The value of g(x) is √2x.
What is a composite function?
A function whose values are obtained from two given functions by first applying one to an independent variable and then using the result to apply the second, and whose domain is made up of those independent variable values for which the first function's result falls within the second function's domain.
Here, we have
g(f(x)) =x√6.
f(x) = 3x²
By applying a composite function
g(f(x)) =√6x
g(3x²) = x√6
g(x) must be √(2x)
because if we substitute x = 3x² in this we get
= (√2(3x^2))
= √2√3√(x²)
= √6 x
Hence, the value of g(x) is √2x.
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Using the calculator below, substitute the values to calculate the interest amount on a the loan using the compound interest formula. Principal: $4,000 time: 10 years rate: 7% number of compounding periods: 4 What is the amount of the compound interest? (interest only)
a. 2,800
b. 4,757
c. 4,006
d. 59,897
Solve the inequality and enter your solution as an inequality comparing the
variable to the solution.
-18+x< 16
Answer here
Solution of the given inequality -18 + x < 16 is equal to x < 34.
As given in the question,
Given inequality is equal to :
-18 + x < 16
Get the value of the variable x by adding 18 both the side of the inequality we get,
-18 + x + 18 < 16 + 18
Collect all like terms together we get,
⇒ x + (-18 + 18 ) < 34
⇒ x + 0 < 34
Solution of the inequality -18 + x < 16 is given by
⇒ x < 34
For the given inequality -18 + x < 16 the value of variable x is less than 34.
Therefore, solution of the given inequality -18 + x < 16 is x < 34.
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What are the corresponding angle pairs in the picture below?
The corresponding angles form the given figure are ∠1 and ∠5, ∠2 and ∠6, ∠4 and ∠8 and ∠3 and ∠7. Therefore, option D is the correct answer.
From the given figure, we need to identify the corresponding angles.
What are corresponding angles?The corresponding angles definition tells us that when two parallel lines are intersected by a third one, the angles that occupy the same relative position at each intersection are known to be corresponding angles to each other.
From the figure, ∠1 and ∠5, ∠2 and ∠6, ∠4 and ∠8 and ∠3 and ∠7 are the corresponding angles.
The corresponding angles form the given figure are ∠1 and ∠5, ∠2 and ∠6, ∠4 and ∠8 and ∠3 and ∠7. Therefore, option D is the correct answer.
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This question number 7 and I need help
The product of two numbers exists done by multiplying a number with the other. The product of a number x and 7 exists 7x.
What is meant by product?The result of multiplying two or more numbers together is known as a product in mathematics. A number that is obtained by multiplying two or more other numbers together is referred to in mathematics as a product.
The outcome of one or more multiplications is referred to as a "product." For instance, the mathematical statement "times equals" would be written with the multiplier, the multiplicand, and their product as the variables.
Let the variable be x
x be a number
So, the product of x and 7 exists calculated as:
Product = 7 × x
Product = 7x
Therefore, the product of a number (x) and 7 exists 7x.
The complete question is:
The product of a number and 7
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Factor 18p-3618p−3618, p, minus, 36 to identify the equivalent expressions.
Choose 2 answers:
Choose 2 answers:
(Choice A)
A
3(9p-12)3(9p−12)3, left parenthesis, 9, p, minus, 12, right parenthesis
(Choice B)
B
9(2p-4p)9(2p−4p)9, left parenthesis, 2, p, minus, 4, p, right parenthesis
(Choice C)
C
2(9p-18)2(9p−18)2, left parenthesis, 9, p, minus, 18, right parenthesis
(Choice D)
D
18(p-2)18(p−2)
After simplification, the equivalent expression is 18(p-2). So the option D is correct.
In the given question,
We have to find factor 18p-36 equivalent expressions.
The given option is
A. 3(9p-12)
B. 9(2p-4p)
C. 2(9p-18)
D. 18(p-2)
The given expression is 18p-36.
We simplify the given expression to find their equivalent expression.
To simplify the expression we take out the common term from both terms.
We can see that 18 is a common multiply of both number 18 and 36. SO we take out 18 from both terms.
Taking common 18
18p-36 = 18(p-2)
Hence, the equivalent expression is 18(p-2). SO the option D is correct.
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What is the quotient of 30 and 0.08
Answer:
30 divided by 0.08 will get you 375
Step-by-step explanation:
Calculate the number of different three-course meals a patron could choose from at the Butcher Shop Steakhouse during Restaurant Week. What conditions had to be met for you to calculate the number of different outcomes for this experiment?
The probability of getting watermelon is 3/58.
The given values are
A pineapple chew was selected 53 Times
A lemon chew was selected 2 times
A watermelon chew was selected 3 times
The probability that you Bella remove from the bag is pineapple chew.
probability is which we can't predict actual it is usually about the prediction
As we know
probability - expected outcome/total outcome
The question Bela perform experiment 58 times then the total outcome will be 58 if you pineapple was selected 53 times the probability of the chew Bella pick of pineapple is 53/58
The probability of Bella pick chew of lemon -2/58
The probability of Bella pick watermelon is - 3/58
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Simplify 2.54 + 1.5 × 4
Which of the following is the correct factorization 64x^3+8?
The correct factorization of the expression, [tex]64x^{3} +8[/tex], is 4[tex](2x-1)^{2}[/tex] (8x+2).
According to the question,
We have the following information:
[tex]64x^{3} +8[/tex]
The factors of this expression can be found using identity because 64[tex]x^{3}[/tex] is the whole cube of 4x and 8 is the cube of 2.
So, we have the following expression:
[tex](4x)^{3} + 2^{3}[/tex]
Now, we can use the following identity to factor the given expression:
[tex]a^{3} +b^{3} = (a+b) (a^{2} -ab+b^{2} )[/tex]
We have a = 8x and b = 2:
(8x+2) {[tex](4x)^{2}[/tex]-16x+[tex]2^{2}[/tex]}
(8x+2) (16[tex]x^{2}[/tex]-16x+4)
Taking 4 as the common factor from the second bracket:
4(8x+2) (4[tex]x^{2}[/tex]-4x+1)
Now, finding the factors of second bracket:
4(8x+2) ([tex]4x^{2}[/tex]-2x-2x+1)
4(8x+2) {2x(2x-1)-1(2x-1)}
4(8x+2) (2x-1) (2x-1)
4[tex](2x-1)^{2}[/tex] (8x+2)
Hence, the correct factorization of the expression, [tex]64x^{3} +8[/tex], is 4[tex](2x-1)^{2}[/tex] (8x+2).
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Q4. Write (5-√5)² in the form a + b√5, where a and b are
integers.
(5-√5)² in the form a + b√5 can be written as 30 - 10√5 where, the integers a and b are 30 and -10 respectively.
What is integer?
Positive, negative, and zero are all examples of integers. The Latin word "integer" means to "whole" or "intact." Therefore, fractions and decimals are not included in integers. In this essay, we will learn more about integers, their definition, and their characteristics.
We know that,
[tex](a-b)^2= a^2 + b^2 - 2ab[/tex]
Using this mathematical identity, putting the values from question,
(5-√5)² = 5² + √5² - 2(5)(√5)
(5-√5)² = 25 + 5 - 10√5
(5-√5)² = 30 - 10√5
This is in the form a + b√5 where, the integers a and b are 30 and -10 respectively.
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hole me out on this thanks
Answer: [tex]5^{2} + 4[/tex]
Step-by-step explanation:
[tex]2 + 3^3[/tex] =?
2 + 27 = 29
10 * 2 - 9 = 20 - 9 = 11
[tex]5^2 + 4[/tex] = 25 + 4 = 29
[tex]5^3\\[/tex] = 5 * 5*5 = 125
3+ 4 * 3 = 3 + 12 = 15
Visit each of the three credit reporting agencies and find an example of a credit report. For each, describe a different portion of the credit report
and how it is evaluated for credit worthiness.
Answer:
Doesn't make a lot of sense. Can you be more specific.
Step-by-step explanation:
The Creditworthiness is how a lender determines that you will default on your debt obligations, or how worthy you are to receive new credit
What are credit reporting agencies?Credit reporting companies, also known as credit bureaus or consumer reporting agencies, are companies that compile and sell credit reports.
Given are three credit reporting agencies.
Creditworthiness is how a lender determines that you will default on your debt obligations, or how worthy you are to receive new credit. Your creditworthiness is what creditors look at before they approve any new credit to you. The 3 C's of credit worthiness are Character, Capacity and Capital. Creditworthiness is determined by several factors including your repayment history and credit score.
Therefore, the Creditworthiness is how a lender determines that you will default on your debt obligations, or how worthy you are to receive new credit.
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2(x+5)=20 what does x===???????????????????/
Answer:
x = 5
Step-by-step explanation:
2(x+5) =20 Distribute the 2
2(x) + 2(5) = 20
2x + 10 = 20 Subtract 10 from both sides of the equation
2x = 10 Divide both sides by 2
x = 5
Answer:
5
Step-by-step explanation:
2(x + 5) = 20 Divide both sides by 2
x + 5 = 10
x = 10 - 5
x = 5
Let f(x) = 4 + 2x and g(x) = 1/2x + 2 . Find f(g(x)) . Simplify the expression.
f(g(x)) = ___
Answer: x + 8
Step-by-step explanation:
[tex]f(g(x))=f(\frac{1}{2}x+2) = 4+2(\frac{1}{2}x+2) = 4+x+4 =x +8[/tex]
There are 121 boys and 116 girls signed up for a trip to an amusement park. The leader first makes groups of 9 students each and then assigns any remaining students to make some of the groups have 10 students. Part A How many groups of 10 students will there be? Explain. Part B How many groups of 9 students will there be? Explain.
The remainder is the amount "leftover" after performing some computation.
Hence,
(A) There are [tex]4[/tex] groups out of [tex]10[/tex] students.
(B) There are [tex]33[/tex] groups of [tex]9[/tex] students.
What is a remainder?
The remainder is the amount "leftover" after performing some computation. In arithmetic, the remainder is the integer "leftover" after dividing one integer by another to produce an integer quotient.
Here given that,
The strength of boys is [tex]121[/tex]
The strength of girls is [tex]116[/tex]
So, the total number of students are
[tex]121+116=337[/tex]
The leader first makes groups of [tex]9[/tex] students and then assigns any remaining students to make some of the groups have [tex]10[/tex] students.
So we divide by [tex]9[/tex] to find out the remainder and the total number of groups are:-
[tex]\frac{337}{9}=37[/tex]
and the remainder value is [tex]4[/tex].
Therefore, there are [tex]37[/tex] groups in the total out of which [tex]4[/tex] are out of [tex]10[/tex]students.
So,
[tex]\frac{37}{4}=33[/tex] groups are of [tex]9[/tex] students.
Hence,
(A) There are [tex]4[/tex] groups out of [tex]10[/tex] students.
(B) There are [tex]33[/tex] groups of [tex]9[/tex] students.
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How is Addy 4+ -4 similar to adding 4+4 how is it different use the words and models to explain
4- (+) (-4) is similar to 4+4 by the rule of addition in integers that is if Negative + Negative then Add the number and put the sign of greater number.
What is integer?Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the corresponding positive numbers are the negative numbers. An integer, pronounced "IN-tuh-jer," is a whole number that can be positive, negative, or zero and is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043. 1.43, 1 3/4, 3.14, and other numbers that are not integers are some examples. Three categories of integers exist: Zero (0) (0) Good integers (Natural numbers) Integer Negatives (Additive inverse of Natural Numbers).
The rules of addition in integers says,
- + - = +
by this,
4-(-4)=8
by concept of addition,
4+4=8
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3
8
13
24
53
123
213
Answer:
321 is the next number that comes in the calculator.
Jan works from 30 to 40 hours per week during the summer. She earns $12.00 per hour. Her friend Rachel also has a job. Rachel's pay for t hours is given by the function r(t) = 11t, where 20 ≤ t ≤ 30. Find the domain and range of each function. Compare their hourly wages and the amount they earn per week.
j(t) domain:
≤ t ≤
j(t) range:
≤ j(t) ≤
r(t) domain:
≤ t ≤
r(t) range:
≤ r(t) ≤
select: Jan or Rachel
earns more per hour than
select: Jan or Rachel
. Jan earns from $ (blank)
to (blank) $
per week and Rachel earns from (Blank) $
to (Blank) $
per week.
Jan earns more than Rachel. The range of what Jan earns is 360 dollars to 480 dollars per week. The range of what Rachel earns is 220 dollars to 330 dollars per week.
How to solve for the Range and the domain of the functionsJan's pay function is given as /(t) = 12 dollars this is the same as 12 dollars in one hour
the time that she has to work is given a 30 hours to 40 hours.
Hence the domain would be written as
domain : 30 ≤ t ≤ 40
we have to make use of the values of t
f(t) = 12 * 30 = 360
f(t) = 12 * 40 = 480
The range of Jan is going to be
range : 360 ≤ t ≤ 480
b. For Rachel, t is going to vary between 20 ≤ t ≤ 30
domain : 20 ≤ t ≤ 30
r*t = 11t
= 11 x 20 = 220
= 11 x 30 = 330
The range is given as
range: 220 ≤ t ≤ 330
Jan earns more per hour than Rachel
The amount earned is, Jan earns from 360 dollars to 480 dollars per week.
Rachel earns from 220 dollars to 330 dollars per week.
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A new student, who has had very little experience solving equations algebraically, has just joined your study group. Show and explain all of the steps necessary to solve the equation 2(x + 1) = 6(x – 1) for x. Be sure to include a step for checking the solution.
The solution of the equation 2(x + 1) = 6(x – 1), is the value of x = 2.
How to Solve an Equation?To solve an equation means to find what the value of the variable of the equation would be that would make the equation true if the value of the variable is plugged into the equation.
The necessary steps taken to find the value of x in the equation, 2(x + 1) = 6(x – 1) are explained below:
2(x + 1) = 6(x – 1) [given]
Apply the distributive property
2x + 2 = 6x - 6
Combine like terms
2x - 6x = -2 - 6
-4x = -8
Divide both sides by -4
-4x/-4 = -8/-4
x = 2
The value of x is 2. To check the solution, plug in the value of x back into the equation:
2(2 + 1) = 6(2 – 1)
2(3) = 6(1)
6 = 6 [true]
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Colton made a scale drawing of a city park. In real life, the soccer field is 90 meters long.
It is 18 millimeters long in the drawing. What scale did Colton use?
By using unitary method it is obtained that -
Scale used my Colton = 1 : 500
What is unitary method?
Unitary method is the process in which the value of single unit can be calculated from the value of multiple unit and the value of multiple unit can be calculated from the value of single unit. Sometimes Value of single unit can be less than the value of multiple unit. For example - The relation between the cost of a commodity and the quantity of the commodity
Sometimes Value of single unit can be more than the value of multiple unit. For example - The relation between the number of men and the number of days taken by those men to do a certain job.
Here unitary method is used
18 mm long field in the drawing is equivalent to 9000 mm long field in real
1 mm long field in the drawing is equivalent to [tex]\frac{9000}{18}[/tex] mm long field in real
1 mm long field in the drawing is equivalent to 500 mm long field in real
Scale used by Colton 1 : 500
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Find sin D, sin E, cos D, and cos E. Write each answer as a fraction in simplest form.
line ED =45
line DF = 27
line EF = 36
sin D =
sin E =
cos D =
cos E =
The value of each term is
sin D = 4/5sin E = 3/5cos D = 3/5cos E = 4/5The length of the line ED = 45 units
The length of the line DF = 27 units
The length of the line EF = 36 units
Here we have to use the trigonometric function
sin θ = Opposite side / Hypotenuse
cos θ = Adjacent side / Hypotenuse
Substitute the value in the equation
sin D = Opposite side / Hypotenuse
= 36/45
= 4/5
sin E = Opposite side / Hypotenuse
= 27/45
= 3/5
cos D = Adjacent side / Hypotenuse
= 27/45
= 3/5
cos E = Adjacent side / Hypotenuse
= 36/45
= 4/5
Hence, the value of each term is
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Members of the student government are planning a movie night on campus. They have asked a random sample of students which of four movies the student would prefer. Here are the results Movie A- 31 students, Movie B- 27 students, Movie C- 34 students, Movie D- 28 students. There are 900 students total on campus. Based on the above information, how many students on campus would we expect to prefer Movie C? Round your answer to the nearest whole number. Do not round any intermediate calculations
There are 255 students who prefer Movie C.
In the given case, the total number of students in the campus = 900
Number of students in the random sample :
= 31 + 27 + 34 + 28
= 120
Number of students who prefer to watch movie C in the chosen sample:
= 34
To get number of students who would prefer to watch the movies C in the total population of 900, we can extrapolate the data from the chosen sample to the entire population.
Thus, number of students expected to prefer movie C in the campus =
34/120 × 900
= 255
Hence the expected number of students are 255.
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( q2 − r2s) ( q4 + q2r2s + r4s2)
what percent is 25 of 100
if we take 25 to be the 100%, what is 100 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 25 & 100\\ 100& x \end{array} \implies \cfrac{25}{100}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{1}{4}=\cfrac{100}{x}\implies x=400[/tex]
Answer:
25
Step-by-step explanation:
25/100=.25x100=25
6 x (2/3 divided by 2) + 0.5
The given expression has a value of 2.5.
The BODMAS rule is named after the letters in the acronym: B - Brackets, O - Order of powers or roots, D - Division, M - Multiplication. A stands for addition, and S stands for subtraction. According to the BODMAS rule, mathematical statements having several operations must be solved from left to right in the BODMAS order.
Given expression 6 x (2/3 divided by 2) + 0.5
To solve this expression, we must employ the BODMAS rule.
First 2/3 divided by 2
(2/3)/2
= 1/3
Now multiply 1/3 with 6
= 1/3 x 6
= 2
Now add both 2 and 0.5
= 2 + 0.5
= 2.5
Therefore the value of the given expression is 2.5
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Find the area of the following figure:
(Use π=3.14 when finding your final answer. Do not round and Do not enter units!)
Area = _______ mm²
Answer:
521 mm2
Step-by-step explanation:
Formulas:
area of circle= 3.14 x radius x radius
area of semicircle = 0.5 x 3.14 x radius x radius
diameter of circle= 20mm
radius=0.5x20mm=10mm
area of trapezium= 0.5 x (base+base) x height
Working:
area of semicircle= 0.5 x 3.14 x 10mm x 10mm = 157mm2
area of trapezium = 0.5 x (20mm+32mm) x 14mm = 364mm2
total area of figure= 157mm2 + 364mm2 =521mm2
For the equation (x) = –3x2 + 2x – 1, explain if the graph will be pointing upward or downward. **20 POINTS**
Answer:
Step-by-step explanation:
the answer is "downward". If you say "why", it is because of the degree coefficient.
in the equation, the latest degree is 2 (which is quadratic equation) so from the degree its coefficient is -3. If it is negative, it should be downward like -3. But if it is positive it should be upward like 3, 1, 44.
Identify the values of the variables. Give your answers in simplest radical form. Help!
Considering the right angle triangle given the values of the variables are
n = 2√3k = 4√3How to determine the values of the variablesInformation from the question
right angle triangle
The values of the variables is worked using SOH CAH TOA
The right angle triangle of sides as described below
hypotenuse = k
opposite = n
adjacent = 6
The variable n is solved using tan, TOA, the angle is 30
tan 30 = Opposite / Adjacent
tan 30 = n / 6
tan 30 * 6 = n
n = 2√3
The variable k is solved using cos, CAH, the angle is 30
cos 30 = Adjacent / Hypotenuse
cos 30 = 6 / k
k = 6 / cos 30
k = 4√3
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A margin of error tells us:
The margin of error tells you how many percentage points your results differ from the true population value.
What is margin of error?The margin of error is a close guess at a given level of probability about the confidence interval. It is denoted as a tiny percentage that is allowed for in the event of an error.
The amount of uncertainty associated with a survey result is referred to as the margin of error. It indicates how confident you can be in the outcome's accuracy. A smaller margin of error indicates that your survey is more precise. A confidence level is the probability that a survey will yield the same results if repeated.
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11/7 Thursday Math Math Hw. Fractions
Answer:
96, $ 144
Step-by-step explanation: