write a solution system for the inequality 3x-2>10

Recall the power series expansions of [tex]\sin(x)[/tex] and [tex]e^x[/tex].

[tex]\displaystyle \sin(x) = \sum_{n=0}^\infty \frac{(-1)^n}{(2n+1)!} x^{2n+1}[/tex]

[tex]\displaystyle e^x = \sum_{n=0}^\infty \frac{1}{n!} x^n[/tex]

By substituting [tex]3x[/tex] for [tex]x[/tex] in the latter series, we have

[tex]\displaystyle e^{3x} = \sum_{n=0}^\infty \frac{1}{n!} (3x)^n = \sum_{n=0}^\infty \frac{3^n}{n!} x^n[/tex]

Then the series expansion of [tex]f(x)[/tex] is

[tex]\displaystyle f(x) = x^3 \sin(x) + e^{3x+2} \\\\ ~~~~~~~~ = x^3 \sum_{n=0}^\infty \frac{(-1)^n}{(2n+1)!} x^{2n+1} + e^2 \sum_{n=0}^\infty \frac{3^n}{n!} x^n \\\\ ~~~~~~~~ = \sum_{n=0}^\infty \frac{(-1)^n}{(2n+1)!} x^{2(n+2)} + e^2 \sum_{n=0}^\infty \frac{3^n}{n!} x^n[/tex]

[tex]f(x)=\sum^{\infty}_{n=0} \frac{(-1)^{n}}{(2n+1)!}x^{2(2n+2)} + e^{2} \sum^{\infty }_{n=0} \frac{1}{n!}3^{n}x^{n}[/tex] is the power series representation for the function f(x) = x³sin(x) + e³ˣ⁺². This can be obtained by using power series representation of each terms, sin x, eˣ and substituting in the function.

In the question the given function is,

⇒ f(x) = x³sin(x) + e³ˣ⁺²

We know that series representation of sin x and eˣ are:

   ⇒ [tex]e^{3x} = \sum^{\infty }_{n=0} \frac{1}{n!}x^{n}[/tex]

             = [tex]\sum^{\infty }_{n=0} \frac{1}{n!}3^{n}x^{n}[/tex]

Substituting the series representation in the function we get,

⇒ f(x) = x³sin(x) + e³ˣ⁺²

⇒ [tex]f(x)=x^{3}\sum^{\infty}_{n=0} \frac{(-1)^{n}}{(2n+1)!}x^{2n+1} + e^{2} \sum^{\infty }_{n=0} \frac{1}{n!}3^{n}x^{n}[/tex]

[tex]f(x)=\sum^{\infty}_{n=0} \frac{(-1)^{n}}{(2n+1)!}x^{2(2n+2)} + e^{2} \sum^{\infty }_{n=0} \frac{1}{n!}3^{n}x^{n}[/tex]

Hence [tex]f(x)=\sum^{\infty}_{n=0} \frac{(-1)^{n}}{(2n+1)!}x^{2(2n+2)} + e^{2} \sum^{\infty }_{n=0} \frac{1}{n!}3^{n}x^{n}[/tex]  is the power series representation for the function f(x) = x³sin(x) + e³ˣ⁺².

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Answer:

Step-by-step explanation:

i doont know

The second tree is 56.4 ft tall.

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are identical, their respective sides are equal in number and their corresponding angles are congruent.

Let the length of the tall tree be x. Thus by similarity of triangles we get,

Length of small tree/ Shadow Length of small tree =

Length of  Tall tree/ Shadow Length of tall tree

Substituting the values we get,

5.6/4.2 = x/42.3

x = 56.4

Thus the second tree is 56.4 ft tall.

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Answer:

2

Step-by-step explanation:

just because all three numbers are even

Hope this helps

The greatest common factor of 30, 22, and 8 will be 2.

The Highest Common Factor (HCF) of two numbers is the highest possible number that is divisible by both numbers.

In other words, the highest common factor is the common factor between the two numbers but it should be the highest among all common factors.

For example in 6 and 12 6 is the highest common factor.

The factor of 30 ⇒ 2,3,5

The factor of 22 ⇒ 2,11

The factor of 8 ⇒ 2,4

The only common factor among 30,22 and 8 is 2 so it will be the greatest common factor.

Hence "The greatest common factor of 30, 22, and 8 will be 2".

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The scale factor from Figure A to Figure B is 4

From the question, we have the following statement:

Figure B is a scaled copy of Figure A.

The corresponding side lengths of figure A and figure B are:

Figure A = 10

Figure B = 40

The scale factor from Figure A to Figure B is then calculated as:

Scale factor = Figure B/Figure A

Substitute the known values in the above equation

Scale factor = 40/10

Evaluate the quotient

Scale factor = 4

Hence, the scale factor from Figure A to Figure B is 4

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The z score that separate the middle 56% of the distribution from the area in the tails of the standard normal distribution is ±0.77.

Given that the z score separates the 56% of the distribution from the area in the tails of the standard normal distribution.

In a normal distribution in with mean μ and standard deviation σ, the z score of a measure X is as under:

Z=(X-μ)/σ

It is used to measure how many standard deviations the measure is from the mean.

After finding the z score we have to look at the z score table and find the p value associated with this z score, which is the percentile of X.

The normal distribution is symmetric which means that the middle 56% is between the 11th and 67th percentile. Looking at the z table the z scores are Z=±0.77.

Hence the z score that separate the middle 56% of the distribution from the area in the tails of the standard normal distribution is ±0.77.

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Answer:

A is the answer

[tex]x = \frac{1}{48} [/tex]

Answer:

x^2/ 16 + y^2/4 = 1

Step-by-step explanation:

The major axis is 4 and that goes with the x variable.  It is the major axis because 4 is a larger value than 2.

4 x 4 = 16

2 x 2 = 4

The equation of the ellipse in standard form is x² / 16 + y² / 4 = 1.

In this problem we know the coordinates of a vertex, a co-vertex and the center of an ellipse. Based on this information, we find an ellipse whose major axis is parallel to the x-axis. whose formula in standard form is:

(x - h)² / a² + (y - k)² / b² = 1     (1)

Where:

The major semiaxis has a length of 4 units and the minor semiaxis has a length of 2 units. If we know that (h, k) = (0, 0), a = 4 and b = 2, then the equation of the ellipse is:

x² / 16 + y² / 4 = 1

The equation of the ellipse in standard form is x² / 16 + y² / 4 = 1.

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Answer:

  180 yards

Step-by-step explanation:

The number of yards she sprints on day 21 can be found by evaluating the formula with n=21.

  a21 = 100 +(21 -1)4 = 100 +(20)(4) = 100 +80 . . . . . use 21 in place of n

  a21 = 180

Marika sprints 180 yards on day 21.

Answer:

4.25 × 10^-4

Step-by-step explanation:

0.00045-2.5x10^-5

= (4.5 × 10^-4) - (0.25 × 10¹ × 10^-5)

= (4.5 × 10^-4) - (0.25 × 10^{1-5} )

= (4.5 × 10^-4) - (0.25 × 10^-4)

= (4.5 - 0.25) × 10^-4

= 4.25 × 10^-4

**Disclaimer** Hi there! I assumed the unit [ mph ] represents miles per hour and [ m/s ] represents meters per second. The following answer will be according to this understanding. If I am wrong, please let me know and I will modify my answer.

Answer: [tex]\Large\boxed{23~m/s}[/tex]

Step-by-step explanation:

Given information

Speed = 52 mph

Given conversion factors

1 mile ≈ 1609 meters

1 hour = 3600 seconds

Convert the unit from mph to m/s using conversion factors

The basic idea is that you utilize the factors and cancel out unnecessary units

[tex]\dfrac{52~miles}{1~hour} \times\dfrac{1~hour}{3600~seconds} \times\dfrac{1609~meters}{1~miles}[/tex]

Simplify by multiplication

[tex]=\dfrac{52~miles}{3600~Seconds} \times\dfrac{1609~meters}{1~miles}[/tex]

[tex]=\dfrac{52\times 1609~meters}{3600~Seconds}[/tex]

Simplify the fraction

[tex]=\dfrac{83668~meters}{3600~Seconds}[/tex]

[tex]\Large\boxed{\approx23~m/s}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

Step-by-step explanation:

7/3=7:

what will seven over three equals seven divide be

7/3 is a division (7:3)

so

your answer is :

3

(7/3=7:3)

Answer:

40° to the left and 3/2 units down

Step-by-step explanation:

See attached image.

The list of the possible outcomes for spinning the spinner with four sectors A, B, C, D, and flipping a fair coin goes as follows,

AH, BH, CH, DH, AT, BT, CT, DT

The possible outcomes for spinning a spinner (assuming that the spinner has four sectors, A, B, C, D) are: A, B, C, D  (4 outcomes)

Now, the possible outcomes for flipping a fair coin are: Tales (T) and Heads (H) (2 outcomes)

For each possible outcome of the spinner, there can be two possible outcomes associated, because of the flipping of the fair coin. Hence, the total possible outcomes for spinning the spinner with four sectors A, B, C, D, and flipping a fair coin are 4 × 2, i.e. 8 outcomes.

These possible outcomes are AH, BH, CH, DH, AT, BT, CT, DT.

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Step-by-step explanation:

the inner WU arc angle is 23x - 5.

the outer WU arc angle is 37x + 5.

together they must be 360°, as this is the full circle.

so, we have

360 = 23x - 5 + 37x + 5 = 60x

x = 6

therefore, the angle at V is

V = 5x + 17 = 5×6 + 17 = 30 + 17 = 47°

inner WU arc angle = 23x - 5 = 133°

outer WU arc angle = 37x + 5 = 227°

this also fits with

V = (outer arc angle - inner arc angle)/2 =

= (227 - 133)/2 = 94/2 = 47°

The solution for the given differential equation is lnlxl = [tex]\frac{-x}{y} +C[/tex]

Given,

[tex](y^{2} +y^{x} )dx - x^{2} dy =0[/tex]

Here,

x = vy, dx = vdy + ydv

y = ux, dy = udx + xdu

Then,

[tex]((ux)^{2} +(ux)x)dx-x^{2} (udx+xdu)=0\\=u^{2} x^{2} dx+ux^{2} dx-x^{2} udx-x^{3} du=0\\=u^{2} x^{2} dx=x^{3} du\\=\frac{x^{2} }{x^{3} } dx=\frac{1}{u^{2} } du[/tex]

Now,

[tex]\int\limits^a_b {\frac{1}{x} } \, dx =\int\limits^a_b {u^{-2} } \, du[/tex]

l[tex]n[/tex]l[tex]x[/tex]l[tex]=\frac{u^{-1} }{(-1)} +C[/tex]

l[tex]n[/tex]l[tex]x[/tex]l[tex]=\frac{-1}{u} +C[/tex]

y = ux

u = [tex]\frac{y}{x}[/tex]

That is l[tex]n[/tex]l[tex]x[/tex]l [tex]=\frac{-x}{y} +C[/tex]

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The independent variable in the function f(c) = 2c + 9 is c whereas the dependent variable is f.

An equation is an expression that shows the relationship between two numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.

The independent variable in the function f(c) = 2c + 9 is c whereas the dependent variable is f.

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Using translation concepts, the expression for h(x) is given as follows:

[tex]h(x) = \sqrt{x + 4} - 1[/tex]

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

For this problem, the parent function is:

[tex]f(x) = \sqrt{x}[/tex]

For the translations, we have that:

Then the expression for h(x) is given as follows:

[tex]h(x) = \sqrt{x + 4} - 1[/tex]

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Answer:

supposed to make the subject y then slope is -2

The claim is wrong, or your question is incorrectly entered.

[tex]x=1 \implies f(3) = f(3) + f(1) \implies f(1) = 0[/tex]

[tex]x=3 \implies f(9) = f(3) + f(3) = 2f(3)[/tex]

[tex]x=9 \implies f(27) = f(3) + f(9) = 3 f(3)[/tex]

[tex]x=27 \implies f(81) = f(3) + f(27) = 4f(3)[/tex]

Then

[tex]f(1) - f(3) - f(9) - f(27) = 0 - f(3) - 2f(3) - 3f(3) = -6f(3) \neq 4f(3) = f(81)[/tex]

at least if [tex]f(3)\neq0[/tex].

Mrs. Corrubi takes 7.5 hours to complete the job alone.

Directly proportional: as one amount increases, another amount increases at the same rate. Direct variation means when one quantity changes, the other quantity also changes in direct proportion

Inversely Proportional: when one value decreases at the same rate that the other increases. An increase in the quantity A leads to a decrease in quantity B and vice versa.

Let the number of hours taken by Mrs Corrubi to do a particular work be x.

∴ The number of hours taken by Mr Corrubi to do a particular work will be 2x.

So according to the condition,

1/x + 1/2x = 1/5

(2+1)/2x = 1/5

3/2x = 1/5

2x = 15

x = 7.5 hours.

Thus Mrs. Corrubi takes 7.5 hours to complete the job alone.

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Answer:

D. 70,244 and 70,632

Step-by-step explanation:

Got it right on PLATO/EDMENTUM

70,244 and 70,632 is the approximate 90% confidence interval for this situation.

A confidence interval, in statistics, refers to the probability that a population parameter will fall between a set of values for a certain proportion of times.

Confidence intervals measure the degree of uncertainty or certainty in a sampling method. They can take any number of probability limits, with the most common being a 95% or 99% confidence level. Confidence intervals are conducted using statistical methods.

Statisticians use confidence intervals to measure uncertainty in a sample variable. For example, a researcher selects different samples randomly from the same population and computes a confidence interval for each sample to see how it may represent the true value of the population variable. The resulting datasets are all different; some intervals include the true population parameter and others do not.

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Answer:

j = 7.8.

Step-by-step explanation:

The slope of the line = difference in y-values / corresponding difference in x-values.

Slope = (7-3) / (j-5) = 10/7

so 10(j - 5) = 7*4

10j - 50 = 28

10j = 78

j = 7.8.

The first inequality is represented by the purple area seen in the picture and the second inequality by the black area seen in the picture, the solutions set is the region where the two areas overlap each other.

In this question we have two inequalities representing constraints that Marissa should satisfy, provided that she wants to make a profit in selling paintings and bracelets.

The first inequality represents the minimum profit required from the sales of paintings (x) and bracelets (y) and the second one represents the minimum number required of sold bracelets. The two inequalities are described below:

15 · x + 7 · y ≥ 800      (1)

y ≥ 60     (2)

Since there are more than one solution, we decided to define a solutions set with the help of graphing tool. The first inequality is represented by the purple area seen in the picture and the second inequality by the black area seen in the picture, the solutions set is the region where the two areas overlap each other.

The statement is incomplete and such issue cannot be resolved. We decided to modify the statement as follows:

Marissa is selling paintings for $ 15 each and bracelets for $ 7 each. Her goal is to sell at least $ 800 in products, and she must sell at least 60 bracelets. Please show the set of all possible solution that will satisfy these constraints?

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Answer:

26 paintings and 61 bracelets

Step-by-step explanation:

if you do 26x15=390 and 61x7=427

390+427=817

so the answer is 26 paintings and 61 bracelets

also, I took the test so I know its right

Answer:

D is correct

Step-by-step explanation:

Since you have 2 parallel lines cut by a transversal, <BAC and <BDE are corresponding angels.  Corresponding angles are congruent.  You are able to prove that 2 pairs of angles are congruent so the triangles are similar.  All of the answers show that the 2 triangles share angle B as the first part of the answer.

Lynn wants to wait because (D) she would likely have to pay more than $55 at the time of purchase for the convenience of using her credit card.

The answer to why Lynn wants to wait would be:

Therefore, Lynn wants to wait because (D) she would likely have to pay more than $55 at the time of purchase for the convenience of using her credit card.

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The complete question is shown below:

Lynn is at a store and wants to buy a new backpack that costs $55. she only has $35 with her, but she has the rest at home. Lynn also has a credit card that does not charge her any interest if she pays the balance in full by the end of the month. why might Lynn want to wait until she has $55 in cash at the store to purchase the backpack, instead of using her credit card?

a. Using a credit would cause the store to lose money because even if she pays back her bill in full, she will still need to pay the credit card company additional dollars for the convenience of borrowing money.

b. Using cash would cause the store to lose a large amount of money because credit card companies offer incentives to stores based on the number of people who use their cards.

c. She might forget to pay the credit card bill, which would make her purchase more expensive due to interest payments and late charges.

d. She would likely have to pay more than $55 at the time of purchase for the convenience of using her credit card.

The mistake that the researcher made is that; neither critical nor obtained Chi squares can have negative values

A chi-square statistic is one way to show a relationship between two categorical variables. In statistics, there are two types of variables: numerical (countable) variables and non-numerical (categorical) variables.

The chi-squared statistic is a single number that tells you how much difference exists between your observed counts and the counts you would expect if there were no relationship at all in the population.

Now, Chi square (χ²) is the sum of a set of squared values, and as such it can never be negative. The minimum chi - squared value would be obtained if each Z = 0 so that χ² would also be 0. There is no upper limit to the χ² value. Similarly, the critical chi square cannot also be negative.

Thus, we can conclude that the mistake that the researcher made is that neither critical nor obtained Chi squares can have negative values

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Answer:

Positive

Step-by-step explanation:

5a < 2a

Divide 2 on both sides

5/2a < a

the number of gallons that must be applied is 94 gallons.

Density is simply defined as the ratio of the mass to the volume occupied by an object or substance.

It is denoted with rho, 'ρ'

The formula for density is given as;

Density = mass/ volume

From the information given, we have that

To determine the volume, we need to make it the subject from the formula

Volume = density × mass

Volume = [tex]\frac{9. 4}{100}[/tex]

Volume = 0. 094

The number of gallons is given as;

= Volume × 1000

= 0. 094 × 1000

= 94 gallons

Thus, the number of gallons that must be applied is 94 gallons.

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A GDP per capita of $13,000 would correspond to the following corruption score of: B. 42.

A scatter plot can be defined as a type of graph which is used for the graphical representation of the values of two variables, with the resulting points showing any association (correlation) between the data set.

Based on the information provided in the table above, we can logically deduce that the situation can be modeled by this linear function:

y = 511x - 8540

Where:

x is the corruption score.

y is GDP per capita in dollars.

Based on the model, a GDP per capita of $13,000 would correspond to the following corruption score:

y = 511x - 8540

13,000 = 511x - 8540

511x = 13,000 + 8540

511x = 21,540

x = 21,540/511

x = 42.1 ≈ 42.

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