For a certain drug, based on standards set by the United States Pharmacopeia (USP) - an official public standards-setting authority for all prescription and over-the-counter medicines and other health care products manufactured or sold in the United States, a standard deviation of capsule weights of less than 0.8 mg is acceptable. A sample of 20 capsules was taken and the weights are provided below:
120.3 120.8 120.1 119.7 120.8
119.4 119.1 120.9 118.9 119.5
120.4 121.1 118.6 119.4 119.3
119.8 120.2 119.5 118.9 119.8
(Note: The average and the standard deviation of the data are respectively 119.8 g and 0.73 g.)
At 5% significance level, test the claim that the standard deviation of capsule weights of the drug is different from 0.8 g.
Procedure: Select an answer One mean Z Hypothesis Test One mean T Hypothesis Test One proportion Z Hypothesis Test One variance χ² Hypothesis Test
Assumptions: (select everything that applies)
Normal population
Sample size is greater than 30
The number of positive and negative responses are both greater than 10
Population standard deviation is unknown
Population standard deviation is known
Simple random sample
Step 1. Hypotheses Set-Up:
H0:H0: Select an answer p σ² μ = , where ? p μ σ is the Select an answer population proportion population standard deviation population mean and the units are ? lbs g mg kg
Ha:Ha: Select an answer μ p σ² ? > ≠ < , and the test is Select an answer Right-Tail Left-Tail Two-Tail
Step 2. The significance level α=α= %
Step 3. Compute the value of the test statistic: Select an answer z₀ f₀ χ²₀ t₀ = (Round the answer to 3 decimal places)
Step 4. Testing Procedure: (Round the answers to 3 decimal places)
CVA PVA
Provide the critical value(s) for the Rejection Region: Compute the P-value of the test statistic:
left CV is and right CV is P-value is
Step 5. Decision:
CVA PVA
Is the test statistic in the rejection region? Is the P-value less than the significance level?
? yes no ? yes no
Conclusion: Select an answer Do not reject the null hypothesis in favor of the alternative. Reject the null hypothesis in favor of the alternative.
Step 6. Interpretation:
At 5% significance level we Select an answer DO DO NOT have sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis.

The inequality is -2 < x ≤ 1 and the interval notation is ( -2 , 1 ]

Given data ,

Let the inequality be represented as A

Now , the value of A is

-2 < x ≤ 1

And , Interval notation: (-2, 1]

In interval notation, the parentheses "(" and ")" represent open intervals, which means the endpoints are not included, and the square bracket "]" represents a closed interval, which means the endpoint is included.

And , Set-builder notation: {x | -2 < x ≤ 1}

In set-builder notation, the vertical bar "|" is read as "such that," and the inequality -2 < x ≤ 1 describes the set of all values of x that satisfy this condition.

Hence , the inequality is -2 < x ≤ 1

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When testing a proportion, we use p and q to represent the proportion of success and failure, respectively.

For example, if we are testing the proportion of students who passed a test, we would use p to represent the proportion who passed and q to represent the proportion who did not pass.

When testing a mean (average), we use n to represent the sample size. For example, if we are testing the average height of a sample of individuals, we would use n to represent the number of individuals in the sample.

In some cases, we may use all three terms when testing both a proportion and a mean. For example, if we are testing the proportion of students who passed a test and the average score of those who passed, we would use p and q to represent the proportion of success and failure, and n to represent the sample size of those who passed. We would also use the mean to represent the average score of those who passed.

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The polynomial long division of 6x³+x²+7x+9 by 2x+1 gives a quotient of 3x² - x + 4

From the question, we have the following parameters that can be used in our computation:

6x³+x²+7x+9 by 2x+1

Using the polynomial long division setup, we have

2x + 1   |  6x³ + x² + 7x + 9

Evaluating the division, we have

              3x² - x + 4

2x + 1   |  6x³ + x² + 7x + 9

              6x³ + 3x²

             ---------------------------------------

                     -2x² + 7x + 9

                     -2x² - x

             ---------------------------------------

                           8x + 9

                           8x + 4

                        ---------------------------------------

                                  5

Hence, the quotient is 3x² - x + 4

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To add polynomials in a horizontal method, combine like terms. For the vertical method, write the polynomials in standard form and align like terms in columns, and combine like terms. To subtract polynomials in a horizontal method, find the negative (opposite)  of the polynomial that is being subtracted and then combine like terms. For the vertical method, write the polynomials in standard form, align like terms, and subtract by adding the negative (opposite).

To add polynomials vertically,  one need to write them in standard form and align like terms in the columns. Combine like terms and add them to the polynomial.

Therefore, note that Polynomials are seen as expressions with variables and coefficients. Combine or subtract like terms when adding or subtracting them.

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WRITE Describe how to add and subtract polynomials using both the vertical and horizontal methods.

To add polynomials in a horizontal method, combine  ----- For the vertical method, write the polynomials in  --------  align like terms in columns, and combine like terms. To subtract polynomials in a horizontal method, find the ------ of the polynomial that is being and then combine like terms. For the vertical method, write the polynomials in standard form, align like terms and  and subtract by adding the  -------

The inequality that can be used to represent the lengths of the glass that will fit in the frame is 12 < x ≤ 122

We are given that the length, x, of a piece of glass must be longer than 12 cm but not longer than 122 cm in order to fit in an existing frame.

This can be represented mathematically using the inequality 12 < x ≤ 122

Therefore, the inequality that can be used to represent the lengths of the glass that will fit in the frame is 12 < x ≤ 122

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The variance of X is 3/80.

Given the probability density function of X,

f(x) = {3x² for 0 < x < 1

{0 otherwise

We can use this to answer the following:

(a) Find P(X < 0.5)

To find P(X < 0.5), we need to integrate the density function from 0 to 0.5:

P(X < 0.5) = ∫[0,0.5] f(x) dx

= ∫[0,0.5] 3x² dx

= [x³]₀.₃

= 0.125

(b) Find the cumulative distribution function of X, F(x)

The cumulative distribution function (CDF) of X is given by:

F(x) = P(X ≤ x) = ∫[0,x] f(t) dt

If x ≤ 0, then F(x) = 0. If 0 < x ≤ 1, then

F(x) = ∫[0,x] f(t) dt

= ∫[0,x] 3t² dt

= [t³]₀.ₓ

= x³

If x > 1, then F(x) = 1. So, the CDF of X is:

F(x) = {0 if x ≤ 0

{x³ if 0 < x ≤ 1

{1 if x > 1

(c) Find the expected value of X, E(X)

The expected value of X is given by:

E(X) = ∫[−∞,∞] x f(x) dx

Since the density function f(x) is zero outside the interval [0,1], we can restrict the integration to this interval:

E(X) = ∫[0,1] x f(x) dx

= ∫[0,1] 3x³ dx

= [3/4 x⁴]₀.₁

= 3/4 * 1⁴ - 0

= 3/4

Therefore, the expected value of X is 3/4.

(d) Find the variance of X, Var(X)

The variance of X is given by:

Var(X) = E(X²) - [E(X)]²

We have already found E(X) in part (c). To find E(X²), we integrate x² times the density function:

E(X²) = ∫[0,1] x² f(x) dx

= ∫[0,1] 3x⁴ dx

= [3/5 x⁵]₀.₁

= 3/5 * 1⁵ - 0

= 3/5

Substituting into the formula for variance:

Var(X) = E(X²) - [E(X)]²

= 3/5 - (3/4)²

= 3/5 - 9/16

= 3/80

Therefore, the variance of X is 3/80.

Complete question: Let X be a random variable defined by the density function

[tex]$$f(x)=\left\{\begin{array}{cl}3 x^2 & 0 \leq x \leq 1 \\0 & \text { otherwise }\end{array}\right.$$[/tex]

Find

(a)[tex]$E(X)$[/tex]

(b) [tex]$E(3 X-2)$[/tex]

(c) [tex]$E\left(X^2\right)$[/tex]

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Answer:

140

Step-by-step explanation:

7/20 = 0.35 = 35% of the 20 players made all five baskets.

If this trend holds up, then we should expect 35% of the 400 people to make all five baskets.

35% of 400 = 0.35*400 = 140

We expect about 140 people will make all five baskets.

Note how 140/400 = 0.35 = 35%

-------------

Through another alternative method, we can solve like this

7/20 = x/400

7*400 = 20*x ... cross multiply

2800 = 20x

20x = 2800

x = 2800/20 ... dividing both sides by 20

x = 140 which is the same result as before

it's going to be 150 baskets made

The 90% confidence interval for the population mean is (-9.05, 15.05).

To construct a confidence interval for a population mean with a known standard deviation when the sample size is less than 30, we use the formula:

CI = x ± z*(σ/√n)

where x is the sample mean, σ is the population standard deviation, n is the sample size, z is the z-score associated with the desired confidence level, and CI is the confidence interval.

Given the information provided, we have:

x = 3

σ = 26

n = 15

The desired confidence level is 90%, which corresponds to a z-score of 1.645 (from the standard normal distribution table)

Substituting these values into the formula, we get:

CI = 3 ± 1.645*(26/√15)

CI = 3 ± 12.05

Therefore, the 90% confidence interval for the population mean is (-9.05, 15.05).

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If a woman pays $2.78 for some bananas and eggs. If each banana costs $0.69 and each egg costs $0.35, then she bought 4 bananas and 6 eggs.

Let's assume the woman bought x bananas and y eggs.

According to the problem, each banana costs $0.69 and each egg costs $0.35.

So the cost of x bananas would be 0.69x and the cost of y eggs would be 0.35y.

The total cost of the bananas and eggs is given as $2.78. So we can write the equation:

0.69x + 0.35y = 2.78

Now we need to solve for x and y.

We can start by multiplying the entire equation by 100 to get rid of the decimals:

69x + 35y = 278

We can also simplify the equation by dividing both sides by 1 (which doesn't change the equation):

69x/1 + 35y/1 = 278/1

Now we can use a system of equations to solve for x and y.

Let's solve for y in terms of x by isolating y on one side of the equation:

35y = 278 - 69x

y = (278 - 69x)/35

Now we can substitute this expression for y into the original equation:

0.69x + 0.35((278 - 69x)/35) = 2.78

Simplifying this equation, we get:

0.69x + 8 - 2x = 2.78

Solving for x, we get:

0.69x - 2x = 2.78 - 8

-1.31x = -5.22

x = 4

So the woman bought 4 bananas.

Now we can substitute this value for x into the expression we derived for y:

y = (278 - 69(4))/35

y = 6

So the woman bought 6 eggs.

Therefore, the woman bought 4 bananas and 6 eggs.

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Therefore, the nth term of the sequence is approximately 29.94.

Assuming that the sequence is formed by alternating between adding 1.5 and multiplying by a constant factor, the nth term can be calculated using the following formula:

nth term = [tex]5.5 * c^{((n-1)//2}) + 1.5 * ((n-1) % 2)[/tex]

Here "//" represents integer division, "%" represents the modulo operator, and c is the constant factor that multiplies each term.

Assuming that the constant factor is 1.5 and the sequence starts with the first term being 5.5, the first few terms of the sequence would be:

5.5, 7, 10.5, 16, 24.5, 37, 55.5, 83, 124.5, ...

Using the formula above, we can find the nth term for any given value of n. For example, the 10th term would be:

nth term = 5.5 * [tex]1.5^4[/tex]+ 1.5 * 1

= 5.5 * 5.0625 + 1.5

= 29.9375

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Correct Question:

What is the nth term of 5.5 7  2008.510 11.5.

The amount of paper used for the label on the can of tune is 12.57 in²

Here, the shape of the can of can is cylindrical.

The area of the cured surface of cylinder is given by formula,

A = 2πrh

where r is the radius of the cylinder

and h is the height of the cylinder

Here, r = 2 in and h = 1 in

so, the area of the lateral surface of cylinder would be,

A = 2 × π × r × h

A = 2 × π × 2 × 1

A = 4 × π

A = 12.57 sq. in.

Therefore, the required amount of paper = 12.57 in²

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Educational psychology provides teachers with research-based principles to guide their teaching.

When teachers go through educational psychology, they are taught on ways to improve their teaching.

These ways will be based on research overtime that have proved efficient in helping students learn from teachers.

Some of these include empowering school social and cultural structures, minimizing bias, implementing an equity pedagogy, the method of knowledge creation, and integrating content (Banks, 1995a).

The main goal of multicultural education is to reduce barriers to educational opportunity and success for students from different cultural backgrounds. The principle that all pupils, regardless of culture, deserve educational equity serves as its cornerstone.

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The Quasilinearization Method is a technique used to approximate solutions for nonlinear differential equations by linearizing them iteratively. It is particularly helpful when solving first-order IVPs.

A maximal solution to a first-order IVP is a solution that exists on the largest possible interval, while a minimal solution exists on the smallest possible interval.

Example 1:
Consider the first-order IVP: dy/dt = y^2, y(0) = 1.

Maximal solution: The maximal solution to this IVP is y(t) = 1/(1 - t) on the interval (-∞, 1).

Minimal solution: The minimal solution is the same as the maximal solution for this example, as there are no other solutions that exist on a smaller interval.

Example 2:
Consider the first-order IVP: dy/dx = x + y, y(0) = 0.

Maximal solution: The maximal solution to this IVP is y(x) = -x + e^x - 1 on the interval (-∞, +∞).

Minimal solution: The minimal solution is the same as the maximal solution for this example since there are no other solutions that exist on a smaller interval.

In both examples, the Quasilinearization Method can be applied to linearize the differential equations and approximate the solutions. The maximal and minimal solutions represent the largest and smallest possible intervals where the solutions are valid.

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A.  The negation of the given statement is "There exists an x such that for all y, y is not greater than x".

B. The negation of the given statement is "For all integers n, 2n² - 5n + 2 is not equal to 0".

E. the statement is true by contraposition.

Integers are a type of number that includes all positive whole numbers (1, 2, 3, ...), zero (0), and negative whole numbers (-1, -2, -3, ...). In mathematical notation, the set of integers is denoted by the symbol Z.

a. The given statement is ∀x ∃y, y > x. Its negation is ¬(∀x ∃y, y > x), which is equivalent to ∃x ¬(∃y, y > x). By De Morgan's law, we can simplify this as ∃x ∀y, ¬(y > x). Therefore, the negation of the given statement is "There exists an x such that for all y, y is not greater than x".

b. The given statement is ∃n ∈ Z, 2n² − 5n + 2 = 0. Its negation is ¬(∃n ∈ Z, 2n² − 5n + 2 = 0), which is equivalent to ∀n ∈ Z, 2n² − 5n + 2 ≠ 0. Therefore, the negation of the given statement is "For all integers n, 2n² - 5n + 2 is not equal to 0".

c. To disprove the statement, we need to find a counterexample where the statement is false. Let x = 10. Then, for any y greater than 10, y is also greater than 6. Therefore, the statement is true for this choice of x, and hence the statement is true.

d. To prove the statement, we can use proof by contradiction. Assume that there exists a real number n such that n ≤ 7 and n > 9. This is a contradiction, and hence our assumption must be false. Therefore, the statement "If n is a real number, then either n > 7 or n ≤ 9" is true.

e. To prove by contraposition, we need to show that if one of the integers is even, then the product of the integers is even. Let's assume that one of the integers is even, say a = 2k. Then, the other integer can be odd or even, but in either case, the product of the integers will be even. Therefore, the statement is true by contraposition.

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81 is the largest number of two-digit which is a perfect square.

Perfect squares are those integers that result from multiplying any number by itself.

1, 4, 9, 16, 25, 36, 49, 64, 81, and 100 are the numbers.

Therefore, there exist 17 two-digit numbers whose digit sums are squares.

The greatest number among those that form a perfect square must be found.

We are aware that the initial number of perfect squares is 100. Furthermore, it is a perfect square of 10.

The number whose square will appear is obviously going to be fewer than 10 today.

The square of 9, which is written as 9²=81, is the first number before 10, so let's start there.

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The surface area of the sphere is 64π square units.

Option B is the correct answer.

We have,

Surface area of a sphere = 4πr² ______(1)

Now,

Radius = 4 units

Substituting in (1)

The surface area of a sphere

= 4πr²

= 4 x π x 4²

= 4π x 16

= 64π square units

Thus,

The surface area of the sphere is 64π square units.

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I think it's 9, tell me if I'm wrong

The area of sector that is bounded by the 180° sector arc, obtained from the formula for the area of circle is 40.5·π square miles

The area of a circle can be obtained from the product of the pi and the square of the radius of the circle.

Mathematically, the area of a circle = π × (Radius)²

The length of the radius of the circle = 9 miles

The angle bounded by the sector = 180°

The area bounded by the sector is therefore;

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The mass of the object to the nearest gram is 29223 grams.

We have,

The volume of the rectangular prism.

V = length x width x height

Substituting the given values, we get:

V = 7 x 6 x 4 = 168 cubic inches

We need to convert the volume to cubic centimeters since the density is given in grams per cubic centimeter.

There are 2.54 centimeters in an inch, so:

V = 168 cubic inches x (2.54 cm/in)³

V = 2755.392 cubic centimeters

Now we can find the mass of the object.

mass = density x volume

Substituting the given density and calculated volume, we get:

mass = 10.6 g/cm³ x 2755.392 cm³

mass = 29223.1232 grams

Rounding to the nearest gram, we get:

mass = 29223 grams

Therefore,

The mass of the object to the nearest gram is 29223 grams.

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Answer:

The Answer Is B "Graph 2 has a larger sample standard deviation than Graph 1"

Step-by-step explanation:

Because the message in the text said the mean of Group 1's data is 2.57 while the sample mean of Group 2's data is 3.337 and from what I understand. 3.337 is a lot more than 2.57

Answer:

  (b)  Graph 2 has a larger sample standard deviation than Graph 1

Step-by-step explanation:

Given the two histograms of hours practiced, you want to know the relationship between the sample standard deviations of the two data sets.

The standard deviation is a measure of data variability. It will tend to be larger for less-symmetrical data distributions, and for those that are skewed one way or another.

The data of Graph 2 is less symmetrical than that of Graph 1, so we expect its standard deviation to be higher. A computation of the standard deviation confirms this.

Graph 1 standard deviation: about 1.40

Graph 2 standard deviation: about 1.53

Graph 2 has a larger sample standard deviation than Graph 1, choice B.

__

Additional comment

In the computation, the first list (L1) is the set of data values. The second list, {2, 3, 4, ...} for example, is their relative frequencies—the heights of the bars in the histogram.

The given mean values seem to show that each bar is represented by its midpoint value, 0.5 for the first bar, for example. For the purpose of the standard deviation calculation, we don't need to make that adjustment.

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Answer:

I'm not quite sure if you are joking or not, but here is your answer:
(a) The point estimate for the population mean price (per 100 pounds) is x = $6.88. The standard deviation is known to be σ = $1.92. The sample size is n = 42. For a 90% confidence interval, the critical value is 1.645 (obtained from a t-distribution table with 41 degrees of freedom). The margin of error is:

Margin of error = Critical value x Standard error

Standard error = Standard deviation / sqrt(sample size) = 1.92 / sqrt(42) = 0.2968

Margin of error = 1.645 x 0.2968 = 0.4882 ≈ 0.49

The lower limit of the confidence interval is:

Lower limit = Point estimate - Margin of error = 6.88 - 0.49 = $6.39

The upper limit of the confidence interval is:

Upper limit = Point estimate + Margin of error = 6.88 + 0.49 = $7.37

Therefore, the 90% confidence interval for the population mean price (per 100 pounds) that farmers in this region get for their watermelon crop is $6.39 to $7.37. The margin of error is $0.49.

(b) The maximal error of estimate is E = 0.25. The confidence level is 90%. The standard deviation is known to be σ = $1.92. We need to find the sample size (n) that satisfies the following formula:

Margin of error = Critical value x Standard error

Standard error = Standard deviation / sqrt(sample size)

For a 90% confidence interval, the critical value is 1.645. Substituting the known values and solving for n, we get:

0.25 = 1.645 x (1.92 / sqrt(n))

sqrt(n) = (1.645 x 1.92) / 0.25

n = [(1.645 x 1.92) / 0.25]^2

n ≈ 113

Therefore, a sample size of 113 farming regions is necessary for a 90% confidence level with maximal error of estimate E = 0.25 for the mean price per 100 pounds of watermelon.

(c) The farm brings 15 tons of watermelon to market, which is equivalent to 30,000 pounds (since 1 ton = 2,000 pounds). The point estimate for the population mean cash value of this crop is unknown. We can use the confidence interval obtained in part (a) to estimate this interval. Multiplying the lower and upper limits by 300 (since 300 pounds of watermelon correspond to $6.88), we get:

Lower limit = 6.39 x 300 = $1917

Upper limit = 7.37 x 300 = $2211

Therefore, the 90% confidence interval for the population mean cash value of this crop is $1917 to $2211. The margin of error is:

Margin of error = (Upper limit - Lower limit) / 2 = (2211 - 1917) / 2 = $147

C(x) is the linear cost function: C(x) = $50x + $300

Where x denotes the number of things manufactured.

A function connects an input with an output. It is analogous to a machine with an input and an output. And the output is somehow related to the input. The standard manner of writing a function is f(x) "f(x) =... "

To find the linear cost function, we need to determine the slope of the cost function and the value of the y-intercept.

Given that 40 items cost $2,300 to produce, we can use this information to find the slope:

Slope = (Change in cost) / (Change in quantity)

Slope = (Total cost for 40 items - Fixed cost) / (40 items - 0 items)

Slope = ($2,300 - $300) / (40 - 0)

Slope = $2,000 / 40

Slope = $50 per item

The fixed cost of $300 represents the y-intercept of the cost function.

Therefore, the linear cost function C(x) is:

C(x) = $50x + $300

Where x represents the number of items produced.

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The given statement, "The mean income of workers who have majored in history is less than $25,000," is an alternative hypothesis.

An alternative hypothesis is a statement that is tested against the null hypothesis, which generally claims no relationship or effect. In this case, the null hypothesis would be, "The mean income of workers who have majored in history is greater than or equal to $25,000."

We must first comprehend the idea of null and alternative hypotheses in hypothesis testing before we can comprehend why the above statement is an alternate hypothesis.

When doing a hypothesis test, we begin with a null hypothesis, which is a claim that there is no connection between the variables under investigation.

The null hypothesis in this situation would be "The mean income of workers with history majors is greater than or equal to $25,000."

On the other side, the competing hypothesis asserts that the median income of people who majored in history is less than $25,000.

The supplied claim, "The mean income of workers who majored in history is less than $25,000," is, therefore, a counterclaim.

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At x equals -5 and x equals 3 our function is discontinuous.

We have been given a rational function:

f(x) = [tex]\frac{x^{2}+7x+1 }{x^{2} +2x-15}[/tex]

We are asked to find the points at which our function is discontinuous.

A rational function is discontinuous when the function is undefined or the denominator is zero.

Let us find what values of x will make our denominator zero.

[tex]x^{2} +2x-15=0[/tex]

We will use factoring to find the zeros of x. By splitting the middle term we will get,

[tex]x^{2} + 5x - 3x -15=0\\\\x(x+5)-3(x+5)=0[/tex]

(x +5)(x - 3) = 0

x = -5 and x = 3

Therefore, at x equals -5 and x equals 3 our function is discontinuous.

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Answer:

$83.60

Step-by-step explanation:

22 x $3.80 = $83.60

LCM stands for "Least Common Multiple". It is the smallest positive integer that is a multiple of two or more numbers

To find a formula for the least common multiple (LCM) of three positive integers a, b, and c.

The formula for LCM(a, b, c) is:
LCM(a, b, c) = LCM(LCM(a, b), c)

To find the LCM of two numbers, you can use the formula:
LCM(a, b) = (a * b) / GCD(a, b)
where GCD(a, b) is the greatest common divisor of a and b.

So, to find the LCM(a, b, c), follow these steps:

1. Calculate GCD(a, b)
2. Calculate LCM(a, b) = (a * b) / GCD(a, b)
3. Calculate GCD(LCM(a, b), c)
4. Calculate LCM(a, b, c) = LCM(LCM(a, b), c) = (LCM(a, b) * c) / GCD(LCM(a, b), c)

That's the formula and the step-by-step process to find the LCM of three positive integers a, b, and c.

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Answer:I can't see the question

Step-by-step explanation:

To write an exponential decay function to the given model and we compare the average rate of changes over the given intervals. Then the average rate of change comes out to be, for situation 1 is-4.065 and situation 2 is -2.667.

It is given that,

Initial value: 50

Decay factor: 0.9

1 ≤ x ≤ 4 and

5 ≤ x ≤ 8

x = 1

f(x) = 50(0.9)¹

f(x) = 45

x = 4

f(x) = 50(0.9)¹

f(x) = 32.805

Now, the average rate of change for situation 1 where x = 1 and x = 4

= (32.805 - 45) / (4 - 1)

= -4.065

average rate of change for situation 2 where x = 5 and x = 8

= (50(0.9)⁵ - 50(0.9)⁸) / (5 - 8)

= 8.0011 / -3

= -2.667

Thus, the average rate of change for situation 1 is-4.065 and situation 2 is -2.667.

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Note that the full question is:

Write an exponential decay function to the model the situation compare the average rates of change over the given intervals

Initial value: 50

Decay factor: 0.9

1 ≤ x ≤ 4 and

5 ≤ x ≤ 8

If right is a scaled copy of the rectangle on the left then the scale factor is  1/2.

The scale factor can be calculated by dividing the corresponding lengths (or widths) of the two rectangles.

The length of the left rectangle is 20 units, and the length of the right rectangle is 10 units.

Therefore, the scale factor for the length is:

scale factor for length = length of right rectangle / length of left rectangle

= 10 / 20

= 0.5

scale factor for width = width of right rectangle / width of left rectangle

= 5 / 10

= 0.5

Since the two scale factors are the same, we can conclude that the rectangles are scaled by the same factor of 0.5 in both the length and the width.

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