in what form is the following linear equation written y=9x+2

       [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:

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: 0.16

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:

First type of fruit drinks: 160 pints

Second type of fruit drinks: 80 pints

Step-by-step explanation:

Let's call A the amount of first type of fruit drinks. 5.5% pure fruit juice

Let's call B the amount of second type of fruit drinks. 100% pure fruit juice

The resulting mixture should have 70% pure fruit juice and 240 pints.

Then we know that the total amount of mixture will be:

[tex]A + B = 240[/tex]

Then the total amount of pure fruit juice in the mixture will be:

[tex]0.55A + B = 0.7 * 240[/tex]

[tex]0.55A + B = 168[/tex]

Then we have two equations and two unknowns so we solve the system of equations. Multiply the first equation by -1 and add it to the second equation:

[tex]-A -B = -240[/tex]

[tex]-A -B = -240[/tex]

                  +

[tex]0.55A + B = 168[/tex]

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

[tex]-0.45A = -72[/tex]

[tex]A = \frac{-72}{-0.45}[/tex]

[tex]A = 160\ pints[/tex]

We substitute the value of A into one of the two equations and solve for B.

[tex]160 + B = 240[/tex]

[tex]B = 80\ pints[/tex]

To make 240 pints of a mixture that is 70% pure fruit juice, you will need 160 pints of the first type of fruit drink (55% pure fruit juice) and 80 pints of the second type of fruit drink (100% pure fruit juice).

To solve this problem, we can set up a system of equations. Let's say x represents the number of pints of the first type of fruit drink (55% pure fruit juice) and y represents the number of pints of the second type of fruit drink (100% pure fruit juice). We know that the total number of pints of the mixture is 240, so we can write the equation x + y = 240. We also know that the desired percentage of pure fruit juice in the mixture is 70%, so we can write the equation (55% * x + 100% * y) / 240 = 70%. To solve this system of equations, we can use substitution or elimination method. Let's use substitution:

From the first equation, we can solve for x in terms of y: x = 240 - y. Substituting this into the second equation, we get ((55% * (240 - y)) + 100% * y) / 240 = 70%. Simplifying the equation, we have (0.55(240 - y) + y) / 240 = 0.70. Distributing and combining like terms, we get (132 - 0.55y + y) / 240 = 0.70. Simplifying further, we have (132 + 0.45y) / 240 = 0.70. Cross multiplying, we get 132 + 0.45y = 0.70 * 240. Simplifying, we have 132 + 0.45y = 168. Multiplying 0.45 with y, we get 0.45y = 168 - 132. Subtracting 132 from 168, we get 0.45y = 36. Dividing both sides of the equation by 0.45, we get y = 36 / 0.45. Evaluating this expression, we get y = 80. So, the number of pints of the second type of fruit drink (100% pure fruit juice) needed is 80. Substituting this value back into the first equation, we can solve for x: x + 80 = 240. Subtracting 80 from both sides of the equation, we get x = 240 - 80. Evaluating this expression, we get x = 160. Therefore, the number of pints of the first type of fruit drink (55% pure fruit juice) needed is 160.

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Final answer:

Train B travels at a speed of 30 miles per hour and train A travels at a speed of 50 miles per hour.

Explanation:

Let's say the speed of train B is x miles per hour. Since train A is 20 miles per hour faster, the speed of train A is x + 20 miles per hour.

Distance = Speed x Time

For train A, Distance = (x +20) * 3

For train B, Distance = x * 3

Since they meet 240 miles apart, the sum of their distances is 240:

(x + 20) * 3 + x * 3 = 240

3x + 60 + 3x = 240

6x = 180

x = 30

Hence, train B travels at a speed of 30 miles per hour and train A travels at a speed of 50 miles per hour.

Answer:

{chocolate, strawberries, peanuts}

Step-by-step explanation:

Given that three sets are

Let A = {vanilla, chocolate, hot fudge, strawberries, sprinkles, peanuts, whipped cream}

Let B = {vanilla, hot fudge, sprinkles, whipped cream}  

Let C = {chocolate, hot fudge, peanuts, whipped cream}

Then Universal set U = AUBUC

= {vanilla, chocolate, hot fudge, strawberries, sprinkles, peanuts, whipped cream}

B'=elements in U but not in B

={chocolate, strawberries, peanuts}

The resulting set is B' = {chocolate, strawberries, peanuts}.

To solve for B', we first need to understand that B' (B complement) consists of elements that are in set A but not in set B.

Given the sets:

Set B includes: vanilla, hot fudge, sprinkles, and whipped cream. Therefore, B' will be the elements of set A excluding those in B.

Thus, B' is:

Therefore, the set B' = {chocolate, strawberries, peanuts}.

This method can help you understand combinations without repetition effectively.

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: 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:

Bailey family's sprinkler was used for 35 hours and Harris family's sprinkler was used for 20 hours.

Step-by-step explanation:

 Set up a system of equations.

Let be "b" the time Bailey family's sprinkler was used and "h" the time Harris family's sprinkler was used.

Then:

[tex]\left \{ {{b+h=55} \atop {15b+40h= 1,325}} \right.[/tex]

You can use the Elimination method. Multiply the first equation by -15, then add both equations and solve for "h":

[tex]\left \{ {{-15b-15h=-825} \atop {15b+40h= 1,325}} \right.\\.............................\\25h=500\\\\h=\frac{500}{25}\\\\h=20[/tex]

Substitute [tex]h=20[/tex] into an original equation and solve for "b":

[tex]b+20=55\\\\b=55-20\\\\b=35[/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:

(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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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: 19.77%

Step-by-step explanation:

Given: Mean : [tex]\mu=74[/tex]

Standard deviation : [tex]\sigma = 7.1[/tex]

The formula to calculate z-score is given by :_

[tex]z=\dfrac{x-\mu}{\sigma}[/tex]

For x= 80, we have

[tex]z=\dfrac{80-74}{7.1}\approx0.85[/tex]

The P-value = [tex]P(z>0.85)=1-P(z<0.85)=1-0.8023374=0.1976626[/tex]

In percent , [tex]0.1976626\times100=19.76626\%\approx19.77\%[/tex]

Hence, the approximate percentage of the test scores during the past year exceeded 80 =19.77%

You probably know that

[tex]\sin x=\displaystyle\sum_{n=0}^\infty\frac{(-1)^nx^{2n+1}}{(2n+1)!}[/tex]

Then

[tex]\mathrm{sinc}\,x=\displaystyle\frac1x\sum_{n=0}^\infty\frac{(-1)^nx^{2n+1}}{(2n+1)!}=\sum_{n=0}^\infty\frac{(-1)^nx^{2n}}{(2n+1)!}[/tex]

when [tex]x\neq0[/tex], and 1 when [tex]x=0[/tex].

By the ratio test, the series converges if the following limit is less than 1:

[tex]\displaystyle\lim_{n\to\infty}\left|\frac{\frac{(-1)^{n+1}x^{2n+2}}{(2n+3)!}}{\frac{(-1)^nx^{2n}}{(2n+1)!}}\right|=|x^2|\lim_{n\to\infty}\frac{(2n+1)!}{(2n+3)!}[/tex]

The limit is 0, so the series converges for all [tex]x[/tex].

[tex]\textbf{Transform}\\ \textrm{log} (7(3x -2)^2) \textbf{ into} \textrm{ log}(7) + \textrm{log}(3x-2)^2\\\\ \textbf{Expand} \\ \text{log}(3x-2)^2\\\\ \text{You can move 2 outside of }\text{log}(3x-2)^2\\\\ \textbf{Answer}\\ \text{log }7 + 2\text{ log}(3x-2)[/tex]

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.

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

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:

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.

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:     [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]

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:

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

The line y = 3 means that x = 0.

The point (-3, y) tells me that x = -3 when y is 3.

So, y = 3 completes the point (-3, 3).

Answer: c) The number 75 is an outlier on the stem and leaf plot.

Step-by-step explanation:

When we look in the given stem-leaf plot, there is no leaf attached to the stem with value 6.

It mean there is no value between 50 and 75.

It shows that the value of 75 is detached from the other values in the data.

⇒ The number 75 is an outlier on the stem and leaf plot.

Answer:

The answer is C

Step-by-step explanation:

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.

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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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)

Answer: The altitude and the base of the sign are 6 meters and 11 meters respectively.

Step-by-step explanation:

Since we have given that

Area of triangular sign = 33 sq. meters

Let the altitude of the triangle be 'x'.

Let the base of the triangle be ' 2x-1'.

As we know the formula for "Area of triangle ":

[tex]Area=\dfrac{1}{2}\times base\times height\\\\33=\dfrac{1}{2}\times x(2x-1)\\\\33\times 2=2x^2-x\\\\66=2x^2-x\\\\2x^2-x-66=0\\\\2x^2-12x+11x-66=0\\\\2x(x-6)+11(x-6)=0\\\\(2x+11)(x-6)=0\\\\x=-\dfrac{11}{2},6\\\\x=-5.5,6[/tex]

Discarded the negative value of x for dimensions:

So, altitude of triangle becomes 6 meters

Base of triangle would be [tex]2(6)-1=12-1=11\ meters[/tex]