9. 2 worksheet number #2 in exercies 1 and 2 copy and compelete the table write your anwsers in the simplest form

The values of x and y in the attached triangle using trigonometric ratios are: x = 59 and y = 51.1

The three primary trigonometric ratios are:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

Now, to find the values of x and y in the attached triangle using trigonometric ratios, we have:

29.5/y = tan 30

y = 29.5/tan 30

y = 51.1

Similarly:

29.5/x = sin 30

29.5/0.5 = x

x = 59

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Yes, $9 for 4 visitors and $18 for 8 site visitors are proportional.

To determine whether or not $9 for 4 visitors and $18 for 8 visitors are proportional, we need to test if the ratio of the value to the number of visitors is the equal for both cases.

The ratio of cost to the quantity of visitors for $9 and four visitors is:

$9/4 visitors = $2.25/ visitors

The ratio of value to the quantity of visitors for $18 and eight visitors is:

$18/8 visitors = $2.25/ visitors

We are able to see that both ratios are equal to $2.25 per visitor.

Therefore, $9 for 4 visitors and $18 for 8 site visitors are proportional.

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The critical value for the goodness-of-fit needed to test the claim is A.11.071

Given:

There are 6 colors.

Df= 6-1=5

Critical chi-square with 5 df at 0.05 level of significance = 11.071

Answer: 11.071

Chi-square serves as a statistical examination that analyzes whether there exists any noteworthy disparity between anticipated and witnessed frequencies present inside a categorical compilation of data.

By assessing the interrelationship between two independent variables, the tool determines the scope of association between them till they become independent.

After scrutinizing the differentiation within the outcome extracted from expected and actual observations, which is then evaluated against predetermined chi-square results, the derived p-value deduces the consequent decision concerning null hypothesis dismissal or affirmation in confirming an absence of interrelation between the two initial variable candidates.

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The delivery person will need 6 gallons of gasoline in his tank for a 9-hour shift.

To find the gallons of gasoline needed for a 9-hour shift, we will use the given functions f(x) and g(y).

Find the number of miles driven in 9 hours using the function f(x) = x^2 + 3x.
f(9) = 9^2 + 3(9) = 81 + 27 = 108 miles

Calculate the gallons of gasoline used for driving 108 miles using the function g(y) = y/18.
g(108) = 108/18 = 6 gallons

So, the delivery person will need 6 gallons of gasoline in his tank for a 9-hour shift.

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Answer:

-12

Step-by-step explanation:

First substitute

Then after evaluating collect the like terms

After collecting the like terns simplify the Numbers

And finally evaluate the answer

Answer: 2x-64x+18x = –44x

Step-by-step explanation:

To answer the question about whether the process standard deviation of the cylindrical metal bar production should be adjusted to (I) a higher level than 0.25 cm or (II) a lower level than 0.25 cm to minimize the chance of production costs exceeding $1000, the suggestion is to adjust the standard deviation to (II) a lower level than 0.25 cm.

By reducing the standard deviation, the variation in the lengths of the produced metal bars will decrease, resulting in more consistent and controlled production. This will ultimately help minimize the chances of the production cost of a metal bar exceeding the $1000 threshold. A lower standard deviation ensures that the production process has fewer outliers and deviations from the mean length of 11 cm, leading to cost efficiency and reduction of waste or rework due to bars not meeting the desired specifications.

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The event that will have a sample space of S = {h, t} is (a) Flipping a fair, two-sided coin

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

Sample space of S = {h, t}

The sample size of the above is

Size = 2

Analyzing the options, we have

Hence, the event is (a)

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The series of transformations correctly show that △CAT≅△DOG is rotate ACAT 180° about the origin, the correct option is A.

We are given that;

△CAT≅△DOG

Now,

To show that ACAT and ADOG are congruent, we need to find a sequence of rigid transformations that maps one onto the other.

One possible sequence is:

This will map A to D, C to O, A to G, and T to O.

Translate the image 2 units left. This will align the image with ADOG.

Therefore, by transformation the answer will be rotate ACAT 180° about the origin.

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The three consecutive odd integers are 27, 29, and 31.

Given that three consecutive odd integers their sum is two times third number plus 25

Let's call the first odd integer "x." Since the integers are consecutive odd numbers, therefore, the next two odd integers would be x+2 and x+4.

Now according to the problem, their sum is equal to two times the third number (x+4) plus 25:

x + (x+2) + (x+4) = 2(x+4) + 25

Simplifying the left side:

3x + 6 = 2x + 8 + 25

Next combining like terms:

3x + 6 = 2x + 33

Subtracting 2x and 6 from both sides:

x = 27

Therefore, the three consecutive odd integers are 27, 29, and 31.

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Answer:

No, it is not. See justification in the diagram.

Step-by-step explanation:

You have to do polynomial long division. My math is shown in the picture below and if you have any questions, please let me know.

At the end, (x+7) does not go into 468.

Answer: 7:8

Step-by-step explanation: just subtract 150-80 and you get 70

80 is the women

The remaining 70 is the men

Now arrange it to men:women

70:80

Now simplify

7:8

Hope that helps :)

The probability that at most 2 columns will fail is 0.98.

This is a binomial distribution problem, where the number of trials n = 16, the probability of success (a column failing) p = 0.05, and we want to find the probability of at most 2 columns failing.

To solve this, we need to calculate the probability of 0, 1, or 2 columns failing and add them up.

P(at most 2 columns failing) = P(0 columns failing) + P(1 column failing) + P(2 columns failing)

P(0 columns failing) = (n choose 0) * p^0 * (1-p)^(n-0) = (16 choose 0) * 0.05^0 * 0.95^16 = 0.45

P(1 column failing) = (n choose 1) * p^1 * (1-p)^(n-1) = (16 choose 1) * 0.05^1 * 0.95^15 = 0.38

P(2 columns failing) = (n choose 2) * p^2 * (1-p)^(n-2) = (16 choose 2) * 0.05^2 * 0.95^14 = 0.15

P(at most 2 columns failing) = 0.45 + 0.38 + 0.15 = 0.98

Therefore, the probability that at most 2 columns will fail is 0.98.

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Answer:

Step-by-step explanation:

first, we convert the minutes into an hour

there are 60 minutes in an hour

so then we do 60 divided by 12

that equals to 5

so 5 miles is the answer

Answer:

Let B {bı, b2} and C = {c1, c2} be bases for R^2 where bı [-1;8]. b2 [1;-5], c1 = [1;4]. Find the change-of-coordinates matrix from B to C and the change-of-coordinates matrix from C to B.

In the given problem, we have the bases B and C as follows:

B = {b1, b2} where b1 = [-1;8] and b2 = [1;-5]

C = {c1, c2} where c1 = [1;4] and c2 = [0;1]

We need to find the change-of-coordinates matrix from B to C and from C to B.

To find the change-of-coordinates matrix from B to C, we need to express the basis vectors of B in terms of the basis vectors of C. We can do this by solving the following equations:

b1 = x1c1 + y1c2

b2 = x2c1 + y2c2

where x1 , y1, x2, and y2 are the coefficients we want to find.

Substituting the given values, we get:

[-1;8] = x1*[1;4] + y1*[0;1]

[1;-5] = x2*[1;4] + y2*[0;1]

Solving these equations, we get:

x1 = -17/4, y1 = 1/4, x2 = 9/4, and y2 = -1/4

Therefore, the change-of-coordinates matrix from B to C is:

[-17/4  9/4]

[ 1/4 -1/4]

To find the change-of-coordinates matrix from C to B, we need to express the basis vectors of C in terms of the basis vectors of B. We can do this by solving the following equations:

c1 = a1b1 + a2b2

c2 = b1b1 + b2b2

where a1 , a2, b1, and b2 are the coefficients we want to find.

Substituting the given values and solving these equations, we get:

a1 = 4/17, a2 = -1/17, b1 = -1/17, and b2 = -5/17

Therefore, the change-of-coordinates matrix from C to B is:

[ 4/17 -1/17]

[-1/17 -5/17]

I hope this helps!

Step-by-step explanation:

Answer:

A. The probability of a temperature from 30 degrees to 90 degrees

Step-by-step explanation:

The range of the graph is from 60 to 160 degrees, so we're looking for options that fit within that range.

A. 30 degrees is lower than 60, outside the range

B. Fits

C. Need more information

D. 30 degrees is too low, outside the range

The inequalities are x ≤ -2 and x <-5.

We have,

x is less than or equal to -2 and x is less than -5.

writing the inequality in mathematical expression as

x is less than or equal to -2  = x ≤ -2.

and, x is less than -5 = x <-5.

Now, for x ≤ -2  the number line start from -2 with closed dot and move towards -3, -4, -5, ....

and, for x < -5 the number line start from -5 with open dot move towards -6, -7, -8, ....

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After 20 years, the value of the fox population will be 640.

The population of the fox after 20 years is calculated as follows;

The given function is;

y = 40 x 4ˣ

Where;

how many 10 years period make up 20 years?

x = 2

The value of the fox population is calculated as follows

y = 40 x 4²

y = 40 x 16

y = 640

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Step-by-step explanation:

We can start by using the formula:

force = pressure x area

The pressure on the floor is given as 55 newtons/m². To find the area, we need to first calculate the base of the prism. We can do this by rearranging the formula for volume:

volume = base x height x depth

30 = base x 5 x depth

base = 6m² (dividing both sides by 5 x depth)

Now we can calculate the force exerted by the prism on the floor:

force = pressure x area

force = 55 x 6

force = 330 newtons

Therefore, the force exerted by the prism on the floor is 330 newtons.

(a)This is because the distance between the slits is such that the waves from S1 and S2 arrive at Y in phase, resulting in constructive interference and a maximum in intensity. (b) The frequency of microwaves is [tex]1.94x10^8 Hz[/tex]. (c)One reason why the maxima observed at W, X, and Y will have different intensities from each other is due to the phenomenon of diffraction.

(a) The pattern of intensity maxima and minima observed in the double-slit experiment can be explained by the principle of interference. The microwaves from S1 and S2 interfere with each other as they propagate through the slits and form a pattern on the screen where they are detected. When the receiver is initially placed at W, it is equidistant from both slits and therefore the path lengths for the waves from each slit are equal, resulting in constructive interference and a maximum in intensity.

As the receiver is moved towards Z, the path length from S1 to the receiver decreases while the path length from S2 to the receiver increases. At X, the path lengths from S1 and S2 differ by one wavelength, resulting in constructive interference and a maximum in intensity. At Y, the path lengths from S1 and S2 differ by half a wavelength, resulting in destructive interference and a minimum in intensity.

The distance from S1 to Y is 1.243m, which is equal to the wavelength of the microwaves, while the distance from S2 to Y is 1.181m, which is also equal to the wavelength of the microwaves. This is because the distance between the slits is such that the waves from S1 and S2 arrive at Y in phase, resulting in constructive interference and a maximum in intensity.

(b) The frequency of the microwaves can be determined using the equation for the wavelength of a wave, which is given by[tex]λ = c/f[/tex], where[tex]λ[/tex]is the wavelength, c is the speed of light, and f is the frequency. We know that the wavelength of the microwaves is 1.243m, so we can rearrange the equation to solve for the frequency: f =[tex]c/λ[/tex] = 2.41 ×[tex]10^8[/tex]m/s ÷ 1.243m =[tex]1.94x10^8 Hz[/tex].

(c) As the waves pass through the narrow slits, they spread out and interfere with each other, creating a diffraction pattern. The intensity of the pattern is determined by the amount of interference, which depends on the size of the slits and the wavelength of the waves.

The intensity of the maxima will be affected by the width of the slits, with narrower slits producing a more intense diffraction pattern. The intensity will also be affected by the distance from the slits to the screen, with further distances producing a less intense diffraction pattern. Therefore, the maxima observed at different points on the screen will have different intensities due to variations in the diffraction pattern.

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If random sample of 1000 applicants, 392 applicants were accepted, then (c) interval is from 36.2% to 42.2%. Since value of 42% lies in interval, Bridgeton's claimed acceptance rate is accurate.

The "Confidence-Interval" is defined as "range-of-values" which contain the "true-value" of a population parameter with a certain probability.

To calculate the 95% confidence interval, we use the formula:

⇒ CI = p ± z × √((p(1-p))/n),

where : p = sample proportion (accepted applicants / total applicants)

⇒ z is = z-score associated with desired "level-of-confidence" (95% corresponds to z = 1.96)

⇒ n is = sample size = (1,000),

First, we calculate the "sample-proportion" (p) :

⇒ p = 392 / 1000 = 0.392,

Substituting the values,

We get,

⇒ CI = 0.392 ± 1.96 × √((0.392(1-0.392))/1000),

⇒ 0.392 ± 0.030,

So, the 95% confidence interval for the proportion of accepted applicants at Bridgeton University is (0.362, 0.422) = 36.2% to 42.2%.

Next, To evaluate whether Bridgeton's claim of accepting 42% of applicants seems accurate, we can check if the claim falls within the confidence interval.

The claim of 42% falls within the 95% confidence interval of (0.362, 0.422). So, acceptance rate claimed by Bridgeton is accurate.

Therefore, the correct option is (c).

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The given question is incomplete, the complete question is

Bridgeton University claims to accept 42% of applicants. In a random sample of 1,000 Bridgeton University applicants, 392 were accepted. Calculate the 95% confidence interval and evaluate whether Bridgeton's claim seems accurate.

(a) The interval is from 36.7% to 41.7%. Since the value of 42% does not lie in the interval, Bridgeton's claimed acceptance rate does not seem accurate.

(b) The interval is from 36.2% to 42.2%. Since almost 40% of the sample was accepted, Bridgeton's claimed acceptance rate seems accurate.

(c) The interval is from 36.2% to 42.2%. Since the value of 42% lies in the interval, Bridgeton's claimed acceptance rate seems accurate.

(d) The interval is from 36.7% to 41.7%. Since only 40% of the sample was accepted, Bridgeton's claimed acceptance rate does not seem accurate.

(a) The probability of selecting a senior on any given selection is 0.65. The probability of selecting a non-senior (either a junior or a sophomore) is 0.35. To select exactly three award-winners until a senior is selected, we need to select two non-seniors followed by a senior. The probability of this sequence is:

0.35 * 0.35 * 0.65 = 0.080

So the probability of selecting exactly three award-winners until a senior is selected is 0.080.

(b) The probability of selecting a junior on any given selection is 0.24. The probability of selecting a non-junior (either a senior or a sophomore) is 0.76. To select at least three award-winners until a junior is selected, we need to select two or more non-juniors followed by a junior. The probability of this sequence is:

(0.76 * 0.76 * 0.24) + (0.76 * 0.24) + (0.24) = 0.334

So the probability of selecting at least three award-winners until a junior is selected is 0.334.

(c) The probability of selecting a sophomore on any given selection is 0.11. The probability of selecting a non-sophomore (either a senior or a junior) is 0.89. To select 2 or fewer award-winners until a sophomore is selected, we need to select 1 or 2 non-sophomores followed by a sophomore. The probability of these sequences is:

(0.89 * 0.89 * 0.11) + (0.89 * 0.11) + (0.11) = 0.214

So the probability of selecting 2 or fewer award-winners, until a sophomore is selected, is 0.214.
(a) To find the probability that we will select exactly three award-winners, and the third one is a SENIOR, we need to consider the following probabilities:

1. First student is not a senior (i.e., a junior or a sophomore)
2. Second student is not a senior (i.e., a junior or a sophomore)
3. Third student is a senior

Probability (not a senior) = 1 - Probability (senior) = 1 - 0.65 = 0.35
Probability (exactly 3 award-winners with the third being a senior) = 0.35 * 0.35 * 0.65 ≈ 0.079625

(b) To find the probability that we will select at least three award-winners until a JUNIOR is selected, we can find the probability of selecting 1 or 2 award-winners and subtract it from 1.

Probability (1 award-winner and it's a junior) = 0.24
Probability (2 award-winners, first is not a junior and second is a junior) = (1-0.24) * 0.24 = 0.1816

Total probability (1 or 2 award-winners) = 0.24 + 0.1816 = 0.4216
Probability (at least 3 award-winners) = 1 - 0.4216 ≈ 0.5784

(c) To find the probability that we will select 2 or fewer award-winners until a SOPHOMORE is selected:

Probability (1 award-winner and it's a sophomore) = 0.11
Probability (2 award-winners, first is not a sophomore and second is a sophomore) = (1-0.11) * 0.11 ≈ 0.0989

Total probability (2 or fewer award-winners) = 0.11 + 0.0989 ≈ 0.2089

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The gradient of the path from the trailhead to the mountain peak can be calculated by dividing the change in elevation (in feet) by the length of the trail (in miles). i.e., Gradient = (Change in Elevation) / (Trail Length)

To calculate the elevation change, we can subtract the elevation at the trailhead from the elevation at the mountain peak:

Change in Elevation = Peak Elevation - Trailhead Elevation
Change in Elevation = 9,262 ft - 3,874 ft
Change in Elevation = 5,388 ft

To calculate the length of the trail in miles, we simply divide the length in feet by the number of feet in a mile:

Trail Length = 3 miles

Now we can calculate the gradient:

Gradient = (Change in Elevation) / (Trail Length)
Gradient = 5,388 ft / 3 miles
Gradient = 1,796 ft/mi

Therefore, the gradient of the path from the trailhead to the mountain peak is 1,796 ft/mi. This means that for every mile traveled along the path, there is an increase in elevation of 1,796 feet. The steepness of this path may pose a challenge to hikers, especially those who are not accustomed to hiking at high elevations. Hikers need to be prepared and take appropriate safety precautions when hiking in mountainous terrain.

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The experimental probability that the next shirt sold will be purple is [tex]2/5[/tex].

The experimental probability means ratio of the number of times the event occurs to the total number of trials or observations.

In this case, the event is the sale of a purple shirt and the trials are the total number of shirts sold.

So, total number of shirts sold is:

= 6 purple shirts + 9 other color shirts

= 15 shirts

The number of purple shirts sold is 6.

The experimental probability of selling a purple shirt on the next sale will be:

= Number of purple shirts sold / Total number of shirts sold

= 6 / 15

= 2 / 5.

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a) The total number of capsules needed for 4 weeks is C, 112 capsules.

b) The total milliliters needed for the month of October is C, 465 ml.

a) To determine the number of Rimactane 150mg capsules needed for a 10-year-old boy weighing 30 kg, who has been prescribed a dose of 10 mg/kg twice daily for 4 weeks, follow these steps:

1. Calculate the total daily dose: 30 kg * 10 mg/kg = 300 mg/day
2. Determine the number of daily doses: 300 mg/day / 150 mg/capsule = 2 capsules/day
3. Calculate the total number of capsules needed for 4 weeks: 2 capsules/day * 7 days/week * 4 weeks = 112 capsules

The answer is C, 112 capsules.

b) To calculate the number of milliliters of Epanutin suspension (phenytoin 30 mg/5 ml) that a 5-year-old boy weighing 18 kg with epilepsy will take at a dose of 5 mg/kg twice daily during the month of October, follow these steps:

1. Calculate the total daily dose: 18 kg * 5 mg/kg = 90 mg/day
2. Determine the number of milliliters needed for each daily dose: 90 mg/day * (5 ml/30 mg) = 15 ml/day
3. Calculate the total milliliters needed for the month of October: 15 ml/day * 31 days = 465 ml

The answer is C, 465 ml.

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Answer:

18.5

Step-by-step explanation:

Make sure the numbers are in order from least to greatest!

To define the median of the lower half, you must first divide the data set in half. Then, find the median of the first half.

17, 18, 19, 20 | 21, 24, 25, 27

To find the median, locate the number(s) in the middle of the data set.

17, 18, 19, 20

There are two numbers in the middle: 18 and 19.

When you have two medians, add the numbers, then divide the sum by 2.

[tex]18+19=37\\37/2=18.5[/tex]

The median of the lower half is 18.5.

Answer:

We can use the concept of probability to determine the likelihood of Mr. Wells handing out a blue eraser next.

The probability of an event happening is equal to the number of favorable outcomes divided by the total number of possible outcomes. In this case, the favorable outcome is Mr. Wells handing out a blue eraser, and the total number of possible outcomes is the total number of erasers in the container.

To find the total number of erasers in the container, we can add up the number of erasers in each color:

3 + 5 + 4 + 2 + 7 = 21

Therefore, there are 21 erasers in the container.

To find the number of blue erasers in the container, we need to use the information given in the problem. We know that Mr. Wells has already handed out 3 blue erasers, so there must be some blue erasers left in the container. However, we do not know how many blue erasers are left.

Since we do not have enough information to determine the exact number of blue erasers left, we can assume that all the remaining erasers in the container are equally likely to be handed out next. This is known as the principle of equally likely outcomes.

Therefore, the probability of Mr. Wells handing out a blue eraser next is equal to the number of blue erasers in the container divided by the total number of erasers in the container:

P(blue eraser) = number of blue erasers / total number of erasers

We do not know the exact number of blue erasers, but we know that there are some blue erasers left. Therefore, the probability of Mr. Wells handing out a blue eraser next is greater than zero.

So, the answer to the question is:

The probability that the next eraser Mr. Wells hands out will be blue is greater than zero, but we cannot determine the exact probability without knowing the number of blue erasers left in the container.

To solve this problem, we need to understand the conditions under which the inequality $x^2 nx 15 < 0$ has no real solutions. This inequality can be rewritten as $nx(x-15/n) < 0$, which tells us that either $n>0$ and $x<0$ or $x>15/n$, or $n<0$ and $x>0$ or $x<15/n$.

In either case, we have a product of two factors that must be negative, which means that either both factors are negative or both factors are positive.
Since we are looking for the number of different possible values of $n$, we need to consider all possible combinations of signs for $n$ and $x-15/n$. If $n>0$, then $x-15/n$ must also be positive, which means that $x>15/n$. If $n<0$, then $x-15/n$ must be negative, which means that $x<15/n$. In either case, we can see that $n$ must be either positive or negative, and that there is only one possible value of $n$ that satisfies the given condition: $n = \frac{15}{x^2}$.

To find the number of different possible values of $n$, we need to consider all possible values of $x$. If $x=0$, then the inequality is trivially true for any value of $n$. If $x\neq 0$, then we can see that $n$ can take any value in the interval $(0,\infty)$ or $(-\infty,0)$, which means that there are infinitely many possible values of $n$ that satisfy the given condition.

Therefore, the answer to the question is that there are infinitely many different possible values of $n$.
To find the number of different possible values of $n$ for which the inequality $x^2 + nx + 15 < 0$ has no real solutions in $x$, we first need to analyze the inequality.

Step 1: Find the discriminant of the quadratic inequality.
The discriminant, $D$, is given by the formula $D = b^2 - 4ac$, where $a$, $b$, and $c$ are the coefficients of the quadratic expression. In this case, $a = 1$, $b = n$, and $c = 15$.

So, $D = n^2 - 4(1)(15) = n^2 - 60$.

Step 2: Determine the condition for the inequality to have no real solutions.
For a quadratic inequality to have no real solutions, the parabola must not intersect the x-axis, which means the discriminant must be less than 0.

So, we need to solve the inequality $D < 0$:

$n^2 - 60 < 0$

Step 3: Solve the inequality for $n$.
To solve the inequality, find the range of values of $n$ that satisfy the inequality.

$(n - \sqrt{60})(n + \sqrt{60}) < 0$

Since $\sqrt{60}$ is between 7 and 8, we can rewrite the inequality as:

$-8 < n < 8$

Step 4: Count the number of possible integer values of $n$.
The inequality indicates that $n$ must be an integer between -8 and 8 (not inclusive). Therefore, the possible values of $n$ are -7, -6, -5, -4, -3, -2, -1, 1, 2, 3, 4, 5, 6, and 7.

There are 14 different possible values of $n$ for which the inequality $x^2 + nx + 15 < 0$ has no real solutions in $x$.

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Answer:

Let xxx be the number of days Addison can afford to rent.

The cost of renting the car for xxx days is 20*x.

The cost of driving 100 miles is 0.10*100 = 10.

The total cost of renting the car and driving is 20*x + 10.

Addison wants to spend at most $80, so we have the inequality 20*x + 10 <= 80.

Solving for xxx, we get x <= 3.

Therefore, Addison can afford to rent the car for at most 3 days.

The solutions are:

(a) 2Cu = (16C, 6C)

(b) 3v = (18, -21)

(c) V - u = (-2, -10)

(d) 2u + 5v = (46, -29)

To find the given values, we need to perform basic vector operations using the given vectors u and v.

(a) 2Cu

We need to multiply the vector u by 2C.

2Cu = 2C(8, 3)

= (16C, 6C)

So, 2Cu = (16C, 6C).

(b) 3v

We need to multiply the vector v by 3.

3v = 3(6, -7)

= (18, -21)

So, 3v = (18, -21).

(c) V - u

We need to subtract the vector u from the vector v.

V - u = (6, -7) - (8, 3)

= (-2, -10)

So, V - u = (-2, -10).

(d) 2u + 5v

We need to multiply vector u by 2 and vector v by 5 and then add the two vectors.

2u + 5v = 2(8, 3) + 5(6, -7)

= (16, 6) + (30, -35)

= (46, -29)

So, 2u + 5v = (46, -29).

Therefore, the solutions are:

(a) 2Cu = (16C, 6C)

(b) 3v = (18, -21)

(c) V - u = (-2, -10)

(d) 2u + 5v = (46, -29)

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