Find f(x) + g(x) for
[ f(x) = 6x – 4
[g(x) = -5x + 24

The geometric average of the five returns is 20.14.%

Geometric average or geometric mean is the average of a set of values calculated using the products of the terms or values.

The geometric average of a data set containing n observations is the nth root of the product of the values.

Calculating the geometric average of the following five returns: -36.81%, 19.14%, 23.77%, -6.34%, 31.17%:

n = 5

Geometric average = \(\sqrt[5]{(-36.81) \times (19.14) \times (23.77) \times (-6.34) \times (31.17)}\)

Geometric average = 20.14%

In conclusion, the geometric average  mean is obtained as the  nth root of the product of the values.

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this line does not pass through the origin (0, 0), since the vector x = [0, 0] does not satisfy the equation Ax = b.

One possible example is:

A = [[1, 2], [2, 4]]

b = [3, 6]

The solution set of Ax = b is the set of all vectors of the form x = [x1, x2] such that:

x1 + 2x2 = 3

2x1 + 4x2 = 6

Solving this system of equations, we get:

x1 = 3 - 2x2

x2 = x2

So the solution set is the set of all vectors of the form x = [3 - 2x2, x2]. This is a line in R² with slope -2 and y-intercept (3, 0)

Note that this line does not pass through the origin (0, 0), since the vector x = [0, 0] does not satisfy the equation Ax = b.

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Answer: D

Step-by-step explanation: 200/4=50, they must sell a minmum of 50 pies to make a minimum of $200. It's D because it denotes any sale of 50 pies or greater. You use a closed circle on a number line when referring to 'greater than or equal to' (at least) and 'less than or equal to' (at most).

The equivalent expression is: \(-x^5 y^3 + 6x^3 y^5\).

Let's simplify the given expression step by step using the given terms:
Expression:

\(3x^3 y^5 + 3x^5 y^3 - (4x^5 y^3 − 3x^3 y^5)\)
Distribute the negative sign outside the parentheses to the terms inside:
\(3x^3 y^5 + 3x^5 y^3 - 4x^5 y^3 + 3x^3 y^5\)
Combine like terms, which are terms that have the same variables raised to the same power:
\((3x^3 y^5 + 3x^3 y^5) + (3x^5 y^3 - 4x^5 y^3)\)
Add or subtract the coefficients of the like terms:
\(6x^3 y^5 - x^5 y^3\)
So, the simplified expression is:
\(6x^3 y^5 - x^5 y^3\)

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The probability of selling more than 3 properties in one week is 0.4044.

This is a binomial probability problem, where the number of trials is the number of properties shown (17) and the probability of success is 0.40 (the chance of selling any one property).

Let X be the random variable representing the number of properties sold in a week. We want to find P(X ≤ 3).

Using the binomial probability formula, we have:

P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

where

P(X = k) = (\(^{n}C_k\)) × \(p^k\) × \((1-p)^{(n-k)}\)

where n is the number of trials, p is the probability of success, and (n choose k) is the number of ways to choose k successes from n trials.

Plugging in the values, we get:

P(X ≤ 3) = (\(^{17}C_0\)) × \(0.4^0\) × \(0.6^{17}\) + (\(^{17}C_1\)) × \(0.4^1\) × \(0.6^{16}\) + (\(^{17}C_2\)) × \(0.4^2\) × \(0.6^{15}\) + (\(^{17}C_3\)) × \(0.4^3\) × \(0.6^{14}\)

Using a calculator or software, we get:

P(X ≤ 3) ≈ 0.4044

Rounding to four decimal places, the probability of selling no more than 3 properties in one week is 0.4044.

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Answer:

The height of the cylinder can be calculated using the formula: height = radius x volume / area. In this case, the volume of the cylinder is equal to the volume of the sphere, so the height of the cylinder is equal to the radius of the sphere.

Step-by-step explanation:

Answer:

25 + x = y

Step-by-step explanation:

Answer:

25+x=y

Step-by-step explanation:

25 plus the birthday cards(x)= total cards(y)

To find the volume of the solid obtained by rotating the region bounded by the curves x+y=2 and \(x=3-(y-1)^2\) about the z-axis, we can use the method of cylindrical shells.Evaluating this integral will give you the volume of the solid obtained by rotating the region about the z-axis.

First, let's find the limits of integration. We can set up the integral with respect to y, integrating from the lower bound to the upper bound of the region. The lower bound is where the curves intersect, which is y=1. The upper bound is the point where the curve \(x=3-(y-1)^2\) intersects with the line x=0. Solving this equation, we get y=2.

Now, let's find the height of each cylindrical shell. Since we are rotating about the z-axis, the height of each shell is given by the difference in x-coordinates between the two curves. It is equal to the value of x on the curve \(x=3-(y-1)^2.\)

The radius of each shell is the distance from the z-axis to the curve x=3-\((y-1)^2\), which is simply x.

Therefore, the volume of the solid can be calculated by integrating the expression 2πxy with respect to y from y=1 to y=2:

Volume =\(∫(1 to 2) 2πx(3-(y-1)^2) dy\)

Evaluating this integral will give you the volume of the solid obtained by rotating the region about the z-axis.

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

Explanation:

x = original price

If she saves 20%, then she still pays the remaining 80% which then converts to the decimal form 0.80

The expression 0.80x represents the new price, or sale price, of the dress. We're told this price is $180

Equate the two expressions and solve for x

0.80x = 180

x = 180/0.80

x = 225

The original price is $225

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

Checking the answer:

20% of 225 = 0.20*225 = 45

She saves $45

225 - 45 = 180

This confirms the answer.

(ii) The function \(x(t) = 3e^(^-^2^t^)\) for t ≥ 0 and x(t) = 0 for t < 0.

(iii) The function \(x(t) = 1 - e^(^-^t^)\) for t ≥ 0 and x(t) = 0 for t < 0.

In part (ii), the function x(t) is defined differently for t ≥ 0 and t < 0. For t ≥ 0, \(x(t) = 3e^(^-^2^t^)\), which means that as t approaches infinity, x(t) approaches 0. The exponential term \(e^(^-^2^t^)\) decays exponentially as t increases, causing the function to decrease rapidly. For t < 0, x(t) is equal to 0, indicating that the function is zero for negative values of t. This function represents an exponentially decaying signal that starts at 3 and approaches 0 as time progresses.

In part (iii), the function x(t) is also defined differently for t ≥ 0 and t < 0. For t ≥ 0, x(t) = \(1 - e^(^-^t^)\) As t approaches infinity, the exponential term e^(-t) approaches 0, and x(t) approaches 1. This means that the function starts at 1 and gradually decreases towards 0 as time passes. For t < 0, x(t) is equal to 0, indicating that the function is zero for negative values of t. This function represents a decaying exponential signal that starts at 1 and decreases towards 0 over time.

These two functions illustrate different behaviors based on the value of t. The first function (ii) exhibits exponential decay starting at 3, while the second function (iii) represents a decaying exponential starting at 1. Understanding these types of functions is important in various fields, including physics, engineering, and signal processing, as they model the behavior of dynamic systems and time-dependent phenomena.

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Answer:

44.1

Step-by-step explanation:

- To find the distance, we have to use the distance formula:

d = √(x2 - x1)² + (y2 - y1)²

d = √(-19 - 5)² + (-12 - 25)²

d = √(-24)² + (-37)²

d = √(576) + (1369)

d = √1945

d = 44.1

1359 college freshmen must be surveyed to cut the stated margin of error in half.

Here, as the company wants to cut the stated margin of error in half, the new margin of error is (0.05/2) = 0.025 (since 0.05 is the previous margin of error).We know that, the Margin of Error formula is given by:

ME = Z*(sqrt{(p*(1-p))/n}),

where

Z is the z-score,

p is the proportion of success, and

n is the sample size.

To determine the number of college freshmen that must be surveyed, we need to find the sample size (n) that would give the new margin of error of 0.025. We can assume a proportion of success as 0.76 (as the proportion of college freshmen who return is 0.76). Now, substituting the given values, we get:

0.025 = Z*(sqrt{(0.76*(1-0.76))/n})

For 95% confidence level, the z-score is 1.96.

Now, substituting the values, we get:

0.025 = 1.96*(sqrt{(0.76*(1-0.76))/n})

Squaring both sides, we get:

0.000625 = (1.96^2)*(0.76*(1-0.76))/n

Now, solving for n, we get:

n = (1.96^2)*(0.76*(1-0.76))/(0.000625)n ≈ 1358.87...n ≈ 1359 (rounded to the nearest whole number)

Therefore, 1359 college freshmen must be surveyed to cut the stated margin of error in half.

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Answer:

A(-6,-8)

Step-by-step explanation:

the graph that goes up the most

Answer: D

Step-by-step explanation:

Because it said she rode her bike 15 feet per second and per means 1 so for every second she rode 15 distance(feet)

I Hope This helped :)

Answer:

Step-by-step explanation:

m - 9 = 12.

It would take 0.58 hours to cover a distance of 1 kilometer.

The speed of a body is defined as the total distance covered by the body per unit time by taken by the body.

S = D/t

where,

S is the speed of the body,

D is the distance covered by the body and

t is the time taken by the body.

Here, in the provided situation,

The distance D to be covered is 1 kilometer.

The speed S at which the body moving is 1.7 km/h.

using formula,

S = D/t

1.7 = 1/t

t = 1/1.7

t = 0.58 hours.

Time taken by the body is 0.58 hours.

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There are total 1680 ways to arrange 4 magazines in a row of 8 choices

What is Permutation?

The term permutation refers to a mathematical computation of the number of possible arrangements of a given collection. Simply said, a permutation is a term that defines the amount of different ways something may be organised or arranged. The order of the arrangement is important in permutations.

Solution:

Since, order of the arrangement matter too

we will use Permutation

Total Ways of Arrangement = 8P4

Total Ways of Arrangement = 8!/4!

Total Ways of Arrangement = 8*7*6*5*4!/4!

Total Ways of Arrangement = 1680 ways

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Answer:

Add -3+8

Step-by-step explanation:

You would do this first because it is in the brackets. Usually you would do (*) first but those are just there because the 4 is negative and if they were not there it would get confusing and look like this::[-3+8]--4. So the next step would be the [*].

HOPE THIS HELPS!!!

Answer:

Use PEMDAS

Step-by-step explanation:

Parenthesis, If there are none move on to exponents if there are no exponents move to multiplication. No multiplication? use division. If you dont see division use addition and lastly if there is no addition use subtraction. In the equation, it looks like you have to make the -3 and 8 positive. So, since the -4 is in the parenthesis(P) multiply(M) 4 by 3 and 8 once the three is positive. So your final answer would be either C or D

Its the best i could do but good luck. I tried...

Answer: x = -8

Step-by-step explanation:

12 ( x + 10 ) = 24

First we divide the two sides of the exercise by 12.

\(\boldsymbol{\sf{x+10=\dfrac{24}{12} }}\)

We divide 24 by 12..

x + 10 = 2

Subtract 10 from both sides.

x = 2 - 10

Subtract 10 from 2 to get. Since the number 10 is greater than 2, the result will be negative.

x = -8

Answer:

\( \sf \: x = - 8\)

Step-by-step explanation:

Given equation,

→ 12(x + 10) = 24

Now the value of x will be,

→ 12(x + 10) = 24

→ 12(x) + 12(10) = 24

→ 12x + 120 = 24

→ 12x = 24 - 120

→ 12x = -96

→ x = -96 ÷ 12

→ [ x = -8 ]

Hence, the value of x is -8.

Answer:

<BAC = 65

<CAE = 115

<DAE = 65

<BAD = 115

Step-by-step explanation:

x + 75 = 3x - 5

-x           -x

75 = 2x - 5

+ 5        + 5

80 = 2x

/2     /2

x = 40

Then we substitute x in the problems and solve

<BAD = x + 75 = 40 + 75 = 115

<CAE = 3x - 5 = 3(40) - 5 = 115

<BAC = 180 - 115 = 65

<DAE = 180 - 115 = 65

We can also confirm this because BAC and DAE are congruent. Also BAD and CAE are congruent due to vertical angles.

the predicted subway fare when the CPI is 80 would be $1.214.

To determine the line of regression that predicts subway fare based on CPI, we need to use linear regression analysis. We can use software like Excel or a calculator to perform the calculations, but since we don't have that information here, we will use the formulas for the slope and intercept of the regression line.

Let x be the CPI and y be the subway fare. Using the given data, we can find the mean of x, the mean of y, and the values for the sums of squares:

$\bar{x} = \frac{30.2 + 48.3 + 112.3 + 162.2 + 191.9 + 197.8}{6} = 110.933$

$\bar{y} = \frac{0.15 + 0.35 + 1.00 + 1.35 + 1.50 + 2.00}{6} = 1.225$

$SS_{xx} = \sum_{i=1}^n (x_i - \bar{x})^2 = 52615.44$

$SS_{yy} = \sum_{i=1}^n (y_i - \bar{y})^2 = 0.655$

$SS_{xy} = \sum_{i=1}^n (x_i - \bar{x})(y_i - \bar{y}) = 22.69$

The slope of the regression line is given by:

$b = \frac{SS_{xy}}{SS_{xx}} = \frac{22.69}{52615.44} \approx 0.000431$

The intercept of the regression line is given by:

$a = \bar{y} - b\bar{x} \approx 1.225 - 0.000431 \times 110.933 \approx 1.180$

Therefore, the equation of the regression line is:

$y = a + bx \approx 1.180 + 0.000431x$

To predict the subway fare when the CPI is given, we can substitute the CPI value into the equation of the regression line. For example, if the CPI is 80, then the predicted subway fare would be:

$y = 1.180 + 0.000431 \times 80 \approx 1.214$

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The answer is 1.79.

Division is breaking a number up into an equal number of parts.

Given that, 5.37 divided by 3

5.37÷3 = 1.79

Hence,  5.37 divided by 3 equals to 1.79.

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Answer:

-15

Step-by-step explanation:

Answer:

iam sorry

i don't know the answer

Answer:

8 minutes

Step-by-step explanation:

Leo has already run 1 mile, leaving him with 4 more to finish the race. At 2 minutes a mile (a ridiculously impressive pace, considering the world record mile time is just a little under 3:45), it will then take him 4 x 2 = 8 minutes to cross the finish line.

Answer:

4 t-shirts

Step-by-step explanation:

75-35 = 40

at most she can buy 4, because if she buys 5, she uses 45 dollars

Answer:

-4/9

Step-by-step explanation:

find two points that cross perfectly and take the ys and subtract and take the xs and subtract and then do y/x

Hope this helps :)

Answer:

there is 2 spaces between them, and that 10 has 2 factors and 12 has 3 factors.

Step-by-step explanation:

The sum of an arithmetic sequence given a partial sum is 35532.

Firstly, we need to identify the common difference of the arithmetic sequence. This can be done by finding the difference between any two consecutive terms. In this case, subtracting 9 from 3 gives us a common difference of 6.

Next, we determine the number of terms in the sequence. To do this, subtract the first term from the given partial sum and divide the result by the common difference. In this case, subtracting 3 from 639 and dividing by 6 gives us 106 terms.

Finally, we can calculate the sum using the arithmetic series formula: Sn = (n/2)(2a + (n-1)d), where Sn represents the sum, n is the number of terms, a is the first term, and d is the common difference. Plugging in the values, we have Sn = (106/2)(2*3 + (106-1)*6). Simplifying this expression, we find that the sum of the arithmetic sequence is 35532.

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