A store sells a box of breakfast cereal for $3. Write an equation to relate the number of boxes b to total sales T.

Answer:

The prime factors of 13195 are 5, 7, 13 and 29. The largest prime factor of the number 600851475143 is 6857

The probability that no two consecutive heads will occur is 13/32.

It should be noted that probability simply means the likelihood of the occurence of an event based on chance.

In this case, the fair coin is tossed 5 times and we simony want it find the probability that no two consecutive heads will occur.

This will be:

Let n be the number of strings of h

Let t be the length n with two adjacent H's.

Therefore, the probability will be:

= (8+5)/2^5

= 13/32

In conclusion, the probability that no two consecutive heads will occur is 13/32.

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Answer: 5

Step-by-step explanation:

11/2-x = 1/3 + 1/6

-x+11/2 = 1/2

   - 11/2   - 11/2

-x = -5

Divide -1 by both sides

And it gives you the answer 5.

Answer:

104.607kph

Step-by-step explanation:

Conversion from mph to kph = 1.609mph

The function that models the independent variable, x, in terms of y, is:

[tex]x = ln(\frac{y}{2.56})/ln(1.04)[/tex]

Here we have the relation:

[tex]y = 2.56*(1.04)^x[/tex]

We want to write x in terms of y, so we just need to isolate x.

We have:

[tex]\frac{y}{2.56} = (1.04)^x[/tex]

Now we can apply the natural logarithm in both sides, so we get:

[tex]ln(\frac{y}{2.56}) = ln((1.04)^x)\\\\ln(\frac{y}{2.56}) = ln((1.04))*x[/tex]

Now we can just isolate x.

[tex]x = ln(\frac{y}{2.56})/ln(1.04)[/tex]

That is the function that models the independent variable, x, in terms of y.

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Step-by-step explanation:

"t t hours" ????

you mean 11 hours ?

13 gallons now.

2 gallons are used (and therefore disappear from the tank) per hour.

so, in 5 hours 5×2 = 10 gallons will be used.

that leaves 13 - 10 = 3 gallons in the tank.

in 11 hours 11×2 = 22 gallons would have been used.

but there are only 13 gallons in the tank.

so, if he does not fill up, he will have 0 gallons left after 11 hours. in fact, already after 13/2 = 6.5 hours.

the point :

when you use 2 gallons per hour, that means in t hours you are using t × 2 or 2t gallons.

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

Explanation:

The 3y in the first equation must add to -3y so the y terms go away. We have -y in the second equation, which is why we triple everything in that equation

2x-y = 1 becomes 6x - 3y = 3 after tripling everything. This is the same as multiplying both sides by 3.

This is the updated equivalent system

[tex]\begin{cases}x+3y = 42\\6x-3y = 3\end{cases}[/tex]

Add the terms straight down

We have the equation 7x = 45 which solves to x = 45/7.

Unfortunately it doesn't turn into a nice single whole number because 45 isn't a multiple of 7. So I would leave it as a fraction.

Optionally you could note that 45/7 = 6.42857 approximately. But I prefer the fraction form since it's most exact.  

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

Use this x value to find y. Pick any equation involving x and y. Plug in that x value and solve for y.

x + 3y = 42

45/7 + 3y = 42

3y = 42 - 45/7

3y = 42*(7/7) - 45/7

3y = 294/7 - 45/7

3y = (294 - 45)/7

3y = 249/7

y = (249/7)*(1/3)

y = 83/7

Like with x, we also don't get a nice whole number.

I used WolframAlpha to confirm the solutions. GeoGebra is another tool you could use.

Using the binomial distribution, it is found that there is a 0.0012 = 0.12% probability at least two of them make it inside the recycling bin.

The formula is:

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

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

The parameters are:

With 5 shoots, the probability of making at least one is [tex]\frac{211}{243}[/tex], hence the probability of making none, P(X = 0), is [tex]\frac{232}{243}[/tex], hence:

[tex](1 - p)^5 = \frac{232}{243}[/tex]

[tex]\sqrt[5]{(1 - p)^5} = \sqrt[5]{\frac{232}{243}}[/tex]

1 - p = 0.9908

p = 0.0092

Then, with 6 shoots, the parameters are:

n = 6, p = 0.0092.

The probability that at least two of them make it inside the recycling bin is:

[tex]P(X \geq 2) = 1 - P(X < 2)[/tex]

In which:

[P(X < 2) = P(X = 0) + P(X = 1)

Then:

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

[tex]P(X = 0) = C_{6,0}.(0.0092)^{0}.(0.9908)^{6} = 0.9461[/tex]

[tex]P(X = 1) = C_{6,1}.(0.0092)^{1}.(0.9908)^{5} = 0.0527[/tex]

Then:

P(X < 2) = P(X = 0) + P(X = 1) = 0.9461 + 0.0527 = 0.9988

[tex]P(X \geq 2) = 1 - P(X < 2) = 1 - 0.9988 = 0.0012[/tex]

0.0012 = 0.12% probability at least two of them make it inside the recycling bin.

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Answer: definition of slope

Step-by-step explanation:

The results in step 7 come from substituting the coordinates into the slope formula.

Answer:

Right option is B.

Step-by-step explanation:

[tex] \sf \longrightarrow \frac{ \sec x \sin( - x) + \tan( - x) }{1 + \sec( - x) } \\ \\ \sf \longrightarrow \frac{ \sec x( - \sin x) - \tan x}{1 + \sec x} \\ \\ \sf \longrightarrow \frac{ - \frac{1}{ \cos x } \times \sin x - \tan x }{1 + \sec x} \\ \\ \sf \longrightarrow \frac{ - \tan x - \tan x}{1 + \sec x} \\ \\ \sf \longrightarrow \frac{ - 2 \tan x}{1 + \sec x} \\ \\ \sf \longrightarrow \frac{ \frac{ - 2 \sin x}{ \cos x} }{1 + \frac{1}{ \cos x} } \\ \\ \sf \longrightarrow \frac{ \frac{ - 2 \sin x}{ \cos x} }{ \frac{ \cos x + 1}{ \cos x} } \\ \\ \boxed{ \sf{\longrightarrow \frac{ - 2 \sin x}{ \cos x + 1} }}[/tex]

Answer:

3.64 × 10(raised to the power 7)

2.6 × 10⁴

The values of x and y in the equation are 15 and 28 respectively

Let's find the x and y values in the equation,

m = 7x + 7

m = 4y

m = 112

Therefore,

4y = 7x + 7

4y - 7x = 7

4y = 112

y = 112 / 4

y = 28

Therefore,

4(28) - 7x = 7

112 - 7x = 7

112 - 7 = 7x

105 = 7x

x = 105 / 7

x = 15

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The logarithmic form of 13^2=169 is [tex]\log_{13}(169) = 2[/tex]

The equation is given as

13^2=169

Take the logarithm of both sides

log(13^2) = log(169)

This gives

2log(13) = log(169)

Divide both sides by log(13)

[tex]\log_{13}(169) = 2[/tex]

Hence, the logarithmic form of 13^2=169 is [tex]\log_{13}(169) = 2[/tex]

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Answer:

10 unit^2.

Step-by-step explanation:

The base of the triangle (CE)

= 6 - 2 = 4 units

The height = 5

Area = 1/2 * 4 * 5

= 10 unit^2.

Answer:

10

Step-by-step explanation:

area = hight ×base÷2

hight = 5-0

= 5

base = 6-2

= 4

area = 4×5÷2

=10

Check the picture below.

The requried measure of the angle m∠C in the given circle is 15°.

In the given circle the m∠DFB is 41°, mArc EF is 52°
To find out the measure of the angle m∠C.

Following the properties of arcs in the circle,
arc BD = 2m∠BFD
arc BD=2*41 = 82

Now we know that,
The angle subtended by two sectants drawn from the single point that lies outside the circle is given by the difference in larger and minor arcs divided by 2.

∠c= BD- EF / 2
∠c = 82°-52°/2
∠c = 15°

Thus, the requried measure of the angle m∠C in the given circle is 15°.

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Based on the given parameters, the 15 ft rope will reach the swimmer

From the question, we have the following equation:

sin 55 = 10/x

Multiply both sides of the equation by x

x * sin 55 = 10/x * x

Evaluate the product

x * sin 55 = 10

Divide both sides by sin 55

x = 10/sin 55

Evaluate sin 55

x = 10/0.8192

Evaluate the quotient

x = 12.21

From the question, the lifeguard tosses a ring in a 15ft rope to the swimmer

15 is greater than 12.21

This means that the 15 ft rope will reach the swimmer

Hence, the 15 ft rope will reach the swimmer

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The option B is a correct option which is y = 26x and y = -0.030(x-500)2 15,900 represent the quadratic and linear function.

According to the statement

we have given that Vertex

(h,k) = (500, 15900)

And One of the points on the graph

(x,y) = (0,8400)

FIRST PART: we have to find the quadratic function

We can find the quadratic function by parabola's equation formula

y = a (x - h)² + k  -(1)

Input the numbers to the formula, to find the value of a

y = a (x - h)² + k

8400 = a(0 - 500)² + 15900

8400 = a (500)² + 15900

8400 = 250000a + 15900

-250000a = 15900 - 8400

-250000a = 7500

a = 7500/-250000

a = 0.03

Now,

Submit a to the formula (1)

y = a (x - h)² + k

y = 0.03 (x - 500)² + 15900

this is the quadratic equation.

SECOND PART: Find the linear function

the total cost = cost each helmet × the number of helmet

y = 26x

So,

The option B is a correct option which is y = 26x and y = -0.030(x-500)2 15,900 represent the quadratic and linear function.

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Disclaimer: This question was incomplete. Please find the full content below.

Question: A company plans to sell bicycle helmets for $26 each. The company's business manager estimates that the cost, y, of making x helmets is a quadratic function with a y-intercept of 8,400 and a vertex of (500, 15900)

x= number of helmets

y = amount in dollars

Which system models this situation?

a) y = 26x and y = 8,400(x-500)2+15,900

b) y = 26x and y = -0.030(x-500)2+15,900

c) y = x/26 and y = -0.030(x-500)2+15,900

d) y = x/26 and y =8,400(x-500)2+15,900

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Answer:

B. y = 26x and y = -0.030(x-500)2+15,900

Step-by-step explanation:

Answer: Choice B

All real numbers except 2 and 5

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

Explanation:

Factor the denominator.  We need to find two numbers that multiply to 10 and add to -7.

Through trial and error, those two numbers are -2 and -5

-2 times -5 = 10

-2 plus -5 = -7

This means the denominator [tex]\text{x}^2 - 7\text{x} + 10[/tex] factors to [tex](\text{x}-2)(\text{x}-5)[/tex]. You can use the FOIL rule to confirm this.

Then each piece is set equal to zero to solve for x

x-2 = 0 leads to x = 2

x-5 = 0 leads to x = 5

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

In short, if x = 2 or x = 5, then it causes the the denominator [tex]\text{x}^2 -7\text{x}+10[/tex] to turn into 0.

Dividing by 0 is not allowed; therefore, x = 2 nor x = 5 is allowed in the domain. Any other x value is valid.

Answer: 9 yards

Step-by-step explanation:

Let's make equations to represent each situation.

The first equation says that the width is 3 less than 4 times the length, so let's put that into an equation:

[tex]w=4l-3[/tex]

Next, we can use the perimeter equation that [tex]P=2l+2w[/tex]. Since we know the perimeter is 24 yards, we can replace it for P.

[tex]24=2l+2w[/tex]

Now that we have two equations with two variables, we can use either elimination or substitution to solve them. Since w is already solved for in the first equation, let's plug it in the second equation.

[tex]24=2l+2(4l-3)\\ 12=l+4l-3\\ 12=5l-3\\ 15=5l\\ l=3[/tex]

Now, let's put l back into the first equation to solve for w.

[tex]w=4(3)-3\\ w=12-3\\ w=9[/tex]

The width is 9 yards

Step-by-step explanation:

what is not clear that you cannot answer this by yourself ?

please let me know what you need explained.

1. Rhombus

2. rectangle

3. square

4. rhombus

5. square

6. rectangle

7. rhombus

8. parallelogram

The proofing of the triangle is illustrated below.

Based on the information, the reflexive property of equality states that an angle or shape is always congruent to itself.

The alternate interior angle theorem is that when two parallel lines are cut by a transversal, then the alternate interior angles are the same.

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Answer:

answer in picture

Step-by-step explanation:

Answer:

x=m/9

Steps:

m=9x

m/9=x

x=m/9

it is a relatively easy way to draw a sample while ensuring randomness is the answer.

Systematic sampling is a probabilistic sampling method in which a researcher selects members of a population at regular intervals. For example, select every 15 people from the list of populations. If the population is in random order, this can mimic the benefits of a simple random sample.

These are generally preferred by researchers because they are easy to implement and understand. The important assumption that the results represent the majority of the normal population ensures that the entire population is sampled equally. The process also provides a higher level of control for systematic sampling compared to other sampling methods. systematic sampling also has a lower risk factor because the data is unlikely to be contaminated.

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From the list of options, the set that is equal to the set  {1, 2, 3, ...} is {x | x N, x ≥ 1}

The set is given as:

{1, 2, 3, ...}

The three dots (...) after 3 implies that the elements of the set include other values such as 4, 5, 6 and so on

Using the above scenario, we can see that the set  {1, 2, 3, ...} contains only positive integers.

All positive integers are natural numbers and they are denoted by N

From the list of options, we have:

{x | x R, x ≥ 1}

This represents the set of all real numbers greater than or equal to 1.

Note that this set includes decimal numbers i.e. 1, 1.5, 1.89 and so on

This does not represent the set  {1, 2, 3, ...}

{x | x R, x > 1}

This represents the set of all real numbers greater than 1.

Note that this set includes decimal numbers i.e. 1.5, 1.89 and so on

This does not represent the set  {1, 2, 3, ...}

{x | x N, x ≥ 1}

This represents the set of all natural numbers greater than or equal to 1.

Note that this set does not include decimal numbers i.e. 1, 2, 3, 4 and so on

This does represent the set  {1, 2, 3, ...}

Hence, the set that is equal to the set  {1, 2, 3, ...} is {x | x N, x ≥ 1}

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Answer:  2.12 × [tex]10^{-3}[/tex]

               The coefficient (in green) will be 2.12

Step-by-step explanation:

     Scientific notation is written by multiplying the number by a power of 10. This number is a number between 1 and 10.

     Since this is a smaller number, we will be multiplying it by a power of 10 to a negative number.

    To get this value to a number between 1 and 10, we must multiply it by 10 3 times (also shown as 10³) which gives us 2.12.

    To get back to the original value, we multiply this by [tex]10^{-3}[/tex]. This gives us our answer.

ANSWER:

Quadrant ll

________________________________

________________________________HOPE IT HELPS

Answer:

Khan Academy.

Step-by-step explanation:

You can go on khan academy and search up "area and graphs." The videos should immediately pop up. there are also lessons if you don't want to risk getting your problem wrong. If you are still confused and do not understand please just comment and I will respond.

Answer:

see explanation

Step-by-step explanation:

to find the intersection equate g(x) and h(x) , that is

(x + 7)(x - 5) = x - 5 ← expand left side using FOIL

x² + 2x - 35 = x - 5 ( subtract x - 5 from both sides )

x² + x - 30 = 0 ← in standard quadratic form

(x + 6)(x - 5) = 0 ← in factored form

equate each factor to zero and solve for x

x + 6 = 0 ⇒ x = - 6

x - 5 = 0 ⇒ x = 5

substitute these values into either g(x) or h(x) for corresponding values of y

substituting into h(x)

h(- 6) = - 6 - 5 = - 11 ⇒ (- 6, - 11 )

h(5) = 5 - 5 = 0 ⇒ (5, 0 )

There are two methods of solving systems of equations:

Substitution is where we substitute one equation into the other by isolating a certain variable, or a group of terms.

Elimination is where we subtract the two equations. Before doing this, we may have to multiply one equation by a certain number to make sure one variable cancels out.

We're given the following equations:

Because they are organized in the same manner (i.e. x [operation] y [equals] number), it is easier for us to use elimination.

First, multiply the first equation by 2:

[tex]x + 3y = 7\\2(x + 3y) = 2(7)\\2x + 6y = 14[/tex]

Now, subtract the second equation from the one we just created:

[tex]\hspace{10}2x + 6y = 14\\-2x + 4y = 11\\\rule{67}{0.3}\\2y=3[/tex]

Solve for y:

[tex]y=\dfrac{3}{2}[/tex]

To solve for x, we can use substitution in the first equation:

[tex]x + 3y = 7\\\\x + 3(\dfrac{3}{2}) = 7\\\\x + \dfrac{9}{2} = 7\\\\x = 7- \dfrac{9}{2}\\\\x = 7- 4.5\\\\x = 2.5\\\\x=\dfrac{5}{2}[/tex]

[tex]x=\dfrac{5}{2}[/tex]

[tex]y=\dfrac{3}{2}[/tex]