A 124- inch board is cut into two pieces. One piece is three times the length of the other. Find the lengths of the tow pieces

The angle of elevation is approximately 36.87 degrees and the horizontal distance is 264.6 feet

a.

The diagram is attached below;

b. We can use the tangent function to find the angle of elevation:

tan(θ) = opposite / adjacent

tan(θ) = 300 / 400

tan(θ) = 0.75

θ = tan^(-1)(0.75)

θ ≈ 36.87 degrees

So the angle of elevation from the boat to the parasail rider is approximately 36.87 degrees.

c. We can use the Pythagorean theorem to find the horizontal distance from the parasail rider to the boat:

d = √(400^2 - 300^2)

d ≈ 264.6 feet

So the horizontal distance from the parasail rider to the boat is approximately 265 feet.

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x² - x - 6 = 0 is the standard form quadratic equation with solutions of -2 and 3.

There are two roots—or solutions—to a quadratic equation with real or complex coefficients. These two possibilities may or may not be distinct, and they may or may not be true. The standard quadratic equation, Y=x2x6, can be solved using the set of solutions 2, 3, which are given.

The elements of a quadratic equation whose solutions are -2 and 3 are (x + 2) and (3, respectively) (x - 3).

The total value of the quadratic equation is 0.

We can add the two elements together to obtain the quadratic equation in standard form:

(x + 2) (x - 3) = x²-3x+2x-6

Simplifying this expression, we get:

x²- x - 6 = 0

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Answer:

Step-by-step explanation:

483278.4

Therefore , the solution of the given problem of ratio comes out to be  8:17 .

The simple formula "a / b," where "b" may be greater than zero, can be used to determine a group of integers "a" and "b" that appear to be equal. Two ratios are combined to form a ratio. If there were only one man and three ladies, the fraction would be 1:1. In the group, there are 3/4 women and 1/4 males. Parts can be a division between things, a figure, or a particular percentage of a component's volume.

Here,

Let x be the price of plastic per square centimetre used to create visage A.

Consequently, the price of the components for aspect A is:

=> 4πx

The metal sector's size on face B is:

=>  (20/360)π(2cm)² = (1/9)π cm²

The plastic sector's size on face B is:

=>  (340/360)π(2cm)² = (17/9)π cm²

Face B's entire surface size is:

=>  (1/9)π + (17/9)π = 2π cm²

Let y be the plastic's expense per square centimetre used to create face B.

Consequently, the price per cm2 of the metal used to create face B is three and a half times the price per cm2 of the plastic, leading to:

=> (3/2)y = (3/2)(2x) = 3x

The material cost for the metal section on face B is inversely correlated with its area, so:

=>  (1/9)π(3x)

The price of the plastic used in the section on face B is inversely proportional to its area, so:

=>  (17/9)πy

=> 8πx : 17πy = 8 : 17

The response is 8:17,

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On average, Miguel loses half a dollar every time he plays.

To check all the events (6), we label the chips.

Suppose one chip with 1 is labeled R1 and the other B1 (as if they were red and blue). Now, lets take all combinations; for the first chip, we have 4 choices and for the 2nd chip we have 3 remaining choices.

Thus there are 12 combinations. Since we dont care about the order, there are only 6 combinations since for example R1, 3 is the same as 3, R1 for us.

The combinations are: (R1, B1), (R1, 3), (R1, 5), (B1, 3), (B1, 5), (3,5)

We have that in 1 out of the 6 events, Miguel wins 2$ and in five out of the 6 events, he loses one.

The expected value of this bet is: 1/6*2+5/6*(-1)=-3/6=-0.5$.

In general, the expected value of the bet is the sum of taking the probabilities of the outcome multiplied by the outcome; here, there is a 1/6 probability of getting the same 2 chips and so on.

On average, Miguel loses half a dollar every time he plays.

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As a result of angle-angle-side (AAS) alignment, we have ABO, DBO, and AEO, CEO.

To prove △BEC≅△DEA:

First, we can see that segment AC and segment BD intersect at point O, which is the point of intersection of the angle bisectors of △BED.

Since AC and BD are angle bisectors, they are perpendicular bisectors of each other, so they divide the angles of △BED into congruent angles.

This means that angle ABO is congruent to angle DBO, and angle AEO is congruent to angle CEO.

Since angle ABO and angle AEO are vertical angles, they are congruent.

Similarly, angle DBO and angle CEO are vertical angles, so they are congruent.

Therefore, we have △ABO≅△DBO and △AEO≅△CEO by angle-angle-side (AAS) congruence.

Since BE is common to both triangles, we can conclude that △BEC≅△DEA by side-angle-side (SAS) congruence.

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the solution (x = 3/2, y = 5) satisfies both equations, and therefore it is the correct solution.

We can solve this system of equations using either substitution or elimination method.

Using substitution method:

From the second equation, we can solve for x in terms of y:

4x + 2y = 16

4x = 16 - 2y

x = 4 - (1/2)y

Substitute this expression for x into the first equation:

4x + 3y = 21

4(4 - (1/2)y) + 3y = 21

16 - 2y + 3y = 21

y = 5

Now, substitute y = 5 into either of the original equations to solve for x:

4x + 2y = 16

4x + 2(5) = 16

4x + 10 = 16

4x = 6

x = 3/2

Therefore, the solution to is x = 3/2 and y = 5.

We can check this solution by substituting x = 3/2 and y = 5 into both equations:

4x + 3y = 21

4(3/2) + 3(5) = 6 + 15 = 21

and 4x + 2y = 16

4(3/2) + 2(5) = 6 + 10 = 16

So the solution (x = 3/2, y = 5) satisfies both equations, and therefore it is the correct solution.

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If P(A) = 7/13, P(B) = 5/13, and P(A and B) = 3/13, then the probability of P(AIB) = 3/5.

Probability is a measure of the likelihood of an event occurring. Many events cannot be predicted with absolute certainty. We can only predict the probability of an event by using it, i.e. the probability of it occurring.

The probability can range from 0 to 1, where 0 means the event is unlikely to happen and 1 means it will definitely happen. All events in the sample space have a probability of 1. For example, when we flip a coin, heads or tails, there are only two possible outcomes (H, T). But when you toss two coins, there are four possible outcomes, namely {(H, H), (H, T), (T, H), (T, T)}.

According to the Question:

Given that:

P(A) = 7/13

P(B) = 5/13

P(A∩B) = 3/13

We know that :

P(A|B) = P(A∩B) / P(B).

(By formula for conditional probability)

P(AIB) = (3/13)÷ (5/13)

          = 3/5

Hence, the value of P(A|B) = 3/5.

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Considering the probability of independent events, if one student is randomly selected from each class, the probability they are both girls is 8/21.

Probability establishes a relationship between the number of favorable events and the total number of possible events.

Then, the probability of any event A is defined as the ratio between the number of favorable cases (number of cases in which event A may or may not occur) and the total number of possible cases:

Probability= number of favorable cases÷ number of possible cases

Two events A and B are said to be independent if and only if the probability of event B is not influenced by the occurrence of event A or vice versa.

For any number of independent events, the probability that all the events will occur is the product of the probabilities that the individual events will occur. That is, if A and B are independent events, P(A and B) = P(A)×P(B).

You know:

If one student is randomly selected from each class, the probability that a girl is selected in each class is calculated as:

Now, the probability that both students selected for the classes are girls, considering that these are independent events, is calculated as:

Probability of both students selected for the classes are girls = Probability in Ms. Brown's class× Probability in Mrs. Ball's class

Probability of both students selected for the classes are girls = 8/15× 10/14

Probability of both students selected for the classes are girls = 8/21

Finally, the probability they are both girls is 8/21.

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[tex]g( \sqrt{55} ) = ( \sqrt{55} ) {}^{2} + 11 = 55 + 11 = 66[/tex]

[tex]f(g(55)) = f(66) = \sqrt{66 - 2} = \sqrt{64} = 8[/tex]

The value of the function f(g(√55)) is 3√7.

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable).

We have the function:

f(x) = √ (x - 2)

and, g(x) = x² + 11.

As, g(√55)

= (√55)² + 11

= 55 + 11

= 66

So, f(g(√55))

= √ (65 - 2)

= √63

= 3√7

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Answer:

The conclusion is false.

Step-by-step explanation:

[tex]\frac{57}{3} = 19\\\\\frac{9}{3} = 3[/tex]

Although 3 and 9 do share some multiples, they must be divisible by 3. For example. 36/3 = 12, and 12 is divisible by 3. However, 57/3 = 19, which is not divisible by 3.

Answer:

[tex]30x +68[/tex]

Step-by-step explanation:

[tex]6(9+5x)+14[/tex]

[tex]\text{Distribute the 6}[/tex]

[tex]30x +68[/tex]

In addition of fractions together student added the denominators together, which is the error in solution. You must have like denominators in order to add fractions together is the strategy for solution. Haley bought 7/8 pound of cheese.

We have a incorrect solution of problem consists addition and subtraction fractions. We have to identify error and solve problem correctly and also share a strategy for solution. Now the problem is defined as : Quantity of mozzarella cheese bought by Haley = [tex] \frac{3}{8} [/tex] pound

Quantity of parmesan cheese bought by Haley = [tex] \frac{1}{2} [/tex] pound

Total pound of cheese that she did bought = sum of parmesan cheese and mozzarella cheese

= [tex] \frac{3}{8} + \frac{1}{2} [/tex]

Incorrect work:

[tex] \frac{3}{8} + \frac{1}{2} = \frac{4}{10}[/tex] [tex]= \frac{2}{5} [/tex]

Identification and Explain the Error :

In the problem student correctly identified that this was addition of fractions however he was incorrect in solving. When adding fractions together you do not add denominators together.

He also forgot that you must have "like" denominators.

Correct Solution:

[tex] \frac{3}{8} + \frac{1}{2} [/tex]

For addition of fractions, make the same denominator in both of fractions. So, multiply the denominator and numentor in fraction 1/2 by 4.

[tex] = \frac{3}{8} + \frac{1 \times 4}{2\times 4} = \frac{3}{8} + \frac{4}{8} [/tex][tex] =\frac{7}{8} [/tex], which is the required solution.

Strategy: We do not add denominator together ever. You must have like denominators in order to add them together. Hence, Haley bought 7/8 pound of cheese.

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Complete question:

Error Analysis Adding and subtracting fractions :

Read the word problem. Look at the students work and solution. Identify the error and describe it. Solve the problem correctly. Then share a strategy this student could use to prevent the same error in the future. Haley bought 3/8 pound of mozzarella cheese and 1/2 pound of parmesan cheese. How many pound of cheese did she buy?

Incorrect work or solution : 3/8 + 1/2

= 4/10 = 2/5

Haley bought 2/5 pound of cheese.

The height of the lighthouse from the top of the cliff is given as 25.3 cm

tan 37.2 = h / 825

h = 825 * 0.7590

h = 626.209

tan 38.3 = 626.209 + a / 825

825 tan 38.3 = 626.209 + a

651.55 = 626.209 + a

a = 651.55 - 626.209

a = 25 . 33 meters

Hence we can say that the height of the  lighthouse from the top of the cliff is given as 25 . 33 meters

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The length of the slide itself in feet would be = 75 ft.

To calculate the length of the water slide the Pythagorean formula should be used which is written as follows;

C² = a² + b²

a = length of the tower = 21 ft

b = distance from the base of the tower = 72ft

C = length of the water slide = ?

c² = 21²+72²

C² = 441 + 5184

c² = 5625

C = √5625

C = 75 ft

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The length of the dock on the scale drawing would be 13.89 inches (250/18 = 13.89).

On a scale drawing of a dock for a marina, 1 inch equals 18 feet. This means that for every inch on the scale drawing, it represents 18 feet in reality. The dock is 250 feet long. To calculate the length of the dock on the scale drawing, divide 250 by 18. This gives the result of 13.89. This means that the length of the dock on the scale drawing is 13.89 inches. This is because for every inch on the scale drawing, it represents 18 feet in reality. Therefore, the length of the dock on the scale drawing is 13.89 inches (250/18 = 13.89). To ensure accuracy, the calculation should be double checked. This can be done by multiplying 13.89 by 18 which should give the result of 250. This confirms that the length of the dock on the scale drawing is 13.89 inches.

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The number line that models the total amount of time Ava will practice piano in all is shown in the figure and  Ava will practice piano for a total of 6 hours.

We can model the total amount of time Ava will practice piano in all using a number line. Since she practiced for 3 hours yesterday and is going to practice for another 3 hours today, we can represent this on a number line as follows:

The number line above represents the total amount of time Ava will practice piano in all. The first mark (0) represents the starting point, which is when she has not started practicing yet. The second mark (3) represents the time she spent practicing yesterday, and the third mark (6) represents the time she will spend practicing today. The distance between the first mark and the third mark (0 to 6) is the total amount of time Ava will practice piano in all, which is 6 hours.

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The volume of the larger cylinder is (25/8)πR³.

Volume is a measure of the amount of space occupied by a three-dimensional object. It is typically measured in units of cubic meters, cubic centimeters, cubic feet.

Let's denote the radius and height of the smaller cylinder as r and h, respectively, and the radius and height of the larger cylinder as R and H, respectively.

We know that the lateral area of a cylinder is given by the formula:

Lateral area = 2πrh

Using this formula for the smaller and larger cylinders, we get:

25π = 2πrh

64π = 2πRH

Dividing both sides of the first equation by 2π, we get:

rh = 25/2π

We also know that the following formula determines a cylinder's volume:

Volume = πr²h

Using this formula for the smaller cylinder, we get:

150π = πr²h

Substituting rh = 25/2π from above, we get:

150π = πr²(25/2π)

r² = 12

Taking the square root of both sides, we get:

r = √12 = 2√3

Substituting this value into rh = 25/2π, we get:

h = 25/(2πr) = 25/(4π√3)

Now, we can use the ratio of the lateral areas to find the ratio of the heights:

25π/64π = (2πrh)/(2πRH)

25/64 = rh/RH

25/64 = (2√3)(25)/(4πR)(H)

H = 2hR/r

Finally, we can use the formula for the volume of the larger cylinder to find its volume:

Volume = πR²H

Volume = πR²(2hR/r)

Volume = 2πR³h/r

Substituting the values we found for r, h, and H, we get:

Volume = 2π(R³)(25/(4π√3))/(2√3)

Volume = (25/8)πR³

Therefore, the volume of the larger cylinder is (25/8)πR³.

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Velocity is given by the change in the distance divided by the change in the time, hence the following equation is built to model the relationship between these three variables:

v = d/t.

The parameters for the trip are given as follows:

Hence the velocity is obtained as follows:

230/7 = 32.86 miles per hour.

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The line is 13 units to the right (or shifted by -13 units).

A mathematical statement known as an equation consists of two algebraic expressions separated by equal signs (=) on either side.

It demonstrates the equality of the relationship between the printed statements on the left and right.

Left side equals right side in all formulas.

To find the values of unknowable variables, which stand in for unknowable quantities, you can solve equations.

A statement is not an equation if it lacks the equals sign.

When two expressions have the same value, a mathematical statement known as an equation will include the symbol "equal to" between them.

According to our question-

The ratio of y to x, which indicates how many units change in y when a specific number of units change in x, is used to express a line's slope.

A has a slope of 2 (x factor) = 2/1.

and as a result, y moves 2 units while x moves 1 unit.

B has a slope of 1 = 1/1.

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The length of the arc of the sector is approximately 34.6 millimeters when rounded to one decimal place.

What is angle ?

An angle is a geometric figure formed by two rays that share a common endpoint, called the vertex of the angle. The rays are often referred to as the sides of the angle. Angles are typically measured in degrees or radians and are used to describe the amount of turn between two lines or surfaces.

In a circle, the measure of the arc of a sector is proportional to the measure of the central angle that it subtends. Therefore, to find the length of the arc of the sector in this problem, we need to first find the measure of the central angle that corresponds to the inscribed angle of 312 degrees.

The measure of the central angle is equal to twice the measure of the inscribed angle, which is 312/2 = 156 degrees. This is because the inscribed angle subtends an arc that is half as long as the arc subtended by the central angle.

The length of the arc of the sector can be calculated using the formula:

arc length = (central angle / 360 degrees) x (2 x pi x radius)

Plugging in the values we have:

arc length = (156/360) x (2 x pi x 4mm)

arc length = (13/30) x (8pi)

arc length = (104/30) x pi

arc length ≈ 34.557mm

Therefore, the length of the arc of the sector is approximately 34.6 millimeters when rounded to one decimal place.

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Answer:efefef

Step-by-step explanation:

efregtythth

The proportion of green apples can be estimated in the same way: expressions  Green apple proportion = (number of green apples) / (Total number of fruits)

In mathematics, you can multiply, divide, add, or subtract. An expression is formed as follows: Expression, number, and math operator Numbers, parameters, and functions make up a mathematical expression. It is possible to contrast phrases and expressions. Every mathematical statement that contains variables, numbers, and a mathematical action between them is referred to as an expression. For example, the phrase 4m + 5 is made up of the phrases 4m and 5, as well as the variable m from the provided equation, all separated by the mathematical sign +.

a) Because the basket contains four different types of fruits, the proportion of cherries can be computed as follows:

Cherry proportion = (number of cherries) / (Total number of fruits)

We can't compute the proportion of cherries without knowing how many fruits are in the basket.

b) The proportion of green apples can be estimated in the same way:

Green apple proportion = (number of green apples) / (Total number of fruits)

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the relationship between x and y given by the values (-3, -4), (2, 6), and (1, 4) is not a direct variation.

To determine whether the relationship between x and y is a direct variation, we need to check if y is directly proportional to x. In other words, we need to check if there is a constant of proportionality that relates the two variables.

To do this, we can calculate the ratio of y to x for each pair of corresponding values:

y/x = (-4)/(-3) = 4/2 = 2

y/x = 6/2 = 3

y/x = 4/1 = 4

If y is directly proportional to x, then the ratio of y to x should be the same for all pairs of corresponding values. However, in this case, the ratios are not equal. Therefore, the relationship between x and y is not a direct variation.

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To work out the volume of the cone, we can use the formula V = (1/3) * π * r² * h, where r is the radius of the base of the cone and h is the height of the cone. The volume of the cone is approximately 171.55 cubic units.

The formula for calculating the volume of a cone is given as V = (1/3) * π * r² * h. In this formula, 'r' represents the radius of the base of the cone, and 'h' represents the height of the cone. By substituting the given values, the volume of the cone is calculated to be approximately 171.55 cubic units. This formula is widely used in various fields, such as architecture, engineering, and manufacturing. Calculating the volume of a cone is useful in determining the amount of material required to construct or fill a cone-shaped object, such as a cone-shaped container or a cone-shaped structure. The formula is also used in solving real-life problems related to cones, such as calculating the volume of ice cream in a cone-shaped ice cream cone or the volume of a cone-shaped tank used for storing liquids.

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Answer:

x =~ 31.2

y =~ 18

z =~ 9

Step-by-step explanation:

cos 30º = 27 / x

0.8660 = 27 / x

x = 27 / 0.8660

x =~ 31.18

w = height (smaller trinagle w, y, z)

tg 30º = w / 27

0.5774 = w / 27

w = 27 * 0.5774

w = 15.5898

tg 30º = z / 15.5898

0.5774 = z / 15.5898

z = 0.5774 * 15.5898

z = 9.00155052

cos 30º = 15.5898 / y

0.8660 = 15.5898 / y

y = 15.5898 / 0.8660

y =~ 18

Answer: 1/6

Step-by-step explanation:

1/1 - 5/6

2    6-5/6

2    1/6

7 number of  students chose all three activities.

To find out how many students chose all three activities, we need to subtract the number of students who chose two activities from the total number of students. There are 76 students who chose sport, 64 students who chose music, and 40 students who chose drama. 12 students chose both music and sport, 7 chose both sport and drama, and 21 chose both music and drama. We can subtract these two-activity choosers from the total number of students to find out how many chose all three activities: 145 - (12 + 7 + 21) = 105. Therefore, 7 students chose all three activities.

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