Tom drank 1 1/4 quarts of water and his sister Jane drank 1.75 quarts of water. Write the amount that Jane drank using a
fraction. Who drank more water?
(Doesn’t have choices)

Answer:

[tex]h \circ m \circ n \text{ where } h(x)=\sqrt{x} \text{ and } m(x)=1+\frac{15}{n} \text{ and } n(x)=x^3-9[/tex]

Step-by-step explanation:

Ok so I see a square root is on the whole thing.

I'm going to let the very outside function by [tex]h(x)=sqrt(x)[/tex].

Now I'm can't just let the inside function by one function [tex]g(x)=\frac{x^3+6}{x^3-9}[/tex] because we need three functions.

So I'm going to play with [tex]g(x)=\frac{x^3+6}{x^3-9}[/tex] a little to simplify it.

You could do long division. I'm just going to rewrite the top as

[tex]x^3+6=x^3-9+15[/tex].

[tex]g(x)=\frac{x^3-9+15}{x^3-9}=1+\frac{15}{x^3-9}[/tex].

So I'm going to let the next inside function after h be [tex]m(x)=1 + \frac{15}{x}[/tex].

Now my last function will be [tex]n(x)=x^3-9[/tex].

So my order is h(m(n(x))).

Let's check it:

[tex]h(m(x^3-9))[/tex]

[tex]h(1+\frac{15}{x^3-9})[/tex]

[tex]h(\frac{x^3-9+15}{x^3-9})[/tex]

[tex]h(\frac{x^3+6}{x^3-9})[/tex]

[tex]\sqrt{ \frac{x^3+6}{x^3-9}}[/tex]

To express the function √(x^3+6)/√(x^3-9) as a composition of non-identity functions, we can rewrite it in terms of exponential and logarithmic functions.

To express the function √(x^3+6)/√(x^3-9) as a composition of three or more non-identity functions, we can start by rewriting √(x^3+6) and √(x^3-9) as powers:

√(x^3+6) = (x^3+6)^(1/2)

√(x^3-9) = (x^3-9)^(1/2)

Next, we can express (x^3+6)^(1/2) and (x^3-9)^(1/2) in terms of powers of its components. Let's denote a = x^3+6 and b = x^3-9:

(x^3+6)^(1/2) = (a)^(1/2)

(x^3-9)^(1/2) = (b)^(1/2)

Finally, we can express these in terms of exponential and logarithmic functions:

(a)^(1/2) = e^(0.5⁢ln(a))

(b)^(1/2) = e^(0.5⁢ln(b))

Therefore, the function √(x^3+6)/√(x^3-9) can be expressed as a composition of three non-identity functions:

√(x^3+6)/√(x^3-9) = e^(0.5⁢ln(a))/e^(0.5⁢ln(b))

Answer:

V = 500 pi in^3

or approximately 1570 in ^3

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h  where r is  the radius and h is the height

The diameter is 10. so the radius is d/2 = 10/2 =5

V = pi (5)^2 * 20

V = pi *25*20

V = 500 pi in^3

We can approximate pi by 3.14

V = 3.14 * 500

V = 1570 in ^3

Answer:

V=1570.8

Step-by-step explanation:

The volume of a cylinder with a diameter of 10 inches and height of 20 inches is 1570.8 inches.

I changed the diameter to radius to make it easier. The radius is half the diameter, making the radius 5 inches.

Formula: V=πr^2h

V=πr^2h=π·5^2·20≈1570.79633

Answer:

First option, Second option and Fourth option.

Step-by-step explanation:

We need to remember that:

 1) Corresponding angles are located on the same side of the transversal (one interior and the other one exterior). They are congruent. Based on this, we can conclude that:

-Angle 1 and Angle 3 are Corresponding angles. Therefore, they are congruent.

-Angle 2 and Angle 4 are Corresponding angles. Therefore, they are congruent.

2)  Alternate interior angles are between the parallel lines,  and on opposite sides of the transversal. They are congruent.

Based on this, we can conclude that:

Angle 3 and Angle 6 are Alternate interior angles. Therefore, they are congruent.

Answer: C.( 0,-21)

Step-by-step explanation: Use the slope-intercept form to find the slope and y-intercept.

Final answer:

The y-intercept of the given line y = 5x - 21 is -21, which means the line crosses the y-axis at the point (0, -21), corresponding to option C.

Explanation:

The y-intercept of a line represented by the equation y = mx + b is the value at which the line crosses the y-axis. To find the y-intercept, one must look at the value of b, which is the constant in the equation. Given the equation y = 5x - 21, the y-intercept would be -21.

Therefore, when x is 0, the value of y would be -21, meaning that the line crosses the y-axis at the point (0, -21). This corresponds to the option C: (0, -21).

Answer:

D. ABC = DBC

Step-by-step explanation:

They are the same length and congruent.

Answer:

d) ABC ≅ DBC

Step-by-step explanation:

∠B in ΔABC and ∠B in ΔDBC is 90°. BC is a common side in both triangles which mean that both triangles have one side of the same length. Side AC in ΔABC is the same length as side DC in ΔDBC. Therefore ∠C in both ΔABC and ΔDBC are the same size. Therefore ΔDBC is a mirror image of ΔABC, which is a form of congruent triangles.

Answer:

[tex]\left ( 3\sqrt{2},135^{\circ} \right )\,,\,\left ( 3\sqrt{2},315^{\circ} \right )[/tex]

Step-by-step explanation:

Let (x,y) be the rectangular coordinates of the point.

Here, [tex](x,y)=(3,-3)[/tex]

Let polar coordinates be [tex](r,\theta )[/tex] such that [tex]r=\sqrt{x^2+y^2}\,,\,\theta =\arctan \left ( \frac{y}{x} \right )[/tex]

[tex]r=\sqrt{3^2+(-3)^2}=\sqrt{18}=3\sqrt{2}[/tex]

[tex]\theta =\arctan \left ( \frac{-3}{3} \right )= \arctan (-1)[/tex]

We know that tan is negative in first and fourth quadrant, we get

[tex]\theta =\pi-\frac{\pi}{4}=\frac{3\pi}{4}=135^{\circ}\\\theta =2\pi-\frac{\pi}{4}=\frac{7\pi}{4}=315^{\circ}[/tex]

So, polar coordinates are [tex]\left ( 3\sqrt{2},135^{\circ} \right )\,,\,\left ( 3\sqrt{2},315^{\circ} \right )[/tex]

Answer:

See explanation

Step-by-step explanation:

a) To prove that DEFG is a rhombus, it is sufficient to prove that:

Using the distance formula; [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]|DG|=\sqrt{(0-(-a-b))^2+(0-c)^2}[/tex]

[tex]\implies |DG|=\sqrt{a^2+b^2+c^2+2ab}[/tex]

[tex]|GF|=\sqrt{((a+b)-0)^2+(c-0)^2}[/tex]

[tex]\implies |GF|=\sqrt{a^2+b^2+c^2+2ab}[/tex]

[tex]|EF|=\sqrt{((a+b)-0)^2+(c-2c)^2}[/tex]

[tex]\implies |EF|=\sqrt{a^2+b^2+c^2+2ab}[/tex]

[tex]|DE|=\sqrt{(0-(-a-b))^2+(2c-c)^2}[/tex]

[tex]\implies |DE|=\sqrt{a^2+b^2+c^2+2ab}[/tex]

Using the slope formula; [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

The slope of EG is [tex]m_{EG}=\frac{2c-0}{0-0}[/tex]

[tex]\implies m_{EG}=\frac{2c}{0}[/tex]

The slope of EG is undefined hence it is a vertical line.

The slope of  DF is [tex]m_{DF}=\frac{c-c}{a+b-(-a-b)}[/tex]

[tex]\implies m_{DF}=\frac{0}{2a+2b)}=0[/tex]

The slope of DF is zero, hence it is a horizontal line.

A horizontal line meets a vertical line at 90 degrees.

Conclusion:

Since [tex]|DG|\cong |GF| \cong |EF| \cong |DE|[/tex] and [tex]DF \perp FG[/tex] , DEFG is a rhombus

b) Using the slope formula:

The slope of DE is [tex]m_{DE}=\frac{2c-c}{0-(-a-b)}[/tex]

[tex]m_{DE}=\frac{c}{a+b)}[/tex]

The slope of FG is [tex]m_{FG}=\frac{c-0}{a+b-0}[/tex]

[tex]\implies m_{FG}=\frac{c}{a+b}[/tex]

The domain in this context, which represents the possible values for time from when the soccer ball was kicked until it landed, is the set of all real numbers from 0 to 4.

In the context of this problem, the domain refers to the possible values for time, from when Vanessa kicked the soccer ball until when it landed again. We know from the problem that the ball was in the air for 4 seconds. Therefore, the domain consists of all real numbers from 0 to 4 (both inclusive). Since time cannot be negative in this context, we start the domain at 0, and end at 4 because that's when the ball hit the ground again. Also, time, which is a continuous quantity, can take any value within this period, therefore it's the set of all real numbers between 0 and 4.

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The domain of the function, which represents the soccer ball's flight, is the time interval it was in the air. Therefore, the domain is from 0 to 4 seconds, written as [0,4].

In the problem, Vanessa kicked a soccer ball and it was in the air for 4 seconds before hitting the ground. In this scenario, the height of the soccer ball is considered to be a function of time. As such, the domain of the function, which represents all possible input values for the function, would be the amount of time the ball is in the air. Therefore, the domain for this function would be the interval from 0 to 4 seconds, often written as [0,4].

It's important to understand that in situations involving time, the domain value cannot be negative, as negative time values have no physical meaning. Therefore, the lower limit of the domain is 0, when Vanessa initially kicked the ball. The upper limit is the time the soccer ball spent in the air, or 4 seconds.

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Answer:

There is no scatter plot provided, but I can tell you how to solve this. You will look at the plot. It should be numbered somewhere 0-10 and tell you that is the point system, the other side should be the students. So, now you will look at the points on the plot and determine where most of them are. If they are low, you would say that she thinks that they are bad. If it's mostly middle, you would say they need improvement, but aren't terrible. If they are high, you would say she thinks that they are very good.

Answer:

D

Step-by-step explanation:

∠ACE is a secant- secant angle and is measured as half the difference of the intersecting arcs, that is

∠ACE = 0.5(m AE - m BD )

          = 0.5 (106 - 48)° = 0.5 × 58° = 29° → D

Answer: D. [tex]29^{\circ}[/tex]

Step-by-step explanation:

In the given picture , we can see that the ∠ ACE is an Secant angle.

Two arcs =  arcBD and arcAE

Now , by considering (1) , we have

[tex]\angle{ACE}=\dfrac{1}{2}(\overarc{AC}-\overarc{BD})\\\\\Rightarrow\ \angle{ACE}=\dfrac{1}{2}(106^{\circ}-48^{\circ})\\\\\Rightarrow\ \angle{ACE}=\dfrac{1}{2}(58^{\circ}))\\\\\Rightarrow\ \angle{ACE}=29^{\circ}[/tex]

Hence, the measure of [tex]\angle{ACE}=29^{\circ}[/tex]

hence, the correct answer is D. [tex]29^{\circ}[/tex]

The expression equivalent to 6(2y - 4) + p is p + 12y - 24, according to the distributive property of multiplication over subtraction.

The task is to find which of the following is equivalent to 6(2y - 4) + p. The first step is to apply the distributive property of multiplication over subtraction to the term 6(2y - 4). This gives us 12y - 24. If we add p to this term, we get our equivalent expression: p + 12y - 24. So, option A. p+ 12y - 24 is equivalent to 6(2y - 4) + p.

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For this case we have that the equation of a line of the point-slope form is given by:

[tex](y-y_ {0}) = m (x-x_ {0})[/tex]

To find the slope we look for two points through which the line passes:

We have to:

[tex](x1, y1) :( 0,2)\\(x2, y2) :( 4, -2)[/tex]

Thus, the slope is:

[tex]m = \frac {y2-y1} {x2-x1} = \frac {-2-2} {4-0} = \frac {-4} {4} = - 1[/tex]

Substituting a point in the equation we have:

[tex](y - (- 2)) = - 1 (x-4)\\y + 2 = - (x-4)[/tex]

Answer:

Option A

Answer:

y = 3x - 10

Step-by-step explanation:

Assuming you require the equation of the parallel line through (2, - 4)

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 3x + 24 ← is in slope- intercept form

with slope m = 3

• Parallel lines have equal slopes, hence

y = 3x + c ← is the partial equation of the parallel line

To find c substitute (2, - 4) into the partial equation

- 4 = 6 + c ⇒ c = - 4 - 6 = - 10

y = 3x - 10 ← equation of parallel line

since we know the endpoints of the circle, we know then that distance from one to another is really the diameter, and half of that is its radius.

we can also find the midpoint of those two endpoints and we'll be landing right on the center of the circle.

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-4}~,~\stackrel{y_1}{-7})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{-5})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{diameter}{d}=\sqrt{[-2-(-4)]^2+[-5-(-7)]^2}\implies d=\sqrt{(-2+4)^2+(-5+7)^2} \\\\\\ d=\sqrt{2^2+2^2}\implies d=\sqrt{2\cdot 2^2}\implies d=2\sqrt{2}~\hfill \stackrel{~\hfill radius}{\cfrac{2\sqrt{2}}{2}\implies\boxed{ \sqrt{2}}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{-4}~,~\stackrel{y_1}{-7})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{-5})\qquad \qquad \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{-2-4}{2}~~,~~\cfrac{-5-7}{2} \right)\implies \left( \cfrac{-6}{2}~,~\cfrac{-12}{2} \right)\implies \stackrel{center}{\boxed{(-3,-6)}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{-3}{ h},\stackrel{-6}{ k})\qquad \qquad radius=\stackrel{\sqrt{2}}{ r} \\[2em] [x-(-3)]^2+[y-(-6)]^2=(\sqrt{2})^2\implies (x+3)^2+(y+6)^2=2[/tex]

Answer:

FIRST OPTION: [tex](x+3)^2+ (y+6)^2 =2[/tex]

Step-by-step explanation:

The equation of the circle in center-radius form is:

[tex](x- h)^2 + (y- k)^2 = r^2[/tex]

Where the center is at the point (h, k) and the radius is "r".

We know that the endpoints of the diameter of this circle are (-4, -7) and (-2, -5), so we can find the radius and the center of the circle.

In order to find the radius, we need to find the diameter. To do this, we need to use the formula for calculate the distance between two points:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Then, substituting the coordinates of the endpoints of the diameter into this formula, we get:

[tex]d=\sqrt{(-4-(-2))^2+(-7-(-5))^2}=2\sqrt{2}[/tex]

Since the radius is half the diameter, this is:

[tex]r=\frac{2\sqrt{2}}{2}=\sqrt{2}[/tex]

To find the center, given the endpoints of the diameter, we need to find the midpoint with this formula:

[tex]M=(\frac{x_2+x_1}{2},\frac{y_2+y_1}{2})[/tex]

This is:

[tex]M=(\frac{-4-2}{2},\frac{-7-5}{2})=(-3,-6)[/tex]

Then:

[tex]h=-3\\k=-6[/tex]

Finally, substituting values  into  [tex](x- h)^2 + (y- k)^2 = r^2[/tex], we get the following equation:

 [tex](x- (-3))^2 + (y- (-6))^2 = (\sqrt{2})^2[/tex]

[tex](x+3)^2+ (y+6)^2 =2[/tex]

We have the following function:

[tex]f(x)=-\frac{3}{x}[/tex]

The graph of this function has been plotted below. So lets analyze each statement:

As you can see x increases from -∞ to 0 and decreases from 0 to +∞

The function is undefined for [tex]x=0[/tex] since x is in the denominator.

Statement is unclear but the range is the set of all real numbers except zero.

The function is a reflection in the x axis of the function [tex]g(x)=\frac{3}{x}[/tex]

This is false since:

[tex]f(3)=-1\neq -27[/tex]

Note. As you can see those statements are false, so any of them is true, except item 3 that is unclear.

Answer:

its b and d

Step-by-step explanation:

i know

16/-8=-2

Whenever dividing a -negative number and +positive number= number will be always -

3  3/7 / 1  1/7= 24/7 *7/8= 3 ( Cross out 7 and 7, divide by 1). Cross out 8 and 24 and divide by 8) ( Also always flip over the second fraction only when dividing)

3 3/7= 24/7 because multiply the denominator and whole number. 3*7=21

Add 21 with the numerator (3)= 21+3=24

-12.2 / (-6.1)=2

Whenever dividing two - negative numbers= + positive number

-2 2/5 / 4/5= -12/5*5/4=-3 Cross out 5 and 5- divide by 5. Cross out 4 and -12, divide by 4

Answers:

- 2 = 16/-8=-2

3= 3  3/7 /( dividing )1 1/7= 3

2= -12.2 / (-6.1)=2

-3=-2 2/5 / ( dividing) 4/5=-3

Answer:

1). -2 = 16 ÷ (-8)

2) 3 = [tex]3\frac{3}{7}[/tex] ÷ [tex]1\frac{1}{7}[/tex]

3). 2 = (-12.2) ÷ (-6.1)

4). -3 = -[tex]2\frac{2}{5}[/tex] ÷ [tex]\frac{4}{5}[/tex]

Step-by-step explanation:

1). 16 ÷ (-8) = -[tex]\frac{16}{8}=-2[/tex]

2). [tex]3\frac{3}{7}[/tex] ÷ [tex]1\frac{1}{7}[/tex]

   = [tex]\frac{24}{7}[/tex] ÷ [tex]\frac{8}{7}[/tex]

   = [tex]\frac{24}{7}\times \frac{7}{8}[/tex]

   = 3

3). (-12.2) ÷ (-6.1)

   = [tex]\frac{12.2}{6.1}[/tex]

   = 2

4). -[tex]2\frac{2}{5}[/tex] ÷ [tex]\frac{4}{5}[/tex]

   = -[tex]\frac{12}{5}[/tex] ÷ [tex]\frac{4}{5}[/tex]

   = -[tex]\frac{12}{5}[/tex] × [tex]\frac{5}{4}[/tex]

   = -3

Answer:

There are 80 marks in total.

Step-by-step explanation:

Let the number of total marks be [tex]x[/tex].

The percentage score of the student can be written as the ratio

[tex]\displaystyle \frac{68}{x} = 85\%[/tex].

However,

[tex]\displaystyle 85\% = \frac{85}{100}[/tex].

Equating the two:

[tex]\displaystyle \frac{68}{x} = \frac{85}{100}[/tex].

Cross-multiply (that is: multiple both sides by [tex]100x[/tex], the product of the two denominators) to get

[tex]85x = 68\times 100[/tex].

[tex]\displaystyle x = \frac{68\times 100}{85} = 80[/tex].

In other words, there are 80 marks in total.

Answer:

B. 19

Step-by-step explanation:

g(x) = x^2+3

Let x=4

g(4) = 4^2 +3

       = 16+3

       =19

Answer:

b

Step-by-step explanation:

all work is shown and pictured

Answer:

12.9

Step-by-step explanation:

Intersecting chord segments are proportional, so:

35×a = 15×30

a = 12.9

The value of a in the intersecting chords is 12.9

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

The intersecting chords

Using the theorem of intersecting chords, we habe the following equation

a * 35 = 15 * 30

This gives

a = 15 * 30/35

Evaluate

a = 12.9

Hence, the value of a is 12.9

Read more about chords at

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For this case we have that by definition, the point-slope equation of a line is given by:

[tex]y-y_ {0} = m (x-x_ {0})[/tex]

We have as data that:

[tex](x_ {0}, y_ {0}): (- 6, -3)\\m = 4[/tex]

Substituting in the equation we have:

[tex]y - (- 3) = 4 (x - (- 6))\\y + 3 = 4 (x + 6)[/tex]

Finally, the equation is: [tex]y + 3 = 4 (x + 6)[/tex]

Answer:

[tex]y + 3 = 4 (x + 6)[/tex]

[tex]\huge{\boxed{y+3=4(x+6)}}[/tex]

Point-slope form is [tex]y-y_1=m(x-x_1)[/tex], where [tex]m[/tex] is the slope and [tex](x_1, y_1)[/tex] is a known point on the line.

Substitute in the values. [tex]y-(-3)=4(x-(-6))[/tex]

Simplify the negative subtraction. [tex]\boxed{y+3=4(x+6)}[/tex]

Answer:

Part A) [tex]x=6[/tex]

Part B) ∠3=29°

Part C) ∠1=29°

Part D) ∠2=151°

Step-by-step explanation:

Part A) If ∠3=5x-1 and ∠5=3x+11, then x=?

we know that

∠3=∠5 ----> by alternate interior angles

so

substitute and solve for x

[tex]5x-1=3x+11[/tex]

[tex]5x-3x=11+1[/tex]

[tex]2x=12[/tex]

[tex]x=6[/tex]

Part B) If ∠3=5x-1 and ∠5=3x+11, then the measure of ∠3=?

we know that

∠3=5x-1

The value of x is

[tex]x=6[/tex]

substitute

∠3=5(6)-1=29°

Part C) If ∠3=5x-1 and ∠5=3x+11, then the measure of ∠1=?

we know that

∠1=∠3 ----> by vertical angles

we have

∠3=29°

therefore

∠1=29°

Part D) If ∠3=5x-1 and ∠5=3x+11, then the measure of ∠2=?

we know that

∠1+∠2=180° ----> by supplementary angles

we have

∠1=29°

substitute

29°+∠2=180°

∠2=180°-29°

∠2=151°

Answer:

slope = 0

Step-by-step explanation:

The line with equation x = - 3 is a vertical line parallel to the y- axis

A perpendicular line is therefore a horizontal line parallel to the x- axis

The slope of the x- axis is zero, hence the slope of the horizontal line is

slope = 0

Answer:

13.7

Step-by-step explanation:

We know that sin(thetha) = BC/AB

In this case, thetha = 41, BC = 9in

→ AB = BC/sin(thetha)

→ AB = 9in/sin(41)

→ AB = 13.7

Therefore, the result is 13.7

Answer:

The correct answer is third option

13.8 in

Step-by-step explanation:

From the figure we can see a right angled triangle ABC, right angled at C,

m<A = 41°, and BC = 9 in

Points to remember

Sin θ = Opposite side/Hypotenuse

To find the value of AB

Sin 41 =  Opposite side/Hypotenuse

 = BC/AB

 = 9/AB

AB = 9/Sin(41)

 =13.8 in

The correct answer is third option

13.8 in

The sum of the length of all the ten movies is [tex]\fbox{\begin\\\ 780\text{ minutes}\\\end{minispace}}[/tex].

Step-by-step explanation:

It is given that a new movie is released each year for [tex]10[/tex] consecutive years so there are total number of [tex]10[/tex] movies released in [tex]10[/tex] years.

The movie released in first year is [tex]60\text{ minutes}[/tex] long and each movie released in the successive year is [tex]4\text{ minutes}[/tex] longer than the movie released in the last year.

So, as per the above statement movie released in first year is [tex]60[/tex] minutes long, movie released in second year is [tex]64[/tex] minutes long, movie released in third year is [tex]68[/tex] minutes long and so on.

The sequence of the length of the movie formed is as follows:

[tex]\fbox{\begin\\\ 60,64,68,72...\\\end{minispace}}[/tex]

The sequence formed above is an arithmetic sequence.

An arithmetic sequence is a sequence in which the difference between the each successive term and the previous term is always constant or fixed throughout the sequence.

The general term of an arithmetic sequence is given as

[tex]\fbox{\begin\\\math{a_{n} =a+(n-1)d}\\\end{minispace}}[/tex]

The sequence formed for the length of the movie is an arithmetic sequence in which the first term is [tex]60[/tex] and the common difference is [tex]4[/tex].

The arithmetic series corresponding to the arithmetic sequence of length of the movie is as follows:

[tex]\fbox{\begin\\\ 60+64+68+72+...\\\end{minispace}}[/tex]

The arithmetic series formula to obtain the sum of the above series is as follows:

[tex]\fbox{\begin\\\math{S_{n} =(n/2)(2a+(n-1)d)}\\\end{minispace}}[/tex]

In the above equation  [tex]n[/tex] denotes the total number of terms, a denotes the first term, d denotes the common difference and Sn denotes the sum of n terms of the series.

Substitute [tex]\fbox{\begin\\\math{a}=60\\\end{minispace}}[/tex],[tex]\fbox{\begin\\\math{n}=10\\\end{minispace}}[/tex] and [tex]\fbox{\begin\\\math{d}=4\\\end{minispace}}[/tex] in the equation [tex]\fbox{\begin\\\math{S_{n} =(n/2)(2a+(n-1)d)}\\\end{minispace}}[/tex]

[tex]S_{10} =(10/2)(120+36) \\S_{10} =780[/tex]

Therefore, the length of the all [tex]10[/tex] movies as calculated above is [tex]\fbox{\begin\\\ 780\text{ minutes}\\\end{minispace}}[/tex]

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Answer details

Grade: Middle school

Subject: Mathematics  

Chapter: Arithemetic preogression  

Keywords: Sequence, series, arithmetic , arithmetic sequence, arithmetic series, common difference, sum of series, pattern, arithmetic pattern, progression, arithmetic progression, successive terms.

Answer:  

The total length of all 10 movies is 780 minutes.  

Further Explanation:  

Arithmetic Sequence: A sequence of numbers in which difference of two successive numbers is constant.  

The sum of n terms of an arithmetic sequence is given by the formula,  

[tex]S_n=\dfrac{n}{2}[2a+(n-1)d][/tex]

Where,  

The first movie is 60 minutes long. This would be the first term of the sequence.  

Thus, First term, a= 60 minutes

A new movie is released each year for 10 years. In 10 years total 10 movies will released.  

Thus, Number of terms, n=10

Each movie is 4 minutes longer than the last released movie. It means the difference of length of two successive movie is 4 minutes.

Thus, Common difference, d=4

Using the sum of arithmetic sequence formula, the total length of all 10 movies is,

[tex]S_{10}=\dfrac{10}{2}[2\cdot 60+(10-1)\cdot 4][/tex]

[tex]S_{10}=\dfrac{10}{2}[2\cdot 60+9\cdot 4][/tex]                          [tex][\because 10-1=9][/tex]

[tex]S_{10}=\dfrac{10}{2}[120+36][/tex]                                  [tex][\because 2\cdot 60=120\text{ and }9\cdot 4=36][/tex]

[tex]S_{10}=\dfrac{10}{2}\times 156[/tex]                                      [tex][\because 120+36=156][/tex]

[tex]S_{10}=5\times 156[/tex]                                         [tex][\because 10\div 2=5][/tex]

[tex]S_{10}=780[/tex]                                                  [tex][\because 5\times 156=780][/tex]

Therefore, The total length of all 10 movies is 780 minutes

Learn more:  

Find nth term of series: https://brainly.com/question/11705914

Find sum: https://brainly.com/question/11741302

Find sum of series: https://brainly.com/question/12327525

Keywords:  

Arithmetic sequence, Arithmetic Series, Common difference, First term, AP progression, successive number, sum of natural number.

Answer:

$102.29 is the original price of the suit.

Explanation:

$x ------- 100% price (full price)

$35.80 --------------- 35% of the original price (100%-65%=35%).

To find x, use cross-products.

x=(35.80×100)/35 =3580/35 = approximately $102.29.

Answer:

The original price of the suit was $102.29.

Step-by-step explanation:

Alex purchased a new suit discounted by 65%.

He paid $35.80 for the suit.

Let the original price (100% price) be x.

After discount the price is given = 100% - 65% = 35%

35% of x = 35.80

0.35x = 35.80

x = [tex]\frac{35.80}{0.35}[/tex]

x = 102.2857 rounded to $102.29

The original price of the suit was $102.29.

Answer:

a. 3/4

Step-by-step explanation:

The expected value is the sum of each outcome times its probability.

If n is the total number of marbles, then the expected value is:

E = (3/8) (n) + (3/8) (n)

E = 3/4 n

sorry wrong question-

[tex]\bf ~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill &\$75000\\ P=\textit{original amount deposited}\\ r=rate\to 3.5\%\to \frac{3.5}{100}\dotfill &0.035\\ t=years\dotfill &10 \end{cases} \\\\\\ 75000=Pe^{0.035\cdot 10}\implies 75000=Pe^{0.35}\implies \cfrac{75000}{e^{0.35}}=P \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill 52851.61\approx P~\hfill[/tex]

Answer:

x = 6, y = 9

Step-by-step explanation:

One of the properties of a parallelogram is that the diagonals bisect each other, thus

y + 3 = 2x → (1)

2y = 3x → (2)

Subtract 3 from both sides in (1)

y = 2x - 3 → (3)

Substitute y = 2x - 3 into (2)

2(2x - 3) = 3x ← distribute left side

4x - 6 = 3x ( subtract 3x from both sides )

x - 6 = 0 ( add 6 to both sides )

x = 6

Substitute x = 6 in (3) for value of y

y = (2 × 6 ) - 3 = 12 - 3 = 9

Hence x = 6 and y = 9

Answer:

1 kg/m³

Step-by-step explanation:

Density is mass divided by volume.

D = M / V

D = 10 kg / 10 m³

D = 1 kg/m³

Answer:

1 kg/m³

Step-by-step explanation:

Answer:

$0.19.

Step-by-step explanation:

Unit rate / ounce = 2.66 / 14

= $0.19.