suppose your given the formula n=3m-2l if you know that l= m+2 how could you rewrite that formula

Answer:

The probability that 25% or more in the sample speak Spanish is 76%.

Step-by-step explanation:

Sample of 75 Americans

If 25% or more in the sample speak Spanish, it can be deduced that 24% do not speak Spanish.

The proportion of those who do not speak Spanish is 18 (24% of 75)

Therefore, the proportion of those who speak Spanish is 57 (75 - 19)

This implies that 57/75 x 100 = 76% of the sample speak Spanish.

This 76% of the sample who speak Spanish is equal to the 25% or more who do speak Spanish in the sample.

Probability is the chance that an event may occur from many other events that could have occurred.  It is an educated guess or estimate of something or one event happening when all the events in the set are given an equal chance.

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:

C

Step-by-step explanation:

Given f(x) then f(x + k) represents a horizontal translation of f(x)

• If k > 0 then shift left by k units

• If k < 0 then shift right by k units

Here the shift is 4 units to the left, thus

y = (x + 4)²

Given f(x) then f(x) + k represents a vertical translation of f(x)

• If k > 0 then shift up by k units

• If k < 0 then shift down by k units

Here the shift is 3 units down, thus

y = (x + 4)² - 3 → C

y = (x+4)²-3 is the result of translating y = x² downward by 3 units and to the left by 4 units

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

We need to find the function is the result of translating y = x² downward by 3 units and to the left by 4 units

A translation is a movement of the graph either horizontally parallel to the -axis or vertically parallel to the axis.

To translate the graph of y = f(x) three units downward, subtract 3 from f(x) which becomes y = x²-3

To translate the graph four units to the left, replace x by x+4

y = (x+4)²-3

Hence,  y = (x+4)²-3 is the result of translating y = x² downward by 3 units and to the left by 4 units

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Answer:

correct answer is 456 sq units.

Step-by-step explanation:

Let us have a look at the formula for Surface Area of a prism:

[tex]A =p \times h+2 \times B[/tex]

Where p is the perimeter of base

h is the height of prism

and B is the base area of prism.

Given that:

h = 7.5 units

Hypotenuse of prism's base = 20 units

One of the Other sides = 12  units

Pythagorean theorem can be used to find the 3rd side of right angled base.

Square of hypotenuse = Sum of squares of other two sides

[tex]20^2=12^2+side^2\\\Rightarrow 400=144+side^2\\\Rightarrow side =\sqrt{256}\\\Rightarrow side =16\ units[/tex]

Area of base = area of right angled triangle:

[tex]B = \dfrac{1}{2} \times \text{Base Length} \times \text{Perpendicular Length}\\\Rightarrow B = \dfrac{1}{2} \times 16\times 12 = 96\ sq\ units[/tex]

Perimeter [tex]\times[/tex] height = (12+20+16) [tex]\times[/tex] 7.5 = (48) [tex]\times[/tex] 7.5 = 360 sq units

Now putting the values in formula:

Surface area, A = 360+96 = 456 sq units

So, correct answer is 456 sq units.

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:

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

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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:

A) Brown-Brown ,Brown-Blue, Blue-Brown, Blue-Blue  B) 1/4 =0,25   C)3/4=0,75

Step-by-step explanation:

Lets mother's  "BROWN" is  "BROWN-M",  

mother's "BLUE"  is  " BLUE-M"

Lets  father's  "BROWN" is "BROWN-F" and

father's  "BLUE " is  "BLUE-F"

The kid can have the genotype as follows (list of possible outcomes) :

1. BROWN-M>BROWN-F   ( received BROWN as from mother as from father)

2. BROWN-M>BLUE-F  ( Received BROWN from mother and BLUE from father)

3. BLUE-M>BROWN-F ( Received BLUE from mother and Brown from father)

4.  BLUE-M>BLUE-F ( Received BLUE as from mother as from father)

b) As we can see in a) only 1 outcome from 4 is BLUE-BLUE.  So the probability of BLUE-BLUE genotype is

P(BLUE>BLUE)=1/4=0.25  

c) As we know that if the child has at least one brown allele, that color will dominate and the eyes will be brown.

It means that outcomes BROWN-BROWN, BROWN-BLUE and BLUE-BROWN determine brown color of eye. So the number of these outcomes is 3. Total amount of outcomes is 4.

So probability that eyes are brown is P(Brown eyes)=3/4 =0.75

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:

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].

Step-by-step explanation:

6

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

Answer:

6√6is the exact answer

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:

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:

12.566370614359172953850573533118

Step-by-step explanation:

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.

Hi

500 *1.025^10 ≈ 640.04

The value of root 10 is between 3 and 3.5

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

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:

0.181818

Step-by-step explanation:

There are total 11 candies. The possibility of combinations is 165 which is found by using computation technique 11C3. It is assumed that order does not matter. There are 3 pieces of candy are selected at random. There are 6C2 which is 15 different ways to select cherry and lemon. There are 30 ways to choose 2 cherry and a lemon combination. The probability is [tex]\frac{30}{165}[/tex] = 0.181818

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:

i think it might be A. 0.2

Step-by-step explanation:

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]

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

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:

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:

There is 9 on each pace and 3 on a row

Step-by-step explanation:

54/6=9

if there is 9 on each side and the same on each side, then it has to be 3 in each row and column. Also, this is a Rubix cube

Please give me brainliest, it really helps! :)

Have a good day!

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:

4x^3 + 2x^2 +8x -9

Step-by-step explanation:

A third degree polynomial is a  is a polynomial whose highest power of x is to the power of three.  Standard form is

Ax^3 + Bx^2 + Cx + D where A is non zero

An example would be

4x^3 + 2x^2 +8x -9

Answer:

Step-by-step explanation:

Step1 : Verify Sn is valid for n = 1