what is the exact area of a circle having diameter 4in

Answer:

The answer is

Step-by-step explanation:

Equation of a line is y = mx + c

where m is the slope

c is the y intercept

4x + y + 1 = 0

y = - 4x - 1

Comparing with the above formula

Slope / m = - 4

Since the lines are parallel their slope are also the same

That's

Slope of the parallel line is also - 4

Equation of the line using point ( 1 , 2) is

y - 2 = -4(x - 1)

y - 2 = - 4x + 4

4x + y - 2 - 4

We have the final answer as

Hope this helps you

The constant of proportionality is 3. The relationship that will have the same constant of proportionality will also have a slope of 3

For us to determine the constant of proportionality of the given graph, we must first find the equation of the line.

The standard equation of a line is expressed as y = mx + b

Using the coordinate points (0, 0) and (2, 6)

Get the slope "m"

[tex]m=\frac{6-0}{2-0}\\m=\frac{6}{2}\\m=3[/tex]

Since the line passed through the origin, the y-intercept is 0

Get the required equation:

y = mx + b

y = 3x + 0

y = 3x

From the equation, the constant of proportionality is 3. The relationship that will have the same constant of proportionality will also have a slope of 3

Learn more here: https://brainly.com/question/13441754

Answer:

Step-by-step explanation:

Equation of the line using point (0, 1) and slope 4/5 is

[tex]y - 1 = \frac{4}{5} (x - 0) \\ \\ 5y - 5 = 4x \\ \\ 5y - 4x = 5[/tex]

Hope this helps you

Answer:

D. [tex]\boxed{5y-4x=5}[/tex]

Step-by-step explanation:

Slope = m = 4/5

y - intercept = b = 1 (As from the point (0,1) , y-intercept is when x = 0)

So, the equation becomes

=> [tex]y = mx+b[/tex]

=> [tex]y = \frac{4}{5} x +1[/tex]

=> [tex]y - \frac{4}{5} x = 1[/tex]

Multiplying both sides by 5

=> [tex]5y-4x = 5[/tex]

Answer:

The equation in the polar form is;

[tex]r = \dfrac{6}{4 + 3 \cdot sin(\theta)}[/tex]

Step-by-step explanation:

 e = 3/4  > 1, we have an hyperbola    

The polar equation of a conic is of the form;

For vertical directrix

[tex]r = \dfrac{k \cdot e}{1\pm e \cdot cos (\theta)}[/tex]

For horizontal directrix

[tex]r = \dfrac{k \cdot e}{1\pm e \cdot sin(\theta)}[/tex]

Where;

k = Distance from the focus to the directrix = 2

We have;

[tex]r = \dfrac{2 \cdot \dfrac{3}{4} }{1 + \dfrac{3}{4} \cdot sin(\theta)}[/tex]

[tex]r = \dfrac{\dfrac{3}{2} }{1 + \dfrac{3}{4} \cdot sin(\theta)}[/tex]

Which gives the equation in the polar form as follows;

[tex]r = \dfrac{6}{4 + 3 \cdot sin(\theta)}[/tex].

Answer:

B

Step-by-step explanation:

Answer:

Consumption in the 20th year  = 82252 (nearest unit)

Step-by-step explanation:

Exponential growth problem.

Current consumption (year 0), P = 31000

growth rate, r = 5%

consumption in nth year

P(n) = P(1+r)^n

for the 20th year,

P(20) = P((1+r)^20) = 31000*1.05^20 = 82252.2 m^3  

(note: annual water consumption in a town is likely to be measured by m^3, please double check)

The required volume of water will be used at 82253 liters.

The annual water usage rate increase 5% annually with current usage is 31000 liters. After 20 years what will be the volume usage? To determine.

The function which is in format f(x) =a^x  where a is constant and x is variable,  the domain of this exponential function lies   (-∞, ∞).

Here, the rate of volume of water usage increases exponentially by 5%, current usage  = 31000. So Usage for the 20th year,
= 31000(1+5%)^20
=31000(1.05)^20
= 82253 liters

Thus, The required volume of water will be used at 82253 liters.

learn more about exponential function here:

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Answer:

£32.4

Step-by-step explanation:

£100 = 216 Swiss francs

x        =  70 francs

70 x 100=7000/216=32.4

Answer:

18

Step-by-step explanation:

You have 25 when you are done, but you made 7, so subtract that from 27.

25-7 equals 18.

Answer:

Option C.

Step-by-step explanation:

It is given that, a menu at a local diner has

Appetizers = 12

Entrees = 8

Choice of desserts = 4

We need to find the different meal combinations which are possible if you select one appetizer, one entree and one dessert form the menu.

Total ways to select an Appetizers = 12

Total ways to select an entrees = 8

Total ways to select a desserts = 4

Now,

Total combinations for different meal [tex]=12\times 8\times 4=384[/tex]

Therefore, the correct option is C.

Answer:

see below

Step-by-step explanation:

the answer is c

Answer:

y = -9/5x + 9/5

Step-by-step explanation:

From this points, we can determine the slope and the y-intercept.

First, we do:   y/x  -  y1/x1

=> 0/3 - (3 - 2)

=> 0-3/ 3 + 2

=> -3/5

So the slope of the equation is -3/5.

The equation is: y = mx + b

In this equation "m" = slope.

=>  b = constant

Now we take the x and y points from the above numbers.

=> Let's take 3 as x and 0 as y.

=> 0 = -3/5 *3 + b

=> 0 = -9/5 + b

=> Take the -9/5 to the other side

=> 9/5 = b

So, the constant number which is not multiplied by the x is 9/5

Now, our equation looks like:

y = -9/5x + 9/5

If you have any doubts about this question, ask me the comments and I will answer it as soon as possible.

Answer:

80%

Step-by-step explanation:

The basic idea of this problem is to convert [tex]\frac{44}{55}[/tex] into a percentage.  [tex]\frac{44}{55}[/tex]  can be simplified to [tex]\frac{4}{5}[/tex] which is also 80%.

Answer:

Step-by-step explanation:

44 out of 55

divide :44/55=0.8

to convert it to decimal  you multiply by 100 and put percentage next to it

0.8*100=80

%80

Answer:

2 ¹/12

Step-by-step explanation:

convert 1 4/12 to an improper fraction

(1×12+4)=16/12

16/12+9/12=25/12

convert 25/12 to a mixed fraction

=2 ¹/12

Answer:

(-1, -2)

Step-by-step explanation:

Look up each point in the choices on the graph. If it is on the line or in the shaded area it is a solution.

Answer: (-1, -2)

Answer:

First & Last

Step-by-step explanation:

See what is in the red portion(Shaded or line), that is what can work to the inequality.

(-1, -2) -- In the red(works)

(-1, 2) -- Out of the red(Nope)

(0, 5.2) -- Out of the red(Nope)

(-2, -1) -- In the red(works)

Answer:

1. 677 inches = 18.056 yards

677 inches  = 56.416 feet

677 inches = 677 inches

2. QP = 23.5 cm

3. The perimeter = 53.5 cm

Step-by-step explanation:

1. To convert, 677 inches to yards, we have;

1 inch = 0.0277778 yards

677 inches = 677*0.0277778 = 18.056 yards

To convert, 677 inches to feet, we have;

1 inch = 0.083333 feet

677 inches = 677*0.083333  = 56.416 feet

To convert, 677 inches to inches, we have;

1 inch = 1 inch

677 inches = 677*1  = 677 inches

2. We have that ∠PRQ and ∠PRS are supplementary angles (angles on a straight line

Given that ∠PRS = 90°, ∠PRQ = 180° - 90° = 90°;

∠PRQ + ∠PQR + ∠RPQ = 180°, sum of angles in a triangle

∠PQR = 24° given

∠PRQ = 90°

∴  ∠RPQ = 180° - 90° - 24° = 66°

∴∠SPQ = ∠SPR + ∠RPQ = 36° + 66° = 102°

∠QSP + ∠SPQ + ∠PQS = 180° (sum of angles in a triangle)

∠QSP = 180° -∠SPQ - ∠PQS = 180° -102° - 24 = 54°

By sine rule, we have;

a/(sin(A)) = b/(sin(B))

Therefore, we have;

11.8/(sin(24)) = QP/(sin(54°))

QP = (11.8/(sin(24))) × (sin(54°)) = 23.5 cm

3. From trigonometric ratios, we have;

tan(43°) = BC/CA = BC/(16.2 cm)

BC = 16.2 cm × tan(43°) = 15.1

By Pythagoras theorem, we have;

AB = √(15.1² + 16.2²) = 22.2

The perimeter = 15.1 + 16.2 + 22.2 = 53.5 cm

Answer:

3. time = 6.4999  approximately 6.5 years

4. $2235.35

5.  $ 3950

Step-by-step explanation:

4. amount of interest =  final amount - principle= 7535.35 - 5300 = 2235.35

5. principle = final amount - interest earned = 4435.25 - 485.25 = 3950

Answer: 2.

Step-by-step explanation:

Number of samples = 121

Average speed (sample mean) = 65mph

Population standard deviation = 22 mph

The standard error of the mean is:

Standard error of the mean(S.Em)

Standard error of the mean is the proportion of the population standard deviation and the square root of the sample size.

S.Em = standard deviation / √same size

S.Em = 22 / √121

S.Em = 22 / 11

S.Em = 2

Answer:

  16 hours

Step-by-step explanation:

In the time it took Ruth to plant 5 bulbs, Terry planted 3 bulbs. So, Terry did 3/8 of the work of planting 8 bulbs in that time.

We expect that Terry alone would take 8/3 of the time that it took when working together with Ruth.

  (8/3)×(6 hours) = 16 hours . . . . . . for Terry to do the job alone

Answer:

25 - 3x^5

Step-by-step explanation:

-2x^4+16+2x^4+9-3x^5

Combine like terms

-2x^4+2x^4+9+16-3x^5

0                 + 25 -3x^5

Answer:

3x^5-25

Step-by-step explanation:

you but the terms with the same power together and don't forget to add the signs that are in front of each terms when combining.

Answer:

  57°

Step-by-step explanation:

There is a right angle at the point of tangency, so the angle of interest is the complement of the one given:

  m∠K = 90° -m∠J = 90° -33°

  m∠K = 57°

Answer:

[tex]\boxed{f[ g(3) ] = 673}[/tex]

Step-by-step explanation:

[tex]f(x) = 4x^2 - 3 \\ g(x) = 5x - 2[/tex]

[tex]f(g(3))[/tex]

[tex]f(5(3)-2)[/tex]

[tex]f(15-2)[/tex]

[tex]f(13)[/tex]

[tex]f(13)=4(13)^2 -3[/tex]

[tex]f(13)=4(169) -3[/tex]

[tex]f(13)=676-3[/tex]

[tex]f(13)=673[/tex]

Answer:

f[g(3)] = 673

Step-by-step explanation:

I took the test

Answer:

A. g(x)=1/2x²

Step-by-step explanation:

Given:

f(x)=x²

We have to find g(x)

Since, we are given that g(2)=2

1. g(x)=1/2x²

x=2

g(x)=1/2(2)²

=1/2(4)

=4/2

=2

2. g(x)=1/4x²

x=2,

g(x)=1/4(2)²

=1/4(4)

=4/4

=1

3. g(x)= 2x²

at x=2,

g(x)=2(2)²

=2(4)

=8

4. g(x)=(1/2x)²

x=2

g(x)={1/2(2)}²

=(1/4)²

=1/16

A. g(x)=1/2x² is the answer

Answer:

7.

Step-by-step explanation:

15 - [7 + (-6)+ 1]^3

Using PEMDAS:

= 15 - [ 7-6+1]^3

Next work out what is in the parentheses:

= 15  - 2*3

Now the exponential:

= 15 - 8

= 7.

Step-by-step explanation:

Hi,

I hope you are searching this, right.

=15[7+(-6)+1]^3

=15[7-6+1]^3

=15[2]^3

=15-8

=7...is answer.

Hope it helps..

Answer:

[tex]\large \boxed{\sf \ \ \dfrac{8}{7} \ \ }[/tex]

Step-by-step explanation:

Hello, please consider the following.

The solutions are, for a positive discriminant:

   [tex]\dfrac{-b\pm\sqrt{\Delta}}{2a} \ \text{ where } \Delta=b^2-4ac[/tex]

Here, we have a = -21, b = -11, c = 40, so it gives:

[tex]\Delta =b^2-4ac=11^2+4*21*40=121+3360=3481=59^2[/tex]

So, we have two solutions:

[tex]x_1=\dfrac{11-59}{-42}=\dfrac{48}{42}=\dfrac{6*8}{6*7}=\dfrac{8}{7} \\\\x_2=\dfrac{11+59}{-42}=\dfrac{70}{-42}=-\dfrac{14*5}{14*3}=-\dfrac{5}{3}[/tex]

We only want x > 0 so the solution is

   [tex]\dfrac{8}{7}[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

The third graph

Step-by-step explanation:

Answer:

probability that a player wins after playing the game once = 5/9

Step-by-step explanation:

To solve this, we will find the probability of the opposite event which in this case, it's probability of not winning and subtract it from 1.

Since, we are told that there are 2 fair six sided die thrown at the same time and that he receives a five or a one on either die ;

Probability of not winning, P(not win) = 4/6.

Thus;

P(winning) = 1 - ((4/6) × (4/6))

P(winning) = 1 - 4/9 = 5/9

Answer:

The answer is

Step-by-step explanation:

f(x) = 36x^5 − 44x⁴ − 28x³

g(x) = 4x²

To find f(x) / g(x) Divide each term of f(x) by g(x)

That's

[tex] \frac{f(x)}{g(x)} = \frac{ {36x}^{5} - {44x}^{4} - {28x}^{3} }{ {4x}^{2} } \\ \\ = \frac{ {36x}^{5} }{ {4x}^{2} } - \frac{ {44x}^{4} }{ {4x}^{2} } - \frac{ {28x}^{3} }{ {4x}^{2} } \\ \\ = {9x}^{3} - {11x}^{2} - 7x[/tex]

Hope this helps you

Answer:

9x³ - 11x² - 7x

Step-by-step explanation:

guy abpove is right or bwlowe

Answer:

Step-by-step explanation:

The first thing we are going to do is to fill in the other angles that we need to solve this problem. You could find ALL of them but all of them isn't necessary. So looking at the obtuse angle next to the 35 degree angle...we know that those are supplementary so 180 - 35 = the obtuse angle in the small triangle. 180 - 35 = 145. Within the smaller triangle we have now the 145 and the 10, and since, by the Triangle Angle-Sum Theorem all the angles have to add up to equal 180, then 180 - (10 + 145) = the 3rd angle, so the third angle is 180 - 155 = 25. Now let's get to the problem. If I were you, I'd draw that out like I did to keep track of these angles cuz I'm going to name them by their degree. In order to find d, we need to first find the distance between d and the right angle. We'll call that x. The reference angle is 35, the side opposite that angle is 12 and the side we are looking for, x, is adjacent to that angle. So we will use the tan ratio to find x:

[tex]tan(35)=\frac{12}{x}[/tex] Isolating x:

[tex]x=\frac{12}{tan(35)}[/tex] so

x = 17.1377 m

Now we have everything we need to find d. We will use 25 degrees as our reference angle, and the side opposite it is 12 and the side adjacent to it is

d + 17.1377, so that is the tan ratio as well:

[tex]tan(25)=\frac{12}{d+17.1377}[/tex] and simplifying a bit:

[tex]d+17.1377=\frac{12}{tan(25)}[/tex] and a bit more:

d + 17.1377 = 25.73408 so

d = 8.59, rounded

Answer:

6

Step-by-step explanation:

6 appears the most

Answer:

6

Step-by-step explanation:

Put the data in order from smallest to largest

5,6,13,2,6,11,6,5,3,14

2,3,5,5,6,6,6,11,13,14

The mode is the number that appears most often

6 appears most often so it is the mode

Given Information:

Monthly payment = MP = $1500/4 = $375

Monthly interest rate = r = 25/12 = 2.083%

Required Information:

Present Value = ?

Answer:

[tex]PV = \$10,110[/tex]

Explanation:

n = 10*4

n = 40 monthly payments

The present value is found by

[tex]$ PV = MP \times \frac{ (1 - \frac{1}{(1+r)^n} )}{r} $[/tex]

Where r is monthly interest rate.

MP is the monthly payment.

[tex]$ PV = 375 \times \frac{ (1 - \frac{1}{(1+0.02083)^{40}} )}{0.02083} $[/tex]

[tex]PV = 375 \times (26.96)[/tex]

[tex]PV = \$10,110[/tex]

Therefore, $10,110 is the present value of 10 quarterly payments of $1500 each at 25% interest rate compounded each month.

Answer:

[tex]\boxed{Volume = 696.9 \ in.^3}[/tex]

Step-by-step explanation:

Diameter = 11 inches

Radius = 11/2 = 5.5 inches

[tex]Volume \ of \ a \ sphere = \frac{4}{3} \pi r^3[/tex]

Where r = 5.5

V = [tex]\frac{4}{3} (3.14)(5.5)^3[/tex]

V = [tex]\frac{4}{3} (3.14)(166.375)[/tex]

V = [tex]\frac{2090.7}{3}[/tex]

V = 696.9 in.³