what is the solution set of y= x^2+2x+7 and y= x+7 ?

Answer:  G ∩ M = {Anael, Max}

G U S = {Acel, Acton, Anael, Barek, Carl, Carlin, Dario, Kai, Max}

Step-by-step explanation:

intersection ∩ - items found in BOTH sets

union U - the joining of the sets. include EVERYTHING in the sets.

G = (Acel, Acton, Anael, Carl, Dario, Max}

S = {Anael, Barek, Bay, Carlin, Kai, Max}

G ∩ S: Anael and Max are found in both sets

G = (Acel, Acton, Anael, Carl, Dario, Max}

S = {Acton, Anael, Barek,  Carlin, Dario, Kai}

G U S: include everything in G and everything in S. If found in both sets, only list it once.

G U S = {Acel, Acton, Anael, Barek, Carl, Carlin, Dario, Kai, Max}

    Notice that Acton and Anael are in both sets but we only list them once.

Answer:

1320 ways

Step-by-step explanation:

To solve we need to use permutations and factorials. If we wanted to find where they would all place 1-12, we would do 12!

12! is the same as 12x11x10x9x8... etc

But in this problem, we are only looking for the top 3.

We can set up a formula

[tex]\frac{n!}{(n-r)!}[/tex]

N is the number of options that are available and r represents the amount we are choosing

In this case, we have 12 teams so n=12

We are looking for the top 3 so r=3

[tex]\frac{12!}{(12-3)!}[/tex]

[tex]\frac{12!}{9!}[/tex]

We expand the equation and cancel out

[tex]\frac{12x11x10x9x8x7x6x5x4x3x2}{9x8x7x6x5x4x3x2}[/tex]

Notice how both sides can cancel out every number 9 and below

That leaves us with 12x11x10

1320 ways

The possible ways for the gold, silver, and bronze medals to be awarded is 1320

A permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements.

The word "permutation" also refers to the act or process of changing the linear order of an ordered set.

Given that, there are 12 teams, each representing a different country, in a women’s Olympic basketball tournament.

We need to find that, in how many ways is it possible for the gold, silver, and bronze medals to be awarded,

Using the concept of permutation, to find the number of ways

ⁿPₓ = n!/(n-x)!

= 12! / (12-3)!

= 12! / 9!

= 1320

Hence, the possible ways for the gold, silver, and bronze medals to be awarded is 1320

Learn more about permutation click;

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Answer:

C(x) = 0.2x^5 - x^2 + 6000

Step-by-step explanation:

Given in the question are restated as follows:

Marginal cos = C'(x) = x^4 - 2x ...................... (1)

Note that marginal cost (C'(x)) refers to the change in the total cost (C(x)) as a result of one more unit increase in the quantity produced. That is, MC refers to the additional cost incurred in order to produce one more unit of a good.

Therefore, TC can be obtained by integrating equation (1) as follows:

C(x) = ∫C'(x) = ∫[x^4 - 2x]dx

C(x) = 1/5x^5 - 2/2x^2 + F ................................ (2)

Where F is the fixed cost. Since the fixed cost is given as $6,000 in the question, we substitute it for F into equation (2) and solve as follows:

C(x) = 0.2x^5 - x^2 + 6000 ......................... (3)

Equation (3) is the total cost function​ C.

Answer:

[tex]\dfrac{1213}{9999}[/tex]

Step-by-step explanation:

We are required to express [tex]0.\overline{1}+0.\overline{01}+0.\overline{0001}[/tex] as a common fraction.

The bar on top of the decimal part indicates the decimal number is a repeating decimal.

Therefore:

[tex]0.\overline{1}=\dfrac{1}{10-1}= \dfrac{1}{9}\\\\0.\overline{01}=\dfrac{1}{100-1}= \dfrac{1}{99}\\\\0.\overline{0001}=\dfrac{1}{10000-1}= \dfrac{1}{9999}\\\\\\$Therefore$:\\0.\overline{1}+0.\overline{01}+0.\overline{0001} \\=\dfrac{1}{9}+\dfrac{1}{99}+\dfrac{1}{9999}\\\\=\dfrac{1213}{9999}[/tex]

Answer:

The 95 percent confidence interval for the true mean metal thickness is between 0.2903 mm and 0.2907 mm

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.95}{2} = 0.025[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.025 = 0.975[/tex], so [tex]z = 1.96[/tex]

Now, find the margin of error M as such

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 1.96\frac{0.000586}{\sqrt{59}} = 0.0002[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 0.2905 - 0.0002 = 0.2903 mm

The upper end of the interval is the sample mean added to M. So it is 0.2905 + 0.0002 = 0.2907 mm

The 95 percent confidence interval for the true mean metal thickness is between 0.2903 mm and 0.2907 mm

Answer:

1. -6.5x+11

2. 6b-5

3. 3p-5.1

Step-by-step explanation:

[tex]1. \\(x-1)+(12-7.5x)=\\x-1+12-7.5x=\\x-7.5x-1+12=\\-6.5x-1+12=\\-6.5x+11\\\\2.\\b-(4-2b)+(3b-1)=\\b-4+2b+3b-1=\\b+2b+3b-4-1=\\3b+3b-4-1=\\6b-4-1=\\6b-5\\\\3.\\(2p+1.9)-(7-p)=\\2p+1.9-7+p=\\2p+p+1.9-7=\\3p+1.9-7=\\3p-5.1[/tex]

Answer:

Step-by-step explanation:

In an isosceles triangle, the base angles are equal. This also means that the length of two sides of the triangle are equal. Looking at triangle ABC, to prove that it is an isosceles triangle, then

Angle CAB = angle CBA

For the second question, to determine how it is known that QS is equivalent to YT, we would recall that the diameter of a circle passes through the center and from one side of the circle to the other side. Assuming R is the center of the circle, then QS and YT are the diameters of the circle and also the diagonals of the rectangle. Thus, the correct option is

The diameters act as diagonals

Answer:

Solution,

Complement of 70°

=90°-70°

=20°

hope this helps...

Good luck on your assignment..

Answer:

20°

Step-by-step explanation:

Complement of 70° is 90°-70°= 20°  

To determine the complement, subtract the given angle from 90.

Answer:

The curvature is modelled by [tex]\kappa = \frac{e^{-t}}{6\sqrt{2}}[/tex].

Step-by-step explanation:

The equation of the curvature is:

[tex]\kappa = \frac{|\dot {x}\cdot \ddot {y}-\dot{y}\cdot \ddot{x}|}{[\dot{x}^{2}+\dot{y}^{2}]^{\frac{3}{2} }}[/tex]

The parametric componentes of the curve are:

[tex]x = 6\cdot e^{t} \cdot \cos t[/tex] and [tex]y = 6\cdot e^{t}\cdot \sin t[/tex]

The first and second derivative associated to each component are determined by differentiation rules:

First derivative

[tex]\dot{x} = 6\cdot e^{t}\cdot \cos t - 6\cdot e^{t}\cdot \sin t[/tex] and [tex]\dot {y} = 6\cdot e^{t}\cdot \sin t + 6\cdot e^{t} \cdot \cos t[/tex]

[tex]\dot x = 6\cdot e^{t} \cdot (\cos t - \sin t)[/tex] and [tex]\dot {y} = 6\cdot e^{t}\cdot (\sin t + \cos t)[/tex]

Second derivative

[tex]\ddot{x} = 6\cdot e^{t}\cdot (\cos t-\sin t)+6\cdot e^{t} \cdot (-\sin t -\cos t)[/tex]

[tex]\ddot x = -12\cdot e^{t}\cdot \sin t[/tex]

[tex]\ddot {y} = 6\cdot e^{t}\cdot (\sin t + \cos t) + 6\cdot e^{t}\cdot (\cos t - \sin t)[/tex]

[tex]\ddot{y} = 12\cdot e^{t}\cdot \cos t[/tex]

Now, each term is replaced in the the curvature equation:

[tex]\kappa = \frac{|6\cdot e^{t}\cdot (\cos t - \sin t)\cdot 12\cdot e^{t}\cdot \cos t-6\cdot e^{t}\cdot (\sin t + \cos t)\cdot (-12\cdot e^{t}\cdot \sin t)|}{\left\{\left[6\cdot e^{t}\cdot (\cos t - \sin t)\right]^{2}+\right[6\cdot e^{t}\cdot (\sin t + \cos t)\left]^{2}\right\}^{\frac{3}{2}}} }[/tex]

And the resulting expression is simplified by algebraic and trigonometric means:

[tex]\kappa = \frac{72\cdot e^{2\cdot t}\cdot \cos^{2}t-72\cdot e^{2\cdot t}\cdot \sin t\cdot \cos t + 72\cdot e^{2\cdot t}\cdot \sin^{2}t+72\cdot e^{2\cdot t}\cdot \sin t \cdot \cos t}{[36\cdot e^{2\cdot t}\cdot (\cos^{2}t -2\cdot \cos t \cdot \sin t +\sin^{2}t)+36\cdot e^{2\cdot t}\cdot (\sin^{2}t+2\cdot \cos t \cdot \sin t +\cos^{2} t)]^{\frac{3}{2} }}[/tex]

[tex]\kappa = \frac{72\cdot e^{2\cdot t}}{[72\cdot e^{2\cdot t}]^{\frac{3}{2} } }[/tex]

[tex]\kappa = [72\cdot e^{2\cdot t}]^{-\frac{1}{2} }[/tex]

[tex]\kappa = 72^{-\frac{1}{2} }\cdot e^{-t}[/tex]

[tex]\kappa = \frac{e^{-t}}{6\sqrt{2}}[/tex]

The curvature is modelled by [tex]\kappa = \frac{e^{-t}}{6\sqrt{2}}[/tex].

Answer:

i think it might be A. 0.2

Step-by-step explanation:

Correct question:

The vector matrix [ [tex] \left[\begin{array}{ccc}2\\7\end{array}\right] [/tex] is dilated by a factor of 1.5 and then reflected across the x axis. If the resulting matrix is [a/b] then a=??? and b=???

Answer:

a = 3

b = 10.5

Step-by-step explanation:

Given:

Vector matrix = [tex] \left[\begin{array}{ccc}2\\7\end{array}\right] [/tex]

Dilation factor = 1.5

Since the vector matrix is dilated by 1.5, we have:

[tex] \left[\begin{array}{ccc}1.5 * 2\\1.5 * 7\end{array}\right] [/tex]

= [tex] \left[\begin{array}{ccc}3\\10.5\end{array}\right] [/tex]

Here, we are told the vector is reflected on the x axis.

Therefore,

a = 3

b = 10.5

Answer:

a = 3

b = -10.5

Step-by-step explanation:

got a 100% on PLATO

Hi

500 *1.025^10 ≈ 640.04

Answer: x =40

Step-by-step explanation:

x +x +100 = 180   They form a straight line so they add to 180 degrees.

2x + 100 = 180      solve for x  by combining like terms

       -100    -100   subtract  100 from both sides

2x = 80             Divide both sides by 2

x =40

Answer:

x might be 40°.

Step-by-step explanation:

angle on a straight line =180°

x+100+x =180

2x =180-100

2x=80

2x/2=80/2

x=40°

The answers are in order

r = −0.08 --> weak negative correlation

r = −0.83 --> strong negative correlation

r = 0.96 --> strong positive correlation

r = 0.06 --> weak positive correlation

The match of each correlation is given by,

r = −0.08  implies a weak negative correlation

r = −0.83  implies a strong negative correlation

r = 0.96  implies strong positive correlation

r = 0.06 implies  weak positive correlation.

We have given that,

The correlation coefficient, r, to its description.

A                                                 B

r = −0.08                             strong negative correlation

r = −0.83                               weak positive correlation                

r = 0.96                               weak negative correlation                    

r = 0.06                                strong positive correlation

We have to match the given relation

If the correlation coefficient is greater than zero, it is a positive relationship. Conversely, if the value is less than zero, it is a negative relationship.

So the correct match is,

r = −0.08  implies a weak negative correlation

r = −0.83  implies strong negative correlation

r = 0.96  implies strong positive correlation.

r = 0.06 is implies  weak positive correlation.

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Answer:

The answer is below

Step-by-step explanation:

What we should do is the following:

First, from the random sample of 852 researchers, it is necessary to obtain the number of adult residents who consumed alcohol in the past year.

After the above, we must calculate the proportion of adult residents who consumed alcohol in the last year by dividing the number of adult residents who consumed alcohol in the last year by 852.

After this, we must compare if the proportion is exactly 70% or different from it.

We have the following hypotheses:

Null Hypothesis: The proportion of adult residents who consumed alcohol in the last year in the state of Wisconsin is exactly 70%

Alternative hypothesis: The proportion of adult residents who consumed alcohol in the last year in the state of Wisconsin is not equal to 70%

Answer:

  30 miles

Step-by-step explanation:

Jose's charges are ...

  j = 5 + 0.30m . . . . . for m miles

Kathy's charges are ...

  k = 8 +0.20m . . . . . for m miles

The charges are the same when ...

 j = k

  5 +0.30m = 8 + 0.20m

  0.30m = 3 + 0.20m . . . . subtract 5

  0.10m = 3 . . . . . . . . . . . . subtract 0.20m

  m = 30 . . . . . . . . . . . . . . . multiply by 10

The charges will be the same for a distance of 30 miles.

Answer:

Step-by-step explanation:

Given that:

[tex]E( \hat \theta _1) = \theta \ \ \ \ E( \hat \theta _2) = \theta \ \ \ \ V( \hat \theta _1) = \sigma_1^2 \ \ \ \ V(\hat \theta_2) = \sigma_2^2[/tex]

If we are to consider the estimator [tex]\hat \theta _3 = a \hat \theta_1 + (1-a) \hat \theta_2[/tex]

a. Then, for  [tex]\hat \theta_3[/tex] to be an unbiased estimator ; Then:

[tex]E ( \hat \theta_3) = E ( a \hat \theta_1+ (1-a) \hat \theta_2)[/tex]

[tex]E ( \hat \theta_3) = aE ( \theta_1) + (1-a) E ( \hat \theta_2)[/tex]

[tex]E ( \hat \theta_3) = a \theta + (1-a) \theta = \theta[/tex]

b) If [tex]\hat \theta _1 \ \ and \ \ \hat \theta_2[/tex] are independent

[tex]V(\hat \theta _3) = V (a \hat \theta_1+ (1-a) \hat \theta_2)[/tex]

[tex]V(\hat \theta _3) = a ^2 V ( \hat \theta_1) + (1-a)^2 V ( \hat \theta_2)[/tex]

Thus; in order to minimize the variance of [tex]\hat \theta_3[/tex] ; then constant a can be determined as :

[tex]V( \hat \theta_3) = a^2 \sigma_1^2 + (1-a)^2 \sigma^2_2[/tex]

Using differentiation:

[tex]\dfrac{d}{da}(V \ \hat \theta_3) = 0 \implies 2a \ \sigma_1^2 + 2(1-a)(-1) \sigma_2^2 = 0[/tex]

⇒

[tex]a (\sigma_1^2 + \sigma_2^2) = \sigma^2_2[/tex]

[tex]\hat a = \dfrac{\sigma^2_2}{\sigma^2_1+\sigma^2_2}[/tex]

This implies that

[tex]\dfrac{d}{da}(V \ \hat \theta_3)|_{a = \hat a} = 2 \ \sigma_1^2 + 2 \ \sigma_2^2 > 0[/tex]

So, [tex]V( \hat \theta_3)[/tex] is minimum when [tex]\hat a = \dfrac{\sigma_2^2}{\sigma_1^2+\sigma_2^2}[/tex]

As such; [tex]a = \dfrac{1}{2}[/tex]       if   [tex]\sigma_1^2 \ \ = \ \ \sigma_2^2[/tex]

Answer:

V  = 23π/6

Step-by-step explanation:

V = 2π ∫ [a to b] (r * h) dx

y = −x² + 23x − 132

y = −(x² − 23x + 132)

y = −(x − 11) (x − 12)

Parabola intersects x-axis (line y = 0) at x = 11 and x = 12 ----> a = 11, b = 12

r = x

h = −x² + 23x − 132

V = 2π ∫ [11 to 12] x (−x² + 23x − 132) dx

V  = 23π/6

Answer:

Step-by-step explanation:

Step1 : Verify Sn is valid for n = 1

Answer:

(2x+16) + (x) = 180

Step-by-step explanation:

The opposite angles of a quadrilateral inscribed inside a circle will be supplementary angles, meaning that A+C=180, and B+D=180. A+C is not given in the answers below, but B+D is, so that is the correct answer.

Hope this helps! Please give brainliest!!

Answer:

C

Step-by-step explanation:

Opposite angles of a quadrilateral are supplementary

Answer:

A margin of error of +/- 3%

Step-by-step explanation:

Strenght of surveys:

The lesser the margin of error, the more precise, stronger, the confidence interval is.

The margin of error depends of the number of people surveyed. The more people are surveyed, lower the margin of error is, giving a stronger interval.

In this question:

We want the smaller margin of error, which is given by:

A margin of error of +/- 3%

Answer:

x = -1.796, 7.796

Step-by-step explanation:

3x² - 18x + 5 = 47

3x² - 18x - 42 = 0

use quadratic equation

x = -1.796, 7.796

Answer:

x = 3 +/- √23

Step-by-step explanation:

got it right on edg

Answer:

10 rows with 6 passengers per row

Step-by-step explanation:

Let x be the number of rows and y the number of passengers per row.

Then we can interpret the story as the following two equations:

xy=60

(x+2)(y-1)=60

Solving these two equations:

y=60/x

(x+2)(60/x-1)=60     (substitute y)

60 - x + 120/x - 2 = 60 (multiply by -x)

x² + 2x - 120 = 0     (factor)

(x-10)(x+12) = 0

x = 10

y = 60/10 = 6

and indeed 10 * 6 = 60 and also 12 * 5 = 60

The value of root 10 is between 3 and 3.5

Answer:

104 degrees

Step-by-step explanation:

The angle of the whole set of lines is 140 degrees. In addition, the partial angle of it is also given--which is 36 degrees. In order to solve for the remaining part, Subtract 36 degrees from 140 degrees to get 104 degrees.

Answer: x = 15, y = 12.5

Step-by-step explanation:

The sum of the three angle measures of a triangle equals 180ᴼ

Since these triangles are vertical, the measures are congruent.

45 + 60 = 105

180 - 105 = 75

So now we know that 5x = 75ᴼ and 6y = 75ᴼ.

To find x, divide 75 by 5

75 / 5 = 15

x = 15

To find y, divide 75 by 6

75 / 6 = 12.5

y = 12.5

Answer:

The maximum height that the object will reach is of 9 feet.

Step-by-step explanation:

Vertex of a quadratic function:

Suppose we have a quadratic function in the following format:

[tex]f(x) = ax^{2} + bx + c[/tex]

It's vertex is the point [tex](x_{v}, f(x_{v})[/tex]

In which

[tex]x_{v} = -\frac{b}{2a}[/tex]

If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]f(x_{v})[/tex]

In this question:

[tex]f(t) = -16t^{2} + 16t + 5[/tex]

So

[tex]a = -16, b = 16[/tex]

The instant of the maximum height is:

[tex]t_{v} = -\frac{16}{2*(-16)} = 0.5[/tex]

The maximum height is:

[tex]f(0.5) = -16*(0.5)^2 + 16*0.5 + 5 = 9[/tex]

The maximum height that the object will reach is of 9 feet.

Answer:

24

Step-by-step explanation:

Answer:

A(s) = 255.8857

Step-by-step explanation:

Find the area of the surface correct to four decimal places by expressing the area in terms of a single integral and using your calculator to estimate the integral. The part of the surface z = e^-x^2-y^2 that lies above the disk x2 + y2 ≤ 81.

Given that:

[tex]Z = e^{-x^2-y^2}[/tex]

By applying rule; the partial derivatives with respect to x and y

[tex]\dfrac{\partial z }{\partial x}= -2xe^{-x^2-y^2}[/tex]

[tex]\dfrac{\partial z }{\partial y}= -2ye^{-x^2-y^2}[/tex]

The integral over the general region D with respect to x and y is :

[tex]A(s) = \int \int _D \sqrt{1+(\dfrac{\partial z}{\partial x} )^2 +(\dfrac{\partial z}{\partial y} )^2 }\ dA[/tex]

[tex]A(s) = \int \int _D \sqrt{1+(-2xe^{-x^2-y^2})^2 +(-2ye^{-x^2-y^2})^2 } \ dA[/tex]

[tex]A(s) = \int \int _D \sqrt{1+4x^2({e^{-x^2-y^2})^2 +4y^2({e^{-x^2-y^2}})^2 }} \ dA[/tex]

[tex]A(s) = \int \int _D \sqrt{1+(4x^2+4y^2)({e^{-x^2-y^2})^2 }} \ dA[/tex]

[tex]A(s) = \int \int _D \sqrt{1+(4x^2+4y^2)e^{-2}({{x^2+y^2}) }} \ dA[/tex]

By relating the equation to cylindrical coordinates

[tex]A(s) = \int \int_D \sqrt{1+4r^2 e^{-2r^2} }. rdA[/tex]

The bounds for integration for the circle within the cylinder [tex]x^2+y^2 =81[/tex] is r =9

[tex]A(s) = \int \limits ^{2 \pi}_{0} \int \limits^9_0 r \sqrt{1+4r^2 e^{-2r^2} }. dr d\theta[/tex]

[tex]A(s) = {2 \pi} \int \limits^9_0 r \sqrt{1+4r^2 e^{-2r^2} }\ dr[/tex]

Using integral calculator to estimate the  integral,we have:

A(s) = 255.8857

Answer:

√75 = 5√3 and √12 = 2√3 so √75 + √12 = 5√3 + 2√3 = 7√3.

Answer:

[tex] 7\sqrt{3} [/tex]

Step-by-step explanation:

[tex] \sqrt{12} \: can \: be \: simplified \: as \: 2 \sqrt{3} \: and \: \sqrt{75} \: canbe \: simplified \: as \: 5 \sqrt{3} \\ after \: simplifying \: we \: can \: add \: them \: up \\ 2 \sqrt{3} + 5 \sqrt{3} = 7 \sqrt{3} [/tex]

Step-by-step explanation:

6

[tex]6 \sqrt{6} [/tex]

Answer:

6√6is the exact answer