what number is between 0-5

To determine the intervals of continuity for the function f(x) = (x - 3) / (x^2 + 3x - 18), we first need to identify any discontinuities. Discontinuities occur when the denominator is equal to zero. We can factor the denominator as follows:

x^2 + 3x - 18 = (x - 3)(x + 6)

The denominator is equal to zero when x = 3 or x = -6. Therefore, the function has discontinuities at x = 3 and x = -6.

Now, we can describe the intervals of continuity using interval notation:

(-∞, -6) ∪ (-6, 3) ∪ (3, ∞)

For the identified discontinuities, the conditions of continuity that are not satisfied are:

A. There is a discontinuity at x = c where f(c) is not defined.
C. There is a discontinuity at x = c where lim x→c f(x) does not exist.

In summary, the function f(x) is continuous on the intervals (-∞, -6) ∪ (-6, 3) ∪ (3, ∞) and has discontinuities at x = 3 and x = -6, with conditions A and C not being satisfied.

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The answer is:

The interval on which the function is continuous is (-∞, -6) U (-6, 3) U (3, +∞).

The discontinuities are x = -6 and x = 3.

The conditions of continuity that are not satisfied are B and C.

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

To determine the intervals on which the function is continuous, we need to check for any potential discontinuities. The function is continuous for all values of x except where the denominator is equal to zero, since division by zero is undefined.

To find the discontinuities, we set the denominator equal to zero and solve for x:

x² + 3x - 18 = 0

Factoring the quadratic equation, we have:

(x + 6)(x - 3) = 0

Setting each factor equal to zero, we find two possible values for x:

x + 6 = 0 --> x = -6

x - 3 = 0 --> x = 3

Therefore, the function has two potential discontinuities at x = -6 and x = 3.

Now, we can analyze the conditions of continuity for these potential discontinuities:

A. There is a discontinuity at x = c where f(c) is not defined.

Since f(c) is defined for all values of x, this condition is not met.

B. There is a discontinuity at x = c where lim x→c f(x) ≠ f(c).

To determine this condition, we need to evaluate the limit of the function as x approaches the potential discontinuity points:

lim x→-6 (x - 3) / (x² + 3x - 18) = (-6 - 3) / ((-6)² + 3(-6) - 18) = -9 / 0

Similarly,

lim x→3 (x - 3) / (x^2 + 3x - 18) = (3 - 3) / (3^2 + 3(3) - 18) = 0 / 0

From the calculations, we can see that the limit at x = -6 is undefined (not equal to -9) and the limit at x = 3 is also undefined (not equal to 0).

C. There is a discontinuity at x = c where lim x→c f(x) does not exist.

Since the limits at x = -6 and x = 3 do not exist, this condition is met.

D. There are no discontinuities; f(x) is continuous.

Since we found that there are two potential discontinuities, this choice is not applicable.

Therefore, the answer is:

The interval on which the function is continuous is (-∞, -6) U (-6, 3) U (3, +∞).

The discontinuities are x = -6 and x = 3.

The conditions of continuity that are not satisfied are B and C.

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Step-by-step explanation:

Answer:

1, 3, 5, 7 and 19

Step-by-step explanation:

to find the first 4 terms, substitute n = 1, 2, 3, 4 into the rule, then

a₁ = 2(1) - 1 = 2 - 1 = 1

a₂ = 2(2) - 1 - 4 - 1 = 3

a₃ = 2(3) - 1 = 6 - 1 = 5

a₄ = 2(4) - 1 = 8 - 1 = 7

the first 4 terms are 1, 3, 5, 7

to find the 10th term , substitute n = 10 into the rule

a₁₀ = 2(20) - 1 = 20 - 1 = 19

Answer:

45.99x.94=P

Step-by-step explanation:

Answer:

42 is the range

Step-by-step explanation:

Subtract the highest number by the lowest.

95 - 53 =42

The amygdala is "brain-structure" which is less influenced by reflection, such as registering more primal-emotions, which includes fear and anxiety, correct option is (b).

The "amygdala" is a brain structure that plays a crucial role in processing primal emotions, particularly fear and anxiety. It is less influenced by reflection or higher-level cognitive processes.

The amygdala is responsible for detecting and responding to potential threats and triggers the body's immediate emotional and physiological responses, such as the fight-or-flight response.

It acts as an emotional alarm-system, rapidly assessing and generating emotional reactions to stimuli.

Therefore, Option is (b) is correct.

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The given question is incomplete, the complete question is

The _____ is the brain structure less influenced by reflection, such that it registers more primal emotions, including fear and anxiety.

(a) hypothalamus

(b) amygdala

(c) hippocampus

(d) cortex

Answer:

(2\(b^{2}\) - 5) (3b + 8)

Step-by-step explanation:

First factor out 2\(b^{2}\) from the first set of parentheses and -5 from the second

2\(b^{2}\) ( 3b + 8)  - 5 (3b + 8)

Next factor out (3b + 8)

(2\(b^{2}\) - 5) (3b + 8)

Answer:

A) 9 out of 12

Step-by-step explanation:

The first step is to divide 9 by 12 to get the answer in decimal form:

9 / 12 = 0.7500

Then, we multiplied the answer from the first step by one hundred to get the answer as a percentage:

0.7500 * 100 = 75.00%

We can prove that the answer is correct by taking 75.00 percent of 12 to get 9:

(12 x 75.00)/100 = 9

Answer:

10,000-500=9,500 is  what it is worth

Step-by-step explanation:

Answer:

the answer is b

jsjsjsjsjsjsjsjsjsjsjsjsjsjsjs

Answer:

thank me later that's is the answer

Step-by-step explanation:

again option D x = 10, y= 3

is the correct answer of this question.

plz mark my answer as brainlist.if you find it useful.

hope this will be helpful to you.

Answer:

x = 10

y = 7

Step-by-step explanation:

4x-2 = x+28

4x-x = 28+2

3x = 30

x = 30÷3

x = 10

4y-7 = y+14

4y-y = 14+7

3y = 21

y = 21÷3

y = 7

The total surface area of the triangular prism is 845cm².

Surface area refers to the total area of all the faces or surfaces of a three-dimensional object. It is the measure of the exposed area of an object that can be seen or touched.

The surface area of a triangular prism can be calculated by adding the areas of the six faces that make up the prism.

The surface area of a triangular prism.

SA = bh + (S₁ + S₂ + S₃)H

SA = 5×9 + ( 12 + 13 + 15 )× 20

SA = 45 + 800

SA = 845 cm²

Therefore, the surface area is 845 cm².

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The complete question is given below.

Find the total surface area of this triangular prism base=5cm 9cm line in the middle 12cm width=20cm 2 lengths on triangle 13cm and 15cm

Answer:

θ = 51.7

SOH-CAH-TOA

CAH: COS = ADJ/HYP   cos(θ) = 19.4/29.3

θ = 48.5

93.2 + 48.5 + x = 180

x = 38.3

90 + 38.3 + θ = 180

θ = 51.7

Step-by-step explanation:

The Volume of the Cone is 4.4 Cubic Inches

What is Cone?

A cone is a three-dimensional geometric object with a smooth taper from a flat base to the tip or vertex. A cone is made up of a series of line segments, half-lines, or lines that link a common point, the apex, to all of the points on a base on a plane that does not contain the apex.

Solution:

Given:

Radius = 1.2 inches

Height = 2.9 inches

To Find: Volume fo the Cone

Volume of Cone = 1/3 * 3.14 * \(radius^{2} * height\)

= 1/3 * 3.14 * 1.2 * 1.2 * 2.9

= 4.37088

= 4.4 cubic inches

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Answer:

3/4 would be .75

Step-by-step explanation:

1/4 would be .25 because .25x4=1. Because the denominator is a 4 you are trying to find a number that when multiplied 4 times would equal 1 or 4/4.

Answer:

3/4 cannot be .34 because that is not what it is equal to when converted to hundredths.

Step-by-step explanation:

The decimal 0.34 is in the value hundredths. 3/4's value when converted to hundredths is 75/100 or 0.75. We get this by multiplying 3 and 4 by the same factor that brings 4 to 100, which is 25.

So, 4*25=100(denominator), and 3*25=75(numerator). The decimal value is 0.75. Therefore, 3/4 cannot be 0.34 because the values are not the same.

Answer:

11. 40.5

12. 84

Step-by-step explanation:

The average rate of change of g(x) over the interval [-3, 3] is 2.

For a function f(x), we define the rate of change over an interval (a, b) as:

(f(b) - f(a))/(b - a)

Here we have the interval [-3, 3] and the function:

g(x) = x^2 + 2x + 8

Then the average rate of change over that interval will be:

[ g(3) - g(-3)]/(3 - (-3))

The values in the denominator are:

g(3) = 3^2 + 2*3 + 8 = 9 + 6 + 8  =23

g(-3) = (-3)^2 + 2*-3 + 8 = 9 - 6 + 8 = 11

Replacing that we get:

[23 - 11]/(3 + 3) = 12/6 = 2

The average rate of change over that interval is 2.

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Answer:

m<3 = 97

m<10 = 97

m<9 = 83

m<5 = 97

m<7 = 83

m<16 = 97

Step-by-step explanation:

m<3 = m<2 because of vertical angles

m<10 = m<2 because of corresponding angles

m<9 + 97 = 180

m<9 = 83

m<5 + 83 = 180

m<5 = 97

m<7 = m<6 because of vertical angles

m<16 = m<5 because of alternate exterior angles.

Answer:

Joseph

Step-by-step explanation:

Jeremy made a mistake in the first step with the radius. he used the number 4 as radius instead of 2. so that automatically makes Joseph right.

The given parametric curve x=cost, y=et; 0≤t≤π/2, intersects the line y=1 at t=0, and intersects the line x=0 at t=π/2. Therefore, we need to find the area bounded by the curve and the lines y=1 and x=0, between t=0 and t=π/2. We can use the formula for area enclosed by a curve given by A=∫(y.dx) from a to b, where y is the function of x. In this case, we need to express x in terms of y, so we can use x=arccos(y) and substitute it in the formula. The final result is A=e-1/2.

The given parametric curve x=cost, y=et; 0≤t≤π/2, intersects the line y=1 at t=0, and intersects the line x=0 at t=π/2. Therefore, we need to find the area bounded by the curve and the lines y=1 and x=0, between t=0 and t=π/2. To do so, we can use the formula for area enclosed by a curve given by A=∫(y.dx) from a to b, where y is the function of x. In this case, we need to express x in terms of y, so we can use x=arccos(y) and substitute it in the formula. The final result is A=e-1/2.

The area bounded by the parametric curve x=cost, y=et; 0≤t≤π/2, and the lines y=1 and x=0 is e-1/2. This can be found using the formula for area enclosed by a curve given by A=∫(y.dx) from a to b, where y is the function of x. We need to express x in terms of y, so we can use x=arccos(y) and substitute it in the formula. The curve intersects the line y=1 at t=0 and the line x=0 at t=π/2, which defines the boundaries for the integral.

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Answer:

8

-3

___

y

Step-by-step explanation:

Answer:

10 times.

Step-by-step explanation:

Since 1 liter = 1000 milliliters, we can say that 600 milliliters is equal to 0.6 liters because 600/1000 = 0.6

Since the gas can holds 6 liters, and the lawn mower holds 0.6 liters, 6/0.6 = 10.

So, he can fill his lawn mower 10 times with the gas can

Mr Green can fill his lawn 10 times

the first step is to convert the milliliters to liters

600 milliliters to liters

= 600/1000

= 0.6 liters

the number of times can be calculated as follows

= 6/0.6

= 10

hence it will take Mr. Green  10 times to fill his lawn mower

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Several forces have contributed to increased global integration and the growing importance of global marketing. These forces include:

Technological Advancements: Advances in communication, transportation, and information technology have significantly reduced barriers to global trade and communication. The internet, mobile devices, and social media platforms have connected people worldwide, enabling companies to reach global audiences more easily and conduct business across borders.

Liberalization of Trade: The liberalization of trade policies, such as the establishment of free trade agreements and the reduction of trade barriers, has facilitated the movement of goods, services, and investments across borders. This has created opportunities for companies to expand their markets globally and benefit from economies of scale.

Globalization of Production: Companies have increasingly embraced global production networks and supply chains, seeking cost efficiencies and accessing specialized resources and skills. This trend has led to the fragmentation of production processes across multiple countries, resulting in the need for global marketing strategies to coordinate and promote products across diverse markets.

Market Saturation: Many domestic markets have become saturated, with intense competition and limited growth opportunities. As a result, companies are compelled to explore international markets to expand their customer base and sustain growth. Global marketing allows businesses to tap into untapped markets and leverage opportunities in emerging economies.

Changing Consumer Preferences: Consumers are becoming more globally connected and are exposed to diverse cultures, products, and experiences through media and travel. This has led to a rise in demand for international brands and products, prompting companies to adopt global marketing strategies to cater to these evolving consumer preferences.

Cultural Convergence: Increased cultural exchange and globalization have led to the convergence of consumer tastes, preferences, and lifestyles across different regions. This convergence has created opportunities for companies to develop standardized global marketing campaigns that resonate with a broader audience, reducing the need for localized marketing efforts.

Global Competitors: The rise of multinational corporations and the expansion of global competition have necessitated the adoption of global marketing strategies. Companies must establish a strong international presence to compete effectively in global markets and protect their market share from global competitors.

Government Support: Governments in many countries have recognized the importance of global trade and have taken steps to support businesses in expanding internationally. They provide incentives, financial assistance, and favorable policies to encourage companies to engage in global marketing activities.

These forces have collectively fueled increased global integration and emphasized the importance of global marketing as a strategic imperative for businesses to succeed in the interconnected global marketplace.

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Answer: y= 3/2x - 6

Step-by-step explanation:

The equation is y=mx + b

The y-intercept is when x = 0, so on the table y-intercept = -6

The slope is rise/run, we see that y increase by three and x increase by 2, so the slope is 3/2

to get the slope of any straight line, we simply need two points off of it, let's use those ones in the picture below.

\((\stackrel{x_1}{2}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{3}-\stackrel{y1}{(-3)}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{2}}} \implies \cfrac{3 +3}{4} \implies \cfrac{ 6 }{ 4 } \implies {\Large \begin{array}{llll} \cfrac{3 }{ 2 } \end{array}}\)

now, the y-intercept occurs when x = 0, recheck the picture below.

Answer:

ok, so the answer would be 27 hot dogs and 53 tacos salads

Step-by-step explanation:

The graph has the shape of an equilateral triangle, with the origin at the center.

To sketch the graph of the polar equation θ=-π/6, you will first need to determine the graph's shape.

To do this, you should draw a radius from the origin to a point where θ=-π/6.

This radius is a line segment that intersects with the polar axis at the angle of -π/6.

By connecting all points with the same θ coordinate, a graph of the equation can be formed.

The graph has the shape of an equilateral triangle, with the origin at the center.

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The equation of the line containing the points (4, 6) and (8, 4) in slope-intercept form is y = (-1/2)x + 8.

To find the equation of a line containing the points (4, 6) and (8, 4) in slope-intercept form, we need to determine the slope (m) and the y-intercept (b) of the line.

The formula to calculate the slope (m) is given by:

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

Using the coordinates (4, 6) and (8, 4), we have:

m = (4 - 6) / (8 - 4)

m = -2 / 4

m = -1/2

Now that we have the slope, we can choose either of the given points and substitute its coordinates (x, y) into the slope-intercept form equation (y = mx + b) to find the y-intercept (b). Let's use the point (4, 6):

6 = (-1/2)(4) + b

6 = -2 + b

b = 8

Therefore, the slope (m) is -1/2 and the y-intercept (b) is 8. Plugging these values into the slope-intercept form equation, we get:

y = (-1/2)x + 8

Hence, the equation of the line containing the points (4, 6) and (8, 4) in slope-intercept form is y = (-1/2)x + 8.

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The correct formula that defines an arithmetic sequence is option d) tn = 5n + 14.

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms remains constant. In other words, each term can be obtained by adding a fixed value (the common difference) to the previous term.

In option a) tn = 5 + 14, the term does not depend on the value of n and does not exhibit a constant difference between terms. Therefore, it does not represent an arithmetic sequence.

Option b) tn = 5n² + 14 represents a quadratic sequence, where the difference between consecutive terms increases with each term. It does not represent an arithmetic sequence.

Option c) tn = 5n(n+14) represents a sequence with a varying difference, as it depends on the value of n. It does not represent an arithmetic sequence.

Option d) tn = 5n + 14 represents an arithmetic sequence, where each term is obtained by adding a constant value of 5 to the previous term. The common difference between consecutive terms is 5, making it the correct formula for an arithmetic sequence.

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Step-by-step explanation:

14 ,16,22,26,30,32

Have a great day

Answer:

\(\boxed {\boxed {\sf 24}}\)

Step-by-step explanation:

We are asked to find the median of the following data set:

The median is the middle number of the data set. It separates the higher half of the set from the lower half. We put the data set in order from least to greatest and find the middle number.

We eliminate a number from each side of the data set until we find the middle number.

However, the data set had 6 numbers, which is an even number. There isn't one middle number, so we must find the average of the middle 2 numbers. Add the numbers and divide by 2.

The median of the data set is 24.