Write this ratio as a fraction in simplest form without any units. 21 feet 8 yards you can use the table below to help convert the units. Length: 1 foot = 12 inches. 1 yard = 3 feet. Weight: 1 pound = 16 ounces Capacity (Volume) 1 quart = 2 pints. 1 gallon = 4 quarts

Answer:

(0, -3)

Step-by-step explanation:

It will help to graph it out.

Also is the phase shift negative or is it just to the right? Im assuming its just right pi over 4

Answer: 0

Step-by-step explanation:

2pi/4 does not equal pi, it equals half of pi. 2pi/2 equals pi. Regardless here's my answer, since it also checks out for a similar function that was confirmed to have a phase shift of pi/2:

The formula for this is asin(bx - c) + d, where

|a| = amplitude

period = 2pi/b

and phase shift = c/b

The amplitude is 3

3sin(bx - c) + d

Phase shift is c/b, in this case, pi/4

3sin(4x - pi) + d  

d is vertical shift

(phase shift, c, is also known as horizontal shift)

We don't see any d here so graph on Desmos as follows....

Graph 3sin(4x - pi)

Looks like the y-intercept is 0

Check by substituting 0 for x:

3sin(4x - pi)

3sin(4(0) - pi)

3sin(-pi) = 0

The answer is 0, checks out.

Answer:

a) 36x-27y-207

b)12x-6y+2

c)300y-60x-195

d)-8x-96

d)8x+272y-576

Step-by-step explanation:

In all of these equations, you multiply the numbers on the outside of the parentheses to all of the terms inside the parentheses to get each of your different answers.

Hope this helps and please award brainliest if possible!

Answer:

Step-by-step explanation:

(a)

(b)

#a

Check IO bisects the FH at 90°.

#b

So the options are

For any square matrix A, if it is invertible, its inverse is given by

[tex]A^{-1} = \dfrac1{\det(A)} \mathrm{adj}(A)[/tex]

where adj(A) is the so-called adjugate matrix, which is the transpose of the cofactor matrix of A. If you don't know what that is, that's not terribly important. What is important is that the inverse does not exist if the determinant, det(A), is zero.

We have

[tex]A=\begin{bmatrix}6&7\\-6&7\end{bmatrix} \implies \det(A) = 6\times7-7\times(-6)=84 \neq 0[/tex]

so the inverse does indeed exist. (And we eliminate D as an answer.)

From the given choices, it's quite clear that C must the correct answer, since we know det(A) = 84, and we can easily confirm that

[tex]\begin{bmatrix}7&-7\\6&6\end{bmatrix} \begin{bmatrix}6&7\\-6&7\end{bmatrix} = \begin{bmatrix}84&0\\0&84\end{bmatrix}[/tex]

so that multiplying by 1/84 recovers the identity matrix.

We are given with a square matrix and we are asked to find it's inverse if it exists . So , let's recall some important points first :-

Now , in this question let's assume that [tex]{\sf A=\begin{bmatrix}6 & 7 \\ -6 & 7\end{bmatrix}}[/tex]

Now , Calculating det(A) :-

[tex]{:\implies \quad \sf det(A)=\begin{vmatrix}6 & 7 \\ -6 & 7 \end{vmatrix}}[/tex]

[tex]{:\implies \quad \sf det(A)=42-(-42)}[/tex]

[tex]{:\implies \quad \sf det(A)=42+42}[/tex]

[tex]{:\implies \quad \sf det(A)=84}[/tex]

As , det(A) ≠ 0 . So , [tex]{\bf A^{-1}}[/tex] exists . Now , we need to find the matrix of cofactors first , but let's find cofactors first , so here ;

[tex]{\blacktriangleright \sf C_{11}=7,\: C_{12}=6,\: C_{21}=-7,\: C_{22}=6}[/tex]

Now , let's assume that matrix of cofactors is C , so putting the cofactors as elements of the matrix , C will be ;

[tex]{:\implies \quad \sf C=\begin{bmatrix}7 & 6 \\ -7 & 6\end{bmatrix}}[/tex]

Now , adj(A) will be found by interchanging it's rows by columns and vice versa.

[tex]{:\implies \quad \sf adj(A)=\begin{bmatrix}7 & -7 \\ 6 & 6\end{bmatrix}}[/tex]

Now as [tex]{\sf A^{-1}}[/tex] is given by [tex]{\bf{A^{-1}=\dfrac{1}{adj(A)}det(A)}}[/tex]

[tex]{:\implies \quad \bf \therefore \quad \underline{\underline{A^{-1}=\dfrac{1}{84}\begin{bmatrix}7 & -7 \\ 6 & 6\end{bmatrix}}}}[/tex]

Hence , Option C) [tex]{\sf \dfrac{1}{84}\begin{bmatrix}7 & -7 \\ 6 & 6\end{bmatrix}}[/tex] is correct :D

Answer:

x=−7

Step-by-step explanation:

(x+4)(2)−3(x+4)−3=0

(x)(2)+(4)(2)+(−3)(x)+(−3)(4)+−3=0(Distribute)

2x+8+−3x+−12+−3=0

(2x+−3x)+(8+−12+−3)=0(Combine Like Terms)

−x+−7=0

Answer:

56

Step-by-step explanation:

8C5 = 56

Answer:

  8C5 = 56

Step-by-step explanation:

The formula for nCk is ...

  nCk = n!/(k!(n-k)!)

Then the value of 8C5 is ...

  8!/(5!(8-5)!) = 8·7·6/(3·2·1) = 8·7

  8C5 = 56

_____

Additional comment

The larger of the denominator factorials will cancel most of the factors of the numerator. The remaining denominator factors can be factored from the remaining numerator values to simplify the problem of doing the math by hand. Most graphing calculators and all spreadsheets can compute this function for you.

  [tex]\dfrac{8!}{5!\cdot3!}=\dfrac{8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1}{(5\cdot4\cdot3\cdot2\cdot1)(3\cdot2\cdot1)}=\dfrac{8\cdot7\cdot6}{3\cdot2\cdot1}=\dfrac{8\cdot7\cdot6}{6}=8\cdot7[/tex]

Answer: See below

Step-by-step explanation:

Event 1:

There are 13 diamond cards in total

A standard deck of cards has a total of 52 cards

Probability = 13/52

P = 1/4 or 25%

Event 2:

There are a total of 6 sides on a standard dice

Probability = 4/6

P = 2/3 or 66.67%

Event 3:

There are 3 blue marbles in a bag of 18 marbles

Probability = 3/18

P = 1/6 or 16.67%

Answer: a) 1/4     b) 2/3     c) 1/6

Step-by-step explanation:

All of these are probability problems. They have this trick.

First, the trick. The chance of taking an x amount of blue marbles out of a bag of y marbles is x/y. Now using this…

a) there are 13 diamonds and 52 total. 13 is x, and 52 is y. It is 13/52 = 1/4

b) There are 4 numbers you need to get, and 6 in total. Therefore; there is a 4/6 chance which simplifies to 2/3.

c) There are 3 marbles you need, and 18 of them in total. It is 3/18 which is 1/6.

I once struggled on these problems, for they can be difficult.

Answer:

y = 2x - 3

Step-by-step explanation:

y - 9 = 2 ( x - 6 )

y - 9 = 2x - 12

Hi! I can help you with a smile! :)

Answer:

y=2x-3

Hope it helps!

~Nature~

Enjoy your day!

Answer:

57/6   60/6    22/6   26/6

Step-by-step explanation:

So the answers for the blanks are 57, 60, 22, 26.

Let me know if I am incorrect.

Answer:

[tex]x=\frac{1}{2}[/tex]

Step-by-step explanation:

equation of a circle:  [tex](x - h)^2+(y-k)^2=r^2[/tex]

where (h, k) = center and r = radius

From inspection, we can see that the center of the circle = (0, 0)

and the radius = 1

[tex]\implies (x - 0)^2+(y-0)^2=1^2[/tex]

[tex]\implies x^2+y^2=1[/tex]

Substitute [tex]y=\frac{\sqrt{3}}{2}[/tex]  into  [tex]x^2+y^2=1[/tex]  and solve for [tex]x[/tex]:

[tex]\implies x^2+(\frac{\sqrt{3}}{2})^2=1[/tex]

[tex]\implies x^2+\frac{3}{4}=1[/tex]

[tex]\implies x^2=\frac{1}{4}[/tex]

[tex]\implies x=\pm \sqrt{\frac{1}{4}}[/tex]

[tex]\implies x=\pm\frac{1}{2}[/tex]

As point P is in quadrant 1, [tex]x[/tex] is positive, so [tex]x=\frac{1}{2}[/tex]

Answer:

March 25, 2021, Mrs. Chaues balance is _____

Step-by-step explanation:

Mrs. Chauke balance in words is Eighteen thousand five hundred eighty-two and seven hundredths

From the complete question, we have the following highlights:

When 18,582,07 is expressed In words, it is:

Eighteen thousand five hundred eighty-two and seven hundredths

Hence, Mrs. Chauke balance on the 25 March 2021 in words is Eighteen thousand five hundred eighty-two and seven hundredths

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Answer:

[tex]6x-7x^{2}[/tex]

Step-by-step explanation:

o= 4x [tex]x[/tex] 2 +7x -3

0= 8x +7x -3

0= 15x -3

- 15x =-3

x= [tex]\frac{1}{5}[/tex]

x= 0.2  , x =[tex]x^{-1}[/tex]

[tex](f+g)(2)[/tex]

[tex]18 - 7x -5-7 \\6-7x\\[/tex]

Answer:Given a normal distribution with μ = 62 and σ = 4., calculate the 68-95-99.7 rule, or three-sigma rule, or empirical rule ranges

Calculate Range 1:

Range 1, or the 68% range, states that 68% of the normal distribution values lie within 1 standard deviation of the mean

68% of values are within μ ± σ

μ ± σ = 62 ± 4.

62 - 4. <= 68% of values <= 62 + 4.

58 <= 68% of values <= 66

Calculate Range 2:

Range 2, or the 95% range, states that 95% of the normal distribution values lie within 2 standard deviations of the mean

95% of values are within μ ± 2σ

μ ± 2σ = 62 ± 2(4.)

62 - 2 x 4. <= 95% of values <= 62 + 2 x 4.

62 - 8 <= 95% of values <= 62 + 8

54 <= 95% of values <= 70

Calculate Range 3:

Range 3, or the 99.7% range, states that 99.7% (virtually ALL) of the normal distribution values lie within 3 standard deviations of the mean

99.7% of values are within μ ± 3σ

μ ± 3σ = 62 ± 3(4.)

62 - 3 x 4. <= 99.7% of values <= 62 + 3 x 4.

62 - 12 <= 99.7% of values <= 62 + 12

50 <= 99.7% of values <= 74

Step-by-step explanation:

The probability that a data value is between 56 and 64 is,

= 64.7%

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

Given that :

Mean (m) = 62

Standard deviation (s) = 4

Hence, Probability that a data value is between 56 and 64

P(56 < x < 64)

Using the relation :

(x - m) / s

P(x < 56) : (56 - 62) / 4

              = - 1.5

P(Z < - 1.5) = 0.10565

( Z probability calculator)

P(x < 64) :

(64 - 62) / 4 = 0.75

P(Z < 0.75) = 0.77337 (Z probability calculator)

Hence, We get;

P(Z < 0.75) - P(Z < - 1.25)

0.77337 - 0.10565

= 0.64772

= 64.7%

Thus, the probability that a data value is between 56 and 64 is,

= 64.7%

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Answer:

LCM of 3, 5, and 11 is 165.

Step-by-step explanation:

The number of people in the room is 91.

The first step is to determine the total number of chairs in the room. In order to determine this value, divide the fraction of the unoccupied chairs by the number of empty chairs.

8 ÷ 1/8

8 x 8 = 64

Number of people sitting on the chairs = 64 - 8 = 52

Number of people in the room = 52 ÷ 4/7

= 52 x 7/4 = 91

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Answer:

1.

Step-by-step explanation:

The greatest common factor is the largest positive integer that divides evenly into all numbers with zero remainder.

So, let's factor each number:

12w⁴: To factor it, factor 12 and w⁴ separately.

12: 1, 2, 3, 4, 12

w⁴: 1, w, w², w³, w⁴

So, the factor of 12w⁴ is all the combinations of the factor of 12 and w⁴.

1, 2, 3, 4, 12, 1w, 2w, 3w, 4w, 12w, 1w², 2w², ..., 12w⁴

5y³: To factor it, factor 5 and y³ separately.

5: 1, 5

y³: 1, y, y², y³

So, the factors of 5y³ are all the combinations of the factor of 5 and y³.

1, 5, 1y, 5y, 1y², ... , 5y³

The only factor that 12w⁴ and 5y³ have in common is 1.

Answer: 1.

Answer:

58

Step-by-step explanation:

the way of the parts of the question

1. We can measure the following two things:

(i) a person's height

(ii) the velocity required to reach Mars.

2. Everything involving a rocket launch needs to be extremely precise; otherwise, it could result in tragedy. However, anything involving a person's height won't result in disaster.

This can be solved using the concept of precision and uncertainty concept.

The accuracy of a material or substance is the distance or degree to which two or more measurements are near to one another. Every time a measurement is performed, a new result is obtained that falls within the uncertainty interval that surrounds the measured value.

1. We don't need to be very precise because we can measure a person's height with a modest degree of accuracy. The person hearing would get a notion of their height if we said, "That individual is roughly 5 feet tall."

On the other hand, if we estimate the rocket speed to Mars incorrectly, it would lead to tragedy in the future, hence we require great precision. In order to ensure that we strike the necessary objective in space, we apply intricate mathematics.

2.  Like we stated in problem 1, everything involving space travel needs extreme accuracy. The spaceship might crash and calamity could ensue if our estimates are incorrect. Engineers utilized the incorrect settings in the one instance where anything went wrong, causing the Mars lander to smash into the planet rather than securely land there.

Due to the enormous expense of these space exploration missions, it is imperative to obtain as many exact and accurate values as possible. Now, details like a person's height don't necessarily need to be accurate because we can just guesstimate a person's height depending on who we're speaking to.

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Prioritize meeting basic needs and invest in education and skill development, while supporting community projects for a fair distribution of funds.

Prioritize basic needs: I would recommend ensuring that everyone's basic needs are met first, such as food, shelter, and healthcare. This promotes fairness by addressing essential requirements for survival and well-being.

Invest in education and skill development: Allocating funds towards education and skill development programs can empower individuals to improve their future prospects and contribute to society. It promotes fairness by providing equal opportunities for personal growth and advancement.

Support community projects: Encouraging investments in community projects, infrastructure development, and social initiatives can benefit a broader range of people. It promotes fairness by aiming to uplift the community as a whole, rather than focusing solely on individual interests.

By following these principles, the recommended approach for spending money can ensure fairness by addressing basic needs, fostering personal development, and benefiting the community at large. Ultimately, the specific allocation of funds would depend on the context, priorities, and values of the individuals involved.

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Answer:

380,460

Step-by-step explanation:

x copies have been sold to date

so 8.7% * x = 33,100

x = 33,100/0.087 = 380,460

Step-by-step explanation:

f'(x)=-2sin(x)+2cos(2x)=0

as cos(2x)=2sin(x)cos(x),

-2sin(x)+4cos(x)sin(x)=0

sin(x)-2cos(x)sin(x)=0

(sin(x))(1-2cos(x))=0

-> x = 0, pi/3

testing these values along with the end points of the interval,

f(0)=2

f(pi/3)=1+(0.5sqrt(3))

f(pi/2)=0

so the min is 0 and the max is 2.

Answer:

6

Step-by-step explanation:

the least common denominator of 3 and 6 is 6

THATS how I got six

Hopped this helped <3

The slope of the line will be -2/3. And the coordinates will be A(-35/4, 6) and B(9, -34/6).

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = -2/3 x + 1/6

The slope of the line is - 2/3.

At y = 6, the value of 'x' is calculated as,

6 = -2/3 x + 1/6

35/6 = -2/3 x

x = -35 / 4

At x = 9, the value of 'y' is calculated as,

y = -2/3 (9) + 1/6

y = -6 + 1/6

y = -35/6

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The possible outcomes are the sample space of the game

The number of possible outcomes in the game is 3

The number of games is given as:

n = 5 i.e. 5 games to finish the season

In each game, the soccer team can either win, lose or tie.

So, we have the outcome of each game to be:

Outcome = {Win, Lose, Tie}

Count the outcomes

Count = 3

Hence, the number of possible outcomes in the game is 3

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Answer:

Letter a is 6:38 and letter b is 2:17

Hope this helps!

Answer:

75200 x 1/100= 752

hope this helps!

Answer:

0.25

Step-by-step explanation:

11/12 = 0.917

2/3 = 0.667

0.917 - 0.667 = 0.25