Use the graph to write the explicit rule of the arithmetic sequence.

The probability that a randomly selected individual will score between 90 and 110 on this test is 0.6826. The score the employer will use to decide job offers is 123.3 to decide job offers for potential "high flyers."

The IQ test is designed to have a mean of 100 and a standard deviation of 10. This means that the test follows a normal distribution with a mean of 100 and a standard deviation of 10.

(a) The probability that a randomly selected individual from the population will score between 90 and 110 on this test can be found using the standard normal distribution table. We need to find the z-scores for 90 and 110 and then use the table to find the corresponding probabilities.

The z-score for 90 is (90 - 100) / 10 = -1
The z-score for 110 is (110 - 100) / 10 = 1

Using the standard normal distribution table, we find that the probability for a z-score of -1 is 0.1587 and the probability for a z-score of 1 is 0.8413.

The probability that a randomly selected individual will score between 90 and 110 is the difference between these two probabilities:

0.8413 - 0.1587 = 0.6826

So the probability that a randomly selected individual will score between 90 and 110 on this test is 0.6826.

(b) The employer wants to identify potential "high flyers" and intends to do this using the outcome of the IQ test. If the employer offers these positions to people with IQs in the top 1% of the population, we need to find the z-score that corresponds to the top 1% of the population.

Using the standard normal distribution table, we find that the z-score that corresponds to the top 1% of the population is 2.33.

Now we can use the z-score formula to find the corresponding IQ score:

z = (x - mean) / standard deviation

2.33 = (x - 100) / 10

Solving for x, we get:

x = (2.33 * 10) + 100 = 123.3

So the employer will use a score of 123.3 to decide job offers for potential "high flyers."

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In response to the supplied query, we may state that Ben's speed, equation rounded to one decimal place, is x + 0.8 = 2.5 mph.

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.

Rate times distance

Let x represent Alan's speed in mph. Ben's speed will then be x + 0.8 mph.

They will have travelled 12.6 kilometres in total when they finally cross paths. The formula is as follows:

[tex]12.6 = (x + x + 0.8) × 3\\12.6 = 6x + 2.4 \s10.2 = 6x \sx = 1.7[/tex]

Alan is moving at a speed of 1.7 mph, decimal place included.

Ben's speed, rounded to one decimal place, is x + 0.8 = 2.5 mph.

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Answer:

​Alan's rate of speed is 1.7 mph.

​Ben's rate of speed is 2.5 mph.

Step-by-step explanation:

We can use the distance-rate-time formula to solve the given problem.

[tex]\boxed{\sf Distance=rate \times time}[/tex]

Create a distance equation for each of the hikers.

Therefore, the equation for Alan's distance in terms of r is:

[tex]\implies \sf d = 3r[/tex]

Therefore, the equation for Ben's distance in terms of r is:

[tex]\implies \sf d = 3(r+0.8)[/tex]

Alan and Ben are 12.6 miles apart and walking toward each other.  

Therefore, their combined distances will equal 12.6 miles.

Set the sum of the found expressions for distance equal to 12.6 and solve for r:

[tex]\implies \sf d_{Alan}+d_{Ben}=12.6[/tex]

[tex]\implies \sf 3r+3(r+0.8)=12.6[/tex]

[tex]\implies \sf 3r+3r+2.4=12.6[/tex]

[tex]\implies \sf 6r+2.4=12.6[/tex]

[tex]\implies \sf 6r=10.2[/tex]

[tex]\implies \sf r=1.7[/tex]

Therefore:

​Alan's rate of speed is 1.7 mph.

​Ben's rate of speed is 2.5 mph.

The solution to an absolute value inequality is all real numbers. Then the correct options are -

Option A: The inequality could be lx - 4| ≥ -24.

Option F: The inequality could be -3 |x - 7| -2 < 10.

What is an inequality?

An inequality in algebra is a mathematical statement that employs the inequality symbol to show how two expressions relate to one another. The phrases on either side of an inequality symbol are not equal. The phrase on the left should be larger or smaller than the expression on the right, or vice versa, according to this symbol.

An absolute value inequality must not impose any limitations on the value of the absolute value expression if the answer contains only real values.

This implies that any positive real integer can be used as the absolute value statement.

Option A: The inequality |x - 4| -24 has an absolute value expression with a non-negative absolute value, hence it satisfies the requirement that the solution set only consist of real values.

Option B and Option E both refer to the solution set's graph as a number line with a 2-value gap.

To know whether the solution set only contains real numbers, however, more information is required.

Depending on the particular absolute value disparity, the range of the number line could be anything.

Option C: Because of the negative absolute value statement of the inequality -4 |x - 11| - 3 ≥ 9, the left-hand side can never be less than 3.

As a result, the solution set has a lower bound and cannot include only real values.

The inequality |x - 12| ≤ -48 has a non-negative absolute value expression, but an absolute value expression cannot be less than or equal to a negative number, as shown in Option D.

There are therefore no effective remedies for this inequity.

Option F: Because the inequality -3 |x - 7| - 2 < 10 has an absolute value expression that is not negative, it satisfies the requirement that the solution set only contain real numbers.

As a result, choices A and F are the proper ones.

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To show that d/dx (csc(x)) = −csc(x)cot(x), we will use the chain rule and the derivative of the inverse function.

The chain rule states that the derivative of a composite function is the product of the derivatives of the individual functions. The derivative of the inverse function is the reciprocal of the derivative of the original function. Here are the steps:

1. Start with the given function: d/dx (csc(x))
2. Rewrite csc(x) as 1/sin(x): d/dx (1/sin(x))
3. Use the chain rule to find the derivative: (d/dx 1)(d/dx sin(x))
4. The derivative of 1 is 0, so the first term becomes 0: (0)(d/dx sin(x))
5. The derivative of sin(x) is cos(x), so the second term becomes cos(x): (0)(cos(x))
6. Simplify the expression: 0
7. Use the derivative of the inverse function to find the derivative of 1/sin(x): -1/sin^2(x)
8. Rewrite sin^2(x) as (sin(x))(sin(x)): -1/(sin(x))(sin(x))
9. Simplify the expression by canceling out one of the sin(x) terms: -1/sin(x)
10. Rewrite 1/sin(x) as csc(x): -csc(x)
11. Rewrite -1/sin(x) as -cot(x): -cot(x)
12. Combine the two terms to get the final answer: −csc(x)cot(x)

Therefore, d/dx (csc(x)) = −csc(x)cot(x).

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The simplified expression is (8x-7) / ((3x-2)[tex]^{((2)/(3)))}[/tex].

To simplify the expression (3(3x-2)[tex]^{((1)/(3))}[/tex] - (x-1)(3x-2)[tex]^{(-(2)/(3)))/((3x-2)}[/tex][tex]^{((2)/(3)))}[/tex] first we need to perform the indicated operations.

1. Using the power rule, we can rewrite (3x-2)[tex]^{((1)/(3))}[/tex] as 3x-2 and (3x-2)^(-(2)/(3)) as 1/(3x-2).  

Therefore, the expression can be rewritten as (3(3x-2) - (x-1)/(3x-2)) / ((3x-2)[tex]^{((2)/(3)))}[/tex].

2.Now, using the distributive property, we can simplify the expression to (9x-6-(x-1)) / ((3x-2)[tex]^{((2)/(3)))}[/tex].

Finally, simplifying further, we get the expression (8x-7) / ((3x-2)[tex]^{((2)/(3)))}[/tex].

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The polynomial function P(x) with a quadratic function zero of 3-4i and an additional zero is P(x) = (x2 - 6x + 25)(x - additional zero).

A polynomial function, P(x), is a function that can be written in the form P(x) = anxn + an-1xn-1 + ... + a1x + a0, where n is a non-negative integer and an, an-1, ..., a1, a0 are real numbers. A quadratic function is a polynomial function of degree 2, which means it can be written in the form P(x) = ax2 + bx + c.

If a polynomial function has a zero of 3-4i, then it must also have a zero of 3+4i, since complex zeros always come in conjugate pairs. This means that the polynomial function must have factors of (x - (3-4i)) and (x - (3+4i)). Multiplying these two factors together gives us (x - 3 + 4i)(x - 3 - 4i) = x2 - 6x + 25.

If the polynomial function also has an additional zero, then it must have a factor of (x - additional zero). Multiplying this factor with the previous one gives us P(x) = (x2 - 6x + 25)(x - additional zero).

So, the polynomial function P(x) with a quadratic function zero of 3-4i and an additional zero is P(x) = (x2 - 6x + 25)(x - additional zero).

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Answer:

Step-by-step explanation:

300

Answer:150 m

Step-by-step explanation:

2cm/25 m = 2 cm: 2500 cm= 1cm:1250 1250x12=15000 convert back to meters 150 m

The probability that there are not greater than 859 defective products in 359 packages is 0.9999.

We are given that;

Distribution: X 0 3 4 1 2 Р 0.02 0.14 0.34 0.36 0.14 1

0(X) = 0.9635 2

Now,

We need to know the probability of success for each package, which is the probability of having a defective product. Assuming that each product has an equal chance of being defective, we can calculate this probability by dividing the number of defective products by the number of products in a package. In this case, we have:

[tex]p = \frac{0.02 + 0.14 + 0.34 + 0.36 + 0.14}{4} = 0.25[/tex]

This means that each product has a 25% chance of being defective, and each package has a binomial distribution with n=4 and p=0.25.

To find the average and the standard deviation of the number of defective products in a package, we can use these formulas³:

[tex]$$E(X) = np$$$$\sigma(X) = \sqrt{np(1-p)}$$[/tex]

Plugging in the values of $n$ and $p$, we get:

[tex]$$E(X) = 4 \times 0.25 = 1$$$$\sigma(X) = \sqrt{4 \times 0.25 \times (1-0.25)} = \sqrt{0.75} \approx 0.866$$[/tex]

Therefore, the average number of defective products in a package is 1, and the standard deviation is 0.866.

To find the probability that there are not greater than 859 defective products in 359 packages, we need to use the binomial distribution again, but with different values of n and p. In this case, we have:

[tex]$$n = 359 \times 4 = 1436$$$$p = 0.25$$[/tex]

We want to find the probability that [tex]$X \leq 859$[/tex], where [tex]$X$[/tex] is the number of defective products in 1436 trials. We can use this formula:

[tex]$$P(X \leq k) = \sum_{i=0}^{k} \binom{n}{i}p^i(1-p)^{n-i}$$Plugging in the values of $n$, $p$, and $k$, we get:$$P(X \leq 859) = \sum_{i=0}^{859} \binom{1436}{i}0.25^i(1-0.25)^{1436-i}$$[/tex]

Therefore, by probability the answer will be 0.9999.

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The volume of the cone that will fill the cone halfway is [tex]198.72 cm3[/tex] by the given base radius of 9/2cm and 14cm deep.

The  formula for the volume of the cone is

[tex]V = (1/3)πr^2h[/tex]

where h is the height of the cone, r is its base's radius and is a mathematical constant roughly equal to 3.14159.

We must first determine the height of the cone that is filled halfway in to calculate the volume of the cone that will fill it halfway.

Half of the cone's entire height, or 14 cm divided by 2, or 7 cm, corresponds to the height of the half-filled cone.

The cone's base has a radius of 9/2 cm.

We can calculate the volume of the cone that will fill the cone halfway using the formula for a cone's volume as follows:

[tex]V = (1/3)πr^2h[/tex]

[tex]V = (1/3)π(9/2)^2(7) (7)[/tex]

[tex]V ≈ 198.72 cm^3[/tex] (rounded to 2 decimal places) (rounded to 2 decimal places)

Therefore, [tex]198.72 cm3[/tex] is the volume of the cone that will fill it halfway.

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Based on the given information, the sample space for the event can be represented using a tree diagram, where the first level consists of the three pants (black, blue, and tan) and the second level consists of the five shirts (white, black, green, blue, and red). Each branch represents a possible combination of a pair of pants and a shirt.

To find the total number of outcomes in the sample space, we can simply multiply the number of options for pants (3) by the number of options for shirts (5), giving us a total of 15 possible outcomes.

For Natalie selecting a pair of pants and shirt that are the same color, the favourable outcomes would be the combinations where the pants and shirt are either both black or both blue. These can be listed as:

Black pants and black shirt

Blue pants and blue shirt

For Natalie selecting a black shirt, the favourable outcomes would be the combinations where the shirt is black. These can be listed as:

Black pants and black shirt

Blue pants and black shirt

Tan pants and black shirt

For Natalie selecting a blue article of clothing, the favourable outcomes would be the combinations where either the pants or the shirt (or both) are blue. These can be listed as:

Black pants and blue shirt

Blue pants and white shirt

Blue pants and black shirt

Blue pants and green shirt

Blue pants and blue shirt

Tan pants and blue shirt

Answer:

1,254 - whole number; 0.13 - terminating; 0.123456789... - non-terminating/non-repetitive; 0.143143143... - repeating decimal

Step-by-step explanation:

A whole number is a number without any decimals or fractions. A terminating number is one that has an end. A non-terminating number is one that continues on forever. A repeating number is one that has the same pattern and continues on forever.

139

because you do 5 dollars times 11 cats equals 55 and 12 dollars times 7 dogs equals 84 add it together is 139

Answer:

0.011

Step-by-step explanation:

Answer:9.05

Step-by-step explanation: uh why? its easy

Answer:

Heterozygous matches up with C

Homozygous dominant is D

Homozygous recessive is E

Genotype is A

and Phenotype is B

a. False. If we form the table with aspirin in the first row (instead of placebo), the confidence interval is (1/2.33, 1/1.44) = (0.43, 0.69).

b. True. We may get a different odds ratio value if we treat marijuana use as the response variable than if we treat alcohol use as the response variable.

c. False. Interchanging two rows or interchanging two columns in a contingency table does have an effect on the value of the X2 or G-chi-squared statistics. Thus, these tests treat both the rows and the columns of the contingency table as nominal scale, and if either or both variables are ordinal, the test takes that information into account.

d. False. Income and gender are not necessarily independent in the 2 x 2 marginal table, even if they are conditionally independent given the type of job.

e. False. The estimated odds ratio between opinion on global warming and whether one is a Democrat or a Republican does not equal 2.96 x 2.08 = 6.2, it equals (2.96/2.08) = 1.42.

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1. Independent Variable: Group (No News or watch news)

Dependent Variable: Depression Scores

2. Null Hypothesis: μ = 0

Alternative Hypothesis: μ < 0

3. Yes, you can reject the null hypothesis at a = 0.05 because there is a considerable difference in the depression ratings of the two groups

1. According to the information provided, the score for depression depends on whether a group watches the news or not.

Group is an independent variable (No News or watch news).

Depression scores are a dependent variable.

2. Null Hypothesis: The two groups do not differ in their depression levels, which is the null hypothesis.

Alternate Hypothesis: Those who don't read or watch the news will score less depressed than people who receive therapy as usual.

μ = 0 is the null hypothesis.

Between the two groups, there is no difference in depression scores.

Differential Hypothesis:  μ < 0

Those who don't read or watch the news will score less depressed than people who receive therapy as usual.

3. Due to the p-value of (0.024) < α(0.05) at α = 0.05, we can rule out the null hypothesis.

The rejection zone of the t-distribution with 12 degrees of freedom has the t-score of -2.58.

As a result, it is clear that there is a considerable difference in the depression ratings of the two groups, with the group that does not watch or read the news scoring significantly lower on the depression scale than the group that continues to get therapy as usual.

The proper response is "Yes".

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The complete question is:

Dr. Z is interested in discovering if there is a difference in depression scores between those who do not watch or read the news and those who continue with therapy as normal. She divides her clients with depression into 2 groups. She asks Group 1 not to watch or read any news for two weeks while in therapy and asks Group 2 to continue with therapy as normal. The dataset score is a record of the results of the measure, administered after 2 weeks.

Independent Samples T-Test

                                   t                          df                          p

Score                      -2.580                    12                      0.024

1. Identify IV and DV.

2. State the null hypothesis and the directional (one-tailed) alternative hypothesis

3. Can you reject the null hypothesis at a = 0.05?

According to the given information, the probabilites are a) 0.159, b)0.107, d) 0.893 e) 0.662 c) expected value is 12.192 f) standard deviation is 3.0121.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

a) Using the binomial probability formula, we have:

P(X = 13) = (48)^13 * (0.254)^13 * (0.746)^35

= 0.159

So the probability that 13 out of 48 flowers will bloom early is 0.159.

b) To find the probability that fewer than 13 flowers will bloom early, we can find the cumulative probability up to 12:

P(X < 13) = P(X = 0) + P(X = 1) + ... + P(X = 12)

= ∑(48 choose k) * (0.254)^k * (0.746)^(48-k) from k=0 to 12

= 0.107

So the probability that fewer than 13 flowers will bloom early is 0.107.

c) The expected value of a binomial distribution is given by n*p, where n is the number of trials and p is the probability of success. In this case, we have:

E(X) = 48 * 0.254

= 12.192

So on average, we expect to observe about 12.192 early blooming flowers.

d) To find the probability that at least 13 flowers will bloom early, we can use the complement rule and find the probability that 12 or fewer flowers will bloom early, and subtract that from 1:

P(X ≥ 13) = 1 - P(X < 13)

= 1 - 0.107

= 0.893

So the probability that at least 13 flowers will bloom early is 0.893.

e) To find the probability that between 9 and 14 flowers (inclusive) will bloom early, we can find the cumulative probability from 9 to 14:

P(9 ≤ X ≤ 14) = P(X = 9) + P(X = 10) + ... + P(X = 14)

= ∑(48 choose k) * (0.254)^k * (0.746)^(48-k) from k=9 to 14

= 0.662

So the probability that between 9 and 14 flowers (inclusive) will bloom early is 0.662.

f) The variance of a binomial distribution is given by np(1-p), and the standard deviation is the square root of the variance. In this case, we have:

Var(X) = 48 * 0.254 * (1-0.254)

= 9.078

SD(X) = sqrt(Var(X))

= sqrt(9.078)

= 3.0121 (rounded to 4 decimal places)

So the standard deviation of the number of flowers that bloom early in a row of 48 flowers is approximately 3.0121.

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In a right-angled triangle, the sum of two acute angles is equal to 90°.

So if α and β are the two acute angles of a right-angled triangle, then α + β = 90°.Using the formula for sin of the difference of two angles, we can write:sin2α = sin(90° − β) = sin90°cosβ − cos90°sinβ = cosβsin2β = sin(90° − α) = sin90°cosα − cos90°sinα = cosαSince sin2α = cosβ and sin2β = cosα, we can conclude that sin2α = sin2β.Now, let's write 3sinx − 5cosx in the form kcos(x+a). Using the formula for cos of the sum of two angles, we can write:3sinx − 5cosx = kcos(x+a) = k(cosxcos a − sinxsin a)Equating the coefficients of sinx and cosx, we get:−5 = kcos a3 = −ksin aSquaring and adding these equations, we get:25 + 9 = k^2(cos^2a + sin^2a) = k^2So k = √34.Taking the ratio of the two equations, we get:−5/3 = cos a/sin a = 1/tan aSo tan a = −3/5.Using the inverse tangent function, we get:a = tan^−1(−3/5)So the final answer is:kcos(x+a) = √34cos(x + tan^−1(−3/5)).

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The first step in finding the given operations for the functions is to substitute the expressions for f(x) and g(x) into the operations.

For the first set of functions, f(x) = x2 and g(x) = 4x − 3, we have:
(f + g)(x) = f(x) + g(x) = x2 + (4x - 3) = x2 + 4x - 3
(f - g)(x) = f(x) - g(x) = x2 - (4x - 3) = x2 - 4x + 3
(fg)(x) = f(x)g(x) = x2(4x - 3) = 4x3 - 3x2
(f/g)(x) = f(x)/g(x) = x2/(4x - 3)

For the second set of functions, f(x) = x2 + 5 and g(x) = 7 - x, we have:
(f + g)(x) = f(x) + g(x) = x2 + 5 + (7 - x) = x2 - x + 12
(f - g)(x) = f(x) - g(x) = x2 + 5 - (7 - x) = x2 + x - 2
(fg)(x) = f(x)g(x) = (x2 + 5)(7 - x) = 7x2 - x3 + 35 - 5x
(f/g)(x) = f(x)/g(x) = (x2 + 5)/(7 - x)

The given operations are:
1.) (f + g)(x) = x2 + 4x - 3, (f - g)(x) = x2 - 4x + 3, (fg)(x) = 4x3 - 3x2, (f/g)(x) = x2/(4x - 3)
2.) (f + g)(x) = x2 - x + 12, (f - g)(x) = x2 + x - 2, (fg)(x) = 7x2 - x3 + 35 - 5x, (f/g)(x) = (x2 + 5)/(7 - x)

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Answer

the answer is b

The simplified form of the rational expression is given as follows:

[(x - 5)/(x² - 3x - 10)] x [(x + 2)/(x² + x - 12)] = 1/[(x + 4)(x - 3)]

The rational expression for this problem is defined as follows:

[(x - 5)/(x² - 3x - 10)] x [(x + 2)/(x² + x - 12)].

To simplify the rational expression, first we must factor the quadratic equations at the denominator of each of the fractions, hence:

The simplification of the first quadratic function, x² - 3x - 10 = (x - 5)(x + 2), means that the numerators of each of the fractions can be simplified.

As the numerators of each of the fractions are simplified along with x² - 3x - 10, the remaining part is x² + x - 12, hence the simplified expression is given as follows:

[(x - 5)/(x² - 3x - 10)] x [(x + 2)/(x² + x - 12)] = 1/[(x + 4)(x - 3)]

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The manufacturer should ship 0 refrigerators to warehouse A and 80 refrigerators to warehouse B to minimize costs. The minimum cost is $800.

The objective of the problem is to minimize the cost of shipping the refrigerators to the two warehouses while also meeting the requirements of shipping at least 100 refrigerators and hiring at least 300 workers. This can be formulated as a linear programming problem with the following decision variables:

x1 = the number of refrigerators shipped to warehouse A
x2 = the number of refrigerators shipped to warehouse B

The objective function is the total cost of shipping the refrigerators:

minimize 12x1 + 10x2

The constraints are the requirements of shipping at least 100 refrigerators, hiring at least 300 workers, and the maximum capacity of each warehouse:

x1 + x2 >= 100
4x1 + 2x2 >= 300
x1 <= 75 (100 - 25)
x2 <= 80 (100 - 20)

Using the graphical method, we can plot the constraints and find the feasible region. The optimal solution will be at one of the corner points of the feasible region.

After plotting the constraints and finding the feasible region, we can evaluate the objective function at each of the corner points to find the minimum cost. The corner points and their corresponding costs are:

(75, 0) -> 12(75) + 10(0) = $900
(0, 80) -> 12(0) + 10(80) = $800
(50, 100) -> 12(50) + 10(100) = $1700
(60, 90) -> 12(60) + 10(90) = $1740

The minimum cost is $800, which occurs when 0 refrigerators are shipped to warehouse A and 80 refrigerators are shipped to warehouse B.

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The vector x whose image under T is b is x = [23/19 -129/19​].

A linear transformation is a function that maps one vector to another vector while preserving the operations of vector addition and scalar multiplication. In this case, the linear transformation T is defined as T(x) = Ax, where A is a matrix and x is a vector.

To find a vector x whose image under T is b, we need to solve the equation Ax = b for x. This can be done by multiplying both sides of the equation by the inverse of A, which gives us x = A-1b.

Using the formula for the inverse of a 2x2 matrix, we can find A-1:

A-1 = (1/(6*4 - 5*1)) * [4 -5​-1 6​] = [4/19 -5/19​-1/19 6/19​]

Now we can multiply A-1 by b to get x:

x = A-1b = [4/19 -5/19​-1/19 6/19​] * [−9−17​] = [(4/19)*(-9) + (-5/19)*(-17) (−1/19)*(-9) + (6/19)*(-17)​] = [23/19 -129/19​]

Therefore, the vector x whose image under T is b is x = [23/19 -129/19​].

The vector x is unique because the inverse of A is unique, and therefore the solution to the equation Ax = b is also unique.

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Answer:

$1.50

Step-by-step explanation:

3 boxes = $4.50

1 box= $4.50÷3

1box= $1.50

Answer:$1.50

Step-by-step explanation:

An ellipse has an equation equal to 9x^2-144x+16y^2+96y+495=0, the eccentricity of the curve is √7/4.

To compute the eccentricity of the curve of an ellipse, we must first complete the square for both x and y terms to put the equation in standard form.

Complete the square for x terms:
9x²- 144x + 495 = -16y² - 96y
9(x² - 16x) + 495 = -16(y² + 6y)
9(x²- 16x + 64) + 495 - 9(64) = -16(y² + 6y)
9(x - 8)² + 39 = -16(y² + 6y)

Complete the square for y terms:
9(x - 8)² + 39 = -16(y² + 6y)
9(x - 8)² + 39 = -16(y² + 6y + 9) + 16(9)
9(x - 8)² + 39 - 16(9) = -16(y + 3)²
9(x - 8)² - 105 = -16(y + 3)²

Move constant term to the right side of the equation and divide by -105:
9(x - 8)² - 16(y + 3)² = 105
-9(x - 8)²/105 + 16(y + 3)²/105 = 1
(x - 8)²/(105/9) + (y + 3)²/(105/16) = 1

Identify the values of a^2 and b^2:
a² = 105/9
b² = 105/16

Compute the eccentricity using the formula e = √(1 - (b²/a²)):
e = √(1 - ((105/16)/(105/9)))
e = √(1 - (9/16))
e = √(7/16)
e = √7/4

Therefore, the eccentricity of the curve is √7/4.

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Local Minima is 5 and 80

The critical numbers, a and b, of f'(x)=x^4−19x^3+135x^2+2 can be found by setting the derivative f'(x) = 0 and solving for x.

The derivative is: f'(x) = 4x^3 − 57x^2 + 270x

By setting the derivative equal to 0, we get:
4x^3 − 57x^2 + 270x = 0

Solving for x, we get:
x = 0, x = 5, x = 9

The critical numbers of f'(x) are 0, 5 and 9. The second derivative f''(x) is undefined at x = 0, so this is a local maximum point, while x = 5 and 9 are local minimum points.

Table:
Critical number | Second derivative (f''(x)) |  Value
0 | Undefined | Local Maximum
5 | -80 | Local Minimum
9 | 80 | Local Minimum

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Answer:

$9 an hour

Step-by-step explanation:

A) 1

B) 18

C) 4

D) 90