the shaded region.

One possible solution would be for Mason to work 8 hours babysitting and 4 hours clearing tables, earning him $56 from babysitting and $40 from clearing tables, for a total of $96.

Step-by-step explanation: