For k(x)= (-x- 1)(x^2 + 3x - 1)(x+2), find the derivative of k(x) at the point = -2 using the product rule.

Answer:

25:16

Step-by-step explanation:

i think its right

Answer:

x >5

Step-by-step explanation:

-4(3-X) > 8

Divide by -4, remembering to flip the inequality

-4/-4(3-X) < 8/-4

3-x < -2

Subtract 3 from each side

3-x-3 < -2-3

-x <-5

Divide by -1, remembering to flip the inequality

x >5

Answer:

[tex]c.[/tex] [tex]5<x[/tex]

Step-by-step explanation:

[tex]-4(3-x)>8\\3-x>-2\\-x>-5\\x>5[/tex]

Answer:

median: 90

mode: 91

mean: 84.2 or round it to 84

Step-by-step explanation:

Let me know if this helps! have a great day! :)

Answer:

a) Median = 91

b) mode = 91

c)Mean 84.2

Step-by-step explanation:

a) Median is the middle term. So, 6th term

Median = 91

b) Mode is the score which occurs more number of times

91 occurs 3 times

Mode = 91

c) Mean= sum of all data's/Number of data's

            = 85 + 91 + 48 +98 + 99 /5

            = 421/5

  Mean = 84.2

Answer:

1. equilateral triangle

2. rectangle

3. circle area

4. trapezoid

5. circle circumference

6. parallelogram

7. regular polygon

8. triangle

Hope that helps.

Answer:

There are 9 llamas.

Step-by-step explanation:

For Billy, we have to find a number that is divisible by four, because he has one group of lambs, and 3 times as many llamas, which gives us 4 groups altogether. The number must be below 10 in order to not go above 17 when Milly's number of animals are included, but above 4 itself in order to reach the target of 17 in the first place.

As you can guess, the only number that fits all the criteria is 8. It's divisible by 4 and below 10, but above 4 itself.

If Billy has three times as many llamas as lambs, then he must have 2 lambs, and 6 llamas, as 2 × 3 = 6.

If we know that Billy has 8 animals, then we also know that Milly must have 9 animals, as 17 - 8 = 9.

We also know that Milly has 3 groups of animals; one group of llamas, and two groups of lambs, meaning we divide the number of animals she has by 3.

9 ÷ 3 = 3.

This tells us Milly has just 3 llamas, because 3 is one group of 9, and 3 × 2 = 6,  because she has twice the amount of lambs.

Billy has 2 lambs and 6 llamas.

Milly has 6 lambs and 3 llamas.

The amount of lambs is irrelevant to our final answer, so we can disregard them and do a final sum of 6 + 3 = 9, which gives us our answer.

Answer:

Billy: Has 4 lots of animals

Milly: Has 3 lots of animals

17 animals in total means that Billy must have 4 lots of 2 (8 animals) and Milly must have 3 lots of 3 (9 animals) So Billy has 6 llamas and Milly has 3, giving 9 llamas in total

Answer:

The probability that the combined sample tests positive  for the virus is 0.083

Since the probability that combined sample test positive for the virus is greater than 0.05, it is not likely for such a combined  sample to test positive.

The probability that the combined sample will test positive is 0.083

Step-by-step explanation:

Given that:

The probability of a randomly selected adult in one country being infected with a certain virus is 0.003.

P = 0.003

number of blood sample size n = 29

The probability mass function of X is as follows;

[tex]P(X=x) = \left[\begin{array}{c}{29}&x\\\end{array}\right] (0.003)^x (1-0.003)^{29-x}[/tex]

Thus; the required probability is;

[tex]P(X \geq 1) = 1 - P ( X < 1)[/tex]

[tex]P(X \geq 1) = 1 - P ( X =0)[/tex]

[tex]P(X \geq 1) = 1 - \left[\begin{array}{c} \dfrac{29!}{0!(29-0)!} \ \ \times 0.003)^0 \times (1-0.003)^{29-0}}\end{array}\right][/tex]

[tex]P(X \geq 1) = 1 - \left[\begin{array}{c} 1 \times 1 \times ( 0.9166)\end{array}\right][/tex]

[tex]P(X \geq 1) = 1 - 0.9166[/tex]

[tex]P(X \geq 1) = 0.0834[/tex]

Therefore; the probability that the combined sample tests positive  for the virus is 0.083

Is it unlikely for such a combined  sample to test positive?

P(combined  sample test positive  for the virus ) = 0.0834

Since the probability that combined sample test positive for the virus is greater than 0.05, it is not likely for such a combined  sample to test positive.

The probability of a randomly selected adult in one country being infected with a certain virus is 0.003.

P = 0.003

number of blood sample size n = 29

The probability mass function of X is as follows;

[tex]P(X=x) = \left[\begin{array}{c}{29}&x\\\end{array}\right] (0.003)^x (1-0.003)^{29-x}[/tex]

Thus; the required probability is;

[tex]P(X \geq 1) = 1 - P ( X < 1)[/tex]

[tex]P(X \geq 1) = 1 - P ( X =0)[/tex]

[tex]P(X \geq 1) = 1 - \left[\begin{array}{c} \dfrac{29!}{0!(29-0)!} \ \ \times 0.003)^0 \times (1-0.003)^{29-0}}\end{array}\right][/tex]

[tex]P(X \geq 1) = 1 - \left[\begin{array}{c} 1 \times 1 \times ( 0.9166)\end{array}\right][/tex]

[tex]P(X \geq 1) = 1 - 0.9166[/tex]

[tex]P(X \geq 1) = 0.0834[/tex]

The probability that the combined sample will test positive is 0.083

Answer:

the answer is 12

Step-by-step explanation:

because (6, 12) x axis is 6, and the 12 is the y axis. Meaning that you would go 12 along the y axis.

Answer:

I believe the answer is 12

Answer:

[tex]\frac{13}{3}[/tex] ÷ [tex](-\frac{5}{6})[/tex]

Step-by-step explanation:

[tex]4\frac{1}{3}/(-\frac{5}{6})=\\\\\frac{13}{3}/(-\frac{5}{6})[/tex]

Answer:

13/3  ÷ - 5/6

Step-by-step explanation:

4 1/3 ÷ - 5/6

Change the mixed number to an improper fraction

4 1/3 = (3*4 +1)/3 = 13/3

13/3  ÷ - 5/6

Answer:

C. -3

Step-by-step explanation:

Plugging both of those points into the slope formula gets you a slope of -3.

Answer:

19.625 cm^2

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h

V = 3.14 * 5^2 * .25

V =19.625 cm^2

Hey there! :)

Answer:

56.7 kg.

Step-by-step explanation:

Use the density formula to solve for the mass:

D = m/V.

Rearrange in terms of mass, or 'm':

DV = m.

Solve for the volume:

0.06 × 0.9 × 1.5 = 0.081 m³.

Plug this into the equation along with the density:

700 × 0.081 = 56.7 kg.

Answer:

The smallest number that is divisible by 1,2,3,4,5,6,7,8,9 and 10 is 2,520.

Step-by-step explanation:

2520/1 = 2520

2520/2 = 1260

2520/3 = 840

2520/4 = 630

2520/5 = 504

2520/6 = 420

2520/7 = 360

2520/8 = 315

2520/9 = 280

2520/10 = 252

Step-by-step explanation:

1.32:24

32/8:24/8

4:3

2.20:32

20/4:32/4

5:8

3.24:76

24/4:76/4

6:19

4.24:32:20

24/4:32/4:20/4

6:8:5

Answer:

Answer:

The y in the second equation

Step-by-step explanation:

hope this helps

Answer:

2/$5.00

Step-by-step explanation:

It's the only one that makes sense

Answer:

4,10

It is the only option on the table

Step-by-step explanation:

Answer:

Since ∠E ≅ ∠A and ∠D ≅ ∠B, the answer is ΔABC ~ ΔEDF.

Answer:

option 2

Step-by-step explanation:

Answer:  A

Since you already have an equation just put in how many stickers and erasers she wants to get: 0.35(2)+0.99(2)+0.59≤4.

Then you multiply: .35(2)=.70. .99(2)=1.98.

Then add: .70+1.98+.59=3.27, so yes she can since 3.27 is less than 4 so the answer is A

Answer:

A. yes, because the total will be $3.27

Step-by-step explanation:

0.35x + 0.99y + 0.59 ≤ 4

0.35(2) + 0.99(2) + 0.59 ≤ 4

0.70 + 1.98 + 0.59 ≤ 4

3.27 ≤ 4

Answer:

segment FG = one half segment FI, segment FH = one half segment FE, and segment HG = one half segment EI; ΔHFG ~ ΔEFI  

Step-by-step explanation:

In the picture attached, the triangles are shown.

After the dilation and reflection, there is proportionality between segment FG and segment FI, segment FH and segment FE, and segment HG  and segment EI. More specifically:

Answer:

segment FG = one half segment FI, segment FH = one half segment FE, and segment HG = one half segment EI; ΔHFG ~ ΔEFI  

Step-by-step explanation:

In the picture attached, the triangles are shown.

After the dilation and reflection, there is proportionality between segment FG and segment FI, segment FH and segment FE, and segment HG  and segment EI. More specifically:

FG = 1/2*FI

FH = 1/2*FE

HG = 1/2*EI

This answer is right! took the test on FLVS and confirmed it :)

Answer:

0.16 P(Yellow or Brown)=0.16

Answer: 0.44

Step-by-step explanation:

0.4 + 0.28 = 0.68

1.00 - 0.68 = 0.32

0.32 divided by 2.0 = 0.16

Total answer is 0.44

GLAD TO HELP:)

HAVE A NICE DAY!

BTW: I WAS DOING A TEST, BUT TOOK MY TIME TO HELP YOU! :)

PLEASE BRAINLEST ME!

Answer:

(a) y = -3/5 x + 13/5

(b) y = 5/3 x + 1/3

Step-by-step explanation:

(a) The slope of the tangent line is dy/dx.  Use implicit differentiation:

x² + y² + 4x + 6y − 21 = 0

2x + 2y dy/dx + 4 + 6 dy/x = 0

2x + 4 + (2y + 6) dy/dx = 0

x + 2 + (y + 3) dy/dx = 0

(y + 3) dy/dx = -(x + 2)

dy/dx = -(x + 2) / (y + 3)

At the point (1, 2), the slope is:

dy/dx = -(1 + 2) / (2 + 3)

dy/dx = -3/5

Using point-slope form of a line:

y − 2 = -3/5 (x − 1)

Simplifying to slope-intercept form:

y − 2 = -3/5 x + 3/5

y = -3/5 x + 13/5

(b) The normal line is perpendicular to the tangent line, so its slope is 5/3.  It also passes through the point (1, 2), so point-slope form of the line is:

y − 2 = 5/3 (x − 1)

Simplifying to slope-intercept form:

y − 2 = 5/3 x − 5/3

y = 5/3 x + 1/3

Answer: 3

Step-by-step explanation:

This problem is looking for the Greatest Common Factor (GCF) of 6 and 15.

Draw a factor tree for each number and see what they have in common.

           Reg         Diet

               6              15

               ∧               ∧

            2   3           3  5

The GCF of 6 and 15 =  3

Each table will contain 2 cans of regular soda and 5 cans of diet soda.

Answer:

I think it's D because the line AC looks like it is splitting the rectangle in half. I think this is right since the angles are congruent. (Angle BAC and Angle ACD)

Answer: 5x + 1

Step-by-step explanation:

f(x) - g(x)

(3x + 2) - (-2x + 1)       Here you distribute the negative sign to (-2x + 1)

3x + 2 + 2x - 1            Here you combine like terms

5x + 1                         This is the answer.

g(x) = (x - 5)^2 + 2x^3

At the root this function is equal to 0

(x - 5)^2 + 2x^3= 0

Rearrange:

(x - 5)^2 = -2x^3

Now if you plot these two functions you need to check how many times they intersect. For this you do not need to be precise just scetch approximately.

If you do that, you will see that they meet once. I cannot really use this site to plot, but you can use other tools for that if you do not know how to do it.

Answer:

≈ 68.2°

Step-by-step explanation:

tan X= 20/8

tan X= 2.5

x= tan ⁻¹ 2.5

x ≈ 68.2°

Answer:

Step-by-step explanation:

 To find the size of YXZ we should use some trigonometry but first let's find the length of YZ

(XZ)²+(ZY)²=(YX)²

YX=[tex]\sqrt{20^{2}+8^{2} }[/tex]

    =4[tex]\sqrt{29}[/tex]

Answer:

D

Step-by-step explanation:

4x^4+3x^2-3x^3-3x+1

Answer:

The found values are:

A = 1/3

B = -8/3

Step-by-step explanation:

We know that general equation is given by:

y = mx + c

where m is the slope and c is a constant.

x + 3y = -5

y = -(1/3)x - 1/3(5)

Slop of the equation is -(1/3). As parallel line have same slope substitute it in the first equation:

Ax + By = 3

By = -Ax - 3

By = (1/3)x - 3

Hence, A = 1/3

Substitute point (-7,2) into the equation:

B(2) = (1/3)(-7) -3

B(2) = -7/3 - 3

B(2) = -16/3

B = -16/6

B = -8/3

Answer:

a) [tex]cos(\alpha)=-\frac{3}{5}\\[/tex]

b)  [tex]\sin(\beta)= \frac{\sqrt{3} }{2}[/tex]

c) [tex]\frac{4+3\sqrt{3} }{10}\\[/tex]

d)  [tex]\alpha\approx 53.1^o[/tex]

Step-by-step explanation:

a) The problem tells us that angle [tex]\alpha[/tex] is in the second quadrant. We know that in that quadrant the cosine is negative.

We can use the Pythagorean identity:

[tex]tan^2(\alpha)+1=sec^2(\alpha)\\(-\frac{4}{3})^2 +1=sec^2(\alpha)\\sec^2(\alpha)=\frac{16}{9} +1\\sec^2(\alpha)=\frac{25}{9} \\sec(\alpha) =+/- \frac{5}{3}\\cos(\alpha)=+/- \frac{3}{5}[/tex]

Where we have used that the secant of an angle is the reciprocal of the cos of the angle.

Since we know that the cosine must be negative because the angle is in the second quadrant, then we take the negative answer:

[tex]cos(\alpha)=-\frac{3}{5}[/tex]

b) This angle is in the first quadrant (where the sine function is positive. They give us the value of the cosine of the angle, so we can use the Pythagorean identity to find the value of the sine of that angle:

[tex]cos (\beta)=\frac{1}{2} \\\\sin^2(\beta)=1-cos^2(\beta)\\sin^2(\beta)=1-\frac{1}{4} \\\\sin^2(\beta)=\frac{3}{4} \\sin(\beta)=+/- \frac{\sqrt{3} }{2} \\sin(\beta)= \frac{\sqrt{3} }{2}[/tex]

where we took the positive value, since we know that the angle is in the first quadrant.

c) We can now find [tex]sin(\alpha -\beta)[/tex] by using the identity:

[tex]sin(\alpha -\beta)=sin(\alpha)\,cos(\beta)-cos(\alpha)\,sin(\beta)\\[/tex]

Notice that we need to find [tex]sin(\alpha)[/tex], which we do via the Pythagorean identity and knowing the value of the cosine found in part a) above:

[tex]sin(\alpha)=\sqrt{1-cos^2(\alpha)} \\sin(\alpha)=\sqrt{1-\frac{9}{25} )} \\sin(\alpha)=\sqrt{\frac{16}{25} )} \\sin(\alpha)=\frac{4}{5}[/tex]

Then:

[tex]sin(\alpha -\beta)=\frac{4}{5}\,\frac{1}{2} -(-\frac{3}{5}) \,\frac{\sqrt{3} }{2} \\sin(\alpha -\beta)=\frac{2}{5}+\frac{3\sqrt{3} }{10}=\frac{4+3\sqrt{3} }{10}[/tex]

d)

Since [tex]sin(\alpha)=\frac{4}{5}[/tex]

then  [tex]\alpha=arcsin(\frac{4}{5} )\approx 53.1^o[/tex]

Answer: B

Step-by-step explanation:

Makes the most sense out of all the options because it’s the most random or unpredictable