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We can calculate limits considering the following rules:

Constant Rule The constant rule of limit calculus is utilized when a function is given in which there is no identical variable available. This rule states that the limit of the constant function remains as it is.

Limu→a k = k

Constant time function rule This rule is utilized when there are stagnant coefficients along with the identical variables of the function. This rule states that the constant coefficient will be written outside the limit notation.

Limu→a kf(u) = k Limu→a f(u)

Sum Rule The sum rule is utilized when there are two or more terms or functions given along with the additional sign among them. This rule states that the denotation of the limit will apply to every function separately.

Limu→a [f(u) + g(u)] = Limu→a [f(u)] + Limu→a [g(u)]

Difference Rule The difference rule is utilized when two or more terms or functions are mentioned along with the minus sign among them. This rule expresses that the notation of the limit will be implied to each function segregation.

Limu→a [f(u) – g(u)] = Limu→a [f(u)] – Limu→a [g(u)]

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Answer:

Step-by-step explanation:

We can calculate limits considering the following rules:

Constant Rule The constant rule of limit calculus is utilized when a function is given in which there is no identical variable available. This rule states that the limit of the constant function remains as it is.

Limu→a k = k

Constant time function rule This rule is utilized when there are stagnant coefficients along with the identical variables of the function. This rule states that the constant coefficient will be written outside the limit notation.

Limu→a kf(u) = k Limu→a f(u)

Sum RuleThe sum rule is utilized when there are two or more terms or functions given along with the additional sign among them. This rule states that the denotation of the limit will apply to every function separately.

Limu→a [f(u) + g(u)] = Limu→a [f(u)] + Limu→a [g(u)]

Difference RuleThe difference rule is utilized when two or more terms or functions are mentioned along with the minus sign among them. This rule expresses that the notation of the limit will be implied to each function segregation.

Limu→a [f(u) – g(u)] = Limu→a [f(u)] – Limu→a [g(u)]

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Josie combines 6.72 ounces of strawberries with 6.47 ounces of blueberries and divides them equally into 3 bowls. There are 2.57 ounces of fruit left over. We need to find the number of ounces of fruit in each bowl.

To find the number of ounces of fruit in each bowl, we need to divide the total amount of fruit by the number of bowls. The total amount of fruit is the sum of the strawberries and blueberries, which is 6.72 + 6.47 = 13.19 ounces.

If we divide 13.19 ounces by 3, we get 4.3967 ounces per bowl. However, we need to consider the fact that there are 2.57 ounces of fruit left over. This means that the 13.19 ounces of fruit cannot be divided equally into 3 bowls.

To distribute the remaining 2.57 ounces of fruit equally among the 3 bowls, we can add 2.57/3 = 0.8567 ounces to each bowl. Adding this amount to the initial division, we get approximately 4.3967 + 0.8567 = 5.2534 ounces per bowl.

Therefore, each bowl contains approximately 5.2534 ounces of fruit.

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Step-by-step explanation:

it is simple for such a line.

x goes to -infinity, and therefore y (or f(x)) also goes to -infinity.

x goes to +infinity, and therefore y (or f(x)) also goes to +infinity.

the difference between x and y values is just a constant factor (the slope). that constant factor becomes irrelevant, when the values approach infinity anyway. only the sign is relevant.

but in our case the slope is +1/+2 (the y value increases by +1 for every increase of x by +2).

so, the line (as we can see in the graph) is

y = 1/2 × x - 1

when x goes to +infinity, "-1" is irrelevant, and

1/2 × +infinity = +infinity.

when x goes to -infinity, again, "-1" is irrelevant, and

1/2 × -infinity = -infinity

If a negative relation exists between two variables, low scores on one variable will be associated with high scores on the other variable.

In a negative relationship between two variables, a decrease in one variable is accompanied by an increase in the other variable. This means that as scores on one variable decrease (i.e., low scores), the scores on the other variable tend to increase (i.e., high scores). The negative relationship implies an inverse pattern where the variables move in opposite directions.

The exact nature and strength of the negative relationship can vary, but the general trend is that low scores on one variable correspond to high scores on the other variable. This negative association provides insights into the behavior and interactions between the variables being examined.

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The difference in the proportion of males and the proportion of females that smoke is 0.08

In a sample of 61 males, 15 smoke, while in a sample of 48 females, 8 smoke.

The given parameters are:

                             Male           Female

Sample                  61                  48

Smokers               15                   8

The proportion is calculated using:

p = Smoker/Sample

So, we have:

Male = 15/61 = 0.25

Female = 8/48 = 0.17

The difference is then calculated as:

Difference = 0.25 - 0.17

Evaluate

Difference = 0.08

Hence, the difference in the proportion of males and the proportion of females that smoke is 0.08

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Answer:

Bella saves more per chore than sweet T

Step-by-step explanation:

The old monthly payment was =  10.67 x 70 = 746.9

The new monthly payment is = 11.72 x 70 = 820.4

The percent increase in his monthly payment is =9.8406%

Given,

Sandra Williams bought a home with a 11.5% adjustable rate mortgage for 20 years. He paid $10.67 monthly per thousand on his original loan

According to the question:

So, per thousand value of $70,000 is 70000/1000 =70

Now, the old monthly payment was =  10.67 x 70 = 746.9

He decides to renew and will now pay $11.10 monthly per thousand on his loan.

So, the new monthly payment is = 11.72 x 70 = 820.4

The percent increase in his monthly payment is= 11.72 /10.67 - 1 x 100

9.8406 % and to nearest tenth it is 9.8406%

Hence,  the old monthly payment was =  10.67 x 70 = 746.9

the new monthly payment is = 11.72 x 70 = 820.4

The percent increase in his monthly payment is =9.8406%

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Answer:

an 8 ounce package would be the lower cost per ounce

Step-by-step explanation:

one pound represents 16 ounces so 1/4 of 16 ounces would be 4 ounces

so it cost $8.25 for 4 ounces of almonds and would cost $16.50 for 8 ounces of almonds instead of the other package that is offering 8 ounces of almonds for $0.50 cheaper

hope this helps and makes sense <3

The correct answer is h(t) = 14.25 + 0.25 * sin((π/26) * t)

To model the hours of daylight in a year using a sinusoidal equation, we can consider the average length of daylight, the amplitude of the variation, and the period of the function.

Given:

Summer solstice (longest day) is 14.5 hours

Winter solstice (longest night) is 14 hours

Let's analyze the information:

Average daylight: The average daylight throughout the year would be the average of the summer and winter solstices. It can be calculated as:

Average daylight = (14.5 + 14) / 2 = 14.25 hours

Amplitude: The difference between the average daylight and the longest day or night is the amplitude. In this case, the amplitude is half the difference between the summer and winter solstices. It can be calculated as:

Amplitude = (14.5 - 14) / 2 = 0.25 hours

Period: We are modeling the function over a year, which we'll consider as 52 weeks. Since we want to measure time in weeks (t), the period of the function is 52 weeks.

Putting all the information together, we can write the sinusoidal equation:

h(t) = Average daylight + Amplitude * sin((2π / Period) * t)

Substituting the values we calculated:

h(t) = 14.25 + 0.25 * sin((2π / 52) * t)

Simplifying further, the sinusoidal equation modeling the hours of daylight in a year is:

h(t) = 14.25 + 0.25 * sin(π/26 * t)

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Answer:

7.9

Step-by-step explanation:

7.87400787401

Answer:

Height of the building = 115.4 ft.

Step-by-step explanation:

Height of building = AB + 46.4 + CD + 30.5

By applying Pythagoras theorem in ΔABP,

(26)² = (10)²+ (AB)²

676 - 100 = AB²

AB² = 576

AB = 24 ft

By applying sine rule in ΔCDE,

cos(60°) = \(\frac{CD}{CE}\)

CD = CE × \(\frac{1}{2}\)

CD = \(\frac{29}{2}\)

CD = 14.5 ft

Total Height = 24 + 46.4 + 14.5 + 30.5

                     = 115.4 ft

Answer:

Below

Step-by-step explanation:

This is a horizontal line ( the y-coordinates are the same )

   Horizontal lines  have a slope of  0

Answer:

integer and rational hth

Step-by-step explanation:

The scale factor from Figure A to Figure B is 4

From the question, we have the following statement:

Figure B is a scaled copy of Figure A.

The corresponding side lengths of figure A and figure B are:

Figure A = 10

Figure B = 40

The scale factor from Figure A to Figure B is then calculated as:

Scale factor = Figure B/Figure A

Substitute the known values in the above equation

Scale factor = 40/10

Evaluate the quotient

Scale factor = 4

Hence, the scale factor from Figure A to Figure B is 4

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Answer:

LM = 45

Step-by-step explanation:

M is the midpoint of LN. If LN = 90, what is LM?

L––––––N

From the question

M is the midpoint of LN.

Hence:

L––M––N

Since M is the Midpoint of LN, it means LN is divided in 2 equal parts

LM , MN

So, LM + MN = LN = 90

If LN = 90, LM = 90/2

LM = 45

\(x^y^z\)   , \(|x|\)  are the output of 1st 2 question and for the second question

the final computation SquareRoot(RaiseToPower(x*y, z)) is doing this:

\(\sqrt{(xy)^z}\)

float x , float y , float z

x = Get new line of  input

y = Get new line of  input

z = Get new line of  input

Place RaiseToPower(x, y) in the output.

Place RaiseToPower(x, RaiseToPower(y, z)) to get output

Put abs(x) to output

where abs(x) is absolute value of x

Place SquareRoot(RaiseToPower(x*y, z)) to get disired output

The very first three lines of code simply declare the float type (a number with decimal points) data type of the x, y, and z variables.

After the initial three lines, the user's input is asked in the following three lines.

Coral's Put instruction is used to output an expression for display on the console.

I'm using Coral's built-in RaiseToPower math function to instruct the interpreter to output the value of x raised to the power of y to the console for the initial Put command.

Although the subsequent calculation RaiseToPower(x, RaiseToPower(y, z)) appears to be nested, it actually performs this: \(x^y^z\)

The next computation is AbsoluteValue(x) is doing this \(|x|\)

And the final computation SquareRoot(RaiseToPower(x*y, z)) is doing this:

\(\sqrt{(xy)^z}\)

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The greatest possible value of $xy$ is $17\times5=\boxed{85}$. To get the greatest possible value of $xy$, we need to maximize the values of $x$ and $y$. We can start by rearranging the equation $5x+3y=100$ to solve for one of the variables in terms of the other:

$5x+3y=100 \implies 5x=100-3y \implies x=\frac{100-3y}{5}$
Since $x$ must be a positive integer, $100-3y$ must be divisible by 5. The largest multiple of 3 less than 100 is 99, so we can try values of $y$ starting from 1 and working up to 33 (because if $y\geq34$, then $5x\leq0$, which is not positive).
When $y=1$, we get $x=\frac{100-3}{5} = 19.4$, which is not an integer.
When $y=2$, we get $x=\frac{100-6}{5} = 18.8$, which is also not an integer.
When $y=3$, we get $x=\frac{100-9}{5} = 18.2$, still not an integer.
When $y=4$, we get $x=\frac{100-12}{5} = 17.6$, still not an integer.
When $y=5$, we get $x=\frac{100-15}{5} = 17$, which is an integer.
From here, we can continue to increase $y$ and see that the values of $x$ will only decrease. Thus, the greatest possible value of $x$ is 17 and the corresponding value of $y$ is 5.

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Answer:

x = 0, y = 4

Step-by-step explanation:

12x - 5y = 20

y = x+4

____________

12x - 5y = 20

-x + y = 4

___________

12x - 5y  = 20

5(-x+y = 4)

___________

12x - 5y = 20

-5x + 5y = 20

____________

7x = 0

x = 0

y = x + 4

y = 0+4

y = 4

The quotient is 154. The remainder is 3.

What is a divisor?

In division, we multiply one number by any other number to produce a second number. Therefore, the dividend here refers to the number that is being divided. The divisor is the number that divides a given number. The quotient is the sum that we arrive at as a result. The remainder is the number that the divisor leaves after partially dividing the original number.

Given that 927 ÷ 6.

The dividend is 6 and the divisor is 927.

6) 927(100+50+4

   600

______

    327

    300

______

        27

        24

_______

            3

The remainder is 3. The quotient is 154.

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Answer: She will use 6 cans of pinto beans .

She will use 6 cans of kidney beans.

Step-by-step explanation:

As per given,

For bean salad : lima beans : pinto beans : kidney beans

= 3:2:2

Let quantity of lima beans = 3x, pinto beans 2x , kidney beans 2x.

if she use 9 cans of lima beans, then

3x=9

⇒x=9

Now, 2x= 2 x 3 =6

Thus , she will use 6 cans of pinto beans and 6 cans of kidney beans.

See attachment for the Venn diagram

The shapes are given as:

As a general rule:

Next, we draw the Venn diagram using the above highlights

See attachment for the Venn diagram

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Answer:

f(0)=0

Step-by-step explanation:

If f(x) is x you don't have to do anything to it.

I'm assuming 2 - 5 is like the problem # or something but just in case... that is -3 lol

Answer:

w = 90/65 (125)

Step-by-step explanation:

Since you are trying to find how much Gabriel can type in 125 seconds, you have to find how much he can type in 1 second. Then you can multiply by 125 to get your answer!

Hope this Helps! :)

Have any questions? Ask below in the comments and I will try my best to answer.

-SGO

My bad

the answer is 16

I'm going to refrain from answering area problems from now on. Deepest Apologies

The area enclosed by the curves y = 3x and \(y = x^2\)  is 13.5 square units (rounded to one decimal place).

To find the area enclosed by the curves y = 3x and \(y = x^2\), we need to find the points of intersection and integrate the difference between the curves with respect to x.

First, we find the points of intersection by setting the two equations equal to each other:

\(3x = x^2x^2 - 3x = 0x(x-3) = 0x = 0 or x = 3\)

So the curves intersect at the points (0,0) and (3,9).

To find the area enclosed between the curves, we integrate the difference between the curves with respect to x from x=0 to x=3:

Area =\(\int\limits (y = x^{2} \ to\ y = 3x) dx\)  from 0 to 3

= \(\int\limits(3x - x^2) dx \ from \ 0 \ to \ 3\)

= \([3/2 x^2 - 1/3 x^3] from 0 to 3\)

= (27/2 - 27/3) - (0 - 0)

= 13.5 square units

Therefore, the area enclosed by the curves y = 3x and \(y = x^2\) is 13.5 square units (rounded to one decimal place).

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Answer:

2 19/56 is the answer.

Step-by-step explanation:

10 5/8 - 8 2/7

or, 85/8 - 58/7

or, (595-464)/56

or, 131/56

= 2 19/56

Answer:

permutations: order matters

combinations: order doesn't matter

Answer:

A combination doesn't need to be in a specific order, unlike permutation which needs to go in order.

Step-by-step explanation:

The expected value of the number of games the two equally strong tennis players will play until one wins three games in a row is 14.

Let's consider the possible sequences of games that can occur until one player wins three games in a row. We will denote the winning player as W and the losing player as L. The sequences can be represented as a combination of W's and L's, such as WWL, WLW, LWW, etc.

The key insight is that for each sequence, the last game played must be won by the player who wins three games in a row. This means that the number of games played until the streak ends is fixed at three. However, the preceding games can have various combinations of wins and losses.

To calculate the expected value, we need to consider all possible sequences and their probabilities. Since each player has a 50% chance of winning each game, the probability of any specific sequence occurring is (1/2)^n, where n is the length of the sequence.

We can calculate the expected value by summing the product of the number of games played in each sequence and its corresponding probability.

Considering all possible sequences and their probabilities, the expected value of the number of games played until one player wins three games in a row is found to be 14.

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Answer:

in about 0.92 hours or 55.2 minutes

Step-by-step explanation:

The time they take to paint the room:

Pragnesh and Qazi  = 2 hours

Pragnesh and Ronghui = 3 hours

Qazi and Ronghui = 4 hours

Meaning, each hour (1)  they'll paint:

Pragnesh and Qazi  =  \(\frac{1}{2th}\) of the room

Pragnesh and Ronghui = \(\frac{1}{3th}\) of the room

Qazi and Ronghui = \(\frac{1}{4th}\) of the room

By summing all their work abilities we can determine how long it would take if all three students worked together to paint the fence, which is:

\(\frac{1}{2} + \frac{1}{3} + \frac{1}{4} = \frac{13}{12th}\) of the room each hour. Therefore the whole (1) room would be painted in 1 ÷ \(\frac{13}{12}\) = \(\frac{12}{13} hours\) or 0.92 hours or 55.2 minutes (0.92 * 60).