Which u-substitution would be useful in evaluating ∫sec²(3x-2) dx?

The equity in the house after three years is $30,000.

Equity in a house is the difference between the current market value of the house and the outstanding mortgage balance (if any). Since the problem does not mention any outstanding mortgage balance, we can assume that the entire purchase price of $250,000 was paid upfront.

Therefore, the equity in the house after three years is:

$280,000 (current market value) - $250,000 (original purchase price) = $30,000

So, you have $30,000 equity in the house after three years.

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Dana will need 8 gallons of fuel for her trip and it will cost her $35.60 in total.

To calculate the total cost of fuel for Dana's trip, we need to determine how many gallons of fuel she will need.

For the trip from New York to Boston, which is a distance of 200 miles, Dana will need 200/50 = 4 gallons of fuel.

For the return trip from Boston to New York, which is another 200 miles, Dana will also need 4 gallons of fuel.

Therefore, the total amount of fuel Dana will need for the round trip is 4 + 4 = 8 gallons.

Since biodiesel fuel costs $4.45 per gallon, the total cost of fuel for Dana's trip will be 8 x $4.45 = $35.60.

So Dana will need 8 gallons of fuel for her trip and it will cost her $35.60 in total.

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The probability that a randomly selected DVD player will have a replacement time less than 4.3 years is approximately 0.0304 or 3.04%.

The standard normal distribution to find the probability that a randomly selected DVD player will have a replacement time less than 4.3 years.

To do this, we first need to standardize the value of 4.3 using the mean and standard deviation of the replacement times:

[tex]z = (x - \mu) / \sigma[/tex]

x is the value we want to standardize, μ is the mean of the distribution, and σ is the standard deviation of the distribution.

Substituting the values given in the problem, we get:

z = (4.3 - 7.3) / 1.6

z = -1.875

A standard normal distribution table or calculator to find the probability that a randomly selected DVD player will have a replacement time less than -1.875.

Since the standard normal distribution is symmetric about zero, we can look up the probability of a z-score of 1.875 and subtract it from 0.5 to get the probability of a z-score less than -1.875:

P(Z < -1.875) = 0.0304

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When matched with examples, the words would be:

The goal of visiting all fifty states during one's lifespan is clearly a great undertaking. Furthermore, the amusement park ride that attempts to realistically reproduce each person's experience of skydiving is an astonishing feat.

Moreover, it is readily apparent the school buses remain stationary and without activity in their parking lot throughout the weekend-- displaying their ordinary idleness. Likewise, electric cars are known to require fewer repairs than those powered by gas engines, offering a tremendous advantage above traditional cars.

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By algebra properties and trigonometric functions, the solution to the trigonometric equation in the given interval is x = 30° or x = 60°.

In this question we find a trigonometric equation whose solution set must be found, this can be done by algebra properties and trigonometric functions. First, write the entire expression:

sin 2x - √3 / 2 = 0

Second, clear the trigonometric function:

sin 2x = √3 / 2

Third, use inverse trigonometric functions to eliminate the trigonometric function:

2 · x = sin⁻¹ (√3 / 2)

Sine function is positive for 0 < 2 · x < 180, then:

2 · x = 60° or 2 · x = 120°

x = 30° or x = 60°

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Answer:

(x+2)^2 - 6

Step-by-step explanation:

The solution is,  the changes in her account is a debit of $11 i.e. -$11

Here, we have,

Given

Polly bought a cracker for $7 and then bought a parrot for $4.

Required

Determine the changes in the account

First, we need to determine the total amount spent;

we have,

Polly bought a cracker for $7

then, bought a parrot for $4.

so, total changes is:

$7 +  $4

=$11

Hence, the changes in her account is a debit of $11 i.e. -$11.

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Reason:

I used the distributive property a(b+c) = ab + ac

Notice that 6p+21 = 3*2p+3*7 which shows each term has the GCF 3.

Answer:

3(2p+7)

Step-by-step explanation:

To find this, you have to find a number that, taken out of 6 and 21, can be taken out to become the factor product.

The GCF is 3, because 3 can go into 6 twice and into 21 7 times.

So,

3(2p+7)

When multiplied to check our work, we get 6p+21, so this is the correct equation.

Hope this helps :)

2/8 of the bars are blue and 3/4 bars are green.

Number of blue bars =4

Number of Green bars=12

Total number of bars = 16

Blue 4/16=1/4

Or the equivalent fraction of 1/4 is 2/8

Green = 12/16

Divide numerator and denominator by 4

Green =3/4

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The value of operated function is -3x²-13x+4.

Given are two functions f(x) = -x²+10x+3 and g(x) = -4x²-3x+7, we need find g(x) - f(x),

So,

g(x) - f(x) = -4x²-3x+7 - (-x²+10x+3)

= -4x²-3x+7 + x²-10x-3

Combining the like terms,

= -4x²+x²-3x-10x+7-3

= -3x²-13x+4

Hence the value of operated function is -3x²-13x+4.

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(5)The measure of the angle, m∠H  is 62⁰.

(6) The measure of arc XY is 120⁰.

(7) The measure of the angle, m∠GEF is 32⁰ and arc EG is 116⁰.

(8) The measure of the variable x is 10 and c is 62.

The measure of the angles is calculated as follows;

question 5.

m∠H + m∠A = 180 (opposite angles of a cyclic quadrilateral)

4x - 6 +  7x - 1 = 180

11x = 187

x = 187/11

x = 17

m∠H = 4(17) - 6 = 62⁰

Question 6.

arc ZY = 2 x ∠X (intersecting chord theorem)

arc ZY = 2 x 55 = 110⁰

arc XY = 360 - (arc ZY + arc XZ) (sum of angles in a circle)

arc XY = 360 - (110 + 130)

arc XY = 120⁰

question 7.

m∠GEF = ¹/₂ arc GF (intersecting chord theorem)

m∠GEF = ¹/₂ x 64

m∠GEF = 32⁰

arc EG = 180 - arc GF (sum of angles of a semicircle)

arc EG = 180 - 64

arc EG = 116⁰

Question 8.

8x + 10x = 180 (opposite angles of a cyclic quadrilateral)

18x = 180

x = 180/18

x = 10

c + 2c - 6 = 180 (opposite angles of a cyclic quadrilateral)

3c - 6 = 180

3c = 186

c = 186/3

c = 62

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The statement "For all integers a, b, and c, if a|bc then a|b or a|c" is false, as it does not hold true for all possible choices of a, b, and c. One counterexample to this statement is (a, b, c) = (2, 3, 4).

Here, a = 2, b = 3, and c = 4.

a|bc means "a divides bc", which is true in this case since 2 divides the product of 3 and 4. However, 2 does not divide either b or c individually, so a does not divide b or c. Therefore, the statement "if a|bc then a|b or a|c" is false for this particular choice of (a, b, c).

This counterexample shows that the statement is not true for all possible choices of a, b, and c, and therefore the statement is false. It is important to note that finding a single counterexample is enough to prove the statement false.

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We can use the fact that the sum of angles in a triangle is 180 degrees, and the sum of angles in a quadrilateral is 360 degrees, to solve for the variables.

For the first three angles:

M = 180 - 54 - 46 = 80

W = 180 - 46 - 130 = 4

K = 360 - 54 - 130 - 46 = 130

For the last two angles:

The sum of angles in a triangle is 180 degrees, so:

3aº + 110° + 180° = 180°

3aº = -110°

This doesn't make sense, since an angle cannot be negative. Therefore, there is no solution for a that satisfies the given conditions.

Answer:

M = 80

W = 4

K = 130

There is no solution for a that satisfies the given conditions.

Based on the given scatterplot the best prediction of weight of the 28 week old dog will be approximately 75 lb pounds.

In the given scatterplot in the x-axis we find the age of the dog in weeks and on the y-axis there is the weight of the dog per each week.

From the given scatterplot after observing closely, we can see that at 28 weeks which is in between 26 and 30, the weight of the dog will be approximately present at 75 lb which is in between 70 lb and 80 lb pounds on the y-axis.

From the above explanation, we can conclude that the weight of the 28 week old dog is 75 lb pounds.

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Given question is not having enough information, so I am attaching the complete question below:

The sequence is arithmetic and the common difference is -8.

The term number 24 is:

A(24) = -206

To check if a sequence is arithmetic, take the difference between the consecutive terms, you should get the same value for all the cases.

Here we have:

-22, -30, -38, -46, ...

The differences give:

-30 + 22 = -8

-38 + 30 = -8

-48 + 38 = -8

We get the same thing in all, so the sequence is arithmetic, and the common difference is -8.

The n-th term of this sequence will be:

A(n) = -22 + (-8)*(n - 1)

Then the 24th term is:

A(24) = -22 + (-8)*(24 - 1)= -206

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The equation of the transformed exponential function g(x) is g(x) = 2^-x - 1

From the question, we have the following parameters that can be used in our computation:

Parent function: y = 2^x

The graph of the transformed exponential function g(x) passes through the points  (-2,3), (-1,1), (0,0), (1,-0.5) and (2, -0.75)

So, we have the following transformation steps:

1st Transformation:

Reflect y = 2^x across the y-axis

So, we have

y = 2^-x

2nd Transformation:

Translate y = 2^-x down by 1 unit

So, we have

y = 2^-x - 1

This means that

g(x) = 2^-x - 1

Hence, the equation of the function g(x) is g(x) = 2^-x - 1

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The differential equation dy/dx = 3x² - 2 with f(-1) = 2 is y = x³ - 2x + 1To solve this differential equation, we need to integrate both sides with respect to x.

dy/dx = 3x² - 2

Integrating both sides:

∫dy = ∫(3x² - 2)dx

y = x³ - 2x + C

Here, C is the constant of integration that we need to find. To do that, we can use the initial condition f(-1) = 2.

Substituting x = -1 and y = 2 in the equation:

2 = (-1)³ - 2(-1) + C

2 = -1 + 2 + C

C = 1

Therefore, the solution to the differential equation is:

y = x³ - 2x + 1

To overlay this solution on a slope field for the differential equation, we need to first draw the slope field. We can do this by calculating the slopes at different points in the x-y plane.

Using the differential equation, we know that the slope at any point (x, y) is given by:

dy/dx = 3x² - 2

We can draw arrows with slopes equal to 3x² - 2 at various points in the plane to get the slope field.

Once we have the slope field, we can overlay the solution y = x³ - 2x + 1 on it by plotting the curve y = x³ - 2x + 1 and checking if the direction of the curve matches the arrows in the slope field.

Overall, the solution to the differential equation dy/dx = 3x² - 2 with f(-1) = 2 is y = x³ - 2x + 1, and we can overlay this solution on the slope field to visualize the behavior of the solution at different points in the plane.

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Answer:

11.40=7.50+0.65x. There are 6 toppings

Step-by-step explanation:

Answer: Equation: 7.50+(0.65 x 6)

6 toppings on the pizza

The correct answer is B. P{z ≥ 1.88}.

To find the p-value for a hypothesis test, you need to determine the probability of observing a test statistic as extreme or more extreme than the one you obtained, assuming that the null hypothesis is true.

In this case, the test statistic is Z = 1.88, which represents the number of standard deviations that the sample mean is away from the hypothesized population mean of 20, under the assumption that the null hypothesis is true.

Since this is a one-tailed test in the positive direction (Ha: μ > 20), we want to find the probability of observing a Z value that is greater than or equal to the observed test statistic of 1.88.

We can use a standard normal distribution table or a calculator to find this probability, which is the p-value.

Using a standard normal distribution table or a calculator, we find that the area to the right of Z = 1.88 is 0.0307, or approximately 0.031.

Therefore, the p-value is P{z ≥ 1.88} ≈ 0.031.

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Answer:

16 quarts left.

Step-by-step explanation:

just subtract.

Using Theorem 4.3.2, we can conclude that the sum of three rational numbers [tex](3(r^2), -2r, and 4)[/tex] is rational. Therefore, [tex]3r^2 - 2r + 4[/tex]is rational.

Theorem 4.3.2 states that the sum of any two rational numbers is rational. Therefore, let r and s be any two rational numbers. Then, r and s can be expressed as r = a/b and s = c/d, where a, b, c, and d are integers and b and d are not zero.

Using Theorem 4.3.2, we can conclude that r + s is also rational.

Now consider the expression[tex]3r^2 - 2r + 4[/tex]. We can express this as:

[tex]3r^2 - 2r + 4 = 3(r^2) - 2r + 4(1)[/tex]

Since [tex]r^2[/tex] is the product of two integers (r and r), it is also an integer. Using Theorem 4.3.1, we know that r is rational, and therefore [tex]3(r^2)[/tex] is the product of an integer and a rational number, making it rational.

Next, we know that -2r is the product of an integer (-2) and a rational number (r), making it rational.

Finally, 4(1) is simply 4, which is an integer.

Using Theorem 4.3.2, we can conclude that the sum of three rational numbers [tex](3(r^2), -2r, and 4)[/tex] is rational. Therefore, [tex]3r^2 - 2r + 4[/tex]is rational.

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The probability that it runs on electrical power and has an alarm is 0.54.

In the collection of clocks at Dr. Zadok's Museum, 28% run on electrical power, 45% have alarms, and 54% either run on electrical power or have alarms.

The number of clocks that do not meet both requirements (i.e., those that do not operate on electrical power or do not have alarms) can be subtracted from the total number of clocks in order to get the number of clocks that do so:

The probability that it runs on electrical power and has an alarm is calculated as,

P = 54 / 100

P = 0.54

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The area of the figure is 13 cm².

We have,

From the figure,

We can make two rectangles.

Now,

Length = 5 cm

Width =  1 cm

Area of one rectangle.

= 5 x 1

= 5 cm²

Length = 4 cm

Width = 2 cm

Area of another rectangle.

= 4 x 2

= 8 cm²

Now,

Area of the figure,

= 5 + 8

=  13 cm²

Thus,

The area of the figure is 13 cm².

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Answer:

The asymptotic behavior of f(x), where the leading term is 3x, is a straight line that grows without bound as x approaches infinity or negative infinity. The function has a slope of 3 and becomes increasingly steep in the positive and negative directions. This means that the function will either constantly increase or constantly decrease without limit as x approaches infinity or negative infinity.

There are 1040 citizens in the community. x is the total number of citizens in the community.

Let's use x to represent the total number of citizens in the community. We know that 400 citizens did not agree with the analysis, which means that the remaining (1 - 5/13) = 8/13 of citizens did agree with the analysis. Therefore, we can set up the following equation:

(8/13)x = number of citizens who agreed with the analysis

We can solve for x by adding the number of citizens who did not agree with the analysis to the number who did agree:

x = (8/13)x + 400

Multiplying both sides by 13, we get:

13x = 8x + 5200

Simplifying, we get:

5x = 5200

Dividing both sides by 5, we get:

x = 1040

Therefore, there are 1040 citizens in the community.

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If 5/13 of citizens believe that difficulty with procrastination led to not agreeing with an analysis, and 400 citizens did not agree with this analysis, how many citizens live in the community?

Miami, FL is higher in altitude than New Orleans, LA.

On the number line, the zero point represents sea level.

Miami, FL has an altitude of about [tex]6\frac{3}{5}[/tex] feet,

so it is represented by a point [tex]6\frac{3}{5}[/tex] units above sea level.

New Orleans, LA has an altitude of about [tex]-6\frac{1}{2}[/tex] feet

so it is represented by a point 6 1/2 units below sea level.

Thus, we can see that Miami, FL is higher in altitude than New Orleans, LA.

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Answer:

f(x) = 3x + 5

Step-by-step explanation:

You can use trial and error by putting each set of points into the equations and seeing which one works.

All four points work for the third function, f(x) = 3x + 5.

The evaluation of the points on the graph of the function indicates;

(a) The intercepts are;

x-intercepts; (-π, 0), (0, 0), (π, 0)

y-intercept; (0, 0)

(b) Domain; [-π, π]

Range [-8, 8]

(c) The interval the function is increasing is; [-π/2, π/2]

The interval the function is decreasing are; [-π, -π/2], [π/2, π]

(d) The function is an odd function

A function is a definition or rule that maps the set of input variables unto the set of output variables, such that each input maps unto exactly one output.

The parameters in the graph of the function f indicates that we get;

(a) The intercepts of the graph are the point where the graph intersects the x and y-axis, therefore;

The intercepts are; (-π, 0), (0, 0), and (π, 0)

Therefore;

The x-intercepts are; (-π, 0), (0, 0), and (π, 0)

The y-intercept is; (0, 0)

(b) The domain is the set of possible x-values, the domain is therefore; -π ≤ x ≤ π

The range is the set of the possible y-values. The graph indicates that the range is; -8 ≤ y ≤ 8

(c) The interval on which the y-values of the graph is increasing is; [-π/2, π/2]

The interval on which it is decreasing are; [-π, π/2], and [π/2, π]

(d) A function is even if f(x) = f(-x)

f(π/2) = 8

f(-π/2) = -8

f(x) ≠ f(-x)

The function is odd if -f(x) = f(-x)

The points on the graph indicates

f(π/2) = 8, -f(π/2) = -8 = f(-π/2)

The function is an odd function

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