Answer:
sqrt(A /pi ) = r
Step-by-step explanation:
The area of a circle is given by
A = pi r^2
Divide each side by pi
A / pi = r^2
Take the square root of each side
sqrt(A /pi ) = sqrt(r^2)
sqrt(A /pi ) = r
Answer:
sqrt(A /pi ) = r
Step-by-step explanation:
the graph of the invertible function ggg is shown on the grid below.
What is the value of g^-1(7)
Answer:
[tex]g^{-1} (7)=5[/tex]
Step-by-step explanation:
We are asked to find [tex]g^{-1} (7)[/tex].
One thing to remember about the inverse of a function is what exactly an inverse means.
If we have the ordered pair [tex](a,b)[/tex] of function [tex]g[/tex], then the corresponding ordered pair of [tex]g^{-1}[/tex] would be [tex](b,a)[/tex].
As we are asked to find [tex](7,b)[/tex] of [tex]g^{-1}[/tex], we can instead find [tex](b,7)[/tex] of [tex]g[/tex].
This means that we are looking for where [tex]g(b)=7[/tex].
From the graph, we can see that for this to be true, [tex]b=5[/tex]
This means that [tex]g^{-1} (7)=5[/tex]
The value of g^-1(7) is 5.
What is the value of g^-1(7)?
What is invertible function?A function f from a set X to a set Y is said to be invertible if for every y in Y and x in X, there exists a function g from Y to X such that f(g(y)) = y and g(f(x)) = x. function is invertible only if each input has a unique output. That is, each output is paired with exactly one input. That way, when the mapping is reversed, it will still be a function.
Given that:
One thing to remember about the inverse of a function is what exactly an inverse means.
If we have the ordered pair (a, b) of function g , then the corresponding ordered pair of g^-1 would be (b, a).
As we are asked to find (7,b) of g^-1, we can instead find (b, 7) of g .
This means that we are looking for where g(b)=7.
From the graph, we can see that for this to be true, b=5.
So, the value of g^-1(7) is 5.
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Imagine there are 5 cards. They are colored red, yellow, green, white, and black. You mix up the cards and select one of them without looking. Then, without putting that card back, you mix up the remaining cards and select another one.
How many possible outcomes there are?
Answer:
There would be a 25% percent chance for each card.
Step-by-step explanation:
5 cards.
You pick 1 and didn't put it back in the deck and mix the cards again
There would be 4 cards left and 100 ÷ 4 would be 25.
There are 4 possible outcomes.
What are possible outcomes?Possible outcomes are the possible results of an experiment. For example, when you flip a coin, the coin could land on heads or the coin could land on tails.
Given that, there are 5 cards they are colored red, yellow, green, white, and black. you mix up the cards and select one of them without looking. then, without putting that card back, you mix up the remaining cards and select another one.
We need to find the possible outcomes,
The initial cards = 5
One is being picked and removed,
5-1 = 4
Hence, there are 4 possible outcomes.
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Find the surface area of the triangular prism. A triangular prism. The base is a right triangle with base 1 foot, height 2 feet and third side 2 point 2 feet. The height of the prism is 3 feet.
Answer:
17.6ft²Step-by-step explanation:
The formula for calculating the surface area of a triangular prism is expressed as shown below:
SA= bh + pH
b= base of the triangle
h- height of the triangle
p= perimeter of the triangle
H= height of the prism
Given b = 1foot
h = 2feet
perimeter of the triangle = sum of all its sides = 1ft + 2ft + 2.2ft
p = 5.2ft
H = 3ft
Substituting the values into the formula for finding the surface area:
SA = 1(2)+5.2(3)
SA = 2+15.6
SA = 17.6ft²
The surface area of the triangular prism is 17.6ft²
Answer:
69 ft^2
Step-by-step explanation:
Como se haya la media de esta distribución normal? "Se estima que la cantidad de dinero que gastan en gasolina los clientes de una estación de servicio sigue una distribución normal con desviación estándar de quince mil pesos. También se ha encontrado que el 4% de los clientes gasta más de 70.000 pesos."
Answer:
43750 pesos
Step-by-step explanation:
The first thing is to establish the formula in this case as it is a normal distribution is as follows:
z = x - m / sd
where x is the point value, m the mean, sd the standard deviation and z is the z score, we can calculate the z score by means of this 4% and it is found in the normal distribution table.
for 4%. z = 1.75
replacing:
1.75 = (70000 - m) / 15000
m = -1.75 * 15000 + 70000
m = -26250 + 70000
m = 43750
therefore we have that the average is 43750 pesos
what is the distance between (2,6) and (5,10)?
Distance formula: d = √(x2-x1)^2 + (y2-y1)^2
d = √(5-2)^2 + (10-6)^2
d = √3^2 + 4^2
d = √9 + 16
d = √25
d = 5
The distance is 5 units.
Best of Luck!
Find \cos(\alpha)cos(α)cosine, left parenthesis, alpha, right parenthesis in the triangle. Choose 1 answer: Choose 1 answer: (Choice A) A \dfrac{20}{29} 29 20 start fraction, 20, divided by, 29, end fraction (Choice B) B \dfrac{20}{21} 21 20 start fraction, 20, divided by, 21, end fraction (Choice C) C \dfrac{21}{29} 29 21 start fraction, 21, divided by, 29, end fraction (Choice D) D \dfrac{21}{20} 20 21
Answer:
Check Explanation
Step-by-step explanation:
The diagram for this question is missing, but from the setup of the question, it is evident that the triangle to obtain cos α from is a right angled triangle.
It is evident from the options provided that the right angled triangle is one with dimensions of 20, 21 and 29.
These three dimensions perfectly form a Pythagorean triple.
So, the value of cos α now depends on the setup of the triangle.
From trigonometric relations, if α is an angle in the right angled triangle, cos α is given mathematically as
Cos α = (Adj/Hyp)
For this Pythagorean triple,
Hyp = hypotenuse side = 29
Adj = Adjacent side = 20 or 21, depending on the triangle's setup.
If the adjacent is 20,
Cos α = (20/29), option A is correct.
If the adjacent is 21,
Cos α = (21/29), option C is correct.
Hope this Helps!!!
7532 Question 1 of 7 The equation 4x – 45 = y is used to find your profit, y, in dollars from buying $45 of supplies and washing cars for $4 each. What does the x stand for?
Answer:
x stands for the number of cars washed with the supplies.
Step-by-step explanation:
Given;
Profit equation; y = 4x - 45
Price of supplies = $45
Amount received per car wahed = $4
From the equation given, we can notice that the higher the value of x the higher the profit generated.
Since, for washing a car brings $4, 2 car is $8 and so on... So the value of x is the number of cars washed with the supplies.
x stands for the number of cars washed with the supplies.
For example, if we wash 15 cars. x = 15
y = 4(15) - 45 = 60 - 45
y = $15
Find the area of the shape?
Answer:
12 pi
Step-by-step explanation:
First find the area of full circle
A = pi r^2 where r is the radius
A = pi (4)^2
A = 16 pi
This is 3/4 of a circle so multiply the area by the fraction of a circle
3/4*16pi = 12 pi
Answer:
[tex]12\pi[/tex] or 37.70 (rounded)
Step-by-step explanation:
To work this out you would first need to work out the area of this circle. You can do this by multiplying pi by the radius of 4 squared, this gives you 50.27 or [tex]16\pi[/tex].
Then in order to work out the area of this part of the circle you would have to divide the area 50.27 or 16pi by 4, this gives you 4 pi or 12.57. This is because the angle of the missing part is 90 degrees or a right angle, and because 360 divided by 4 is 90 this meant that the question is asking to work out [tex]\frac{3}{4}[/tex]of a circle and so by dividing it by 4 we are working out the area of one quadrant.
Then the final step is to multiply 4 pi or 12.57 by 3, this gives you 12 [tex]\pi[/tex] and 37.70.
1) Multiply pi by 4 squared.
[tex]\pi*4^{2} =16\pi or 50.27[/tex]
2) Divide 50.27 by 4.
[tex]16\pi or 50.27 /4=4\pi or 12.57[/tex]
3) Multiply 12.57 by 3.
[tex]12.57*3=12\pi or 37.70[/tex]
Here are two steps from the derivation of the quadratic formula (picture included)
what took place between the first step and the second step?
A. factoring a perfect square trinomial
B. completing the square
C. taking the square root of both sides
The mathematical operation which took place between the first step and the second step from the derivation of the quadratic formula is: B. completing the square.
What is a quadratic equation?A quadratic equation can be defined as a mathematical expression (equation) that can be used to define and represent the relationship that exists between two or more variable on a graph. In Mathematics, the standard form of a quadratic equation is given by;
ax² + bx + c = 0
The derivation of quadratic formula.Mathematically, the quadratic formula can be derived as follows:
x² + b/ax +c/a = 0
x² + b/ax = -c/a
x² + b/ax + (b/2a)² = - c/a + (b/2a)² [completing the square]
(x + b/2a)² = b²/4a² - c/a
x + b/2a = √(b²/4a² - c/a)
[tex]x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}[/tex]
In conclusion, the step which is shown in the image above for the derivation of the quadratic formula was derived by using completing the square method.
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Answer: THE CORRECT ANSWER IS Factoring a perfect square trinomial
Step-by-step explanation:
In ΔVWX, the measure of ∠X=90°, the measure of ∠W=20°, and XV = 58 feet. Find the length of VW to the nearest tenth of a foot.
Answer:
169.6
Step-by-step explanation:
We can use trig to find the missing side (sin specifically). sin(x)=opposite/hypotenuse. where x is the angle. VWX is 20 degrees. The side opposite to that angle is VX or 58. We dont know the hypotenuse. If we were to substitute values into sin(x)=opposite/hypotenuse, we would get sin(20)=58/hypotenuse. sin(20) in the calculator is 0.342020143... so we can rewrite the equation as 0.342020143=58/hypotenuse. Lets call the hypotenuse h. If we multiply h on both sides, we can try to find what h is equal to. 0.342020143h=58. Now we can divide 0.342020143 on both sides to isolate h. h=169.58... or if we round it, we get 169.6
What value of x makes the
equation true?
5x = 20
Answer:
4
Step-by-step explanation:
5x = 20
x= 20/5
x = 4!
hope this helps ! <3
mark brainliest plz!
Answer:
4
Step-by-step explanation:
Divide 20 by 5 to find x
Find the standard form of the equation of the parabola with a focus at (0, 6) and a directrix at y = -6.
A) y equals 1 divided by 24 x squared
B) y2 = 6x
C) y2 = 24x
D) y equals 1 divided by 6 x squared
Answer:
None of the options represent the right answer. (Real answer: [tex]y = 24\cdot x^{2}[/tex])
Step-by-step explanation:
The parabola shown above is vertical and least distance between focus and directrix is equal to [tex]2\cdot p[/tex]. Then, the value of p is determined with the help of the Pythagorean Theorem:
[tex]2\cdot p = \sqrt{(0-0)^{2}+[6-(-6)]^{2}}[/tex]
[tex]2\cdot p = 12[/tex]
[tex]p = 6[/tex]
The general equation of a parabola centered at (h,k) is:
[tex]y-k = 4\cdot p \cdot (x-h)^{2}[/tex]
It is evident that parabola is centered at origin. Hence, the equation of the parabola in standard form is:
[tex]y = 24\cdot x^{2}[/tex]
None of the options represent the right answer.
Answer:
y equals 1 divided by 24 x squared
Step-by-step explanation:
Just took the test
The given system of eqqations models the coins in a jar containing n nickels, d dimes, and a quarters. Which statement is
modeled by one of the equations in the system?
q- dun
0 250+ 0 100+ 0.05n-6.05
+0+-36
The number of nickels is equal to the total number of dimes and quarters
The total value of the coins in the jar is $36
There is a total of 36 coins in the jar
There is an equal number of nickels, dimes, and quarters
Answer:
Option (3).
Step-by-step explanation:
This question is incomplete; find the compete question in the attachment.
Equation (1): q = d + n
"Total number of quarters is equal to the sum of number of dimes and nickels."
Equation (2): 0.25q + 0.10d + 0.05n = 6.05
"Total value of the coins in the jar is $36"
Equation (3) : q + d + n = 36
"There are a total of 36 coins in the jar."
By comparing the options given, we find the third option which matches with equation (3)
Therefore, option (3) is the correct answer.
Please help!!! A plane takes off from the airport and climbs at a steady rate. If the plane travelled
5.4km after take-off and gained 1120m of elevation (vertical gain), what angle did the plane take off at?
Answer:
[tex] 12.0^\circ [/tex]
Step-by-step explanation:
Think of a right triangle. It may help you to draw it.
Start at a point. Draw a point and label it point A. That is where the plane takes off from. Now draw a diagonal segment tilted up to the right and stop at a point and label it B. Segment AB is the path of the airplane. Now draw a segment down vertically to a point you will label C, so that points A and C are on the same horizontal line. Connect points A and C.
You now have a right triangle. Angle C is the right angle. AB is the hypotenuse and is 5.4 km. That is the actual distance the plane traveled. BC is 1.12 km (since 1120 m = 1.12 km) and is a leg of the right triangle. The angle you are looking for is angle A.
For angle A, BC is the opposite leg. AB is the hypotenuse.
The trig ratio that relates the opposite leg to the hypotenuse is the sine.
[tex] \sin A = \dfrac{opp}{hyp} [/tex]
[tex] \sin A = \dfrac{1.12~km}{5.4~km} [/tex]
[tex] \sin A = 0.2074 [/tex]
[tex] A = \sin^{-1} 0.2074 [/tex]
[tex] A = 12.0^\circ [/tex]
Answer: 12.0 degrees
Find the measure of the reference angle for each given angle. Part 2
13. θ = -160°
14. θ = 345°
15. θ = =130°
Answer:
13. 20°
14. 15°
15. 50°
Step-by-step explanation:
Please see the attached pictures for full solution.
For negative angles, the arrow turns clockwise.
Answer:
13. 20°
14. 15°
15. 50°
Step-by-step explanation:
From a mathematical point of view, the reference angle is the smaller of α and (180°-α), where α = θ mod 180°.
That is, add or subtract multiples of 180° until the result is in the range 0–180°. Then choose the smaller of the angle and its supplement.
It is convenient to let a spreadsheet calculate these when you have a bunch of them.
__
From a geometrical point of view, the reference angle is the positive angle between the terminal ray and the nearest x-axis.
__
For the angles here, the reference angles (in degrees) are shown in the attachment.
Greg has a bag that contains 25 colored tiles. Of all the tiles in this bag, 10 are blue. Suppose another bag contains 250 colored tiles. Of all the tiles in this bag, 75 are blue. From which bag is Greg less likely to pick a blue tile? Explain.
Answer:
he is less likely to pick a blue tile in the second bag
Step-by-step explanation:
divide 10 by 25 which will give you 40%
divide 75 by 250 which will give you 30%
this makes it less likely for Greg to pick blue from the second bag, as the first bag has a higher percentage chance
The sound of thunder from a bolt of lightning was heard 2.6 seconds after the lightning hit,from 895 meter away.What was the speed of sound to the nearest tenth of a meter of a meter per person
Answer:
344.2m/s
Step-by-step explanation:
The parameters given are:
Distance=895meter
Time=2.6seconds
Therefore the speed of sound is:
Speed of sound= distance/time taken
= 895/2.6
=344.23
=344.2m/s ( to the nearest tenth)
Answer:
d 344.2 meters per second
Step-by-step explanation:
edge 2021
A plane is descending into an airport. When its altitude is 3 1/2 miles, it is 250 miles from the airport. When its altitude is 1 mile, it is 75 miles from the airport. At 2 1/2 miles, it is 175 miles from the airport. Problem 6 a. If the pilot follows the same pattern, what will the plane's altitude be at 25 miles from the airport? *
Answer: 1/2 miles
Step-by-step explanation:
Given the following:
Altitude (miles) - - - - - - - - - - distance (miles)
3 1/2 - - - - - - - - - - - - - - - - - - - 250
2 1/2 - - - - - - - - - - - - - - - - - - - - 175
Calculate the plane's altitude at 25miles from the airport
7/2 = 250
5/2 = 175
(7/2 - 5/2) miles = (250 - 175)miles
1 mile = 75 miles
From the above, the plane craft 's altitude reduces by 1 mile for every 75 miles moved
Therefore, at a distance of 25 mile from the airport,
Distance moved = (250 - 25)miles = 225miles
225miles / 75 miles = 3
Therefore, the altitude will reduce by 3 miles from the initial altitude at 250 miles
Therefore,
( 3 1/2 - 3) miles = 1/2 miles
Therefore, the plane craft will have an altitude of 1/2
Would a piece of wood with a mass of 48 grams and a volume of 47.4 cm^3 float in water?
The piece of wood would sink if a piece of wood with a mass of 48 grams and a volume of 47.4 cubic cm, and a density is 1 g/cm³.
What is density?It is defined as the mass-to-volume ratio. The density indicates the object's density and is represented by the symbol. The density is measured in kilograms per cubic meter.
We have:
Mass of the piece of wood = 48 grams
The volume of the piece of wood = 47.4 cubic cm
As we know, from the definition of density, density is the mass-to-volume ratio.
d = mass/volume
d = 48/47.4
d = 1.01 g/cm³ ≈ 1 g/cm³
As we know,
It will float if the volume is larger than the mass and sink if the reverse is true.
Thus, the piece of wood would sink if a piece of wood with a mass of 48 grams and a volume of 47.4 cubic cm, and a density is 1 g/cm³.
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Maria earned $20 walking her neighbor's dogs last week. She went shopping today and spent $8 on shampoo and conditioner. What is her current financial standing? *
20 is what percent of 60
Answer:
30%
Step-by-step explanation:
Answer:
33.333333333333%
Step-by-step explanation:
Find the area of the figure
Answer:
11000
Step-by-step explanation:
Seventy-five percent of the flowers in the arrangement are roses and the rest are tulips. Of the tulips, 50 percent are pink. To the nearest whole percent, what is the probability that a randomly chosen flower from the arrangement is a pink tulip?
Answer: 13% :D
Step-by-step explanation: Hope it helps
Answer:
13%
Step-by-step explanation:
:D
What is the area of the triangle below?
Answer:l think it's 6
Step-by-step explanation:
You 1/2×4×3
=6
The table gives the mass of liquids with a volume of 5 cm3. A 2-column table with 4 rows. Column 1 is labeled liquid with entries water, glycerin, milk, olive oil. Column 2 is labeled Mass (grams) with entries 5, 6.3, 5.15, 4.9. Density is the ratio of mass to volume. Density = mass volume What is the density of milk? Use the drop-down menu to complete the statement. The density of milk is StartFraction grams Over centimeters cubed EndFraction.
The answer would be 1.03! hopes this helps!
Answer:
1.03
Step-by-step explanation:
i did the assignment on edg 2020/2021
(6^4)(6^−2) = please help will get brainliest!
Answer:
4-2=2 6^2=36
Step-by-step explanation:
Answer:
= 36 3/35
Step-by-step explanation:
(6)^4 × (6^-2)
= 1290 × 1/36
= 1290/36
= 36 3/35
IM SO DUMB I NEED HELP
Answer:
[tex]76.0m^2[/tex] (you have to have the .0 since it says to round to the nearest tenth)
Step-by-step explanation:
The formula for the surface area of a rectangular prism is:
[tex]A=2(wl+hl+hw)[/tex]
So just plug in the values.
Height= 4
Width=2
Length=5
[tex]A=2((2)(5)+(4)(5)+(4)(2))\\A=2(10+20+8)\\A=2(38)\\A=76m^2[/tex]
7/2x + 1/2x = 22 + 9/2
Answer:
[tex]x = \frac{53}{8} [/tex]
alternative form:
[tex]x = 6 \frac{5}{8} \: or \: x = 6.625[/tex]
Step-by-step explanation:
[tex] \frac{7}{2} x + \frac{1}{2} x = 22 + \frac{9}{2} \\ add \: \frac{7}{2}x \: to \: \frac{1}{2} x \\ \\ 4x = 22 + \frac{9}{2} \\ add \: 22 \: to \: \frac{9}{2} \\ \\ 4x = \frac{53}{2} \\ divide \: both \: sides \: by \: 4 \: \\ \\ x= \frac{53}{8} [/tex]
If you spun the spinner 1 time, what is the probability it would land on a white piece?
Answer:
4/7
Step-by-step explanation:
Since there are 7 possible outcomes because there are 7 triangles the denominator will be 7. Since there are 4 white squares the chances of landing on one is 4/7
Which of the following statements is true for the logistic differential equation?
The graph has a horizontal asymptote at y = 18.
y is growing the fastest when y = 9.
The limiting value for y is 18.
All of the above.
Answer:
All of the above
Step-by-step explanation:
dy/dt = y/3 (18 − y)
0 = y/3 (18 − y)
y = 0 or 18
d²y/dt² = y/3 (-dy/dt) + (1/3 dy/dt) (18 − y)
d²y/dt² = dy/dt (-y/3 + 6 − y/3)
d²y/dt² = dy/dt (6 − 2y/3)
d²y/dt² = y/3 (18 − y) (6 − 2y/3)
0 = y/3 (18 − y) (6 − 2y/3)
y = 0, 9, 18
y" = 0 at y = 9 and changes signs from + to -, so y' is a maximum at y = 9.
y' and y" = 0 at y = 0 and y = 18, so those are both asymptotes / limiting values.
