How do the average rates of change for the pair of functions compare over the given​ interval?
​f(x)x
​g(x)x
x
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Part 1
The average rate of change of​ f(x) over x is

enter your response here. The average rate of change of​ g(x) over x is

enter your response here. The average rate of change of​ g(x) is

enter your response here times that of​ f(x). ​(Simplify your answers. Type integers or​ decimals. )

Moreover, we should evaluate the model's goodness of fit and take into expressions account additional elements that can influence plant development.

Mathematical operations include doubling, dividing, adding, and subtracting. A phrase is constructed as follows: Expression, monetary value, and mathematical operation Numbers, parameters, and functions make up a mathematical expression. It is possible to use words and terms in contrast. Every mathematical statement including variables, numbers, and a mathematical operation between them is called an expression, sometimes referred to as an algebraic expression. For example, the expression 4m + 5 is composed of the expressions 4m and 5, as well as the variable m from the above equation, which are all separated by the mathematical symbol +.

In the formula, h is the height, t is the time, and a and b are the parameters that need to be approximated.

The information in the table may be used to estimate the values of a and b. The equation is first transformed to yield:

[tex]log(b*t) = log(h/a)[/tex]

[tex]19 = 19.24 * log(53.89*t)[/tex]

t = 0.186 months, or approximately 5.58 days, or log(53.89*t) = 1 53.89*t = 10

Hence, 5.58 days is the best guess for the age of the plant at 19 inches tall. Seeing that this is a very little period of time, it is probable that the model will not be correct for values of t this low. Moreover, we should evaluate the model's goodness of fit and take into account additional elements that can influence plant development.

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The roots of the equation x^(2)-12x+61=0 in simplest a+bi form are 6 + 5i and 6 - 5i.

The roots of the equation x^(2)-12x+61=0 in simplest a+bi form can be found using the quadratic formula.

The quadratic formula is x = (-b ± √(b^(2)-4ac))/(2a), where a, b, and c are the coefficients of the equation. In this case, a = 1, b = -12, and c = 61.

Plugging in the values into the quadratic formula, we get:

x = (-(-12) ± √((-12)^(2)-4(1)(61)))/(2(1))

Simplifying the equation, we get:

x = (12 ± √(144-244))/2

x = (12 ± √(-100))/2

Since the square root of a negative number is a complex number, we can write the equation as:

x = (12 ± 10i)/2

Simplifying further, we get:

x = 6 ± 5i

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Jaylon and Paula should expect the pointer to land on 4 around 30 and 43 times respectively.

A probability calculated by a series of tests is known as experimental probability.

The given table is as follows:

              1    2    3    4

Jaylon:   6    8    9    7

Paula:    8     5     7   10

To determine the experimental probability of the pointer landing on 4 for Jaylon, we add up the number of times the pointer landed on 4 for Jaylon and divide by the total number of spins:

Experimental probability for Jaylon = (number of times the pointer landed on 4 for Jaylon) / (total number of spins)

= 7 / 30

Similarly,

Experimental probability for Paula:

= 10 / 30

Expected number of times the pointer will land on 4 = (experimental probability) x (total number of spins)

For Jaylon: (7 / 30) × 130 = 30.33

For Paula: (10 / 30) × 130 = 43.33

Therefore, Jaylon and Paula should expect the pointer to land on 4 around 30 and 43 times respectively.

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The missing table has been attached below.

Answer:

The family will save $896 on airfare by vacationing to Vancouver

Step-by-step explanation:

Tickets to Fairbanks - $958 each (4 total people)

Total cost - 958 times 4 = $3832

Tickets to Vancouver - $734 each (4 total people)

Total cost - 734 times 4 = $2936

$3832 - $2936 = $896

Answer:

The two polynomials cannot be factored using integer coefficients. Therefore, we need to use the quadratic formula to find their roots:

For x² - 3x + 2 = 0:

a = 1, b = -3, c = 2

x = (-(-3) ± √((-3)² - 4(1)(2))) / (2(1)) = (3 ± √1) / 2

x = 1 or x = 2

For x² + x + 2 = 0:

a = 1, b = 1, c = 2

x = (-1 ± √(1² - 4(1)(2))) / (2(1)) = (-1 ± √(-7)) / 2

x = (-1 ± i√7) / 2

Therefore, the LCM of x² - 3x + 2 and x² + x + 2 is:

(x - 1)(x - 2)(x - (-1/2 + i√7/2))(x - (-1/2 - i√7/2))

In response to the supplied query, we may state that Therefore, equation  g(12) = 8.

Using the equals symbol (=) to indicate equivalence, a math equation links two statements. Algebraic equations prove the equality of two mathematical expressions by a mathematical assertion. The equal sign, for example, provides a gap between the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. You can use a mathematical formula to understand the connection between the two phrases that are written on opposite sides of a letter. Most of the time, the logo and the particular software match. e.g., 2x - 4 = 2 is an example.

To find g(3), we substitute x=3 into the function g(x):

g(3) = 2(3)/3

g(3) = 6/3

g(3) = 2

Therefore, g(3) = 2.

To find g(12), we substitute x=12 into the function g(x):

g(12) = 2(12)/3

g(12) = 24/3

g(12) = 8

Therefore, g(12) = 8.

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Answer:

25%

Step-by-step explanation:

p/w =x/100 for a percentage

93.75/125 = x/100

93.75×100= 9375

9375 = 125x

9375/125 =75

x=75

So she paid 75% of the original price, meaning the jeans were 25% off.

The measure of ∠FGH is 28 - 4x.

A three-sided polygon with three angles is known as a triangle. It is a basic geometric shape that can be classified based on its sides and angles.

Since G is the midpoint of DF, we have m∠DGF = m∠FGC (vertical angles are equal), so m∠FGD = m∠CGF = (180 - m∠DGF)/2 = (180 - m∠FGC)/2 = m∠GFC. Similarly, m∠FHE = m∠HEC, so m∠FHE = m∠CGF = m∠GFC.

Using angle sum property, we have:

m∠DEF + m∠FED + m∠FDE = 180

60 - 5x + 2(46 + 2x) + m∠FGH = 180

152 + 4x + m∠FGH = 180

m∠FGH = 180 - 152 - 4x

m∠FGH = 28 - 4x

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There is a zero for f(x) between a and b.

Using the Intermediate Value Theorem, we can show that the function f(x)=2x3+6x2-3a-2 has a zero between a and b.

The Intermediate Value Theorem states that if a continuous function f(x) takes on different values at two points a and b, then there must exist at least one value c in between a and b such that f(c) = 0. Since f(x) is a continuous function, it takes on different values at a and b.

Thus, by the Intermediate Value Theorem, there must exist at least one value c in between a and b such that f(c) = 0, meaning that there is a zero for f(x) between a and b.

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Answer: G=(3, 4) R=(4, 8) A=(7, 8) M=(6, 4)

Step-by-step explanation:

translation is the movement of a point so 11 units right add 11 to the x value and 2 to the y value then do the opposite for going left and down

The x-values at a distance of 22 or less from the number 9 are all the numbers in the interval [-13, 31].

The x-values at a distance of 22 or less from the number 9 can be found by solving the inequality |x-9|≤22.

Step 1: Break up the absolute value inequality into two separate inequalities:
x-9≤22 and x-9≥-22

Step 2: Solve each inequality for x:
x≤31 and x≥-13

Step 3: Combine the two inequalities using the "and" operator (∩):
-13≤x≤31

Step 4: Write the solution in interval notation:
[-13, 31]

So, the x-values at a distance of 22 or less from the number 9 are all the numbers in the interval [-13, 31].

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Answer:

42

Step-by-step explanation:

you asding it all up

"The expressions are equivalent." We can use the distributive property to determine whether or not the expressions are equivalent.

First, let's apply the distributive property to the first expression:

3(x+2) + 8 = 3x + 6 + 8

Next, let's simplify the expression by combining like terms:

3x + 6 + 8 = 3x + 14

Now, we can see that the two expressions are equivalent because they both simplify to the same expression, 3x + 14. Therefore, we can conclude that the expressions are equivalent.

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In the given triangle, using congruency, ∠JHI is congruent to ∠SJT.

What is Triangle ?

Triangle can be defined in which it consists of three sides, three angles and sum of three angles is always 180 degrees.

In the given figure, we can see that there are two pairs of vertically opposite angles, which are opposite to each other at the intersection of two straight lines. These angles are:

According to the ASA Rule, triangles are congruent to one another if any two angles and the side between them are comparable to the corresponding angles and side. According to the AAS Rule, the triangle's angles and excluded side are equal in the same way.

In the given triangle, using congruency, ∠JHI is congruent to ∠SJT

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The missing value that cοmpletes the frequency table is 174.

A frequency distributiοn table is a table that displays the number (οr frequency) οf οbservatiοns that fall within each interval after grοuping the data intο intervals. It is an effective tοοl fοr cοmprehending data distributiοn and spοtting patterns οr trends.

Typically, the table has twο cοlumns. The intervals, οr "bins," intο which the data is divided are listed in the first cοlumn. The frequency, οr quantity οf οbservatiοns, that fall intο each bin is displayed in the secοnd cοlumn. Depending οn the data and the level οf precisiοn required, the bins may be identical οr vary in width.

The analysis οf a variety οf data types, including numerical, categοry, and οrdinal data, can be dοne using frequency distributiοn tables. As well as calculating descriptive statistics like the mean, median, and mοde, as well as measures οf variability like the range and standard deviatiοn, they can alsο be used tο generate these statistics.

All things cοnsidered, frequency distributiοn tables οffer a quick and effective apprοach tο summarize a lοt οf data and learn mοre abοut its distributiοn and prοperties.

Tο cοmplete the frequency table, we need tο determine the frequency fοr the interval 28 ≤ x < 30.

We can see frοm the histοgram that the interval 28 ≤ x < 30 has a width οf 2. Since the tοtal frequency is the sum οf the frequencies in each interval, we can use the infοrmatiοn prοvided in the frequency table tο sοlve fοr the missing value:

110 + 36 + 180 + frequency fοr 28 ≤ x < 30 = tοtal frequency

We can simplify this expressiοn:

326 + frequency fοr 28 ≤ x < 30 = tοtal frequency

We knοw that the tοtal frequency is the number οf mοbile phοnes that were tested, sο we can assume that this is a knοwn quantity. Let's say that the manufacturer tested 500 mοbile phοnes. Then we can sοlve fοr the missing frequency:

326 + frequency fοr 28 ≤ x < 30 = 500

frequency fοr 28 ≤ x < 30 = 174

Therefοre, the missing value that cοmpletes the frequency table is 174. The cοmpleted frequency table is:

Battery life, x(hοurs) Frequency

15 < x < 20                   110

20 ≤ x < 22                  36

22 ≤ x < 28                  180

28 ≤ x < 30                   174

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The measure of angle FLI is 56=

The sum of angles of a triangle equals the straight angle. A triangle has three angles, one at each vertex, bounded by a pair of adjacent sides. It was unknown for a long time whether other geometries exist, for which this sum is different.

Therefore the sum of angle in a triangle is 180

Since FIL is right angle , then angle FLI =

180-(90+34)

= 180- 124

= 56°

therefore the measure of angle FLI is 56°

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The solution is then:

l = 6cm

w = 2cm

h = 2cm

The surface area of a cuboid is the total area of all of the faces of a cuboid. If, the length (l), width (w), and height (h) of the cuboid

then, use the formula: surface area (SA)=2lw+2lh+2hw.

here, we have,

We know that the formula for the volume of a box is:

V = l*w*h

Where:

l = length

w = width

h = height

The formula of the surface area of a box is:

SA = 2(lw+lh+wh)

Based on the given we know the following:

24 =  l*w*h

and

56 =  2(lw+lh+wh)

If we factor out the given volume, you can come up with 3 numbers that will satisfy the surface area formula:

24 = 6*2*2

Let:

l = 6cm

w =2cm

h =2cm    

Now let's try this on the surface area formula:

56 = 2(6*2+6*2+2*2)

so, 56 = 56

The answer is then:

l = 6cm

w = 2cm

h = 2cm

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The scale factοr οf dilatiοn is 1/40 and the cοοrdinates οf F" are (1440, 600)

Labelling the image οf the triangle

The image οf the label is attached

The scale factοr οf the dilatiοn

Given that

D'E' = 36 units

Then, we have

D"E" = 0.9 units

The scale factοr is calculated as

Scale factοr = D"E"/D'E'

Sο, we have

Scale factοr = 0.9/36

Evaluate

Scale factοr = 1/40

Sο, the scale factοr οf dilatiοn is 1/40

The cοοrdinates οf F"

This is calculated as

F = F'/Scale factοr

Sο, we have

F = (36, 15)/(1/40)

F = (1440, 600)

The trigοnοmetry ratiοs

The trigοnοmetry ratiοs are calculated as

sin(D") = EF/DF

cοs(D") = DE/DF

tan(D") = EF/DE

Sο, we have the fοllοwing apprοximated values

sin(D") = 15/39 = 0.36

cοs(D") = 36/39 = 0.92

tan(D") = 0.36/0.92 = 0.39

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Answer:

5x4

Step-by-step explanation:

The dimensions of the rectangle are 20x16

The reducing factor is 0.25.

Multiple 20 * 0.25= 5

Multiple 16 * 0.25= 4

Therefore the new dimensions are 5x4.

The little monsters will do an overhead press and a squat at the same instant 3 times during the drill.

The process of calculating a value using operands and a math operator is referred to as a "operation" in mathematics. The math operator's symbol has predetermined rules that must be obeyed for the provided operands or integers. The five fundamental operations in mathematics are addition, subtraction, multiplication, division, and modular forms.

The prime factorizations of 12 and 30 are 2² x 3 and 2 x 3 x 5, respectively.

Hence, 2² x 3 x 5 = 60 is the smallest common multiple of 12 and 30.

This means that the little monsters will do an overhead press and a squat at the same instant every 60 seconds.

To find out how many times this will happen during the 200-second drill, we can divide 200 by 60:

200 ÷ 60 = 3 remainder 20

This means that there will be 3 complete cycles of both exercises during the 200-second drill, with an additional 20 seconds left over.

Therefore, the little monsters will do an overhead press and a squat at the same instant 3 times during the drill.

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The correct representations of the inequality –3(2x – 5) < 5(2 – x) are given as follows:

The four inequality symbols, along with their meaning, are presented as follows:

The inequality for this problem is defined as follows:

–3(2x – 5) < 5(2 – x)

Expanding the operations, the solution is obtained as follows:

-6x + 15 < 10 - 5x

-6x + 5x < 10 - 15

-x < -5

x > 5.

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The number of each kind of coins Sharah have is 23 dimes and 12 quarters.

Let's use a system of equations to solve this problem. Let x be the number of dimes and y be the number of quarters that Sharah has. Then, we can write the following equations:

x + y = 35 (the total number of coins)

0.10x + 0.25y = 5.30 (the total value of the coins)

We can use the first equation to solve for one of the variables in terms of the other. Let's solve for x:

x = 35 - y

Now we can substitute this into the second equation:

0.10(35 - y) + 0.25y = 5.30

3.50 - 0.10y + 0.25y = 5.30

0.15y = 1.80

y = 12

Now we can use this value of y to solve for x:

x = 35 - 12 = 23

So Sharah has 23 dimes and 12 quarters.

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The profit for buying pencils for $2 each and selling them for $2.40 is $6.40 and there is no loss.

The profit is the difference between the selling price and the cost price of the pencils. In this case, the profit per pencil is $2.40 - $2 = $0.40.

Since the total sales amount is $40, the number of pencils sold is $40/$2.40 = 16.67, which we can round down to 16 pencils. Therefore, the total profit is 16 * $0.40 = $6.40.

There is no loss in this scenario, as the selling price is higher than the cost price. Loss occurs when the selling price is lower than the cost price.

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The solution to the inequality 16 + 12x < 19x + 12 is all the values of x between the interval notation (4/7, ∞).

To solve the inequality 16 + 12x < 19x + 12, we need to isolate the variable x on one side of the inequality. We can do this by subtracting 12x from both sides and subtracting 12 from both sides:

16 + 12x - 12x - 12 < 19x + 12 - 12x - 12

4 < 7x

Solving for x, we can divide both sides by 7:

4/7 < x or x > 4/7

In interval notation, this would be (4/7, ∞). Therefore, the solution to the inequality is (4/7, ∞) in interval notation.

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Answer: (0, 48)

Step-by-step explanation:

To find the y-intercept, plug the x and y values in the equation y = -3x + b, and leave the b the same.

I will use (11, 15)

15 = -3(11) + b

15 = -33 + b

48 = b

The y-intercept is (0, 48)

Equation is y = -3x + 48

Hope this helps!

Based on the data showing the ordered pairs of a linear function, we can find the slope of the line, which will be: 2.4. The closest correct option is letter c.

We need to use the following formula to find the intended result:

Slope = (change in y) / (change in x)

To calculate slope, we can pick any two points from the table. Choosing the points (0, -9) and (10, 15) we have:

Therefore, using two points from the table, we find that the slope of the line is 2.4. The option c) 2.1 is the closest to the result.

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If the extra large box have a dilation scale factor of 4, then the extra large box contain 76.8ounces.

If the extra large box is a dilation of the single serving box with a scale factor of 4, then

The ratio of the volumes of the extra large box to the single serving box will be 4³,

We know that, Volume is a three-dimensional measurement and is affected by the cube of the scale factor.

So, the volume of the extra large box will be;

⇒ 4³ × 1.2 ounces = 4×4×4×1.2 ounces = 76.8 ounces,

Therefore, the extra large box will contain 76.8 ounces of cereal.

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Answer:

(a) The probability that all 4 calls are for medical help can be calculated using the binomial probability formula:

P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)

where:

n is the number of trials (in this case, 4)

k is the number of successes (in this case, 4)

p is the probability of success on a single trial (in this case, 0.81)

Plugging in the values, we get:

P(X = 4) = (4 choose 4) * 0.81^4 * (1 - 0.81)^(4 - 4)

P(X = 4) = 0.5314

Therefore, the probability that all 4 calls are for medical help is 0.5314, rounded to 4 decimal places.

(b) The probability that at least 1 of the calls is not for medical help can be calculated using the complement rule:

P(at least 1 call not for medical help) = 1 - P(all 4 calls for medical help)

We already calculated the probability of all 4 calls being for medical help in part (a), which is 0.5314. So, using the complement rule, we get:

P(at least 1 call not for medical help) = 1 - 0.5314

P(at least 1 call not for medical help) = 0.4686

Therefore, the probability that at least 1 of the calls is not for medical help is 0.4686, rounded to 4 decimal places.

(c) The calculation in part (a) may not be valid if we choose 4 consecutive calls to the station because the 4 consecutive calls being medical may not be independent events. For example, if a large accident or a natural disaster occurs in the area, there may be a higher probability of multiple consecutive medical calls due to the same incident or cause. In that case, the assumption of independence between the events would not hold, and the binomial probability formula would not be applicable.

Step-by-step explanation:

We have shown that a line L is tangent to a circle C at a point P if and only if L is perpendicular to the line OP.

A line L is said to be tangent to a circle C at a point P if and only if L meets C at P and at no other point besides P. Given a circle centered at a point O, a point P on the circle, and a line L passing through P, we can show that L is tangent to the circle at P if and only if L is perpendicular to the line OP.

Let us assume that L is perpendicular to OP. Then, since L is perpendicular to the radius at P, it is also perpendicular to the circumference of the circle at P. This means that the line L only meets the circumference of the circle at the one point P, and so L is tangent to the circle at P.

Conversely, let us assume that L is tangent to the circle at P. This implies that the line L only meets the circumference of the circle at the one point P. Thus, since the line L must pass through the point P, it must be perpendicular to the line OP.

Therefore, we have shown that a line L is tangent to a circle C at a point P if and only if L is perpendicular to the line OP.

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