Liberty bought a make-your-own salad when she went out to lunch at a restaurant. The salad cost $4, plus $0.85 for each salad topping. Liberty spent $9.95 on the salad. Which equation can be used to find t, the number of toppings that Liberty ordered on her salad

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.

Learn more probability about here:

https://brainly.com/question/23846068

#SPJ4

Answer:

Option B

Step-by-step explanation:

Subscribe to RANDOM TOPICS TRENDING on youtub. Thank you.

Answer:

D. T= I/PR

Step-by-step explanation:

PRT are multiplyed so you divide PR to get T by itself.

Answer:

First payment (50%) would be 512$

The next two payments would be 32$ each

Explanation:

.5(1024)= 512

.25(512)=128

.25(128)= 32

Answer:

22 units

Step-by-step explanation:

Known Quantities:

Calculations:

Final Calculations:

Answer:

x= -1

Step-by-step explanation:

2(x -5) -6 = -18

2x -10 -6 =-18

2x -10 -6 =-18

2x -16 = -18

2x =16 += -18

2x -16 +16 = -18 +16

2x = -2

2x/2 = -2/2

x=-1

x = -1

Answer: No

Step-by-step explanation:

The range and the Domain aren’t equal

Answer:

Step-by-step explanation:

[tex]7a(3b - 2c + 4)\\\\\mathrm{Distribute\:parentheses}\\\\=7a\times \:3b+7a\left(-2c\right)+7a\times\:4\\\\\mathrm{Apply\:minus-plus\:rules}\\\\+\left(-a\right)=-a\\\\=7\times\:3ab-7\times\:2ac+7\times\:4a\\\\Simplify\\\\21ab-14ac+28a[/tex]

Answer:

x+10

Step-by-step explanation:

sum = addition (+)

number = variable because we don't know what the number is yet (x)

ten=ten

So by this we can get x+10

Answer:55.6

Step-by-step explanation:

Answer:

55.6

Step-by-step explanation:

Answer:

x = 6

Step-by-step explanation:

7 + 5x = 2x + 25

first subtract 7 from both sides to isolate 5x on the left

5x = 2x + 18

then subtract 2x from both sides to isolate all of the x terms to one side

3x = 18

then divide 18 by 3 to solve for x

x = 6

hope this helped!! :)

Answer:

i got you, i wrote it out and all gimme brilliantness

Step-by-step explanation:

Answer:

The slope of this line is -2/3x.

Step-by-step explanation:

The slope can be found by getting x1 and y1 (0,3) and x2 and y2 (3,1). Once you have these you would do y2 - y1 / x2 - x1.

And the equation then is

1 - 3 / 3 - 0.  After simplifying this you get -2/3.

Answer:

-5/3

Step-by-step explanation:

m=−9−6/10−1

m=−15/9

Slope=

−15/9=−5/3

Answer:

????

Step-by-step explanation:

Answer:

where's the shape

Step-by-step explanation:

what's the length and width, maybe I can help

Answer:

0 -1

Step-by-step explanation:

because the line is going down which is negative

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

Learn more on exponential function here: https://brainly.com/question/12940982

Answer:

width = 15

Step-by-step explanation:

a² + b² = c² This the the formula

(PLUG IN)

8² + b² = 17²

64 + b² = 289 (subtract 64 on both sides)

b² = 225 (square root)

b = 15

Hope this helps ya!!

-33.33333333333333 %A change from 27 to 18 represents a negative change (decrease) of -33.33333333333333%

Use the formula found below on this webpage to find the percent changeby replacing the given values:Percent change = New - Old|Old|  100%Percent change = 18 - 27|27|  x 100 = -927  x 100 = -33.33333333333333decrease)

Where: 27 is the old value and 18 is the new value. In this case we have a negative change (decrease) of -33.33333333333333 percent because the new value is smaller than the old value.

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:

1:2

Step-by-step explanation:

You didn't really specify, but I'm going to assume you meant as simplified as possible. If you write it as a fraction, it will be ½ or as a decimal it will be 0.5.

Answer:

1:2

Step-by-step explanation:

Simplifying a ratio is like simplifying a fraction.

Simply put the number to the left as the numerator, and the number to the right as the denominator.

In this case, 3/6 = 1/2.

Hence, plug the numbers right back in and you get 1:2.

Hope this helped!

Answer:

Yes.

Step-by-step explanation:

First, find the unit rate for 1 bookcase.

65 ÷ by 13 = 5 (unit rate)

Then, multiply the unit rate by the bookcases the carpenter wants to make.

6 · 5 = 30

Finally, subtract the shelves the carpenter wants to use by 30.

32 - 30 = 2 shelves.

Therefore, 32 shelves is enough to build 6 more bookcases. <3

Answer:

12+18x is the perimeter

Step-by-step explanation:

4+6x+4+6x+1/2(4+6x)+1/2(4+6x)=

3(4+6x)=

12+18x

Answer:

slope - (-4/5)

y- intercept - (0,-2)

Step-by-step explanation:

Answer:

the slope is -4/5 and the y intercept is -2

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

Answer:

x = 7

Step-by-step explanation:

Given the equations

2x + 3y = 17 → (1)

2y + z = 1 → (2)

5x + 10z = 25 → (3)

Rearrange (2) expressing z in terms of y

z = 1 - 2y

Substitute z = 1 - 2y into (3)

5x + 10(1 - 2y) = 25

5x + 10 - 20y = 25 ( subtract 10 from both sides )

5x - 20y = 15 → (4)

Multiply (1) by 20 and (4) by 3, then add to eliminate the y- term

40x + 60y = 340 → (5)

15x - 60y = 45 → (6)

Add (5) and (6) term by term to eliminate y, that is

55x = 385 ( divide both sides by 55 )

x = 7

Answer:

[tex]x = 7[/tex]

Step-by-step explanation:

From the equation [tex]2y + z = 1[/tex] , we can separate [tex]z[/tex] so that [tex]z = 1-2y[/tex].

The equation [tex]5x+10z = 25[/tex] can then be turned into:

[tex]5x+10(1-2y) = 25[/tex]

[tex]5x+10-20y = 25[/tex]

[tex]5x -20y = 15[/tex]

[tex]x-4y = 3[/tex] (divide by [tex]5[/tex] on both sides)

We can now use elimination to solve for one of the variable:

[tex]2(x-4y) = 2\times3[/tex] (times 2 to get [tex]2x[/tex] for elimination)

[tex]2x-8y=6[/tex]

[tex]2x+3y-(2x-8y) = 17-6[/tex]

[tex]11y = 11[/tex]

[tex]y = 1[/tex]

Now, we can use substitution to solve for [tex]x[/tex]:

[tex]2x+3y = 17[/tex]

[tex]2x+3 = 17[/tex]

[tex]x = 7[/tex]

Hope this helps :)

Answer:

Step-by-step explanation:

The two integers are 10 and 9

10 + 9 = 19

10 x 9 = 90

The two numbers are 9 and 10.

A number without a decimal or fractional element is known as an integer, which can be both positive and negative, including zero

Let the two integers be x and y.

Given that, the sum of the integers is 19, therefore,

x + y = 19

x = 19 - y

Given that, the product of the integer is 90:

xy = 90

(19-y)y = 90

19y - y² = 90

y² -19y + 90 =0

y² -10y - 9y + 90 = 0

y(y - 10) -9(y - 10) = 0

(y -9)(y - 10) = 0

y = 9 and y = 10

Hence, the two numbers are 9 and 10.

Learn more about integers:

https://brainly.com/question/15276410

#SPJ2

Answer:

y=mx+b no judgement i think this is right but i coukldbe completely off

Step-by-step explanation:

Answer: C. 3(b-2)=24

Step-by-step explanation: See since b equals ten and by the rules of P.E.M.D.A.S the parenthesis/brackets comes first so 10-2 equals 8 and three times 8 is 24 therefore the answer is 24