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The is used to measure volume.
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meter
gram
liter

The expected number of times the mosquito will visit 0 before the first time she visits 4 is 3/4 by using concept of probability and geometric series.

Given that repeatedly throwing a fair tetrahedral die, trying to get a 4 (success) before getting a number from 1 to 3 (failure), which follows a geometric distribution.

To find the expected number of visits to 0 before reaching 4, analyze two cases:

By the given data, the probabilities of two cases are:

P(success) p = 1/4,

P(failure)=3/4.

The expected count of failures, X, can be found in terms of success probability p as

[tex]E[X]=\sum_{x=0}^{+\infty}[x(1-p)^xp][/tex]

On substituting p = 1/4 gives:

[tex]E(X) = 0(1/4)+1(3/4)(1/4)+2(3/4)^2(1/4)+3(3/4)^3(1/4)+.........[/tex]

On taking (1/4) gives

[tex]E(X) = 1/4[3/4+(3/4)^2+(3/4)^3+......+\infty]----(1)[/tex]

Consider [tex]3/4+(3/4)^2+(3/4)^3+......+\infty[/tex]

This forms a geometric series tends to infinity and the sum is given by :

[tex]S_\infty = a/(1-r)[/tex]

Here: a= 3/4

r = 3/4

Plugging these values into formula gives:

[tex]3/4+(3/4)^2+(3/4)^3+......+\infty = S_\infty[/tex]

[tex]S_\infty= 3/4/(1-3/4)[/tex]

On subtracting the denominator gives:

= 3/4/(1/4)

On taking reciprocal gives:

= 3/4 * 4

On simplifying gives:

= 3

Substituting these value into given equation 1 gives:

E(X) = 1/4*[3]

On multiplying gives:

E(X) = 3/4.

Therefore, the  expected number of times the mosquito will visit 0 before the first time she visits 4 is 3/4 by using concept of probability and geometric series.

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An equation for each situation, in terms of t, is y = 850e^35t and

y = 700e^70t

The required equation will be in the form y = Ae^kt

where:

If High School A currently has 850 students and is projected to grow by 35 students each year, hence;

Substituting into the formula, we will have:

y = 850e^35t

If High School B currently has 700 students and is projected to grow by 60 students each year, hence;

Substituting into the formula, we will have:

y = 700e^70t

An equation for each situation, in terms of t, is y = 850e^35t and

y = 700e^70t

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Answer:

b

Step-by-step explanation:

Answer:

ACD

Step-by-step explanation:

VNQLW3M2L,Q;KJ52KQ

Answer:

Step-by-step explanation:

[tex]X + Y \geq 15\\\\10X + 5Y \leq 100[/tex]

we want to put it into terms of Y

[tex]y \geq 15 - x\\and\\5y \leq 100 - 10x\\y \leq 20 - 2x[/tex]

the graph is in the attached image. Any point in the shaded overlap region where x is greater than or equal to 0 (assuming you cannot have negative coins) works, e.g. (2, 14)

The solution of the inequalities is required.

One of the solutions is [tex](5,10)[/tex]

Number of dimes is [tex]x[/tex]

Number of nickels is [tex]y[/tex]

Minimum number of coins is 15.

So, [tex]x+y\geq 15[/tex]

Maximum total value of the coins is $1

So, [tex]0.1x+0.05\leq 1[/tex]

The equations are

[tex]x+y=15[/tex]

[tex]0.1x+0.05y=1[/tex]

Points of the first equation

[tex](0,15)[/tex] and [tex](15,0)[/tex]

Graph the points and draw a line through them.

Points of the second equation

[tex]x=0[/tex]

[tex]y=\dfrac{1}{0.05}=20[/tex]

[tex]y=0[/tex]

[tex]x=\dfrac{1}{0.1}=10[/tex]

[tex](0,20)[/tex] and [tex](10,0)[/tex]

Graph the points and draw a line through them.

The shaded regions can be determined by substituting the point in the equations.

One of the solutions is [tex](5,10)[/tex]

This means there are 5 dimes and 10 nickels.

[tex]5+10=15\geq 15[/tex]

[tex]0.1\times 5+0.05\times 10=1\leq 1[/tex]

Hence, one of the solutions is [tex](5,10)[/tex].

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speed =  [tex]\frac{distance}{time}[/tex]

speed = [tex]\frac{100}{2.5}[/tex]

speed = 40 feet per second

Answer:

1

Step-by-step explanation:

Given table:

     x      -1    1   3   5

     y      -2   0   2  4

Unknown:

Slope of the line  = ?

Solution:

Each x and y pair on the table lies on the line. Therefore, we can use them to find the slope;

  Slope  = [tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]  

 let us take;

x₁ = -1        x₂ = 3

y₁ = -2        y₂ = 2

Insert the parameters and solve;

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

The slope of the line is 1

Answer: 7 x 10 + 2 x 1 + 6 x 1/10+ 3 x 1/1000

Step-by-step explanation: just had this question on the test

Answer:

3.5

Step-by-step explanation:

 3.5 inches would represent 350 feet.

Relationship between inches and feet is that one inch is equal to [tex]\boldsymbol{100}[/tex] feets as per the map.

So,[tex]350[/tex] feet represent [tex]\frac{350}{100}=3.5[/tex] inches.

Therefore, [tex]\boldsymbol{3.5}[/tex] inches would represent [tex]350[/tex] feet in decimal.

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Answer:

It depends on what x is

Step-by-step explanation:

I cant help

Answer:

0

Step-by-step explanation:

well if its just 4, then that means it doesnt have a y value

Answer:

4 x 10⁵

so that i think will be OD)

Answer:

i believe its the rise and the run of the slope.

Step-by-step explanation:

i believe its something similar to this photo

Answer:

y = 3x + 7.

To graph the line mark off the 2 points and draw a line through them.

Step-by-step explanation:

The slope = (-2-7) / (-3-0)

= -9/-3

= 3.

The value of b is found using the point-slope form of a line:

y - y1 = m(x - x1)

using m = 3, (x1, y1) = (0, 7):

y - 7 = 3(x - 0)

y = 3x + 7.

Answer:

Step-by-step explanation:

Volume of the cuboid = Length * Width * Height

Given

Length = 4cm

Width = (x+1)cm

Height = (x-11)cm

Volume of the cuboid = 4(x+1)(x+11)

Volume of the cuboid = 4(x^2+11x+x+11)

Volume of the cuboid = 4(x^2+12x+11)

Volume of the cuboid = 4x*2+48x+44

925 = 4x*2+48x+44

4x*2+48x+44-925 = 0

4x*2+48x-881 = 0

Divide through by 4

x^2 + 12x - 220.25 = 0

Factorize using the general formula;

x = -12±√12²-4(-220.25)/2

x = -12±√144+881/2

x = -12±√1025/2

x = -12±32/2

x = 12+32/2

x = 20/2

x = 10

Hence the dimension of the cuboid is 4cm, (10+1)cm and (10+11)cm

Dimension is 4cm by 11cm by 21cm

Answer:

(4,3)

Step-by-step explanation:

2y = x + 2

x - 3y = -5

Rearrange the second equation to equal y.

x - 3y = -5

x + 5 = 3y

(x+5)/3 = y

Substitute into the first equation.

2y = x +2

2[(x+5)/3] = x + 2

(2x + 10)/3 = x + 2

2x + 10 = 3(x + 2)

2x + 10 = 3x + 6

10 - 6 = 3x - 2x

4 = x

Therefore, the correct ordered pair is (4,3) since x is equal to 4.

Answer:

X=17

Step-by-step explanation:

73+x=90 90-73=17

Answer:

x = ± [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

[tex]|a|= \left \{ {a,if{a\geq 0} \atop-a, if {a<0}} \right.[/tex]

~~~~~~~~~~~~

7 | 3x | + 2 = 16

7 | 3x | = 14

| 3x | = 2

1). 3x = 2

x = [tex]\frac{2}{3}[/tex]

2). - 3x = 2

x = - [tex]\frac{2}{3}[/tex]

Answer:-15/28

Step-by-step explanation:

2/1*x5/7x-3/8=-30/56 ÷2=-15/28

Answer: No

Step-by-step explanation:

The range and the Domain aren’t equal

Answer:

Step-by-step explanation:

D = { - 4 , 0 , 2 , 7 }

R = { - 8 , - 1 , 3 }

Yes the relation is a function.

Answer:

D

Step-by-step explanation:

let the number of songs Byron have be s songs.

s + 26 = 75

Answer:

D

Step-by-step explanation:

s= number of songs played.

s+26=75

s-26=75-26

s=49

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

Explanation:

Check out figure 1 in the attached images below. In this figure, I've plotted the function y = 6/(2x-3) on a 2D grid system. The function curve is in blue. Then I've plotted (2,0) and (3,0) on the x axis. Point A is somewhere between those endpoints. Point A is also on the x axis. Directly above A is point B such that B is on the blue function curve.

The distance from A to B is found by subtracting the y values of each point.

The y coordinate of A is y = 0. The y coordinate of B is y = 6/(2x-3)

Therefore, the distance from A to B is 6/(2x-3) units. This will form the radius of each cylindrical slice as figure 2 shows. Note the color coding to help see how the 2D view corresponds to the 3D view. The xy plane has been laid flat on the floor. So we're viewing the function curve at a downward angle now. Each of those gray cylinders combine to form an approximate 3D volume. The more cylinders we have, and the finer the cuts, the more accurate the total volume.

So it comes down to finding the volume of each cylindrical slice and adding up the volumes. This is effectively what integral calculus is all about.

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

Since the radius of each cylinder is y = 6/(2x-3), this means r = 6/(2x-3) is plugged into the formula

V = pi*r^2*h

which is the volume of a cylinder formula

The height of each cylinder is delta x, which we'll use dx for short. So this is where the dx comes from in integrals.

This is what the integral will look like

[tex]\displaystyle V = \int_{2}^{3} \pi*\left(\frac{6}{2x-3}\right)^2dx[/tex]

which turns into

[tex]\displaystyle V = 36\pi\int_{2}^{3}\frac{1}{(2x-3)^2}dx[/tex]

after a bit of algebra. We're able to factor the 36pi out because it's a constant

From here we use u-substitution. Let u = 2x-3

This leads to du/dx = 2 which can be solved to dx = du/2

Since u = 2x-3, the lower endpoint x = 2 leads to

u = 2x-3 = 2*2-3 = 1

and x = 3 leads to

u = 2x-3 = 2*3-3 = 3

So the interval 2 < x < 3 turns into 1 < u < 3

After using u-sub, making the proper replacements, and integrating, we get

[tex]\displaystyle V = 36\pi\int_{2}^{3}\frac{1}{(2x-3)^2}dx\\\\\\\displaystyle V = 36\pi\int_{1}^{3}\frac{1}{u^2}\frac{du}{2}\\\\\\\displaystyle V = 36\pi*\frac{1}{2}\int_{1}^{3}\frac{1}{u^2}du\\\\\\\displaystyle V = 18\pi\int_{1}^{3}u^{-2}du\\\\\\\displaystyle V = 18\pi\left[-u^{-1}+C\right]_{1}^{3}\\\\\\\displaystyle V = 18\pi\left[-\frac{1}{u}+C\right]_{1}^{3}\\\\\\[/tex]

Let's evaluate that to get the following

[tex]\displaystyle V = 18\pi\left[-\frac{1}{u}+C\right]_{1}^{3}\\\\\\\displaystyle V = 18\pi\left[\left(-\frac{1}{3}+C\right)-\left(-\frac{1}{1}+C\right)\right]\\\\\\\displaystyle V = 18\pi\left(-\frac{1}{3}+1\right)\\\\\\\displaystyle V = 18\pi\left(\frac{2}{3}\right)\\\\\\\displaystyle V = 12\pi\\\\\\[/tex]

So the 3D volume formed by rotating that region (under the curve from x = 2 to x = 3) is exactly 12pi cubic units

Answer:

1/3

Step-by-step explanation:

Answer:

20 mobile sets.

Step-by-step explanation:

Every mobile set costs:

40000 / 8

= 5000 Rs.

Therefore, for 100,000 Rs, the number of mobile sets that can be purchased is:

100,000 / 5000

= 20 mobile sets.

Hope this helped!

Answer:

8

Step-by-step explanation:

we can say that AD is congruent to DC

so your equation for x is: 4x - 1 = 2x

solve this to get x = 0.5

plug x into and equation and multiply you answer by 2 to find the hypotenuse of triangle ABC and DEF

4(0.5) - 1 = 1

hypotenuse: 1 x 2 = 2

since we know x is 0.5, plug this into 4x + 1 to find the length of the leg FE,

4(0.5) + 1 = 3

In the diagram, it shows that the legs of triangle are congruent

this means that FE, ED, BA, and BC are all congruent

since we know FE is 3, we know that all the other sides are 3 as well

this means that the perimeter of the triangle is: leg + leg + hypotenuse

so 3 + 3 + 2

the perimeter is 8