Find an explicit rule for the nth term of the arithmetic sequence.

-9, -4, 1, 6, ...

Answer:

381/90

Step-by-step explanation:

x = 4.2333.... ----------(I)

Number of digit after decimal is 2 ( 4 , 3). So multiply both sides by of equation 100

100x = 423.333..... (II)

One digit (3) is repeating.So, multiply by both sides of equation (I) by 10

10x = 42.333....... -----(III)

Subtract Equation (III) from (II)

(II)     100x = 423.333......

(III)        10x =  42.333......  {Subtract}

         90x   = 381

                x = 381/90

Answer:

Step-by-step explanation:

Answer:

14.3

Step-by-step explanation:

sin73 = opposite/hypotenuse = x/15

x = 15sin73 = 14.344571 = 14.3

Answer:

45g

Step-by-step explanation:

The amount of salt left once the whole water is evaporated can be calculated as follows

= 12% × 375

= 12/100 × 375

= 0.12×375

= 45

Hence 45g of salt is left after the evaporation of water

Answer:

45g

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

[tex]8x \sqrt{2} - 4 \sqrt{2} [/tex]

Answer:

The standard deviation of the sampling distribution of the sample wait times is of 0.8 minutes.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30. Otherwise, the mean and the standard deviations holds, but the distribution will not be approximately normal.

Standard deviation 4 minutes.

This means that [tex]\sigma = 4[/tex]

A sample of 25 wait times is randomly selected.

This means that [tex]n = 25[/tex]

What is the standard deviation of the sampling distribution of the sample wait times?

[tex]s = \frac{4}{\sqrt{25}} = 0.8[/tex]

The standard deviation of the sampling distribution of the sample wait times is of 0.8 minutes.

Answer:

m=4

Step-by-step explanation:

m = y2 - y1/x2 - x1

(y2=8, y1=0, x2= 2, x1=0)

m = y2 -y1/x2 - x1

= 8 - 0/2 - 0

= 8/2

=4

Answer:

y = 4x - 12

Step-by-step explanation:

y = 4x + b

8 = 4(5) + b

8 = 20 + b

-12 = b

[tex] \green{ \boxed{\boxed{\begin{array}{cc} \maltese \bf \: \: \: we \: know \: that \: \\ \sf \: if \: any \: equation\:of \: line \: which \: slope (m) \\ \sf \: and \: passes \: through \: (x_1,y _1) \: \: then \: its \\ \sf equation \: is \: : \\ \\ \red{ \boxed{ \bf y - y_1 = m(x - x_1)}}\bf\end{array}}}}[/tex]

Given that,

A equation of the line with a slope of m = 4 and that contains / passes through the point (5, 8).

So,

[tex] \green{ \boxed{\boxed{\begin{array}{cc} \bf \: x_1 = 5 \: \: \: \\ \bf y_1 = 8 \\ \bf \: m \: = 4 \: \: \end{array}}}}[/tex]

NOW,

The equation is :

[tex] \green{ \boxed{\boxed{\begin{array}{cc} \bf \: y - 8 = 4(x - 5) \\ \\ = > \bf \: y - 8 = 4x - 20 \\ \\ = > \pink{ \boxed{\bf\:4x - y - 12 = 0}} \end{array}}}}[/tex]

Answer:

1) The total displacement vector is ((16 + √2)/2, -(6+11·√2)/2)

2) The number of miles they'd have to walk is approximately 13.856 miles

Step-by-step explanation:

1) The distance, direction, and location of the path of the walk the person takes,  are listed as follows;

Start location, (0, 0)

6 miles East walk to location, (6, 0)

6 miles Southeast to location, (6 + 3·√2, -3·√2)

3 miles South to location, (6 + 3·√2, -3·√2 - 3)

5 miles Southwest to location, (6 + 3·√2 - 2.5·√2, -3·√2 - 3 - 2.5·√2)

2 miles East to location, (6 + 3·√2 - 2.5·√2 + 2, -3·√2 - 3 - 2.5·√2)

(6 + 3·√2 - 2.5·√2 + 2, -3·√2 - 3 - 2.5·√2) = ((16 + √2)/2, -(6+11·√2)/2)

Therefore the destination coordinates is ((16 + √2)/2, -(6+11·√2)/2)

The total displacement vector, [tex]\underset{d}{\rightarrow}[/tex] = ((16 + √2)/2, -(6+11·√2)/2)

d =  (16 + √2)/2)·i - (6+11·√2)/2)·j

2) If the person walked straight home, the number of miles they'd have to walk, [tex]\left | \underset{d}{\rightarrow} \right |[/tex], is given as follows;

[tex]\left | \underset{d}{\rightarrow} \right | = \sqrt{\left(\dfrac{16 +\sqrt{2} }{2} \right)^2 + \left(-\dfrac{6 + 11 \cdot \sqrt{2} }{2} \right)^2 } = \sqrt{134 + 41 \cdot \sqrt{2} }[/tex]

Therefore;

If the person walked straight home, the number of miles they'd have to walk [tex]\left | \underset{d}{\rightarrow} \right | \approx 13.856 \ miles[/tex]

Answer:

1/2

Step-by-step explanation:

You need to see how much times bigger or smaller the shape is after it's changed, that's the scale factor

The dialated image (blue one where it says J'K'T'P') seems like half the size of the black one, so we'll say the scale factor is half or 1/2 (if it's double then the scale factor is 2, for triple, it's 3)

Answered by GAUTHMATH

Answer:

divide, 2x+9

Step-by-step explanation:

got it right

Answer:

69.3

Step-by-step explanation:

if you put it into 2D, you get a right triangle with leg lengths 62 (vertical height) and 31 (1/2 the base's length). Using Pythagorean's Theorem you get sqrt((62^2)+(31^2))= 69.318. Rounding to the nearest tenth you get 69.3

Answer:

Step-by-step explanation:

Mean of the data = sum of the data / number of frequencies:

Correct choice is d

Answer:

3(13x-5)

Step-by-step explanation:

first step open your bracket,u have

=4x²+20x-3x-15-4x²+22x then collect like terms

=4x²-4x²+20x-3x+22x-15

=0x²+39x-15

=39x-15

further simplifying u have:

=3(13x-5)

Answer:not a man but I think you should just relax and be yourself, high school isn’t scary at all. When you go in for orientation walk around the school and find your classes so you have a good map of where you need to go in your head already! Best of luck

Step-by-step explanation:

Step-by-step explanation:

Hope you understand through the steps on the attachment, if not kindly reach out

Answer:

the answer to your question is D

Answer:

c

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Using the Cosine rule to find AC

AC² = BC² + AB² - (2 × BC × AB × cosB )

      = 18² + 12² - ( 2 × 18 × 12 × cos75° )

      = 324 + 144 - 432cos75°

      = 468 - 111.8

      = 356.2 ( take the square root of both sides )

AC = [tex]\sqrt{356.2}[/tex] ≈ 18.9

-----------------------------------------

Using the Sine rule to find ∠ A

[tex]\frac{18}{sinA}[/tex] = [tex]\frac{18.9}{sin75}[/tex] ( cross- multiply )

18.9 sinA = 18 sin75° ( divide both sides by 18.9 )

sinA = [tex]\frac{18sin75}{18.9}[/tex] , then

∠ A = [tex]sin^{-1}[/tex] ( [tex]\frac{18sin75}{18.9}[/tex] ) ≈ 66.9°

Answer:

x is 30 degrees

Step-by-step explanation:

Answer:

(27xy +3)/5x^2 +6x

Step-by-step explanation:

((15xy^2 )/ x^2 + 5x + 6 ) × ((2x^2 + 7x + 3) / 5x^2y)

(3y ×(2x+ 7x + 3)) / 5x^2 +6x)

Answer:

Step-by-step explanation:

Given,

m || n

So,

35° = y° [Alternate interior angles]

And,

y° + x° = 180° [Since linear pair]

=> x + 35 = 180

=> x = 180 - 35

=> x = 145°

Hence,

x = 145°, y = 35°

Answer:

x = 145

y = 35

Step-by-step explanation:

35 and y are alternate interior angles and alternate interior angles are equal when the lines are parallel

35 = y

x+y = 180 because x and y form a straight line

x+35 = 180

x = 180-35

x = 145

Answer:

A

Step-by-step explanation:

The recursive rule allows any term to be found by multiplying the previous term by the common ratio r

Here r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{20}{4}[/tex] = 5

Then

f(n) = 5 . f(n - 1) , for n ≥ 2 → A

Answer:

Step-by-step explanation:

Look at the y-values as x-values are same for all tables.

We see that:

Answer:

[tex]1 \frac{7}{15} [/tex]

Step-by-step explanation:

[tex] - \frac{1}{3} \times 2 + x = \frac{4}{5} \\ - \frac{2}{3} + x = \frac{4}{5} \\ x = \frac{4}{5} + \frac{2}{3} \\ x = \frac{12 + 10}{15} \\ x = \frac{22}{15} \\ x = 1 \frac{7}{15} [/tex]

Answer:

58%

Step-by-step explanation:

10*5=50

7*3=21

21/50 chance to choose inside small rectangle

21/50*2 = 42/100 chance to choose inside small rectangle

100-42=58%

Answer:

[tex]{ \tt{x = \sqrt{ {10}^{2} - {8}^{2} } }} \\ { \tt{x = \sqrt{36} }} \\ { \tt{x = 6}}[/tex]

Answer:

X = 6

Step-by-step explanation:

This is a right angled triangle. Thus, pythagoras theorem will be best for its solution.

Hypotenuse squared = height squared + base squared

SH² = H² + B²

10² = x² + 8²

100 = x² + 64

10 – 64 = x² + 64 – 64 (grouped like terms)

36 = x²

Root of both sides

Therefore x = 6

Answer:

[tex]\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\la\la\la\la\ddddddddddddddddddddddddddddddddcleverdddddd\ffffffffffffffffffffffffffffffffffffffff\pppppppppppppppppppppppppppppppppppp\dddddd \displaystyle \Large \boldsymbol{} t_1=\boxed{5} \\\\d=\boxed{-4} \\\\t_n=\boxed{9-4n}[/tex]

Step-by-step explanation:

[tex]\displaystyle\large \boldsymbol{Rule: t_n=S_{n}-S_{n-1}} \\\\\\S_n=7n-2n^2 \ \ \ \ then \\\\\Longrightarrow S_{n-1}=7(n-1)-2(n-1)^2 =7n-7-2n^2+4n-2 \\\\then \\\\\\S_{n}-S_{n-1}=7n\!\!\!\!\!\!\diagup-2n^2\!\!\!\!\!\!\diagup-7n\!\!\!\!\!\!\diagup+7+2n^2\!\!\!\!\!\!\diagup-4n+2=9-4n \\\\t_n=9-4n => t_1=5\\\\d=t_2-t_{1}=1-5=-4[/tex]

Answer:

Total number in favour:

Probability:

Total number in against:

Probability: