please help me in this duty

The correct statement about the angle measures in the diagram is given as follows:

m < 1 + m < 2 = 180º.

To obtain the angle measures for this diagram, we must consider the exterior angle theorem, which states that an angle is supplementary with it's exterior angle.

When two angles are supplementary, it means that the sum of their measures is of 180º.

In this problem, angle 1 is the exterior angle pair of angle 2, hence the correct statement is given as follows:

m < 1 + m < 2 = 180º.

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1. The youngest is Jade she is 12 years old.

2. The expression representing the age of Jane is:- Jane = 2 x Jade

3. The oldest age is Jane she is 24 years old.

4. The age of Jade is 12 years.

5. The expression for the sum of the ages will be:-

Jane + Jade + Jem = 55

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Mr and Mrs Torres have three pretty daughters, Jane, Jade and Jem. Jane is twice old as Jade, and Jem is 5 years younger than Jane. If n represents the age of Jade and the sum of their ages is 55.

From the given data following equations can be made:-

Jane = 2 x Jade

Jem = Jane - 5

Jane + Jade + Jem = 55

From the three equations the following equation can be made:-

2 Jade + Jade + 2Jade - 5 =  55

4Jade - 5 = 55

4Jade = 60

Jade = 60 / 5 = 12 years

Jane = 2 x Jade = 2 x 12 = 24 years

Jem = Jane - 5 = 24 - 5 = 19 years

The answers can be written as:-

1. Jade, who is 12 years old, is the youngest.

2. Jane's age is represented by the formula Jane = 2 x Jade.

3. Jane, who is 24 years old, is the oldest.

4. Jade is twelve years old.

5. Jane + Jade + Jem = 55 will be the formula for the total age.

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The total volume of the ice cream is -4.76 cubic inches.

The volume of the frustum of a cone can be calculated as follows:

V = (1/3) × π × h × (r1² + r2² + r1 × r2), where r1 and r2 are the radii of the top and bottom base of the cone.

And the volume of a sphere can be calculated as follows:

V = (4/3) × π × r³, where r is the radius of the sphere.

To calculate the total volume of the ice cream, we need to subtract the volume of the cone from the volume of the sphere.

Let's first calculate the radii of the top and bottom base of the cone.

r1 = (di/2) = (1.25/2) = 0.625 in.

r2 = (d0/2) = (2.25/2) = 1.125 in.

Now, we can estimate the volume of the cone.

V_cone = (1/3) × π × h × (r1² + r2² + r1 × r2)

= (1/3) × π × 2 × (0.625² + 1.125² + 0.625 × 1.125)

= 6.45 cubic inches.

Next, let's calculate the radius of the sphere.

r_sphere = (di/2) = (1.25/2) = 0.625 in.

And finally, we can calculate the volume of the sphere.

V_sphere = (4/3) × π × 0.625³

= 1.69 cubic inches.

So, the total volume of the ice cream is given by:

V_ice_cream = V_sphere - V_cone

= 1.69 - 6.45

= -4.76 cubic inches.

Note: Since the volume of the cone is larger than the volume of the sphere, the total volume of the ice cream will be negative, indicating that it is not possible to fill a frustum of a cone with ice cream in the manner described.

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--The given question is incomplete; the complete question is

"A frustum of a cone is filled with ice cream such that the portion above the cone is a hemisphere. Define the variables di=1.25 in., d0=2.25 in., h=2 in., and determine the volume of the ice cream."--

x>-4 is the solution of the inequality -8x < 32

A relationship between two expressions or values that are not equal to each other is called 'inequality.

The given inequality is -8x < 32

Minus eight times of x less than thirty two.

We need to solve for x which is a variable.

Divide both sides by 8

-x<4

x>-4

Hence, x>-4 is the solution of the inequality -8x < 32

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The correct option regarding the addition of vectors t and v is given as follows:

A. <-1, -11>.

The standard notation of a vector is given as follows:

<x,y>.

In which:

To add two vectors, we add the elements at the same component.

Then the addition of vectors t and v is given as follows:

t + v = <2, -10> + <-3, - 1> = <2 - 3, -10 -1> = <-1, -11>.

From the result obtained above, the correct option in the context of this problem is given by option A.

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The model used by Victor in the linear equation is incorrect,

The parameters are that;

Victor saved: $89.25

Cost of the bicycle = $129.85

Thus, to find the amount extra that he will need to purchase the bicycle, the equation model should be;

$89.25 + x = $129.85

This can be expressed in words as;

The amount of money he already has saved + the amount of money he still requires = the total price of the bike.

An equation that correctly represents this problem can show the sum of the amount of money he already has and the amount of money he needs equals the total cost of the bicycle

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Complete question is;

Victor has saved $89.25 for the bicycle that he wants. The bicycle costs $129.85. Victor writes the equation below to help him determine the additional amount that he needs to solve to have enough to buy the bicycle.

89.25 + 129.85 = x

Does Victor's equation correctly model the problem?

The number of such sequences of strings of length 14 is 172.

Let [tex]$a_n$[/tex] and [tex]$b_n$[/tex] denote, the number of sequences of length n ending in A and B, respectively.

If a sequence ends in an A, then it must have been formed by appending two A's to the end of a string of length (n-2).

If a sequence ends in a B, it must have either been formed by appending one Bs to a string of length (n-1) ending in an A, or by appending two Bs to a string of length (n-2) ending in a B.

Thus, we get the recursions as follows -

[tex]a_n &= a_{n-2} + b_{n-2}[/tex]

[tex]b_n &= a_{n-1} + b_{n-2}[/tex]

By counting further, we find that [tex]$a_1[/tex]= 0, [tex]b_1[/tex] = 1, [tex]a_2[/tex] = 1, [tex]b_2[/tex] = 0.

Similarly, we will get the following table -

Therefore, the number of such strings of length 14 is [tex]$a_{14} + b_{14}[/tex] = 80 + 92 = 172.

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A linear system that is underdetermined either has no solution or infinitely many solutions. has an infinite number of solutions and is consistent, for example, (x, y, z) = (1, 2, 2), (2, 3, 2), and (3, 4, 2).

If there are more equations than unknowns in a system of linear equations or a system of polynomial equations, it is said to be underdetermined (in contrast to an overdetermined system, where there are more equations than unknowns). The notion of constraint counting can be used to clarify the vocabulary. It is possible to think of each unknown as a potential degree of freedom. One degree of freedom is constrained by each equation that is added to the system.

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Slopes of all four sides are 1, -2/3, 1 and -2/3.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The given points are J(-4,-1), K(-7,-4), L((2, -10), M(5, -7)

For JK, Slope=-4 - (-1)) / (-7 - (-4)) = -3 / -3 = 1

For KL, slope= (-10 - (-4)) / (2 - (-7)) = -6 / 9 = -2/3

For LM, slope= (-7 - (-10)) / (5 - 2) = 3 / 3 = 1

For MJ, Slope=(-1 - (-7)) / (-4 - 5) = 6 / -9 = -2/3

Hence, slopes of all four sides are 1, -2/3, 1 and -2/3.

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The money factor that will be used to calculate bob’s payment is C) 0.00333

Money Factor can be converted to Annual Percentage Rate (APR) and vice versa.

So the money factor can be solved:

APR = 2400 x Money Factor

Money Factor = APR / 2400

Money Factor = 8% / 2400 = 0.0033333

Basically, APR is short for Annual Percentage Rate, which means an annual percentage. APR is widely applied to the money you are going to borrow. Like when you apply for a motor vehicle loan, credit card, consumer loan, loan for education, or home ownership loan.

The APR will display a calculation of the amount of interest that will be charged if you apply for a loan. The lower the APR, the less interest you will have to pay.

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The distance between the third base and the player is 150 feet.

Pythagoras' theorem states that “In a right-angled triangle,  the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base, and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle of 90°. The sides of a right triangle (say a, b, and c) which have positive integer values, when squared, are put into an equation, also called a Pythagorean triple.

In the diagram attached, we can see the locations of the 1st base, 2nd base, 3rd base, and Home plate.

Since these four points form a square of which diagonals are equal in size.

So if we find the distance between the 1st and 3rd base that will be equal to the distance between the Home plate to the second base.

To find the nearest distance,

By applying "Pythagoras' Theorem"

[tex]nearest \ distance =\sqrt{120^2+90^2}\\\\=\sqrt{22500}\\\\=150\ feet.[/tex]

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The perimeter and area of the figure are 40.8 units and 110 square units respectively.

Using the distance formula:

d = √[(x₂ - x₁)² + (y₂ - y₁)²],

where d is the distance between the points (x₁, y₁) and (x₂, y₂).

we shall evaluate the distance between each points as follows:

AB = √[(8-8)² + (9-2)²] = 7

BC = √[(3-8)² + (13-9)²] = 6.4

CD = √[(-3-3)² + (9-13)²] = 7.2

DE = √[(-3+3)² + (9-13)²] = 9

EA = √[(8+3)² + (2-0)²] = 11.2

DB = √[(8+3)² + (9-9)²] = 11

perimeter of the figure = AB + BC + CD + DE + EA.

perimeter of the figure = 7 + 6.4 + 7.2 + 9 + 11.2

perimeter of the figure = 40.8 units.

The figure is observed to be a trapezium ABDE and a triangle BCD. Triangle BCD have base length DB = 11 with height from C to DB equal to 4.

Trapezium ABDE have sides AB and DE parallel to each other, and height DB = 11.

area of triangle BCD = 1/2 × 11 × 4 = 22 square units

area of trapezium ABDE = 1/2 × (7 + 9) × 11 = 88 square units

total area of the figure ABCDE = 22 + 88

total area of the figure ABCDE = 110 square units

Therefore, the perimeter and area of the figure are 40.8 units and 54 square units respectively.

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The pairs of sample size n and population proportion p would produce the greatest standard deviation is D) n = 100 and p is close to 0

The entire group about whom you want to make conclusions is referred to as a population.

The particular group from which you will gather data is known as a sample. The sample size is always smaller than the population as a whole.

We know, The standard deviation for a population proportion is, [tex]\sigma_p = \sqrt\frac{p(1-p)}{n}[/tex].

Now, The pairs of sample size n and population proportion p would produce the greatest standard deviation for the sampling distribution of a sample proportion p is when n = 100 and p is close to 0 let's say we took

n = 100 and p = 0.1 then [tex]\sigma_p = \sqrt\frac{p(1-p)}{n}[/tex] will be = 0.09 and when n = 100 and

p = 0.5 then [tex]\sigma_p = \sqrt\frac{p(1-p)}{n}[/tex] = 0.05.

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In rare instances, the numerical value of the standard deviation might be 0. The standard deviation, defined as the square root of the variance, is a measure of the dispersion of a collection of data. A collection of data's variance is the average of the squared departures from the mean.

The standard deviation represents the average level of variation in your dataset. It informs you how far each number deviates from the mean on average. A high standard deviation implies that values are spread out from the mean, whereas a low standard deviation shows that values are close to the mean. The standard deviation quantifies the data's dispersion around the mean value. It is useful for comparing data sets that have the same mean but a different range. The mean of the following two numbers, for example, is the same: 15, 15, 15, 14, 16 and 2, 7, 14, 22, 30. The second, on the other hand, is plainly more dispersed.

Here,

When all of the data points in a collection are equal, the deviations from the mean are all 0, and so the variance is likewise zero. When the variance is zero, the square root of the variance (the standard deviation) is likewise zero. As a result, the standard deviation can only be 0 if all of the data points in the collection are equal.

In other words, the standard deviation is 0 when there is no fluctuation or dispersion in the data.

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The ratio notation and decimal notation to describe the relationship between the number of double basses and the total number of instruments in the string section are:

4 : 44 and 0.01.

The ratio shows how many times one value is contained in another value.

Example:

There are 3 apples and 2 oranges in a basket.

The ratio of apples to oranges is 3:2 or 3/2.

We have,

The number of instruments in the string section.

= 7 cellos + 4 double basses + 11 first violins + 11 second violins + 11 violas

= 7 + 4 + 11 + 11 + 11

= 44

Now,

The number of double basses.

= 4

Now,

Ratio notation to describe the relationship between the number of double basses and the total number of instruments in the string section is.

= 4 : 44

The decimal notation to describe the relationship between the number of double basses and the total number of instruments in the string section is.

= 4/44

= 1/11

= 0.01

Thus,

The ratio notation is 4:44.

The decimal notation is 0.01.

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The elevation gain of Mount Everest is 15,028 feet, a very impressive feat considering it is the highest elevation gain of any mountain in the world.

The difference between the height at the base of Mount Everest, which is 14,000 feet and the summit, which is 29,028 feet is 15,028 feet. This is also known as the elevation gain. It can be calculated using the following formula:

Elevation Gain = Summit Height - Base Height

So in this case, Elevation Gain = 29,028 ft - 14,000 ft

Which gives us: Elevation Gain = 15,028 ft

The elevation gain of Mount Everest is 15,028 feet, a very impressive feat considering it is the highest elevation gain of any mountain in the world. It is also the highest mountain in the world, with the summit standing at an impressive 29,028 feet. This is a testament to the power of nature and the sheer scale of Mount Everest.

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The length of the segment is approximately 2.2.

The length of the segment can be found using the Pythagorean theorem.

Given points (x1,y1) and (x2,y2), the length of the segment between them is given by:

√((x2-x1)^2 + (y2-y1)^2)

Plugging in the given points:

√((-3-(-4))^2 + (3-1)^2) = √(1^2 + 2^2) = √5

Rounding to the nearest tenth:

√5 ≈ 2.2

So the length of the segment is approximately 2.2.

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If a ski resort charges $55 for renting a snowboard or skis and $11 per hour for a lift ticket. If julian spent a total of $121. The number of hours is 6.

Let's call the number of hours Julian spent at the ski resort "h".

We know that:

55 (the cost of the equipment rental) + 11h (the cost of the lift ticket) = 121 (the total amount Julian spent).

So we can subtract 55 from both sides to isolate the lift ticket cost:

11h = 121 - 55 = 66

Finally, we divide both sides by 11 to find the number of hours:

h = 66 / 11 = 6

Therefore, Julian was at the ski resort for 6 hours.

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Answer:

x < -6

Step-by-step explanation:

-9x > 54

Divide both sides by -9, this process will switch the inequality sign:

[x < -6]

Since Point A is an element of a direct variation, the other points that are elements of this direct variation include the following:

B. [-2, -8].

E. [2, 8].

In Mathematics, a direct variation is also referred to as direct proportion and it can be modeled by using the following mathematical expression or function:

y = kx

Where:

In direct proportion, the value of x represent an independent variable while the value of y represents the dependent variable. Therefore, an equation that models the situation is given by:

-4 = -k

k = 4

y = 4x

When x = 8, the equation y = 4x is given by:

y = 4(8) = 32.

When x = -2, the equation y = 4x is given by:

y = 4(-2) = -8 (True).

When x = 4, the equation y = -4x is given by:

y = 4(4) = 16.

When x = 2, the equation y = 4x is given by:

y = 4(2) = -8 (True).

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The rationalized surds are;

1) 20 + 5√3/13

2) 12√7 - 24/7

3) 6√2  + 6√3/5

The surd has to do with an irrational number. In this case we are asked to find the value of the following surds.

1) The conjugate of the denominator is; 4 + √3 and the rationalize we have;

5/4 - √3 * 4 + √3/4 + √3

20 + 5√3/16 + 4√3 - 4√3 - 3

20 + 5√3/13

2) The conjugate of the denominator is; √7 - 2

To rationalize we have;

12/√7 + 2 * √7 - 2/√7 - 2

12√7 - 24/7 -2√7 + 2√7

12√7 - 24/7

3) The conjugate of the denominator is √2 + √3

To rationalize we have;

6/√2 - √3 * √2 + √3/√2 + √3

6√2  + 6√3/2 + √6 - √6 + 3

6√2  + 6√3/5

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The number of atoms in the compound will be 54 atoms.

Chemistry's fundamental building block is an atom. It is the smallest fraction of matter into which electrically charged particles cannot be released. It is also the smallest piece of substance with chemical element-like characteristics.

The number of atoms in 2 Sr3(PO4)2 can be determined by counting the number of each type of atom present in the compound. In 2 Sr3(PO4)2, there are:

2 x 3 = 6 Sr atoms

2 x 2 x 4 = 16 P atoms

2 x 2 x 8 = 32 O atoms

So, there are a total of 6 + 16 + 32 = 54 atoms in 2 Sr3(PO4)2.

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The number  300 can be written as 300/1 as a quotient of integers to show that it is rational.

A rational number is a number of the form p/q, where q not equal to 0 and p  and q must be co-primes.

To write a number in the form of quotient of integer, we write it as , where p/q.

Here,  300 can be written as  300/1 or 600/2 .

But we should also take care that p and q must be co-primes.

Co-primes are the pairs of numbers that have only one common factor which is 1.

So, 300 can be written as 300/1

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A closed-ended question is one that doesn't permit many different answers.

Closed-ended questions are those that can only be answered by choosing one of a small number of possibilities. These questions are typically multiple-choice with a single-word response, such as "yes" or "no," or they can use a rating system (e.g. from strongly agree to strongly disagree).

Close-ended questions, such as "yes/no" or multiple choice questions with predetermined answers, are questions that demand a certain response from the respondent. Closed-ended inquiries are frequently used to collect quantitative data from respondents.

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Given that in a △ABC, ∠A:∠B:∠C=11:5:4

Let the angles of the given triangle be 11xo,5xo,4xo.

We know that the sum of the angles of a triangle is 180o

11xo+5xo+4xo=180o⇒20xo=180o

xo=12110o​=15o

So, the angles of the triangle are 70o,60o,45o.

Answer:

A

Step-by-step explanation:

y = 3.8 − 0.4x.

y =  − 0.4x + 3.8

so slope = -0.4 negative slope

intercept = 3.8

Answer:From the question, we have the following parameters that can be used in our computation:

The graph

On the graph, we have

x = dozen

y = cookies

This means that

(3, 36) means 3 dozens required 36 cookies

What ordered pair describes the unit rate?

Using the ordered pair in (a):

The unit rate of the pair (3, 36) is 36/3 = 12.

This means that for every 1 dozen change, there is a corresponding 12 cookies change

Step-by-step explanation:

The sector area for the figure below is 268.19.

The quantity of space included within the sector's perimeter is referred to as the sector's area in a circle. A sector always starts at the circle's center. The area of a circle encompassed between its two radii and the arc next to them is known as the sector of a circle. The sector of a circle that most often symbolizes half of a circle is a semicircle.

The area of sector is given by the formula:

A = (pi)r² × α/360

where, r is the radius and α is the angle of the sector.

Substituting the value of r and α in the formula we have:

A = pi (16)² × 120/ 360

A = 268.19

Hence, the sector area for the figure below is 268.19.

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Answer: 15

Step-by-step explanation: