LESSON 12 SESSION 1


3 Tameka pilots a hot air balloon. She lowers the balloon


five times, going down an equal distance each time. In


all, Tameka lowers the balloon 75 m.


a. What integer represents the change in the hot air


balloon's elevation each time Tameka lowers it?


What does this integer tell you? Show your work.


75/5=-15

The given problem is about finding the linear speed of a vehicle when each of its tire has a diameter of 32 inches and is moving at 800 revolutions per minute. In order to solve this problem, we will use the formula `linear speed = (pi) (diameter) (revolutions per minute) / (1 mile per minute)`.

Since the diameter of each tire is 32 inches, the radius of each tire can be calculated by dividing 32 by 2 which is equal to 16 inches. To convert the units of revolutions per minute and inches to miles and hours, we will use the following conversion factors: 1 mile = 63,360 inches and 1 hour = 60 minutes.

Now we can substitute the given values in the formula, which gives us:

linear speed = (pi) (32 inches) (800 revolutions per minute) / (1 mile per 63360 inches) x (60 minutes per hour)

Simplifying the above expression, we get:

linear speed = 107200 pi / 63360

After evaluating this expression, we get the linear speed of the vehicle as 5.36 miles per hour. Rounding this answer to the nearest tenth gives us the required linear speed of the vehicle which is 5.4 miles per hour.

Therefore, the linear speed of the vehicle is 5.4 miles per hour.

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Answer:

A student has passed 60 percent of the 20 quizzes he has written so far successfully mean:

successfully quizzes = 60 % of 20 quizzes = ( 60 / 100 ) * 20 = 60 * 20 / 100 = 1200 / 100 = 12

The remaining quizzes = 50 - 20 = 30 quizzes

80 percent of the remaining quizzes successfully mean:

The remaining successfully quizzes = 80 % of 30 = ( 80 / 100 ) * 30 = 80 * 30 / 100 = 2400 / 100 = 24

Total successfully quizzes = 12 + 24 = 36

Average = ( 36 / 50 ) * 100 % = 0.72 * 100 % = 72 %

Pls rate Brainliest!

Answer:73%

Step-by-step explanation:A student has passed 60 percent of the 20 quizzes he has written so far successfully mean:

successfully quizzes = 60 % of 20 quizzes = ( 60 / 100 ) * 20 = 60 * 20 / 100 = 1200 / 100 = 12

The remaining quizzes = 50 - 20 = 30 quizzes

80 percent of the remaining quizzes successfully mean:

The remaining successfully quizzes = 80 % of 30 = ( 80 / 100 ) * 30 = 80 * 30 / 100 = 2400 / 100 = 24

Total successfully quizzes = 12 + 24 = 36

Average = ( 36 / 50 ) * 100 % = 0.72 * 100 % = 72 %

We solve as follows:

We have that the solutions for the problem are x = 7sqrt(3) or x = -7sqrt(3).

Answer:

C. Distributive property

The power to which a number or expression is raised is called the exponent.

1. An exponent is a mathematical notation that represents the power to which a number or expression is raised. It is written as a superscript number or variable placed above and to the right of the base number or expression.

2. The base number or expression is the number or expression that is being multiplied repeatedly by itself, raised to the power of the exponent.

3. The exponent tells us how many times the base number or expression should be multiplied by itself. For example, in the expression \(2^3\), the base is 2 and the exponent is 3. This means that 2 should be multiplied by itself three times: 2 * 2 * 2 = 8.

4. The exponent can be a positive whole number, a negative number, zero, or a fraction. Each of these cases has different interpretations:

  - Positive exponent: Indicates repeated multiplication. For example, \(2^4\)means 2 multiplied by itself four times.

  - Negative exponent: Indicates the reciprocal of the base raised to the positive exponent. For example, \(2^{-3\) means 1 divided by \(2^3\).

  - Zero exponent: Always equals 1. For example, \(2^0\) = 1.

  - Fractional exponent: Represents a root. For example, \(4^{(1/2)\)represents the square root of 4.

5. Exponents follow certain mathematical properties, such as the product rule \((a^m * a^n = a^{(m+n)})\), the quotient rule \((a^m / a^n = a^{(m-n)})\), and the power rule \(((a^m)^n = a^{(m*n)})\).

Remember to use these rules and definitions to correctly interpret and evaluate expressions involving exponents.

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Answer:

3√3+4

Step-by-step explanation:

Given the vectors u = <√3, -1> and v = <3, -4>

u · v =  <√3, -1> *<3, -4>

u · v = 3√3 + (-1*-4)

u · v = 3√3+(4)

u · v  =  3√3+4

Hence the dot product is 3√3+4

Answer:

D.

Step-by-step explanation:

just took test

Answer:

x = -2

Step-by-step explanation:

Let the number be x

12 -2x = 8x +32

Add 2x to each side

12 -2x +2x = 8x+32+2x

12 = 10x+32

Subtract 32 from each side

12-32 = 10x+32-32

-20 =10x

Divide each side by 10

-20/10=10x/10

-2 =x

The maximum number of terms fourth-degree polynomial function in standard form can have is 5

The general form of an nth degree polynomial is:

\(p(x) = a_nx^n+a_{n-1}x^{n-1}+a_{n-2}x^{n-2} + ....+a_1x+a_0\)

The maximum number of terms that an nth -degree polynomial can have is n+1

For a fourth degree polynomial, n = 4

Substitute n = 4 into \(p(x) = a_nx^n+a_{n-1}x^{n-1}+a_{n-2}x^{n-2} + ....+a_1x+a_0\)

\(p(x) = a_4x^{4}+a_{4-1}x^{4-1}+a_{4-2}x^{4-2}+a_{4-3}x^{4-3}+a_{4-4}x^{4-4}\\\\p(x) = a_4x^4+a_3x^3+a_2x^2+a_1x+a_0\)

The maximum number of terms of p(x) above, when n = 4 is (4+1)

The maximum number of terms fourth-degree polynomial function in standard form can have is 5

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Answer:

  C.  142°

Step-by-step explanation:

You want the angle between vectors u=3i+√3j and v=-2i-5j.

There are a number of ways the angle between the vectors can be found. For example, the dot-product relation can give you the cosine of the angle:

  u•v = |u|·|v|·cos(θ) . . . . . . where θ is the angle of interest

You can find the angles of the vectors individually, and subtract those:

  u = |u|∠α

  v = |v|∠β

  θ = α - β

When the vectors are expressed as complex numbers, the angle between them is the angle of their quotient:

  \(\dfrac{\vec{u}}{\vec{v}}=\dfrac{|\vec{u}|\angle\alpha}{|\vec{v}|\angle\beta}=\dfrac{|\vec{u}|}{|\vec{v}|}\angle(\alpha-\beta)=\dfrac{|\vec{u}|}{|\vec{v}|}\angle\theta\)

This method is used in the calculation shown in the first attachment. The angle between u and v is about 142°.

A graphing program can draw the vectors and measure the angle between them. This is shown in the second attachment.

__

Additional comment

The approach using the quotient of the vectors written as complex numbers is simply computed using a calculator with appropriate complex number functions. There doesn't seem to be any 3D equivalent.

The dot-product relation will work with 3D vectors as well as 2D vectors.

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Answer:

the answer is 1.713 x 106

Step-by-step explanation:

To approximate the solution and maximize the given objective function we need to find the steepest ascent direction and iteratively update the values of x₁ and x₂ to approach the maximum value of z.

The method of steepest ascent involves finding the direction that leads to the maximum increase in the objective function and updating the values of the decision variables accordingly. In this case, we aim to maximize the objective function z = -(x₁ - 3)² - (x₂ - 2)².

To find the steepest ascent direction, we can take the gradient of the objective function with respect to x₁ and x₂. The gradient represents the direction of the steepest increase in the objective function. In this case, the gradient is given by (∂z/∂x₁, ∂z/∂x₂) = (-2(x₁ - 3), -2(x₂ - 2)).

Starting with initial values for x₁ and x₂, we can update their values iteratively by adding a fraction of the gradient to each variable. The fraction determines the step size or learning rate and should be chosen carefully to ensure convergence to the maximum value of z.

By repeatedly updating the values of x₁ and x₂ in the direction of steepest ascent, we can approach the solution that maximizes the objective function z. The process continues until convergence is achieved or a predefined stopping criterion is met.

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Answer:

12.6

Step-by-step explanation:

9*3.6-6.6*3=S

S=12.6feet^2

Answer:

= a(7b + 1)

Step-by-step explanation:

7ab + a

a(7b + 1).

Answer:

Step 1

Step 2: Simplify the powers of i, specifically remember that i2 = –1.

Step 2

Step 3: Combine like terms, that is, combine real numbers with real numbers and imaginary numbers with imaginary numbers.

Step 3

Answer:

Step-by-step explanation:

1:-9 - 15 i

2: 12 + 6 i

3: -343 - 392 i

Answer:

1

Step-by-step explanation:

m=2

3m²- 2m- 7

3(2)² -2(2) -7

3(4)- 4- 7

12- 4- 7= 1

A measure of the dispersion of observations in a process distribution is called: range.

This is further explained below.

Generally, The range of a collection of data is the difference between the highest and smallest values in the set. This difference is calculated by subtracting the sample maximum and minimum from the sample size. It is written out using the same units that were used for the data.

In conclusion, The term "range" refers to a measure of the dispersion of observations included within a process distribution.

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Answer:

1. 537.1

2. 8.15

3. 9.77

4. 26.75

Step-by-step explanation:

Answer:

48% of 75 is 36 so then 60% of 45 is 27, so then we do simple subtraction and do 36-27 which gives us 9

Step-by-step explanation:

The number for years that it would take 1600 workers to build 25 ziggurats is 66.67 years.

To find out how many years it would take 1600 workers to build 25 ziggurats, you can use the formula:

(time taken by 1200 workers to build 3 ziggurats) x (1600 workers / 1200 workers) x (25 ziggurats / 3 ziggurats) = time taken by 1600 workers to build 25 ziggurats

Plugging in the given values:

(8 years) x (1600 / 1200) x (25 / 3) = 8 years x (4/3) x (25/3)

= 8*25/3

= 200/3

= 66.67 years

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Answer:

sir, this is a english app, search a spanish app

señor, esta es una aplicacion en ingles, busque una en español

Step-by-step explanation:

Brainly.lat

The polynomial function \(\(f(x) = 2(x^2+3)(x+1)^2\)\) has zeros at -3 with multiplicity 1, and -1 with multiplicity 2. The graph of the function crosses the x-axis at -3 and -1.

To find the zeros and their multiplicities, we set \(\(f(x)\)\) equal to zero and solve for \(\(x\).\)

Setting \(\(f(x) = 0\),\) we have:

\(\[2(x^2+3)(x+1)^2 = 0\]\)

Since the product of two factors is zero, at least one of the factors must be zero. Thus, we solve for \(\(x\)\) in each factor separately:

1. \(\(x^2 + 3 = 0\):\)

  This equation does not have real solutions since the square of a real number is always non-negative. Therefore, this factor does not contribute any real zeros.

2. \(\(x + 1 = 0\):\)

  Solving for \(\(x\), we find \(x = -1\).\) This gives us a zero at -1 with multiplicity 1.

Since the factor \(\((x+1)^2\)\) is squared, the zero -1 has a multiplicity of 2.

Therefore, the zeros for the polynomial function are -3 with multiplicity 1 and -1 with multiplicity 2. The graph of the function crosses the x-axis at both zeros.

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Answer:

They washed 18 cars in 2 hours, and each hour they washed 2 fewer.

16 cars in 4 hours,

14 cars in 6 hours,

12 in  8 hours, etc.

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

doin it rn

Answer:

2/5

Step-by-step explanation:

.4 is 40% out of a 100 so it is 2/5

Answer:

4 over 10

Step-by-step explanation:

the .4 is in the 10 place in the destimal sot here forever when u make it a fraction it would be ⁴/10

Answer:

12/54

Step-by-step explanation:

Answer:

B) p<5

Step-by-step explanation:

Answer:

54 choose 42 =  3,081,149,592 ways

The regression equation for the given data set is y = -0.51x + 100.12.

To find the regression equation, we need to first calculate the slope and intercept of the regression line. Using the formula for slope (b) and intercept (a) of the regression line, we get:

b = r(Sy/Sx)

a = y-bar - b(x-bar)

where r is the correlation coefficient, Sy and Sx are the standard deviations of y and x respectively, and y-bar and x-bar are the means of y and x respectively.

Using the given data, we can calculate the means, standard deviations, and correlation coefficient. Then, we can substitute these values into the formulas to get the regression equation.

After calculating, we get the equation y = -0.51x + 100.12. This equation represents the line of best fit for the given data, which can be used to predict the value of y for any given value of x.

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Answer:

see explanation

Step-by-step explanation:

Under a rotation ( clockwise or anticlockwise ) about the origin of 180°

a point (x, y ) → (- y, - x ), thus

A(5, 3 ) → A'(- 3, - 5 )

B(8, 10 ) → B'(- 10, - 8 )

C(11, 3 ) → C'(- 3, - 11 )

(a) The sample size needed is 1,498 if the researcher uses the prior proportion of 0.669.

n = 1.497.87 or 1,498

(b)  The researcher should use a sample size of 1,692 if the proportion is unknown.

n = 1,691.06 or 1,692

When a researcher is designing a sampling study to measure a population parameter, like the proportion, the sample size must be determined. The key to calculating sample size is the margin of error the researcher desires. The smaller the margin of error, the larger the sample size needed.

(a) The sample size needed is 1,498 if the researcher uses the prior proportion of 0.669.

To find sample size for the proportion use the equation:

\(n=\frac{Z^2\pi (1-\pi )}{e^2}\)

Where:

Substituting values:

\(n=\frac{1.6449^2*0.50*0.331}{0.02^2}\)

n = 1.497.87 or 1,498

(b) The researcher should use a sample size of 1,692 if the proportion is unknown.

Use the same equation as in part (a). However, to maximize \(\pi (1-\pi )\) use 0.5 for \(\pi\).

Substituting the values:

\(n=\frac{1.6449^2*0.50*0.500}{0.02^2}\)

n = 1,691.06 or 1,692

Always round up because it is impossible to have a fraction of an observation.

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