As a borrower, you have the option to choose between two 30-year, monthly-payment loans: 7% interest rate with 3 points, versus 7.5% interest with one-half point.
(a) Which loan option would you choose if you had a 10-year expected prepayment horizon?
(b) Which would you choose if you expect to pay off this loan in 5 years?

This is not a simple random sample because not all combinations of 100 toys could have been chosen.

A factory has 20 assembly lines producing a popular toy.

This is not a simple random sample because not all combinations of 100 toys could have been chosen. We know that it will be a random sample if all the 100 toys will ne chosen randomly but in this question not all the 100 toys will be chosen. The answer is No, because not all combinations of 100 toys could have been chosen.

Therefore, quality control staff randomly selected 5 toys from each output, and this is not a simple random sample because not all combinations of 100 toys could have been chosen.

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The rule of dilation can be defined as to  enlarge or reduce any shape or graph of any function, to create a new graph or shape.

We have to write a rule for the dilation,

A transformation is termed as an operation that moves, flips, and create a new shape.

Dilation is also a type of transformation that enlarges or reduces any shape or graph of any function, to create a new graph or shape.

The scale factor, k determines how much large or small the dilation figure will be as compared to the previous shape or figure.

So, the rule of dilation can be defined as to  enlarge or reduce any shape or graph of any function, to create a new graph or shape.

Hence, the rule of dilation can be defined as to  enlarge or reduce any shape or graph of any function, to create a new graph or shape.

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The upper limit of blood pressure is 123.4.

The lower limit of blood pressure is 116.6..

The applicant's blood pressure limit does not meet the standards limit of blood pressure to qualify for study.

we have given that,

mean , μ = 120

standard deviation , σ = 4

The z - distribution of the 60% is,

P( -z < Z < z ) = 0.60

P( Z < z ) - P( Z < -z ) = 0.60

2× P(Z < z ) - 1 = 0.60

2× P(Z < z ) = 1 + 0.60

P( Z < z ) = 1.60 / 2

P( Z < z ) = 0.80

P( Z < -0.84) = 0.80

z = -0.84 and z = 0.84

let X be the required mean of sample .

Using z - score formula,

X = (z × σ )+ μ

= -0.84 × 4 + 120

= 116.6

and

X = z × σ + μ

= 0.84 × 4 + 120

= 123.4

Hence , Lower blood pressure limit = 116.6

Upper blood pressure limit = 123.4

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Complete question:

To qualify for a medical study, an applicant must have a systolic blood pressure in the 60% of the middle range. If the systolic blood pressure is normally distributed with a mean of 120 and a standard deviation of 4, find the upper and lower limits of blood pressure a person must have to qualify for the study. Round final answers to 1 decimal place and intermediate-value calculations to 2 decimal places. Applicants must have a lower blood pressure limit of 118.48 and an upper blood pressure limit of 124.16 to qualify for the study.

I don't know the answer but I believe it could be the 3rd one

For six tests, the Bonferroni corrected p value is 120.

Given,

Bonferroni adjustment;-

The Bonferroni technique is an easy procedure that permits the construction of several confidence intervals or comparison statements while maintaining a constant overall confidence coefficient.

Here,

Divide the initial alpha level (often set to 0.05) by the total number of tests to make the adjustment. The result of the calculation is a Bonferroni-corrected p value, which will serve as the new cutoff point for classifying a single test as significant.

So,

6/0.05 = 120

That is,

The Bonferroni corrected p value is 120 for 6 number of tests.

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We call this a triple zero, or a zero with multiplicity 3. For zeros with even multiplicities, the graphs touch or are tangent to the x-axis at these x-values

What is the multiplicity of 0 3?

We call this a triple zero, or a zero with multiplicity 3. For zeros with even multiplicities, the graphs touch or are tangent to the x-axis at these x-values. For zeros with odd multiplicities, the graphs cross or intersect the x-axis at these x-values.

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The inverse of the functions are f⁻¹(x) = 1/2(x + 3), f⁻¹(x) = 1/2√(x + 5) and A⁻¹(r) = 1/2√(r/pi)

Function (a)

This function is given as

f(x)=1/(2x)-3

The function needs to be represented as an equation

So, we have

y = 1/(2x) - 3

Swap the positions of x and y

x = 1/(2y) - 3

So, we have

1/(2y) = x + 3

Take the inverse of both sides

2y = 1/(x + 3)

Divide by 2

y = 1/2(x + 3)

So, the inverse function is

f⁻¹(x) = 1/2(x + 3)

Function (b)

This function is given as

f(x)=4x²-5

The function needs to be represented as an equation

So, we have

y = 4x²-5

Swap the positions of x and y

x = 4y² - 5

So, we have

4y²= x + 5

Divide both sides by 4

y²= 1/4(x + 5)

Take the square roots

y= 1/2√(x + 5)

So, the inverse function is

f⁻¹(x) = 1/2√(x + 5)

Function (c)

This function is given as

A(r) = 4(pi)r²

The function needs to be represented as an equation

So, we have

y = 4(pi)r²

Swap the positions of r and y

r = 4(pi)y²

So, we have

y²= r/(4pi)

Take the square roots

y = 1/2√(r/pi)

So, the inverse function is

A⁻¹(r) = 1/2√(r/pi)

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1÷2×8x+32=3x+18

4x+16=3x+18

4x-3x=18-16

x=2

The mean of the 4 and 7  numbers is 5.5.

What is mean?

A amount that includes a price intermediate between those of the acute members of some set is known as mean.

Main body:

In this question we have to find the mean of the 4 and 7 numbers. Whole numbers are all non-negative integers which start from 0. Now the mean of the 4 and 7 numbers as the count of numbers from 4 and 7 is 2. Use this concept to reach the answer.

Mean of numbers is equal to the sum of the numbers divided by the count of the numbers that is

Mean = sum of numbers/ total numbers    

mean = 4+7/2

          = 5.5

HENCE , mean of 4 and 7 is 5.5

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The total number of no votes are 4422.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

Given:   The ratio of yes votes to no votes is 5 to 6 i.e.

          yes votes /no votes = 5/6

  It means there are total 11 votes ( 5 votes for yes and 6 votes for no)

  which gives

                    no votes/total votes= 6/11---(i)

But in the given question total votes are 8107,

so let us consider there are x votes for no which implies

                       no votes/total votes= x/8107

From (i), we have

                   x/8107 = 6/11

               ⇒ x = 6*8107/11 = 4422.

Then the total number of no votes is 4422.

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NOTE: The question given in the portal is incomplete. Here is the complete question.

Question: The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 5 to 6. If there were 8107 total votes, how many no votes were there?

The given Fibonacci sequence ,

b)  First term of the Fibonacci sequence is 8.

c) First term = y-x.

Fourth term = x+y

Fifth term = y+30.

What is Fibonacci Sequence?

 A series in which each number is the sum of the two numbers before it is known as the Fibonacci Sequence. We must specify values for the first two terms in order to complete the Fibonacci Sequence. In the Fibanocci sequence we can find next term by adding previous terms.

Here the given Fourth term = 30 and Fifth term = 49.

Here second and third terms are x and y. Let us take first term as a.

We know that the Fibonacci sequence is sum of previous terms.

The sequence are,

=> a , x , y , 30 ,49 ,...

Here Fourth term = 30

=> second term + third term = 30

=> x+y = 30----->1

Now the fifth term is third term + fourth term = 49

=> y+30 =49

=> y =19.

Put y=19 into 1 then,

=> x+19=30

=> x = 30-19 =11

Now third term is first term+second term = third term

=> a+x =y

=> a+11=19

=> a =19-11 =8.

b) First term of the Fibonacci sequence is 8.

c) Third term = first term+second term

=> y = first term +x

=> First term = y-x.

Fourth term = Second term+third term

=>Fourth term = x+y

Fifth term = third term+fourth term

=> Fifth term = y+30.

Therefore the given Fibonacci sequence ,

b)  First term of the Fibonacci sequence is 8.

c) First term = y-x.

Fourth term = x+y

Fifth term = y+30.

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A table can be used to solve equational systems.

A list of particular points from the straight-line graphs is called a table of values. On a graph, the y-values at the points where the lines converge will be the same. We'll be looking for the x-location in the tables where the y-values are equal.

In a table solution, the system's two linear equations are changed with x-values. The solution is established when the same y-value appears in both equations.

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The probability of getting 5 heads and 5 tails is 0.246

Given that,

No. of head = No of tail,

The probability of getting 5 heads and 5 tails

P(X = x ) = nCₓPˣQⁿ⁻ˣ

There x = 5, n=10 p= 1/2 and Q=1/2

P ( x = 1 ) = 10C₅(1/2)⁵(1/2)⁵

= 252 ( 0.000 9765625 )

P ( X = 5 )= 0.2460

First three flips are head stored no of Outcome 2^10 = 1024

X = {H,H,H....}

The remaining 7 position can be flued with Either head or tail

Therefore ,the possible favourable outcomes = 2^7

No of favourable outcomes

: P(X) =No of favorable outcomes /total no of outcomes

P(X) = 0.125

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Cartlon's score is 4.5434.

Given that,

Carlton has a z-score 1.74 on the achievement test.

From the z-table we get the value 0.959.

We know the formula for standard deviation,

z = (x - μ) / σ

where x = score, σ = standard deviation, μ =  mean

Now z-score corresponding to 98th percentile is 2.06

substituting the values in the above equations,

2.06 = (x - 0.959) / 1.74

i.e. x - 0.959 = 2.06 * 1.74

                    x = 3.5844 + 0.959

                    x = 4.5434

Therefore carlton's score is 4.5434.

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The correct answer is the equation of the line is y = [tex]-\frac{2}{3} x - 2[/tex]

Given the equation of the parallel line is 2x + 3y = 3

and the required line passes through the point (3, -4) where x is 3 and y is -4

We can write the given equation  as:

⇒ 3y = 3 - 2x

Dividing both sides by 3

[tex]y = 1 - \frac{2x}{3}[/tex]

On comparing this equation with y= mx+b, thus m = [tex]-\frac{2}{3}[/tex] and the slopes of parallel lines are always equal.

Using the point slope form, we will derive the equation of line

⇒ [tex]y-y_1 =m ( x- x_1)[/tex]

⇒ [tex]y- (-4) = -\frac{2}{3} (x-3)[/tex]

⇒ [tex]y+4= -\frac{2}{3} (x) - \frac{2}{3} (-3)[/tex]

⇒ [tex]y = -\frac{2}{3} (x) +2-4[/tex]

⇒ [tex]y = -\frac{2}{3} (x) - 2[/tex]

Hence, the equation of the required line is [tex]y = -\frac{2}{3} (x) - 2[/tex]

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Making an interval estimate for the population mean requires making the following assumptions about the population:

a. The population is thought to have a normal distribution.

b. The central limit theorem is presumptively true.

Given,

Making an interval estimate for the population mean requires making the following assumptions about the population:

a. The population is thought to have a normal distribution.

b. The central limit theorem is presumptively true.

The distribution of a variable's values is described by a normal distribution. There are 50% of the data to the left and 50% to the right of the mean in this probability distribution, which is symmetrical about the mean. The majority of the data are centered around the mean, meaning that they are more likely to occur or be located close to the mean than distant from it. A bell curve will represent the normal distribution's graph form. Mean = mode = median describes a normal distribution.

According to the Central Limit Theorem, when a variable does not follow a normal distribution, repeated random samples from the population will result in sample means that are normally distributed, regardless of the underlying distribution of the sample. This indicates that as the sample size increases, the sampling distribution of the sample means moves closer to a normal distribution.

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Elimination and substitution is one approach to solve linear equation problems.

Put the equations in actually Standard Form as a first step, which really is quite significant. Choose which sort of variable to basically remove in step two, which particularly is quite significant. 3, very further showing how 3 in a basically major way. Multiply the equations and really find the solutions, so 3, fairly further showing how 3, which for all intents and purposes is quite significant. Step 4: Reconnect the plug to particularly locate the particularly second variable, which really shows that for the most part choose which basically variable to kind of remove in step two in a sort of major way.

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Answer:

[tex]\huge\boxed{\sf 2 \ unit^2}[/tex]

Step-by-step explanation:

Since both base and perpendicular are the same, let's denote both of them by one variable i.e. x

Using Pythagoras Theorem because it is a right-angled triangle.

[tex](Hypotenuse)^2=(Base)^2+(Perp)^2[/tex]

Where,

Base, Perp = x

Hypotenuse = [tex]2\sqrt{2}[/tex]

So,

[tex](2\sqrt{2})^2=(x)^2+(x)^2 \\\\4 \times 2 = x^2+x^2\\\\8 = 2x^2\\\\Divide \ both \ sides \ by \ 2\\\\4 = x^2\\\\Take \ sqrt\\\\2 = x \\\\x = 2[/tex]

So, Base and Perpendicular both equal 2.

[tex]\displaystyle =\frac{1}{2} (Base)(Perp)\\\\= \frac{1}{2} (2)(2)\\\\= 2 \ unit^2\\\\\rule[225]{225}{2}[/tex]

Answer:

2 unit^2

Step-by-step explanation:

a^2 +b^2=c^2 is the formula we use we can turn both a and b to x since they are the same legnth and c is 2√2

X^2+x^2=2√2^2

2x^2=4(2)

2x^2=8

/2.   /2

x^2=4

Square root both sides

x=2

so the base and the height is 2

So we use triangle formula

1/2(2)(2)

1/2(4)

2

The area is 2

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Emerson actually hit the ball 32% of times at bat.

Since in Game 1, Emerson struck out 30 times in 90 times at bat; in Game 2, he struck out 40 times in 120 times at bat; and in Game 3, Emerson struck out 42 times in 140 times at bat; To determine what percentage of times at bat did Emerson actually hit the ball, the following calculation must be performed:

(30 + 40 + 42) / (90 + 120 + 140) = X

112/350 = X

0.32 = X

Therefore, Emerson actually hit the ball 32% of times at bat.

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Each person will pay $516.44.

To split an expense means to divide it into equal parts among the data given.

Over here we have, three friends so we will split the amount among them.

Here, sharing the cost of living means first calculating their total expenses (rent and other costs), which must then be divided among them.

They spend $859.32 on additional expenses in addition to their $690 rent payment.

Their total expenses are rent and other costs.

$690 + $859.32 = $1549.32.

We must now divide the money among the three friends 1554.32/3 =$516.44.

Therefore each individual will pay $516.44.

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The probability of red on the second spin 1/12. the probability of blue on the second spin 1/18.  the probability of not spinning cyan on either spin is 25/36.

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

The ratio of favorable outcomes to all possible outcomes is used as the formula to determine an event's probability. Probabilities are always in the 0 to 1 range.

Probability = Number of Favorable Outcomes / Total Number of

we know the formula of probability;

probability=favorable outcomes/total number of outcomes

so for red:

P(red) = 3/6 = 1/2

so for blue:

P(blue) = 2/6 = 1/3

so for cyan

P(cyan) = 1/6

Now totally;

P( cyan then red) =  1/6 * 1/2 = 1/12

P(cyan then blue) =  1/6 * 1/3 = 1/18

P( no cyan on 2 spins) = (1/2+1/3)* (1/2+1/3) = 5/6 * 5/6 = 25/36

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Answer:

8x+3<15
x<1.5

Step-by-step explanation:

8x+3<15
   -3. -3

8x<12
/8.  /8

x<1.5

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The estimated age of the archaeological sample  as calculated from the given data is  = 2622.58333 years

Half life given is 5730

t₆.₅ = Ln2/k

k= ln 2/ 5730

The rate constant ,

k = 0.00012 year⁻¹

Given that 73 % of the 14C remains

then |A1|/|A2|  = 0.73

As we know ,

|A1|/|A2| = e ⁻₍kt₎

Hence, on solving the equation we get ,

ln(0.73)= -0.00012t

t = -0.31471/ -0.00012

 = 2622.58333 years

Half-life (symbol t½) is the time required for a quantity (of substance) to reduce to half of its initial value. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo radioactive decay or how long stable atoms survive. The term is also used more generally to characterize any type of exponential (or, rarely, non-exponential) decay.

For example, the medical sciences refer to the biological half-life of drugs and other chemicals in the human body. The converse of half-life (in exponential growth) is doubling time.

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The probability of winning is 30/59.

What is a probability simple definition?

A probability is a number that expresses the possibility or likelihood that a specific event will take place.

                 Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

probability = wanted outcomes / total outcomes

odds = wanted outcomes / unwanted outcomes

odds of 29/30 losing means 29 losing outcomes and 30 winning outcomes.

The total outcomes is 59

The probability of losing is 29/30. Yet we want the probability of winning.

Provability of winning is 1 - probability of losing.

1 - 29/59 = 30/59

The probability of winning is 30/59.

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The coefficient of lift is 1.17

C1 = Cn cos α - Ca sin α

Here, α

Cn is the normal force coefficient, and Ca is Substitute 12· for the axial force coefficient for α

C1 = 1.2cos12.-0.03sin 12.

= 1.16

≈1.17

What is the coefficient of normal force?

The Greek letter mu () typically serves as a symbol for it. From a mathematical perspective, = F/N, where F is the normal force and N is the frictional force. The coefficient of friction has no dimensions because both F and N are measured in force units like newtons or pounds.

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The solutions of x in the interval [0°, 360°) are 3[tex]\pi[/tex]/4 and 5[tex]\pi[/tex]/4 respectively.

What is a quadrant?

The quadrant is the area that is bounded by the point where the X and Y axes connect.

A plane is split into four sections in the cartesian system, the X-axis, a horizontal line, and the Y-axis, a vertical line. The term "quadrant" refers to these four areas.

Given, 2cos x + √2 = 0

       or, 2cos x = -√2

       or, cos x = -√2/2 = -1/√2 = - cos ([tex]\pi /4[/tex] )

As the given cos(x) is negative, then it must lie in quadrants II and III respectively for the given interval  [0°, 360°).

Then, cos x = cos ([tex]\pi[/tex] - [tex]\frac{\pi}{4}[/tex])             and, cos x = cos ([tex]\pi +\frac{\pi }{4}[/tex])

       or, x = 3[tex]\pi[/tex]/4                                 or, x = 5[tex]\pi[/tex]/4

Hence, the required solutions of x are 3[tex]\pi[/tex]/4  and 5[tex]\pi[/tex]/4.

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The amount Amy is expected to pay on rent and utilities each year is $15,600. (Option D)

Rent and utilities refer to the amount paid each month for utilization of accommodation and for utility services which are products, services and equipment related to energy, telecommunications, water, and sewerage respectively.

Based on the information provided in the salary analysis table, Amy’s monthly rent and utilities are:

Total = Amy’s Rent + Amy’s Utilities = $1100 + $200 = $1300

As there are 12 months in a year, the yearly total is:

Total = $1300 x 12 = $15,600

Hence, the amount Amy is expected to pay on rent and utilities each year is $15,600.

Note: The question is incomplete. The complete question probably is Amy is analyzing a job offer. How much should she expect to pay on rent and utilities each year? A) $1,300 B) $2,400 C) $13,200 D) $15,600.

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Answer:

5/6

Step-by-step explanation:

The results of previous dice rolls don't have any effect on the result the next time the die is rolled.

The relative frequency of getting a 5 on the next roll is 5/6

Relative frequency is the ratio of the considered sub group's count to the total count. (so its frequency of the considered sub group relative to the total frequency). Conditional relative frequency is relative frequency conditional to some special characteristic.

We are given that a fair die is rolled 25 times. it landed on the number 5 eight times.

We need to find the relative frequency of getting a 5 on the next roll

relative frequency = 5/6

The results of previous dice rolls that have any effect on the result the next time the die is rolled.

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