Final answer:
To solve the equation 4x=7(x-3), distribute 7, simplify, isolate the variable, and divide by -3 to find that x=7.
Explanation:
To solve the equation 4x=7(x-3) step by step:
1. First, distribute 7 to (x-3), resulting in 4x=7x-21. (Reason: applying the distributive property)
2. Next, subtract 7x from both sides of the equation, giving us 4x-7x=-21. (Reason: isolating the variable term)
3. Combine like terms on the left side to get -3x=-21. (Reason: simplifying the equation)
4. Finally, divide both sides of the equation by -3 to solve for x, resulting in x=7. (Reason: isolating the variable)
After solving the given equation, that is, 4x=7(x-3), we get the answer x=7.
City A and City B had two different temperatures on a particular day. On that day, four times the temperature of City A was 8° C more than 3 times the temperature of City B. The temperature of City A minus twice the temperature of City B was −3° C. What was the temperature of City A and City B on that day?
Your answer:
City A was 5° C, and City B was 4° C.
City A was 3° C, and City B was −1° C.
City A was 8° C, and City B was −3° C.
City A was 5° C, and City B was −5° C.
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.
diane charges $10 for a house call plus $35 an hour for electrical work. if she made $150 on one job,how many hours did she work?
Explain when the median of a data set is a better measure of center than the mean
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.
The law of cosines is used to find the measure of Q.
242 = 202 + 342 – 2(20)(34)cos(Q)
576 = 400 + 1156 – (1360)cos(Q)
576 = 1556 – (1360)cos(Q)
–980 = –(1360)cos(Q)
To the nearest whole degree, the measure of angle Q _____ is
degrees
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.
Which is the correct input-output table for the function f(x) = 7 – 4.5x?
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
For an object whose velocity in ft/sec is given by v(t) = −t^2 + 4, what is its displacement, in feet, on the interval t = 0 to t = 3 secs?
7.67
−3.00
−0.33
3.00
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.
For the values a = 3.4 and b = 2.6, which are legs of a right triangle, find c, the hypotenuse, to the nearest tenth.
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
What are five properties preserved under a translation?
If y = 285 when x = 57, what is y when x = 81?
Jack has 2,613 songs saved on his computer. Dexter has 4 times as many songs saved on his computer as Jack has. How many songs does Dexter have saved on his computer?
Suppose an airplane climbs 15 feet for every 40 feet it moves forward. What is the slope of this airplane's ascent?
Answer:
D) 3/8
Step-by-step explanation:
If triangle ABC is congruent to triangle XYZ, then which of the following is congruent to ∠A?
∠C
∠X
∠Y
∠Z
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.
CPCTC (congruent parts of corresponding angles are congruent) tells that if two triangles are congruent then the corresponding angles and sides are congruent .To get to work, a commuter must cross train tracks. the time the train arrives varies slightly from day to day, but the commuter estimates that he'll get stopped on about 15% of work days. during a certain 5-day work week, what is the probability that he doesn't get stopped all week long?
The probability that the commuter doesn't get stopped all week long is approximately 0.44.
Explanation: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%.
Explanation: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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A time-ordered plot of representative sample statistics is called a:
Factor completely 4x5 − 20x4 − 36x3. (1 point)
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.
HEEEEEEEEEEEELP 20 POINTS FOR REAL
Shayla is baking muffins that require 1/2 cup vegetable oil. She only has 1/3 cup left. How much more does she need?
An appointment lasted from 2:30 pm until 5:15 pm. how long was the appointment?
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
Frederick needs to borrow $3000 for a down payment on a new car. His uncle decided to loan him the money as a 4.5% loan. Frederick doesn't want to pay more than $810 in interest. How many years does Frederick have to pay back the loan?
how would the expression x^3-3sqrt(3) be rewritten using difference of cubes?
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]
Determine the function which corresponds to the given graph. a natural logarithmic function crossing the y axis at zero and going through the point 2,1.
The asymptote is x = -1.
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.
Find the measures of angles x,y, and z
how do you make this equation 13+5y=6x into slope-intercept form?
When is g(x) = 0 for the function g(x) = 5⋅23x + 4?
when x = 0
when x = 1
when x = 4
never
The formula to convert Celsius to Fahrenheit is f= 9/5c+32. Convert 45degreesF to Celsius. Round to the nearest degree.
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.
Approximately how many times greater is 9.75×106 than 1.25×102 ? 7.8 7800 78,000 780,000
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:
The sum of three consecutive integers is 267. What is the largest integer?
PLEASE HELP! Complete the truth table and determine whether or not the following statement is a tautology, a contradiction, or neither. ∼(∼p∧q)∧(p∨q)∼(∼p∧q)∧(p∨q). I attached an image.
Identify a benefit of applying statistical forecasting methods
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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Expressed as a percent, 0.325 is less than 100%. True False
Quiz/Survey Quiz Week 4 - Unexpected Events A
1. What happens if you don't pay your car insurance premium for your vehicle? Your car payments will increase
You are not insured
You are driving illegally
Any insurance claim isn't processed and your car doesn't get fixed
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.
Your friend will likely go to jail for theft of your car and destruction of property. Your friend will likely receive fines for driving without insurance.
Your insurance will likely pay for the damages and add your friend's accident to your record.
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.
John and Alyson have the option to choose the less expensive liability-only insurance coverage.
Alyson and Jared have the option to choose the less expensive liability-only insurance coverage.
John, Alyson and Jared all have 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?
$1,550
$750
$0
$1,100
$500
$800
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
The original cost to build the house
The cost to rebuild the house
The appraised value of the house
6. How can understanding risk management topics help in everyday life?
It can help you evaluate the risks involved with situations you might face while driving, hanging out with friends, or being adventurous.
It can help you avoid large medical bills incurred because you have no medical insurance.
It can help safeguard your credit and protect you from lawsuits.
All answers are correct
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.