6. The value, V(t), of a new car is decreasing according to the function V(t) = 22,465 (0.88)', where time t is
measured in years and V(t) is given in dollars. Which of the following represents the average rate of decrease
in the value of the car over the first 5 years of ownership?

The two numbers are x = 3 and y = 8.

Let x and y represent two numbers.

x + y = 16

xy = 24

To solve for the values of x and y, we can use the two equations given. We can first solve for x by dividing both sides of the second equation by y:

xy/y = 24/y

x = 24/y

We can substitute this value for x in the first equation and solve for y:

x + y = 16

(24/y) + y = 16

24 + y^2 = 16y

y^2 - 16y + 24 = 0

(y - 8)(y - 3) = 0

y = 8 or y = 3

Now that we have values for y, we can substitute them into the second equation and solve for x:

xy = 24

(8)(x) = 24

x = 3

(3)(3) = 24

So, the two numbers are x = 3 and y = 8.

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Complete question

Given two numbers x and y such that x + y = 16 and xy = 24, find the values of x and y.

The correct option is a low return rate; eliminating interviewer bias. Mail surveys have the concern of low return rate but have the advantage of eliminating interviewer bias.

A mail survey is a form of a self-administered survey in which the questionnaire is sent to the respondent through the post. Mail surveys are convenient because they allow participants to respond on their schedule and in the privacy of their own homes.

Mail surveys have the concern of a low return rate but have the advantage of eliminating interviewer bias. The concern of mail surveys is a low return rate. One of the greatest advantages of mail surveys is that they do not require any interaction between the researcher and the respondent. Mail surveys' response rate is typically lower than phone or face-to-face surveys. However, it eliminates interviewer bias.

Interviewer bias occurs when the interviewer's characteristics or behavior have an impact on the participant's responses. Interviewer bias can occur in face-to-face interviews or phone surveys. Respondents may attempt to please the interviewer or present themselves in a more favorable light than they otherwise would in order to avoid social disapproval.

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By dragging the number cards to form the lowest sum possible and substituting that sum into the formula for x, we can make the value of x as small as possible.

The formula for x is x = (a + b + c + d)/4. In order to minimize the value of x, we should aim to make the sum of a, b, c, and d as small as possible. To do this, we can drag the number cards to form the lowest sum possible. For example, if the number cards are 5, 6, 7, and 8, we can drag them to form the sum of 26 (5 + 6 + 7 + 8 = 26). To calculate the value of x, we can substitute the sum of the numbers in the formula and divide it by 4. In this example, x = (26/4) = 6.5. By using this strategy, we can minimize the value of x and make it as small as possible.

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Complete question:

What is the smallest value for x when you drag the number cards?

Answer:

(6, -1)

Step-by-step explanation:

The midpoint formula, (y2+y1)/2 and (x2+x1)/2 will help us find our answer. So (2-4)/2= -1 and (7+5)/2=6, so (6,-1) is the midpoint of segment AB.

The area of the given trapezoid would be 176 feet² with the length of the parallel sides of the trapezoid is 13 feet and 31 feet respectively and the height of the trapezoid given is 16 feet.

Given that,

The length of the parallel sides of the trapezoid is 13 feet and 31 feet

The height of the trapezoid given is 16 feet.

We know that area of trapezoid is (a+b)×h/2

Where, (a) and (b) are Length of the parallel sides of trapezoid and h is the height of trapezoid.

Thus, Area = (13+31) × 16/2

 Area = 22×8

  Area = 176 feet²

Hence the area of the given trapezoid would be 176 feet² with the length of the parallel sides of the trapezoid is 13 feet and 31 feet respectively and the height of the trapezoid given is 16 feet.

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After calculations, we find that the company saves a total of $12 x 160 = $1,920 per month by having Alex work instead of a paid employee.

In this scenario, the company has three unpaid interns, including P. Alex, who are working in exchange for college credit. This means that the company does not have to pay these interns any salary or wages.

If the company were to hire a paid employee instead of having an intern like Alex work, they would have to pay that employee $12 per hour for the work that needs to be done. This is the amount that the company would have to spend in wages for each hour worked by the employee.

Now, we know that Alex works for the full 8 hours per day, and for 20 workdays in a month. This means that she works a total of 8 x 20 = 160 hours in a month.

Therefore, the total amount of money the company would have to pay a paid employee for the same amount of work that Alex does would be $12 per hour x 160 hours = $1,920.

Since Alex is working for the company without any payment, the company saves the entire amount of $1,920 per month that they would have had to pay a paid employee to do the same work.

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The sample standard deviation of Ervin's scores is 41.81.

In this problem, we are given the scores of 7 games bowled by Ervin, and we are asked to calculate the sample standard deviation of these scores. To calculate the sample standard deviation, we first need to calculate the sample mean, which is the sum of the scores divided by the number of games:

mean = (155 + 165 + 138 + 172 + 127 + 193 + 142) / 7 = 138.57

Next, we need to calculate the variance, which is the sum of the squared differences from the mean, divided by the number of games minus one:

variance = [(155-138.57)² + (165-138.57)² + (138-138.57)² + (172-138.57)² + (127-138.57)² + (193-138.57)² + (142-138.57)²] / (7-1) = 1749.62

Finally, we can calculate the sample standard deviation by taking the square root of the variance:

standard deviation = √(variance) = √(1749.62) = 41.81

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The expected loss for the retailer is $2288.4.

The retailer receives some products from three suppliers: S1, S2, and S3. The probability of successfully delivering the products in time by the suppliers are 0.85 for $1, 0.82 for $2, and 0.91 for S3. The manufacturer orders 500 units of a raw material from $1, 120 units from $2, and 156 units from $3. In case of failure to receive the materials in time, the manufacturer will bear $20 per unit for the product supplied by S1, $30 for the product supplied by S2, and $10 for the product supplied by S3. We have to calculate the expected loss for the retailer.

Let's calculate the expected loss for each supplier separately.Expected loss for supplier S1:Number of units ordered from S1 = 500The probability that the product will not be delivered in time = 1 - 0.85 = 0.15The expected loss per unit = $20Total expected loss for the products supplied by S1 = Expected loss per unit × Number of units ordered from S1 × Probability that the product will not be delivered in time= 20 × 500 × 0.15= $1500Expected loss for supplier S2:Number of units ordered from S2 = 120The probability that the product will not be delivered in time = 1 - 0.82 = 0.18

The expected loss per unit = $30Total expected loss for the products supplied by S2 = Expected loss per unit × Number of units ordered from S2 × Probability that the product will not be delivered in time= 30 × 120 × 0.18= $648 Expected loss for supplier S3:Number of units ordered from S3 = 156The probability that the product will not be delivered in time = 1 - 0.91 = 0.09The expected loss per unit = $10Total expected loss for the products supplied by S3 = Expected loss per unit × Number of units ordered from S3 × Probability that the product will not be delivered in time= 10 × 156 × 0.09= $140.4The total expected loss for the retailer = Expected loss for supplier S1 + Expected loss for supplier S2 + Expected loss for supplier S3= $1500 + $648 + $140.4= $2288.4

Hence, the expected loss for the retailer is $2288.4.

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The first withdrawal from the account is $200 and another is $150

A mathematical expression made up of variables, coefficients, constants, and operations like addition, subtraction, multiplication, and division is called an algebraic expression. In general, something is considered equal if two of them are the same. Similar to this, analogous expressions in mathematics are those that hold true even when they appear to be different. Yet, both forms provide the same outcome when the values are entered into the formula.

A checking account has a balance of $350

A customer makes two withdrawals

first is $50 more than the other,

let another withdrawal is $x

then first withdrawal is $(50+x)

then,

x+(50+x)=350

2x=300

x=$150

hence first withdrawal is $200

and another is $150

Then he makes a deposit of $75,

So the remaining balance in the account is $75.

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The standard deviation of the costs is 37 Dhs

The given mean is 173 and 3% of costs exceed 243. We have to calculate the standard deviation of the cost. Therefore, let's first start by calculating the z-score as follows;z-score formula = `(x - μ) / σ`z-score = `243 - 173 / σ`z-score = `70 / σ`We need to find the standard deviation of the costs. Since the z-score formula includes standard deviation, we can first calculate the z-score and then use it to calculate the standard deviation.Using the z-table, we can find the z-score for 3% = -1.88-1.88 = (243 - 173) / σσ = (243 - 173) / -1.88σ = -70 / -1.88σ = 37.23≈ 37The standard deviation of the costs is 37 Dhs. Hence, the correct option is as follows.Option D is the correct option.

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The area of the given kite to the nearest tenth would be = 135.10mm².

A kite is defined as the type of quadrilateral that has two pairs of sides that are equal in length and which are adjacent to each other.

To calculate the area of the kite given such as ABCD, the formula = ½ × AC × BD.

Given the sides such as:

AP = 6 mm

PB = 6√3 mm

PD = 7mm

But AC = 6mm × 2 = 12mm

BD = 6√3+7 = 13√3mm

Therefore the area = 1/2 × 12× 13√3

= 6×13√3

= 135.10mm²

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(a) i) The price of the television on the first day of the sale is £360

    ii) The price of the television on the third day of the sale is £288

(a)

i) On the first day of the sale, the price of the television is reduced by 20% of £450, which is:

20/100 × £450 = £90

So the price of the television on the first day of the sale is:

£450 - £90 = £360

ii) On the third day of the sale, the price of the television is reduced by 20% of the price on the second day of the sale. To find the price on the second day, we need to calculate the reduction on the first day and subtract it from the original price:

Reduction on first day = 20/100 × £450 = £90

Price on second day = £450 - £90 = £360

On the second day of the sale, the price of the television is reduced by 20% of £360, which is:

20/100 × £360 = £72

So the price of the television on the third day of the sale is:

£360 - £72 = £288

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The equation will be 26(p − 1.50) = 65 and the amount of money, p, each paint set normally costs is $4.

Ms. Delgado purchases 26 watercolor paint sets

reduced the price of each paint set = $1. 50.

Ms. Delgado spends $65 in all.

we need to find the equation to find p.

The original price of each watercolor paint set.

Solution:

Ms. Delgado purchases 26 Watercolor paint by spending $65 in all.

with a reduction in price of $39

Let 'p' be the original price of each watercolor paint set.

The equation to find p is,

26p - 39 = 65

26p = 65 + 39

26p = 104

p = 4

The original price of each watercolor paint set is $4

The equation to find p, the original price of each watercolor paint set is

26(p − 1.50) = 65 or 26p - 39 = 65

The original price of each watercolor paint set is $4

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He can feed 15 cows till 36 days because earlier he feed 12 cows till 42 days. So we see we uses the concepts inversely proportional.

In this type of proportional is if their are two quantities then if first one is increase then automatically second one is decrease.

Suppose if a, b are two variables , and if they are indirectly proportional then we can write it as a ∝ 1/b , that means xy = k(where k is constant).

Let number of day be x days.

and, total number of cows = 12 + 3 (After he buy 3 more cow)

then, Number of cows and the number of days are inversely proportion.

So, we can write  [tex]\frac{12}{15} = \frac{x}{45}[/tex]

[tex]= x * 15 = 12 * 45[/tex]

[tex]\implies x = 36\ days[/tex]

So, He can feed 15 cows till 36 days.

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Question in English :

A farmer has feed to feed his 12 cows for 45 days. if he buys 3 more cows, How long does the feed last?

The length of PQ is 16 units. ST is the midsegment of PQR, UV is the midsegment of STR, and WX is the midsegment of UVR. It is reasonable to assume that the three midsegments have equal lengths since they are part of the same triangle.

In a triangle, the midsegment is a line segment that connects the midpoints of two sides of the triangle and is parallel to the third side. In the given triangle PQR, the length of PQ is 16 units. ST is the midsegment of PQR, UV is the midsegment of STR, and WX is the midsegment of UVR. Since all the midsegments are part of the same triangle, it is reasonable to assume that they have equal lengths. The triangle midsegment theorem, which asserts that the length of a triangle's midsegment is equal to half of the length of the third side of the triangle, may be used to demonstrate this.. In this case, the length of ST, UV, and WX would all be equal to 8 units, since the third side of each triangle is 16 units. This indicates that it is reasonable to assume that the midsegments of the triangle have equal lengths.

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The probability that the next chew Myesha removes from the bag will be a flavor other than lime is 82%.

What is probability?

Probability is the measure of the likelihood or chance of an event occurring. It is a numerical value between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain to occur. Probabilities between 0 and 1 represent the degree of uncertainty about whether the event will occur or not.

Out of the 17 times Myesha performed the experiment, a lime chew was selected 3 times. Therefore, the probability that the next chew Myesha removes from the bag will be a lime chew is 3/17.

To find the probability that the next chew Myesha removes from the bag will be a flavor other than lime, we need to subtract the probability of getting a lime chew from 1.

P(flavor other than lime) = 1 - P(lime)

P(flavor other than lime) = 1 - 3/17

P(flavor other than lime) = 14/17

To express this probability as a percent to the nearest whole number, we multiply by 100 and round to the nearest integer:

P(flavor other than lime) = 14/17 x 100

P(flavor other than lime) = 82.35

P(flavor other than lime) ≈ 82%

Therefore, the probability that the next chew Myesha removes from the bag will be a flavor other than lime is approximately 82%.

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Answer:

C)  Both pairs of opposite sides are parallel because mPN = mLM = (1/2) and mPL = mMN = - 2.

Step-by-step explanation:

The corners of a rectangle are all right angles.  The two sets of sides are parallel.  In this example:

 PL ║ MN and

 LM ║ NP

To prove that the corners are all right angles, we could compre the slopes of the two lines that form each corner.  They will be perpendicular if they are 90°.

In this example:

PL ⊥ LM and

MN ⊥ NP

So one approach Sherry may have taken is to compare the slopes of all four lines.  To prove the object is a rectangle she could show that:

1.  The sets of parallel lines have equal slopes, and

2.  The sets of perpendicular lines have slopes that are the negative inverse of each other.  (e.g., if a line has slope 5, a perpendicular line will have slope -(1/5))

To prove these points, Sherry probably used a spreadsheet to calculate each line's slopes.  See the attached spreadsheet for how she may have set up the calculations.  The slopes are the Rise/Run for each line.  Rise is the change in y and x is the change in x between the two points.

Note the green cells.  These are the slopes.  Sherry found that:

a)  PL ║ MN and LM ║ NP,  since PL and MN both have slopes of -2; and  LM and NP both have slopes of -0.5

b)  PL ⊥ LM and MN ⊥ NP, since PL and LM and MN and NP both have slopes that are the negative inverse of each other (-2 and -(1/-2) or 0.5)

Without having checked whether any of the other answer options are viable options, Sherry will likely have seen, and done, enough to have chosen option C as proof that quadrilateral PLMN is a rectangle.

Check the picture below.

[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2\implies c=\sqrt{a^2 + o^2} \end{array} \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{9}\\ o=\stackrel{opposite}{8} \end{cases} \\\\\\ c=\sqrt{ 9^2 + 8^2}\implies c=\sqrt{ 81 + 64 } \implies c=\sqrt{ 145 }\implies c\approx 12.04~ft[/tex]

The simplified expression of (x - 4)/2(x - 3) - (x - 1)/2x is -3/(2x).

The given expression (x - 4)/2(x - 3) - (x - 1)/2x can be simplified to;

(x - 4)/(2x - 6) - (x - 1)/2x

To solve this expression, we need to first find a common denominator for the two fractions.

The least common multiple of the denominators 2x and 2x - 6 is;

2x( x - 3)

So we'll multiply the first fraction by (x - 3)/(x - 3) and the second fraction by (x - 3)/(x - 3) to get a common denominator:

((x - 4)/(2x - 6)) · ((x - 3)/(x - 3)) - ((x - 1)/(2x)) · ((x - 3)/(x - 3))

Now we can combine the numerators over the common denominator:

((x - 4)(x - 3) - (x - 1)(x - 3))/(2x(x - 3))

Expanding the parentheses and combining like terms, we get:

(x² - 7x + 12 - x² + 4x - 3)/(2x(x - 3))

Simplifying the numerator, we get:

(-3x + 9)/(2x(x - 3))

Now we can factor out a -3/2 and simplify:

(-3/2) · (x - 3)/(x(x - 3))

The (x - 3) terms cancel out, leaving us with:

(-3/2) · 1/x

= -3/(2x)

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Therefore, the apportionment under Hamilton's method is:

State Apportionment

A             18

B             22

C             13

D             30

E             17

What is Hamilton's method?

To use Hamilton's method, we need to calculate each state's priority by dividing its population by the geometric mean of its current seat and the next higher integer seat.

Then, we assign seats based on priority until we reach the total number of seats (in this case, 100).

State Population Standard Quota

A              5.6                      18

B              6.8                      22

C              3.6                      12

D              3.2                      10

E              5.2                      17

To calculate priorities, we first find the geometric mean of the current seat and the next higher integer seat for each state:

State A: sqrt(18*19) ≈ 18.49

State B: sqrt(22*23) ≈ 22.94

State C: sqrt(12*13) ≈ 12.68

State D: sqrt(10*11) ≈ 10.49

State E: sqrt(17*18) ≈ 17.89

Then, we divide each state's population by its corresponding priority:

State A: 5.6/18.49 ≈ 0.303

State B: 6.8/22.94 ≈ 0.296

State C: 3.6/12.68 ≈ 0.284

State D: 3.2/10.49 ≈ 0.305

State E: 5.2/17.89 ≈ 0.291

We then assign seats based on priority, starting with the highest priority and rounding down to the nearest integer:

State D: 30 seats

State A: 18 seats

State E: 17 seats

State B: 22 seats

State C: 13 seats

This adds up to 100 seats, as required.

Therefore, the apportionment under Hamilton's method is:

State Apportionment

A             18

B             22

C             13

D             30

E             17

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The volume of the composite figure can be divided into two separate figures: a cylinder and a half-sphere, with the total volume being 108 cubic centimeters.

The composite figure can be divided into two separate figures: a cylinder and a half-sphere.

The formula for the volume of a cylinder is:

Volume of the cylinder = π[tex]r^2[/tex]h, where r is the radius of the cylinder and h is the height of the cylinder.

In this case, the radius of the cylinder is 3 centimeters and the height of the cylinder is 10 centimeters, so the volume of the cylinder is:

Volume of the cylinder = π[tex](3cm)^2(10cm)[/tex] = 90π [tex]cm^3[/tex]

The formula for the volume of a half-sphere is:

Volume of half-sphere = (2/3)π[tex]r^3[/tex], where r is the radius of the half-sphere.

In this case, the radius of the half-sphere is also 3 centimeters, so the volume of the half-sphere is:

Volume of half-sphere = (2/3)π[tex](3cm)^3[/tex] = 18π [tex]cm^3[/tex]

To find the total volume of the composite figure, we add the volume of the cylinder and the volume of the half-sphere:

Total volume = Volume of cylinder + Volume of half-sphere

Total volume = 90π [tex]cm^3[/tex] + 18π [tex]cm^3[/tex]

Total volume = 108π [tex]cm^3[/tex]

Therefore, the exact volume of the composite figure is 108π cubic centimeters.

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70% of the time, it takes more than 6.04 minutes to find a parking space. Rounded to two decimal places, the answer is 6.04 minutes.

The length of time it takes to find a parking space at 9 a.m. follows a normal distribution with a mean of 5 minutes and a standard deviation of 2 minutes. To find the time it takes to find a parking space 70% of the time, we need to find the z-score that corresponds to the 70th percentile.

Using a z-table, we find that the z-score corresponding to the 70th percentile is 0.52. Using the formula z = (x - μ) / σ, where x is the value we are trying to find, μ is the mean, and σ is the standard deviation, we can plug in the values and solve for x:

0.52 = (x - 5) / 2

x - 5 = 0.52 * 2

x - 5 = 1.04

x = 6.04

Therefore, 70% of the time, it takes more than 6.04 minutes to find a parking space. Rounded to two decimal places, the answer is 6.04 minutes.

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7 out of the 30 individuals—or 25%—would be predicted to own both a dog and a cat for two events based on laws of probability multiplication.

The probability multiplication method can be used to determine the number of persons who own both a dog and a cat if we assume that owning either one is an independent occurrence.

We are aware that 15 out of the 30 people—or 50%—have cats. Also, 12 out of the 30 people, or 40%, are dog owners. The likelihood of owning both a cat and a dog is just the sum of the probabilities of owning both a cat and a dog if we believe that these events are unrelated:

P(having a dog and a cat) = P(having a cat) * (owning a dog)

P (having a dog and a cat) equals (15/30) * (12/30).

P(having a dog and a cat) = 0.25

7.5 out of the 30 individuals—or 25%—would be predicted to own both a dog and a cat. We cannot allow a fraction of a person to possess both a cat and a dog though, as we are dealing with a discrete number of people. As a result, we can round to the next whole number or down. As there cannot be a half of a person in this situation, we would round down to 7 people having both a dog and a cat.

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The total percent of the data falling between 62. 6 and 71. 8 is around 68%

Mean score = 67.2

Standard deviation = 4.6

Standardizing the values of interest by converting them into z-scores by -

z = (x - μ) / σ

where x is the score, μ is the mean, and σ is the standard deviation.

Calculating for the lower bound of 62.6:

z1

= (62.6 - 67.2) / 4.6

= - 4.6/4.6

= -1

Similarly,

Calculating for the upper bound of 71.8:

z2

= (71.8 - 67.2) / 4.6

= 4.6/4.6

= 1

Getting the area under curve between these two z-scores using a table of common normal probability. The normal distribution is symmetric, thus, the area between z1 and z2, can be then subtracted from the area to the left of z2. The Left of z1 is an area of 0.1587 and the left of z2 is an area of 0.8413. Therefore, the area between z1 and z2 is:

= 0.8413 - 0.1587

= 0.6826

Converting this area to a percentage -

0.6826 × 100%

= 68.26%

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is it a option ? or no cuz im a litlle confused

The area of composite figure composed of a sector and triangle is 95.52 cm²

An equation is an expression that shows the relationship between two or more numbers and variables. Equations can either be linear, quadratic, cubic and so on depending on the degree.

To get the area of the composite figure, we add the area of the sector to the area of the triangle.

Area of circle sector = (Ф / 360) * π * radius²

but Ф = 82°, radius = 10 cm, π = 3.14, hence:

Area of circle sector = (82 / 360) * 3.14 * 10² = 71.52 cm²

Area of triangle = (1/2) * base * height

but base = 6 cm, height = 8 cm, therefore:

Area of triangle = (1/2) * 6 * 8 = 24 cm²

Area of composite figure = 24 cm² + 71.52 cm² = 95.52 cm²

The area of composite figure is 95.52 cm²

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Answer:

n = -3 or n = -6

Step-by-step explanation:

Solve for n over the real numbers:

n^2 + 9 n + 18 = 0

Subtract 18 from both sides:

n^2 + 9 n = -18

Add 81/4 to both sides:

n^2 + 9 n + 81/4 = 9/4

Write the left-hand side as a square:

(n + 9/2)^2 = 9/4

Take the square root of both sides:

n + 9/2 = 3/2 or n + 9/2 = -3/2

Subtract 9/2 from both sides:

n = -3 or n + 9/2 = -3/2

Subtract 9/2 from both sides:

Answer: n = -3 or n = -6

Answer:

Step-by-step explanation:

[tex]\frac{5\pm\sqrt{-4} }{3} =\frac{5\pm2\sqrt{i} }{3}[/tex]             (since [tex]i=\sqrt{-1}[/tex])

          [tex]=\frac{5}{3} \pm\frac{2}{3}\sqrt{i}[/tex]

[tex]\frac{10\pm\sqrt{-16} }{2} =\frac{10\pm4\sqrt{i} }{2}[/tex]

             [tex]=5 \pm2\sqrt{i}[/tex]

[tex]\frac{-3\pm\sqrt{-144} }{6} =\frac{-3\pm12\sqrt{i} }{6}[/tex]

                [tex]=-\frac{1}{2} \pm2\sqrt{i}[/tex]

There will be enough room for Mike since the diagonal is more than 13 inch

The diagonal of a cuboid is a line segment that connects two opposite corners of the cuboid. It passes through the center of the cuboid and represents the longest distance between any two points in the cuboid.

If the diagonal is less than 13 inch then there will not be enough room if otherwise then there will be enough room

To find the diagonal of a cuboid, you can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

In a cuboid, if we label the length, width, and height

diagonal = √(length^2 + width^2 + height^2)

diagonal = √(10^2 + 8^2 + 12^2)

diagonal = √308

diagonal = 17.5 to 1 decimal place

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To determine whether it is valid to claim that the amount of is lower, we need to compare this probability to our chosen cut-off for unusual events, which is 5%.

To find the probability of randomly selecting 37 with a mean of   [tex]0.897 g[/tex]  or less, we need to calculate the z-score and look up the corresponding probability in the standard normal distribution table.

Where X is the sample mean   [tex](0.897 g),[/tex] μ is the population mean (0.951 g), σ is the population standard deviation [tex](0.299 g)[/tex]  , and n is the sample size (37).

Plugging in the values, we get:

[tex]z = (0.897 - 0.951) / (0.299 / sqrt(37)) = -1.731[/tex]

Looking up the corresponding probability in the standard normal distribution table, we find that   [tex]P(Z < -1.731) = 0.0419[/tex] (rounded to 4 decimal places).

Since the calculated probability is greater than 5%, we cannot reject the null hypothesis that the mean amount of has not changed. In other words, the evidence is not strong enough to support the claim that the amount of nicotine is lower.

Therefore, the probability of randomly selecting 37 with a mean of  [tex]0.897 g[/tex] or less is [tex]0.0419[/tex] .

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