each team has a race one racer runs 5/6 the second racer swims 1/12 the third racer bicycles 7/8 what is the total distance the team must cover

ANS : 2√(3 × 43) + √(1254) - √(38)

Let's break down the expression step by step:

Expression: √(516) + √(1254) - √(38)

Step 1: Identify prime factors of each number in the Square roots.
- Prime factors of 516: 2^2 × 3 × 43
- Prime factors of 1254: 2 × 3^1 × 11 × 19
- Prime factors of 38: 2 × 19

Step 2: Simplify the square roots using prime factors.
- √(516) = √(2^2 × 3 × 43) = 2√(3 × 43)
- √(1254) = √(2 × 3 × 11 × 19) (This square root cannot be simplified further.)
- √(38) = √(2 × 19) (This square root cannot be simplified further.)

Step 3: Substitute simplified square roots back into the expression.
- 2√(3 × 43) + √(1254) - √(38)

Since we cannot simplify the square roots of 1254 and 38 further, and there are no common terms to combine, the given expression is already in its simplest form:

Answer: 2√(3 × 43) + √(1254) - √(38)

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The probability of selecting a blue or green ball on the first draw is 2/3 or approximately 0.67.

What is probability ?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 indicates that the event is impossible, and 1 indicates that the event is certain to occur. If an event has a probability of 0.5, it means that the event is equally likely to occur or not occur. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
Probability is an important concept in mathematics, statistics, and many other fields, as it allows us to make predictions and decisions based on the likelihood of certain outcomes.

According to the question:
The total number of balls in the bag is:

6 blue balls + 5 yellow balls + 4 green balls = 15 balls

The probability of selecting a blue or green ball on the first draw can be found by dividing the number of blue and green balls by the total number of balls:

P(blue or green) = (number of blue balls + number of green balls) / (total number of balls)

P(blue or green) = (6 + 4) / 15

P(blue or green) = 10 / 15

P(blue or green) = 2/3

Therefore, the probability of selecting a blue or green ball on the first draw is 2/3 or approximately 0.67.


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let's firstly convert the mixed fractions to improper fractions.

[tex]\stackrel{mixed}{3\frac{1}{2}}\implies \cfrac{3\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{7}{2}}~\hfill \stackrel{mixed}{1\frac{1}{4}} \implies \cfrac{1\cdot 4+1}{4} \implies \stackrel{improper}{\cfrac{5}{4}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{~~ \frac{ 7}{ 2} ~~}{\frac{5}{4}}\implies \cfrac{7}{2}\cdot \cfrac{4}{5}\implies \cfrac{7}{5}\cdot \cfrac{4}{2}\implies \cfrac{7}{5}\cdot 2\implies \cfrac{14}{5}\implies 2\frac{4}{5}\implies 2.8[/tex]

The inverse of the equation y = log(1/4)[tex]x^{5}[/tex] is x = 1/([tex]y^{(log(4)/5)}[/tex]).

What is an inverse equation?

To find the inverse of the equation y = log(1/4)[tex]x^{5}[/tex], we can follow these steps:

Step 1: Interchange the x and y variables to obtain x = log(1/4)[tex]y^{5}[/tex].

Step 2: Solve for y in terms of x. To do this, we need to isolate the y term on one side of the equation. We can start by taking both sides of the equation to the power of 1/5:

[tex]x^{1/5}[/tex] = log(1/4)y

y = [tex](1/4)^{(1/log(x^(1/5)))}[/tex]

Step 3: Simplify the expression. Recall that [tex]a^b^{c}[/tex], so we can rewrite the exponent in the denominator as log([tex]x^{1/5}[/tex]) = (1/5)log(x). Substituting this into the expression for y, we get:

y = [tex](1/4)^{(1/(log(x^(1/5))))}[/tex]

 = [tex](1/4)^{(1/((1/5)log(x)))}[/tex]

 = [tex](1/4)^{(log(x)/5)}[/tex]

 = [tex]x^{(log(1/4)/5)}[/tex]

 = [tex]x^{(-log(4)/5)}[/tex]

 = 1/([tex]x^{(log(4)/5)}[/tex])

Therefore, the inverse of the equation y = log(1/4)[tex]x^{5}[/tex] is x = 1/([tex]y^{(log(4)/5)}[/tex]).

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Complete question is: The inverse of the equation y = log(1/4)[tex]x^{5}[/tex] is x = 1/([tex]y^{(log(4)/5)}[/tex]).

Part (a) replies provide us with the instantaneous rates of change in sales derivatives at t=2, t=3, and t=4 months, respectively. These are 372, 327, and 252 in tens of thousands of dollars each month, respectively.

In mathematics, the derivative of a function with real variables measures how sensitively the function's value varies in reaction to changes in its parameters. Derivatives are the fundamental tools of calculus. Differentiation (the rate of change of a function with respect to a variable in mathematics) (in mathematics, the rate of change of a function with respect to a variable). The use of derivatives is essential in the solution of calculus and differential equation problems. The definition of "derivative" or "taking a derivative" in calculus is finding the "slope" of a certain function. Because it is frequently the slope of a straight line, it should be enclosed in quotation marks. Derivatives are rate of change metrics that apply to almost any function.

a) find the derivatives,

[tex]S(t) = 31t^3 - 501t^2 + 220t + 150\\S'(t) = 3(31t^2) - 2(501t) + 220\\S'(2) = 3(31(2)^2) - 2(501(2)) + 220 = 372\\S'(3) = 3(31(3)^2) - 2(501(3)) + 220 = 327\\S'(4) = 3(31(4)^2) - 2(501(4)) + 220 = 252\\[/tex]

b) To find S(2), S(3), and S''(4), we use the original expression for S(t):

[tex]S(2) = 31(2)^3 - 501(2)^2 + 220(2) + 150 = 662\\S(3) = 31(3)^3 - 501(3)^2 + 220(3) + 150 = 669\\S''(t) = (S'(t))' = 6(31t) - 2(501)\\S''(4) = 6(31(4)) - 2(501) = 264\\[/tex]

c) Part (a) replies provide us with the instantaneous rates of change in sales at t=2, t=3, and t=4 months, respectively. These are 372, 327, and 252 in tens of thousands of dollars each month, respectively.

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For any number n > 1, the given complex equation will always be less than 1.

What is a complex equation?

Complex numbers are described as equations of the type z= a+ib, where a and b are real numbers. Re z = a and Im z = ib are used to signify the real and imaginary parts, respectively.

We are given an expression as [tex]|(\frac{1}{2} +\frac{2}{3} i)^{n}|[/tex].

On taking the LCM, we get

⇒ [tex]|(\frac{3 +4i}{6})^{n}|[/tex]

Now, using the exponent rule, we get

⇒ [tex]|(\frac{(3 +4i)^{n} }{6^{n} }|[/tex]

Now, let us assume n = 2.

By substituting this, we get

⇒ [tex]|(\frac{(3 +4i)^{2} }{6^{2} }|[/tex] < 1

Hence, for any number n > 1, the given complex equation will always be less than 1.

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The complete question has been attached below.

Answer:

Step-by-step explanation:

Step-by-step explanation:

[tex] \frac{1237568 \times 646773}{5373737} = \frac{800425568064}{5373737} = 148951 \frac{2068177}{5373737} [/tex]

First, multiply the numbers that are in numerator

Then divide the product of the numerator by the denominator

And lastly take out the whole part of the fraction and write what remains

It think that's it

In linear equation,  85.60 deductible amount does the policy show.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) component, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                                   Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations with variables of power 1 are known as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.

As you can see in the above table

Insurance for A =  Bodily injury + Property damage + Medical payments + Comprehensive  + Collision + Additional Coverages + Towing and labor + loss of use

= 115+49.5+18.2+38.9+250+250+2+20

= 743.6

Calculation for B :

As you can see in the above table

Insurance for B =  Bodily injury + Property damage + Medical payments + Comprehensive  + Collision + Additional Coverages + Towing and labor + loss of use

=  118.2 + 45.9+ 18.2 +42.3 + 250+250+ 2 +20

= 746.6

Calculations for C :

Total each vehicle:2015 sports  = A + extra passangers * Uninsurared motorised bodily injury

                                                  = 743.6 + 1*0 = 743.6

Calculations for D :

Total each vehicle:2018 minivan  = B + extra passengers * Uninsured motorized bodily injury

                                                  = 746.6 + 1*76.1 = 822.7

Calculations for E:

= C + D

= 743.6 + 822.7

= 1566.3

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x*2+11 = 25

25 - 11 / 2 = x

14/2 = x

7 = x

x = 7

The equation representing the above statement is 2x + 11 = 25 and the value of the unknown number, x is 7.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

Let x be the unknown number.

The unknown number is first doubled, which is represented as 2x.

Then the doubled number is added to 11, which is represented as 2x + 11.

The resulting number is 25.

So, the equation representing the situation can be represented as,

2x + 11 = 25

Subtracting both sides by 11,

2x = 14

Dividing both sides by 2,

x = 7

Hence the value of the unknown number, x is 7.

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Answer:

80 minutes

Step-by-step explanation:

80x3 is 240

240 mins=4 hrs

(i promise its right this time- i bet)

Answer:

c. 80 minutes

Step-by-step explanation:

Some problems give you too much information, and you need to choose only the information you need. The number of pages is not important. Here you only need the time, 4 hours, and the number of assignments, 3.

4 hours × 60 minutes / hour = 240 minutes

240 minutes / 3 assignments = 80 minutes/assignment

Answer: c. 80 minutes

Answer:

C

Step-by-step explanation

The Y axis becomes the opposite when being reflected across the X axis

In this scenario, Y becomes -7

The same thing with X when something is reflected across the Y axis

Answer:

For packages of 8: She will need 13 packages

For packages of 12: She will need 9 packages

Step-by-step explanation:

Number of barbecues sandwiches = 100 (given)

For packages of 8 we have, (100/8) = 12 (without the remainder)

We then add one extra package so that the 100 barbecue sandwiches are served.

So, for packages of 8, packages of barbecue buns = 12 + 1 = 13

For packages of 12 we have, (100/12) = 8 (without the remainder)

We then add one extra package so that the 100 barbecue sandwiches are served.

So, for packages of 12, packages of barbecue buns = 8 + 1 = 9

Answer:

Step-by-step explanation:

3 3 more than x x " can be written as the algebraic expression x+ 3 x +3. But why? Why use math if we can describe things in words? One of the many reasons is that math is more precise and easier to work with than words are. This is a question you should keep thinking about as we dig deeper into algebra.

10: Missing length, x = 16 cm

area of the composite figure = 240 cm²

perimeter = 72 cm

11: Missing length, x = 37 mm

area of the composite figure = 240 mm²

perimeter = 90 mm

To find the area and perimeter of a composite figure, you can break it down into simpler shapes such as triangles, rectangles, circles, etc. and then find the area of each individual shape and add them together.

No. 10

You will notice that the triangle is sharing one side with the square. And the length of the side is 12 cm. Thus:

x = √(20² - 12²)    (Pythagoras)

x = 16 cm

area of the figure = area of square + area of triangle

area of the figure =  L²  + (1/2 * base * height)

area of the figure =  12²  + (1/2 * 16 * 12)

area of the figure = 240 cm²

perimeter = 12 + 12 + 12 + 20 + 16 = 72 cm

No. 11

You will notice that the small triangle is sharing one side with the big triangle. And the length of the side is unknown. Let's call it y. Thus:

y = √(13² - 5²)    (Pythagoras)

y =  12 mm

x = √(35² + 12²)    (Pythagoras)

x = 37 mm

area of the figure = area of small triangle + area of big triangle

area of the figure =  (1/2 * base * height)   + (1/2 * base * height)

area of the figure =  (1/2 * 5 * 12) + (1/2 *  35 * 12)  

area of the figure = 240 mm²

perimeter = 5 + 13  + 37 + 35 = 90 mm

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Answer:

$38.40

Step-by-step explanation:

20% = 0.2

32 x 0.2 = $6.40

20% tip = $6.40

How much money should they leave for the bill and a 20% tip?

We take

32 + 6.40 = $38.40

So, they should leave $38.40 for the bill and a 20% tip.

Answer:

C ) 18

Step-by-step explanation:

2×5(16÷2-2×3)-2

= 2×5(8-2×3)-2 (16 ÷ 2 = 8)

= 2×5(8-6)-2 (2×3 = 6)

= 2×5(2)-2

= 10(2)-2

= 20-2

= 18

To calculate the monthly lease payment, we need to use the formula:

Monthly Payment = Depreciation + Finance Charge

The depreciation represents the portion of the car's value that is lost during the lease period, while the finance charge is the interest charged on the lease.

First, let's calculate the depreciation:

MSRP = $51,500

Residual Value = 49% of MSRP = 0.49 x $51,500 = $25,235

Depreciation = (Negotiated Price - Residual Value - Down Payment) / Lease Term

Depreciation = ($49,000 - $25,235 - $4,000) / 36 = $541.53

Next, let's calculate the finance charge:

Lease Balance = (Negotiated Price - Down Payment) - Residual Value

Lease Balance = ($49,000 - $4,000) - $25,235 = $19,765

Money Factor = Annual Interest Rate / 2400

Money Factor = 7.8% / 2400 = 0.00325

Finance Charge = Lease Balance x Money Factor

Finance Charge = $19,765 x 0.00325 = $64.26

Finally, we can calculate the monthly payment:

Monthly Payment = Depreciation + Finance Charge

Monthly Payment = $541.53 + $64.26 = $605.79

Therefore, the monthly lease payment is $605.79.

Answer:

1. The number of suite seats is 10% of the highest-priced seats, which is 10% of 92,000 = 9,200 seats.

2. The number of non-suite seats is 90% of the highest-priced seats, which is 90% of 92,000 = 82,800 seats.

3. The revenue generated from suite seats if all are purchased for one game is 9,200 x $200 = $1,840,000.

4. The revenue generated from non-suite seats if all are purchased for one game is 82,800 x $60 = $4,968,000.

5. The revenue earned at one sold-out game is the sum of the revenue from suite seats and non-suite seats: $1,840,000 + $4,968,000 = $6,808,000.

6. The net revenue of one sold-out game in which the nonconference team plays at the big stadium is the revenue earned at one sold-out game minus the payment to the nonconference team: $6,808,000 - $1,500,000 = $5,308,000.

Step-by-step explanation:

Answer:

m = -2

Step-by-step explanation:

-m^3 + 17m + 44 = -(m + 2)(m^2 - 2m - 22)

m + 2 = 0 or m^2 - 2m - 22 = 0

m = -2 or m = 1 ± √23

The equation for p is p + 6 = 14, which means that the number of pieces left is equal to the difference between the total number of pieces (14) and the number of pieces served (6).

Ron's mother bakes a pizza and divides it into 14 pieces. After serving 6 pieces to Ron and his friends, she has a certain number of pieces left. To determine this number, we can use the equation p + 6 = 14. This equation states that the number of pieces left (p) is equal to the difference between the total number of pieces (14) and the number of pieces served (6). Therefore, the equation for p is p + 6 = 14. By solving this equation, we can determine that the number of pieces left is 8. This means that Ron's mother has 8 pieces left after serving 6 pieces to Ron and his friends.

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Answer:

a < 12

Step-by-step explanation:

500 - 25a > 200

500 - 200 > 25a

300 > 25a

divide both sides by 25

300/25 > 25a/25

12 > a

therefore, a < 12

The number is 300, as stated in the sentence. A histogram:

One common plotting instrument is the histogram. It is employed to present interval-scaled summaries of discontinuous or continuous data. It is commonly applied to easily represent the key features of the information's distribution.

To create a histogram of the weights of the miniature poodles, we would first divide the weight range into a series of intervals, or bins. The bin width should be chosen so that each bin has a similar number of observations.

According to the histogram and table: the height of a cell represents 10 15 ≤ x < 20: 120 ÷ 12=10

28 ≤ x <30 has 30 cells, so the frequency is 30 × 10=300

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The width of the walkway around the rectangular garden should be approximately 2.061 feet wide.

What is rectangle?

A rectangle is a type of quadrilateral with four sides and four right angles (90-degree angles). It is characterized by two pairs of parallel sides of equal length.

Let's represent the width of the brick walkway by "x" feet.

Then the dimensions of the entire rectangle including the brick walkway will be [tex]$(25+2x)$[/tex] feet by [tex]$(13+2x)$[/tex] feet.

The area of the rectangle with the walkway will be:

[tex]$$(25+2x)(13+2x)$$[/tex]

We know that the area of the walkway itself is 287 square feet. So we can set up the following equation:

[tex]$$(25+2x)(13+2x) - 25\cdot 13 = 287$$[/tex]

Simplifying and solving for x, we get:

[tex]$$4x^2 + 86x - 216 = 0$$[/tex]

Using the quadratic formula, we get:

[tex]$x = \frac{(-86 \pm \sqrt{86^2 - 4(4)(-216)})}{2(4)}$$[/tex]

[tex]$$x \approx 2.061 \text{ or } x \approx -26.311$$[/tex]

Since the width of the walkway cannot be negative, we reject the negative solution. Therefore, the width of the walkway should be approximately 2.061 feet wide (rounded to the nearest thousandth).

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GCD (119, 378) = 7 and x = 25 and y = -6 is the value by using Euclidean alogorithm.

What does Euclidean algorithm mean?

By dividing the larger by the smaller, the smaller by the remainder, the first remainder by the second remainder, and so on, until an exact division is achieved, the greatest common divisor is the exact divisor. Euclid's algorithm is also known as.

by Euclidean division algorithm,

378 = 3 × 119 +21

119 = 5 × 21 + 14

21 = 1 × 14 + 7

14 = 2 × 7 + 0

Therefore 7 is GCD of 119 and 378.

so, GCD(119 , 378) = 119x + 378y = 7

now 7 = 119x + 378y

⇒7 = 7 × 13x + 7 × 54y

⇒1 = 13x + 54y

⇒13 × 25 + 54 × (-6) = 13x + 54y

on comparing we get, x = 25 and y = -6

Therefore GCD (119, 378) = 7 and x = 25 and y = -6

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The area of the shaded region is 176 m² and area of compound shapes are 208 m² and 16 m².

What is rectangle?

A rectangle is a two-dimensional geometric shape with four straight sides and four right angles (90 degrees). It is a type of quadrilateral, which means it has four sides. The opposite sides of a rectangle are equal in length, and the adjacent sides are perpendicular to each other.

The formula for calculating the area of a rectangle is A = l x w, where "A" is the area, "l" is the length, and "w" is the width. The perimeter of a rectangle can be calculated by adding the lengths of all four sides, which is given by the formula P = 2(l + w).

Rectangles are commonly found in many aspects of everyday life, such as in buildings, furniture, electronic devices, and books. They can be used in architecture and engineering for creating stable and functional structures. In mathematics, rectangles are often used in geometry and algebraic expressions, as well as in statisticalanalysis and graphing.

Here we have a rectangle with length 16m and breadth 13 m.

Now, area of the rectangle is length × breath = 13×16 = 208 m².

And here we also have two square parts with side 4 m .

So, area of the square is side × side = 4×4 = 16 m².

Now, numbers of square are 2.

So, total area of two square is (2×16) = 32 m².

If we will subtract the total area of two square from area of the rectangle then we will get the area of shaded region .

So, area of the shaded region [tex] = 208 - 32 = 176 \: {m}^{2} [/tex]

Therefore, area of the shaded region is 176 m² .

Here compound shapes are one rectangle and two squares.

So, area of compound shapes are 208 m² and 16 m².

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Answer:

1) A

2) D

3)  B

Step-by-step explanation:

Math

:)

Answer:

Step-by-step explanation:

If the value of the tent depreciates by 12% each year, then its value at the end of each year is 100% - 12% = 88% of its value at the beginning of the year.

So after the first year, the value of the tent will be:

$866 x 0.88 = $761.28

After the second year, the value of the tent will be:

$761.28 x 0.88 = $670.58

After the third year, the value of the tent will be:

$670.58 x 0.88 = $590.99

Therefore, the tent will be worth $590.99 in 3 years, to two decimal places.

Answer:

After one year, the value of the tent will be worth 100% - 12% = 88% of its original value.

After two years, the value of the tent will be worth 88% - 12% = 77.44% of its original value.

After three years, the value of the tent will be worth 77.44% - 12% = 68.1472% of its original value.

To find out how much the tent will be worth in 3 years, we can use the following formula:

Value after 3 years = original value x (1 - depreciation rate)^number of years

Value after 3 years = $866 x (1 - 0.12)^3 = $518.98

Therefore, the tent will be worth $518.98 in 3 years.

In circulation is 6% cumulative preferred stock for ABC Corporation. ABC distributed a 6% preferred dividend two years ago. ABC distributed a 4% preferred stock dividend last year. The minimum payout to preferred stockholders is 8%.

As per the given information, ABC Company has outstanding 6% cumulative preferred stock. This means that the preferred shareholders are entitled to receive a dividend at a fixed rate of 6% every year before any dividend is paid to the common shareholders.

The term "cumulative" implies that any unpaid dividends from previous years must be paid before any dividends can be paid to the common shareholders.

Now, we are given that two years ago, ABC paid a 6% preferred dividend. This means that the preferred shareholders received their full dividend payment for that year.

ABC distributed a 4% preferred stock dividend last year. This means that the preferred shareholders did not receive their full dividend payment for that year, and there is an unpaid amount of 2% (6% - 4%) from the previous year.

Since the preferred stock is cumulative, the unpaid dividends from the previous year must be paid before any dividend is paid to the common shareholders. Therefore, this year, ABC must pay the preferred shareholders their full dividend of 6% for the current year, as well as the unpaid amount of 2% from the previous year, totalling 8%.

To summarize, this year, ABC must pay the preferred shareholders a dividend of 8% before any dividend is paid to the common shareholders.

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