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Answer:

The third choice is the one you want.

Step-by-step explanation:

The formula for an arithmetic sequence is as follows:

[tex]a_{n}=a_{1}+d(n-1)[/tex]

Our first number is 8, so a1 = 8.  If the second term is 5, then d = -3.  Filling in our formula gives us this:

[tex]a_{n}=8-3(n-1)[/tex]

Now we need domain.  Our choices are n ≥ 1 and n ≥ 0 so let's try both.  Replace n in the formula with each one, one at a time, and see what the result is.

If n ≥ 0:

[tex]a_{0}=8-3(0-1)[/tex] so [tex]a_{0}=8-(-3)[/tex] which gives you that the first term, defined by [tex]a_{0}[/tex] is 11.  That's not correct.  Let's check n ≥ 1[tex]a_{1}=8-3(1-1)[/tex]

and [tex]a_{1}=8-0[/tex] which is 8, the first term.

Answer:

A. Permutation; number of ways = 720

Step-by-step explanation:

For the first medal, we have 6 runners that can earn it.  

For the second medal, we have 5 runners because there's one who won the first one.

For the third, we have 4 runners.

And so on up to the 6th medal where we have just one runner left.

As this happens all at the same time, we have to multiply them.

Ways to award the medals = 6*5*4*3*2*1 = 6! = 720

Remember that a permutation is a combination where the order matters. So, in this case, is a permutation because each medal is different.

Answer:

a) Permutation; number of ways = 720

Step-by-step explanation:

Answer:

  8r^4

Step-by-step explanation:

√(64r^8) = √((8r^4)^2) = 8r^4

_____

You can make use of either or both of these rules of exponents:

  (a^b)^c = a^(b·c) . . . . . used above

  [tex]\sqrt[n]{a}=a^{\frac{1}{n}}[/tex]

Using the second rule, you can write the expression as ...

[tex]\sqrt{64r^8}=\sqrt{64}\cdot r^{8\cdot\frac{1}{2}}=8r^4[/tex]

Answer:

B

Step-by-step explanation:

edg21

[tex]\bf \qquad \qquad \textit{sum of a finite geometric sequence} \\\\ \displaystyle S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases} n=\textit{last term's}\\ \qquad position\\ a_1=\textit{first term}\\ r=\textit{common ratio} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \begin{cases} r=-5\\ n=3\\ S_3=147 \end{cases} \implies 147=a_1\left( \cfrac{1-(-5)^3}{1-(-5)} \right)\implies 147=a_1\left( \cfrac{1-(-125)}{1+5} \right) \\\\\\ 147=a_1\cdot \cfrac{126}{6}\implies 147=21a_1\implies \cfrac{147}{21}=a_1\implies 7=a_1[/tex]

The first term of the geometric sequence with a common ratio of -5 and the sum of the first 3 terms being 147 is 7.

The first term of a geometric sequence where the common ratio is -5 and the sum of the first 3 terms is 147. A geometric sequence is denoted by a, ax, ax2, ax3, ..., where 'a' is the first term and 'x' is the common ratio.

Given the common ratio (x) is -5, we can express the first three terms of this geometric sequence as:

First term: a

Second term: a(-5) = -5a

Third term: a(-5)2 = 25a

The sum of these three terms equals 147:

a - 5a + 25a = 147

Combining like terms we get:

21a = 147

Now, dividing both sides by 21 to isolate 'a', we find:

a = 7

Therefore, the value of the first term of the sequence is 7.

Answer: The first box is circle and second box is rectangle.

Step-by-step explanation:

If you are asking about the shape of the cross section for a right circular cylinder, that is the case. A parabola or triangle can't be sliced so the cross section is parallel or perpendicular to the base.

If the cross section is parallel to the base, it is a circle.

If the cross section is perpendicular to the base, it is a rectangle.

Answer:

√129

Step-by-step explanation:

The distance formula between two points is:

d² = (x₂ − x₁)² + (y₂ − y₁)² + (z₂ − z₁)²

Plugging in:

d² = (4 − (-4))² + (-1 − 7)² + (-2 − (-3))²

d² = 8² + 8² + 1²

d² = 129

d = √129

Answer:

  $5308.79

Step-by-step explanation:

The future value can be computed from ...

  FV = P(1 +r/n)^(nt)

where P is the principal invested, r is the annual interest rate, n is the number of times per year it is compounded, and t is the number of years.

Filling in the given numbers, we have ...

  FV = $5000(1 +.03/12)^(12·2) ≈ $5308.79

Myron's withdrawal will be in the amount of $5308.79.

Answer: 24%

Step-by-step explanation:

2610+8120 = The undergraduates and graduates combined.

That is 10730. You are figuring out the probability the student is a graduate when those two graduates are combined, because that is all the data given. So you would do 2610/10730 in your calculator, resulting in 24.324324324%. As it says rounded to the nearest percent in parentheses, it has to round to the whole number, 24%, and .3 rounds down.

Answer:

  see below

Step-by-step explanation:

Eric will drive between 70 -4 = 66 mph and 70+4 = 74 mph. He will not drive less than 66 or more than 74 mph.

Answer:

Step-by-step explanation:

In general, solutions to absolute value inequalities, as in this case, take two forms:

If | x | <a, then x<a or x> -a.

If | x |> a, then x> a or x <-a.

In this case, you have |x − 70| ≤ 4. So, you have two cases:

x − 70 ≤ 4 and x − 70 ≥ -4

Solving both equations:

x − 70 ≤ 4      

x ≤ 4 + 70

x≤ 74

and

x - 70 ≥ -4

x ≥ -4+70

x ≥ 66

It is convenient to graph both solutions, as shown in the attached image .

The intersection between both conditions is the solution to the inequality (that is, in the image it is shown as the interval painted by both colors). In this case, the solution is 66≤x≤74

This indicates that Eric can drive within this speed range.

The range of speeds Eric would not drive at under the given conditions is x≤66 and x≥74,  as shown in the other image.

Answer with Step-by-step explanation:

Tara can spend at most $700

Restaurant charges $450 for the first 25 people and  $15 for each additional guest

Let x be the number of additional guest

⇒ 450+15x<700

⇒ 15x<250

⇒ x<250/15

⇒ x<16.67

Hence, Maximum additional guest can be 16

25+16=41

Hence,  the greatest number of people who can attend the shower is:

41

Answer:

t = 5.48

Step-by-step explanation:

f(x) = -5x² + 200

given f(t) = 50 when x = time(t)

Hence,

50 = -5t² + 200

5t² = 200 - 50

5t² = 150

t² = 30

t = √30 = 5.48

The number of seconds are 5.48, the correct option is C.

A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is  ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

We are given that;

f(x) = –5x2 + 200

Now,

To find the time when the ball is 50 meters from the ground, we need to solve the equation:

f(x) = 50

Substituting f(x) with -5x^2 + 200 and simplifying, we get:

-5x^2 + 200 = 50

-5x^2 = -150

x^2 = 30

x = ±√30

Since x represents time, we only consider the positive value of x. Therefore,

x ≈ 5.48

Therefore, by the quadratic equations the answer will be 5.48

Learn more about quadratic equations;

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Answer:

  Yes

Step-by-step explanation:

(3/8)·64 = 24 seats in the first class carriage are being used.

(7/13)·(78)·3 = 126 seats in the standard carriages are being used, for a total of ...

  24 + 126 = 150 . . . occupied seats

The number of available seats is ...

  64 +3·78 = 298

so half the seats on the train will be 298/2 = 149 seats.

  150 > 149, so more than half the seats on the train are being used.

Answer:

The surface area is [tex]SA=384\ mm^{2}[/tex]

Step-by-step explanation:

we know that

The surface area of the cube is equal to

[tex]SA=6s^{2}[/tex]

we have

[tex]s=8\ mm[/tex]

substitute

[tex]SA=6(8)^{2}[/tex]

[tex]SA=384\ mm^{2}[/tex]

Answer:

(-7,4)

Step-by-step explanation:

goal: (y-k)^2=4p(x-h)

y^2-8y=4x+12    Rearranged and added 4x and 12 on both sides

y^2-8y+(-8/2)^2=4x+12+(-8/2)^2 complete square time (add same thing on both sides)

y^2-8y+(-4)^2=4x+12+(-4)^2 (simplify inside the squares)

(y-4)^2=4x+12+16  (now write the left hand side as a square)

(y-4)^2=4x+28

(y-4)^2=4(x+7)    factored...

vertex is (-7,4)

Answer:

(-7,4)

Step-by-step explanation:

The answer is:

The correct option is A. 8.3.

To calculate the number of weeks that will pass, we need to use the given information.From the statement we know that we need to use the value of $600 substituting it as "y", and then, isolate "x", so, calculating we have:

[tex]log(y)=0.30x+0.296\\\\log(600)=0.30x+0.296\\\\2.78=0.30x+0.296\\\\2.78-0.296=0.30x\\\\x=\frac{2.78-0.296}{0.30}=8.28=8.3[/tex]

Hence, the correct option is A. 8.3.

Have a nice day!

Answer:

0

1

Step-by-step explanation:

First question:

You are given a side, a, and its opposite angle, A. You are also given side b. Use that in the law of sines and solve for the other angle, B.

[tex] \dfrac{a}{\sin A} = \dfrac{b}{\sin B} [/tex]

[tex] \dfrac{10}{\sin 30^\circ} = \dfrac{40}{\sin B} [/tex]

[tex] \dfrac{1}{0.5} = \dfrac{4}{\sin B} [/tex]

[tex] \sin B = 2 [/tex]

The sine function can never equal 2, so there is no triangle in this case.

Answer: no triangle

Second question:

You are given a side, b, and its opposite angle, B. You are also given side c. Use that in the law of sines and solve for the other angle, C.

[tex] \dfrac{b}{\sin B} = \dfrac{c}{\sin C} [/tex]

[tex] \dfrac{10}{\sin 63^\circ} = \dfrac{}{\sin C} [/tex]

[tex] \sin C = \dfrac{8.9\sin 63^\circ}{10} [/tex]

[tex] C = \sin^{-1} \dfrac{8.9\sin 63^\circ}{10} [/tex]

[tex] C \approx 52.5^\circ [/tex]

One triangle exists for sure. Now we see if there is a second one.

Now we look at the supplement of angle C.

m<C = 52.5°

supplement of angle C: m<C' = 180° - 52.5° = 127.5°

We add the measures of angles B and the supplement of angle C:

m<B + m<C' = 63° + 127.5° = 190.5°

Since the sum of the measures of these two angles is already more than 180°, the supplement of angle C cannot be an angle of the triangle.

Answer: one triangle

In the first case with measures a=10, b=40, A=30°, no triangle can be formed as a is smaller than b sin(A). In the second case with measures b=10, c=8.9, B=63°, one triangle can be formed because b is greater than c.

In the context of the Ambiguous Case of the Law of Sines, we can find the number of triangles formed given the measures. For the first case, a = 10, b = 40, and A = 30°, no triangle can be formed because a is less than b sin(A), which means the given side (a) is too short to reach the other side (b).

For the second case, b = 10, c = 8.9, and B = 63°, one triangle can be formed. Here, b is greater than c and therefore capable of forming one valid triangle as per the Ambiguous Case of the Law of Sines.

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Answer:

56.3 cm

Step-by-step explanation:

(sinA)/(27) = (sinC)/c

(sin28°)/(27) = (sin102°)/c

For this case we have that by definition, the sum of the internal angles of a triangle is 180 degrees.

Then we look for the measure of the third angle:

[tex]102 + 28 + x = 180\\x = 180-102-28\\x = 50[/tex]

According to the Law of sines:

[tex]\frac {sin (50)} {a} = \frac {Sin (28)} {27}\\a = \frac {27 * sin (50)} {sin (28)}\\a = \frac {0.76604444 * 27} {0.46947156}\\a = 44.06[/tex]

Answer:

[tex]a = 44.1[/tex]

Answer:

  1

Step-by-step explanation:

The constant term in a perfect square trinomial with leading coefficient 1 is the square of half the coefficient of the linear term.

  (2/2)² = 1

The missing constant term is 1.

Answer:  The correct answer is:  " 1 " .

_____________________________________________________

                               →   "  x²  +  2x  +    1     =   (x + 1)²  " .

_____________________________________________________

_____________________________________________________

Step-by-step explanation:

_____________________________________________________

Let us assume that the question asks us to solve for the "missing constant term in the following equation:  

      →   " x² + 2x + b = 0 " ;  

      →  in which:  " b " is the "missing constant term" for which we shall solve.

_____________________________________________________

The form of an equation in the perfect square would be:

                →  (x + b) ² =  x² + 2bx + b²  ;

                →  In our case, "b" ; refer to the "missing constant term" for which we shall solve.

_____________________________________________________

      →   " x² + 2x + b = 0 " ;  

       Note that the term in the equation with the highest degree (highest exponent) is:  

            →  " x² " ;  with an "implied coefficient" of: " 1 " (one) ;

      →   {since "any value" , multiplied by " 1 " , results in that same initial value.}.

      →   Since the term with the highest degree has a "co-efficient" of " 1 " ;

  we can solve the problem;   i.e. "Solve for "b" ;  accordingly:

_____________________________________________________

      →   " x² + 2x + b = 0 " ;

Subtract "b" from each side of the equation:

      →   " x² + 2x + b - b = 0 - b " ;

      →  to get:

      →   x² + 2x  =  - b

Now we want to complete x² + 2x into a perfect square.

To do so, we take the:  "2" (from the:  "+2x" );  

     →  and we divide that value {in our case, "2"};  by "2" ;

to get:  "[2/2]" ;  and then we "square" that value;

     →  to get:  " [2/2]² " .

_____________________________________________________

Now, we add this "squared value" to:  " x² + 2x " ;  as follows:

     →  " x² + 2x + [2/2]² " ;  and simply:  " [2/2]² = [1]² = 1 ."

_____________________________________________________

     x² + 2x + (2/2)² = x² + 2x + 1 ;

                              =  (x + 1)² ;

_____________________________________________________

Now:  " x² + 2x = - b " ;

 We add "(2/2)² " ;  to each side of the equation;

 →  In our case,  " [2/2]² = [1]² = 1 " ;

 →  As such, we add:  " 1 " ;  to each side of the equation:

              →   x² + 2x + (2/2)² =  - b + (2/2)² ;

              →  Rewrite;  substituting " 1 " [for:  " (2/2)² "] :

              →   x² + 2x + 1  =  1 - b ;                                          

              →   x² + 2x + 1   = 1 - b ;

_____________________________________________________

And assume "b" would equal "1" ;

 since assuming the question refers to the equation:

     "x²  +  2x  ±   b = 0 " ;  solve for "b" ;  

And:   "b = 1 " ;

Then:  " x² + 2x + 1 = ?  1 - b  ??

       →  then:   " 1 - b = 0 "  ;  Solve for "b" ;

       →  Add "b" to each side of the equation:

                      " 1 - b + b = 0 + b " ;

       →  to get:  " 1 = b "  ;   ↔ " b =  1 "  ;  Yes!

___________________________________________________

Also, to check our work:

_____________________________________________________

Remember, from above:

_____________________________________________________  

" The form of an equation in the perfect square would be:

                →  (x + b)²  =  x²  +  2bx + b² " ;  _____________________________________________________

   →  Let us substitute "1" for all values of "b" :

                  →   "  (x + 1) ²  =   x² + 2*(b)*(1)  +   1²  "  ;

                  →   "  (x + 1)²   =   x²  +  (2*1*1)   +  (1*1) "  ;

                  →   "  (x + 1)²   = ?  x²  +  2  +  1 "  ?? ;  Yes!

                  →  However, let us check for sure!

 _____________________________________________________

→   Expand:  " (x + 1)²  " ;  

→  " (x + 1)² = (x + 1)(x + 1) " ;

_____________________________________________________

   →  " (x + 1)(x + 1) " ;  

_____________________________________________________

Note the following property of multiplication:

_____________________________________________________

 →   " (a + b)(c + d)  =  ac  +  ad  +  bc  +  bd " ;

_____________________________________________________

As such:

_____________________________________________________

         →  " (x + 1)(x + 1) " ;

              =  (x*x) + (1x) + (1x) + (1*1) ;

              =  x²  +  1x + 1x + 1 ;

        →  Combine the "like terms" :

              + 1x + 1x = + 2x ;  

And rewrite:

              =   x²  +  2x + 1 .

_____________________________________________________

"  (x + 1)²   = ?  x²  +  2  +  1 "  ?? ;  Yes!

_____________________________________________________

    →   So:  The answer is:  " 1 " .

_____________________________________________________

   →  " x² + 2x +  1    =  (x + 1)²  " .

_____________________________________________________

Hope this answer helped!

    Best wishes to you in your academic endeavors

            — and within the "Brainly" community!

_____________________________________________________

Answer:

x= -5/7

Step-by-step explanation:

The equation involves only one variable x.

so, we have to isolate the variable to get the solution of the equation

Given

[tex]2(4 - 2x) - 3 = 5(2x + 3)\\8-4x -3 = 10x+15\\5-4x = 10x+15\\-4x = 10x +15 -5\\-4x-10x=10\\-14x = 10\\x = \frac{10}{-14}\\ x = -\frac{x=5}{7}[/tex]

Hence the value of x or solution is

x= -5/7

Answer:

B) 16 ft, 10.5 in

Step-by-step explanation:

There are a few different ways you can work this. Since we want to know the difference between length and heigh of the model and we are given skull length of the model, it makes a certain amount of sense to find the corresponding measurements of the actual skeleton.

The actual skeleton's length was 40 ft and its height was 13 ft, so the difference between these dimensions is ...

40 ft - 13 ft = 27 ft

The actual skull is 5 ft long, so the difference is ...

(27 ft)/(5 ft) = 5.4

times the length of the skull.

The same ratio will apply to the model, so the difference between the model height and model length is 5.4 times the length of the model skull:

desired difference = 5.4 × 3 ft 1.5 in = 16.2 ft + 8.1 in

= 16 ft 10.5 in

[tex]\bf \qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &8227\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ t=\textit{elapsed time}\ \end{cases} \\\\\\ A=8227(1-0.07)^t\implies A=8227(0.93)^t[/tex]

Final answer:

An exponential decay model represents the car's value decreasing each year by 7%, with the equation V = 8227 x (1 - 0.07)^t, where V is the car's value and t is the time in years.

Explanation:

The student is dealing with a depreciation problem in which a car decreases in value by a fixed percentage each year. To express this situation mathematically, we can use an exponential decay model. With an initial value of $8227 and an annual decrease rate of 7%, the equation to represent the car's value V at any time t in years can be written as:

V = 8227 times (1 - 0.07)^t

This equation models the car's value as it depreciates 7% per year from its initial value. When t is 0 (at the time of purchase), V will be $8227, indicating the initial value.

Answer:

Domain is 2 and range is 4

Step-by-step explanation:

William Jones

The number pi (π) is a platonic concept and has been used for 4000 years. The number pi can be approached but never reached. In general, this number means the constant ratio of the circumference to the diameter of any circle. Ancient Babylonians, Egyptians, and even Archimedes, one of the greatest mathematicians of the ancient world tried to approximate the value of pi, but in the 1700s, mathematicians began using the Greek letter π that was introduced by William Jones, in his second book Synopsis Palmariorum Matheseos or A New Introduction to the Mathematics base. Then, this symbol was popularized and adopted in 1737 by the greatest mathematician Leonhard Euler.

The inequality that represents Sam's situation is: x <= 18.67

To determine the inequality that represents Sam's situation, we can use the following formula for compound interest:

A = P(1 + r/n)^(nt)

where:

A is the final amount

P is the principal amount

r is the interest rate

n is the number of compounding periods per year

t is the number of years

We know that Sam initially invested $4,500 (P = 4500) and that the interest rate is 3% (r = 0.03). We also know that Sam wants to determine the number of years, x (t = x), for which the account will have less than or equal to $7,020 (A = 7020).

Substituting these values into the formula, we get the following inequality:

7020 <= 4500(1 + 0.03/1)^(1x)

Solving for x, we get:

x <= log(7020/4500) / (0.03/1)

x <= 18.67

Therefore, the inequality that represents Sam's situation is:

x <= 18.67

For such more question on inequality

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1. To sketch the function f(x) = (2/3)x - 3, we first need to find two points that we can later join to sketch the line, for example the x- and y-intercepts.

a) The x-intercept occurs when f(x) = 0, so if f(x) = 0, then:

f(x) = (2/3)x - 3

0 = (2/3)x - 3

3 = (2/3)x (Add three to both sides)

3*(3/2) = x (Multiply both sides by 3/2)

9/2 = x

We have now found the x-intercept at (9/2, 0)

b) The y-intercept occurs when x = 0, so:

f(x) = (2/3)x - 3

f(0) = (2/3)*0 - 3

f(0) = -3

Now we know that the y-intercept is at (0, -3)

c) All that's left is to sketch the graph axes and label them, plot the two points, join them together using a ruler and label their coordinates.

2. The Domain is the range of x-values for which the function exists, and the Range is the range of y-values for which the function exists.

Since there haven't been any constraints specified, we can say that both the Domain and Range are (-∞, ∞), since the graph continues forever both along the x- and y-axis.

(Note that this isn't always the case and would change if, for example, the question stipulated that there was a domain of [0, 5] and you had to find the range. Then, you would calculate the value of y at each end of the domain (if x = 0, y = -3 and if x = 5, y = 1/3) - in my example, the range would thus be [-3, 1/3].)

Answer:

D=5/2

Step-by-step explanation:

Circumference of a circle = πD where D is the diameter of the circle.

In the question Circumference is =55/7 and π provided =22/7

55/7 = (22/7)D

We multiply both sides with the reciprocal f 22/7

D = (55/7) (7/22)

D = 5/2

Answer:

  $851.62

Step-by-step explanation:

The value multiplier wll be ...

  (1 +r/n)^(nt)

where r is the annual interest rate (3.8%), n is the number of compoundings per year (12), and t is the number of years (3). Filling in these numbers, we see the ending value will be ...

  A = $760(1 +.038/12)^(12·3) = $760(1.0031667^36) = $851.62

Answer:

$851.62

Step-by-step explanation:

Answer: The height of the robot is 200 millimeters

Step-by-step explanation:

Answer:

It is 1,200

Step-by-step explanation:

Answer:

168

Step-by-step explanation:

The first equation given as  [tex]10.50a+3.75b=2071.50[/tex]

Where a is the number of adults and b is the number of students

Since, the number of students are given as 82, we can plug 82 into b and then do algebra and solve for a (shown below):

[tex]10.50a+3.75b=2071.50\\10.50a+3.75(82)=2071.50\\10.50a+307.5=2071.50\\10.50a=2071.50-307.5\\10.50a=1764\\a=\frac{1764}{10.50}\\a=168[/tex]

Thus, 168 adult tickets were sold

Answer:

It's 224.

Step-by-step explanation:

We use the power rule for a derivative.

If f(x) = ax^n then the derivative  f'(x) = anx^(n-1).

So the derivative of 12x^2 + 8x

= 2*12 x^(2-1) + 8x^(1-1)

= 24x + 8x^0

= 24x + 8.

When x = 9 the derivative = 24(9) + 8

=  224.

The value of first order derivative with x=9 is 224. Therefore, option D is the correct answer.

The process of finding derivatives of a function is called differentiation in calculus. A derivative is the rate of change of a function with respect to another quantity.

The given function is f(x)=12x²+8x at x=9.

Here, first order derivative is

f'(x)=24x+8

= 24×9+8

= 224

Therefore, option D is the correct answer.

To learn more about the differentiation of an equations visit:

https://brainly.com/question/25731911.

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