7. Kim knows that one angle of an isosceles triangle is 48°.
He says that one of the other angles must be 66°. Is Kim correct?
If yes explain why?

Answer:

-2,-1,1,2

Step-by-step explanation:

The term root is just another name for the x intercept so just look at where your line crosses the x axis and you will have your answer. Remember the y axis is not involved so it cannot be a co-ordinate.

The process takes approximately 14 iterations to reach the desired accuracy.

The Bisection Method will take approximately 14 iterations to find the approximate root of the equation within an error tolerance of 0.001. The mathematics calculations involve finding the midpoint of a given interval [a, b] and then determining whether the midpoint is a root of the equation. If it is not a root, then the interval is divided into two halves, and the process is repeated on the subinterval where the sign of the function changes. This process is repeated until the midpoint is within the desired error tolerance.

To calculate the number of iterations required, we begin by noting that the initial interval used is [1, 0]. The midpoint of this interval is 0.5. This value is then plugged into the function to determine if it is a root. Since it is not, the interval is then divided into two halves and the process is repeated. This process is repeated until the midpoint is within the desired error tolerance of 0.001. In this case, it takes approximately 14 iterations to reach the desired accuracy.

The complete question is:

Given the function f(x) = x^3 - x^2 - 4 and an initial approximation of x = 1, how many iterations of the Bisection Method are required to find the approximate root of the equation within an error tolerance of 0.001?

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Answer:

\(\dfrac{1}{729}\)

Step-by-step explanation:

\(\left(\dfrac{}{}(-3)^2\dfrac{}{}\right)^{-3}\)

First, we should evaluate inside the large parentheses:

\((-3)^2 = (-3)\cdot (-3) = 9\)

We know that a number to a positive exponent is equal to the base number multiplied by itself as many times as the exponent. For example,

\(4^3 = 4 \, \cdot\, 4\, \cdot \,4\)

       ↑1 ↑2 ↑3 times because the exponent is 3

Next, we can put the value 9 into where \((-3)^2\) was originally:

\((9)^{-3}\)

We know that a number to a negative power is equal to 1 divided by that number to the absolute value of that negative power. For example,

\(3^{-2} = \dfrac{1}{3^2} = \dfrac{1}{3\cdot 3} = \dfrac{1}{9}\)

Finally, we can apply this principle to the \(9^{-3}\):

\(9^{-3} = \dfrac{1}{9^3} = \boxed{\dfrac{1}{729}}\)

The range of possible distances from the beach to the theater is 2 km to 16 km, calculated by subtracting the distance between the theater and the house (7 km) from the distance between the beach and the house (9 km), and adding it back.

To calculate the range of possible distances from the beach to the theater, we can use the information provided

Start with the distance between the beach and the house: 9 km.

Subtract the distance between the theater and the house: 7 km.

9 km - 7 km = 2 km.

This gives us the minimum possible distance from the beach to the theater: 2 km.

Add the distance between the theater and the house: 7 km.

9 km + 7 km = 16 km.

This gives us the maximum possible distance from the beach to the theater: 16 km.

Therefore, the range of possible distances is from 2 km to 16 km.

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--The given question is incomplete, the complete question is given below " Describe the range of possible distances from the beach to the theater "--

Answer:

-6

Step-by-step explanation:

use PEMDAS

start with the exponent: (-4)^2=16

-12 / 3 * (-8 + 16 - 6) +2

then the parentheses: (-8+16-6)=2

-12 / 3 * 2 +2

next is multiplication/division, division comes first so: -12/3=-4

-4 * 2 +2

then multiplication: -4*2=-8

-8+2=-6

Answer: Part A:

To find the x-intercepts of the graph of f(x), we need to set f(x) equal to zero and solve for x:

-16x2 + 60x + 16 = 0

Divide both sides by -4 to simplify:

4x2 - 15x - 4 = 0

We can use the quadratic formula to solve for x:

x = (-b ± sqrt(b2 - 4ac)) / 2a

Where a = 4, b = -15, and c = -4.

x = (-(-15) ± sqrt((-15)2 - 4(4)(-4))) / 2(4)

x = (15 ± sqrt(385)) / 8

Therefore, the x-intercepts are approximately 0.256 and 3.194.

Part B:

The coefficient of the x2 term in f(x) is -16, which is negative. This means that the graph of f(x) opens downward, so the vertex is a maximum.

The x-coordinate of the vertex can be found using the formula:

x = -b / 2a

Where a = -16 and b = 60.

x = -60 / 2(-16) = 1.875

To find the y-coordinate of the vertex, we can plug in this value of x into the equation for f(x):

f(1.875) = -16(1.875)2 + 60(1.875) + 16 = 80.25

Therefore, the coordinates of the vertex are (1.875, 80.25).

Part C:

To graph f(x), we can use the information we obtained in Part A and Part B. We know that the x-intercepts are approximately 0.256 and 3.194, and the vertex is at (1.875, 80.25).

We can also find the y-intercept by plugging in x = 0:

f(0) = -16(0)2 + 60(0) + 16 = 16

Therefore, the y-intercept is (0, 16).

Using all of this information, we can sketch the graph of f(x) as a downward-opening parabola with x-intercepts at approximately 0.256 and 3.194, a vertex at (1.875, 80.25), and a y-intercept at (0, 16).

Step-by-step explanation:

Answer:

$93 per hour ?

125-405 = 280

280÷3= 93 per hour

The GCD of a and b in the ring of integers is the same as their GCD in the ring of Gaussian integers because both conditions of Gaussian integers are satisfied.

To show that the greatest common divisor (GCD) of integers a and b is the same in the ring of integers and the ring of Gaussian integers, we need to prove two things:

1. GCD(a, b) in the ring of integers divides both a and b.
2. Any common divisor of a and b in the ring of Gaussian integers also divides a and b in the ring of integers.

Let's start with the first point. If GCD(a, b) in the ring of integers divides a and b, it must also divide any linear combination of a and b. Since the ring of Gaussian integers is a subset of the ring of integers, any linear combination of a and b in the ring of Gaussian integers is also a linear combination of a and b in the ring of integers. Therefore, GCD(a, b) in the ring of integers divides any linear combination of a and b in the ring of Gaussian integers.

For the second point, any common divisor of a and b in the ring of Gaussian integers also divides a and b in the ring of integers because the ring of Gaussian integers is a subset of the ring of integers.

In conclusion, the GCD of a and b in the ring of integers is the same as their GCD in the ring of Gaussian integers because both conditions are satisfied.

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The number 13 is very close to 11.511. Then the correct option is C.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Jovana makes $11.25 per hour at her part-time job. During one week, she also earned $30 in tip money, and her final pay for the week was $159.50.

Let 'x' be the number of weeks. Then the equation is given as,

11.25x + 30 = 159.50

11.25x = 129.5

x = 11.511

The number 13 is very close to 11.511. Then the correct option is C.

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Answer: 4

Step-by-step explanation:

2(x+7) = x + 18

2x + 14 = x + 18

x + 14 = 18

x = 4

Answer:

C. 4

Step-by-step explanation:

\(2(x + 7) = x + 18\)

\(2(x+7) = 2x + 2×7\)

\(=2x+14\)

\(2x + 14 = x + 18\)

\(2x + 14-x=18\)

\(2x - x = 18 - 14\)

\(x=18-14\)

\(x = 4\)

ANSWER

f(-4) = -21

EXPLANATION

We have that:

f(x) = 6x + 3

We want to find f(-4)

To do this, we replace x with -4:

f(-4) = 6(-4) + 3

f(-4) = -24 + 3

f(-4) = -21

That is the answer.

Since none of the 13 classmates had been given math homework between the original survey and Kelly's second survey, the sum of the values in the second data set is the same as the sum of the values in the original data set. Therefore, the change in the means can be determined without calculating the mean of either data set by considering the number of data points in each set.

Since both data sets have the same number of data points, the change in the means will be zero. This is because the mean is calculated by dividing the sum of the values by the number of data points, and since the sum of the values is the same in both data sets, the means will also be the same.

In other words, the change in the mean is calculated as follows:

Change in mean = Mean of second data set - Mean of first data set

Since none of the values in the second data set have changed, the mean of the second data set is the same as the mean of the first data set. Therefore, the change in the mean is:

Change in mean = Mean of second data set - Mean of first data set

= Mean of first data set - Mean of first data set

= 0

Thus, the change in the means between Kelly's original survey and her second survey is zero.

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The probability that you will catch a t-shirt that is not of medium size would be 0.7

What is the probability?

Probability is a branch of mathematics that deals with numerical descriptions of how likely an event is to occur or how likely a proposition is to be true. The probability of an event is a number between 0 and 1, where 0 indicates the event's impossibility and 1 indicates certainty.

Small=S=20, M=medium=30,

L = Either large or extra large=50

P(T-shirt that is not a medium)= 1 - P(T-shirt is medium)

                                           = 1 - 30/100

                                           = 1 - 0.3

                                           = 0.7

Hence, the probability that you will catch a t-shirt that is not of medium size would be 0.7

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Answer:

Erosion

Step-by-step explanation:

Erosion is the movement of sediment from one place to another. Erosion is the mechanical process of wearing or grinding somethin down. It condition in which the earth’s surface is worn away by the action of water and wind.

Therefore, the answer is erosion.

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Answer:

7/6 miles

Step-by-step explanation:

As, Distance for 1 hour = x

For 2 hours = 2 1/3

For 2 hours = 2(x)

So, 2(x)= 2 1/3

2(x)= 7/3

So, x = 7/3 ÷ 2

So x= 7/3 x 1/2

Therefore, x = 7/6

Final answer= 7/6 miles per hour

Answer:I don’t Knowt Try To Answer it yourself

Step-by-step explanation:

Answer:

Replace y with f−1(x) f - 1 ( x ) to show the final answer. Verify if f−1(x)=x3+73 f - 1 ( x ) = x 3 + 7 3 is the inverse of f(x)=3x−7 f ( x ) = 3 x - 7

Step-by-step explanation:

To verify the identity sin(θ) / 1-cos^2θ = cosθ, we start by manipulating the left-hand side of the equation using trigonometric identities. We can use the Pythagorean identity cos^2θ + sin^2θ = 1 to rewrite the denominator as 1-sin^2θ. Then, using the reciprocal identity sinθ/cosθ = tanθ, we can simplify the left-hand side to 1/cosθ.

We can start by manipulating the left-hand side of the equation using trigonometric identities:

sin(θ) / (1-cos^2θ)

= sin(θ) / sin^2θ (using the Pythagorean identity cos^2θ + sin^2θ = 1)

= 1/cosθ (using the reciprocal identity sinθ/cosθ = tanθ)

Now, we can simplify the right-hand side using the definition of cosine:

cosθ = cosθ/1 (multiplying numerator and denominator by 1)

= sin^2θ/cosθsinθ (using the definition of sine and cosine: sinθ = opposite/hypotenuse, cosθ = adjacent/hypotenuse)

= sinθ/sin^2θ (using the Pythagorean identity cos^2θ + sin^2θ = 1)

= 1/cosθ (using the reciprocal identity sinθ/cosθ = tanθ)

Therefore, we have shown that:

sin(θ) / (1-cos^2θ) = cosθ

The identity is verified.

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It's important to note that the ratio doesn't mean that it takes akiko 6 min to get to school.

Ratio simply means the comparison of numbers. In this case, when akkiko rides her bike to school ahe travels 1 mi for every 6 min.

In this case, let's day the school is 10 miles, the minutes used will be:

= 10 × 6

= 60 minutes.

In this case, it doesn't mean that he will get to school in 6 minutes.

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(a) The doubling time of the population is approximately 13.86 years., (b) It takes approximately 23.10 years for the population to triple in size, (c) It takes approximately 27.72 years for the population to quadruple in size.

To calculate the doubling time of the population, we need to find the time it takes for the population to double from its initial value. In this case, the initial population is 9 million.

(a) Doubling Time:

Let's set up an equation to find the doubling time. We know that when the population doubles, it will be 2 times the initial population.

2P(0) = P(t)

Substituting P(t) = 9e^(0.05t), we have:

2 * 9 = 9e^(0.05t)

Dividing both sides by 9:

2 = e^(0.05t)

To solve for t, we take the natural logarithm (ln) of both sides:

ln(2) = 0.05t

Now, we can isolate t by dividing both sides by 0.05:

t = ln(2) / 0.05

Using a calculator, we find:

t ≈ 13.86

Therefore, the doubling time of the population is approximately 13.86 years.

(b) Time to Triple the Population:

Similar to the doubling time, we need to find the time it takes for the population to triple from its initial value.

3P(0) = P(t)

3 * 9 = 9e^(0.05t)

Dividing both sides by 9:

3 = e^(0.05t)

Taking the natural logarithm of both sides:

ln(3) = 0.05t

Isolating t:

t = ln(3) / 0.05

Using a calculator, we find:

t ≈ 23.10

Therefore, it takes approximately 23.10 years for the population to triple in size.

(c) Time to Quadruple the Population:

Similarly, we need to find the time it takes for the population to quadruple from its initial value.

4P(0) = P(t)

4 * 9 = 9e^(0.05t)

Dividing both sides by 9:

4 = e^(0.05t)

Taking the natural logarithm of both sides:

ln(4) = 0.05t

Isolating t:

t = ln(4) / 0.05

Using a calculator, we find:

t ≈ 27.72

Therefore, it takes approximately 27.72 years for the population to quadruple in size.

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We have the system of equations

Using substitution, we have that

Solving for x, we have that

but this is a contradiction, therefore the system of equations don't have a solution.

We also can notice this if we graph the equations.

From the graph we see that the equations do not intersect, then the system don't have a solution.

The given equation is

First, we add 4 on each side.

Then, we multiply 10 on each side.

Seventeen-year-old Simon went through a period of conflict over issues relating to his identity, but now he feels comfortable with the choices and commitment he has made. Thomas has achieved what Erik Erikson would call: integrated identity

Thomas has achieved what Erik Erikson would call "identity achievement." Erikson's theory of psychosocial development proposes that during adolescence, individuals go through a stage called identity versus role confusion.

This stage is marked by a period of conflict and exploration in which adolescents seek to establish a sense of identity and make meaningful life choices.

Identity achievement refers to the successful resolution of this conflict, where individuals have gone through a process of exploration, self-reflection, and decision-making, ultimately arriving at a clear and coherent sense of self. They have made commitments to particular values, beliefs, relationships, and life goals, and feel a sense of comfort and confidence in their choices.

In the case of seventeen-year-old Simon, who has experienced conflict but now feels comfortable with his choices and commitments, he has likely reached the stage of identity achievement according to Erikson's theory. He has successfully navigated the complexities of adolescence and emerged with a clear and solid sense of his own identity.

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Complete Question:

Seventeen-year-old Simon has gone through a period of conflict over issues relating to his identity, but now he feels comfortable with the choices and commitment he has made. Thomas has achieved what Erikson would call a(n): ___________.

The allowable is a term used in advertising and marketing to refer to the maximum cost per acquisition (CPA) that a business can afford to pay. So, the given statement is False.

"The allowable" is a term used in advertising and marketing to refer to the maximum cost per acquisition (CPA) that a business can afford to pay to acquire a customer while still remaining profitable. It is not directly related to the conversion rate needed to break even.

To determine the conversion rate needed to break even, you would need to consider the cost of acquiring a customer, the profit margin on the product or service being sold, and the total revenue generated by each customer. This calculation can help determine the minimum conversion rate needed to achieve profitability.

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The distance from the home plate is described by variable z. Then, the increasing rate is described by the derivative of z with respect to time, t.

Applying the Pythagorean theorem, the relation between z, x, and y is:

The derivative of x with respect to time is the speed of the player, that is,

-2 - 10 + (-3)^3

= -12 - 27

= -39

Answer:

-39

Step-by-step explanation:

Substitute v and k

v - 10 + k³

-2 - 10 -3³

Multiply the 3 and the power of thirds together

-2 -10 + 27

Combine like terms

If the probability that the insurer pays at least 1.20 on a random loss is 0.30, the probability that the insurer pays at least 1.44 on a random loss is 0.18.

Let X be the loss covered by the insurance policy. Since X is uniformly distributed on [0, 2], its probability density function is f(x) = 1/2 for 0 <= x <= 2.

Let D be the deductible amount. Then the insurer pays at least 1.20 on a random loss if and only if X - D >= 1.20. Using the cumulative distribution function F(x) of X, we have:

P(X - D >= 1.20) = P(X >= D + 1.20) = 1 - F(D + 1.20)

We are given that P(X - D >= 1.20) = 0.30. Therefore,

1 - F(D + 1.20) = 0.30

F(D + 1.20) = 0.70

Using the formula for the cumulative distribution function of a uniform distribution, we have:

F(x) = (x - a)/(b - a), for a <= x <= b

where a = 0 and b = 2.

Therefore,

F(D + 1.20) = (D + 1.20 - 0)/(2 - 0) = (D + 1.20)/2

Setting this equal to 0.70, we get:

(D + 1.20)/2 = 0.70

D + 1.20 = 1.40

D = 0.20

So the deductible amount is $0.20. Now we can find the probability that the insurer pays at least 1.44 on a random loss:

P(X - D >= 1.44) = P(X >= D + 1.44) = 1 - F(D + 1.44)

Using the formula for F(x) and plugging in D = 0.20, we get:

1 - F(D + 1.44) = 1 - F(1.64) = 1 - (1.64 - 0)/(2 - 0) = 0.18

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