THINK
12. SOLVE
EXPLAIN
SHORT RESPONSE During a vacation,
Alice went fly-fishing. She rented a
driftboat.
Rick's Rental
fishing rod
driftboat
$12
$8/hour
If she spent a total of $96, write and
solve an equation to find how many
hours she rented the boat.
Answer:

Part A: The actual dimensions of the pool are 10 feet long and 5 feet wide.

Part B: the cost of the cover for the pool would be $15.00.

Dimension is a measure of a physical property of an object, such as its length, breadth, height, or mass.

Part A: The actual dimensions of the pool can be determined by using the given scale. To do this, we need to convert the given measurements in inches to feet. We can do this by dividing the given measurements in inches by the scale, which is 2 inches equals 7 feet.

The actual length of the pool is 20 ÷ 2 = 10 feet.

The actual width of the pool is 10 ÷ 2 = 5 feet.

Therefore, the actual dimensions of the pool are 10 feet long and 5 feet wide.

Part B: To calculate how much it would cost to buy a cover for the pool, we need to determine the area of the pool. We can do this by multiplying the length by the width of the pool.

Area = length x width

Area = 10 ft x 5 ft

Area = 50 ft²

Therefore, the cost of the cover for the pool would be

$0.30 x 50 ft² = $15.00.

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Question :

The blueprint of a pool has a scale of 2 inches equals 7 feet. The scale drawing is shown below. the length is 20 and the width is 10

Part A What are the actual dimensions of the pool? Blueprint: 10 in. Actual: ft Blueprint: 20 in. Actual: ft

Part B How much would it cost to buy a cover for the pool that costs $0.30 per square foot?

The interest that is paid on the loan in 6 years will be $4,200.

The amount of interest that is saved is $2,100.

The simple interest is a linear function of the number of years of the loan, value of the loan and the duration of the loan. The higher either of these values are, the higher the simple interest.

Simple interest = loan x time x interest rate

Simple interest if the loan is paid off after 6 years: $12,500 x 6 x 0.056 = $4,200

Simple interest if the loan is paid off after 3 years: $12,500 x 3 x 0.056 = $2100

Interest saved = $4200 - $2100 = 2100

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The mass of the individual can be up to 87.27 kg for the hot-weather training strategy to be appropriate.

Given that the training strategy is appropriate for a BSA less than 2.0, we need to find the maximum mass (M) for the individual with a height (H) of 165 cm. The equation for BSA is:

BSA = √(H x M) / 3600

We can rearrange the equation to solve for M:

M = (BSA^2 x 3600) / H

Since we want the maximum mass for a BSA less than 2.0, we can use BSA = 2.0 as the upper limit:

M = (2.0^2 x 3600) / 165

M = (4 x 3600) / 165

M = 87.27 kg

The above question is in response to the full question as seen in the image;

A sports medicine specialist determines that a hot-weather training strategy is appropriate for a 165 cm tall individual whose BSA is less

than 2.0. To the nearest hundredth, what can the mass of the individual be for the training strategy to be appropriate?

The equation for BSA is BSA = √(H x M)/3600

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The  X, Y, and Z values ​​are 84, 90, and 90, respectively. To answer this question, we need to understand the meaning of the words "median", "mean" and "range".

Median is the middle number of a set of numbers - it is the number in the middle when the numbers are ordered from smallest to largest.

Since the median is 90, this means that Y (the mean number) is 90. Since the average is 92, this means that the sum of the three numbers is 276 (92 x 3). The interval is 6, which means that the difference between the largest number and the smallest number is 6.

To solve for X and Z, we can use the equation X Y Z = 276. We know that Y is 90, so we can plug 90 into Y:

X 90 Z = 276

Then we can  subtract 90 from both sides to find the value of X and Z:

X Z = 186

Since the range of the three numbers is 6, this means that X and Z must be 6 plus. The only two numbers that differ by six and add up to 186 are 84 and 90.

Therefore the  X, Y, and Z values ​​are 84, 90, and 90, respectively.

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It will take around 3.72 months to pay off the credit card debt.

The formula for APR is:

A = P * [tex](1 + r/n)^{nt}[/tex]

In which,

A = amount after compounding.

P = balance amount

r = rate of interest.

n = number of time compounded.

Initial balance: $30,000.

Payments per month = $200.

Expenses = $100

Balance amount = 30,000 - 12 *(200 - 100)

Balance amount = $28800

So, time taken for paying off credit card debt.

30,000 = 28800  [tex](1 + 0.24/1)^{1*t}[/tex]

[tex](1.24)^{t}[/tex] = 30,000 / 28800

[tex](1.24)^{t}[/tex] = 1.04

Solve by using logarithmic function.

t = ln (1.04) / 1.24

t = 0.31  year

t = 3.72 months

Thus, it will take around 3.72 months to pay off the credit card debt.

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Answer:

31000 - y = x

Step-by-step explanation:

Solve for x

[tex]12000\times5=9500+9500+10000+x+y[/tex]

Add and multiply the integers

[tex]60000=29000+x+y[/tex]

Subtract 29000 on both sides

[tex]31000=x+y[/tex]

Subtract y on both sides

[tex]31000-y=x[/tex]

Answer:

When you divide 233 by 6 using long division, you get:

38

---

6|233

 216

 ---

  17

Therefore, 233 ÷ 6 = 38 with a remainder of 17

Answer:

38.83 (the 3 goes on and on)

29 + 14 = 44 by decomposing numbers to add and make a new 10.

Decomposition of numbers involves breaking a number down into its constituent parts or smaller numbers that add up to the original number. This can be done in different ways depending on the purpose and context of the problem.

For example, one common way of decomposing a number is by place value. In this case, the number is broken down into its digits, which represent different powers of ten. For instance, the number 562 can be decomposed into 500 + 60 + 2.

Another way of decomposing numbers is by factoring. In this case, the number is expressed as a product of its factors. For example, the number 12 can be decomposed as 2 x 2 x 3.

Decomposing numbers is a useful skill in many areas of mathematics, including arithmetic, algebra, and geometry. It is often used to simplify problems, make computations easier, and facilitate further analysis.

To decompose 29 to make a new 10, we can break it into 9 and 20. Then, to decompose 14 to make a new 10, we can break it into 6 and 8.

So, we have:

29 + 14 = (9 + 20) + (6 + 8)

Now, we can regroup the numbers to make a new 10:

= (9 + 1) + (20 + 6) + 8

= 10 + 26 + 8

= 44

Therefore, 29 + 14 = 44 by decomposing numbers to add and make a new 10.

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The probability that John's drive to work will take between 36 and 40 minutes is 0.3413.

Probability is the measure of how likely an event is to occur. It is expressed as a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain to occur. Probability is used in many areas of life, such as gambling, finance, and science. It is also used to make decisions in everyday life, such as estimating the likelihood of rain or the chance of winning a bet.

Using the normal distribution, the probability of John's drive taking between 36 and 40 minutes can be calculated using the standard normal distribution table. The formula for calculating the probability is: P(x<X<y) = P(y) - P(x).

For the given problem, the lower boundary is 36 minutes and the upper boundary is 40 minutes. Using the standard normal distribution table, the probability of John's drive taking between 36 and 40 minutes can be calculated by subtracting the probability of 36 minutes from the probability of 40 minutes. This gives us a probability of 0.3413.

Therefore, the probability that John's drive to work will take between 36 and 40 minutes is 0.3413.

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The probability that John's drive to work will take between 36 and 40 minutes is 0.3829.

Probability is the measure of how likely an event is to occur. It is expressed as a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain to occur. Probability is used in many areas of life, such as gambling, finance, and science. It is also used to make decisions in everyday life, such as estimating the likelihood of rain or the chance of winning a bet.

The probability that John's drive to work will take between 36 and 40 minutes can be calculated using a normal distribution table. The mean of the distribution is µ = 38 minutes, and the standard deviation is σ = 5 minutes.

To calculate the probability, we need to convert the given range (36 minutes to 40 minutes) into standard normal scores. This is done by subtracting the mean (µ = 38 minutes) from the lower bound (36 minutes) and then dividing by the standard deviation (σ = 5 minutes). The result is a standard normal score of -0.4. The same calculation is carried out for the upper bound (40 minutes) and the result is a standard normal score of 0.4.

Using a normal distribution table, we can then determine the probability that John's drive to work will take between 36 and 40 minutes. This probability is equal to the area under the normal curve between the two standard normal scores of -0.4 and 0.4. The result is a probability of 0.3829.

Therefore, the probability that John's drive to work will take between 36 and 40 minutes is 0.3829.

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The value of x does not exist.

What is Quadratic equation?

A quadratic equation is a second-degree polynomial equation in a single variable of the form ax^{2} + bx + c = 0, where a, b, and c are constants and x is the variable. The highest exponent of the variable in a quadratic equation is 2, and the equation can be written in standard form, where the coefficient of the squared term (a) is not equal to zero.

The given expression is:

5x² - √3x + 2

This is a quadratic expression in the variable x, which means that it can be written in the form of ax² + bx + c, where a, b, and c are constants. In this case, we have:

a = 5

b = -√3

c = 2

We can use the quadratic formula to find the roots of this expression:

x = [-b ± √(b² - 4ac)] / 2a

Now, putting the values of a, b, and c, we get:

x = [-(-√3) ± √((-√3)² - 4(5)(2))] / 2(5)

Now, Simplifying the expression under the square root, we get:

x = [√3 ± √(-71)] / 10

Since the expression under the square root is negative, there are no real roots to this equation. Therefore, the expression 5x² - √3x + 2 has no real solutions.

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Try going to the store and they should be surprisingly cheap.

Answer: here it is.

Step-by-step explanation:

1. Making a topic relevant to an audience can involve finding ways to connect the subject matter to their cultural, social, or personal experiences.

2. The audience can learn a great deal from a well-crafted presentation that effectively conveys important information and insights.

For example, if the topic is about climate change, one might discuss how it affects their local community or how it relates to their personal lifestyle choices. Similarly, if the topic is about a historical event, one might highlight its relevance to current social issues or draw connections to cultural traditions and values.

For instance, they may gain a deeper understanding of a particular issue or topic, or learn about new ideas and perspectives. A good presentation can also inspire the audience to take action or make changes in their own lives.

In order to achieve these outcomes, it is important for the presenter to communicate clearly and engagingly, and to connect the topic to the interests and concerns of the audience. By doing so, the presentation can be a valuable learning experience for everyone involved.

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To determine which of these methods apply, you'll need to analyze the given information about angles and side lengths in triangles AMNO and AQRS.

To prove that triangles AMNO and AQRS are similar (~), we need to show that their corresponding angles are congruent, and their corresponding sides are proportional. Here are some methods to do that:

1. Angle-Angle (AA) similarity: If two pairs of corresponding angles in triangles AMNO and AQRS are congruent, then the triangles are similar.

2. Side-Angle-Side (SAS) similarity: If two pairs of corresponding sides in triangles AMNO and AQRS are proportional, and the included angles between these sides are congruent, then the triangles are similar.

3. Side-Side-Side (SSS) similarity: If all three pairs of corresponding sides in triangles AMNO and AQRS are proportional, then the triangles are similar.

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The measure οf ∠Y is 51 degrees.

An inscribed angIe in a circIe is an angIe fοrmed by twο chοrds in the circIe that have a cοmmοn endpοint, with the vertex οf the angIe οn the circIe. The measure οf the inscribed angIe is haIf the measure οf the intercepted arc that Iies inside the angIe.

The measure οf ∠Y can be determined using the prοperty that an inscribed angIe in a circIe is haIf the measure οf the intercepted arc.

Since the arc XZ is 86 degrees, the measure οf the inscribed angIe XYZ is 86/2 = 43 degrees.

AngIe X Y Z is the sum οf angIes XYZ and YXZ. Let's caII the measure οf angIe YXZ as α.

AngIe X Y Z = ∠XYZ + ∠YXZ

∠Y = 180° - ∠XYZ - ∠YXZ = 180° - 43° - α

Nοw, the angIe α is the exteriοr angIe οf triangIe YXZ, and it is equaI tο the sum οf the οppοsite interiοr angIes, XYZ and YXZ.

α = ∠XYZ + ∠YXZ

α = 43° + α/2

SοIving fοr α, we get:

α = 86°

Substituting α = 86° in the expressiοn fοr ∠Y, we get:

∠Y = 180° - 43° - 86° = 51°

Therefοre, the measure οf ∠Y is 51 degrees.

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This is a contradiction, so our original assumption that g(x) = f(x) must be false. Therefore, the solution is not true algebraically.

What are functions ?

In mathematics, a function is a rule that maps each element in a set (the domain) to a unique element in another set (the range). It is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. Functions are commonly represented using function notation, where the symbol "f" is used to represent the function, and the input value is placed inside parentheses. For example, if the function takes the input "x" and returns the output "y"

According to the question:
To prove algebraically that g(x) = f(x), we need to show that the expressions for g(x) and f(x) are equivalent for all values of x. That is, we need to show that:

2x²+3x-1 = x²-3

We can start by simplifying both sides of the equation:

2x²+3x-1 - (x²-3) = 0

Simplifying the left side, we get:

2x²+3x-1 - x²+3 = x²+3x+2

Now we can simplify the right side:

x²+3x+2 = (x+1)(x+2)

Substituting this expression back into the equation, we get:

2x²+3x-1 - x²+3 = (x+1)(x+2)

Simplifying the left side again, we get:

x²+3x-4 = (x+1)(x-4)

Now we have:

(x+1)(x-4) = (x+1)(x+2)

We can cancel out the factor of (x+1) from both sides, since it is not equal to zero for any value of x:

x-4 = x+2

Subtracting x from both sides, we get:

-4 = 2

This is a contradiction, so our original assumption that g(x) = f(x) must be false. Therefore, the solution is not true algebraically.

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The correct equation relating the volume of mulch purchased (v) and the total cost of the purchase (c) is: c = 33v + 720

The total cost formula is used to combine the variable and fixed costs of providing goods to determine a total.

The cost of the mulch depends on the volume purchased, so the equation relating the volume of mulch purchased (v) and the cost of the purchase (c) is:

c = 33v

The cost for 5 yards of edge material is $60, so the cost for 60 yards of edge material is:

60/5 x 60 = $720

Therefore, the total cost of the purchase is the sum of the cost of the mulch and the cost of the edge material:

total cost = cost of mulch + cost of edge material

c = 33v + 720

So the correct equation relating the volume of mulch purchased (v) and the total cost of the purchase (c) is: c = 33v + 720

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The interest rate paid by Scott is 4.25% for the 72 months.

We can determine the simple interest of the given problem by the simple interest formula which is given as :

I=PRT

Where,

I=Interest

P=principal

R=rate in decimal

T=time in years

Converting the given 72 months into years we get time t :

1 year = 12months

72 months / 12months = 6 years

t=6

From the given data

I=8925

P=35000

R=r

T=6

Substituting the above values in the simple interest equation we get:

8925 = 35000*r*6

8925 = 210000*r

divide both sides by 210000

R = 0.0425

Therefore, the interest rate is 4.25%

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The value of the variable x for the similar triangles is equal to 25

The triangles BDR and QDC are similar, this implies that the length DC of the smaller triangle is similar to the length DR of the larger triangle

and the length DQ of the smaller triangle is similar to the length DB of the larger triangle

so;

x/(15 + x) = 40/64

64x = 40(15 + x) {cross multiplication}

64x = 600 + 40x

64x - 40x = 600 {subtract 40x from both sides}

24x = 600

x = 600/24

x = 25

Therefore, the value of the variable x for the similar triangles is equal to 25

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Answer: yes correct i love math

Step-by-step explanation:

The quadratic equation in the given graph can be written in the vertex-form as:

y = -2(x - 1)² + 4

We can see the graph of a quadratic equation. Remember that a quadratic equation with a vertex (h, k) and a leading coefficient a can be written as:

y = a*(x - h)² + k

in the graph we can see that the vertex is (1, 4), replacing that we will get:

y = a*(x - 1)² + 4

In the graph we also can see that the curve passes through the point (0, 2), replacing thesevalues in the equation we will get:

2 = a*(0 - 1)² + 4

2 = a + 4

-2 = a

Then the quadratic is:

y = -2(x - 1)² + 4

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The length of the base is 6 inches.

What is triangle?

A triangle is a three-sided polygon, which is a flat shape with straight sides. It is a basic shape in geometry and has many interesting properties that are useful in mathematics and other fields.

The formula for the area of a triangle is A = 1/2 * b * h, where A is the area, b is the length of the base, and h is the height of the triangle.

In this case, we know that the area of the triangle is 21 in² and the height is 7 in. So we can substitute these values into the formula and solve for the base:

21 = 1/2 * b * 7

Multiplying both sides by 2:

42 = b * 7

Dividing both sides by 7:

6 = b

Therefore, the length of the base is 6 inches.

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Complete question : The area of the triangle is 21 in² ad the height is 7 in. what is the length of the base?

Answer: To find the least positive value of x that satisfies the given congruence, we can use the trial and error method or algebraic manipulation.

Using the trial and error method, we can start by plugging in values of x and checking if the congruence is satisfied.

For x = 1, (x + 3) = 4, so 89 ≡ 0 (mod 4), which is not a multiple of 3.

For x = 2, (x + 3) = 5, so 89 ≡ 1 (mod 4), which is not a multiple of 3.

For x = 3, (x + 3) = 6, so 89 ≡ 2 (mod 4), which is not a multiple of 3.

For x = 4, (x + 3) = 7, so 89 ≡ 3 (mod 4), which is not a multiple of 3.

For x = 5, (x + 3) = 8, so 89 ≡ 0 (mod 4), which is a multiple of 3.

Therefore, the least positive value of x that satisfies the congruence is x = 5.

Alternatively, we can use algebraic manipulation to solve the congruence. We have:

89 ≡ (x + 3) (mod 4)

=> 89 ≡ x + 3 (mod 4)

=> 86 ≡ x (mod 4) (subtracting 3 from both sides)

Now we need to find the least positive value of x that satisfies this congruence and is a multiple of 3.

The solutions for this congruence are x = 2 (mod 4) and x = 6 (mod 4).

Plugging in x = 2, we get 89 ≡ 5 (mod 4), which is not a multiple of 3.

Plugging in x = 6, we get 89 ≡ 3 (mod 4), which is not a multiple of 3.

Therefore, the least positive value of x that satisfies the congruence and is a multiple of 3 is x = 10 (which is equivalent to x = 2 (mod 4) and x = 6 (mod 4)), but this is not the answer to the original question since x must be positive.

Plugging in x = 14, we get 89 ≡ 1 (mod 4), which is not a multiple of 3.

Plugging in x = 18, we get 89 ≡ 3 (mod 4), which is not a multiple of 3.

Finally, plugging in x = 22, we get 89 ≡ 1 (mod 4), which is not a multiple of 3.

Plugging in x = 26, we get 89 ≡ 3 (mod 4), which is not a multiple of 3.

Since we want x to be positive, we can stop here and conclude that the least positive value of x that satisfies the given congruence is x = 5.

Step-by-step explanation:

Step-by-step explanation:

Quadrilateral Sum Theorem. The total sum of the interior angles of a quadrilateral is 360°. A quadrilateral is formed by joining four non-collinear points. A quadrilateral has four sides, four vertices and four angles. Therefore, that is the Quadrilateral Sum Theorem.

Hello and regards kiann09.

So the solution of the equation is:

  y = x - 2

  y = 3x + 5

We substitute the given value of y into the equation y = 3x + 5.

   x - 2 = 3x + 5

We solve the equation for x.

     x - 2 - 3x = 5

We move the variable to the left side and change its sign.

The sign of the variable must be changed because, in the process of "moving the variable", we are adding its opposite to both sides.

     x - 2 - 3x = 5

Now we move the constant to the right hand side and change its sign.

      x - 3x = 5 + 2

We group like terms.

      -2x = 5 + 2 ⇒ We add the numbers ⇒ -2x + 7

We must divide both sides by -2.

      x = - 7/2

We substitute the given value of x into the equation y = x - 2.

       y = (-7/2)-2

We solve the equation for y. We write all the numerators above the common denominator.

              y = -(7 + 4)/2

              y = - 11/2

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Answer:

y=2x+10

Explanation: They start with paying $10 and have to pay and extra $2 for each time at the concession stand.

Algebraic expressions are useful for solving different and complex equations in mathematics, as well as for modelling real-life situations such as revenue, cost, inference, etc

The algebraic expression is: [tex]6x - 9[/tex].

To represent the sentence as an algebraic expression, we can follow these steps: Identify the variable. In this case, “a number” is x. Identify the operation. In this case, “less than” means subtraction and “times” means multiplication.

An algebraic expression is an expression that contains variables, constants and mathematical operations. Algebraic expressions are useful because they can help us solve different and complex equations.

For example, if you want to calculate the area of a rectangle with length x and width y, you can use the algebraic expression xy to represent the area.

Write the expression using the order of operations. In this case, we need to multiply six by x first, then subtract nine from the result.

Therefore, The algebraic expression is: [tex]6x - 9[/tex]

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Answer:

Step-by-step explanation:

To calculate the equal monthly payments under this loan, we can use the formula for the present value of an annuity due, since the payments are due at the end of each period. The present value of the equal monthly payments can then be set equal to the loan amount of R250,000, and we can solve for the payment amount.

First, we need to calculate the present value factor for an annuity due with 12 payments per year over a four-year period, using a nominal annual rate of 6%.

PVIFA(due) = (1 - (1 + r/n)^(-nt))/((r/n)(1 + r/n))

Where:

r = nominal annual rate = 6%

n = number of compounding periods per year = 12

t = number of years = 4

PVIFA(due) = (1 - (1 + 0.06/12)^(-12*4))/((0.06/12)(1 + 0.06/12)) = 43.232

Next, we can use the formula for the present value of an annuity due to calculate the equal monthly payments:

PMT = PV / PVIFA(due)

Where:

PV = present value of the loan = R250,000

PMT = 250000 / 43.232 = R5,785.97

Therefore, your equal monthly payments will be R5,785.97. At the end of the four-year period, you will also need to make a final balloon payment of R50,000 to fully pay off the loan.

Answer:

3. 216 cm^3

4a. A = 5 ft, B = 4 ft.

4b. 88 ft^3

Step-by-step explanation:

3. Separate into two rectangular prisms:

Volume of first one: 4cm*2cm*3cm = 24cm^3

Volume of second one: 4cm*12cm*4cm = 192cm^3

Add them together: 24 + 192 = 216cm^3

4a.

Length A = 8-3 = 5ft.

Width B = 8-4 = 4ft.

4b. Separate into two rectangular prisms:

Volume of first one: 2ft*3ft*4ft = 24ft^3

Volume of second one: 8ft*4ft*2ft = 64ft^3

Add them together: 24 + 64 = 88ft^3