The Bells obtain a 25​-year, ​$150,000 conventional mortgage at a 10.0​% rate on a house selling for ​$190,000. Their monthly mortgage​ payment, including principal and​ interest, is ​$1363.50. They also pay 3 points at closing.

The number of times that the band played an encore at 7 out of the next 14 shows.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The band should do an encore at a rate of 2 out of every 4 gigs, or 2/4 = 1/2 shows, according to the available statistics.

We may use the following percentage to determine how many of the following 14 performances will likely have an encore:

1/2 = x/14

14 = 2x

x = 7

Therefore, we can expect the band to play an encore at 7 out of the next 14 shows.

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Answer: Number 2

Step-by-step explanation: yes

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the line above, since a parallel line will have the same slope anyway

\((\stackrel{x_1}{4}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-1}-\stackrel{y1}{3}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{4}}} \implies \cfrac{ -4 }{ -3 } \implies {\Large \begin{array}{llll} \cfrac{ 4 }{ 3 } \end{array}}\)

I assume the equation is

\(x \, dy - (y^2 - 4y) \, dx = 0\)

since separating variables leads to

\(x\,dy = y(y-4) \, dx\)

\(\dfrac{dy}{y(y-4)} = \dfrac{dx}x\)

for which the condition that \(x>0\) is actually relevant, as opposed to the simpler differential equation

\(x \, dx - (y^2-4y)\, dy = 0 \implies y(y-4) \, dy = x \, dx\)

(though it's a bit more work to solve for \(y(x)\) in this case)

That the slope \(\frac{dy}{dx}\) is non-zero tells us that

\(\dfrac{dy}{dx} = \dfrac{y(y-4)}x \neq 0 \implies y\neq0 \text{ and } y \neq 4\)

Integrate both sides.

\(\displaystyle \int \frac{dy}{y(y-4)} = \int \frac{dx}x\)

On the left, expand into partial fractions.

\(\displaystyle \frac14 \int \left(\frac1{y-4} - \frac1y\right) \, dy = \int \frac{dx}x\)

\(\dfrac14 (\ln|y-4| - \ln|y|) = \ln|x| + C\)

With the given initial value, we find

\(y(1) = 2 \implies \dfrac14 (\ln|2-4| - \ln|2|) = \ln|1| + C \implies C = 0\)

so the particular solution is

\(\dfrac14 (\ln|y-4| - \ln|y|) = \ln|x|\)

By definition of absolute value, with the initial condition of \(0 < y=2 < 4\) and the condition \(x>0\), we can remove the absolute values.

\(\dfrac14 (\ln(4-y) - \ln(y)) = \ln(x)\)

Solve for \(y\).

\(\ln\left(\dfrac{4-y}y\right) = 4 \ln(x) = \ln\left(x^4\right)\)

\(\dfrac{4-y}y = \dfrac4y - 1 = x^4\)

\(\implies y(x) = \dfrac4{1 + x^4}\)

Then

\(10y\left(\sqrt2\right) = \dfrac{40}{1 + \left(\sqrt2\right)^4} = \boxed{8}\)

On the off-chance you meant the other equation I suggested, we find

\(\displaystyle \int y(y-4) \, dy = \int x \, dx\)

\(\displaystyle \frac{y^3}3 - 2y^2 = \frac{x^2}2 + C\)

\(y(1) = 2 \implies \dfrac83 - 2\cdot4 = \dfrac12 + C \implies C = -\dfrac{35}6\)

Solving for \(y(x)\) involves picking the right branch of the cube root that agrees with \(y(1)=2\). With the cube root formula, we find

\(y(x) = 2 - \xi(1 - i\sqrt3) - \dfrac1\xi (1+i\sqrt3)\)

where

\(\xi = \dfrac{2\sqrt[3]{4}}{\sqrt[3]{3x^2 - 3 + \sqrt{9x^4 - 18x^2 - 1015}}}\)

With a calculator, we find

\(10y\left(\sqrt2\right) \approx 18.748\)

Answer:

Its A. Medera turned the phone off while playing in the soccer game

Step-by-step explanation:

Answer:

It is A.Medera turned the phone off while playing in a soccer game.

Step-by-step explanation:

got a 100 on the test

Answer:

→402 is not a term in the given sequence.

Step-by-step explanation:

Given sequence is 8,13,18,23,...

First term = 8

Common difference = 13-8= 5

⇛18-13=5

⇛23-18=5

Since the common difference is same throughout the sequence

⇛8,13,18,23,... are in the AP.

Let nth term = 402

We know that

nth term of an AP = an = a+(n-1)d

Now,

an = 402

⇛8+(n-1)(5) = 402

⇛8+5n-5 = 402

⇛5n+3 = 402

⇛5n = 402-3

⇛5n = 399

⇛n = 399/5

n can not be rational number it should be a positive integer.

402 is not a term in the given sequence.

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Answer:

d. Definite integral can be used to calculate area under a curve in a given interval

General Formulas and Concepts:

Calculus

Integration

Area of a Region Formula:                                                                                    \(\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx\)

Step-by-step explanation:

We know that by definition, an integral is an antiderivative.

Also by definition, an integral is also the area under the curve. This can be extended to area between 2 curves.

We have a formula specifically to find an area under a curve (region), as listed above.

∴ our answer is D.

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

The inequality represented by the graph is given as follows:

y > 3x - 4.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The graph crosses the y-axis at y = -4, hence the intercept b is given as follows:

b = -4.

When x increases by 1, y increases by 3, hence the slope m is given as follows:

m = 3.

Hence the equation of the line is:

y = 3x - 4.

The inequality is composed by the values to the right (greater) of the line, and has an open interval due to the dashed line, hence:

y > 3x - 4.

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Answer:

Step-by-step explanation:

By using a statistical calculator, the actual sample mean and sample standard deviation are:

Actual sample mean = 46.1500.

Actual ample standard deviation = 8.6256.

In Mathematics and Geometry, the sample mean for any set of data can be calculated by using the following formula:

Mean = ∑x/(n - 1)

In Mathematics and Geometry, the sample standard deviation for any set of data can be calculated by using the following formula:

Standard deviation, δx = √(1/N × ∑(x - \(\bar{x}\))²)

By using a statistical calculator, the actual sample mean and sample standard deviation are as follows;

Actual sample mean = 46.1500.

Actual ample standard deviation = 8.6256.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

not sure if the 4 is seperate but if it is then (30+26)+(6-33)

Step-by-step explanation:

Answer:

3/2^3=3/8 and (-1/4)^2 = 1/16

Step-by-step explanation:

1. You know what 2^3 is, right? That's 2*2*2. 2*2 is 4, and then 4*2 is 8. So that is 3/8.

2. (-1/4)^2 is (-1/4)*(-1/4), right? So that is (-1*-1)/(4*4). Two negatives make a positive, so -1*-1=1. 4*4 is 16, so we have 1/16.

Answer:

(x + 4)^2 + (y + 7)^2 = 36

Step-by-step explanation:

The given information describes a circle with its center at (-4, -7) and tangent to the vertical line x = 2. To determine the radius of the circle, we need to find the distance between the center and the tangent line.

The distance between a point (x1, y1) and a line Ax + By + C = 0 is given by:

d = |Ax1 + By1 + C| / sqrt(A^2 + B^2)

In this case, the equation of the line is x = 2, which can be written as 1x + 0y - 2 = 0. Therefore, A = 1, B = 0, and C = -2. The center of the circle is (-4, -7), so x1 = -4 and y1 = -7. Substituting these values into the formula, we get:

d = |1*(-4) + 0*(-7) - 2| / sqrt(1^2 + 0^2)

d = |-6| / sqrt(1)

d = 6

Therefore, the radius of the circle is 6 units. The equation of a circle with center (h,k) and radius r is given by:

(x - h)^2 + (y - k)^2 = r^2

Substituting the values we have found, we get:

(x + 4)^2 + (y + 7)^2 = 36

This is the equation of the circle that satisfies the given conditions.

If you do a reflection on the x-axis, you're taking the points from (x , y) to (x , -y).

The only case where the circle won't change its center it is when the center is located at the x-axis(when y = 0).

From the examples given in the question, only the circle C won't change its center.

The answer would be:

Circle A: Support

Circle B: Support

Circle C: Refute

Circle D: Support

Answer:

A

Step-by-step explanation:

To prove that line segment a is parallel to line segment d, based on the given information, we can utilize the properties of perpendicular and parallel lines.

Given that a is perpendicular to b and b is perpendicular to c, we know that angles formed between a and b, as well as between b and c, are right angles. Let's denote these angles as ∠1 and ∠2, respectively.

Now, since c is parallel to d, we can conclude that the corresponding angles ∠2 and ∠3, formed between c and d, are congruent.Considering the fact that ∠2 is a right angle, it can be inferred that ∠3 is also a right angle.

By transitivity, if ∠1 is a right angle and ∠3 is a right angle, then ∠1 and ∠3 are congruent.Since corresponding angles are congruent, and ∠1 and ∠3 are congruent, we can deduce that line segment a is parallel to line segment d.

Thus, we have successfully proven that a is parallel to d based on the given information and the properties of perpendicular and parallel lines.

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The equations that are true for x = -2 and x = 2 are x² + 4 = 0 and 4x² = 16. So, the correct option is A) and D).

To determine which equations are true for x = -2 and x = 2, we simply substitute these values into each equation and check if the equation is true or not. Here are the results

x² - 4 = 0

Substituting x = -2 gives (-2)² - 4 = 0, which is true. Substituting x = 2 gives 2² - 4 = 0, which is also true. Therefore, this equation is true for both x = -2 and x = 2.

x² = -4

Substituting x = -2 gives (-2)² = -4, which is not true. Substituting x = 2 gives 2² = -4, which is also not true. Therefore, this equation is not true for either x = -2 or x = 2.

3x² + 12 = 0

Substituting x = -2 gives 3(-2)² + 12 = 0, which is true. Substituting x = 2 gives 3(2)² + 12 = 24, which is not equal to zero. Therefore, this equation is true for x = -2 but not for x = 2.

4x² = 16

Substituting x = -2 gives 4(-2)² = 16, which is true. Substituting x = 2 gives 4(2)² = 16, which is also true. Therefore, this equation is true for both x = -2 and x = 2.

2(x - 2)² = 0

Substituting x = -2 gives 2(-2 - 2)² = 0, which is true. Substituting x = 2 gives 2(2 - 2)² = 0, which is also true. Therefore, this equation is true for both x = -2 and x = 2.

Therefore, the two equations that are true for both x = -2 and x = 2 are x² - 4 = 0 and 4x² = 16. So, the correct answer is A) and D).

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The solution of the inequality is 8 ≥  x  or x > 10. The graph of the solution is attached

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value e.g. 5 < 6, x ≥ 2, etc.

Solving for x:

11≥ 2x - 5 or 2x - 5 > 15

Collect like terms:

11 + 5 ≥ 2x  or 2x > 15 + 5

16 ≥ 2x  or 2x > 20

8 ≥  x  or x > 10

Note:  8 ≥  x can also be written as x ≤ 8

We can combine the two as follow:

Inequality notation: 8 ≥  x > 10

The graph of the solution is attached

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Based on the interval, the average rate of change of the function is 4.0

The graph that completes the question is added as an attachment

From the graph, we can see  that the equation of the graph is a quadratic equation

Also, from the question:

We have the interval to be:

The interval is given as

x = -4 to x = 2

This can be represented as

(a, b) = (-4, 2)

From the attached graph, we have

f(-4) = 22

f(2) = -2

The estimate of the average rate of change f is calculated as(to one decimal place)

Rate = [f(b) - f(a)]/[b - a]

Substitute the known values in the above equation

This gives

Rate = [f(2) - f(-4)]/[2 + 4]

Substitute the known values in the above equation

So, we have

Rate = [-2 - 22]/[2 + 4]

Evaluate

Rate = -4.0

Hence, the estimate (to one decimal place) of the average rate of change of the graph is 4.0

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The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

We have,

To solve the integral ∫ (log(1 + x²) / (x + 1)²) dx, we can use the method of substitution.

Let's substitute u = x + 1, which implies du = dx. Making this substitution, the integral becomes:

∫ (log(1 + (u-1)²) / u²) du.

Expanding the numerator, we have:

∫ (log(1 + u² - 2u + 1) / u²) du

= ∫ (log(u² - 2u + 2) / u²) du.

Now, let's split the logarithm using the properties of logarithms:

∫ (log(u² - 2u + 2) - log(u²)) / u² du

= ∫ (log(u² - 2u + 2) / u²) du - ∫ (log(u²) / u²) du.

We can simplify the second integral:

∫ (log(u²) / u²) du = ∫ (2 log(u) / u²) du.

Using the power rule for integration, we can integrate both terms:

∫ (log(u² - 2u + 2) / u²) du = log(u² - 2u + 2) / u - 2 ∫ (log(u) / u³) du.

Now, let's focus on the second integral:

∫ (log(u) / u³) du.

This integral does not have a simple closed-form solution in terms of elementary functions.

It can be expressed in terms of a special function called the logarithmic integral, denoted as Li(x).

Therefore,

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

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Using central angle theorem,

The measure of the arc BC = 110°.

An angle with its vertex in the middle of the circle it creates with its two radii is said to be central.

Here in the question,

As per the central angle theorem:

(2x -30) ° + x° = 180°

⇒ 2x - 30 + x = 180

⇒ 3x - 30 = 180

Adding 30 on both sides:

⇒ 3x = 180 + 30

⇒ 3x = 210

Dividing both sides by 3.

⇒ x = 70°

Now BC = 2x-30

= 2 × 70 -30

= 140 - 30

= 110°

Therefore, the measure of BC = 110°.

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Answer:

it is too blury to read

Step-by-step explanation:

Answer:

0.25M + 0.75B + 1.25C - 50 = total money raised

Step-by-step explanation:

0.25 for each muffin so if 78 are sold we do 78*0.25 = 19.5

0.75*56 = 42 for brownies

1.25*30 = 37.5

19.5+42+37.5 = 99

99 -50 = 49

9514 1404 393

Answer:

Step-by-step explanation:

Your calculator can do this for you.

1. 2/4 = 1/2 = 5/10 = 0.5

__

2. The long division immediately becomes repetitive. The decimal equivalent is repeating 4s: 0.444...

_____

The long division is shown in the attachments. When the remainder is the same as the initial dividend, you know the quotient will repeat.

Answer:

the absolute value of 5 is 5 and absolute value of -5 is also 5.

Step-by-step explanation:

the absolute value of a number refers to how many spaces away a number is from 0, so it doesn't matter if the number is positive or negative, the absolute value is always positive. the absolute value of -7 is 7, the absolute value of 24 is 24, the absolute value of -435,706 is 435,706, the absolute value of 1,234,567,890 is 1,234,567,890.

i hope this helped :))

Answer:

the first 2

Step-by-step explanation:

let me know if it is wrong

The match for the items are:  exponential function, characteristic, common logarithm,  mantissa, characteristic, antilog,  matrix

The items in the question can be matched below

Here's the match for the items:

y = 2* ----> exponential function

exponents ----> characteristic

log 100 = g ----> common logarithm

0.8395 when log 6,910 = 3.8395 ----> mantissa

3 when log 6,910 = 3.8395 ----> characteristic

6,910 when log 6,910 = 3.8395 ----> antilog

rectangular array of numbers ----> matrix

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The value of x when the secant intersect is 5.

When two secants intersect outside a circle, the circle divides the secants into segments that are proportional with each other.

Therefore,

(4 + 5)4 = (x - 2 + x + 4)(x - 2)

9(4) = (2x + 2)(x - 2)

36 = 2x² - 4x + 2x - 4

2x² - 2x - 4 - 36 = 0

2x² - 2x - 40 = 0

x² - x - 20 = 0

x² - 5x + 4x  - 20 = 0

x(x - 5) + 4(x - 5) = 0

(x + 4)(x - 5) = 0

(x - 5)(x + 4) = 0

x = 5 or x = -4

Therefore,

x = 5

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Answer:

  -1

Step-by-step explanation:

You want the slope of the line through the points (-3, 4) and (2, -1).

The slope is given by the formula ...

   m = (y2 -y1)/(x2 -x1)

Using the given points, we find the slope to be ...

  m = (-1 -4)/(2 -(-3)) = -5/5 = -1

The slope of the line through the given points is -1.