Answers
Answer: 15. f(1)=3
16. g(3)=1
Step-by-step explanation:
15. (fog)(1)=
f(g(1))=
f(1)=3
16. (gof)(5)=
g(f(5))=
g(3)=1
Related Questions
For a ride on a rental scooter, Jose paid a $6 fee to start the scooter plus 8 cents per minute of the ride. The total bill for Jose's ride was $16.48 . For how many minutes did Jose ride the scooter?
Answers
Answer:
40
Step-by-step explanation:
Answer:
6+8x=
16.8
x=
Step-by-step explanation:
If an arrow is shot upward on the moon with a velocity of 58 m/s, its height in meters after t seconds is given by y=58t−.83t2.
(a) Find the average velocity over the given time intervals:
(1) [1,1.5]
(2) [1,1.1]
(3) [1,1.01]
(4) [1,1.001]
(b) Find the instantaneous velocity after one second (to the nearest hundredth).
(1) m/s
(2) m/s
(3) m/s
(4) m/s
(b) m/s
Answers
The 58 m/s initial velocity of the arrow with height, y = 58•t - 0.83•t², gives;
(1) 55.925 m/s
(2) 56.257 m/s
(3) 56.3317 m/s
(4) 56.33917 m/s
(b) 56.34 m/s
How can the average and instantaneous velocity be calculated?Initial velocity of the arrow = 58 m/s
Height of the arrow is; y = 58•t - 0.83•t²
The above kinematic equation can be analyzed as follows;
(1) The height at t = 1 is found as follows;
y = 58 × 1 - 0.83 × 1² = 57.17
Height at t = 1.5 s. is y = 58×1.5 - 0.83×1.5² = 85.1325
Average velocity = ∆y/∆tWhich gives;
Average velocity = (85.1325-57.17)/(1.5-1) = 55.925
The average velocity in the interval [1, 1.5] is therefore;
55.925 m/s(2) [1, 1.1]
Height at t = 1.1 s. is y = 58×1.1 - 0.83×1.1² = 62.7957
Which gives;
Average velocity = (62.7957-57.17)/(1.1-1) = 56.257
The average velocity is 56.257 m/s(3) [1, 1.01]
Height at t = 1.01 s. is y = 58×1.01 - 0.83×1.01² = 57.733317
Which gives;
Average velocity = (57.733317-57.17)/(1.01-1) = 56.3317
The average velocity is 56.33 m/s
(4) [1, 1.001]
Height at t = 1.01 s. is y = 58×1.001 - 0.83×1.001² = 57.22633917
Which gives;
Average velocity = (57.22633917-57.17)/(1.001-1) = 56.33917
The average velocity is 56.33917 m/s(b) The equation for the instantaneous velocity is found as follows;
v = dy/dt = 58 - 2×0.83•t
After 1 second, we have;
t = 1
v = 58 - 2×0.83 × 1 = 56.34
The instantaneous velocity at t = 1 seconds is 56.34 m/s
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Find the inverse of the linear function
Answers
Answer:
D [tex] \frac{1}{3} x - \frac{2}{3} [/tex]
Step-by-step explanation:
[tex] f(x) = 3x + 2[/tex]
[tex] {f}^{ - 1} (x) = \frac{x}{3} - \frac{2}{3} ⟹ \frac{1}{3} x - \frac{2}{3} [/tex]
A toilet manufacturer has decided to come out with a new and improved toilet. The fixed cost for the production of this new toilet line is $16,600 and the variable costs are $67 per toilet. The company expects to sell the toilets for $157. Formulate a function P(x) for the total profit from the production and sale of x toilets.
Answers
The function P(x) for the total profit from the production and sale of x toilets is P(x) = 90x - 16600
How to formulate a function P(x) for the total profit from the production and sale of x toilets?The given parameters are
Fixed cost = 16600
Variable cost = 67 per toilet
Cost of toilet = 157 per toilet
Let the number of toilets be x
So, the cost function is
C(x) = Fixed cost + Variable cost * Number of toilets
This gives
C(x) = 16600 + 67x
Also, we have the revenue function to be
R(x) = Cost of toilet * Number of toilets
This gives
R(x) = 157x
The function P(x) for the total profit from the production and sale of x toilets is
P(x) = R(x) - C(x)
So, we have
P(x) = 157x - 16600 - 67x
Evaluate
P(x) = 90x - 16600
Hence, the function P(x) for the total profit from the production and sale of x toilets is P(x) = 90x - 16600
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True or False : If a collection has two sets of values that appear the same amount of time and more than any other number in the set , it is considered bimodal .
Answers
Answer:
Step-by-step explanation
it is true
Solve
4x + 8y = 16 for X.
Solve for x
Answers
Answer:
x = 4 - 2y
Step-by-step explanation:
4x + 8y = 16
or, x + 2y = 4
or, x = 4 - 2y
Answer:4-2y
Step-by-step explanation:
Decide if each statement below is
true or false.
45 tens is equal to 450.
12.3 is equal to 123 ones.
80 tens is greater than 6 hundreds.
43,200 is less than 50 thousands.
60 hundreds = 6,000
Answers
(a) 45 tens is equal to 450. :- True
(b) 12.3 is equal to 123 ones. :- True
(c) 80 tens is greater than 6 hundreds. :- True
(d) 43,200 is less than 50 thousands. :- True
(e) 60 hundreds = 6,000 :- True
Consider the first statement,
45 tens are equal to 450
So, 45 tens mean 45 times 10 is written as:
45 × 10 = 450
Hence, it's true.
Consider the second statement,
12.3 is equal to 123 ones.
Now, 123 ones is equal to 123 times 1.
123 × 1 = 123
Hence, the statement is true.
Consider the third statement,
80 tens is greater than 6 hundreds.
Now 80 tens = 80 × 10 = 800
Now, 6 hundreds = 6 × 100 = 600
Now, 800 > 600
Hence, the statement is true.
Consider the fourth statement.
43,200 is less than 50 thousands.
Now, 50 thousands = 50 × 1000 = 50,000
We know,
50,000 > 43,200
Therefore, the statement is true.
Consider the fifth statement,
60 hundreds = 6000
Now, 60 hundreds = 60 × 100 = 6000
Therefore, the statement is true.
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Find last year's salary if, after 2% pay raise, this year's salary is 37,740
Answers
The last year's salary is found as 33078.43.
How do you calculate the percentage of a number?Divide the value by the total value as well as multiply the result by 100 to get the percentage. (amount/total amount), the formula for determining the percentage is 100%.
A percentage is defined as a portion of the whole expressed in the form of 100. There are two ways to calculate a percentage:
The unitary method is implemented.By changing the denominator of the fraction to 100.As per the given question;
The salary for the current year is given as 37,740.
There is the increase in 2%.
Let the last year's salary be x.
Then 2% of x will be;
x + 2%of x = 37,740
x + 2x/100 = 37,740
x + 0.02x = 37,740
1.02x = 37,740
x = 37,740/1.02
x = 33500
Therefore, the value of last year's salary is was 33,500.
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How we use scientific calculator
Answers
Answer:
I'll answer the question in the picture first.
log(6) = 1.788
log(8) = 2.079
ln(6) = 1.792
ln(8)= 2.08
How to use a scientific calculator?
There are many different types of scientific calculators, so it is difficult to give a single answer to this question. However, most scientific calculators have a variety of buttons that perform different functions. Typically, there are buttons for the four basic operations ( addition, subtraction, multiplication, and division), as well as buttons for more complex functions such as square roots and exponential operations. To use a scientific calculator, simply press the buttons corresponding to the operations you want to perform.
Step-by-step explanation:
greg sets his watch for the correct time exactly one week later he finds that his watch 1 1 over 3 minutes it loses time at the same rate for eight weeks write a multiplication expression that describes the sittuation find the product and explain how it is related to the problem?
Answers
The product or overall change in time for 8 weeks will be 29.33 minutes.
What is a statement?A statement is a declarative sentence that is either true or false but not both. A statement is sometimes called a proposition. The key is that there must be no ambiguity. To be a statement, a sentence must be true or false, and it cannot be both.
Given:
After one week, Greg's watch has lost 11/3 minutes. If the watch continues to lose time at the same rate, we can say that the change in time is 11/3 minutes per week.
According to given question we have
(11/3 minutes/week) x (8 weeks) = 29.33 minutes
Therefore, the product or overall change in time for 8 weeks will be 29.33 minutes.
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A mobile phone manufacturing unit produces a certain number of mobile phones in a day. The cost of each phone was found to be 55 minus the number of mobile phones produced in a day. On a particular day, the total cost of production was $750, find the number of mobile phones produced on that day.
Answers
Answer:
−55x+750=0
Step-by-step explanation:
If the difference of a number and eight is tripled, the result is six more than the number. Find the number. Round your answer to the nearest integer, if necessary.
Answers
The number that is six less than the product of three and the difference of the number and eight is; 15
How can the required number in the word problem be found?The verbal expression of the equation in the word problem is presented in mathematical form as follows;
(x - 8) × 3 = x + 6Expanding the left hand side gives;
3•x - 3×8 = x + 6
3•x - 24 = x + 6
3•x - x = 24 + 6 = 30
2•x = 30
x = 30/2 = 15
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what is the solution to -3/8x-11=4
Answers
Answer: -40
Step-by-step explanation:
Answer:
-1/40
Step-by-step explanation:
-3/8x -11+11=4+11
-3/8x=15
-3/8x x=15x
-3/8=15x
15x/15= -3/8/15
x=-1/40
Hope this helps!^^
The sum of a number and seven
Answers
Answer:
x + 7
___________________________________________________
What are variables?
A variable is a quantity that may change within the context of a mathematical problem or experiment. Typically, we use a single letter to represent a variable. The letters x, y, and z are common symbols used for variables!
How do we describe variables in word form?
When we describe an expression in words that includes a variable, we're describing an algebraic expression (an expression with a variable).
In this case "The sum of a number" has no definite correlation to a number, therefore, it is automatically considered a variable.
Then, since it says "The sum" we know we are adding. Adding what? We are adding an unknown term to the number 7.
Henceforth, the answer is x + 7.
___________________________________________________
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could anyone help me with this?
Answers
Answer: Domain: -2<=x<=2
Range: -2<=y<=2
Not a function
Step-by-step explanation:
Domain: x goes from -2 to 2
-2<=x<=2
Range: y goes from -2 to 2
-2<=y<=2
Not a function since there are several y-coordinates that have the same x-coordinate, so the graph doesn't pass the vertical line test. Example: (0, -2) and (0, 2).
Question 2
2 pts
James wants to have earned $8,388 amount of interest in 22 years. Currently he finds that his
annual interest rate is 7.34%. Calculate how much money James needs to invest as his principal in
order to achieve this goal.
Answers
The money James needs to invest as his principal in order to achieve this goal is $ 5, 197. 67
How to determine the amount
The formula for simple interest is expressed as;
Simple Interest, I = PRT/100
Where:
P is the principal amountR is the rateT is the timeSubstitute the values
8388 = P × 7. 34 × 22/ 100
cross multiply
161. 48 P = 838800
Make 'P' the subject of formula
P = 838800/ 161. 38
Divide through
P = $ 5, 197. 67
Thus, the money James needs to invest as his principal in order to achieve this goal is $ 5, 197. 67
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how do i d+2 in words
Answers
Answer:
9
Step-by-step explanation:
Can someone help me get the points I’ll make u brilliant the points are S T R U
Answers
Using translation concepts, the coordinates of the vertices after a rotation 180º clockwise around the origin is:
S': (-4,-10), R'(-4,-3), U'(-8,-3) and T'(-8,-10).
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
For this problem, the coordinates (x,y) of the vertices are given as follows:
S(4,10), R(4,3), U(8,3), T(8,10).
The rule for a rotation 180º clockwise around the origin is:
(x,y) -> (-x,-y).
Hence the vertices of the rotated image will be given as follows, applying the above rule:
S': (-4,-10), R'(-4,-3), U'(-8,-3) and T'(-8,-10).
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Only answer if you are beinggreat78!
Answers
[tex]s = \frac{cardinality(s)}{cardinality( \omega)} = \frac{15}{100} = \frac{1.5}{100} [/tex]
The shaded region represents 1.5 grids
[tex]1.5 = 1 \frac{0.5}{1} = 1 \frac{5}{10} = 1\frac{1}{2} [/tex]
Option AAnswer:
D
Step-by-step explanation:
The answer and work is in the attached screenshot! :)
21x5-12+31 Order of Operations
Answers
Answer:625
Step-by-step explanation:(2+3)^4
5^4
a bucket holds c liters of water but a jar holds d liters more how much water do they hold together
Answers
The bucket and the jar together will hold (c + d) litres of water.
What is defined as linear equation on two variables?A linear function does have a positive relationship, so increasing one variable (input variable) causes a rise in the second variable (output variable), implying that the variables have always been directly proportional. As a result, the graph of such a linear function is a straight line with a constant slope.Correspondingly, a linear equation is a first-order algebraic equation with two variables and terms with exponents of one.A linear equation in 2 variables [x and y] is any equation with the form:
ax + by = c and at least one of a or b being non-zero.
This is known as the equation's General Form.
For the given question;
The water hold by bucket = c litres.
The water hold by jar = d litres.
Thus, the water hold by both bucket and jar is is linear equation with two variable c and d.
Total water = c + d
By, varying any value the total amount of the water will also get change.
Thus, total water hold by jar and bucket is (c + d) litres.
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use the discriminant to find the number of real solutions of the equation
3x 2 -5x +4=0
Answers
Answer:
zero real solutions
Step-by-step explanation:
You want the number of real roots of 3x² -5x +4 = 0 and determined by using the discriminant.
DiscriminantThe discriminant of a quadratic equation ax²+bx+c=0 is ...
d = b² -4ac
When d < 0, both roots are complex. When d = 0, there is one (repeated) real root. The number of real solutions is 2 when d > 0.
ApplicationFor this equation, a=3, b=-5, c=4, so the discriminant is ...
d = b² -4ac = (-5)² -4(3)(4) = 25 -48 = -23
This means both roots are complex. There are no real solutions.
__
Additional comment
As confirmation, we can look at the graph. It does not cross the x-axis, so there are no (real) values of x that make the value of the quadratic be zero.
is this proportion or not a meal delivery service cost $10 to sign up ,plus $24.99 each month ASAP
Answers
Answer:
This is not proportional.
Step-by-step explanation:
If there was no meal delivery cost than it would be proportional.
What is the equation 5y+22=5x-33 written in slope intercept form
Answers
Answer:
y = x - 11
Step-by-step explanation:
5y + 22 = 5x - 33
5y = 5x - 33 - 22
5y = 5x - 55
y = x - 11
how should i find the volume of the sphere?
Answers
Answer:
Volume of sphere = 4.187x³
Step-by-step explanation:
[tex]\textsf {Volume of a sphere = $\dfrac{4}{3} \pi {r^2 }$}[/tex]
Here r = x
[tex]\textsf {Volume = $\dfrac{4}{3} \pi {x^2 }$}[/tex]
[tex]\textsf {Volume of cuboid = $4x^3$}\\[/tex]
[tex]\textsf {volume of sphere = $\dfrac{4}{3}\pi \cdot x^3$}[/tex]
[tex]\textsf {Since $\pi \approx 3.14$, this is} \approx \dfrac{4\cdot (3.14)}{3} x= 4.187x[/tex]
So volume of sphere of radius x = 4.187x³ is greater than cuboid volume of 4x³
Given the following values, find the perimeter of the figure shown below:
AB = 8 cm, BC = 3 cm, CD = 1 cm, DE = 2 cm, EF = 3 cm, and FG = 1 cm.
Do not include "cm" with your response.
Answers
The perimeter of the given figure for the given values is equal to 24units.
As given in the question,
Given values of the figure,
AB = 8 cm, BC = 3 cm, CD = 1 cm, DE = 2 cm, EF = 3 cm, and FG = 1 cm
HG = AB - (EF + CD)
= 8- (3 +1)
= 4 units
AH = (BC-DE)+FG
= (3-2)+1
=2units
Perimeter of the given figure
= AB + BC+ CD+ DE+ EF+ FG+ GH+ HA
= 8+ 3+ 1+ 2+ 3+ 1+ 4+ 2
=24 units
Therefore, the perimeter of the given figure for the given values is equal to 24units.
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If y varies directly as x, and y = 8 when x = 4, find y when x = 24.
Answers
The value of y is 48
How to calculate the value of y in the variation ?y= kx
let's solve for k which is the constant
y= 8 , x= 4
k= 8/4
k= 2
Next is to calculate the value of y when x is 24
y = 2 × 24
y= 48
Hence the value of y is 48
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Find the slope of a line perpendicular to the line -3x + 4y = 7.
Answers
Answer:
perpendicular slope = - [tex]\frac{4}{3}[/tex]
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
- 3x + 4y = 7 ( add 3x to both sides )
4y = 3x + 7 ( divide through by 4 )
y = [tex]\frac{3}{4}[/tex] x + [tex]\frac{7}{4}[/tex] ← in slope- intercept form
with slope m = [tex]\frac{3}{4}[/tex]
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{3}{4} }[/tex] = - [tex]\frac{4}{3}[/tex]
NEED ANSWERS ASAP WE NEED IT TOMORROW GRADE SIX MATH
1.What is the difference when ⅓ is subtracted from ¾?
2.The sum of ³/⁷ and ½ is equal to? ___
3.The difference between ⅘ and ¼ is ___
4. The sum of 2¼ and 1³/²⁴ subtracted by 1¾ is ______
Answers
f has a range of (-4, infinity), and a graph that is symmetric about the line x = -1 , and has a y- intercept of -3
Answers
The graph of the parabola is given at the end of the answer.
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient.
Considering the range and the symmetry line, the vertex of the function is at (-1,-4) and:
h = -1, k = -4.
Hence:
y = a(x + 1)² - 4.
It has a y-intercept of -3, that is, when x = 0, y = -3, hence we use it to find a as follows.
-3 = a - 4
a = 1.
Hence the function is:
y = (x + 1)² - 4.
The graph of this function is given at the end of the answer.
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