Find the general solution of the differential equation: y′+3y=te^−4t.Use lower case c for the constant in your answer.

Answer:40

Step-by-step explanation:

Width x length x height

4 x 2 = 8 x 5 = 40

According to the statement the coefficient bo is -1.The coefficient b1 is equal to -5.1.The coefficient b2 is equal to -12.9.The coefficient b3 is equal to 6.9.

Newton interpolation is an algorithm used for the purpose of interpolation. The algorithm is based on constructing a polynomial curve that passes through the given data points of the data set. By evaluating this polynomial curve at the point x, we can find the interpolated value of the function f(x).

Here is the Newton Interpolation equation: P3 (x) = bo + b1 (x - x1) + b2 (x - x1)(x - x2) + b3 (x - x1)(x - x2)(x - x3)Given the data set xi | 1.0 | 2.0 | 3.0 | 4.0yi | -1.0 | -6.1 | -19 | -12.1Now, let us use Newton Interpolation to calculate the coefficients.bo = y0 = -1b1 = Δy0/x0_1 = (-6.1 + 1)/1 = -5.1b2 = Δy1/x1_2 = (-19 + 6.1)/(3 - 2) = -12.9b3 = Δy2/x2_3 = (-12.1 + 19)/(4 - 3) = 6.9Therefore, the coefficient bo is -1.

The coefficient b1 is equal to -5.1.The coefficient b2 is equal to -12.9.The coefficient b3 is equal to 6.9.The above Newton Interpolation gives the polynomial equation P3(x) = -1 - 5.1(x - 1) - 12.9(x - 1)(x - 2) + 6.9(x - 1)(x - 2)(x - 3).Hence, this is the answer of the given problem.

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Answer:

0.70=y

Step-by-step explanation:

Hope this helps:)

The probability that any one of the ways identified in problem 3 is: 0.03.

In statistical hypothesis testing, the probability of observing a particular test statistic or a more extreme one under the null hypothesis is called the p-value. A small p-value indicates that the observed result is unlikely to occur by chance alone, and thus provides evidence against the null hypothesis.

In this case, problem 3 is not specified, so it is not possible to calculate the p-value. However, the hint suggests using the second part of the binomial equation. This might refer to the formula for calculating the probability of obtaining k or more successes in n independent Bernoulli trials, each with probability p of success. This formula is:

P(X ≥ k) = ∑(k to n) (n choose i) p^i (1-p)^(n-i)

where X is the number of successes, n is the number of trials, p is the probability of success in each trial, (n choose i) is the binomial coefficient, and the summation is taken from k to n inclusive.

If the null hypothesis is true, the probability of success is equal to the significance level α, which is typically chosen to be small (e.g., 0.05 or 0.01). The value of k depends on the specific problem and the test being performed.

Using this formula, we can calculate the probability of observing k or more successes in n trials when the null hypothesis is true. If this probability is small (i.e., less than α), we reject the null hypothesis in favor of the alternative hypothesis.

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The probability that Juan loses his next tennis match is 48%

From the question, we have the following parameters

The proportion of tennis matches won

p = 52%

This proportion implies that the probability that the player will win his next tennis match

So, we have the following representations

Probability of winning, p = 52%

Express the percentage as decimal

So, we have the following representations

Probability of winning, p = 0.52

The probability of losing the next match is the complement of the probability of winning

This is represented as

Probability of losing = 1 - Probability of winning,

Substitute the known values in the above equation

So, we have the following equation

Probability of losing = 1 - 0.52

Evaluate

Probability of losing = 0.48

Hence, the probability is 0.48 or 48%

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Answer:

300

Step-by-step explanation:

375 divided by 5=75

Each “1”=75

4x75=300

There are 300 boys.

Hope this makes sense

Answer:

300 boys

Step-by-step explanation:

Let the number of boys = x

Girls: 375

boys : girls = 4 : 5

total in the ratio is 9

girls are 5/9 of total, and are 375

boys are 4/9 of total

5/9 x = 375

x = 375 × 9/5

x = 675

Boys are 4/9 of total.

4/9 × 675 = 300

Answer:

A ratio must be positive.

Step-by-step explanation:

A ratio is comparing two things. For example, the number of sisters as a ratio to the number of brothers. If you have 2 sisters, and 1 brother, the ratio of sisters and brothers would be 2:1. this number does not make sense as -2:1.

Out of the 500 people surveyed, we would expect approximately 155 of them to consider reading books or surfing the Internet as the best entertainment value.

To calculate the expected number of people who considered reading books or surfing the Internet as the best entertainment value out of the 500 surveyed, we need to calculate the percentage corresponding to reading books and surfing the Internet.

The percentage for reading books is 22% and the percentage for surfing the Internet is 9%. To find the combined percentage, we add these two percentages:

22% + 9% = 31%

Now, we can calculate the expected number by multiplying the combined percentage by the total number of people surveyed:

Expected number = 31% of 500 = (31/100) * 500 = 155

The complete question is:

Out of 500 people surveyed, how many would you expect considered reading books or surfing the Internet as the best entertainment value?

Best Entertainment Value

Type of Entertainment               Percent

Playing Interactive Games            48

Reading Books                              22

Renting Movies                              10

Going to Movie Theaters               10

Surfing the Internet                          9

Watching Television                         1

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Answer:

30 cubic feet

Step-by-step explanation:

Base of 10 sq ft x 3 ft = 30 cubic feet

3. The scale factor is of: 1 : 360.

The lengths and scale factors are given as follows:

4. Length of 7.5 in and scale factor of 1 : 96.

5. Length of 48 cm and scale factor of 1 : 400

6. Length of 18 in and scale factor of 1 : 9.

The meaning of the scale of a drawing is how much each unit in the drawing represents in actual distance.

The scale factor is the ratio between the ratio of the dimension of the drawn shape by the actual dimension.

Each feet is composed by 12 inches, hence the scale factor for item 3 is given by:

1/(20 x 12) = 1 : 360.

The lengths for items 4, 5 and 6 are given by the division of the actual length by the measure represented by a single unit, hence:

The scale factors are given as follows:

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a) Hence the distance between U and N is d=5 units.

b)Hence the slope of UF is \(\frac{1}{6}\)

The triangle FUN has vertices located at F(-2,-3), U(4,-2) and N(1,2)

a) Find the length of the UN,

We know that distance between two points is-

let two points (x,y) and (s,t) then

d=√((s-x)²+(t-y)²)

We have U(4,-2) and N(1,2)

d=√(1-4)²+(2+2)²

d=√9+16

d=√25

d=5

Hence the distance between U and N is d=5 units.

b) Find the slope of UF

We know that the formula for slope of (x,y) and (s,t)

\(m=\frac{t-y}{s-x}\\\)

We have U(4,-2) and F(-2,-3)

\(m=\frac{-3+2}{-2-4}\\\\m=\frac{-1}{-6}\\\\m=\frac{1}{6}\)

Hence the slope of UF is \(\frac{1}{6}\)

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Answer:

$8170.10

Step-by-step explanation:

Given data

P=$3230

R= 5.8%

T= 16 years

The given expression for the account is

V = P*e^(rt)

substotute

V = 3230*e^0.058*16

V= 3230 e^ 0.928

V=3230*2.5294452249

V=$8170.10

Hence the balance is $8170.10

Answer:

8170.11

Step-by-step explanation:

3230e^0.058(16)

Answer:

x=9

Step-by-step explanation:

plug in the number 9

-2(9)= -18

-18+3= -15

Answer:

No and yes. it depends on what type of function you are looking for this will be a Linear Function.

The force required to make the car turn in a circle of radius 120 m is 7500 N (Newtons).

To calculate the force required to make the car turn in a circle of the given radius, we need to find the centripetal force. The formula for centripetal force is:

F_c = m * a_c

Where F_c is the centripetal force, m is the mass of the car (1000 kg), and a_c is the centripetal acceleration.

To find the centripetal acceleration, use the formula:

a_c = v^2 / r

Where v is the speed of the car (30 m/s) and r is the radius of the circular track (120 m).

Step 1: Calculate centripetal acceleration:
a_c = (30 m/s)^2 / 120 m
a_c = 900 m^2/s^2 / 120 m
a_c = 7.5 m/s^2

Step 2: Calculate centripetal force:
F_c = 1000 kg * 7.5 m/s^2
F_c = 7500 N

So, the force required to make the car turn in a circle of radius 120 m is 7500 N (Newtons).

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Answer:

2(6x)_>10?a._>4b_>6d

Answer:

Solution given:

1:

-1/8=\(\frac{-1³}{2³}=(\frac{-1³}{2³}=-1³*2^{-3}=-2^{-3}\)

2. -64/27

=\(\frac{-4^{3}}{3³}=\frac{-4³}{3³}=(\frac{-4}{3})^{3}\)

Express in rational number

1. (-3/2)=-3/2*2/2=-(3*2)*(2/2)=-6/4

2. (1/5)=1/5*5/5=5/25

and

(-4/3)³(2/5)-⁴ ÷ (7/4)

(-4³/3³)(2-⁴/5-⁴)÷7/4

(-64/27)(5⁴/2⁴)÷7/4

(-64/27)(625/16)÷7/4

(-64*625/(27*16))*4/7

-2500/27*4/7

-10000/169

(-100/13)²

The statement that proves that polygon ABCD is not a rectangle is: C. Slope of AD × slope of AB ≠ -1 and slope of BC × slope of AB ≠ -1.

A rectangle is a quadrilateral that has four right angles, this means that two sides of the rectangle intersect each other perpendicularly to form right angles.

Thus, the slope of each pair of sides that intersect perpendicularly equals -1.

Therefore, for polygon ABCD to be a rectangle, we must prove that each pair of intersecting sides that meet have a a slopes that gives -1 when multiplied together. If the product of their slopes is not equal to -1, then the polygon is not a rectangle.

Conclusively, the statement that proves that polygon ABCD is not a rectangle is: C. Slope of AD × slope of AB ≠ -1 and slope of BC × slope of AB ≠ -1.

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Answer:

55%

Step-by-step explanation:

first, you set up the problem as two fractions: 11 is to 20 as x is to 100. you cross multiply the 11 and 100, then divide that by 20 which gives you 55, which you divide by 100 for the percentage answer.

Answer:

Sorry , I might be wrong : 35664

Step-by-step explanation:

So, first, we can find 33% of 53,200

That is 17,556

Then, we can subtract 17556 from 53,200

We get 35664

ANSWER

y = 3.5x + 56

EXPLANATION

The slope of a line passing through points (x1, y1) and (x2, y2) is,

And the slope-intercept form of the equation of a line is,

Where m is the slope and b is the y-intercept.

In this problem, we have to use points (5, 73) and (7, 80) to find the equation of the line. First, we can find the slope,

For now, the equation is,

We have to find the y-intercept, by replacing x and y for the coordinates of one of the given points,

And solve for b,

The equation is,

The slope as a decimal is 3.5 and the y-intercept, rounded to the nearest whole number is 56, so the equation is y = 3.5x + 56

`The total number T of people at the sport's award banquet is ;

the capacity C of each table is given as;

To determine the number of tables N needed for the sport's award banquet, we will divide the total number of people by the capacity of each table;

Substituting the values of T and C, we have;

The number of tables needed is 58 tables

Answer: 54

Step-by-step explanation:

The statement that best describes why ∫₁^∞ ²/(3x + 2)² dx will converge or diverge is option B. It will diverge because the corresponding limit does not exist.

To evaluate the convergence or divergence of the integral, examine the behavior of the integrand as x approaches infinity. In this case, as x gets larger, the denominator 3x + 2 also grows without bound. Therefore, the integrand ²/(3x + 2)² approaches zero as x goes to infinity.

However, the convergence or divergence of the integral is not totally determined by the behavior of the integrand; it also depends on the behavior of the limits of integration.

In this case, the lower limit is 1, and integrating from 1 to infinity. Since the integrand approaches zero but does not tend to a finite value as x goes to infinity, the integral ∫₁^∞ ²/(3x + 2)² dx does not converge. Hence, it diverges.

Therefore, the correct statement is option B. It will diverge because the corresponding limit does not exist.

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Answer:

45.00%

Step-by-step explanation:

The total answers count 40 - it's 100%, so we to get a 1% value, divide 40 by 100 to get 0.40. Next, calculate the percentage of 18: divide 18 by 1% value (0.40), and you get 45.00% - it's your percentage grade.

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\( \sqrt{4 \frac{53}{169} } \)

\( \sqrt{ \frac{729}{169} } \)

\( \sqrt{ \frac{27}{13} } \)

Solution

For this case we can see that QT is perpendicular to PR and we want to find the correct proportional rule and for this case is:

C. PT/TQ = PR/TQ

Answer:

lol is this possible i tried doing it but couldnt haha i googled it and well it said 2.6532977e+40

Step-by-step explanation:

Answer:

2.65329771×10 to the power of 40

Step-by-step explanation:

Use scientific notation to get the simplest answer

Answer: The first 3 options

Step-by-step explanation:

You have to make sure that the given variable would be able to equal -5. The  \(\geq\) sign in the second and third answer show that the variable could be equivalent to -5.

Answer:

g > -7, f ≤ -5 and g ≥ -5

Step-by-step explanation:

the < and > symbols mean less than and greater than respectively, but not including. Therefore -5 cannot be a valid solution if the range is (for example) g > -5. However, ≤ and ≥ mean less/greater than or equal to, so -5 would be a valid solution for g ≥ -5 (for example).