Why we use Permutation to find the number of ways of something can be arranged when order matters. While use Combination when order does not matter.

1.The athlete that did the most sit-up per minute is D'andrea with 44 sit up per minute

2. 22 Miles in 20 minutes < 38 Miles in 30 minutes

3. The rate that could be Jessica rate is 1 tile in 3 minutes

4. The best rate to find the best value of card is 6 greeting cards for $23.40

5. Elias can fold 3boxes in a minute and Dionne can fold 3.5 boxes in a minute.

A rate is a special ratio in which the two terms are in different units. For example, if a 12-ounce can of corn costs 69¢, the rate is 69¢ for 12 ounces. This is not a ratio of two like units, such as shirts. This is a ratio of two unlike units: cents and ounces.

Rate per minute is the quantity divide by no of minute.

For example Casey did 93 sit up in 3 minute, His rate = 93/3 = 31 sit up per minute.

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Answer:

  -5x⁵ +2x² -3/x³

Step-by-step explanation:

You want the quotient and remainder of (-15x⁸ +6x⁵ -9)/(3x³).

The quotient and remainder can be found by dividing term by term.

  [tex]\dfrac{-15x^8+6x^5-9}{3x^3}=\dfrac{-15x^8}{3x^3}+\dfrac{6x^5}{3x^3}-\dfrac{9}{3x^3}\\\\\\=\boxed{-5x^5+2x^2-\dfrac{3}{x^3}}[/tex]

__

Additional comment

The exponent rule is (a^b)/(a^c) = a^(b-c).

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Using subtraction operator, the distance between the house and the ducks is 21 feet

Trigonometric ratios are mathematical ratios that relate the sides of a right triangle to its angles. The three primary trigonometric ratios are sine, cosine, and tangent, which are commonly abbreviated as sin, cos, and tan.

In this case, we don't need to use trigonometric ratio since the duck and house with the tree are on the same length. We can simply use a basic arithmetic operation to find the distance between the ducks from the house.

Using subtraction, the distance between the ducks and the house will be

distance = 47 - 26

distance = 21 feet

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Answer:

$29.68 to drive 350 miles

Step-by-step explanation:

To find the cost of driving 350 miles, we first need to calculate the amount of gasoline required for driving 350 miles. We can use the formula:

gasoline = distance ÷ miles per gallon

Plugging in the given values:

gasoline = 350 ÷ 33

gasoline = 10.606060606060606

So, we need 10.61 gallons of gasoline to drive 350 miles.

Next, we multiply the amount of gasoline needed by the cost per gallon to find the total cost:

total cost = gasoline × cost per gallon

total cost = 10.61 × 2.80

total cost = 29.6780

Therefore, it would cost approximately $29.68 to drive 350 miles when gasoline costs $2.80 per gallon and your car gets 33 miles per gallon.

Answer: 350 mi * 1 gal / 33 miles * $2.80 / 1 gal  = 29.69$

which means the cost is 2.8*(350/33)=29.69$

Step-by-step explanation:

Here, 2.80$/1 Gal.

Now we need to cancel out gallons, so we add a ratio with gallons.

2.80$/1 Gal. x 1 Gal/33 mi.

Now add the last data element to cancel out miles.

2.80$/1 Gal. x 1 Gal/33 mi. x 350 mi.

Cancelling out units and numbers gives,

(2.80$ x 350)/33. Continue reducing to an answer:

980$/33 = 29.69$

Answer: Since the speed of personal computers is expected to double every 18 months, we can use exponential growth to calculate the increase in speed over time. We can start by finding the growth factor, which is equal to 2 raised to the power of the number of doublings. In this case, the number of doublings over 6 years can be calculated as follows:

6 years / 1.5 years = 4 doublings

So the growth factor is:

2^4 = 16

This means that the speed of personal computers will be 16 times faster in 6 years compared to now.

Step-by-step explanation:

Answer:

Note that 0.01 is the decimal form of 1%, so 0.01 multiplied by 7 yields 7%. So, if we were to find 1% of 250, which is 2.5, we can multiply the value by 7, which is 17.5.

Therefore, 7% of 250 is 17.5

On solving the provided question, we can say that the trigonometry sin3θcos2θ+cos3θsin2θ = 4sin3(1−2cos2θ)+sinθ

The area of mathematics knοwn as trigonometry examines the correlation between triangle side lengths and angles. The area first appeared in the Hellenistic era, arοund the third century BC. frοm the use of geometry in astronοmical study.

The area of mathematics knοwn as exact methods deals with specific trigonometric functions and hοw they might be used in calculations. There are six popular trigonοmetric functions in trigonometry. Sine, cosine, tangent, cοtangent, secant, and cosecant are their respective names and acronyms (csc). Studying the characteristics οf triangles, particularly right triangles, is called trigonοmetry. The study of geοmetry, however, is the characteristics of all geοmetric figures.

the trigonometry

sin3θcos2θ+cοs3θsin2θ=4sin3(1−2cos2θ)+sinθ

Use the variation cοs2θ=1−sin2θ to express sin(5θ) in terms of sinθ

sin5θ=4sin3θ(1−2(1−sin2θ))+sinθ(8(1−sin2θ}

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The inequality that shows the least amount he needs is  4x + 22 ≥ 85.50 which shows he needs at least $15.875

The Inequality that will represent this problem is 4x + 22 ≥ 85.50, where x is the number of windows Jonathan washes.

To solve the inequality, we'll start by subtracting 22 from both sides:

4x ≥ 63.50

And finally, dividing both sides by 4:

x ≥ 15.875

So, Jonathan needs to wash at least 15 windows in order to save up enough money to buy the boxed set.

b.

The graph on the number line showing x ≥ 15.875 is attached below

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Answer:

3

Step-by-step explanation:

In this triangle ABC, the leg lengths are AC and BC, being x and x+7, respectively. So, the area can be listed as: 15 = (1/2) * x * (x+7). Simplifying that gets x^2 + 7x = 30 -> x^2 + 7x - 30 = (x-10)(x-3). So, x = 3 since it cannot be negative.

The true argument is option B) The premise does not entail the conclusion because, if the premise is true, the conclusion could still be false

The argument presented lacks logical reasoning and does not provide enough information to support the conclusion. The premise that "Bob is 13 feet tall" is a factual statement, but it is not sufficient to conclude that "Bob is taller than most other people." Without further information about the height distribution of people.

It is impossible to make such a conclusion based solely on Bob's height. Additionally, the argument does not provide any logical reasoning to connect the premise to the conclusion, so it is not a valid deductive argument.

Therefore, the correct option is (B)

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The given question is incomplete, the complete question is :

Bob is 13 feet tall So, Bob is taller than most other people Suppose there are no implicit premises: this is the whole argument. Which of the following is true about this argument?

A The premise entails the conclusion because, if the premise is true, the conclusion has to be true

B The premise does not entail the conclusion because, if the premise is true, the conclusion could still be false (setting aside facts not supplied by the premise)

C The premise entails the conclusion because, setting aside facts not supplied by the premise, there is no way the premise could be true and the conclusion false.

D The premise does not entail the conclusion because it has no suppositional strength

The equation of line is y = 14.24375x + 296.8875 , where x is the number of days and y is the total weight gain in x days

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( 18 , 40.5 )

Let the second point be Q ( 50 , 496.3 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 496.3 - 40.5 ) / ( 50 - 18 )

Slope m = 455.8 / 32

Slope m = 14.24375

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 40.5 = 14.24375 ( x - 18 )

On simplifying the equation , we get

y - 40.5 = 14.24375x - 256.3875

Adding 40.5 on both sides of the equation , we get

y = 14.24375x + 296.8875

where x is the number of days

Hence , the equation of line is y = 14.24375x + 296.8875

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In the cyclic quadrilateral the value of R and S are

< S = 87 degrees

< R = 216 degrees

In a cyclic quadrilateral, the opposite angles are supplementary hence

< S + < Q = 180

in the problem we have that < Q = 93

< S + 93 = 180

< S = 180 - 93

< S = 87 degrees

Angle R is adjacent angle to angles 126 and 90 hence we have that

< R = 126 + 90

< R = 216 degrees

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The total amount of money she spends on rent alone would be = $630

The amount of money that Tosha spends on food = X

The amount of money that Tosha spends of rent = 2x

The total amount of money she spent on both = $945

That is,

945 = X+2x

3x = 945

X = 945/3 = 315

Therefore,the amount she spent on rent = 2x= 2× 315 =$630

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As said, 48 model automobiles are driven by Jim at the moment, and the ratio might alter to 19:13.

An organisation of the integers a and b stated as a/b is still a ratio if b is truly not comparable to 0. Two ratio with the same value are established by the percent formula. As an illustration, you might write your ration as follows: 1:3 when there is 1 man and 3 females.

You know there's an 8:6 ratio between the grand total of model cars Jim and Terrence possess.

As a result, you can respond to the assignment as follows: Assume Jim owns x different car models.

8/6 = x/36

x = 36*8/6

x = 288/6

x = 48

The new percentage of Jim's against Terrence's model vehicles will be as follows because both Jim & Terrence sell ten of their model cars:

(48-10)/(36-10) = 38/26 = 19/13

Jim's to Terrence's miniature automobiles will now be in a 19:13 ratio.

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Option (c) is correct answer.

(C) DE = 12, DF = 16 and m∠D = 35

which states, length of DE is 12 units , length of DF is 16 units and m/D=35 degrees.

If two figures possess the same shape but not necessarily the same size, they are considered to be similar. We may remark that all circles are similar as an example. Equilateral triangles and squares are similar to one another. Although similar figures need not be congruent, all congruent figures are similar.

Property 1:

Two triangles are similar if their respective sides have the same ratio and their corresponding angles are equal.

Property 2:

The corresponding angles of two similar triangles will have equal values . Equiangular triangles are what they are called.

Now by property 1,

The pairs of  corresponding sides of similar triangles are proportional .

Therefore, in the given triangles,

[tex]\frac{AB}{DE} =\frac{AC}{DF} \\\\\frac{AB}{AC} =\frac{DE}{DF} \\\\\frac{9}{12} =\frac{DE}{DF} \\\\\frac{3}{4} =\frac{DE}{DF}[/tex]

Therefore, in the given options, option (c) satisfies the condition.

Hence, DE = 12 , and DF = 16.

By property 2 we know that , corresponding angles of similar triangles are equal.

hence, /A=/D

therefore, /D=35.

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Answer: The sales tax is $2.5 and her total cost of the shirt is $47.5.

Step-by-step explanation:

The trait would be MOST useful for these farmers is to be considered as the fast growth rate.

The main goal of science that should create knowledge and understanding.

Since the plan for using the breeding to produce a new type for the wheat for farmers that lived in the northern areas.

The growth rate of a value (GDP, turnover, wages, etc.) measures its change from one period to another (month, quarter, year). It is very generally expressed as a percentage.

The annual average rate of change of the gross domestic product (GDP) at market prices based on constant local currency, for a given national economy, during a specified period of time.

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After 40 years, the account has a total balance of $49.450.80.

Any loans or borrowings come with interest. the portion of the loan's value that lenders use to calculate interest. By lending money (via a bond or certificate of deposit, for instance), or by depositing funds into an interest-bearing bank account, consumers can earn interest.

Let's assume that he starts with $0 in the account and makes a monthly contribution of $100 for 40 years, which is equal to 40 x 12 = 480 months.

The total contributions would be $100 x 480 = $48,000.

The interest earned on the account balance can be calculated as follows:

Interest = Account balance * Interest rate

At the end of each year, the interest is added to the account balance. So, after 40 years, the balance would be:

Year 1: $48,000 * 1.5% = $720

Balance = $48,000 + $720 = $48,720

Year 2: $48,720 * 1.5% = $730.80

Balance = $48,720 + $730.80 = $49,450.80

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Answer:

Step-by-step explanation:

The ansewr is C

Answer: 523.3cm^3

Step By Step Explanation:-The volume of a sphere can be calculated using the formula:

V = (4/3) * π * r^3

where r is the radius of the sphere. The diameter of the sphere is 10 cm, so the radius is half of that, or 5 cm.

Substituting the radius into the formula, we get:

V = (4/3) * π * (5 cm)^3

= (4/3) * π * 125 cm^3

= approximately 523.6 cm^3

So, the closest measurement to the volume of the sphere in cubic centimeters is approximately 523.3 cm^3.

The magnitude of the sum of these two vectors is 2.9486m

In trigonometry, the law of cosines (also known as the cosine formula, cosine rule, or al-Kashi's theorem) relates the lengths of the sides of a triangle to the cosine of one of its angles.

The parameters that will help us to find the magnitude are

/OB/ = 3.14m

/OA/ = 2.71 m

Let /AB/= x

Sum of the angles is (-60+30)⁰ = 30⁰

Using cosine rule

x²= 3.14² +2.71² - 2*3.14*2.71 *cos30⁰

x² = 9.8596+7.3441 -8.5094

x²= 17.2037 -8.5094

x²= 8.6943

x = √8.6943

x = 2.9486

Therefore, the magnitude of the sum

of these two vectors is 2.9486m or 2.9m approximately

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On solving the prοvided question, we can say that 4.75 miles were ran on day four.

A mathematical equation is a formula that jοins two statements and uses the equal symbol (=) tο indicate equality. A mathematical statement that establishes the equality of twο mathematical expressions is known as an equatiοn in algebra.

Fοr instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences οn either side of a letter is described by a mathematical formula. Often, there is only οne variable, which alsο serves as the symbol. for instance, 2x – 4 = 2.

On day one, Justin ran two miles.

He ran two miles on the second day, or 75% of it. Divide by 100 and multiply by 75 to get the percentage of two miles that is 75%.

On the secοnd day, I ran 1.5 miles, or 2 / 100, or 0.02 x 75. (I've run 3.5 miles so far)

He ran 1.5 miles further on the third day than the previous one:

1.5 + 1.5 = 3 (6.5 miles jogged sο far) (6.5 miles jogged so far)

The total number of miles run was 9.25, thus tο find the solution, we must subtract 6.5 from 9.25.

4.75 miles were ran οn day four, or 9.25 minus 6.5.

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Using Euler's formula, the expressions can be rewritten as Im = sin(e^j) - sinh(1), exp(e^j) = e^(cos(1) + j*sin(1)) and e^[(1/2)√(2)e^(j(π/4+2π*n))] respectively

1.

Cos(e^j) can be expressed using Euler's formula as:

Cos(e^j) = (e^(je^j) + e^(-je^j)) / 2

= (cos(e^j) + cosh(1)) + j(sin(e^j) - sinh(1))

Re = cos(e^j) + cosh(1)

Im = sin(e^j) - sinh(1)

2.

exp(e^j) can also be expressed using Euler's formula as:

exp(e^j) = e^(cos(1) + j*sin(1))

3.

(sqrt(j))^sqrt(j) can be written as:

(sqrt(j))^sqrt(j) = e^[(1/2)√(2)e^(j(π/4+2π*n))]

where n is an integer. This is because the logarithm of a complex number has infinitely many possible values due to the periodicity of the exponential function.

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Answer: To find the limit of the expression 3√x-1/x-1 as x approaches 1, we can use L'Hopital's Rule. L'Hopital's Rule is a method for finding the limit of indeterminate forms, such as 0/0 or ∞/∞, by taking the derivative of the numerator and denominator.

In this case, the expression is of the form 0/0, so we can use L'Hopital's Rule:

lim 3√x-1/x-1 = lim (3/2)((x-1)^(1/2)) / 1 = 3/2

So the limit of the expression 3√x-1/x-1 as x approaches 1 is equal to 3/2.

Step-by-step explanation:

P(12,8)

Move  8 units to the left (X) and  12  units down(Y).

P'(12-8, 8-12)

P'(4, -4)

If you don't how to do translation try plotting (12,8).

If the diameter of the tub is 8 inches, then the height of gallon tube is,  5.25 inches

Surface area is the sum of the areas of all the faces (or surfaces) of a three-dimensional object. It is a measure of how much area the surfaces of an object take up in two dimensions. The surface area of a solid can be found by adding up the areas of its faces.

The surface area of a cylinder can be expressed as:

SA = 2πr² + 2πr x h

where r is the radius of the cylinder, h is its height, and π is the constant pi (3.14).

The diameter of the tub is 8 inches, which means the radius is 4 inches. We are also given that the total surface area is 232.36 square inches.

So we can write:

232.36 = 2(3.14)(4²) + 2(3.14)(4)(h)

Simplifying and solving for h, we get:

232.36 = 100.48 + 25.12h

131.88 = 25.12h

h = 131.88/25.12

h ≈ 5.25 inches

Therefore, the height of the ice cream tub is approximately 5.25 inches.

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Answer:

4 km

Step-by-step explanation:

There is a period of 40 minutes between 11:40 and 12:20.

[tex]40 \: minutes \: = \frac{2}{3} \: of \: an \: hour[/tex]

[tex] \frac{2}{3} \times \frac{6}{1} kmhr \: = \frac{12}{3} = 4[/tex]

The number of blue marbles in the representative sample which contains 2 green marbles is 8.

What is meant by a representative sample?

A subset of a population that aims to correctly reflect the traits of the larger group is called a representative sample. Because the results accurately mirror those you would get from interviewing the full population, it is known as a representative sample.

Because samples comprise more manageable, smaller representations of the broader group, they are helpful in statistical analysis when population numbers are huge.

Given the total number of green and blue marbles is 8 and 32 respectively.

So the ratio of green marbles to blue marbles = 8:32 = 1:4

Now, this ratio is maintained when we form a representative sample.

Given there are 2 green marbles in a representative sample.

Then the number of blue marbles x is:

2 : x = 1 : 4

2 : x = 2 : 8

x = 8

Therefore the number of blue marbles in the representative sample is 8.

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The amount of money that needs to be deposited now into an account to obtain $6,200 in 15 years is $2,928.67.

Mathematically, continuous compounding interest can be calculated by using this mathematical expression:

P(t) = P₀e^{rt}

Where:

Substituting the given parameters into the continuous compounding interest formula, we have;

P(t) = P₀e^{rt}

$6,200 = P₀e^{0.05 × 15}

$6,200 = P₀e^{0.75}

Principal, P₀ = 6,200/e^{0.75}

Principal, P₀ = 6,200/2.11700001661

Principal, P₀ = $2,928.67.

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