A student has 5 ninths gallons of popcorn to give away. He wants to split it evenly between his 4 friends. How much popcorn does each friend receive?

20 over 9 gallons
1 gallon
5 over 13 gallons
5 over 36 gallons

Answer: f(k)=4k² - 6k +7

Step-by-step explanation:

f(x)=4x² - 6x +7

f(k)=4k² - 6k +7

Answer:

Step-by-step explanation:

The answer is 110

hope this helps :)

The right triangle that shows the length of the two sides is 5.2 and 3.1.

It is required to find the triangle.

The branch of mathematics dealing with the relations of the sides and angles of triangles and with the relevant functions of any angles.

Given:

In trigonometry function, in a right triangle, a tangent of an angle x is equal to the ratio of the opposite side to angle x to the adjacent side to angle x.

According to given question we have:

Given that angle x will be:

[tex]x=tan^{-} \frac{3.1}{5.2}[/tex]

The opposite to angle x or perpendicular = 3.1 units

The adjacent side to angle x or base angle  = 5.2 units

Therefore, the right triangle that shows the length of the two sides is 5.2 and 3.1.

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Answer:

b

Step-by-step explanation:

Answer:

Step-by-step explanation:

#1 Number of ways picking 2 from 6 = 6C2 = 15

#2 Arranging them in a circle (consider 1 pair AB)

can be done

1,5  (ABBBBB)   or (5,1)

2,4 ( AABBBB) or (4,2)

3,3

1,1 (ABABAB)

all up = 7 ways

#3 = product of #1 and #2 = 15x7 = 105

There are 60 different ways the students can place the beads on the necklace using exactly two colors.

To find the number of different ways the students can place the beads on the necklace using exactly two colors, we need to consider the different arrangements that can be made.

We can first choose the two colors to be used, which can be done in C(6, 2) = 15 ways (where C(n, r) represents the combination of n items taken r at a time).

Once the colors are chosen, we can arrange the beads on the necklace in two ways: either clockwise or counterclockwise.

We can also flip the necklace to get a different arrangement.

Therefore, for each combination of colors, there are 2 x 2 = 4 different arrangements possible.

Thus, the total number of different ways the students can place the beads on the necklace is 15 x 4 = 60.

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Answer:

Step-by-step explanation:

The equation of the line is written in the slope-intercept form, which is: y = mx + b, where m represents the slope and b represents the y-intercept. In our equation, y = 6x + 2, we see that the slope of the line is 6.

Hope this helps :)

Answer:

See below

Step-by-step explanation:

Slope intercept form for a line equation is :

  y = m x + b      m is the slope of the line

                          b is the y-axis intercept ( this occurs when x = 0)

You can add and subtract radicals by ensuring that they have same radical parts.

It should be noted that a radical expression is an expression that contains the radical symbol which is ✓.

The necessary steps to add or subtract radicals include:

Identify the radical parts.

Add them together.

If there's unlike radical parts, one will manipulate the parts involved before solving.

Example: Add ✓63 + 5✓7

It should be noted that ✓63 = ✓9 × ✓7 = 3✓7

Therefore, ✓63 + 5✓7 will be:

= 3✓7 + 5✓7

= 8✓7.

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Answer:

No one can answer this

Step-by-step explanation:

You need to add a picture or something because we need more information. This could be a graph, a number line, etc.

Answer:

(Image 1)

d(A,C)=10d(C,B)=8

d(A,B)=d(A,C)+d(C,B)=10+8=18

(Image 2)

AB=AC−BC

=10−8=2

Step-by-step explanation:

The width of rectangle is 5 feet.

Let us assume the length of rectangle to be x. So, the width of rectangle will be (x - 3).

Now, as per the known fact, perimeter, length and width of rectangle are related by the formula -

Perimeter = 2 × (length + width)

Keep the values in formula to find the value of width

26 = 2 × (x + x - 3)

Performing addition of variables inside the bracket

26 = 2 × (2x - 3)

Shifting 2 to other side of equation to find the value of x

2x - 3 = [tex]\frac{26}{2}[/tex]

Performing division to find the value of x

2x - 3 = 13

Shifting 3 to other side of equation to find the value of x

2x = 13 + 3

Performing addition to find the value of x

2x = 16

Shifting 2 as denominator to other side of equation to find the value of x

x = [tex]\frac{16}{2}[/tex]

Performing division to find the value of x

x = 8

So, length of rectangle is 8 feet

Width of rectangle = x - 3

Width of rectangle = 8 - 3

Width of rectangle = 5 feet

Hence, the width of rectangle is 5 feet.

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Answer:

Step-by-step explanation:

it should be Venus

hmmm. im thinking its venus

The possible widths of the play area is  mathematically given as

This is further explained below.

Generally, the equation for perimeter  is  mathematically given as

P =2(l+w)

180 =2(l+w)

2(l+w) =180

[tex]l+w = \frac{180}{2}[/tex]

l+w =90

A =l \times w

1800 &=l *w

l *w =1800

l *w =1800

Substitute Eq. 3 in the Eq. 2:

l *w=1800

(90-w) *w=1800

90w-ww=1800

90w-w^2=1800

w^2-90 w+1800=0

Therefore

w^2-90 w+1800 =0

[tex]\left(w^2-30 w\right)+(-60 w+1800) =0[/tex]

w(w-30)-60(w-30) =0

(w-30)(w-60) =0

Thereofre

w =30

w=60

In conclusion, Because of this, the width of the rectangular play space is either thirty or sixty feet.

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Answer:

-13, -7.9, -7.7, -3.3, 0.1, 2.4

Step-by-step explanation:

Answer: p - 1 > 6, or p > 7

Step-by-step explanation:

   We will write an expression from the sentence given.

difference of a number (p) and 1 ➜ p - 1

is greater than ➜ >

    The difference of a number p and 1 is greater than 6​ ➜ p - 1 > 6

   To solve for the possible values of p, we will add 1 to both sides of the equation;

p > 7

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Answer:

The width of Tyrone's actual patio is 16 feet

Step-by-step explanation:

[tex]\frac{2ft}{1in}[/tex] =  [tex]\frac{x}{8}[/tex]   If we look at what we know, we see that the scale tells us that 1 inch is proportional to 2 ft.  What do we need to multiple 1 inch by to get 8 inches?  8.  So, we multiply 2 feet by 8 to get the actual size of the patio which is 16 feet.

P= 3

b=4

By using pythagorus therom,

h^2=p^2+b^2

=3^2+4^2

=9+16

=25

h =5

now,

sin(theta)= p÷h

=3÷5

Answer:

5X - 2 = 18

Step-by-step explanation:

5 x 4 = 20

20 - 2 = 18

Using the mean concept, it is found that LeBron scored 10 more points per game on his last two games than on his first two.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.

For his first two games, he scored 20 + 15 = 35 points, hence the mean is:

35/2 = 17.5 points per game.

For his last two games, he scored 25 + 30 = 55 points, hence the mean is:

55/2 = 27.5 points per game.

The difference is:

27.5 - 17.5 = 10.

On average, LeBron scored 10 more points per game on his last two games than on his first two.

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Answer:

$31.44

Step-by-step explanation:

$125.76 ÷ 4 = $31.44

Lauren $31.44

Friend 1 $31.44

Friend 2 $31.44

Friend 3 $31.44

+ ________

$125.76

She is diminutive (a very, very small person). She can ask others to hit the top elevator buttons for him because he can't reach them. On rainy days, he presses the buttons with his umbrella.

A statement, question, or phrase with a hidden or double meaning that is presented as a problem to be answered is called a riddle. Enigmas, which are difficulties typically presented in metaphorical or allegorical language that call for inventiveness and careful thought to solve, and conundra, which are questions that rely on puns in either the question or the answer, are two different forms of riddles.

Riddles from hundreds of various civilizations, including Finnish, Hungarian, American Indian, Chinese, Russian, Dutch, and Filipino sources, are cited by Archer Taylor in his statement that "we may definitely claim that riddling is a global art. Riddles and riddle motifs are common across the world.

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Answer:

Alright

Ignore the 20, We have 5(x-2)
Brackets mean Multiplication

So, Multiply 5 with x and multiply 5 with 2

=> 20 = 5x - 10

Transpose the 20 to the other side

the twenty being transposed to the other side becomes Minus because it is in plus

And bring 5x in front of the =

=> 5x = 20 - 10
=> 5x = 10

So now we have 5x but we need x so transpose the 5 to the other side

by transposing the five becomes division because its in positive so

=> x = 10 ÷ 5

=> x = 2

Kaboom, All done!

The value of expression using PEMDAS rule is 28 .

Given : expression [ 8 ( 2 ) - [tex]( 4 )^{2}[/tex]] + 7 ( 4 )

To find : value of expression

Calculation : Using V-BODMAS

[ 8 ( 2 ) - [tex]( 4 )^{2}[/tex]] + 7 ( 4 )

= [ ( 8 * 2 ) - ( 4 * 4 ) ] + ( 7 * 4 )

= [ 16 - ( 4 * 4 ) ] + ( 7 * 4 )

= [ 16 - 16 ] + ( 28 )

= [ 0 ] + ( 28 )

= 28

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It looks like the system of ODEs is

[tex]\begin{cases} 2x' + y' - 4x - 4y = e^{-t} \\ x' + y' + 2x + y = e^{4t} \end{cases}[/tex]

Differentiate both sides of both equations with respect to [tex]t[/tex].

[tex]\begin{cases} 2x'' + y'' - 4x' - 4y' = -e^{-t} \\ x'' + y'' + 2x' + y' = 4e^{4t} \end{cases}[/tex]

Eliminating the exponential terms, we have

[tex](2x' + y' - 4x - 4y) + (2x'' + y'' - 4x' - 4y') = e^{-t} + (-e^{-t}) \\\\ \implies (2x'' - 2x' - 4x) + (y'' - 3y' - 4y) = 0[/tex]

[tex](x'' + y'' + 2x' + y') - 4 (x' + y' + 2x + y) = 4e^{4t} - 4\cdot e^{4t} \\\\ \implies (x'' - 2x' - 8x) + (y'' - 3y' - 4y) = 0[/tex]

Now we can eliminate [tex]y[/tex] and it derivatives.

[tex]\bigg((2x'' - 2x' - 4x) + (y'' - 3y' - 4y)\bigg) - \bigg((x'' - 2x' - 8x) + (y'' - 3y' - 4y)\bigg) = 0 - 0 \\\\ \implies x'' + 4x = 0[/tex]

Solve for [tex]x[/tex]. The characteristic equation is [tex]r^2 + 4 = 0[/tex] with roots at [tex]r=\pm2i[/tex], hence the characteristic solution is

[tex]\boxed{x(t) = C_1 \cos(2t) + C_2 \sin(2t)}[/tex]

Solve for [tex]y[/tex]. Substituting [tex]x[/tex] into the second ODE gives

[tex]x' + y' + 2x + y = e^{4t} \\\\ \implies y' + y = e^{4t} + C_1 \cos(2t) + C_2 \sin(2t)[/tex]

The characteristic equation this time is [tex]r + 1 = 0[/tex] with a root at [tex]r=-1[/tex], hence the characteristic solution is

[tex]y(t) = C_3 e^{-t}[/tex]

Assume a particular solution with unknown coefficients [tex]a,b,c[/tex] of the form

[tex]y_p = ae^{4t} + b \cos(2t) + c \sin(2t) \\\\ \implies {y_p}' = 4ae^{4t} - 2b\sin(2t) + 2c\cos(2t)[/tex]

Substituting into the ODE gives

[tex]5ae^{4t} + (b+2c) \cos(2t) + (-2b+c) \sin(2t) = e^{4t} + C_1 \cos(2t) + C_2 \sin(2t) \\\\ \implies \begin{cases}5a = 1 \\ b+2c = C_1 \\ -2b+c = C_2\end{cases} \\\\ \implies a=\dfrac15, b=\dfrac{C_1-2C_2}5, c=\dfrac{2C_1+C_2}5[/tex]

so that the general solution is

[tex]\boxed{y(t) = \dfrac15 e^{4t} + \dfrac{C_1-2C_2}5 \cos(2t) + \dfrac{2C_1+C_2}5 \sin(2t) + C_3 e^{-t}}[/tex]

The number that contains digits where the hundreds digit is 1/10 the value of the thousand's digit is: 748917.

Firstly, refer to the image attached for the complete question.

Now,

Given: The value of the digit in the hundreds place in 653,841 is: 800

Now, the following cases arise for the given options:

Value of digit in the thousands place = 8000

=> 1/10 the value of the digit =  [tex]\frac{1}{10}(8000) = 800[/tex]

Value of digit in the thousands place = 9000

=> 1/10 the value of the digit = [tex]\frac{1}{10}(9000) = 900[/tex]

Value of digit in the thousands place = 4000

=> 1/10 the value of the digit = [tex]\frac{1}{10}(4000) = 400[/tex]

Value of digit in the thousands place = 7000

=> 1/10 the value of the digit = [tex]\frac{1}{10}(7000) = 700[/tex]

Out of all the options, as shown above, only Option A satisfies the given condition.

Hence, the correct Option is A, i.e., The number that contains digits where the hundreds digit is 1/10 the value of the thousand's digit is: 748917.

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The equation, in slope-intercept form, of the line zw is y = x.

It is given that, equation of the line pq is:-

y = -x + 2

Also, line pq is perpendicular to line zw

zw passes through the point z (11,11).

We have to find the equation, in slope-intercept form, of the line zw.

The slope intercept form of a line is:-

y = mx + b

Where,

m represents slope of the line,

(x,y) represents every point on the line

b represents the y-intercept of the line

We know that, when two lines are perpendicular, the product of slopes of the lines is -1.

Let the slope of the line zw be m.

Hence,

m*(-1) = -1

m = 1

As it passes from the point z(11,11).

Hence, we can write,

11 = 1(11) + b

11 = 11 + b

b = 0

Hence, the slope intercept form of the line zw is y = x .

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Answer:

the anser in 60

Step-by-step explanation:

Let the original number be x.

According to the question we can write as (2/3)x+20x

On rearranging x−(2/3)x=20

Now taking the L.C.M od 1 and 3 is 3

(3x−2x)/3=20

x/3=20

Again by transposing x=60

So the original number is 60

Answer:

4/36 but reduce to lowest terms.

Step-by-step explanation:

The rolls that add up to 5 are 1 and 4, 4 and 1, 2 and 3, and 3 and 2 for a total of 4 possibilities. then divide 4 by the total number of possibilities which is 6 times 6.

4/36 which you can also reduce to lowest terms.

Answer:

A.

B.✅

C.✅

D.✅

E.

F.✅

Step-by-step explanation:

[tex](4x-1)² = 11 \\ 4x-1 = \sqrt{11 } \\ 4x = \sqrt{11} + 1 \\ x = \frac{ \sqrt{11} + 1 }{4} [/tex]

If the total cost before tax was $11.5, then the cost of each bottle of juice j= $1.6 which can be found by the equation 5j + $3.50 = $11.50.

The cost of each bottle can be determined by using an algebraic expression.

An algebraic expression can be defined as the use of both numerals and letters in a mathematical equation.

To find the cost of each bottle, an algebraic expression can be given as,

Cost of a 5-pack of juice bottles + Cost of popcorn = Total cost before tax

5j + $3.50 = $11.50

Solving for j,

5j = 11.50 - 3.50

5j = 8

j = 8/5

j = $1.6

Hence, the cost of each bottle from a 5-pack of juice bottles is calculated to be $1.6

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Answer:

Step-by-step explanation:

It is asking for the "mode" which is the data element you see the most, therefore it is 2.