A COUPLE PLAN TO HAVE THREE CHILDREN.
A) LIST ALL THE POSSIBILITIES FOR THE SAMPLE SPACE.
B) WHAT IS THE PROBABILITY THAT THEY HAVE AT MOST TWO BOYS?
C) WHAT IS THE PROBABILITY THAT THEY HAVE AT LEAST TWO GIRLS?
D) WHAT IS THE PROBABILITY THAT THEY ARE ALL OF THE SAME SEX?

Answer:

Step-by-step explanation:

answer: 47

add the heights then divide by 5

Answer:

f(x) = -3x + 3

Step-by-step explanation:

Answer:

e

Step-by-step explanation:

[tex]volume~of~cone=\frac{1}{3}volume ~of~cylinder\\volume~of~cylinder=3 \times volume ~of~cone=3 \times15=45 \\volume ~of~two~cylinders=2 \times45=90[/tex]

For a standard normal distribution, the probability of the 2 - scores P(-1.64 < z < 0.2) is 0.52876

We want to find the p-value between 2 z-scores expressed as;

P(-1.64 < z < 0.2)

To solve this, we will solve it as;

P(-1.64 < z < 0.2) = 1 - [P(z < -1.64)  + P(z > 0.2)]

From normal distribution table, we have that;

P(x < -1.64) = 0.050503

P(x > 0.2) = 0.42074

Thus;

P(-1.64 < z < 0.2) = 1 - (0.050503 + 0.42074)

P(-1.64 < z < 0.2) = 0.52876

Thus, For a standard normal distribution, the probability of the 2 - scores P(-1.64 < z < 0.2) is 0.52876

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The value of k such that the graph of f and the graph of g only intersect one is equal to 2.

The value of k such that the graph of f and the graph of g only intersect one is equal to 2. According to the image attached below, functions f(x) and g(x) intersect at point (x, y) = (0, 4) for k = 2.

Herein we have a system formed by two nonlinear equations, a quadratic equation and a cubic equation. Given the constraint that both function must only intersect once, we have the following expression:

f(x) - x² - k · x = 4       (1)

g(x) - x² - k · x = x³ + 2 · k        (2)

x³ + 2 · k = 4

x³ + 2 · (k - 2) = 0

If f and g must intersect once, then the roots must of the form:

(x - r)³ = x³ + 2 · (k - 2)

x³ - 3 · r · x² + 3 · r² · x - r³ = x³ + 2 · (k - 2)

Then, the following conditions must be met: - 3 · r · x² = 0, 3 · r² · x = 0. If x may be any real number, then r must be zero and the value of k must be:

2 · (k - 2) = 0

k - 2 = 0

k = 2

Therefore, the value of k such that the graph of f and the graph of g only intersect one is equal to 2. According to the image attached below, functions f(x) and g(x) intersect at point (x, y) = (0, 4) for k = 2.

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The surface area of the figure illustrated will be 286 yards²

The surface area of a solid object simply implies the measure of the total area which the surface of an object occupies. This is typically done by adding all the areas on the surface of the object.

It should be noted that the surface area of a cuboid will be:

= 2(lw + lh + wh)

w = width = 7

l = length = 9

h = height = 5

Surface area = 2(lw + lh + wh)

= 2(7 × 9) + 2(9 × 5) + 2(7 × 5)

= 126 + 90 + 70

= 286 yards²

Therefore, the surface area of the solid will be 286 yards².

Complete question:

Find the surface area of the solid given that the length is 9 yards, the width is 7 yards, and the height is 5 yards.

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Answer:

Step-by-step explanation:

[tex]2x > 30+\frac{5}{4x} \\2x-\frac{5}{4x} > 30\\\frac{8x^2-5}{4x} > 30\\case~1\\if~x > 0\\8x^2-5 > 120x\\8x^2-120x > 5\\x^2-15x > \frac{5}{8} \\adding~(-\frac{15}{2} )^2~to~both~sides\\(x-\frac{15}{2} )^2 > \frac{5}{8}+\frac{225}{4} \\(x-\frac{15}{2} )^2 > \frac{455}{8} \\x-\frac{15}{2} < -\sqrt{\frac{455}{8} } \\x < \frac{15}{2}-\sqrt{\frac{455}{8} } \\or~x < 0\\rejected~as~x > 0[/tex]

[tex]x-\frac{15}{2} > \sqrt{\frac{455}{8} } \\x > \frac{15}{2} +\sqrt{\frac{455}{8} }[/tex]

case~2

[tex]if~x < 0\\8x^2-5 < 120x\\8x^2-120x < 5\\x^2-15x < \frac{5}{8} \\adding~(-\frac{15}{2} )^2\\(x-\frac{15}{2} )^2 < \frac{5}{8} +(-\frac{15}{2} )^2\\|x-\frac{15}{2} | < \frac{5+450}{8} \\-\sqrt{\frac{455}{8} } < x-\frac{15}{2} < \sqrt{\frac{455}{8} } \\\frac{15}{2} -\sqrt{\frac{455}{8} } < x < \frac{15}{2} +\sqrt{\frac{455}{8} } \\but~x < 0\\7.5-\sqrt{\frac{455}{8} } < x < 0[/tex]

Comparing g(x) with f(x), you can see that the function f(x) is translated to the right by 6 units to produce g(x) which is equivalent to (x-6)²

Transformation is a techniques use to change the position of an object on an xy-plane.

Given the parent function f(x) = x² and the function g(x) = x²-12x +36

Factorize g(x);

g(x) = x²-6x-6x+36

g(x)=x(x-6)-6(x-6)

Group the terms to have;

g(x) = (x-6)²

Comparing g(x) with f(x), you can see that the function f(x) is translated to the right by 6 units to produce g(x) which is equivalent to (x-6)²

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(i) The expanded form of (1 / 2 - 2 · x)⁵ in ascending form is 1 / 32 - (5 / 8) · x + 5 · x² - 20 · x³ + 40 · x⁴ - 32 · x⁵.

(ii) The coefficient of x³ from (1 + a · x + 3 · x²) · (1 / 2 - 2 · x)⁵ is - 265 / 8.

In this problem we must apply the concept of Pascal's triangle to expand the power of a binomial of the form (x + y)ⁿ and further algebra properties.

(i) First, we proceed to expand the power binomial (1 / 2 - 2 · x)⁵ in ascending order:

(1 / 2 - 2 · x)⁵ = (1 / 2)⁵ + 5 · (1 / 2)⁴ · (- 2 · x) + 10 · (1 / 2)³ · (- 2 · x)² + 10 · (1 / 2)² · (- 2 · x)³ + 5 · (1 / 2) · (- 2 · x)⁴ + (- 2 · x)⁵

( 1 / 2 - 2 · x)⁵ = 1 / 32 - (5 / 8) · x + 5 · x² - 20 · x³ + 40 · x⁴ - 32 · x⁵

(ii) Second, we proceed to expand the following product of polynomials by algebra properties:

(1 + a · x + 3 · x²) · (1 / 2 - 2 · x)⁵ = (1 + a · x + 3 · x²) · [1 / 32 - (5 / 8) · x + 5 · x² - 20 · x³ + 40 · x⁴ - 32 · x⁵]

(1 + a · x + 3 · x²) · (1 / 2 - 2 · x)⁵ = 1 / 32 + (a / 32 - 5 / 8) · x + (- 5 · a / 8 + 163 / 32) · x² + (- 175 / 8 + 5 · a) · x³ + (65 - 20 · a) · x⁴ + (- 92 + 40 · a) · x⁵ + (120 - 32 · a) · x⁶ - 96 · x⁷

In accordance with the statement, we find that:

- 5 · a / 8 + 163 / 32 = 13 / 2

- 5 · a / 8 = 45 / 32

a = - 9 / 4

Thus, the coefficient of x³ is:

C = - 175 / 8 + 5 · (- 9 / 4)

C = - 265 / 8

The coefficient of x³ from (1 + a · x + 3 · x²) · (1 / 2 - 2 · x)⁵ is - 265 / 8.

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6 decks of cards = 60 cards

---> 60/8 = 15/2 = 7.5

7.5 cards = 0.75 decks of cards

Therefore, each student will get 0.75 decks of cards.

Answer:

1

Step-by-step explanation:

Everyone gets 1 and there's 2 left over

Answer:

57

Step-by-step explanation:

-7a + 4b

Let a = -3  b = 9

Substitute the values in

-7(-3) + 4(9)

Multiply

21 + 36

Add

57

Answer:

y = (constant variable x time) + independent variable

y = 60x + 30    ← Health Club B

y = 27x + 50    ← Health Club A

Step-by-step explanation:

I can't see the question at the bottom due to the covering but if you comment I can edit this and give a proper answer. Otherwise this is all I can give you.

The length of the diagonal that he cut to the nearest whole inch is 36 inches

A red dotted line crosses the rectangle from the upper left corner to the lower right corner to form a triangle.

Length of the diagonal of a rectangle;

Hypotenuse² = adjacent² + opposite²

= 18² + 36²

= 324 + 1296

hyp² = 1620

hyp = √1620

hyp = 35.4964786985976

Approximately,

hypotenuse = 36 inches

Therefore, the length of the diagonal that he cut to the nearest whole inch is 36 inches.

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Using the permutation formula, there are 157,410 ways for the medals to be distributed.

The number of possible permutations of x elements from a set of n elements is given by:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

In this problem, 3 athletes are chosen from a set of 55, hence the number of ways is given by:

P(55,3) = 55!/52! = 157,410

157,410 ways for the medals to be distributed.

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Answer:

1) 13m, 2) 10ft, 3) 11.4ft, 4) 12.7m

Step-by-step explanation:

Since all of these triangles are right triangles, we can use the Pythagorean Theorem: a^2+b^2 = c^2

1) 5^2+12^2 = c^2 = 25+144 = c^2 = 169 = c^2 = 13 = c

2) 6^2+8^2 = c^2 = 36+64 = c^2 = 100 = c^2 = 10 = c

3) 5^2+10.3^2 = c^2 = 25+106.09 = c^2 = 131.09 = c^2 = 11.4494541 = 11.4 = c

4) 8.6^2+9.4^2 = c^2 = 73.96+88.36 = c^2 = 162.32 = c^2 = 12.7404866 = 12.7 = c

Answer: 320 mL

Step-by-step explanation:

Given information

The bottle is currently 3/8 full

Current Volume = 240 mL

Concept:

Imagine the water in the bottle being separated into 8 parts

Currently, 3 parts are being occupied

Determine the volume for 1 part

3 parts = 240 mL

1 part = 240 / 3 = 80 mL

Determine the volume for half-full (4 parts)

1 part = 80 mL

4 parts = 80 × 4 = [tex]\Large\boxed{320~mL}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

The difference between Alok and Prabir share exists 8000.

Given: Invested by Alok = Rs 90, 000

Invested by Prabir = Rs 1,20000

The time period of Alok = 3 months

The time period of Prabir = 2 years

They earn a profit = Rs 96,000.

Profit exists directly proportional to the product of the amount invested and the time period of investment.

8000 = 90000 [tex]*[/tex] 24/120000 [tex]*[/tex] 21

= 5/7

5x + 7x = 96000

x = 8000

first = 40000

second = 48000

so the difference exists at 8000.

The difference between Alok and Prabir share exists 8000.

Therefore, the correct answer is 8000.

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Answer:

f^-1(x)=x-14

Step-by-step explanation:

change f(x) to y :y=x×14

interchange variables :x=y+14

move constant(14) to the left :x-14=f^-1(x)

Answer:

39 pages

Step-by-step explanation:

If 13 pages are read in 1/3 of an hour, we need to multiply 13 by 3 to get the number of pages read in 1 hour. 13*3 = 39 pages

The equation of parabola is a [tex]\frac{-(x+ 3)^{2}}{64} + \frac{ (y-1)^{2}}{4} = 1[/tex] and the coordinates of center is (0,0) And asymptote is become 16.

According to the statement

we have to find the centers, foci, vertices and asymptotes of the hyperbola from the given equations.

So, For this purpose,

Hyperbola is a a plane curve generated by a point so moving that the difference of the distances from two fixed points is a constant.

So, The given equation is:

16y²-x² - 6x - 32y = 57

So, rearrange it then

-x² - 6x - 32y + 16y² = 57

-(x² + 6x) + (16y² - 32y ) = 57

-(x² + 6x) + 16(y² - 2y ) = 57

-(x² + 6x + 9) + 16(y² - 2y +1 ) = 57 +1(16) + 9(-1)

-(x+ 3)²  + 16 (y-1)²  = 64

-(x+ 3)²  + 16 (y-1)²  = 64

divide whole equation by 64 then

[tex]\frac{-(x+ 3)^{2}}{64} + \frac{16 (y-1)^{2}}{64} =\frac{64}{64}[/tex]

then equation become

[tex]\frac{-(x+ 3)^{2}}{64} + \frac{ (y-1)^{2}}{4} = 1[/tex]

This become the equation of hyperbola.

So,

here coordinates of center is (0,0)

And asymptote is become 16.

So, The equation of parabola is a [tex]\frac{-(x+ 3)^{2}}{64} + \frac{ (y-1)^{2}}{4} = 1[/tex] and the coordinates of center is (0,0) And asymptote is become 16.

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Answer:

[tex]3x^{2} - 4xy + 2y { }^{2} - 1 \\ 3 \times ( - 3) { }^{2} - 4 \times ( - 3) \times 5 + 2 \times 5 {}^{2} - 1 \\ (3 \times 9) - ( - 60) + 50 - 1 \\ 27 + 60 + 50 - 1 \\ 165 [/tex]

Answer: 136

Substitute -3 for x and 5 for y.

[tex]3x^2 - 4xy + 2y^2 - 1[/tex]

[tex]3(-3)^2-4(-3)(5)+2(5)^2-1[/tex]

[tex]3(9)-4(-15)+2(25)-1[/tex]

[tex]27+60+50-1[/tex]

[tex]87+50-1[/tex]

[tex]137-1[/tex]

[tex]136[/tex]

hope this helped!

Answer:

simplification of the original equation is below/

Step-by-step explanation:

9+4t=-3(1-2t) can be simplified into

9+4t=-3+6t because of distributing the -3 to both the 1 and -2t.

however, this can simplified to

4t-6t=-3-9

and this can simplify to

-2t=-12

which can simplify to

t = 6

give brainliest please!

hope this helps :)

Answer: 28

Step-by-step explanation:

[tex]8+(7+1)2+4\\\\8+(8)2+4\\\\8+16+4\\\\24+4\\\\28[/tex]

The second number line best shows how to solve –4 – (–8). This can be obtained by finding the value of –4 – (–8) and checking which number line has the required arrow mark.

The value of  –4 – (–8) is obtained.

–4 – (–8) =  –4 + 8

–4 – (–8) = 4

The arrow should move from zero to - 4 and the second arrow should move from - 4 to 4.

From the question given the number lines,

The first arrow is moving from zero to - 4.

First condition is satisfied.

The second arrow is moving from - 4 to  8.

Second condition is not satisfied.

The first arrow is moving from zero to - 4.

First condition is satisfied.

The second arrow is moving from - 4 to  4.

Second condition is satisfied.

Hence the second number line best shows how to solve –4 – (–8).

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Given the following:

The economic order quantity is 24.

Eoq = √2 * demand * ordering cost / holding cost)

= √(2 * 1050 * 15 / 55)

EOQ = 24

The  Average inventory = EOQ / 2

= 24 / 2

= 12

Expected number of orders = demand / EOQ

= 1050 / 24

= 44

Annual holding cost (AHC) = (EOQ / 2) * Holding cost

= (24 / 2) * 55

= 660

Annual ordering cost (AOC) = (demand / EOQ) * ordering cost

= (1050 / 24) * 15

= 656

Thus,

Total cost of managing = AHC + AOC

= 660 + 656

TCM = 1,316

5. For holding cost of 60

EOQ= √(2 * demand * ordering cost / holding cost)

= √(2 * 1050 * 15 / 60)

= 23

Annual holding cost = (EOQ / 2) * holding cost

this gives us

= (23 / 2) * 60

= 690

Annual ordering cost = (demand / EOQ) * ordering cost

= (1050 / 23) * 15

= 685

Total cost of managing = AHC+ AOC

= 690 + 685

= 1375

Change in total annual cost = new - old

= 1375 - 1316

= 59

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Answer:

  x = 3

Step-by-step explanation:

Maybe you want the value of x such that ...

  4(6^x) = 864

Dividing by 4 gives ...

  6^x = 216

You may know that 216 = 6^3. Using that, we can equate exponents:

  6^x = 6^3

  x = 3

Alternatively, we can use logarithms to find x. Taking logs gives ...

  x·log(6) = log(216)

  x = log(216)/log(6) = 3

The formula that can be used to illustrate consecutive even numbers is a + 2.

It should be noted that the information is incomplete. Therefore, an overview will be given.

It should be noted that consecutive even numbers we the numbers that follow each other and have a difference of 2.

Examples of such numbers include 2, 4, 6,8, 10, etc.

In this case, the formula that can be used to illustrate consecutive even numbers is a + 2.

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Answer: Pr(4.19 ≤ X ≤ 4.81)

Step-by-step explanation:

First of all, let's calculate the mean;

x¯ = (4.3 + 5.1 + 3.9 + 4.5 + 4.4 + 4.9 + 5.0 + 4.7 + 4.1 + 4.6 + 4.4 + 4.3 + 4.8 + 4.4 + 4.2 + 4.5 + 4.4)/17

x¯ = 76.5/17

x¯ = 4.5

We are given standard deviation; s = 0.31

Now, z-value for a 68% Confidence interval is 1

Range in which the data falls is;

Range = x¯ ± zs

Range = 4.5 ± (1 × 0.31)

Range is;

Pr[(4.5 - 0.31) ≤ X ≤ (4.5 + 0.31)]

Pr(4.19 ≤ X ≤ 4.81)

Answer:

Pr (3.57 ≤ X ≤ 5.43)

Step-by-step explanation:

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