Find the dimensions of the rectangle

The numerical values of the mean and standard deviation are 4 and 1.55, respectively

The given parameters are:

n = 10

π = 0.4

The probability is then calculated as:

[tex]P(x) = ^nC_x * \pi^x *(1-\pi)^{n-x}[/tex]

So, we have:

[tex]P(6) = ^{10}C_6 * 0.4^6 *(1-0.4)^4[/tex]

Apply the combination formula

[tex]P(6) = \frac{10!}{6!4!} * 0.4^6 *0.6^4[/tex]

So, we have:

[tex]P(6) = 210 * 0.4^6 *0.6^4[/tex]

Evaluate

P(6) = 0.1115

Hence, the numerical value of the probability that x = 6 is 0.1115

The mean value is:

[tex]\bar x = n\pi[/tex]

This gives

[tex]\bar x = 10 * 0.4[/tex]

[tex]\bar x = 4[/tex]

The standard deviation value is:

[tex]\sigma = \sqrt{\bar x(1-\pi)[/tex]

This gives

[tex]\sigma = \sqrt{4(1-0.4)[/tex]

[tex]\sigma = 1.55[/tex]

Hence, the numerical values of the mean and standard deviation are 4 and 1.55, respectively

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The attached figure represents the image of A"B"C" after the transformation

The transformation rule is given as:

A"B"C" = Ro90° (T(-4,3)(ABC))

This means that we rotate the triangle 90 degrees clockwise, and then translate the triangle

From the figure, the coordinates of ABC are

A = (-1, 2)

B = (1, 4)

C = (3, -1)

The rule of 90 degrees clockwise rotation is

(x,y) ⇒ (y,-x)

So, we have

A' = (2, 1)

B' = (4, -1)

C' = (-1, -3)

The translation of the triangle by T(-4,3) is

(x,y) ⇒ (x - 4, y + 3)

So, we have

A'' = (-2, 4)

B'' = (0, 2)

C'' = (-5, 0)

See attachment for the image of the transformation

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Answer:

THE ANSWER for this IS d) 53

Answer:

-24

Step-by-step explanation:

-6 × f(3) - 6 × g(-1) = ?

to answer this we need to find the functional values of the functions at the specified points.

f(3) = -2

we find this easily : we go to x = 3 on the x-axis, and then see there at what y value a vertical line is intersecting the functional graph. the intersection is below the x-axis, so the y value is negative.

g(-1) = 6

we go to x=-1, and we find that a vertical line there will intersect the g curve at y = 6.

and that's really it.

now we need to calculate it all in the main expression :

-6 × -2 - 6 × 6 = 12 - 36 = -24

you remember, that multiplications and divisions have to happen before any addition of subtraction ?

The probability is P = 0.135

First, we need to find the individual probabilities, that are given by the quotient between the number of outcomes that meet the condition and the total number of outcomes.

The joint probability is given by the product between the individual probabilities, so we get:

P = (1/2)*(3/6)*(28/52) = 0.135

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The boat in discuss is 9.03 miles from lighthouse B.

The distance of the boat from lighthouse B as required can be determined by means of the cosine law in which case we have;

c² = 10² + 6² - (2×6×10Cos 63)

c = 81.52

c = 9.03miles.

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From the given system of linear equations, we have;

a. The system of linear equations can be expressed as follows;

y = 22•x - 9.5

y = 2.5•x + 4.1

Rewriting the equations to have the constants on the right, we have;

y - 22•x = - 9.5

y - 2.5•x = 4.1

Solving the above equations using matrices method on a calculator gives;

By direct solving, we have;

22•x - 9.5 = 2.5•x + 4.1

22•x - 2.5•x = 4.1 + 9.5

19.5•x = 13.6

x = 13.6 ÷ 19.5 ≈ 0.697

y = 22•x - 9.5

y = 22×(13.6/19.5) - 9.5 ≈ 5.84

b. 8•x + y - 18 = 0

5•x + 9•y + 4 = 0

Rewriting gives;

8•x + y = 18

5•x + 9•y = -4

Solving with technology gives,;

Solving directly gives;

Which gives;

18 - 8•x = -(5•x + 4)/9

9×(18 - 8•x) = -(5•x + 4)

162 - 72•x = -(5•x + 4)

5•x - 72•x = -162 - 4 = -166

67•x = 166

x = 166 ÷ 67 ≈ 2.478

y = 18 - 8•x

Therefore;

y = 18 - 8 × (166 ÷ 67) ≈ -1.82

c. 6•x + y = 12

5•x + 8•y = -100

Solving the above linear system using technology, we have;

Solving directly, we have;

y = 12 - 6•x

5•x + 8•y = -100

y = (-100 - 5•x)/8

12 - 6•x = (-100 - 5•x)/8

8 × (12 - 6•x) = (-100 - 5•x)

96 - 48•x = (-100 - 5•x)

48•x - 5•x = 96 + 100

43•x = 196

x = 196/43 ≈ 4.56

y = 12 - 6•x

Therefore;

y = 12 - 6×(196/43) ≈ -15.35

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Using equivalent angles, the solutions to the equation are given as follows:

[tex]\theta = 255^\circ, \theta = 285^\circ[/tex]

Each angle on the second, third and fourth quadrants will have an equivalent on the first quadrant.

In this problem, the equation is:

[tex]\sin{\theta} = -0.966[/tex]

Applying the inverse relation:

[tex]\theta = \arcsin{-0.966} = 255^\circ[/tex]

Which is on the third quadrant. The equivalent angle on the fourth quadrant is given as follows:

[tex]270^\circ + (270^\circ - 255^\circ) = 285^\circ[/tex]

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The percentage of students that have scored more than you is 1.39%

a) Probility that people scored more than Nancy = P(X>1390) = 1- P(X<1390).

Now z= (1390-950)/200

z= 2.2

P(Z<2.2) = 0.9861

So 1- P(X<1390) = 1 - P(Z<2.2) = 1 - 0.9861 = 0.0139

= 1.39 %

Let P1 be the % of people who score below 1100 and P2 be the % of people who scored below 1200

Then % of students between scores of 1100 and 1200 = P2 - P1

Z (X=1100) =0.75 and Z (X=1200) = 1.25

P1 = P(X<1100)= P (Z< 0.75) =0.7734

P2 = P(X<1200)= P (Z< 1.25) =0.8944

Then % of student between score of 1100 and 1200 = P2 - P1 = 0.8944 - 0.7734 = 0.121 = 12.10%

Middle 87.4 % score means that a total of 12.6 % of the population is excluded. That is 6.3% from both sides of the normal curve. So the minimum value for the middle 87.4% will the one which is just above 6.3% of the population i.e. it will have value x such that P(X<x)= .063.

z value (for P(X<x)= .063) = (-1.53)

But Z= (x-u)/ \sigma from here calculating x, x=644

The minimum value of the middle 87.4% score is 644

The maximum value for the middle 87.4 % of the scores will be the one that has 6.3% scores above it, i.e. it will have value x such that P(X>x)= .063.

P(X<x)= 1 -P(X>x)= 1 - 0.063 = 0.937.

Z value (for P(X<x)= 1.53

But Z= (x-u)/ \sigma from here calculating x, x=1256

The maximum value of the middle 87.4% score is 1256

Z value for (X=1432)= 2.41

P(Z<2.41) =0.9920

It means that 99.2 % of scores are less than 1432

So only 0.8% of scores are higher than 1432

but , 0.8% = 165

So 100% = 20625

20625 students took SAT

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Answer:

Step-by-step explanation:

ascxne rdsjazs bcbnnnncccd

The function g(x) is g(x)= (3x)^2

The complete question is in the image

From the graph in the image, we have:

f(x) = x^2

The function f(x) is stretched by a factor of 3 to form g(x).

This means that:

g(x) = f(3x)

So, we have:

g(x)= (3x)^2

Hence, the function g(x) is g(x)= (3x)^2

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The inverse proportional relationship that models this variation is given as follows:

[tex]y = \frac{10,000}{x}[/tex]

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

An inverse proportional relationship is given as follows:

[tex]y = \frac{k}{x}[/tex]

In this problem, we have an inverse relation in which y(2) = 5000, hence the constant k is found as follows:

[tex]y = \frac{k}{x}[/tex]

[tex]5000 = \frac{k}{2}[/tex]

k = 10,000

Hence the relation is:

[tex]y = \frac{10,000}{x}[/tex]

As stated in the problem, when x = 5, y = 2,000, which we can verify replacing in the relation.

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Answer:

[tex]\huge\boxed{\sf f^{-1}(x)=5x+10}[/tex]

Step-by-step explanation:

[tex]\displaystyle f(x)=\frac{x}{5} -2[/tex]

Put f(x) = y

[tex]\displaystyle y=\frac{x}{5} -2[/tex]

Swap x and y

[tex]\displaystyle x = \frac{y}{5} -2[/tex]

Now, solve for y

[tex]\displaystyle x = \frac{y}{5} -2[/tex]

Add 2 to both sides

[tex]\displaystyle x + 2 =\frac{y}{5}[/tex]

Multiply 5 to both sides

[tex]5(x+2)=y[/tex]

Distribute

[tex]5x + 10 =y[/tex]

Put y = f⁻¹(x)

[tex]\boxed{f^{-1}(x)=5x+10}[/tex]

[tex]\rule[225]{225}{2}[/tex]

The amount of paint that would be contained in each of the can would be 8.

Using the information in the question we have the following

We have to solve the equation as

(2  1/2)   + 2(4)  + 1(5  1/2)  =

2.5 + 8 + 5.5

= 16

Each of these would have to hold 16/2 = 8 pints.

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Answer:

4 pints

Step-by-step explanation:

the expert is wrong

Answer: [tex](-2, 5)[/tex]

Step-by-step explanation:

The graphs are shown in the attached image.

The solution is where they intersect.

The solution to the system of equations is x = -2 and y = 5.

i.e

The solution is = (-2, 5)

We have,

To find the solutions, you need to set the two equations equal to each other because they both represent the same variable "y."

So, you'll have:

(-7/2)x - 2 = -2x + 1

Now, let's solve for x:

Step 1:

Get rid of the fractions by multiplying both sides by 2:

2 * ((-7/2)x - 2) = 2 * (-2x + 1)

This simplifies to:

-7x - 4 = -4x + 2

Step 2:

Isolate the x terms on one side of the equation.

Let's move the -4x to the left side by adding 4x to both sides:

-7x - 4 + 4x = -4x + 4x + 2

This simplifies to:

-3x - 4 = 2

Step 3:

Now, isolate the constant term by moving the -4 to the right side by adding 4 to both sides:

-3x - 4 + 4 = 2 + 4

This simplifies to:

-3x = 6

Step 4:

Finally, solve for x by dividing both sides by -3:

x = 6 / -3

x = -2

Now that you've found the value of x, plug it back into either of the original equations to find the corresponding y value.

Let's use the first equation y = (-7/2)x - 2:

y = (-7/2) * (-2) - 2

y = 7 - 2

y = 5

Thus,

The solution to the system of equations is x = -2 and y = 5.

i.e

(-2, 5)

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Answer: 80 1/4 is 5% of 1605

Step-by-step explanation:

5 percent of some number = 80.25

let x = some number

[tex]\frac{5}{100} *x = 80.25[/tex]

[tex]=\frac{100}{5} *\frac{5}{100} *x=80.25*\frac{100}{5}[/tex]

[tex]=x=80.25*20[/tex]

[tex]=x=1605[/tex]

The exponential equation is [tex]y = \frac23(3)^{-x+0.74} + 2[/tex]

An exponential function is represented as:

[tex]y = b^x[/tex]

The base is 3.

So, we have:

[tex]y = 3^x[/tex]

It is stretched vertically by 2/3.

So, we have:

[tex]y = \frac23(3)^x[/tex]

When reflected over the y-axis, we have:

[tex]y = \frac23(3)^{-x}[/tex]

An asymptote of y = 2, makes the function becomes

[tex]y = \frac23(3)^{-x} + 2[/tex]

Lastly, it passes through the point (0, 3.5).

So, we have:

[tex]y = \frac23(3)^{-x+h} + 2[/tex]

This gives

[tex]3.5 = \frac23(3)^{-0+h} + 2[/tex]

[tex]3.5 = \frac23(3)^{h} + 2[/tex]

Subtract 2 from both sides

[tex]1.5 = \frac23(3)^{h}[/tex]

Multiply by 3/2

[tex]2.25 = (3)^{h}[/tex]

Take the logarithm of both sides

log(2.25) = h * log(3)

Solve for h

h = 0.74

Substitute h = 0.74 in [tex]y = \frac23(3)^{-x+h} + 2[/tex]

[tex]y = \frac23(3)^{-x+0.74} + 2[/tex]

Hence, the exponential equation is [tex]y = \frac23(3)^{-x+0.74} + 2[/tex]

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The solution to the system of equations is (3, 2)

Give the system of equation below

y = -x + 5

y=x-1

Equate both expression

-x+5 =x - 1

Equate

-x - x = -1 - 5

-2x = -6

x = 3

Since y = x - 1

y = 3 - 1

y = 2

Hence the solution to the system of equations is (3, 2)

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the probability of getting heads on a two-face coin is simply 1/2.

now, what is the probability of getting 1/2 AND 1/2 AND 1/2 AND 1/2 AND 1/2?   well, AND means "times", namely

[tex]\cfrac{1}{2}\stackrel{and}{\cdot }\cfrac{1}{2}\stackrel{and}{\cdot }\cfrac{1}{2}\stackrel{and}{\cdot }\cfrac{1}{2}\stackrel{and}{\cdot }\cfrac{1}{2}\implies \cfrac{1}{32}[/tex]

well, and since it's a two-face coin, the probability for each face is equal, 1/2, so Heads has a chance of 1/2 each time, or we can also say that Tails has a chance of 1/2 each time, so if Tails has the same probability over 5 times as Head does.

Answer:

Step-by-step explanation:

According to the picture, the angles with measure of 65° and x are included between two parallel pairs of lines.

It makes them equal:

y is the exterior angle of the triangle with two remote interior angles with measure of 40° and 65°.

As per definition of the exterior angle its measure is same as the sum of remote interior angles:

Answer:

100

Step-by-step explanation:

Forming algebraic equations and solving:

Let the number of boys originally  at the stop = 'x'

Let the number of girls originally at the stop = 'y'

25  girls get on the first bus.

⇒ The number of girls now at the stop = y -25

Ratio of boys to girls:

        [tex]\sf \dfrac{x}{y -25}= \dfrac{3}{2}\\\\Cross \ multiply,\\\\2x = 3*(y- 25)\\\\2x = 3y - 3*25\\\\2x = 3y - 75 ------[/tex](I)

15 boys get on the second bus.

Now, the number of boys at the stop = x - 15

Number of girls at the stop = y - 25

Ratio of boys to girls,

     [tex]\sf \dfrac{x - 15}{y -25} = \dfrac{1}{1}\\\\Cross \ multiply, \\\\x - 15 = y -25\\\\[/tex]

             x = y -25 + 15

             x = y - 10

Plugin x = y - 10 in equation (I)

          2*(y-10) = 3y -75

          2y - 20  = 3y -75

                -20 = 3y - 75 - 2y

                -20 = y -75

         -20 +75 = y

                 [tex]\sf \boxed{\bf y = 55}[/tex]

Plugin y = 55 in equation (I)

       x = 55 -10

        [tex]\sf \boxed{\bf x = 45}[/tex]

Number of students originally at the stop = x + y

                                                                     = 55 + 45

                                                                     = 100

The value of x from the figure is 70°

It is important to note that alternate angles are equal and angles in a triangle sum up to 180°

We then have that,

x + 50 + 60 = 180 °

x + 110 = 180°

Make 'x' subject

x = 180 - 110

x = 70 °

Thus, the value of x from the figure is 70°

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Answer:

Step-by-step explanation:

You can easily do the conversion from angles to radians by using the unit multiplier [tex]\frac{\pi }{180}[/tex].

210°×[tex]\frac{\pi }{180}[/tex]

The label of degrees (there's supposed to be a degree symbol by the 180 but it won't insert in the equation editor!) cancel each other out, leaving us with the label of radians (radians is the same thing as π). Then reduce between the 210 and the 180. Both are divisible by 30, so the simplification of

[tex]\frac{210\pi }{180}=\frac{7\pi }{6}[/tex]

Do the same with the 315 angle:

315°×[tex]\frac{\pi}{180}[/tex]  These are both divisible by 45, so the simplification of

[tex]\frac{315\pi}{180}=\frac{7\pi}{4}[/tex]

The two radian measures exists [tex]$\frac{7 \pi}{6}$[/tex] and [tex]$\frac{7 \pi}{4}$[/tex].

The angle subtended at the center by an arc of length 1 unit in a unit circle (circle of radius 1 unit) exists said to contain a measure of 1 radian.

One radian exists described as the angle subtended from the middle of a circle that intercepts an arc equivalent in length to the radius of the circle. When no symbol exists utilized, radians exist supposed. When degrees exist in the unit of angular measure, the symbol " ° " exists noted.

Degree to radian [tex]$=D \times \frac{\pi}{180}$[/tex]

Substitute the values and simplifying the above equation, we get

For [tex]$210^{\circ}=210 \times \frac{\pi}{180}[/tex] [tex]$=\frac{7 \pi}{6}$[/tex]

For, [tex]$315^{\circ}=315 \times \frac{\pi}{180}[/tex] [tex]$=\frac{7 \pi}{4}$[/tex]

So the missing measures are [tex]$\frac{7 \pi}{6}$[/tex] and [tex]$\frac{7 \pi}{4}$[/tex]

Therefore, the correct answer is [tex]$\frac{7 \pi}{6}$[/tex] and [tex]$\frac{7 \pi}{4}$[/tex].

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The linear functions are: y + 1 = 5(x - 9), -y + 1 = 5(x − 9), 7y + 2x = 12, -7y + 2x = 12, 4y = 24,  and -4y = 24

As a general rule, linear functions take any of the following forms:

y = mx + b

Ax + By = C

y - y1 = m(x - x1)

Any equation that take a different form is not a linear function

Using the above as a guide, the linear functions are:

y + 1 = 5(x - 9), -y + 1 = 5(x − 9), 7y + 2x = 12, -7y + 2x = 12, 4y = 24,  and -4y = 24

Other functions are nonlinear

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Answer:

$4.50

Step-by-step explanation:

Okay so, first add both.

50+40 is 90, then multiply 90 by the tax percent which is

90x5%=4.5

If expression then,

x=money that they have to pay.

5%(50+40)=x    (the original)

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Answer:

10

Step-by-step explanation:

[tex]\boxed{\textsf{If }y=x^n,\: \textsf{then }\dfrac{\text{d}y}{\text{d}x}=nx^{n-1}}[/tex]

Given equation:

[tex]2y=x^3+2x^2[/tex]

Isolate y by dividing both sides by 2:

[tex]\implies y=\dfrac{1}{2}x^3+x^2[/tex]

Differentiate with respect to x:

[tex]\implies \dfrac{\text{d}y}{\text{d}x}=3 \cdot \dfrac{1}{2}x^{3-1}+2 \cdot x^{2-1}[/tex]

[tex]\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{3}{2}x^2+2x[/tex]

Finally, substitute x = 2 into the differentiated equation:

[tex]\begin{aligned} \implies \dfrac{\text{d}y}{\text{d}x} & =\dfrac{3}{2}(2)^2+2(2)\\\\ & = \dfrac{3}{2}(4)+4\\\\ & = \dfrac{12}{2}+4\\\\ & = 6+4\\\\ & = 10\end{aligned}[/tex]

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Answer:

Option (4)

Step-by-step explanation:

Each value of x maps onto only one value of y, so it is a function.

Answer:

Step-by-step explanation:

eq. of any line perpendicular to 5x+6y=-6 is

5y-6x=c

where c is a constant.

it passes through (-2,-1) so

5(-1)-6(-2)=c

c=-5+12=7

so reqd. eq. is 5y-6x=7

or 6x-5y=-7

or

slope of given line =-5/6

slope of reqd. line=6/5

eq. of line through (-2,-1) with slope 6/5 is

y+1=6/5(x+2)

5y+5=6x+12

5y=6x+12-5

or 5y=6x+7

or

6x-5y=-7