Determine pnorm using R, assuming that the variable has a Normal
distribution with a mean of 5.5 and SD of 15.
less than -12
between -6 and 6 months
greater than 12
either less than -24 or greater th

The solution of the equation is 115.

The solution of the equation is calculated as follows;

The equation: 2√(x + 6) - 3 = 19

Collect similar terms;

2√(x + 6)  = 19 + 3

2√(x + 6) = 22

Square 2 and add it into the root;

√(4(x + 6) = 22

square both sides;

4(x + 6) = 22²

4(x + 6) = 484

x + 6 = 484/4

x + 6 = 121

x = 121 - 6

x = 115

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Juan is 13 years old.

Andrés is 34 years old.

We have,

Let's assume that Juan's age is x.

Then, we know that Andrés' age is x + 21.

We also know that the sum of their ages is 47:

x + (x + 21) = 47

Simplifying the equation:

2x + 21 = 47

Subtracting 21 from both sides:

2x = 26

Dividing by 2:

x = 13

So Juan is 13 years old.

To find Andrés' age, we can substitute Juan's age into the equation we used earlier:

x + 21 = 13 + 21 = 34

Thus,

Juan is 13 years old.

Andrés is 34 years old.

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The complete question.

Juan is 21 years younger than Andrés and we know that the sum of their ages is 47. How old is each of them?

The recurrence relation for the total prize money in the tournament is T(n) = 2T(n/2) + 100n, under the condition that tournament has n contestants, where n is a power of 2.



Let's us consider there are n players in the tournament where n is a power of 2. Each player wins k hundreds of dollars, where k is the number of people in the sub-tournament won by the player.

Let us present T(n) as the total prize money in a tournament with n players. We observe that  T(1) = 100 since there is only one player who loses in the first round and gets $100.

For n > 1, we can divide the tournament into two sub-tournaments each with n/2 players. Let's denote k as the number of people in a sub-tournament won by a player. Then we can see that k = n/2 for each player since each player wins one of two sub-tournaments.

Therefore, each player wins k hundreds of dollars where k = n/2. The total prize money for each sub-tournament is T(n/2). Therefore, we can write:

T(n) = 2T(n/2) + 100n

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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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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.

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:

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

Value of a is $52,427.69

To find the value of "a" in this situation, we can use the formula for the present value of an annuity:

PV = a * [1 - (1 + r)^(-n)] / r

where PV is the present value of the loan, a is the amount of each payment, r is the annual interest rate (expressed as a decimal), and n is the number of payments.

In this case, we know that PV = $335,000, r = 0.14, and n = 15. We want to solve for a.

Substituting these values into the formula, we get:

$335,000 = a * [1 - (1 + 0.14)^(-15)] / 0.14

Simplifying, we get:

a = $52,427.69

Therefore, the person assuming responsibility for this loan would need to make 15 equal payments of $52,427.69 each year for the next 15 years in order to repay the loan. The total amount paid would be $786,415.35, which includes both the principal amount of $335,000 and $451,415.35 in interest.

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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:

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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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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If you have just arrived at the downtown bus stop, you should expect to wait about 26 minutes for a bus to arrive.

To calculate the expected waiting time, we need to find the weighted average of the waiting times for each interval, where the weights are the probabilities of each interval occurring.

Let t1, t2, and t3 be the waiting times for intervals of 20 minutes, 40 minutes, and 2 hours, respectively.

Then, we have:

t1 = 10 minutes (half the interval time)

t2 = 20 minutes (half the interval time)

t3 = 60 minutes (half the interval time)

The probabilities of each interval are 0.2, 0.4, and 0.4, respectively.

Therefore, the expected waiting time is:

E(waiting time) = 0.2 * t1 + 0.4 * t2 + 0.4 * t3

= 0.2 * 10 + 0.4 * 20 + 0.4 * 60

= 26 minutes

So, on average, you should expect to wait about 26 minutes for a bus to arrive.

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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.

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.

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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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.

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.

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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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 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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(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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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 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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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.

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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(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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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