Given a function f : a → b and a subset y ⊆ b, is f (f −1 (y)) = y always true? prove or give a counterexample
If the subset y is the empty set, then the statement is false. That is the counterexample.
Is the statement true?
We know that for an invertible function, we always have that:
[tex]f(x) = y\\f^{-1}(y) = x[/tex]
Now, the range of f(x) is the set b. This means that the domain of the inverse is the set b. Such that:
f^{-1} is defined on b→a
Now we want to work on a subset y ⊆ b.
And here comes the problem.
The empty set {∅} is a subset of ay other set. So, if y is the empty set, there are no elements where we can evaluate the inverse function. From that counterexample, we conclude that the statement is false.
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the money in a bank account increased from $400 to $1000.
copy and complete these sentences.
a) $1000 is ........% of $400.
b) the money has increased by .......%
Answer:
a).1000/400*100
= (1000*100)/400
= 100000/400 = 250
b).600
Step-by-step explanation:
a). Percentage solution with steps:
Step 1: We make the assumption that 400 is 100 % since it is our output value.
Step 2: We next represent the value we seek with x.
Step 3: From step 1, it follows that 100 % = 400.
Step 4: In the same vein, x % = 1000 .
Step 5: This gives us a pair of simple equations:
100 % = 400(1).
x % = 1000(2).
Step 6: By simply dividing equation 1 by equation 2 and taking note of the fact that both the LHS
(left hand side) of both equations have the same unit (%); we have
100 % / x % = 400/1000
Step 7: Taking the inverse (or reciprocal) of both sides yields
x/100 = 1000/400
x = 250 %
Therefore, 1000 is 250 % of 400.
b) $1000-$400= 600
= $400+$600=$1000
Doubling the dimensions of a rectangle increases the area by a factor of 4.
If p represents doubling the dimensions of a rectangle and q represents the area increasing by a factor of 4, which are true? Select two options.
p → q represents the original conditional statement and the contrapositive of the original conditional statement. Then the correct options are A and E.
The missing options are given below.
What is dilation?Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.
There is no effect of dilation on the angle.
Doubling the dimensions of a rectangle increases the area by a factor of 4.
If p represents doubling the dimensions of a rectangle and q represents the area increasing by a factor of 4.
Then the true statement will be
Then the correct options are A and E.
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The surface area of the cone below is about 151.58 inches squared. The radius of the base is 4 inches. What is the slant height? Use 3.14 for Pi. Round your answer to the nearest whole number.
The slant height of the given cone will be 12.06 inches.
What is slant height?The measurement from the base to the peak along the "center" of a lateral face of an object, such as a cone, is its slant height.
Given that:-
The surface area of the cone below is about 151.58 inches squared. The radius of the base is 4 inches.The slant height will be calculated as:-
Surface area = π r l
151.58 = π x 4 x l
l = 151.58 / ( π x 4 )
l = 12.06 inches.
Therefore slant height of the given cone will be 12.06 inches.
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Estimate the roots of f(x)
Answer:
Step-by-step explanation:
If T(x) = x + 0.14x, then find the value of T(290).
Answer:
330.6
Step-by-step explanation:
You have to enter 290 for x.
T(290) = 290 + 0.14(290)
T(290) = 290 + 40.6
T(290) = 330.6
A sample of substance x that has a mass of 326.0 g releases 4325.8 cal when it freezes at its freezing point. if substance x has a molar mass of 58.45 g/mol, what is the molar heat of fusion for substance x? use q equals n delta h.. 13.31 cal/mol 74.00 cal/mol 775.6 cal/mol 19054.7 cal/mol
The molar heat of fusion for substance X , given the data is 775.6 cal/mol
How to determine the mole of the substance XMass = 326 gMolar mass = 58.45 g/molMole = ?Mole = mass / molar mass
Mole = (326 / 58.45) moles
How to determine the heat of fussionMole (n) = (326 / 58.45) molesHeat (Q) = 4325.8 calHeat of fusion (ΔHf) = ?
Q = n × ΔHf
4325.8 = (326 / 58.45) × ΔHf
4325.8 = (326 × ΔHf ) / 58.45
Cross multiply
326 × ΔHf = 4325.8 × 58.45
Divide both sides by 326
ΔHf = (4325.8 × 58.45) / 326
ΔHf = 775.6 cal/mol
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What is the greatest area of a rectangle with a perimeter of 60cm? What is the length and width of this rectangle?
The length and width of this rectangle are 15 cm respectively
How to determine the greatest area?The perimeter is given as:
Perimeter, P = 60
The greatest area is calculated as:
Greatest = (P/4)^2
Substitute 60 for P
Greatest = (60/4)^2
Evaluate the quotient
Greatest = 15^2
Evaluate the exponent
Greatest = 225 square centimeters
Hence, the greatest area is 225 square centimeters
How to determine the length and widthWe understand that the area is the greatest.
In such a scenario;
Length = Width
This means that:
Area =Length^2 =Width^2
So, we have:
Length^2 =Width^2 = 225
Take the square root
Length =Width = 15
Hence, the length and width of this rectangle are 15 cm respectively
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Suzanna’s doctor told her to lose 9 kg, which was 10% of her body weight.
a) How much did Suzanna weigh?
b) If Suzanna lost 12% of her body weight, what is her new weight?
(a) 10% of x = 9
x = 9 ⋅ (100/10)
x = 90 kg
(b) 12% of x = 12/100 of 90
Weight she lost = 10.8
Her new weight = 90 - 10.8
= 79.2kg
Which statement about proportional relationships is false?
A proportional relationship must graph as a line.
A graph of a proportional relationship must pass through (0, 0).
Each point (or pair) in a proportional relationship must share the same ratio.
O Each point (or pair) in a proportional relationship must share the same difference.
Mark this and return
Save and Exit
Next
Submit
Answer:
Each point (or pair) in a proportional relationship must share the same difference is the false statement.
City worker drain a community pool that contains 403,920 gallons of water. The pump they use removes water at a rate of 40 cubic feet per minute. One cubic foot of water contains 7.48 gallons how long in hours will it take to remove all the water from the pool
Answer:
22.5 hours
Step-by-step explanation:
One cubic foot of water contains 7.48 gallons, so 40 cubic feet of water would equal 7.48 × 40, or 299.2 gallons. So the pumping rate is 299.2 gallons per minute. Multiplying 299.2 by 60, we have
299.2 × 60, or 17952 gallons per hour. Finally, divide 403,920 by 17,952 to find the number of hours to remove all the water: 403,920 ÷ 17,952 = 22.5 hours
Set up a proportion to solve for x in the following similar triangles
Answer:
[tex] \frac{18}{12} = \frac{24}{x - 2} [/tex]
What is 5 x -1 =
Doing summer homework
Answer:
x=1/5
Step-by-step explanation:
You have to isolate x. First, add the one to the sider to give you 5x=1. In order to get the x by itself, you have to divide the 5 into both sides. In the end, this gives you x=1/5.
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Which set of angle measures could be the measures of the interior angles of a triangle?
O 90°, 42°, and 58°
O 60°, 60°, and 60°
O 100°, 48°, and 42°
O 31°, 75°, and 70°
TIME REMAI
42:34
Answer:
1) -
2) +
3) -
4) +
Step-by-step explanation:
сумма внутренних углов треугольника не должна превышать 180 градусов
Chocolate cost $1.50 and was paid for with $5 which three coins were given as change
Answer: $3.5
Step-by-step explanation:
If a product cost $1.50 and you paid $5, the change will be equal to
$5 - $1.50 = $3.5 for change
A box in the shape of a rectangular prism has a width that is 5 inches greater than the height and a length that is 2 inches greater than the width. Write a polynomial expression in standard form for the volume of the box. Explain the meaning of any variables used.
The volume of the rectangular prism can be express in standard polynomial as follows:
x³ + 12x² + 35x
How to find the volume of a rectangular prism?volume of a rectangular prism = lwh
where
l = lengthw = widthh = heightTherefore,
let
height = x
width = x + 5
length = x + 5 + 2 = x + 7
Therefore,
volume = x(x + 5)(x + 7)
volume = x(x² + 7x + 5x + 35)
volume = x(x² + 12x + 35)
volume = x³ + 12x² + 35x
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Given: cot = -0.59 in QII, find sin
The value of sin x in Q II is 0.86 .
What are Trigonometry ?This the field in Maths which deals with a right angled triangle and the other angles in the triangle.
It is given that cot = -0.59
cot x = cos x / sin x
Using online trigonometric calculator
sin x in Q II is 0.86 .
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A green gold bracelet weighs 56g. The bracelet is made from 75% gold, 20% silver and 5% copper.
(a) What is the mass of the gold in the bracelet?
(b) What is the mass of the copper in the bracelet?
Answer:
a. 42 g
b. 2.8 g
Step-by-step explanation:
a. Since the entire thing weighs 56g and gold is 75% of the mass you simply find 75% of the mass. This is done by converting the 75% into decimal form by dividing it by 100 to get 0.75 and then multiply it by the 56 g to get (0.75 * 56 g) = 42 g
b. same thing here as the previous answer. 5%/100 = 0.05. (0.05 * 56 g) = 2.8 g
Work out the angle of elevation from the
rabbit to the top of the tree.
18 m
9√3m
Not drawn accurately
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:Angle \:\: of \:\: elevation= 30° [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
Let the angle of elevation be " x "
[tex]\qquad \tt \rightarrow \: \cos(x) = \dfrac{9 \sqrt{3} }{18} [/tex]
[tex]\qquad \tt \rightarrow \: \cos(x) = \dfrac{ \sqrt{3} }{2} [/tex]
[tex]\qquad \tt \rightarrow \: x = \cos {}^{ - 1} \bigg( \cfrac{ \sqrt{3} }{2} \bigg ) [/tex]
[tex]\qquad \tt \rightarrow \: x = 30 \degree \: \: or \: \: \cfrac{ \pi}{6} \: \: rad[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Answer:
The angle is 60 degree.
Step-by-step explanation:
First of all, we will find the height if the tree by using Pythagorean theorm.
Let, height of tree be x.
18^2=(9(3^1/2))^2+x^2
324=243+x^2
x^2=324-243
x^2=81
x=9
Now, let the angle be y.
tan y= x/base
tan y=9/9×(3^1/2)
tan y=1.73
y=cot 1.73
y= 60
find the measure of arc DB in P
please hurry if you can
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:m\overbrace{DB}= 90 \degree[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex] \qquad \tt \rightarrow \: m \overbrace{DB} + m \overbrace{TB} = 180 \degree[/tex]
[ linear pair ]
[tex] \qquad \tt \rightarrow \: m \overbrace{DB} + 90 \degree = 180 \degree[/tex]
[tex] \qquad \tt \rightarrow \: m \overbrace{DB} = 180 \degree - 90 \degree[/tex]
[tex] \qquad \tt \rightarrow \: m \overbrace{DB} = 90 \degree[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
A shipment of tile cost $64,500. each tile costs 15 dollars. how many pieces of tile are in the shipment?
Answer:
4,300
Step-by-step explanation:
total cost of the shipment of tile cost =$64,500
each tile cost =$15
how many pieces will now be the total cost of shipment tile divided by the cost of each tile
which will be
64500/15
=4,300 tiles are there
i am glad I helped
5(2x - 12) + 21 = 2x + 41
05
08
O 10
072
Answer:
x = 10
Step-by-step explanation:
5(2x - 12) + 21 = 2x + 41 ← distribute parenthesis and simplify left side
10x - 60 + 21 = 2x + 41
10x - 39 = 2x + 41 ( subtract 2x from both sides )
8x - 39 = 41 ( add 39 to both sides )
8x = 80 ( divide both sides by 8 )
x = 10
