For the following geometric sequence find the explicit formula.
(12, -6, 3, ...]

The average of the five consecutive numbers ending with b in discuss when expressed in terms of a is; Choice D; a+3.

First, since it was given in the task content that the average of six positive consecutive odd integers starting with a is equal to b, it therefore follows that;

(a+a+2+a+4+a+6+a+8+a+10)/6 = b

6b=6a+30

b=a+5

Also, let the average of the consecutive intergers ending with b be denoted by; x.

(b+b-1+b-2+b-3+b-4)/5 = x

=(5b-10)/5

=b–2

The average, x=b – 2 (where b = a-5)

Ultimately, the value of the required average is; = a+5-2 = a+3.

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Answer:

About 1/4 scored higher and 3/4 scored lower

Step-by-step explanation:

84 is on the right side line

Each line represents 25 % of the score

It is 75 percent ( 3 lines) of the way

She scored higher than 75% of the students and lower than 25% of the students

About 1/4 scored higher and 3/4 scored lower

Answer:

8.5 years

Step-by-step explanation:

It will take 102 more payments

8.5 years

Interest will be $26,239

It would take approximately 15 years to pay back the loan of 95000 which is compounding monthly and the rate of interest is 6%.

Compound interest is basically the interest which is calculated on the primcipal with addition to aggregate interest. The formula of sum after compounding is as under:

S=P[tex](1+r/n)^{nt}[/tex] in which P is principal amount, r is rate per annum, n is number of times of compounding and t is time period.

We have been given that the amount of loan is $95000, installment is $1200 , rate of interest is 6% and it is compounded monthly.

First of all we have to find the effective rate=6%/12=0.005.

The future value of 95000 at a rate of 6% compunded monthly should be equal to the amount of all installments. So,

95000[tex](1+0.005)^{12n}[/tex]=12*1200*n

95000[tex]1.005^{12n}[/tex]=14400n

[tex]1.005^{12n}[/tex]=14400n/95000

[tex]1.005^{12n}[/tex]=0.1515n

We have to make graph of this to find the value of n which after graphing will come approx 15.

Hence it would take 15 years to pay back loan amount.

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The value of x which S(x) is a global minimum is x = 1/2

From the question, we have:

This means that:

S(x) = 1/x + 4x^2

From the question, we understand that x is a positive number.

This means that the domain of x is x > 0

As a notation, we have (0, ∞)

Recall that:

S(x) = 1/x + 4x^2

Differentiate the function

S'(x) = -1/x^2 + 8x

Set to 0

-1/x^2 + 8x = 0

Multiply through by x^2

-1 + 8x^3 = 0

Add 1 to both sides

8x^3 = 1

Divide by 8

x^3 = 1/8

Take the cube root of both sides

x = 1/2

To prove the point is a global minimum, we have:

S'(x) = -1/x^2 + 8x

Determine the second derivative

S''(x) = 2/x^3 + 8

Set x = 1/2

S''(x) = 2/(1/2)^3 + 8

Evaluate the exponent

S''(x) = 2/1/8 + 8

Evaluate the quotient

S''(x) = 16 + 8

Evaluate the sum

S''(x) = 24

Because S'' is positive, then the single critical point is a global minimum

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We get $593,940

Answer:

Solution Given:

1 second = $ 521

19 minutes=19*60=1140 seconds

1140 seconds =$521*1140 =$593,940

Answer:

$593,940

Step-by-step explanation:

$521 for every second

First, you need to multiply 60 with 19, since there are 60 seconds in a minute.

We get: 60 × 19 = 1140

Now multiply $521 with 1140

We get: 521 × 19 = 593,940

Final result: $593,940

Hope this helps :)

Hi

if he has 24 point he scored 24/ 6 = 4 times

As he score points every 11 ennemies,

He had : 4*11= 44 ennemies.

Using Euler's Formula, the number of faces is given by: 8.

It states that the number of vertices, edges and faces is related by the following equation:

V - E + F = 2.

In this problem, the parameters are given as follows:

E = 15, V = 9.

Hence the number of faces is given by:

V - E + F = 2.

9 - 15 + F = 2

F - 6 = 2

F = 8.

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Answer:

Length = 30ft, Width = 5ft

Step-by-step explanation:

Let x be the width.

Area of Rectangle = Length * Width

Given from the information in the question,

Length = 6x ft

Width = x ft

Substitute the values into the formula:

6x * x = 150

[tex]6x^{2}[/tex] = 150

[tex]x^{2} =\frac{150}{6}[/tex]

[tex]x^{2} =25[/tex]

[tex]x=\sqrt{25}[/tex]

x = 5 ft.

Therefore,

Length = 6 * 5 = 30ft

Width = 5 ft.

Answer: 120

Step-by-step explanation: The pattern is a very weird pattern, but still a pattern.

The pattern starts with number 2 to the power of 2, and then subtract 1. This is 3.

Then we keep using this same pattern, keeping the exponent the same but increasing the numbers. 3^2 is 9, and subtracting 1 gives 8.

Then the pattern skips two numbers 4 and 5. So for every 2 numbers that is squared and subtracted 1, 2 other numbers are not apart of the pattern.

So the next is 6^2, which is 36-1 which is 35.

Then 7^2 is 49 and subtracting 1 is 48.

Then, ignoring the next 2 numbers because of the pattern, we have 10^2 which is 100, and subtracting 1 is 99.

Now the next number is 11^2 which is 121, and subtracting 1 is 120.

Hope this helped! If it did, please mark as Brainliest.

Answer:

105°

Step-by-step explanation:

EFGH is an isosceles trapezoid (a trapezoid with congruent legs is an isosceles trapezoid)

∠G=75° (base angles of an isosceles trapezoid are congruent)

∠F=105° (same-side interior angles theorem)

Answer:

-181 - 79x

Step-by-step explanation:

I am not sure your comment fits the given problem.

I get the following approach and solution :

T(1 + 4x) = 1×a + 4x×b = 2 + 2x

a = 2 + 2x - 4xb

T(4 + 15x) = 4×a + 15x×b = -3 + 3x

4×(2 + 2x - 4xb) + 15xb = -3 + 3x

8 + 8x - 16xb + 15xb = -3 + 3x

11 + 5x - xb = 0

11 + 5x = xb

b = (11 + 5x)/x

a = 2 + 2x - 4x(11 + 5x)/x = 2 + 2x - 44 - 20x = -42 - 18x

T(3 - 5x) = 3×a - 5xb = 3(-42 - 18x) - 5x(11 + 5x)/x =

= -126 - 54x - 55 - 25x = -181 - 79x

control :

T(1 + 4x) = a + 4xb = -42 - 18x + 44 + 20x = 2 + 2x

T(4 + 15x) = 4a + 15xb = -168 - 72x + 165 + 75x = -3 + 3x

Answer:

Equation of a line has a form as below:

y=ax+b

Given:

b ( the y intercept)= -5

a ( the slope)= -3

so, y= -3x -5 is the equation of the line.

Please give me Brainliest [:)

Answer:

AD-DB

Step-by-step explanation:

Because ti joins altogether

Answer:

4th option

Step-by-step explanation:

given Δ ABD and Δ CBD are congruent then corresponding sides are congruent, that is

AB ≡ BC

[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

[tex]\qquad \sf  \dashrightarrow \: 1 \: \: cm {}^{3} = \cfrac{1}{1000000} \: \: m {}^{3} [/tex]

[tex]\qquad \sf  \dashrightarrow \: 1 \: \: cm {}^{3} = \cfrac{1}{10 {}^{6} } \: \: m {}^{3} [/tex]

[tex]\qquad \sf  \dashrightarrow \: 1 \: \: cm {}^{3} = {}{10 {}^{ - 6} } \: \: m {}^{3} [/tex]

Converting the portions to decimal, the grade that has the greatest portion of students is: 3rd grade.

The bigger the digit that is close to the decimal point, the bigger the number given.

Also, percentage can be converted to decimal by dividing the given percent by 100. Percent means over 100.

Fractions can also be converted to decimals by simply dividing the numerator by the denominator.

To compare the portion of students interested in playing an instrument in each grade, let all the portions be in decimals.

Converting 25/36 to decimal, we have: 0.694 (3rd grade)

Converting 61.24% to decimal, we have: 61.24/100 = 0.6124 (4th grade)

From the rest of the portions given, 0.694 is greater than the others.

Therefore, the grade that has the greatest portion of students is: 3rd grade.

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One way to capture the domain of integration is with the set

[tex]D = \left\{(x,y) \mid 0 \le x \le 1 \text{ and } -x \le y \le 0\right\}[/tex]

Then we can write the double integral as the iterated integral

[tex]\displaystyle \iint_D \cos(y+x) \, dA = \int_0^1 \int_{-x}^0 \cos(y+x) \, dy \, dx[/tex]

Compute the integral with respect to [tex]y[/tex].

[tex]\displaystyle \int_{-x}^0 \cos(y+x) \, dy = \sin(y+x)\bigg|_{y=-x}^{y=0} = \sin(0+x) - \sin(-x+x) = \sin(x)[/tex]

Compute the remaining integral.

[tex]\displaystyle \int_0^1 \sin(x) \, dx = -\cos(x) \bigg|_{x=0}^{x=1} = -\cos(1) + \cos(0) = \boxed{1 - \cos(1)}[/tex]

We could also swap the order of integration variables by writing

[tex]D = \left\{(x,y) \mid -1 \le y \le 0 \text{ and } -y \le x \le 1\right\}[/tex]

and

[tex]\displaystyle \iint_D \cos(y+x) \, dA = \int_{-1}^0 \int_{-y}^1 \cos(y+x) \, dx\, dy[/tex]

and this would have led to the same result.

[tex]\displaystyle \int_{-y}^1 \cos(y+x) \, dx = \sin(y+x)\bigg|_{x=-y}^{x=1} = \sin(y+1) - \sin(y-y) = \sin(y+1)[/tex]

[tex]\displaystyle \int_{-1}^0 \sin(y+1) \, dy = -\cos(y+1)\bigg|_{y=-1}^{y=0} = -\cos(0+1) + \cos(-1+1) = 1 - \cos(1)[/tex]

The preparation of the Cost of Goods Sold Budget for MingWare Ceramics Inc. in September is as follows:

Beginning inventory of finished goods $11,850

Cost of goods manufactured                485,310

Ending inventory of finished goods      (12,670)

Cost of Goods Sold                          $484,490

The cost of goods sold budget sums the costs of the beginning inventory of finished goods with the cost of goods manufactured and subtracts the ending inventory of finished goods.

The cost of goods sold budget is based on the cost of goods manufactured budget.

Direct materials:                            Enamel        Paint     Porcelain      Total    

Total direct materials purchases

budgeted for September            $35,870    $7,530    $139,890  $183,290

Estimated inventory, September 1   1,730        4,150          6,920      12,800 Desired inventory, September 30 (2,980)      (2,710)         (7,150)    (12,840)

Materials used in production                                                          $183,250

Direct labor cost:           Kiln Department    Decorating Department   Total

Total direct labor cost

 budgeted for September    $51,550                   $149,500        $201,050

Finished goods inventories:             Dish       Bowl     Figurine             Total

Estimated inventory, September 1  $5,810   $3,310     $2,730        $11,850

Desired inventory, September 30    3,720    4,590       4,360         12,670

Work in process inventories:

 Estimated inventory, September 1      $3,540

Direct materials used in production $183,250

Direct labor costs                              $201,050

Total factory overhead costs             $99,450

 Desired inventory, September 30       (1,980)

Cost of goods manufactured           $485,310

Indirect factory wages $80,400

Depreciation of plant and equipment 10,550

Power and light 5,110

Indirect materials 3,390

Total 99,450

Thus, to prepare the cost of goods sold, as above, MingWare Ceramics, requires to determine the cost of goods manufactured for September.

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The area of the square in terms of x unit is x²/ 2

The expression for the diagonal of a square is written as'

d^2=s^2+s^2

Where

But from the given question we have that the diagonal of the said square is 'x'

Now, let's substitute the values into the expression of the diagonal given above,

d^2=s^2+s^2

d² = s² + s²

We have,

x² = s² + s²

Collect and add like terms

x² = 2s²

But we know that s² represents the area of the square

So,

x² = 2 × area

Make 'area' subject of formula

Area = x²/ 2

Now, we can say that the area of the square in terms of x units is x²/2

Therefore, the area of the square in terms of x unit is x²/ 2

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Answer:

B. 45.7

Step-by-step explanation:

20/6=3.33

3.33*14=46.62

46.62 is closest to 45.7

Therefore, 45.7 is the best answer.

The slope of another line is changed to 20 degree to keep the segments parallel.

According to the statement

We have given that the If ac is parallel to bd and m <5 is decreased by 20 degrees And we have to find that the how must m <2 be changed to keep the lines parallel.

So, For this purpose,

We know that the Slope or gradient of a line is a number that describes both the direction and the steepness of the line.

And here

The slopes of two lines will only same when these lines are parallel.

In other words, Only parallel lines have a same slope.

So, if slope of one line is decreased by 20 degree then we have to kept these line parallel. Then we have to decrease the slope of other line by 30 degree also.

So, The slope of another line is changed to 20 degree to keep the segments parallel.

Disclaimer: This question was incomplete. Please find the full content below.

Question:

If ac is parallel to bd and m <5 is decreased by 20 degrees how must m <2 be changed to keep the lines parallel?

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[tex]y = \frac{ - 1}{4} x + \frac{1}{2} [/tex]

Considering the given quadratic equation for the number of automobiles, we have that:

A) The equation to be solved is: x² + 12x - 133 = 0

B) The first year was of 1987.

A quadratic function is given according to the following rule:

[tex]y = ax^2 + bx + c[/tex]

The solutions are:

In which:

[tex]\Delta = b^2 - 4ac[/tex]

The number of automobiles, in x years after 1980, is modeled by:

A(x) = 2x² + 24x + 300.

The amount is of 566,000 when A(x) = 566, hence the equation is:

2x² + 24x + 300 = 566

2x² + 24x - 266 = 0

x² + 12x - 133 = 0

The coefficients are a = 1, b = 12, c = -133, hence:

Time is a positive measure, hence we take the solution of 7, 1980 + 7 = 1987, which is the year.

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a. The area on [0, 10] is that of a trapezoid with bases 5 and 15 and height 10, so

[tex]\displaystyle \int_0^{10} f(x) \, dx = \frac{5+15}2\cdot10 = \boxed{100}[/tex]

b. By linearity of the definite integral, we have

[tex]\displaystyle \int_0^{25} f(x)\,dx = \int_0^{10} f(x)\,dx + \int_{10}^{25} f(x)\,dx[/tex]

and the area on [10, 25] is another trapezoid with bases 15 and 7.5 and height 15, so that

[tex]\displaystyle \int_{10}^{25} f(x)\,dx = \frac{15+7.5}2\cdot15 = 168.75[/tex]

Then the total area on [0, 25] is

[tex]\displaystyle \int_0^{25} f(x)\,dx = \boxed{268.75}[/tex]

c. The area on [25, 35] is that of a triangle with base 10 and height 15. However, [tex]f(x)<0[/tex] on this interval, so we multiply this area by -1 to get

[tex]\displaystyle \int_{25}^{35} f(x)\,dx = -\frac{10\cdot15}2 = \boxed{-75}[/tex]

d. The area on [15, 25] is the same as the area on [25, 35] because it's another triangle with the same dimensions. But the area on [15, 25] lies above the horizontal axis, so

[tex]\displaystyle \int_{15}^{25} f(x)\,dx = \int_{15}^{25} f(x)\,dx + \int_{25}^{35} f(x)\,dx = \boxed{0}[/tex]

e. The plot of [tex]|f(x)|[/tex] lies above the horizontal axis. We know the area on [15, 25] is the same as the area on [25, 35], but now both areas are positive, so

[tex]\displaystyle \int_{15}^{35} |f(x)| \, dx = \int_{15}^{25} f(x)\,dx - \int_{25}^{35} f(x)\,dx = 2 \int_{15}^{25} f(x)\,dx = \boxed{150}[/tex]

f. Changing the order of the limits in the integral swaps the sign of the overall integral, so

[tex]\displaystyle \int_{10}^0 f(x)\,dx = -\int_0^{10} f(x)\,dx = \boxed{-100}[/tex]

Answer:

x³+3x²-28x

Step-by-step explanation:

(x-4)(x-0)(x+7)

(x-4)(x)(x+7)

(x-4)(x+7)=(x²+3x-28)

(x²+3x-28)(x)=x³+3x²-28x

Using linear functions, we have that:

A linear function is modeled by:

y = mx + b

In which:

We consider the initial values as the y-intercepts. Randall's house decayed 58 thousand dollars in 3 years, hence the slope is:

m = -58/3 = -19.

Hence the function for the value, in thousands of dollars, is:

f(t) = -19t + 234.

Damien's initial value was of 110, and it increased 44 thousand in 3 years, hence the slope is:

m = 44/3 = 14.67

Hence the function for the value of Damien's house, in thousands of dollars, in t years after 2003, is:

g(t) = 14.67t + 110

They will have the same value when:

f(t) = g(t)

-19t + 234 = 14.67t + 110

33.67t = 124

t = 124/33.67

t = 3.68

They will have the same value in 3.68 years since the start of 2000.

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Answer:

If the question asked mixed fraction:

7/3 = 2 1/3

4/2 = 2

Step-by-step explanation:

I converted it to mixed fraction because it is already improper fraction.

Answer:

6x<48

Step-by-step explanation:

ik its this one because theres 48 players and 6 teams both are even numbers so if you did 48÷6x you would get 8 but theres fewer than 48 kids

Answer:

40

Step-by-step explanation:

[tex]\frac{RW}{24}=\frac{30}{18} \\ \\ RW=40[/tex]

Answer:

20 minutes

Step-by-step explanation:

Rate x Time = jobs

The rate is 3 jugs/ 4 minutes.

The number of jobs is 15

Use T for time

3/4T = 15  Multiply both sides by 4/3 to get the variable T by itself

(4/3) 3/4 T = 15(4/3)

T = 20 minutes