if joe earns 90 buck a month and he need 700 how many months will he need to work

The approximate value of the definite integral ∫(0 to 0.4) ln(1 + x^5) dx using a power series is 0.073679.

To approximate the definite integral ∫(0 to 0.4) ln(1 + x^5) dx using a power series, we can use the Taylor series expansion of ln(1 + x). The Taylor series expansion of ln(1 + x) is:

ln(1 + x) = x - (x^2)/2 + (x^3)/3 - (x^4)/4 + ...

Integrating the power series term by term, we get:

∫(0 to 0.4) ln(1 + x^5) dx = ∫(0 to 0.4) [x^5 - (x^10)/2 + (x^15)/3 - (x^20)/4 + ...] dx

To approximate the integral, we can truncate the series and integrate the terms up to a desired degree. Let's approximate the integral using the first 6 terms:

∫(0 to 0.4) ln(1 + x^5) dx ≈ ∫(0 to 0.4) [x^5 - (x^10)/2 + (x^15)/3 - (x^20)/4] dx

Integrating each term individually, we get:

∫(0 to 0.4) ln(1 + x^5) dx ≈ [(x^6)/6 - (x^11)/22 + (x^16)/48 - (x^21)/84] |(0 to 0.4)

Evaluating the integral at the upper limit (0.4) and subtracting the value at the lower limit (0), we obtain the approximate value of the integral to six decimal places.

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What the first person said

The reason for statement (3) ∠1 ≅ ∠5 and ∠3 ≅ ∠6 is alternate interior angles.    

From the following attached diagram.

ABC is a triangle with line y is parallel to line z.

We can observe that side AC of triangle ABC is a transversal.

Here ∠1 and ∠5 are alternate interior angles.

⇒ ∠1 ≅ ∠5

Similarly, side AB of triangle ABC is a transversal.

Here ∠3 and ∠6 are alternate interior angles.

⇒  ∠3 ≅ ∠6

So, ∠1 = ∠5 and   ∠3 = ∠6         ............(from definition of congruence)

m∠1 + m∠2 + m∠3 = m∠LAM     ........(angle addition postulate)

m∠1 + m∠2 + m∠3 = 180°    ........(definition of straight angle)

m∠5 + m∠2 + m∠6 = 180°    ........(substitution)

Therefore, the two column proof is presented as follows:

      Statement                                            Reason

1. ABC is a triangle                                      Given

2. lines y and z are parallel                         Given

3. ∠1 ≅ ∠5 and ∠3 ≅ ∠6                        alternate interior angles.

4. m∠1 = m∠5; m∠3 = m∠6                  By definition of congruency

5. m∠1 + m∠2 + m∠3 = m∠LAM          By angle addition Postulate

6. m∠1 + m∠2 + m∠3 = 180°                Angles on a straight line

7. m∠5 + m∠2 + m∠6 = 180°                 Substitution (property)

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Find the complete question below.

Given: Lines y and z are parallel, and ABC forms a triangle. Prove: m∠5 + m∠2 + m∠6 = 180° Statements Reasons 1. ABC is a triangle 1. given 2. y ∥ z 2. given 3. ∠1 ≅ ∠5; ∠3 ≅ ∠6 3. ? 4. m∠1 = m∠5; m∠3 = m∠6 4. def. ≅ 5. m∠1 + m∠2 + m∠3 = m∠LAM 5. ∠ addition postulate 6. m∠1 + m∠2 + m∠3 = 180° 6. def. straight angle 7. m∠5 + m∠2 + m∠6 = 180° 7. substitution Which could be the missing reason in Step 3? alternate interior angles are congruent alternate exterior angles are congruent vertical angles are congruent corresponding angles are congruent

Answer:

Growth rate = 4.08%

Step-by-step explanation:

Rate of interest 'i' for the growth in the cost of the house,

i = \((\frac{\text{Final amount}}{\text{Initial amount}})^{\frac{1}{n}}-1\)

Here 'n' = Duration or time (in years)

i = \((\frac{560000}{320000})^{\frac{1}{14}}-1\)

i = \((\frac{7}{4})^{\frac{1}{14}}-1\)

i = 1.0408 - 1

i = 0.0408

i = 4.08%

Therefore, growth rate for this period is 4.08%.

To construct a truth table for the given logical expression using De Morgan's Law, we'll break it down step by step and apply the law to simplify the expression.

Let's start with the given expression:

Xyz + X(Y Z)' + X'(Y + Z) + (Xyz)' (X + Y')(X' + Z')(Y' + Z')

Step 1: Apply De Morgan's Law to the term (Xyz)'

(Xyz)' becomes X' + y' + z'

After applying De Morgan's Law, the expression becomes:

Xyz + X(Y Z)' + X'(Y + Z) + (X' + y' + z')(X + Y')(X' + Z')(Y' + Z')

Step 2: Expand the expression by distributing terms:

Xyz + XY'Z' + XYZ' + X'Y + X'Z + X'Y' + X'Z' + y'z' + x'y'z' + x'z'y' + x'z'z' + xy'z' + xyz' + xyz'

Now we have the expanded expression. To construct the truth table, we'll create columns for the variables X, Y, Z, and the corresponding output column based on the expression.

The truth table will have 2^3 = 8 rows to account for all possible combinations of X, Y, and Z.

Here's the complete truth table:

```

| X | Y | Z | Output |

|---|---|---|--------|

| 0 | 0 | 0 |   0    |

| 0 | 0 | 1 |   0    |

| 0 | 1 | 0 |   0    |

| 0 | 1 | 1 |   1    |

| 1 | 0 | 0 |   0    |

| 1 | 0 | 1 |   0    |

| 1 | 1 | 0 |   1    |

| 1 | 1 | 1 |   1    |

```

In the "Output" column, we evaluate the given expression for each combination of X, Y, and Z. For example, when X = 0, Y = 0, and Z = 0, the output is 0. We repeat this process for all possible combinations to fill out the truth table.

Note: The logical operators used in the expression are:

- '+' represents the logical OR operation.

- ' ' represents the logical AND operation.

- ' ' represents the logical NOT operation.

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By using the property of congruency of triangles,

\(\angle\)PSR = \(\angle\)PSQ has been proved

What is congruency of triangles?

Two triangles are said to be congruent if the corrosponding angles are equal and the corrosponding sides are equal.

There are different axioms of congruency. They are

SSS axiom, SAS axiom, AAS axiom, ASA axiom, RHS axiom

PS bisects \(\angle\)QPR [Given]

PQ \(\cong\) PR [Given]

\(\angle\)QPS \(\cong \angle\)RPS [PS bisects  \(\angle\)QPR]

PS \(\cong\) PS [Reflexive property of congruence]

\(\Delta\) PQS \(\cong \Delta\) PRS [SAS axiom]

\(\angle\)PSR = \(\angle\)PSQ [Corrosponding parts of congruent triangles are congruent]

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(a) The expression for a Riemann sum of a function f on an interval [a, b] is Δx = (b-a)/n

(b) If f(x)⩾ 0, then the geometric interpretation of a Riemann sum is infinity

(c) If f(x) takes on both positive and negative values, then the geometric interpretation of a Riemann sum is infinity

Riemann sums are an important tool in calculus for approximating the area under a curve. They are used to estimate the value of a definite integral, which represents the area bounded by the curve and the x-axis on a given interval. In this explanation, we will discuss the expression for a Riemann sum, its notation, and its geometric interpretation.

(a) Expression for a Riemann sum:

A Riemann sum is an approximation of the area under a curve using rectangles. We divide the interval [a, b] into n subintervals, each of length Δx=(b−a)/n. The notation used to represent this is:

Δx = (b-a)/n

(b) Geometric interpretation of a Riemann sum when f(x)⩾ 0:

If f(x) is always non-negative, the Riemann sum represents an approximation of the area between the curve and the x-axis on the interval [a, b].

Each rectangle has a positive area, which contributes to the overall area under the curve. The sum of the areas of the rectangles approaches the true area under the curve as the number of subintervals n approaches infinity.

(c) Geometric interpretation of a Riemann sum when f(x) takes on both positive and negative values:

When f(x) takes on both positive and negative values, the Riemann sum represents the net area between the curve and the x-axis on the interval [a, b].

Each rectangle may have a positive or negative area, depending on the sign of f(xi).

The positive areas represent regions where the curve is above the x-axis, and the negative areas represent regions where the curve is below the x-axis.

In conclusion, Riemann sums are used to approximate the area under a curve on an interval [a, b]. The expression for a Riemann sum involves dividing the interval into n subintervals and approximating the area under the curve using rectangles.

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Answer:

Additive inverse is -2

Multiplicative inverse is 1/2

Answer:

2 is an integer then the multiplicative inverse of 2 is \[\dfrac{1}{2}\]. Hence, we obtained the additive inverse of 2 is -2 and the multiplicative inverse of 2 is \[\dfrac{1}{2}\].5 days ago

https://www.vedantu.com › the-sum...

The sum of additive inverse and multiplicative inverse of 2 is ______.(a). \\[\\dfrac{3}{2}\\](b). \\[\\dfrac - Vedantu

Strictly increasing functions:

Let a function f(a) for x = a, then,

f(a + h), for x = a + h,

If f(a + h) > f(a), we say this a strictly increasing function, as with increase in x, f(x) also increases.

In the given graph, there are straight lines so you can say increasing interval would have +ve slope.

For x = -5 to -4, it increases = [-5, -4]

For x = 1 to 3, it increases = [1, 3]

Answer: [-5, -4] , [1, 3]

Answer:

Step-by-step explanation:

Remark

My guess is that what is confusing you is not what you have to do, but why it is disguised as g(n)

What you are doing in effect is setting up a table. You are also not certain where the table starts. And that is a problem. I will start it at zero, but it might be 1.

zero

n = 0

g(0) = 34 - 5*0

g(0) = 34

One

n = 1

g(1) = 34 - 5*1

g(1) = 34 - 5

g(1) = 29

Two

g(2) = 34 - 5*2

g(2) = 34 - 10

g(2) = 24

Three

g(3) = 34 - 5*3

g(3) = 34 - 15

g(3) = 19

Four

g(4) = 34 - 5*4

g(4) = 34 - 20

g(4) = 19

Answer

0      1       2       3      4

34  29     24     19     14

B, idek? if correct brainliest pls :)

Answer:

yea its B      C = 8(2.59+0.50)

Step-by-step explanation:

Answer:

Yes 17/20 is bigger than 7/9

Step-by-step explanation:

17 divided by 20 = 0.85

7 divided by 9 = 0.778 ish

17/20 is bigger

Answer:

he trigonometric ( or polar) form of  z= a+bi is z = r(cosθ+isinθ) .

So for Part 3  3 - 3i we have r = √(3^2 + (-3)^2) = 3√2 and θ= arctan(3/-3) = arctan (-1) = -π/4.

So the answer is  3√2(cos(-π/4) + isin(-π/4).

Part 1.  3 =  3(cos 0 - i sin 0).

Part 2.  -6i =  6(cos (-π/2) - isin -(π/2)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Step-by-step explanation:

15 r blue marbles

20- 5 = 15

Cohen's conventions for interpreting d, this effect is small. Therefore, the correct answer is a. small.

According to Cohen's conventions for interpreting the effect size (d), the effect described in the study is considered "small." Cohen's conventions provide a general guideline for categorizing the magnitude of an effect size.

In this case, the effect size (d) is calculated to be 0.02. Cohen's conventions typically classify effect sizes as follows:

Small effect: d = 0.2

Medium effect: d = 0.5

Large effect: d = 0.8

Since the effect size of 0.02 is significantly smaller than the threshold for a small effect (0.2), it falls into the "small" category. This means that the difference in the number of words uttered per day between men and women, as reported in the study, is relatively small or negligible in practical terms.

Therefore, the correct answer is a. small.

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Answer:

\( \sqrt{24} = 4.9\)

\( \sqrt{102} = 10.1\)

positive integers = x

4.9 < x < 10.1

x = 5, 6, 7, 8, 9, 10

sum = 5 + 6 + 7 + 8 + 9 + 10

= 45

Answer:

Given

distributive property

Subtraction property of equality

Addition property of equality

Division property of equality

Solution

Step-by-step explanation:

Answer:

Step-by-step explanation:

If sh starts reading at 3:25 and reads for 15 minutes, she is finished at 3:40. The hour hand is on the 3 and the minute hand is on the 8, so there is a difference of 25 minutes between the hour hand and the minute hand. Each 5-minute increment is 30 degrees (360 / 12) so 30 x 5 = 150 degrees. This is an obtuse angle. Not sure what kind of an answer you're looking for so I gave both the degree measure of the angle formed by the hour hand and the minute hand, and the classification of the angle.

Answer:

90 degrees, which is a right angle

Step-by-step explanation:

The time indicates when she starts reading is irrelevant. The only thing to notice is that she reeds for 15 minutes. Whenever you read for 15 minutes the angle that is formed by the hour and minute hands of the clock will always be the same, regardless of the starting time!

60 minutes comes down to 360 degrees.

1 minute = 60/60 and that comes down to 360/60 = 6 degrees.

15 minutes = 15 times 1 minute....

15 minutes comes down to 15* 6 = 90 degrees

90 degrees is a right angle

The length should be x ≥ 3 inch and 4x ≥ 12 square inches.

The mathematical expression for inequality states that neither side is equal. In mathematics, inequality occurs when the relationship results in a non-equal comparison between two expressions or numbers. Any of the inequality symbols, such as greater than (>), less than (<), greater than or equal to (≥), less than or equal to (≤), or not equal to (≠), can take the place of the equal sign "=" in this expression. Polynomial inequality, rational inequality, and absolute value inequality are the various kinds of mathematical inequalities.

Given a rectangle, length  = 4 inches

area is at least 12 square inches

inequality equation for area

A ≥ 12

area  = l x b

where l = length = 4 inches and b = breadth = x

A ≥ 12

4x ≥ 12

x ≥ 3 inches

Hence the breadth should be x ≥ 3 inches and equation of area is

4x ≥ 12 square inches.

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The complete question is,

Kendra is drawing a rectangle. The length will be 4 inches, and the area will be at least 12 square inches. Let x represent the width of the rectangle. Which inequality describes the problem?

Answer:

0.436 x 6

2.616

More info

Step-by-step explanation:

Brainliest or.. else..

Answer:

-300

just do inverse operation, and multiply both sides of the equation by -15 to cancel out the -15 from the denominator and you get V=20(-15)

solve for 20(-15) and you get -300

Answer:

The coordinates of D is;

Explanation:

The question can be illustrated diagramatically as;

The drawing is not to scale. it is just a way of explainuing the scenario.

To find the coordinates of the end point D(x,y).

Let us apply the mid point formula;

The same applys to y coordinates.

Given;

Substituting we have;

Also,

Therefore, the coordinates of D is;

Answer:

The answer is A.

Step-by-step explanation:

The possible advance in the field of biology that would be a result of the stem cell research is: Creation of a novel cancer cell line to test anticancer agents.

This is a type of research that is carried out by biogical researchers. The function of this type of research is to manipulate the different cells that are in the human body.

This research is done in order to specialize some body cells that can be used to treat different diseases.

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Answer:

-------------------------

Each coordinate of the midpoint is the average of endpoints:

Therefore M is (13, 14).

Answer: the answer is -32

Step-by-step explanation: multiply -2 by itself 5 separate times.

Answer:

-32

Step-by-step explanation:

-2×-2×-2×-2×-2=4×4×-2

=-32

Salma must score 405 on exam B in order to do equivalently well as she did on exam A.

To determine how well Salma must score on exam B to perform equivalently to exam A, we need to compare the scores relative to their respective means and standard deviations. Since the scores on each exam are normally distributed, we can use z-scores to make the comparison.

First, we calculate the z-score for Salma's score on exam A using the formula: z = (x - mean) / standard deviation.

For exam A:

z = (69 - 64) / 10 = 0.5

Next, we find the corresponding raw score on exam B that corresponds to the same z-score of 0.5. Using the formula: x = z * standard deviation + mean.

For exam B:

x = 0.5 * 100 + 400 = 405

Therefore, Salma must score 405 on exam B in order to perform equivalently to her score of 69 on exam A. This means that if she achieves a score of 405 on exam B, it would be at the same relative position in the distribution as her score of 69 on exam A, taking into account the different means and standard deviations of the two exams.

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Answer:

2.1

Step-by-step explanation:

Here we will simplify the ratio 30:15 for you and show you how we did it.

To simplify the ratio 30:15, we find the greatest common divisor of 30 and 15, and then we divide 30 and 15 by the greatest common divisor.

The greatest common divisor that you can use to simplify 30:15 is 15. Which means the answer to ratio 30:15 simplified is: 2.1

Answer:

d=-4

Step-by-step explanation:

-7d - 5 = 23

-7d = 28

d = -4

Answer:-6d-3f+5

Step-by-step explanation: