4. Michelle and Joyce had an equal number of stickers.
After Michelle gave away 8 stickers to her sister and
Joyce bought twice as many stickers as what she had at first,
Joyce had 4 times as many stickers as Michelle.
How many stickers did Joyce buy?

Find the critical points of [tex]f_1[/tex] and [tex]f_2[/tex].

By the fundamental theorem of calculus,

[tex]{f_1}'(x) = \displaystyle \prod_{j=1}^{21} (x-j)^j = (x-1) (x-2)^2 (x-3)^3 \cdots (x-21)^{21}[/tex]

and [tex]{f_1}'=0[/tex] for [tex]x\in\{1,2,3,\ldots,21\}[/tex]. The stationary points at odd values have odd multiplicity, while the even ones have even multiplicity. At the points of odd multiplicity, [tex]{f_1}'[/tex] passes through the [tex]x[/tex]-axis and the sign of [tex]{f_1}'[/tex] changes, while at the points of even multiplicity, [tex]{f_1}'[/tex] is tangent the to [tex]x[/tex]-axis. We also have

[tex]\displaystyle \lim_{x\to-\infty} {f_1}'(x) = (-1)^{1+3+5+\cdots+21} \infty = (-1)^{11^2} \infty = -\infty[/tex]

[tex]\displaystyle \lim_{x\to\infty} {f_1}'(x) = \infty[/tex]

so the plot of [tex]{f_1}'[/tex] looks more or less like the attached curve. (Not drawn to scale)

Wherever the sign of [tex]{f_1}'[/tex] changes from negative to positive, as it does in the case of [tex]x\in\{1,5,9,13,17,21\}[/tex], there is a local minimum, so [tex]m_1 = 6[/tex]. Similarly, wherever the sign changes from negative to positive, as it does when [tex]x\in\{3,7,11,15,19\}[/tex], there is a local maximum, so [tex]n_1 = 5[/tex].

Repeat for [tex]f_2[/tex].

[tex]{f_2}'(x) = 4900 (x-1)^{49} - 29400 (x-1)^{48} = 4900 (x-1)^{48} (x-7)[/tex]

has roots at [tex]x=1[/tex] and [tex]x=7[/tex], but only the latter is a critical point due to odd multiplicity. A rough sketch of the plot of [tex]{f_2}'[/tex] is also attached. The sign of [tex]{f_2}'[/tex] changes from negative to positive at [tex]x=7[/tex], so [tex]m_2 = 1[/tex] and [tex]n_2=0[/tex].

We conclude that

Q.9) [tex]2m_1+3n_1+m_1n_1 = \boxed{57}[/tex]

Q.10) [tex]6m_2+4n_2+8m_2n_2 = \boxed{6}[/tex]

Answer:

the answer is two because ur multiplying hope this helps

Answer: $5.75

Step-by-step explanation: 2.75 x 2 = 5.5    1.25 x 3 = 2.75    2.75 + 5.5 = 9.25     $15 - $9.25 = $5.75

On 4/5 gallon of gasoline, hybrid car will travel a distance of 48 miles.

Suppose, non hybrid car travel "x" distance in 1 gallon of gasoline

Then, hybrid will travel " 1 ⁹/₁₁ * x" distance in 1 gallon of gasoline

Given that, non hybrid car travel distance per gallon is; x = 33 miles per gallon

Then, hybrid car travel,  1 ⁹/₁₁ * x =  1 ⁹/₁₁ * x * 33 = 60 miles per gallon

On 1 gallon of gasoline hybrid car travel 60 miles

On 4/5 gallon of gasoline hybrid car will travel = 4/5 * 60 = 48 miles

On 4/5 gallon of gasoline, hybrid car will travel 48 miles of distance.

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Answer and Explanation:

The problem provides the following information:

Hypotenuse

=

h

y

p

=

5129

ft

Vertical drop

=

o

p

p

=

1275

ft

To find the angle of depression, the best trigonometric ratio to use is the sine ratio. After equating it with the ratio of the opposite side over the hypotenuse, get the inverse of the sine ratio as shown:

sin

θ

=

o

p

p

h

y

p

θ

=

sin

−

1

(

o

p

p

h

y

p

)

θ

=

sin

−

1

(

1275

ft

5129

ft

)

θ

=

sin

−

1

(

0.2485864691

)

θ

=

14.3938824691

≈

14.4

∘

The angle of depression is

14.4

Answer: total household present are 136

Step-by-step explanation:

Given:

82.1% of Cincinnati households have a computer.

111.804 households in Cincinnati have a computer.

According to ratio and proportions we have:

let total number of houses be x;

then

(111.804/x)*100=percentage of Cincinnati households having  a computer.    [[tex]gain/total*100 =gain %[/tex]]

then

(111.804/x)*100=82.1

cross multiplying we have

x=(111.804*100)/82.1

x=136 households  (Round to the nearest whole number.)

so total household present are 136

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Answer:

OD

Step-by-step explanation:

move the -8 to the right, and change its sign

x > 5

Answer:

the slope of the table is -0.857

Answer:

x < 3

Step-by-step explain: I used quizlet

The set X is convex.

In geometry, a subset of an affine space over the real numbers, or more broadly a subset of a Euclidean space, is said to be convex if it contains the entire line segment connecting any two points in the subset. A solid cube is an example of a convex set, whereas anything hollow or with an indent, such as a crescent shape, is not. Alternatively, a convex region is a subset that crosses every line into a single line segment.

b)The set X is convex as any two points on the set X is included in the whole set as x>0. So a line joining any two points on the set X is completely inside the set x.

c)set X is not a closed set as the compliment of the set is not an open set.

d)Set X is not bounded. If a set S contains both upper and lower bounds, it is said to be bounded. A set of real numbers is therefore said to be bounded if it fits inside a defined range. hence set x is not bounded.

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Answer: -8, -3, 2, |-6|

Step-by-step explanation:

-3 , -8, |-6|, 2

|-6|=6

6>2

-3>-8 since a negative number closer to 0 is the greater number.

Order: -8, -3, 2, 6 ==> -8, -3, 2, |-6|

The value of 4 gal 6 qt 112 oz expressed in standard notation is; 6.375

Standard notation of a number is defined as when a number is written with only number digits. This is the typical way to write numbers since words are not used in standard number notation.

Now, from conversions, we know that;

1 oz = 0.0078125 gallons

1 qt = 0.25 gallons

Thus, 4 gal 6 qt 112 oz expressed in gallons is;

4 + (6 * 0.25) + (112 * 0.0078125)

= 4 + 1.5 + 0.875

= 6.375

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Answer:

x∈(-3;0)∪(3;+∞).

Step-by-step explanation:

1) if to solve the inequality x³-9x>0, then

x(x-3)(x+3)>0, and solution is

x∈(-3;0)∪(3;+∝).

2) the graph is provided in the attachment (it is marked with red colour).

If you contribute $400 every quarter for 20 years, the amount of  interest you would  earn during the 20 years is $22,447.52

What future value formula is applicable in this case?

The applicable future value formula is that of an ordinary annuity which determines the future worth of $400 quarterly savings for 20 years bearing in mind that the quarterly interest rate is the annual interest rate divided by 4

FV=PMT*(1+r)^N-1/r

FV=worth of the annuity after 20 years=unknown

PMT=quarterly deposit=$400

r=quarterly interest rate=5%/4=1.25%

N=number of quarterly savings in 20 years=20*4=80

FV=$400*(1+0.0125)^80-1/0.0125

FV=$54,447.52

interest=$54,447.52-($400*80)

interest=$ 22,447.52

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Using proportions, it is found that the exact value of 41% of 379 is of 155.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

The proportion of 41% of 379 is given as follows:

0.41 x 379 = 155.39.

Since 0.39 < 0.5, the exact value is rounded to 155.

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Answer:

[tex]\textsf{1.} \quad x=-6, \quad x=6[/tex]

[tex]\textsf{2.} \quad x=-5, \quad x=2[/tex]

[tex]\textsf{3.} \quad x=-3, \quad x=7[/tex]

[tex]\textsf{4.} \quad x=\dfrac{-5 +\sqrt{57} }{4}, \quad x=\dfrac{-5 -\sqrt{57} }{4}[/tex]

[tex]\textsf{5.} \quad x=\dfrac{7+ \sqrt{309} }{10}, \quad x=\dfrac{7-\sqrt{309} }{10}[/tex]

Step-by-step explanation:

Method: Extracting the Square Root

[tex]\begin{aligned}& \textsf{Given}: & x^2 & = 36\\& \textsf{Square root both sides}: & \sqrt{x^2} & = \sqrt{36}\\& \textsf{Simplify}: & x & = \pm 6\\&\textsf{Solution}:&x& = -6, 6\end{aligned}[/tex]

Method: Factoring

[tex]\begin{aligned}& \textsf{Given}: & x^2+3x-10 & = 0\\& \textsf{Split the middle term}: & x^2+5x-2x-10 & = 0\\& \textsf{Factor the first two and the last two terms}: & x(x+5)-2(x+5)&=0\\& \textsf{Factor out the common term $(x+5)$}: & (x-2)(x+5)&=0\\& \textsf{Apply the zero-product property}: & (x-2)=0 \implies x&=2\\ &&(x+5)=0 \implies x&=-5\\ & \textsf{Solution}: & x&=-5,2\end{aligned}[/tex]

Method: Factoring

[tex]\begin{aligned}& \textsf{Given}: & x^2-4x-21 & = 0\\& \textsf{Split the middle term}: & x^2-7x+3x-21 & = 0\\& \textsf{Factor the first two and the last two terms}: & x(x-7)+3(x-7)&=0\\& \textsf{Factor out the common term $(x-7)$}: & (x+3)(x-7)&=0\\& \textsf{Apply the zero-product property}: & (x+3)=0 \implies x&=-3\\&&(x-7)=0 \implies x&=7\\& \textsf{Solution}: & x & = -3, 7\end{aligned}[/tex]

Method: Quadratic  Formula

[tex]\boxed{\begin{minipage}{4 cm}\begin{center}\underline{Quadratic Formula}\end{center}\\\\\begin{center}$x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$\end{center}\\\\\\\begin{center}when $ax^2+bx+c=0$\end{center}\end{minipage}}[/tex]

Given:

[tex]5x-4=-2x^2[/tex]

Rearrange into standard form by adding 2x² to both sides:

[tex]\implies 2x^2+5x-4=0[/tex]

Therefore:

[tex]a=2, \quad b=5, \quad c=-4[/tex]

Substitute the values into the quadratic formula and solve for x:

[tex]\implies x=\dfrac{-5 \pm \sqrt{5^2-4(2)(-4)} }{2(2)}[/tex]

[tex]\implies x=\dfrac{-5 \pm \sqrt{25+32} }{4}[/tex]

[tex]\implies x=\dfrac{-5 \pm \sqrt{57} }{4}[/tex]

Therefore, the solutions are:

[tex]x=\dfrac{-5 +\sqrt{57} }{4}, \quad x=\dfrac{-5 -\sqrt{57} }{4}[/tex]

Method: Quadratic  Formula

[tex]\boxed{\begin{minipage}{4 cm}\begin{center}\underline{Quadratic Formula}\end{center}\\\\\begin{center}$x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$\end{center}\\\\\\\begin{center}when $ax^2+bx+c=0$\end{center}\end{minipage}}[/tex]

Given:

[tex]5x^2-7x-13=0[/tex]

Therefore:

[tex]a=5, \quad b=-7, \quad c=-13[/tex]

Substitute the values into the quadratic formula and solve for x:

[tex]\implies x=\dfrac{-(-7) \pm \sqrt{(-7)^2-4(5)(-13)} }{2(5)}[/tex]

[tex]\implies x=\dfrac{7 \pm \sqrt{49+260} }{10}[/tex]

[tex]\implies x=\dfrac{7 \pm \sqrt{309} }{10}[/tex]

Therefore, the solutions are:

[tex]x=\dfrac{7+ \sqrt{309} }{10}, \quad x=\dfrac{7-\sqrt{309} }{10}[/tex]

Using translation concepts, the new location after the jump will be at (9,9).

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

The translation rule for this problem is:

(x,y) -> (x + 4, y + 9).

Which means that the coordinates move 4 units right and 9 units up.

The initial position is:

(5,0).

Hence the final position is:

(5,0) -> (5 + 4, 0 + 9) = (9,9).

The new location after the jump will be at (9,9).

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Answer:

(9c) - 4=5

Step-by-step explanation:

Product means 'The answer when you multiply' So we are working in multiplication. ( x )

9c is the multiplication.

It says 'less' which means subtracting to our answer. So we subtract 4. So far our equation is: (9c) - 4 (Brackets are needed as we are multiplying 9 by c and not multiplying 9 by c - 4)

Lastly, it says the answer must be 5 so we add that at the end. So the answer is:

(9c) - 4=5

Answer:

6-9x

Step-by-step explanation:

Converted from word to standard form.

Hope it helps!

The segment bisector of line segment XY is line n.

The length of the line segment XY is 6 units.

A line segment is a section of a line with two endpoints. A line segment, unlike a line, has a fixed length.

As per the given diagram in the question.

It is clear that the line segment XY is being divided by another line named n.

Thus,

The two segment of the line segment XY must be equal.

XM = MY

Substitute the values from the diagram;

5x + 8 = 9x + 12

Simplifying;

4x = -4

x = -1

Put the values in each segment;

XM = 5x + 8

XM = 5(-1) + 8

XM = 3 units.

Put the value in MY

MY = 9x + 12

MY = 9(-1) + 12

MY = 3 units.

As, it is clear from above values that the both segment are equal of 3 units each.

XY = XM + MY

XY = 3 + 3 = 6

Therefore, the value of XY is 6 units.

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C.78893

Step-by-step explanation:

-_-_+_(*;#-✓✓

Answer:

[tex]xy\left(7.2x-0.9y\right)[/tex]

Step-by-step explanation:

[tex]Rule: a^{b+c}=a^ba^c\\(x^2y=xxy,\:xy^2=xyy)\\=7.2x(xy)-0.9xyy\\=xy\left(7.2x-0.9y\right)[/tex]

hi

if he takes 1/3 , then remains 2/3

then 2/3 X = 10

             X =  10 / 2/3

            X =  10 * 3/2

              X = 30/2

              X = 15

let's check :  

1/3 of  15 =   15/3 = 5

15 -5 = 10

all macth, so answer is correct

The required inequality solution is x ≤ 8.

What is inequality?

x represents the number(no.) of people who can go to the amusement park.

They have no more than $125(one hundred twenty-five) to spend

Parking 15.00(fifteen), Tickets 12.50(12.five zero) per person

$15 + $12.50x ≤ $125

x = 110/12.5 ≤ 8.8

x ≤ 8

Therefore, the required inequality solution is x ≤ 8.

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Answer:

Inequality: 20p+9 ≤ 125

Answer: p ≤ 5.8

Step-by-step explanation:

Solve:

20p+9≤125

subtract -9 from both sides

20p≤116

20p/20 ≤ 116/20 Divide both sides by 20

p ≤ 5.8

Answer: -10s +15

-10 = 10 meters down

s = seconds

+ 15 = 15 meters risen

Answer:

Movie duration:1.5hrs

Answer:

A because of the way the pipe is designed