Answer:
[tex]\mathbf{g^{-1} (t) = log _2 \ 20 \ t}[/tex]
Step-by-step explanation:
Here is the full question
A standard piece of paper is 0.05 mm thick. Let's imagine taking a piece of paper and folding the paper in half multiple times. We'll assume we can make "perfect folds," where each fold makes the folded paper exactly twice as thick as before - and we can make as many folds as we want.
Write a function g that determines the thickness of the folded paper (in mm) in terms of the number folds made, n. (Notice that g(0) 0.05,)
[tex]g(n )= (05)2^n[/tex]
The function g has an inverse. The function g⁻¹ determines the number of folds needed to give the folded paper a thickness of t mm. Write a function formula for g⁻¹).
SOLUTION:
If we represent g(n) with t;
Then
[tex]\mathbf{t = (0.05)2^n} \\ \\ \mathbf{\dfrac{t}{0.05} = 2^n} \\ \\ \mathbf{\dfrac {100 \ t }{ 5} = 2^n} \\ \\ \mathbf{20 t = 2^n}[/tex]
Taking logarithm of both sides; we have :
[tex]\mathbf{log (20 t) = n log 2} \ \ \ \mathbf{(since \ , log \ a^b = b \ log \ a) } \\ \\ \mathbf{n = \dfrac{log \ 20 t }{log \ 2 }} \\ \\ \mathbf{g^{-1} (t) = \dfrac{log \ 20 t }{log \ 2 }} \\ \\ \mathbf{g^{-1} (t) = log _2 \ 20 \ t}[/tex]
Can u please answer this question in the picture below or above I guess
Answer: B. 72ᴼ alternate exterior angles theorem
Step-by-step explanation:
Alternate exterior angles because they’re angles on the outside of the transversal.
Alternate exterior angles are also congruent to each other, so that’s why 2 is congruent to 72ᴼ
Please answer correctly !!!!!!! Will mark brianliest answer !!!!!!!!!!
Answer:
g(-4) =1
Step-by-step explanation:
g(-4) we want to find the value of the graph when x = -4
Got over to x=-4
Got up to the blue line
read the value of the y coordinate
y=1
g(-4) =1
the base of a pyramid is equilateral triangle of side 8cm long. If the altitude of the pyramid is 15cm ,find it's volume
Answer:
V = 80√3 cm³
Step-by-step explanation:
V = Ab×h/3
Ab = l²√3/4 = 64√3/4 = 16√3 cm²
V = 16√3cm²×15cm/3
= 16√3cm²×5cm
= 80√3 cm³
Answer:
138.56cm2
Step-by-step explanation:
B.a×hx1/3
B.a=1/2×8×8sin60=27.71cm2
1/3×27.71×15=138.56cm2
Raj was asked to fully simplify this polynomial and put it into standard form.
2x2y + 8x3 – xy2 – 2x3 + 3xy2 + 6y3
Raj simplified the polynomial with a final term of 6y3. What is the first term of the polynomial Raj ended up with?
6x3
8x3
2xy2
3xy2
Step-by-step explanation:
The first term is 6x3
Because he subtracted like terms 8x3 and 2x3
Answer:
6x³
Step-by-step explanation:
2x²y + 8x³ – xy² – 2x³ + 3xy² + 6y³=
6x³+2x²y+2xy²+6y³
Mr Hassan gave his year 7 class a test on Friday. the highest possible mark for the test was 10.
Answer:
To solve this question, we just need to observe the given graph.
(A) How many pupils scored more than 8 in the test?
Each little square is equivalent to 0.5 units, so there are 5 students who fot more than 8. Specifically, 1 got 8 points and 4 students got 10.
(B) How many pupils are there in Mr. Hassan's Year 7 class?There are 33 pupils in total, remember that each little square is equivalent to 0.5 units.
(C) What assumption have you made in answering part b)?The assumption was that the majority of pupils scored less than 8.
A circle centered at the origin contains the point (0, –9). Does (8, StartRoot 17 EndRoot) also lie on the circle? Explain.No, the distance from the center to the point (8, StartRoot 17 EndRoot) is not the same as the radius. No, the radius of 10 units is different from the distance from the center to the point (8, StartRoot 17 EndRoot). Yes, the distance from the origin to the point (8, StartRoot 17 EndRoot) is 9 units. Yes, the distance from the point (0, –9) to the point (8, StartRoot 17 EndRoot) is 9 units.
Answer:
Step-by-step explanation:
No it does not cause the 8 To the 17 overpasses the coordinates 0,-9 so the perimeter of the imaginary circle it expands loosely over the designated area
Answer:
Answer C
Step-by-step explanation:
EDGE2021
the weights of cars passing over a Bridge have a mean of 3550 lb and a standard deviation of 870 lb. Assume that the weights of the cars passing over the bridge, Lee distributed. Use the empirical rule to estimate the percentage of the cars going over the bridge whose weights are more than 4420 lbs.
Answer:
a. 16%
Step-by-step explanation:
The difference from the mean is ...
(x - µ) = 4420 lb -3550 lb = 870 lb
Then the minimum Z-score of the traffic of interest is ...
(x - µ)/σ = (870 lb)/(870 lb) = 1
__
The "empirical rule" tells you that 68% of a normal distribution is within 1 σ (Z = ±1) of the mean. If 68% is inside that range, then the remaining 32% is outside that range. The normal distribution is symmetrical about the mean, so half that quantity is below Z = -1, and the other half, 16%, is above Z=1.
About 16% of the cars have weights more than 4420 pounds.
find the mean deviation of the following set of numbers: 10,12,14,15, 17 and 19
(A). 2.5
(B). 2.6
(C). 2.7
(D). 2.8
Answer:
2.5
Step-by-step explanation:
I'm sorry I don't know how to explain it but I'm pretty sure the answer is a. 2.5
What is -3 1/2 ÷ 4/9 = ???
Answer: -7.875
Step-by-step explanation:
What are the x-intercepts of y=4x^2-16
Answer:
(-2,0) and (2,0)
Step-by-step explanation:
To find the x intercepts of a graph, you need to set the y to 0. This is because a graph only intersects the x axis at the line y=0. Hence:
[tex]4x^2-16=0[/tex]
Factor:
[tex]4(x^2-4)=0 \\\\4(x-2)(x+2)=0 \\\\x=2,-2[/tex]
The x intercepts are at (-2,0) and (2,0). Hope this helps!
Answer:
The x intercepts are -2 and 2
Step-by-step explanation:
y=4x^2-16
Set equal to zero to find the x intercepts
0 =4x^2-16
Factor
0 = 4(x^2 -4)
Factor again, noticing the difference of squares ( a^2 - b^2) = (a-b)(a+b)
0 = 4(x-2) (x+2)
Using the zero product property
0 = x-2 0 = x+2
x =2 x = -2
The x intercepts are -2 and 2
The two segments formed as a result of a bisector will
always be______?
1Proportional
2Perpendicular
3Congruent
4Parallel
What is the discriminant of the quadratic equation 0 = 2x² + 3x - 5?
-37
-31
43
49
Answer:
D 49
Step-by-step explanation:
just did it
A biologist uses a box-shaped fish trap that measures 1/4meter by 2/3meter by 3/5meter. What is the volume of the trap in the cubic meters.
To find the volume of a box-shaped fish trap, we have to multiply the three dimensions of it:
(1/4 m)* (2/3 m)* (3/5 m)
= (1*2*3)/ (4*3*5) m^(3)
= 6/ 60 m^(3)
= 1/10 m^(3)
= 0.1 m^(3)
The volume of the box-shaped fish trap is 0.1 m^(3).
Hope this is helpful~
find the size of angle yxz give your answer to 3 significant figures 20cm 8cm
tan X = |YZ| / |XZ| = 20/8 = 5/2
X = arctan(5/2) = 68.2°
Answer: 68.2°
The size of angle ∠YXZ is 68.3° given that sides YZ=20cm and XZ=8cm by using trigonometric ratios.
What are trigonometric ratios?In a right angled triangle, if A is an angle other than right angle then trigonometric ratios are
sin A =[tex]\frac{opposite side}{hypotenuse}[/tex]
cos A=[tex]\frac{adjacent side}{hypotenuse}[/tex]
tan A =[tex]\frac{opposite side}{adjacent side}[/tex]
Calculate the angle ∠YXZGiven YZ=20cm and XZ=8cm
Since the triangle is right angled, and opposite side and adjacent side are given we can find tan(∠YXZ )
tan (∠YXZ ) =20/8 =2.5
∠YXZ = arctan (2.5) =68.2°
Hence the size of angle ∠YXZ is 68.2° given that sides YZ=20cm and XZ=8cm.
Learn more about trigonometric ratios here :
brainly.com/question/22384999
#SPJ2
Evaluate A² for A = 2.3
Answer:
5.29
Step-by-step explanation:
From A=2.3, A^2=2.3^2.3=2.3*2.3=5.29
What is the probability that a card drawn randomly from a standard deck of 52 cards is a red eight Express your answer as a fraction in
lowest terms or a decimal rounded to the nearest millionth
Answer:
=1/26
Step-by-step explanation:
In a 52 card deck there are 2 red 8's ( hearts and diamonds)
P(red 8) = number of red 8's / total
=2/52
=1/26
Find the values of x and y in the diagram.
Answer:can you put some angle degrees on it plz
Step-by-step explanation:
Timothy Bergling is designing a logo. The logo is a polygon whose shape is a square attached to an equilateral triangle. The square and the equilateral triangle have side lengths of 2 centimeters, and the equilateral triangle has a height of about 1.7 cm. Find the area of the logo.
Answer:
The logo has an area of 5.7 cm².
Step-by-step explanation:
The area of the logo must be equal to the sum of the square's area and the triangle's one, therefore we will calculate each individually. The triangle is attached to the square, this means that its base has the same length as the side of the square.
[tex]square = side^2 = 2^2 = 4 \text{ cm}^2[/tex]
[tex]triangle = \frac{b*h}{2} = \frac{2*1.7}{2} = 1.7 \text{ cm}^2[/tex]
The total area of the figura is:
[tex]total = square + triangle = 4 + 1.7 = 5.7 \text{ cm}^2[/tex]
The logo has an area of 5.7 cm².
What is the product? Assume x greater-than-or-equal-to 0 (StartRoot 3 x EndRoot + StartRoot 5 EndRoot) (StartRoot 15 x EndRoot + 2 StartRoot 30 EndRoot)
Answer:
[tex]3\sqrt5 x+ \sqrt x (6 \sqrt{10} +5\sqrt{3}) +10 \sqrt6[/tex]
Step-by-step explanation:
To find the product :
[tex](\sqrt{3x} +\sqrt5)(\sqrt{15x} +2\sqrt{30})[/tex]
[tex]\sqrt{3x}(\sqrt{15x} +2\sqrt{30}) +\sqrt5(\sqrt{15x} +2\sqrt{30})\\\Rightarrow \sqrt{3x}\times \sqrt{15x} +\sqrt{3x}\times 2\sqrt{30} +\sqrt5 \times \sqrt{15x} +\sqrt5\times 2\sqrt{30}\\\Rightarrow \sqrt{45} \times x + 2 \sqrt{90x} + \sqrt{75x} + 2 \sqrt{150}\\\Rightarrow \sqrt{5 \times 9} \times x + 2 \sqrt{9\times 10x} + \sqrt{25 \times 3x} + 2 \sqrt{25 \times 6}\\\Rightarrow 3\sqrt5 x+ 2 \times 3 \sqrt{10x} +5\sqrt{3x} +2 \times 5 \sqrt6\\\Rightarrow 3\sqrt5 x+ 6 \sqrt{10x} +5\sqrt{3x} +10 \sqrt6[/tex]
[tex]\Rightarrow 3\sqrt5 x+ \sqrt x (6 \sqrt{10} +5\sqrt{3}) +10 \sqrt6[/tex]
Some identities used:
1. [tex](a+b)(c+d) = a (c+d) + b(c+d)[/tex]
2. [tex]\sqrt9 =3[/tex]
3. [tex]\sqrt{25} =5[/tex]
4. [tex]\sqrt x \times \sqrt x=x[/tex]
5. [tex]\sqrt a \times \sqrt b = \sqrt{ab}[/tex]
So, the solution is [tex]3\sqrt5 x+ \sqrt x (6 \sqrt{10} +5\sqrt{3}) +10 \sqrt6[/tex]
Answer:it’s b
Step-by-step explanation:
On edge
Please help me with my question!!
We know that the area of each tile is 3 1/2in^2
All we need to do is divide.
210 / 3.5 = 60
So, she will need 60 tiles to cover the entire bathroom floor.
Best of Luck!
What’s the answer I need help plssssssssss
Answer:
[tex]\frac{\sqrt[3]{19} }{\sqrt[3]{x} }[/tex]
So A is the answer
Step-by-step explanation:
[tex]y=\frac{19}{x^3}\\\mathrm{Interchange\:the\:variables}\:x\:\mathrm{and}\:y\\x=\frac{19}{y^3}\\\mathrm{Solve}\:x=\frac{19}{y^3}\:\mathrm{for}\:y\\y=\sqrt[3]{\frac{19}{x}}\\\sqrt[3]{\frac{19}{x}}\\\frac{\sqrt[3]{19} }{\sqrt[3]{x} }[/tex]
6+
Зу + 4 < 6
helppppppppp
Step-by-step explanation:
6 + 3y + 4 < 6
10 + 3y < 6
3y < -4
y < -4/3
Answer:
y < -4/3
Step-by-step explanation:
6+ Зу + 4 < 6
Combine like terms
10 +3y < 6
Subtract 10 from each side
10 +3y - 10 < 6-10
3y < -4
Divide each side by 3
3y/3 < -4/3
y < -4/3
What is the answer to 2+5(11-6)+12/3?
Answer:
39
Step-by-step explanation:
From left to right but first parenthesis
11-6=5
5+2=7
7x5=35
12/3=4
35+4=39
Answer:
39
Step-by-step explanation:
1. Never forget to use P.E.M.D.A.S
11 - 6 = 5
2 + 5 (5) + 12/3
39
what is the solution to -5x-7=3
Answer:
x = -2
Step-by-step explanation:
-5x - 7 = 3
-5x = 10
x = 10/-5
x = -2
What is the completely factored form of f(x) = 683 – 1332 - 4x + 15?
Answer:-637
Step-by-step explanation:
How many prime numbers have squares between 100 and 300?
Answer:
there are 62 prime numbers with squares
Answer:
i believe it is 3...?
11, 13, and 17
Step-by-step explanation:
11 = 121
13= 169
17 = 289
these are prime numbers
What is the difference between -4 and 6
[tex]answer = - 10 \\ solution \\ - 4 - 6 \\ = - 10 \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment[/tex]
Answer:
[tex] - 10[/tex]
Step-by-step explanation:
We know that,
[tex]( - ) \times ( + ) = ( - )[/tex]
[tex]( - ) + ( - ) = ( - )[/tex]
Let's solve
[tex] - 4 - ( + 6) \\ - 4 - 6 \\ = - 10[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
At a pet store, Davina counted 12 parrots out of 20 birds. Which is an equivalent ratio of parrots to birds at the pet store?
Answer:
3 to 5 This is because if you simplify the ratio by dividing each number in the ratio by 4, therefore for every group of 5 birds 3 of them are parrots
Step-by-step explanation:
Answer:
answer d
Step-by-step explanation:
edg 2020
i’ve been stuck on this one
[tex]the \: right \: answer \: is \: of \: option \: a \\ please \: see \: the \: attached \: picture \: for \\ full \: solution \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment[/tex]
what is called circle
Answer:
A round plane figure whose boundary (the circumference)consists of points equidistant from a fixed point (the center)
Answer:
A round plane figure
Step-by-step explanation: