a game show releases its secrets about how it chooses contestants from its audience. they say the probability of being chosen for the first round on the show is 130; the probability of being chosen for the second round on the show is 215; the probability of being chosen for both rounds on the show is 0. let event a be being chosen for the first round, and event b being chosen for this second round. are events a and b mutually exclusive, independent, both, or neither?

Thus {u, v} is linearly independent if and only if {u v, u − v} is linearly independent

It is given that {u,v} be a linearly independent set of a set S.

This means that there exist constant a,b such that if:

                               au+bv=0

                            then a=b=0

Now we are asked to prove that:

{u+v,u-v} is a linearly independent set.

Let us consider there exists constant c,d such that:

                           c(u+v)+d(u-v)=0

To show:   c=d=0

The expression could also be written as:

cu+cv+du-dv=0

( Since, using the distributive property)

Now on combining the like terms that is the terms with same vectors.

cu+du+cv-dv=0

i.e.

(c+d)u+(c-d)v=0

Since, we are given that u and v are linearly independent vectors this means that:

c+d=0------------(1)

and c-d=0 i.e c=d-----------(2)

and from equation (1) using equation (2) we have:

2c=0

i.e. c=0

and similarly by equation (2) we have:

        d=0

Hence, we are proved with the result.

We get that the vectors {u+v,u-v} is linearly independent.

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Answer:

b is 10.5 c is 11

Step-by-step explanation:

9+1.5

10.5

3(5)-4

15-4

11

There were 2.07 times as much people that applied in the fourth month than in the first month.

An exponential function is one that grows or decreases in an exponential manner. Thus, for any exponential function we can write; f(x) = ax^±n. The term a is the initial value x is the rate of change while n is the time elapsed. The positive sign is used for an exponential increase while the negative sign is used for an exponential decrease.

Thus we have;

f(x) = 27(1.2)^4

This shows us that the time elapsed is four months and f(x) = 2.07.

Therefore, there were 2.07 times as much people that applied in the fourth month than in the first month.

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The given proof that all horses are the same color is a fallacy of circular reasoning or proof by induction.                                

   Here’s why: There is a fallacy in the statement given in the proposition P(k) is true, so that all the horses in any set of k horses are the same color. The fallacy is that it assumes the truth of the proposition to be proven by circular reasoning. By saying that all horses in any set of k horses are the same color, it means that all horses in a set of 1 horse, which is the basis step, are the same color. But this is false because a horse, as a solitary individual, can be of any color.                                

So, the statement, "all horses in any set of k horses are the same color" assumes the conclusion to be proven. This flaw invalidates the entire proof by induction. Therefore, the "proof" that all horses are the same color is wrong.

What is induction?                                                                                                                                                                                                             Induction is the process of establishing a general statement or principle by looking at examples or instances. It involves a specific observation or case that leads to a general conclusion. It is useful in mathematical proofs, scientific inquiry, and problem-solving.
The issue with this "proof" that all horses are the same color lies in the inductive step. To clarify, let's go through the proof by induction process:

1. Basis Step: P(1) is true since there is only one horse, and it must be the same color as itself.
2. Inductive Step: Assume P(k) is true for some arbitrary k (all k horses have the same color).

Now, proof consider a set of k + 1 horses. You claimed that the first k horses have the same color and the last k horses have the same color. However, this argument fails when k = 1. In this case, you would have a set of 2 horses (k+1), and there is no overlap between the first horse and the second horse, so you cannot conclude that they have the same color based on the induction assumption.

Thus, the inductive step does not hold for all cases, and the proof that all horses are the same color is incorrect.

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Answer:

20,300

Step-by-step explanation:

Convert 1.5% to a decimal (.015)

20,000 x .015 = 300

20,000 + 300 = 20,300

A "99% confidence" in a confidence interval means that we can be 99% confident that the true population parameter lies within the interval.

We have,

In a statistical context, "99% confidence" refers to the level of confidence associated with a confidence interval.

A 99% confidence interval means that if we were to repeat the sampling process many times and construct 99% confidence intervals for the population parameter of interest, approximately 99% of those intervals would contain the true population parameter.

In simpler terms, it means that we are 99% confident that the true value of the population parameter lies within the calculated confidence interval.

It provides a measure of the uncertainty associated with the estimation process and indicates the level of confidence we have in the accuracy of the interval estimate.

Thus,

A "99% confidence" in a confidence interval means that we can be 99% confident that the true population parameter lies within the interval.

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Answer:

three half.

Step-by-step explanation:

short and simple

Answer:

D. 3/2                      

Step-by-step explanation:

I got the question right on the quiz

Answer:

first if a=d that 62=5x+8

62-8=5x+8-8 ...substract by same number

54=5x ....simplifying

54/5=5x/5 ....divided by two equal part

10.8=x

Answer:

A

Step-by-step explanation:

a) The monthly payment for this fully amortising mortgage is approximately $10,331.25.
b) The monthly payment for this interest-only mortgage is approximately $14,360.33.

c) The new monthly payment after the interest rate increase is approximately $9,090.70.

d) The remaining loan balance is approximately $625,014.72.

A) To calculate the monthly payment of a fully amortising mortgage, we can use the formula:

M = P * (r * (1+r)^n) / ((1+r)^n - 1)

Where:
M = Monthly payment
P = Loan amount
r = Monthly interest rate
n = Total number of payments

For the given question, the loan amount is 81% of $1,175,378, which is $952,622.38. The annual interest rate is 11.6%, so the monthly interest rate would be 11.6% / 12 = 0.9667%. The mortgage term is 21 years, which means a total of 21 * 12 = 252 payments.

Plugging these values into the formula, we can calculate the monthly payment:

M = 952,622.38 * (0.009667 * (1+0.009667)^252) / ((1+0.009667)^252 - 1)

The monthly payment for this fully amortising mortgage is approximately $10,331.25.

B) To calculate the monthly payment of an interest-only mortgage, we can use the formula:

M = P * r

Where:
M = Monthly payment
P = Loan amount
r = Monthly interest rate

For the given question, the loan amount is 80% of $1,495,863, which is $1,196,690.40. The annual interest rate is 14.4%, so the monthly interest rate would be 14.4% / 12 = 1.2%.

Plugging these values into the formula, we can calculate the monthly payment:

M = 1,196,690.40 * 0.012

The monthly payment for this interest-only mortgage is approximately $14,360.33.

C) To calculate the new monthly payment after an interest rate increase, we can use the same formula as in part A:

M = P * (r * (1+r)^n) / ((1+r)^n - 1)

For the given question, the remaining loan balance is $700,134. The current interest rate is 14.5% per annum, and the loan term is 12 years.

To calculate the new interest rate, we need to add 1% to the current interest rate, which gives us 15.5% per annum, or 15.5% / 12 = 1.2917% as the monthly interest rate.

Plugging these values into the formula, we can calculate the new monthly payment:

M = 700,134 * (0.012917 * (1+0.012917)^144) / ((1+0.012917)^144 - 1)

The new monthly payment after the interest rate increase is approximately $9,090.70.

D) To calculate the remaining loan balance, we can use the formula:

B = P * ((1+r)^n - (1+r)^p) / ((1+r)^n - 1)

Where:
B = Remaining loan balance
P = Loan amount
r = Monthly interest rate
n = Total number of payments
p = Number of payments made

For the given question, the monthly payment is $8,364. The annual interest rate is 12.4%, so the monthly interest rate would be 12.4% / 12 = 1.0333%. The remaining loan term is 10 years, which means a total of 10 * 12 = 120 payments have been made.

Plugging these values into the formula, we can calculate the remaining loan balance:

B = P * ((1+0.010333)^120 - (1+0.010333)^360) / ((1+0.010333)^360 - 1)

The remaining loan balance is approximately $625,014.72.

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Answer:5 hours

Step-by-step explanation:

55*5=275 and 25*5+150=275

Answer:

6

Step-by-step explanation:

Answer:

11.75

Step-by-step explanation:

the angles of a triangle should add to 180

5x + 3x - 4 +90 = 180

now solve for x

8x = 94

94/8 = 11.75

(a)the area between -1 and 1 is approximately 0.6827 (b) the area between -√3.84146 and √3.84146 is approximately 0.9500.

(a) To track down P(z^2 < 1), we can revamp it as P(- 1 < z < 1) since the square of a standard typical irregular variable is generally certain.

We know that P(-1  z  1) is the same as the area under the standard normal curve between -1 and 1. This is based on the properties of the standard normal distribution.

Using statistical software or looking up the values in the standard normal distribution table, also known as the Z-table, we discover that the range from -1 to 1 is roughly 0.6827.

As a result, P(z2  1)  0.6827.

(b) To track down P(z^2 < 3.84146), we can again modify it as P(- √3.84146 < z < √3.84146) since the square of a standard typical irregular variable is dependably sure.

We can determine the area under the standard normal curve between -√3.84146 and √3.84146 by utilizing the characteristics of the standard normal distribution.

Using statistical software or the standard normal distribution table, we determine that the range between -3.84146 and 3.84146 is approximately 0.9500.

Consequently, P(z2  3.84146)  0.9500.

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Answer:

-0.1155

Step-by-step explanation:

-5.5 x 0.021

a negative multiplied by a positive is negative

- (5.5 x 0.021)

-0.1155

Answer:

Step-by-step explanation:

sum of ratio=3+6=9

Jeff invest=3/9×146,000=146000/3=48666 2/3 $

Trudy invest=6/9×146,000=292,000/3=97,333 1/3 $

We can say that whenever x changes by 1, the value of y becomes 1.7 times as large as its previous value.

Given that,

With respect to x, the value of y varies exponentially, and the 1-unit growth factor is 1.7.

We have to find which of the following best describes the significance of this growth factor.

We know that,

The required expression for y with respect to x is

y=(1.7)ˣ------>equation(1)

1.7=1- unit growth factor.

When ever x changes by 1.

x=x-1----->equation(2)

Putting equation (2) in (1)

y'=1.7ˣ⁺¹

y'=1.7ˣ×1.7----->equation(3)

Here [ y is new value after increase]

Taking ratio of (3) and (1)

y'/y= (1.7)ˣ×(1.7)/(1.7)ˣ

y'=(1.7)y

Therefore, We can say that whenever x changes by 1, the value of y becomes 1.7 times as large as its previous value.

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The formula to find  the total number of shaded triangles in the first 10 sierpinski triangles is Sn = (1 - 310)/(-2).

The Sierpiski triangle, also known as the Sierpiski gasket or Sierpiski sieve, is a fractal appealing fixed set with the general shape of an equilateral triangle that is subdivided recursively into smaller equilateral triangles. The name Sierpiski is derived from the Polish language. This is one of the simplest instances of self-similar sets, meaning it is a mathematically generated pattern that can be replicated at any magnification or reduction. It was initially built as a curve.

The Sierpinski triangle can be divided into three self-similar sections (n=3), each of which can then be enlarged by a factor of two (m=2) to produce the full triangle. N = md, where n is the number of self-similar pieces and m is the magnification factor, is the formula for dimension d.

The formula to find  the total number of shaded triangles in the first 10 sierpinski triangles is Sn = (1 - 310)/(-2).

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We can conclude that (A) "Yes since the appropriate probability is greater than​ 0.05, it is a significantly high numbe"r is the correct reason for the question.

So,

Number of Girls x

​P(x)

(0)

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

Results from groups of 8 births from 8 different parent sets are shown in the accompanying table.

Therefore, (A) "yes, since the appropriate probability is greater than​ 0.05, it is a significantly high number" is the correct reason for the question.

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Answer: 565.3 cubic cm

Step-by-step explanation:

V= 1/3Bh

V= 1/3π r^2h

= 1/3 π (6 cm) ^2 (15 cm)

= 1/3 π (36 cm squared) (15 cm)

= 180π cubic cm

about 565.2 cubic cm

π is about 3.14

The value of the volume of a cone with a radius of 6 centimeters and a height of 15 centimeters is,

⇒ 565.2 cubic cm

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

In cone,

Radius = 6 cm

Height = 15 cm

Now, We know that;

Volume of cone is,

V = 1/3π r²h

Substitute all the values we get;

V = 1/3 π (6 cm)² (15 cm)

V = 1/3 π (36) (15)

V = 180π

V = 565.2 cubic cm

Thus, The value of the volume of a cone with a radius of 6 centimeters and a height of 15 centimeters is,

⇒ 565.2 cubic cm

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\(Hello\) \(There!\)

Let's do step-by-step explanation!

\(10+(\frac{1}{2})\) \(4\) · \(48\)

Multiply and divide (left and right) \((\frac{1}{2} )\) · \(4\) · \(48: 96\)

\(=10+96\)

Add and subtract (left to right) \(10+96:106\)

Answer:

\(106.\)

Hopefully, this helps you!!

\(Emilychu\)

The number of tractors lent by the first, second and third stations results in a system of three simultaneous equations which indicates;

The first originally station had 39 tractors, the second station had 21 tractors and the third station originally had 12 tractors

Simultaneous equations are a set of two or more equations that have common variables.

Let x represent the number of tractors at the first station, let y represent the number of tractors at the second tractor station, and let z, represent the number of tractors at the third tractor station

According to the details in the question, after the first transaction, we get

Number of tractors at the first station = x - y - z

Number of tractors at the second station = y + y = 2·y

Number of tractors at the third station = z + z = 2·z

After the second transaction, we get;

Number of tractors at the first station = 2·x - 2·y - 2·z

Number of tractors at the second station = 2·y - (x - y - z) - 2·z = 3·y - x - z

Number of tractors at the third station = 2·z + 2·z = 4·z

After the third transaction, we get;

Number of tractors at the first station = 2 × (2·x - 2·y - 2·z) = 4·x - 4·y - 4·z

Number of tractors at the second tractor station = 6·y - 2·x - 2·z

Number of tractors at the third tractor station = 4·z - (2·x - 2·y - 2·z) - (3·y - x - z) = 7·z - x - y

The three equations after the third transaction are therefore;
4·x - 4·y - 4·z = 24...(1)

6·y - 2·x - 2·z = 24...(2)

7·z - x - y = 24...(3)

Multiplying equation (2) by 2 and subtracting equation (1) from the result we get;

12·y - 4·x - 4·z - (4·x - 4·y - 4·z) = 16·y - 8·x = 48 - 24 = 24

16·y - 8·x = 24...(4)

Multiplying equation (3) by 2 and multiplying equation (2) by 7, then adding both results, we get;

14·z - 2·x - 2·y = 48

42·y - 14·x - 14·z = 168

42·y - 14·x - 14·z + (14·z - 2·x - 2·y) = 48 + 168

40·y - 16·x = 216...(5)

Multiplying equation (4) by 2 and then subtracting the result from equation (5), we get;

40·y - 16·x - (32·y - 16·x) = 216 - 48 = 168

8·y = 168

y = 168/8 = 21

The number of tractors initially at the second station, y = 21

16·y - 8·x = 24, therefore, 16 × 21 - 8·x = 24

8·x = 16 × 21 - 24 = 312

x = 312 ÷ 8 = 39

The number of tractors initially at the first station, x = 39

7·z - x - y = 24, therefore, 7·z - 39 - 21 = 24

7·z = 24 + 39 + 21 = 84

z = 84/7 = 12

The number of tractors initially at the third station, z = 12

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Answer:

x = 5,-2

Step-by-step explanation:

Multiply the whole equation by 3(x+1) to get rid of the denominator.

\( \large{ \frac{x + 2}{3} \times 3(x + 1) = \frac{2(x + 2)}{x + 1} \times 3(x + 1)} \\ \large{(x + 2)(x + 1) = 2(x + 2) \times 3} \\ \large{ {x}^{2} + 3x + 2 = 6(x + 2)} \\ \large{ {x}^{2} + 3x + 2 = 6x + 12}\)

Then we solve the equation.

\( \large{ {x}^{2} + 3x + 2 - 6x - 12 = 0} \\ \large{ {x}^{2} - 3x - 10 = 0} \\ \large{(x - 5)(x + 2) = 0} \\ \large{x = 5, - 2}\)

Since we are also solving rational equation, make sure that x ≠ -1 for this problem. Because if x = -1, the denominator is 0 which is undefined. Since our solutions are x = 5,-2 and not -1. Therefore the answer is x = 5,-2

150 students scored between 42 and 56 on the district geometry test.

Box whisker plots are used to abstract a collection of data that has been approximated using an interval scale. Just a box plot is another name for it. They are mostly employed while interpreting data. It is one of the graphical approaches that shows how the dataset's data varies from one another. The histogram may be used to display the data as well. Yet a histogram offers a useful presentation. Box and whisker plots are preferable to histograms because they may exhibit numerous sets of data on a single graph, which adds more information.

From the box whisker plot we see that the lower quartile is 42 and the median is 56.

The median represents the 50th percentile whereas lower quartile is 75%.

The difference is:

75 - 50 = 25%.

Now, for 600 scores we have:

25% of 600

= 25/100 (600) = 150

Hence, 150 students scored between 42 and 56 on the district geometry test.

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To obtain an amount of 3 / 2 cups of flour, then we need three halves of cup by means of a 1 / 2 cup measuring cup.

In this problem we have the case of recipe that requires 3 / 2 cups of flour in terms of certain number of measuring cups with an amount of 1 / 2 cups. The number of measuring cups (n) is equal to the total required by the recipe (M) divided by the amount of the measuring cup (m), both in cups. That is:

n = M / m

If we know that m = 1 / 2 cup and M = 3 / 2 cup, then the number of measuring cups is:

n = (3 / 2 cup) / (1 / 2 cup)

n = 3

In other words, we need 3 halves of a cup of flour to obtain the required amount of 3 / 2 cups.

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Answer:

\(2 + 3 + 7 + x = 4 \times 5 \\ x = 20 - 12 = 8\)

Answer: $329.00

Explanation: To reconstruct an original price from a sale price, use:

Original Price – Original Price * Mark-down-percent = Sale Price, or

Original Price * (1 - Mark-down-percent) = Sale Price

To do a double mark-down problem, we must do this twice.  For the 10%:

Original Sale Price * (1 – 10%) = $207.27

Original Sale Price = $207.27/0.9 = $230.30.

For the pre-all-discount price,

Original Price * (1 – 30%) = $230.30

Original Price = $230.30/0.7 = $329.00.

Answer:

Examine this system of linear equations.

y – 3x = –2,

y = 4

Which is a solution of the system of equations?

(0, 4)

(2, 2)

(2, 4)=this is the correct answer

(4, 2)

Step-by-step explanation:

thats the answer

(2,4)