A circle is centered at the point (-3, 2) and passes through the point (1, 5). The radius of the circle is

Given:

The function is

[tex]f(x)=(x-5)^2(3-x)^2[/tex]

To find:

The derivative of the given function.

Solution:

Chain rule of differentiation:

[tex][f(g(x))]'=f'(g(x))g'(x)[/tex]

Product rule of differentiation:

[tex][f(x)g(x)]'=f(x)g'(x)+g(x)f'(x)[/tex]

We have,

[tex]f(x)=(x-5)^2(3-x)^2[/tex]

Differentiate with respect to x.

[tex]f'(x)=(x-5)^2\dfrac{d}{dx}(3-x)^2+(3-x)^2\dfrac{d}{dx}(x-5)^2[/tex]

[tex]f'(x)=(x-5)^2[2(3-x)(0-1)]+(3-x)^2[2(x-5)(1-0)][/tex]

[tex]f'(x)=(x^2-10x+25)(-6+2x)+(9-6x+x^2)(2x-10)[/tex]

[tex]f'(x)=(x^2)(-6)+(-10x)(-6)+(25)(-6)+(x^2)(2x)-10x(2x)+25(2x)+(9)(2x)+(-6x)(2x)+x^2(2x)+9(-10)+(-6x)(-10)+x^2(-10)[/tex]

On further simplification, we get

[tex]f'(x)=-6x^2+60x-150+2x^3-20x^2+50x+18x-12x^2+2x^3-90+60x-10x^2[/tex]

[tex]f'(x)=(2x^3+2x^3)+(-6x^2-20x^2-12x^2-10x^2)+(60x+50x+18x+60x)+(-90-150)[/tex]

[tex]f'(x)=4x^3-48x^2+188x-240[/tex]

Therefore, the derivative of the given function is [tex]f'(x)=4x^3-48x^2+188x-240[/tex].

the one we barely see in the photo you took seems a good fit. on the left wich 3 blue stripes and one white. and with stripes of half the size, 6 blue and two white

Answer:

Answer is a because it has

Step-by-step explanation:

3 blue and 6 blue trust me

Answer:

y = 5x – ¼

Step-by-step explanation:

The equation for the slope intercept form is given by:

y = mx + c

Where m and c are the slope and intercept on the y-axis respectively.

From the equation i.e y = mx + c, we can see that y is the subject of the equation.

Now, comparing the equation of the slope intercept form (i.e y = mx + c) with those given in the question above, we can see that only the equation:

y = 5x – ¼

has y as the subject of the equation.

Therefore, y = 5x – ¼ gives the correct answer to the question.

Answer:

40

Step-by-step explanation:

The median is the middle number

There are 10 numbers

The middle is between 5th and 6th number

Take the 5th and 6th numbers and average them

(39+41)/2 = 80/2 = 40

The median is 40

Mass of each rock in Nija's collection is 40.

Answer:

The median is the middle number

n=10 numbers

The middle is between 5th and 6th number

Taking the 5th and 6th numbers:

average(39+41)/2 = 80/2 = 40

Answer:

3(5x + 4y)

Step-by-step explanation:

Given

15x + 12y ← factor out 3 from each term

= 3(5x + 4y) ← in factored form

Work it out yourself lad

Answer:

three

Step-by-step explanation:

answer might be 3... shortest name length

Answer:

D No; even though there is a strong positive correlation, playing violin doesn't cause students to get better grades

Answer:

0.383 (3 d.p.)

Step-by-step explanation:

Probability formula

[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]

Let P(A) = probability that the student owns a credit card

Let P(B) = probability that the student is a freshman

Use the given table to calculate the probability that the student is a freshman and owns a credit card:

[tex]\implies \sf P(B \cap A)=\dfrac{23}{100}=0.23[/tex]

Use the given table to calculate the probability that the student is a freshman:

[tex]\sf \implies P(B) = \dfrac{60}{100}=0.6[/tex]

To find the probability that the student owns a credit card given that they are a freshman, use the conditional probability formula:

Conditional Probability Formula

The probability of A given B is:

[tex]\sf P(A|B)=\dfrac{P(B \cap A)}{P(B)}[/tex]

Substitute the found values into the formula:

[tex]\implies \sf P(A|B)=\dfrac{0.23}{0.6}=0.383333...[/tex]

Therefore, the probability that the student owns a credit card given that they are a freshman is 0.383 (3 d.p.).

P(Freshman credit card holder)

P(Freshman)

P(Freshman credit holder|Freshman)

9514 1404 393

Answer:

  the correct answer is marked

Step-by-step explanation:

The circle with center (h, k) and radius r has equation ...

  (x -h)² +(y-k)² = r²

For the given center, that is ...

  (x -1)² +(y +1)² = r²

The value of r² can be found by using the given point for x and y, and seeing what value of r² makes the equation true.

  (5 -1)² +(7 +1)² = 4² +8² = 16 +64 = 80

So, r² = 80 makes the equation true, and that equation is ...

  (x -1)² +(y +1)² = 80

Answer:

[tex]P(x \le 3.24) = 0.97725[/tex]

Step-by-step explanation:

Given

[tex]\bar x = 2.5[/tex]

[tex]\sigma = 0.37[/tex]

Required

Percentage that is not more than 3.24

The above implies that:

[tex]x = 3.24[/tex]

Calculate z score

[tex]z = \frac{x - \bar x}{\sigma}[/tex]

[tex]z = \frac{3.24 - 2.5}{0.37}[/tex]

[tex]z = \frac{0.74}{0.37}[/tex]

[tex]z = 2[/tex]

So, the probability is represented s:

[tex]P(x \le 3.24) = P(z \le 2)[/tex]

From z probability

[tex]P(z \le 2) = 0.97725[/tex]

Hence:

[tex]P(x \le 3.24) = 0.97725[/tex]

=============================================================

Explanation:

1/6 is the probability of rolling a '3' since there is one side we want out of 6 total.

The probability of getting an ace is 4/52 because there are 4 aces out of 52 cards total.

If that card isn't put back, then we have 52-1 = 51 cards left. That means the probability of drawing a black 2 is 2/51. The numerator 2 has nothing to do with the card value of '2'. It has to do with the fact we have 2 black cards (2 of spades, 2 of clubs) out of 51 left over.

We multiply the fractions to get the final answer

(1/6)*(4/52)*(2/51)

(1*4*2)/(6*52*51)

8/15912

1/1989

When using a calculator, we can see that,

1/1989 = 0.0005 = 0.05%

There is a very small chance of all three events happening at the same time.

Answer:

The expected number of hunters who hit the duck they aim at is 3.6

Step-by-step explanation:

Given;

number of hunters, n = 6

the probability of killing a duck, p = 0.6

The expected number of hunters who hit the duck they aim at?

In binomial distribution, the expected value is equal to the product of the number of trials and the probability of success.

The expected number of hunters who hit the duck they aim at is calculated as follows;

E = np

E = 0.6 x 6

E = 3.6

Therefore, the expected number of hunters who hit the duck they aim at is 3.6

Answer:

d. employed individuals aged 25-29

Step-by-step explanation:

"Population" in a research study is the comprehensive group that the experimenter or the researcher is interested in.

It is given that US Census Bureau, showed that percentage of the employed individual who are of age group 25 years to 29 years are college educated and is at all time high.

The research study focuses on the specific age group of individuals those who graduated form college or at least have a bachelor degree.

Thus the population of the research study those who studied in each of the four years are the employed individuals aged from 25-29.

Answer:

a. 81 square inches

b. 108 inches

Step-by-step explanation:

The area of all 5 squares combined is 405 square inches. This is 5 times the area of 1 square. 405/5 = 81. The area of 1 square is 81 square inches.

Since this is a square, the sides are equal. Thankfully the area of 1 square is a perfect square so the length of one side of the square is a full number, which is 9. All of the squares are congruent as shown in the diagram so we simply add every length together (there are 12 sides, each side is 9 inches).

12*9 = 108 and that is the perimeter.

Answer:

area

Step-by-step explanation:

a = 405/5 = 81

a =81 square inches

perimeter

p = √81

= 9

=4×9×5

=180 inches

Answer:

y=4x-5

Step-by-step explanation:

-3y = -12x+15. y = (-12x+15)/(-3). y = (-12x/-3)+(15/-3). y = 4x-5.

Answer:

Hello! answer: 20

Step-by-step explanation:

These are vertical angles meaning they will have the same measure so... 20 + 40 = 60 20 × 3 = 60 therefore x = 20 hope that helps!

In the given scenario, the value of x is 20. The correct option is A.

A parallelogram is a quadrilateral with two pairs of parallel sides. This means that opposite sides of a parallelogram are parallel and congruent, and opposite angles are congruent as well.

To find the value of x in the given diagram, we need to use the fact that the opposite sides of a parallelogram are equal in length.

Therefore, we can set the expressions for the opposite sides equal to each other and solve for x:

x + 40 = 3x

Simplifying the equation, we get:

40 = 2x

Dividing both sides by 2, we get:

x = 20

Therefore, the value of x is 20.

For more details regarding parallelogram, visit:

https://brainly.com/question/29147156

#SPJ7

9514 1404 393

Answer:

  108 square units

Step-by-step explanation:

The area of a trapezoid is given by the formula ...

  A = 1/2(b1 +b2)h

This trapezoid has bases 8 and 1, and a height of 24. Its area is ...

  A = (1/2)(8 +1)(24) = 108 . . . square units

Answer:

A) -8x+2

Step-by-step explanation:

-8x + 7 - 5 - 5x + 5x

-8x -5x + 5x + 7 - 5

- 8x+2

The answer is B

the method use to solved this is called foil

Answer:

730

Step-by-step explanation:

separate each rectangle

use the formula to calculate the area of each rectangle.

1st rectangle

area = length ×breadth

length =5, breadth =8+25+8=41

A1=5×41=205

2nd rectangle

A2=8×25=200

....

A3=5×25=125

A4=8×25=200

Add all As and you have your ans 730

Answer:

The equation would be d - (d×0.2)

Answer:

seems to be the same as the other angle

Step-by-step explanation:

i use desmos for these graphs btw

Answer:

If Florence Griffith Joyner and Usain Bolt were running at their world-record speed in the same race, Florence Griffith Joyner would finish 8.67 m behind Usain Bolt.

Step-by-step explanation:

Step 1: Determine the speed of each athlete in m/s

Speed = distance / time

Distance = 100 m

Usain Bolt's speed: 100m / 9.58 s = 10.438 m/s

Florence Griffith Joyner's speed: 100 m/ 10.49 s = 9.533 m/s

Step 2: Determine the distance covered by Florence Griffith Joyner in 9.58 s

Distance = Speed × time

Distance covered by Florence Griffith Joyner = 100 m/ 10.49 s × 9.58 s = 91.32 m

Step 3: Determine the difference in the distance covered by Usain Bolt and Florence Griffith Joyner after 9.58 s

After 9.58 s, Usain Bolt have covered a distance of 100 m

After 9.58 s, Florence Griffith Joyner have covered a distance of 91.33 m

Difference between the distances = (100 - 91.33) m = 8.67 m

Therefore, if Florence Griffith Joyner and Usain Bolt were running at their world-record speed in the same race, Florence Griffith Joyner would finish 8.67 m behind Usain Bolt

Answer:

The graph of function g is the graph of function f shifted 6 units up

Step-by-step explanation:

If you plug in the values, [tex]g(x) = 2^{x} + 6[/tex]. If the 6 was added or subtracted from the x in the exponent, it would shift horizontally (left and right), but adding 6 to f(x) separately moves the graph vertically (up and down). Hope this helps.

Answer: 2√17 A website to use for this would be "M a t h w a y"!!! Good luck, hope I helped!!!

Answer:

9.3 hours

Step-by-step explanation:

Given

[tex]y = 2.89\sin(0.0145x-1.40) + 10.99.[/tex]

Required

Hours of sunlight on Feb 21, 2013

First, calculate the number of days from Jan 1, 2013 to Feb 21, 2013

[tex]days = 52[/tex]

So:

[tex]x = 52[/tex]

So, we have:

[tex]y = 2.89\sin(0.0145x-1.40) + 10.99.[/tex]

[tex]y = 2.89\sin(0.0145*52-1.40) + 10.99.[/tex]

[tex]y = 2.89\sin(0.754-1.40) + 10.99.[/tex]

[tex]y = 2.89\sin(-0.646) + 10.99.[/tex]

[tex]y = 2.89*-0.6020 + 10.99.[/tex]

[tex]y = -1.740 + 10.99.[/tex]

[tex]y = 9.25[/tex]

[tex]y = 9.3[/tex] --- approximated