HELPPP PLSSS Write the equation of the arithmetic sequence defined by a1 = 3 and a4 = 0. (Type your answer in the form an= and please do NOT use spaces.)

Answer:

Kindly check explanation

Step-by-step explanation:

Given the following :

Yellow (Y) toys = 5

Red (R) toys = 4

Total toys = yellow + red = (5 +4) = 9

WITH REPLACEMENT :

Probability that two toys of same color will be picked.

From the tree diagram.

Two toys of the same color

a.)P(Y, Y) + P(R, R) = (25/81) + (16 / 81) = 41/81

b) toys of different color :

P(Y, R) + P(R, Y) = (20/81) + (20/81) = 40/81

c.) A red toy will be picked first :

P(R, Y) = 20/81

d.) Atleast one red toy will be picked

P(Y, R) + P(R, Y) + P(R, R)

20 /81 + 20/81 + 16/81 = 56/81

2) WITHOUT REPLACEMENT :

a.)P(Y, Y)+P(R, R) = (20/72) + (12/72) = 32/72 = 4/9

b) P(Y, R)+P(R, Y) = (20/72)+(20/72)= 40/72 = 5/9

c) p(R, Y) = 12/72 = 1/6

d) P(Y, R) + P(R, Y) + P(R, R) = 20/72 + 20/72 + 12/72 = 52/72 = 13/ 18

Answer:

The value of M₁₁ is -6.

Step-by-step explanation:

The minor, [tex]M_{ij}[/tex] is the determinant of a square matrix, say P, formed by removing the ith row and jth column from the original square matrix, P.

The matrix provided is as follows:

[tex]A=\left[\begin{array}{ccc}7&9&-3\\3&-6&5\\4&0&1\end{array}\right][/tex]

The matrix M₁₁ is:

Remove the 1st row and 1st column to form M₁₁,

[tex]M_{11}=\left|\begin{array}{cc}-6&5\\4&0\end{array}\right|[/tex]

Compute the value of M₁₁ as follows:

[tex]M_{11}=\left|\begin{array}{cc}-6&5\\4&0\end{array}\right|[/tex]

       [tex]=(-6\times 1)-(5\times 0)\\\\=-6-0\\=-6[/tex]

Thus, the value of M₁₁ is -6.

Answer:

see explanation

Step-by-step explanation:

I will begin with part two, first.

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius.

Given

x² - 18x + y² - 10y = - 6

Using the method of completing the square

add ( half the coefficient of the x/ y terms )² to both sides

x² + 2(- 9)x + 81 + y² + 2(- 5)y + 25 = - 6 + 81 + 25, that is

(x - 9)² + (y - 5)² = 100 ← in standard form

with centre = (9, 5 ) and r = [tex]\sqrt{100}[/tex] = 10

Answer:

The formula for speed is s=(distance traveled)/(time elapsed)

Answer:

[tex]\huge \boxed{S =\frac{d }{t} }[/tex]

[tex]\rule[225]{225}{2}[/tex]

Step-by-step explanation:

The formula to find speed is as follows:

[tex]\Longrightarrow \ \ \displaystyle \sf speed =\frac{distance \ travelled }{time \ taken}[/tex]

[tex]\Longrightarrow \ \ \displaystyle S =\frac{d }{t}[/tex]

[tex]\rule[225]{225}{2}[/tex]

Answer:

(5 1/3)/7

Step-by-step explanation:

Divide 4 by 3, then times it by four and put it over the 7

●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●

               Hi my lil bunny!

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

Lets do this step by step.

This is the trigonometric form of a complex number where [tex]|z|[/tex] is the modulus and [tex]0[/tex] is the angle created on the complex plane.

[tex]z = a + bi = |z| (cos ( 0 ) + I sin (0))[/tex]

The modulus of a complex number is the distance from the origin on the complex plane.

[tex]|z| = \sqrt{a^2 + b^2}[/tex] where [tex]z = a + bi[/tex]

Substitute the actual values of a = -5 and b = -5.

[tex]|z| = \sqrt{(-5) ^2 + (-5) ^2}[/tex]

Now Find [tex]|z|[/tex] .

Raise - 5 to the power of 2.

[tex]|z| = \sqrt{25 + (-5) ^2}[/tex]

Raise - 5 to the power of 2.

[tex]|z| = \sqrt{25 + 25}[/tex]

Add 25 and 25.

[tex]|z| = \sqrt{50}[/tex]

Rewrite 50 as 5^2 . 2 .

[tex]|z| = 5\sqrt{2}[/tex]

Pull terms out from under the radical.

[tex]|z| = 5\sqrt{2}[/tex]

The angle of the point on the complex plane is the inverse tangent of the complex portion over the real portion.

[tex]0 = arctan (\frac{-5}{-5} )[/tex]

Since inverse tangent of  [tex]\frac{-5}{-5}[/tex]  produces an angle in the third quadrant, the value of the angle is [tex]\frac{5\pi }{4}[/tex] .

[tex]0 = \frac{5\pi }{4}[/tex]

Substitute the values of [tex]0 = \frac{5\pi }{4}[/tex] and [tex]|z| = 5\sqrt{2}[/tex] .

[tex]5\sqrt{2} ( cos( \frac{5\pi}{4}) + i sin (\frac{5\pi}{4}))[/tex]

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●

Hope this helped you.

Could you maybe give brainliest..?

❀*May*❀

The complex number (5 - 5i) in trigonometric form is

5√2 [cos(-π/4) + i sin(-π/4)]

An imaginary number is denoted by i.

The value of i is √-1.

We have,

To express the complex number (5 - 5i) in trigonometric form,

We first need to find its modulus (r) and argument (θ).

The complex number (a - bi) in trigonometric form is

|r| [cosФ + i sinФ]

Now,

Modulus (r).

|r| = √(5² + (-5)²)

= √(50)

= 5√(2)

And,

Argument (θ).

θ = [tex]tan^{-1}[/tex](-5/5)

  = -π/4

(since the complex number is in the fourth quadrant)

Therefore,

The complex number (5 - 5i) in trigonometric form is

5√2 [cos(-π/4) + i sin(-π/4)]

Learn more about imaginary numbers here:

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Answer:

5

Step-by-step explanation:

Given

[tex]\frac{30b}{6b}[/tex]

Cancel the b on the numerator/ denominator.

Also the 30 and 6 can both be cancelled by 6 , thus

[tex]\frac{30b}{6b}[/tex] = [tex]\frac{30}{6}[/tex] = 5

Answer:

[tex]\boxed{5}[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{30b}{6b}[/tex]

[tex]\sf Simplify[/tex]

[tex]\displaystyle \frac{30}{6} \times \frac{b}{b}[/tex]

[tex]5 \times 1[/tex]

[tex]=5[/tex]

Answer:

[tex] L_o= 1500 cm[/tex]

And we know that the level is decreasing 20% each day so then we can use the following model for the problem

[tex] L_f = L_o (1-0.2)^t[/tex]

Where t represent the number of days and L the level for this case we want to fnd the level after two days so then t =2 and replacing we got:

[tex] L_f = 1500cm(0.8)^2 = 960cm[/tex]

Step-by-step explanation:

For this case we know that the initial volume of water is:

[tex] L_o= 1500 cm[/tex]

And we know that the level is decreasing 20% each day so then we can use the following model for the problem

[tex] L_f = L_o (1-0.2)^t[/tex]

Where t represent the number of days and L the level for this case we want to fnd the level after two days so then t =2 and replacing we got:

[tex] L_f = 1500cm(0.8)^2 = 960cm[/tex]

Answer:

16

Step-by-step explanation:

perimeter of B = 21

divide by 3 to get each side: 21/3 = 7 = Y

perimeter of hexagon is 50. subtract 2Y: 50 - 14 = 36

divide 36 by 4 to find X = 9

add X + Y

Answer:

283 cm^2

Step-by-step explanation:

Solution:-

We have a cone with a circular base of radius r = 5 cm

The height of the cone is h = 12 cm

The slant height of the cone is L = 13 cm

We are to determine the surface area of the cone. The surface area of the cone is comprised of two parts:

         Base Area : Circle

               [tex]A_1 = \pi r^2\\\\A_1 = \pi 5^2\\\\A_1 = 25\pi[/tex]

        Curved Surface: conical

                [tex]A_2 = \pi * r*L\\\\A_2 = \pi * 5*13\\\\A_2 = 65\pi[/tex]

The total surface area of the cone can be written as ( A ):

               [tex]A = A_1 + A_2\\\\A = (25 + 65 )*\pi \\\\A = 90*(3.14) \\\\A = 282.7433 cm^2[/tex]

Answer: The surface area of the cone to nearest whole number would be 283 cm^2

Answer:

[tex]\large \boxed{\sf \ \ x=\pm8 \ \ or \ \ x=\pm2 \ \ }[/tex]

Step-by-step explanation:

Hello, please consider the following.

First of all, we can assume that x and y are different from 0, as we cannot divide by 0.

And from the first equation we can write y as a function of x as below.

[tex]y=\dfrac{16}{x}[/tex]

And then, we replace it in the second equation to get.

[tex]\dfrac{x}{\frac{16}{x}}+\dfrac{\frac{16}{x}}{x}=\dfrac{17}{4}\\\\<=> \dfrac{x^2}{16}+\dfrac{16}{x^2}=\dfrac{17}{4}\\\\\text{*** We multiply by }16x^2 \text{ both sides ***}\\\\x^4+16*16=\dfrac{17*16}{4}x^2\\\\x^4-68x^2+3600=0\\\\\text{*** The product of the zeroes is 3600 = 64*4 and the sum is 64+4=68 ***}\\\\\text{*** So we can factorise *** }\\\\x^4-64x^2-4x^2+3600=x^2(x^2-64)-4(x^2-64)=(x^2-64)(x^2-4)=0\\\\x^2=64=8^2 \ \ or \ \ x^2=4\\\\x=\pm8 \ \ or \ \ x=\pm2\\[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

The correct option is;

(0, -3), (-1, 0) and (3, 0)

Step-by-step explanation:

From the given graph of the function we have the following observations;

There are two x-intercepts which are;

1) To the left of the vertical y-axis having coordinates (-1, 0)

2) To the the right of the y-axis having coordinates (3, 0)

There is only one y-intercept  having coordinates, (0, -3)

Therefore, all the intercepts of the function are, (0, -3), (-1, 0) and (3, 0).

Answer:

(0, -3), (-1, 0) and (3, 0)

Step-by-step explanation:

Answer:

127 500

Step-by-step explanation:

Let x be the missing value.

● 510 000 => 100

● x => 25

x = (25*51000)÷100 = 127 500

Answer:

hope it helps

Step-by-step explanation:

25 percent of 510,000 = 127,500

Answer:

5.5

Step-by-step explanation:

We use right triangle XVW.

For <W, VX is the opposite leg.

WX is the hypotenuse.

The trig ratio that relates the opposite leg to the hypotenuse is the sine.

[tex] \sin W = \dfrac{opp}{hyp} [/tex]

[tex] \sin W = \dfrac{VX}{WX} [/tex]

[tex] \sin 43^\circ = \dfrac{VX}{8~mi} [/tex]

[tex] VX = 8~mi \times \sin 43^\circ [/tex]

[tex] VX = 5.5~mi [/tex]

Answer:

c. jasper has apparently decreased the volume of items in his ending inventory as compared to the number of items in his beginning inventory

Step-by-step explanation:

First In First Out  FIFO is a type of inventory system in accounting, it literally implies that  the oldest purchase goes out first when you made a sale. The oldest purchase are charged based on cost of good sold. If price are rising, :

FIFO will yield a lower cost of good sold

FIFO will yield a higher net income

FIFO will yield higher tax liability

FIFO will yield a higher inventory

From the information given:

the business records show that the cost of the stores inventory items has been steadily increasing. the cost of the end of the year inventory is 200,000 and the cost of the beginning of the year inventory was 250,000.

What the statement implies is that:

jasper has apparently decreased the volume of items in his ending inventory as compared to the number of items in his beginning inventory

Answer:

a. 11/25

b. 11/25

Step-by-step explanation:

We proceed as follows;

From the question, we have the following information;

Three urns A, B and C contains ( 3 black balls 7 white balls), (7 black balls and 13 white balls) and (12 black balls and 8 white balls) respectively.

Now,

Since events of choosing urn A, B and C are denoted by Ai , i=1, 2, 3

Then , P(A1 + P(A2) +P(A3) =1 ....(1)

And P(A1):P(A2):P(A3) = 1: 2: 2 (given) ....(2)

Let P(A1) = x, then using equation (2)

P(A2) = 2x and P(A3) = 2x

(from the ratio given in the question)

Substituting these values in equation (1), we get

x+ 2x + 2x =1

Or 5x =1

Or x =1/5

So, P(A1) =x =1/5 , ....(3)

P(A2) = 2x= 2/5 and ....(4)

P(A3) = 2x= 2/5 ...(5)

Also urns A, B and C has total balls = 10, 20 , 20 respectively.

Now, if we choose one urn and then pick up 2 balls randomly then;

(a) Probability that the first ball is black

=P(A1)×P(Back ball from urn A) +P(A2)×P(Black ball from urn B) + P(A3)×P(Black ball from urn C)

= (1/5)×(3/10) + (2/5)×(7/20) + (2/5)×(12/20)

= (3/50) + (7/50) + (12/50)

=22/50

=11/25

(b) The Probability that the first ball is black given that the second ball is white is same as the probability that first ball is black (11/25). This is because the event of picking of first ball is independent of the event of picking of second ball.

Although the event picking of the second ball is dependent on the event of picking the first ball.

Hence, probability that the first ball is black given that the second ball is white is 11/25

​​

Answer:

From sin²θ + cos²θ = 1, we have;

sin⁴θ + cos⁴θ = 1 - 2·sin²θ·cos²θ

Step-by-step explanation:

The given equation is (sin⁴θ + cos⁴θ) = 1 - 2 sin²θ·cos²θ

We have;

(sin⁴θ + cos⁴θ) = 1 - 2 sin²θ·cos²θ gives;

(sin⁴θ + cos⁴θ) + 2 sin²θ·cos²θ= 1

Which is equivalent to sin⁴θ + 2 sin²θ·cos²θ +cos⁴θ  = 1

From which we can get;

(sin²θ + cos²θ)·(sin²θ + cos²θ)  = 1

Given that sin²θ + cos²θ = 1

Therefore;

1 × 1 = 1

To get to the initial equation in the question, we have;

sin²θ + cos²θ = 1

(sin²θ + cos²θ) × (sin²θ + cos²θ) = 1

(sin⁴θ + sin²θ·cos²θ + sin²θ·cos²θ + cos⁴θ = 1

∴ sin⁴θ + cos⁴θ = 1 - sin²θ·cos²θ + sin²θ·cos²θ  = 1 - 2·sin²θ·cos²θ

Therefore;

sin⁴θ + cos⁴θ = 1 - 2·sin²θ·cos²θ.

Answer:

A

Step-by-step explanation:

Using ZPP we get x = 0, 2x + 4 = 0, x + 5 = 0. Solving these, we get x = 0, x = -2, x = -5.

Answer:

m = -9/4

Step-by-step explanation:

Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Simply plug in the coordinates into the slope formula:

m = (16 - 7)/(2 - 6)

m = 9/-4

m = -9/4

Answer:

(f ∘ g)(x) = 0.9x - 100

Step-by-step explanation:

Here in this question, we are interested in calculating (f ∘ g)(x)

From the question, we are given;

f(x) = x -100

g(x) = 0.9x

So (f ∘ g)(x) simply means we shall be representing the x in f(x) with the totality of the value of g(x)

Mathematically, what we are saying is that;

Find (f ∘ g)(x) = 0.9x - 100

Answer:

The coordinates of the triangle, (3, 6), (3, -3), and (3, 3), dilated by a magnitude of 3 is;

(9, 18), (9, -9), and (9, 9)

Step-by-step explanation:

The vertices of the given triangle are;

(3, 6), (3, -3), and (3, 3)

A dilation with a magnitude of 3 can be found as follows;

For each value of the x, and y-coordinates of the vertices, we multiply by the magnitude of dilation

As an example, the coordinate of the points on a line, (x₁, y₁) and (x₂, y₂), dilated by a scale factor of m, will become, (m·x₁, m·y₁) and (m·x₂, m·y₂)

Therefore, we have foe a magnitude of 3;

(3, 6), (3, -3), and (3, 3) becomes, (3×3, 3×6), (3×3, 3×(-3)), and (3×3, 3×3)

(9, 18), (9, -9), and (9, 9).

Answer:

(9, 18), (9, -9), and (9, 9)

Step-by-step explanation:

Answer: 108 square inches

Step-by-step explanation:

The formula for any square is base*height/2. The formual to find the area of a square is base*height. If you draw out a square and cut it in half diagonaly, you get a right triangle. That is why you divide it by 2. (sorry if the explanation was clunky/ hard to understand)

1. You would multiply 18*12 which equals 216.

2. Divide 216 by 2. 216/2= 108.

The answer is 108. Hope this helped you:)

The area of the triangle is 108 square inches.

The area of the triangle is defined as the product of half the base and the height of the triangle.

The area of the triangle = 1/2 x b x h

If we draw out a square and cut it in half diagonaly, you get a right triangle. That is why we need to divide it by 2.

The area of the triangle = 1/2 x b x h

The area of the triangle = 1/2 x 12  x 18

= 216/2= 108.

The area of the triangle is 108 square inches.

Learn more about the area;

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Answer: 13/20 - 2/5 = 1/4 ( Using LCD)

Step-by-step explanation:

Given: 13/20 - 2/5 = ? Use LCD

1) First we need find the least common multiple of the denominator (20 and 5) which is 20.

2) Since we know the least common multiple we know need to switch the two fractions up but since one of the denominator is already 20 ( 13/20) we now need to fix the other fraction (2/5).

3) We need to make it the same for both fractions so we want the same denominator as the first fraction (20) so we multiply 5 by 4 since 5 x 4 = 20 and we get 20, while also doing the same thing with the numerator. So we times 2 by 4 and we get 8.

4) Now our two fractions are now 13/20 and 8/20.

5) Our next step is to subtract the numerator, so its 13-8 which we get 5.

6) So now we have 5/20 and we want to simply to the smallest fraction so we find a number that is divisible and can make the smallest fraction which is 5.  

5/5 and 20/5 and we get 1/4.

Answer:

This graph is nonlinear

The initial displacement of the weight is 40cm

The weight first returns to equilibrium when t=1/2

Step-by-step explanation:

thats the answer i only had time to give not to explain

Answer:

the answer is in the photo ^^

Step-by-step explanation:

the correct thing is there for confirmation ;)

Answer:

2/13

Step-by-step explanation:

In a standard deck of cards, there are 52 cards total, 4 kings, and 4 queens.

Probability is calculated by (number of favorable outcomes)/(number of possible outcomes), so our probability would be 8/52, which can be simplified to 2/13.

Hope this helps!

Answer:

MN = 14 ft

Step-by-step explanation:

NP tangent => ∡PNM = 90°

Pythagoras

MN = √MP² - NP²

= √50² - 48²

= √(50 - 48)(50 + 48)

= √2×98

= √196

= √14²

= 14 ft

Answer: The coordinates of D are (1,-12) .

Step-by-step explanation:

Given : Translation rule : (x, y) → (x + 6, y – 10)  is applied to figure ABCD.

From the figure below, we have figure ABCD in which

The coordinates of D = (-5,-2)

According to the given translation rule :

D(-5,-2) → D'(-5 + 6, -2 – 10)    (coordinates of image point D')

i.e. D(-5,-2) → D'(1, -12)    [-5+6 = 1, -2-10 = -12]

Hence, the coordinates of D are (1,-12) .

Answer:

B. (1, –12)

Step-by-step explanation:

edge2021

[tex](1-3i)(1-i)(1+i)(1+3i)=\\(1^2-(3i)^2)(1^2-i^2)=\\(1+9)(1+1)=\\10\cdot2=20[/tex]

Answer:

[tex]\huge\boxed{(1-3i)(1-i)(1+i)(1+3i)=20}[/tex]

Step-by-step explanation:

[tex](1-3i)(1-i)(1+i)(1+3i)\\\\\text{use the commutative property}\\\\=(1-3i)(1+3i)(1-i)(1+i)\\\\\text{use the associative property}\\\\=\bigg[(1-3i)(1+3i)\bigg]\bigg[(1-i)(1+i)\bigg]\\\\\text{use}\ (a-b)(a+b)=a^2-b^2\\\\=\bigg[1^2-(3i)^2\bigg]\bigg[1^2-i^2\bigg]\\\\=\bigg(1-9i^2\bigg)\bigg(1-i^2\bigg)\\\\\text{use}\ i=\sqrt{-1}\to i^2=-1\\\\=\bigg(1-9(-1)\bigg)\bigg(1-(-1)\bigg)\\\\=\bigg(1+9\bigg)\bigg(1+1\bigg)\\\\=(10)(2)\\\\=20[/tex]

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

The value of y is 7.

The graph of the two-equation is given below.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 9 is an equation.

We have,

3x = y - 13 ____(1)

x + 2y = 12 _____(2)

From (1) we get,

x = (y - 13)/3 _____(3)

Putting (3) in (2) we get,

(y - 13)/3 + 2y = 12

y - 13 + 6y = 36

7y = 36 + 13

7y = 49

y = 7

The graph of the equation is given below.

Thus,

The value of y is 7.

The graph of the two-equation is given below.

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Answer:

iii

Step-by-step explanation:

because of the amount taken from the cashews.and nuts and 1 of 3 were taken away