(a) Find the average rate of change of the area of a circle with respect to its radius r as r changes from 2 to each of the following.
(i) 2 to 3
(ii) 2 to 2.5
(iii) 2 to 2.1
(b) Find the instantaneous rate of change when r =2.

Answer:

Box dimensions:

x =  3.42 cm

y = 6.84 cm

C(min) = 14.04 $

Step-by-step explanation:

We need the surface area of the cube:

S(c)  =  2*S₁ ( surface area of top or base) +  4*S₂ ( surface lateral area)

S₁  = x²        2*S₁  = 2*x²

Surface lateral area is:

4*S₂  =  4*x*h                          V(c) =  80 cm³  =  x²*h          h  =  80/x²

4*S₂  = 4*80/x

4*S₂  = 320 / x

Costs

C (x)  =  0.2* 2*x²   +  0.1 * 320/x

Taking derivatives on both sides of the equation we get:

C´(x)  =    0.8*x   -  32/x²

C´(x)  =  0            0.8*x - 32/x²  = 0

0.8*x³  -  32  =  0            x³  =  32/0.8

x³  =  40  

x =  3.42 cm

h =  80/(3.42)²          h  = 6.84 cm

To find out if x = 3.42 brings a minimum value for C we go to the second derivative

C´´(x) =  64/x³       is always positive for  x > 0  

The C(min) = 0.4*(3.42)²  +  32/(3.42)

C(min)  =  4.68 +  9.36

C(min)  = 14.04 $

Complete question is;

Components arriving at a distributor are checked for defects by two different inspectors (each component is checked by both inspectors). The first inspector detects 83% of all defectives that are present, and the second inspector does likewise. At least one inspector does not detect a defect on 34% of all defective components. What is the probability that the following occurs?

(a) A defective component will be detected only by the first inspector?

b) A defective component will be detected by exactly one of the two inspectors?

(c) All three defective components in a batch escape detection by both inspectors (assuming inspections of different components are independent of one another)?

Answer:

A) 0.17

B) 0.34

C) 0

Step-by-step explanation:

a) We are told that the first inspector(A) detects 83% of all defectives that are present, and the second inspector(B) also does the same.

This means that;

P(A) = P(B) = 83% = 0.83

We are also told that at least one inspector does not detect a defect on 34% of all defective components.

Thus;

P(A' ⋃ B') = 0.34

Also, we now that;

P(A ⋂ B) = 1 - P(A' ⋃ B')

P(A ⋂ B) = 1 - 0.34

P(A ⋂ B) = 0.66

Probability that A defective component will be detected only by the first inspector is;

P(A ⋂ B') = P(A) - P(A ⋂ B)

P(A ⋂ B') = 0.83 - 0.66

P(A ⋂ B') = 0.17

B) probability that a defective component will be detected by exactly one of the two inspectors is given as;

P(A ⋂ B') + P(A' ⋂ B) = P(A) + P(B) - 2P(A ⋂ B)

P(A) + P(B) - 2P(A ⋂ B) ; 0.83 + 0.83 - 2(0.66) = 0.34

C) Probability that All three defective components in a batch escape detection by both inspectors is written as;

P(A' ⋃ B') - (P(A ⋂ B') + P(A' ⋂ B))

Plugging in the relevant values, we have;

0.34 - 0.34 = 0

Answer:

a) 0.0062 = 0.62% probability that the return will exceed 55%.

b) 0.3085 = 30.85% probability that the return will be less than 25%

c) 30%.

d) The 75th percentile of returns is 36.75%.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean 30% and standard deviation 10%.

This means that [tex]\mu = 30, \sigma = 10[/tex]

(a) Find the probability that the return will exceed 55%.

This is 1 subtracted by the p-value of Z when X = 55. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{55 - 30}{10}[/tex]

[tex]Z = 2.5[/tex]

[tex]Z = 2.5[/tex] has a p-value of 0.9938

1 - 0.9938 = 0.0062

0.0062 = 0.62% probability that the return will exceed 55%.

(b) Find the probability that the return will be less than 25%

p-value of Z when X = 25. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{25 - 30}{10}[/tex]

[tex]Z = -0.5[/tex]

[tex]Z = -0.5[/tex] has a p-value of 0.3085

0.3085 = 30.85% probability that the return will be less than 25%.

(c) What is the expected value of the return?

The mean, that is, 30%.

(d) Find the 75th percentile of returns.

X when Z has a p-value of 0.75, so X when Z = 0.675.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]0.675 = \frac{X - 30}{10}[/tex]

[tex]X - 30 = 0.675*10[/tex]

[tex]X = 36.75[/tex]

The 75th percentile of returns is 36.75%.

Answer:

the anwer is B ( i mean second option)

And you can try it

you will find ;

[tex]y = \frac{x}{3} - 1[/tex]

HAVE A NİCE DAY

Step-by-step explanation:

GREETİNGS FROM TURKEY ツ

Answer:

[tex]-\infty < x < \infty[/tex]

Step-by-step explanation:

Given

[tex]f(x) = (-\frac{5}{6}) \cdot (\frac{3}{5})^x[/tex]

Required

The domain

There are no undefined points such as denominator of x or square roots.

Hence, the domain is:

[tex]-\infty < x < \infty[/tex]

Answer:

option one is the correct answer

Answer:

1/625

Step-by-step explanation:

Answer:

Hello good evening friend

Answer:

0.502

64.1666

Step-by-step explanation:

Detained explanation of the product operation and division operation is attached below.

2.51 * 0.2 = 0.502

(after multiplying) the number of decimal places of the town values is added and counted from the right in the product to place the data Comal point appropriately.

77/1.2 ; values were multiplied by 10 in other to obtain inter values for the denominator.

10x-5

Answer:

5(2x-1)

5*2x 5*-1

10x-5

Hey there!

5(2x - 1)

= 5(2x) + 5(-1)

= 10x - 5

Therefore, your answer should be: 5x - 5

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

see below

Step-by-step explanation:

[tex] \displaystyle AB = DE[/tex]

[given]

[tex] \displaystyle \boxed{BC = EF}[/tex]

[given]

[tex] \displaystyle AB + BC = AC[/tex]

[segment addition Postulate]

[tex] \displaystyle \boxed{DE+ EF=DF}[/tex]

[segment addition Postulate]

[tex] \rm\displaystyle DE+ BC = AC \: \: \text{and} \: \: DE+ BC = DF[/tex]

[Substitution Property of Equality]

[tex] \displaystyle \boxed{AE= DE}[/tex]

[Proven]

Answer:

The probability that exactly 12 buyers would prefer green

=0.00555

Step-by-step explanation:

We are given that

p=50%=50/100=0.50

n=14

We have to find the probability that exactly 12 buyers would prefer green.

q=1-p

q=1-0.50=0.50

Using binomial distribution formula

[tex]P(X=x)=nC_r p^r q^{n-r}[/tex]

[tex]P(x=12)=14C_{12}(0.50)^{12}(0.50)^{14-12}[/tex]

[tex]P(x=12)=14C_{12}(0.50)^{12}(0.50)^2[/tex]

[tex]P(x=12)=14C_{12}(0.50)^{14}[/tex]

[tex]P(x=12)=\frac{14!}{12!2!}(0.50)^{14}[/tex]

[tex]P(x=12)=\frac{14\times 13\times 12!}{12!2\times 1}(0.50)^{14}[/tex]

[tex]P(x=12)=91\cdot (0.50)^{14}[/tex]

[tex]P(x=12)=0.00555[/tex]

Hence, the probability that exactly 12 buyers would prefer green

=0.00555

Answer:

B

Step-by-step explanation:

Divide both sides by 3

Take square root of both sides.

Add 9 to both sides.

Answer:

Step-by-step explanation:

Total sales = x

Correct choice is C

Answer:

Monthly taxes = $250.63 (Approx.)

Step-by-step explanation:

Given:

Amount of purchase = $205,950

Loan amount = $164,760

Assessed value = $200,500

Tax rate is 1.5%

Find:

Monthly taxes

Computation:

Tax always calculated on Assessed value

Annual tax amount = 200,500 x 1.5%

Annual tax amount = 3,007.5

Monthly taxes = Annual tax amount / 12

Monthly taxes = 3,007.5 / 12

Monthly taxes = 250.625

Monthly taxes = $250.63 (Approx.)

Answer:

A: x = 0

B: x = All real numbers

Step-by-step explanation:

A.

Any number to the power of (0) equals one. This applies true for the given situation; one is given an expression which is as follows;

[tex](6^2)^x=1[/tex]

Simplifying that will result in;

[tex]36^x=1[/tex]

As stated above, any number to the power of (0) equals (1), thus (x) must equal (0) for this equation to hold true.

[tex]36^0=1\\x=0[/tex]

B.

As stated in part (A), any number to the power (0) equals (1). Therefore, when given the following expression;

[tex](6^0)^x=1[/tex]

One can simplify that;

[tex]1^x=1[/tex]

However, (1) to any degree still equals (1). Thus, (x) can be any value, and the equation will still hold true.

[tex]x=All\ real \ numbers[/tex]

Answer:

188 degrees

Step-by-step explanation:

The measure of the arc is the center angle, that is double of the circumference one

94 * 2 = 188 degrees

Answer:

a) 0.000016 = 0.0016% probability of selecting and finding that all three bags are overweight.

b) 0.729 = 72.9% probability of selecting and finding that all three bags are satisfactory

Step-by-step explanation:

The condition of the bags in the sample is independent of the other bags, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

a) What is the probability of selecting and finding that all three bags are overweight?

2.5% are overweight, which means that [tex]p = 0.025[/tex]

3 bags means that [tex]n = 3[/tex]

This probability is P(X = 3). So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 3) = C_{3,3}.(0.025)^{3}.(0.975)^{0} = 0.000016[/tex]

0.000016 = 0.0016% probability of selecting and finding that all three bags are overweight.

b) What is the probability of selecting and finding that all three bags are satisfactory?

90% are satisfactory, which means that [tex]p = 0.9[/tex]

3 bags means that [tex]n = 3[/tex]

This probability is P(X = 3). So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 3) = C_{3,3}.(0.9)^{3}.(0.1)^{0} = 0.729[/tex]

0.729 = 72.9% probability of selecting and finding that all three bags are satisfactory

Answer:

[tex]x=4[/tex]

Step-by-step explanation:

We have the quadratic function:

[tex]\displaystyle y=0.3(x-4)^2-2.5[/tex]

And we want to determine its axis of symmetry.

Notice that this is in vertex form:

[tex]y=a(x-h)^2+k[/tex]

Where (h, k) is the vertex of the parabola.

From our function, we can see that h = 4 and k = -2.5. Hence, our vertex is the point (4, -2.5).

The axis of symmetry is equivalent to the x-coordinate of the vertex.

The x-coordinate of the vertex is 4.

Therefore, the axis of symmetry is x = 4.

(a) The region Y₁ < 1/2 and Y₂ > 1/4 corresponds to the rectangle,

{(y₁, y₂) : 0 ≤ y₁ < 1/2 and 1/4 < y₂ ≤ 1}

Integrate the joint density over this region:

[tex]P\left(Y_1<\dfrac12,Y_2>\dfrac14\right) = \displaystyle\int_0^{\frac12}\int_{\frac14}^1 (y_1+y_2)\,\mathrm dy_2\,\mathrm dy_1 = \boxed{\dfrac{21}{64}}[/tex]

(b) The line Y₁ + Y₂ = 1 cuts the support in half into a triangular region,

{(y₁, y₂) : 0 ≤ y₁ < 1 and 0 < y₂ ≤ 1 - y₁}

Integrate to get the probability:

[tex]P(Y_1+Y_2\le1) = \displaystyle\int_0^1\int_0^{1-y_1}(y_1+y_2)\,\mathrm dy_2\,\mathrm dy_1 = \boxed{\dfrac13}[/tex]

Y₁ and Y₂ are not independent because

P(Y₁ = y₁, Y₂ = y₂) ≠ P(Y₁ = y₁) P(Y₂ = y₂)

To see this, compute the marginal densities of Y₁ and Y₂.

[tex]P(Y_1=y_1) = \displaystyle\int_0^1 f(y_1,y_2)\,\mathrm dy_2 = \begin{cases}\frac{2y_1+1}2&\text{if }0\le y_1\le1\\0&\text{otherwise}\end{cases}[/tex]

[tex]P(Y_2=y_2) = \displaystyle\int_0^1 f(y_1,y_2)\,\mathrm dy_1 = \begin{cases}\frac{2y_2+1}2&\text{if }0\le y_2\le1\\0&\text{otherwise}\end{cases}[/tex]

[tex]\implies P(Y_1=y_1)P(Y_2=y_2) = \begin{cases}\frac{(2y_1+1)(2y_2_1)}4&\text{if }0\le y_1\le1,0\ley_2\le1\\0&\text{otherwise}\end{cases}[/tex]

but this clearly does not match the joint density.

Answer:

50 bags ;

£750

Step-by-step explanation:

The dimension of the rectangular lawn is 500ft by 300 ft

The area of the lawn an e obtained thus :

Area of rectangle = Length * width

Area of rectangle = 500 ft * 300 ft

Area of rectangle = 150000 feets

1 bag of fertilizer covers 3000 feets

The minimum bags of fertilizer required :

Area of rectangle / Area covered by 1 bag of fertilizer

Minimum bags of fertilizer required :

(150,000 / 3000) = 50 bags

50 bags of fertilizer

Cost per bag = 15

Total cost = 15 * 50 = £750

Answer:

Step-by-step explanation:

356 * 80 = 28 480

275 * 60 = 16 500

369 * 45 = 16 605

sum = $ 61 585

Answer:

Step-by-step explanation:

answer C looks good  

Answer:

option c is answer

Step-by-step explanation:

as we can see r^2 =(d/2)^2

r^2=(6/2)^2

r^2=36/4=9

A=πr^2

A=9π

Answer:

c. 1.29

Step-by-step explanation:

Z-score:

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Andy 70578 60000 8200

This means that [tex]X = 70578, \mu = 60000, \sigma = 8200[/tex]

What is the z-score of Andy's salary?

This is Z, so:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{70578 - 60000}{8200}[/tex]

[tex]Z = 1.29[/tex]

So the correct answer is given by option c.

Answer:r=v^2/A

Step-by-step explanation: To solve for r means you have to isolate r on one side and put all the other terms on the other. To get r out from under the fraction, multiply both sides by r. This leaves:

A*r=v^2     so to isolate r, divide by A and get:

r=v^2/A.

Answer:

This problem has not solution

Step-by-step explanation:

lets the  integers be:

x

x+1

x+2

x+3

so:

x+(x+1)+(x+2)+(x+3)=2021

x+x+x+x+1+2+3=2021

4x+6=2021

4x=2021-6=2015

x=2015/4=503.75

x is not a integer

Answer:

1,108 in²

Step-by-step explanation:

SA = (12×20) + (2×20×5 + 2×12×5) + (2×½×12×9)

+ (2×20×11)

= 240+320+108+440

= 1,108 in²

Answer:

22=4

Step-by-step explanation:

0977-=ytb

6

+

4

−

8

Step-by-step explanation:

Please mark me as brain list and please like my answer and rate also

Answer:

hope this will help you more

Answer:

Step-by-step explanation:

circumference = πd ≅ 250 ft

d ≅ 250/π ≅80 ft

Answer:

[tex]K = L[/tex]

Step-by-step explanation:

Given

Circle A

[tex]r = b[/tex] --- radius

[tex]p = c[/tex] ---- perimeter

Circle B

[tex]r = y[/tex] --- radius

[tex]p =z[/tex] --- perimeter

[tex]K = \frac{c}{b}[/tex]

[tex]L = \frac{z}{y}[/tex]

Required

Select the true option

The perimeter of a circle is:

[tex]Perimeter = 2\pi r[/tex] ------ the circumference

So, we have:

[tex]c = 2\pi b[/tex] --- circle A

[tex]z = 2\pi y[/tex] --- circle B

Calculate K

[tex]K = \frac{c}{b}[/tex]

[tex]K = \frac{2\pi b}{b}[/tex]

[tex]K = 2\pi[/tex]

Calculate L

[tex]L = \frac{z}{y}[/tex]

[tex]L = \frac{2\pi y}{y}[/tex]

[tex]L = 2\pi[/tex]

So, we have:

[tex]K = L = 2\pi[/tex]