Find the equation in slope- intercept form that matches the table of solutions.

The value of the limit for the given function [tex]\lim_{x \to 5} \frac{x^2 - 5x}{x^2 - 25}[/tex] = 1/2.

A general technique for assessing indeterminate forms like 0/0 or / is the L'Hospital rule. L'Hospital's rule is applied to calculate the limits of indeterminate forms for calculus derivatives. It is possible to use the L Hospital rule many times. This rule is still valid after being applied, and it will take any indefinite form. L'Hospital's Rule cannot be applied if the issue is not of the indeterminate types.

The given function is:

[tex]\lim_{x \to 5} \frac{x^2 - 5x}{x^2 - 25}[/tex]

Substituting the value of limit we can see that the function is of the indeterminate form 0/0.

Using the L'Hospital rule we have:

[tex]\lim_{x \to 5} \frac{x^2 - 5x}{x^2 - 25}\\\\\lim_{x \to 5} \frac{2x - 5}{2x}\\[/tex]

Substitute the value of limits:

[tex]=\frac{2(5) - 5}{2(5)}\\ \\=\frac{1}{2}[/tex]

Hence, the value of the limit for the given function [tex]\lim_{x \to 5} \frac{x^2 - 5x}{x^2 - 25}[/tex] = 1/2.

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Answer:

Step-by-step explanation:

Given the function f(x) = 4 - 9x, the indicated values are:

(a) f(-8) = 4 - 9(-8) = 4 + 72 = 76

(b) f(0) = 4 - 9(0) = 4

(c) f(9) = 4 - 9(9) = 4 - 81 = -77

So, the values of f(-8), f(0), and f(9) are 76, 4, and -77, respectively.

a) The bearing of D from C is 250.

b) The bearing of D from C is 145.

Angles are measured in bearings clockwise from north. The direction of north must be identified before taking a bearing measurement. The math exam question will typically include this north direction. The required angle is then measured in a clockwise fashion.

Given:

a) 250°N, 110°D

As, we know that Bearings are angles, measured clockwise from north. To measure a bearing, we must first know which direction is north.

So, the bearing of D from C is 250.

b) The bearing of D from C in second case is 145.

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The solution of the expression ( 10z - 3 ) is equal to 37.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that the expression is 10z - 3. The value of the expression at z = 4 will  be calculated below,

Evaluate for z = 4,

E = 10x - 3

E = (10)(4)−3

E = (10)(4)−3

E = 37

Therefore, the solution for the expression is 37.

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The given sequence is convergent and the limit is 1.

What is a sequence?

In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members. The number of elements is called the length of the sequence.

Here, we have

Given: aₙ = (n/2) sin(2/n)

First, we will find the limit of a given sequence.

aₙ = [tex]\lim_{n \to \infty} (n/2)sin(2/n)[/tex]

We apply L'hospital's rule here and we get

aₙ = [tex]\lim_{n \to \infty} {cos(2/n)(-2/n^2)}/(-2/n^2)[/tex]

aₙ = [tex]\lim_{n \to \infty} cos(2/n)[/tex]

aₙ = 1

We concluded that the given series is convergent.

Hence, the given sequence is convergent and the limit is 1.

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Take the PSI value and divide it by 14.696 or 14.7 to convert PSI to atm.

What is atmospheric pressure?

The force per unit area that an atmospheric column exerts is known as atmospheric pressure, also known as barometric pressure (that is, the entire body of air above the specified area). A mercury barometer (hence the commonly used synonym barometric pressure) can be used to measure atmospheric pressure because it displays the height of a mercury column that precisely balances the weight of the atmosphere over the barometer. An aneroid barometer, which uses one or more hollow, partially evacuated, corrugated metal discs supported against collapse by an inside or outside spring, can also be used to measure atmospheric pressure. The change in the disk's shape with changing atmospheric pressure can be recorded using a pen arm and a clock-driven revolving drum.

The Imperial system of measurement measures pressures in pounds per square inch (PSI). PSI is frequently used to calculate the pressure of liquids or gases (hydraulic pressure).

The model equation is ATM = PSI/14.7

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Answer:

A) <5 and <6 are commentary

B) 72

C < 4 = 22

<3 = 68

Step-by-step explanation:

A) The square drawn over the 2 angles shows that the angles together measure 90 degrees

B) 90 - 18 = 72

C) 4x -10 + 5x + 28 = 90  Combine like terms

9x + 18 = 90  Subtract 18 from both sides

9x = 72   Divide both sides by 9

x = 8

<4

4x - 10

4(8) - 10

32 - 10

<4 = 22

<3

5x + 28

5(8) + 28

40 + 28

68

<3 = 68

Answer:

Part A: Yes, ∠5 and ∠6 are complementary angles because they add up to 90°.

Part B: If the measure of ∠6 is 18°, then the measure of ∠5 is 72° because ∠6+∠5=90° so 90°-18°=72°.

Part C: ∠4+∠3=90°

(4x-10)°+(5x+28)°=90°

add 10 to both sides

4x+5x+28=100

subtract 28 from both sides

4x+5x=72

combine like terms

9x=72

divide both sides by 9

x=8

now plug 8 in for x

∠4=(4(8)-10)°

∠4=22°

∠3=(5(8)+28)

∠3=68°

22°+68°=90°

An increase in consumer incomes would lead to a decrease in the demand and price of potatoes, and an increase in supply and quantity.

When consumer incomes increase, the demand for inferior goods such as potatoes usually decreases. This is because as people's incomes rise, they tend to switch to buying more superior goods, which are generally more expensive than inferior goods.

At the same time, the supply of potatoes may also increase as farmers respond to the potential for higher prices by growing more potatoes.

With both a decrease in demand and an increase in supply, the market price for potatoes is likely to fall. The quantity of potatoes supplied will likely increase as well, as the lower price attracts both consumers and producers.

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Applying inequality, the minimum height of her brother is: 26 inches.

An inequality is a mathematical statement that shows the relationship between two values or expressions, where one value is either greater than, less than, greater than or equal to, or less than or equal to the other value. It is represented using symbols such as ">", "<", "≥", or "≤".

Let's call the height of Adriana's little brother "x".

So Adriana's height is 2x + 8 inches.

And because Adriana is at least 60 inches tall, we can write the following inequality:

2x + 8 ≥ 60

Subtracting 8 from both sides:

2x ≥ 52

Dividing both sides by 2:

x ≥ 26

So the minimum height of Adriana's little brother is 26 inches.

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The solution to the initial value problem is y(t) = 5e^8t.

y(t) = 5e^8t

This is a separable differential equation. Separating the variables, we have

dy/dt = 8y

dy = 8y dt

Integrating both sides, we have

∫dy = ∫8ydt

y = 4e^8t + C

To find C, we use the initial condition, y(1) = 5

5 = 4e^8(1) + C

C = 5e^-8

Substituting C into the equation, we have

y(t) = 5e^8t

The solution to the initial value problem is y(t) = 5e^8t.

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This is quite simple. You just need to multiply. 130 × 3 = 390

Therefore, you would have driven 390 km.

Answer:

A

Step-by-step explanation:

Surface area of sphere is 4 pi r^2

                     144 pi   = 4 pi r^2

                          144 pi / (4 pi) = r^2

                             36 = r^2

                               r = 6 ft

The area of circle can be calculated by using the formulas: Area = π x r2, in terms of radius 'r'. Area = (π/4) x d2,

State area  of circle?

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The volume of cone B is calculated as: 384 cm³.

If the ratio of the surface area of cone A to the surface area of cone B is 25:4, then the ratio of the radii of the cones is 5:2 (since the surface area of a cone is proportional to the square of the radius).

Since the cones are similar, the ratio of their volumes is also the ratio of the cubes of their radii, which is 125:8.

So, if the volume of cone A is 6000 cm³, then the volume of cone B is (6000 * 8) / 125 = 384 cm³.

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Step-by-step explanation:

triangle BOY is congruent with triangle MAN by ASA (angle-side-angle) : 2 angles are the same and the side between them has the same length.

that is sufficient to declare the triangles congruent.

Teresa would need to work 10 weeks in order to earn the same total amount as the second job.

Assuming Teresa takes the first job, she would need to work for 10 weeks in order to earn the same total amount as the alternate job. The total amount earned from the first job can be calculated by (400 x 10) + 200 = 6000. The total amount earned from the second job can be calculated by (420 x 10) = 4200. Thus, in order to earn the same amount from the total of both jobs, Teresa would need to work 10 weeks at the first job. This can be expressed by the following formula: (400 x n) + 200 = 420 x n, working for n is the number of weeks. Solving for n gives n = 10.

Thus, Teresa would need to work 10 weeks in order to earn the same total amount as the second job.

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This strategy works for all cases with 40 or fewer total tiles. The pattern observed here is that XORing pattern.

If there are 5 red tiles and 7 blue tiles, the binary representation of these numbers is 101 and 111, respectively. Taking the bitwise XOR of these numbers gives 010, which is 2. Hence, the player should take 2 tiles of either color, leaving 3 tiles of one color and 5 tiles of the other color. This leaves the other player in a losing position.

The pattern observed here is that XORing all the numbers together effectively cancels out all the common bits, leaving only the unique bits. The player should then take a number of tiles such that the unique bits become 0.

Unique bits refer to the concept of binary representation of numbers in mathematics. The binary system is a base-2 numeral system where each digit can either be 0 or 1. Unique bits refers to the distinct and non-repeating number of binary digits used to represent a number. It is a measure of the number of bits needed to represent a unique number.

The unique bits in mathematics is a concept that is widely used in computer science, information theory and cryptography. The more unique bits used, the greater the number of unique combinations that can be produced and hence, the greater the accuracy in representation. For example, using 8 unique bits in binary representation can result in up to 256 unique combinations, compared to using only 7 unique bits, which can only result in 128 unique combinations. Unique bits plays a crucial role in ensuring the accuracy and efficiency of information representation and transmission.

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9 m, 23 m, and 23 m are the triangle's measurements.

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The ratios of  the areas in the following sets or similar triangles are:

1. 9:1,         2. 4:1,         3. 25:9,

4. 46:9,     5. 9:4,        6. 4:1,

7. 25:4,      8.9:4,         9. 9:1.

Having three edges and three vertices, a triangle is a three-sided polygon. The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic. This characteristic is known as the triangle's angle sum property.

Given a set of triangles is similar,

for similar triangles the ratio of their corresponding sides is equal,

so A/a = B/b = C/c

where A, B, and C are sides of larger triangles and a, b, and c are sides of small triangles.

area of small triangle = 1/2*b*h

here b =base and h = height

area of large  triangle = 1/2*B*H

here B =base and H = height

the ratio of areas = area of the large  triangle/area of the small triangle

the ratio of areas = [1/2*B*H]/[1/2*b*h]

the ratio of areas = BH/bh

since the triangles are similar, B/b = H/h

the ratio of areas = B²/b²

or the ratio of areas = (SIDE)²/(side)²

1. given side of large triangle = 3

side of small triangle = 1

ratio of areas = 3²/1²

ratio of areas = 9/1 = 9:1

2.  given side of large triangle = 4

side of small triangle = 2

ratio of areas = 4²/2²

ratio of areas = 16/4 = 4:1

3. given side of large triangle = 5

side of small triangle = 3

ratio of areas = 5²/3²

ratio of areas = 25/9 = 25:9

similarly for other questions,

4.ratio of areas = 16/9 = 16:9

5. ratio of areas = 9/4 = 9:4

6. ratio of areas = 64/16 = 4:1

7. ratio of areas = 25/4 = 25:4

8. ratio of areas = 36/16 = 9:4

9. ratio of areas = 4/1 = 4:1

Hence the ratios are as possible.

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Answer: 2 bags

Step-by-step explanation:

To determine the number of bags Clay can fill, we need to divide the total amount of the trail mix by the amount of trail mix in each bag.

First, we'll convert the amounts to a common denominator of fifths:

4/5 of a pound of trail mix is 4/5 * 5/5 = 4 fifths

2/5 of a pound is 2/5 * 5/5 = 2 fifths

Now, we can divide the total amount of trail mix by the amount in each bag:

4 fifths ÷ 2 fifths/bag = 2 bags

So, Clay can fill 2 bags with 2/5 of a pound of trail mix each.

The parabola function has a minimum value of -4.

The given parameters are:

Declines through (-5,-2), (-3,-4)

Rises through  (-2, -3), (-1, -2), (0, 0), (0, 2) and (1, 4)

Because the parabola declines before it rises, it means that the function has a minimum

From the point of decline;

-4 is less than -2

Hence, the parabola function has a minimum value of -4.

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The expression for the cost is cost = 0.35x + 7.5 and the total cost for a small yogurt with no toppings and a large yogurt with 3 toppings is $8.55

To write an expression to show how much it costs to buy a small yogurt with no toppings,
The expression for the costs of a small yogurt with no toppings and a large yogurt with x toppings will be:

Cost = 2.85 + (4.65 + 0.35x)

Cost = 2.85 + 4.65 + 0.35x

Cost = 0.35x + 7.5

To find the total cost for a small yogurt with no toppings and a large yogurt with 3 toppings, substitute x = 3 into the above expression. That is:

Cost = 0.35x + 7.5

Cost = 0.35(3) + 7.5

Cost = $8.55

Thus, the total cost is $8.55

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Answer: The estimate of the airplane's climb angle while climbing 250 feet for every 1000 feet it travels is approximately 14°

Step-by-step explanation:

The climb angle of an airplane can be estimated using the tangent of the rise over the run. To do this, you need to know the rise (the vertical distance the airplane is climbing) and the run (the horizontal distance the airplane is traveling).

In this case, the rise is 250 feet and the run is 1000 feet. The tangent of the angle is the rise divided by the run:

tan(angle) = rise / run = 250 / 1000 = 0.25

To find the angle in degrees, you need to take the inverse tangent (arctan) of 0.25:

angle = arctan(0.25) = 14.0°

So, the estimate of the airplane's climb angle while climbing 250 feet for every 1000 feet it travels is approximately 14°.

In an experiment, the variable being measured or tested is known as the dependent variable.

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Answer:14 meters

Step-by-step explanation:

Answer:

The equation is y = 1,460e^(2%)x, and the balance will be $2,067.54 in 8 years

The surface area of a cone is given by the formula:

S = πl + πr^2

Solving for l, we can start by isolating l on one side of the equation:

S - πr^2 = πl

Dividing both sides by π:

(S - πr^2) / π = l

Therefore, the length l can be found by subtracting the product of π and r^2 from the surface area S, and dividing the result by π.

Sandy's experimental probability was closest to the theoretical probability in the experiment with 100 flips.

In Sandy's experiment, she used a virtual coin toss app to simulate the results of flipping a coin 100 times, 500 times, and 1,000 times. The experimental probability is the probability obtained from the observed outcomes of the experiment, while the theoretical probability is the probability calculated based on mathematical principles and assumptions.

Based on the information given, it is stated that Sandy's experimental probability was closest to the theoretical probability in the experiment with 100 flips. This suggests that the observed outcomes of the 100 flips aligned more closely with the expected outcomes based on the theoretical probability.

It is important to note that experimental probability tends to converge towards theoretical probability as the number of trials increases. Therefore, it is expected that the experimental probability would be closer to the theoretical probability in the experiment with 1,000 flips compared to the experiment with 500 flips.

Without further information, it is not possible to determine whether Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments. However, based on the given statement, it can be concluded that Sandy's experimental probability was closest to the theoretical probability in the experiment with 100 flips.

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In Sandy's experiment, the experimental probability was closest to the theoretical probability in the experiment with 100 flips.

In Sandy's experiment, she used a virtual coin toss app to simulate the results of flipping a coin 100 times, 500 times, and 1,000 times. The experimental probability is the probability obtained from the observed outcomes of the experiment, while the theoretical probability is the probability calculated based on mathematical principles and assumptions.

Based on the information given, it is stated that Sandy's experimental probability was closest to the theoretical probability in the experiment with 100 flips. This suggests that the observed outcomes of the 100 flips aligned more closely with the expected outcomes based on the theoretical probability.

It is important to note that experimental probability tends to converge towards theoretical probability as the number of trials increases. Therefore, it is expected that the experimental probability would be closer to the theoretical probability in the experiment with 1,000 flips compared to the experiment with 500 flips.

Without further information, it is not possible to determine whether Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments. However, based on the given statement, it can be inferred that the experimental probability was closest to the theoretical probability in the experiment with 100 flips.

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The function is continuous on [−2,2], and its derivative is f′(x)=4 x 3−9 x 2. Because x=9/4 is not in the interval [−2,2], the only critical point occurs at   x = 0 which is (0,−1).

What is meant by function ?

To the complete questions is;    

Find the maximum and minimum values of f(x)= x 4−3 x 3−1 on [−2,2].

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The analyst could use the geom_jitter() function to make the points easier to find.

What is data analyst ?

Analytics is the systematic computational analysis of data or statistics. It is used for the discovery, interpretation, and communication of meaningful patterns in data.

The function geom_jitter() can help to resolve this issue by randomly offsetting the x and y position of each point. By adding a small amount of "jitter" to each point, the overlap is reduced and the individual data points become more visible. In ggplot2 library, which is a popular plotting library in R, geom_jitter() is used as a layer in a plotting pipeline to add jitter to a scatterplot.

To use geom_jitter(), you will first create a scatterplot using the geom_point() function, then add a geom_jitter() layer to it. This will apply the jitter to the points and improve their visibility. For example, in ggplot2 the following code would create a scatterplot with jittered points:

ggplot(data, aes(x=x, y=y)) +

 geom_jitter() +

 geom_point()

The analyst could use the geom_jitter() function to make the points easier to find.

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The analyst could use the geom_jitter() function to make the points easier to find.

Analytics is the systematic computational analysis of data or statistics. It is used for the discovery, interpretation, and communication of meaningful patterns in data.

The function geom_jitter() can help to resolve this issue by randomly offsetting the x and y position of each point. By adding a small amount of "jitter" to each point, the overlap is reduced and the individual data points become more visible. In ggplot2 library, which is a popular plotting library in R, geom_jitter() is used as a layer in a plotting pipeline to add jitter to a scatterplot.

To use geom_jitter(), you will first create a scatterplot using the geom_point() function, then add a geom_jitter() layer to it. This will apply the jitter to the points and improve their visibility. For example, in ggplot2 the following code would create a scatterplot with jittered points:

ggplot(data, aes(x=x, y=y)) +

geom_jitter() +

geom_point()

The analyst could use the geom_jitter() function to make the points easier to find.

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