A couple is planning to have 3 children. Assuming that having a boy and having a girl are equally likely, and that the gender of one child has no influence on (or, is independent of) the gender of another, what is the probability that the couple will have exactly 2 girls? The "random experiment" in this case is having 3 children, as odd as that may sound in this context. The next and most important step is to determine what all of the possible outcomes are, and list them (i.e., list the sample space S). In this case, each outcome represents a possible combination of genders of 3 children (note that examples with the same number of boys and girls but a different birth order must be listed separately).

Answer:

  550 mm^2

Step-by-step explanation:

A net can be drawn as shown in the first figure attached. Each square represents 5 mm by 5 mm, so is 25 mm^2. Altogether, there are 22 of them, so the total area is ...

  (25 mm^2)·22 = 550 mm^2

The second attachment shows that net folded up to make the given figure.

_____

In the first attachment, the green shades represent the left- and right-side faces. (Darker green is left side.) The red and blue shades represent the front- and back-side faces. The white rectangles represent the top and bottom faces. The dark black lines are the cut lines. If you want to fold the figure up, the lighter lines are the fold lines.

The second attachment is just verification that all faces are accounted for and the net actually corresponds to the given figure.

Answer:

y = 700 (0.969)^t

Step-by-step explanation:

Using the depreciation formula after a given period of time.

A = P (1- r/100)^n

Where, A is the initial value

P is the original value

r is the rate of depreciation and

n is the time taken in years

Therefore;

A will be the new mass of the sample after decay,y

P is the original mass of the sample before decay, 700 mg

r is the rate of decay each year, 3.1% and

n is the number of years, t

Hence;

y = 700 (1- 3.1/100)^t

y = 700 (96.9/100)^t

y = 100(0.969)^t

The relationship between the mass of the radioactive sample (y) and the number of years since the start of the study (t) can be represented by the exponential function y = 700 * (1 - 0.031) ^ t.

This is a problem related to exponential decay. In general, the formula for an exponential decay is given as Y = A * (1 - r) ^ t where 'A' represents the initial amount, 'r' is the rate of decay (as a decimal), and 't' is the time period.

For this problem, the initial amount of the radioactive substance is 700 milligrams (A = 700), the rate of decay is 3.1% per year (r = 0.031), and 't' is represented as the number of years since the start of the study.

Using these values, we can write the exponential function showing the relationship between the mass of the sample 'y' and the number of years 't' as follows:

y = 700 * (1 - 0.031) ^ t

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[tex]\ln(n+3)-\ln n=\ln\dfrac{n+3}n=\ln\left(1+\dfrac3n\right)[/tex]

We can show the sequence is bounded and monotonic.

Boundedness: [tex]1+\dfrac3n>1[/tex] for all [tex]n>0[/tex], so [tex]\ln\left(1+\dfrac3n\right)>\ln1=0[/tex] for all [tex]n>0[/tex].

Monotonicity: Consider the function

[tex]f(x)=\ln\left(1+\dfrac3x\right)[/tex]

which has derivative

[tex]f'(x)=\dfrac{1+\frac3x}{-\frac3{x^2}}=-\dfrac3{x^2+3x}[/tex]

which has negative sign for all [tex]x>0[/tex], and so [tex]f(x)[/tex] is strictly decreasing.

[tex]\ln(n+3)-\ln n[/tex] is bounded and monotonic, so the sequence converges.

As [tex]n\to\infty[/tex] we have [tex]\dfrac3n\to0[/tex], leaving us with the limit

[tex]\displaystyle\lim_{n\to\infty}(\ln(n+3)-\ln n)=\lim_{n\to\infty}\ln\left(1+\frac3n\right)=\ln\left(1+\lim_{n\to\infty}\frac3n\right)=\ln1=0[/tex]

The sequence an = ln(n + 3) - ln(n) converges with a limit of 0. This is determined by simplifying the expression and observing its behavior as n approaches infinity.

Firstly, the question pertains to the study of the convergence or divergence of a sequence. In this case, we're looking at the sequence an = ln(n + 3) - ln(n). Using logarithmic properties, this can be rewritten as ln((n+3)/n). As n approaches infinity, the sequence converges to the limit ln(1), which equals 0. Therefore, the sequence converges and its limit is 0.

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The scale factor of the lengths of two similar octagons with areas 4 m² and 9 m² is obtained by taking the square root of the ratio of their areas, yielding a scale factor of 1.5.

The subject of this question is Mathematics, particularly dealing with geometry and scale factors. For two similar shapes, the ratio of their areas is equal to the square of the scale factor of their lengths.

Given the areas of the two similar octagons as 4 m² and 9 m², we find the square root of the ratio of the areas to obtain the scale factor of the lengths. That is, √(9/4) = √2.25 = 1.5.

Therefore, the scale factor of the lengths of the two similar octagons is 1.5.

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The scale factor of the lengths of the two similar octagons is 1.5.

To find the scale factor of the lengths of two similar octagons, we can use the formula:

Scale factor = sqrt(Area2 / Area1)

Where Area1 is the area of the first octagon, and Area2 is the area of the second octagon.

Plugging in the given values, we get:

Scale factor = sqrt(9 m² / 4 m²) = sqrt(2.25) = 1.5

Therefore, the scale factor of the lengths of the two octagons is 1.5.

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Answer:

Step-by-step explanation:

2 meter is like 6.4 yards

so i would say B is the answer

Final answer:

The work done by the crane in lifting 50 Newtons over a distance of 2 meters is 100 Nm.

Explanation:

The work done by a crane can be calculated by multiplying the force applied by the distance over which the force is applied. In this case, the crane is lifting 50 Newtons over a distance of 2 meters. Therefore, the work done is:

Work = Force x Distance

Work = 50 N x 2 m = 100 Nm

So, the correct answer is 100 Nm.

Answer:

21.5

Step-by-step explanation:

x is the radius of the circle.

If we draw a line from the circle's center to either end of the horizontal line, that line will also be a radius, so it will have length x.  This forms a right triangle with side lengths 10 and 19 and hypotenuse x.

Using Pythagorean Theorem:

c² = a² + b²

x² = 10² + 19²

x² = 461

x ≈ 21.5

Check the picture below.

so is filled with those cubes, recall that a cube has all equal sides, in this case 1/3, so the volume of each cube is simply the product of length*width*height.

[tex]\bf \stackrel{\textit{volume of one cube}}{\cfrac{1}{3}\cdot \cfrac{1}{3}\cdot \cfrac{1}{3}\implies \cfrac{1}{27}}\qquad \qquad \stackrel{\textit{if there are \underline{x} cubes inside then their total volume is}}{\cfrac{1}{27}x~~~~=~~~~\stackrel{\textit{volume of prism}}{4}} \\\\\\ x=27\cdot 4\implies x=108[/tex]

Answer:

A = (16π -32) in²

P = (4π +8√2) in

Step-by-step explanation:

The area is that of a quarter-circle of radius 8 inches less half the area of a square with side length 8 inches. Two formulas are useful:

area of a circle = πr² . . . . .r = radius

area of a square = s² . . . . s = side length

Then your area is ...

A = (1/4)π(8 in)² - (1/2)(8 in)² = (64 in²)(π/4 -1/2)

A = (16π -32) in²

____

The applicable formulas for the side lengths of your figure are ...

arc BD = (1/4)(2πr) = π(r/2) = π(8 in)/2 = 4π in

segment BD = (8 in)√2

The perimeter is the sum of these lengths, so is ...

P = (4π +8√2) in

_____

Of course, you are very familiar with the fact that an isosceles right triangle with side lengths 1 has a hypotenuse of length √(1²+1²) = √2. Scaling the triangle by a factor of 8 inches means the segment AB will be 8√2 inches long.

Answer:

[tex]\dfrac{2\sqrt{15\pi}}{\pi}[/tex]

Step-by-step explanation:

[tex]\displaystyle\sqrt{\frac{60}{\pi}}=\sqrt{\frac{4\cdot 15\pi}{\pi^2}}=\frac{2}{\pi}\sqrt{15\pi}[/tex]

Answer:

24

Step-by-step explanation:

If you use Pascal's triangle, which I did, you will look at the 5th row of the triangle which contains the numbers 1, 4, 6, 4, 1

If we expand using a = 2x and b = -1, then the expansion looks like this:

[tex]1(2x)^4(-1)^0+4(2x)^3(-1)^1+6(2x)^2(-1)^2+4(2x)^1(-1)^3+1(2x)^0(-1)^4[/tex]

If you simplify all that down by multiplying, you'll get

[tex]16x^4-32x^3+24x^2-8x+1[/tex]

If you don't know how to use Pascal's triangle, you need to learn.  It's so very cool!

Answer:

Answer me please??!!

Step-by-step explanation:

Answer: [tex]x=-11[/tex]

Step-by-step explanation:

You can use the Method of substitution.

Substitute the equation [tex]y=3-\frac{1}{2}x[/tex] into the equation [tex]3x + 4y = 1[/tex] and then you must solve for the variable x:

[tex]3x + 4y = 1\\\\3x + 4(3-\frac{1}{2}x) = 1\\[/tex]

Apply Distributive property:

[tex]3x + 12-\frac{4}{2}x = 1\\3x+12-2x=1[/tex]

Subtract 12 from both sides of the equation and then add the like terms. Then you get:

[tex]3x+12-2x-12=1-12\\3x-2x=-11\\x=-11[/tex]

Answer:

A'(-2, -1), B'(0, 1), C'(-2, 0)

Step-by-step explanation:

When dilation is about the origin, the scale factor multiplies each individual coordinate.

  A' = (1/3)A = (-6/3, -3/3) = (-2, -1) . . . . for example

The rest is mental arithmetic, since all given coordinate values are divisible by 3.

Answer:

125,970

Step-by-step explanation:

Even if jury are assigned numbers, the order in which they are picked has no importance.  That means that it's a combination, not a permutation.

The formula to calculate possible combinations is:

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

Where n is the global population, and r is the number of selected items.

In our case, n = 20 and r = 12, so...

[tex]C(20,12) = \frac{20!}{(12! (20-12)!)} = 125970[/tex]

There are 125970 different ways to select 12 jury members out of 20 people.

there are 125970 different 12 person juries that can be chosen from a pool of 20 people.

The question is asking how to determine the number of different ways to choose a 12-person jury from a pool of 20 potential jurors. This type of problem is solved using the concept of combinations in mathematics, specifically the binomial coefficient formula which is given by the following:

C(n, k) = n! / (k!(n - k)!)

where:

n represents the total number of items (in this case, jurors).

k represents the number of items to choose (jurors to be selected for the jury).

n! means factorial of n, which is the product of all positive integers up to n.

In this scenario, n = 20 and k = 12. Therefore, the number of different 12 person juries that can be chosen is calculated as:

C(20, 12) = 20! / (12!(20 - 12)!)

Further calculation yields:

C(20, 12) = 20! / (12!8!) = 125970

Therefore, there are 125970 different 12 person juries that can be chosen from a pool of 20 people.

Answer:

Your Awnser would be 597,000

Step-by-step explanation:

Answer:

The actual answer for this question should be 200.

Step-by-step explanation:

Answer:

square; 60; 225.

Step-by-step explanation:

1) using the vectors rules to calculate the lengths of the sides AB; BC; CD and AD. When AB=BC=CD=AD it means, the shape is a square of rhombus.

2) using the vectors rules to calculate the lengths of the diagonales AC and BD. When AC=BD it means, the shape is a square.

3) The perimeter of the square ABCD is 15*4=60.

4) The area of the square ABCD is 15*15=225.

All the details are in the attached picture; answers are marked with colour.

Answer: 740 miles

Step-by-step explanation:

You know that [tex]\frac{3}{8}inches[/tex] on the map is actually 60 miles and the distance between these two cities is [tex]4\ \frac{5}{8}inches[/tex].

You can express this distance as a decimal number:

[tex](4+0.625)inches=4.625inches[/tex]

Therefore, let be "d" the distance in miles between these two cities.

Then, you get:

[tex]d=\frac{(4.625inches)(60miles)}{(\frac{3}{8}inches)}\\\\d=740miles[/tex]

She will take 6 weeks.

Answer:

She will take 6 weeks.

hope this helps

Answer:$76

Step-by-step explanation:

JEANS: (5x8)= 40

SHIRTS:(4x6)= 24

SHOES BUY ONE GET ONE FREE: (12x2 - 12)= 12

40 + 24 + 12 = 76

Answer:

6.9

Step-by-step explanation:

12 x 4 = x^2

48 = x^2

x = 6.9

Answer:

6.9

explanation:

I did the test.

hope this helps you!

:D

Answer:

106

Step-by-step explanation:

VPL=1/2VkP

VKP=148

VPL=74

JPV+VPL=180

JPV=106

The measurement of angle JPV from the considered situation is found as m∠JPV = 106°

The radius which touches the point where the tangent touches too on a specified circle, is perpendicular to the tangent (90 degrees angle with the tangent).

Referring to the image attached below, we're provided that:

m arcVKP = central angle arc VKP subtends = m∠VOP = 148°

The perpendicular from center O on the line VP (VP is a chord) bisects it, and therefore, the triangle ODP and ODV are congruent by SAS congruency [ side OD is common, the angle (the 90 degree) on either side of OD is of same measure, and VD and DP are of same measure due to OD bisecting VP).

Thus, we get:

[tex]m\angle POD = m\angle VOD[/tex]

But since we have:

m∠POD + m∠VOD  = m∠VOP = 148°

thus, m∠POD + m∠POD = 148°

or  m∠POD = 148°/2 = 74° = m∠VOD

Now, as sum of angles in a triangle is 180°, therefore, for triangle OPD, we get:

[tex]m\angle OPD + m\angle ODP + m\angle POD = 180^\circ\\x^\circ + 90^\circ + 74^\circ = 180^\circ\\x = 16[/tex]

Thus, we get the measurement of angle JPV as:

[tex]m\angle JPV = m\angle JPO + m\angle OPD\\ m\angle JPV = 90^\circ + x^\circ = (90 + 16)^\circ = 106^\circ[/tex]

Thus, the measurement of angle JPV from the considered situation is found as m∠JPV = 106°

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Answer:

The lines of symmetry are the diameters, any straight line passing through the origin and touching both ends of the circle.

Step-by-step explanation:

Without graphing, this is the equation of a circle with center at the origin,

(0, 0) and with a radius of 3 units. The general equation of a circle with center (a, b) and with radius r units is given as;

[tex](x-a)^{2}+(y-b)^{2}=r^{2}[/tex]  

The graph of the function is as shown in the attachment below;

A line of symmetry cuts the graph of a function into two equal parts such that these parts become mirror images of each other.

For the case of a circle, the line that divides the circle into two equal portions is the diameter. Any given circle has infinite number of diameters.

Therefore, the lines of symmetry are the diameters, any straight line passing through the origin and touching both ends of the circle.

ANSWER

[tex]Area = 2\sqrt{3} \: {cm}^{2} [/tex]

EXPLANATION

We need to use the Pythagoras Theorem to find the height of the triangle.

[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]

[tex] ({2 \sqrt{3}) }^{2} + {b}^{2} = {4}^{2} [/tex]

[tex]12 + {b}^{2} = 16[/tex]

[tex] {b}^{2} = 16 - 12[/tex]

[tex]{b}^{2} = 4[/tex]

Take positive square root to get;

[tex]b = \sqrt{4} = 2[/tex]

Area =½bh

[tex]Area = \frac{1}{2} \times 2\sqrt{3} \times 2[/tex]

[tex]Area = 2\sqrt{3} \: {cm}^{2} [/tex]

Answer:

[tex]f^{-1} (x)=-\frac{1}{6}x+1[/tex]

Step-by-step explanation:

To find the inverse of a function in equation form, first I recommend changing the f(x) to a y:

y = -6x + 6

Next step is to switch the x and y:

x = -6y + 6

Now solve for the new y:

x - 6 = -6y and

[tex]-\frac{1}{6}x + 1=y[/tex]

You can put the inverse notation back in for y like I did in the answer section above.

3) For Zach, if his heart beats 15 times in 10 seconds, his heart beats 1.5 times in 1 second. Multiply this by 25 to get the number of times his heart will beat in 25 seconds → 1.5 * 25 = 27.5 times per 25 seconds. 1.5 * 60 = 90 times per minute. 1.5 * 120 = 180 times per two minutes. Do the same for your heart beats. 14 beats per 10 seconds is 1.4 beats per second. 1.4 * 25 = 35 times per 25 seconds. 1.4 * 60 = 84 times a minute. 1.4 * 120 = 168 times per two minutes.

4) Zach's equation would be H = 1.5n and yours would be H = 1.4n

5) Your heat beats just a little bit slower than Zachs. Everyone is different and there are many different things that can affect heart rate. Maybe he walked a little more than you did or maybe he was stressing about something which made his heart beat a little faster.

I hope this helps you!

Answer:

A. x² -3x -30

Step-by-step explanation:

Using the distributive property to eliminate parentheses, we get ...

3x² +5x -12 -2x² -8x -18

Then, collecting terms gives ...

= (3-2)x² +(5-8)x +(-12-18)

= x² -3x -30 . . . . . . . . . . . . . matches selection A

Answer:

  2. 90°

  3. 65°

Step-by-step explanation:

2. Points A, B, and D are on a semicircle centered at C. The angle A is inscribed in that semicircle, so is 90°. Then angles B and D sum to 90°.

__

3. Triangle ABC is similar to triangle EDC by SAS, so angle x has the same measure as the third angle of triangle EDC: 180° -80° -35° = 65°.

___

The relevant relationship in both cases is that the sum of angles in a triangle is 180°. Also, for problem 2, you need to know that an inscribed angle has half the measure of the arc it subtends. And for problem 3, it helps to understand the relationships in similar triangles.

Answer: 1,7 and 1,5 on coefficient

Step-by-step explanation:

Equation at the end of step  1  :

 (((5•(x4))+(x3))+3x2)-7

Step  2  :

Equation at the end of step  2  :

 ((5x4 +  x3) +  3x2) -  7

Step  3  :

Checking for a perfect cube :

3.1    5x4+x3+3x2-7  is not a perfect cube

Trying to factor by pulling out :

3.2      Factoring:  5x4+x3+3x2-7  

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1:  3x2-7  

Group 2:  5x4+x3  

Pull out from each group separately :

Group 1:   (3x2-7) • (1)

Group 2:   (5x+1) • (x3)

3.3    Find roots (zeroes) of :       F(x) = 5x4+x3+3x2-7

Polynomial Roots Calculator is a set of methods aimed at finding values of  x  for which   F(x)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  x  which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number  P/Q   then  P  is a factor of the Trailing Constant and  Q  is a factor of the Leading Coefficient

In this case, the Leading Coefficient is  5  and the Trailing Constant is  -7.

The factor(s) are:

of the Leading Coefficient :  1,5

of the Trailing Constant :  1 ,7

The factor of the constant is [tex]\rm (x+1) (5x^3-4x^2+7x-7) =0\\\\[/tex].

Given

Expression; [tex]\rm 5x^4+x^3+3x^2-7[/tex]

The leading coefficient of the polynomial of the term has the highest degree of the polynomial.

The factors of the constant term;

[tex]\rm 5x^4+x^3+3x^2-7=0\\\\ 5x^4-4x^3+7x^2-7x+5x^3-4x^2+7x-7=0\\\\(x+1) (5x^3-4x^2+7x-7) =0\\\\[/tex]

Hence, the factor of the constant is [tex]\rm (x+1) (5x^3-4x^2+7x-7) =0\\\\[/tex].

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Answer:

We have to prove

sin⁡(α+β)-sin⁡(α-β)=2 cos⁡ α sin ⁡β

We will take the left hand side to prove it equal to right hand side

So,

=sin⁡(α+β)-sin⁡(α-β)      Eqn 1

We will use the following identities:

sin⁡(α+β)=sin⁡ α cos⁡ β+cos⁡ α sin⁡ β

and

sin⁡(α-β)=sin⁡ α cos ⁡β-cos ⁡α sin ⁡β

Putting the identities in eqn 1

=sin⁡(α+β)-sin⁡(α-β)

=[ sin⁡ α cos ⁡β+cos⁡ α sin⁡ β ]-[sin⁡ α cos ⁡β-cos ⁡α sin ⁡β ]

=sin⁡ α cos⁡ β+cos⁡ α sin ⁡β- sin⁡α cos⁡ β+cos ⁡α sin ⁡β

sin⁡α cos⁡β will be cancelled.

=cos⁡ α sin ⁡β+ cos ⁡α sin ⁡β

=2 cos⁡ α sin ⁡β  

Hence,

sin⁡(α+β)-sin⁡(α-β)=2 cos ⁡α sin ⁡β