For waht values of x do the vectors -1,0,-1), (2,1,2), (1,1, x) form a basis for R3?

Answer:

A. Switch S1 is Open

Step-by-step explanation:

I attach the missing figure in the image below

Since you are getting a reading of 6V which is the maximum voltage of your circuit, you can conclude that

A. Switch S1 is Open

- If the Switch S1 was closed, we would be getting a reading of 0V. This is not the case.

- Because the switch is open, there is no current going through the circuit and therefore there is not any voltage drop across the resistors. This is why their values don't affect the reading.

Answer:

  d.  (1, 5, 2)

Step-by-step explanation:

A suitable calculator can find the reduced row-echelon form for you. Some scientific calculators and many graphing calculators have this capability, as do on-line calculator. The one below is supported by ads.

a and c  both have √x  , so they will both be in brackets multiplied by √x.

b is the only term with √y  so it will be outside of the brackets.

So the answer will be:

(a - c)√x  + b√y

We can check this by expanding the brackets:

  (a - c)√x  + b√y

= a√x  - c√x  + b√y

We can rearrange this to get the same original expression:

a√x  - c√x  + b√y

= a√x  + b√y  - c√x

____________________________________

Answer:

Last option: (a - c)√x  + b√y

Answer:

choice 3 is correct  √x(a - c) + b√y

explanation:

You simplify by looking for the common multiplier which is √x

meaning it will be

√x(a - c)  + b√y

Answer: Option D

[tex]t_{max} =19\ s[/tex]

Step-by-step explanation:

Note that the projectile height as a function of time is given by the quadratic equation

[tex]h = -12t ^ 2 + 456t[/tex]

To find the maximum height of the projectile we must find the maximum value of the quadratic function.

By definition the maximum value of a quadratic equation of the form

[tex]at ^ 2 + bt + c[/tex] is located on the vertex of the parabola:

[tex]t_{max}= -\frac{b}{2a}[/tex]

Where [tex]a <0[/tex]

In this case the equation is: [tex]h = -12t ^ 2 + 456t[/tex]

Then

[tex]a=-12\\b=456\\c=0[/tex]

So:

[tex]t_{max} = -\frac{456}{2*(-12)}[/tex]

[tex]t_{max} =19\ s[/tex]

Answer:

  $270,314.08

Step-by-step explanation:

The multiplier each month is 1+0.08/12 ≈ 1.0066667, so after 120 months, the amount is multiplied by (1.0066667)^120 ≈ 2.2196402. The amount needed is ...

  $600,000/2.2196402 ≈ $270,314.08

To reach a retirement goal of $600,000 in 10 years with an 8% interest rate compounded monthly, you would need to deposit approximately $277,002.66 now.

In this case, we're using a formula to determine the amount needed to deposit today (P) for a future goal ($600,000) using an interest rate (r) of 8% compounded monthly for ten years. The formula to use is P = F / (1 + r/n)^(nt), where:

So, you need to plug these figures into the equation: P = 600,000 / (1 + 0.08/12)^(12*10). After doing the math, you would need to deposit around $277,002.66 now to reach your retirement goal of $600,000 in ten years given an 8% annual interest rate compounded monthly.

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The length of the ramp required can be determined by using conservation

of energy principle.

The length of the ramp should be approximately 154.97 meters.

Reasons:

Given parameters are;

The angle of inclination of the ramp, θ = 6.0°

Coefficient of friction, μ = 0.30

Mass of the truck, m = 15,000 kg

Speed of the truck, v = 35 m/s

Required;

The length of the ramp to stop the truck

Solution:

From the law of conservation of energy, we have;

Kinetic energy = Work done against friction + Potential energy gained by the truck at height

K.E. = [tex]W_f[/tex] + P.E.

Kinetic energy of the truck, K.E. = [tex]\frac{1}{2} \cdot m \cdot v^2[/tex]

Therefore;

K.E. = [tex]\frac{1}{2} \times 15,000 \times 35^2 = 9,187,500[/tex]

The kinetic energy of the truck, K.E. = 9,187,500 J

Friction force,[tex]F_f[/tex] = m·g·cos(θ)·μ

Therefore;

[tex]F_f[/tex] = 15,000 × 9.81 × cos(6) × 0.30 = 43,903.169071

Friction force,[tex]F_f[/tex] = 43,903.169071 N

Work done against friction = [tex]F_f[/tex] × d

Therefore;

Work done against friction, [tex]W_f[/tex] = 43,903.169071·d

Potential energy gained, P.E. = m·g·h

The height, h = d × sin(6.0°)

∴ P.E. = 15,000 × 9.81 × d × sin(6.0°) = 147150 × d × sin(6.0°)

Which gives;

9,187,500 J = 43,903.169071·d + 147150 × d × sin(6.0°)

[tex]d = \dfrac{9187500}{43,903.169071 + 147150 \times sin(6.0^{\circ})} \approx 154.97[/tex]

The length of the ramp, d ≈ 154.97 m.

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For this case we propose a system of equations:

x: Variable representing the weight of large boxes

y: Variable that represents the weight of the small boxes

So

[tex]x + y = 80\\55x + 70y = 4850[/tex]

We clear x from the first equation:

[tex]x = 80-y[/tex]

We substitute in the second equation:

[tex]55 (80-y) + 70y = 4850\\4400-55y + 70y = 4850\\15y = 450\\y = 30[/tex]

We look for the value of x:

[tex]x = 80-30\\x = 50[/tex]

Large boxes weigh 50 pounds and small boxes weigh 30 pounds

Answer:

Large boxes weigh 50 pounds and small boxes weigh 30 pounds

Answer: A large box weighs 50 pounds and a small box weighs 30 pounds.

Step-by-step explanation:

Set up a system of equations.

Let be "l" the weight of a large box and "s" the weight of a small box.

Then:

[tex]\left \{ {{l+s=80} \atop {55l+70s=4,850}} \right.[/tex]

You can use the Elimination method. Multiply the first equation by -55, then add both equations and solve for "s":

[tex]\left \{ {{-55l-55s=-4,400} \atop {55l+70s=4,850}} \right.\\.............................\\15s=450\\\\s=\frac{450}{15}\\\\s=30[/tex]

Substitute [tex]s=30[/tex] into an original equation and solve for "l":

[tex]l+(30)=80\\\\l=80-30\\\\l=50[/tex]

Answer:

0.23

Step-by-step explanation:

A standard deck has 4 suits (spade, club, diamond, and heart), and each suit has 13 ranks (ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, and king).

We want to know the probability of drawing an ace, a 2, or a 3.  There are four aces, four 2's, and four 3's in a deck (one for each suit).  That's a total of 12 cards.  So the probability is:

12 / 52 ≈ 0.23

Using the probability concept, it is found that there is a 0.2308 = 23.08% probability of selecting a number less than 4.

--------------------------

Thus, the probability of selecting a number less than 4 is:

[tex]p = \frac{D}{T} = \frac{12}{52} = 0.2308[/tex]

0.2308 = 23.08%

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The probability of writing the first 7 digits of your phone number is 1/60480.

To determine the probability of choosing the first 7 digits of your phone number in the given scenario, we need to calculate the probability of choosing each digit correctly and in order. Since there are 10 digits to choose from, the probability of choosing the first digit correctly is 1/10. The probability of choosing the second digit correctly is 1/9, since one digit has already been chosen. Continuing this pattern, the probability of choosing all 7 digits correctly and in order is:

P(choosing all seven numbers correctly) = P(choosing 1st number correctly) * P(choosing 2nd number correctly) * ... * P(choosing 7th number correctly)

So, the probability is:

1/10 * 1/9 * 1/8 * 1/7 * 1/6 * 1/5 * 1/4 = 1/60480

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The probability of writing the first 7 digits of your phone number is 1/604,800.

The probability of writing the first 7 digits of your phone number depends on the specific digits in your phone number. However, assuming that all digits are equally likely to be chosen, the probability can be calculated by multiplying the probabilities of choosing each digit correctly. Since there are 10 digits to choose from and you are picking 7, the probability would be:

To calculate the overall probability, you multiply these individual probabilities together:

So, the probability of writing the first 7 digits of your phone number is 1/604,800.

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Answer:

8418

Step-by-step explanation:

1 + 2 + ... + n is (n^2 + n)/2

46 + 47 + ... + 137

is the same as

1 + 2 + ... + 137 - (1 + 2 + ... + 45)

or

(137^2 + 137)/2 - (45^2 + 45)/2

= 8418

Answer:

The solutions are x = -9 , x = -5

Step-by-step explanation:

* Lets find the vertex of the parabola

- In the quadratic equation y = ax² + bx + c, the vertex of the parabola

 is (h , k), where h = -b/2a and k = f(h)

∵ The equation is y = x² + 14x + 45

∴ a = 1 , b = 14 , c = 45

∵ h = -b/2a

∴ h = -14/2(1) = -14/2 = -7

∴ The x-coordinate of the vertex of the parabola is -7

- Lets find k

∵ k = f(h)

∵ h = -7

- Substitute x by -7 in the equation

∴ k = (-7)² + 14(-7) + 45 = 49 - 98 + 45 = -4

∴ The y-coordinate of the vertex point is -4

∴ The vertex of the parabola is (-7 , -4)

- Plot the point on the graph and then find two points before it and

 another two points after it

- Let x = -9 , -8 and -6 , -5

∵ x = -9

∴ y = (-9)² + 14(-9) + 45 = 81 - 126 + 45 = 0

- Plot the point (-9 , 0)

∵ x = -8

∴ y = (-8)² + 14(-8) + 45 = 64 - 112 + 45 = -3

- Plot the point (-8 , -3)

∵ x = -6

∴ y = (-6)² + 14(-6) + 45 = 36 - 84 + 45 = -3

- Plot the point (-6 , -3)

∵ x = -5

∴ y = (-5)² + 14(-5) + 45 = 25 - 70 + 45 = 0

- Plot the point (-5 , 0)

* To solve the equation x² + 14x + 45 = 0 means find the value of

  x when y = 0

- The solution of the equation x² + 14x + 45 = 0 are the x-coordinates

 of the intersection points of the parabola with the x-axis

∵ The parabola intersects the x-axis at points (-9 , 0) and (-5 , 0)

∴ The solutions of the equation are x = -9 and x = -5

* The solutions are x = -9 , x = -5

Answer:

  344 ft²

Step-by-step explanation:

The area of the square is (40 ft)² = 1600 ft².

The area of the four circles is ...

  4×(πr²) = 4×3.14×(10 ft)² = 1256 ft²

Then the area that is not covered by the circles is ...

  1600 ft² -1256 ft² = 344 ft²

The area not sprinkled is 344 ft².

Answer:     [tex]\text{Mean length}=590.5\ mm\\\\\text{Variance of the lengths}=0.03\ mm[/tex]

Step-by-step explanation:

The mean and variance of a continuous uniform distribution function with parameters m and n is given by :-

[tex]\text{Mean=}\dfrac{m+n}{2}\\\\\text{Variance}=\dfrac{(n-m)^2}{12}[/tex]

Given : [tex] m=590.2\ \ \ n=590.80[/tex]

[tex]\text{Then, Mean=}\dfrac{590.2+590.8}{2}=590.5\ mm\\\\\text{Variance}=\dfrac{(590.8-590.2)^2}{12}=0.03\ mm[/tex]

You must know that percent are ALWAYS taken out of 100. This means that 100 subtracted by 65 will give the percent that this event won't happen:

100 - 65 = 35

This event has 65% probability of happening and a 35% of NOT happening

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

Option C

Step-by-step explanation:

96ft2

Answer:

Area of pyramid = [tex]96[/tex]. square feet.

Step-by-step explanation:

Given : A square pyramid is 6 feet on each side. The height of the pyramid is 4 feet.

To find:  What is the total area of the pyramid.

Solution : We have given

Each side of square pyramid = 6 feet .

Height = 4 feet .

Area of pyramid = [tex](side)^{2} + 2* side\sqrt{\frac{(side)^{2}}{4} +height^{2}}[/tex].

Plug the values side =  6 feet  , height = 4 feet .

Area of pyramid = [tex](6)^{2} + 2* 6\sqrt{\frac{(6)^{2}}{4} + 4^{2}}[/tex].

Area of pyramid = [tex]36+ 12\sqrt{\frac{36}{4} + 16}[/tex].

Area of pyramid = [tex]36+ 12\sqrt{9 +16}[/tex].

Area of pyramid = [tex]36+ 12\sqrt{25}[/tex].

Area of pyramid = [tex]36+ 12 *5[/tex].

Area of pyramid = [tex]36+ 60[/tex].

Area of pyramid = [tex]96[/tex]. square feet.

Therefore, Area of pyramid = [tex]96[/tex]. square feet.

1.

a. 30

b. 44

c. 36

d. 40

2. I don't really remember how to do these but if you cant make the denominator smaller then I belive it's

a. 24

b. 20

c. 4

d. 5

3.

a. =

b. not =

c. not =

d. not =

4. Gary

5.

a. 5/6

b. 5/12

c. 19/45

d. 13/14

e. 7/11

f. 1/2

6.

a. 2/3

b. 8/9

c. 3/10

d. 9/11

e. 3/4

f. 1/5

7.

a. 36/40

b.

c.

8.

a. yes

b. no

c. no

d. no

9. no

10. yes

11.

a. 40

b. 48

c. 77

d. 48

12. 4,620

c. 27⁄90

d. 63⁄77

e. 24⁄32

f. 73⁄365

7.What is the next fraction in each of the following patterns?

a. 1⁄40, 4⁄40, 9⁄40, 16⁄40, 25⁄40 . . .?

b. 3⁄101, 4⁄101, 7⁄101, 11⁄101, 18⁄101, 29⁄101. . .?

c. 5⁄1, 10⁄2, 9⁄2, 18⁄4, 17⁄8, 34⁄32, 33⁄256. . .?

8.In each pair, tell if the fractions are equal by using cross multiplication.

a. 5⁄30 and 1⁄6

b. 4⁄12 and 21⁄60

c. 17⁄34 and 41⁄82

d. 6⁄9 and 25⁄36

1.

a. 30

b. 44

c. 36

d. 40

2.

a. 24

b. 20

c. 4

d. 5

3.

a. =

b. not =

c. not =

d. not =

4. Gary

5.

a. 5/6

b. 5/12

c. 19/45

d. 13/14

e. 7/11

f. 1/2

6.

a. 2/3

b. 8/9

c. 3/10

d. 9/11

e. 3/4

f. 1/5

7.

a. 36/40

b.

c.

8.

a. yes

b. no

c. no

d. no

9. no

10. yes

11.

a. 40

b. 48

c. 77

d. 48

12. 4,620

Step-by-step explanation:

Step-by-step answer:

Given:

alarm clocks that fail at 15.7% on any day.

Solution

Probability of failure of a single clock = 15.7% = 0.157

(a)

probability of failure of a single clock on any given day (final exam or not)

= 15.7%  (given)

(b)

probability of failure of two independent alarm clocks on the SAME day

= 0.157^2

= 0.024649  (from independence of events)

(c)

probability of failure of three independent alarm clocks on the SAME day

= 0.157^3

= 0.00387  (from independence of events)

(d)

Since the probability of failure has been reduced from 0.157 to 0.00387, we can conclude that yes, even though malfunction of all three clocks is not impossible, it is unlikely at a probability of 0.00387 (less than 1 %)

Using the binomial distribution, it is found that:

a) 15.7% probability that the​ student's alarm clock will not work on the morning of an important final​ exam.

b) 0.0246 = 2.46% probability that they both fail on the morning of an important final​ exam.

c) 0.0039 = 0.39% probability of not being awakened if the student uses three independent alarm​ clocks.

d)

(C) ​Yes, because total malfunction would not be​ impossible, but it would be unlikely.

---------------------------

For each alarm clock, there are only two possible outcomes. Either it works, or it does not. The probability of an alarm working is independent of any other alarm, which means that the binomial 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:

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

And p is the probability of a success on a single trial.

---------------------------

Item a:

---------------------------

Item b:

The probability of both falling is the probability that none works, thus P(X = 0).

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

[tex]P(X = 0) = C_{2,0}.(0.843)^{0}.(0.157)^{2} = 0.0246[/tex]

0.0246 = 2.46% probability that they both fail on the morning of an important final​ exam.

---------------------------

Item c:

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

[tex]P(X = 0) = C_{3,0}.(0.843)^{0}.(0.157)^{3} = 0.0039[/tex]

0.0039 = 0.39% probability of not being awakened if the student uses three independent alarm​ clocks.

---------------------------

Item d:

(C) ​Yes, because total malfunction would not be​ impossible, but it would be unlikely.

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Answer:

a(12) = 35

Step-by-step explanation:

Given

a(12) = 50- 1.25x

Value of x is 12

50 - 1.25(12)

Simplify

50 - 15

Solve

a(12) = 50 - 15

a(12) = 35

Answer:

Step-by-step explanation:

The formula of an area of a square with side length a:

[tex]A=a^2[/tex]

The big square:

[tex]a=x+5[/tex]

Substitute:

[tex]A_B=(x+5)^2[/tex]           use  [tex](a+b)^2=a^2+2ab+b^2[/tex]

[tex]A_B=x^2+2(x)(5)+5^2=x^2+10x+25[/tex]

The small square:

[tex]a=x-2[/tex]

Substitute:

[tex]A_S=(x-2)^2[/tex]       use  [tex](a-b)^2=a^2-2ab+b^2[/tex]

[tex]A_S=x^2-2(x)(2)+2^2=x^2-4x+4[/tex]

The area of a shaded region:

[tex]A=A_B-A_S[/tex]

Substitute:

[tex]A=(x^2+10x+25)-(x^2-4x+4)=x^2+10x+25-x^2+4x-4[/tex]

combine like terms

[tex]A=(x^2-x^2)+(10x+4x)+(25-4)=14x+21[/tex]

Answer: 0.9730

Step-by-step explanation:

Let A be the event of the answer being correct and B be the event of the knew the answer.

Given: [tex]P(A)=0.9[/tex]

[tex]P(A^c)=0.1[/tex]

[tex]P(B|A^{C})=0.25[/tex]

If it is given that the answer is correct , then the probability that he guess the answer [tex]P(B|A)= 1[/tex]

By Bayes theorem , we have

[tex]P(A|B)=\dfrac{P(B|A)P(A)}{P(B|A)P(A)+P(C|A^c)P(A^c)}[/tex]

[tex] =\dfrac{(1)(0.9)}{(1))(0.9)+(0.25)(0.1)}\\\\=0.972972972973\approx0.9730[/tex]

Hence, the student correctly answers a question, the probability that the student really knew the correct answer is 0.9730.

Answer: 0.16

Step-by-step explanation:

Given: The probability that a student graduating from Suburban State University has student loans to pay off after graduation is =0.60

Then the probability that a student graduating from Suburban State University does not have student loans to pay off after graduation is =[tex]1-0.6=0.4[/tex]

Since all the given event is independent for all students.

Then , the probability that neither of them has student loans to pay off after graduation is given by :-

[tex](0.4)\times(0.4)=0.16[/tex]

Hence, the probability that neither of them has student loans to pay off after graduation =0.16

Answer:

(a) The probability of P(A), P(B), and P(C) are 0.35, 0.6 and 0.65 respectively.

(b) The probability of P(A ∩ B) is 0.2.

(c) The probability of P(A ∪ B) is 0.75.

(d) Events A and C mutually exclusive because the intersection of set A and C is null set or ∅.

Step-by-step explanation:

The given sample space is

[tex]S=\{E_1,E_2,E_3,E_4,E_5,E_6,E_7\}[/tex]

[tex]P(E_1)=0.1, P(E_2)=0.15,P(E_3)=0.15,P(E_4)=0.2,P(E_5)=0.1,P(E_6)=0.05, P(E_7)=0.25[/tex]

It is given that

[tex]A=\{E_1,E_4,E_6\}[/tex]

[tex]B=\{E_2,E_4,E_7\}[/tex]

[tex]C=\{E_2,E_3,E_5,E_7\}[/tex]

(a)

[tex]P(A)=P(E_1)+P(E_4)+P(E_6)=0.1+0.2+0.05=0.35[/tex]

[tex]P(B)=P(E_2)+P(E_4)+P(E_7)=0.15+0.2+0.25=0.6[/tex]

[tex]P(C)=P(E_2)+P(E_3)+P(E_5)+P(E_7)=0.15+0.15+0.1+0.25=0.65[/tex]

Therefore the probability of P(A), P(B), and P(C) are 0.35, 0.6 and 0.65 respectively.

(b)

A ∩ B represent the common elements of set A and set B.

[tex]A\cap B=\{E_4\}[/tex]

[tex]P(A\cap B)=P(E_4)=0.2[/tex]

The probability of P(A ∩ B) is 0.2.

(c)

A ∪ B represent all the elements of set A and set B.

[tex]A\cup B=\{E_1,E_2,E_4,E_6,E_7\}[/tex]

[tex]P(A\cup B)=P(E_1)+P(E_2)+P(E_4)+P(E_6)+P(E_7)[/tex]

[tex]P(A\cup B)=0.1+0.15+0.2+0.05+0.25=0.75[/tex]

The probability of P(A ∪ B) is 0.75.

(d)

Set A and C has no common element. So, the intersection of set A and C is empty set.

Yes, events A and C mutually exclusive because the intersection of set A and C is null set or ∅.

The probability of events A, B, and C are calculated by summing the individual probabilities of their constituent sample points. The probability of the intersection of events A and B is equal to the probability of the common sample point. The probability of the union of events A and B is obtained by subtracting the probability of the intersection from the sum of their individual probabilities. Events A and C are not mutually exclusive because they have common sample points.

(a) Probability of events A, B, and C:

(b) Probability of intersection of events A and B:

P(A ∩ B) = P(E4) = 0.2

(c) Probability of union of events A and B:

P(A ∪ B) = P(A) + P(B) - P(A ∩ B) = 0.35 + 0.6 - 0.2 = 0.75

(d) Mutually exclusive events A and C:

No, events A and C are not mutually exclusive because they have common sample points in E2 and E7.

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Answer:

First city: $5,500

Second city: $5,000

Step-by-step explanation:

Let's define x as the hotel price in the first city and y the hotel price in the second city.  We can start with this equation:

y = x - 500 (The hotel before tax in the 2nd city was $500 lower than in the 1st.)

Then we can say

0.065x + 0.045y = 582.50  (the sum of the tax amounts were $582.50)

We place the value of y from the first equation in the second equation:

0.065x + 0.045 (x - 500) = 582.50

0.065x + 0.045x - 22.50 = 582.50 (simplifying and adding 22.5 on each side)...

0.11x = 605

x = 5,500

The cost of the first hotel was $5,500

Thus, the cost of the second hotel was $5,000 (x - 500)

       [tex]f'(x)= \dfrac{-1}{2\sqrt{9-x}}[/tex]

The function f(x) is given by:

   [tex]f(x)=\sqrt{9-x}[/tex]

The domain of the function is the possible values of x where the function is defined.

We know that the square root function [tex]\sqrt{x}[/tex] is defined when x≥0.

Hence, [tex]\sqrt{9-x}[/tex] will be defined when [tex]9-x\geq 0\\\\i.e.\\\\x\leq 9[/tex]

Hence, the domain of the function f(x) is: [tex]x\leq 9[/tex]

Also, the definition of derivative of x is given by:

[tex]f'(x)= \lim_{h \to 0}  \dfrac{f(x+h)-f(x)}{h}[/tex]

Hence, here by putting the value of the function we get:

[tex]f'(x)= \lim_{h \to 0} \dfrac{\sqrt{9-(x+h)}-\sqrt{9-x}}{h}\\\\i.e.\\\\f'(x)= \lim_{h \to 0} \dfrac{\sqrt{9-(x+h)}-\sqrt{9-x}}{h}\times \dfrac{\sqrt{9-(x+h)}+\sqrt{9-x}}{\sqrt{9-(x+h)}+\sqrt{9-x}}\\\\\\f'(x)= \lim_{h \to 0} \dfrac{(\sqrt{9-(x+h)}-\sqrt{9-x})(\sqrt{9-(x+h)}+\sqrt{9-x})}{(\sqrt{9-(x+h)}+\sqrt{9-x})\times h}\\\\\\f'(x)= \lim_{h \to 0} \dfrac{9-(x+h)-(9-x)}{(\sqrt{9-(x+h)}+\sqrt{9-x})\times h}[/tex]

Since,

[tex](a-b)(a+b)=a^2-b^2[/tex]

Hence, we have:

[tex]f'(x)= \lim_{h \to 0} \dfrac{-h}{(\sqrt{9-(x+h)}+\sqrt{9-x})\times h}\\\\\\f'(x)= \lim_{h \to 0} \dfrac{-1}{(\sqrt{9-(x+h)}+\sqrt{9-x})}\\\\\\i.e.\\\\\\f'(x)= \dfrac{-1}{2\sqrt{9-x}}[/tex]

Since, the domain of the derivative function is equal to the derivative of the square root function.

Also, the domain of the square root function is: [tex]x\leq 9[/tex]

Hence, domain of the derivative function is:  [tex]x\leq 9[/tex]

Answer:

-1/sqrt(1-9x)

Step-by-step explanation:

This is the answer

Answer: .11

Step-by-step explanation:

Let F be the event that the first truck is available and S be the event that the second truck is available.

The probability of neither truck being available is expressed as P([tex]F^{C}[/tex]∩[tex]S^{C}[/tex]) , where P([tex]F^{C}[/tex]) is the probability that the event F doesn't happen and P([tex]S^{C}[/tex]) is the probability that the event S doesn't happen.

P([tex]F^{C}[/tex])= 1-P(F) = 1-0.73 = 0.27

P([tex]S^{C}[/tex])=1-P(S) = 1-0.59 = 0.41

Since  [tex]F^{C}[/tex] and [tex]S^{C}[/tex] aren't mutually exclusive events, then:

P([tex]F^{C}[/tex]∪[tex]S^{C}[/tex]) = P([tex]F^{C}[/tex]) + P([tex]S^{C}[/tex]) - P([tex]F^{C}[/tex]∩[tex]S^{C}[/tex])

Isolating the probability that interests us:

P([tex]F^{C}[/tex]∩[tex]S^{C}[/tex])= P([tex]F^{C}[/tex]) + P([tex]S^{C}[/tex])- P([tex]F^{C}[/tex]∪[tex]S^{C}[/tex])

Where P([tex]F^{C}[/tex]∪[tex]S^{C}[/tex]) = 1 - 0.43 = 0.57

Finally:

P([tex]F^{C}[/tex]∩[tex]S^{C}[/tex]) = 0.27+ 0.41 - 0.57 = 0.11

Answer:

The cost of 1 pint of the medication would be $1.875.

Step-by-step explanation:

The AWP of 3785 ml ( 1 gallon ) cough syrup = $18.75

After an additional 20% discount from wholesaler the price would be

New price = 18.75 - (0.20 × 18.75)

                 = 18.75 - 3.75

                 = $15.00

Since 1 gallon ( 3785 ml) = 8 pints

Therefore, the price for 1 pint = [tex]\frac{15}{8}[/tex] = $1.875

The cost of 1 pint of the medication would be $1.875.

Answer:  The mean number of checks written per​ day  [tex]=0.3452[/tex]

Standard deviation[tex]=0.5875[/tex]

Variance  [tex]=0.3452[/tex]

Step-by-step explanation:

Given : The total number of checks wrote by person in a year = 126

Assume that the year is not a leap year.

Then  1 year = 365 days

Let the random variable x represent the number of checks he wrote in one​ day.

Then , the mean number of checks wrote by person each days id=s given by :-

[tex]\lambda=\dfrac{126}{365}\approx0.3452[/tex]

Since , the distribution is Poisson distribution , then the variance must equal to the mean value i.e. [tex]\sigma^2=\lambda=0.3452[/tex]

Standard deviation : [tex]\sigma=\sqrt{0.3452}=0.5875372328\approx0.5875[/tex]

Step-by-step explanation:

The probability of winning at least once is equal to 1 minus the probability of not winning any.

P(x≥1) = 1 - P(x=0)

P(x≥1) = 1 - (1-0.11)^4

P(x≥1) = 1 - (0.89)^4

P(x≥1) = 0.373

The probability is approximately 0.373.

Answer:

37.26% probability of winning at least once

Step-by-step explanation:

For each play, there are only two possible outcomes. Either you win, or you do not win. The probability of winning on eah play is independent of other plays. So we use the binomial probability distribution 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.

The probability of winning something on a single play at a slot machine is 0.11.

This means that [tex]p = 0.11[/tex]

After 4 plays on the slot machine, what is the probability of winning at least once

Either you do not win any time, or you win at least once. The sum of the probabilities of these events is decimal 1. So

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

We want [tex]P(X \geq 1)[/tex]. So

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

In which

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

[tex]P(X = 4) = C_{4,0}.(0.11)^{0}.(0.89)^{4} = 0.6274[/tex]

[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.6274 = 0.3726[/tex]

37.26% probability of winning at least once

Answer: 0.59

Step-by-step explanation:

Probability is a measure that quantifies the likelihood that events will occur.

Probabilities can be numerically described by the number of desired outcomes divided by the total number of all outcomes .

In this case, the number of desired outcomes is 307 (surveyed voters who plan to vote to reelect the mayor), and the total number of all outcomes is 520 (total of surveyed voters) .

Then, the probability that a surveyed voter plans to vote to reelect the mayor is calculated as:

[tex]\frac{307}{520}=0.59[/tex]

The probability that a surveyed voter plans to vote to reelect the mayor is 0.59.

To find the probability that a surveyed voter plans to vote to reelect the mayor, we divide the number of surveyed voters who plan to reelect the mayor by the total number of surveyed voters.

Given that 307 out of 520 likely voters plan to reelect the incumbent mayor, the probability is:

Probability = Number of surveyed voters who plan to reelect the mayor / Total number of surveyed voters

Probability = 307 / 520 = 0.59 (rounded to two decimal places)

[tex](f+g)(x)=3x^2-2+4x+2=3x^2+4x\\\\(f+g)(2)=3\cdot2^2+4\cdot2=12+8=20[/tex]