Henry buys a large boat for the summer, however he cannot pay the full amount of $32,000 at
once. He puts a down payment of $14,000 for the boat and receives a loan for the rest of the
payment of the boat. The loan has an interest rate of 5.5% and is to be paid out over 4 years.
What is Henry’s monthly payment, and how much does he end up paying for the boat overall?

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:

[tex]308.4579\ inches^2[/tex]

Step-by-step explanation:

We are given the height and radius

[tex]h=19\ inches\\r=5\ inches[/tex]

The formula for lateral area is:

[tex]LA = \pi rl[/tex]

We have to find lateral height first

[tex]l = \sqrt{r^2+h^2}\\  =\sqrt{5^2+19^2}\\ =\sqrt{25+361}\\=\sqrt{386}\\l=19.647\ inches[/tex]

Now,

[tex]LA = \pi rl\\= 3.14*5*19.647\\=308.4579\ inches^2[/tex]

Answer: [tex]308.61\ in^2[/tex]

Step-by-step explanation:

In order to calculate the lateral area of the traffic cone, we can use the following formula:

[tex]LA=\pi rl[/tex]

Where "r" is the radius and "l" is the slant height of the cone.

We need to find the slant height.  Knowing the height and the radius, we can calculate it with the Pythagorean Theorem:

[tex]a^2=b^2+c^2[/tex]

Where "a" is the hypotenuse and "b" and "c" are the legs of the triangle.

For this case, we can say that:

[tex]a=l\\b=19\ in\\c=5\ in[/tex]

Substituting anf solviing for "l", we get:

[tex]l^2=(19\ in)^2+(5\ in)^2\\\\l=\sqrt{(19\ in)^2+(5\ in)^2}\\\\l=19.6468\ in[/tex]

Now we can substitute values into the formula for calculate the lateral area of the traffic cone. This is:

[tex]LA=\pi (5 in)(19.6468\ in)=308.61\ in^2[/tex]

Answer:

Step-by-step explanation:

[tex]2x-3(x+4)=-5\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\2x+(-3)(x)+(-3)(4)=-5\\\\2x-3x-12=-5\qquad\text{add 12 to both sides}\\\\-x=7\qquad\text{change the signs}\\\\x=-7[/tex]

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:

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

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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]

Answer:

1+cot ²∅=csc² ∅

Step-by-step explanation:

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

Answer:

The quotient to the problem 806 ÷ 6 is 134.3333 and so forth.

The quotient of the expression 806 ÷ 6 will be 134.33.

What is Division method?

Division method is used to distributing a group of things into equal parts.

Given that;

The expression is,

806 ÷ 6

Now, Solve the expression by using long division as;

6 ) 806 ( 134.333.....

  - 6

---------

    20

  - 18

 -----------

      26

   -  24

    -------

         20

       - 18

       -------

           2

Thus, The quotient of the expression 806 ÷ 6 will be 134.33.

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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]

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-

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!

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:

The conjecture is that the sum is [tex]30^2+30=930[/tex].

Step-by-step explanation:

I don't see your table... but let's see if we can make a conjecture about the sum of the first 30 positive even numbers.

What is the sum of the first even number? 2=2

What is the sum of the first two even numbers? 2+4=6

What is the sum of the first three even numbers? 2+4+6=12

What is the sum of the first four even numbers? 2+4+6+8=20

What is the sum of the first five even numbers? 2+4+6+8+10=30

What is the sum of the first six even numbers? 2+4+6+8+10+12=42

Alright, let's stop there for a second.

So we have the following sequence of numbers to find a pattern for:

2,6,12,20,30,42,...

Let's look at the common differences:

6-2 ,  12-6 , 20-12 , 30-20, 42-30,...

 4  ,    6     ,  8      ,   10     , 12

No common difference here so let's move on too the second common differences:

6-4  ,  8-6,   10-8,   12-10

 2   ,    2  ,     2  ,     2

So there is a 2nd common difference which means the pattern is a quadratic.

So our expression is of the form [tex]ax^2+bx+c[/tex]

Let's plug in our numbers to come up with a system to solve:

If x=1 , then [tex]ax^2+bx+c=2[/tex]

That is, [tex]a(1)^2+b(1)+c=2[/tex] .

Simplifying this gives: [tex]a+b+c=2[/tex].

If x=2, then [tex]ax^2+bx+c=6[/tex]

That is, [tex]a(2)^2+b(2)+c=6[/tex]

Simplifying this gives: [tex]4a+2b+c=6[/tex].

If x=3, then [tex]ax^2+bx+c=12[/tex]

That is [tex]a(3)^2+b(3)+c=12[/tex]

Simplifying this gives: [tex]9a+3b+c=12[/tex].

So we have this system of equations:

 a+  b+  c=2

4a+2b+  c=6

9a+3b+  c=12

I'm going to set this up as a matrix:

[ 1    1    1    2 ]

[4   2    1    6 ]

[9   3    1    12]

Multiply first row by -4:

[ -4   -4    -4    -8 ]

[  4     2     1     6 ]

[  9     3     1     12]

Add equation 1 to 2:

[ -4    -4    -4     -8]

[   0    -2    -3    -2]

[   9    3      1      12]

Divide first row by -4:

[ 1     1        1       2]

[ 0    -2     -3     -2]

[9      3      1       12]

Multiply top row by -9:

[-9    -9      -9    -18]

[0    -2      -3       -2]

[ 9    3       1         12]

Add equation 3 to 1:

[0    -6      -8     -6]

[0    -2      -3      -2]

[9     3        1        12]

Multiply the second equation by -3:

[ 0    -6     -8     -6]

[0      6      9      6]

[9       3      1     12]

Add equation 1 to 2:

[0      -6    -8    -6]

[0       0     1       0]

[9       3      1       12]

Let's stop there the second row gives us c=0.

So the first row gives us -6b-8c=-6 where c=0 so -6b-8(0)=-6.

Let's solve this:

-6b-8(0)=-6

-6b-0=-6

-6b    =-6

  b    =1

So we have b=1 and c=0 and we haven't used that last equation yet:

9a+3b+c=12

9a+3(1)+0=12

9a+3+0=12

9a+3=12

9a=9

a=1

So your expression for the pattern is [tex]x^2+x+0[/tex] or just [tex]x^2+x[/tex].

Let's test it out for one of our terms in our sequence:

"What is the sum of the first four even numbers? 2+4+6+8=20"

So if we plug in 4 hopefully we get 20.

[tex]4^2+4[/tex]

[tex]16+4[/tex]

[tex]20[/tex]

Looks good!

Now we want to know what happens when you plug in 30.

[tex]30^2+30[/tex]

[tex]900+30[/tex]

[tex]930[/tex]

If you don't like this matrix way, I can think of something else let me.

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]

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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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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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:

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:

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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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.

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:

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°

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:

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]

[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:

$0.19.

Step-by-step explanation:

Unit rate / ounce = 2.66 / 14

= $0.19.

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!!!

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.

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:

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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