A scuba diver dives 80 feet below the surface. After a while, the diver rises 3 feet per
minute. Which integer describes the position if the diver in relation to the surface of
the water 8 minutes after beginning to rise?
A. -56
B. -66
C. -72
D. -88

The counting rule that is used for counting the number of experimental outcomes when n objects are selected from a set of n objects where order of selection is important is called the counting rule for permutations.

What is a counting rule? Counting rule is a mathematical technique that aids in determining the number of ways that certain events or observations can occur. The counting principle is a basic method of calculating the number of feasible events, allowing us to determine the likelihood of different events occurring when several possibilities are available.

What is permutation? Permutations are the ways in which a group of objects or symbols can be ordered or arranged. The order of selection is important in permutations, and each permutation is unique because of this. The formula for computing the permutations of n objects taken r at a time is:

nPr = n! / (n - r)!, where n is the number of objects and r is the number of objects being chosen for the permutation.

This is different from combinations which is used when order of selection is not important, independent events which involves two or more events that are unrelated, and multiple-step random experiments which are experiments that involve two or more random steps.
Therefore, the counting rule that is used for counting the number of experimental outcomes when n objects are selected from a set of n objects where order of selection is important is called the counting rule for permutations.

To learn more about permutations and combinations visit : https://brainly.com/question/28065038

#SPJ11

[tex]\textit{internal division of a line segment using ratios} \\\\\\ P(1,-2)\qquad Q(4,10)\qquad \qquad \stackrel{\textit{ratio from P to Q}}{2:1} \\\\\\ \cfrac{P\underline{T}}{\underline{T} Q} = \cfrac{2}{1}\implies \cfrac{P}{Q} = \cfrac{2}{1}\implies 1P=2Q\implies 1(1,-2)=2(4,10)[/tex]

[tex](\stackrel{x}{1}~~,~~ \stackrel{y}{-2})=(\stackrel{x}{8}~~,~~ \stackrel{y}{20}) \implies T=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{1 +8}}{2+1}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{-2 +20}}{2+1} \right)} \\\\\\ T=\left( \cfrac{ 9 }{ 3 }~~,~~\cfrac{ 18}{ 3 } \right)\implies T=(3~~,~~6)[/tex]

a. We get that it will take approximately 108 months, or 9 years, to double the value of the tithe. b. annual interest rate of approximately 5.84% c. approximately $27,714.28.

In finance, interest refers to the cost of borrowing money or the return on invested money. It is the compensation paid by a borrower to a lender for the use of their money or the compensation paid by an institution to an individual or organization for depositing money with them.

a. Using the TVM Solver with the given information, we get:

Present value (PV) = -$35,000 (since it is a tithe, we are starting with a negative value)

Future value (FV) = $70,000 (since we want the tithe to double in value)

Interest rate (I/Y) = 7.75/12 (since the APR is compounded monthly)

Number of periods (N) = ? (this is what we want to find)

Solving for N, we get that it will take approximately 108 months, or 9 years, to double the value of the tithe.

b. Using the compound interest formula, we have:

A = P(1 + r/n)ⁿˣ

where A is the future value, P is the present value, r is the annual interest rate, n is the number of times per year the interest is compounded, and x is the number of years.

Plugging in the given values, we get:

$50,000 = $22,500(1 + r/2)²*¹⁴

Solving for r, we get that an annual interest rate of approximately 5.84% (compounded semi-annually) is required for the $22,500 to accumulate to $50,000 in 14 years.

c. Using the TVM Solver with the given information, we want to solve for the present value (PV):

Future value (FV) = $40,000

Interest rate (I/Y) = 4.25/4 (since the APR is compounded quarterly)

Number of periods (N) = 9

Payment (PMT) = 0 (since there are no regular payments)

Solving for PV, we get that the present value required to return $40,000 in 9 years at 4.25% APR compounded quarterly is approximately $27,714.28.

To know more about rate visit:

https://brainly.com/question/199664

#SPJ1

The area of the composite figure is 47 cm².

The perimeter of the composite figure is 36 cm.

The figure above is a composite figure because it's compose of two shapes.

Therefore, we have to find the area of the individual shape and sum it  to get the area of the composite figure.

Hence,

area of the composite figure = area of the rectangle1 + area of the rectangle2

55 mm = 5.5 cm

area of the rectangle1  = 2 × 5.5 = 11 cm²

60mm = 6 cm

l = 2 + 6 = 8cm

w = 10 - 5.5 = 4.5 cm

area of the rectangle2 = 8 × 4.5

area of the rectangle2 = 36 cm²

Therefore,

area of the composite figure = 36 + 11 = 47 cm²

perimeter of the composite figure = 2 + 10 + 8 + 4.5 + 6 + 5.5

perimeter of the composite figure =  36 cm

learn more on composite figure here: https://brainly.com/question/870536

#SPJ1

Answer:  The correct option is (A) -28.

Step-by-step explanation:  The given system of linear equations is as follows :

We are to find the y-determinant for the above system of equations.

The given system can be written as :

Therefore, the y-determinant of the system will be

Thus, the required value of the y-determinant is -28.

Option (A) is CORRECT.

Answer:

yes this is because to find similarity of triangles two interior angles must be the same which automatically means that the lat angle would be the same

Answer:

7

Step-by-step explanation:

f(x) = 6 + 3 - 2

= 7

f(x) = 13 + 3 - 2

= 14

Answer:

1256 in.3

Step-by-step explanation:

V = pi x r^2 x h
V = 3.14 x 20/2 x 4
V = 3.14 x 10 x 4

V = 1256in^3

Answer:

1256 in³

Step-by-step explanation:

To calculate volume of a cylinder the formula is: π · r2 · h

Since Pi is already given to us as 3.14, we now have to find the radius

The radius is always the diameter cut in half meaning it will be 20/2 which gives us 10 (radius is figured)

The height is given to us as 4 meaning the equation will be

3.14 x 10 x 10(seeing as it's radius squared) x 4

10x10 = 100

100 x 4 = 400

400 x 3.14 = 1256

The answer is in cubed(³) because it is volume

Answer:

Step-by-step explanation:

its a

Answer :

1.00478853497

Step-by-step explanation :

'Square root of decimal is the value of a decimal number to the power 1/2. For example, the square root of 24.01 is 4.9 as (4.9)2 = 24.01. The square root of a decimal number can be calculated by using the estimation method.

Let's find the square root of 31.36.

Step 1: Find the nearest perfect square numbers to 31.36. 25 and 36 are the perfect square numbers nearest to 31.36.

Step 2: √25 = 5 and √36 = 6. This implies that √31.36 lies between 5 and 6.

Step 3: Now, we need to see if √31.36 is closer to 5 or 6. Let us consider 5.5 and 6.

Step 4: 5.52 = 30.25 and 62= 36. Thus, √31.36 lies between 5.5 and 6 and is closer to 5.5.

Thus, the square root of 31.36 is close to 5.5.'

I got the answer from long division, which you can also find on the article.

Source for step-by-step explanation : https://www.cuemath.com/algebra/square-root-of-decimals/

Sean and his six companions will each receive 1/7 of the original action figures.

Let's assume Sean originally had x action figures. After donating some, he has 1/3 of them left, which is (1/3)x.

To find out how many action figures Sean has left, we can use the equation:

(1/3)x = x - y

where y is the number of action figures Sean donated.

Simplifying this equation, we get:

y = (2/3)x

Now, Sean wants to share his remaining action figures with 6 friends, so they will split the total number of action figures into 7 equal parts (Sean + 6 friends).

Therefore, each person will get 1/7th of the total number of action figures.

To find out what fraction of the original action figures each person will get, we need to divide the number of action figures each person will get by the original number of action figures (x):

1/7 = [tex]\frac{[(\frac{1}{3} )x - y]}{x}[/tex]

Substituting y = (2/3)x, we get:

1/7 = [tex]\frac{[(\frac{1}{3} )x - (\frac{2}{3} )x]}{x}[/tex]

1/7 = (1/3)

Therefore, each person will get 1/7th of the original number of action figures.

To learn more about fraction, refer:-

https://brainly.com/question/10354322

#SPJ1

Robert Wadlow's height is more extreme than Chandra Bahadur Dangi's height.

Robert Wadlow is more extreme than Chandra Bahadur Dangi. To calculate this, we need to use the formula for standard deviation:

Standard Deviation (SD) = (Individual measurement - Mean) / SD

For Robert Wadlow, his height of 272 cm is 97.88 cm higher than the mean of 174.12 cm. Using the formula, this translates to a standard deviation of 13.77:

SD = (272 - 174.12) / 7.10 = 13.77

For Chandra Bahadur Dangi, his height of 54.6 cm is 119.52 cm lower than the mean of 174.12 cm. Using the same formula, this translates to a standard deviation of 16.87:

SD = (54.6 - 174.12) / 7.10 = -16.87

Since Robert Wadlow has a larger standard deviation than Chandra Bahadur Dangi, his height is more extreme.

Learn more about Standard Deviation here:

https://brainly.com/question/23907081

#SPJ4

The graph of [tex]y=x^2+10x+21[/tex] includes a vertex at (-5, 17) and two roots at (-6, 0) and (-4, 0).

To graph the equation [tex]y=x^2+10x+21[/tex], we can complete the square to find the vertex and use the quadratic formula to find the roots.

First, we'll find the vertex. We can do this by adding and subtracting [tex](10/2)^2 = 25[/tex] inside the parentheses:

[tex]y = x^2 + 10x + 21[/tex]

[tex]y = (x^2 + 10x + 25) - 4 + 21[/tex]

[tex]y = (x + 5)^2 + 17[/tex]

So the vertex is (-5, 17).

Next, we'll find the roots using the quadratic formula:

x = (-b ± sqrt([tex]b^2 - 4ac[/tex]))/(2a)

where a = 1, b = 10, and c = 21.

x = (-10 ± sqrt([tex]10^2 - 4[/tex](1)(21)))/(2(1))

x = (-10 ± sqrt(4))/(2)

x = -5 ± 1

So the roots are x = -6 and x = -4.

Now we can plot the vertex at (-5, 17) and the roots at (-6, 0) and (-4, 0) on the accompanying set of axes.

To learn more about vertex please click on below link        

https://brainly.com/question/12563262

#SPJ1

The radius of the cylinder is 3.385 inches.

In geometry, cylinder is one of the basic 3d shapes,  which has two parallel circular bases at a distance. The two circular bases are joined by a curved surface, at a fixed distance from the center are called height of the cylinder.

Given that the volume of right cylinder is V= π × r²× h-------(1)

where r is the radius and h is the height of the cylinder.

π = 3.14

The volume of the cylinder is 72m cubic inches and the height of the cylinder is 2 inches,

Putting the values in equation (1) we get,

       72= π×r²×2

Dividing both sides by 2 we get,

       36= π×r²

dividing both sides by π= 3.14 we get,

r²= 11.46

r= √11.46

r= 3.385

Hence, the radius of the cylinder is 3.385 inches.

To know more about cylinder

https://brainly.com/question/16134180

#SPJ1

Answer:

Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

To compare the central tendency, spread, and variability of the two sets of data, we can find their median, range, and IQR.

For NY Giants:

Median: The middle value of the data set is 28.

Range: The difference between the maximum and minimum values is 11.

IQR: The difference between the first quartile (Q1) and the third quartile (Q3) is 4.

For NY Jets:

Median: The middle value of the data set is 28.

Range: The difference between the maximum and minimum values is 11.

IQR: The difference between the first quartile (Q1) and the third quartile (Q3) is 3.

Comparing the median, we can see that the two teams have the same middle value.

Comparing the range, we can see that the two teams have the same spread.

Comparing the IQR, we can see that the NY Giants have a slightly larger IQR than the NY Jets.

Therefore, we can conclude that the two teams have similar median and range, but the NY Giants have slightly greater variability in their ages.

Answer:x=4, y=4

Step-by-step explanation:

2)

Let x = dress pants

let y = jeans

equation 1: x+y = 8

equation 2: 70x+20y=360

First step: isolate x: x=8-y

Second step: Plug in x to the other equation: 70(8-y)+20y = 360

Simplify: 560-70y + 20y = 360, 560-50y = 360, -50y = -200, y=4

Plug in first equation for x: x+4=8, c=4

result: x = 4; y=4

The approximate probability of acceptance if the true proportion of non conformances in the lot is 10% is 0.964

To find the approximate probability of acceptance, we can use the binomial distribution. Let's define the following variables

n = 50 (sample size)

p = 0.1 (true proportion of nonconformances in the lot)

q = 1 - p = 0.9 (true proportion of conformances in the lot)

k = 0, 1, 2, ..., 5 (number of nonconformances allowed)

The probability of accepting the lot is the probability of observing k or fewer nonconformances in a sample of size n

P(X ≤ k) = Σ [n choose i] p^i q^(n-i), i=0 to k

Using a binomial calculator or software, we can find the probability of acceptance to be

P(X ≤ 5) ≈ 0.964

Learn more about probability here

brainly.com/question/29350029

#SPJ4

Explanation:

There are 12 makes and 16 total free throws.

The ratio of makes to total is 12:16. The order is important. We list the makes first, then the total second.

Divide both parts of that ratio by the GCF 4

12:16 reduces to 3:4

It means for every 3 free throws made, the basketball player has attempted 4 free throws total.

The given scenario can be estimated using a single linear model. Using the model, the estimate for games sold after 48 months is around 65,800.

This information could be reasonably estimated using a single linear model because the data points show a general increasing trend over time, which could be modeled using a linear equation.

If so, use the model to estimate the number of games sold after 48 months.

To estimate the number of games sold after 48 months using a linear model, we need to first find the slope and intercept of the line. We can use the two data points (12, 4000) and (36, 15000) to find these values:

Slope = (y2 - y1) / (x2 - x1) = (15000 - 4000) / (36 - 12) = 1100

Intercept = y1 - slope * x1 = 4000 - 1100 * 12 = 14800

Therefore, the linear equation that models the number of games sold over time is:

y = 1100x + 14800

where y is the number of games sold and x is the number of months.

To estimate the number of games sold after 48 months, we simply substitute x = 48 into the equation:

y = 1100(48) + 14800 = 65800

Therefore, we can estimate that the company will sell around 65,800 games after 48 months.

To know more about linear model:

https://brainly.com/question/29757372

#SPJ4

Answer:

answer is b (36/7)

Step-by-step explanation:

Answer:

  36/23

Step-by-step explanation:

You want the value of y in the solution to the system of equations ...

Since we only want the y-value, it is convenient to eliminate x using substitution. The second equation gives an expression for x that can be used in the first equation:

  5(5 -3/2y) -4y = 7

  25 -15/2y -4y = 7 . . . . eliminate parentheses

  50 -15y -8y = 14 . . . . . multiply by 2 to eliminate fractions

  36 = 23y . . . . . . . . . . . add 23y-14

  y = 36/23 . . . . . . . . . . divide by 23

Answer:

The amount for loss would be RM 600 and the amount for profit would be RM 600.

Step-by-step explanation:

Loss percent

25=loss/CP *100

25/100=L/CP *100

25/100=100L/240,000

10000L/10000=240,000*25/10000

L=24*25

L=RM 600

Profit percent

25/100=P/240,000 *100

25/100= 100P/240000

10000P/10000=240000*25/10000

P=RM 600

Answer:

Step-by-step explanation:

RM (⁠≧⁠▽⁠≦⁠)

The we can infer that the cardinality of s is less than or equal to the cardinality of t multiplied by k.

Given that s and t are finite sets and there is a function f such that f is a k-to-1 correspondence. We need to determine what can be inferred about the cardinality of s and t.

Definition of K to 1 function: A function f is k-to-1 correspondence if the function f maps at most k distinct elements of the domain to a given element of the range.

Let |s| and |t| be the cardinalities of s and t respectively. According to the pigeonhole principle,
|s| <= k |t| This implies that the cardinality of s is less than or equal to the cardinality of t multiplied by k.

Note: We cannot infer anything about the equality of cardinalities of s and t, as the k-to-1 correspondence allows a function to map a single element of the domain to k elements of the range.

Learn more about Cardinality

brainly.com/question/29093097

#SPJ11

Answer: x = 27

Step-by-step explanation:

we know that vertical angles are equal to each other, so

4x + 7 = [ 5 (x - 4) ]

distribute

4x + 7 = 5x - 20

subtract 4x from each side to combine variables

4x - 4x + 7 = 5x - 4x - 20

simplify

7 = x - 20

add 20 to both sides to solve for x

7 + 20 = x -20 + 20

simplify

27 = x

check your work, substitute value of x into equation

4x + 7 = 5x - 20

4(27) + 7 = 5(27) - 20

108 + 7 = 135 - 20

115 = 115

solution equals and is true, problem solved!

The original price of the goods was RM 39.13

Suppose that the original price is P, if we have an increase of x (where x is the decimal form of a percentage) the new price will be given by:

P' = P*(1 + x)

In this case the percentage is 15%, then x = 15%/100% = 0.15

Now we know that the final price is RM 45, then we can write the equation:

45 = P*(1 + 0.15)

45 = P*1.15

Solving this for P:

P = 45/1.15 = 39.13

The original price was RM 39.13

Learn more about percentages:

https://brainly.com/question/843074

#SPJ1

The ratio of the area of circle A to the area of circle B is 100 : 64.

What is ratio?

A ratio is a mathematical expression that compares the magnitude or size of two or more quantities.

The circumference of a circle is directly proportional to its radius. Therefore, if the circumference of circle B is 80% of the circumference of circle A, then the ratio of their radii is also 80%.

Let's assume that the radius of circle A is r. Then, the radius of circle B is 0.8r.

The area of a circle is proportional to the square of its radius. Therefore, the ratio of the areas of circle A to circle B is:

[tex](Area of circle A) : (Area of circle B) = r^2 : (0.8r)^2\\\\= r^2 : 0.64r^2\\\\= 100 : 64[/tex]

Therefore, the ratio of the area of circle A to the area of circle B is 100 : 64.

To learn more about ratio visit:

https://brainly.com/question/12024093

#SPJ9

Answer:

see explanation

Step-by-step explanation:

let length be l and width be w , then perimeter P is

P = 2(l + w)

given P = 20 , then

2(l + w) = 20 ( divide both sides by 2 )

l + w = 10 ( subtract w from both sides )

l = 10 - w → (1)

area (A) is calculated as

A = lw

given A = 24 , then

lw = 24

substitute l = 10 - w into this equation

(10 - w)w = 24

10w - w² = 24 ( subtract 24 from both sides )

10w - w² - 24 = 0 ( multiply through by - 1 and rearrange )

w² - 10w + 24 = 0 ← in standard form

(w - 4)(w - 6) = 0 ← in factored form

equate each factor to zero and solve for w

w - 4 = 0 ⇒ w = 4

w - 6 = 0 ⇒ w = 6

substitute these values into (1)

w = 4 : l = 10 - 4 = 6

w = 6 : l = 10 - 6 = 4

Then

length = 6 cm , width = 4 cm

or

length = 4 cm , width = 6 cm

The probability that exactly two couples state incompatibility as the reason is equal to the probability of two couples citing incompatibility and two couples not citing it.

HTML formatted answer: Given: 65% of all divorce cases cite incompatibility as the underlying reason. To find: Probability that exactly two will state incompatibility as the reason. Solution: As per the given data, The probability of citing incompatibility as the underlying reason for divorce is 65%.

Then, the probability of citing any other reason is (100% - 65%) = 35%.Let the probability of citing incompatibility by any couple as A, and the probability of not citing incompatibility by any couple as B. Here, the total couples filing for divorce = 4. Probability of two couples citing incompatibility and two couples not citing it.P(2C, incompatibility and 2C, not incompatibility)= \[\left( \begin{matrix}
  4  \\
  2  \\
\end{matrix} \right)\] × 0.65² × 0.35²The probability of choosing any 2 out of 4 couples = \[\left( \begin{matrix}
  4  \\
  2  \\
\end{matrix} \right)\] = 6The probability of 2 couples citing incompatibility = 0.65²The probability of 2 couples not citing incompatibility = 0.35²Hence,The probability that exactly two couples state incompatibility as the reason isP(2C, incompatibility) = \[\left( \begin{matrix}
  4  \\
  2  \\
\end{matrix} \right)\] × 0.65² × 0.35² = 6 × 0.4225 × 0.1225 = 0.3218Therefore, the required probability is 0.3218.

Learn more about Incompatibility

brainly.com/question/28235190

#SPJ11

Answer:

width = 44

Step-by-step explanation:

let l be length then width = 4l

the perimeter (P)  of a rectangle is calculated as

P = 2(l + w)

given P = 110 , then

2(l + 4l) = 110 ( divide both sides by 2 )

l + 4l = 55

5l = 55 ( divide both sides by 5 )

l = 11

then

width = 4l = 4 × 11 = 44

Answer:

with = 44

Step-by-step explanation:

let the lenght l, = x

b or width = 4x

Perimeter of rectangle = 2(l + b)

110 = 2( x + 4x )

110 = 2( 5x )

110 = 10x

10x = 110

x = 110/10

x = 11

Therefore width = 4x

width = 4 (11)

with = 44

take a picher of   that your working on

Answer:

C: 3,350

Step-by-step explanation:

took test 2023