Answers
The functions and its domain are a representation of their dependance on one another.
Functionsfunction, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). In the given question, we have two functions and we are required to find the composite of which ever form of the functions as well as the domain of the said function.
[tex]f(x) = \frac{3}{x}, g(x) = 2x + 8;\\(f.g)(x) = \frac{3}{2x + 8}[/tex]
The domain of the function is given as
[tex]domain = (-\infty , -4) U (-4, \infty)\\[/tex]
In the second composition of the function,
[tex](g.f) = \frac{6}{x} + 8\\domain = (-\infty, 0) U (0, \infty)[/tex]
The third composition of function
[tex](f.f) = x\\domain = (-\infty, \infty)[/tex]
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Related Questions
what is the daily recommended amount of vitamin A if 15% is 150 mcg?
Answers
If x is the daily amount of Vitamin A and we know that 15% of x is 150 mcg, we can calculate x as:
[tex]\begin{gathered} 15\%\cdot x=\frac{15}{100}x=0.15x=150 \\ x=\frac{150}{0.15} \\ x=1000 \end{gathered}[/tex]Answer: the recommended daily amount of Vitamin A is 1000 mcg.
Ben has £24
He gives £16 to Rhys.
a) What fraction of the £24 does Rhys get?
Give your answer in its simplest form.
b) What fraction of the £24 does Ben have now?
Give your answer in its simplest form.
Answers
Answer:
[tex]\frac{2}{3}[/tex] and [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
(a)
fraction Rhys gets is [tex]\frac{16}{24}[/tex] = [tex]\frac{2}{3}[/tex]
(b)
Ben is left with £24 - £16 = £8
then fraction Ben has left is
[tex]\frac{8}{24}[/tex] = [tex]\frac{1}{3}[/tex]
Bridget sold a total of $135 at her yard sale. If she sold a lamp for $35.50 more than the cost of everything else, what was the cost of the lamp and everything else.
Answers
The cost of lamp and everything else will be equal to $85.25 and $49.75 respectively.
This question can be solved by converting it into the form of linear equation. A linear equation can be expressed in the form of y = ax + b where a, b are coefficients and x, and y are independent and dependent variables. We know the total sale which is equal to $135. Let us assume the cost of everything else as x. Now, the cost of lamps is $35.50 more than cost of everything else that is equal to x + 35.50. Now, the linear equation will be written as
135 = x + (x + 35.50)
135 = 2x + 35.50
=> 2x = 99.5
=> x = $49.75 which is the cost of everything else and cost of lamp = x + 35.50 = $85.25.
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A country's education department reported that in 2015, 64.8% of students enrolled in college or a trade school within 12 months of graduating high school. In 2017, a random sample of 179 individuals who graduated from high school 12 months prior was selected. From this sample, 112 students were found to be enrolled in college or a trade school. Complete parts a through c. a. Construct a 90% confidence interval to estimate the actual proportion of students enrolled in college or a trade school within 12 months of graduating from high school in 2017.
The confidence interval has a lower limit of
and an upper limit of
(Round to three decimal places as needed.)
Answers
Answer:
Step-by-step explanation:
4/5 equals blank over 100
Answers
We solve as follows:
[tex]\frac{4}{5}=\frac{x}{100}\Rightarrow x=80[/tex]So, the value of "blank" is 80.
3] If the p.d.f., of the random variable X is given byf(x)= K sqrt x &0 1)(c) P(|X| < 3)(d) E(2X - 2)(e) V(3X)
Answers
Are the triangles similar! If yes state how?are the triangles similar if yes State how
Answers
Part 1
Remember that
If two triangles are similar , then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
so
Verify the proportion
38.5/14=22/8
38.5*8=14*22
308=308 -----> is true
that means
the triangles are similarPart 3
Verify the proportion
22/9=30/12=25/10
2.44=2.5=2.5 ------> is not true
that means
the triangles are not similarSchool Supplies Pencils $0.25 each Notebooks $2.50 each Backpacks $32 each- . Hugh bought x notebooks. Write an expression for the cost of the notebooks.
Answers
Pencils: $0.25 each
Notebooks: $2.50 each
Backpacks: $32 each
The cost of the notebooks (C) must be equal to the price of each notebook (2.50) multiplied by the number of notebooks bought (x)
C = 2.50x
For what value of x will 3x + 4 = x - 6 be a true statement?
A x = -5
В. x = -5/2
C x = -1
D x = - 1/2
Answers
Answer:
A
Step-by-step explanation:
3x + 4 = x - 6 ( subtract x from both sides )
2x + 4 = - 6 ( subtract 4 from both sides )
2x = - 10 ( divide both sides by 2 )
x = - 5
Answer:x 1= x. Examples: 41=4. 5)
Step-by-step explanation:
Simplify the fractiom
7/21
4/38
Answers
2. 4/38 = 2/19
If you roll a 6-sided die 72 times, what is the best prediction possible for the number of times you will roll a one?
Answers
The prediction of outcomes of the number of 1 is 12
How to determine the number of times?The given parameters are
Device = A die
Number of rolls = 72
From the question, the die is six-sided
This means that the sample space is
S = {1, 2, 3, 4, 5, 6}
So, the probability of rolling a 1 is
P(1) = 1/6
When the die is rolled 72 times, the number of outcomes of 1 is
Outcomes = P(1) * n
Where n = 72
So, we have
Outcomes = 1/6 * 72
Evaluate
Outcomes = 12
Hence, the prediction is 12
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What is the area of ΔABC given m∠B = 95°, a = 22 feet, and c = 17 feet?use area = 1/2 ac sin B
Answers
area = 1/2 ac sin B
1/2 ( 22) ( 17) * (sin 95)
187 sin 95
186.2884085 ft^2
the domain of a function is all of the second value of ordered pairs
true or false?
Answers
Answer:
False
Step-by-step explanation:
Domain is the x-axis, range is the y-axis. In an ordered pair, the x-values go first, not second.
aIn a class of students, the following data table summarizes how many students passeda test and complete the homework due the day of the test. What is the probability thata student who passed the test did not complete the homework?Passed the test Failed the testCompleted the homework112.2Did not complete the homework3N
Answers
According to the given table, the number of students that passed the test and did not complete the homework is
[tex]3.[/tex]Also, from the table, we get that the total number of students that passed the test is
[tex]11+3=14.[/tex]Therefore, the probability that a student that passed the test did not complete the homework is:
[tex]\frac{3}{14}\text{.}[/tex]Answer:
[tex]\frac{3}{14}\text{.}[/tex]Kathy Runde, age 66 and retired, receives a $20,000 partial distribution from her 401(k) plan. The plan does not pay out an annuity. Immediately before the distribution, her account balance is $50,000, including $10,000 in nondeductible contributions. How much of the $20,000 distribution must Kathy include in gross income?
Answers
The whole twenty thousand dollars that were distributed has to be accounted for as part of the gross revenue.
This is further explained below.
What is gross income?Generally, A person's or a household's gross income is the whole amount of money earned before any deductions or taxes are taken out of that income. This includes all wages, salaries, profits, interest payments, rentals, and other types of earnings.
Because it is treated as regular income, the amount that was withdrawn is subject to taxation at the same rate as ordinary income under the federal income tax system.
If, on the other hand, Kathy makes the decision to convert her 401(k) to a Roth 401(k), then any money she takes out of the account will not be subject to taxes.
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Find the product of 21 and the difference between one whole number 1/2 and -1/2
Answers
The product of 21 and the difference between one whole number 1/2 and -1/2 is; 42
What is the product of the two numbers?We want to find the product of 21 and the difference between one whole number 1/2 and -1/2. This can be expressed as;
21 * (1¹/₂ - (-¹/₂))
Let us first solve the bracket out using the order of operations rule named PEMDAS which stands for P- Parentheses, E- Exponents, M- Multiplication, D- Division, A- Addition, and S- Subtraction to get;
1¹/₂ - (-¹/₂)
= 1¹/₂ + ¹/₂
= 2
Thus;
21 * (1¹/₂ - (-¹/₂)) = 21 * 2
= 42
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please help me with this. I have been trying to figure it out for a long time and I need to have dinner with my family very soon.
Answers
To subtract this polynomial, we would have to open the bracket
[tex]\begin{gathered} 9x^4+8x^3-6-(5x^2-8x+6) \\ 9x^4+8x^3-5x^2+8x-6-6=9x^4+8x^3-5x^2+8x-12^{} \end{gathered}[/tex]Remember, we only add and subtact directly , Algebraic characters of the same type only
and the same power only.
A hiker on the Appalachian Trail planned to increase the distance covered by 10% each day. After 7 days, the total distance traveled is 75.897 miles.Part A: How many miles did the hiker travel on the first day? Round your answer to the nearest mile and show all necessary math work. (4 points)Part B: What is the equation for Sn? Show all necessary math work. (3 points)Part C: If this pattern continues, what is the total number of miles the hiker will travel in 10 days? Round your answer to the hundredths place and show all necessary math work. (3 points)
Answers
Answer with explanation: A hiker has increased his distanced covered by 10% each day since the start, the total distance covered at the end of the 7th day is 75.897mile:
(A) The number of miles on the first day:
[tex]\begin{gathered} \text{let x be the distance covered on first day:} \\ x,1.1x,1.21x,1.331x,\ldots. \\ \text{ This is a Geomatric sequence:} \\ S_n=\frac{a(r^n-1)}{r-1} \\ a=x \\ r=\frac{1.1x}{x}=1.1 \\ r=1.1 \\ n=7 \\ S_n=\frac{x((1.1)^7-1)}{1.1-1}\Rightarrow(0) \end{gathered}[/tex]Substituting the total miles covered on the 7th day in equation(0) gives:
[tex]\begin{gathered} 75.897=\frac{x((1.1)^7-1)}{1.1-1} \\ 7.5897=0.9487171x \\ x=7.9999612107761101807904590314647 \\ x\approx7.9999mi \end{gathered}[/tex]Therefore on the first day, the hiker covered about 7.99 miles:
(B) The equation for the S:
[tex]\begin{gathered} S_n=\frac{a(r^n-1)}{r-1} \\ S_n=\frac{7.99((1.1)^n-1)}{1.1-1}\Rightarrow(1) \end{gathered}[/tex]The equation (1) gives the number of miles hiked on the nth day.
(C) miles covered on 10th day:
The number of miles covered on the 10th day is calculated using the equation(1) as follows:
[tex]\begin{gathered} S_n=\frac{7.99((1.1)^n-1)}{1.1-1}\Rightarrow n=10 \\ S_{10}=\frac{7.99((1.1)^{10}-1)}{1.1-1} \\ S_{10}=127.340mi \end{gathered}[/tex]The number of miles covered on the 10th day is 127.340miles.
About the formula used:
[tex]\begin{gathered} S_n=\frac{a-ar^n}{1-r}\Rightarrow\text{ Your formula} \\ \text{Multiply by:} \\ \frac{(-1)}{(-1)} \\ \therefore\Rightarrow \\ S_n=\frac{(-1)}{(-1)}\times\frac{(a-ar^n)}{(1-r)}=\frac{(-1)\cdot(a-ar^n)}{(-1)\cdot(1-r)}=\frac{-a+ar^n}{-1+r}=\frac{ar^n-a}{r-1} \\ S_n=\frac{ar^n-a}{r-1}=\frac{a(r^n-1)}{r-1} \\ S_n=\frac{a(r^n-1)}{r-1}\Rightarrow\text{ My formula} \end{gathered}[/tex]In conclusion, the formula used is the same as the one that was required to be used.
The average daily profit of an electronics store is $27,235. The company estimates that 15% is lost each day to returns, with a margin of error
of 13%. What is the maximum the company can expect for returned items?
O $3268.20
$3668.30
O$4425.60
O $4902.30
Answers
Using proportions, it is found that the maximum the company can expect for returned items is of:
$4,616.
What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using basic arithmetic operations such as multiplication or division along with the unit rates in the context of this problem.
The lost amount to returns each day is of 15% of 27235, and this amount is calculated as follows:
0.15 x 27235 = $4,085.25
(the decimal equivalent of the percentage is multiplied by the original amount to find the equivalent amount).
The margin of error is of 13%, hence this amount can still be increased by 113, that is, multiplied by 1.13, hence:
4085.25 x 1.13 = $4,616.
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Answer:
The answer is D $4902.30
Step-by-step explanation:
Write the equation of the line with a slope of -3 that passes through (-5,20)
Answers
SUBSTITUTE THE KNOWNS IN THE GIVEN GENERAL EQUATION BELOW AND SIMPLIFY TO GET c
[tex]y = mx + c \\ 20 = - 3( - 5) + c \\ 20 = 15 + c \\ c = 20 - 15 \\ c = 5[/tex]
Meaning
[tex]y = - 3x + 5[/tex]
IS THE EQUATION
Nicholas is typing a book report at an average of 30 words per minute. Which equation could Nicholas use to find tea the amount the amount of time in minutes he will spend typing his report has W words?
Answers
The equation could Nicholas use to find tea the amount the amount of time in minutes he will spend typing his report has W words is w = 30t .
What is speed?In contrast to velocity, which describes the speed and direction of an object's movement, speed is the rate of movement along a path. Alternatively, velocity is a vector while speed is a scalar quantity. Velocity and speed are denoted by the letters v and v, respectively (boldface). The symbol has a bar over it for average values. How swiftly something is going, being done, or something that is moving quickly is measured in terms of speed. Driving an automobile 45 miles per hour is an illustration of speed. Someone cleaning a room in 10 minutes would be an example of quickness. the definition of speed. a direction or speed at which an object's location changes.
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Which number comes first
5
1/3 -1. √3. - 12/21
6
3.4
Answers
-3.4 is the number which will come first.
What is simplifying?To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue. the act of simplifying something such that it is simpler to carry out or understand, or the thing that is the product of this simplifying process: The group offers suggestions for streamlining business processes. This grossly oversimplifies what actually transpired.
Given Data
5, 1/3 -1. √3. - 12/21,6,3.4
Simplifying,
5, [tex]\frac{1}{3}[/tex] - 1, √3. -[tex]\frac{12}{21}[/tex], 6, -3.4
5, -0.6 , [tex]\sqrt{3}[/tex] , -0.5 ,6,-3.4
-3.4 is the number which will come first.
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Elinor wanted to order an 18 inch hoagie, which cost $7.99. The sandwich shop is out of 18 inch buns. They only have 12 inch buns.
Answers
The price of 12 inch bun purchased by Elinor is $5.32.
What is defined as the method of unitary?The unitary method determines the value of a unit and afterwards the value of such a necessary number of units. The value of a unit amount is determined first in the unitary method before calculating the value of many other units. It comes in two varieties.Variation in DirectVariation in the inverseFor the given question;
Elinor wanted to have a bun.
The cost of 18 inch hoagie bun is $7.99.
As there is only 12 inch bun present, the price of 12 inch bun is calculated by unitary method.
The price can be written as;
18 inch -------> $7.99
For 1 inch bun, divide both side by 18.
18/18 inch -------> $7.99/18
1 inch -------> $7.99/18
For 12 inch, multiply each side by 12.
12 inch -------> $7.99×12/18
12 inch -------> $5.32
Thus, the price of 12 inch bun is $5.32.
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If you could please help me with this it makes no sence to me.
Answers
Answer:
A = 7986 m²
Step-by-step explanation:
the field is in the form of a trapezium.
the area (A) of a trapezium is calculated as
A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )
where h is the perpendicular distance between the bases b₁ and b₂
here h = 66 , b₁ = 102, b₂ = 140 , then
A = [tex]\frac{1}{2}[/tex] × 66 × (102 + 140) = 33 × 242 = 7986 m²
Answer:
7986 m²
Step-by-step explanation:
The field geometric shape is a trapezoid whose bases are 102 m and 140 m and height of 66m
The equation for the area of a trapezoid is given by
[tex]A = \dfrac{a + b}{2} h\\\\[/tex]
where a and b are the two sides and h is the height
Here a = 102, b = 140 and h = 66
Substitute these values directly into the equation for area
[tex]A = \dfrac{102 + 140}{2} \times 66\\\\A = (102 + 140) \times \dfrac{66}{2}\\\\\\102 + 140 = 242\\\\\dfrac{66}{2} = 33\\\\\\A = 242\ \times 33 = 7986\; m^2[/tex]
Tristan is building steps up to a deck that is 1 yards above the ground. The steps must all be the same height. If he wants to make 8 steps, how high should he make each step?
Answers
Tristan should make 8 pieces of length 0.125 yards each to make a steps to the deck 1 yards above.
What is division?Division is breaking a number up into an equal number of parts. Mathematically, we can write "[a] divided by [b]" as a ÷ b. The division algorithm is given by -
D = dq + r
[D] - Dividend
[d] - Divisor
[q] - Quotient
[r] - remainder
Given is Tristan who is building steps up to a deck that is 1 yards above the ground. The steps must all be the same height an he wants to make 8 steps.
Total number of steps to be made = [n] = 8
Height of deck = [h] = 1 yard.
Now, we have to divide 1 yard into 8 equal parts. Therefore, assume
that -
A = 1 ÷ 8
A = 1/8
0.125
We get the length of each step to be 0.125 yards.
Therefore, Tristan should make 8 pieces of length 0.125 yards each to make steps to the deck 1 yards above.
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Find an equation in point-slope form for the line having the slope m=-3 and containing the point (4,2).
Answers
The equation of a line in point-slope form is given by
[tex]y-y_1=m(x-x_1)[/tex]Where
[tex]\begin{gathered} m=-3 \\ y_1=2 \\ x_1=4 \end{gathered}[/tex]Thus, if we substitute the above values into the equation:
[tex]y-2=-3(x-4)[/tex]Need help with a statistics question please!
Answers
Please help me work this out and explain it.
Answers
Answer:
a) DE = 15 cm
b) AB = 6 cm
Step-by-step explanation:
Explanation #a)
- Relating the triangle ABC with triangle DCE, a scale factor fomula is used;
[tex]{ \rm{ \frac{ \bar{DE}}{ \bar{BC} }} = \frac{ \bar{CE}}{ \bar{AC} } } \\ \\ { \rm{ \frac{\bar{DE}}{5} = \frac{24}{8} }} \\ \\ { \rm{\bar{DE}} = \frac{24 \times 5}{8} } \\ \\ { \rm{\bar{DE}} = 15 \: cm}[/tex]
Explanation #b)
[tex]{ \rm{ \frac{ \bar{CE}}{ \bar{AC}} } = \frac{ \bar{CD}}{ \bar{AB} }} \\ \\ { \rm{ \frac{24}{8} = \frac{18}{\bar{AB}} }} \\ \\ { \rm{\bar{AB} = \frac{18 \times 8}{24} }} \\ \\ { \rm{\bar{AB} = 6 \: cm}}[/tex]
- Therefore, the scale factor is 2, triangle CDE = 2ABC
[tex]{ \boxed{ \red{ \delta}}}{ \underline{ \red{ \mathfrak{ \: \: creed}}}}[/tex]
Ingrid hit a golf ball. the height of the golf ball (in meters above the ground) t seconds after being hit is modeled by h(t)=-5t²+30tIngrid wants to know when the ball reached its highest point 1) rewrite the function in a different form (factored or vertex) where the awnser appears as a number in the equationh(t)=___2) How many seconds after being hit does the ball reach its highest point?____ seconds
Answers
Write the equation in vertex form to find the maximum height, as well as the time when the maximum height is reached.
The vertex form of a quadratic equation is:
[tex]y=a(x-h)+k[/tex]Where (h,k) is the vertex of the parabola, k is the maximum or minimum value and h is the value of x where that maximum or minimum is reached.
To write h in vertex form, complete the square:
[tex]\begin{gathered} h(t)=-5t^2+30t \\ =-5(t^2-6t) \\ =-5(t^2-6t+9-9) \\ =-5((t-3)^2-9) \\ =-5(t-3)^2-5(-9) \\ =-5(t-3)^2+45 \end{gathered}[/tex]We can see that in this case, the vertex is (3,45).
Therefore:
1)
[tex]h(t)=-5(t-3)^2+45[/tex]2)
The ball reaches the maximum height 3 seconds after being hit.
For each of the variables described below, indicate whether it is a quantitative or a categorical (qualitative) variable. Also, indicate the level of measurement for the variable: nominal, ordinal, interval, or ratio. Make sure your responses are the most specific possible.
Answers
Part A.
From the given table, we can see that the variable occupation is a Categorical variable becasue the occupation can divide a set of people into groups. Then, the level of measurement is Nominal because the occupation describes the objects by labels, with no quantitative value.
Part B.
Temperature is a Quantitave variable because we can measure the temperature of an object. Regarding the level of measurement, the temperature is an Interval variable because zero temperature is not the lowest possible temperature.
Part C.
The price is a Quantitative variable because the price is a numerical value with a meaningful order. Regarding the level of measurement, the price is a Ratio variable because it has a true zero, meaning that we can take ratios of values.