What is the equation for the linear model in the scatter plot obtained by choosing the two points closest to the line?
A)Y = -3 x+ 56
B)Y = -2 x +46
C)Y = -2 x +56
D)Y = 2 x + 56

The lengths of the sides of the kite LM is 13√2.

According to the Pythagorean theorem, the hypotenuse of a right-angled triangle's other two sides add up to a square whose length equals the hypotenuse's.

The hypotenuse (longest side) of a right-angled triangle's square is equal to the sum of its other two sides, according to the Pythagoras theorem (base and perpendicular). Hypotenuse2 = Base2 + Perpendicular2 is how this is expressed. A2 + B2 = C2 is the formula for the hypotenuse.

According to question:-

LM = 13√2

Hypotenuse = Base 2 + Perpendicular 2.

So,

LM = √7² + 17²

LM = √49 + 289

LM = √338

LM = 13√2.

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The correct answer is   A.  {(-8,-14), (-7,-12), (-6,-10), (-5,-8)} which  sets of ordered pairs represents a function.

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

Here, we have,

sets of ordered pairs represents a function are,

{(-8,-14), (-7,-12), (-6,-10), (-5,-8)}

{(-4,-14), (-9,-12), (-6,-10), (-9,-8)}

{(8,-2), (9,-1), (10,2), (8,-10)}

{(-8,-6), (-5,-3), (-2,0), (-2,3)}

Now, we know that,

A function has no repeated values of the independent variable.

So, we have now,

Only choice A meets that requirement.

And,

B: (-9, 12) and (-9, 8) both have -9 as a first value; not a function.

C: (8, -2) and (8, -10) both have 8 as a first value; not a function.

D: (-2, 0) and (-2, 3) both have -2 as a first value; not a function.

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A. Commutative property of addition

B. Distributive property

C. Commutative property of addition

D. Associative property of multiplication

Answer:

2.7n + 6.6 or 6.6 + 2.7n

Step-by-step explanation:

Algebraic Expressions are just like Numerical Expressions but instead of numbers, alphabets are used, these alphabets can also be used as variables. (BODMAS rule applies to Algebraic Expressions as well.)

Eg. 45x + 31x(2) = 45x + 62x = 107x

Given from the question:

[tex]0.3(9n + 22) \\ = 2.7n + 6.6 \: or \: 6.6 + 2.7n[/tex]

The dimensions length is 10 feet, width is 10 feet and height is 5 feet and the smallest possible surface area is 300 square feet.

Volume=lbh

lbh=500 cubic feet

h=500/lb

Surface area S=lb+2bh+2lh...(1) {rectangular tank has no top}

S=lb+2b(500/lb)+2l(500/lb) {substituting the value of h in 1}

S=lb+1000/l+1000/b { partially differentiating S with respect to l and b}

for S to be minimum dS/dl=0 and dS/db=0

dS/dl= b-1000/l^2

dS/dl=0

b=1000/l^2...(2)

dS/db= l-1000/b^2

dS/db=0

l=1000/b^2

l=1000/(1000/l^2)^2 {substituting the value of b from 2}

l=(1000 x l^4)/(1000000)

1000000/1000=l^4/l

1000=l^3

l=10  feet

b=1000/l^2

b=1000/100=10  feet

lbh=500

h=500/(10x10(

h=5  feet

S=10x10+2x5x10+2x10x5

S=300 square  feet

Length is 10 feet, width is 10 feet and height is 5 feet and the smallest possible surface area is 300 square feet of the  rectangular tank.

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Sine of an angle is defined as the ratio of the side opposite (perpendicular side) to that angle divided by hypotenuse of the triangle.

sin is a trigonometric ratio.

If θ is one of the acute angles in a triangle, then the sine of theta is the ratio of the opposite side to the hypotenuse.

sin Q = perpendicular / hypotenuse.

sin Q is the base of the trigonometry ratios and it is one of the ratio.

sine is an acute angle.

some formula of sine angle are ,

1- sine Q = 1/ cosec Q .

2- sin ^2 Q = 1- cos^2 Q .

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20 dodgeballs have been pumped up by Ttaloc.

Ttaloc has 36 additional pumped-up balls.

The complete ball's original number is 14.

The relationship between two or more numbers is expressed by the ratio. It displays the frequency of how often one value is encapsulated by another value (s).

The number of dodgeballs Ttaloc pumped up = (5/14) x 56 = 20

The number of other balls Ttaloc pumped up = (9/14) x 56 = 36.

A ratio in mathematics demonstrates how many times one number is present in another.

A ratio can have any number of quantities, such as counts of people or things or measurements of length, weight, time, etc. Both numbers must be positive in most situations.

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Answer:

9 loaves of bread

Step-by-step explanation:

We know

8 days = 6 loaves of bread

1 day = 0.75 loaves of bread

12 days = 0.75 x 12 = 9 loaves of bread

So, she should pack 9 loaves of bread for a 12-day hiking trip.

Answer: Kendra will need to back 9 loaves of bread for a 12 day hiking trip.

Step-by-step explanation:

Alright, the first step to solve any math problem is to take a look at the information we have. We know that Kendra has eaten through 6 loaves over the course of 8 days. We want to know how much bread she needs if she takes a 12 day hiking trip.

Because she's eating the same amount of bread each day, we need to find out how much of a loaf she eats daily. In order to find that number, we have to divide. In this case, it would be 6/8. (Amount of bread she has/Time taken to eat that bread).

This gives us 0.75. This means that Kendra eats 0.75 of a loaf of bread daily. In order to find out how much bread she needs for a 12 day hiking trip, all we have to do is multiply by 12.

0.75 * 12 = 9.

Kendra will need to back 9 loaves of bread for a 12 day hiking trip.

P.S. You could also do this with fractions by simplifying 6/8 to 3/4 (divide the numerator and denominator by 2, as they're both divisible by 2), and then multiply like 12 in the same way. They both yield the same answer, so it's a matter of preference. I used decimals as I found them easier to work with!

Answer:

1004 is the smallest four-digit palindrome that is divisible by 4.

Answer:

0

Step-by-step explanation:

625 / 25 = 25

55g + 25 = 25

55g = 25 - 25

55g = 0

g = 0/55

g = 0

Answer:

[tex] \sf \: g = 0[/tex]

Step-by-step explanation:

Given equation,

→ 55g + 25 = 625 ÷ 25

Now the value of g will be,

→ 55g + 25 = 625 ÷ 25

→ 55g + 25 = 25

→ 55g = 25 - 25

→ g = 0 ÷ 55

→ [ g = 0 ]

Hence, the value of g is 0.

After combine they hold 115.84 ounces.

A process of combining or adding two or more numbers is called addition.

We have to given that;

One bottle holds 67.34 ounces and another bottle holds 48.5 ounces.

So, After combine, we get;

Both bottle hold = 67.34 ounces + 48.5 ounces

                         = 115.84 ounces

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The exponential function to describe the given sequence of numbers, 10, 60, 360, 2160, 12960, ... is aₙ = 10 × [tex]6^{n-1}[/tex].

The given series 10, 60, 360, 2160, 12960, ... is a geometric progression.

a = 10

The common difference r = 60/10 = 6

As we know the general formula of the nth term of a geometric series is

aₙ = a × [tex]r^{n-1}[/tex]

Now, put the values of a = 10, r = 6 and n in the general formula,

aₙ = 10 × [tex]6^{n-1}[/tex]

Therefore, the required exponential function to describe the given sequence of numbers, 10, 60, 360, 2160, 12960, ... is aₙ = 10 × [tex]6^{n-1}[/tex].

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By fraction , 3  3/7   will it take 7 men to do the job if they work at the same rate.

What is fraction in maths?

In mathematics, the portion or component of the complete item is represented by a fraction. It stands for the proportionate pieces of the whole.

                The denominator and numerator are the two components of a fraction. The top number is referred to as the numerator, and the bottom number is referred to as the denominator.

per person per hour

           1/4*6  = 1/24

7 men per hour

       1/24 * 7 =   7/24

  total times

          1 ÷ 7/24  =  1   *  24/7  

                   =  3  3/7

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The three variable system is written as (x, y, z).

Here we have to find the definition of three variable system.

basically a solution of a system in three variables is an ordered triple (x, y, z) that makes all three equations true.

On the other hand it is what they all three have in common.

Where as the solution to a system of three equations in three variables (x, y, z) is called an ordered triple.

In order to solve these one we have to do the following:

First we have to pick any two pairs of equations from the system.

And then we have to eliminate the same variable from each pair using the Addition/Subtraction method.

Final step is to solve the system of the two new equations using the Addition/Subtraction method.

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=========================================

Explanation:

L = 6 inches = length

W = 3 inches = width

H = 5 inches = height

----------------------

V = volume

V = L*W*H

V = 6*3*5

V = 90 cubic inches is the volume

----------------------

SA = Surface Area

SA = 2*(LW + LH + WH)

SA = 2*(6*3 + 6*5 + 3*5)

SA = 126 square inches is the surface area

-----------------------

Unfortunately there isn't enough information to know the material cost. Please post the full problem, and any other relevant information connected to this question.

Function: This means that 2.7 x 10^3 is about 201.593 times smaller than 5.481 x 10^5. This can also be expressed as 0.049 or 4.9%.

A function is a mathematical relation between two sets of values, usually between an input and an output. It can be thought of as a machine that takes a certain input and produces a certain output.

2.7 x 10^3 is about 0.049 times smaller than 5.481 x 10^5.
To determine this, we can divide the two numbers. 5.481 x 10^5 divided by 2.7 x 10^3 equals about 201.593.
This means that 2.7 x 10^3 is about 201.593 times smaller than 5.481 x 10^5. This can also be expressed as 0.049 or 4.9%.

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The value of the polynomial "5x - 4x^2 + 3" at x =- 1 is -6.

The polynomial is 5x - 4x^2 + 3, and it is required to find its value at x = -1,

Now solve the polynomial by putting the value of x equal to -1:

5(-1) - 4(-1)^2 + 3        ,  x =  - 1

-5 - 4 ( 1 ) + 3             , squaring -1 gives + 1

minus 5 minus 4 plus 3

( - 9 + 3)

( - 6 )

Hence, is shown that the value - 6 is obtained when the given polynomial "5x - 4x^2 + 3" is solved for x = -1.

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Answer: To determine the games in which a person who buys a ticket for each game every day for the next 400 days could expect to lose less than a total of $200, we need to find the games in which the probability of winning is greater than the probability of losing.

Since the tickets for all of the games cost $2 per ticket, the probability of winning any given game is equal to the prize money divided by the ticket cost. For example, if the prize money for a game is $10, the probability of winning is $10/$2 = 1/2.

If the probability of winning a game is greater than the probability of losing, the expected value of the game is positive, which means that the person can expect to win more than they lose over time. On the other hand, if the probability of winning is less than the probability of losing, the expected value of the game is negative, which means that the person can expect to lose more than they win over time.

Therefore, to determine which games the person could expect to lose less than $200 in total, we need to find the games in which the prize money is greater than $2 per ticket.

Step-by-step explanation:

Answer: C

Step-by-step explanation:

Based on the graph, we know that it is negative if it is under the x-axis. It is also indicated by the negative labels.

A: incorrect

Looking at choice A, it says the interval is from -3<x<-2. This means we have to find x=-3 and x=-2. On the graph, that interval is above the x-axis, so it is positive, not negative.

B: incorrect

Looking at choice B, it says the interval is from 2<x<3. This means we have to find x=2 and x=3. On the graph, that interval is above the x-axis, so it is positive, not negative.

C: correct

Looking at choice C, it says the interval is from 4<x<5. This means we have to find x=4 and x=5. On the graph, that interval is under the x-axis, so it is negative.

Therefore, C is the correct answer.

The volume of the prism in the attached figure is calculated to be

672 m³

In the given problem, the formula used for volume of prism is

= area of base * height

Assuming a triangular base

area of triangular base = 1/2 * base * height

where

base = 12 m

height = 14 m

area of triangular base = 1/2 * 12 * 14

area of triangular base = 84 m²

The volume of the prism with a triangular base

volume of the prism = area of triangular base * height

where

area of triangular base = 84 m²

height = 8 m

volume of the prism = 84 * 8

volume of the prism = 672 m³

The volume of the prism is solved to be 672 m³

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Answer:

1. 30 − 6q

3. −7d − 14 OR -7d + -14

4. = −4x + 24y

5. a) −3b − 15           b)−12x + 24

6. For the first answer to this question: 3x + 3y OR 3x = t

For the second answer to this question: 3x = t and it costs 15 dollars in total with x = 5.

To prove the inverse :

You assemble the functions (that is, insert x into one function, plug that function into the suggested inverse function, then simplify) and check that you end up with simply "x" to establish (or refute) that two functions are the inverses of one another. The functions are inverses if you get x; otherwise, they are not.

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Answer: The odds against an event occurring are the ratio of the probability that the event will not occur to the probability that the event will occur. To find the odds against an event, you can use the formula:

Odds against = (1 - probability of event occurring) / probability of event occurring

In this case, the event is that exactly 5 cars will pass over the bridge in a 4-minute period. The probability that this event will occur is 0.16. Therefore, the odds against this event occurring are:

Odds against = (1 - 0.16) / 0.16

= 0.84 / 0.16

= 5.25

So, the odds against exactly 5 cars passing over the bridge in a 4-minute period are 5.25 to 1.

It means that there are 5.25 times more likely that it will not happen compare to happen.

Step-by-step explanation:

Answer:

C = $30 + $0.05M

Step-by-step explanation:

We know that renting the car will cost $30, regardless of whether you drive it any where or not

So far

C = $30

On the end of this equation, we want to be able to add another value, that can vary depending on the quantity of M (number of miles)

The second value is $0.05 multiplied by how many miles are travelled

Also expressed as $0.05M

Finally, just fix the two parts together

Answer:

Step-by-step explanation:

We know that renting the car will cost $30, regardless of whether you drive it any where or not

So far

C = $30

On the end of this equation, we want to be able to add another value, that can vary depending on the quantity of M (number of miles)

The second value is $0.05 multiplied by how many miles are travelled

Also expressed as $0.05M

Finally, just fix the two parts together

C = $30 + $0.05M

Answer:

26 - 11√5

Step-by-step explanation:

(4√5-3)(√5-2)

= 4√5 (√5-2) -3 (√5-2)

= 4√5 √5 + 4√5 ⋅ -2 -3 (√5-2)

= 4√5 √5 + 4√5 ⋅ -2 -3√5 -3 ⋅ -2

= 26 - 11√5

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Answer:

Answer:

Foci: (±5, 0)

Vertex: ( ±4 , 0)

Eccentricity: e = 5/4

Step-by-step explanation:

Hyperbola:

Write the equation of hyperbola in the form,

\boxed{\dfrac{x^2}{a^2}-\dfrac{y^2}{b^2}=1}

a

2

x

2

−

b

2

y

2

=1

9x² - 16y² = 144

Divide the entire equation by 144,

\begin{gathered}\sf \dfrac{9x^2}{144}-\dfrac{16y^2}{144}=\dfrac{144}{144}\\\\\\ \dfrac{x^2}{16}-\dfrac{y^2}{9}=1\\\\\\\dfrac{x^2}{4^2}-\dfrac{y^2}{3^2}=1\end{gathered}

144

9x

2

−

144

16y

2

=

144

144

16

x

2

−

9

y

2

=1

4

2

x

2

−

3

2

y

2

=1

a = 4 and b =3

Eccentricity: e

\boxed{e=\sqrt{1+\dfrac{b^2}{a^2}}}

e=

1+

a

2

b

2

\begin{gathered}\sf = \sqrt{1+\dfrac{9}{16}}\\\\=\sqrt{\dfrac{16}{16}+\dfrac{9}{16}}\\\\=\sqrt{\dfrac{25}{16}}=\sqrt{\dfrac{5*5}{4*4}}\\\\\\=\dfrac{5}{4}\end{gathered}

=

1+

16

9

=

16

16

+

16

9

=

16

25

=

4∗4

5∗5

=

4

5

Foci:

(ae, 0) & (-ae , 0)

\begin{gathered}\sf \left(4*\dfrac{5}{4},0 \right) \ ; \ \left( -4*\dfrac{5}{4},0 \right)\\\\\\(5, 0) \ ; \ (-5,0)\end{gathered}

(4∗

4

5

,0) ; (−4∗

4

5

,0)

(5,0) ; (−5,0)

Vertex of hyperbola:

The vertex of the hyperbola is a point where the hyperbola cuts the axis. (-a , 0) ; (a , 0)

Vertex : (-4 , 0) ; (4 , 0)

Time taken to travel from North Carolina to Florida driving an average speed of 70 mph is 7 hours.

Calculating average speed involves dividing the total distance traveled by the total time it took to cover that distance.

Given,

Time taken to travel = 9hours

average speed =55 mph

distance between North Carolina to Florida = speed x distance

distance= 55 x 9

distance= 495 miles

if driving at speed of 70 mph

time taken = distance/speed

time taken=495/70

time taken=7 hours

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