Cubes having side lengths of 3/4in. are used to fill the right rectangular prism shown.

Answer:

0.2048 = 20.48% probability that exactly two of the five sample families will have no children.

Step-by-step explanation:

For each children, there are only two possible outcomes. Either they have no children, or they do have children. The probability of a family not having children is independent of any other family. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

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

And p is the probability of X happening.

20% of the families have no children at all.

This means that [tex]p = 0.2[/tex]

Five families:

This means that [tex]n = 5[/tex]

What is the chance that exactly two of the five sample families will have no children?

This is P(X = 2).

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 2) = C_{5,2}.(0.2)^{2}.(0.8)^{3} = 0.2048[/tex]

0.2048 = 20.48% probability that exactly two of the five sample families will have no children.

Answer:

[tex]f(x) = \frac{10}{x} - 4 \\ \delta \: f(x) = \frac{f(8) - f(2)}{2} \\ = \frac{(\frac{10}{8} - 4) - ( \frac{10}{2} - 4)}{2} \\ = \frac{ \frac{ - 11}{4} - 1}{2} \\ = \frac{ \frac{ - 15}{4} }{2} \\ = - \frac{15}{8} [/tex]

Answer:

-4x-31

Step-by-step explanation:

1.6(5x-10)-(12x+15)

8x-16-12x-15

-4x-31

The simplified expression is -4x - 31.

We know,

In mathematics, an expression refers to a combination of numbers, variables, operations, and mathematical symbols that represents a mathematical statement or computation. It can involve arithmetic operations (addition, subtraction, multiplication, division).

We have Equation,

1.6(5x - 10) - (12x + 15)

Now simplifying the equation

1.6(5x - 10) - (12x + 15)

= 8x - 16 - 12x - 15

= -4x - 31

Thus, the simplified expression is -4x - 31.

Learn more about Equation here:

https://brainly.com/question/29538993

#SPJ1

Answer:

third

Step-by-step explanation:

arctan of ( opp/adj) = arctan( 10/15 )

the shadow is 15 so 10 must be the height of the streetlight and

arctan (10/15) is the angle between the ground and the line from the edge of the shadow to the top of the streetlight

Answer:

Step-by-step explanation:

Cos(A + B) = Cos(A)*Cos(B) - Sin(A)*Sin(B)

Find The Hypotenuse of A

Tan(A) = Opposite / Adjacent

Tan(A) = 15/8

Opposite = 15

Adjacent = 8

Hypotenuse = c

c^2 = opposite^2 + Adjacent^2

c^2 = 15^2 + 8^2

c^2 = 225 + 64

c^2 = 289

sqrt(c^2) = sqrt(289)

c = 17

Find the opposite of B

Adjacent = 12

Hypotenuse = 37

Opposite = b

adjacent^2 + opposite^2 = hypotenuse^2

12^2 + b^2 = 37^2

144 + b^2 = 1369

b^2 = 1369 - 144

b^2 = 1335

b = 35

Definitions

Sin(A) = Opposite / hypotenuse = 15/17

Sin(B) = opposite / hypotenuse =  35/37

Cos(A) = 8/17

Cos(B) = 12/37

Answer

Cos(A + B) = Cos(A)*Cos(B) - Sin(A)*Sin(B)

Cos(A + B) = 8/17 * 12/37 - 15/17*35/37

Cos(A + B) = 96/629 - 525/629

Cos(A + B) = -429/629

Answer:

BC = 6.9

Step--step explanation:

Reference angle = 30°

Adjacent = BC

Hypotenuse = 8

Apply trigonometric function, CAH:

Cos 30° = Adj/Hypotenuse

Cos 30° = BC/8

8*Cos 30° = BC

6.92820323 = BC

BC = 6.9 (to the nearest tenth)

Answer:

65*

Step-by-step explanation:

12x-7+16x+19=180

28x=168

x=6

12(6)-7=65

Answer:

A) 9/2x3/8

Step-by-step explanation:

Answer:

45.584

;)

Have a nice day

Answer:

104 softballs

Step-by-step explanation:

26 x 4 = 104

Answer: 88

Step-by-step explanation:

got it right 2022 edge

Let u = (1, 0) and v = (0, 1). Then

T (u) = (2*1 - 3*0, 1 + 4, 5*0) = (2, 5, 0)

T (v) = (2*0 - 3*1, 0 + 4, 5*1) = (-3, 4, 5)

=>   T (u) + T (v) = (-1, 9, 5)

but

T (u + v) = T (1, 1) = (2*1 - 3*1, 1 + 4, 5*1) = (-1, 5, 5)

=>   T (u + v) ≠ T (u) + T (v)

which means T does not preserve addition, so it is not linear.

the answer is 35 I did a lot of work I can't show you here

Answer:

27.5

Step-by-step explanation:

Answer:

Step-by-step explanation:

110/4 is 27.5

Answer:

M(x)  =  452,56 in

Step-by-step explanation:

The volume of the open box is  500 in³

V = Area of the base times height

V(b) =  x² * h               where x is the side of the square and h the heigh

Then     500 =  x²*h

Total material to use is: material of the base + material of 4 sides

material of the base is  x²

material of one side is x*h  we have 4 sides then  4*x*h

Total material M(b)

M(b)  =  x²  +  4*x*h

And    as    h  =  500/ x²

M(x)  =  x²  +  4* x* 500/x²

M(x)  =  x²  +  2000/x

Tacking derivatives on both sides of the equation

M´(x)  =  2*x   - 200/x²

M´(x)  =  0         2*x  -  200/x²  = 0

x³ -  100  =  0

x³   =  100

x   =  4,64 in

And By substitution     h  =  500/x²

h  =  500/(4,64)²           h  =  23,22  in

How do we know that x = 4,64 make V(x) minimum

we get the second derivative

M´´(x)  =  2  +  200*2x/ x⁴    =  2  +  400/x³

M´´(x) is always positive

M´´(x) > 0     then M(x) has a minimum for  x= 4,64 in

The least amount of material is:

M(x)  =  x²    +    2000/x

M(x)  =  (4,64)²  *  2000/4,64

M(x)  = 21,53  +  431,03

M(x)  =  452,56 in

9514 1404 393

Answer:

  the correct choice is marked

Step-by-step explanation:

The line has a rise of 2 for a run of 1, so a slope of 2. The line crosses the y-axis at y=-2, so the y-intercept is -2. The slope-intercept equation for the line is ...

  y = mx + b . . . . . . for slope m and y-intercept b

  y = 2x -2

Answer:

the answer is c y=2x-2

Step-by-step explanation:

:)

Answer:

[tex]Volume = \frac{1}{3} \pi r^2 h \\\\r= 5\\Volume = 100\pi\\\\Find \ h.\\\\h = 3\frac{V}{\pi r^2} = 3 \times \frac{100 \pi}{\pi \times 5^2} = 3\times \frac{100}{25} = 3 \times 4 = 12[/tex]

Answer:

63%.

Step-by-step explanation:

There are 12 scores below 45 and total number of scores = 19.

So percentile rank= (12/19) * 100

=  63%.

Answer: c

Step-by-step explanation:

Answer:

C. 13 gallons

Step-by-step explanation:

150 divided by 6 is 25. 325 divided by 25 is 13.

To travel 325 miles the van needs C. 13 gallons of gas.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, A van travels 150 miles on 6 gallons of gas.

So, In one gallon the van travels (150/6) = 25 miles.

∴ To travel 325 miles the van needs (325/25) = 13 gallons of gas.

learn more about the unitary method here :

https://brainly.com/question/28276953

#SPJ2

Answer:

A. A triangle can be equilateral and obtuse at the same time

Step-by-step explanation:

All angles in an equilateral triangle are 60° therefore they cannot be above 90° and less than 180°

The probability that at least three plants produce two or more seeds is 0.793915.

Binomial distributions consist of n independent Bernoulli trials.

Bernoulli trials are those trials that end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))

The probability that out of n trials, there be x successes is given by

Use binomial distribution, with p =0.20, n=5, x=3

[tex]P(X=x)=C(n,x)p^x (1-p)^{n-x}[/tex]

P(X> = 3)

[tex]=1-(P(X=0)+P(X=1)+P(X= 5 ))\\=1-(C(20,0)0.2^0 (0.8)^{20-0}+C(20,1)0.2^1 (0.8)^{20-1}+C(20,2)0.2^2 (0.8)^{20-2})[/tex]

=1-(0.0115292+0.057646+0.136909)

=1-0.206085

=0.793915

Hence, the probability that at least three plants produce two or more seeds is 0.793915.

Learn more about binomial distribution here:

brainly.com/question/13609688

#SPJ12

Answer:

Hello! answer: x = 40

Step-by-step explanation:

These are vertical angles meaning they will have the same measure.

40 × 3 = 120 120 - 16 = 104 therefore x = 40 hope that helps!

Answer: The answer would be y = x + 8

Step-by-step explanation:

Answer:

#2. 6x3.14=1080 which is more than 18

9514 1404 393

Answer:

  (-5, -4)

Step-by-step explanation:

Compare the given equation to vertex form:

  y = a(x -h)² +k

You see that a=2, h=-5, k=-4.

The vertex is (h, k) = (-5, -4).