Answers
Answer:
To solve these first swap x and y, solve for y and name it inverse function3. y = -8x + 2
x = -8y + 28y = -x + 2y = -x/8 + 2/8y = -(18)x + 1/4f⁻¹(x) = -(18)x + 1/4
-----------------------------------------
4. y = (2/3)x - 5
x = (2/3)y - 5(2/3)y = x + 5y = (3/2)x + (3/2)5y = 1.5x + 7.5f⁻¹(x) = 1.5x + 7.5
-----------------------------------------
5. f(x) = 2x² - 6
x = 2y² - 62y² = x + 6y² = 1/2x + 3y = [tex]\sqrt{1/2x + 3}[/tex]f⁻¹(x) = [tex]\sqrt{1/2x + 3}[/tex]
-----------------------------------------
6. y = (x - 3)²
x = (y - 3)²[tex]\sqrt{x}[/tex] = y - 3y = 3 + [tex]\sqrt{x}[/tex]f⁻¹(x) = 3 + [tex]\sqrt{x}[/tex]
Related Questions
Find the volume of the figure. Round to the nearest hundredth if necessary. (Figure is not to scale)
Answers
Answer:
360 mi^3
Step-by-step explanation:
The figure is composed by two parallelepipeds. For find the volume we have to find the volume of both the solids and the added up the two values
solid 1
length = 11 - 4 = 7 mi
base area = length x width = 7 x 4 = 28 mi^2
V = base area x height = 28 x 6 = 168 mi^3
solid 2
base area = 8 x 4 = 32 mi^2
V = 32 x 6 = 192 mi^3
total volume: 168 + 192 = 360 mi^3
The volume of the figure is 360 mi³.
What is Volume?Volume of a three dimensional shape is the space occupied by the shape.
Given is a figure where two rectangular boxes are put on top of each other.
Volume of a rectangular prism = L × W × H
Here L is the length, W is the width and H is the height.
The dimensions of the rectangular prism are :
Larger one having L = 11 mi, W = 6 mi and H = 4 mi
Smaller one on top having L = 4 mi, W = 6 mi and H = 8 - 4 = 4 mi.
Volume of the figure = volume of larger box + Volume of smaller box
= (11 × 6 × 4) + (4 × 6 × 4)
= 264 + 96
= 360 mi³
Hence the volume of the figure is 360 mi³.
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The number of mold spores on a piece of bread after a different amount of time or listed in the table below
Which function models the number of mold spores on the bread after X days
Answers
Answer:
Option (4)
Step-by-step explanation:
From the table attached,
Ratio of spores in day 2 and day 1 = [tex]\frac{400}{200}[/tex]
= 2
Ratio of spores in day 3 and day 2 = [tex]\frac{800}{400}[/tex]
= 2
There is a common ratio of 2 in each successive to the previous term of the Mold spores.
Therefore, spores are growing exponentially.
Let the function representing exponential function is,
y = a(b)ˣ
Here, y = Number of spores after time 'x'
x = Number of days
a and b are the constants.
On day 1,
x = 1
y = 200
By substituting these values in the exponential function,
200 = a(b)¹
ab = 200 -------(1)
On day 2,
x = 2
y = 400
400 = a(b)² -------(2)
Divide equation 2 by equation 1,
[tex]\frac{400}{200}=\frac{ab^{2} }{ab}[/tex]
b = 2
By substituting the value of b in equation (1),
a(2) = 200
a = 100
Therefore, equation of the function will be,
y = 100(2)ˣ
Option (4) will be the answer.
Which is bigger? 2^4 or 4^2?
Answers
Answer:
Both are equal
Step-by-step explanation:
[tex]2^4 = 16 \\ \\ {4}^{2} = 16 \\ \\ \implies \: {2}^{4} = {4}^{2} [/tex]
Answer:
Step-by-step explanation:
2^4=16 and 4^2=16
They both equal the same thing so im guessing neither. They are both the same value.
Hope this helped!
PLS let me know if i'm wrong so i can correct my mistake!!
Which of the following equations will produce the graph shown below?
Answers
Answer:
x-1/8y^2=0
Step-by-step explanation:
just took the test
Calculate the number of edges of the solid. Given it has 8 faces; 4 hexagons & 4 triangles
Answers
Answer:
20 Edges
Step-by-step explanation:
As this figure shows only 10 edges..so to meet the given condition (8 faces; 4 hexagons & 4 triangles) same figure is present at the back making total of 20 Edges.
What is the measure of DEF
Answers
The calculated measure of the arc DEF is 204 degrees
Calculating the measure of arc DEFFrom the question, we have the following parameters that can be used in our computation:
The circle
The measure of the arc intercepted by the angle DEF is calculated as
Arc DF = 2 * DEF
When the given values are substituted in the above equation, we have the following equation
Arc DF = 2 * 78
So, we have
Arc DF = 156
The measure of arc DEF is then calculated as
Arc DEF = 360 - 156
Evaluate
Arc DEF = 204
Hence, the measure of the arc DEF is 204 degrees
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please show an actual answer i need help
Answers
Answer:
1. wire is approx. 143.96 ft
2. pole is approx. 106.55 ft
Step-by-step explanation:
Mapping the information on the SOHCAHTOA picture below:
Φ = 46
wire = hypotenuse
adjacent side = 100
CAH is most suitable:
cos 46° = 100/wire => wire = 100/cos 46 ≈ 143.96
pole = opposite side + 3
TOA is most suitable:
tan 46° = (pole-3)/100 => pole = 3 + 100 * tan 46 ≈ 106.55
How many moles are present in 4.51x1015 atoms of Aluminum (Al)?
Answers
Answer:
divide by avagadro number to get the amount of moles in the atoms you have
what is 8w+5=4(2w+1)
Answers
Answer:
No solution
Step-by-step explanation:
1. Distribute the right side.
8w+5=8w+4
2. This has no solution.
Two sisters, sister A and sister B, play SCRABBLE with each other every evening. Sister A is a statistician, and she draws a random sample of 30 results from the 1,420 total games that have been played to construct a confidence interval estimate of p, the proportion of SCRABBLE games between her and her sister that she has won. Her 95% confidence interval estimate of p is LCL = 0.36, UCL = 0.69.
A 95% confidence interval estimate of the total number of games sister A has won out of the 1,450 games that have been played is LCL =___________ and UCL = ___________
The Illinois State Toll Highway Authority is conducting a study to estimate the proportion of low-income commuters who drive to work on a toll road. The project manager wants to estimate the proportion to within 0.03 with 95% confidence, and the project manager believes that p will turn out to be approximately 0.11.
A sample size no smaller than __________ is needed.
Answers
Answer:
First question: LCL = 522, UCL = 1000.5
Second question: A sample size no smaller than 418 is needed.
Step-by-step explanation:
First question:
Lower bound:
0.36 of 1450. So
0.36*1450 = 522
Upper bound:
0.69 of 1450. So
0.69*1450 = 1000.5
LCL = 522, UCL = 1000.5
Second question:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The project manager believes that p will turn out to be approximately 0.11.
This means that [tex]\pi = 0.11[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The project manager wants to estimate the proportion to within 0.03
This means that the sample size needed is given by n, and n is found when M = 0.03. So
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 1.96\sqrt{\frac{0.11*0.89}{n}}[/tex]
[tex]0.03\sqrt{n} = 1.96\sqrt{0.11*0.89}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.11*0.89}}{0.03}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96\sqrt{0.11*0.89}}{0.03})^2[/tex]
[tex]n = 417.9[/tex]
Rounding up
A sample size no smaller than 418 is needed.
Find the height of ABD
Answers
Answer:
[tex]Height=\boxed{10\sqrt{2}} [/tex]
[tex] Area =\boxed{165\sqrt{2}} [/tex]
Step-by-step explanation:
By geometric mean theorem:
[tex] AC=\sqrt{25\times 8}[/tex]
[tex] AC=\sqrt{5^2 \times 2^2 \times 2}[/tex]
[tex] AC=5\times 2\sqrt{2}[/tex]
[tex] AC=10\sqrt{2}[/tex]
So,
[tex]Height=\boxed{10\sqrt{2}} [/tex]
[tex] Area = \frac{1}{2} \times base\times height [/tex]
[tex] \therefore Area = \frac{1}{2} \times (25+8)\times 10\sqrt{2} [/tex]
[tex] \therefore Area =33\times 5\sqrt{2} [/tex]
[tex] Area =\boxed{165\sqrt{2}} [/tex]
Two imaginary roots
A.144
B.O
D.-4
C.36
Answers
Answer:
D) -4 (with imaginary roots ±2i)
Step-by-step explanation:
Since you cannot take the square root of a negative number to produce a real result, the only option that has two imaginary roots is D) -4, where the two imaginary roots are 2i and -2i.
HELP WILL GIVE BRANLIEST
Answers
Answer:
The answer would be B [tex]120ft^{3}[/tex]
Step-by-step explanation:
volume of triangular prism is 30 and volume of the cube is 90 :)
How do we solve this in factor form? X^2-11x+24=0
Answers
Answer:
x=8, 3
Step-by-step explanation:
24 has 8 factors: 1,2,3,4,6,8,12,24
8 and 3 make 11
If you factor it out, the equation is (x-8)(x-3)=0
to get 0, only one of the expressions has to equal 0
so x can have 2 different values
Please help me with this ASAP ASAP please please help please please
Answers
Answer:
Step-by-step explanation:
Base perimeter: 5 x 2 x π = 10π
LA = 10π x 2 = 20π
Base area : 5^2π = 25π
SA = 25π x 2 + 20π = 70π
V : 25π x 2 = 50π
What’s the correct answer for this question?
Answers
Answer:
$16 is correct answer
Hope it helps you
Step-by-step exploration:
One CD lets be x
Five CDs - 5x
5x=80
x=80/5=16
Find the value of x in the diagram below( HELP PLEASE)
Answers
9514 1404 393
Answer:
x = 30
Step-by-step explanation:
The sum of exterior angles of a convex polygon is 360°. Here, that means ...
3x° +x° +2x° +2x° +4x° = 360°
12x = 360
x = 360/12 = 30
The value of x is 30.
Answer:
Solution :-Sum of all angles = 360⁰
[tex] \to \sf \: 2x + 2x + x + 4x + 3x = 360[/tex]
[tex] \to \: 12x = 360[/tex]
[tex] \to \: x = \dfrac{360}{12} [/tex]
[tex] \sf \: x = 30[/tex]
Find the minimum value of
C = 2x + 3y subject to the following constraints:
(4x + 3y > 29
X + 2y 11
x20
y > 0
C = [?]
Answers
x+2y>=11 (*4)
=> 4x+8y>=44 and 4x+3y>=29
=> 5y>=15
=> y>=3 => 3y>=9
x>=11-2y => x>=5 => 2x>=10
=> 2x+3y>= 19
C=[19]
WITH THE STEPS
FOR THE 2 SHAPE
Answers
Answer:
70 in
Step-by-step explanation:
7 * 7 = 49 {that's the square}
(7 * 6) * 1/2 = 21 {that's the triangle}
49 + 21 = 70
Answer:
the square SxS= 7x7 = 49
the triangle is hxs÷2=(7×6 )÷2 =42 ÷2 = 21
On a coordinate plane, a line goes through (negative 4, 0) and (4, negative 4). A point is at (2, 3).
What is the equation of the line that is parallel to the given line and passes through the point (2, 3)?
x + 2y = 4
x + 2y = 8
2x + y = 4
2x + y = 8
Answers
9514 1404 393
Answer:
(b) x +2y = 8
Step-by-step explanation:
The only offered line that includes the given point is ...
x +2y = 8
__
We can check the other choices:
x + 2y = 2 +2(3) = 2+6 = 8 . . . matches B (not A)
2x +y = 2(2) +3 = 4+3 = 7 . . . . not a choice
_____
Getting there from scratch
The standard form equation for a line can be written from ...
(y2 -y1)x -(x2 -x1)y = constant
(-4 -0)x -(4 -(-4))y = constant . . . . using the given points (-4, 0) and (4, -4)
-4x -8y = constant
For standard form, we need the leading coefficient to be positive, and we need common factors removed. We can get there by dividing by -4.
x +2y = constant
The value of the constant will be whatever it takes for the given point to lie on the line. For (x, y) = (2, 3) to be a solution, we must have ...
x +2y = (2) +2(3) = constant = 8
The desired line has the equation ...
x +2y = 8
Answer:
B on edge
Step-by-step explanation:
PLEASE ANSWER ILL GIVE BRIA LIEST
Answers
Answer:B
Step-by-step explanation:
A company wanted to estimate the mean lifetime of its new model of lightbulbs. They use a method for testing bulbs that accelerates the process so the bulbs burn out relatively quickly, and the company can accurately calculate the corresponding lifetime under regular usage. They took a random sample of 555 of these new bulbs and calculated their lifetimes. Here are the data and summary statistics:
Bulb 1 2 3 4 5
Lifetime 14.2 12.2 13.4 12.6 14.6
Mean= 13.4 years
Standard deviation= sx =1.02 years
Required:
Wrtite a 90% confidence interval for the mean lifetime in years) for this type of bulb.
Answers
Answer:
13.4±2.132(1.02/5)
Step-by-step explanation:
Khan Academy
The confidence interval for the mean life time is; CI = 13.4 ± 3.678(1.02/5)
What is the confidence interval?
Formula for confidence interval is;
CI = x' ± z(s/√n)
We are given;
Mean; x' = 13.4
Standard deviation; s = 1.02
Sample size; n = 5
z-score at confidence level of 90% = 1.645
Thus;
CI = 13.4 ± 1.645(1.02/√5)
CI = 13.4 ± 3.678(1.02/5)
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The number of hamburgers H sold and the dollar amount of sales S taken in. what is the independent variable and what is the dependent variable?
Answers
Answer:
H = independent variable
S = dependent variable
Step-by-step explanation:
number of hamburgers sold isnt affected by other factors
sales taken in depend on Hamburgers sold
What is the perimeter?? Please help!
Answers
Step-by-step explanation:
perimeter of the given figure=24cm+24cm+30cm+20cm+20cm+20cm+5cm+5cm
=148cm
Answer:
148mm aka 1.48cm aka 1cm48mm
Step-by-step explanation:
to obtain the small thing between the"24mm" and"20mm":
(30mm-20mm)÷2
=5mm
so add up all those given information:
24mm+24mm+20mm+20mm+20mm+30mm+5mm+5mm
comment below if you still don't get it ;)
The scale below represents which equation or inequality?
S or T
A. S = t
B. s > t
C. s < t
Answers
Answer:
B
Step-by-step explanation:
s>t because s is on top of the scale and t is below the scale
Answer plz due in a few min
Answers
Answer:
40
Step-by-step explanation:
24^2+32^2=c^2
square root of 1600 is 40
Answer:40
Step-by-step explanation:Because
a^2 + b^2=c^2
Could someone help me figure this out??
Answers
Answer:
180
Step-by-step explanation:
What is the lateral surface area of a cone that has a slant height of 17 inches and a diameter of 13 inches? (Recall the formula L A = pi r l)
107.5 pi inches squared
110.5 pi inches squared
201 pi inches squared
221 pi inches squared
Answers
Answer:
[tex]A=110.5\pi \ inches^2[/tex]
Step-by-step explanation:
Given that,
The slant height of a cone, l = 17 inches
The diameter of a cone, d = 13 inches
Radius, r = (D/2) = 6.5 inches
We need to find the lateral surface area of a cone. The formula for the lateral surface area of a cone is given by :
[tex]A=\pi rl[/tex]
Put all the values,
[tex]A=\pi \times 6.5\times 17\\\\A=110.5\pi \ inches^2[/tex]
So, the lateral surface area of the cone is equal to [tex]110.5\pi \ inches^2[/tex].
Answer:
B 110.5
Step-by-step explanation:
A die is rolled. What is the probability of getting an even number?
A. 1/6
B. 1/2
C. 1/3
D. 1/4
Answers
Answer:
I wanna say 1/3 because there 3 even numbers on a dice
Step-by-step explanation:
What is a formula for the nth term of the given sequence 13,17,21
Answers
Answer:13+4(n-1)
Step-by-step explanation: