A probability experiment is conducted in which the sample space of the experiment is S={3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}. Let event E={4, 5, 6, 7, 8}Assume each outcome is equally likely.a. List the outcomes in E^c (Use a comma to separate answers as needed.)b. Find P(E^c)..

A machine must produce a bearing that is within 0.02 inches of the correct diameter 4.1 inches. By writing this statement using absolute value notation is:

| x - 4.1 | ≤ 0.02

This notation expresses the requirement that the diameter of the bearing, represented by x, must be within 0.02 inches of the correct diameter of 4.1 inches. The absolute value of the difference between x and 4.1 must be less than or equal to 0.02 for the bearing to meet the specification.

The absolute value function is used to ensure that the difference between x and 4.1 is always positive, regardless of whether x is greater than or less than 4.1. This is important because the requirement is concerned with the magnitude of the difference, rather than its sign. If the absolute value of the difference is less than or equal to 0.02, then the diameter of the bearing is considered to be within the required tolerance.

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The absolute value of the x-values of the coordinates of A and B = |2 - 5| = 3 units.

The absolute value of the y-values of the coordinates of B and C = |6 - 3| = 3 units.

If two points lie on a coordinate plane, the distance between them represents the length of the segment both points form, which is determined by finding the absolute difference between the values of their coordinates that lie on the same axis.

Given that a square has the points, A (2, 6), B (5, 6), C (5, 3), D (2, 3), its dimensions can be found as explained below:

Length of AB is found by calculating the absolute value of the x-values of the coordinates of A and B, while to find the length of BC, is the absolute value of the y-values of the coordinates of B and C.

Therefore:

AB = |2 - 5| = 3 units

BC = |6 - 3| = 3 units

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A is the answer

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The number of ordered triples (a, b, c) where a, b, and c are positive integers and a is a factor of b, a is a factor of c, and abc=N, is 64.

To find the ordered triplets, Firstly Factorize N into its prime factors.For each prime factor. we can choose its exponent as the value of a, b, and c. The total number of ordered triples (a, b, c) is (number of exponents + 1)^3.

let N = 24. The prime factorization of 24 is 2^3 * 3^1.

The number of possible values of a is 4 (from 0 to 3), so the number of possible values of b and c is also 4.

The number of ordered triples is 4^3 = 64.

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In the figure, angles ∠5 and ∠1 are complementary angle.

The sum of two or more angle is 90 degree then the angle is called the complementary angle.

Given that;

Angles are shown in figure.

Now, By the figure we have;

⇒ ∠ 1 and ∠ 4 are vertically opposite angles, hence both are equal.

Here, ∠4 and ∠5 are complementary angles.

⇒ ∠4 + ∠5 = 90°

⇒ ∠1 + ∠5 = 90°

Hence,  Angles ∠5 and ∠1 are complementary angle.

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The linear function relationship between the change in the median home value and the year, indicates that we get;

a) The home values increased at a higher rate in Connecticut

b) The median home value in West Virginia in 2010 is $80,721

c) The home values in both states are equal in 1915

A linear function relationship can be expressed in the form; y = m·x + c. Where, m is the slope of the graph of the function and c is the y-intercept.

a) The rate of increase of the home value, where the values of the house change linearly can be found as follows;

Rate of change of home value for West Virginia =  [tex]\frac{72800-33200}{200-1950} = 792[/tex]

The home values in West Virginia increases by about $792 per year

Rate of change of home values for Connecticut = [tex]\frac{166900-71900}{2000-1950} =1900[/tex]

The home values in Connecticut increases by $1900 each year

Therefore;

b) The increase in the home value in West Virginia per year is $792, therefore, the home value in 2010 can be found as follows;

The number of years between 2010 and 2000 = 2010 - 2000 = 10

Home value in 2010 = Home value in 2000 + 792 × 10

Home value in 2010 = $72800 + $792 × 10 = $80720

c) The equation for the median home value for West Virginia can be presented as follows;

y - 33200 = 792×(x - 1950)

y = 792×(x - 1950) + 33200

The equation for the median home value for Connecticut can be presented as follows;

y - 71900 = 1900×(x - 1950)

y = 1900×(x - 1950) + 71900

When the home values in West Virginia is equal to the home value in Connecticut, we get;

792 × (x - 1950) + 33200 = 1900 × (x - 1950) + 71900

1900·x - 792·x = 1900 × 1950 - 792 × 1950 + 33200 - 71900 = 2121900

1108·x = 2121900

x = 2121900/1108 ≈ 1915.07

The year the median value will be the same in both states is about 1915

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To determine how many cakes Lionel makes in one hour, we can use the following formula:

cakes per hour = total cakes / total hours worked

On Monday, Lionel made 7 cakes in some number of hours, so we don't know how many cakes he made per hour that day. However, on Tuesday, he made an additional 6 cakes (13 total cakes - 7 cakes made on Monday), and he worked for 2 hours longer than he did on Monday. Therefore:

cakes per hour on Tuesday = 6 cakes / 2 hours = 3 cakes per hour

So Lionel made 3 cakes per hour on Tuesday. We don't have enough information to determine how many cakes he made per hour on Monday.

The trigonometry ratio values are tan(50) = 1.19 and cos(70) = 0.34

This can be calculated using a calculator

So, we have

tan(50) = 1.19 and cos(70) = 0.34

This can be calculated using a calculator

So, we have

sin(84) = 0.9945 and tan(75) = 3.7321

Here, we make use of the laws of cosines and sines

So, we have

cos(X) = 15/17 = 0.8824

sin(C) = 36/45 = 0.8

Here, we make use of the laws of tangents and sines

So, we have

tan(?) = 6/13 = 0.4615

? = 24.77

sin(?) = 41/59 = 0.6949

? = 44.01

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The solution is, the required probability is p= 1/10.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

here, we have,

from the given information we get,

We have 5 possible parts colored red, green, blue, purple and yellow

The cube for this case have 6 possible numbers 1,2,3,4,5,6

We have the following even numbers: 2,4,6

Then the probability of obtain an even number is:

p1= 3/6= 1/2

Then the probability of obtain a blue color on the spinner is:

p2= 1/5

Then we want this probability:

Obtain an even number AND sppining a blue on the spinner

Then since the events are independent we can do this:

p = 1/2 * 1/5= 1/10

Hence, The solution is, the required probability is p= 1/10.

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The interquartile range of the data is

The interquartile range (IQR) is a measure of variability in a dataset that is calculated as the difference between the third quartile (Q3) and the first quartile (Q1).

The IQR is the range of the middle 50% of the data, and it provides a measure of the spread of the central part of the distribution.

From the given information, we have:

Minimum value = 4

Q1 = 11

Median = 14

Q3 = 16

Maximum value = 20

To find the IQR, we subtract Q1 from Q3:

IQR = Q3 - Q1 = 16 - 11 = 5

Therefore, the interquartile range of the data is 5.

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Answer:

Step-by-step explanation:

The equation that models the population of bats, y, after x years can be found using the formula:

y = P(1 + r)^x

where P is the initial population, r is the annual growth rate as a decimal, and x is the number of years.

In this case, the initial population P is 345,000, the annual growth rate r is 1.2% or 0.012 as a decimal, and x is the number of years. Substituting these values into the formula, we get:

y = 345,000(1 + 0.012)^x

Simplifying the expression in the parentheses, we get:

y = 345,000(1.012)^x

Therefore, the equation that models the population of bats, y, after x years is:

y = 345,000(1.012)^x

Step-by-step explanation:

the other answer is correct.

I just want to point out some mechanism used here :

the increase by 1.2%

an increase by x% means adding x% to the original 100%.

so, we end up with (100 + x)%.

"%" just stands for 1/100.

so, if y = 100%, an increase by x% is

y×(100 + x)/100 = y×(1 + x/100)

in our case here that is

345,000 × (1 + 0.012) = 345,000 × 1.012

and since the increase rate of 1.2% applies per year, we multiply the end population of every year by 1.012 for the following year.

so, each year a new factor of 1.012 is being integrated into the calculation.

it goes then

345,000×1.012×1.012×1.012×...×1.012 x times after x years.

and we get

y = 345,000 × (1.012)^x

The amount of interest that Laura will be paid in the first 5 years is $600.

The simple interest formula is expressed as;

I = P × r × t

Where I is interest, P is principal, r is interest rate and t is time.

Given that;

Plug the given values into the above formula and solve for interest I.

I = P × r × t

I = $3,000 × 0.04 × 5

I = $3,000 × 0.2

I = $600

Therefore, the amount of interest payable is $600.

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The shape of this histogram is skewed to the right since the highest frequency is found in the first class, and the frequencies decrease as the numbers increase.

The class width, also known as the class interval, is the difference between the upper and lower boundaries of a class. In this frequency distribution, the class width is 9 since the lower boundary of the first class is 54.5 and the upper boundary of the last class is 90.5. We can calculate the frequency of each class by counting how many numbers fall within the class boundaries. For example, the first class has 72 observations since there are 72 numbers that fall between 54.5 and 63.5. To calculate the relative frequency of each class, we divide the frequency of each class by the total frequency. For example, the relative frequency of the first class is 0.312 since 72/231 = 0.312. Once the frequencies and relative frequencies have been calculated, a histogram can be made to represent the data. The shape of this histogram is skewed to the right since the highest frequency is found in the first class, and the frequencies decrease as the numbers increase.

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Answer:

Step-by-step explanation:

First, let's simplify the equation:

(x – 3)² + 9 = 0

(x – 3)² = -9

Now we can apply the square root principle:

x – 3 = ±√(-9)

x – 3 = ±3i

Solving for x:

x = 3 ± 3i

Therefore, the answer is (a) x = 3 + 3i, 3 – 3i.

The efficiency of the a and b from the uniform distribution on the interval a:X-1/2 and b:Xn-n/n+1 is x.

The probability distribution known as the uniform distribution comes in two varieties: the discrete case and the continuous case. Both types of uniform distributions, as their names imply, have constant or uniform probabilities for all possible values of the random variable.

The random sample X1,X2,....,Xn is taken from the uniform distribution on the interval (0,θ).

δlog(L(x,θ))/δθ = -n/θ + ∑(xt)/θ² = 0

n/θ = ∑(xt) /θ²

θ = x

Now derivate it again with respect to θ,

∂²log(L(x;θ)) / ∂θ²

=nθ²−2∑t(xt) / θ³<0

Since, the second derivative is less than 0, ^θ is maximum likelihood estimate of θ.

Therefore, the maximum likelihood estimate of θ is ¯x.

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Answer:

b = -9

Step-by-step explanation:

-3 (3b + 6) = 36 - 3b

-9b - 18 = 36 - 3b

-6b - 18 = 36

-6b = 54

b = -9

Let's check

-3(3(-9) + 6) = 36 - 3(-9)

-3( -27 + 6) = 36 + 27

-3( -21) = 63

63 = 63

So, b = -9 is the correct answer.

Step-by-step explanation:

-3(3b+6)=36-3b

-9b-18=36-3b

-9b+3b=36+18

-6b=54

divide both sides by -6

b= -9

The angle that the flagpole makes with the ground is 20°.

There are three commonly used trigonometric identities.

Sin x = 1/ cosec x

Cos x = 1/ sec x

Tan x = 1/ cot x or sin x / cos x

Cot x = cos x / sin x

We have,

Flagpole height = 16  feet

From figure  B,

The angle of elevation has increased this means,

The flagpole is leaning.

Now,

The angle that the flagpole makes with the ground.

Cos m = 15/16

Cos m = 0.9375

m = [tex]cos^{-1}[/tex] 0.9375

m = 20.36

m = 20°

Thus,

The angle that the flagpole makes with the ground is 20°.

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it is not advisable to make only the minimum payment on a credit card if Jason wants to minimize the amount of interest he has to pay and pay off his debt faster.

A credit card is a payment card issued to users to enable the cardholder to pay a merchant for goods and services based on the cardholder's accrued debt.

Jason may not be doing the right thing by making only the minimum payment on his credit card, depending on the interest rate and penalty charges.

When a credit card holder makes only the minimum payment, the remaining balance accrues interest, which is added to the principal amount.

This means that the total amount owed on the credit card increases every month, even if no additional purchases are made.

The interest rate charged by the credit card company can significantly impact how much Jason ends up paying over time.

Hence, it is not advisable to make only the minimum payment on a credit card if Jason wants to minimize the amount of interest he has to pay and pay off his debt faster.

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Answer:

64.34 feet.

Step-by-step explanation:

To solve this problem, we can use trigonometric ratios, specifically the tangent ratio.

Let's denote the height up the wall that the ladder reaches as "h". We can then set up the following equation:

tan(65°) = h/30

To solve for h, we can multiply both sides by 30:

30 tan(65°) = h

Using a calculator, we can find that tan(65°) is approximately 2.1445. Multiplying this by 30 gives us:

h ≈ 64.34 feet

Therefore, the ladder reaches approximately 64.34 feet up the wall. Rounded to the nearest hundredth of a foot, the answer is 64.34 feet.

a. The probability that a person could give up her cell phone would be 0.69.

b. Probability that a person who could give up her cell phone could also give up television would be 0.45

c. The probability that a person who could not give up her ell phone could give up television would be 0.55.

d. Probability of giving up television is higher for people who could not give up their cell phone than for those who could give up their cell phone.

What is probability?

Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.

a. The probability that a person could give up their cell phone is the sum of the probabilities in the "Could Give Up" column: 0.31 + 0.38 = 0.69.

Therefore, The probability that a person could give up her cell phone would be 0.69.

b. The probability that a person who could give up their cell phone could also give up television is the conditional probability of "Could Give Up Television" given "Could Give Up Cellphone." This is calculated by dividing the joint probability of "Could Give Up Television" and "Could Give Up Cellphone" (0.31) by the probability of "Could Give Up Cellphone" (0.69): 0.31 / 0.69 = 0.4493 or approximately 0.45.

c. The probability that a person who could not give up their cell phone could give up television is the conditional probability of "Could Give Up Television" given "Could Not Give Up Cellphone." This is calculated by dividing the joint probability of "Could Give Up Television" and "Could Not Give Up Cellphone" (0.17) by the probability of "Could Not Give Up Cellphone" (0.31): 0.17 / 0.31 = 0.5484 or approximately 0.55.

d. To compare the probabilities of giving up television for people who could or could not give up their cell phone, we need to calculate the conditional probabilities of "Could Give Up Television" given "Could Give Up Cellphone" and "Could Give Up Television" given "Could Not Give Up Cellphone" respectively.

Probability of giving up television if one could give up a cell phone: 0.31 / 0.69 = 0.4493 or approximately 0.45.

Probability of giving up television if one could not give up a cell phone: 0.17 / 0.31 = 0.5484 or approximately 0.55.

The probability of giving up television is higher for people who could not give up their cell phone than for those who could give up their cell phone.

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Answer:

71%

Step-by-step explanation:

We know

Tyler went to the gym on 22 of the last 31 days.

Which of the following is closest to the percentage of days that Tyler went to the gym?

We take

22 divided by 31, times 100 = 71%

So, the answer is 71%

The scale factor that has been used is 1/2

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

Side length on red = 6 units

Corresponding side length on green = 3 units

Given that the red rectangle is the pre-image and the green rectangle is the image

We have

Scale factor = Green/Red

So, we have

Scale factor = 3/6

Evaluate

Scale factor = 1/2

Hence, the scale factor is 1/2

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Invested in each vehicle is $40,000 if the annual investment income is $944.25.

Let

CD's = x

Bonds = x + 60000

Stocks = y

x + x + 60000 + y = 140000 ----> 2x + y = 80000 .......(1)

Using I = Prt; t = 1; I = Pr

2x + 3.7(x + 60000) + 11.1y = 7800(100× )  × Since I used an exact proportion, the opposite side needs to be multiplied by 100.

5.7x + 11.1y = 558000 .......(2)

Either elimination or substitution;

x = 20000 y = 40000

So CD's = 20000, Bonds = 80000, Stocks = 40000

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Divide the 8-digit student ID by the leftmost 3 digits to find q and r using the Quotient Remainder Theorem. If your 8-digit student ID is 12345678, then d = 123, n = 45,678, q = 371, and r = 45.

Suppose your 8-digit understudy ID is 12345678. Then, at that point, we can take the furthest left three digits to get d = 123. Also, we can take the excess 5 digits to get n = 45,678.

To find q and r, we can utilize the condition n = dq + r and address for q and r.

To begin with, we really want to see as the biggest various of d that is not exactly or equivalent to n. We can do this by separating n by d and taking the floor of the outcome:

q = ⌊n/d⌋ = ⌊45,678/123⌋ = 371

Then, we can track down the rest of taking away the result of d and q from n:

r = n - dq = 45,678 - 123 × 371 = 45,678 - 45,633 = 45

Along these lines, in the event that your 8-digit understudy ID is 12345678, d = 123, n = 45,678, q = 371, and r = 45.

The Remainder Leftover portion Hypothesis expresses that for any whole number n and positive whole number d, there exist whole numbers q and r with the end goal that n=dq+r, where q is the remainder and r is the rest of. We can track down q and r by separating n by d and taking the floor of the outcome for q, and deducting the result of d and q from n for r.

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Measure of angle G is 62.5°.

For a regular polygon of any number of sides, the sum of its exterior angle is 360° (full angle).

In triangle EFG,

Measure of angle E = 55°

Measure of angle F should be less than 180 = x/2°

By the triangle sum theorem, the Sum of measures of all interior angles of triangle = 180°

m(∠E) + m(∠F) + m(∠G) = 180°

55° + x/2° + x/2= 180°

x= 180° - 55°

x = 125

Measure of angle G = 125/2 = 62.5

Therefore, measure of angle G is 62.5°.

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area of square 1 is 28 square units and its side length is[tex]$2\sqrt{7}$[/tex] units.

Let the side length of square 1 be x units. Then the areas of squares 1, 2, and 3 are [tex]$x^2$[/tex], 64, and 36 square units, respectively.

Since square 2 has an area of $64$ square units, its side length is [tex]$\sqrt{64}=8$[/tex] units. Similarly, square 3 has a side length of[tex]$\sqrt{36}=6$[/tex]units.

We can now set up an equation based on the fact that the sum of the areas of squares 1 and 3 is equal to the area of square 2:

[tex]$$x^2+36=64$$[/tex]

Solving for x, we get:

[tex]$$x^2=28$$[/tex]

Therefore, the area of square 1 is [tex]$x^2=28$[/tex] square units, and its side length is [tex]$\sqrt{28}=2\sqrt{7}$[/tex] units.

In summary, the area of square 1 is 28 square units and its side length is[tex]$2\sqrt{7}$[/tex] units.

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The properties are listed below.

Properties of addition and multiplication are defined for the various conditions and rules of addition and multiplication.  The properties are:

The product between any number and this one is zero. This comes from the existence of zero, which states that there must exist a value that represents nothingness, the zero.

This is the associative property of addition,

This is the reflexive property of equality, which says that every number is equal to itself.

This is the distributive property of addition which says ,

C*(A + B) = C*A + C*B

This is the inverse property of addition, this property says that for any real number x there exists a real number -x such that x+(-x)=0.

This is the symmetric property.

This is the transitive property, we can apply it in the next way

then x = z

This is the identity property of multiplication.

This is identity property of addition is that when a number n is added to zero, the result is the number itself i.e. n + 0 = n.

This is inverse property of multiplication. It states that if you multiply a number by its reciprocal, also called the multiplicative inverse, the product will be 1

Hence, the properties are identified.

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Answer:28

Step-by-step explanation: because add z and x

Experimental Probability

Just because the odds are 50% for both genders doesn't mean there is any reason for it to be even. It's like flipping a coin six times. there's no reason for it to land on tails 3 times and heads 3 times. Its just more likely