The straight line L has equation y = 1/2x+7 The straight line M is parallel to L and passes through the point (0, 3). Write down an equation for the line M.

a must be the least upper bound of S because it satisfies both conditions: it is an upper bound of S, and any other upper bound b for S must be greater than or equal to a.

What is the difference between the least upper bound and upper bound?

An upper bound of a set S of real numbers is any real number that is greater or equal to all numbers in S. A lower bound is any which is less than or equal to all numbers in S. A least upper bound is an upper bound that is less than or equal to all upper bounds.

To prove that a is the least upper bound (LUB) of the set S, we need to show that a satisfies two conditions:

a is an upper bound of S, meaning that for every element x in S, x <= a.

If there is another upper bound b for S, then a <= b.

First, we already know that a is an upper bound of S because it is given that a is an upper bound of the set S.

Next, suppose there is another upper bound b for S such that b > a. Then, since the sequence xₙ converges to a, there exists a positive integer N such that for all n >= N, xₙ is arbitrarily close to a, meaning that |xₙ - a| < (b - a)/2. This means that xₙ < b for all n >= N, which contradicts the assumption that b is an upper bound of S, since xₙ is an element of S and xₙ < b.

Therefore, a must be the least upper bound of S because it satisfies both conditions: it is an upper bound of S, and any other upper bound b for S must be greater than or equal to a.

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A fully inflated professional basketball has a circumference of 78 centimetres, hence the football's radius is 12.42 cm.

A circle is created when almost every point there in plane that is a specific distance away from another point does so (center). As a conclusion, it is a curve made up of segments that are spaced from each other in the plane. It is rotationally homogeneous about the centre in anyway angles. All pair of points in the grid that make up a circle are evenly spaced away from the "centre" and create a closed, two-dimensional object. A specular parity line is generated by a line that passes through circle. It is rotationally symmetric about just the centre at all angles.

given

The football's circumference is 12.42 cm.

Football's circumference is 78 cm.

The formula for the football's circumference is C = 2pir

= 78 r

= 78/2pi r

= 12.42 cm.

A fully inflated professional basketball has a circumference of 78 centimetres, hence the football's radius is 12.42 cm.

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The triangle is congruent by the Angle side Angle property.

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other. The meaning of congruency is that the two shapes are similar as well as equal in size.

The Angle side Angle Congruence Theorem (ASA) defines two triangles to be congruent to each other if the included two angles and one side of one are congruent to the included angle and corresponding two sides of the other triangle.

The three parameters that are congruent are:-

BV ≅ BV ( common side)

∠1 ≅ ∠2  ( Bisector)

∠3 ≅ ∠4  ( Bisector)

Hence, the two triangles are congruent with each other.

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In linear equation, The effect of the time of day a science class is taught on test scores being studied in an experiment will be the length of the class period.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                                 The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times. Equations with variables of power 1 are referred to as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.

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Answer:

84

Step-by-step explanation:

Let's call the father's present age "F" and the son's present age "S".

Five years ago, the father's age was F - 5 and the son's age was S - 5.

According to the first statement, F - 5 = 6(S - 5), so F = 6S - 35.

Two years in the future, the father's age will be F + 2 and the son's age will be S + 2.

According to the second statement, F + 2 = 3(S + 2) + 1, so F = 3S + 7.

We can now substitute the first equation into the second:

3S + 7 = 6S - 28,

3S - 6S = -35 - 7 = -42,

-3S = -42,

S = 14.

Finally, the father's present age is F = 6S - 35 = 84.

Answer:

The dad is 35 and the son is 10

Step-by-step explanation:

Let f =  the father's age

let s - the son's age

In the equations f-5 and s-5 represents the father and son's ages 5 years ago.   f + 2 and s +2 represent the father and son's ages two years in the future.

Answer:

4 events

Step-by-step explanation:

you divide 12.50 by 50 then you get 4

The number in question is 28.

To make solving this problem easier, we need to consider the number.

Let the number is ab.

So that,

4 × a = b

4a = b

We spread the numbers on the options.

28

(4 × 2 = 8) → True

32

(4 × 3 = 2) → False

15

(4 × 1 = 5) → False

25

(4 × 2 = 5) → False

We prove what number of 28 is when the digits is reversed to be greater than 54.

28 ⇄ 82

It is proved that the number 82 is greater than the number 54.

So, the number in question is 28.

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There are 353925 committees of 10 persons that can be chosen with exactly 8 men.

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

People = 15 men and 11 women

Committee = 10 persons (8 men)

The number of ways is then calculated as

Ways = Men * Women

So, we have

Ways = C(15, 8) * C(11, 2)

Evaluate the products

Ways = 353925

Hence, the number of committee is 353925

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10 divided by 0 problem would NOT have a solution.

Given:

a. 10 divided by 2

b. 10 divided by 5

c. 10 divided by 0

d. 0 divided by 10

We know that ,

Integer divided by an integer is an integer

Therefore (a) and (b) will have a proper solution

We also know that ,

Zero divided by anything is Zero

Therefore (d) also have a unique answer that is zero

Now , We know that

Any numeric value divided by Zero tends to infinity .

Hence, 10 divided by 0 problem would NOT have a solution.

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Answer:

Step-by-step explanation:

you take away 1 from 2 and that leaves you with 1

Answer:

Let's say I have two apples. You want one too! I give you one, and how many do I have left? 1

What I am explaining here is that if you take one away from two, it becomes one.

Answer:

Step-by-step explanation:

We can find the rental cost for each movie and each video game by dividing the total cost by the number of movies and video games rented, respectively.

For the movies:

Rental cost for each movie = Total cost of movies rented / Number of movies rented

= $33 + $24 = $57

= $57 / 6 = $9.50 per movie

For the video games:

Rental cost for each video game = Total cost of video games rented / Number of video games rented

= $18 + $24 = $42

= $42 / 4 = $10.50 per video game.

A system of equations in standard form to model this scenario include the following:

2x + 10y = 74.

x + y = 17.

In order to write a system of linear equations that could be used to model the situation and determine the number of small boxes shipped and the number of large boxes shipped, we would assign variables to the number of small boxes that were shipped, the number of large boxes that were shipped respectively as follows:

Next, we would translate the word problem into system of linear equations as follows:

Since x small boxes weigh 2 pounds each and y large boxes weigh 10 pounds each and  all the boxes she ships is 74 pounds;

2x + 10y = 74.

Additionally, she is shipping 17 boxes altogether;

x + y = 17.

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Answer: The answer is D

Answer:

B. False

Step-by-step explanation:

The domain is the set of values of x.

There is no restriction on the value of x.

x can be any real number.

Answer: B. False

For a set of data in which the sample mean is 83.3 and the sample standard deviation is 6.3 the z-score given that x = 79.8 would be -0.555

We know that the formula for calculating a z-score is :

z = (x - μ) / σ

where z is the standard z - score

x is the observed value

μ is the mean of the sample

σis the standard deviation of the sample

here, set of data in which the sample mean is 83.3 and the sample standard deviation is 6.3

i.e., μ = 83.3,  σ = 6.3

We calculate the z-score for x = 79.8

Using above formula,

z = (x - μ) / σ

z = (79.8 - 83.3) / (6.3)

z = (-3.5) / (6.3)

z = -0.555

Therefore, the z-score is:  -0.555

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The lines are skew is Lines AD and BF.

Skew lines are two lines that do not intersect, are not parallel, and are not coplanar. This means that the skew lines never cross and are not parallel to each other. For lines to be two-dimensional or coplanar, they can intersect or be parallel. This property does not apply to diagonal lines, which are always non-coplanar and exist in three or more dimensions.

In real life, cities have different types of roads, such as highways and overpasses. These streets are supposed to be on different levels. Lines drawn on such roads never intersect, creating skew lines instead of being parallel to each other.

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The relationship between the price of balloons and the amount earned is 56f + 120 dollars

The price of the balloons if 400 dollars is earned on friday and saturday is 5 dollars on friday and 8 dollars on saturday

a) If f is the price of a balloon on Friday, then the price of a balloon on Saturday would be f + 3 dollars. The total amount Thomas earns on Friday would be 16 balloons * f dollars/balloon = 16f dollars. The total amount Thomas earns on Saturday would be 40 balloons * (f + 3 dollars/balloon) = 40f + 120 dollars. Hence, the total amount earned on Friday and Saturday would be 16f + 40f + 120 dollars = 56f + 120 dollars.

Therefore, the equation to describe the relationship between the price of a balloon on Friday and the total amount earned is: t = 56f + 120 dollars.

b) We are given that Thomas earns 400 dollars on Friday and Saturday, so we can set t = 400 dollars in the equation derived above:

400 = 56f + 120

Solving for f, we have:

280 = 56f

f = 5 dollars

The price of a balloon on Friday is $5, and the price of a balloon on Saturday would be f + 3 = 5 + 3 = $8.

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I believe its 44,880

The sum of the squares of the differences between each data value and the mean is given as follows:

828.

The mean of the data-set in this problem is given as follows:

33.

The data-set is given as follows:

28, 34, 27, 42, 52 and 15.

Hence the sum of the squares of the differences between each data value and the mean is obtained as follows:

(28 - 33)² + (34 - 33)² + (27 - 33)² + (42 - 33)² + (52 - 33)² + (15 - 33)² = 828.

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Answer: To find the distance fallen after 1.6 seconds, we simply plug this value into the function and solve for h:

h = t^2 * 16

h = 1.6^2 * 16

h = 2.56 * 16

h = 40.96 feet

So, the object has fallen 40.96 feet after 1.6 seconds.

Step-by-step explanation:

Answer:

we on top

Step-by-step explanation:

Answer:

Step-by-step explanation:

you gotta be kidding me right now b r u h.  Aint no way bro is posting this hahahha get it i guess

The number of the 3 / 5 in a tape diagram is 3.

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator. Any number of equal parts is represented by a fraction, which also represents a portion of a whole.

A fraction is a number that is a component of a whole. By breaking a whole into a number of parts, it is evaluated.

Given that the fraction is 3 / 5. When we add the fraction three times we will get the value that is closest to 2.

E = 3 / 5 + 3 / 5 + 3 / 5

E = ( 3 + 3 + 3 ) / 5

E = 9 / 5

E = 1.8 ≅ 2

Hence, in a tape diagram, the 3/5 is represented by the number 3.

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As a result, the length is 8.5 cm and the breadth is 3.5 cm, and the total perimeter is 22 cm.

what is perimeter ?

An enclosed line that surrounds, distinguishes, or incorporates a two-dimensional contour or a three-dimensional length is referred to as a boundary. The edge of an ellipse or circle refers to its broadest area. The perimeter calculation has many useful properties. The rim of a form is its edge's radius. Understand how to determine the perimeter by adding the lengths of such sides of various forms. You can always measure the perimeter of a shape by multiplying its side lengths. The perimeter of an object is the space around it. At your house, any enclosed terrace is one illustration. The border of anything is the area encircling it. For a 50 feet x 50 feet yard, a 200 foot fence is required.

given

let the length of the rectangular wallet be x

the width be x - 5

perimeter = sum of all the sides = 22

x + x - 5 = 22

2x - 5 = 22

2x = 17

x = 8.5

length is 8.5 and width is 8.5 - 5 = 3.5

As a result, the length is 8.5 cm and the breadth is 3.5 cm, and the total perimeter is 22 cm.

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Answer:

40h = e

Step-by-step explanation:

40 x 11 = 440

Therefore , the solution of the given problem of test statistic comes out to be rounding to two decimal places, the z-score is -0.26.

The Z-statistic, which demonstrates that the ordinary ordinary neutral hypothesis is true, has been used as the statistic for anything resembling a Z-test. Let's say you run two separate X-y tests with a 0.05 level of significance, and the variable results show that you got a 2.5 R t. (also  Z-value). The p-value for this Z-value is 0.0124.

Here,

To find the z-scores corresponding to the oldest and youngest senators of age 86% and 41%, respectively, we can use the standard normal distribution formula:

z = (x - μ) / σ

where z is the z-score, x is the given value, μ is the mean, and σ is the standard deviation.

For the oldest senators of age 86%, we can find the corresponding z-score as follows:

z = (x - μ) / σ

z = (0.86 - 0.5) / 0.3413

z = 1.055

Rounding to two decimal places, the z-score is 1.06.

For the youngest senators of age 41%, we can find the corresponding z-score as follows:

z = (x - μ) / σ

z = (0.41 - 0.5) / 0.3413

z = -0.264

Rounding to two decimal places, the z-score is -0.26.

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The probabilities are obtained as -

a) P(X = 1) = 0.006377

b) P(X ≤ 2) = 0.0296075

c) P(X = 4) = 0.091137

d) P(X = 8) = 0.130251

What is Poisson Distribution?

The Poisson distribution is a discrete probability function that means the variable can only take specific values in a given list of numbers, probably infinite. A Poisson distribution measures how many times an event is likely to occur within “x” period of time.

The mean of the Poisson distribution is given by λ.

The cumative distribution function is -

P(X = π) = (e^(-λ)λ^π) / π!, where π = 0,1,2,...

a) So, putting π = 1, λ = 7 in the above formula -

P(X = 1) = (e^(-7)7^1) / 1!

P(X = 1) = (0.000911 × 7) / 1

P(X = 1) = 0.006377

Therefore, the value is P(X = 1) = 0.006377.

b) P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)

P(X ≤ 2) = (e^(-7)7^0) / 0! + (e^(-7)7^1) / 1! + (e^(-7)7^2) / 2!

P(X ≤ 2) = 0.000911 + 0.006377 + 0.022319

P(X ≤ 2) = 0.0296075

Therefore, the value is P(X ≤ 2) = 0.0296075.

c) So, putting π = 4, λ = 7 in the above formula -

P(X = 4) = (e^(-7)7^4) / 4!

P(X = 4) = (0.000911 × 2401) / 24

P(X = 4) = 0.091137

Therefore, the value is P(X = 4) = 0.091137.

c) So, putting π = 8, λ = 7 in the above formula -

P(X = 8) = (e^(-7)7^8) / 8!

P(X = 8) = (0.000911 × 5764801) / 24

P(X = 8) = 0.130251

Therefore, the value is P(X = 8) = 0.130251.

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For the system of equations, y = 10 + 2z and y = 38 - 5z the value of y and z are 18 and 4 respectively.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

The first equation is : y = 10 + 2z

The second equation is : y = 38 - 5z

Subtract equation (1) and (2) -

y - y = 10 + 2z - (38 - 5z)

0 = 10 + 2z - 38 + 5z

Collect the like terms -

2z + 5z = -10 + 38

7z = 28

z = 28/7

z = 4

Substitute the value of z in equation (1) -

y = 10 + 2(4)

y = 10 + 8

y = 18

Therefore, the value of y = 18 and z = 4.

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Answer:

Step-by-step explanation:

Sorry I don’t know

The translation of the sentence 'The sum of 15 and Delia’s age is 65'

is 15 + d = 65.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Let, The age of Delia be 'd'.

Therefore, The equation for the statement 'The sum of 15 and Delia’s age is 65'  can be expressed as,'

15 + d = 65.

d = 65 - 15.

d = 50.

So, The age of Delia is 50 years.

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The solutions for all the equations are:

1) x = 4

2) x = ±7

3) x = 5²´³

4) x = ±5³´²

The first equation is:

x³ = 64

If we apply the cubic root in both sides we will get:

∛x³ = ∛64

x = ∛64 = 4

2) now we have:

x² = 49

If we apply the square root:

√x² = ± √49

(remember the plus minus sign when you use a even degree root)

x = ±7

In this case we have two solutions.

3) x³ =25

Like in the first case:

x = ∛25 = ∛5² = 5²´³

Now we can't simplify this, so we leave it in this way.

4) x² = 125

Remember that 125 = 5³, then:

x² = 5³

x = ±√5³ = ±5³´²

These are all the solutions.

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