Answers
The operations between functions are:
a) h(f(3)) = 5
b) (f×g)(4) = -8
c) f( g(h(0))) -1
How to operate with functions?
The first thing we want to find is a composition, we want to find:
h(f(3))
That means that we need to evaluate h(x) in f(3), look at the graph and you can see that f(3) = -4
Replacing that we get:
h(f(3)) = h(-4)
And on the graph, we can see that h(-4) = 5
then h(f(3)) = 5
b) Now we have the product:
(f×g)(4) = f(4)*g(4)
Again, looking at the graph:
f(4) = -4
g(4) = 2
Then:
(f×g)(4) = f(4)*f(4)
(f×g)(4) = -4*2
(f×g)(4) = -8
c) Finally we have other composition:
f( g(h(0)))
So we have 2 compositions, first we find:
h(0) = 5
f( g(h(0))) = f(g(5))
Then:
g(5) = 0
f( g(5)) = f(0)
Finally, look at the graph and you can see that f(0) = -1
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Related Questions
Points B, D, and F are midpoints of the sides of
AACE. EC 32 and DF = 20. Find AC.
The diagram is not to scale.
A
F
B
Answers
The value of the side AC is 40 if the points B, D, and F are midpoints of
the sides of ΔACE.
What is the mid-point of a triangle?The midpoint theorem states that in order to determine the midpoints of a triangle's sides, "a line segment linking any two of its midpoints is said to be parallel to the triangle's third side and also half the length of the third side."
Divide the distance between the two endpoints by 2, then do it again. The two terminal x coordinates can alternatively be combined, then the result divided by two. Draw a line from a midway to the opposite corner. The centroid of a triangle is the point at where the three medians intersect.
Given,
The points B, D, F are midpoints of the sides of a triangle ACE.
And also given that,
EC =32 and DF=20, AC=?
So, FD=1/2(AC)
AC=2(FD)
AC=2(20)
AC=40
Therefore, the value of the side AC is 40 if the points B, D, and F are
midpoints of the sides of ΔACE.
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A new streaming service sent out a survey to 350 households to see who would be interested in its service. The company found that it could charge $55 per month, with a margin of error of ±1.3. If 1,000 people signed up for the service, what is the least amount of monthly revenue the company should expect?
$52,815
$53,700
$54,915
$56,300
Answers
Answer:
B) $53700-------------------------------------
The charge of $55 with error margin of ± 1.3 results in the least value of $(55 - 1.3) = $53.7 and greatest value of $(55 + 1.3) = $56.3.
If 1000 people signed up for the service, then the least total amount is:
$53.7*1000 = $53700Correct choice is B.
Answer question #9
The response is incorrect and I need help on getting the correct answer
Answers
Answer:
congruence is compatibility or agreement while equal is the same or equivalent to one another.
Find the perimeter and total area of the composite shape shown below. All measurements are given in inches. Use = 3.14 in
any formulas used.
Answers
The area of the composite shape is 292.96 in² and the perimeter of the composite shape is 65.12 inches
Area of Half circle:The quantity of surface contained within a semicircle's perimeter is known to as its area.
The formula for the Area of a half circle with a Radius (r) is given by
Area of Half circle = πr²/2
The formula for the perimeter of a half circle with a radius (r) is given by
Perimeter of Half circle = πr
Here we have
A picture of a Rectangle with a half circle
Dimensions of Rectangle = 16 in × 12 in
=> Area of rectangle = 16 in × 12 in = 192 in²
=> Perimeter of rectangle shape = 12 + 16 + 12 = 40 inches
[ Here we only take one side of the rectangle since one of the sides is connected with a Half circle ]
The radius of half circle = 8 inch
=> Area of Half circle = π(8)² = (3.14)(64)/2 = 100.96 in²
=> Perimeter of Half circle = πr =(3.14)(8) = 25.12 in
Area of the composite shape
= Ractangle's Area + Half circle's Area
= 192 in² + 100.96 in²
= 292.96 in²
The perimeter of the composite shape
= Ractangle perimeter + Half circle perimeter
= 40 inches + 25.12 inches
= 65.12 inches
Therefore,
The area of the composite shape is 292.96 in² and the perimeter of the composite shape is 65.12 inches
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A piece of cheese is shaped like a triangle. It has a height of 2.5 inches and a base that is 4.75 inches long. If 1 inch = 2.54 centimeters, find the area of the cheese in square centimeters. Round the answer to the nearest square centimeter. Please answer this thank you!
Answers
Answer:
[tex]A \approx 38 \, \textrm{cm}^2[/tex]
Step-by-step explanation:
The area of a triangle is defined as:
[tex]A_\triangle = \dfrac{1}{2}bh[/tex]
where [tex]b[/tex] is the length of its base and [tex]h[/tex] is its height.
So, we can plug the given values into this formula along with the inch to centimeter conversion to get the answer to this problem.
[tex]A=\dfrac{1}{2}\left(4.75\, \textrm{in} \times \dfrac{2.54 \, \textrm{cm}}{1 \, \textrm{in}}\right)\left(2.5\, \textrm{in} \times \dfrac{2.54 \, \textrm{cm}}{1 \, \textrm{in}}\right)[/tex]
And simplify.
[tex]A \approx 38 \, \textrm{cm}^2[/tex]
A coach is buying snacks for 22 players at a soccer match. She pays a total of $77 to
buy each player a bottle of water and an energy bar. The price of one energy bar is $2.
Let w equal the price of a bottle of water. Write an equation that
represents the situation.
Answers
Answer: 22( w + 2 ) =77 and the amount of the water bottle would be 1.50
Step-by-step explanation: i dont know what to write??
Use the formula y = mx + b and use point slope form to write an equation for a line given with the given information.
Answers
Either the slope intercept form or the point-slope form can be used to express the equation of a line-, the line's equation is - 3x - 5.
What is Slope?A line's steepness and direction are measured by the line's slope.
Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.
Any two distinct points on a line can be used to calculate the slope of any line.
The ratio of "vertical change" to "horizontal change" between two different points on a line is calculated using the slope of a line formula.
According to our question-
the points are given as
(x1,y1)=0,-5
(x2,y2)=-3,4
m = y2-y2/x2-x2
Hence, the line's equation is - 3x - 5.
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an item is regularly priced at . it is on sale for off the regular price. how much (in dollars) is discounted from the regular price?
Answers
An item is regularly priced at, 1.98$ is discounted from the regular price.
A percentage is a portion of a whole expressed as a number between 0 and 100 rather than as a fraction. All of something is 100 percent, half of it is fifty percent, none of something is zero percent. To determine a percentage, you divide the portion of the whole by the whole itself and multiply by 100.
Given that,
First, change the percentage into decimal:
Let us assume,
Sale of regular price = 1%
1% = 1/100 = 0.01
Assume, item regular price is = 2$
Multiply 2 with 0.01:
2 * 0.01 = 0.02
Note that this number 0.02 (0.01 of 2) is the amount off from the original price (2). Subtract 2 from 0.02
2 - 0.02 = 1.98
Therefore,
An item is regularly priced at, 1.98$ is discounted from the regular price.
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Please reply urgent I need it now
step by step
Answers
Answer:
x ≥ 5
Step-by-step explanation:
5 + 2 (2x - 3) ≥ 3x + 4
5 + 4x - 6 ≥ 3x + 4
-1 + 4x ≥ 3x + 4
4x ≥ 3x + 5
x ≥ 5
Usually Cassandra tap dances 1 7/8 hours a day. Today she reduced this time by half. For how long did she tap dance today?
Answers
Answer: 15/16 hour
Step-by-step explanation:
two thirds of a number b is no more than 12.
Answers
two thirds of a number b which is no more than 12, is b ≤ 18
What is inequality ?
In mathematics, an inequality represents the connection between two values in an imbalanced algebraic statement. A sign of inequality can be used to show that one of the two variables is larger than, greater than or equal to, less than, or equal to another value.
According to question
two thirds of a number b = (2/3)b
Given two thirds of number b is no more than 12
⇒ (2/3)b ≤ 12
⇒ 2b ≤ 12*3
⇒ b ≤ (12*3)/2
⇒ b ≤ 36/2
⇒ b ≤ 18
hence the number b whose 2/3 is no more than 12 is, b ≤ 18
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Somebody please help I’m studying for finals and I’m losing my mind
Answers
The perimeter of the image is 70 meters and its area is 210 square meters.
What is meant by perimeter?The circumference of a shape is known as its perimeter. The lengths of all four sides must be added in order to get a rectangle's or square's perimeter. The sum of the lengths of all the sides in a rectangle is its perimeter, or P. A rectangle's opposite sides are equal, hence it has two equal lengths and two equal widths. The following formula is used to determine a rectangle's perimeter: Diameter is equal to the sum of the following dimensions: length, width, height, and width.
There are numerous practical uses for calculating the perimeter. The size of the fence needed to enclose a yard or garden is known as the calculated perimeter.
Area=(1/2)×base× height
=(1/2)×21×20
=210 square meters
Perimeter=a+ b+ c
=21+20+29
=70meters
Therefore, The perimeter of the image is 70 meters and its area is 210 square meters.
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In the first week of July a record 1,120 people went to the local swimming pool in the second week 125 fewer people went to the pool than in the first week in the third week 130 more people went to the pool than in the second week in the fourth week 229 fewer people went to the pool than in the third week what is the percent decrease in the number of people who went to the pool over these four weeks
Answers
There is 20% decrease in the number of people who went to the pool over these four weeks.
What is percentage?
A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.
There is no dimension to percentages. As a result, it is known as a dimensionless number. When we say a number is 50% of anything, we mean that it is 50% of everything.
Attendance of pool in first week of July = 1120
In second week, 125 fewer people joined.
Thus, attendance in second week is = 1120-125 = 995
In third week, 130 more people joined.
Thus, attendance in third week is = 995+130 = 1125
In fourth week, 229 fewer people joined.
Thus, attendance in fourth week is = 1125-229 = 896
Difference of attendance in first and fourth week = 1120-896 = 224
Percentage decrease = (Decrease number/Initial number)×100%
= (224/1120)×100%
= 0.20×100%
= 20%
Thus, there has been a 20% decrease over the four weeks.
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identify the measure of angle X:
Answers
Since the line is linear, the sum of the angles should be 180 degrees
x + 28 + 73 = 180
x = 180 - 28 - 73
x = 79 degrees
Hope this helped :)
if w denotes weight, n denotes number of items, m denotes maximum capacity constraint, and x =0 or 1, what would be the valid bounding condition/conditions for the sum of the subset problem?
Answers
So the valid bounding conditions for the sum of the subset problem are:
0 <= x[i] <= 1 (for all i such that 1 <= i <= n)
∑(w[i] * x[i]) <= m (for all i such that 1 <= i <= n)
The valid bounding condition for the sum of the subset problem is:
0 <= x[i] <= 1 (for all i such that 1 <= i <= n)
This means that each item can either be included in the subset (x[i] = 1) or not included in the subset (x[i] = 0).
The sum of the weights of the items in the subset should not exceed the maximum capacity constraint, m. So the bounding condition for the weight of the subset is:
∑(w[i] * x[i]) <= m (for all i such that 1 <= i <= n)
This means that the sum of the weights of the items in the subset should be less than or equal to the maximum capacity constraint.
So the valid bounding conditions for the sum of the subset problem are:
0 <= x[i] <= 1 (for all i such that 1 <= i <= n)
∑(w[i] * x[i]) <= m (for all i such that 1 <= i <= n)
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Please help me. I don't want to get the answer wrong
Answers
Answer:
photo?
Step-by-step explanation:
Find the values of x and y
Answers
Answer:
x = 20
y = 70
Step-by-step explanation:
It's rather difficult to explain since nothing is labeled but those are the answers
PLEASE HELP!!!!!!!!
Given 2 and one-eighth times negative 7 times five tenths, determine the product.
negative fourteen and five eightieths
negative 7 and seven sixteenths
fourteen and five fortieths
7 and one eighth
Answers
Answer:
Negative seven and seven sixteenths
Step-by-step explanation:
2⅛ x (-7) x 5/10
= 17/8 x (-7) x 1/2
= - 119/16
= - 7 7/16
what is the conditional probability that a randomly-generated 4-bit string contains two consecutive 1s, given that the first bit of the string is a 1?
Answers
The conditional probability that a randomly-generated 4-bit string contains two consecutive 1s is 3 / 8 .
total length of four-bit strings = 16
Let S represent the collection of all four-bit bit strings.
Let A represent the occurrence of a randomly generated string beginning with 1.
Let B represent the scenario where a string created at random contains two consecutive 0s.
S has 8 strings that begin with the letter "1."
P( A ) = 8 / 16 = 1 / 2
Strings in S starting with 1 and having two consecutive zeros are 1000 , 1001 , 1100
P(A ∩ B) = 3 / 16
Conditional probability that at least two consecutive 0s will appear in a randomly generated bit string of length four is ,
3/16 / 1/2
= 3 / 8
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Given △
△
M
T
S
and △
△
S
Q
P
, find SP.
Answers
Answer:
22
Step-by-step explanation:
Corresponding sides of similar triangles are proportional.
[tex]\frac{3x+2}{5x-4}=\frac{15}{20}=\frac{3}{4} \\ \\ 12x+8=15x-12 \\ \\ 3x=20 \\ \\ \therefore SP=20+2=22[/tex]
If A=45° B = 30°, prove that
Sin (A-B) = sinAcos B - Cos Asin B
Answers
To prove that Sin (A-B) = sinAcos B - Cos Asin B, we can use the angle subtraction formula for sine:
Sin (A-B) = Sin A Cos B - Cos A Sin B
This formula is derived from the identity:
Sin (A-B) = Sin A Cos B - Cos A Sin B
which can be derived by using the double angle identities for sine and cosine:
Sin (2A) = 2 Sin A Cos A
Cos (2A) = Cos^2 A - Sin^2 A = 2 Cos^2 A - 1 = 1 - 2 Sin^2 A
Substituting these identities into the identity above, we get:
Sin (A-B) = Sin A Cos B - Cos A Sin B
What is an angle subtraction?Angle subtraction formulas is otherwise known as angle subtraction identities. This angle subtraction formulas permit us to find the exact values of less common trigonometric angles by expressing the less common angle as the difference of two common angles. For example, 15 degrees = 45 degrees - 30 degrees.
Therefore, Sin (A-B) = sinAcos B - Cos Asin B.
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n divided by 6 equals 42 please explain
Answers
The value of n when is divided by 6 and it gives 42 is 252
What is division?Division is the opposite of multiplication. If 3 groups of 4 make 12 in multiplication, 12 divided into 3 equal groups give 4 in each group in division and 12 divided by 4 gives 3 in each group. This means that 3 and 4 are factors of 12
When dividing a number by another number that is not it's factor, there will be remainder for example 12 divided by 5 . It will give 2 remainder 2. This is because 5 is not a factor of 12.
Similarly, n divided by 6 to give 42. This means that 42 and 6 are factors of n
Therefore to find n we multiply 42 and 6.
n = 42×6
n = 252
therefore the value of n is 252
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2(x+6)+3x+4=
what it equals
Answers
Answer:
5x + 16
Step-by-step explanation:
First you have to distribute the 2 into the parentheses
2 times x is 2x
2 times 6 is 12
so now the equation is
2x + 12 + 3x + 4
add the 2x and 3x and that is 5
so now the equation is...
5x + 12 + 4
add 12 + 4 and that is 16
so now the answer is
5x + 16
Given ab, and c is not parallel to a or b, which statements
must be true?
Select each correct answer.
O
□m/4=m/8
m/8=m/9
m/2=m/7
m/7=m/10
a
C
1/2
3/4
5/6
7/8
9/10
11/12
Answers
please solve for x
5x+10y=25
Answers
[tex]5x+10y=25[/tex]
Add -10y to both sides:
[tex]5x+10y+-10y=25+-10y[/tex]
[tex]5x=-10y+25[/tex]
Divide both sides by 5:
[tex]\dfrac{5x}{5} =\dfrac{-10y+25}{5}[/tex]
[tex]\fbox{y = -2y + 5}[/tex]
5x = 25 - 10y
x = 25/5 - 10/5 y
x = 5 - 2y
Seven days a year, Tiger Stadium becomes the fifth largest city in the state of Louisiana. Over 92,000 fans pack the stadium to watch the Tigers play. After the game, if the fans leave at a rate of 10% per minute, how long will it take before the stadium is half empty?
Answers
It will take 5 minutes before the stadium is half empty
Given that:
Over 92,000 fans pack the stadium to watch the Tigers play
The fans leave at a rate of 10% per minute
The number of fans that leave per minute will be:
10% of 92,000 = 10/100 × 92, 000 = 9,200
The stadium will be fully empty in:
time = 92,000/9,200 = 10 minutes
The stadium will be half empty in:
time = 10 minutes / 2 = 5 minutes
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lonzo borrowed 15000$ at 1.2% simple interest to buy a car . after 9 months how much will lonzo owe the bank in interest
Answers
The simple interest implies that Lonzo owes $1513.5
How to determine the amount Lonzo owes?The given variables can be represented as:
Loan amount P = $1500
Rate of interest, R = 1.2%
Time to pay back the loan, t = 9 months i.e. 0.75 year
The amount from a simple interest can be calculated using:
A = P(1 + RT)
Substitute the known values in the above equation, so, we have the following representation
A = 1500 * (1 + 1.2% * 0.75)
Evaluate
A = 1513.5
Hence, the amount owed is $1513.5
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find the least commmon multiple (LCM) for each pair of numbers.To solve the riddle the letters to the numberd lines below 2,5 3,15 6,12 2,15 2,3 8,24 4,10 6,9 7,9
Answers
The LCM of the given pairs are 10, 15,12,30,6,24,20,18, and 63 respectively.
What is LCM?The least common multiple (LCM) of two numbers is the lowest possible number that can be divisible by both numbers.
There are 9 pairs, so let's name them using the letters A to I.
The LCM of the first pair A (2, 5) is 10.
The LCM of the pair B (3, 15) is 1*3*5 = 15.
The LCM of the pair C (6, 12) is 3*2*1*2 = 12.
The LCM of the pair D (3, 15) is 2*3*1*5 = 30.
The LCM of the pair E (2, 3) is 1*3*2 = 6.
The LCM of the pair F (8, 24) is 2*2*2*1*3 = 24.
The LCM of the pair G (4, 10) is 2*2*5 = 20.
The LCM of the pair H (6, 9) is 3*2*3 = 18.
The LCM of the pair I (7, 9) is 7*9 = 63.
Hence, 10,15,12,30,6,24,20,18,63 are the LCM of the given pairs.
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Insert terms to make a identity replace *
(*-0.2n)^2=*-1.2mn+0.04n^2
Answers
The unidentified term is 3m.
What is equation?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, an equation (x-0.2n)² = x-1.2mn+0.04n²
We know that, (a-b)² = a²-2ab+b²
Comparing the given equation with the above identity, we get,
a = x, b = 0.2n and 2ab = 1.2mn
Therefore, 2x×0.2n = 1.2mn
x = 3m
Hence, the unidentified term is 3m
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Simplify the expression 10^log5
Answers
Answer:
5
Step-by-step explanation:
The logarithm function, denoted as "log," is the inverse of the exponentiation function. This means that if we have the expression "log(x) = y," then "x" is the base "b" raised to the power "y." In other words, "x" is equal to "b^y."
Using this definition, we can simplify the expression "10^log5" as follows:
10^log5 = 10^y
Where "y" is the exponent to which the base "10" must be raised to produce the result "5."
To find the value of "y," we can use the property of logarithms that states "log(b^y) = y." Applying this property to our expression, we have:
log(10^y) = y
Since "10^y" is equal to "5," we can substitute "5" for "10^y" in the above equation:
log(5) = y
Solving for "y," we find that "y = log(5)."
Therefore, the expression "10^log5" can be simplified to:
10^log(5) = 10^(log(5)) = 5
So the simplified result is 5.
