A sweater that originally cost $40 is on sale for 10 percent off. What is the amount of the discount?

The homogeneous linear ODE

\(y^{(4)} + y''' + y'' = 0\)

has characteristic equation

\(r^4 + r^3 + r^2 = r^2 (r^2 + r + 1) = 0\)

with a double root at \(r=0\) and two complex roots

\(r^2 + r + 1 = 0 \implies r = -\dfrac{1 \pm i\,\sqrt3}2\)

Hence the characteristic solution is

\(y = C_1 e^{0x} + C_2x e^{0x} + C_3 e^{((-1/2)-i(\sqrt3/2))x} + C_4 e^{((-1/2)+i(\sqrt3/2))x}\)

\(y = C_1 + C_2x \\\\ ~~~~~~~~~~ + C_3 e^{-x/2} \left(\cos\left(\dfrac{\sqrt3}2x\right) - i\, \sin\left(\dfrac{\sqrt3}2x\right)\right) \\\\ ~~~~~~~~~~ + C_4 e^{-x/2} \left(\cos\left(\dfrac{\sqrt3}2x\right) + i\,\sin\left(\dfrac{\sqrt3}2x\right)\right)\)

\(y = C_1 + C_2x + C_3 e^{-x/2} \cos\left(\dfrac{\sqrt3}2x\right) + C_4 e^{-x/2} \sin\left(\dfrac{\sqrt3}2x\right)\)

Answer: 7x - 1

Step-by-step explanation: use the distributive property to multiply 3 by x + 2. subtract 7 from 6 to get -1. Combine 3x and 4x to get 7x.

Answer: For 3 Batches, 6 butter & 9 flour

For 5 Batches, 10 butter & 15 flour

Step-by-step explanation:

1 Batch = 2:3

So, whatever we times up by in batches we can do the same to the ingredients.

1 batch = 2:3

multiply 3

3 batches = 6:9

and so on…

For 3 batches 6 ounces of butter and 9 ounces of flour are required for 5 batches 10 ounces of butter and 15 ounces of flour are required.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other.

Given that for one batch of cookies, the ratio of ounces of butter to ounces of flour is 2 to 3. The proportions of butter and flour will be calculated as:-

3 batches = 2 Butter : 3 Flour = 6 Butter : 9 Flour

5 batches = 2 Butter : 3 Flour = 10 Butter : 15 Flour

Therefore, for 3 batches 6 ounces of butter and 9 ounces of flour are required for 5 batches 10 ounces of butter and 15 ounces of flour are required.

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Therefore, the intersection of the arcs that Victor drew must be the midpoint of segment XY.

the midpoint is the point that is exactly halfway between two other points. It is the point that divides the line segment into two equal halves.

The midpoint of a line segment can be found by taking the average of the x-coordinates and the y-coordinates of the two endpoints of the segment. For example, if the endpoints of a line segment are (x1, y1) and (x2, y2), then the midpoint of the segment is\(((x_1 + x_2)/2,(y_1+y_2)/2).\)

by the question.

If Victor drew an arc centered at X and then drew an arc of the same radius centered at Y, the intersection of these arcs will be equidistant from X and Y. This is because the points on the arcs are all a fixed distance away from their respective centers.

Since Victor is drawing a perpendicular segment to XY, the intersection of the arcs he drew will be the midpoint of XY. This is because the perpendicular segment will divide XY into two equal segments, and the intersection of the arcs is equidistant from X and Y.

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The lifting force if the speed is 220 miles per hour is F' = 708.53 N.

The force of light, or simply light, is the sum of all forces on an object that cause the object to move perpendicular to the direction of flow.

The most common type of lift is the wing lift. But there are many other common uses, such as propellers on airplanes and ships, rotors on helicopters, fan blades, sails on sailboats, and wind turbines.

We have,

The lifting force, F, exerted on an airplane wing varies jointly as the area, A, of the wing's surface and the square of the plane's velocity, v. It, means that,

\(F=kAv^{2}\)

Where

k is constant

If, A = 190 Ft², v = 220 mph, F = 950 pounds

Now, find k first from the above data. So,

    \(k=\frac{F}{Av^{2} }\)

⇒ \(k=\frac{950}{190* (220)^2}\)

⇒ k = 0.0001033

It is required to find the lifting force on the wing if the plane slows down to 190 miles per hour.

Let F' is a new force. So,

    F' = 0.0001033 × 190 × (190)²

⇒ F' = 708.53 pounds.

So, the lifting force is 708.53 pounds if the plane slows down to 190 miles per hour.

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The possible values for (\overline{ab}) are: 12, 13, 21, 23, 31, 32.

And the possible values for (\overline{cd}) are: 11, 12, 13, 14, 21, 22, 23, 24, 31, 32, 33, 34.

Given the digits 1, 2, 3, 1, 2, 3, and 44 arranged to form two two-digit numbers ((\overline{ab}) and (\overline{cd})), we need to determine the possible values for (\overline{ab}) and (\overline{cd}).

To find the possible values, we need to consider the given digits and their arrangement.

We have the following digits: 1, 2, 3, 1, 2, 3, and 44.

Since we are forming two two-digit numbers, (\overline{ab}) and (\overline{cd}), we can assign the digits in the following way:

(\overline{ab}): The tens digit is represented by a, and the ones digit is represented by b.

(\overline{cd}): The tens digit is represented by c, and the ones digit is represented by d.

To find the possible values for (\overline{ab}) and (\overline{cd}), we need to consider the available digits and their arrangement.

From the given digits, we have 1, 2, 3, 1, 2, 3, and 44.

To form two two-digit numbers, we need to select the appropriate digits for each place value.

The tens digit for (\overline{ab}) (represented by a) can be chosen from {1, 2, 3}.

The ones digit for (\overline{ab}) (represented by b) can also be chosen from {1, 2, 3}.

Similarly, the tens digit for (\overline{cd}) (represented by c) can also be chosen from {1, 2, 3}.

The ones digit for (\overline{cd}) (represented by d) can be chosen from {1, 2, 3, 4}.

Since the problem states that the numbers are randomly arranged, we need to consider all possible combinations of digits.

Now, let's determine the possible values for (\overline{ab}) and (\overline{cd}):

Possible values for (\overline{ab}):

(\overline{12}), (\overline{13}), (\overline{21}), (\overline{23}), (\overline{31}), (\overline{32})

Possible values for (\overline{cd}):

(\overline{11}), (\overline{12}), (\overline{13}), (\overline{14}), (\overline{21}), (\overline{22}), (\overline{23}), (\overline{24}), (\overline{31}), (\overline{32}), (\overline{33}), (\overline{34})

Please note that the number 44 counts as a single digit since it represents a two-digit number itself.

Therefore, the possible values for (\overline{ab}) are: 12, 13, 21, 23, 31, 32.

And the possible values for (\overline{cd}) are: 11, 12, 13, 14, 21, 22, 23, 24, 31, 32, 33, 34.

These are the possible combinations of two two-digit numbers that can be formed using the given digits.

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Answer:

c

Step-by-step explanation:

The red line represents the critical value, and the shaded region on the right-hand side of the red line represents the rejection region. If the calculated test statistic is greater than the critical value of z, which is 1.88 in this case, we will reject the null hypothesis.

The critical value(s) and rejection region(s) for the type of z-test with a level of significance a = 0.03 and a right-tailed test are as follows :Step 1: Determine the critical value of  zThe critical value is calculated by using the normal distribution table and the level of significance. A right-tailed test will have a critical value of zα. For a level of significance of 0.03, we will look for the z-value that corresponds to 0.03 in the normal distribution table.Critical value for a = 0.03 is z = 1.88 (approx).Step 2: Determine the Rejection Region The rejection region for a right-tailed test is defined as any z-value that is greater than the critical value. That is, if the test statistic is greater than 1.88, we reject the null hypothesis at the 0.03 level of significance, and if it is less than or equal to 1.88, we fail to reject the null hypothesis.Therefore, the rejection region for a right-tailed test with a level of significance of 0.03 is as follows:Rejection Region: Z > 1.88  OR  Z ≤ -1.88Graph: The graph for the given values will be as follows:The red line represents the critical value, and the shaded region on the right-hand side of the red line represents the rejection region. If the calculated test statistic is greater than the critical value of z, which is 1.88 in this case, we will reject the null hypothesis.

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Harley will need 125 pallets from the 625 bags of cement that he was loading

let y represent the amount of pallets Harley will need

1/5 = y/625

Cross multiply both sides

5y= 625

Divide by the coefficient of y which is 5

y= 625/5

y= 125

Hence Harley needs 125 pallets

The question is incorrect, here is the correct question

Harley is loading 625 bags of cement onto small pallets. Each pallet holds five bags how many pallets will Harley need

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We must know the following exponent rules to help us solve this question:

\(3^p=\dfrac{\sqrt[3]{9}}{3}\)

⇒ Rewrite \(\sqrt[3]{9}\) as \(9^\frac{1}{3}\):

\(3^p=\dfrac{(3^2)^\frac{1}{3}}{3}\)

⇒ Multiply:

\(3^p=\dfrac{3^\frac{2}{3}}{3}\)

⇒ Subtract:

\(3^p=3^{\frac{2}{3}-1}\)

\(p=\dfrac{2}{3}-1\\\\p=-\dfrac{1}{3}\)

\(p=-\dfrac{1}{3}\)

Null hypothesis, \(H_{0}\) P.1 = P2 (The proportion of tablets owned by men and women are equal.)

Alternative hypothesis,\(H_{0}\)  P1\(\neq\)P2 (The proportion of tablets owned by men and women are not equal.)

Sample proportion for men who own tablets  ≈0.433

Sample proportion for women who own tablets ≈0.466

p value of the test  is 0.3320.

Test whether the survey results provide evidence of a difference in the proportion owning a tablet between men and women.

Let p, be the proportion of all men who own tablets and p, be the proportion of all women who own tablets.

Null hypothesis, \(H_{0}\) P.1 = P2 (The proportion of tablets owned by men and women are equal.)

Alternative hypothesis,\(H_{0}\)  P1\(\neq\)P2 (The proportion of tablets owned by men and women are not equal.)

The notations for the sample statistic are  p p1 p2

Pooled proportion p = \(\frac{x_{1}+x_{2} }{n_{1}+n_{2} }\)= 197+235/455+504

                                               ≈ 0.45

Sample proportion for men who own tablets,

                               p1 = \(\frac{x_{1} }{n_{1} }\)= 197/455

                                           ≈0.433

Sample proportion for women who own tablets,

                              p2 = \(\frac{x_{2} }{n_{2} }\) = 235/506

                                          ≈0.466

Since p1<p2  women group has higher tablet ownership.

Sample statistic, p1-p2

                          = 0.433-0.466

p value of the test  is 0.3320.

In mathematics, statistics deals with the study of surveys and reports of numerical data. For questions, we need to define a hypothesis. In general, there are two types of hypotheses. One is the null hypothesis and the other is the alternative hypothesis.

In probability and statistics, the null hypothesis is the general statement or default state that  zero  or nothing will happen. For example, there is no association between groups or no association between two measured events. Here, a hypothesis is generally assumed to be true until  other evidence is presented to disprove the hypothesis.

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Answer:

They would need 24 pints of chocolate to make 6 boxes of candy

Omar should go back and regroup the terms in step 1 as (3x^3 – 15x^2) – (4x + 20). In step 2, Omar should factor only out of the first expression.

When factoring polynomials, it is essential to look for common factors that can be factored out. In this case, Omar noticed that there are no common factors in the given polynomial. To proceed, he should go back and regroup the terms in step 1 as (3x^3 – 15x^2) – (4x + 20).

This regrouping allows Omar to factor out of the first expression, which can potentially lead to further factoring or simplification. However, without additional information about the polynomial or any specific instructions, it is not possible to determine the exact steps Omar should take after this point.

In summary, regrouping the terms and factoring out of the first expression is a reasonable next step for Omar to explore the polynomial further.

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Answer:

there is no more number than one

Step-by-step explanation:

Answer:

$13.50

Step-by-step explanation:

The total is $103.50.

Answer:

999,960

Step-by-step explanation:

let x be a multiple of 120

120x ≤ 999,999

999,999 / 120 = 8333.325

8333 ≤ x ≤ 8334

8333(120) = 999,960

8334(1200) = 1,000,080  this is a 7-digit number

Therefore, the largest 6-digit number that is exactly divisible by 120 is 999,960

Answer:

the thired one

Step-by-step explanation:

Answer:

option D. 10

Step-by-step explanation:

\(\frac{34}{85} = \frac{4}{x}\\\\34 \times x = 4 \times 85\\\\x = \frac{340}{34} = 10\)

Answer:

x = 10

Step-by-step explanation:

\( \dfrac{34}{85} = \dfrac{4}{x} \)

Cross multiply.

34x = 4 × 85

34x = 340

Divide both sides by 34.

x = 10

Answer:

The slope-intercept form is simply the way of writing the equation of a line so that the slope (steepness) and y-intercept (where the line crosses the vertical y-axis) are immediately apparent. Often, this form is called y = mx + b form. This form of a line is one of the most commonly used in algebra classes.

Answer:

okay so IM not 100 percent sure but I think its 64 = 92

Answer:

well I'm not gonna explain it but

#1 is C or the 3rd one (DOMIAN)

#2 is B or the second one (RANGE)

Answer:

DOMAIN OF THE FUNCTION :-

all real numbers

RANGE :-

all real numbers greater than or equal to - 2

as we the graph's vertex is at -2 so basically -2 is the lowest value of the function.

Answer:

The variance of Y is given by the expression (2/5) * y^(5/2) - y.

Step-by-step explanation:

To calculate the variance of a continuous random variable, we use the formula:

Var(X) = E[X²] - (E[X])²

Let's start with calculating var(X):

The probability density function (PDF) of X is given as:

f(x) = 2x² for 0 < x ≤ 2, and f(x) = 0 for other values.

To calculate the variance of X, we need to find the expected value E[X] and the expected value of the square E[X²].

First, let's calculate E[X]:

E[X] = ∫(x * f(x)) dx

For 0 < x ≤ 2, f(x) = 2x²:

E[X] = ∫(x * 2x²) dx

= ∫(2x³) dx

= [1/2 * x⁴] from 0 to 2

= 1/2 * (2⁴ - 0⁴)

= 8/2

= 4

Next, let's calculate E[X²]:

E[X²] = ∫(x² * f(x)) dx

For 0 < x ≤ 2, f(x) = 2x²:

E[X²] = ∫(x² * 2x²) dx

= ∫(2x⁴) dx

= [1/2 * x⁵] from 0 to 2

= 1/2 * (2⁵ - 0⁵)

= 16/2

= 8

Now, we can calculate var(X):

Var(X) = E[X²] - (E[X])²

= 8 - (4)²

= 8 - 16

= -8

However, variance cannot be negative, so the variance of X is not meaningful in this case.

Moving on to var(Y):

The probability density function (PDF) of Y is given as:

f(y) = 1/(2√y) for 0 ≤ y ≤ 1, and f(y) = 0 for other values.

To calculate the variance of Y, we again need to find the expected value E[Y] and the expected value of the square E[Y²].

First, let's calculate E[Y]:

E[Y] = ∫(y * f(y)) dy

For 0 ≤ y ≤ 1, f(y) = 1/(2√y):

E[Y] = ∫(y * 1/(2√y)) dy

= ∫(1/(2√y)) dy

= (1/2) ∫(1/√y) dy

= (1/2) * 2√y + C

= √y + C

Since E[Y] is the expected value, it should be a constant. Therefore, C must be 0.

E[Y] = √y

Next, let's calculate E[Y²]:

E[Y²] = ∫(y² * f(y)) dy

For 0 ≤ y ≤ 1, f(y) = 1/(2√y):

E[Y²] = ∫(y² * 1/(2√y)) dy

= ∫(y^(3/2)) dy

= (2/5) * y^(5/2) + C

= (2/5) * y^(5/2) + C

Again, since E[Y²] is the expected value, C must be 0.

E[Y²] = (2/5) * y^(5/2)

Now, we can calculate var(Y):

Var(Y) = E[Y²] - (E[Y])²

= (2/5) * y^(5/2) - (√y)²

= (2/5) * y^(5/2) - y

So, the variance of Y is given by the expression (2/5) * y^(5/2) - y.

Var(X) is approximately -17.07 and Var(Y) is approximately 0.1. Variance measures the spread of a dataset and shows how much individual data points differ from the mean. A higher variance means there is greater diversity among the data points.

To calculate the variance of a continuous random variable, we need to use the following formula:

Var(X) = \(\int[(x - E(X))^2 \times f(x)] dx\)

where E(X) is the expected value or mean of X.

For the first random variable X with the probability density function f(x) = 2x² for 0 < x ≤ 2, we first need to calculate the mean:

E(X) = \(\int [x \times f(x)] dx\)

= \(\int [x \times 2x^2] dx\)

= 2∫[x³] dx

= 2[x⁴/4] evaluated from 0 to 2

= 2(2⁴/4 - 0⁴/4)

= 2(16/4)

= 8

Now, we can calculate the variance:

Var(X) = \(\int [(x - 8)^2 \times 2x^2] dx\)

=\(2\int [(x - 8)^2 \times x^2] dx\)

=\(2\int [x^4 - 16x^3 + 64x^2] dx\)

= 2[x⁵/5 - 4x⁴ + 64x³/3] evaluated from 0 to 2

= 2[(2⁵/5 - 4(2⁴) + 64(2³)/3) - (0⁵/5 - 4(0⁴) + 64(0³)/3)]

= 2[(32/5 - 4(16) + 64(8)/3) - (0 - 0 + 0)]

= 2[(32/5 - 64 + 512/3) - 0]

= 2[-128/15]

= -256/15

≈ -17.07 (rounded to two decimal places)

For the second random variable Y with the probability density function f(y) = 1/(2√y) for 0 ≤ y ≤ 1, the mean is:

E(Y) = \(\int [y \times f(y)] dy\)

= \(\int [y \times 1/(2\sqrt{y})] dy\)

= \(\int [1/(2\sqrt{y} )] dy\)

=\(\int [y^{(-1/2)}/2] dy\)

=\((y^{(1/2)}/2)\) evaluated from 0 to 1

= (1/2 - 0/2)

= 1/2

= 0.5

Now, let's calculate the variance:

Var(Y) = \(\int [(y - 0.5)^2 \times (1/(2\sqrt{y} ))] dy\)

= \(\int [(y - 0.5)^2/(2\sqrt{y} )] dy\)

= \(\int [(y^2 - y + 0.25)/(2\sqrt{y} )] dy\)

= \((1/2)\int [(y^{(3/2)} - y^{(1/2)} + 0.25y^{(-1/2)})] dy\)

=\((1/2)[(2/5)y^{(5/2)} - (2/3)y^{(3/2)} + 0.5y^{(1/2)}]\) evaluated from 0 to 1

=\((1/2)[(2/5)(1^{(5/2)}) - (2/3)(1^{(3/2)}) + 0.5(1^{(1/2)})] - (0 - 0 + 0)\)

= (1/2)[(2/5) - (2/3) + 0.5]

= (1/2)[(6/15) - (10/15) + 0.5]

= (1/2)[-4/15 + 0.5]

= (1/2)[-4/15 + 7/15]

= (1/2)[3/15]

= 3/30

= 1/10

= 0.1

Therefore, Var(X) ≈ -17.07 and Var(Y) = 0.1. Variance provides insight into the variability and volatility of a set of values, with a higher variance indicating greater diversity among the data points.

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Answer:

I think it would be the addition property of equality

Step-by-step explanation:

Answer:

Step-by-step explanation:

We worry about 2 things:

-terms power

-coefficient for each term

(3x-4)^5, has 2 terms 3x and -4

-Start with the first term to the highest power 5 and second term to the lowest power 0, then the high power goes down and low power increases until the first term has the lowest power 0 and the second term has the highest power 5.

-The coefficients for each term we take it from the Pascal triangle.

For the the power 5 the coefficients are 1, 5, 10, 10, 5, 1

\((3x-4)^{5} = 1*(3x)^{5} *(-4)^{0} +5*(3x)^{4} *(-4)^{1} +10*(3x)^{3} *(-4)^{2}+10*(3x)^{2} *(-4)^{3}+5*(3x)^{1} *(-4)^{4}+1*(3x)^{0} *(-4)^{5}\)

Simplify:

\((3x-4)^{5} = 3^{5} x^{5} -20*3^{4} x^{4} +160*3^{3} x^{3}-640*3^{2} x^{2}+1280*3x-1024\)

\((3x-4)^{5} = 243 x^{5} -1,620x^{4} +4,320 x^{3}-5,760x^{2}+3,840x-1024\)

Answer:

9/8

Step-by-step explanation:

3/16 x 6

= 3/16 x 6/1

= 18/16

= 9/8

Answer:

15:5 is the ratio of apples to oranges and 5:15 if reverse

Answer: 22

Step-by-step explanation:

24+x-4

Simplify

24+2-4

Simplify

24-2 = 22

(i think you didn't insert everything lol)

Answer:

Quartiles Quartiles:

Q1 --> 396

Q2 --> 423.5

Q3 --> 552

Step-by-step explanation:

Mean x¯¯¯ 461.91666666667

Median x˜ 423.5

Mode 420

Range 218

Minimum 375

Maximum 593

Count n 12

Sum 5543

Quartiles Quartiles:

Q1 --> 396

Q2 --> 423.5

Q3 --> 552

Interquartile

Range IQR 156

Outliers none

As we have proved that the line created works exclusively with the three points by justifying how the x-value and y-value fit into the equation for the line.

Let's start by defining what a linear function is. A linear function is an equation of the form y = mx + b, where m is the slope of the line and b is the y-intercept. The slope represents the rate of change of the line, and the y-intercept represents the value of y when x is equal to zero. To create a linear function, we need two points on the line.

Now, let's create another linear function using points B and C:

slope (m) = (y₂ - y₁) / (x₂ - x₁) = (6 - 4) / (5 - 3) = 1

y-intercept (b) = y - mx = 4 - 1 * 3 = 1

Therefore, the linear function that passes through points B and C is also y = x + 1. We can check if point A lies on this line by substituting its x and y values into the equation:

2 = 1 + 1

This is true, so point A lies on the line created by points B and C. Therefore, we have also proved that the line created works exclusively with these three points.

In conclusion, we have created two linear functions using three points and proved that they work exclusively with those three points.

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The stress-strain curve of structural steel with a yield point can generally be divided into three stages: elastic deformation, yielding, and plastic deformation.

In the first stage, known as elastic deformation, the steel material exhibits a linear relationship between stress and strain. This means that when stress is applied, the steel deforms elastically and returns to its original shape once the stress is removed. The steel behaves like a spring during this stage, with the deformation being directly proportional to the applied stress.

The second stage is the yielding stage. At this point, the stress-strain curve deviates from linearity, and plastic deformation begins to occur. The steel reaches its yield point, which is the stress level at which a significant amount of plastic deformation starts to take place. The material undergoes permanent deformation during this stage, even when the stress is reduced or removed.

The third stage is the plastic deformation stage. In this stage, the steel continues to deform plastically under increasing stress. The stress-strain curve shows a gradual increase in strain with increasing stress. The material may exhibit strain hardening, where its resistance to deformation increases as it continues to stretch. Ultimately, the steel may reach its ultimate strength, after which it may experience necking and eventual failure.

Overall, the stress-strain curve of structural steel with a yield point is characterized by the initial linear elastic deformation, followed by yielding and plastic deformation. These stages represent the steel's ability to withstand and accommodate varying levels of stress before reaching its breaking point.

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