Consider the function f(x) = (x^2 - 4)/(x - 2). What is the limit of f(x) as x approaches 2?

based on this website i saw;

take the deravative

f'(x) = 4x - 12

0 = 4x - 12

x = 3

plug into the equation;

2(3)^2 - 12(3) + 9 = - 9

(3,-9)

Step-by-step explanation:

Clients have ordered 48 yards of fencing  for their rectangular garden bed.

Let the width is x and then length is 2x.

Amount of fencing required is equal to the perimeter of the rectangular garden i.e.

2(x+2x)=48

2(3x)=48

6x=48

x=8 yards

Width of the garden is 8 yards

Length of the garden is 2x = 2(8) = 16 yards

Area of a rectangle is given by :

A = L×B

A = 8 × 16

A = 128 sq yards

Hence, this is the required solution.

The probability of an adult having hypertension is  0.344 and an adult having hypertension and being classified as a low level of obesity is 0.102, having hypertension given he/she is classified as a high level of obesity is 0.540. If an adult has hypertension, the probability that he/she also has a high level of obesity is  0.444.

Probability is a branch of mathematics that deals with the likelihood of an event occurring. It is the measure of the likelihood of an event occurring divided by the number of possible outcomes. Probability is used to determine the chances of a particular outcome occurring and can range from 0 to 1.

a)The probability of an adult having hypertension is (34 + 30 + 51) / (34 + 30 + 51 + 119 + 99 + 82) = 115 / 334 = 0.344.

b) The probability of an adult having hypertension and being classified as a low level of obesity is 34 / (34 + 30 + 51 + 119 + 99 + 82) = 34 / 334 = 0.102.

c) The probability of an adult having hypertension given he/she is classified as a high level of obesity is 51 / (30 + 51 + 82) = 51 / 163 = 0.312.

d) The probability of an adult being classified as a high or average level of obesity is (30 + 51 + 99) / (34 + 30 + 51 + 119 + 99 + 82) = 180 / 334 = 0.540.

e) If an adult has hypertension, the probability that he/she also has a high level of obesity is 51 / (34 + 30 + 51) = 51 / 115 = 0.444.

f) No, an adult's hypertension status and obesity categorization are not independent. This is because the probability of an adult having hypertension given he/she is classified as a high level of obesity (0.312) is not the same as the probability of an adult having hypertension (0.344).

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Complete Question

ymposium is part of a larger work referred to as Plato's Dialogues. Wishart and Leach† found that about 21.4% of five-syllable sequences in Symposium are of the type in which four are short and one is long. Suppose an antiquities store in Athens has a very old manuscript that the owner claims is part of Plato's Dialogues. A random sample of 498 five-syllable sequences from this manuscript showed that 129 were of the type four short and one long. Do the data indicate that the population proportion of this type of five-syllable sequence is higher than that found in Plato's Symposium? Use = 0.01.  

a. What is the value of the sample test statistic? (Round your answer to two decimal places.)  

b. Find the P-value of the test statistic. (Round your answer to four decimal places.)

Answer:

a) \(Z=2.45\)

b) \(P Value=0.0073\)

Step-by-step explanation:

From the question we are told that:

Probability of Wishart and Leach \(P=21.4=>0.214\)

Population Size \(N=498\)

Sample size \(n=12\)

Therefore

\(P'=\frac{129}{498}\)

\(P'=0.2590\)

Generally the Null and Alternative Hypothesis is mathematically given by

\(H_0:P=0.214\)

\(H_a:=P>0.214\)

Test Statistics

\(Z=\frac{P'-P}{\sqrt{\frac{P(1-P)}{n}}}\)

\(Z=\frac{0.2590-0.214}{\sqrt{\frac{0.214(1-0.214)}{498}}}\)

\(Z=2.45\)

Therefore P Value is given as

\(P Value =P(Z\geq 2.45)\)

\(P Value =1-P(Z\leq 2.45)\)

\(P Value =1-0.99268525\)

\(P Value=0.0073\)

Answer:

x = 35

Step-by-step explanation:

since the figures are similar then the ratios of corresponding parts are in proportion, that is

\(\frac{x}{10}\) = \(\frac{14}{4}\) = \(\frac{7}{2}\) ( cross- multiply )

2x = 7 × 10 = 70 ( divide both sides by 2 )

x = 35

The speed of both car A and car B are the same which is 0.7 miles per minute

An equation is an expression containing numbers and variables linked together by mathematical operations such as addition, subtraction, division, multiplication and exponents.

Let x represent the distance travelled by car A and y represent the distance travelled by car B

Speed of car A = x /20

Car B reaches in 50 minutes, hence:

Speed of car B = y/50

Since both speed are same;

x/20 = y/50

20y = 50x    (1)

Car B is 21 miles farther, then:

y - x = 21     (2)

x = 14, miles y = 35 miles

Speed of car A = speed of Car B = 14/20 = 35/50 = 0.7 miles per minute

The speed is 0.7 miles per minute

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An odd integer can be expressed as x = 2n+1 where n is an integer. (Therefore making 2n an even number and 2n+1 an odd number).

Three consecutive odd integers can then be expressed as  (2n+1), (2n+3), and (2n+5).

The sum of the first two integers is (2n+1) + (2n+3) = 4n+4 = 4(n+1). It is supposed to be 24 less than 4 times the third integer, or

4(2n+5)-24.

Setting both equal and solving for n:

4(n+1) = 4(2n+5)-24

24 = 4·6, so you can factor out 4 in the right-hand expression.

4(n+1) = 4(2n+5-6)   or   4(n+1) = 4(2n-1)

Cancel out factor 4 and solve for n.

n+1 = 2n-1      this yields   n=2

Now plug in into your three consecutive odd integer expressions:  (2n+1) = 5, (2n+3) = 7, (2n+5) = 9. The sum is therefore 5+7+9 = 21.

Double check your answer:  

Sum of first two integers:  5+7 = 12

24 less than 4 times third integer:  4·9 - 24 = 36-24 = 12.

Answer:

              vertex

ray

Step-by-step explanation:

The point where the rays intersect, upper right, is the vertex.

One side of the angle, bottom left, is a ray.

Answer:

the leaf would be 9 and 2

Step-by-step explanation:

Stem | leaf

  3      9 & 2

Answer:

19 7/20 feet

Step-by-step explanation:

1. \(2\frac{5}{8}\) pieces of wood

\(2\frac{5}{8} * 6 = 15\frac{3}{4}\)

2. \(1\frac{1}{5}\) pieces of wood

\(1\frac{1}{5} * 3 = 3\frac{3}{5}\)

3. Combined

\(15\frac{3}{5} +3\frac{3}{5} = 19\frac{7}{20}\)

Based on the information we can infer that the area of the image is: 50.24 in²

To find the area of the figure we must take into account that this figure is a circle. To find the area of this figure we must use the following mathematical formula:

A = πr²

Then we must replace the values and find the result, the formula would look like this:

A = π4²

A=3.14*4²

A=3.14*16

A = 50.24in

According to the above, the area of the circle would be 50.24 in. Additionally, we learned the formula for circle area.

Note: This question is incomplete; here is the missing information:

Find the area of the figure below.

r = 4 in

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Given:

Find:

Value of x with the help of quadratic formula.

Sol:

Quadratic formula:

Use the formula :

So the value of "x" is -1.25 and 0.5

The range is {y | −7 ≤ y ≤ 2}.

Range is defined as the difference between the largest and smallest item in a distributiοn.

The range οf the functiοn is {y | −7 ≤ y ≤ 2}.

The graph starts at an οpen circle at negative 3 cοmma negative 7 and increases tο a maximum pοint at 0 cοmma 2 befοre decreasing again tο a clοsed circle at 2 cοmma negative 2. Therefοre, the lοwest pοint οf the graph is at y = -7 and the highest pοint is at y = 2.

Since the graph is cοntinuοus and the parabοla is symmetric arοund its vertex, every y value between -7 and 2 is included in the range.

Hence, the range is {y | −7 ≤ y ≤ 2}.

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After answering the presented question, standard deviation t Lower bound = X - \((t * (s/\sqrt(n))) = 1271.89 - (1.860 * (34.753/\sqrt(9))) = 1238.94\)

A statistic that expresses the variability or variation of a bunch of values is the standard deviation. A high standard deviation indicates that the values are more distributed, whereas a low standard deviation indicates that the numbers are closer to the set mean. The standard deviation is a measure of how far the data are from the mean (or ). When the standard deviation is small, the data tends to cluster around the mean; when it is great, the data is more spread. The standard deviation represents the average variability of the data collection. It displays the average deviation from the mean of each score.

Next, we need to find the t-value for a 90% confidence interval with 8 degrees of freedom (n-1):

t = t(0.05, 8) = 1.860

Now we can calculate the lower and upper bounds of the confidence interval:

Lower bound = X - \((t * (s/\sqrt(n))) = 1271.89 - (1.860 * (34.753/\sqrt(9))) = 1238.94\)

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Answer:

7/12 teaspoons

fraction

Step-by-step explanation:

Amount of salt that would be used = 1\(\frac{3}{4}\) x \(\frac{1}{3}\)

Convert \(1\frac{3}{4}\) to an improper fraction

to convert to improper fraction, take the following steps :  

1. Multiply the whole number  by the denominator

2. Add the numerator to the answer gotten in the previous step

3. divide the number gotten in the previous step by the denominator

(1 x 4) + 3 = \(\frac{7}{4}\)

7/4 x 1/3 = 7/12

Answer:

The formula says that the sum of the first n terms of our arithmetic sequence is equal to n divided by 2 times the sum of twice the beginning term, a, and the product of d, the common difference, and n minus 1. The n stands for the number of terms we are adding together.

Answer:

its 85

Step-by-step explanation:

The relationship between the dates of spread and the number of people infected can vary depending on various factors such as the infectiousness of the disease, the effectiveness of containment measures, population density, and individual behaviors.

However, there is a general rule that can describe the relationship:As the dates of spread progress, the number of infected individuals tends to increase initially, reaching a peak, and then gradually decreasing over time.

This pattern is often referred to as the epidemic curve or the epidemiological curve. In the early stages of an outbreak, the number of cases may grow rapidly as the disease spreads through a susceptible population. This rapid increase is often influenced by factors such as the contagiousness of the disease, population density, and social interactions.

As containment measures, such as vaccination campaigns, public health interventions, and behavioral changes, are implemented, the rate of new infections may start to decline. This can lead to a peak in the number of cases, after which the curve gradually decreases as the disease is brought under control and fewer susceptible individuals remain.

It's important to note that the specific shape, duration, and magnitude of the epidemic curve can vary significantly depending on the disease and the effectiveness of the response measures implemented. Additionally, emerging variants, changes in behavior, and other factors can impact the trajectory of the epidemic curve.

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1. Tha rate of return is 11.12%

2. The investor will not be happy in case the market interest rates fall

n is NPER 5 (called back in 5yrs)

Coupon payment / PMT = 1000 * 10% = 100,

Purchase price PV (PV is entered as a negative value) -1000

Called for value is FV Call premium is 7% hence FV = 107% * 1000 = 1070

You can use the RATE function in excel

Rate(nper, PMT, PV,FV, Type)

RATE(5,100,-1000,1070)

= 11.12%

The investor was promised a fixed return rate of 10%, but since the bond was called after 5 years, the actual return was 11.12%, so the investor had good reason to be pleased.

In the event that market interest rates decline, the investor will not be pleased because, had the bond not been called, he would have continued to receive his fixed 10% coupon payments of $100 per year.

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Answer:

\(P(B\ u\ S) = 0.48\)

Step-by-step explanation:

Given

\(P(S) = 0.40\)

\(P(B) = 0.20\)

\(P(B\ n\ S) = 0.12\)

Required

Determine \(P(B\ u\ S)\)

In probability, the relationship between the given parameters and the required is:

\(P(B\ u\ S) = P(S) + P(B) - P(B\ n\ S)\)

Substitute values for P(S), P(B) and P(B n S)

\(P(B\ u\ S) = 0.40 + 0.20 - 0.12\)

\(P(B\ u\ S) = 0.48\)

Hence;

The probability that of purchasing or recalling is 0.48

After answering the presented question, we can conclude that As a radius result, a titanium sphere with a radius of 11 cm would weigh roughly 25.1 kg (rounded to 1 decimal place).

In more modern parlance, the length of a circle or sphere is the same as its radius in classical geometry, which is one of the line segments from its centre to its circumference. The term was derived from the Latin word radius, which also refers to the spokes of a waggon wheel. The radius of a circle is the distance between its centre and any point on its periphery. It is usually denoted by "R" or "r." A radius is a line segment with one endpoint in the centre and one on the circle's circumference. The radius of a circle matches its diameter. The diameter of a circle is the segment that passes through its centre and has ends on the circle.

The formula for the volume of a sphere of radius "r" is:

V = (4/3)πr³

Substituting the specified radius value (r = 11 cm), we get:

V = (4/3)π(11)³ \sV = 5575.279 cm³

Now we must compute the weight of the titanium sphere, which can be found by multiplying its volume by its density:

Density = Volume Weight

Weight = 25121.811974 g Weight = 5575.279 cm3 4.506 g/cm3

When we divide 1000 by 1000 to convert grammes to kilogrammes, we get:

The weight is 25.121811974 kg.

As a result, a titanium sphere with a radius of 11 cm would weigh roughly 25.1 kg (rounded to 1 decimal place).

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Answer:

C

Step-by-step explanation:

there would have to be one more zero between 0 and 8 for both of them

The value of 'n' for which the division of x^(2n-1) by x + 3 leaves a remainder of -80 is n = 1.

To find the value of 'n' for which the division of x^(2n-1) by x + 3 leaves a remainder of -80, we can use polynomial long division. Let's perform the division step by step:

Write the dividend and divisor in polynomial long division format:

_________________________

x + 3 │ x^(2n-1) + 0x^(2n-2) + 0x^(2n-3) + ...

Divide the leading term of the dividend (x^(2n-1)) by the leading term of the divisor (x). The result is x^(2n-1)/x = x^(2n-2).

Multiply the divisor (x + 3) by the quotient obtained in the previous step (x^(2n-2)). The result is x^(2n-2) * (x + 3) = x^(2n-1) + 3x^(2n-2).

Subtract the result obtained in step 3 from the original dividend:

x^(2n-1) + 0x^(2n-2) + 0x^(2n-3) + ... - (x^(2n-1) + 3x^(2n-2)) = -3x^(2n-2) + 0x^(2n-3) + ...

Bring down the next term of the dividend (which is 0x^(2n-3)) and repeat steps 2-4 until the remainder is constant.

Since we are given that the remainder is -80, we can set the remainder equal to -80 and solve for 'n'.

-3x^(2n-2) + 0x^(2n-3) + ... = -80

Since the remainder is constant (-80), it means that all the terms with x have been canceled out in the division process. Therefore, we can deduce that the highest power of x in the divisor (x + 3) is 0.

This implies that x^(2n-2) = 0, and for any value of 'n', the exponent 2n-2 should be equal to zero. Solving this equation:

2n-2 = 0

2n = 2

n = 1

Therefore, the value of 'n' for which the division of x^(2n-1) by x + 3 leaves a remainder of -80 is n = 1.

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Answer:

the coordinates of the vertex are (-7/2, -25/4), and we should plot this point and the x-intercepts on both sides of the vertex.

Step-by-step explanation:

To find the x-intercepts, we set y = 0 and solve for x:

0 = (x+6)(x+1)

x + 6 = 0 or x + 1 = 0

x = -6 or x = -1

So the x-intercepts are (-6, 0) and (-1, 0).

To find the coordinates of the vertex, we first expand the equation:

y = x^2 + 7x + 6

Then we use the formula for the x-coordinate of the vertex, which is -b/2a:

x = -7/(2*1) = -7/2

To find the y-coordinate of the vertex, we substitute this value of x into the equation:

y = (-7/2)^2 + 7(-7/2) + 6

y = 49/4 - 49/2 + 6

y = -25/4

So the coordinates of the vertex are (-7/2, -25/4), and we should plot this point and the x-intercepts on both sides of the vertex.

Answer:

the slope intercept form is   y = (1/2)x - 1

Step-by-step explanation:

The slope-intercept form is, y = mx + b

We see from looking at the graph that,

at x = 0, y = -1

So, from this we find that b = -1

at x = 2, y = 0,

now, we find the slope m,

using,

\(m = \frac{y_{2} -y_1}{x_2-x_1}\)

Using x_2 = 2, y_2 = 0,

x_1 = 0, y_1 = -1, we get,

m = (0-(-1))/(2-0)

m = 1/2

So, the slope intercept form is,

y = (1/2)x - 1

Answer:

É 5x3=15

Step-by-step explanation:

Answer:

0.

Step-by-step explanation:

I am (not 100%) but quite sure that X = 0.

hope that helps !

:)