Andre sells vegetables for a farmer at the local market the farmer pays him $50 a day plus a 9% commission on his sales. On Saturday, he had $130 in sales. Andre wants to know how much he will be paid for his work on Saturday

∂g/∂u is equal to 21u⁵cos⁴(v)sin⁴(v)(cos(v) + u³cos⁴(v)sin²(v)sin(v)).

To find the indicated derivative, we need to use the chain rule. Let's differentiate step by step:

Given:

g(u, v) = f(x(u, v), y(u, v))

f(x, y) = 7x³y³

x(u, v) = ucos(v)

y(u, v) = usin(v)

To find ∂g/∂u, we differentiate g(u, v) with respect to u while treating v as a constant:

∂g/∂u = (∂f/∂x) * (∂x/∂u) + (∂f/∂y) * (∂y/∂u)

To find ∂f/∂x, we differentiate f(x, y) with respect to x:

∂f/∂x = 21x²y³

To find ∂x/∂u, we differentiate x(u, v) with respect to u:

∂x/∂u = cos(v)

To find ∂f/∂y, we differentiate f(x, y) with respect to y:

∂f/∂y = 21x³y²

To find ∂y/∂u, we differentiate y(u, v) with respect to u:

∂y/∂u = sin(v)

Now, we can substitute these partial derivatives into the equation for ∂g/∂u:

∂g/∂u = (21x²y³) * (cos(v)) + (21x³y²) * (sin(v))

To find the simplified form, we substitute the given values of x(u, v) and y(u, v) into the equation:

x(u, v) = ucos(v) = u * cos(v)

y(u, v) = usin(v) = u * sin(v)

∂g/∂u = (21(u * cos(v))²(u * sin(v))³) * (cos(v)) + (21(u * cos(v))³(u * sin(v))²) * (sin(v))

Simplifying further, we get:

∂g/∂u = 21u⁵cos⁴(v)sin⁴(v)(cos(v) + u³cos⁴(v)sin²(v)sin(v))

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The solution of the quadratic equation is \(x = \dfrac{5\pm\sqrt5}{2}\).

A quadratic equation is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.

Given that the quadratic equation is x²-5x+5=0. The equation can be solved as below:-

x²-5x+5=0

a = 1 , b = -5 , c = 5

\(x = \dfrac{-b \pm\sqrt{(b^2-4ac}}{2a}\)

\(x=\dfrac{5\pm\sqrt{25 - 4\times1\times5}}{2}\)

\(x = \dfrac{5\pm\sqrt5}{2}\)

The value of x for the quadratic equation will be \(x = \dfrac{5\pm\sqrt5}{2}\).

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Answer:

If you have a party and your pizza was split up into 16 pieces, 8 people should be able to have 2 pieces.

Step-by-step explanation:

Answer:

B. 20

Step-by-step explanation:

60 = 2x + 20

40 = 2x

40/2 = 2x/2

20 = x

Hope this helps :)

Answer:

B. 20

Step-by-step explanation:

The minimum value of F is 136.

To solve the optimization problem, we can use the method of Lagrange multipliers. Let L(x,y,λ) = 34x^2 + 34y^2 + λ(xy^2 - 16) be the Lagrangian function. Then, we need to find the critical points of L(x,y,λ).

Taking partial derivatives of L with respect to x, y, and λ and setting them to 0, we get:

∂L/∂x = 68x + λy^2 = 0
∂L/∂y = 68y + 2λxy = 0
∂L/∂λ = xy^2 - 16 = 0

From the first equation, we get λ = -68x/y^2. Substituting this into the second equation, we get:

68y - 2(68x/y^2)(xy) = 0
68y^3 - 136x^2y = 0
y(68y^2 - 136x^2) = 0

Since y cannot be 0 (because xy^2 = 16), we have:

68y^2 - 136x^2 = 0
y^2 = 2x^2

Substituting this into xy^2 = 16, we get:

x(2x^2)^(3/2) = 16
x^4 = 64/8
x = 2

Then, y = sqrt(2x^2) = 2sqrt(2).

Finally, we can compute F = 34x^2 + 34y^2 = 34(2^2) + 34(2sqrt(2))^2 = 136 + 136(2) = 408.

Therefore, the minimum value of F is 408.
To solve this optimization problem, we will first express y in terms of x using the constraint xy^2 = 16, and then substitute it into the objective function F(x, y) = 34x^2 + 34y^2.

From the constraint:
xy^2 = 16
y^2 = 16/x
y = ±√(16/x)

We'll use the positive root for now, as y will represent the same square term in the objective function:
y = √(16/x)

Now, substitute y into the objective function:
F(x) = 34x^2 + 34(16/x)^2

To minimize F(x), find the critical points by taking the derivative of F(x) with respect to x and setting it equal to 0:
dF/dx = 68x - 1088/x^2 = 0

Now, solve for x:
68x^3 = 1088
x^3 = 16
x = 2

Now, substitute the value of x back into the expression for y:
y = √(16/2)
y = 2

Now that we have the values for x and y, we can find the minimum value of F:
F(2, 2) = 34(2^2) + 34(2^2) = 136

So, the minimum value of F is 136.

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Answer:

c

Step-by-step explanation:

Answer:

The answer is 3391.2 cm3

Step-by-step explanation:

The central angle of the sector described is 210 degrees.  To find the central angle of the sector, we need to use the formula:θ_sector = θ x (A_sector/A_circle)where A_sector is the area of the sector.

Therefore, the central angle of the sector described is 210 degrees.

However, this is the angle for the entire circle. To find the angle for the sector, we need to multiply by the ratio of the sector area to the circle area:θ_sector = θ x (a/A)

= 263.53 x (263.42/563.24) degrees

= 210 degrees

Therefore, the central angle of the sector described is 210 degrees. To find the central angle of the sector described, we can use the formula for the area of a sector: A = (1/2)r²θwhere A is the area of the sector, r is the radius of the circle, and θ is the central angle of the sector (in radians).

We are given that the area of the sector is 263.42 cm² and the area of the entire circle is 563.24 cm². We can use these values to find the radius of the circle: r = sqrt(A/π) = sqrt(563.24/π) = 15.01 cm Now we can use the formula for the central angle of the sector:θ = 2A/r² = 2(263.42)/15.01² = 4.60 radians .To find the central angle of the sector, we need to use the formula:θ_sector = θ x (A_sector/A_circle)where A_sector is the area of the sector and A_circle is the area of the entire circle. Substituting the given values, we have: θ_sector = 263.53 x (263.42/563.24) = 210 degrees

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1. The perimeter of the shape is 9x²+ 7x +8

2. The third side of the triangle is 2x²+x+4

The perimeter of a shape is the total measurement of all the edges of a shape e.g. a triangle has three edges, so its perimeter is the total of those three edges added together.

1. The trapezium has 4 sides, and the perimeter is found by adding all the sides. Therefore,

5x²+7 + x²+2x + 2x²+3x -4+ x²+2x+5

= 9x²+7x + 8

2. A triangle has 3 sides, therefore the other side is found by;

5x²-6x+7 -( x²+2x+1+ 2x²-5x+2)

= 5x²-6x +7 - ( 3x²-7x+3)

= 2x²+x+4

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The Chi-square test is a statistical test used to determine if there is a significant difference between observed and expected frequencies in categorical data. In this example, the test is used to assess whether there is a significant difference in the mean breaking strengths of two types of cables.

The Chi-square test of significance is employed when dealing with categorical or nominal data. It compares the observed frequencies with the frequencies that would be expected if the variables were independent. In this case, the breaking strengths of the two cables are the variables of interest.

To perform the test, the first step is to define the null hypothesis (H0) and the alternative hypothesis (Ha). In this example, H0 assumes that there is no difference in the mean breaking strengths of the two cables, while Ha suggests that there is a difference.

Next, the test statistic, denoted by X2 (chi-square), is calculated using the formula X2 = Σ[(O - E)²/E], where O represents the observed frequencies and E represents the expected frequencies under the assumption of independence.

To determine the expected frequencies, we need to estimate the means and variances of the breaking strengths. Here, x = 1925 and sigma = 40 for the first cable, and x = 1905 and sigma = 30 for the second cable.

Once the test statistic is calculated, it is compared to a critical value from the Chi-square distribution with degrees of freedom equal to (r - 1)(c - 1), where r is the number of rows and c is the number of columns in the contingency table. The significance level of 0.01 determines the critical value.

If the calculated X2 value is greater than the critical value, we reject the null hypothesis and conclude that there is sufficient evidence to indicate a difference in the mean breaking strengths of the two cables. Conversely, if the calculated X2 value is less than or equal to the critical value, we fail to reject the null hypothesis and conclude that there is no significant difference.

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Answer:

$464.24095

Step-by-step explanation:

8 1/4% = NY sales-tax rate

8 1/4 % = .0825

428.86 x .0825 = 35.38095

428.86 + 35.38095 = $464.24095

The values of the missing sides are;

a.  x = 35. 6 degrees

b. x = 15

c. x = 22. 7 ft

d. x = 31. 7 degrees

To determine the values, we have;

a. Using the tangent identity;

tan x = 5/7

Divide the values

tan x = 0. 7143

x = 35. 6 degrees

b. Using the Pythagorean theorem

x² = 9² + 12²

find the square

x² = 225

x = 15

c. Using the sine identity

sin 29= 11/x

cross multiply the values

x = 11/0. 4848

x = 22. 7 ft

d. sin x = 3.1/5.9

sin x = 0. 5254

x = 31. 7 degrees

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Answer:

$36

Step-by-step explanation:

22+14=36

Measures of central tendency, measures of variation, and crosstabulation are all types of descriptive statistics.

Descriptive statistics summarize and describe the main features of a data set, including the typical or central values (measures of central tendency) and the spread or variability of the data (measures of variation). Crosstabulation, also known as contingency tables, is a way to summarize the relationship between two variables by displaying their frequency distributions in a table format.
Measures of central tendency, measures of variation, and crosstabulation are types of descriptive statistics. Descriptive statistics are used to summarize and describe the main features of a dataset in a simple and meaningful way.

Central tendency refers to the measures that help identify the center or typical value of a dataset, such as mean, median, and mode. Variation measures describe the spread or dispersion of data, including range, variance, and standard deviation. Crosstabulation is a method of organizing data into a table format to show the relationship between two categorical variables.

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Answer: 3 1/4 + 2 1/3 = 67/

12

= 5 7/

12

≅ 5.5833333

Step-by-step explanation:

Answer:

                  \(\bold{r=\dfrac{V^2}A}\)

Step-by-step explanation:

\(\bold{A=\dfrac{V^2}r}\\^{\cdot r}\qquad ^{\cdot r}\\\bold{Ar=V^2}\\ ^{\div A}\quad\ ^{\div A}\\\bold{r=\dfrac{V^2}A}\)

For given function f(x) = x+2/(x + 4) (x + 1), the graph of function is as shown below and the end behaviour of function is as x → -∞, f(x)→0, as x → +∞, f(x)→0

In this question, we have been given a function  f(x) = x+2/(x + 4) (x + 1)

We need to gaph the given function.

From given function we can observe that the function f(x) is not defined for x = -4 and x = -1

Also, the degree of numerator = 1 and the degree of denominator is 2

We know that if the degree of the denominator > degree of the numerator, then a horizontal asymptote is at y = 0 (x - axis)

The graph of function f(x) is as shown below.

The x-intercept for the graph  function f(x) is at (-2, 0)

Also, as x → -∞, f(x)→0

and as x → +∞, f(x)→0

Therefore, for given function f(x) = x+2/(x + 4) (x + 1), the graph of function is as shown below and the end behaviour of function is as x → -∞, f(x)→0, as x → +∞, f(x)→0

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Answer:

An arithmetic sequence is an ordered set of numbers where the difference between each consecutive term is the same (this is called the "common difference").

The formula for each term in an arithmetic sequence is:

\(\sf a_n=a+(n-1)d\)

where:

Example

Sequence:  3, 10, 17, 24, 31, ...

The first term in the sequence is 3, therefore a = 3

The common difference can be found by subtracting one term from the next:  d = 10 - 3 = 7

Substituting these values into the equation for the nth term:

\(\implies \sf a_n=3+(n-1)7\)

\(\implies \sf a_n=3+7n -7\)

\(\implies \sf a_n=7n -4\)

Therefore, if we want to find the 5th term of the sequence, simply input
n = 5 into the found equation:

\(\implies \sf a_5=7(5)-4=31\)

Yes we can find terms

The formula is

Where

Mika has described a proportional relationship because the ordered pairs are linear and the line passes through the origin.

The slope-intercept representation of a linear function is given as follows:

y = mx + b

The coefficients of the function have the description presented as follows:

A proportional relationship is a special case of a linear relationship that has an intercept of 0, that is, passing through the origin.

From the given table, we have that:

Hence the correct option is given as follows:

Mika has described a proportional relationship because the ordered pairs are linear and the line passes through the origin.

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Answer:

A

Step-by-step explanation:

\([25.318\ ,\ 31.121]\) is a 95% confidence interval for the population variance.

A confidence interval in statistics denotes the probability/likelihood that a population parameter will fall between a set of values for a given proportion of the time. Analysts often use confidence intervals that include 95% or 99% of the expected observations.

Given,

Sample = 21 23 25 27 28 35 30 32 33.

confidence level = 95%

sample size =9

To determine confidence interval use formula,

\(C.I=mean \pm z(\frac{S}{\sqrt{n}})\)

where,

S=standard deviation

n=sample size

z-value for 95% =1.96

At first,

\(Mean=\frac{sum\ of\ numbers}{total\ numbers}\\\\Mean=\frac{21+23+25+27+28+35+30+32+33}{9}\\\\Mean=28.22\)

Now calculate standard deviation,

\(S=\sqrt{\frac{1}{n}\sum(x_i-mean)^2}\\\\S=\sqrt{\frac{1}{9}((21-28.22)^2+(21-28.22)^2+(23-28.22)^2+...+(33-28.22)^2}\\\\\\S=4.441\)

Now, calculate confidence interval,

\(C.I=28.22 \pm 1.96(\frac{4.441}{\sqrt{9}})\\\\C=28.22 \pm 2.901\\\\C=25.318\ ,\ 31.121\)

Thus, the confidence level is  \(C=[25.318\ ,\ 31.121]\)

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Your question is incomplete, here is the complete question.

The values taken from a normally distributed population are 21 23 25 27 28 35 30 32 33. Which of the following is a 95% confidence interval for the population variance.

[2.03, 16.30]

[10.12, 81.43]

[9.00, 72.41]

[11.39, 91.64]

[25.31, 31.12]

The sum of the series Σ (n=0 to infinity) 3n! / (8^n * n!) is 1.6.

To find the sum of the series, we can rewrite the terms using the concept of the exponential function. The term 3n! can be expressed as (3^n * n!) / (3^n), and the term n! can be written as n! / (n!) = 1.

Now, we can rewrite the series as Σ (n=0 to infinity) (3^n * n!) / (8^n * n!).

Next, we can simplify the expression by canceling out common terms in the numerator and denominator:

Σ (n=0 to infinity) (3^n * n!) / (8^n * n!) = Σ (n=0 to infinity) (3^n / 8^n)

Notice that the resulting series is a geometric series with a common ratio of 3/8.

Using the formula for the sum of an infinite geometric series, S = a / (1 - r), where 'a' is the first term and 'r' is the common ratio, we can determine the sum.

In this case, a = 3^0 / 8^0 = 1, and r = 3/8.

Substituting these values into the formula, we get:

S = 1 / (1 - 3/8) = 1 / (5/8) = 8/5 = 1.6

Therefore, the sum of the series is 1.6.

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The solutions to the given algebraic expressions are;

1) 3x + 4 = 7x - 8; Letter C

2) 2x = 7x - 5; Letter E

3) 5x - 8 = 5x + 12; Letter D

1) We are given the algebraic expression as;

3x + 4 = 7x - 8

Add 8 to both sides to get;

3x + 12 = 7x

Subtract 3x from both sides to get;

12 = 4x

divide both sides by 4 to get;

x = 3

2) 2x = 7x - 5

Add 5 to both sides to get;

2x + 5 = 7x

Subtract 2x from both sides to get;

5x = 5

divide both sides by 5 to get;

x = 1

3) 5x - 8 = 5x + 12

Subtract 5x from both sides gives;

-8 = 12

Thus, no solution

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The correct answer is C. To increase the strength of a solenoid, you need to increase the number of loops or the amount of electric current. A solenoid is a type of electromagnet that consists of a coil of wire with an electric current running through it, creating a magnetic field.

A solenoid is a type of electromagnet that consists of a coil of wire with an electric current running through it, creating a magnetic field. The strength of the magnetic field is directly proportional to the number of loops of wire and the amount of current flowing through the coil. Therefore, to increase the strength of a solenoid, you can either increase the number of loops in the coil or increase the amount of current flowing through the coil.

Option A (plugging up multiple items in the circuit) and option D (arranging the resistors of the circuit in a series circuit) do not increase the strength of a solenoid. These options relate to the circuit's resistance, which can affect the amount of current flowing through the solenoid but does not directly impact its strength.

Option B (arranging the resistors of the circuit in a parallel circuit) could potentially increase the current flowing through the solenoid, but it would not increase the number of loops in the coil, which is necessary to increase the strength of the solenoid. Therefore, option C is the correct answer.

In summary, to increase the strength of a solenoid, you need to increase the number of loops or the amount of electric current flowing through the coil.

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Answer:

ywes

Step-by-step explanation:

Answer:

＼(◎o◎)／

♪～(´ε｀ ) ╮(. ❛ ᴗ ❛.)╭

Answer:

A: law

B:  The opposite of a number is its additive inverse. The sum of a number and its opposite is zero. (This is sometimes called the property of opposites ).

C: To add integers having the same sign, keep the same sign and add the absolute value of each number. To add integers with different signs, keep the sign of the number with the largest absolute value and subtract the smallest absolute value from the largest. Subtract an integer by adding its opposite.

Step-by-step explanation:

I hope this helps. :)

Answer:

8

Step-by-step explanation:

1+2+3=6

4+5+6=15

15-6=9-1=8

X is a binomial random variable such that n = 15 and p = 0.33, the mean, μ, and standard deviation σ respectively are;μ = np = 15 x 0.33 = 4.95σ = √npq = √15 x 0.33 x (1 - 0.33)σ = 1.805

In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n independent experiments, each asking a yes-no question, and each with its own Boolean-valued outcome: a random variable containing binary data.A binomial random variable is a count of the number of successes in a binomial experiment. Here, suppose X is a binomial random variable such that n = 15 and p = 0.33, then, the mean and standard deviation are calculated. In this case, the mean, μ, and standard deviation σ are;μ = np = 15 x 0.33 = 4.95σ = √npq = √15 x 0.33 x (1 - 0.33)σ = 1.805

Therefore, the mean is 4.95 and the standard deviation is 1.805.

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Answer:

About 250 attendance

Step-by-step explanation:

Answer:

The attendance of 250

Step-by-step explanation:

You would see where the 125 containers is on the left is and then you would just go right from there until you hit a meeting point on the straight line which would be at 250