1. S = 10 mm
V= S×S×S
=___×___×___
=____ mm3

​

Answer:

a = 2

b = 5

Step-by-step explanation:

Given :

(ar^b)^4 = 16r^20 ; a and b are positive integers :

Opening the bracket :

a^4r^4b = 16r^20

a^4 = 16 - - - - - (1)

r^4b = r^20 - - - (2)

a^4 = 16

Take the 4th root of both sides :

(a^4)^(1/4) = 16^1/4

a = 2

From (2)

r^4b = r^20

4b = 20

Divide both sides by 4

4b/4 = 20/4

b = 5

Hence ;

a = 2

b = 5

Answer:

n>2 2/3

Draw a filled dot at a little more than 2 1/2 and continue the line to the right.

Step-by-step explanation:

Subtract 1/3 from both sides to get

2 2/3

Flip the inequality

n> 2 2/3

I hope this helps!

Hello!

The answer is a.

Good luck! :)

Answer:

40

Step-by-step explanation:

10/x = 25/100

Cross multiply 10 and 100 = 1000.

Then, divide 1000 by 25 = 40.

10/40 = 0.25 = 25%

Answer:

[tex]A = 200,000(1+.025) ^{t}[/tex]

[tex]A = 200,000(1+.025) ^{10}[/tex]

Step-by-step explanation:

Answer:

4 different ways

Step-by-step explanation:

Total number of children = 4

Distribution of the 4 children :

Number of boys = 3 ; Number of girls = 1

Boy = B ; Girl = G

Possible combinations :

BBBG ; GBBB ; BBGB ; BGBB

From the pascal triangle number of e; number of outcomes = 2

Having exactly 3 boys and 1 girl

Hence, of any of the 4 four total children, 3 must be boys and 1 girl ;

Answer:

19.0%

Step-by-step explanation:

The probability that a student in the sample data is enrolled in painting Given that the student is female is a conditional probability and can be defined as :

Let,

F = Female ; P = painting

P(Painting Given female) = P(P|F) = (PnF) / F

From the table :

(PnF) = 16

F = 84

Hence,

P(P|F) = 16 / 84 = 0.19047 = 0.19047 * 100%

P(P|F) = 19.0%

Answer:

B. [tex] y + 5 = 2(x + 2) [/tex]

Step-by-step explanation:

Point-slope equation is given as [tex] y - b = m(x - a) [/tex], where,

(a, b) = (-2, -5)

[tex] m = slope = \frac{y_2 - y_1}{x_2 - x_1} [/tex]

Using two points on the line (-2, -5) and (0, -1),

Slope (m) = (-1 -(-5))/(0 -(-2)) = 4/2

m = 2

✔️To write the equation in point-slope form, substitute a = -2, b = -5, and m = 2 into [tex] y - b = m(x - a) [/tex]

Thus:

[tex] y - (-5) = 2(x - (-2)) [/tex]

[tex] y + 5 = 2(x + 2) [/tex]

9514 1404 393

Answer:

  (b)  the correct table is marked

Step-by-step explanation:

Direct variation is characterized by the ratio of y to x being a constant for all values in the table. That constant is the constant of proportionality. For the values in the second table (marked), the ratio is ...

  y/x = 8/6 = 12/9 = 16/12 = 4/3

The constant of proportionality is 4/3.

I'll use the integrating factor method for the first DE, and undetermined coefficients for the second one.

(a) Multiply both sides by exp(7t ):

exp(7t ) dx/dt + 7 exp(7t ) x = 5 exp(7t ) cos(2t )

The left side is now the derivative of a product:

d/dt [exp(7t ) x] = 5 exp(7t ) cos(2t )

Integrate both sides:

exp(7t ) x = 10/53 exp(7t ) sin(2t ) + 35/53 exp(7t ) cos(2t ) + C

Solve for x :

x = 10/53 sin(2t ) + 35/53 cos(2t ) + C exp(-7t )

(b) Solve the corresonding homogeneous DE:

d²x/dt ² + 6 dx/dt + 8x = 0

has characteristic equation

r ² + 6r + 8 = (r + 4) (r + 2) = 0

with roots at r = -4 and r = -2. So the characteristic solution is

x (char.) = C₁ exp(-4t ) + C₂ exp(-2t )

For the particular solution, assume an ansatz of the form

x (part.) = a cos(3t ) + b sin(3t )

with derivatives

dx/dt = -3a sin(3t ) + 3b cos(3t )

d²x/dt ² = -9a cos(3t ) - 9b sin(3t )

Substitute these into the non-homogeneous DE and solve for the coefficients:

(-9a cos(3t ) - 9b sin(3t ))

… + 6 (-3a sin(3t ) + 3b cos(3t ))

… + 8 (a cos(3t ) + b sin(3t ))

= (-a + 18b) cos(3t ) + (-18a - b) sin(3t ) = 5 sin(3t )

So we have

-a + 18b = 0

-18a - b = 5

==>   a = -18/65 and b = -1/65

so that the particular solution is

x (part.) = -18/65 cos(3t ) - 1/65 sin(3t )

and thus the general solution is

x (gen.) = x (char.) + x (part.)

x = C₁ exp(-4t ) + C₂ exp(-2t ) - 18/65 cos(3t ) - 1/65 sin(3t )

Answer:

2/7

Step-by-step explanation:

d=2n+3

 [tex]\frac{d-7}{2n-4} = \frac{4}{13}[/tex]

13(2n+3) -91 =8n - 16

26n+39 -91 = 8n-16

18n=36

n=2

d=7

Answer:

The maximum number of possible combinations are 9.

Step-by-step explanation:

There are three types of juices :

Orange, Mango and Blue lemonade

There are three types of biscuits:

Oreo, Skyflakes and Rebisco

So, the number of possible combinations are

= (3 C 1) x (3 C 1)

= 3 x 3 = 9

The maximum number of possible combinations are 9.

This question is incomplete, the complete question is;

We know that the remainder R[tex]_n[/tex] will satisfy | R[tex]_n[/tex] | ≤ b[tex]_{ n + 1[/tex] = 1 / ( n + 1 )9[tex]^{ n + 1[/tex].

We must make n large enough so that this is less than 0.0001.

Rounding to five decimal places,

we have b₂ = _________ , b₃ =_________and b₄ =__________

Answer:

b₂ = 0.00617, b = 0.00046 and  b₄ = 0.00004

Step-by-step explanation:

Given the data in the question;

| R[tex]_n[/tex] | ≤ b[tex]_{ n + 1[/tex] = 1 / ( n + 1 )9[tex]^{ n + 1[/tex]

Now,

b[tex]_{ n + 1[/tex] = 1 / ( n + 1 )9[tex]^{ n + 1[/tex]

b₂ = b[tex]_{ 1 + 1[/tex] = 1 / ( 1 + 1 )9[tex]^{ 1 + 1[/tex] = 1 / (2)9² = 1 / 162 = 0.00617   { 5 decimal places }

b₃ = b[tex]_{ 2 + 1[/tex] = 1 / ( 2 + 1 )9[tex]^{ 2 + 1[/tex] = 1 / (3)9³ = 1 / 2187 = 0.00046 { 5 decimal places }

b₄ = b[tex]_{ 3 + 1[/tex] = 1 / ( 3 + 1 )9[tex]^{ 3 + 1[/tex] = 1 / (4)9⁴ = 1 / 19683 = 0.00004 { 5 decimal places }

Therefore, b₂ = 0.00062, b = 0.00046 and  b₄ = 0.00004

Answer:

363,000,000

..........

Answer:

6x6

Step-by-step explanation:

Answer:

t = [tex]\frac{75}{n}[/tex]

Step-by-step explanation:

Use the inverse variation equation, y = [tex]\frac{k}{x}[/tex]

Replace y with t, and replace x with n, since those are the variables in this situation:

t = [tex]\frac{k}{n}[/tex]

Plug in 3 as t and 25 as n, and solve for k:

3 = [tex]\frac{k}{25}[/tex]

75 = k

Create the equation by plugging in 75 as k:

t = [tex]\frac{75}{n}[/tex]

So, the equation is t = [tex]\frac{75}{n}[/tex]

Answer:

i^−3 = i

i^−2 = −1

i^−1 = −i

i^0 = 1

i^1 = i

i^2 = −1

i^3 = −i

i^4 = 1

i^5 = i

i^ 6 = −1

See the pattern

Answer:

C. 15.6

Step-by-step explanation:

Perimeter of WXYZ = WX + XY + YZ + ZW

Use the distance formula, [tex] d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex] to calculate the length of each segment.

✔️Distance between W(-1, 1) and X(1, 2):

Let,

[tex] W(-1, 1) = (x_1, y_1) [/tex]

[tex] X(1, 2) = (x_2, y_2) [/tex]

Plug in the values

[tex] WX = \sqrt{(1 - (-1))^2 + (2 - 1)^2} [/tex]

[tex] WX = \sqrt{(2)^2 + (1)^2} [/tex]

[tex] WX = \sqrt{4 + 1} [/tex]

[tex] WX = \sqrt{5} [/tex]

[tex] WX = 2.24 [/tex]

✔️Distance between X(1, 2) and Y(2, -4)

Let,

[tex] X(1, 2) = (x_1, y_1) [/tex]

[tex] Y(2, -4) = (x_2, y_2) [/tex]

Plug in the values

[tex] XY = \sqrt{(2 - 1)^2 + (-4 - 2)^2} [/tex]

[tex] XY = \sqrt{(1)^2 + (-6)^2} [/tex]

[tex] XY = \sqrt{1 + 36} [/tex]

[tex] XY = \sqrt{37} [/tex]

[tex] XY = 6.08 [/tex]

✔️Distance between Y(2, -4) and Z(-2, -1)

Let,

[tex] Y(2, -4) = (x_1, y_1) [/tex]

[tex] Z(-2, -1) = (x_2, y_2) [/tex]

Plug in the values

[tex] YZ = \sqrt{(-2 - 2)^2 + (-1 -(-4))^2} [/tex]

[tex] YZ = \sqrt{(-4)^2 + (3)^2} [/tex]

[tex] YZ = \sqrt{16 + 9} [/tex]

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

[tex] YZ = 5 [/tex]

✔️Distance between Z(-2, -1) and W(-1, 1)

Let,

[tex] Z(-2, -1) = (x_1, y_1) [/tex]

[tex] W(-1, 1) = (x_2, y_2) [/tex]

Plug in the values

[tex] ZW = \sqrt{(-1 -(-2))^2 + (1 - (-1))^2} [/tex]

[tex] ZW = \sqrt{(1)^2 + (2)^2} [/tex]

[tex] ZW = \sqrt{1 + 4} [/tex]

[tex] ZW = \sqrt{5} [/tex]

[tex] ZW = 2.24 [/tex]

✅Perimeter = 2.24 + 6.08 + 5 + 2.24 = 15.56

≈ 15.6

Answer:CCCCCCCCCCCCCCCCC

Step-by-step explanation:

x = 100° (using definition of vertical angles)

23/200

Hope this helps! :)

Answer:

23/2000

Step-by-step explanation:

0.0115 can be written as 115/10000

=23/2000

Please mark me as brainliest.

Answer:

measurement m<GEM+m<MEO=m<GEO

Answer:

1d = -3

2b = 2

2c = 1

3a = 3

3d = 4

Step-by-step explanation:

Polynomial 1: [tex]x^2-8x+15[/tex]

Multiply the leading coefficient, 1, and the last term, 15. You get: 15.

Then, list out the factors of 15 and the addends of -8 until you get two of numbers that are the same:

Factors of 15: -5 * -3

Addends of -8: -5 + -3

Replace the -8x with -5x - 3x:

[tex]x^2-5x-3x+15[/tex]

Put parentheses around the first 2 terms & last 2 terms and factor like so:

[tex](x^2-5x)-(3x+15)[/tex]

[tex]x(x-5)-3(x-5)[/tex]

[tex](x-5)(x-3)[/tex]

Looking at the answer (ax + b)(cx + d), d would correspond with -3.

Polynomial 2: [tex]2x^3-8x^2-24x[/tex]

First factor out the x:

[tex]x(2x^{2}-8x-24)[/tex]

Divide the polynomial inside by 2 and place the 2 outside with the x:

[tex]2x(x^2-4x-12)[/tex]

Then find the factors of 1*-12 and the addends of -4 and see which two numbers match:

Factors of -12: -6 * 2

Addends of -4: -6 + 2

Replace the -8x with -6x + 2x:

[tex]2x(x^2-6x+2x-12)[/tex]

Put parentheses around the first 2 terms & last 2 terms and factor like so:

[tex]2x((x^2-6x)+(2x-12))[/tex]

[tex]2x(x(x-6)+2(x-6))[/tex]

[tex]2x((x+2)(x-6))[/tex]

[tex]2x(x+2)(x-6)[/tex]

Looking at the answer (2x)(ax + b)(cx + d), b & c would correspond with 2 & 1.

Polynomial 3: [tex]6x^2+14x+4[/tex]

Divide the polynomial by 2:

[tex](2)(3x^2+7x+2)[/tex]

Find the factors of 3*2 and the addends of 7 and see which two numbers match:

Factors of 6: 6 * 1

Addends of 7: 6 + 1

Replace the 7x with 6x + x:

[tex](2)(3x^2+6x+x+2)[/tex]

Put parentheses around the first 2 terms & last 2 terms and factor like so:

[tex](2)((3x^2+6x)+(x+2))[/tex]

[tex](2)(3x(x+2)+(x+2))[/tex]

[tex](2)((3x+1)(x+2))[/tex]

[tex](2)(3x+1)(x+2)[/tex]

Then multiply the 2 with the (x+2) and here's your final answer:

[tex](3x+1)(2x+4))[/tex]

Looking at the answer (ax + b)(cx + d), a & d correspond with 3 & 4.

Hope that helps (●'◡'●)

(This took a while to write, sorry about that)

Answer:

The point of intersection of angle bisectors of the 3 angles of triangle ABC is the incenter (denoted by I). The incircle (whose center is I) touches each side of the triangle.

Answer:

Step-by-step explanation:

we need a photo..

9514 1404 393

Answer:

Step-by-step explanation:

The formula for figuring the amount that can be borrowed (P) is shown on the first line of the attachment. (The second line rounds it to the nearest cent.) In this formula, ...

  a = monthly payment, r = annual interest rate, t = number of years

The amounts requested by the problem statement are shown in the attachment, and above. b is the amount that can be borrowed, p is the total of payments, and i is the interest paid. There are 360 monthly payments in 30 years, so the total paid is 360 times the monthly payment amount.

Answer:

-3,-1

Step-by-step explanation:

x²+4x+3=0

x²+4x=-3

x²+4x+(2)²=-3+(2)²

(x+2)²=-3+4

(x+2)²=1

Take square root of both sides

x+2=±1

x=-2±1

x=-1 or-3