Suppose y varies directly with x. If y = –4 when x = 8, what is the equation of direct variation? Complete the steps to write the equation of direct variation. Start with the equation of direct variation y = kx. Substitute in the given values for x and y to get . Solve for k to get . Write the direct variation equation with the value found for k. The equation is

Answer:

45 degrees Fahrenheit = 7.3 Celsius

Step-by-step explanation:

The formula to convert Celsius to Fahrenheit is given by :

[tex]F=\dfrac{9}{5}C+32[/tex]

In this case, it is required to convert degree Fahrenheit to Celsius. It can be simply done by putting the value of F = 45 degrees Fahrenheit to Celsius. So,

[tex]C=\dfrac{(F-32)5}{9}[/tex]

[tex]C=\dfrac{(45-32)5}{9}[/tex]

C = 7.222

or

T = 7.3 Celsius

So, 45 degrees Fahrenheit is equal to 7.3 Celsius. Hence, this is the required solution.

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

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]

City A = x

City B = y

1st equation: 4x-8 =3y

 2nd equation: x-2y = -3 , rewrite as x = 2y-3

replace x in eq. 1 with equation 2

4(2y-3) -8 =3y

8y-12-8=3y

8y-20 = 3y

-20 = -5y

y = -20/-5 = 4

x = 2y-3 = 2(4)-3 = 5

City A was 5° C, and City B was 4° C. 

Answer: Option 'B' is correct.

Step-by-step explanation:

Since we have given that

Number of members in the easton west high school marching = 52

Number of members in the weston high school marching = 65

We need to find the number of rows so that each row has the same number of players.

For this we will do L.C.M. of 52 and 65.

So, L.C.M. of 52 and 65 = 13

Hence, there are 13 rows in all.

Therefore, Option 'B' is correct.

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.

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.

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.

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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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.

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:

D) 3/8

Step-by-step explanation:

Answer:

Sample Response: When there is an outlier in the data set, the dot plot or histogram will be skewed. In a skewed representation, the mean is pulled up or down toward the tail of the data. Therefore, skewed data affects the mean more than the median.

What did you include in your response? Check all that apply.

The dot plot or histogram will be skewed.

The mean is pulled up or down toward the tail.

The mean is affected more than the median.

regular earnings  + overtime = 421.00 + 78.00 = 499.00

add all the deductions: 29.59 + 30.75 + 18.30 + 25.00 + 7.50 + 5.00 = 116.14

subtract deductions from pay:

499.00 - 116.14 = 382.86

 Answer is B $382.86

Answer:

The function for the given description is y = ln (x + 1) - 0.098 .

Step-by-step explanation:

As you can see in the problem the asymptote is x = -1. This means that the function is not defined for x= -1 and as you know, natural logarithm is not defined for zero. So, it implies that when x tends to -1 the function tends to infinite. So it must be a number adding to x that makes -1 + b = 0 ⇒ b= 1.

Then, you have y = ln (x + 1). If you check, when you replace the point given in the problem (2,1), you find that y = ln (2 + 1) ⇒ y = ln(3) ⇒ y = 1.098, so you can introduce a correction factor ⇒ y = ln (x + 1) - 0.098.

Summarizing, the function decribed before can be y = ln (x + 1) - 0.098.

The 5 employees work per day is [tex]31\frac{1}{3}[/tex].

A subfield of mathematics known as arithmetic operations deals with the study and application of numbers to all other subfields of mathematics. Operations like addition, subtraction, multiplication, and division make up the bulk of it.

These essential numerical tasks (+, - , ×, and ÷) we use in our regular day to day existence. Arithmetic operations are used in every aspect of our lives, whether we need to figure out the annual budget or divide something equally among several people.

Given total employees in flower shop = 5

each employee work [tex]6\frac{4}{15}[/tex] hours per day

[tex]6\frac{4}{15}[/tex] can be solved as = 6 + 4/15 = 94/15

total work time of 5 employees can be calculated by

94/15 + 94/15 + 94/15 + 94/15 + 94/15 = 470/15 = 94/3

or 5 x 94/15 = 94/3

dividing 94 by 3  we get [tex]31\frac{1}{3}[/tex] in mixed fraction.

Hence the total work 5 employees do in a day is [tex]31\frac{1}{3}[/tex].

Learn more about arithmetic operations;

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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.

hypotenuse = c

c^2 = 3.4^2 + 2.6^2

c^2 = 11.56 + 6.76

c^2 = 18.32

c = sqrt(18.32) = 4.28

rounded to nearest tenth = 4.3

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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