1. Suppose you have a variable X~N(8, 1.5). What is the probability that you have values between (6.5, 9.5)

The amount of interest is $252. The equations  or  represent the relation relationship between p, (r), (t) and (i).

Step-by-step explanation:

The formula of simple interest is

Where, principal amount (p), rate of interest (r), period of investment in years (t), and interest earned (i).

The principal amount is $1,400, interest rate of 6% and the time period of 3 years.

The amount of interest is

Therefore the amount of interest is $252.

The equations  or  represent the relation relationship between p, (r), (t) and (i).

The amount of interest is $252. The equations or represent the relation relationship between p, (r), (t) and (i).

The formula of simple interest is

Where, principal amount (p), rate of interest (r), period of investment in years (t), and interest earned (i).

The principal amount is $1,400, interest rate of 6% and the time period of 3 years.

The amount of interest is

Therefore the amount of interest is $252.

The equations or represent the relation relationship between p, (r), (t) and (i).

Answer:

  f(x +h) = 4x² +4h² +8xh +5x +5h +3

  (f(x+h) -f(x))/h = 4h +8x +5

  f'(x) = 8x +5

Step-by-step explanation:

For f(x) = 4x² +5x +3, you want the simplified expression f(x+h), the difference quotient (f(x+h) -f(x))/h, and the value of that at h=0.

Put (x+h) where h is in the function, and simplify:

  f(x+h) = 4(x+h)² +5(x+h) +3

  = 4(x² +2xh +h²) +5x +5h +3

  f(x +h) = 4x² +4h² +8xh +5x +5h +3

The difference quotient is ...

  (f(x+h) -f(x))/h = ((4x² +4h² +8xh +5x +5h +3) - (4x² +5x +3))/h

  = (4h² +8xh +5h)/h

  (f(x+h) -f(x))/h = 4h +8x +5

When h=0, the value of this is ...

  f'(x) = 4·0 +8x +5

  f'(x) = 8x +5

__

Additional comment

Technically, the difference quotient is undefined at h=0, because h is in the denominator, and we cannot divide by 0. The limit as h→0 will be the value of the simplified rational expression that has h canceled from every term of the difference. This will always be the case for difference quotients for polynomial functions.

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Answer:

4

Step-by-step explanation:

Answer:

Step-by-step explanation:

what do u need help with

Answer:

The triangles are similar.

Explanation:

Similar triangles have 3 pairs of congruent angles. In this diagram, we can see that the triangles WXP and WYZ share angle W, which is congruent to itself; therefore, they have at least 1 pair of congruent angles. We are given that angle X is congruent to angle Y, so that is a second pair of congruent angles. Finally, we know that angle P is congruent to angle Z because if two pairs of corresponding angles are congruent, then the third pair must also be congruent because the measures of the interior angles of both triangles have to add to 180°.

Answer and Step-by-step explanation:

We are given:

A side length of 7

An angle of 30.

We will use trigonometric functions to solve for a.

We will use the sine trig function.

\(sin(Angle) = \frac{Opposite (Side)}{Hypotenuse (Side)}\)

\(sin30 = \frac{7}{a}\)

Multiply a by both sides, then divide by sin30 on both sides.

\(a = \frac{7}{sin30}\)

Now, use a calculator and do 7 divided by sin of 30.

We get a to be:

14

a is equal to 14

#teamtrees #WAP (Water And Plant)

Btw you look cute in that picture you took

Answer:

21

Step-by-step explanation:

Answer:

x = 16

Step-by-step explanation:

We know that line a and b are parallel so they each have the same slope therefore, (7x + 2) = (8x - 14).

First we have so isolate a number value and x.

So we subtract 7x from 8x, which looks like:

2 = (x - 14)

Then we have to get that -14 to the other side, so we add and that looks like:

16 = x

Therefore, we have our answer, x = 16.

Answer:

1-3+2-5+-1-11

Step-by-step explanation:

I hope this helps :’)

Answer:

72 square units

Step-by-step explanation:

move above the dotted line to make a rectangel then the numbers are 6 and 12 then times them to get 72

Answer:

Yes it its!!! It goes on for a long time!! Keep that in mind when you are doing problems like this!  

:)

Step-by-step explanation:

Answer: Come up with questions that make sence. That are good solvablequestions. Make sure that you are able to take data off of it to see how people result in it.

Step-by-step explanation:

Answer:

180

Step-by-step explanation:

87b-179+957/87

Replace b with 4

87*4-179+957/87

Evaluate 87*4=348 and 958/87=11

348-179+11=169+11=180

Answer:

2.275%

Step-by-step explanation:

Given that:

Mean, m = 6

Standard deviation, s = 1

x ≥ 8

P(x ≥ 8)

Zscore = (x - m) / s

Zscore = (8 - 6) / 1

Zscore = 2

P(Z ≥ 2) = 1 - P(Z ≤ 2)

P(Z ≤ 2) = 0.97725

P(Z ≥ 2) = 1 - 0.97725

P(Z ≥ 2) = 0.02275

0.02275 * 100%

= 2.275

Answer:

idek and i dont ;like how this is working!

Step-by-step explanation:

Answer:

Step-by-step explanation:

The parallel lines create similar triangles, so corresponding sides are proportional.

  AC/AD = AB/AE

  (x -5)/(2x +3) = 15/(15+40)

Cross-multiplying gives ...

  55(x -5) = 15(2x +3)

  55x -275 = 30x +45 . . . . eliminate parentheses

  25x = 320 . . . . . . . . . . . . add 275-30x

  x = 12.8 . . . . . . . . . . . . . . .divide by 25

__

CD = AD -AC = (2x +3) -(x -5) = x +8 = 12.8 +8

CD = 20.8

Two polygons are similar if their respective sides have a constant ratio and their corresponding angles are congruent (in other words, if they are proportional).

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Answer:

Step-by-step explanation:

100%-10%=90%

90/100=0.9%

3000*0.9^10 years= 1046.04

Step-by-step explanation:

For annually,

3000×(1.10)^10= 7781.23

For quarterly,

3000×(1.10)^40= 135777.77

For montly,

3000×(1.10)^120=278127206.5

The equation that represents a line that passes through (-9, -3) with a slope of -6 is D. y+3=-6(x+9). I made a mistake when I was solving it to double-check.

Answer:

Clock

Step-by-step explanation:

The answer is Clock because the time changes from AM to PM and there are many things inside that cause it to work.

Answer:

Step-by-step explanation:

Required equation is:

Solution:

0 and 1 are the numbers that do not represent the probabilities of complementary events.

Probability is a measure of the possibility or chance that an event will occur.It is a value between 0 and 1, with 0 indicating that the event will not happen and 1 indicating that the event will almost likely happen. The number of favourable outcomes divided by the total number of possible outcomes is the probability of an event. Probability is utilised extensively in a wide range of professions, including mathematics, statistics, science, economics, and engineering.

In probability theory, complementary events are two events that together encompass all possible outcomes, and their probabilities add up to 1. The complement of an event A is the absence of A, indicated by A'.  Therefore, the probability of the complement of A is 1 minus the probability of A, or P(A') = 1 - P(A).

In the given pair, 0 represents the probability of an impossible event, and 1 represents the probability of a certain event. These events are not complementary, as there is no other event that can occur apart from a certain event, and their probabilities do not add up to 1. Therefore, this pair does not represent the probabilities of complementary events.

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Plane ADF is another way to label Plane J.

In order to determine which of the given options is another way to label Plane J, we need to first identify the key characteristics of Plane J.

These characteristics are its points, lines, and planes that it contains. We can then use these characteristics to compare and match them with the given options.

Here are the key characteristics of Plane J: Points: J, A, D Lines: JA, JD, AD Planes: Plane J Now let's examine each option to see which one matches the characteristics of Plane J: Option A: Plane h This option is not a match since Plane h is not one of the planes that contain the points J, A, and D.

Option B: Plane ABD This option is not a match since Plane ABD contains points A, B, and D but not point J.

Option C: Plane EFG This option is not a match since Plane EFG contains points E, F, and G but not point J.

Option D: Plane ADF This option is a match since Plane ADF contains points A, D, and F which are all points that are contained in Plane J.

Therefore, Plane ADF is another way to label Plane J.

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Answer:

rational

Step-by-step explanation:

Answer:

A rational because it is

Answer:

112.5$

Step-by-step explanation:

\(80 - 60 = 20 \\(20 \div 80)100 = 25\% \\ 75\% \times 150 = 112.5 \)

The difference in mean growth per week is 3.7cm/week

From the graph given :

Growth per week for Basil = 2, 6, 9, 10, 14, 16

Growth per week for Mint = 1, 2, 4, 7, 9, 12

Mean growth per week = (2+6+9+10+14+16) / 6 = 9.5 cm/week

Mean growth per week (Mint) = (1+2+4+7+9+12)/6 = 5.83 cm/week

The difference cannbe obtained by subtracting the mean Values thus ;

Difference in average growth = 9.5 - 5.83 = 3.67 cm/week

Therefore, the difference in mean growth per week is 3.7cm/week

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Answer:

5.5 X \(10^{8}\)

Step-by-step explanation:

This is the Scientific Notation.

Answer:

(a)\(x^TAx=3x_1^2+4x_1x_2+2x_2^2+2x_2x_3\)

(b) 12

(c)\(2\frac{3}{4}\)

Step-by-step explanation:

\(G$iven A=\left[\begin{array}{ccc}3&2&0\\2&2&1\\0&1&0\end{array}\right]\)

We are to compute the quadratic form \(x^TAx\) for A.

Part A

\(x=\left[\begin{array}{ccc}x_1\\x_2\\x_3\end{array}\right]\)

\(x^TAx = \left[\begin{array}{ccc}x_1&x_2&x_3\end{array}\right]\left[\begin{array}{ccc}3&2&0\\2&2&1\\0&1&0\end{array}\right]\left[\begin{array}{ccc}x_1\\x_2\\x_3\end{array}\right]\)

\(= \left[\begin{array}{ccc}x_1&x_2&x_3\end{array}\right]\left[\begin{array}{ccc}3x_1+2x_2+0x_3\\2x_1+2x_2+1x_3\\0x_1+1x_2+0x_3\end{array}\right]\)

\(= x_1(3x_1+2x_2+0x_3)+x_2(2x_1+2x_2+1x_3)+x_3(0x_1+1x_2+0x_3)\\= x_1(3x_1+2x_2)+x_2(2x_1+2x_2+x_3)+x_3(x_2)\)

\(= 3x_1^2+2x_1x_2+2x_1x_2+2x_2^2+x_2x_3+x_2x_3\\\\x^TAx=3x_1^2+4x_1x_2+2x_2^2+2x_2x_3\)

Part B

\(x=\left[\begin{array}{ccc}-2\\-1\\5\end{array}\right]\\x^TAx=3x_1^2+4x_1x_2+2x_2^2+2x_2x_3\\=3(-2)^2+4(-2)(-1)+2(-1)^2+2(-1)(5)\\=3*4+4*2+2-10\\=12+8+2-10\\=12\)

Part C

\(x=\left[\begin{array}{ccc}\frac{1}{2}\\\frac{1}{2}\\\frac{1}{2}\end{array}\right]\\x^TAx=3x_1^2+4x_1x_2+2x_2^2+2x_2x_3\\=3(\frac{1}{2})^2+4(\frac{1}{2})(\frac{1}{2})+2(\frac{1}{2})^2+2(\frac{1}{2})(\frac{1}{2})\\\\=\frac{3}{4}+1+ \frac{1}{2}+\frac{1}{2}\\\\=2\frac{3}{4}\)

Answer:

4m + 2m = 6m

Step-by-step explanation: