Was $15.60 now is $34.80 Percent increase or percent decrease

Step-by-step explanation:

x=10

y=24

r=√10²+24²=√100+576=√676=26

sin = y/r = 24/26

cos = x/r =10/26

tan=y/x = 24/10

csc = r/y=26/24

sec= r/x = 26/10

tan = x/y = 10/24

The conclusion of the symbolised argument is that N implies (O and P). This can be proven using conditional proof and the eighteen rules of inference, or using the rule of conjunctive simplification.

The symbolic argument's conclusion is that N implies (O and P). This can be demonstrated using conditional proof and the eighteen inference rules.

Proof:

1. N ⊃ O (Premise)

2. N ⊃ P (Premise)

3. N (Assumption)

4. O (1,3 Modus Ponens)

5. P (2,3 Modus Ponens)

6. O•P (4,5 Conjunction)

7. N ⊃ (O•P) (3-6 Conditional Proof)

8. N ⊃ (O•P) (2,7 Disjunctive Syllogism)

This leads us to the conclusion that N implies (O and P).

Without the use of conditional proof, the identical result can be reached. The conjunctive simplification rule can be used to do this.

Proof:

1. N ⊃ O (Premise)

2. N ⊃ P (Premise)

3. N (Assumption)

4. O (1,3 Modus Ponens)

5. P (2,3 Modus Ponens)

6. O•P (4,5 Conjunction)

7. N ⊃ (O•P) (Conjunctive Simplification)

Therefore, we have derived the conclusion that N implies (O and P).

Complete Question:

Use conditional proof and the eighteen rules of inference to derive the conclusions of the following symbolized arguments. Having done so, attempt to derive the conclusions without using conditional proof.

1. N ⊃ O

2. N ⊃ P / N ⊃ (O • P)

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To write the expression with a rationalized denominator, you need to eliminate the square root from the denominator. Here's the expression you provided: (3√2) / (3√4). Let's rationalize the denominator step by step:

1. Evaluate the square root in the denominator: √4 = 2.
  So, the expression becomes: (3√2) / (3 * 2).

2. Simplify the denominator: 3 * 2 = 6.
  The expression now is: (3√2) / 6.

3. Since there is no square root in the denominator, it is already rationalized.

So, the expression with a rationalized denominator is (3√2) / 6.

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False. The symbol x¯ represents the population mean of all possible sample means of size n.

The symbol x¯ (x-bar) represents the sample mean, not the population mean of all possible sample means of size n. The population mean of all possible sample means of size n is denoted by μ (mu). The sample mean, x¯, is calculated by taking the average of the observations in a specific sample.

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We now have three equations, so we can solve them.

Let's define the length of the 3 boards in terms of x:

F=x

S=2x-3

T=2

F+S+T =26

x+2x-3+2 =26

3x =26+1=27

x =27/3 = 9 feet for First section

2x-3 =18-3 = 16 feet = Second

2 = Third

9+16+2 = 27

27 is the length of the shortest piece.

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Answer:

2x^2-4x+8

Step-by-step explanation:

Answer:

rational #, natural #, whole #

Step-by-step explanation:

Answer:

See below ↓

Step-by-step explanation:

19.

20.

Answer:

He has to route 23 calls

Step-by-step explanation:

If he spends 2 mins in each phone call, and he'll spend 46 mins routing calls. Your answer is 23 sense 46 divided by 2 is 23

 Robert have to route 23 phone calls to spend a total of  46 minutes on the phone.

" Time is defined as ongoing sequence of certain event during a fixed period."

According to the question,

Time taken by Robert for routing each incoming phone = 2minutes.

Number of phone calls Robert route in 1 minute = 1 / 2

Number of phone calls Robert route in 46 minutes = (1 / 2) × 46

                                                                                       = 23 phone calls

Hence,  Robert have to route 23 phone calls to spend a total of  46 minutes on the phone.

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a) The 90% confidence interval for the population proportion is approximately (0.7777, 0.8423).

b) The 95% confidence interval for the population proportion is approximately (0.7737, 0.8463).

To calculate the confidence intervals for the population proportion, we can use the formula:

Confidence Interval = sample proportion ± margin of error

The margin of error can be calculated using the formula:

Margin of Error = critical value * standard error

where the critical value is determined based on the desired confidence level and the standard error is calculated as:

Standard Error = \(\sqrt{((p * (1 - p)) / n)}\)

Given that the sample proportion (p) is 0.81 and the sample size (n) is 500, we can calculate the confidence intervals.

a. 90% Confidence Interval:

To find the critical value for a 90% confidence interval, we need to determine the z-score associated with the desired confidence level. The z-score can be found using a standard normal distribution table or calculator. For a 90% confidence level, the critical value is approximately 1.645.

Margin of Error = \(1.645 * \sqrt{(0.81 * (1 - 0.81)) / 500)}\)

≈ 0.0323

Confidence Interval = 0.81 ± 0.0323

≈ (0.7777, 0.8423)

Therefore, the 90% confidence interval for the population proportion is approximately (0.7777, 0.8423).

b. 95% Confidence Interval:

For a 95% confidence level, the critical value is approximately 1.96.

Margin of Error = \(1.96 * \sqrt{(0.81 * (1 - 0.81)) / 500)}\)

≈ 0.0363

Confidence Interval = 0.81 ± 0.0363

≈ (0.7737, 0.8463)

Thus, the 95% confidence interval for the population proportion is approximately (0.7737, 0.8463).

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It is a continuous variable, as it can take on any value within a certain range (i.e., any value between a positive delay and a negative early arrival).

The variable described is quantitative, as it represents a numerical measurement of time, which is a continuous variable that can take on any value within a certain range. The range includes both positive values, representing delays, and negative values, representing early arrivals. This variable is a useful metric for tracking the performance of transportation systems or airlines, as it provides an objective measure of the amount of time a flight is delayed or arrives early. By analyzing the distribution of arrival delay times, policymakers and transportation providers can identify patterns, trends, and potential areas for improvement in their service delivery.

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the answer to this problem is 63

Answer:

A

Step-by-step explanation:

47+58=105 then you just subtract 7 from 75 and you get 68 than you divide 68 by 2

9514 1404 393

Answer:

  (3) y + 1 = -1/2(x + 6)

Step-by-step explanation:

The slope of the line between the two points can be found from the slope formula:

  m = (y2 -y1)/(x2 -x1)

  m = (-1 -1)/(6 -2) = -2/4 = -1/2

Then the point-slope form of the equation of the line through the given points can be written as either of ...

  y -1 = -1/2(x -2)

  y +1 = -1/2(x -6)

We note that only choices (2) and (3) have slopes of -1/2, so are parallel. Choice (2) matches the first equation above, so is the identical line, not one that is parallel.

Choice (3) matches neither of the equations of the line through the given point, so that is the choice of interest.

point B is located in quadrant II (option B)

Point A: (6, 3) = (x, y)

reflection of point A across the y axis:

The x coordinate will be negative and the y coordinate will remain the same

reflection of point A across the y axis = (-6, 3)

Attaching the graph showing the point after reflection:

Since point B is the reflection of point A.

Hence, point B is located in quadrant II (option B)

The total distance traveled over the interval 0 < t < 8 is: 32/3 + 16/3 + 176/3 = 224/3.

To find the displacement over the given interval, we need to integrate the velocity function:

∫v(t)dt = ∫(t^3 - 10t^2 + 24t)dt = (1/4)t^4 - (10/3)t^3 + 12t^2

Now we can evaluate the displacement over the different intervals:

0 < t < 4:

(1/4)(4)^4 - (10/3)(4)^3 + 12(4)^2 = 32/3

4 < t < 6:

(1/4)(6)^4 - (10/3)(6)^3 + 12(6)^2 - [(1/4)(4)^4 - (10/3)(4)^3 + 12(4)^2]

= -16/3

6 < t < 8:

(1/4)(8)^4 - (10/3)(8)^3 + 12(8)^2 - [(1/4)(6)^4 - (10/3)(6)^3 + 12(6)^2]

= 176/3

Therefore, the displacement over the entire interval 0 < t < 8 is:

32/3 - 16/3 + 176/3 = 64/3

To find the distance traveled over the given interval, we need to break down the motion into the different intervals of direction:

0 < t < 4: The particle is moving in the positive direction, so the distance traveled is the same as the displacement, which is 32/3.

4 < t < 6: The particle is moving in the negative direction, so the distance traveled is the absolute value of the displacement, which is 16/3.

6 < t < 8: The particle is moving in the positive direction, so the distance traveled is the same as the displacement, which is 176/3.

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The total distance traveled over the interval 0 < t < 8 is: 32/3 + 16/3 + 176/3 = 224/3.

To find the displacement over the given interval, we need to integrate the velocity function:

∫v(t)dt = ∫(t^3 - 10t^2 + 24t)dt = (1/4)t^4 - (10/3)t^3 + 12t^2

Now we can evaluate the displacement over the different intervals:

0 < t < 4:

(1/4)(4)^4 - (10/3)(4)^3 + 12(4)^2 = 32/3

4 < t < 6:

(1/4)(6)^4 - (10/3)(6)^3 + 12(6)^2 - [(1/4)(4)^4 - (10/3)(4)^3 + 12(4)^2]

= -16/3

6 < t < 8:

(1/4)(8)^4 - (10/3)(8)^3 + 12(8)^2 - [(1/4)(6)^4 - (10/3)(6)^3 + 12(6)^2]

= 176/3

Therefore, the displacement over the entire interval 0 < t < 8 is:

32/3 - 16/3 + 176/3 = 64/3

To find the distance traveled over the given interval, we need to break down the motion into the different intervals of direction:

0 < t < 4: The particle is moving in the positive direction, so the distance traveled is the same as the displacement, which is 32/3.

4 < t < 6: The particle is moving in the negative direction, so the distance traveled is the absolute value of the displacement, which is 16/3.

6 < t < 8: The particle is moving in the positive direction, so the distance traveled is the same as the displacement, which is 176/3.

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The total cost of the apples would be $3.50 given that Tina and her friend picked 2.5 pounds of apples. So, the apples would cost $3.50.

The cost of the apples can be calculated by multiplying the weight of the apples by the cost per pound.

In this case, Tina and her friend picked 2.5 pounds of apples.

To find the cost, we need to multiply the weight (2.5 pounds) by the cost per pound ($1.40).

Therefore, the total cost of the apples would be 2.5 pounds * $1.40/pound = $3.50.

So, the apples would cost $3.50.

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Answers:

Domain: all real numbers

Range: \(y \le 6\)

Graph is below.

====================================================

Explanation:

This is a piecewise function that is composed of two parts:

This piecewise function has split identities or multiple aliases so to speak. It all depends on what the x input is.

The graph is shown below.

The domain is the set of all real numbers since any x value will lead to some y output. Even x = 0 itself is allowed. Note the arrows indicate the graph stretches on forever to the left and to the right.

The range on the other hand isn't all real numbers. Instead, it's \(y \le 6\) indicating that y = 6 is the largest y can get. Simply locate the highest point on the graph (similar to the concept of the vertex) and you'll spot the highest y value.

Side notes:

Based on the provided sample data, the hypothesis that the population has a variance of σ^2 = 40 and a mean of µ = 220 is tested.

To test the hypothesis, we can perform a hypothesis test using the sample data. The null hypothesis (H0) states that the population variance is 40 and the mean is 220. The alternative hypothesis (Ha) suggests that these values are not true.For testing the variance, we can use the chi-square test statistic. Since the sample size is small (n = 21), we can compare the chi-square statistic with the critical value from the chi-square distribution with (n-1) degrees of freedom.

To calculate the chi-square statistic, we need the sample variance. The sample standard deviation (s) is given as 35, so the sample variance (s^2) is 35^2 = 1225.Using the formula chi-square = (n - 1) * s^2 / σ^2, we can compute the chi-square statistic. Plugging in the values, we get chi-square = 20 * 1225 / 40 = 612.5.

Next, we compare the chi-square statistic to the critical value at a chosen significance level (e.g., α = 0.05). If the chi-square statistic exceeds the critical value, we reject the null hypothesis in favor of the alternative hypothesis.Consulting the chi-square distribution table or using statistical software, we find the critical value for (n-1 = 20) degrees of freedom and α = 0.05 is approximately 31.41.

Since the chi-square statistic (612.5) is greater than the critical value (31.41), we reject the null hypothesis. This indicates that the data does not support the hypothesis that the population has a variance of σ^2 = 40.

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Answer:

2.9 meters.

Step-by-step explanation:

First we multiply the length, 3.8, by the width, 1.5, to get the base, 5.7 (this step is not entirely necessary, but makes it much easier).  Then we divide the volume, 16.53, by the base, 5.7, to get the height, 2.9 meters.

Answer:

i think its 21.83 i may be wrong but im pretty sure its 21.83

Step-by-step explanation:

We have the parabola with equation y = 4x².

We have to determine the shape and direction of it.

If we compare it to the standard equation y = ax² + bx + c, we can see that a = 4, b = 0 and c = 0.

As the value of a is positive, the parabola will open upward.

The parameter has an absolute value greater than 1. This means that y increases "faster" relative to x that a parabola with a = 1.

This means that the parabola will be narrow about its line of symmetry which we call vertical strecth.

Answer:

Because a is positive the parabola opens upward.

Because a has an absolute value larger than 1 the parabola is narrow about its line of symmetry which we call vertical stretch.

Answer:

Step-by-step explanation:

(-2+3)/2 = 1/2

(5 - 17)/2 =  -12/6= -2

(1/2, -2)

Answer:

Find the coordinates of the midpoint of a segment with the given endpoints. (-3,5) (7,-1)

Step-by-step explanation:

Answer:

x=125

Step-by-step explanation:

suppose the number is x

72% of x is 90

=> 0.72x=90

=> x=90/0.72

=> x=125

The 90 is 72 percent of approximately 125. In other words, if the unknown number is 125, 72 percent of 125 would be equal to 90.

To calculate the number that 90 is 72 percent of, we can set up the proportion:

90 is to x as 72 is to 100.

This proportion can be expressed as:

90/x = 72/100.

To solve for x, we can cross-multiply:

90 * 100 = 72 * x.

Simplifying the equation:

9000 = 72x.

Next, divide both sides of the equation by 72:

9000/72 = x.

x ≈ 125.

Hence, 90 is 72 percent of approximately 125. In other words, if the unknown number is 125, 72 percent of 125 would be equal to 90.

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Answer:

True

Step-by-step explanation:

The answer is "True". Let me explain.

Let's say that we have a line segment which we will call AB, construct a perpendicular bisector. The following steps will be taken;

1) Draw a semi circle with its centre at point A and passing through point B.

2) Draw a semi circle with its centre at point B and passing through point A.

3) The two semicircles will intersect at two points with one being above and the other being below the straight line segment AB. Now, a line will have to be drawn that passes through those two intersecting points. This drawn line is called the perpendicular bisector for line segment AB.

Answer:

True

Step-by-step explanation:

Make sure you’re paying attention to if your question says “were able to” or “were not able to”.

Given equation is: (x + 1)²y" + 5(x + 1)y + 4y = 0

To solve the given equation, we have to determine the following: (a) Find all ordinary points and singular points of this equation. For singular points, are they regular or irregular? Explain your reason.(b) Find the general solution of the equation.

(a) Here, the coefficient of y" is (x + 1)².

The singular point(s) of the given equation occurs where (x + 1)² = 0.

Since (x + 1)² ≥ 0 for all x, then it follows that (x + 1)² = 0 if and only if

x = -1.∴ x = -1 is the singular point of the given equation.

Since the coefficient of y" in the given equation is zero at x = -1, then it follows that the singular point x = -1 is an irregular singular point of the given equation.

(b) To find the general solution of the given equation, let us try to write the given equation in the form of a hypergeometric equation.

Let y = (x + 1)α. Then

y' = α(x + 1)α - 1 y, and

y" = α(α - 1)(x + 1)α - 2.

Substituting these derivatives of y into the given equation, we have

(α² - α) (x + 1)α + 5α(x + 1)α + 4(x + 1)α = 0

Canceling (x + 1)α from the above equation, we have

=(α² + 4α + 4) - α - 4α

= (α + 2)² - 5α

= 0Or (α + 2)²

= 5α Or α² - α + 4

= 0

Therefore, \(a= \frac{1 \pm \sqrt{1 - 16}}{2}\) or \(a = -2 \pm \frac{3i}{2}\)

There are three cases to consider when finding the general solution of the given equation.

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Answer:

805.5 out of 900

Step-by-step explanation:

A test is out of 100 and because there are 9 tests: 9 x 100 which equals 900.

To get the average we add up each test mark and divide by the number of tests. The same can be applied here but reversed. So because there were 9 tests we can multiply 89.5 by 9 which gives us 805.5. Beverly scored 805.5 marks out of 900 which makes her average 89.5% for 9 tests.

The total cost of going to the carnival is $30. The independent variable is the carnival fee and the dependent is the cost of rides.

In any equation, the variables that represent the input and output are referred to as independent and dependent variables, respectively. An independent variable is the one for which we enter the values. The dependent variable is the one that reflects the output value. In mathematics, data techniques, and quantitative sciences, there are dependent and independent variables. Dependent variables are so named because, during an experiment, their values are examined under the presumption or requirement that they do, in fact, depend on other variables' values.

The cost of admission fee at the carnival = $9(independent variable)

Cost of each ride = $1.75

Let the number of rides = x (dependent variable)

The cost of 12 rides = 12 x

= 12( 1.75)
= $21

So, the cost to go to the carnival and 12 rides is

= $9+ $21

= $30

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Part A: To find the equation of the line tangent to the solution curve at the point (0, 5), we need to find the slope of the tangent line. The slope of the tangent line is equal to the derivative of the solution curve at that point.

Given the differential equation: dy/dx = 5(2x + 3)sin(x^2 + 3x + π/2)

Taking the derivative of the right-hand side with respect to x:

d/dx [5(2x + 3)sin(x^2 + 3x + π/2)] = 10sin(x^2 + 3x + π/2) + 5(2x + 3)cos(x^2 + 3x + π/2)

Now we substitute x = 0 into the derived expression to find the slope at (0, 5):

slope = 10sin(0^2 + 3(0) + π/2) + 5(2(0) + 3)cos(0^2 + 3(0) + π/2)

= 10sin(π/2) + 5(3)cos(π/2)

= 10(1) + 15(0)

= 10

Therefore, the slope of the tangent line is 10. The equation of the line tangent to the solution curve at (0, 5) is given by:

y - 5 = 10(x - 0)

y - 5 = 10x

y = 10x + 5

Part B: To find the second derivative at (0, 5) and determine the concavity of the solution curve at that point, we need to differentiate the given differential equation one more time.

Taking the derivative of the given differential equation:

d^2y/dx^2 = d/dx [5(2x + 3)sin(x^2 + 3x + π/2)]

= 10cos(x^2 + 3x + π/2)(2x + 3) + 5(2)sin(x^2 + 3x + π/2)

Now we substitute x = 0 into the derived expression to find the second derivative at (0, 5):

d^2y/dx^2 = 10cos(0^2 + 3(0) + π/2)(2(0) + 3) + 5(2)sin(0^2 + 3(0) + π/2)

= 10cos(π/2)(3) + 5(2)sin(π/2)

= 10(0)(3) + 5(2)(1)

= 10

The second derivative at (0, 5) is 10. Since the second derivative is positive, the concavity of the solution curve at that point is concave up.

Part C: To find the particular solution y = f(x) with the initial condition f(0) = 5, we can solve the given differential equation.

dy/dx = 5(2x + 3)sin(x^2 + 3x + π/2)

To solve the differential equation, we can integrate both sides with respect to x:

∫dy = ∫5(2x + 3)sin(x^2 + 3x + π/2) dx

Integrating the right-hand side may require the use of techniques like substitution or integration by parts. Once the integration is performed, we can add the constant of integration (C) to obtain the particular solution

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Answer:

Yes ,because of SAS similarity theorem

Step-by-step explanation:

In ΔYOM , ΔTON

∠YOM = ∠TON        

\(\frac{OY}{OT}=\frac{96}{84}=\frac{8}{7}\\\\\frac{OM}{ON}=\frac{104}{91}=\frac{8}{7}\)

SAS similarity theorem

Answer:

Hello,

Answer C

Step-by-step explanation:

\(\dfrac{96}{104}=? \dfrac{84}{91} \\\\Calculating\ crossed\ products\\96*91=8736\\104*84=8736\\they\ are\ equals\\\\\\\dfrac{YO}{MO} =\dfrac{OT}{ON} \\\\\\Triangles\ are\ similar\ because \ SAS \theorem\\\\\)

The numeric value of the composite function at x = 1 is given as follows:

(h ∘ k)(1) = 28.

The composite function of f(x) and g(x) is given by the rule presented as follows:

(f ∘ g)(x) = f(g(x)).

For the composition of two functions, we have that the output of the inner function, in this example g(x), serves as the input of the outer function, in this case f(x).

Hence the numeric value at x = 1 for the function in this problem is:

h(k(1)).

The numeric value of k at x = 1 is:

k(1) = 3.

Then, as the numeric value of h at x = 3 is of 28, the composite function is:

(h ∘ k)(1) = 28.

The problem is given by the image presented at the end of the answer.

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