Two plans for reaching a goal are given below.
Plan A: Save $450 over the next 8 weeks by working 9 hours per week at $7.20 per hour.
Plan B: Save $450 over the next 6 weeks by working 15 hours per week at $6.50 per hour.
Which of the following is a true statement?
a.
Only plan A will work for achieving the goal.
b.
Only plan B will work for achieving the goal.
c.
Both plans will work for achieving the goal.
d.
Neither plan will work for achieving the goal.

Answer:

D) 3/8

Step-by-step explanation:

Answer:

78,000

Step-by-step explanation:

9.75 is 7.8 times larger than 1.25.

However, we have powers of 10.  In the first number, 10 is raised to the 6th power; in the second number, 10 is raised to the 2nd power.  This means that the first number is 10⁴ times bigger than the second one, or 10000 times bigger.

This means in total, the first number is 7.8(10000) = 78000 times larger than the second one.

This can be confirmed by dividing the two; 9.75(10⁶)÷1.25(10²) = 78000

Answer:

78000

Step-by-step explanation:

$2500 is invested at an interest rate of 4.5% per year, compounded daily for 2 years will amount to $5225.

Borrowers are required to pay interest on interest in addition to principal since compound interest accrues and is added to the accrued interest from prior periods.

We know the formula for compound interest is,

A = P(1 + r/100)ⁿ.

Where, A = amount, P = principle, r = rate, and n = time in years.

Given,  $2500 is invested at an interest rate of 4.5% per year, compounded daily, and assuming it is for 2 years.

∴ The amount compounded daily will be,

A = P(1 + (r/365)/100)ⁿˣ³⁶⁵ as compounded daily.

A = 2500(1 + (4.5/365)/100)²ˣ³⁶⁵.

A = 2500( 1 + 0.00101)⁷³⁰.

A = 2500(1.00101)⁷³⁰.

A = 2500×2.09 dollars.

A = 5225 dollars.

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To calculate the future value of an investment of $2500 at a 4.5% interest rate compounded daily for 5 years, we use the compound interest formula. Assuming 5 years of growth, the future value would be approximately $3117.14.

If $2500 is invested at an interest rate of 4.5% per year, compounded daily, we need to find the value of the investment after a certain number of years. The formula to calculate the future value of an investment with daily compounding is given by:

FV = P × (1 + r/n)^(n×t)

where:

To calculate the future value, we plug in the values into the formula. However, the number of years, t, has not been specified, so we'll need that to give a final answer. For our purposes, let's assume the student asks for the value after 5 years. Using the formula:

FV = $2500 × (1 + 0.045/365)^(365×t)

FV = $2500 × (1 + 0.00012328767)^(1825)

FV = $2500 × 1.246856823

FV = $3117.14 (rounded to the nearest cent)

After 5 years, the investment would be worth approximately $3117.14.

Ronnie cut a total of 9 inches of wood. This is determined by multiplying the number of sections he cut (12) by the length of each section (3/4 inch).

Ronnie cut 12 sections of wood, each measuring 3/4 inch to make his birdhouse's roof. In order to find out the total length of wood he used, we need to multiply the number of sections he cut by the length of each section. This is a basic multiplication problem in fractions.

So, 12 (sections) x 3/4 (inches/section) = 9 inches.

This means Ronnie cut a total of 9 inches of wood to make the birdhouse roof.

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Final answer:

The total duration of the appointment was 2 hours and 45 minutes.

Explanation:

To determine how long the appointment lasted, we need to calculate the time difference between the start time and the end time. The appointment started at 2:30 pm and ended at 5:15 pm.

First, take note of the start time: 2:30 pm.

Then, take note of the end time: 5:15 pm.

Calculate the hours by subtracting the start hour from the end hour: 5 pm - 2 pm = 3 hours.

Next, calculate the minutes by subtracting the start minutes from the end minutes: 15 minutes - 30 minutes. Since you cannot have a negative number of minutes, you need to borrow an hour from the 3 hours calculated, making it 2 hours, and add 60 minutes to the 15 minutes. Now, 75 minutes - 30 minutes = 45 minutes.

Combine the total hours and minutes: 2 hours and 45 minutes

Answer:

Correct option is:

C. [tex](x-\sqrt{3})(x^2+3+x\sqrt{3} )[/tex]

Step-by-step explanation:

x^3-3sqrt(3)

=  [tex]x^3-3\sqrt{3} \\\\=x^3-\sqrt{3}^3[/tex]

= [tex](x-\sqrt{3})(x^2+3+x\sqrt{3} )[/tex]

(since, [tex]a^3-b^3=(a-b)(a^2+b^2+ab)[/tex])

Hence, the correct option is:

   C.    [tex](x-\sqrt{3})(x^2+3+x\sqrt{3} )[/tex]

1. What happens if you don't pay your car insurance premium for your vehicle?

Your are not insured and are driving illegally.

2. Suppose that you only have liability and comprehensive car insurance and you allow your roommate (who doesn't have car insurance) to drive your car to run an errand. What will likely happen if there is a single-car accident causing moderate damage to your car while your roommate is driving?

Your insurance policy will likely not cover the damages to your car.

3. John, Alyson and Jared all selected identical new cars at the same price. John bought the car with some of his own money and the rest a car loan. Alyson bought the car with cash. Jared leased the car. What is true about their options for car insurance?

Alyson has the option to choose the less expensive liability-only insurance coverage.

4. William pays his $500 premium every 6 months for automobile insurance with collision coverage. His deductible is $750. William caused a minor accident that resulted in $700 of damages to his car and $1,100 of damages to the other car. William's car looks and drives fine and he chooses not to file a claim to repair his car. How much will William pay out-of-pocket to have the other car fixed?

$0

5. When Lisa purchased her house, the mortgage lender required her homeowner's insurance to cover 100% of the loan amount. After many years, Lisa paid off her mortgage. If Lisa decided to comparison shop for homeowner's insurance now, what should the insurance coverage amount be based on…

The market value of the house.

6. How can understanding risk management topics help in everyday life?

All answers are correct.

The total travel time one way is 288 minutes.

To find the total travel time one way, we need to add up the time spent on each part of the journey. The salesman spends 1 hour and 48 minutes commuting from his house to the airport. Let's convert this to minutes, which gives us 60 + 48 = 108 minutes.

Next, we add the flight time. The question doesn't specify the duration of the flight, so we can't determine that. We'll assume it takes 2 hours, which is 120 minutes. Finally, we add the time spent on the bus. Again, the question doesn't provide this information, so let's assume it takes 1 hour (60 minutes) by bus.

Adding up the commute time, flight time, and bus time, we get 108 + 120 + 60 = 288 minutes. Therefore, the total travel time one way is 288 minutes.

The probability that the commuter doesn't get stopped all week long is approximately 0.44.

To find the probability that the commuter doesn't get stopped all week long, we need to find the probability of not getting stopped on each day and then multiply those probabilities together. Since the commuter estimates that he gets stopped on about 15% of work days, the probability of not getting stopped on a single day is 1 - 15% = 85%. To find the probability of not getting stopped all week, we raise 85% to the power of 5, since there are 5 work days in a week:

Probability of not getting stopped all week = (85%)5 = 0.85 * 0.85 * 0.85 * 0.85 * 0.85 = 0.44370515625.

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The probability that the commuter doesn't get stopped by the train all week long is 44%.

This question falls under the category of probability in mathematics. The commuter estimates he'll get stopped 15% of work days, which implies that he'll have a smooth commute 85% of the time (100% - 15%). In a 5-day work week, the probability that he doesn't get stopped at all can be computed by multiplying the probability of not getting stopped each day. Therefore, the answer is (0.85)^5 or approximately 0.44, which represents 44%.

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There are 36 boys in the school choir.

The numerical relationship between two values that demonstrates how frequently one value contains or is contained within another.

Given:

There are 18 girls in the school choir.

The ratio of girls to boys is 1 to 2.

That means,

Girls / boys = 1/2

Substituting the values,

18 / boys = 1/2

Boys = 2 x 18

Boys = 36

Therefore, there are 36 boys.

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Answer:

The factored form of given polynomial is [tex]x^3(4x^2-5x-9)[/tex]

Step-by-step explanation:

Given the polynomial [tex]4x^5 - 20x^4 - 36x^3[/tex]

We have to factor the above polynomial completely.

[tex]4x^5 - 20x^4 - 36x^3[/tex]

Take [tex]x^3[/tex] common from each term.

[tex]x^3(4x^2-5x-9)[/tex]

Here, the quadratic polynomial is prime i.e it cannot be factored into lower degree polynomial. It has complex roots.

Hence, the factored form of given polynomial is [tex]x^3(4x^2-5x-9)[/tex]

Answer: 4x^3(x^2 - 5x - 9)

Proof of validity is shown below.

Answer:

The function is given to be :

f(x) = 7 - 4.5x

Now, to make a correct input-output table for the given function write the given function in the form of y and x

⇒ y = 7 - 4.5x

Now, in this equation x is independent variable and y  is dependent variable.

So, give the input values to the variable x and note down the output values of variable y.

The required table is :

x      0         1           2             3

y      7        2.5       -2           -6.5

the right answer is 44.

Answer:

44 degrees.

Step-by-step explanation:

We are asked to find the measure of angle Q using law of cosines.

Law of cosines:

[tex]c^2=a^2+b^2-2ab\times cos(C)[/tex]

Upon substituting our given values in above formula we will get,

[tex]24^2=20^2+34^2-2\times 20\times 34\times cos(Q)[/tex]

[tex]576=400+1156-1360\times cos(Q)[/tex]

[tex]576=1556-1360\times cos(Q)[/tex]

[tex]576-1556=1556-1556-1360\times cos(Q)[/tex]

[tex]-980=-1360\times cos(Q[/tex]

Upon dividing both sides of our equation by -1360 we will get,

[tex]\frac{-980}{-1360}=\frac{-1360\times cos(Q}{-1360}[/tex]

[tex]0.7205882352941176=cos(Q)[/tex]

Now we will use arccos to solve for the measure of angle Q.

[tex]cos^{-1}(0.7205882352941176)=Q[/tex]

[tex]43.896932391182=Q[/tex]

[tex]Q\approx 44[/tex]

Therefore, the measure of angle Q is 44 degrees.

Answer: ∠X

Step-by-step explanation:

If ΔABC is congruent to ΔXYZ then their corresponding parts must be congruent by CPCTC.

To find the corresponding angle to ∠A, just check the position of A in the name of ΔABC,

A is the first letter in the name of ΔABC, thus the angle corresponding to  ∠A is ∠X.

Answer:

The answer is 3 feet

Step-by-step explanation:

The displacement  function is the integration of the velocity formula, so:

[tex]d(t)=\int\limits^0_t \, (-t^{2} +4) dt \\d(t)=\int\limits^0_t{} \, (-t^{2}) dt + \int\limits^0_t{} \, 4 dt \\\\d(t)=(\frac{-t^{3} }{3} + C ) + (4t + C)\\\\\\\ d(t)=frac{-t^{3} }{3} + 4t + C\\[/tex]

if we evaluate the displacement for the upper and lower limit it would be

D = total displacement = d(3) - d(0)

[tex]D=(\frac{-3^{3}  }{3}  + 12 + C) - (\frac{-0^{3} }{3}  + 4*0 + C)\\\\D=(-9  + 12 + C) - (0  + 0 + C)\\\\\\D=(3 + C) -  C\\\\\\D=3[/tex]

Answer:

3 feet

Step-by-step explanation:

The relationships between displacement (position), velocity and acceleration are:

[tex]\boxed{\boxed{\begin{array}{c}\textbf{DISPLACEMENT (s)}\\\\\text{Differentiate} \downarrow\qquad\uparrow\text{Integrate}\\\\\textbf{VELOCITY (v)}\\\\\text{Differentiate}\downarrow\qquad\uparrow \text{Integrate}\\\\\textbf{ACCELERATION (a)}\end{array}}}[/tex]

Displacement is an object’s distance from a particular point (often its starting point), measured in a straight line. It’s not necessarily the same as the total distance travelled.

To find the displacement of an object in its first 3 seconds of travel, we need to integrate its velocity function on the interval [0, 3] seconds.

[tex]\begin{aligned}\displaystyle \int^3_0 (-t^2+4)\; \text{d}t&=\left[\dfrac{-t^{2+1}}{2+1}+4t\right]^3_0\\\\&=\left[-\dfrac{t^{3}}{3}+4t\right]^3_0\\\\&=\left(-\dfrac{(3)^{3}}{3}+4(3)\right)-\left(-\dfrac{(0)^{3}}{3}+4(0)\right)\\\\&=-9+12+0-0\\\\&=3\end{aligned}[/tex]

Therefore, the displacement of the object on the interval [0, 3] seconds is 3 feet.

One benefit of applying statistical forecasting methods is the ability to make informed predictions and decisions based on historical data.

Statistical forecasting methods utilize historical data and mathematical models to make predictions about future outcomes. By analyzing patterns, trends, and relationships within the data, statistical forecasting methods can provide valuable insights and estimates for various industries and fields.

One key benefit of applying statistical forecasting methods is the ability to make informed decisions and plan for the future. By utilizing historical data and statistical models, organizations can anticipate future demand, sales, or resource needs. This enables them to optimize their operations, allocate resources efficiently, and make strategic decisions.

Statistical forecasting methods also provide a level of objectivity and reliability in the prediction process. These methods are based on rigorous mathematical techniques and statistical principles, ensuring that the forecasts are grounded in sound methodology. This allows decision-makers to have confidence in the accuracy and validity of the forecasts, reducing uncertainty and aiding in effective planning.

Overall, applying statistical forecasting methods provides a systematic and data-driven approach to predicting future outcomes. It enables organizations to anticipate and adapt to changing circumstances, optimize their resources, and make informed decisions, leading to improved efficiency, profitability, and overall performance.

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