The complete set of Hannah Montana DVDs costs $149.99. The first 1,000
orders will receive a discount of 40%.
How much is the discount?
How much is the sale price?

Answer:2 4  −  1 8

Step-by-step explanation:

a) The GCD of 9 and 11 can be expressed as: 1 = 9 - 4(11) + 5(9).

b) The GCD of 33 and 44 can be expressed as: 11 = 44 - 1(33)

c) The GCD of 35 and 78 can be expressed as: 1 = 35 - 4(78) + 11(35) - 22(8).

d) The GCD of 21 and 55 can be expressed as: 1 = 21 - 2(55) + 3(21) - 4(13) + 7(8) - 11(5) + 18(3) - 29(2).

Using the technique used in Example 17, let's go through each pair of integers and determine their greatest common divisor (GCD) as a linear combination of the numbers.

a) Pair: 9, 11

We start by dividing the larger number by the smaller number:

11 ÷ 9 = 1 remainder 2

Next, we divide the smaller number (9) by the remainder (2):

9 ÷ 2 = 4 remainder 1

We continue this process until we obtain a remainder of 0:

2 ÷ 1 = 2 remainder 0

The last non-zero remainder is 1, which is the GCD of 9 and 11.

To express the GCD (1) as a linear combination of 9 and 11, we backtrack through the divisions:

1 = 9 - 4(2) + 1(1)

So, the GCD of 9 and 11 can be expressed as: 1 = 9 - 4(11) + 5(9)

b) Pair: 33, 44

44 ÷ 33 = 1 remainder 11

33 ÷ 11 = 3 remainder 0

The GCD of 33 and 44 is 11.

Expressing the GCD (11) as a linear combination:

11 = 44 - 1(33)

So, the GCD of 33 and 44 can be expressed as: 11 = 44 - 1(33)

c) Pair: 35, 78

78 ÷ 35 = 2 remainder 8

35 ÷ 8 = 4 remainder 3

8 ÷ 3 = 2 remainder 2

3 ÷ 2 = 1 remainder 1

2 ÷ 1 = 2 remainder 0

The GCD of 35 and 78 is 1.

Expressing the GCD (1) as a linear combination:

1 = 35 - 4(8) + 2(3) - 1(2)

So, the GCD of 35 and 78 can be expressed as: 1 = 35 - 4(78) + 11(35) - 22(8)

d) Pair: 21, 55

55 ÷ 21 = 2 remainder 13

21 ÷ 13 = 1 remainder 8

13 ÷ 8 = 1 remainder 5

8 ÷ 5 = 1 remainder 3

5 ÷ 3 = 1 remainder 2

3 ÷ 2 = 1 remainder 1

2 ÷ 1 = 2 remainder 0

The GCD of 21 and 55 is 1.

Expressing the GCD (1) as a linear combination:

1 = 21 - 1(13) + 1(8) - 1(5) + 1(3) - 1(2)

So, the GCD of 21 and 55 can be expressed as: 1 = 21 - 2(55) + 3(21) - 4(13) + 7(8) - 11(5) + 18(3) - 29(2)

These are the expressions of the greatest common divisors of each pair of integers as linear combinations of the integers.

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Answer:

i believe its 50

Step-by-step explanation:

because all the angles are congruent to each other

Answer:

12 miles below sea level

Step-by-step explanation:

Answer:

Hi...

a^2+b^2=c^2

b^2=c^2-a^2

b^2=22500-3600=18900

So...b=137/4

Answer:

(4,18)

Step-by-step explanation:

Answer:

(4,18)

Step-by-step explanation:

We can just pluck the x values into the equation: y = 5x -1 to see if the y values fit.

1. y = 5(4) - 1

    = 20 - 1

    = 19 (Nope, 18 is not 19)

2. y = 5(3) - 1

     = 15 - 1

     = 14 (Yep, same as option)

3. y = 5(0) - 1

     = 0-1

     = -1 (Yep, same as option)

4. y = 5(2) - 1

     = 10 - 1

     = 9 (Yep, same as option)

The theoretical probability of event E, denoted by P(E), is the number of favorable outcomes divided by the total number of possible outcomes.

The theoretical probability of an event E, denoted by P(E), is the ratio of the number of favorable outcomes to the total number of possible outcomes in a given sample space.

In other words, it represents the likelihood of occurrence of event E based on the underlying theoretical assumptions.

Theoretical probability is derived from a theoretical or mathematical model and is based on the assumption that all outcomes in the sample space are equally likely.

It provides a theoretical expectation of the probability of an event occurring under ideal conditions.

To calculate the theoretical probability, we divide the number of favorable outcomes (the outcomes that meet the criteria for event E) by the total number of possible outcomes in the sample space.

This ratio represents the probability of event E occurring.

For example, if we have a fair six-sided die and we want to calculate the theoretical probability of rolling a 3, there is only one favorable outcome (rolling a 3) out of six possible outcomes (numbers 1 to 6).

Therefore, the theoretical probability of rolling a 3 is 1/6 or approximately 0.1667.

It's important to note that theoretical probability assumes ideal conditions and equal likelihood of all outcomes, which may not always reflect the real-world situation.

In practice, empirical probability based on observed frequencies is often used when actual data is available.

In summary, the theoretical probability of event E is the ratio of the number of favorable outcomes to the total number of possible outcomes in the sample space, providing a mathematical estimate of the likelihood of event E occurring.

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Answer:

{c,d,e}

Solution,

P n Q n R

={a,b,c,d,e} n { a,c,e,d,t} n {t,d,c,b,e}

={c,d,e}

In case of intersection,

we have to list the common elements which are present in all sets.

Hope it helps

Good luck on your assignment

Answer:

Step-by-step explanation:

when it says to list the intersection ,

we have to list the letters which are present in all the sets.

intersection = P n Q n R

Let's list the set now.

P n Q n R. = { c , d , e}

hope this helps

brainliest appreciated

good luck! have a nice day!

Notice that

Then, the factors of both quantities are:

and

Then, the GCF is 5x^2

Answer:

at 3

Step-by-step explanation:

because iin a number line we have positives and negatives if rlR is at nine then S is at 3

The value of the union of sets A and B is, P(A ∪ B) is 0.64.

The union of two sets means the total elements in both the sets combined.

Given: sets P(A) = 0.38, P(B) = 0.83, and  intersection P(A ∩ B) = 0.57

We need to find the union of P(A ∪ B).

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

Let us substitute the given values in the formula.

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

=0.38+0.83-0.57

=1.21-0.57

=0.64

Therefore, the value of union of sets P(A ∪ B) is 0.64.

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Answer:

sq rt of 32 units

Step-by-step explanation:

use the pythagorean theorem:

4^2 + 4^2 = c^2

16 + 16 = c^2

32 = c^2

sq rt of 32 = c

The length of the hypotenuse of a right triangle is 4√2.

The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.

Given:

P= 4 units, B= 4 units

Now, using Pythagoras theorem

H² = P² + B²

H² = 4² + 4²

H²= 16+ 16

H² =32

H= √32

H= 4√2

Hence, the Hypotenuse is 4√2.

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Answer:

24 g

Step-by-step explanation:

60/100x40

2400/100

24

Answer:

ur correct

Step-by-step explanation:

if ∠N and ∠Y are the same then we know the missing angle is 30.°  

30

Step-by-step explanation:

do angle sum property

x + z + y = 180

60 + 90 + y = 180

150 + y = 180

y = 180-150

y = 30

Hence, there are 725,760 ways to seat the ten people together in a row, taking into account the two individuals who insist on sitting side-by-side.

If two of the ten people insist on sitting side-by-side, we can consider them as a single entity or a pair. So, essentially, we have nine entities (including the pair) to be seated in a row.

The number of ways to arrange these nine entities in a row is 9!, which is the factorial of 9.

However, within the pair, the two individuals can be arranged in 2! = 2 ways.

Therefore, the total number of ways to seat the ten people together, considering the pair as one entity, is 9! * 2!.

Simplifying this expression:

9! * 2! = 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 * 2 = 725,760

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Solution

For this case we know that one base angle is 67.5º

Then the other base angle is 67.5º

Then we can find the vertex angle like this:

180 - 67.5- 67.5= 45º

Then the answer for this case is:

45º

Answer:

132 cm²

Step-by-step explanation:

To find the area of the figure, start by dividing the figure into smaller rectangles.

Area of figure

= area of shaded rectangle +area of unshaded rectangle

\(\textcolor{steelblue}{\text{Area of rectangle= length ×breadth}}\)

Shaded rectangle

Length= 4 cm

Breadth= 6 cm

Area

= 4(6)

= 24 cm²

Unshaded rectangle

Length= 9 cm

Breadth= 12 cm

Area

= 9(12)

= 108 cm²

After finding the area of each rectangle, we can add the two areas together to obtain the total area of the figure.

Area of figure

= 108 +24

= 132 cm²

Answer:

17in, 49in, 35in

Step-by-step explanation:

I did this in my RSM homwork and it is correct.

First, I added the two inches shorter to the 101, then subtracted 1 longer and got 102.

then divide 102 by how many second lengths, 6. so 102 ÷ 6 = 17

17 is the second length.

3x17-2=49 (another length)

2x17+1=35 (last length)

and there is your answer!

First side : 49

Second side : 17

Third side : 35

If triangle has sides a, b, c , then the perimeter of that triangle will be P= a +b +c.

Now, according to the question

Let  second side be (b) = x unit

then, First side will be  (a)= 3x-2 unit

and Third side will be  (c)= 2x + 1 unit

since , perimeter is 101

P = a + b + c

x + 3x -2 + 2x + 1 = 101

6x - 1 = 101

x= 17

hence , b = 17 unit

a= 3*17 - 2 =49 unit

c = 2*17 +1 = 35 unit

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Lucy has $7 less than Kristine and $5 more than Nina together, the three have $35. Lucy has $11.

Let's denote the amount of money that Kristine has as K, the amount of money that Lucy has as L, and the amount of money that Nina has as N.

According to the given information, we can form two equations:

Lucy has $7 less than Kristine: L = K - 7

Lucy has $5 more than Nina: L = N + 5

We also know that the three of them have a total of $35: K + L + N = 35

We can solve this system of equations to find the values of K, L, and N.

Substituting equation 1 into equation 3, we get:

K + (K - 7) + N = 35

2K - 7 + N = 35

Substituting equation 2 into the above equation, we get:

2K - 7 + (L - 5) = 35

2K + L - 12 = 35

Since Lucy has $7 less than Kristine (equation 1), we can substitute K - 7 for L in the above equation:

2K + (K - 7) - 12 = 35

3K - 19 = 35

Adding 19 to both sides:

3K = 54

Dividing both sides by 3:

K = 18

Now we can substitute the value of K into equation 1 to find L:

L = K - 7

L = 18 - 7

L = 11

Finally, we can find the value of N by substituting the values of K and L into equation 3:

K + L + N = 35

18 + 11 + N = 35

N = 35 - 18 - 11

N = 6

Therefore, Lucy has $11.

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Answer:

x = 19

Step-by-step explanation:

1 = x - 18

1 + 18 = x

x = 19

Answer:

1

Step-by-step explanation:

1)( then remove the parenthesis and came up with 1.

Answer:

√m^4 + n^4 +2m²n²

Step-by-step explanation:

Given the following

Opposite= m²-n²

adjacent = 2mn

Using pythagoras theorem

hyp² =  (m²-n²)²+(2mn)²

hyp² = m^4-2m²n²+n^4+4m²n²

hyp² = m^4 + n^4 +2m²n²

hyp = √m^4 + n^4 +2m²n²

hence the required expression is  √m^4 + n^4 +2m²n²

To find f(g(x)), substitute g(x) into f(x). Simplifying gives f(g(x)) = log6(36g(x)). For range of y in f(x) + g(x), Take possible values . Since log6(36x) is defined for x > 0, and 6 is positive, the range of y is (0, ∞).

a) To find f(g(x)), we substitute g(x) into f(x):

f(g(x)) = f(6x) = log6(36(6x)) = log6(216x) = log6(6^3x) = 3log6(6x) = 3(log6(6) + log6(x)) = 3(1 + log6(x)) = 3 + 3log6(x).

Thus, f(g(x)) simplifies to 3 + 3log6(x).

(b) To find the range of y in f(x) + g(x), we need to consider the possible values of f(x) and g(x). Since log6(36x) is defined for x > 0, and 6* is always positive, the range of f(x) is (0, ∞). Similarly, g(x) = 6* is always positive, so the range of g(x) is also (0, ∞).When we add f(x) and g(x), we are adding two positive functions, resulting in values greater than 0. Therefore, the range of y in f(x) + g(x) is (0, ∞).

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For confidence interval: support of the association rule A to B is 0.5 and the confidence of the association rule A to B is 0.5.

For Support and confidence of the association rule A - B

To determine the support and the confidence of the association rule A → B, where A = {1, }, B = {1}, we use the formulas given below:

Support(A → B) = frequency of (A, B) / N

Confidence(A → B) = frequency of (A, B) / frequency of A

where N is the number of transactions in the database.

To find the frequency of (A, B) and the frequency of A.

Thus Frequency of (A, B) = 1

Since there is only one transaction in the database where both A and B occur, the frequency of (A, B) is 1.

Frequency of A = 2

The itemset {1, } occurs in two transactions T₁ and T₂.

Hence, the frequency of A is 2.

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Magnification if lens #2 were absent: M1 = 1

Properties of the final image: real, enlarged, and upright.

To determine the magnification if lens #2 were absent (i.e., the magnification of lens #1), we need to consider the properties of the lenses in combination.

Given the options for the magnification of lens #1, we can eliminate some options based on the properties of the final image:

real, enlarged and inverted

virtual, enlarged and upright

virtual, reduced and inverted

virtual, enlarged and inverted

real, reduced and upright

real, enlarged and upright

real, reduced and inverted

virtual, reduced and upright

Lens #2, being absent, does not contribute to the overall magnification of the system. Therefore, the magnification of the entire system is determined solely by lens #1.

From the given options, we can see that the only possible choice for the magnification of lens #1 that matches the properties of the final image is:

M1 = 1 (real, enlarged, and upright)

As for the properties of the final image for the present two-lens problem, we can conclude:

real, enlarged, and upright

Therefore, the correct answers are:

Magnification if lens #2 were absent: M1 = 1

Properties of the final image: real, enlarged, and upright.

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The amount of time Carl represent is 25-m on the problems.

The statement "Davis spent 25 minutes working on math problems. Carl worked on math problems for m fewer minutes" means that Carl spent some amount of time working on math problems, but that amount is m minutes less than what Davis spent.

To represent the amount of time Carl worked on math problems, we can use the variable X. We know that X is equal to the amount of time Carl worked on math problems, and that X is equal to 25 minus m.

This is because Davis spent 25 minutes on math problems, and Carl worked on them for m fewer minutes. So if we subtract m from 25, we get the amount of time Carl worked on math problems.

Therefore, the equation X = 25 - m represents the amount of time Carl worked on math problems, where X is the amount of time in minutes and m is the number of minutes Carl worked less than Davis.

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Answer:

-23

Step-by-step explanation:

16 x 1/4^2 - 4 x 6 = -23

The correct statement is c. The Adjusted R-squared is a measure used in multiple regression analysis that is between 0 and 1. It is different from the R-squared value in simple linear regression.

The Adjusted R-squared can decrease if the addition of another X regressor does not sufficiently lower the sum of squared residuals (SSR) relative to the impact of increasing the number of predictors (k). It measures the proportion of the variance explained by the predictors, adjusted for the number of predictors and the sample size, rather than the ratio of the sum of squared residuals to the total sum of squares. It provides a measure of how well the regression model fits the data, and it ranges between 0 and 1. A value closer to 1 indicates that a higher proportion of the variance in the dependent variable is explained by the predictors.

Adding another X regressor to the multiple regression model can impact the Adjusted R-squared. If the additional regressor does not significantly contribute to reducing the sum of squared residuals (SSR) relative to the increase in the number of predictors (k), the Adjusted R-squared can decrease. This means that the added regressor does not improve the model's ability to explain the variance in the dependent variable adequately.

However, the Adjusted R-squared does not directly measure the ratio of the sum of squared residuals to the total sum of squares. Instead, it represents the proportion of the variance explained by the predictors, adjusted for the number of predictors and the sample size. It penalizes models with a large number of predictors that may overfit the data, thereby providing a more reliable measure of the model's goodness of fit.

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The life expectancy will reach 75 years old in the year 1970.

We have,

Let's start by defining the variables:

L = life expectancy in years

t = time in years since 1900

We know that from 1900 to 1960, life expectancy increased at a constant rate of 0.401 years per year.

So, we can write the following equation to represent the relationship between L and t:

L = 0.401t + b

where b is the life expectancy in 1900.

To find b, we can use the fact that the life expectancy in 1900 was around 47 years old.

b = 47

So, the equation becomes:

L = 0.401t + 47

We also know that in 1942, the life expectancy was 62.9 years old.

So, we can use this information to find the value of t in 1942:

62.9 = 0.401t + 47

Solving for t, we get:

t = (62.9 - 47) / 0.401 = 39.15

In 1942,

t = 39.15.

To find the year when the life expectancy reaches 75 years old, we can plug in L = 75 into the equation and solve for t:

75 = 0.401t + 47

Solving for t.

t = (75 - 47) / 0.401 = 69.82

So, the life expectancy will reach 75 years old in the year:

1900 + 69.82 = 1969.82

Therefore,

The life expectancy will reach 75 years old in the year 1970.

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so,  -11-\(\sqrt{2}\)i and 3 + 4i are roots of polynomial function f(x) so 11 + \(\sqrt{2}\)i and

3 - 4i are roots of f(x)  

Therefore, option D is correct

Polynomial function:

A polynomial function, in general, is also stated as a polynomial or polynomial expression, defined by its degree. The degree of any polynomial is the highest power present in it.

given that

Patricia is studying a polynomial function f(x). three given roots of f(x) are

-11-\(\sqrt{2}\)i , 3 + 4i and 10 . Patricia concludes that f(x) must be a polynomial with degree 4.

so -11-\(\sqrt{2}\)i and 3 + 4i are roots of polynomial function f(x) so 11 + \(\sqrt{2}\)i and

3 - 4i are roots of f(x)  

Therefore, option D is correct

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