the art club charges 2x+12 dollars for any number of X paintings. they announce that they will be selling art for half the price this weekend. Factor the expression to determine the cost of paintings this weekend

Answer:

\(( x_1 , y_1 , z_1 ) = < -7 + 4\sqrt{3} , -4 + 2\sqrt{3} , 7 - 2\sqrt{3} >\\\\( x_2 , y_2 , z_2 ) = < -7 - 4\sqrt{3} , -4 - 2\sqrt{3} , 7 + 2\sqrt{3} >\\\)

Step-by-step explanation:

Solution:-

- We are given a parametric form for the vector equation of line defined by ( t ).

- The line vector equation is:

                        L: < 3 + 2t , t + 1 , 2 -t >

- The same 3-dimensional space is occupied by a unit sphere defined by the following equation:

                          \(S: x^2 + y^2 + z^2 = 1\)

- We are to determine the points of intersection of the line ( L ) and the unit sphere ( S ).

- We will substitute the parametric equation of line ( L ) into the equation defining the unit sphere ( S ) and solve for the values of the parameter ( t ):

                        \(( 3 + 2t )^2 + ( 1 + t )^2 + ( 2 - t)^2 = 1\\\\( 9 + 12t + 4t^2 ) + ( t^2 + 2t + 1 ) + ( 4 + t^2 -4t ) = 1\\\\t^2 + 10t + 13 = 0\\\\\)

- Solve the quadratic equation for the parameter ( t ):

                       \(t = -5 + 2\sqrt{3} , -5 - 2\sqrt{3}\)

- Plug in each of the parameter value in the given vector equation of line and determine a pair of intersecting coordinates:

                      \(( x_1 , y_1 , z_1 ) = < -7 + 4\sqrt{3} , -4 + 2\sqrt{3} , 7 - 2\sqrt{3} >\\\\( x_2 , y_2 , z_2 ) = < -7 - 4\sqrt{3} , -4 - 2\sqrt{3} , 7 + 2\sqrt{3} >\\\)

The value of x for the given expression, x + 20 ≤ -10 will be -30. The value of x is obtained by applying the arithmetic operation.

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

For the inequality, we have to apply the arithmetic operation in which we do the multiplication of x and apply the inequality for the given data.

It is given that the expression is,

x + 20 ≤ -10

Rearrange the expression as

x≤ -10-20

x≤ -30

Thus, the value of x for the given expression, x + 20 ≤ -10 will be -30. The value of x is obtained by applying the arithmetic operation.

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The coefficient of variation or CV of the given numbers is 45.64%.

Given numbers are,

5, 8, 9, 2, 6

We have to find Coefficient of variation.

CV = (Standard deviation / sample mean ) × 100

Sample mean = Sum of the values / total number of values

                       = (5 + 8 + 9 + 2 + 6) / 5

                       = 6

Standard deviation = √[(Σ(x - mean)² / (n - 1)]

Σ(x - mean)² = (5 - 6)² + (8 - 6)² + (9 - 6)² + (2 - 6)² + (6 - 6)²

                    = 30

Standard deviation = √(30 / (5 - 1) = 2.7386

CV = (2.7386 / 6) × 100

     = 45.64%

Hence CV is 45.64%.

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Answer:

4!

Step-by-step explanation:

40 x 4 = 160

160+ 140 = 300

Answer:

4 dresses

Step-by-step explanation:

If she starts with $300 and ends up with $140, that means that she spent $160. So, since each dress costs $40, you divided $160 by $40, which equals 4. So Michelle bought 4 dresses.

(hope this helps!)

This type of data can be analyzed using a two-way analysis of variance (ANOVA) to determine the effect of both the day of the week (weekday or weekend) and the shift (morning or evening) on chair production. The manager can use this information to make predictions about future production based on the day of the week and shift.

The manager can start by creating a table to show the average number of chairs produced on each day of the week and shift. Then, a two-way ANOVA can be performed to determine if there is a significant difference in the mean number of chairs produced between weekdays and weekends, and between morning and evening shifts.

If the results of the ANOVA show that there is a significant effect of the day of the week and/or the shift on chair production, the manager can use this information to make more accurate predictions about future chair production. For example, if the results show that chair production is higher on weekdays compared to weekends, the manager can make predictions based on this information and allocate resources accordingly.

It is important to note that other factors such as the availability of materials, number of workers, and machine downtime can also impact chair production and should be considered when making predictions.

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Answer:

Part A:

To find the percentage of survey respondents who liked neither hamburgers nor burritos, we need to calculate the frequency in the "Does not like hamburgers" and "Does not like burritos" categories.

Frequency of "Does not like hamburgers" = Total in "Does not like hamburgers" category = 135

Frequency of "Does not like burritos" = Total in "Does not like burritos" category = 54

Total respondents who liked neither hamburgers nor burritos = Frequency of "Does not like hamburgers" + Frequency of "Does not like burritos" = 135 + 54 = 189

Percentage of survey respondents who liked neither hamburgers nor burritos = (Total respondents who liked neither hamburgers nor burritos / Total respondents) x 100

Percentage = (189 / 205) x 100 = 92.2%

Therefore, 92.2% of the survey respondents liked neither hamburgers nor burritos.

Part B:

To find the marginal relative frequency of all customers who like hamburgers, we need to divide the frequency of "Likes hamburgers" by the total number of respondents.

Frequency of "Likes hamburgers" = 110 (given)

Total respondents = 205 (given)

Marginal relative frequency = Frequency of "Likes hamburgers" / Total respondents

Marginal relative frequency = 110 / 205 ≈ 0.5366 or 53.66%

Therefore, the marginal relative frequency of all customers who like hamburgers is approximately 53.66%.

Part C:

To determine if there is an association between liking burritos and liking hamburgers, we can compare the joint and marginal frequencies.

Joint frequency of "Likes hamburgers" and "Likes burritos" = 29 (given)

Marginal frequency of "Likes hamburgers" = 110 (given)

Marginal frequency of "Likes burritos" = 70 (calculated by adding the frequency of "Likes burritos" in the table)

To assess the association, we compare the ratio of the joint frequency to the product of the marginal frequencies:

Ratio = Joint frequency / (Marginal frequency of "Likes hamburgers" x Marginal frequency of "Likes burritos")

Ratio = 29 / (110 x 70)

Ratio ≈ 0.037 (rounded to three decimal places)

The answer is A.

An indefinite integral is a function that, when differentiated, equals the original function. It is denoted by ∫f(x)dx, where f(x) is the function to be integrated. An indefinite integral always has an arbitrary constant of integration, which is denoted by C. This is because the derivative of any constant is zero, so the derivative of ∫f(x)dx+C is still equal to f(x).

A definite integral is the limit of a Riemann sum as the number of terms tends to infinity. It is denoted by ∫

a

b

​

f(x)dx, where a and b are the limits of integration. A definite integral does not have an arbitrary constant of integration, because the limits of integration specify a unique value for the integral.

In other words, an indefinite integral is a family of functions that share the same derivative, while a definite integral is a single number.

The value of 57.17 as a mixed number is - 57 17/100.

A mixed number is said to be in its simplest form if its fractional part's highest common factor, or HCF, is 1. When mixed numbers are simplified, the fraction value remains constant. We can say that the simplified mixed number and the actual mixed number are fractions that are equivalent.

A mixed number is made up of three components: a whole number, a numerator, and a denominator. The numerator and denominator are both components of the proper fraction that results in the mixed number.

In this case, -57.17 will be:

= -57 + (17/100)

= -57 17/100.

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Step-by-step explanation: To solve for x in this literal equation, I would first distribute the C through the parentheses to get y = cx + cb.

Now subtract cb from both sides to get y - cb = cx.

Finally, divide both sides by c to get y - cb / c = x.

Answer:

189 students

Step-by-step explanation:

Answer:

\(\mathbf{A = \dfrac{8}{3} \bigg (2 \pi + 3\sqrt{3} \bigg ) }\)

Step-by-step explanation:

From the information given:

Lets first change the given relations into polar coordinates

So, the region of the inner circle into polar coordinates is as follows:

(x - 4)² + y² = 16

x² + y² - 8x = 0

r² - 8r cos θ = 0

r = 8 cos θ

For the outside circle:

x² + y² = 16

r² = 16

Thus, the intersection point are:

64cos²θ = 16

cos²θ = 1/4

θ = -(π/3) , (π/3)

Now: if we are to represent the sketch on a graph, the region of the integration D will be:

\(D = \bigg \{ (r,\theta )\bigg |-\dfrac{\pi}{3}\leq \theta \leq \dfrac{\pi}{3}, 4 \leq r \leq 8 cos \theta \bigg \}\)

Therefore, the are of the required region can now be computed as follows:

\(A = \int \int _D \ dA\)

\(A = \int ^{\pi/3}_{-\pi/3} \int ^{8 \ cos \theta}_{4} \ r dr d \theta\)

\(A = \int ^{\pi/3}_{-\pi/3} \bigg (\dfrac{r^2}{2} \bigg ) ^{8 \ cos \theta}_{4} \ d \theta\)

\(A = \int ^{\pi/3}_{-\pi/3} \dfrac{1}{2} \bigg (64 \ cos ^2 \theta - 16 \bigg ) \ d \theta\)

\(A = \int ^{\pi/3}_{-\pi/3} \dfrac{16}{2} \bigg (4 \ cos ^2 \theta - 1 \bigg ) \ d \theta\)

\(A = \dfrac{16}{2} * 2 \int ^{\pi/3}_{0} \bigg (4 \bigg ( \dfrac{ 1+ cos 2 \theta}{2} \bigg) - 1 \bigg ) \ d \theta\)

\(A = 16 \int^{\pi/3}_{0} (1 + 2 cos 2 \theta ) d \theta\)

\(A =16 ( \theta + sin2 \theta )^{\pi/3}_{0}\)

\(A = 16 \begin {bmatrix} \bigg (\dfrac{\pi}{3} + \dfrac{\sqrt{3}}{2} \bigg ) - (0-0) \end {bmatrix}\)

\(A = 16 \begin {bmatrix} \bigg (\dfrac{\pi}{3} + \dfrac{\sqrt{3}}{2} \bigg ) \end {bmatrix}\)

\(\mathbf{A = \dfrac{8}{3} \bigg (2 \pi + 3\sqrt{3} \bigg ) }\)

The area of the region is equal to \(8\sqrt{3} + \frac{16\pi}{3}\) square units.

The double integral formula for the area of a given curve is described below:

\(A = \iint\,r(\theta) \,dr\,d\theta\) (1)

Where:

We notice that \(r \in [4, 8\cdot \cos \theta]\) and \(\theta \in \left[-\frac{\pi}{3}, \frac{\pi}{3} \right]\), then we have the following integral:

\(A = \int\limits_{-\frac{\pi}{3} }^{+\frac{\pi}{3} } \int \limits_{r= 4}^{r = 8\cdot \cos \theta}\,r\,dr\,d\theta\)

Now we proceed to integrate the expression:

\(A = \frac{1}{2}\int\limits_{-\frac{\pi}{3} }^{+\frac{\pi}{3} } \,(64\cdot \cos^{2}\theta -16)\,d\theta = 32 \int\limits^{+\frac{\pi}{3} }_{-\frac{\pi}{3} } \,\cos^{2}\theta \, d\theta - 8\,\int\limits^{+\frac{\pi}{3} }_{-\frac{\pi}{3} } \, d\theta\)

\(A = 16\int\limits^{+\frac{\pi}{3} }_{-\frac{\pi}{3} } {\cos 2\theta} \, d\theta + 8\int\limits^{+\frac{\pi}{3} }_{-\frac{\pi}{3} } \, d\theta\)

\(A = 8\sqrt{3}+\frac{16\pi}{3}\)

The area of the region is equal to \(8\sqrt{3} + \frac{16\pi}{3}\) square units.

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Answer:

D.

Step-by-step explanation:

The graph that shows the image of ∠B after a rotation of 180∘ about the origin has the coordinates B' - (-1, 8)(attached)

The 180-degree rotation, whether clockwise and anticlockwise, is one of the most basic and frequent geometric transformations. The coordinates of B (x, y) after the rotation will only have the opposite signs of the initial values if B (x, y) is a point that needs to be rotated 180 degrees the about origin.

The camera may move wherever on its side in accordance with the 180-degree rule, but it must not cross the axis. The performers maintain the same left/right interaction with one another while the camera is on one side of the 180-degree line.

It is demonstrated to rotate 180 degrees around the origin.

From the question:

The coordinates of B are - B(1, -8).

Thus, the formula is (x,y)→(−x,−y)  for a 180° rotation of the origin.

B' - (-1 ,-(- 8))

B' - (-1, 8)

The graph that shows the image of ∠B after a rotation of 180∘ about the origin has the coordinates B' - (-1, 8): . (attached)

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Answer:b

Step-by-step explanation:

Answer:

8.5 feet

Step-by-step explanation:

1.5 times 4

Answer:

\(\tan\theta + \sec\theta + C\)

Step-by-step explanation:

This cool problem uses an old trick:  multiplying by a cleverly chosen expression for 1 (a fraction with the same numerator and denominator).

\(\int \frac{\sec\theta}{\sec\theta-\tan\theta} \cdot \frac{\sec\theta+\tan\theta}{\sec\theta+\tan\theta}\, d\theta\\\\=\int\frac{\sec\theta(\sec\theta+\tan\theta)}{\sec^2\theta-\tan^2\theta}\)

That denominator looks kind of familiar.  Remember one of the so-called Pythagorean identities?

\(1+\tan^2\theta=\sec^2\theta\\\\\sec^2\theta - \tan^2\theta =1\)   The denominator of the integrand is just 1 !!!

The integral is now

\(\int \sec\theta(\sec\theta+\tan\theta) \, d\theta = \int(\sec^2\theta+\sec\theta\tan\theta) \, d\theta\\=\int \sec^2\theta \, d\theta + \int \sec\theta\tan\theta \, d\theta\\=\tan\theta + \sec\theta + C\)

That little trick is good to know.  You may have used it before to rationalize a denominator.  Example:

\(\frac{1}{\sqrt{7}-3}\cdot\frac{\sqrt{7}+3}{\sqrt{7}+3}=\frac{\sqrt{7}+3}{7-9}=\frac{\sqrt{7}+3}{-2}\)

In the context of this problem all the solutions to the polynomial equation is correct because they all make sense.

The given polynomial equation  can be expressed as ;

x³ + 6x² - 40x = 192 and the given solutions can be written as ; x = -8, x = -4, and x = 6

We can test if the solution is the best for the given euation because this will help us to know if these valueas are the solution for the equation

x = -8

[(-8)³ + 6(-8)² - 40(-8)]

= 192

[-512 + 384 + 320]

= 192

x = -4,

[(-4)³ + 6(-4)² - 40(-4)]

[-64 + 96 + 160 ]

= 192

x = 6

[(6)³ + 6(6)² - 40(6) ]

216 + 216 - 240

= 192

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Answer:

Step-by-step explanation:

A,B

x = –8

x = –4

el perimetro de la figura en la imagen es 96 centimetros.

Sabemos que para cualquier figura el perimetro se define como la suma de las longitudes de sus lados.

Para la figura en la imagen, el perimetro será:

AH + AB + BC + CD + DE + EF + FG + GH

Para la figura en la imagen, es bastante claro que:

AH = BC + DE + FG

AB = CD + EF + GH

Y tambien podemos ver que:

AH = 33cm

AB = 15cm

Entonces en la formula del perimetro podemos rerescribir:

AH + AB + BC + CD + DE + EF + FG + GH

AH + (BC + DE + FG) + AB + (CD + EF + gH)

AH + AH + AB + AB

33cm + 33cm + 15cm + 15cm = 66cm + 30cm = 96cm

De esta forma, concluimos que el perimetro de la figura en la imagen es 96 centimetros.

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Answer:

4x -y + 8=0

Step-by-step explanation:

:)

The equation 2 log₅ x = log₅ 4 + log₅ 9 has two solutions: x = 6.

To solve the equation 2 log₅ x = log₅ 4 + log₅ 9, we can use logarithmic properties to simplify and find the value of x.

Using the properties of logarithms, we can rewrite the equation as follows:

2 log₅ x = log₅ (4 * 9)

Next, we simplify the right side:

2 log₅ x = log₅ (36)

Now, we can use the property of logarithms that states logₐ b = c is equivalent to aᶜ = b. Applying this property, we have:

x² = 36

Taking the square root of both sides, we get:

x =  √36

Since the square root of 36 can be either positive or negative, we have two possible solutions:

x = 6

It's important to note that when working with logarithmic equations, we must always check if the obtained solutions satisfy the domain restrictions of the original equation. In this case, since the logarithm has a base of 5, the solution x = 6.

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Answer:

  x = 1

Step-by-step explanation:

You want to know the value of x in the trapezoid with adjacent angles (43x+2)° and 135°.

The two marked angles can be considered "consecutive interior angles" where a transversal crosses parallel lines. As such, they are supplementary.

  (43x +2)° +135° = 180°

  43x = 43 . . . . . . . . . . . . . . divide by °, subtract 137

  x = 1 . . . . . . . . . . . . . . . divide by 43

The value of x is 1.

__

Additional comment

Given that the figure is a trapezoid, we have to assume that the top and bottom horizontal lines are the parallel bases.

<95141404393>

The Lim household used 225 kWh of electricity in that month. The solution has been obtained by using the arithmetic operations.

What are arithmetic operations?

All real numbers are thought to be adequately described by the four basic operations, often known as "arithmetic operations." The mathematical operations quotient, product, sum, and difference come after division, multiplication, addition, and subtraction.

We are given that the Lim household paid $45 for electricity usage in a certain month and each electricity (in kWh) is charged at $0.20​.

Let the electricity used be x.

So, we get an equation as

⇒ 0.20x = $45

Using the division operation, we get

⇒ x = 225 kWh

Hence, the Lim household used 225 kWh of electricity in that month.

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Solution: C. X=-2

Analysis:

When we graph the derivative of a function, we can find a local maximum or minimum point, where the graph takes a maximum or minimum value, it's a maximum point for the initial function.

In this case, the point would be X=-2. At that point, the graph has a minimum value.

9514 1404 393

Answer:

  u'(1) = 0

  v'(5) = -2/3

Step-by-step explanation:

There are several ways to go at this. One is to write the function composition, then differentiate that. Another is to make use of the derivative relations only at the point of interest. (The first method is used in the graph.)

At x=1

u(x) = f(x)g(x)

u'(1) = f'(1)g(1) +f(1)g'(1)

The derivatives of the functions will be their slopes at the point of interest.

  f(1) = 2, f'(1) = 2

  g(1) = 1, g'(1) = -1

u'(1) = (2)(1) +(2)(-1)

u'(1) = 0

__

At x=5

v(x) = f(x)/g(x)

v'(5) = (g(5)f'(5) -f(5)g'(5))/g(5)²

The relevant function values are ...

  f(5) = 3, f'(5) = -1/3

  g(5) = 2, g'(5) = 2/3

v'(5) = ((2)(-1/3) -(3)(2/3))/(2²) = (-2/3 -2)/4 = (-8/3)/4

v'(5) = -2/3

_____

Additional comment

The functions used in each of the compositions are only defined on the relevant interval [0, 2] or (2, ∞).

Answer:

Simon used 50 blocks

Ron used 60 blocks

Together, they used 110 blocks.

Here is the question as an equation-

(5x10)+(6x10)=

Using the radius of the Ferris wheel and the angle between the two positions, the time spent on the ride when they're 28 meters above the ground is 12 minutes

The radius of the Ferris wheel is 30 / 2 = 15 meters.

The highest point on the Ferris wheel is 15 + 4 = 19 meters above the ground.

The time spent higher than 28 meters is the time spent between the 12 o'clock and 8 o'clock positions.

The angle between these two positions is 180 degrees.

The time spent at each position is 10 minutes / 360 degrees * 180 degrees = 6 minutes.

Therefore, the total time spent higher than 28 meters is 6 minutes * 2 = 12 minutes.

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