a triangle is inscribed inside a circle. one vertex of the triangle is at the center of the circle, and the other two vertices are on the circle. if the angle at the center of the circle measures 80 degrees, what is the measurement of one other angle?

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let the number of pages in each chapter be x,

total number of pages is equal to

so,

number of pages in each chapter = x = 31

Answer: There are 31 pages in one chapter

Step-by-step explanation:

6-chapters - ? pages  ; Introduction -8

Therefore, the required answer is that the coordinates of the local minimum and absolute minimum points are (3/2, -7/4), and the ordered pair for the absolute maximum point is not provided as it is not asked in the question.

To determine the local extreme and absolute extreme points and inflection points, we first need to find the first and second derivatives of the given function, which is:

y = x² - 3x + 5So,dy/dx = 2x - 3and d²y/dx² = 2These are the first and second derivatives of the given function.

Now, we can find the critical points of the function by equating the first derivative to zero.

So,2x - 3 = 0x = 3/2

This gives us a critical point x = 3/2.Substituting this value in the second derivative, we can determine the nature of this critical point as follows:

When x = 3/2,d²y/dx² = 2 > 0So, the critical point is a point of local minimum.

Now, let's find the y-coordinate of the critical point by substituting x = 3/2 in the given function:y = (3/2)² - 3(3/2) + 5y = 9/4 - 9/2 + 5y = -7/4

Therefore, the coordinates of the point of local minimum are:(3/2, -7/4)

As there are no more critical points, this is also the point of absolute minimum.

On the graph of the function, the point of local minimum and absolute minimum can be shown as:OA.

As we have found the point of absolute minimum to be (3/2, -7/4), we can write it as an ordered pair as follows:

OA: (3/2, -7/4)

Therefore, the required answer is that the coordinates of the local minimum and absolute minimum points are (3/2, -7/4), and the ordered pair for the absolute maximum point is not provided as it is not asked in the question.

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Answer:

\(\textsf{C)} \quad 4\frac{1}{2}\)

Step-by-step explanation:

PEMDAS

The PEMDAS rule is an acronym representing the order of operations in math:

Given expression:

\(\dfrac{1}{4}(15-6)+\dfrac{3^3}{12}\)

Carry out the operation inside the parentheses:

\(\implies \dfrac{1}{4}(9)+\dfrac{3^3}{12}\)

Carry out the exponent:

\(\implies \dfrac{1}{4}(9)+\dfrac{3 \cdot 3 \cdot 3}{12}\)

\(\implies \dfrac{1}{4}(9)+\dfrac{9 \cdot 3}{12}\)

\(\implies \dfrac{1}{4}(9)+\dfrac{27}{12}\)

Carry out the multiplication:

\(\implies \dfrac{9}{4}+\dfrac{27}{12}\)

Rewrite 27 as 3 · 9 and 12 as 3 · 4:

\(\implies \dfrac{9}{4}+\dfrac{3 \cdot 9}{3 \cdot 4}\)

Cancel the common term 3:

\(\implies \dfrac{9}{4}+\dfrac{9}{4}\)

\(\textsf{Apply the fraction rule} \quad \dfrac{a}{c}+\dfrac{b}{c}=\dfrac{a+b}{c}:\)

\(\implies \dfrac{9+9}{4}\)

\(\implies \dfrac{18}{4}\)

Reduce the fraction by dividing the numerator and denominator by 2:

\(\implies \dfrac{18 \div 2}{4 \div 2}\)

\(\implies \dfrac{9}{2}\)

Rewrite 9 as 8 + 1:

\(\implies \dfrac{8+1}{2}\)

\(\textsf{Apply the fraction rule} \quad \dfrac{a+b}{c}=\dfrac{a}{c}+\dfrac{b}{c}:\)

\(\implies \dfrac{8}{2}+\dfrac{1}{2}\)

Divide 8 by 2:

\(\implies 4+\dfrac{1}{2}\)

\(\implies 4\frac{1}{2}\)

Answer:

C) \(\sf 4\frac{1}{2}\)

Step-by-step explanation:

The given equation is,

\( \sf \: → \frac{1}{4} (15 - 6) + \frac{ {3}^{3} }{12} \)

The value of the equation is,

\( \sf \rightarrow \frac{1}{4} (15 - 6) + \frac{ {3}^{3} }{12} \)

\( \sf \: \rightarrow \frac{1}{4} (9) + \frac{27}{12} \)

\( \sf → \frac{9}{4} + \frac{27}{12} \)

\( \sf → \frac{(27 + 27)}{12} \)

\( \sf → \frac{(54 \div 6)}{(12 \div 6)} \)

\( \sf → \frac{9}{2} = 4 \frac{1}{2} \)

Hence, the required value is 4 1/2.

The answer is the 3rd one

Answer:

Common factor from the two pairs

n2+2n-n-2 or

n(n+2)-1(n+2)

Rewrote in factored form

n(n+2)-1(n+2)or

(n-1)(n+2)

Solution

(n-1)(n+2)

Therefore, Jozef had 15 dimes and 27 quarters in his piggy bank.

An equation is a mathematical statement that shows that two expressions are equal. It typically consists of variables, constants, and mathematical operations. Equations can be solved by manipulating the expressions to find the value of the variables that satisfy the equation. Equations can be used to model real-world situations, and they are an important tool in many fields, including mathematics, physics, engineering, and economics.

Here,

Let's use the following variables to represent the number of dimes and quarters in Jozef's piggy bank:

d: the number of dimes

q: the number of quarters

We know that Jozef has a total of 42 dimes and quarters, so we can write the equation:

d + q = 42

We also know that the total value of the coins is $8.25. We can express this value in cents as:

10d + 25q = 825

We can simplify this equation by dividing both sides by 5:

2d + 5q = 165

Now we have two equations with two variables:

d + q = 42

2d + 5q = 165

We can use the first equation to solve for one of the variables in terms of the other. For example, we can solve for q:

q = 42 - d

Now we can substitute this expression for q into the second equation:

2d + 5(42 - d) = 165

Simplifying and solving for d, we get:

2d + 210 - 5d = 165

-3d = -45

d = 15

So Jozef had 15 dimes in his piggy bank. We can use the first equation to find the number of quarters:

15 + q = 42

q = 27

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Answer:

h=3

Step-by-step explanation:

The area bounded by the parabola \(\(y = x^2\)\) and the line \(\(y = x\)\) is \(\(\frac{1}{6}\)\) square units.

To find the area bounded by the parabola \(\(y = x^2\)\) and the line \(\(y = x\)\), we need to determine the points of intersection between the parabola and the line. These points will form the bounds of the region.

Setting the equations equal to each other:

\(\(x^2 = x\)\)

\(\(x^2 - x = 0\)\)

\(\(x(x - 1) = 0\)\)

\(\(x = 0\) or \(x - 1 = 0\)\)

This gives us two intersection points: (0, 0) and (1, 1).

To find the area between the parabola and the line, we need to calculate the definite integral of the difference between the two functions within the bounds of x = 0 and x = 1:

\(\(\text{Area} = \int_0^1 (x - x^2) \, dx\)\)

\(\(\text{Area} = \left[\frac{x^2}{2} - \frac{x^3}{3}\right]_0^1\)\\\(\text{Area} = \left(\frac{1^2}{2} - \frac{1^3}{3}\right) - \left(\frac{0^2}{2} - \frac{0^3}{3}\right)\)\\\(\text{Area} = \left(\frac{1}{2} - \frac{1}{3}\right) - \left(0 - 0\right)\)\\\(\text{Area} = \frac{1}{6}\)\)

Therefore, the area bounded by the parabola \(\(y = x^2\)\) and the line \(\(y = x\)\) is \(\(\frac{1}{6}\)\) square units.

Complete Question:

Find the area bounded by the parabola y = x² & the line y=x.

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A rotation maps a line to a line, a ray to a ray, a segment to a segment, and an angle to an angle.

A rotation preserves lengths of segments.

A rotation preserves measures of angles. Step-by-step explanation:

You Welcome :)!

Answer:

160

Step-by-step explanation:

4 × 10 × 4 = 160

(Random words to hit the character limit please ignore)

Answer:

-5x²y²z + 7xy - x²y²z - 5xy

Step-by-step explanation:

Answer:

4.7 ~~~ :D

Step-by-step explanation:

t = total...i = initial amount ridden......d = days..... m = average amount of miles

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

t = i +dm

26.8 = 8 + 4m

----------------- solve -----------------

26.8 = 8 + 4m ----> 18.8 = 4m ----> 4.7 = m

The expression is 26.8 = 8 + 4m and the average number of, miles he would have to ride each day to meet his goal is 4.7.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Let the attributes be, t = total,  i = initial amount ridden, d = days, and m = average amount of miles.

The required expression can be written as below:-

t = i +dm

26.8 = 8 + 4m

The value of average miles will be calculated by solving the expression:-

26.8 = 8 + 4m

18.8 = 4m

4.7 = m

Therefore, the expression is 26.8 = 8 + 4m and the average number of, miles he would have to ride each day to meet his goal is 4.7.

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Answer:

here's your answer.........

To find Pedro's exam score, we can use the formula for calculating the z-score:

z = (x - μ) / σ,

where z is the z-score, x is the exam score, μ is the mean, and σ is the standard deviation.

Given that Pedro's z-score was 3, we can rearrange the formula to solve for x:

3 = (x - 68) / 10.

Multiplying both sides of the equation by 10, we get:

30 = x - 68.

Adding 68 to both sides, we find:

x = 30 + 68 = 98.

Therefore, Pedro's exam score was 98.

The z-score measures how many standard deviations an individual's score is above or below the mean. In this case, Pedro's z-score of 3 indicates that his exam score was 3 standard deviations above the mean of 68.

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When comparing the means between two independent samples, the alternative hypothesis should be stated as: "There is a significant difference between the means of the two independent samples."

In this context, the alternative hypothesis (often denoted as H1 or Ha) proposes that there is a meaningful or notable difference between the means of the two groups being compared, suggesting that the observed difference is not due to chance or sampling error.

The alternative hypothesis is tested against the null hypothesis (H 0), which states that there is no significant difference between the means of the two independent samples. In other words, the null hypothesis suggests that any observed difference is simply due to random chance or sampling variability.

When conducting a hypothesis test, researchers use statistical tests, such as the t-test or ANOVA, to determine the likelihood of the observed difference between the means occurring by chance alone. If the probability of obtaining the observed difference under the null hypothesis is sufficiently low (typically less than 0.05), the null hypothesis is rejected in favor of the alternative hypothesis, indicating that there is a significant difference between the means of the two independent samples.

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We need to first identify the center of the circle.

We see that the coordinate point of the center of the circle is (-1, -2).

The equation of a circle is given with the equation

where h is x, k is y, and r is the radius of the circle.

Therefore, we can plug in the coordinates first to find the h and k of the equation.

Then, we need to determine r.

The circle intersects points (-6, -2) and (4, -2). We can simply subtract the x-coordinates from each other to find the diameter of the circle.

Finally, we know the radius is half of the diameter:

We can plug in the radius into the equation.

Therefore, our final equation is Choice D:

We have to order 36 yoga pants.

We have the following information from the question is:

Yoga pants are number one for women's clothing sales in your store.

and, she ordered one gross last time.

According to trend, it reports states that you should increase your order by 25%.

Now, we have to calculate how many should you order.

Now, According to the question:

We know that :

1 gross = 144

We have to should order yoga pants are:

25% × 144 = 36

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Linear pairs are the angles which formed a straight line

Look at your figure

Which angle pairs formed a straight line

Angle 1 and angle 5 formed a straight line

The sum of them = 180 degrees

Angles 1, 2, and 3 formed a straight line

The sum of them = 180 degrees

Angles 2, 3, and 4 formed a straight line

The sum of them is 180 degrees

Angles 4 and 5 formed a straight line

The sum of them = 180 degrees

So, the linear pairs are

Angle 1 and angle 5

Angle 4 and angle 5

a) the population cannot be negative, the limiting population is 4300.

b)the population is increasing when 0 < p < 4300 and decreases when p > 4300.

c)the equilibrium solutions are p = 0 and p = 4300.

(a) To determine when the population is increasing or decreasing, we need to look at the sign of dp/dt.

\(\frac{dp}{dt} = 1.2p(1 - \frac{p}{4300})\)

For dp/dt to be positive (i.e. population is increasing),

we need\(1 - \frac{p}{4300} > 0, or \ p < 4300.\)

For dp/dt to be negative (i.e. population is decreasing),

we need\(1 - \frac{p}{4300} < 0, or p > 4300.\)

Therefore, the population is increasing when 0 < p < 4300 and decreases when p > 4300.

(b) To find the limiting population, we need to find the value of p as t approaches infinity.

As t approaches infinity,\(\frac{dp}{dt}\)approaches 0. Therefore, we can set \(\frac{dp}{dt}\) = 0 and solve for p.

0 = 1.2p(1 - p/4300)

Simplifying, we get:

0 = p(1 - p/4300)

So, either p = 0 or 1 - p/4300 = 0.

Solving for p, we get:

p = 0 or p = 4300.

Since the population cannot be negative, the limiting population is 4300.

(c) Equilibrium solutions occur when\(dp/dt = 0.\)We already found the equilibrium solutions in part (b): p = 0 and p = 4300.

Therefore, the equilibrium solutions are p = 0 and p = 4300.

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a)  The population is increasing when 0 < p < 4300, and  decreasing when p > 4300.

b)  The population cannot be negative, the limiting population is 4300.

c)  these are the equilibrium solutions.  At p = 0, the population is not

increasing or decreasing, and at p = 4300,  the population is decreasing

but not changing in size.

(a) To determine when the population is increasing or decreasing, we

need to find the sign of dp/dt. We have:

dp/dt = 1.2p(1 - p/4300)

This expression is positive when 1 - p/4300 > 0, i.e., when p < 4300, and

negative when 1 - p/4300 < 0, i.e., when p > 4300.

Therefore, the population is increasing when 0 < p < 4300, and

decreasing when p > 4300.

(b) To find the limiting population, we need to solve for p as t approaches infinity. To do this, we set dp/dt = 0 and solve for p:

1.2p(1 - p/4300) = 0

This equation has two solutions: p = 0 and p = 4300. Since the population cannot be negative, the limiting population is 4300.

(c) To find the equilibrium solutions, we need to solve for p when dp/dt = 0. We already found that the only solutions to dp/dt = 0 are p = 0 and

p = 4300.

Therefore, these are the equilibrium solutions.

At p = 0, the population is not increasing or decreasing, and at p = 4300,

the population is decreasing but not changing in size.

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Confidence intervals of treatment effects estimation in panel data models with interactive fixed effects A confidence interval (CI) is an interval estimate for an unknown parameter.

The most commonly used level of confidence is 95 percent, although other levels of confidence can also be used. The range is calculated from a given set of sample data using a statistical method. In this case, we are looking at confidence intervals of treatment effects estimation in panel data models with interactive fixed effects.

Panel data models with interactive fixed effects are commonly used in economics to analyze the effects of treatments on outcomes over time. These models account for both individual-level and time-level variation, and they can be used to estimate treatment effects more accurately than other types of models.

In addition, panel data models with interactive fixed effects allow for the estimation of fixed effects that vary by individual and time, which can provide important insights into the dynamics of treatment effects over time.

However, several methods have been developed to estimate confidence intervals for treatment effects in panel data models with interactive fixed effects. These methods typically involve bootstrapping or simulation techniques that account for the correlation structure of the data.

Overall, the estimation of confidence intervals for treatment effects in panel data models with interactive fixed effects is an important area of research that has the potential to improve the accuracy of treatment effect estimates in economics and other social sciences.

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Answer:

The answer you're looking for is 1470.

Step-by-step explanation:

The method I used was PEMDAS

Since there was no parenthesis, I simplified the exponents.

2.130 x 10³ - 6.6 x 10² = ?
2.130 x 1000 - 6.6 x 100 = ?

After that, I multiplied all terms next to each other.

2.130 x 1000 - 6.6 x 100 = ?
2130 - 660 = ?

The final step I did was to subtract the two final terms and ended up with 1470 as my final answer.

1470 = ?

I hope this was helpful!

The amount of paint needed to paint the front of the building knowing that 0.5 kg of paint is needed per m^2 is 20 kg.

We know that,

Area of rectangle = L * W

where L = Length of the rectangle

and W  = Width of the rectangle.

Area of triangle = 1/2 * B * H

where B = Base of the triangle

and H  = Height of the triangle.

From the figure, we are given;

The front of the building has two rectangles that represent the floor and one triangle.

The rectangles are of the same size and it's given;

L = 8 m

W = 4 m

Area of rectangle = L * W = 8 * 4 = 32 m^2

The dimension of the triangle is:

B = 8 m

H = 2 m

Area of triangle = 1/2 * B * H = 1/2 * 8 * 2 = 8 m^2

The total area of the front of the building = 32 + 8 = 40 m^2

Amount of paint required

= total area of the front of the building * paint is needed per m^2

= 40 * 0.5 = 20 kg

So, 20 kg of paint is needed.

Thus, the amount of paint needed to paint the front of the building knowing that 0.5 kg of paint is needed per m^2 is 20 kg.

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Answer: The midpoint  is MZ midpoint = (0.5,1)

Step-by-step explanation:

\(MP= (\frac{x_1+x_2}{2}),(\frac{y_1+y_2}{2} ) \\MP= (\frac{-4+3}{2}),(\frac{-1+3}{2} )\\MP= (\frac{-1}{2}),(\frac{2}{2} ) \\\\MP= (-0.5 ,1)\)

Answer:

n= -1.2

Step-by-step explanation:

I think because if you use slope equation to find the slope which is 3/5 and then you use point slop equation to find out what the equation would be. y=3/5x and then you substitue y for 18 and solve/simplify the equation to get -1.2.

(a) For y''+4y=sin2t+(2t+1)cos2t+tsint, we need to find a particular solution Y(t) using the method of undetermined coefficients.

Since the right-hand side of the equation contains sin(2t), cos(2t), and tsin(t), we can assume that the particular solution has the form:

Y(t) = A sin(2t) + B cos(2t) + Ct sin(t) + Dt cos(t) + Et + F

where A, B, C, D, E, and F are undetermined coefficients to be determined.

(b) For y''-4y'+4y=t^2(e^(2t)-1), we need to find a particular solution Y(t) using the method of undetermined coefficients. Since the right-hand side of the equation contains t^2e^(2t) and t^2, we can assume that the particular solution has the form:

Y(t) = (At^2 + Bt + C)e^(2t) + Dt^2 + Et + F

where A, B, C, D, E, and F are undetermined coefficients to be determined.

(c) For y''+2y'+2y=3e^(-t)+2e(-t)cos(t)+4(t^2)e^(-t)sin(t), we need to find a particular solution Y(t) using the method of undetermined coefficients. Since the right-hand side of the equation contains e^(-t), e^(-t)cos(t), and t^2e^(-t)sin(t), we can assume that the particular solution has the form:

Y(t) = Ae^(-t) + (Bt + C)e^(-t)cos(t) + (Dt + Et^2) e^(-t)sin(t) + F

where A, B, C, D, E, and F are undetermined coefficients to be determined.

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The value of X = 25.

Solution:

The two equations are

(i) the first condition is difference of x and y is 14

x - y = 14 ---------equation 1

(ii) the second condition of the given data is value of x is 3 times more than two times of y value.

x - 2y = 3 --------equation 2

From equation 2, we have to separate two variables x and y,

x = 3 + 2y  --------equation 3

We have to Substitute equation 3 in equation 1

3 + 2y - y = 14

3 + y = 14

y = 14 - 3

y = 11

Substitute y = 11 in equation 1........

x - 11 = 14

x = 14 + 11

x = 25

So, the value of x is 25 and y is 11.

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Answer:

Step-by-step explanation:

Given the difference of x and y is 14, and the difference of x and 2y is 3, you want two equations, their graph, and the value of x.

The difference of 'a' and 'b' is (a -b). Here, the two differences are expressed as the equations ...

The attachment shows a graph of these equations. Their point of intersection is (25, 11), meaning the value of x is 25.

The graph of the first equation is easily drawn by recognizing the x- and y-intercepts are 14 and -14, respectively.

The graph of the second equation will go through the x-intercept point of (3, 0) and the y-intercept point of (0, -3/2). It is probably easier to graph this by hand by considering the x-intercept point and the slope of 1/2.

Since we're only interested in the value of x, it is convenient to eliminate the variable y. We can to that by subtracting the second equation from twice the first:

  2(x -y) -(x -2y) = 2(14) -(3)

  x = 25 . . . . . . . . . simplify