Answer:
i think the answer is 7776
for two dice its 6x6 36 then 36×6 216 then 216×6 1296 then 1296×6 7776
Answer: 7776 possible outcomes
Step-by-step explanation:
You know that each dice has 6 possible results.
1, 2, 3, 4 , 5 , 6
Then, if you throw 2 dice, the possible results are 6(for the first one)*6(for the second one) = 6*6 = 36
then, as you add another die, you add another 6 to that equation, this means that for 5 dice we have
combinations = 6*6*6*6*6 = 6^5 = 7776
But in this situation most of the numbers can be repeated, for example, then number 6, can be made from (1 + 1 + 1 + 1 + 2), (1 + 2 + 1 + 1 + 1), (1 + 1 + 1 + 2 + 1 +1)
etc, this means that the die that rolls a 2 can change, but the end result of the addition is the same, in this case the total range of possible values is the amount of dice times the biggest value minus the amount of dice times the smallest value:
5*6 - 5*1 = 30 - 5 = 25 possible results
So you have 7776 combinations that give a only 25 possible results (a number between 5 and 30)
what is the measure of ACE shown in the diagram below
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:
The secant angle is exactly half of the difference between the measure of the two arcs formed by it . (1)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]
Finding the Domain and Range of a Graph
Determine the domain and range for the graph below. Write your answer in interval notation and in set builder form using a compound inequality.
Domain written in interval notation:
Range written in interval notation:
Domain written in set builder form
Use a compound inequality:
{x| _________ }
Range written in set builder form
Use a compound inequality:
{y|_________ }
Answer:
Step-by-step explanation:
By looking at the graph I notice an open circle at (-4, -5) which means the function is not evaluable at -4, this restricts the domain.
The Domain of a function represents the set of values for which the function has an output.
The Range of a function is the set containing all the possible values associated with all input.
Domain in interval notation: (-4, 3]. The parenthesis denotes that the interval does not contain the extreme point -4. The brackets are the opposite.
Domain in set builder notation: [tex]$\{x |-4<x \leq 3 \}$[/tex]
Range in interval notation: (-5, -3]
Range in set builder notation: [tex]$\{y |-5<y \leq 3 \}$[/tex]
Answer:
1) Domain = {x ∈ R | -4 < x ≤ 3}
Step-by-step explanation:
In this case, we have a line segment made up by two points (-4,-5) and (3,-3)
1) To find the Domain, is to find the set of values x may assume for a function.
We can also write it as compound inequality which is a complete form of writing it since inform us the set, the conditions.
{x ∈ R | -4 < x ≤ 3}
Or simply the interval (-4,3]
2) Range or Image is the set of values y may assume once you plug it in valid values for the Domain.
{y ∈ R| -5>y≥-3} or Simply (-5, -3]
What is the y-intercept of the line given by the equation y=5x-21
O A. (0.21)
O B. (0,5)
O C. (0, -21)
O D. (0,-5)
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).
A 14-ounce can of tomato sauce costs $2.66. What is the unit rate per ounce? A. $0.16. B. $0.17. C. $0.18. D. $0.19.
Answer:
$0.19.
Step-by-step explanation:
Unit rate / ounce = 2.66 / 14
= $0.19.
A student gets 68 marks n therefore gets 85 percent total marks are?
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.
which of the following is equivalent to
6(2y - 4) + p
A. p+ 12y - 24
B. 6y + p - 24
C. p - 6(2y - 4)
D. 24 + 12y + p
Plz explain or show work on how you got the answer :)
The expression equivalent to 6(2y - 4) + p is p + 12y - 24, according to the distributive property of multiplication over subtraction.
Explanation: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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If x is a number that is 7 more than y, how do you express x as a function of y?
A. x = f(y) = 7 + x
B. x = f(y) = 7 + y
c. y = f(x) = 7x
D. y=f(x) =y-7
E. y=f(x) = 7+y
Answer:
B.
Step-by-step explanation:
We are given x is a number that is 7 more than y.
This means when you add 7 to y you get x.
So the equation for this is 7+y=x.
We want x as a function of y. So we want to replace x with f(y).
This means we have the function 7+y=f(y) or f(y)=7+y by symmetric property of equality.
Your answer is B.
Answer:
the answer is x = f(y) = 7 + y
Step-by-step explanation:
If / and m are parallel, which pairs of angles are congruent
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.
what is the slope of the line that contains the points (-1 8) and (5 -4)
Answer:
-2
Step-by-step explanation:
The slope of the line can be found using
m = (y2-y1)/ (x2-x1)
= (-4-8)/(5--1)
= (-4-8)/(5+1)
= -12/6
= -2
Answer:
The slope is -2.
Step-by-step explanation:
The slope formula is [tex]\Rightarrow \displaystyle \frac{Y_2-Y_1}{X_2-X_1}[/tex].
[tex]\displaystyle \frac{(-4)-8}{5-(-1)}=\frac{-12}{6}=-2[/tex]
[tex]\Large\textnormal{Therefore, the slope is -2, which is our answer.}[/tex]
Hope this helps!
Solve the formula Ax+By=C for y.
Step-by-step explanation:
Step-by-step explanation:
Ax+By=C
By=C-Ax
y=(C-Ax)/B
To solve the equation Ax + By = C for y, first subtract Ax from both sides to get By = C - Ax. Then, divide by B to isolate y, resulting in y = (C - Ax) / B.
Explanation:In order to solve the given formula Ax+By=C for y, we need to isolate y in the equation. The steps are as follows:
Subtract Ax from both sides of the equation. This gives us: By = C - Ax.Now, we want to solve for 'y'. To do this, we divide both sides of the equation by 'B'. So: y = (C - Ax) / B.And that's it! This is the formula solved for 'y'. It shows y in terms of A, B, C, and x.
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what the answer when you factor this polynomial expression.
3x2 + 30x + 75
Answer:
3(x + 5)(x+ 5)
Step-by-step explanation:
3x² + 30x + 75
Here's one way to do it.
Step 1. Factor out the highest common factor of all three terms.
You can factor out a 3.
3(x² +10x +25) = 0
Step 2. Factor the remaining polynomial
We must find two numbers whose product is 25 and whose sum is 10.
A little trial-and-error gives us 5 and 5.
5 × 5 = 25; 5 + 5 = 10
We can factor the expression as
3(x + 5)(x + 5)
To factorize a polynomial implies that, we want to get several algebraic expressions from the polynomial.
When [tex]3x^2 +30x + 75[/tex] is factored, the result is: [tex]3(x + 5)(x + 5)[/tex]
Given
[tex]3x^2 +30x + 75[/tex]
Factor out 3
[tex]3x^2 +30x + 75 = 3 \times (x^2 + 10x + 25)[/tex]
Expand the bracket
[tex]3x^2 +30x + 75 = 3 \times (x^2 + 5x + 5x + 25)[/tex]
Factorize
[tex]3x^2 +30x + 75 = 3 \times (x(x + 5) + 5(x + 5))[/tex]
Factor out x + 5
[tex]3x^2 +30x + 75 = 3 \times ((x + 5)(x + 5))[/tex]
So, we have:
[tex]3x^2 +30x + 75 = 3(x + 5)(x + 5)[/tex]
Hence, the factors of [tex]3x^2 +30x + 75[/tex] are 3 and (x + 5)
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I Need The Answer Plz Geometry Is Hard!!
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
Fatima wants to find the value of sin theta, given cot theta =4/7. Which identity would be best for Fatima to use?
Answer:
1+cot ²∅=csc² ∅
Step-by-step explanation:
Prove that the segments joining the midpoint of consecutive sides of an isosceles trapezoid form a rhombus.
Find the slope of DE and FG.
Answer:
See explanation
Step-by-step explanation:
a) To prove that DEFG is a rhombus, it is sufficient to prove that:
All the sides of the rhombus are congruent: [tex]|DG|\cong |GF| \cong |EF| \cong |DE|[/tex]The diagonals are perpendicularUsing 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]
A body of made 10kg and volume 10m³. Find the density of the body.
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:
How much money should be invested today in an account that earns 3.5%, compound daily, in order to accumulate $75000 in 10 years (assume n=365)
[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]
Solve for x,y, and z
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°
through: (2,-4), parallel to y=3x+24)
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
find the volume of a cylinder with a diameter of 10 inches and height of 20in
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
A bag contains red and blue marbles, such that the probability of drawing a blue marble is 3 over 8. an experiment consists of drawing a marble, replacing it, and drawing another marble. The two draws are independent. A random variable assigns the number of blue marbles to each outcome. Calculate the expected value of the random variable. a. 3 over 4 b. 1 over 3 c. 3 over 8 d. 2 over 3
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-
Drag the tiles to the correct boxes to complete the pairs.
Match each division expression to its quotient.
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
Vanessa kicked a soccer ball laying on the ground. It was in the air for 4 seconds before it hit the ground. While the soccer ball was in the air it reached a height of approximately 20 feet. Assuming that the soccer ball’s height (in feet) is a function of time (in seconds), what is the domain in the context of this problem?
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.
Explanation: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].
Explanation: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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Can someone helpppppp
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
What is the value of a to the nearest tenth?
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
How to determine the value of afrom 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
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Solve the equation. Show your work. 3x – 10 = 5x + 32
Answer:
-21 =x
Step-by-step explanation:
3x – 10 = 5x + 32
Subtract 3x from each side
3x-3x – 10 = 5x-3x + 32
-10 =2x +32
Subtract 32 from each side
-10 -32 = 2x+32-32
-42 = 2x
Divide each side by 2
-42/2 = 2x/2
-21 =x
Answer: [tex]x=-21[/tex]
Step-by-step explanation:
To solve the equation you need to find the value of "x".
First, you need to subtract 32 from both sides of the equation:
[tex]3x - 10 -32= 5x + 32-32\\\\3x - 42= 5x[/tex]
Now you must subtract [tex]3x[/tex] from both sides of the equation:
[tex]3x - 42-3x= 5x-3x\\\\- 42= 2x[/tex]
And finally divide both sides of the equation by 2. Then:
[tex]\frac{-42}{2}=\frac{2x}{2}\\\\x=-21[/tex]
A new movie is released each year for 10 years to go along with a popular book series. Each movie is 4 minutes longer than the last to go along with a plot twist. The first movie is 60 minutes long. Use an arithmetic series formula to determine the total length of all 10 movies.
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]
Learn more:
A problem to complete the square of quadratic function brainly.com/question/12992613A problem to determine the slope intercept form of a line brainly.com/question/1473992Inverse function brainly.com/question/1632445Answer 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,
a is the first term of the sequence. d is a common difference.n is number of terms[tex]S_n[/tex] is sum of n terms of the sequence.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.
Given point (-6, -3) and a slope of 4, write an equation in point-slope form. a. y - 3 = 4(x - 6) c. y + 3 = 4(x + 6) b. y + 3 = 4(x - 6) d. y - 3 = 4(x + 6) Please select the best answer from the choices provided A B C D
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]
Currently, you're working as a cashier at the grocery store. Your hourly wage is $11.55. If you earned $1074.15 over a two-week period how many hours did you work?
Answer:
93
Step-by-step explanation:
$11.55 per hour.
$1074.15 in two weeks.
1074.25 ÷ 11.55 = 93.
Answer:
93 hours.
Step-by-step explanation:
The question states that $1074.15 has been earned in a two weeks time (in 14 days total). The hourly wage rate is $11.55. To calculate the total number of hours worked in the two week time, following formula will be used:
Number of hours worked = Total income / Hourly wage rate.
Number of hours worked = 1074.15/11.55 = 93 hours.
Therefore, 93 hours have been worked in 2 weeks to earn the total money of $1074.15!!!
Could some please help with this math question
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
Determine two pairs of polar coordinates for the point (3, -3) with 0°≤ θ < 360°
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]