Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.
f of x equals eight divided by x and g of x equals eight divided by x
Rasheed needs to save $231. To earn money,he plans to wash cars and charge $12 per car.Write two estimates Rasheed could use to determine how many cars he needs to wash
Coin can be tossed until a tail appears or until it has been tossed 3 times. Given that tail does not occur on the first toss, whats probability that the coin is tossed 3 times?
Put these numbers in order from least to greatest 11, 7, 8, 3, 6, three, 16, 10, 16
What are the approximate solutions of 7x^2 4x-9=0??
What is the total interest on a ten-year. 6.1% loan with a principal of $32,000?
Final answer:
The total interest on a ten-year, 6.1% loan with a principal of $32,000 is $19,520.
Explanation:
To find the total interest, we need to use the formula:
Interest = Principal × Rate × Time
Given that the principal is $32,000, the interest rate is 6.1%, and the time is 10 years, we can substitute these values into the formula to calculate the total interest:
Principal: $32,000
Rate: 6.1%
Time: 10 years
Interest = $32,000 × 0.061 × 10 = $19,520
Therefore, the total interest on a ten-year, 6.1% loan with a principal of $32,000 is $19,520.
Heather writes the equations below to represent two lines drawn on the coordinate plane.
–6x + 18y = 0
4x – 12y = 20
After applying the linear combination method, Heather arrived at the equation 0 = 60. What conclusion can be drawn about the system of equations?
The equation has no solution; therefore, the system of equations has no solution.
The equation has a solution at (0, 60); therefore, the system of equations has a solution at (0, 60).
The equation has infinite solutions; therefore, the system of equation as infinite solutions.
The equation has a solution at (0, 0); therefore, the system of equations has a solution at (0, 0).
Answer:
its A if you are taking the unit test
Step-by-step explanation:
1, 6, 11, 16, 21, . . .
Use inductive reasoning to predict the next term in the sequence.
A.26B.31C.36D.37 ?
Carol sells candles and Yankee Candle. She earns $8.50 per hour plus 6% commission on sales. Last week Carol worked 40 hours. What was Carol’s weekly gross salary if her total sales were $250? *
$590.51
$352.16
$355.00
$340.00
Answer:$352.16
Im in a rush so cant add explaination
There are 6 quarters in a jar. Jill adds 2 quarters to the jar every day. Which linear equation represents the total amount of quarters in the jar after x days?
y = 6x + 2
y = 1/6x + 2
y = 2x + 6
6y = 2x
Answer: [tex]y = 2x + 6[/tex]
Step-by-step explanation:
Let x represents the number of days .
Given : There are 6 quarters in a jar.
Jill adds 2 quarters to the jar every day.
Then, the number of quarters added in x days = 2x
Now, the total number of quarters in the jar after x days = 2x+6
Hence, the linear equation represents the total amount of quarters in the jar after x days will be:-
[tex]y = 2x + 6[/tex]
Find dy/dx and d2y/dx2. x = et, y = te−t
The question is about finding the first and second derivatives of y with respect to x. The first derivative dy/dx is found to be (1+t)e^-2t, and the second derivative d2y/dx2 is found to be -2e^-2t.
Explanation:The derivatives are found by differentiating each function with respect to t first, using the product and chain rules, respectively: the derivatives dy/dt and dx/dt are dy/dt = e^-t - te^-t and dx/dt = e^t. Then, dy/dx can be found as (dy/dt)/(dx/dt), and the second derivative d2y/dx2 can be obtained by differentiating dy/dx with respect to x, which will utilize the quotient rule. Specifically, dy/dx = (e^-t(1+t))/(e^t) which simplifies to (1+t)e^-2t, and after a relatively complex differentiation for d2y/dx2, we get -2e^-2t.
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Sixteen is 64% of what number?
A.12
B.25
C.32
D.48
Which fraction is equivalent to 2/6?
how to solve sin(pi/2) without a calculator ...?
By the definition of the functions of trigonometry, the sine of is equal to the -coordinate of the point with polar coordinates , giving . Similarly, , since it is the -coordinate of this point. Filling out the rest trigonometric functions then gives
How many pints are in 7.5 gallons?
a. 120 pt
b. 90 pt
c. 60 pt
d. 30 pt
In a sample of students, 12 out of 24 students in a class wanted a sandwich for lunch. using the data from the sample, predict how many students would want sandwiches for lunch in a school of 400
Out of 400 students in school, 200 students would want sandwich in school.
The question is asking to predict how many students would want sandwiches for lunch in a school of 400 based on a sample of 24 students where 12 wanted a sandwich.
Calculate the proportion of students in the sample wanting a sandwich: 12/24 = 0.5
Apply the proportion to the larger school: 0.5 x 400 = 200 students.
PLEEEEEEEEEEEEEEEAAAAAAAAAAAAAAAASE HELP ME!!!!
Which is the equation of the given line?
A. x=-3
B. x=3
C. y=-3
D. y=3
slope -2 and passes through (1, 1)
Write 9 as a power of the base 3
The number 9 can be expressed as a power of 3 by finding the appropriate exponent that, when raised to the base 3, equals 9. This exponent is 2, making 9 written as a power of 3 to be 3².
To write the number 9 as a power of the base 3, we look for an exponent that can be raised to the base 3 to result in the number 9. This is achieved by recognizing that 3 squared (3²) equals 9. So, 9 expressed as a power of 3 is 3².
When raising a number to a power, such as generating the cubing of exponentials, you cube the digit term normally and multiply the exponent by 3. However, in this case of 9 as a power of 3, we are not cubing but rather finding which power results in the number 9 when using the base 3. The process involves simple experimentation or recollection that 3¹ = 3, 3² = 9, and so on.
In mathematics, writing numbers in exponential form is essential, as it simplifies operations and understanding of scale. It's a useful concept, not only for integer powers but also when dealing with decimal or negative exponents.
for the sequencing of 3/16, 4/25, 5/36, 6/49
would it be (n+1)/(n^2)? ...?
An insurance company charges a 35-year old non-smoker an annual premium of $118 for a $100,000 term life insurance policy. The premiums for 45-year olds and 55-year old no smokers are $218 and $563, respectively. Write a quadratic model for the premium p as a function of age a.
Answer:
[tex]p=\dfrac{49}{40}a^2-88a+\dfrac{13579}{8}[/tex]
Step-by-step explanation:
Let premium p for age of a , (p,a)
# An insurance company charges a 35-year old non-smoker an annual premium of $118 for a $100,000 term life insurance policy.
(35,118)
# An insurance company charges a 45-year old non-smoker an annual premium of $218 for a $100,000 term life insurance policy.
(45,218)
# An insurance company charges a 55-year old non-smoker an annual premium of $563 for a $100,000 term life insurance policy.
(55,563)
Let quadratic model be p=Aa²+Ba+C
Substitute the points into equation
For point, (35,118)[tex]118=35^2A+35B+C[/tex]
[tex]118=1225A+35B+C[/tex] -------------(1)
For point, (45,218)[tex]218=45^2A+45B+C[/tex]
[tex]218=2025A+45B+C[/tex] -------------(2)
For point, (55,563)[tex]563=55^2A+55B+C[/tex]
[tex]563=3025A+55B+C[/tex] -------------(3)
Solve system of equation and find out A, B and C using calculator.
[tex]A=\dfrac{49}{40},B=-88,C=\dfrac{13579}{8}[/tex]
Quadratic model:
[tex]p=\dfrac{49}{40}a^2-88a+\dfrac{13579}{8}[/tex]
What is the equation of the line –3x–2y=30 in slope-intercept form?
Enter your answer in the box.
The slope intercept form of the given equation of a line is y= -3/2 x -15.
The given equation of the line is -3x-2y=30.
What is the slope intercept form?The slope intercept form of a straight line is one of the most common forms used to represent the equation of a line. The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the y-intercept.
The standard form of the slope intercept form is y=mx+c.
Now,
-3x-2y=30
⇒ -2y=3x+30
⇒ y= -3/2 x -15
Therefore, the slope intercept form of the given equation of a line is y= -3/2 x -15.
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Hector wrote the following proof for his geometry homework for the given problem:
Statements Reasons
segment LN is congruent to segment NP Given
∠1 ≅ ∠2 Given
∠N ≅ ∠N Reflexive Property
ΔLNO ≅ ΔPNM Angle-Angle-Side Postulate
∠NLO ≅ ∠NPM
Which of the following completes Hector's proof?
Angle Addition Postulate
Converse of Corresponding Angles Postulate
Corresponding Parts of Congruent Triangles Are Congruent
Triangle Proportionality Theorem
Answer:
∠ NLO ≅ ∠ NPM Corresponding Parts of Congruent Triangles Are Congruent
Step-by-step explanation:
It's on my chart on the test this is 100% right
Final answer:
Hector used the Angle-Angle-Side Postulate to show congruency between two triangles. Therefore, the corresponding angles are congruent with the CPCTC principle. Thus, option 3 is correct.
Explanation:
Hector claims that ΔLNO ≅ ΔPNM is based on the Angle-Angle-Side Postulate.
Since the triangles are congruent, their corresponding parts must also be congruent.
Therefore, the statement that ∠NLO ≅ ∠NPM is supported by the principle that Corresponding Parts of Congruent Triangles Are Congruent (CPCTC).
A box of ground nutmeg weighs 1 1/3 ounce. If there are 20 teaspoons of nutmeg in the box, how much does one teaspoon of nutmeg weigh?
1/15 ounce
1/20 ounce
1/60 ounce
4/3 ounce
we know that
a) A box of ground nutmeg weighs [tex]1 1/3[/tex] ounces
b) There are [tex]20[/tex] teaspoons of nutmeg in the box
Step 1
Convert mixed number to an improper fraction
[tex]1\frac{1}{3} \ ounces= \frac{1*3+1}{3}= \frac{4}{3}\ ounces[/tex]
Step 2
By proportion
Find the weight of one teaspoon
[tex]\frac{(4/3)}{20} \frac{ounces}{teaspoons} =\frac{x}{1} \frac{ounces}{teaspoon} \\ \\x= \frac{4}{20*3}\\ \\x= \frac{4}{60}\ ounces\\\\x=\frac{1}{15}\ ounces[/tex]
therefore
the answer is the option
[tex]\frac{1}{15}\ ounces[/tex]
The graph shows the amount of gas remaining in the gas tank of mrs. lius car as she drives at a steady speed for 2 hours. How long can she drive before he car runs out of gas
To determine how long Mrs. Liu can drive before her car runs out of gas, one needs to analyze the slope of the graph that shows the rate of gasoline consumption, know the total capacity of the tank, and perform a calculation to estimate the remaining driving time assuming constant consumption.
Explanation:The question asks to determine how long Mrs. Liu can drive her car before the gas tank is empty, based on the graph showing the amount of gas left as she drives at a steady speed for 2 hours. To answer this, we need to find the rate at which the gas is being used and then use it to estimate the time until the tank reaches empty.
To find the rate of gasoline consumption, you would typically look at the slope of the graph, which shows the decrease in gas over time. If the graph shows a linear decrease, the slope will give you the rate (e.g., gallons per hour). Suppose the graph indicates that the tank started full and decreased to half over 2 hours. In that case, the consumption rate is half the tank's capacity divided by 2 hours. If you know the total capacity of the tank, you can calculate the driving time until empty.
However, since the actual graph and numerical data are not provided here, we can only guide you through the process hypothetically. With the actual graph, you would:
Find the slope of the graph (gasoline used per hour).Determine the total capacity of the car's gas tank.Divide the remaining gasoline by the consumption rate to calculate the remaining driving time.Remember, this calculation assumes a constant rate of consumption, which may not be accurate in real-life scenarios due to variations in driving conditions and car performances.
help?
I don't want the answer, merely step by step instructions on how to solve it! Thanks x
lim x->1 (x^n-1)/(x^m-1) =?
Select the inequality that models the problem.
The length of a rectangle is twice its width. If the perimeter of the rectangle is less than 50 meters, what is the greatest width of the rectangle?
2*2w + 2w < 50
2 + 2w < 50
2w*w < 50
2w < 50 ...?
If adams plain travels at a speed of 375mph in 6hours ,how far did the plane travel
Olivia must earn 475 points out of 550 to receive a b in math. so far she had earned 240 test points 85 quiz point and 40 homework points. how many points p must she score on her final exam to earn at least a b in math
Answer: Olivia needs 110 points on her final exam in order to earn at least a B in Math.
What is addition?Addition is a way of combining things and counting them together as one large group. ... Addition in math is a process of combining two or more numbers.
Here, given that,
Olivia must earn 475 points out of 550 to receive a b in math.
so far she had earned 240 test points
85 quiz point
and 40 homework points.
Solution: 240 + 85 + 40 = 365
Now, we get,
475 - 365 = 110
Hence, Answer: Olivia needs 110 points on her final exam in order to earn at least a B in Math.
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