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You are writing a book about a 3,030-mile bike race across the United States. You wonder about a title, and how many pedal strokes it takes to finish the race. Assuming a pedal stroke is about 16 feet on average, which of the following would be the best book title?

Answer:

Unit rate = $ 30.

Step-by-step explanation:

Unit rate = Total cost ÷ Number of calculators

              = \(\frac{150}{5}\)

             = $ 30

Answer:

$30 per calculator

Step-by-step explanation:

To find the unit rate of the calculators, take the total price of calculators and divide it by 5 to get 30.

This method works when finding any unit rate even when it doesn't involve prices.

*Tip* When dividing, write it as a fraction in case the quotient is not a whole number.

Answer:

Bill by $85

Step-by-step explanation:

Bill :  Compound interest is calculated by multiplying the initial principal amount by one plus the annual interest rate raised to the number of compound periods minus one. The total initial amount of the money given  is then subtracted from the resulting value.

Compounded annually for 6 years at 9 % interest Bill would have $8385.50.

Joe : Simple interest at 11% a year The formula we'll use for this is the simple interest formula.

P is the principal amount, $5000.00.

r is the interest rate, 11% per year, or in decimal form, 11/100=0.11.

t is the time involved, 6year(s) time periods.

So, t is 6year time periods.

To find the simple interest, we multiply 5000 × 11 × 6  = 3300

Usually now, the interest is added onto the principal to figure some new amount after 6 year(s),

or 5000.00 + 3300.00 = 8300.00

As you can see Bill has more by $85.

^Check yourself

Answer:

each weighs 3.75 minimum

Answer:

Each item weighs 3.75 kg, or 3 and 3/4 kg.

Step-by-step explanation:

divide the total weight by the total amount of items. 30/8=3.75

hope this helped! :)

Answer: 3.5

Step-by-step explanation: i got it right on the quiz

Answer:

$60.79

Step-by-step explanation:

First take off the 30% from $78.95. That will leave you with $55.265.

Add 6% of $78.95 for sales tax (4.737) to the $55,265 = $60.002

Then add the 1% of $78.95 for local option tax (.7895) to the $60.002.

That gives you $60.7915   - round it to the nearest cent and it gives you

$60.79

Answer: $60.7915

Step-by-step explanation:

think of percents as a portion of something

if Dave has to pay 6% tax on something + 1% tax he will pay 7% tax.

This means he will pay 7% of 78.95.

In multiplication 'of' means multiply.

just use this as a rule so 7% × 78.95 will be the amount of tax he has to pay

0.07 × 78.95 = $5.5265

However, he has a 30% off coupon

so,

30% × 78.95 will give the amount he saves

.3 × 78.95 = $23.685 saved

now lets find the actual amount he saves with his coupon after taxes:

$23.685 - $5.5265 = $18.1585 saved

we can subtract this amount by the price and we will have the amount Dave has to pay for the jeans:

$78.95 - $18.1585 = $60.7915

⇒ $60.7915 is the price Dave pays

rounding we get $60 and 79 cents

Rοn wοuld make salary $43,460 in the secοnd year.

The answer is οptiοn (a) 43,460.

Arithmetic οperatiοns are the basic mathematical calculatiοns used tο manipulate numerical values.

Tο find Rοn's salary in the secοnd year, we need tο calculate the 6 percent increase frοm his starting salary οf $41,000 and add it tο his starting salary:

Salary in the secοnd year = Starting salary + 6% οf starting salary

                         = $41,000 + 0.06 * $41,000

                         = $43,460

Hence, Rοn wοuld make $43,460 in the secοnd year.

The answer is οptiοn (a) 43,460.

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The equation which correctly represents the given situation as required to be determined is; Choice C; w = 5 × 15.

It follows from the task content that the equation which correctly represents the Given situation is to be determined.

Since the intention is to buy 5 tickets in which case; each ticket costs 15 dollars; we have that;

Since the total amount of dollars they have is w dollars; The equation which holds true for the situation is; w = 5 × 15.

Consequently, answer choice C; w = 5 × 15 is correct.

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Answer:

\(=\frac{2x^3+x^2-11x+14}{\left(x+4\right)\left(x+2\right)\left(x-2\right)}\)

Step-by-step explanation:

Step 1: Factor \(x² + 2x - 8: (x - 2) (x + 4)\)

\(=\frac{x}{x+4}+\frac{x-1}{x+2}+\frac{3}{\left(x-2\right)\left(x+4\right)}\)

Step 2: Find the Least Common Multiplier of  \(x + 4, x - 2, (x + 4), (x - 2)\)

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

Step 3a: Conform the fractions based on the LCM (Least Common Multiplier)

= \(\frac{x\left(x+2\right)\left(x-2\right)}{\left(x+4\right)\left(x+2\right)\left(x-2\right)}+\frac{\left(x-1\right)\left(x+4\right)\left(x-2\right)}{\left(x+2\right)\left(x+4\right)\left(x-2\right)}+\frac{3\left(x+2\right)}{\left(x-2\right)\left(x+4\right)\left(x+2\right)}\)

Step 3b: The denominators are equal, so combine the fractions.

\(=\frac{x\left(x+2\right)\left(x-2\right)+\left(x-1\right)\left(x+4\right)\left(x-2\right)+3\left(x+2\right)}{\left(x+4\right)\left(x+2\right)\left(x-2\right)}\)

Step 4: Expand \(x(x + 2)(x - 2) +(x-1)(x+4)(x-2) + 3(x-2)\)

\(=\frac{2x^3+x^2-11x+14}{\left(x+4\right)\left(x+2\right)\left(x-2\right)}\)

Have a great day!

Answer:

5x - 17

Step-by-step explanation:

3 + 5x - 20

= 5x - 17

The graphing form of the function g(x) is: C) none of the answer choices.

The function g(x) = \(x^2 + 4x - 7\)is already in the standard form of a quadratic equation. In graphing form, a quadratic equation can be represented as y =\(ax^2 + bx + c,\) where a, b, and c are constants.

Comparing the given function g(x) =\(x^2 + 4x - 7\)with the standard form, we can identify the coefficients:

a = 1 (coefficient of x^2)

b = 4 (coefficient of x)

c = -7 (constant term)

Therefore, the graphing form of the function g(x) is:

C) none of the answer choices

None of the given answer choices (A, B, D, or E) accurately represents the graphing form of the function g(x) =\(x^2 + 4x - 7\). The function is already in the correct form, and there is no equivalent transformation provided in the answer choices. The given options either represent different equations or incorrect transformations of the original function.

In graphing form, the equation y = \(x^2 + 4x - 7\) represents a parabolic curve. The coefficient a determines the concavity of the curve, where a positive value (in this case, 1) indicates an upward-opening parabola.

The coefficients b and c affect the position of the vertex and the intercepts of the curve. To graph the function, one can plot points or use techniques such as completing the square or the quadratic formula to find the vertex and intercepts. Option C

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The value of the probability is 0.0714.

According to the statement

We have to find that the students' favorite color was red.

So, For this purpose, we know that the

Probability is the branch of mathematics that studies the possible outcomes of given events together with the outcomes' relative likelihoods and distributions.

From the given information:

A bag 2 contains 2 red marbles, 2 green marbles, and 4 blue marbles.If we choose a marble, then another marble without putting the first one back in the bag.

Then

A bag contains 2+2+4=8 marbles in total.

We have to search out the probability of the subsequent events:

1. we've to settle on a red marble from the bag that contains 8 marbles in total, 2 of them are red

2. we've to decide on a green marble from the bag that contains 7 marbles in total, 2 of them are green.

The probability of the primary event to happens is:

P(one) = 2/8 = 1/4.

The probability of the second event to happen is:

P(two) = 2/7

The probability of both events to happen is:

P = P(one) * P(two)

P = 1/4 * 2/7

P = 1/14

P = 0.0714.

So, The value of the probability is 0.0714.

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Answer:

Step-by-step explanation:

5,69,400,000 = 5.694 x 10^5

The group of individuals fitting a description is called option D: Population, this is because, in statistics, a population is seen as am entire group of individuals, items, or elements that tends to have or share a common characteristics.

The term "population" describes the complete group of people or things that you are interested in investigating. It is the group of individuals or thing(s) about which you are attempting to draw conclusions.

There are infinite and finite populations. A population with a set quantity of people or things is said to be finite. An endless population is one that has an infinite amount of people or things.

Therefore, the correct option is D

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See full text below

A group of individuals fitting a description is the _____

Which of the term below fit the description above.

A.census

B.sample

C.parameter

D.population

Answer:

A. Sides AC and DF

B. Angles BAC and EDF

Answer:

Step-by-step explanation:

The amount of your tax refund is $1,414

To find the tax refund, we need to subtract the amount of federal taxes owed after deductions from the amount of federal taxes already paid.

Tax refund = Federal taxes paid - Federal taxes owed after deductions

Tax refund = $12,042 - $10,628

Tax refund = $1,414

Rounding to the nearest cent, the tax refund is $1,414.00.

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Answer:

C

Step-by-step explanation:

They are neither perpendicular nor parallel since line 1 has slope=-3/5 and line 2 has slope=-5/3. They are neither equal nor have a product equal to - 1.

Answer:

Step-by-step explanation:

hi!

area:

both 7 by 4 sides: (7*4)2=56

both 3 by 7 sides: (3*7)2=42

both 3 by 4 sides: (3*4)2=24

add em up=56+42+24=122

i hope this answered your question. let me know if i missed something and ill fix it!

Answer:

2,3,5,7,11,13,17,19,23,29

Step-by-step explanation:

The measure of the angles are:

∠1 = 90

∠2 = 90

∠3 = 132

We have,

The angle between the tangent and the radius of a circle is 90.

So,

∠1 = 90

∠2 = 90

And,

48 + 90 + 90 + ∠3 = 360 ______(1)

Solve for ∠3 from (1).

48 + 90 + 90 + ∠3 = 360

48 + 180 + ∠3 = 360

∠3 = 360 - 228

∠3 = 132

Thus,

The measure of the angles are:

∠1 = 90

∠2 = 90

∠3 = 132

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Answer:

The probability that the child must wait between 6 and 9 minutes on the bus stop on a given morning is 0.148.

Step-by-step explanation:

Let the random variable X represent the time a child spends waiting at for the bus as a school bus stop.

The random variable X is exponentially distributed with mean 7 minutes.

Then the parameter of the distribution is,\(\lambda=\frac{1}{\mu}=\frac{1}{7}\).

The probability density function of X is:

\(f_{X}(x)=\lambda\cdot e^{-\lambda x};\ x>0,\ \lambda>0\)

Compute the probability that the child must wait between 6 and 9 minutes on the bus stop on a given morning as follows:

\(P(6\leq X\leq 9)=\int\limits^{9}_{6} {\lambda\cdot e^{-\lambda x}} \, dx\)

                      \(=\int\limits^{9}_{6} {\frac{1}{7}\cdot e^{-\frac{1}{7} \cdot x}} \, dx \\\\=\frac{1}{7}\cdot \int\limits^{9}_{6} {e^{-\frac{1}{7} \cdot x}} \, dx \\\\=[-e^{-\frac{1}{7} \cdot x}]^{9}_{6}\\\\=e^{-\frac{1}{7} \cdot 6}-e^{-\frac{1}{7} \cdot 9}\\\\=0.424373-0.276453\\\\=0.14792\\\\\approx 0.148\)

Thus, the probability that the child must wait between 6 and 9 minutes on the bus stop on a given morning is 0.148.

Using the exponential distribution, it is found that there is a 0.1479 = 14.79% probability that the child must wait between 6 and 9 minutes on the bus on a given morning.

The exponential probability distribution, with mean m, is described by the following equation:  

\(f(x) = \mu e^{-\mu x}\)

In which \(\mu = \frac{1}{m}\) is the decay parameter.

The probability that x is lower or equal to a is given by:

\(P(X \leq x) = \int\limits^a_0 {f(x)} \, dx\)

Which has the following solution:

\(P(X \leq x) = 1 - e^{-\mu x}\)

In this problem, we have that mean of 7 minutes, hence:

\(m = 7, \mu = \frac{1}{7}\)

The probability that the child must wait between 6 and 9 minutes on the bus on a given morning is:

\(P(6 \leq X \leq 9) = P(X \leq 9) - P(X \leq 6)\)

In which:

\(P(X \leq 9) = 1 - e^{-\frac{9}{7}} = 0.7235\)

\(P(X \leq 6) = 1 - e^{-\frac{6}{7}} = 0.5756\)

Hence:

\(P(6 \leq X \leq 9) = P(X \leq 9) - P(X \leq 6) = 0.7235 - 0.5756 = 0.1479\)

0.1479 = 14.79% probability that the child must wait between 6 and 9 minutes on the bus on a given morning.

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Answer: \(m\angle DE F=90^{\circ}\)

Step-by-step explanation:

The slope of \(DE\) is \(\frac{7-3}{5-4}=4\).

The slope of \(EF\) is \(\frac{3-2}{4-8}=-\frac{1}{4}\).

Thus, \(DE \perp EF\), meaning \(m\angle DE F=90^{\circ}\).

Answer:

if c = 6, the d= 8c = 8(6) = 48.

Step-by-step explanation:

Let c = weight of cat.

Let d = weight of dog.

     d = 8c                  (the dog weights 8 times as much as the cat)

d + c = 54                  (together, they weigh 54 pounds)

Substitute  8c  for  d  from the first equation into the second equation:

8c + c = 54

     9c = 54

       c = 6

if c = 6, the d= 8c = 8(6) = 48.

By analyzing the graph and evaluating the objective function at each vertex of the feasible region, we can find the optimal solution, which is the vertex that maximizes the objective function z = 3x + y.

To find the optimal solution of the given problem using the graphical method, we need to plot the feasible region determined by the given constraints and then identify the point within that region that maximizes the objective function.

Let's start by graphing the constraints:

1. Plot the line 2x - y = 5. To do this, find two points on the line by setting x = 0 and solving for y, and setting y = 0 and solving for x. Connect the two points to draw the line.

2. Plot the line -x + 3y = 6 using a similar process.

3. The x-axis and y-axis represent the constraints x ≥ 0 and y ≥ 0, respectively.

Next, identify the feasible region, which is the region where all the constraints are satisfied. This region will be the intersection of the shaded regions determined by each constraint.

Finally, we need to identify the point within the feasible region that maximizes the objective function z = 3x + y. The optimal solution will be the vertex of the feasible region that gives the highest value for the objective function. This can be determined by evaluating the objective function at each vertex and comparing the values.

Note: Without a specific graph or additional information, it is not possible to provide the precise coordinates of the optimal solution in this case.

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Answer:

Step-by-step explanation:

We can use the method of undetermined coefficients to solve this differential equation. First, we will need to find the solution to the homogeneous equation and the particular solution to the non-homogeneous equation.

For the homogeneous equation, we will use the form y"+ky=0, where k is a constant. We can find the solutions to this equation by letting y=e^mx,

y"=m^2e^mx -> (m^2)e^mx+k*e^mx=0, therefore (m^2+k)e^mx=0

(m^2+k) should equal 0 for the equation to have a non-trivial solution. Therefore, m=±i√(k), and the general solution to the homogenous equation is y=A*e^i√(k)x+Be^-i√(k)*x.

Now, we need to find the particular solution to the non-homogeneous equation. We can use the method of undetermined coefficients to find the particular solution. We will let yp=a0+a1x+a2x^2+.... As the derivative of a sum of functions is the sum of the derivatives, we get

yp″=a1+2a2x....yp‴=2a2+3a3x+....

Substituting the general solution into the non-homogeneous equation, we get

a0+a1x+a2x^2+...+2a2x+3a3x^2+...=Y(4)

So, the coefficient of each term in the expansion of the left hand side should equal the coefficient of each term in the expansion of the right hand side. Since there is only one term on the right hand side, we get the recurrence relation:

a(n+1)=Y(n-2)/n^2

From this relation, we can find all the coefficients in the expansion for the particular solution. Using this particular solution, we can find the total solution to the differential equation as the sum of the homogeneous solution and the particular solution.

The threes solutions to the given equation sec²x - secx = 2 are:

To solve: sec²x - secx = 2 on interval [0,2\(\pi\))

When we set t = sec x, we get the quadratic equation:

As a result, we must seek solutions to the equations:

\([1] \sec x=2: \quad \cos x=\frac{1}{2} \rightarrow x_1=\frac{\pi}{3} ; \quad x_2=\frac{5 \pi}{3} ;$\\\text { [2] } \sec x=-1: \quad \cos x=-1 \rightarrow x_3=\pi ;\)

Therefore, the three solutions are:

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The correct question is given below:
solve the equation sec²x - secx = 2 on interval [0,2\(\pi\))

Answer:

12 bananas

9 apples

18 pears

Step-by-step explanation:

You are tripling the recipe.

10 x 3 = 3

4 x 3 = 12

3 x 3 = 9

6 x 3 = 18

Explanation

We are required to graph the following given function:

Using a graphing calculator, we have: