Find the length of side DF

The probability of having, at most, 9 girls, is 0.9515

The probability that a random baby is a girl is:

p = 0.5

And the probability that a random baby is a boy is:

q = 0.5

Then the probability that, at most, 9 out of 11 babys are girls, is given by:

1 - p(10) - p(11)

Where P(10) is the probability that 10 of the babies are girls and p(11) is the probability that the 11 babies are girls.

p(10) = C(11, 10)*(0.5)^10*(0.5)^1 = C(11, 9)*(0.5)^11

Where C(11, 10) is the combinations of 10 elements that we can make with a set of 11 elements, such that:

C(11, 10)=  11!/(11 - 10)!*10! = 11

Replacing that, we get:

P = 11*(0.5)^11 = 0.0054

p(11) = C(11, 11)*0.5^11 = 1*0.5^11 = 0.0005

Then the probability is:

P = 1 - 0.0054 - 0.0005 = 0.9515

The probability of having, at most, 9 girls, is 0.9515

If you want to learn more about probability:

https://brainly.com/question/25870256

#SPJ1

The green mathematics tells about the impulse response of an in homogeneous linear differential operator.

According to the statement

we have to explain the green mathematics.

In mathematics, Actually there is a Green Function which was founded by a mathematician George Green.

In this function, a Green's function is the impulse response of an in homogeneous linear differential operator defined on a domain with specified initial conditions or boundary conditions.

The example of green function is the Green's function G is the solution of the equation LG = δ, where δ is Dirac's delta function; the solution of the initial-value problem Ly = f is the convolution (G ⁎ f), where G is the Green's function.

Actually in this function, it gives the relationship between the line integral of two dimensional vector over a closed path by a integral.

In this there is a green theorem, which  relates a line integral around a simply closed plane curve C and a double integral over the region enclosed by C.

So, The green mathematics tells about the impulse response of an in homogeneous linear differential operator.

Learn  more about FUNCTION here https://brainly.com/question/2328150

#SPJ1

Answer: 13.6

Step-by-step explanation: Use a theorem which exists s. then you use pythagoreom

The length of the segment indicated is 13.6

From the question, we have the following parameters that can be used in our computation:

The circle

Assuming that lines which appear to be tangent are tangent, we have

?² = (2 * 6)² + 6.4²

Evaluate

?² = 184.96

So, we have

? = 13.6

Hence, the length of the segment indicated is 13.6

Read mroe about circle at

https://brainly.com/question/32192505

#SPJ6

Considering the critical points of the function, we have that:

The critical points of a function are the values of x for which:

[tex]f^{\prime}(x) = 0[/tex]

In this problem, the function is:

[tex]f(x) = 3x^3 - 16x + 2[/tex]

The derivative is:

[tex]f^{\prime}{x} = 6x^2 - 16[/tex]

The critical points are given as follows:

[tex]6x^2 - 16 = 0[/tex]

[tex]x^2 = \frac{16}{6}[/tex]

[tex]x = \pm \sqrt{\frac{16}{6}}[/tex]

[tex]x = \pm 1.63[/tex]

For x < -1.63, one example of the derivative is:

[tex]f^{\prime}{-2} = 6(-2)^2 - 16 = 8[/tex]

Positive, hence increasing.

For -1.63 < x < 1.63, one example of the derivative is:

[tex]f^{\prime}{0} = 6(0)^2 - 16 = -16[/tex]

Negative, hence decreasing.

For x > 1.63, one example of the derivative is:

[tex]f^{\prime}{2} = 6(2)^2 - 16 = 8[/tex]

Positive, hence increasing.

Hence:

More can be learned about critical points at https://brainly.com/question/2256078

#SPJ1

1) Quadrilateral PAST, TX=AX, [tex]\overline{TP} \parallel\overline{AS}[/tex] (given)

2) [tex]\angle XPT \cong \angle XSA[/tex] and [tex]\angle XTP \cong \angle XAS[/tex] (alternate interior angles theorem)

3) [tex]\triangle TXP \cong \triangle AXS[/tex] (AAS)

4) [tex]\overline{TP} \cong \overline{AS}[/tex] (CPCTC)

5) PAST is a parallelogram (a quadrilateral with two pairs of opposite congruent sides is a parallelogram)

(Adding to the other person's answer)

For the 5th step reason, put this: A quadrilateral is a parallelogram if a pair of opposite sides are parallel and congruent.

It won't work to just say something like the def. of parallelograms.

All the relevant transformations are as shown in the explanations below.

We are given the original function as y = x and told the transformation is as follows;

1) y = x + 5; This means that the function was shifted 5 units to the left.

2) y = ³/₈x; This means that the function was vertically stretched by a scale factor of  ³/₈.

3) y = -x - 2 or y = -(x + 2); This means that the function was first shifted by 2 units to the left before being reflected over the x-axis.

4) y = 6x + 1; This means that the function was stretched by a factor of 6 and then shifted 1  unit to the left.

5) y = x - 11; This means that the function was shifted 11 units to the right.

6) y = 8x; This means that the function was vertically stretched by a scale factor of  8.

7) y = -1/3x; This means that the function was horizontally stretched by a scale factor of  1/3.

Read more about Transformations at; https://brainly.com/question/4289712

#SPJ1

Answer: No

Step-by-step explanation:

There is only one pair of congruent angles that can be determined, but to prove triangles similar, there needs to be two pairs of congruent angles.

Answer:

[tex]6x^{2} -24x-10[/tex] with remainder -5

Answer:

[tex]6^2-24x-10-\frac{5}{x+4}[/tex]

In other words, [tex]6x^2-24x-10[/tex] is the answer and -5 is the remainder

Step-by-step explanation:

I used long division for this, and I uploaded an image for the steps. The final answer I got was [tex]6x^2-24x-10-\frac{5}{x+4}[/tex]

[tex] \sqrt{5612} = \frac{5612 + 5625}{2 \sqrt{5625} } = \frac{11237}{2 \times 75} = 74.913333[/tex]

The new mean and standard deviation is 26 and 15, when each score in data set is multiplied by 5 and then 7 is added.

According to the question,

Original mean is 10 and original standard deviation is 5 . In order to find to new mean and standard deviation when each score in data set is multiplied by 5 and then 7 is added.

First "change of scale" when every score in a data set is multiplied by a constant, its mean and standard deviation is multiplied by a same constant.

Mean: 10*3 = 30

Standard deviation: 5*3 = 15

Secondly "change of origin" when every score in a data set by a constant, its mean get  added or subtracted by the same constant and standard deviation remains constant.

Applying change of origin in the above mean and standard deviation  

Mean: 30 - 4 = 26

Standard deviation: Remains same = 15

Hence, the new mean and standard deviation is 26 and 15, when each score in data set is multiplied by 5 and then 7 is added.

Learn more about Mean and standard deviation here

https://brainly.com/question/26841432

#SPJ4

The equation of the unique function exists g(x) = -4(x-3)².

The polynomial of degree two exists named a quadratic polynomial and the equation corresponding to a quadratic polynomial P(x) exists named a quadratic equation.

Given: F(x) = x²

The vertical stretch by a factor of 4 exists can be satisfied by (b)

if we use a vertical stretch, it transforms the y-values which causes it to seem skinnier when graphed.

Multiply 4 by f(x) which provides 4x².

As the reflection over the x-axis, so multiply it by -1 to f(x), which results in -4x².

Shift the graph right 3 which exists by moving it right, so by adjusting the x values indicating use f(x-3), to obtain this subtract the value from x when you move right, and add the value to x when you move left.

Hence, the unique graph would be g(x) = -4(x-3)²

Therefore, the correct answer is option B. g(x) = -4(x-3)².

To learn more about  equations refer to:

https://brainly.com/question/2273184

#SPJ9

Answer:

B. (5,12,13)

Step-by-step explanation:

The only answer with two side lengths that are greater than the largest side length.

Answer:

Step-by-step explanation:

We will assume that the first two columns are the numbers sold for Plain Wrapping and Decorative Wrapping.  The third colum does not equal the sum of the first two, so we'll assume it is the total paid for both options.  Let set the price of Plain Wrapping to x and the Decorative Wrapping to y.  The number of gift wrappings times the cost per warpping is the product of x or y timers the number wrapped as shown in columns 1 and 2.

Take the first row and set it as an equation:

10x+9y = 47   [10 Plain Wraps and 9 Decorative Wraps bring a total of $47]

Do the same for the second and third rows:

25x + 12y = 86, and

16x +12y =  68

===========

We can take any equation and rearrange it to isolate one of the 2 variables, x or y.  I'll pick 10x = 47-9y and isolate x:

10x = 47-9y

x = (47-9y)/10

-------------------

Now use this definition of x in another equation.  I'll use 25x + 12y = 86.

25x + 12y = 86

25(47-9y)/10 + 12y = 86     [since x = (47-9y)/10 from above]

117.5 - 22.5y + 12y = 86

-10.5y = -31.5

y = 3                                     [the price for decorative wrapping is $3]

If y = 3, then we can use this in any of the equations to find x:

x = (47-9y)/10

x = (47-9(3))/10     [Use y = 3]

x = (47-27)/10

x = 2                              [The price for plain wrapping is $3]

======================

Check to see if these values will expalin the total value of the three rows of numbers:

CHECK:

______UNITS____         $2 each          $3 each

PlainW DecG Total      PlainW ($)      DecG ($)      Total ($)

   x           y                          x                       y

   10         9        $47          $20                    $27              $ 47         OK

   25        12       $86          $50                    $36              $ 86         OK

   16        12       $68          $32                    $36              $ 68         OK

The values work.  Merry Christmas.

Answer:

The team charged $2 to wrap a gift with no bow and $3 to wrap a gift with a bow.

Step-by-step explanation:

just did it in edg

3.60

t = r√n − 2/1 − √r2

= 0.6√25 − 2/√1 − 0.62

= 3.5969 t or about 3.60 rounded to two decimal places.

Hypothesis Testing:

Hypothesis testing is a form of statistical inference that uses data from a sample to draw conclusions about a population parameter or a population probability distribution. First, a tentative assumption is made about the parameter or distribution. This assumption is called the null hypothesis and is denoted by H0.

Learn more about Hypothesis Testing on:

https://brainly.com/question/4232174

#SPJ4

Answer:

51 liters.

Step-by-step explanation:

By proportion  number of litres for 1428 miles

=  17 * 1428/476

= 17 * 3

= 51 liters.

Answer:

we spend maths class in a. day =85m

.:we spend in a maths class in a 9 week period=85x9x7:- 24=223.125

Using translation concepts, the graph that represents a reflection across the x-axis of [tex]g(x) = \frac{3}{4}(3)^x[/tex] is:

On a coordinate plane, an exponential function approaches y = 0 in quadrant 4. The function comes up from quadrant 3 and increases into quadrant 4. It goes through (negative 2, negative 5), (0, negative 3), and (4, negative 1).

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

A reflection across the x-axis of g(x) means that:

f(x) = -g(x).

g(x) increases from the second quadrant into the first, hence for f(x) it will be from quadrant 3 into quadrant 4.

More can be learned about translation concepts at https://brainly.com/question/4521517

#SPJ1

Answer:

Option B

Step-by-step explanation:

Edge 2022

The area of the circle is 78.5 unit square.

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point.

The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the centre.

The formula for area of circle is;

Area = [tex]\pi[/tex](radius)²

The distance between the two points are calculated by distance formula.

[tex]\begin{aligned}&d=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}} \\&d=\text { distance } \\&\left(x_{1}, y_{1}\right)=\text { coordinates of the first point } \\&\left(x_{2}, y_{2}\right)=\text { coordinates of the second point }\end{aligned}[/tex]

Calculation for the area of the circle;

As, the radius of the circle is xy.

The distance between x and y points will be calculated by the distance formula.

x=(0,3)  y=(-3,-1)

[tex]\begin{aligned}&d=\sqrt{\left(-3-0\right)^{2}+\left(-1-3\right)^{2}} \\\end{aligned}[/tex]

[tex]\begin{aligned}&d=\sqrt{\left(-3\right)^{2}+\left(-4\right)^{2}} \\\end{aligned}[/tex]

[tex]\begin{aligned}&d=\sqrt{25} \\\end{aligned}[/tex]

[tex]d=5[/tex]

As, distance between x and y point is 5 units which is the radius of the circle.

Area of circle = [tex]\pi[/tex](radius)²

                      = 3.14×(5)²

                      = 78.5

Therefore, the area of the circle is 78.5 unit square.

To know about the properties of circle, here

https://brainly.com/question/4244936

#SPJ4

Answer:

24.4

Step-by-step explanation:

Answer:

  (c)  f(x) = 3(x -3)(x -7)

Step-by-step explanation:

The correct function can be chosen by looking at the x-intercepts and the behavior around the vertex.

The graph crosses the x-axis at x=3 and x=7. Each x-intercept x=p gives rise to a factor (x -p). These two x-intercepts mean the function will have factors ...

  (x -3)(x -7) . . . . . . . . eliminates choices A and D

The vertical scale factor of the quadratic is easily found by looking at the function behavior near the vertex. Specifically, the scale factor is the change in y-value at a distance of 1 unit either side of the vertex.

Here, the y-value at the vertex (x=5) is -12. The y-value at x=4 and x=6 is -9, three units up from the value at the vertex. This means the vertical scale factor (leading coefficient) is 3. (This eliminates choice B.)

Putting these observations together, we have determined the equation of the function to be ...

  f(x) = 3(x -3)(x -7) . . . . . . matches choice C

Answer:

{x  = -1 + √13  ,  x  = -1 - √13}

Step-by-step explanation:

Completing the square:

f(x) = x² + 2x - 12

     = x² + 2x + 1 - 1 - 12

     = (x² + 2x + 1) - 1 - 12

     = (x + 1)² - 13

Solving:

f(x) = 0

⇔ (x + 1)² - 13 = 0

⇔ (x + 1)² = 13

⇔ x + 1 = √13  or  x + 1 = -√13

⇔ x  = -1 + √13  or  x  = -1 - √13

Answer:

Step-by-step explanation:

rounded to the nearest cent his answer would be $212.24

Answer: D

Step-by-step explanation:

The function that describes the graph is an exponential function

From the graph, we have the following highlights:

The above is the description of an exponential function

Hence, the function that describes the graph is an exponential function

Read more about exponential function at:

https://brainly.com/question/11464095

#SPJ1

Step-by-step explanation:

12 inches

djaikfnshaidifb

The factored form of the equation are as follows;

Converting a quadratic function to factored form is called factoring.

Therefore,

let's factor the equation,

a.

d² - 7d + 6 = 0

d² - d - 6d + 6 = 0

d(d - 1) - 6(d - 1) = 0

(d - 6)(d - 1) = 0

b.

x² + 18x + 81 = 0

x² + 9x + 9x + 81 = 0

x(x + 9) + 9(x + 9) = 0

(x + 9)(x + 9) = 0

c.

u² + 7u - 60 = 0

u² - 5u + 12u - 60 = 0

u(u - 5) 12(u - 5) = 0

(u + 12)(u - 5) = 0

learn more on equation here: https://brainly.com/question/12055751

#SPJ1

First transformation.

Duadrilateral ABCD has vertices with such coordinates:

A(15,10);

B(15,20);

C(20,15);

D(20,5).

Apply a rotation by 90°counterclockwise around point A to this quadrilateral, then

A(15,10)→A'(15,10);

B(15,20)→B'(5,10);

C(20,15)→C'(10,15);

D(20,5)→D'(20,15).

Second transformation.

1. A reflection across the y axis has a rule:

(x,y)→(-x,y).

Then

A'(15,10)→A''(-15,10);

B'(5,10)→B''(-5,10);

C'(10,15)→C''(-10,15);

D'(20,15)→D''(-20,15).

2. A translation 20 units down has a rule:

(x,y)→(x,y-20).

Then

A''(-15,10)→G(-15,-10);

B''(-5,10)→H(-5,-10);

C''(-10,15)→I(-10,-5);

D''(-20,15)→J(-20,-5).

Answer: first blank -B, second blank - B.

Answer:

Step-by-step explanation:

Answer:

153

Step-by-step explanation:

i = square root of -1

i = √-1

(3+12√-1) (3-12√-1)

√a times √b = √ab

a√b times c√d = (a times c) √ (b times d)

9 - (36√-1) + (36√-1) - (144(√-1)^2) =

9 - 0 - (144 * -1) =

9 - 0 - (-144) =

9 - (-144) =

9 + 144 =

153

*** funny thing is if you put

(3+12i) (3-12i)  

in a calculator

it works!

it gives you the answer 153

another way:

Expand the expression using

(a-b) (a+b) =

a²-b² :

3²-(12i)²

Simplify using exponent rule with same exponent

(a*b)^n =

a^n*b^n:

3²-12²* i²

Calculate the power:

9-144* i²

Rewrite by definition

i²=-1:

9–144×(−1)

Calculate the product or quotient: 9+144

Calculate the sum or difference: 153

Answer: 153

gathmath