the equations of motion of a two-degree-of-freedom system can be expressed in terms of the displacement of either of the two masses.true or false

The student is male, which is P(male).Using the rule of complementary events, P(male) = 1 - P(female)P(male) = 1 - 0.572 = 0.428Therefore, the probability that the student is male is 0.428 or 42.8%.

The complimentary event is a part of probability theory. It is the event that occurs when the event E does not occur. In other words, it is a set of outcomes in the sample space that are not included in the outcomes of event E. The notation for the complement of E is E'. Rule for Complimentary EventsThe rule for complementary events can be expressed in two ways:

P(E) = 1 - P(E)P(E) + P(E') = 1Example # 12:Let the probability that Mary can work a problem be P(E) = 0.70.We need to find the probability that Mary cannot work the problem, which is P(E').Using the rule of complementary events,P(E') = 1 - P(E)P(E') = 1 - 0.70 = 0.30Therefore, the probability that Mary cannot work the problem is 0.30 or 30%.Example # 13:Let P(female) be the probability that the student is female. We are given that P(female) = 0.572.

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Serena leans a 24-foot ladder against a 22.8-foot-tall building to climb on the roof is 71.8 degree.

Measurement of Angle:

The measurement of angles is done using basic geometric tools such as protractors and compasses. This tool helps to find precise measurements of angles. A protractor helps provide accurate measurements of angles, while compasses help construct angles. Angles are measured in three ways: degrees, radians, and revolutions.

According to the Question:

Suppose the measure of angle is θ, then we have

   Sinθ = 22.8/24

⇒ Sinθ = 0.95

Therefore,

θ = Sin⁻¹ (0.95)

  = 71.8 degree.

Therefore, Serena leans a 24-foot ladder against a 22.8-foot-tall building to climb on the roof is 71.8 degree.

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Answer: Associative property

Step-by-step explanation:

The definition of the associative property is the answer is the same no matter how the terms are grouped. Hope this helped!

Answer: There were 52 Republicans and 46 Democrats.

Step-by-step explanation:

Let's represent the number of Republicans as "x" and the number of Democrats as "y".

From the problem, we know that:

x + y = 98 (since the total number of senators is 98)

y = x - 6 (since there were 6 fewer Democrats than Republicans)

We can substitute the second equation into the first equation to get:

x + (x-6) = 98

2x - 6 = 98

2x = 104

x = 52

Now that we know that there were 52 Republicans, we can substitute that into the second equation to find the number of Democrats:

y = x - 6

y = 52 - 6

y = 46

Therefore, there were 52 Republicans and 46 Democrats.

Answer:

There were 52 Republicans and 46 Democrats.

Step-by-step explanation:

Let's make a system of equations to represent this! D = democrats and R = republicans.

[tex]d + 6 = r[/tex]

[tex]r + d = 98[/tex]

Now let's set them both equal to d.

To do this for the first equation, subtract 6 from both sides to get:

[tex]d =r - 6[/tex]

To do this for the second equation, subtract r from both sides to get:

[tex]d = 98 - r[/tex]

Now, let's set them equal to eachother.

[tex]r - 6 = 98 - r[/tex]

Add r to both sides

[tex]2r -6 = 98[/tex]

Add 6 to both sides

[tex]2r = 104[/tex]

Divide both sides by two

[tex]r = 52[/tex]

There were 52 republicans. Now let's sub 52 in for r in one of the equations.

[tex]d + 6 = 52[/tex]

subtract six from both sides

[tex]d = 46[/tex]

There were 46 democrats.

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Answer:

235.6 cm²

Step-by-step explanation:

The formula to find the area of a sector is,

[tex]\sf A=\frac{\theta}{360}*\pi r^2[/tex]

Here,

Θ = angle

r = radius

Let us find it now.

[tex]\sf A=\frac{\theta}{360}*\pi r^2\\\\\sf A=\frac{270}{360}*\pi *10*10\\\\\sf A=\frac{270}{360}*\pi *100\\\\A = 235.61 cm^2[/tex]

Answer:

£234.36

Step-by-step explanation:

Answer: y is equal to 8

Step-by-step explanation:

by substituting the x for its vale of three we can add the two values to get 8 or y=8

Answer:

x = 1.5

y = 12.99

Step-by-step explanation:

let's call cost of 1 song is x and cost of 1 album is 6

6x + y = 21.99

4x + 3y = 44.97

6x + y = 21.99 => y = -6x + 21.99

Substitute into 4x + 3y = 44.97

4x + 3(-6x + 21.99) = 44.97

4x - 18x + 65.97 = 44.97

-14x = -21

x = -21/-14 = 1.5

y = -6x + 21.99 = -6(1.5) + 21.99 = 12.99

Answer:

No solution

Step-by-step explanation:

They have the same slope, which makes them parallel to each other. The y-intercepts are different so they do not overlap. If they overlap, then you know they have either one or infinite solutions. They do not so the answer is no solution.

The surface area of the triangular prism is 2016 [tex]feet ^2[/tex], we get to the answer by adding area of all faces in this prism.

What is surface area ?

Surface area is the sum of the areas of all the faces or surfaces of a 3D object, measured in square units.

To find the surface area of the triangular prism, we need to calculate the area of each of its faces and then add them up.

First, let's find the area of the triangular base.

Area of triangle = (1/2) x base x height

Area of triangle = (1/2) x 18 x 24

Area of triangle = 216 [tex]feet ^2[/tex]

Next, let's find the area of each rectangular face.

Area of rectangle = length x width

Area of rectangle 1 = 24 x 22 = 528 [tex]feet ^2[/tex]

Area of rectangle 2 = 18 x 22 = 396 [tex]feet ^2[/tex]

Area of rectangle 3 =  22 x 30 = 660 [tex]feet ^2[/tex]

Now, we can add up the areas of all three faces to get the total surface area of the prism:

Surface area = area of rectangle (1+2+3) + 2 x area of triangle

Surface area = 528 + 396 + 660 + 2(216)

Surface area = 2016 [tex]feet ^2[/tex]

Therefore, the surface area of the triangular prism is 2016 [tex]feet ^2[/tex].

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An expression equivalent to (a - b)³ is a³ - 3a²b + 3ab² - b³.

The fractions 4/10, 6/15, 8/20, etc. are identical to 2/5. In the reduced form, equivalent fractions have the same value. Explanation: When writing equivalent fractions, the numerator and denominator should be multiplied or divided by the same number.

One way to expand (a - b)³ is to use the binomial formula:

(a - b)³ = C(3,0) * a³ * (-b)^0 + C(3,1) * a² * (-b) + C(3,2) * a * (-b)² + C(3,3) * a * (-b)³

where C(n,k) denotes the number of ways there are to select k objects from a set of n objects, and "n choose k" is the binomial coefficient.

Simplifying the above expression, we get:

(a-b)³ = a³-3a²b+3ab²-b³.

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Therefore , the solution of the given problem of volume comes out to be the response is 900 cubic units.

A three-dimensional object's volume, which is expressed in cubic units, indicates how much space it takes up. These symbols for cubic dimensions are liter and in3. However, understanding an object's volume is necessary to calculate its measurements. It is standard practice to convert the weight of an object into mass units like grams and kilograms.

Here,

The formula V = Bh, when B is the area of the bottom and h is the height of the prism, determines the volume of a right triangle prism.

The prism has an area of because its foundation is a right triangle with 8 and 15-foot-long legs.

=> B = (1/2)bh = (1/2)(8)(15) = 60

The prism's height is specified as 15 inches.

As a result, the prism's capacity is:

=>  900 cubic units are equal to V = Bh = 60(15).

Therefore, the response is 900 cubic units.

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Answer:

900 cubic units

Step-by-step explanation:

In the context of this problem, if we reject the null hypothesis, we can conclude that the new design is more effective in terms of accuracy. If we fail to reject the null hypothesis, we can't conclude anything about the effectiveness of the new design

When given the resulting p-values, we reject the null hypotheses (assuming a 0.05 significance level) if the p-value is less than 0.05. We fail to reject the null hypotheses if the p-value is greater than or equal to 0.05.If we reject the null hypothesis, it means that there is strong evidence against it, and we can say that the alternative hypothesis is supported by the data. If we fail to reject the null hypothesis, it means that there is insufficient evidence to reject it, and we can't say that the alternative hypothesis is supported by the data.

In the context of this problem, if we reject the null hypothesis, we can conclude that the new design is more effective in terms of accuracy. If we fail to reject the null hypothesis, we can't conclude anything about the effectiveness of the new design.In either case, whether we reject or fail to reject the null hypothesis, we wouldn't proceed with changing the design of the arrow based solely on the statistical analysis. We would need to consider other factors such as cost, feasibility, and practicality before making any decisions about changing the design.

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(theta + gamma) = 45 degrees, which is equal to 180/4.

tangent of an angle is defined as the ratio of the opposite side to the adjacent side of a right-angled triangle.

Let's consider a right-angled triangle ABC, where angle B is 90 degrees, and angle A(theta ) and angle C(gamma) are the angles whose tangent values are given.

Using the given information, we can say that:

tan(A) = 5/6

tan(C) = 1/11

We can now use the following trigonometric identity:

tan(A + C) = (tan(A) + tan(C)) / (1 - tan(A) * tan(C))

Substituting the given values, we get:

tan(A + C) = (5/6 + 1/11) / (1 - 5/6 * 1/11)

tan(A + C) = (55/66 + 6/66) / (66/66 - 5/66)

tan(A + C) = 61/61 = 1

Now, we know that:

tan(180/4) = tan(45) = 1

Therefore, we can conclude that:

A + C = 180/4 = 45 degrees

Hence, we have shown that (theta + gamma) = 45 degrees, which is equal to 180/4.

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Answer:

Step-by-step explanation:

First, we need to find the coordinates of the center of the circle. Since the equation of the circle is x^2 + y^2 = 40, we have x^2 = 40 - y^2. Substituting this into the equation of the tangent line I, we get:

(40 - y^2) + y(2x) = 40

2xy - y^2 = 0

y(2x - y) = 0

Since the line I crosses the x-axis at point P, we have y = 0 at that point. Therefore, 2x - y = 0, and we can solve for x:

2x = y

2x = 6

x = 3

So the center of the circle is at the point (3, 0).

Next, we need to find the radius of the circle. Since A is on the circle, we have:

3^2 + 6^2 = r^2

r^2 = 45

r = sqrt(45) = 3sqrt(5)

Now we can find the coordinates of point O, which is the center of the circle:

O = (3, -3sqrt(5))

Finally, we can find the area of triangle OAP:

OA = sqrt((2-3)^2 + (6+3sqrt(5))^2) = sqrt(69)

AP = 2

Using the formula for the area of a triangle, we have:

Area(OAP) = 1/2 * OA * AP = 1/2 * sqrt(69) * 2 = sqrt(69)

Therefore, the area of triangle OAP is sqrt(69) square units.

Step-by-step explanation:

There are 8 fluid ounces in a cup....

   divide the number of ounces by 8 to find the number of cups

# ounces /  8 ounces/cup    =    cups

The probability that a household views television between 5 and 11 hours a day is approximately 0.7291, and that a household views television more than 3 hours a day is approximately 0.9830.

(a) To find the probability that a household views television between 5 and 11 hours a day, we need to find the area under the normal distribution curve between the values of 5 and 11, with a mean of 8.35 and a standard deviation of 2.5. We can use a standard normal distribution table or calculator to find the corresponding probabilities.

First, we need to standardize the values of 5 and 11 using the formula:

z = (x - μ) / σ

where z is the standardized score, x is the value we want to standardize, μ is the mean, and σ is the standard deviation.

For x = 5: z = (5 - 8.35) / 2.5 = -1.34

For x = 11: z = (11 - 8.35) / 2.5 = 1.06

Using a standard normal distribution table, we can find the area under the curve between z = -1.34 and z = 1.06 to be approximately 0.7291.

Therefore, the probability that a household views television between 5 and 11 hours a day is approximately 0.7291.

(b) To find how many hours of television viewing a household must have in order to be in the top 3% of all television-viewing households, we need to find the z-score corresponding to the top 3% of the distribution, and then use the formula:

z = (x - μ) / σ

to solve for x, where x is the number of hours of television viewing and μ and σ are the mean and standard deviation of the distribution, respectively.

Using a standard normal distribution table, we can find that the z-score corresponding to the top 3% of the distribution is approximately 1.88.

Therefore, we can solve for x as follows:

1.88 = (x - 8.35) / 2.5

x - 8.35 = 4.7

x = 13.05

Therefore, a household must view more than 13.05 hours of television per day to be in the top 3% of all television-viewing households.

(c) To find the probability that a household views television more than 3 hours a day, we need to find the area under the normal distribution curve to the right of the value of 3, with a mean of 8.35 and a standard deviation of 2.5. We can again use a standard normal distribution table or calculator to find the corresponding probability.

First, we need to standardize the value of 3 using the formula:

z = (x - μ) / σ

where z is the standardized score, x is the value we want to standardize, μ is the mean, and σ is the standard deviation.

For x = 3: z = (3 - 8.35) / 2.5 = -2.14

Using a standard normal distribution table, we can find the area under the curve to the right of z = -2.14 to be approximately 0.9830.

Therefore, the probability that a household views television more than 3 hours a day is approximately 0.9830.

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X is a discrete random variable and Y is a discrete random variable because they both measure countable values rather than continuous values.

X is a discrete random variable because the time until the box arrives is measured in discrete, countable intervals such as days, weeks, or months. Y is a discrete random variable because the number of harmonicas that work properly is a countable number, rather than a continuous, measured value.

For example, the box could arrive in one week, or it could arrive in one month. Therefore,[tex]X[/tex] is discrete. Similarly, Y is discrete because there will be a certain number of harmonicas that work properly, such as 12, 15, 20, etc. So, Y is also discrete.

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Answer:

for the tringle:

area=[tex]p^{2} -2p-3[/tex]

for the frame:

area=[tex]8x+28[/tex]

Step-by-step explanation:

For the tringle:-

Area=1/2bh

Area=1/2(2p-6)(p+1)

Area=1/2([tex]2p^{2} -4p-6[/tex])

Area=[tex]p^{2} -2p-3[/tex]

For the picture frame:-

part 1:the area of the big frame

Area=lw

Area=(x+7)(x+4)

Area=[tex]x^{2} +11x+28[/tex]

part 2:the area of the small frame

Area=lw

Area=(x+3)(x)

Area=[tex]x^{2} +3x[/tex]

To find the area of the shaded regions:

Area of shaded region=area of the big frame-the area of the small frame

Area of shaded region=[tex](x^{2} +11x+28)-(x^{2} +3x)[/tex]

Area of shaded region=[tex]8x+28[/tex]

The fixed amount Hester earns for each television is $65.

A straight line in a two-dimensional coordinate system is described by a linear equation. Using m as the line's slope and b as the y-intercept, it has the generic form y = mx + b.

Mathematical applications of linear equations include algebra, geometry, and calculus. They are employed to represent and examine interactions between different variables, such as the connection between time and space in a straightforward linear motion issue.

Let us suppose the fixed amount = x.

Then, for 15 televisions she earns:

15*$25 = $375

Now, she earned a total of 1350, thus:

15x + $375 = $1,350

15x = $975

x = $65

Therefore, the fixed amount Hester earns for each television is $65.

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Answer:

b = 12.12 (or) 7 sqrt 3

Step-by-step explanation:

a^2 + b^2 = c^2

7^2 + b^2 = 14^2

49 + b^2 = 196

-49 -49

b^2 = 147

b = sqrt 147

decimal form:

b = 12.12

exact form:

b = 7 sqrt 3

The cost of 9 gallons of gas is 24.75$

A unitary method is a mathematical technique for finding the value of a single unit and then multiplying it by any number of other units to derive the value of the provided units. Employing the unitary method, we can solve the above problem.

Given that,

The cost of 8 gallons of gas =  22$

The cost of 1 gallon of gas = 22 ÷ 8

                                            = 2.75$

Therefore, the cost of  9 gallons of gas = 2.75 × 9

                                                                 = 24.75$.

Hence, the cost of 9 gallons of gas is 24.75$.

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The Law of Sines says that for a given triangle, the ratio between the sine of an angle and the length of the opposite side is the same for all three angles in a triangle. the sine values of all three internal angles will be the samethe sine values of all three internal angles will be proportional to each otherthe ratio between the sine of the angle and the opposite side will match for all three internal anglesthe sine values of all three angles will be different

In a triangle, we have three angles and three sides. The Law of Sines says that for any triangle, the ratio between the sine of an angle and the length of the opposite side will be the same for all three angles. In other words, the sine values of each angle are proportional to the length of the opposite side.

To put this in mathematical terms, let's consider a triangle with angles A, B, and C, and sides a, b, and c respectively. The Law of Sines can be written as:

sin(A)/a = sin(B)/b = sin(C)/c

This means that if we know the length of any two sides and the measure of the angle opposite one of those sides, we can use the Law of Sines to find the measure of the other angles and sides.

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The relationship between the sides and angles of the triangles indicates that the information provided by Jared, satisfies the Side-Angle-Angle, SAA congruence rule, therefore, Jared only is correct. The correct option is therefore;

A. Jares only

Congruent triangles are triangles that have both the same shape and size.

The specified information are;

Regina is trying to figure out if triangles ΔABC and ΔDEF are congruent

Regina knows that side AC is the same length as DF, therefore;

AC ≅ DF

∠A is the same measure as ∠D, therefore; m∠A = m∠D

The information Jared tells Regina is; If ∠B and ∠E are the same measure, Regina will know that the triangles are congruent.

The information Isaac tells here is; If BC and EF are the same length, she'll know that the triangles are congruent

In ΔABC and ΔDEF, AC ≅ DF, m∠A = m∠D

The relationship between the triangles if ∠B and ∠E are congruent therefore is; Side-Angle-Angle, SAA, which is a condition for congruence, therefore, Jared is correct

The relationship between the triangles if BC is congruent to EF is Side-Angle-Angle, SAA, which is not a condition for congruence, therefore, Isaac is not correct

Therefore, Jared only is correct. The correct option is option A.

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If the two removed squares have the same color, then it is possible to cover the truncated checkerboard with non-overlapping dominoes. If they have different colors, then it will be impossible to cover the truncated checkerboard with non-overlapping dominoes.

To prove that the chess board can be completely covered by non-overlapping dominoes, where each domino covers exactly two squares, we can color the board alternatively in black and white. The two colors will make the board have 32 black squares and 32 white squares. Each domino will cover one white and one black square. Since there are the same number of black and white squares, there is an equal number of squares that each domino can cover so it is possible to cover the entire board with dominoes without overlap.

To determine whether the cut checkerboard can be covered by non-overlapping dominoes, note that we have 62 squares, 31 of which are black, and 31 white. This means that one color will have one extra square, in this case black. Therefore, if the two removed squares are of different colors, it will be impossible to cover the cut checkerboard with non-overlapping dominoes.However, if the two removed squares have the same color, then it will be possible to cover the checkerboard with non-overlapping dominoes. This is because we will still have an equal number of black and white squares even after the removal of the two squares.The same logic applies to the truncated checkerboard.

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The regression result of 0.320, the beta of 0.136, and the p-value of 0.000.

The strongest predictor in the MLRA summary Table is past history of depression. This is shown by the regression result of 0.320, the beta of 0.136, and the p-value of 0.000. This means that past history of depression has a strong and statistically significant influence on predicting depression at wave 2.

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As a result, there are 180 students in the seventh grade.

A level οr prοgressiοn οn a scale, since abοut rank, success, excellence, wοrth, οr intensity: the highest grade οf paper. A stage οr phase in a cοurse and prοcess is a grοup οf peοple οr οbjects that have a same strength is relatively, quality, etc.

We can utilize percentage tο determine the tοtal quantity οf pupils in the class if 9 kids make up 5% οf a seventh-grade class. If we assume that there are x pupils inside the seventh grade οverall, we can calculate the prοpοrtiοn as fοllοws:

9 / x = 5 / 100

We may crοss-multiply and simplify tο find x's value:

9 × 100 = 5 × x

900 = 5x

x = 900 / 5

x = 180

In the seventh grade, there are 180 students.

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Answer:

$9

Step-by-step explanation:

We know

They start at 10:15 and end at 11:45. It is 1 hour 30 minutes long.

1 hour 30 minutes = 90 minutes

The boat rental costs $1.50 for every 15 minutes.

How much will they pay?

We Take

90 divided by 15, then time 1.50 = $9

So, they pay $9

Answer:

Scott and Tom will pay a total of $9 for the boat rental.

Step-by-step explanation:

If Scott and Tom rent the boat between 10:15 and 11:45, then the total time they rented the boat is 1 hour and 30 minutes.

To convert 1 hour and 30 minutes to units of 15 minutes, we can divide the total number of minutes by 15:

⇒ 1 hour = 60 minutes

⇒ 1 hour and 30 minutes = 60 + 30 = 90 minutes

⇒ 90 minutes / 15 minutes = 6

Therefore, there are 6 units of 15 minutes in 1 hour and 30 minutes.

Given the cost for renting the boat is $1.50 per 15-minute interval, the total cost for renting the boat is:

⇒ 6 × $1.50 = $9

Therefore, Scott and Tom will pay $9 for the boat rental.

The answer is 12units

Answer:

Step-by-step explanation:

e