Solve the following ode:
y^(4) – 4y"' + 6y" – 4y' + y = 0, y(0) = 0, y'(0) = 1, y" (0) = 0, y"; (0) = 1

Answer:

b

Step-by-step explanation:

Answer:

between 10 and 12

Step-by-step explanation:

Given the measure of angles:

m∠B = 70°

m∠C = 60°

m∠A = 50°

Following this information, since the side lengths are directly proportional to the angle measure they see:

Angle B is the largest angle. Therefore, side AC is the longest side of the triangle since it is opposite of the largest angle.

Angle C is the smallest angle, so the side AB is the shortest side.

Therefore, side BC must be between 10 and 12 inches.

Answer:

He must sell 8 cards to reach the minimum goal.

Step-by-step explanation:

Giving the following information:

He wants to earn more than $50 at the fair.

He sells his cards for $2 and he has already earned $36.

First, we need to calculate the money required to reach the minimum goal:

51 - 36= $15

Now, we write the inequality:

2*x >15

x= number of cards sold.

x>15/2

x> 7.5

He must sell 8 cards to reach the minimum goal.

We know that 2+2 is 4.

34 - 4 is 30.

Therefore, the legnth, a, is half of thirty.

30/2 = 15

a = 15

\(\bf a= 15\;\; millimetetrs\)

Step-by-step explanation:

perimeter: 34 millimetetrs

perimeter= \(\tt a+2+a+2=34\)

\(\tt 2a+4=34\)

\(\tt 2a+4-4=34-4\) (Subtract 4 from both sides)

\(\tt 2a=30\) (Simplify)

\(\tt \cfrac{2a}{2}=\cfrac{30}{2}\) (Divide both sides by 2)

\(\tt a=15\)

Therefore, a= 15 millimetetrs.

~

Solve for y.

y=4−3x

Rewrite in slope intercept form.

y=-3x+4

Use the slope intercept form to find the slope and y intercept

Slope: -3

Y-intercept: 4

Any line can be graphed using two points. Select two x values, and plug them into the equation to find the corresponding y values.

(1,1) (2,-2)

Graph the line using the slope and the y-intercept, or the points.

Slope: −3

y-intercept: 4

(1,1) (2,-2)

The inequality that can be used to represent the number of miles, x, Jaime could bicycle on the 4th week to meet his goal is 240 + 310 + 320 + x ≥ 4 (280).

What is inequality?

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other.

For the next four weeks, Jaime wants to log at least 280 miles per week on average. Jamie's objective can be graphically expressed by the inequality: T4, or alternatively T 4 if T is the total number of miles he will pedal his bicycle for four weeks (280).

The sum of the distances Jamie has covered and has yet to cover is the total number of miles Jamie will cycle during this time. Hence,  T = 240 + 310 + 320 + x. Replacing this term into the inequality T ≥ 4(280) gives 240 + 310 + 320 + x ≥ 4(280). Therefore, choice D is the correct answer.

Thus, the correct answer is  240 + 310 + 320 + x ≥ 4 (280).

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Answer:

34

Step-by-step explanation:

Given function:

\(f(x)=3x^2-2x+1\)

To find the value of f(-3), substitute x = -3 into the function and solve:

\(\begin{aligned}x=-3 \implies f(-3)&=3(-3)^2-2(-3)+1\\&=3(9)-2(-3)+1\\&=27+6+1\\&=33+1\\&=34 \end{aligned}\)

The principal sum is approximately Rs 461.538. The interest compounded annually is approximately Rs 76.80.

1. Let's write P for the main amount. We can use the following formula to calculate compound interest:

A = P(1 + r/n)nt

Where:

A is the sum after interest.

r is the annual interest rate in decimal form.

n = Number of annual compoundings of interest

t = The number of years.

Since the interest is compounded yearly in this instance, n = 1 and t = 2.

The difference between the simple interest and compound interest is reported as Rs 76.80. Thus, we can construct the following equation:

P(1 + 0.08/1)^(1*2) - P = 76.80

To make the calculation easier:

P(1.08)2 - P = 76.80 - 1.1664P = 76.80 P = 76.80 / 0.1664P = 76.80

P ≈ 461.538

Consequently, the principal amount is roughly Rs 461.538.

2. We can deduct the principal amount from the compound amount to get the interest compounded annually:

Annual interest compounding equals A P equals P(1 + r/n)(nt).

P is equal to P[(1 + r/n)(nt) - 1]

= 461.538[(1 + 0.08/1)(1*2) - 1]

= 461.538[(1.08)2 - 1]

=461.538[0.1664]
= 76.80

Therefore, the interest compounded annually is approximately Rs 76.80.

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Answer:D

Step-by-step explanation:

the dots are forming a mixed up line going across the plot. D best fits the line.

An equation for which the solution is the speed of this automobile is 200 = 0.5v + v²/51.2.

In Mathematics and Science, stopping distance can be defined as a measure of the distance between the time when a brake is applied by a driver to stop a vehicle that is in motion and the time when the vehicle comes to a complete stop (halt).

Based on the information provided above, the speed of this car is represented by the following equation;

d = vs + v²/64m

Where:

By substituting the given parameters, we have:

200 = 0.5v + v²/64(0.8)

200 = 0.5v + v²/51.2

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Answer:

208

Step-by-step explanation:

4*30 = 120

(15-4) * 8 = 88

88 + 120 = 208

Answer:

208 cm

Step-by-step explanation:

Solving right side first. 8*15=120

Take out 8cm from 30. 30 - 8 = 22

22*4= 88

88 + 120 = 208

Check work I found the total area and the white rectangle.

15*30=450 which in total area

15-4=11 11 is the left/right side of the white rectangle

30-8=22 22 is the top/bottom side of the white rectangle.

22*11= 242

208+242=450

Answer:

c = 5n

Step-by-step explanation:

The cost is equal to the price times the number of notebooks

Answer: Z is less than Zc ∴ 1.342 < 1.96

Therefore, Null hypothesis is not Rejected.

There is no sufficient evidence to claim that students turning in their test first score is significantly different from the mean.

Step-by-step explanation:

Given that;

U = 75

X = 78

standard deviation α = 10

sample size n = 20

population is normally distributed

PROBLEM is to test

H₀ : U = 75

H₁ : U ≠ 75

TEST STATISTIC

since we know the standard deviation

Z =  (X - U) / ( α /√n)

Z = ( 78 - 75 ) / ( 10 / √20)

Z = 1.3416 ≈ 1.342

Now suppose we need to test at ∝ = 0.05 level of significance,

Then Rejection region for the two tailed test is Zc = 1.96

∴ Reject H₀ if Z > Zc

and we know that Z is less than Zc ∴ 1.342 < 1.96

Therefore, Null hypothesis is not Rejected.

There is no sufficient evidence to claim that students turning in their test first score is significantly different from the mean.

Testing the hypothesis, it is found that since the p-value of the test is 0.1802 > 0.05, which means that the average test score earned by the first 20 students to turn in their tests was not significantly different from the overall mean.

At the null hypothesis, we test if the mean is of 75, that is:

\(H_0: \mu = 75\)

At the alternative hypothesis, we test if the mean is different of 75, that is:

\(H_1: \mu \neq 75\)

The test statistic is:

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

In which:

For this problem, we have that:

\(X = 78, \mu = 75, \sigma = 10, n = 20\)

The value of the test statistic is:

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

\(z = \frac{78 - 75}{\frac{10}{\sqrt{20}}}\)

\(z = 1.34\)

Since this is a two-tailed test, the p-value of the test is P(|z| < 1.34), which is 2 multiplied by the p-value of z = -1.34.

Looking at the z-table, z = -1.34 has a p-value of 0.0901.

2(0.0901) = 0.1802

The p-value of the test is 0.1802 > 0.05, which means that the average test score earned by the first 20 students to turn in their tests was not significantly different from the overall mean.

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Answer:

The question might be centered on computation on the hourly rate earned by the three friends:

Nina $12.69

Ty $8.25

Kim  $8.60

Step-by-step explanation:

Hourly rate earned=total earnings/hours worked

Nina:

Nina earned $177.60 for 14 hours,hence hourly rate is $ 12.69   ($177.60/14)

Ty:

Ty earned $148.50 for 18 hours period of work,thus earned $8.25  ($148.50/18)

Kim earned $137.60 for 16 hours duration of work,invariably Kim earned  $8.60 ($137.60/16)

From the above analysis it is clear that Nina earned the highest hourly rate of $12.69 per hour

Answer:

Step-by-step explanation:

The question might be centered on computation on the hourly rate earned by the three friends:

Nina $12.69

Ty $8.25

Kim  $8.60

Hourly rate earned=total earnings / hours of work

Nina:

Nina earned $177.60 for 14 hours,

\(=\frac{177.60}{14}\)

=  $ 12.69 per hour

Ty:

Ty earned $148.50 for 18 hours period of work,

\(=\frac{148.50}{18}\)

=  $8.25 per hour 

Kim

Kim earned $137.60 for 16 hours period of work,

\(\frac{137.60}{16}\)

 $8.60 per hour

From the  analysis it is obvious that Nina earned the highest hourly rate of $12.69 per hour

Answer:

No

Step-by-step explanation:

A recent report estimates that four out of every five dentists recommend a brand of toothpaste situation involves Inferential statistics.

Inferential statistics are widely employed to compare the differences between the treatment groups. Inferential statistics compare the treatment groups and make generalizations about the subject population using data from the experiment's sample of subjects. To offer answers for a situation or phenomena, inferential statistics is helpful. It differs fundamentally from descriptive statistics, which do not allow for result extrapolations and merely report the data that has already been measured.

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Answer:

\(c = 8.60232526704263\)

\(c \approx8.6\)

Step-by-step explanation:

\( {c}^{2} = {a}^{2} + {b}^{2} \)

\(c = \sqrt{ {a}^{2} + {b}^{2} } \)

\(c = \sqrt{ {5}^{2} + {7}^{2} } \)

\(c = \sqrt{25 + 49} \)

\(c = \sqrt{74} \)

\(c = 8.60232526704263\)

\(c \approx8.6\)

The statement which best describes a graph of a two-year-old child's height over the course of a year is it may not be straight, but it will slope up and to the right. The Option D is correct.

A graph of a two-year-old child's height over the course of a year may not be a straight line, but it will generally slope up and to the right. This is because children typically experience rapid growth and development during their early years, and their height tends to increase steadily over time.

However, there may be some variations in the rate of growth and development from month to month, and there may be periods of rapid growth followed by periods of slower growth. These fluctuations may cause the graph of the child's height to curve or bend at certain points, rather than forming a straight line.

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Using synthetic division, we can divide the polynomial x³ + 7x² - 12x + 14 by the divisor 1. Performing the synthetic division, we obtain a quotient of x² + 6x - 6 and a remainder of 8.

To divide the polynomial x³ + 7x² - 12x + 14 by the divisor 1 using synthetic division, we set up the synthetic division table as follows:

1  |   1   7  -12   14

We begin by bringing down the coefficient of the first term, which is 1, and place it on the line below the division bar. Then we multiply the divisor, 1, by the value we brought down and write the result under the next coefficient. Adding the values in the second row, we obtain the new value. We continue this process for each term until we reach the last term.

1  |   1   7  -12   14

 1   8  -4     10

The values in the last row represent the coefficients of the quotient polynomial. Therefore, the quotient is x² + 6x - 6. The remainder, which is the last value in the last row, is 10. Since the divisor is 1, the remainder does not affect the quotient. Hence, the result of the division is x² + 6x - 6 with a remainder of 10.

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Answer:

The class in the second and longest bar graph (the one labeled 3) has the most students.

Step-by-step explanation:

When looking for the largest amount of something in bar graphs, the largest bar graph is correct. In this case the second bar graph is the longest, and we can see it indicates the class contains 28 students.

The probability that less than 7 of the 30 students are left-handed is given as follows:

0.9742 = 97.42%.

The mass probability formula, giving the probability of x successes, is of:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are given by:

The parameter values for this problem are given as follows:

n = 30, p = 0.1.

The probability that less than 7 of the 30 students are left-handed is given as follows:

P(X < 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6).

Using a binomial distribution calculator with the parameter, finding each of the probabilities and adding them, we have that:

P(X < 7) = 0.9742 = 97.42%.

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Jeff's claim that any positive number raised to the -1 power is always less than the number is not true.

We will show that Jeff's claim is incorrect by providing a counterexample.

Let's choose a positive number for Part A and then calculate its value when raised to the -1 power in Part B.
Part A: 1/2 (a positive number)
Part B: (1/2)^(-1) = 2

Summary: We chose 1/2 as our positive number for Part A. When we raised it to the -1 power in Part B, we got 2. In this case, the value raised to the -1 power (2) is greater than the original number (1/2). Therefore, Jeff's claim is incorrect.

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Answer:

5 bags

Step-by-step explanation:

because there are 12 inches

Answer:

I think the answer is 4

Step-by-step explanation:

I think you need to find the area of the rectangle first which is 120 (12 x 10) then you divide 120 by 30 to get 4.

I might have gotten it wrong but  I think the answer is 4.

For an angle in standard position e terminates in quadrant II, with cos θ = a/5, the value of tan θ is 5 √(1 - (a/5)²) / a.

In mathematics, a quadrant refers to one of the four regions or sections into which the Cartesian coordinate plane is divided. The Cartesian coordinate plane consists of two perpendicular lines, the x-axis and the y-axis, which intersect at a point called the origin.

We need to find the value of tan θ.

Using the given information, let us find the value of sin θ using the formula of sin in the second quadrant is positive.

i.e. sin θ = √(1-cos²θ) = √(1 - (a/5)²)

Next, let us find the value of tan θ by dividing sin θ by cos θ as shown below:

tan θ = sin θ / cos θ

= (sin θ) / (a/5)

Multiplying and dividing by 5, we get,

= (5/1) (sin θ / a)

= 5 (sin θ) / a

Substituting the value of sin θ we get

,= 5 √(1 - (a/5)²) / a

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Answer:

8 is the atomic number

Step-by-step explanation:

Atomic number = 8  (meaning it has 8 protons in its nucleus)

Atomic weight = 15.999

O = symbol for oxygen

The answers are presented below:

The quadratic function can be represented by a quadratic equation in the Standard form: ax²+bx+c=0 where: a, b and c are your respective coefficients. In the quadratic function the coefficient "a" must be different than zero (a≠0) and the degree of the function must be equal to 2.

The vertex of an up-down facing parabola of the form ax²+bx+c is \(x_v=\frac{-b}{2a}\)  . Knowing the x-coordinate of vertex, you can find the y-coordinate of vertex. When a vertical line passes through the vertex of the parabola, it  is called the axis of symmetry.

The y-intercept is the point where the function crosses the y-axis. And, the x-intercept is the point where the function crosses the x-axis, in other words, when y=0.

First, you should convert the given equation to Standard form.

f(x) = -(c+7)² + 4

f(x)= - (c²+14c+49)+4

f(x)= -c²-14c-49+4

f(x)= -c²-14c-49+4

f(x)= -c²-14c-45

After that, you should check each option of the question.

Correct because present a degree 2 -- f(x)= -c²-14c-45

Incorrect because it is a quadratic function and this function is represented by a parabola.

The coefficients are: a=-1, b=-14, c=-45. Therefore,

\(c_v=\frac{-b}{2a}=-\frac{-14}{2*(-1)} =-\frac{-14}{-2}=-(7)=-7\)

Incorrect because x-coordinate of vertex is -7

Correct because  \(c_v=\frac{-b}{2a}=-\frac{-14}{2*(-1)} =-\frac{-14}{-2}=-(7)=-7\)

You can find the y-intercept using c=0, then f(x)= -c²-14c-45 will be:

f(x)=-45.

Incorrect because the y-intercept is (0,-45).

The coefficient a of a quadratic function is negative, thus the function has a point maximum. A relative maximum point is defined as the point where the function changes your direction. In other words, the values of the function increase before the relative maximum and the values decrease after the relative maximum.

Correct, see the attached image.

It is possible to find the number of roots or solutions from discriminant.

For quadratic equation the discriminant is determined by D=b²-4ac, where: a, b and c are coefficients.

If D > 0 - the function will have two real solutions;

If D = 0 - the function will have one real solution;

If D < 0 - the function will have imaginary solutions;

For given equation, the coefficients are: a=-1, b=-14, c=-45. Thus, D=(-14)²-4*(-1)*(-45)

D=196-180=16

D=16 thus D > 0

Incorrect because the D>0.

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Positional numeration is a system of representing numbers using positional notation. In this system, each digit represents a multiple of the base of the number system, which is usually 10 in our decimal system. The number 3.15569 x 10^7 in positional numeration is 31,556,900.

The value of a digit is determined by its position, with the rightmost digit representing the ones place, the next digit to the left representing the tens place, and so on. To convert the given number, 3.15569 x 10^7, into positional numeration, we first need to express it in scientific notation. In scientific notation, a number is expressed as a product of a coefficient and a power of 10. In this case, the coefficient is 3.15569, and the power of 10 is 7. Therefore, the given number can be expressed as: 3.15569 x 10^7

To convert this number into positional numeration, we can simply multiply the coefficient by the power of 10. This can be done by moving the decimal point of the coefficient 7 places to the right, since 10^7 is a power of 10 with exponent 7. The resulting number is: 31,556,900

Therefore, the number 3.15569 x 10^7 in positional numeration is 31,556,900. It is important to remember that positional numeration is a system of representing numbers using positional notation based on the base of the number system, which is usually 10 in our decimal system.

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Answer:

I think its positive

Step-by-step explanation:

it was just giving to be honest

Answer: It's positive Zero

Step-by-step explanation: It usually is 0 not -0

Answer:

13√ 2

Step-by-step explanation:

√ 26*(26/2)

=√ 26*13 = √ 338 = 13√ 2

The length of the segment  cut from the line by the two other sides of the triangle is \(13\sqrt{2\)

The length of the side is given as:

L= 26 inches

The length (d) of the line that divides the segment is calculated as:

\(d = \sqrt{(L/2)^2 + (L/2)^2\)

So, we have:

\(d = \sqrt{(26/2)^2 + (26/2)^2\)

Evaluate the quotients

\(d = \sqrt{13^2 + 13^2\)

Rewrite the expression as:

\(d = \sqrt{13^2* 2\)

Take the square root

\(d = 13\sqrt{2\)

Hence, the length of the segment is \(13\sqrt{2\)

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Answer:

11 hours

Step-by-step explanation:

640-200=440

440%40=11

so it would take them a additional 11 hours