Suppose f(x) is a degree three polynomial with ⋅ a root of multiplicity 2 at x=1⋅ a root of multiplicity 1 at x=−2⋅ a y-intercept at (0,4).Find a formula for f(x).

Answer:

3 if 2d, 2 if 3D

I think have an amazing day and stay safe and stay home

Answer:

a) 8 days

b) 84 miles

Step-by-step explanation:

a) L (d) = 201 - 9d

9d = 201 - L (d)

9d = 201 - 129

9d = 72

9d/9 = 72/9

d = 8

b) L (d) = 201 - 9d

L (13) = 201 - 9 (13)

= 201 - 117

= 84

Answer:

  E.  a^(1/3)b^(1/6)

Step-by-step explanation:

You want an expression equivalent to (a^(2/3)b^(1/3))^(1/2).

The applicable rules of exponents are ...

  (a^b)^c = a^(bc)

  (ab)^c = (a^c)(b^c)

The given expression simplifies to ...

  \((a^{2/3}b^{1/3})^{1/2}=a^{(2/3)(1/2)}b^{(1/3)(1/2)}=\boxed{a^{1/3}b^{1/6}}\)

The covariance of two random variables X and Y is defined as

Cov(X, Y) = E[(X - E[X]) (Y - E[Y])]

where E is expectation.

If we replace Y with X, then this reduces to just the variance of X, which is defined as

Var(X) = E[(X - E[X])²]

Answer:a) 28

Step-by-step explanation:

10-2=8

8 objects currently 6 placements for next week = 28 combinations of people of who could stay or leave

Answer:

A

Step-by-step explanation:

The answer is the first one: 28 :) Have a good day everyone!

Answer: 18(a)-89=217

Step-by-step explanation:

If a = 17 then you substitute/replace the a with the 17. Making 18(a) into 18(17). 18(17)= 306 - 89 = 217.

Hope this helped.

Answer:217

Step-by-step explanation:

putting the value of a in the equation.

18×17-89= 217

Answer:

D

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = \(\frac{1}{2}\) x + 3 ← is in slope- intercept form

with slope m = \(\frac{1}{2}\)

• Parallel lines have equal slopes , then

y = \(\frac{1}{2}\) x + c ← is the partial equation

to find c substitute (2, - 4 ) into the partial equation

- 4 = \(\frac{1}{2}\) (2) + c = 1 + c ( subtract 1 from both sides )

- 5 = c

y = \(\frac{1}{2}\) x - 5 ← equation of parallel line

The linear equation for the first scenario is y = 500 while for the second scenario is y = 20x

The equation of a straight line is given by:

y = mx + b;

where y,x are variables, m is the slope of the line and b is the y intercept.

let x represent the number of sales and y represent the total salary for a weeks.

For scenario 1, there is a constant salary of $500. The linear equation becomes:

y = 500

For scenario 2, there is a commission of $20 per sale. The linear equation becomes:

y = 20x

Based on mathematical operations, the lowest amount that Annabel can pay for pencils is $15.20

The lowest amount that Annabel can pay for pencils can be determined using the mathematical operations of multiplication and division.

Multiplication and division are two of the four basic mathematical operations, including addition and subtraction.

If Annabel chooses to purchase the first pencil at 30p each, she would pay £22.80 (£0.30 x 76).

If Annabel chooses to purchase the second pencil class of a pack of 10 pencils for £2, she would pay £15.20 [£2 x (76 ÷ 10)].

Pencils for sale

30p each

Pack of 10 pencils for £2

Thus, if Annabel wants to buy the pencils, she can either pay £15.20 or £22.80, but using mathematical operations, the lowest amount she can pay is £15.20.

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Answer:

c) 108

Step-by-step explanation:

All angles of a regular polygon are the same.

Answer:

x = 3.25 Each diagonal = 34.25. Step-by-step explanation: LMNP is a rectangle and it has diagonals LN and MP. Now, given that LN = 13x - 8 and MP = 9x + 5 Now, we know that the two diagonals of a rectangle are of the same length. So, LN = MP   ⇒ 13x - 8 = 9x + 5 ⇒ 4x = 13 ⇒ x = 3.25 (Answer) Therefore, the each diagonal is of (13 × 3.25 - 8) = 35.25 length. (Answer)

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Step-by-step explanation:

Answer:

Can you provide an Attachment?

Step-by-step explanation:

^^

Answer:

the second one I'm pretty sure

Step-by-step explanation:

Answer:

its definitely B

Step-by-step explanation:

Answer:

Hope this helps

Step-by-step explanation:

to get the slope of any straight line we only need two points off of it, hmmm let's use the points in the picture below.

\((\stackrel{x_1}{2}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{8}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{8}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{2}}}\implies \cfrac{4}{2}\implies 2\)

The 98% confidence interval for the true mean statistics anxiety score (μ) is approximately (39.037, 39.763).

To calculate the 98% confidence interval for the true mean statistics anxiety score (μ) for all undergraduate students in the U.S., we can use the formula:

Confidence interval = sample mean ± (critical value * standard error)

First, we need to find the critical value associated with a 98% confidence level. Since we are assuming a normal distribution, we can use the Z-table or a statistical software to find this value. For a 98% confidence level, the critical value is approximately 2.33.

Next, we calculate the standard error (SE) using the formula:

SE = standard deviation / √sample size

In this case, the standard deviation is 0.9 and the sample size is 33. Plugging these values into the formula, we get: SE = 0.9 / √33 ≈ 0.156

Now, we can calculate the confidence interval:Confidence interval = 39.4 ± (2.33 * 0.156)

Simplifying the expression:Confidence interval ≈ 39.4 ± 0.363

This gives us the interval (39.037, 39.763). This means we are 98% confident that the true mean statistics anxiety score for all undergraduate students in the U.S. falls within this interval.

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Answer:

D 7a - 11b

Step-by-step explanation:

9a- b -2a - 10b

7a - b -10b

7a - 11b

Answer:

I believe the correct answer is D.

Step-by-step explanation:

Answer:

0.42

Step-by-step explanation:

To solve the problem, we need to add the probability of picking a club to the probability of picking a face card, and then subtract the probability of picking a club that is also a face card (because we would have counted it twice).

There are 13 clubs in a standard deck, so the probability of picking a club is 13/52 or 0.25.

There are 12 face cards (4 jacks, 4 queens, and 4 kings) in a standard deck, so the probability of picking a face card is 12/52 or 0.23.

However, there are 3 cards that are both clubs and face cards (the jack of clubs, queen of clubs, and king of clubs), so we need to subtract the probability of picking one of those cards. There are 3 of them out of 52 total cards, so the probability of picking a club that is also a face card is 3/52 or 0.06.

Therefore, the probability of picking a club OR a face card is:

0.25 + 0.23 - 0.06 = 0.42 (rounded to two decimal places).

So the answer is 0.42.

We are given the following two points

Let us find the slope of the line that passes through these points

The slope of a line is given by

Let us substitute the given points into the above slope formula

Therefore, the slope of this line is 0.

This means that it is a horizontal line.

9514 1404 393

Answer:

  A.  (4, 12)

Step-by-step explanation:

Adding the second equation to twice the first will eliminate y.

  2(10x +2y) +(3x -4y) = 2(64) +(-36)

  23x = 92 . . . . . . . . simplify

  x = 4 . . . . . . . . . divide by 23

This value matches choice A: (4, 12).

Answer:

(a) y intercept is approximately 4.3

(b) \(y = 1.5x+4.5\)

Step-by-step explanation:

Given

See attachment for graph

Solving (a) The y intercept

This is the point where \(x =0\)

From the attached graph; By observation

\(y \approx 4.3\) when \(x =0\)

So, the y intercept is approximately 4.3

Solving (b): The equation of best fit.

First, calculate the slope of the line using:

\(m = \frac{y_2 - y_1}{x_2 - x_1}\)

Where

\((x_1,y_1) = (9,18)\)

\((x_2,y_2) = (8,16.5)\)

So:

\(m = \frac{16.5- 18}{8 - 9}\)

\(m = \frac{-1.5}{- 1}\)

\(m = 1.5\)

The equation is then calculated using:

\(y =m(x - x_1) + y_1\)

Where: \(m = 1.5\) and \((x_1,y_1) = (9,18)\)

\(y = 1.5(x - 9) + 18\)

\(y = 1.5x - 9*1.5 + 18\)

\(y = 1.5x - 13.5 + 18\)

\(y = 1.5x+4.5\)

Answer:

-16

Step-by-step explanation:

2xy + 3yz - xyz

x = 2, y = -2, z = 4

First, plug these values into the equation.

2(2)(-2) + 3(-2)(4) - (2)(-2)(4) = ?

Next, multiply the parentheses.

(-8) + (-24) - (-16) = ?

When you add a negative, you are actually subtracting the number. And when you subtract a negative, you are actually adding the number. Apply this to the equation.

-8 - 24 + 16 = ?

Now, simplify from left to right.

-32 + 16

-16

Your answer is -16.

Hope this helps!

(a) 41.6m/sec is the average rate of change for the distance driven from zero seconds to four seconds.

(b) 16.7 m/sec is the average rate of change for the distance driven from six seconds to ten seconds.

Given,

In the question:

Amy is driving a racecar. The table below gives the distance D (t) (in meters) she has driven at a few times t (in seconds) after she starts.

To see the table in the figure.

Now, According to the question:

(a) To find the average rate of change for the distance driven from zero seconds to four seconds.

According to the table we can get t(0 ~ 4 seconds) the average rate

\(V_{a}\) = 166.4 ÷ 4

     = 41.6 m/sec

(b) To find the average rate of change for the distance driven from six seconds to ten seconds.

\(V_{b}\) = (239.6 - 172.8) ÷ (10 - 6)

\(V_{b}\) = 66.8 ÷ 4

\(V_{b}\) = 16.7 meters per seconds.

Speed is equal to distance divided by time .

Hence, (a) 41.6m/sec is the average rate of change for the distance driven from zero seconds to four seconds.

(b) 16.7 m/sec is the average rate of change for the distance driven from six seconds to ten seconds.

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Answer:

Step-by-step explanation:

11.04 = 10(1.02)^n

1.104 = 1.02^n

ln 1.104 = ln 1.02^n

ln 1.104 = n ln 1.02

n = ln 1.104/ ln 1.02

n = 4.99630409516

4.99 can be rounded to 5.

So a reasonable domain would be 0 ≤ x < 5

PART B)

f(0) = 10(1.02)^0

f(0) = 10(1)

f(0) = 10

The y-intercept represents the height of the plant when they began the experiment.

f(1) = 10(1.02)^1

f(1) = 10(1.02)

f(1) = 10.2

(1, 10.2)

f(5) = 10(1.02)^5

f(5) = 10(1.1040808)

f(5) = 11.040808

f(1)=10(1.02)^1

f(1)=10.2

Average rate= (fn2-fn1)/(n2-n1)

                     =11.04-10.2/(5-1)

                    =0.22

the average rate of change of the function f(n) from n = 1 to n = 5 is 0.22.  

Answer:

Part A

The domain should be 0 ≤n≤5

Part B

f(n) = 10(1.02)^n

The function is in the form y =a b^x  where a is the y intercept

The y intercept is 10.  This is the value when n =0 days.

Part C

The average rate of growth over the 4 days is .21 cm per day

Step-by-step explanation:

f(n) = 10(1.02)^n

Part A

Let f(n) = 11.04

11.04 = 10 * 1.02 ^n

Divide each side by 10

11.04/10 = 1.02^n

1.104 = 1.02^n

Taking the log of each side

log 1.104 = log 1.02^n

We know log a^b = b log a

log 1.104 = n log 1.02

log 1.104 / log 1.02 = n

4.99630=n

Rounding n to 5

The domain should be 0 ≤n≤5

Part B

f(n) = 10(1.02)^n

The function is in the form y =a b^x  where a is the y intercept

The y intercept is 10.  This is the value when n =0 days.

Part C

To find the average rate of change

f(5) - f(1)

-----------

5-1

f(5) = 11.04  

f(1) = 10 *1.02 =10.2

11.04 - 10.2

-----------

5-1

.84

-----

4

.21 cm per day

The average rate of growth over the 4 days is .21 cm per day

Answer:

  987

Step-by-step explanation:

You want to determine a three-digit combination based on clues about which digits are right and/or correctly placed.

This tells you one of digits 1, 2, or 7 is correct and correctly placed.

Clue 2 tells you that digit is not 1. Clue 4 tells you that digit is not 2.

  7 is correctly placed as the 3rd digit

We already know that 1 is not the correct digit. This means 3 must be the first digit, or 8 must be the first or second digit.

We already know that 7 is a correct digit, properly placed as the 3rd digit. Since 1 is not a correct digit, 9 must be a correct digit, properly placed as the 1st digit.

  9 is correctly placed as the 1st digit

Combining this fact with Clue 2 means ...

  8 is correctly placed as the 2nd digit

The combination is 987.

__

Check

Clues 4 and 5 are consistent with this combination.

We need to find angle a in the figure.

We know that:

x = 9.342 inches

y = 6.692 inches

z = 2.952 inches

We can do so by finding the legs in the following triangle:

The adjacent leg is x. And the opposite leg is found by subtracting z from y, and then dividing the result by two (assuming the figure is symmetric):

Thus, we have:

Step-by-step explanation:

\(a {}^{3} + b {}^{3} \)

Notice how that for both a and b are raised to an odd power. This means we can factor this by a binomial raised to an odd power.

Let divide this by

\(a + b\)

Since that is also a odd power.

\(( {a}^{3} + {b}^{3} ) \div (a + b)\)

We get

a quotient of

\(( {a}^{2} - ab + {b}^{2} )\)

So our factors are

\((a + b)( {a}^{2} - ab + {b}^{2} )\)

Answer:

\((a+b)(a^{2} -ab+b^{2} )\)

Step-by-step explanation:

\(\textbf{We need to factor this expression}\) \(\textbf{by applying the sum of two cubes rule:}\)

\(\Longrightarrow\) \(A^{3} +B^{3} =(A+B)(A^{2} -AB+B^{2} )\)

Here,  

A= a

B= b

So, \((a+b)(a^{2} -ab+b^{2} )\)

\(\leadsto\leadsto\leadsto\leadsto\leadsto\leadsto\leadsto\leadsto\leadsto\leadsto\)

\(\textsl{OAmalOHopeO}\)

Answer:

180

Step-by-step explanation:

Considering that it is counting by 6's, just multiply 6 by 30 to get the 30th term of the sequence

Answer:

the first third and 5th one i think, check my answer first XD

Step-by-step explanation:

Answer:

–81

Step-by-step explanation:

Answer:

1. 63 or

2. 37.8

step-by-step explanation:

1. $125,$78, $66, $45, $13 take out $125 and $13 then add $78, $66, $45 and you get $189 then divided by 3 and you $63

2.$125,$78, $66, $45, $13 take out $125 and $13 then add $78, $66, $45 and you get $189 then divided by 5 and you $37.8

Answer:

ITS 63

Step-by-step explanation:

JUST DID DA TEST CUZ