Ladies dress blouses are on sale for $18.00. That price is after a 25%
discount. How much money do shoppers save on each blouse they buy?

Answer:

r= 4

Step-by-step explanation:

\(\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }\)

where (x₁, y₁) is the 1st coordinate and (x₂, y₂) is the second coordinate

\( \frac{3}{2} = \frac{r - ( - 5)}{10 - 4} \)

\( \frac{3}{2} = \frac{r + 5}{6} \)

Cross multiply:

2(r +5)= 3(6)

Expand:

2(r) +2(5)= 18

2r +10= 18

-10 on both sides:

2r= 18 -10

2r= 8

Divide both sides by 2:

r= 8 ÷2

r= 4

Answer:

m

Step-by-step explanation:

To find a polynomial function f(x) of least degree having only real coefficients and zeros of 5 and 2-i, we know that the complex conjugate of 2-i, which is 2+i, must also be a zero. This is because complex zeros of polynomials always come in conjugate pairs.

So, we can start by using the factored form of a polynomial:

f(x) = a(x - r1)(x - r2)(x - r3)...

where a is a constant and r1, r2, r3, etc. are the zeros of the polynomial. In this case, we have:

f(x) = a(x - 5)(x - (2-i))(x - (2+i))

Multiplying out the factors, we get:

f(x) = a(x - 5)((x - 2) - i)((x - 2) + i)
f(x) = a(x - 5)((x - 2)^2 - i^2)
f(x) = a(x - 5)((x - 2)^2 + 1)

To make sure that f(x) only has real coefficients, we need to get rid of the complex i term. We can do this by multiplying out the squared term and using the fact that i^2 = -1:

f(x) = a(x - 5)((x^2 - 4x + 4) + 1)
f(x) = a(x - 5)(x^2 - 4x + 5)

Now, we just need to find the value of a that makes the degree of f(x) as small as possible. We know that the degree of a polynomial is determined by the highest power of x that appears, so we need to expand the expression and simplify to find the degree:

f(x) = a(x^3 - 9x^2 + 24x - 25)
Degree of f(x) = 3

Since we want the least degree possible, we want the coefficient of the x^3 term to be 1. So, we can choose a = 1:

f(x) = (x - 5)(x^2 - 4x + 5)
Degree of f(x) = 3

Therefore, the polynomial function f(x) of least degree having only real coefficients and zeros of 5 and 2-i is:

f(x) = (x - 5)(x^2 - 4x + 5)
To find a polynomial function f(x) of least degree with real coefficients and zeros of 5 and 2-i, we need to remember that if a polynomial has real coefficients and has a complex zero (in this case, 2-i), its conjugate (2+i) is also a zero.

Step 1: Identify the zeros
Zeros are: 5, 2-i, and 2+i (including the conjugate)

Step 2: Create factors from zeros
Factors are: (x-5), (x-(2-i)), and (x-(2+i))

Step 3: Simplify the factors
Simplified factors are: (x-5), (x-2+i), and (x-2-i)

Step 4: Multiply the factors together
f(x) = (x-5) * (x-2+i) * (x-2-i)

Step 5: Expand the polynomial
f(x) = (x-5) * [(x-2)^2 - (i)^2] (by using (a+b)(a-b) = a^2 - b^2 formula)
f(x) = (x-5) * [(x-2)^2 - (-1)] (since i^2 = -1)
f(x) = (x-5) * [(x-2)^2 + 1]

Now we have a polynomial function f(x) of least degree with real coefficients and zeros of 5, 2-i, and 2+i:
f(x) = (x-5) * [(x-2)^2 + 1]

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Answer: 11 percent

Step-by-step explanation:

Answer:

24%

Step-by-step explanation:

Answer:

11.16in^2

Step-by-step explanation:

Area of a sector = theta/360 * πr²

Area of a sector = 80/360 * 3.14*4²

Area of a sector = 8/36 * 50.24

Area of a sector  = 401.92/36

Area of a sector = 11.16in^2

Hence the Area of the sector is 11.16in^2

Answer:

11.16 in²

Step-by-step explanation:

I took the test

Solution:

If we choose a usual coordinate axis, an object going down would be traveling a negative distance, so a possible answer would be:

C. skiing 161 ft down a mountain.

On the other hand, An expense of money involves a waste of money, which is negative. So another possible answer would be:

D. spending $spending $161 on vacation.

Then, we can conclude that the correct answer would be:

C. skiing 161 ft down a mountain.

D. spending $spending $161 on vacation.

Answer:

Either (A.) or (D.)

Step-by-step explanation:

not quite sure

The selling price of the bicycle, with a wholesale cost of $98.75 and a 33.3% markup, is approximately $131.59.

To find the selling price of the bicycle, we need to calculate the markup amount and add it to the wholesale cost. The markup amount can be calculated as a percentage of the wholesale cost. In this case, the markup percentage is 33.3% of $98.75.

Markup amount = 33.3% of $98.75

= 0.333 * $98.75

= $32.84 (rounded to the nearest cent)

Now, to find the selling price, we add the markup amount to the wholesale cost:

Selling price = Wholesale cost + Markup amount

Selling price = $98.75 + $32.84

= $131.59 (rounded to the nearest cent)

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Answer:

The True Statements

The sale's price of the items was $41.40.

Mrs. Bolden payed $2.76 on her purchase.

Altogether, Mrs. Bolden payed $43.88 on the shirts and flip-flops.

Step-by-step explanation:

$19 + $19 + $8 = $46

10% of $46 = $4.60

$46 - $4.60 = $41.40

6% of $46 = $2.76

+$2.76 - $4.60 = -$2.12

$46 - $2.12 = $43.88

Answer:

3 1/5

Step-by-step explanation:

(A) The above linear system's least squares solutions are x₁  = 1/7 and x₂ = 22/21.

(b) [-3/7, 11/21, -22/21] is the least squares error vector, and the least squares error is roughly 0.8571.

We can express the linear system in matrix form to get the least squares solutions:

A * X = B

Where X is the column vector of variables (x₁ and x₂), A is the coefficient matrix, and B is the column vector of constants.

The following is a rewrite of the provided linear system:

| 3 -1 | | x1 | | 4 |

| 1 -2 | * | x2 | = | 3 |

| 2 3 | | 2 |

Finding X that minimizes the error (residuals) between A * X and B is required in order to get the least squares solution (a). The standard equation can be solved to obtain the least squares answer:

A^T * A * X = A^T * B

Where A^T is the transpose of matrix A.

First, let's calculate A^T * A:

= | 3 1 2 | | 3 -1 | | 33 + 11 + 22 3(-1) + 1*(-2) + 2*3 |

= | 1 -2 |

= | 2 3 |

= | 14 -4 |

= | -4 14 |

Next, let's calculate A^T * B:

= | 3 1 2 | | 4 |

= | 3 |

= | 2 |

= | 17 |

= | 7 |

Let's now resolve the standard equation:

| 14 -4 | | x1 | | 17 |

| -4 14 | * | x2 | = | 7 |

Simplifying, we have:

14×1 - 4×2 = 17

-4×1 + 14×2 = 7

Solving this system of equations, we find:

x1 = 1

x2 = 2

So, the least squares solution of the given linear system is x1 = 1 and x2 = 2.

Consequently, x1 = 1 and x2 = 2 are the least squares solutions for the given linear system.

(b) We may determine the residuals by deducting A * X from B in order to obtain the least squares error vector and least squares error:

Residuals = B - A * X

Substituting the values, we have:

| 4 | | 3 -1 | | 1 |

| 3 | - | 1 -2 | * | 2 |

| 2 | | 2 3 | |

| 4 | | 3 - (-1) | | 1 | | 5 |

| 3 | - | 1 - (-2) | * | 2 | = | 2 |

| 2 | | 2 - 3 | | -1 |

The least squares error vector is therefore [5, 2, -1].

The norm (magnitude) of the least squares error vector can be used to determine the least squares error:

Least squares error = ||Residuals||

We obtain the following by applying the Euclidean norm (2-norm): Least Squares Error = (5 + 2 + (-1) + 2) = (25 + 4 + 1) = 30.

As a result, the least squares error is roughly 30.

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The transformation of function and their algebraic representation are shown below:

From it we notice that to reflect the function about the y-axis we need to change the sign of the variable, then we have:

Therefore, the expression of g is:

Answer:

108

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

24:40

Step-by-step explanation:

3:5

This means there are 8 divisions altogether - 8 parts to be split (3+5=8)

64 / 8 = 8

8x3 = 24

8x5 = 40

£24:£40

Hope this makes sense!

The statement is false because adding a vector to a set of vectors can increase its span, but the new span is not necessarily the same as the original span.

The statement is false. To prove this, consider three vectors u1, u2 and u3 that span R3, and a vector u4 that is not a linear combination of

u1, u2 and u3.

The span of

{u1, u2, u3, u4}

will be a subset of the span of

{u1, u2, u3}.

This means that the span of

{u1, u2, u3, u4}

will contain all the vectors that the span of {u1, u2, u3} contains, plus the vector u4. However, it does not necessarily mean that the span of

{u1, u2, u3, u4} will be the same as the span of {u1, u2, u3},

as there may be other vectors that are in the span of

{u1, u2, u3, u4}

but not in the span of {u1, u2, u3}. Hence, the statement is false.

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The complete question is

Determine if the statement is true or false, and justify your answer. If (u1, u2, u3) spans R3, then so does (u1, u2, uz, u). O False. Consider u4 =0 True, the span of a set of vectors can only increase (with respect to set containment) when adding a vector to the set. O True, since the span of {ul, u2, u3, u4} is a subset of the span of {u1, u2, us), O False. Consider u4 = 0. The span of {u1, u2, u3, u4} is a subset of the span of {u1, u2, us}, but the span of {u1, u2, u3, u4} is not the same as the span of {u1, u2, us}.

The required answer is the limit of (-5)^∞ is not well-defined, that the limit Does Not Exist

To find the first five terms of the sequence, we simply substitute n=1,2,3,4,5 into the formula given:

a1=(1-6(1)+5)^1=-1
a2=(1-6(2)+5)^2=0
a3=(1-6(3)+5)^3=27
a4=(1-6(4)+5)^4=256
a5=(1-6(5)+5)^5=3125

To determine whether the sequence converges, we take the limit as n approaches infinity:

limn→[infinity](1−6n+5)n=limn→[infinity](−5n+6)n

We can apply L' Hopital's rule to evaluate this limit:

limn→[infinity](−5n+6)n=limn→[infinity](−5)(−5n+6)n−1=limn→[infinity]−5(−5+6n−2)(n−1)n−2

This limit evaluates to -5, which is a finite number, so the sequence converges.
 If such a limit exists, the sequence is called convergent.A sequence that does not converge is said to be divergent. The limit of a sequence is said to be the fundamental notion on which the whole of mathematical analysis ultimately rests

To find the limit of the sequence, we simply take the limit of the formula for an as n approaches infinity:

limn→[infinity](1−6n+5)n=limn→[infinity](−5n+6)n=(-5)^∞

The limit of (-5)^∞ is not well-defined, so we say that the limit Does Not Exist (DNE).
To find the first five terms of the sequence an = (1 - 6n + 5)n, we'll plug in the values n = 1, 2, 3, 4, and 5.

a1 = (1 - 6(1) + 5)(1) = (0)(1) = 0
a2 = (1 - 6(2) + 5)(2) = (-1)(2) = -2
a3 = (1 - 6(3) + 5)(3) = (-2)(3) = -6
a4 = (1 - 6(4) + 5)(4) = (-3)(4) = -12
a5 = (1 - 6(5) + 5)(5) = (-4)(5) = -20

Now, let's examine the limit as n approaches infinity:

A sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members (also called elements, or terms). The number of elements (possibly infinite) is called the length of the sequence. Unlike a set, the same elements can appear multiple times at different positions in a sequence, and unlike a set, the order does matter. Formally, a sequence can be defined as a function from natural numbers (the positions of elements in the sequence) to the elements at each position. The notion of a sequence can be generalized to an indexed family, defined as a function from an arbitrary index set.

lim(n→∞)(1 - 6n + 5)n

Since the term (1 - 6n + 5) keeps getting smaller (more negative) as n increases, and the term n keeps getting larger, their product will continue to decrease without bound. Therefore, the limit does not exist.

Your answer:
a1 = 0
a2 = -2
a3 = -6
a4 = -12
a5 = -20
lim(n→∞)(1 - 6n + 5)n = DNE

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Answer:

$9

Step-by-step explanation:

Since Anna is saving 15%, she is paying 85%. So you find 85% of $60 by multiplying 60*0.85=51.

Anna pays $51 for the bag. But to find out how much she saved, you do 60-51=9.

Answer:

i think its 6 and 8

Step-by-step explanation:

sorry if i get it wrong

can you tell me if it is right or wrong

Answer:

30

Step-by-step explanation:

Answer:

First Of this is split up cayse the first question is already answered but 2+4+4+5+6+1+8=30

Step-by-step explanation:

2+4=6/ 6+4=10/10+5=15/15+6=21/21+1=22+8=30 So that's your answer.

Answer:

I think x equals 7.5

Step-by-step explanation:

Please let me know if this was correct or what you were looking for. Thanks!

To prove the opposite, we need to show that if G is not a pseudorandom generator (PRG), then Construction 3.17 cannot be EAV-secure.

Assume that G is not a PRG, which means it fails to expand the seed sufficiently. Let's suppose that G is computationally indistinguishable from a truly random function on its domain, but it does not meet the requirements of a PRG.

Now, consider the private-key encryption scheme Π described in Construction 3.17 using G as the pseudorandom generator. If G is not a PRG, it means that its output is not sufficiently pseudorandom and can potentially be distinguished from a random string.

Given this scenario, an adversary A could exploit the distinguishability of G's output and devise an attack to break the security of the encryption scheme Π. The adversary could potentially gain information about the plaintext by analyzing the ciphertext and the output of G.

Therefore, if G is not a PRG, it implies that Construction 3.17 cannot provide EAV-security, as it would be vulnerable to attacks by distinguishing the output of G from random strings. This contradicts Theorem 3.18, which states that if G is a PRG, then Construction 3.17 achieves indistinguishable encryptions.

Hence, by proving the opposite, we conclude that if G is not a PRG, then Construction 3.17 cannot be EAV-secure.

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The algebraic expression representing the description given is 5w + 2w

We can rewrite the description as Gerald earns $5 each time he mows a lawn

Let amount earned for lawn mowing = $5Let amount earned for trimming = $2

We can then rewrite the description as Gerald earns $5 each time he mows a lawn. He mows his neighbor's lawn each week.

He also earned an additional $2 for trimming trees one week.

An algebraic expression for the description

Number of weeks = w

Amount earned for any given number of weeks is ;

Amount earned= 5w + 2w = 7w

Hence, the algebraic expression for the description is 5w + 2w

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Answer:

5/7

Step-by-step explanation:

hope this helps :)

4 2 add y 2 root that

it's pretty easy and thanks for the high points ur welcome ur in the matrix kid

Answer:

Point Q is further from A than point P, therefore, they are not the same point

Step-by-step explanation:

The given information are;

Point P partitions the directed segment from A → B into the ratio of 1:3

Point Q partitions the directed segment from B → A into the ratio of 1:3

We note that the properties of a directed segment are that it has a length and direction with a defined starting or initial point.

Hence the two segments when arranged in the same direction are;

A B and B A

Hence point P is at a the point 1/(1 + 3) or 1/4 of AB or 1/4 times the length of AB from A

Point Q is at a the point  1/4 of B/A or 1/4 times the length of AB from B which is 3/4 times the length of AB from A

Therefore, point Q is further from A than point P which means they are not the same point.

Answer:

No, P is One-fourth the distance from A to B, and Q is One-fourth the distance from B to A.

Step-by-step explanation:

Answer:

(5,-1/2)

Step-by-step explanation:

Midpoint formula is x1 +x2 /2 is equal to the x-value, y2+y1 /2 is the y-value. Simply plug it into the formula to get the answer

If A and B are independent variables, P(A and B) =0.12. Therefore, option B is the correct answer.

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

Given that, p(a)=0.60 and p(b)=0.20.

If A and B are independent variables,

P(A and B) =P(P∩B)= P(A) × P(B)

Here, P(P∩B)=0.60×0.20

= 0.12

Therefore, option B is the correct answer.

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