Which of the following is a true statement?

Answer:

1600N

Step-by-step explanation:

Force = 400 N

Angle with horizontal = 60°

Displacement in horizontal direction = 8 m

work done formula when angle is included: Force * distance * cos(angle)

400 * 8 * cos(60)

= 400 * 8 * 1/2

= 1600N

Answer:

The equation of [tex]f(x) = e^{-3\cdot x}[/tex] by Maclaurin series is [tex]f(x) = \Sigma\limits_{i=0}^{\infty} \frac{(-3\cdot x)^{i}}{i!}[/tex].

Step-by-step explanation:

The Maclaurin series for [tex]f(x)[/tex] is defined by the following formula:

[tex]f(x) = \Sigma\limits_{i = 0}^{\infty} \frac{f^{(i)}(0)}{i!} \cdot x^{i}[/tex] (1)

Where [tex]f^{(i)}[/tex] is the i-th derivative of the function.

If [tex]f(x) = e^{-3\cdot x}[/tex], then the formula of the i-th derivative of the function is:

[tex]f^{(i)} = (-3)^{i}\cdot e^{-3\cdot x}[/tex] (2)

Then,

[tex]f^{(i)}(0) = (-3)^{i}[/tex] (2b)

Lastly, the equation of the trascendental function by Maclaurin series is:

[tex]f(x) = \Sigma\limits_{i=0}^{\infty} \frac{(-3)^{i}\cdot x^{i}}{i!}[/tex]

[tex]f(x) = \Sigma\limits_{i=0}^{\infty} \frac{(-3\cdot x)^{i}}{i!}[/tex] (3)

Answer:

I belive it has no x intercepts

it looks weird, but it can be a function. the x-intercept and the y-intercept can also be found in the table above.

to draw a line that can represent a function with these point, we would need to cross y=0 multiple times, so it will have more then one x-intercept.

option A

key takeaway: just draw stuff you find complicated:)

Answer:

Step-by-step explanation:

the first and last choices look good  

Answer:

The unlimited mileage plan would save money for Lia from 410 miles onwards.

Step-by-step explanation:

Since Lia can rent a van for either $ 90 per day with unlimited mileage or $ 50 per day with 250 free miles and an extra 25 ¢ for each mile over 250, to determine for what number of miles traveled in one day would the unlimited mileage plan save Lia money, the following calculation must be performed:

90.25 - 50 = 40.25

40.25 / 0.25 = 161

161 + 250 = 411

Therefore, the unlimited mileage plan would save money for Lia from 410 miles onwards.

Answer: [tex]\dfrac{3}{16},\ \dfrac{1}{2}, \dfrac{7}{2}\ \text{inch}[/tex]

Step-by-step explanation:

Given

Javier created a table for the amount of water evaporated in each week

After two weeks, the amount of water evaporated is

[tex]\Rightarrow \dfrac{2}{16}+\dfrac{1}{16}\\\\\Rightarrow \dfrac{2+1}{16}=\dfrac{3}{16}\ \text{inch}[/tex]

Total amount of water evaporated in four weeks is

[tex]\Rightarrow \dfrac{2}{16}+\dfrac{1}{16}+\dfrac{3}{16}+\dfrac{2}{16}\\\\\Rightarrow \dfrac{2+1+3+2}{16}=\dfrac{8}{16}\\\Rightarrow \dfrac{1}{2}\ \text{inch}[/tex]

If Javier originally puts 4 inches of water, amount of water left in the bucket

[tex]\Rightarrow 4-\dfrac{1}{2}\\\\\Rightarrow \dfrac{4\times 2}{2}-\dfrac{1}{2}\\\\\Rightarrow \dfrac{8-1}{2}=\dfrac{7}{2}\ \text{inch}[/tex]

Answer:

115

Step-by-step explanation:

Answer:

D. 60

Step-by-step explanation:

Range is the difference between the maximum value and the minimum value.

The minimum value is at the extreme end of the whisker of the box plot to your left = 65

The maximum value is at the extreme end of the whisker of the box plot to your right = 125

Range = 125 - 65 = 60

Answer:

Step-by-step explanation:

Answer:

-1.28 AND 2.61

Step-by-step explanation:

[tex]10= -4x+3x^2\\ 3x^2 -4x - 10 = 0\\\\[/tex]

use quadratic formula

x =  [tex]\frac{-b+\sqrt{b^{2} -4ac} }{2a}[/tex]   x =  [tex]\frac{-b-\sqrt{b^{2} -4ac} }{2a}[/tex]

Solution/X-Intercepts: -1.28 AND 2.61    

Answer:

The correct answer is:

(a) Mean = 170,

    Standard deviation = 30

(b) 1700

Step-by-step explanation:

Given:

(a)

Mean of monthly expenses will be:

= [tex]\frac{\mu}{2}[/tex]

= [tex]\frac{2040}{2}[/tex]

= [tex]170[/tex]

Standard deviation will be:

= [tex]\frac{\sigma}{12}[/tex]

= [tex]\frac{360}{12}[/tex]

= [tex]30[/tex]

(b)

The total amount of monthly expenses will be:

= [tex]n\times \frac{\mu}{12}[/tex]

= [tex]100\times 170[/tex]

= [tex]1700[/tex]

Answer:

22

Step-by-step explanation:

3x-14= 4(x-9)

3×-14= 4x-36

4x-36-3x+14=0

×-22÷0

x=22

Answer:

yes I look this problem in this figure

Answer:

B. 200 cu. units

Step-by-step explanation:

Volume of the triangular prism = ½*b*h*l

Where,

b = 8 units

h = 5 units

l = 10 units

Plug in the values

Volume of the prism = ½*8*5*10

= 4*5*10

= 200 cu. units

Answer:

There are 8 penguins and 6 reindeers.

Step-by-step explanation:

Since Brian, the gorilla, was planning a party for his zoo friends, and he sent his elves Jamie and Nancy into the North Pole exhibit to count the penguins and reindeer, and Jamie said there were 40 legs and Nancy said there were 14 heads To determine how many penguins and reindeer were in the exhibit, the following calculation must be performed:

Penguins: 1 head and 2 legs

Reindeers: 1 head and 4 legs

40 - (14 x 2) = X

40 - 28 = X

12 = X

12/2 = 6

14 - 6 = 8

8 x 2 + 6 x 4 = X

16 + 24 = X

40 = X

Therefore, there are 8 penguins and 6 reindeers.

Some symbols and numbers are missing. I assume the system is supposed to read

2x - y + 2z + w = -3

x + 2y - 3z + w = 12

3x - y - z + 2w = 3

-2x + 3y + 2z - 3w = -3

In matrix form, this is

[tex]\begin{bmatrix}2&-1&2&1\\1&2&-3&1\\3&-1&-1&2\\-2&3&2&-3\end{bmatrix}\begin{bmatrix}x\\y\\z\\w\end{bmatrix}=\begin{bmatrix}-3\\12\\3\-3\end{bmatrix}[/tex]

which we can strip down to the augmented matrix,

[tex]\left[\begin{array}{cccc|c}2&-1&2&1&-3\\1&2&-3&1&12\\3&-1&-1&2&3\\-2&3&2&-3&-3\end{array}\right][/tex]

Now for the row operations:

• swap rows 1 and 2

[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\2&-1&2&1&-3\\3&-1&-1&2&3\\-2&3&2&-3&-3\end{array}\right][/tex]

• add -2 (row 1) to row 2, -3 (row 1) to row 3, and 2 (row 1) to row 4

[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&8&-1&-27\\0&-7&8&-1&-33\\0&7&-4&-1&21\end{array}\right][/tex]

• add 7 (row 2) to -5 (row 3), and row 3 to row 4

[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&8&-1&-27\\0&0&16&-2&-24\\0&0&4&-2&-12\end{array}\right][/tex]

• multiply through rows 3 and 4 by 1/2

[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&8&-1&-27\\0&0&8&-1&-12\\0&0&2&-1&-6\end{array}\right][/tex]

• add -4 (row 4) to row 3

[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&8&-1&-27\\0&0&0&3&12\\0&0&2&-1&-6\end{array}\right][/tex]

• swap rows 3 and 4

[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&8&-1&-27\\0&0&2&-1&-6\\0&0&0&3&12\end{array}\right][/tex]

• multiply through row 4 by 1/3

[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&8&-1&-27\\0&0&2&-1&-6\\0&0&0&1&4\end{array}\right][/tex]

• add row 4 to row 3

[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&8&-1&-27\\0&0&2&0&-2\\0&0&0&1&4\end{array}\right][/tex]

• multiply through row 3 by 1/2

[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&8&-1&-27\\0&0&1&0&-1\\0&0&0&1&4\end{array}\right][/tex]

• add -8 (row 3) and row 4 to row 2

[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&0&0&-15\\0&0&1&0&-1\\0&0&0&1&4\end{array}\right][/tex]

• multiply through row 2 by -1/5

[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&1&0&0&3\\0&0&1&0&-1\\0&0&0&1&4\end{array}\right][/tex]

• add -2 (row 2) and 3 (row 3) and -1 (row 4) to row 1

[tex]\left[\begin{array}{cccc|c}1&0&0&0&-1\\0&1&0&0&3\\0&0&1&0&-1\\0&0&0&1&4\end{array}\right][/tex]

Then the solution to the system is (x, y, z, w) = (-1, 3, -1, 4).

Answer:

The slope of the green line is 3

Step-by-step explanation:

The lines are perpendicular, so the slopes are negative inverses

-1/(-1/3)

3

Answer:

0.2

Step-by-step explanation:

The total number of points in PS is a sum of the number of points in :

PQ + QR + RS ;

PQ = 7 ; QR = 13 ; RS = 5

PS = (7 + 13 + 5) = 25

Probability that point selected at random is in RS ;

Required outcome = point in RS

Total possible outcomes = points in PS

Probability = RS / PS = 5 / 25 = 0.2

9514 1404 393

Answer:

  (c)  x = 12.5

Step-by-step explanation:

  -0.2(x -4) = -1.7

  -0.2x +0.8 = -1.7 . . . eliminate parentheses using the distributive property

  -0.2x = -2.5 . . . . . . subtract 0.8

 x = 12.5 . . . . . . . . divide by -0.2

Answer:

13

Step-by-step explanation:

1. Round 19.625 up to 20.

2. Round 6.77 up to 7.

3. Calculate the equation. Ans is 13.

Answer:

Scott invested $ 3,000 at 12% annually, and $ 2,400 at 8% annually.

Step-by-step explanation:

Since Scott invested a total of $ 5400 at two separate banks, and one bank pays simple interest of 12% per year while the other pays simple interest at a rate of 8% per year, if Scott earned $ 552.00 in interest during a single year, to determine how much did he deposit in each bank, the following calculation must be performed:

5400 x 0.12 + 0 x 0.08 = 648

4400 x 0.12 + 1000 x 0.08 = 608

3000 x 0.12 + 2400 x 0.08 = 552

Therefore, Scott invested $ 3,000 at 12% annually, and $ 2,400 at 8% annually.

9514 1404 393

Answer:

  True

Step-by-step explanation:

Your calculator can tell you this is true. Or, you can simplify the given expression:

  [tex]\left(\dfrac{32}{3125}\right)^{2/5}=\left(\dfrac{2^5}{5^5}\right)^{2/5}=\dfrac{2^2}{5^2}=\boxed{\dfrac{4}{25}}[/tex]

__

The applicable rule of exponents is (a^b)^c = a^(bc).

Answer:

[tex] \frac{67}{30} \: \text{or} \:2 \frac{7}{30} [/tex]

Step-by-step explanation:

5/6 ÷ 1/3 - 2/3 (2/5)

Hope it helps you! ＼(^ᴥ^)／

Answer:

The answer is "0.18"

Step-by-step explanation:

[tex]10\% \ of \ 50= 5 \text{are left handed}\\\\45\ \text{are right handed}\\\\[/tex]

If the probability exactly 4 were heft handed

 [tex]=^{50}_{C_4}\times (\frac{5}{50})^4 \times (\frac{45}{50})^{4b}\\\\=^{50}_{C_4} \times (0.1)^4 \times (0.9)^{4b}\\\\=230300 \times (0.1)^4 \times (0.9)^{4b}\\\\=0.181 \approx 0.18[/tex]

Answer:

37.94

Step-by-step explanation:

the 9th percentile is equal to a zscore of -1.34

-1.34=(x-50)/9

x=37.94

Answer:

a. $10  

b. 10.46  

c. 10.46  

d. 0.096