To find the constant c that makes the given piecewise function continuous for all real numbers, the two parts of the piecewise function need to be equal at x = 2. By setting these two equal and solving for c, you will find the value that makes the function continuous.
Explanation:The question presents a piecewise function and asks for which value of the variable c does it become continuous for all real numbers. To make a function continuous at a certain point, both parts of the function must be equal at that point. In this case, the two parts meet at x = 2. We need to set the two parts equal to each other at x = 2 and then solve for c.
For the first part of the piecewise function,
[tex]f(x) = cx^2 + 2x[/tex], when we substitute x = 2, it becomes f(2) = 4c + 4.
For the second part of the piecewise function,
[tex]f(x) = x^3 - cx[/tex], substituting x = 2 again gives us f(2) = 8 - 2c.
In order for the function to be continuous, these two results must be equal. We set 4c + 4 = 8 - 2c and solve it for c. Solving this equation will provide the value of c for which the function is continuous for all x .
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A. Given the equation 2(3x − 4) = 5x + 6, solve for the variable
47 is the result when 12 and x are added. what is the value of x?
Solve for x: 1 over 4 (2x − 14) = 4. 15 15 over 2 9 11
Simplify (1.5 • 10^9) - (7.8 • 10^8) expressed in scientific notation
If AB - 27 and BC=13 then find the length of AC
what is the answer to 2h x 3u
A shop rents bikes for a $4.00 insurance charge plus $2.40 for each hour. for how many hours can a person rent a bike with $19.60?
If JK LM , which statement is true ?
The lumberyard where you work sold a customer two boards . They measure 10 1/4 feet and 8 2/4 feet what is the total of the two boards
Please help asap!! What is the rate of change from x = π to x = 3 pi over 2 ? (6 points)
Initially there were 2 liters of blue paint and 8 liters of crimson paint. a paint job uses 20% of the blue and 80% of the crimson paint. (a) what percentage of the total combined amount of paint is used during the job?
Final answer:
68% of the total combined amount of paint is used for the job, calculated by using 20% of the blue paint and 80% of the crimson paint from the initial amounts of 2 liters and 8 liters, respectively.
Explanation:
To calculate the percentage of the total combined amount of paint used during the job, we first identify the amount of blue and crimson paint used separately. From the question we know that there were initially 2 liters of blue paint and 8 liters of crimson paint.
20% of the blue paint is used, which is 0.20 × 2 liters = 0.4 liters.80% of the crimson paint is used, which is 0.80 × 8 liters = 6.4 liters.Now, we compute the total paint used and the initial total paint:
Total paint used = 0.4 liters (blue) + 6.4 liters (crimson) = 6.8 liters.Initial total paint = 2 liters (blue) + 8 liters (crimson) = 10 liters.To find the percentage of the total paint used, we divide the total paint used by the initial total paint and multiply by 100:
Percentage used = (Total paint used / Initial total paint) × 100
Percentage used = (6.8 liters / 10 liters) × 100 = 68%
Therefore, 68% of the total combined amount of paint is used for the job.
How to find the domain and range for this one
Find the perimeter of triangle XYZ with vertices X(3,7), Y(-1,-5) & Z (6,-4)
The perimeter of triangle XYZ with vertices X(3,7), Y(-1,-5) & Z (6,-4) will be [4√10 + 5√2 + √130] units.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
The perimeter of the triangle is determined by adding together all of its sides.
The vertices are given below.
X(3,7), Y(-1,-5) & Z (6,-4)
The length of XY is given as,
(XY)² = (7 + 5)² + (3 + 1)²
(XY)² = 144 + 16
XY = 4√10 units
The length of YZ is given as,
(YZ)² = (- 4 + 5)² + (6 + 1)²
(YZ)² = 1 + 49
YZ= 5√2 units
The length of XZ is given as,
(XZ)² = (7 + 4)² + (3 - 6)²
(XZ)² = 121 + 9
XZ = √130 units
The perimeter of triangle XYZ is given as,
P = 4√10 + 5√2 + √130
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50 students in 4 buses how many in each bus
The daily dose of ampicillin for the treatment of an ear infection is 115 mg/kg of body weight. what is the daily dose for a 34 lb child?
Answer: 1773.54 mg
Step-by-step explanation:
Given: The daily dose of ampicillin for the treatment of an ear infection is 115 mg/kg of body weight.
The weight of a child = 34 lb
We know that 1 pound = 0.453592 kg
Then , the weight of child in kilograms = [tex]0.453592\times34=15.422128\text{ kg}[/tex]
Now, the daily dose of ampicillin for the treatment of an ear infection for the child is given by :-
[tex]115\times15.422128=1773.54472\approx1773.54\text{ mg}[/tex]
Hence, the daily dose for a 34 lb child = 1773.54 mg
The conversion rate from Ib(pounds) to kg(kilograms)
1 Ib = 0.453592kg
Step 1
We convert the weight of the child to from lb to kg
1 Ib = 0.453592kg
34 lb = ?
Cross Multiply
34 x 0.453592kg
= 15.4221 kg
The weight of the child in kg = 15.4221 kg
Step 2
The daily dose of ampicillin for the treatment of an ear infection is 115 mg/kg of body weight.
Therefore the daily dose of ampicillin for the treatment of ear infection for the child = 15.4221 kg x 115 mg/kg
= 1,773.5415 mg
The daily dose for a 34 lb child is approximately to nearest whole number is 1,774 mg
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One cubic foot holds 7.48 gallons of water, and one gallon of water weighs 8.33 pounds. how much does 6.26.2 cubic feetfeet of water weigh in pounds? in ounces
Can you square root both sides of inequality
.help me please thanks
the map shows the route for a race. you are at a, which is 6000 feet from the first checkpoint b. the second checkpoint c is located at the midpoint between b and the end of the race d. the total race is 3 miles. how far apart are the 2 checkpoints? (hint: there are 5280 feet in a mile.) 5280 feet 6000 feet 4920 feet 9840 feet i will draw the picture!
How do you solve R= us for u
I need help ASAP!!
Maria is doing a probability experiment. She has a bag containing marbles of different colors. The probability of selecting each color of marble is given below.
Blue - 1/2
Green - 1/8
Red - 5/16
Yellow - 1/16
What is the probability that Maria randomly selects a green marble, replaces the marble, and then randomly selects a red marble?
How to find the opposite and the reciprocal of the number 500
Hello pls help it's for pre calc composition of functions
The composite function that converts temperatures from degrees Kelvin to degrees Fahrenheit is:
K to F = 9/5 * K - 241.15
The image shows a question about how to convert temperatures from degrees Celsius to degrees Fahrenheit using composite functions. The question provides two functions:
[tex]$F(x) = \frac{9}{5}x + 32$[/tex] converts from degrees Celsius to degrees Fahrenheit
[tex]$C(x) = x - 273.15$[/tex]converts from degrees Kelvin to degrees Celsius
We are asked to find the composite function [tex]$C \circ F$[/tex] that converts from degrees Kelvin to degrees Fahrenheit.
To find the composite function, we simply substitute the output of the first function, [tex]$F(x)$[/tex], into the input of the second function, [tex]$C(x)$[/tex]. This gives us:
[tex]```(C \circ F)(x) = C(F(x)) = F(x) - 273.15 = \frac{9}{5}x - 241.15```[/tex]
Therefore, the composite function that can be used to convert temperatures from degrees Kelvin to degrees Fahrenheit is:
[tex]```(C \circ F)(x) = \frac{9}{5}x - 241.15```[/tex]
A composite function is a function that is created by composing two or more other functions. In other words, it is a function that takes the output of one function as the input to another function. Composite functions are often used to solve complex problems that cannot be solved using a single function.
For example, the composite function that we found above,[tex]$(C \circ F)(x)$[/tex], can be used to convert temperatures from degrees Kelvin to degrees Fahrenheit. This is a useful function for scientists and engineers who work with temperatures in different units.
Another example of a composite function is the product rule in calculus. The product rule states that the derivative of the product of two functions [tex]$u(x)$[/tex]and [tex]$v(x)$[/tex] is equal to the sum of the product of the derivatives of [tex]$u$[/tex] and [tex]$v$[/tex] and the product of [tex]$u$[/tex] and the derivative of [tex]$v$[/tex]. This can be expressed mathematically as follows:
[tex]```\frac{d}{dx}[u(x)v(x)] = u'(x)v(x) + u(x)v'(x)```[/tex]
The product rule is a composite function because it takes the output of two functions, [tex]$u$[/tex] and [tex]$v$[/tex], and their derivatives,[tex]$u'$[/tex] and [tex]$v'$[/tex], and produces a new function, [tex]$\frac{d}{dx}[u(x)v(x)]$[/tex].
Composite functions are a powerful tool that can be used to solve a wide variety of problems in mathematics, science, and engineering.
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If the APR of a savings account is 1.9% and interest is compounded semiannually, what is the approximate APY of the account
A. 1.9166%
B. 1.9136%
C. 1.9090%
D. 1.9151%
Answer:
C. 1.9090%
Step-by-step explanation:
We have been given that the APR of a savings account is 1.9% and interest is compounded semiannually. We are asked to find the APY of the account.
To solve our given problem, we will use APY formula.
[tex]APY=(1+\frac{r}{n})^n-1[/tex], where,
r = Annual interest rate in decimal form,
n = Number of times interest is compounded per year.
Let us convert our given rate in decimal form.
[tex]1.9\%=\frac{1.9}{100}=0.019[/tex]
Upon substituting [tex]r=0.019[/tex] and [tex]n=2[/tex] in APY formula we will get,
[tex]APY=(1+\frac{0.019}{2})^2-1[/tex]
[tex]APY=(1+0.0095)^2-1[/tex]
[tex]APY=(1.0095)^2-1[/tex]
[tex]APY=1.01909025-1[/tex]
[tex]APY=0.01909025[/tex]
Since APY is in decimal form, so we will multiply APY by 100 to get as percentage.
[tex]APY=0.01909025\times 100[/tex]
[tex]APY=1.909025\%\approx 1.9090\%[/tex]
Therefore, the the approximate APY of the account 1.9090% and option C is the correct choice.
Please,please,please someone answer this!! It's for a math performance task and It's overdue by a couple days so I need to finish it soon!! Please,please,please someone help me!! Worth 50 points PLUS I'll give the person who answers FIRST and BEST the brainlest answer.
Using complete sentences, create your own scenario involving the United States' national debt with any two decades listed in the table. The scenario should include multiplication or division between the numbers in scientific notation. YearUS Nation Debt (in US dollars) 1960 $286,330,760,848.37 1970 $370,918,706,949.93 1980 $907,701,000,000.00 1990 $3,233,313,451,777.25 2000 $5,674,178,209,886.86 2010 $13,561,623,030,891.79
The scenario describes calculating the multiple of growth in the US national debt from 1970 to 1990 using scientific notation, showing that the debt was nearly 9 times larger in 1990 than in 1970
Let's create a scenario involving the United States' national debt from two different decades using multiplication in scientific notation. Imagine the government wanted to compare the debt from 1970 to that of 1990 to analyze the growth. The debt in 1970 was approximately $370.9 billion, and in 1990, about $3,233.3 billion. To find out how many times larger the debt was in 1990 compared to 1970, we'd convert these numbers into scientific notation and divide the 1990 figure by the 1970 figure.
In scientific notation, the 1970 debt is 3.709 x 1011 dollars, and the 1990 debt is 3.2333 x 1012 dollars. To perform the division, we have (3.2333 x 1012) / (3.709 x 1011) which gives us approximately 8.71. This means the national debt in 1990 was nearly 9 times larger than it was in 1970
Anna is 4ft 9in tall. Express Anna's height infeet only by using a mixed number. If necessary, simplify the fravtion part of the mixed number.
12 inches in a foot so 9 inches = 9/12 of a foot
9/12 reduces to 3/4
so 4 ft 9 inches = 4 3/4 feet
You reach into a bag of coins and withdrew two coins without replacement. What is the probability you withdrew a nickel and then a dime if the bag held ten pennies, six nickels, and five dimes?
1.30/44
2.5/14
3.1/14
Answer:
Option 3. 1/14
Step-by-step explanation:
The bag held some coins that are
pennies = 10
nickels = 6
dimes = 5
total coins = 10 + 6 + 5 = 21 coins
You drew 2 coins without replacement,
so the probability that first draw will be nickel = [tex]P_{1}[/tex] = 6/21 = 2/7
Second draw will be a dime = [tex]P_{2}[/tex] = 5/20 = 1/4
P = [tex]\frac{2}{7}[/tex] × [tex]\frac{1}{4}[/tex] = 2/28 = 1/14
Option 3. 1/14 would be the answer.
Final answer:
The probability of withdrawing a nickel and then a dime from the bag without replacement is 1/14, calculated by multiplying the independent probabilities of drawing each coin in sequence (6/21 for the nickel and 5/20 for the dime).
Explanation:
The student has asked for the probability of withdrawing first a nickel and then a dime from a bag containing ten pennies, six nickels, and five dimes, without replacement. To solve this, we calculate the probability of each event independently and then multiply these probabilities, since the events are dependent.
First, the probability of drawing a nickel: There are six nickels and a total of 21 coins, so the probability is 6/21. After drawing a nickel, there are five dimes left out of 20 coins total, thus the second probability is 5/20. Multiplying these together gives us:
(6/21) * (5/20) = 30/420 = 1/14
So, the probability of drawing a nickel and then a dime without replacement from this bag of coins is 1/14.
solve for h
ab - s - 2d - 3t = 4h
? = h
if an employee owes 250 for payroll taxes how much will the employer need to pay for payroll taxes
The employer would need to pay $19.13 in payroll taxes for this employee.
What is payroll tax?Payroll tax is a tax that employers are required to deduct from their employee's wages and pay to the government on their behalf.
It is a tax on the wages or salaries that employees earn and is used to fund various government programs, such as Social Security, Medicare, and unemployment insurance.
We have,
The amount an employer needs to pay for payroll taxes depends on several factors.
The employee's gross wages
The type of payroll taxes.
The tax rates are in effect.
Now,
The two primary types of payroll taxes that employers are responsible for are:
Social Security tax:
This tax funds the Social Security program and is calculated as a percentage of the employee's gross wages, up to a certain limit.
In 2023, the Social Security tax rate is 6.2% for both employers and employees, and the wage base limit is $147,000.
Medicare tax:
This tax funds the Medicare program and is calculated as a percentage of the employee's gross wages, with no limit.
In 2023, the Medicare tax rate is 1.45% for both employers and employees.
Assuming the employee owes $250 for Social Security and Medicare taxes combined, and the employer is responsible for paying the same percentage rate as the employee,
The employer would need to pay an additional $250 in payroll taxes.
i.e
Social Security tax.
= $250 x 6.2%
= 250 x 6.2/100
= $15.50
Medicare tax.
= $250 x 1.45%
= 250 x 1.45/100
= $3.63
Total payroll taxes owed by the employer.
= $15.50 + $3.63
= $19.13
Therefore,
The employer would need to pay $19.13 in payroll taxes for this employee.
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Which mathematical term cannot be defined for all cases in a system of geometry?
Answer:
The answers are :
1. parallel lines
2. midpoint of a line segment
Step-by-step explanation:
The mathematical terms that cannot be defined for all cases in a system of geometry are:
1. parallel lines and
2. midpoint of a line segment.
A parallel line cannot be defined as lines do not occupy any space. It is a straight one dimensional figure with no thickness and it extends infinitely in both directions.
The points also do not have any dimension like length, area, volume etc.