A state park charges a $6.00 entry fee plus $7.50 per night of camping. Write an algebraic expression for the cost in dollars of entering the park and camping for n nights.

The probability that a randomly selected student drives to school is [tex]\( \frac{2}{45} \)[/tex].

The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. In this case, the number of sophomores who drive to school is 2, and the total number of sophomores is the sum of those who drive, take the bus, and walk: 2 + 25 + 3 = 30. Therefore, the probability for sophomores is [tex]\( \frac{2}{30} \)[/tex]. Similarly, for juniors, it is [tex]\( \frac{13}{35} \)[/tex], and for seniors, it is [tex]\( \frac{25}{35} \)[/tex]. To find the overall probability, we take the weighted average:

P(driver to school) = [tex]\frac{\text{(Number of sophomores)} \times P(\text{sophomores}) + \text{(Number of juniors)} \times P(\text{juniors}) + \text{(Number of seniors)} \times P(\text{seniors})}{\text{Total number of students}}[/tex]

[tex]\[ P(\text{driver to school}) = \frac{2 \times \frac{2}{30} + 13 \times \frac{13}{35} + 25 \times \frac{25}{35}}{30 + 35 + 35} \][/tex]

After calculating, the final answer is [tex]\( \frac{2}{45} \)[/tex], representing the probability that a randomly selected student drives to school. This approach considers the distribution of students across different grades, giving a more accurate representation of the overall likelihood.

Answer:

add 1/2x to both sides

multiply both sides by 6/7

Answer: Add 1/2x to both sides.

Multiply both sides by 6/7.

Step-by-step explanation: credit to the person above or below me

Answer:

[tex]P= 26\text{ inches}[/tex]

Step-by-step explanation:

We are given the following in the question:

Dimensions of rectangle:

Length of rectangle,l = 9 inches

Width of rectangle, w = 4 inches

Perimeter of rectangle =

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

Putting values, we get,

[tex]P= 2(9) + 2(4)\\P= (18) + (8)\\P= 26\text{ inches}[/tex]

Thus, the perimeter of rectangle is 26 inches.

Answer:

Step-by-step explanation:

The first function is

[tex]f(x)=2x^{2} -8x+1[/tex]

The second function is

x   g(x)

-2    2

-1    -3

0     2

1     17

The vertex has coordinates of [tex]V(h,k)[/tex], where [tex]h=-\frac{b}{2a}[/tex] and [tex]k=f(h)[/tex].

Let's find the vertex for the first function where [tex]a=2[/tex] and [tex]b=-8[/tex].

[tex]h=-\frac{-8}{2(2)}=2[/tex]

[tex]k=f(2)=2(2)^{2} -8(2)+1=8-16+1=-8+1=-7[/tex]

Therefore, the vertex of the first function is at [tex](2,-7)[/tex].

Now, the minimum value of the second function can be deducted from its table, which is [tex](-1,-3)[/tex].

Therefore, [tex]f(x)[/tex] has -7 as minimum value and [tex]g(x)[/tex] has -3 as minimum vale.

So, the right answer is B, because -7 is less than -3.

Answer:

1300π

Step-by-step explanation:

The volume of a cylinder is

V = Area of base * height

The base is a circle, so its area is

A = πr^2

The radius is half the diameter: 20/2 = 10 ft.

A = π10^2 = 100π

Plug this back into the volume formula:

V = 100π * height

   = 100π * 13

   = 1300π ft

Answer:

35.36 cm

Step-by-step explanation:

The diagonal of a square will be given by

[tex]D=\sqrt {a^{2}+b^{2}}[/tex]

Where a is the length of one side and b is the length of another side. For a square, botj sides are equal hence the diagonal calculations will be as follows

Given that a is 25 then

[tex]D=\sqrt {25^{2}+25^{2}}[/tex]

D=35.3553390593274

Rounding off the nearest two decimal place

D=35.36 cm

The length of the diagonal (c) of the square paper that measures 25 cm on a side can be found using the Pythagorean Theorem (a² + b² = c²). In this case, a = 25cm, b = 25cm, and by solving for c we get c = √(25² + 25²) ≈ 35.36 cm.

In order to answer your question about the length of the diagonal of a square, you would need to use the Pythagorean Theorem. The Pythagorean Theorem is a mathematical principle which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be expressed as: a² + b² = c².

In a square, all sides are equal, so we can consider the given measurement of 25 cm for both 'a' and 'b'. Hence, a = 25cm and b = 25cm. That would make our equation: 25² + 25² = c². When you calculate it, we get 625 + 625 = c², summing them up you get 1250 = c². To find 'c', you will take the square root of 1250 which equals approximately 35.36 cm. So, the length of the diagonal of the square paper is around 35.36 cm.

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Answer:

Step 1: −8x2−15x+2

Step 2: (−8x+1)(x+2)

Step 3: Say thank you

The factors of quadratic equation are : (8x -1) and (x + 2)

Given ,

-8x² -15x + 2 =​ 0

Now,

Firstly multiply the equation with -1 to make the coefficient of x² positive .

8x² + 15x -2 = 0

Now taking the factors,

8x² + 16x - 1x -2 = 0

8x(x + 2) -1 (x + 2) = 0

(8x -1) (x + 2) = 0

Thus,

The factors are (8x -1) and (x + 2).

The values of x are 1/8 and -2 .

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Answer:

Its A.

Step-by-step explanation:

Answer:

The circumference of a circle is the length of its side, the area is the amount of space within it.

Step-by-step explanation:

Answer:

The circumference of a circle is the length of its side, the area is the amount of space within it.

Have a good day! (:

Answer:

B. 106.2

Step-by-step explanation:

We have been given that at 7 am you drink a 12-ounce cup of coffee which has 140 mg of caffeine. The liver metabolizes caffeine at a rate of 12.9% per hour. We are asked to find the milligrams of caffeine left in your body after 2 hours.

We will use exponential decay formula to solve our given problem.

[tex]y=a\cdot (1-r)^x[/tex], where,

y = Final value,

a = Initial value,

r = Decay rate in decimal form,

x = Time.

Let us convert 12.9% in decimal form.

[tex]12.9\%=\frac{12.9}{100}=0.129[/tex]

Initial value is 140 mg.

[tex]y=140\cdot (1-0.129)^x[/tex]

[tex]y=140\cdot (0.871)^x[/tex]

Now we will substitute [tex]x=2[/tex] in our equation as:

[tex]y=140\cdot (0.871)^2[/tex]

[tex]y=140\cdot (0.758641)[/tex]

[tex]y=106.20974\approx 106.2[/tex]

Therefore, approximately 106.2 milligrams of caffeine will be in your body after 2 hours.

Answer:

470(32 - n)

Step-by-step explanation:

Here are the given:

> 32 volunteers

> n volunteers who didn't donate

> 470 mL each

So your expression is: 470(32 - n).

Why?

Subtract the 32 volunteers who want to donate blood from the volunteers who were not able to donate then multiply it by 470.

Hope this helps!

Answer:

2% or less likely

Step-by-step explanation:

At the age of 53.5136 years, an average man expects to have half his hair left.

Given information:

Starting at the age of 40, an average man loses 5% of his hair every year.

So, at the age of 40 years, an average man will have 95% of total hairs left.

Let t be the number of years after the age of 40 years.

So, the value of t so that the man will have 50% of hairs left can be calculated as,

[tex]50\%=(1-5\%)^t\\0.5=(1-0.05)^t\\0.5=0.95^t\\log0.5=t\rm \;log0.95\\\it t=\rm 13.5136[/tex]

So, the age of the man with 50% hairs left will be 40+13.5136=53.5136 years.

Therefore, at the age of 53.5136 years, an average man expects to have half his hair left.

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Answer:

5.64

Step-by-step explanation:

set up a ratio problem

5 ounces/2.35 = 12 ounces/x

5x = 28.2

x = 5.64

Answer:

5.64

Step-by-step explanation:

5x2.4=12

SO,

2.35x2.4=5.64

Assume number =x,

x(2x+5) = 75

=> 2x^2 + 5x -75 = 0

=> 2x^2+ 15x -10x -75 =0

=> x(2x+15)-5(2x+15)=0

=>(x-5)(2x+15)=0

x = 5, or x = -15/2

Answer:

84,500

Step-by-step explanation:

8.45*10^4

8.45 * (10*10*10*10)

8.45 * 10000

84500

the decimal place moves to the right for however many zeros you have :)

i hope this helps :)

Answer: 331.5 inches²

Step-by-step explanation:

To solve for the area of a regular octagon, we can use the formula that is shown below:

Area = 1/2 × apothem × perimeter

In this problem, we have been given the following values:

Apothem = 10 inches

Perimeter = 66.3 inches

To solve for the area,

Area = 1/2 × apothem × perimeter

Area = 1/2 × 10 × 66.3

Area = 331.5 inches²

Answer:

397

Explanation: 9+7 =16 and 3 is odd

Answer:

397

Step-by-step explanation:

379 or 397 with fit the criteria

Answer:

The cost for this appliance is $0.02604

Step-by-step explanation:

In order to solve this problem we need to apply the appliance's values to the provided formula as shown bellow:

cost = {[w*(m/60)]/1000}*c

cost = {[500*(25/60)]/1000}*0.125

cost = {[12500/60]/1000}*0.125

cost = {208.4/1000}*0.125

cost = 0.2084*0.125 = 0.02604

The cost for this appliance is $0.02604

Answer:

$1.68

Step-by-step explanation:

If the function modelled for finding the cost of running the appliance for m minutes is given by the formula (w(m/60))/1000 c, and the following datas are given:

W = 500watts

m = 25minutes

c = cost per kWhr = $0.125

Cost of running an appliance that requires 500 watts for 25 minutes at a cost of $0.125 per kWh will be gotten by substituting the given data in the modelled function.

C= {500(25/60)}/1000 (0.125)

C =(500×0.42)/125

C = 210/125

C = $1.68

The cost of running the appliance will be $1.68

Answer:

1. Juan's marathon training schedule is an example of a geometric sequence

2. Lizzy's marathon training schedule is an example of an arithmetic sequence

3. Lizzy will be better prepared for the marathon

Step-by-step explanation:

In the arithmetic sequence there is a common difference between each two consecutive terms

In the geometric sequence there is a common ratio between each two consecutive terms

Juan's Schedule

∵ Juan's will run one mile on the first day of the week

∴ [tex]a_{1}[/tex] = 1

∵ He will double the amount he runs each day for the next

   6 days

- That means he multiplies each day by 2 to find how many miles

   he will run next day

∴  [tex]a_{2}[/tex] = 1 × 2 = 2 miles

∴  [tex]a_{3}[/tex] = 2 × 2 = 4 miles

∴  [tex]a_{4}[/tex] = 4 × 2 = 8 miles

∴  [tex]a_{5}[/tex] = 8 × 2 = 16 miles

∴  [tex]a_{6}[/tex] = 16 × 2 = 32 miles

∴  [tex]a_{7}[/tex] = 32 × 2 = 64 miles

That means there is a common ratio 2 between each two consecutive days

1. Juan's marathon training schedule is an example of a geometric sequence

Lizzy's Schedule

∵ Lizzy's will run 10 miles on the first day of the week

∴ [tex]a_{1}[/tex] = 10

∵ She will increase the amount she runs by 3 miles each day for

   the next six days

- That means she adds each day by 3 to find how many miles

    she will run next day

∴  [tex]a_{2}[/tex] = 10 + 3 = 13 miles

∴  [tex]a_{3}[/tex] = 13 + 3 = 16 miles

∴  [tex]a_{4}[/tex] = 16 + 3 = 19 miles

∴  [tex]a_{5}[/tex] = 19 + 3 = 22 miles

∴  [tex]a_{6}[/tex] = 22 + 3 = 25 miles

∴  [tex]a_{7}[/tex] = 25 × 3 = 28 miles

That means there is a common difference 3 between each two consecutive days

2. Lizzy's marathon training schedule is an example of an arithmetic sequence

The rule of the sum of nth term in the geometric sequence is [tex]S_{n}=\frac{a_{1}(1-r^{n})}{1-r}[/tex]

∵ [tex]a_{1}[/tex] = 1 , r = 2 and n = 7

∴  [tex]S_{7}=\frac{1(1-2^{7})}{1-2}[/tex]

∴  [tex]S_{7}[/tex] = 127

∴ Juan will run 127 miles in the final week

The rule of the sum of nth term in the arithmetic sequence is [tex]S_{n}=\frac{n}{2}[a_{1}+a_{n}][/tex]

∵ n = 7,  [tex]a_{1}[/tex] = 10  and  [tex]a_{7}[/tex] = 28

∴ [tex]S_{7}=\frac{7}{2}(10+28)[/tex]

∴ [tex]S_{7}[/tex] = 133

∴ Lizzy will run 133 miles in the final week

∵ 133 miles > 127 miles

∴ Lizzy will run more miles than Juan

3. Lizzy will be better prepared for the marathon

Answer: There are 96 green pens sold.

Step-by-step explanation:

Since we have given that

Number of pens in each pack of black pens = 3

Number of pens in each pack of red pens = 5

Number of pens in each pack of green pens = 6

Ratio of number of packs sold of black, red and green pens = 7: 2: 4

Number of total pens sold = 220

So, ratio of pens in number of packs would be

[tex]7\times 3:2\times 5:4\times 6\\\\=21:10:24[/tex]

So, Number of green pens sold would be

[tex]\dfrac{24}{55}\times 220\\\\=24\times 4\\\\=96\ pens[/tex]

Hence, there are 96 green pens sold.

96 green pens were sold.

Since the number of packs sold of black, red and green pens are in the ratio  7 : 2 : 4

Also, a total 220 pens were sold. Let x represent the total number of packs, hence:

Number of black pens = 7x/13 * 3 = 21x/13

Number of red pens = 2x/13 * 5 = 10x/13

Number of green pens = 4x/13 * 6 = 24x/13

Hence:

21x/13 + 10x/13 + 24x/13 = 220

21x + 10x + 24x = 2860

55x = 2860

x = 52

Number of green pens = 24x/13 = 24(52)/13 = 96

Hence  96 green pens were sold.

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Answer: 83 inches

Step-by-step explanation:

1 foot = 12 inches

In the mane, she used 6 feet of ribbon. 6×12 = 72 inches

 She used an additional 11 inches of ribbon around her front right leg

Altogether she use 72 + 11 = 83 inches

Answer:

log5(125)=3 The 5 should be smaller and a little lower.

Step-by-step explanation:

Answer:

18 s

Step-by-step explanation:

We are given that

Distance between Bob and John=450 feet

Speed of Bob=11ft/s

Speed of John=14 ft/s

We have to find the time after they will meet when they are travel towards to each other.

Total distance traveled by Bob and John in 1 s=11+14=25 ft

25ft covered by Bob and John in 1 s

1 ft covered by Bob and John in [tex]\frac{1}{25}s[/tex]

450 ft covered by Bob and John  in [tex]\frac{1}{25}\times 450=18 s[/tex]

Hence, they will meet after 18 s.

Answer:

18 seconds

Step-by-step explanation:

450 divided by 11+14=18

Answer:

middle square top row =9 middle row left square= 7   middle row right square=3 bottom row left square =6 bottom row middle square 1

Step-by-step explanation:

every row = 15 so just start with the rows and columns that only need one square until you've filled it in enough that every row needs one and the solve from there

A magic square consists of a grid of numbers where each row, column, and diagonal add up to the same total. For a 3x3 magic square using numbers 1 through 9, this total is 15. Possible solutions include the rotations of the groupings 9, 5, 1 and 6, 2, 7.

A magic square is a grid of numbers where the values in each row, column, and diagonal add up to the same total. The key to solving such a puzzle is understanding that total. Since we are using the numbers 1 through 9, the total sum of these numbers is 45; because there are 3 rows (or columns or diagonals) in a 3x3 grid, each must add up to 15.

The only way to get 15 with three numbers in the 1-9 range is to either group 9, 5, and 1 or their rotations (such as 5, 1, 9 or 1, 9, 5) or use 6, 2, and 7 or their rotations. This leads to the following magic square:

8 1 6

3 5 7

4 9 2

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Answer:

1.3 x 3.14 x 3 x 3 x 3 = 27 x 1.3 x 3.14 = 113.04

formula is 4/3 x pi x radius to the power of three

Step-by-step explanation:

I may have used google...

Answer:

It's 113.04 in. 3

Step-by-step explanation:

I used the formula from the person on top, credits to them ^^

It takes 10.5 minutes for both the computers to do the work by working together

What is a Fraction?

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator.

Given data ,

The time for which the slower computer can send all the mails = 35 minutes

The time for which the faster computer can send all the mails = 15 minutes

So ,

The slower computer can complete the work in = 1 / 35 min

The faster computer can complete the work in = 1 / 15 min

Let the total work done by both computers together be = W

The total work completed when both the computers work together is 1 / W =
The work completed by slower computer + The work completed by slower computer

The total work completed when both the computers work together 1 / W =
1 / 35 +  1 / 15

And ,

1 / W = 1 / 35 +  1 / 15

1 / W = 10 / 105

Taking reciprocals , we get

W = 105 / 10

W = 10.5 minutes

Hence , The time taken by both the computers to do the work together is 10.5 minutes

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Final answer:

To find the combined time for two computers to complete a job, calculate their work rates individually and add them up.

Explanation:

To solve this problem, we can use the concept of work rates.

Calculate the work rate of each computer:

Slower computer's work rate = 1 job / 35 minutes = 1/35 job per minute

Faster computer's work rate = 1 job / 15 minutes = 1/15 job per minute

When both computers work together:

Total work rate = 1/35 + 1/15 = 5/105 + 7/105 = 12/105 jobs per minute

Calculating the time taken:

Time taken = 1 job / Total work rate = 105 / 12 = 8.75 minutes

Therefore, both computers working together will complete the job in 8.75 minutes.

Answer:

See below where I explain line by line.

Step-by-step explanation:

If two lines are parallel, their slopes are equal.

Look at line 1: Both lines have slope 1/2. Since both slopes are 1/2, the slopes are equal, and the lines are parallel.

Look at line 7: slope 4/8, slope 1/2. Reduce 4/8. It reduces to 1/2. Both lines have slope 1/2. The lines have equal slopes, so they are parallel.

If two lines are perpendicular, then their slopes are opposite reciprocals. Reciprocals are two numbers that when when written as a fraction, when you flip one, you get the other. For example, 4/5 and 5/4. They are reciprocals because is you flip 4/5, you get 5/4. For two lines to be perpendicular, their slopes need to be reciprocals and opposites. That means their signs must be different (one positive and one negative) in addition to being reciprocals. For example, two lines with slope 5/8 and -8/5 are perpendicular since the slopes are both reciprocals and opposites.

Look at line 2: -2/3 and 3/2. If you flip -2/3, you get -3/2. The opposite of -3/2 is 3/2. That means each slope is the opposite reciprocal of the other, so they are perpendicular.

Line 5: slope 4, slope -1/4. Write 4 as a fraction. Now you have 4/1. Flip 4/1 to get 1/4. Then make it the opposite, -1/4. The second line does have slope -1/4, so they are perpendicular.

Line 6: slope -1/6, slope 6. Flip -1/6. You get -6/1. Find its opposite: 6/1. 6/1 is the same as 6. That means that -1/6 and 6 are opposite reciprocals and the lines are perpendicular.

Lines that are neither parallel nor perpendicular.

Look at line 3: 5/2 and 2/5. If you flip 5/2, you get 2/5. The slopes are reciprocals, but they are not opposites since they are both positive. The lines are not perpendicular. Also 5/2 is not equal to 2/5, so the lines are not parallel either.

Look at line 4: slope -3; slope -1/3. Start with -3. Write it as a fraction: -3/1. Now flip it: -1/3. Now find its opposite: 1/3. If the slopes were -3 and 1/3, the lines would be perpendicular because they'd be reciprocal and opposite. The second slope is -1/3, not 1/3, so they are not opposite, and the lines are not perpendicular. Also, -3 and -1/3 are not equal, so the lines are also not parallel.

Answer:

Hanna donated b/50 books

Step-by-step explanation:

In this problem, we have:

n = 150 number of students at Hanna's school

b = ? number of total books donated by the students

Also, Hannah has donated 3 times as many as the average number of books each student donated.

The average number of books each student donated can be written as:

[tex]\frac{b}{150}[/tex]

And calling

h = number of books donated by Hannah

This means that

[tex]h=3(\frac{b}{150})[/tex]

Simplifying, this can be rewritten as

[tex]h=\frac{b}{50}[/tex]

Answer:

b/50

Step-by-step explanation: