If ABC is an equilateral triangle, then the mA =60

A. If the mA = 60, then ABC is an equilateral triangle.
B. If ABC is not an equilateral triangle, then the mA does not equal 60.
C. If the mA does not equal 60, then ABC is not an equilateral triangle.

Answer is C!

The possible values of k for the equation of circle are -4 and 7.

A circle is a two-dimensional figure with a radius and circumference of 2πr.

The area of a circle is πr².

We have,

The equation of a circle is (x - 1)² + (y - k)² = 50

The equation of the circle passes through the point (2, 3) = (x, y).

Now,

(2 - 1)² + (3 - k)² = 50

1 + (3 - k)² = 50

(3 - k)² = 50 - 1

3 - k = √49

3 - k = ±7

Now,

3 - k = 7

3 - 7 = k

k = -4

3 - k = -7

3 + 7 = k

k = 10

Thus,

The possible values of k are -4 and 10.

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Based on the given clues, we can determine the person, drink, and price paid for each individual:

Calvin: Root Beer, $4.99

Dean: Lemonade, $7.99

Kelli: Water, $6.99

Lee: Iced Tea, $5.99

From clue 1, we know that either Calvin or the person who got the Root Beer paid $4.99. Since Calvin paid more than Lee according to clue 4, Calvin cannot be the one who got the Root Beer. Therefore, Calvin paid $4.99.

From clue 2, Kelli paid $6.99.

From clue 3, the person who got the water paid $1 less than Dean. Since Dean paid the highest price, the person who got the water paid $1 less, which means Lee paid $5.99.

From clue 5, the person who got the Root Beer paid $1 less than the person who got the Iced Tea. Since Calvin got the Root Beer, Lee must have gotten the Iced Tea.

Therefore, the final assignments are:

Calvin: Root Beer, $4.99

Dean: Lemonade, $7.99

Kelli: Water, $6.99

Lee: Iced Tea, $5.99

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Answer:

$54

Step-by-step explanation:

45 increase 20% =

45 × (1 + 20%) = 45 × (1 + 0.2) = 54

Answer:

Option B is the correct answer

Step-by-step explanation:

B. x2 + y2 = 25

Answer:

11 and 8

Step-by-step explanation:

11+8=19

11-8=3

Answer:

8 and 11

Step-by-step explanation:

The x-intercepts of a quadratic function are the points where the function graph intersects the x-axis. To find the x-intercepts of the given quadratic function, we need to determine the values of x when the y-value (or the function value) is equal to 0.

From the given information, we can see that the quadratic function passes through the points (-2, 0) and (1, 0), which indicates that the function intersects the x-axis at x = -2 and x = 1. Therefore, the quadratic function x-intercepts are (-2, 0) and (1, 0).

The correct answers are (d) (-2, 0) and (1, 0).

Answer:

x = 95

Step-by-step explanation:

angles that form a straight line add up to equal 180

Thus, x + 85 = 180

180 - 85 = 95

Hence, x = 95

Answer:

The first one is non-linear.

The second is linear.

The value of the angle U in the triangle is 92.10 degrees.

The angle U in the triangle can be found using cosine rule as follows:

Let's use cosine formula to find the angle U

c² = a² + b² - 2ab cos C

Hence,

Therefore,

a = 58.8

b = 38.4

c = 71.4

Hence,

71.4²  = 58.8² +  38.4² - 2(58.8)(38.4) cos U

5097.96 = 3457.44 + 1474.56 - 4515.84 cos U

5097.96 - 4932 =  - 4515.84 cos U

165.96 = - 4515.84 cos U

divide both sides by - 4515.84

cos U = 165.96 / - 4515.84

cos U = - 0.03675063775

U = cos⁻¹ - 0.03675063775

U = 92.1032274244

Therefore,

U = 92.10 degrees

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The limit of (x + x²)/(2 − 3x²) as x approaches infinity is -1/3.

To find the limit of (x + x²)/(2 − 3x²) as x approaches infinity, we can use l'Hospital's Rule.

First, we need to check if the limit is in the indeterminate form 0/0 or ∞/∞. As x approaches infinity, both the numerator (x + x²) and the denominator (2 - 3x²) approach infinity.

Therefore, the limit is in the indeterminate form ∞/∞, and we can apply l'Hospital's Rule.

l'Hospital's Rule states that if the limit is in the indeterminate form 0/0 or ∞/∞, we can take the derivative of the numerator and denominator separately, and then find the limit of the ratio of their derivatives.

Numerator's derivative: d/dx(x + x²) = 1 + 2x Denominator's derivative: d/dx(2 - 3x²) = -6x

Now, we'll find the limit of the ratio of their derivatives as x approaches infinity: lim (1 + 2x)/(-6x) as x→∞

We can use l'Hospital's Rule again, as this limit is also in the indeterminate form ∞/∞. Numerator's second derivative: d/dx(1 + 2x) = 2

Denominator's second derivative: d/dx(-6x) = -6

Now, we'll find the limit of the ratio of their second derivatives as x approaches infinity: lim (2)/(-6) as x→∞ Since the limit involves constants only, it does not depend on x, and we can directly compute the limit: 2 / (-6) = -1/3

Therefore, the limit of (x + x²)/(2 − 3x²) as x approaches infinity is -1/3.

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Answer:

A and B

Step-by-step explanation:

96% of 25

= \(\frac{96}{100}\) × 25 ( per cent means out of 100 ) → A

= 0.96 × 25 ( divide 96 by 100 ) → B

Using the given conditions that sin(20) = cos(2u) = tan(24) = 3, we can find the exact values of sin(2u), cos(2u), and tan(2u) using the double-angle formulas. By substituting the known values into the formulas, we can determine the exact values of these trigonometric functions.

Given sin(20) = 3, we can use the double-angle formula for sine to find sin(2u).

The double-angle formula for sine is sin(2u) = 2sin(u)cos(u). We know that sin(u) = -3/5, so we can substitute this value into the formula to calculate sin(2u).

Therefore, sin(2u) = 2(-3/5)(cos(u)).

Given cos(2u) = 3, we can use the double-angle formula for cosine to find cos(2u).

The double-angle formula for cosine is cos(2u) = cos^2(u) - sin^2(u). Since we already know sin(u) = -3/5 and cos(u) can be calculated using the Pythagorean identity (cos^2(u) = 1 - sin^2(u)), we can substitute these values into the formula to determine cos(2u).

Finally, given tan(24) = 3, we can use the double-angle formula for tangent to find tan(2u).

The double-angle formula for tangent is tan(2u) = (2tan(u))/(1 - tan^2(u)). By substituting the known value of tan(24) = 3 into the formula, we can calculate the exact value of tan(2u).

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Answer:

So, the probability of selecting a number from 1 to 100 that is divisible by 5 or 7 is 0.32.

Hope this helped!

The inflection point occurs at approximately 17.34 days of practice, where the proficiency growth rate starts to decrease.

The inflection point of the sigmoid curve happens when the pace of expansion in capability begins to diminish. This is the point at which the second derivative of the curve equals zero.

To find the inflection point of the curve P(t) = 100/(1 + 40e^(0.3t)), we want to track down the second derivative of P(t) with respect to t:

P(t) = 100/(1 + 40\(e^{(0.3t)}\))

P'(t) = (- 1200\(e^{(0.3t)}\))/(1 + 40\(e^{(0.3t)}\))²

P''(t) = (10800\(e^{(0.6t)}\))/(1 + 40\(e^{(0.3t)}\))³ - (3600\(e^{(0.3t)}\))/(1 + 40\(e^{(0.3t)}\))^2

Setting P''(t) equivalent to nothing and addressing for t, we get:

(10800\(e^{(0.6t)}\))/(1 + 40\(e^{(0.3t)}\))³ - (3600\(e^{(0.3t)}\))/(1 + 40\(e^{(0.3t)}\))² = 0

Working on this articulation by duplicating the two sides by (1 + 40\(e^{(0.3t)}\))³, we get:

10800\(e^{(0.6t)}\) - 3600\(e^{(0.3t)}\)(1 + 40\(e^{(0.3t)}\)) = 0

Partitioning the two sides by 3600\(e^{(0.3t)}\), we get:

3\(e^{(0.3t)}\) - (1 + 40\(e^{(0.3t)}\)) = 0

Expanding and simplifying this expression, we get:

3\(e^{(0.3t)}\) - 1 - 40\(e^{(0.3t)}\) = 0

39\(e^{(0.3t)}\) = 1

\(e^{(0.3t)}\) = 1/39

Taking the natural logarithm of both sides, we get:

0.3t = ln(1/39)

t = (ln(1/39))/0.3

t ≈ 17.34 days

As a result, the proficiency development rate starts to slow down after about 17.34 days of practice, which is the inflection point.

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Check the picture below.

\(\stackrel{\textit{\LARGE Areas}}{ \stackrel{\textit{two triangles}}{2\left[\cfrac{1}{2}(\underset{b}{8})(\underset{h}{6}) \right]}~~ + ~~\stackrel{\textit{three rectangles}}{(14)(6)~~ + ~~(14)(8)~~ + ~~(14)(10)}} \\\\\\ 48~~ + ~~84~~ + ~~112~~ + ~~140\implies \text{\LARGE 384}~cm^2\)

Answer:

Domain is all x values

Range is all y values

Step-by-step explanation:

Your image is not clear enough for me to see the x or y coordinates so hope that helps you to figure it out on your own

Answer:  The long division method is a way to solve division problems by hand. Here are the steps to do long division:

Write the dividend (the number being divided) inside a long division bracket, and write the divisor (the number doing the dividing) outside of the bracket.

Divide the first digit of the dividend by the divisor. Write the answer (the quotient) above the dividend, and write any remainder (what’s left over) below the first digit of the dividend.

Bring down the next digit of the dividend next to the remainder.

Repeat step 2 until you’ve brought down all of the digits of the dividend.

The final answer is your quotient with any remainder written as a fraction.

The equation represented by the model is 3x²-4x+1=(3x-1)(x-1).

Given model represents a polynomial of the form ax²+bx and model is in figure.

Consider the given table.

The first row in the table represents first term of the polynomial.

In first row first three terms are variables and last term are constant.

Write all the terms of the first row in the form of sum.

+x+x+x-1=3x-1

The first column in the table represents second term of the polynomial.

In first column first term are variable and last term are constant.

Write all the terms of the first column in the form of sum.

+x-1=x-1

The product of first term of polynomial (3x-1) and second term of polynomial (x-1) is equal to the sum of all remaining terms in this table.

+x²+x²+x²-x-x-x-x+1=3x²-4x+1.

We can also check this by multiplying (3x-1) and (x-1) as

(3x-1)(x-1)=3x(x-1)-1(x-1)

(3x-1)(x-1)=3x(x)-3x(1)-1(x)+1(1)

(3x-1)(x-1)=3x²-3x-x+1

(3x-1)(x-1)=3x²-4x+1

Hence, the equation represented by the given model in the form of polynomial ax²+bx is (3x-1)(x-1)=3x²-4x+1.

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Answer:

N+1

Step-by-step explanation:

It begins with = 2

then n+1=3

then n+2=4 and so on it is n+1

The correct 95% confidence interval for the proportion of drivers who react more quickly to the new light is (0.53, 0.67).

To calculate the confidence interval for the proportion of drivers who react more quickly to the new light, we can use the formula:

CI = p ± zα/2 √((p(1-p))/n)

where p is the proportion of drivers who react more quickly to the new light, n is the sample size, and zα/2 is the z-score for the desired confidence level (in this case, 95% corresponds to zα/2 = 1.96).

Substituting the given values, we get:

CI = 0.6 ± 1.96 √((0.6*0.4)/n)

Since we don't know the sample size, we can't calculate the exact confidence interval. However, we can see that the margin of error is proportional to 1/√n, which means that larger sample sizes will result in narrower confidence intervals.

Based on the given answer choices, we can see that the margin of error is 0.07, which corresponds to a sample size of around 200. So, if we assume that the sample size is large enough to use the normal approximation, we can calculate the confidence interval as:

CI = 0.6 ± 0.07

which gives us (0.53, 0.67) as the correct answer.

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Answer:

x = 56

MKL = 56

KML=  63

MLK = 61

Step-by-step explanation:

We know that the sum of the interior angles of a triangle = 180 degrees.

So, x+ (x+7)+ ( x+5) = 180

3x+ 12= 180

3x= 180-12 = 168

168/3 = x

therefore, x= 56 degrees.

So MKL = 56

KML= 56+ 7 = 63

MLK = 56+5 = 61

The length of the path described by the parametric equations

 is 3/2units.

We can find the length of the path described by the parametric equations x=cos³t and y=sin³t by using the arc length formula.

The arc length formula for a parametric curve given by:

x=f(t) and y=g(t) is given by:

L = ∫[a,b] √[f'(t)² + g'(t)²] dt

where f'(t) and g'(t) are the derivatives of f(t) and g(t), respectively.

In this case, we have:

x = cos³t, so x' = -3cos²t sin t

y = sin³t, so y' = 3sin²t cos t

Therefore,

f'(t)² + g'(t)² = (-3cos²t sin t)² + (3sin²t cos t)²

= 9(cos⁴t sin²t + sin⁴t cos²t)

= 9(cos²t sin²t)(cos²t + sin²t)

= 9(cos²t sin²t)

Thus, we have:

L = ∫[0,2π] √[f'(t)² + g'(t)²] dt

= ∫[0,2π] √[9(cos²t sin²t)] dt

= 3∫[0,2π] sin t cos t dt

Using the identity sin 2t = 2sin t cos t, we can rewrite the integral as:

L = 3/2 ∫[0,2π] sin 2t dt

Integrating, we get:

L = 3/2 [-1/2 cos 2t] from 0 to 2π

= 3/4 (cos 0 - cos 4π)

= 3/2

Therefore, the length of the path described by the parametric equations x=cos³t and y=sin³t is 3/2 units.

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The integer that represents the change in the hot air balloon's elevation each time Tameka lowers it is -15.

To calculate the change in elevation, we can divide the total change in elevation (75 m) by the number of times the balloon is lowered (5).

75 m / 5 = -15

The negative sign indicates that the balloon is being lowered, and the number 15 represents the distance in meters by which the balloon is descending each time it is lowered.

Let's break down the calculation further to understand why this integer represents the change in elevation.

Tameka lowers the balloon five times, and the total change in elevation is 75 meters. Since the balloon is lowered an equal distance each time, we can divide the total change by the number of times lowered to find the change in elevation per lowering.

75 meters / 5 = 15 meters

However, since the balloon is being lowered, the change in elevation is negative. This means that for each lowering, the balloon descends 15 meters downward.

Hence, the integer -15 represents the change in the hot air balloon's elevation each time Tameka lowers it. It tells us that the balloon is being lowered by 15 meters during each lowering, resulting in a total descent of 75 meters when repeated five times.

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The linear regression method forecasts the values for 2019 as 87.3723, 83.7387, 89.0824, and 84.9406.

To provide a step-by-step explanation of the linear regression method used to forecast the values for 2019:

Linear regression is a statistical technique used to model the relationship between a dependent variable and one or more independent variables. In this case, the dependent variable is the forecasted value for 2019, and the independent variable is time.

The given forecast values, 87.3723, 83.7387, 89.0824, and 84.9406, represent the predicted values for the corresponding time periods.

The linear regression method estimates a straight line that best fits the historical data, allowing for the prediction of future values. In this case, the method estimates the relationship between time and the forecasted values.

By fitting a linear regression model to the historical data, the method calculates the coefficients for the line equation, which represents the trend or pattern observed in the data.

Once the coefficients are determined, the linear regression model can be used to forecast values for future time periods. The model assumes that the relationship between time and the forecasted values will continue to follow the estimated trend.

In this case, the linear regression method predicts the values 87.3723, 83.7387, 89.0824, and 84.9406 for the year 2019 based on the observed trend in the historical data.

It's important to note that without additional context or information about the specific dataset and variables involved, it's difficult to provide a more detailed explanation. The linear regression method relies on the assumption that the relationship between the dependent and independent variables is linear and that there are no other significant factors influencing the forecasted values.

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The subgame perfect Nash equilibrium involves Player 1 receiving a piece that is no less than 1/4 of the original cake, Player 2 receiving a piece that is no less than 1/2 of the cake, and Player 3 receiving a piece that is no less than 1/4 of the cake. Player 2 obtains the largest piece at 1/2 of the cake, while Player 1 gets a share that is no less than 1/4 of the cake, which is larger than Player 3's share of the remaining cake.

The subgame perfect Nash equilibrium and complete strategies are as follows:

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Solving an equation in algebra - mathematics will BOMDAS rule. Multiplication, division, addition, and subtraction are performed before.

However, in order to simplify things, if there are any exponential or logarithmic components, solve them first before applying BOMDAS to reduce them to a single solvable term. This is required by the rules.

So the list goes as

1. Exponents

2. Roots

3. Multiplication

4. Division

5. additional

6. Subtraction

However. Using a regular or scientific calculator will generate a lot of debate. A scientific calculator will adhere to the principles, while a typical calculator will evaluate from left to right or precisely the operator used first.

Using a scientific calculator, 5+2x3=11 instead of the normal one's 5+2x3=21.

Furthermore, the preferred behavior norm for division and multiplication is different.

Thus, people's difficulty with mathematics is not unjustified. The choice of how you want to approach it is ultimately up to you.

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The product of -1.8 and = -1.8 x ?

3 more than a number = 3 + n

The product of -1.8 and 3 more than a number = -1.8(3 + n)

Is the same as 1/10 = equals (equal sign) 1/10

Full Equation: -1.8(3 + n) = 1/10

Steps to solve:

1. Divide both sides by -1.8 (or - 9/5)

(3 + n) = 1/10 x -5/9

3 + n = -5/90

2. Subtract 3 from both sides

n = -5/90 - 270/90

n = -30 5/9

Hope this helps!