In the following parts, define a rationil number to be any number that can be written as a fraction b where a and b are integers and b \neq 0 . Part A Phineas Phoole claims that

We can write an equation for the interior angles, and we will see that x = 13

We want to find the value of x, we can see two adjacent angles on a rectangle, then the sum of these two is equal to 180°, we can write:

3x + 78 + x + 50 = 180

4x + 128 = 180

4x = 180 - 128

4x = 52

x = 52/4 = 13

The value of x is 13.

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Answer: y = 2(x + 2)² - 5

Step-by-step explanation:

          We are going to use the completing the square method to transform this quadratic equation from standard form to vertex form.

Given:

     y = 2x² + 8x + 3

Factor the 2 out of the first two terms:

     y = 2(x² + 4x) + 3

Add and subtract \(\frac{b}{2} ^2\):

     y = 2(x² + 4x + 4 - 4) + 3

Distribute the 2 into -4 and combine with the 3:

     y = 2(x² + 4x + 4) - 5

Factor (x² + 4x + 4):

     y = 2(x + 2)² - 5

Answer:

y = 10x - 8

Step-by-step explanation:

The slope is "m", or how much the y-value changes on a line when the x-value changes by one.

The y-intercept is the y value of the line when it is intersecting the y-axis, or when the x-value is 0.

To find the slope, take 2 points from the graph and plug into the slope formula:

\(\frac{y_2-y_1}{x_2-x\\_1}\)

I'll use (0, -8) and (1,2).

Plug into the formula.

\(\frac{2--8}{1-0}\)

\(\frac{10}{1}\)

10

Slope = 10

To find the y-intercept, look at the table. What is the y-value when the x-value is equal to 0?

-8

y-intercept: -8

Slope-Intercept form:

y = mx + b

m: slope

b: y-intercept

y, x: leave as variables

y = 10x - 8

Answer:

t = 10

Step-by-step explanation:

z^t ⋅ z^5 = z^15

We know that a^b*a^c = a^(b+c)

z^(t+5) = z^15

Since the bases are the same, the exponents are the same

t+5 = 15

t = 15-5

t = 10

Answer:

-4,-3,-2,-1,1

Step-by-step explanation:

these numbers can be expressed in a fraction

Yes, you can show significant differences using superscripts in an ANOVA (Analysis of Variance) single-factor test.

In an ANOVA test, superscripts are commonly used to indicate significant differences between the means of different groups or treatments.

Typically, letters or symbols are assigned as superscripts to denote which groups have significantly different means. These superscripts are usually presented adjacent to the mean values in tables or figures.

The specific superscripts assigned to the means depend on the statistical analysis software or convention being used. Each group or treatment with a different superscript is considered significantly different from groups with different superscripts. On the other hand, groups with the same superscript are not significantly different from each other.

By including superscripts, you can visually highlight and communicate the significant differences between groups or treatments in an ANOVA single-factor test, making it easier to interpret the results and identify which groups have statistically distinct means.

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In the graph of the simple linear regression equation, the parameter ß1 is the slope of the true regression line.

The simple linear regression equation represents a linear relationship between a dependent variable and an independent variable. It can be written as y = ß0 + ß1x, where ß0 is the intercept and ß1 is the slope of the regression line.

The slope (ß1) determines the rate of change in the dependent variable (y) for each unit change in the independent variable (x). It represents the steepness or inclination of the regression line. The sign of ß1 indicates whether the line has a positive or negative slope, indicating the direction of the relationship between the variables.

Thus, in the context of the simple linear regression equation, the parameter ß1 is the slope of the true regression line.

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The value of X in the semiannual deposit sequence is $100. Let's break down the problem to find the value of X. We know that Barbara makes 22 semiannual deposits, and the pattern alternates between X and 2X.

This means that the sequence looks like this: X, 2X, X, 2X, X, 2X, and so on. To find the value of X, we need to consider the future value of these deposits after 8 years, which is given as $10,800. Since the interest is compounded annually, we can convert the semiannual deposits into an equivalent annual deposit.

Since there are 22 semiannual deposits, we can divide them into 11 equivalent annual deposits. The first deposit of X will grow for 8 years, the second deposit of 2X will grow for 7 years, the third deposit of X will grow for 6 years, and so on.

Using the compound interest formula, we can calculate the future value of these deposits. By summing up the individual future values, we find that the total future value after 8 years is $10800. Solving this equation, we get the value of X as $100.

Therefore, the value of X in the semiannual deposit sequence is $100.

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We will use the formula for a confidence interval for the population mean to determine the confidence level associated with a confidence interval of 6.42 ± 0.1916 for the population mean μ, and we found that it represents a 95% confidence interval.

In statistics, confidence intervals are used to estimate the range of values that a population parameter is likely to fall in. A confidence interval is an interval estimate computed from a sample of data, which is used to describe the range of plausible values of the population parameter. In this scenario, we have a sample of 203 adults who were asked how long they slept last night. We are given the mean and standard deviation of their responses, and we are asked to determine the confidence level associated with a confidence interval of 6.42 ± 0.1916 for the population mean μ.

To determine the confidence level associated with a confidence interval of 6.42 ± 0.1916 for the population mean μ, we need to use the formula for a confidence interval for the population mean:

Confidence Interval = mean ± Zα/2 * (σ / √n) where: sample mean, Zα/2 = the critical value of the standard normal distribution at the desired confidence level (α) divided by 2, σ = population standard deviation (which we estimate using the sample standard deviation, s), n = sample size

In this scenario, first, we need to find the critical value of the standard normal distribution at the desired confidence level (α) divided by 2. We can use a standard normal distribution table or a calculator to find this value. For example, if we want a 95% confidence interval, α = 0.05, and the critical value is Zα/2 = 1.96.

Next, we can substitute the values into the formula and solve for the confidence interval: 6.42 ± 1.96 * (1.56 / √203) = 6.42 ± 0.1916

We can see that the interval 6.42 ± 0.1916 represents a 95% confidence interval for the population mean μ. This means that if we were to take multiple random samples of the same size from the population and calculate their confidence intervals, about 95% of these intervals would contain the true population mean.

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The infusion time for the IV solution that will be prescribed 480 mins.

The time taken by the saline to be dripped in the infusion is called as the infusion time.

To calculate the infusion time the formula for IV drip rate is used which is;

Drip rate = volume/time × Drop factor

Drip rate = 5gtt/min

Volume = 120mL

Drop factor= 20 gtt/mL

Time = ?

From the formula above, make time the subject of the formula. That is,

Time = vol × drop factor/drip rate

Time = 120 × 20/5

Time= 120 x 4

Time= 480 mins

Therefore, the infusion time for the IV solution that was prescribed = 480 mins

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The amount of money that Brandon would have more than Julian is $16,564.

The formula for calculating future value when there is continuous compounding is :

FV = A x e^r x N

Where:

Future value of Brandon's investment = $1,100 x 2.718^0.0775 x 18 = $21,395.36

The formula for calculating future value when there is monthly compounding:

FV = P (1 + r)^nm

Where:

FV = 1100 x (1 + 0.006875)^(18 x 12) = $4,831.85

Difference in the amount that Brandon and Julian has  = $21,395.36 - $4,831.85 = $16,563.51≈ $16,564

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We can iterate through the array and compute the cumulative sum to see if there is a place in a non-empty array where the sum of the integers on one side equals the sum on the other.

To record the sum on each side, we cumulative two variables, leftSum and rightSum. RightSum is initially set to the total of the array's elements. After that, we compare the values of leftSum and rightSum and deduct each element in the array from . We return true if they are equal. After the loop, if such a location cannot be located, we return false. The temporal complexity of this approach is O(n), where n is the length of the array.

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we find that the numerical approximation using Euler's method gives y(2) ≈ 1.865, while the analytical solution gives y(2) = 2.5.

Using the formula y(n+1) = y(n) + Δx * f(x(n), y(n)), where f(x, y) = x² √y, we can calculate the values of y at each step. Here's the step-by-step calculation:

Step 1: For x = 0, y = 1 (initial condition).

Step 2: For x = 0.2, y = 1 + 0.2 * (0.2)² * √1 = 1.008.

Step 3: For x = 0.4, y = 1.008 + 0.2 * (0.4)² * √1.008 = 1.024.

Step 4: For x = 0.6, y = 1.024 + 0.2 * (0.6)² * √1.024 = 1.052.

Step 5: For x = 0.8, y = 1.052 + 0.2 * (0.8)² * √1.052 = 1.094.

Step 6: For x = 1.0, y = 1.094 + 0.2 * (1.0)² * √1.094 = 1.155.

Step 7: For x = 1.2, y = 1.155 + 0.2 * (1.2)² * √1.155 = 1.238.

Step 8: For x = 1.4, y = 1.238 + 0.2 * (1.4)² * √1.238 = 1.346.

Step 9: For x = 1.6, y = 1.346 + 0.2 * (1.6)² * √1.346 = 1.483.

Step 10: For x = 1.8, y = 1.483 + 0.2 * (1.8)² * √1.483 = 1.654.

Step 11: For x = 2.0, y = 1.654 + 0.2 * (2.0)² * √1.654 = 1.865.

Therefore, using Euler's method with a step size of Δx = 0.2, we approximate y(2) to be 1.865.

To obtain the analytical solution to the ODE, we can separate variables and integrate both sides:

∫(1/√y) dy = ∫x² dx

Integrating both sides gives:

2√y = (1/3)x³ + C

Solving for y:

y = (1/4)(x³ + C)²

Using the initial condition y(0) = 1, we can substitute x = 0 and y = 1 to find the value of C:

1 = (1/4)(0³ + C)²

1 = (1/4)C²

4 = C²

C = ±2

Since C can be either 2 or -2, the general solution to the ODE is:

y = (1/4)(x³ + 2)² or y = (1/4)(x³ - 2)²

Now, let's evaluate y(2) using the analytical solution:

y(2) = (1/4)(2³ + 2)² = (1/4)(8 + 2)² = (1/4)(10)² = 2.5

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Answer:

90 feet

Step-by-step explanation:

1 yard is equivalent to 3 feet so 30 yards is equal to 30*3 = 90 feet.

Hope this helps :)

The half-life of the material can be determined by comparing the initial mass with the mass after a certain period of time. Therefore, the half-life of the material is 4 hours.

To find the half-life, we need to determine the time it takes for the mass to decrease by half. In this case, the mass decreased from 3 kg to 750 g. The difference in mass is 3 kg - 750 g = 2250 g.

The half-life is the time it takes for half of the radioactive material to decay. In this case, the material is not radioactive, but the concept of half-life can still be applied. The fact that the mass of the material decreased from 3 kg to 750 g indicates that it is undergoing some form of decay or degradation. By comparing the initial mass with the mass after a certain period of time, we can determine the time it takes for the mass to decrease by half, which gives us the half-life of the material. In this case, the mass decreased by half in 4 hours, so the half-life is 4 hours.

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Answer:

z = 70°

x = 15

Step-by-step explanation:

70° and z are opposite from each other, so they are equal.

70° and (6x+20°) are adjacent, so they equal 180°.

70° + (6x+20°) = 180°

70° + 20° + 6x = 180°

90° + 6x = 180°

-90° -90°

6x = 90°

Divide each side by 6

x = 15

Answer:

Hope it helps you..............

that is my I hope it helps you

We have the following:

as a sum

The answer is the option b

Answer:

B.     $2253.65

Step-by-step explanation:

Use the formula for compound interest.

F = P(1 + r/n)^(nt)

F = future value

P = present value

r = interest rate (written as decimal)

n = number of times interest is compounded each year

t = number of years

F = unknown

P = $2000

r = 4% = 0.04

n = 4

t = 3

F = $2000(1 + 0.04/4)^(4 × 3)

F = $2253.65

Answer:

See below

Step-by-step explanation:

8

3 in one times two plus two.

Please mark brainliest!!

There are 8 "1/3's" in 2 2/3.

The solution is 8.

Here,

To find out how many 1/3's are in 2 2/3,

we can divide the whole number part by the fraction part:

2 2/3 = (2 + 2/3)

         = (6/3 + 2/3)

         = 8/3

Now, we need to divide 8/3 by 1/3 to find the number of 1/3's:

(8/3) ÷ (1/3)

= 8/3 * 3/1

= (8 * 3) / (3 * 1)

= 24 / 3

= 8

So, there are 8 "1/3's" in 2 2/3.

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Choice B) Jacket world has the better deal.

Choice D) Both stores are offering a 25% discount on the jacket.

Choice E) The difference in sale prices at the two stores is $7.50

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

Explanation:

25% = 0.25

25% of $190 = 0.25*190 = 47.50

190 - 47.50 = 142.5

This indicates the price at Jacket World is $142.5 instead of $150

Therefore, choice A is false.

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

Choice B on the other hand is true because $142.50 at Jacket World is a lower price compared to $150 at Clothes Are Us. Jacket World has the better deal.

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

Because choice B was shown to be true, there's no way choice C can be true as well. Otherwise, we'd have a contradiction. So we can rule out choice C.

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

Let's find the percentage discount for Clothes Are Us.

The original price is $200 and its sale price is $150. So you save 200-150 = 50 dollars.

Divide that over the original price to find the discount: 50/200 = 0.25 = 25%

Therefore, Clothes Are Us has the same discount percentage as Jacket World. Both have a 25% discount. Choice D is true.

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

Comparing the two sale prices of $150 (Clothes Are Us) and $142.50 (Jacket World), the difference in price is 150-142.50 = 7.50; this means choice E is a true statement.

Answer:

CotR = -√3

Step-by-step explanation:

In the 4th quadrant, sin is negative;

Since Cos R = √3/2,

Adjacent = √3

Hypotenuse = 2

Get the opposite;

opp^2 = 2^2 -(√3)^2

opp^2 = 4 - 3

opp^2 = 1

Opp = 1

Get sinR

Sin R = opp/hyp

SinR=  -1/2

CotR = cosR/sinR

CostR = (√3/2)/(-1/2)

CotR = √3/2* -2/1

CotR = -√3

Answer:

3/5

Step-by-step explanation:

Probability calculates the likelihood of an event occurring. The likelihood of the event occurring lies between 0 and 1. It is zero if the event does not occur and 1 if the event occurs.

For example, the probability that it would rain on Friday is between o and 1. If it rains, a value of one is attached to the event. If it doesn't a value of zero is attached to the event.

Experimental probability is based on the result of an experiment that has been carried out multiples times

experimental probability that she will see birds in her garden on July 1 = number of days she saw a bird in June / total number of days in June

= 18/30

To transform to the simplest form. divide both the numerator and the denominator by 6

Answer:

permutations: order matters

combinations: order doesn't matter

Answer:

A combination doesn't need to be in a specific order, unlike permutation which needs to go in order.

Step-by-step explanation:

Answer:

15 apples in total

Step-by-step explanation:

The function f(x, u) = 2√3x + cos(u) can be linearized using the Taylor series expansion around the operating point x_o = 3 and u_o = 0, neglecting terms of order 2 and above.

To linearize the function f(x, u) = 2√3x + cos(u) around the operating point x_o = 3 and u_o = 0, we can use the Taylor series expansion. The Taylor series expansion represents a function as an infinite sum of terms, where each term represents the function's derivative evaluated at a specific point.

The first step is to calculate the first-order partial derivatives of f(x, u) with respect to x and u. Taking the derivative of 2√3x with respect to x gives 2√3, and the derivative of cos(u) with respect to u is -sin(u). Evaluating these derivatives at the operating point x_o = 3 and u_o = 0, we obtain 2√3 and -sin(0), which simplifies to 0, respectively.

Next, we can write the linearized form of the function as f(x, u) ≈ f(x_o, u_o) + ∂f/∂x * (x - x_o) + ∂f/∂u * (u - u_o), neglecting terms of order 2 and above. Plugging in the values we obtained, the linearized function becomes f(x, u) ≈ 2√3 * (x - 3) + 0 * (u - 0), which simplifies to f(x, u) ≈ 2√3 * (x - 3).

Therefore, the linearized form of the function f(x, u) = 2√3x + cos(u) around the operating point x_o = 3 and u_o = 0, neglecting terms of order 2 and above, is f(x, u) ≈ 2√3 * (x - 3). This linear approximation provides an estimation of the original function's behavior in the vicinity of the operating point.

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Problem 1

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

Work Shown:

\(|4n - 15| = |n|\\\\4n - 15 = n \ \text{ or } \ 4n-15 = -n\\\\-15 = n-4n \ \text{ or } \ -15 = -n-4n\\\\-15 = -3n \ \text{ or } \ -15 = -5n\\\\-3n = -15 \ \text{ or } \ -5n = -15\\\\n = \frac{-15}{-3} \ \text{ or } \ n = \frac{-15}{-5}\\\\n = 5 \ \text{ or } \ n = 3\\\\\)

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

Problem 2

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

Work Shown:

\(|2c+8| = |10c|\\\\2c+8 = 10c \ \text{ or } \ 2c+8 = -10c\\\\8 = 10c-2c \ \text{ or } \ 8 = -10c-2c\\\\8 = 8c \ \text{ or } \ 8 = -12c\\\\8c = 8 \ \text{ or } \ -12c = 8\\\\c = \frac{8}{8} \ \text{ or } \ c = \frac{8}{-12}\\\\c = 1 \ \text{ or } \ c = -\frac{2}{3}\)