The positive variables p and c change with respect to time 1. The relationship between p and c is given by the equation p^2 = (20-c)^3 . At the instant when dp/dt = 41 and c = 15 , what is the value of dc/dt ？

The angular size of the minor arc AB can be calculated using the formula: Angular size = Arc length/Radius. Therefore, the angular size of the minor arc AB is 16 cm/12 cm = 1.333 radians.

The angular size of the minor arc AB can be calculated using the formula: Angular size = Arc length/Radius. To calculate the angular size of the minor arc AB, we need to know the length of the chord AB and the radius of the circle. In this case, the chord AB is 16 cm long and the radius of the circle is 12 cm. Therefore, we can calculate the angular size of the minor arc AB by dividing the length of the chord AB by the radius of the circle, which is 16 cm/12 cm = 1.333 radians. The angular size of the minor arc AB is 1.333 radians.

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The proportional relationship between time spent skateboarding and the number of calories burned will be y = 10x.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

Let 'x' be the number of minutes and 'y' be the number of calories burned. And at x = 0, the value of y is also zero. Then we have

0 = m(0) + c

c = 0

Then the equation is given as,

y = mx

At x = 5, the value of y is 50. Then we have

50 = m(5)

5m = 50

m = 50 / 5

m = 10 calories per minute

The proportional relationship between time spent skateboarding and the number of calories burned will be y = 10x.

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The missing graph is attached below.

Answer:

6 cm

Step-by-step explanation:

a = 1/2bh

42 = 1/2(14)h

42 = 7h  Divide both sides by 7

6 = h

The slope of the line is given by the equation m = -3

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be represented as P ( 2 , -1 )

Let the second point be represented as Q ( 1 , 2 )

Now , the slope of the line between the points is

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 2 - ( -1 ) ) / 1 - 2

Slope m = 3 / -1

Slope m = -3

Hence , the slope of the line is decreasing as m = -3 and has a negative value

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The numeric value of f(x) = x - 3 at x = 7 is given as follows:

f(7) = 4.

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

The function for this problem is defined as follows:

f(x) = x - 3.

To obtain the numeric value of the function at x = 7, we replace the lone instance of x by 7, hence:

f(7) = 7 - 3 = 4.

The function for this problem is defined as follows:

f(x) = x - 3.

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671 runs and their winning percentage was 0.406.  They should have allowed the runs are 333.42.

The Mariners just need ten games to clinch their first postseason berth since the momentous 2001 campaign. On paper, the route there appears to be quite straightforward, with many factors going Seattle's way.

Felix Hernandez now holds the record for most victories in Seattle Mariners history with 169 victories as of November 2022. With a total of 145 games won, Hernandez is followed in this position by Jamie Moyer.

671 runs and their winning percentage was 0.406.

671 * 0.406 = 272.42

272 + 61 =333.42

They should have allowed the runs are 333.42.

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The length of diagonal JL of the rectangle is equal to 93

A quadrilateral is a shape with two opposed sides that are equal and parallel. It is a polygon with four sides and four 90-degree angles. The shape of a rectangle is two dimensional.

The diagonal is the line that passes across the middle of a square, rectangle, or other geometric shape and connects one corner to the opposing corner. Every square with two diagonals is an equal-sized square.

Considering the problem, in a rectangle, the length of the diagonals are equal hence we can say that JL = IK = 93

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The length of the diagonal JL in the rectangle is 93 units.

A rectangle is a quadrilateral with opposite sides parallel to each other and opposite sides equal to each other.

The angle in a rectangle is 90 degrees each. The sum of angles in a triangle is 360 degrees.

The diagonals of a rectangle are congruent. The diagonal of a rectangle bisects each other.

The opposite central angles are equal in the diagonals.

Therefore, the diagonal IK is congruent to diagonal JL.

Hence,

IK = JL = 93 units.

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Answer:

3

Step-by-step explanation:

Let x represent the missing value.

(-3) = x + (-6)

6 + (-3) = x + 6 + (-6)

3 = x

The Polynomial 4 will be 3x^2 - 2. The solution is obtained using arithmetic operations.

What are arithmetic operations?

There are four basic operations which are listed as follows:

⇒Polynomial 1 = x^2 - x^2 + x + x + x + x - 1 + 1 - 1

⇒Polynomial 1 = 4x - 1

⇒Polynomial 2 = x + x + x - x - x^2 - x^2 - 1 + 1 - 1

⇒Polynomial 2 = 2x - 2x^2 - 1

⇒Polynomial 2 = -2x^2 + 2x  - 1

⇒Polynomial 3 = 1 + 1 + 1 + 1 - x - x + x - x^2 + x^2 - x^2

⇒Polynomial 3 = 4 - x - x^2

⇒Polynomial 3 = -x^2 - x + 4

We are given sum of all four expressions = 5x

So,

4x - 1 + (-2x^2 + 2x  - 1) + (-x^2 - x + 4) + Polynomial 4 = 5x

On simplifying the equation,

⇒4x - 1 - 2x^2 + 2x  - 1 - x^2 - x + 4 + Polynomial 4 = 5x

⇒5x - 3x^2 + 2 + Polynomial 4 = 5x

⇒Polynomial 4 = 5x - (5x - 3x^2 + 2)

⇒Polynomial 4 = 5x - 5x + 3x^2 - 2

⇒Polynomial 4 = 3x^2 - 2

Hence, polynomial 4 is 3x^2 - 2 which will be 3 big black squares and 2 small white squares.

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Answer:

24

Step-by-step explanation:

Because of similar triangles,

UV/UG = UW/UH

132/24 = 132/UH

UH = 24

Answer:

24

Step-by-step explanation:

GU.U.V=HU. UW

24×132=HU×132

3168=132HU

HU=24

The domain of the function is all real numbers[tex]$\{x|x\in \mathbb{R}\}$[/tex] greater or equal to 0, because the number of players $n$ can not be negative.

The graph of the function is a line with a slope of 1.5 and a y-intercept of 2.5. This can be seen by considering the equation c(n) = 1.5n + 2.5. As the number of new players n increases, the cost c increases by 1.5 for each new player added. For example, if you add 3 new players, the total cost c is 1.5(3) + 2.5 = 6.5. Similarly, if you add 5 new players, the total cost is 1.5(5) + 2.5 = 8.5.

For example, if you want to add 10 new players, the cost will be $c=1.50\times10+2.50=17.50$. Substituting $n=10$ into the function gives $c=17.50$. The graph of this function is a straight line that passes through the origin and has a positive slope of 1.50.

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The percentage of the variation in height that is explained by a regression on age is 0.64, which is the right answer.

from the aforementioned case, The relationship between children's age and height is strongly correlated, as evidenced by the correlation coefficient R of 0.8. Given the correlation coefficient value, we can calculate the coefficient of determination (R2), which indicates the proportion of variation that the regression model can account for.

Therefore, R2 = 0.82 = 0.64, which is the coefficient of determination. Therefore, the proportion of the variation in children's height that can be attributed to age is 0.64 and the remaining 0.36 can be attributed to other factors.

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We can conclude that an is a positive number and that b is a negative amount from the aforementioned inequalities.

Given,

y<-x + a and y > x + b

The above inequalities have a solution of (0,0) as indicated.

[tex]& \Rightarrow 0 < 0+a \text { and } 0 > 0+b \\[/tex]

[tex]& \Rightarrow a > 0 \text { and } b < 0[/tex]

As a result, we can infer from the aforementioned inequalities that b is a negative quantity and an is a positive number.

As a result, a>b can be considered to be true.

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Answer:

[tex]\begin{array}{|c|c|c|c|}\cline{1-4}\vphantom{\dfrac12}\sf Bank & \sf Basic\;Fee\times 12 & \sf Bill\;Paying\;Fee\times 12 & \sf Checks\;Written-Limit\\\cline{1-4}\vphantom{\dfrac12}\sf A&\$18&\$27&20\\\cline{1-4}\vphantom{\dfrac12}\sf B&\$30&\$27&10\\\cline{1-4}\vphantom{\dfrac12}\sf C&\$18&\$21&10\\\cline{1-4}\vphantom{\dfrac12}\sf D&\$30&\$21&20\\\cline{1-4}\end{array}[/tex]

[tex]\begin{array}{|c|c|c|}\cline{1-3}\vphantom{\dfrac12}\sf Bank & \sf Column\;4\times Cost\;per\;bill\times 12 & \sf Annual\;Total\\\cline{1-3}\vphantom{\dfrac12}\sf A&\$24&\$69\\\cline{1-3}\vphantom{\dfrac12}\sf B&\$18&\$75\\\cline{1-3}\vphantom{\dfrac12}\sf C&\$24&\$63\\\cline{1-3}\vphantom{\dfrac12}\sf D&\$48&\$99\\\cline{1-3}\end{array}[/tex]

Step-by-step explanation:

Jane wants to compare the cost of online banking across 4 different banks. We are told that she writes an average of 40 checks each month.

Given monthly charges for four different banks:

[tex]\begin{array}{|c|c|c|c|c|}\cline{1-5}\vphantom{\dfrac12}\sf Bank & \sf Basic\;Monthly\;Fee& \sf Bill\;Paying\;Monthly\;Fee & \sf Limit& \sf Cost\;per\;bill\;beyond\;limit\\\cline{1-5}\vphantom{\dfrac12}\sf A&\$1.50&\$2.25&20&\$0.10\\\cline{1-5}\vphantom{\dfrac12}\sf B&\$2.50&\$2.25&30&\$0.15\\\cline{1-5}\vphantom{\dfrac12}\sf C&\$1.50&\$1.75&30&\$0.20\\\cline{1-5}\vphantom{\dfrac12}\sf D&\$2.50&\$1.75&20&\$0.20\\\cline{1-5}\end{array}[/tex]

The "limit" is the number of checks Jane is not charged a fee to write per month.  For each check Jane writes above this monthly limit, she will be charged a fee (fifth column).

To complete the first table:

[tex]\begin{array}{|c|c|c|c|}\cline{1-4}\vphantom{\dfrac12}\sf Bank&\sf Basic\;Fee\times12&\sf Bill\;Paying\;Fee\times12&\sf Checks\;Written-Limit\\\cline{1-4}\vphantom{\dfrac12}\sf A&\$1.50\times12=\$18&\$2.25\times12=\$27&40-20=20\\\cline{1-4}\vphantom{\dfrac12}\sf B&\$2.50\times12=\$30&\$2.25\times12=\$27&40-30=10\\\cline{1-4}\vphantom{\dfrac12}\sf C&\$1.50\times12=\$18&\$1.75\times12=\$21&40-30=10\\\cline{1-4}\vphantom{\dfrac12}\sf D&\$2.50\times12=\$30&\$1.75\times12=\$21&40-20=20\\\cline{1-4}\end{array}[/tex]

To complete the second table:

[tex]\begin{array}{|c|c|c|}\cline{1-3}\vphantom{\dfrac12}\sf Bank & \sf Column\;4\times Cost\;per\;bill\times 12 & \sf Annual\;Total\\\cline{1-3}\vphantom{\dfrac12}\sf A&20\times\$0.10\times12=\$24&\$18+\$27+\$24=\$69\\\cline{1-3}\vphantom{\dfrac12}\sf B&10\times\$0.15\times12=\$18&\$30+\$27+\$18=\$75\\\cline{1-3}\vphantom{\dfrac12}\sf C&10\times\$0.20\times12=\$24&\$18+\$21+\$24=\$63\\\cline{1-3}\vphantom{\dfrac12}\sf D&20\times\$0.20\times12=\$48&\$30+\$21+\$48=\$99\\\cline{1-3}\end{array}[/tex]

Answer:

24

Step-by-step explanation:

Try 1 of each:

1 nickel is worth $0.05

1 dime is worth $0.10

1 quarter is worth $0.25

Add them up: $0.05 + $0.10 + $0.25 = $0.40

Divide $10 by $0.40:

$10/$0.40 = 25

25 coins of each will give a total value of $10.

That means you can only have up to 24 coins of each.

Answer: 24

smith should spend 12 min to make computer and 48 min to make calculator and jones should spend 1 hour to make calculators.

the production rate of producing calculators by smith=100 per hour.

the production rate of producing computer by smith=10 per hour.

the production rate of producing calculators by jones=120 per hour

the production rate of producing computer by jones=6 per hour.

the time spend to make one calculator by smith=60/100=0.6min

the time spend to make one computer by smith=60/10=6 min

the time spend to make one calculator by jones=60/120=0.5 min

the time spend to make one computer by jones=60/6=10 min

both produce 220 calculator per hour,

so, one calculator makes in 60/220 =0.272min

time spent to make 200 calculators=0.272*220= approx. 1 hour

time spent to make 2 computers=0 hour

so, according to above calculations.

smith should spend 12 min to make computer and 48 min to make calculator and jones should spend 1 hour to make calculators.

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The values of the variance and expected value expressions are

From the question, we have the following parameters that can be used in our computation:

E(Y1) = 10

E(Y2) = 2

The above parameters are calculated as follows:

a. Expected value

E(4Y1 – 2Y2 + 6) = 4E(Y1) – 2E(Y2) + 6

= 4(10) – 2(2) + 6

= 40 - 4 + 6

= 42

So E(4Y1 – 2Y2 + 6) = 42

b. Variance

V(4Y1 – 2Y2 + 6) = 4^2 * V(Y1) + (-2)^2 * V(Y2)

= 16 * V(Y1) + 4 * V(Y2)

The variances of Y1 and Y2 are not given

This means that the value of the expression cannot be calculated

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Answer: she will receive a grade of zero if she gets one more question incorrect.

Step-by-step explanation: She gets 2 questions correct which equals 4 points and 3 questions wrong which is minus 3 points

4-3=1 so if she were to get one more incorrect she would receive a zero

Let's use v1(t) and v2(t) to represent the speed of the first and second runners, respectively, at time t. The functions v1 and v2 must both be continuous in the time variable t, hence this assumption must be made.

So, their difference, a(t), is similarly a continuous function in the variable t, with the formula a(t) = v1(t)-v2(t).  

Now, using the principle of contradiction, one may demonstrate that t1, t2, such that a(t1) is less than or equal to 0 and a(t2) is higher than or equal to 0, exist because the overall average speed of both runners is identical.

Now, we may utilize the continuous function a's Intermediate Value Property to locate a t0 between t1 and t2, where a(to)=0 and the runners are moving at the same speed at this point.

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Data Retention Settings. This feature allows you to specify how long user-level and event-level data is stored by analytics before being automatically deleted. You can set up data retention periods for different types of data, such as individual user data, event data, and session data.

Data Retention Settings is a feature available in many analytics platforms that allows you to control how long user-level and event-level data is stored. This helps ensure that the data stored is only relevant to your project. You can set up different data retention periods for different types of data, such as individual user data, event data, and session data. This allows you to specify how long the data should be stored before being automatically deleted. Data retention settings are important as they help protect user privacy and ensure that only the data necessary for your project is stored. They also help you manage your storage costs by allowing you to set a maximum amount of data that can be stored for a certain period of time. Data Retention Settings is a valuable tool for managing the data collected by your analytics platform.

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The complete question is

which of these features lets you control how long user-level and event-level data is stored by analytics Data Retention Policies.

Answer: 33

Step-by-step explanation: because like its 33% and its a number between them + its in the range of sample

The total amount of money that Edison spends on salad and pizza is equal to e.

e = s * $2 + p * $3

This equation can be used to calculate the amount of money Edison spends on salad and pizza. The first part of this equation, s * $2, calculates the cost of the bowls of salad. The cost of one bowl of salad is $2, and the number of bowls of salad that Edison buys is represented by s.

The second part of this equation, p * $3, calculates the cost of the slices of pizza. The cost of one slice of pizza is $3 and the number of slices of pizza that Edison buys is represented by p.

When added together, the total amount of money that Edison spends on salad and pizza is equal to e. For example, if Edison buys four bowls of salad (s=4) and six slices of pizza (p=6), the total amount of money he spends (e) is equal to (4 * $2) + (6 * $3) = $24.

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The value of the expression → q(p(-2)) will be → -1.5.

        [tex]${\displaystyle \forall x\in X,\forall y\in Y,\forall z\in Y,\quad ((x,y)\in R\land (x,z)\in R)\implies y=z.}[/tex]

        [tex]${\displaystyle \forall x\in X,\exists y\in Y,\quad (x,y)\in R.}[/tex]

Given are the graphs of two function as shown in the image.

We have to find -

q(p(-2))

Now, we can see from the graph that -

p(-2) = 0

Then, q(p(-2)) will be -

q(0) = - 1.5

Therefore, the value of the expression → q(p(-2)) will be → -1.5.

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The graph that represents the situation is added as an attachment

From the question, we have the following parameters that can be used in our computation:

This means that the graph would be represented using a distance/time graph

Such that the distance would be on the y-axis and the time would be on the x-axis

See attachment for the graph

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The volume of the cube with side of (4m⁸n⁴) unit is (64m²⁴n¹²) unit³

An equation is an expression showing two or more numbers and variables linked together by a mathematical operation. Types of equations are linear, quadratic, cubic and so on depending on the degree of the variable.

Volume is the amount of space that a three dimensional object occupies. For a cube, all the sides are equal, that is length = width = height

The volume of the cube is:

Volume = length³

Given that length = 4m⁸n⁴

Hence:

Volume = length³ = (4m⁸n⁴)³ = 64m²⁴n¹²

The volume of the cube is (64m²⁴n¹²) unit³

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The equation be (x - 10)(x + 10) then x² - 100.

In addition to the monomial, binomial, and polynomial types of expressions, there are two further categories into which an algebraic expression can be placed: Expression in numbers. adjustable expression.

Using the operations + , – , × or ÷ a group of numbers or variables can be combined to form an expression. Expressions in algebra that include variables, numbers, and mathematical operators differ from expressions in arithmetic that simply contain numbers and mathematical operators.

Let the equation be (x - 10)(x + 10)

(x - 10)(x + 10)

simplifying the above equation, we get

= x² - 100

The equation be (x - 10)(x + 10) then x² - 100.

The complete question is:

How do you simplify (x - 10)(x + 10) ?

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This is a system of equations problem. Let x be the number of dimes and y be the number of nickels.

From the problem, we know the following:

x + y = n (where n is the total number of coins)

y = 3x - 9 (because the number of nickels is three times the number of dimes minus nine)

We also know that the total value of the coins is $2.55 and that a dime is worth $0.10 and a nickel is worth $0.05. So we can create an equation using the total value of the coins:

0.10x + 0.05y = 2.55

Now we have a system of three equations and three variables. To solve for x, y and n, we can use substitution or elimination method.

First equation and second equation:

x+3x-9 = n

4x-9=n

4x = n+9

x = (n+9)/4

By substituting the value of x in equation 3

0.10*(n+9)/4 + 0.05*(3*(n+9)/4-9) = 2.55

Solving this equation we get n = 63

Thus, x = (63+9)/4 = 18 dimes

y = 3x - 9 = 3*18 - 9 = 45 nickels

So, Carolyn has 18 dimes and 45 nickels.

a) 2 years: The value of the investment after 2 years would be $2090.45.

b) 4 years: The value of the investment after 4 years would be $2186.63.

c) 12 years: The value of the investment after 12 years would be $2712.20.

a) 2 years: Value = 2000 x e^(0.045 x 2) = $2090.45

b) 4 years: Value = 2000 x e^(0.045 x 4) = $2186.63

c) 12 years: Value = 2000 x e^(0.045 x 12) = $2712.20

The value of a continuously compounded interest rate can be calculated using the formula: Value = P x e^(r x t), where P is the principal amount, r is the interest rate per year, and t is the time in years.

Using this formula, the value of a $2000 investment with an interest rate of 4.5% after 2 years would be $2090.45. This can be calculated by plugging the values into the formula: Value = 2000 x e^(0.045 x 2) = $2090.45.

The value of the same investment after 4 years would be $2186.63, which can be calculated in the same way: Value = 2000 x e^(0.045 x 4) = $2186.63.

The value of the same investment after 12 years would be $2712.20, which can be calculated by plugging the values into the formula: Value = 2000 x e^(0.045 x 12) = $2712.20.

Continuously compounded interest rates are a great way to earn money on investments, as the compounding of interest leads to higher returns over time.

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The length of the trail is given as follows:

32 km.

The length of the trail is obtained applying the proportions in the context of this problem.

The fractions hiked each day are given as follows:

The total fraction after the second day is given as follows:

1/8 + 4/7 x 7/8 = 5/8.

On the third day, one third of the remaining was hiked, hence:

5/8 + 1/3 x 3/8 = 6/8.

Meaning that the remaining distance of 8 km is 2/8 = 1/4 of the total distance, hence:

x/4 = 8

x = 32 km.

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Answer:A

Step-by-step explanation:

1440:15=96