A cylindrical tank with radius 6 m is being filled with water at a rate of 2 m3/min. How fast is the height of the water increasing? Step 1 If h is the water's height, the volume of the water is V = r2h. We must find dV/dt. Differentiating both sides of the equation gives the following.

The equation that could be used to solve for the time t in hours that she drove before her stop is 80t + 100(8/3 - t) = 250.

An algebraic expression is the combination of numbers and variables in expressing and solving a particular mathematical question. An equation is the equality of expressions.

Let t = time she drove before her stop

If the total trip time is 3 hours including the stop, which took 20 minutes, then the time she drove after the stop is 3 - t - 1/3 or 8/3 - t.

If altogether she drove a distance of 250 km, then the sum of the products of the rate of speed and time each drive is equal to 250.

(80 km/h)(t) + (100 km/h)(8/3 - t) = 250

Simplify the equation.

80t + 100(8/3 - t) = 250

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The use of a "thumbs-up" gesture to symbolize the statement "good luck" is a common practice in many cultures. This gesture is typically used to express approval or agreement, but it can also be used to convey positive wishes, such as wishing someone good luck before an exam or a job interview.

It is believed that this gesture originated in ancient Rome, where it was used as a sign of approval in the gladiatorial arena. Today, the thumbs-up gesture has become a universal symbol of positivity and encouragement. So, if you want to wish someone good luck, a thumbs-up gesture is a great way to do it!

The use of a "thumbs-up" gesture to symbolize the statement "good luck" involves the following steps:

1. Extend your arm: To perform the thumbs-up gesture, first extend your arm in the direction of the person you want to wish good luck.
2. Make a fist: Close your fingers into a fist, with your thumb pointing upwards.
3. Show your thumb: Ensure that the thumb is clearly visible and pointing upwards. This represents the "thumbs-up" gesture.
4. Make eye contact: Look at the person you're wishing good luck to, so they know the gesture is directed at them.

By performing the thumbs-up gesture, you're using a universally recognized symbol to convey your positive sentiment and wish someone good luck in their endeavors.

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7) The factors of the expression (x² + 17x + 60) is, (x + 5) (x + 12)

8) The factors of the expression (x² - 6x - 27) is, (x + 3) (x - 9)

9) The factors of the expression (2x² - 18x + 28) is, 2 (x - 2) (x - 7)

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Now, We can factor as;

7) The factors of the expression (x² + 17x + 60) is,

⇒ x² + 17x + 60

By using quadratic formula as;

⇒ x = - 17 ± √(17² - 4×1×60 / 2

⇒ x = - 17 ± √289 - 240 / 2

⇒ x = - 17 ± √49 / 2

⇒ x = - 17 ± 7 / 2

⇒ x = - 17 + 7 / 2

⇒ x = - 10/2

⇒ x = - 5

And, x = - 17 - 7 / 2

⇒ x = - 24/2

⇒ x = - 12

Thus, The factors of the expression (x² + 17x + 60) is,

⇒ (x + 5) (x + 12)

8) The factors of the expression (x² - 6x - 27) is,

⇒ x² - 6x - 27

⇒ x² - 9x + 3x - 27

⇒ x (x - 9) + 3 (x - 9)

⇒ (x + 3) (x - 9)

Thus, The factors of the expression (x² - 6x - 27) is,

⇒ (x + 3) (x - 9)

9) The factors of the expression (2x² - 18x + 28) is,

⇒ 2x² - 18x + 28

⇒ 2 (x² - 9x + 14)

⇒ 2 (x² - 7x - 2x + 14)

⇒ 2 (x (x - 7) - 2 (x - 7))

⇒ 2 (x - 2) (x - 7)

Thus, The factors of the expression (2x² - 18x + 28) is,

⇒ 2 (x - 2) (x - 7)

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The 16th term of the arithmetic sequence is -60.

To find the 16th term of an arithmetic sequence with a first term of 0 and a common difference of -4

we can use the formula for the nth term of an arithmetic sequence:

nth term = a + (n - 1)d

where:

a = first term

d = common difference

n = term number

Substituting the given values, we have:

16th term = 0 + (16 - 1) × (-4)

= 0 + 15(-4)

= 0 - 60

= -60

Therefore, the 16th term of the arithmetic sequence is -60.

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Answer:

40 minutes is your answer

Answer: It will take a 1/2 hour or 30min to paint one full wall.

After 12 minutes, the concentration of sugar in the tank is approximately 0.0773 pounds per gallon.

To find the concentration of sugar in the tank after 12 minutes, we need to consider the amount of sugar and water added during that time period.

The tank initially contains 100 gallons of water with 5 pounds of sugar mixed in. Over the course of 12 minutes, the tap pours in 10 gallons per minute of water and 1 pound per minute of sugar.

After 12 minutes, the total amount of water added is 10 gallons/minute * 12 minutes = 120 gallons. The total amount of sugar added is 1 pound/minute * 12 minutes = 12 pounds.

Therefore, the final volume of water in the tank is 100 gallons (initial) + 120 gallons (added) = 220 gallons.

To find the concentration of sugar in the tank after 12 minutes, we divide the total amount of sugar (5 pounds initial + 12 pounds added) by the final volume of water (220 gallons):

Concentration of sugar = (Total amount of sugar) / (Final volume of water)

= (5 pounds + 12 pounds) / 220 gallons

= 17 pounds / 220 gallons

Simplifying the expression, we get:

Concentration of sugar = 0.0773 pounds/gallon

Therefore, after 12 minutes, the concentration of sugar in the tank is approximately 0.0773 pounds per gallon.

It's important to note that in this scenario, we assume perfect mixing of the sugar and water in the tank. Also, the concentration of sugar may vary over time as more water and sugar are added.

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The measure of angles becomes:

∠a = 30°

∠b = 60°

∠c = 105°

Three vertices make up a triangle, a three-sided polygon. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.

∠a and 30° are vertical angles and vertical angles are equal

∠a = 30°

We have a triangle with a, b and a right angle. Triangles have angles that add to 180°.

∠a + ∠b + 90° = 180°

30° + ∠b + 90° =180°

120° + ∠b = 180

∠b = 180° - 120°

∠b = 60°

Angle c and 70 form a straight line and straight lines are 180 degrees

∠c + 75° = 180°

∠c = 180° - 75°

∠c = 105°

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Answer: 22.5° F at 12 noon

Step-by-step explanation:

If it is already 12° F. at 5:00 am then there is only 7 hours to go till 12 noon. So if there is only 7 hours to go and it rises 1.5° F per hour, you would take 1.5 times 7 hours left and get that it will rise 10.5° F in that 7 hours and it is already 12° F so they will combine to make it 22.5° F at 12 noon.

Pseudocode refers to a language that uses a combination of informal English language and a programming language. It's utilized to specify the steps that a computer program will follow to achieve a particular aim. In the context of programming, pseudocode is commonly used to explain a program's algorithm before it is turned into actual code.

In a nutshell, pseudocode is a way of expressing computer code in a human-readable format that can be easily interpreted. Here is the pseudocode for the manager's scenario:

1. Declare variable: sales = 0, vat = 0.

2. Request input of sales amount in Rands from user.

3. Multiply sales by 15% to calculate the VAT payable.

4. Add VAT payable to the sales amount to determine the total sales amount.

5. Display total sales amount and VAT payable.

the pseudocode for a scenario where a food store manager wants to keep track of the amount of sales of food and the amount of VAT that is payable on it will entail the use of variables, multiplication, and display functions. In addition, requesting input from the user is a critical step that cannot be ignored.

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Answer:

24 is 40% of 60

Step-by-step explanation:

Given two predictor variables with a correlation of 0.32879, we should expect there to be multicollinearity between them.

In a data set with a, b, c, d, e, and f numeric variables, given there is a strong correlation of these pairs (f, a), (f, c), (d, e), (a, d), we can set up a regression model as

Of-a + c Of-a + b + c + d + e Of-a + C + d + e Of-a + C + e.

Given two predictor variables with a correlation of 0.32879, we should expect there is multicollinearity between them.

The statement that is true regarding the given two predictor variables with a correlation of 0.32879 is:

we should expect there to be multicollinearity between them.

Multicollinearity is a situation in which two or more predictor variables in a multiple regression model are highly correlated with one another. Multicollinearity complicates the understanding of which predictor variables are significant in the regression model's estimation.

Therefore, given two predictor variables with a correlation of 0.32879, we should expect there to be multicollinearity between them.

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The percentage reduction in space mean speed at the vicinity of the work zone is 40%.

The space mean speed (SMS) is determined using the Greenshields' model:

SMS = (f f - d ) / f f  × V f

Where: ff = Free-flow speed = 50 mph, d = Density = 160 veh/mile, Vf = Flow speed

Vf = Density × SMS = 160 × SMS

Since the road carries 1600 veh/hr and the work zone capacity is 1200 veh/hr, the traffic reduction is:

Traffic Reduction = 1600 - 1200 = 400 veh/hr

Given that the Greenshields' model defines the normal capacity at 1600 veh/hr, the road capacity during the work zone closure is 1200/1600 = 0.75.

So the density in the work zone, assuming uniform flow, can be calculated as:

D = 160 veh/mile × 0.75 = 120 veh/mile

Using the Greenshields' model:

SMS = (50 - 120/160 × SMS) × 50

SMS = 30 mph

Thus, the space mean speed decreases by 50 - 30 = 20 mph.

Reduction in SMS = (20/50) × 100 = 40%

The percentage reduction in space mean speed is approximately 40%.

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Answer:

14. 20

15. 101

16. 260

Step-by-step explanation:

First of all, refer to the properties of a kite. If we use those, your kite will look like the image below:

Since ΔAED and ΔAEB are right triangles, you can use the Pythagorean Theorem to solve for x:

21² + x² = 29²

441 + x² = 841

x² = 400

√x² = √400

x = 20

Now that you have x, you can use the Pythagorean Theorem to solve for y:

20² + 99² = y²

400 + 9801 = y²

10201 = y²

√10201 = √y²

101 = y

y = 101

Now that you have y, you can find the perimeter of the kite:

P = \(side_{1}\) + \(side_{1}\) + \(side_{2}\) + \(side_{2}\)

P = 2 (\(side_{1}\)) + 2 (\(side_{2}\))

P = 2 (29) + 2( 101)

P = 58 + 202

P = 260

The recent fervor surrounding personal privacy has a significant impact on direct marketing and promotions, particularly in the context of email advertising and collecting information at events.

As you design a campaign, it is essential to consider and address these privacy concerns to build trust and ensure compliance with relevant regulations. Here are some key considerations:

Consent and Permission: Obtain explicit consent from individuals before sending them marketing emails or collecting their personal information at events.

Implement clear opt-in mechanisms and provide transparency regarding the purpose and use of their data.

Privacy Policies: Clearly communicate your privacy policies, outlining how you collect, store, and use personal information.

Make it easily accessible to individuals and ensure compliance with applicable data protection laws, such as the General Data Protection Regulation (GDPR) or the California Consumer Privacy Act (CCPA).

Data Security: Implement robust data security measures to protect the personal information you collect. This includes encryption, secure storage, and regular data audits to mitigate the risk of data breaches.

Data Minimization: Only collect the necessary information required for your marketing campaign. Minimize the data you collect to reduce privacy risks and ensure compliance with the principle of data minimization.

Opt-out Options: Provide individuals with clear and simple mechanisms to opt out of receiving marketing emails or having their data collected. Respect their preferences and promptly honor any opt-out requests.

Third-Party Data: Be cautious when using third-party data sources for your marketing campaigns. Ensure that the data providers have obtained proper consent and comply with privacy regulations.

Personalization and Relevance: Focus on delivering personalized and relevant content to individuals based on their preferences and interests. This can help build trust and engagement while respecting privacy boundaries.

By considering these factors and addressing personal privacy concerns, you can develop a campaign that respects individuals' privacy rights, builds trust, and maintains compliance with privacy regulations.

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The correct answer is C. The Mode.

Data is the collection of data term that is organized and formatted in a specific way it's typically contains fact observation or statistics that are collected through a process of measurement or research data set can be used to answer question and help make informed decision they can be used in a variety of ways such as to identify trends on cover patterns and make prediction.

This measure of centre is most meaningful when the data is qualitative because it shows the value that appears most frequently in the data set. The mode can be used to identify the most popular item or most commonly occurring outcome. It is the only measure of centre that can be used for qualitative data, as the other measures (mean, median, and range) require numerical data.

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Answer:

C

Step-by-step explanation:

f(x) × g(x)

= \(\sqrt{x^2+12x+36}\) × (x³ - 12)

= \(\sqrt{(x+6)^2}\) × (x³ - 12)

= (x + 6)(x³ - 12) ← distribute the parenthesis

= \(x^{4}\) - 12x + 6x³ - 72

= \(x^{4}\) + 6x³ - 12x - 72

Answer:

27/220

Step-by-step explanation:

With regards to the above, Pita would have to pick 2 pound coins and 1 50p coin to get £2.50

Then, the probability of picking 1 pound then 1 pound, then 50 Pound

= 3/12 × 2/11 × 9/10

= 9/220

It therefore means that the number of arrangement possible of 2 pounds and 1 50 pounds

= £ - £ - 50 , £ - 50 - £ and 50 - £ -£

= 3

Hence, the required probability

= 3 × 9/220

= 27/220

Answer: 20/9

or 2 2/9

Step-by-step explanation:

Step-by-step explanation:

x+55+80=180(sum of triangle)

or,x+135=180

or,x=180-135

or,x=45

Therefore,x=45°

The value of X or angle C is 45 degrees.

Given:

Two angles of triangle ABC are 80 degrees and 55 degrees.

It is required to find the value third angle X of the triangle.

The sum of three angles of a triangle is 180°.

So, the third angle, X, can be calculated as,

\(80+55+x=180\\135+x=180\\x=45^{\circ}\)

Thus, we can conclude that the value of X is 45°.

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Answer:

5 inches

Step-by-step explanation:

In summary: 5 and 5/29 is equivalent to the improper fraction 150/29. 3/12/13 simplifies to 13/4.

To simplify the mixed number 5 and 5/29 and the fraction 3/12/13, let's break it down step by step.

Starting with 5 and 5/29:

To convert the mixed number 5 and 5/29 into an improper fraction, we multiply the whole number (5) by the denominator of the fraction (29) and add the numerator (5) to obtain the new numerator. The denominator remains the same.

5 and 5/29 = (5 * 29 + 5)/29 = (145 + 5)/29 = 150/29

Therefore, 5 and 5/29 is equivalent to the improper fraction 150/29.

Now, let's simplify the fraction 3/12/13:

To simplify this fraction, we need to understand how it is written. A fraction with multiple denominators separated by slashes ("/") can sometimes be confusing. However, based on the context and the numbers given, it appears that the fraction is 3 divided by the fraction 12/13.

So, 3/12/13 = 3 ÷ (12/13)

To divide by a fraction, we multiply by its reciprocal (flipping the numerator and denominator):

3 ÷ (12/13) = 3 * (13/12)

we multiply across:

(3 * 13)/(1 * 12) = 39/12

To simplify this fraction, we can find the greatest common divisor (GCD) of the numerator and denominator and divide both by that number:

The GCD of 39 and 12 is 3, so dividing both numerator and denominator by 3 gives us:

(39/3) / (12/3) = 13/4

Therefore, 3/12/13 simplifies to 13/4.

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Answer:

Jalen lost 12 pounds in the first 3 weeks

12/3=4 per week

than the weight loss slowed by half, meaning he lost 6 pounds in 3 weeks

6/3=2 per week

84-12=72 to loose after 3 weeks

72/2=36 weeks

to loose 84 pounds you need 3+36=39 week

pls mark me as brainlist

The matrix exponential eAt can be expressed as:

eAt = (5/4)*e^(3t/2) * [1 3/5; 2/5 1]

Sketching the phase plane, we can see that it represents a spiral source. The solution X(t) satisfying X(0) = [-2] can be found by substituting

t=0 and X(0) = [-2] in the general solution as follows:

X(t) = e^(3t/2) * [1 3/5; 2/5 1] * [-2]X(t) = [-2e^(3t/2)*(3/5) + 2e^(3t/2); -4e^(3t/2)/5 + 2e^(3t/2)]

Hence, the solution X(t) satisfying

X(0) = [-2] is X(t) = [-2e^(3t/2)*(3/5) + 2e^(3t/2); -4e^(3t/2)/5 + 2e^(3t/2)].

Given system of differential equation is

X'

= AX, where [2 - A

= 3 2

We need to find the general solution, sketch the phase plane and determine its type.The general solution is given by: X(t)

= eAt X(0)

Where eAt is the matrix exponential. Since A is a 2x2 matrix, we can find eAt by using the formula:

eAt

= (I + tA + (t^2/2!)A^2 + (t^3/3!)A^3 + ....)

The matrix exponential eAt can be expressed as:

eAt

= (5/4)*e^(3t/2) * [1 3/5; 2/5 1]

Sketching the phase plane, we can see that it represents a spiral source. The solution

X(t) satisfying X(0)

= [-2]

can be found by substituting t

=0 and X(0)

= [-2] in the general solution as follows:

X(t)

= e^(3t/2) * [1 3/5; 2/5 1] * [-2]X(t)

= [-2e^(3t/2)*(3/5) + 2e^(3t/2); -4e^(3t/2)/5 + 2e^(3t/2)]

Hence, the solution X(t) satisfying

X(0)

= [-2] is X(t)

= [-2e^(3t/2)*(3/5) + 2e^(3t/2); -4e^(3t/2)/5 + 2e^(3t/2)].

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The probability of choosing a subcommittee of 3 members with no graduate students is 0.2, or 20%.

The number of possible subcommittees that contain only undergraduate students can be calculated by choosing 3 members from the 4 undergraduate students. This can be done in

(4 choose 3) = 4 ways.

The total number of possible subcommittees of three students that can be formed from the 6 members of the committee can be calculated by choosing 3 members from the 6 students. This can be done in

(6 choose 3) = 20 ways.

Therefore, the probability that there will be no graduate students on the subcommittee is:

Number of subcommittees with only undergraduate students / Total number of possible subcommittees

= 4 / 20

= 1/5

= 0.2

So, the probability of choosing a subcommittee of 3 members with no graduate students is 0.2, or 20%.

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Answer:

Step-by-step explanation:A. ​Solution:

So we know that Ann and Cammy are playing Chess, and Stephen is playing by himself, which would mean he is playing -ONE-player games. So we have Rake and Dora, when you see their names, it creates a word. Cammy, Ann, Rake, Dora, and Stephen.

                                                                                                                                          C           A      R        D              S

So Rake and Dora are playing cards. But what kind of cards? The ONE is spotlighted for clues, we have Spanish. So -ONE- in Spanish is UNO. If you search UNO, its a card game, TAAAAADDDDDDDDDAAAAAAAAA.

The money will last approximately 20.0 years before it runs out.

To determine how long the money will last, we need to calculate the number of semiannual withdrawals the child can make before the account balance is depleted. Initially, the child receives $107,440 as a gift, which will serve as the principal amount in the bank account. The account is compounded semiannually at a 6% interest rate. To calculate the number of withdrawals, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = the final amount after t years

P = the principal amount (initial gift) = $107,440

r = the annual interest rate (converted to decimal) = 0.06

n = the number of times interest is compounded per year = 2 (since it's compounded semiannually)

t = the number of years

The child makes withdrawals of $5,000 at the end of each half year, reducing the principal amount by $5,000. We need to find the value of t that will make the account balance reach zero. Once we calculate the value of t using the compound interest formula, we find that t is approximately 20.0 years. Therefore, the money will last around 20.0 years before it runs out.

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Answer:

-5

Step-by-step explanation:

6 - 5 = 1

so 6 + -5 is also equal to 1

Answer:

   q = -5

Step-by-step explanation:

Step  1  :  Simplify:  6/q

Step  2  :

Rewriting the whole as an Equivalent Fraction

Equation at the end of step  2  :

 (6 - q)    

 ——————— -  2  = 0  

    q      

Step  3  :

Rewriting the whole as an Equivalent Fraction

Step  4  :

Pulling out like terms

Answer:    q = -5

Hope this helps.