A local radio station surveyed people going into a grocery store about whether or not they liked country and if they listed to that station. The results are shown in the table.
Is listening to the radio station independent of liking country music? Explain.
A) No, the probability of not liking country is the same as the probability of not liking country given that they listen to the station.
B) Yes, the probability of not liking country is the same as the probability of not liking country given that they listen to the station.
C) No, the probability of not liking country is different from the probability of not liking country given that they listen to the station.
D) Yes, the probability of not liking country is different from the probability of not liking country given that they listen to the station.
Answers
Answer:
B
Step-by-step explanation:
51 /22= 2.3
19/8=2.3
The correct option is D) Yes, the probability of not liking country is different from the probability of not liking country given that they listen to the station.
What is the probability?Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty.
We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it.
Given that, a local radio station surveyed people going into a grocery store about whether or not they liked country and if they listed to that station,
We need to determine that if listening to the radio station independent of liking country music,
So, here the answer will be yes, because both the events are not connected to each other.
The probability of not liking or liking the country music is nowhere related to whether a person is listening to the radio station or not.
Hence, the correct answer is D
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Related Questions
Please help me solve this?
Answers
Answer:
[tex]15x^4y^5z^2[/tex]
Step-by-step explanation:
The applicable rule of exponents is ...
(a^b)(a^c) = a^(b+c)
[tex]3xy^4z^2\cdot 5x^2yx=(3\cdot 5)x^{1+2+1}y^{4+1}z^2=15x^4y^5z^2[/tex]
_____
Comment on the rule of exponents
You can see where the rule comes from when you consider that an exponent signifies repeated multiplication.
x² = x·x . . . . . . the 2 signifies that x is a factor 2 times
x³ = x·x·x . . . . the 3 signifies that x is a factor 3 times
The product of these is ...
(x²)(x³) = (x·x)(x·x·x) = x·x·x·x·x = x⁵ = x²⁺³
The base of a regular pyramid is a hexagon.
What is the area of the base of the pyramid?
Enter your answer in the box. Express your answer in radical form.
cm²
Answers
ANSWER
[tex] 96 \sqrt{3} {cm}^{2} [/tex]
EXPLANATION
The area of a regular polygon is
[tex]Area= \frac{1}{2} ap[/tex]
where 'a' is the apothem of the polygon and 'p' is the perimeter of the polygon.
From the diagram,
[tex] \sin(60) = \frac{a}{8} [/tex]
a=8sin(60)
[tex]a = 4 \sqrt{3} [/tex]
[tex] \cos(60) = \frac{l}{8} [/tex]
[tex]l = 8 \cos(60) [/tex]
[tex]l = 4[/tex]
The length of one side of the hexagon is 2×4=8.
The perimeter of the hexagon is
p=6×8=48
The area of the hexagon is
[tex] = \frac{1}{2} \times 4 \sqrt{3} \times 48[/tex]
[tex] = 96 \sqrt{3} {cm}^{2} [/tex]
Kyle poured 9 ounces of juice into 17 cups for his family. How many total ounces of water did Kyle pour into all the glasses?
Answers
Answer:
none. he didn't pour water, he poured juice.
Step-by-step explanation:
please help me out
The equation 9(w + 7) = 27 solved in several steps below.
For each step, choose the reason that best justifies it.
The options are the same for each one.
Answers
For this case we have the following equation:
[tex]9 (w + 7) = 27[/tex]
To solve we follow the steps below:
We apply Distributive Property to the terms of parentheses:
[tex]9w + 63 = 27[/tex]
We apply Subtraction Property of equality by subtracting 63 from both sides of the equation:
[tex]9w + 63-63 = 27-63\\9w = -36[/tex]
We apply Division Property of equality by dividing by 9 on both sides of the equation:
[tex]\frac {9w} {9} = \frac {-36} {9}[/tex]
simplifiying
w = -4
Answer:
[tex]w = -4[/tex]
a 4 sided cube, numbered 1-4, is rolled twice. Determine the sample space. how many possible outcomes are there?
Answers
Answer:
16
Step-by-step explanation:
1 1
1 2
1 3
1 4
2 1
2 2
2 3
2 4
Three and four are done exactly the same way. the total is 16 ways.
You buy a new home in Metropolis (CONGRATULATIONS!) for $374,848. Prices of homes in your area are continuously increasing by 5% per year. How much should your new home be worth in 13 years?
Answers
Answer:
618499.2
answer step by step
5%×13=65
65%×374848=243651.2
243651.2+374848=618499.2
What is the sum of the first 80 terms of the sequence 53, 54, 55, 56, ...?
Answers
Answer:
7,400
Step-by-step explanation:
First, we have to see that this is an arithmetic sequence... since to get the next element we add 1 to it. (a geometric sequence would be a multiplication, not an addition)
So, we have a, the first term (a = 53), and we have the difference between each term (d = 1), and we want to find the SUM of the first 80 terms.
To do this without spending hours writing them down, we can use this formula:
[tex]S = \frac{n}{2} * (2a + (n - 1) * d)[/tex]
If we plug in our values, we have:
[tex]S = \frac{80}{2} * (2 * 53 + (80 - 1) * 1) = 40 * (106 + 79 * 1)[/tex]
S = 40 * (106 + 79) = 40 * 185= 7,400
If the length of each edge of the cube is doubled, the surface area will increase 2 times.True or false
Answers
Answer:
False. The surface area of the cube will increase to four times its initial value.
Step-by-step explanation:
Consider a cube with edge of lengths [tex]a[/tex]. What will be its surface area?
Each face of a cube is a square. The lengths of sides of the square are also [tex]a[/tex].
The area of each square will be the square of its sides: [tex]a \cdot a = a^{2}[/tex].
It takes six such squares to make a cube. The sum of the area of the sube [tex]6a^{2}[/tex] will also be the surface area of the cube.
In case the length of each side of the cube is doubled to [tex]2a[/tex].
The area of each face will become [tex](2a)^{2} = 4a^{2}[/tex].The sum of the area of the six sides will become [tex]6 \times 4a^{2} = 24a^{2} = 4 \times 6a^{2}[/tex], which is four times the initial surface area of [tex]6a^{2}[/tex].find the surface area of the figure
Answers
Answer: First Option
[tex]A = 790.90 cm^2[/tex]
Step-by-step explanation:
The surface area of a circular cone is equal to the area of the cone surface plus the area of the circular base
[tex]A = \pi r ^ 2 + \pi rs[/tex]
Where r is the radius of the base and s is the inclined height of the pyramid.
In this case we know that:
[tex]r = \frac{19}{2}[/tex]
[tex]s = 17[/tex]
Then the surface area of the cone is:
[tex]A = \pi (9.5) ^ 2 + \pi (9.5)(17)[/tex]
[tex]A = 790.90 cm^2[/tex]
A right cone has a radius of 13 cm and an altitude of 52 cm. Find its surface area.
A. 2,668.7 cm2
B. 865.8 cm2
C. 849.5 cm2
D. 2,720.0 cm2
Answers
Answer:
Option B. [tex]865.8\pi\ cm^{2}[/tex]
Step-by-step explanation:
we know that
The surface area of the cone is equal to
[tex]SA=\pi r^{2} +\pi rl[/tex]
we have
[tex]r=13\ cm[/tex]
[tex]h=52\ cm[/tex]
Find the slant height l
Applying Pythagoras \theorem
[tex]l^{2}=r^{2} +h^{2}[/tex]
substitute the values
[tex]l^{2}=13^{2} +52^{2}[/tex]
[tex]l^{2}=2,873[/tex]
[tex]l=53.6\ cm[/tex]
Find the surface area
[tex]SA=\pi(13)^{2} +\pi(13)(53.6)=865.8\pi\ cm^{2}[/tex]
For each vector field f⃗ (x,y,z), compute the curl of f⃗ and, if possible, find a function f(x,y,z) so that f⃗ =∇f. if no such function f exists, enter none. (a) suppose f⃗ (x,y,z)=(2yze2xyz+4z2cos(xz2)i⃗ +(2xze2xyz)j⃗ +(2xye2xyz+8xzcos(xz2))k⃗ . curl(f⃗ )
Answers
[tex]\vec f(x,y,z)=(2yze^{2xyz}+4z^2\cos(xz^2))\,\vec\imath+2xze^{2xyz}\,\vec\jmath+(2xye^{2xyz}+8xz\cos(xz^2))\,\vec k[/tex]
Let
[tex]\vec f=f_1\,\vec\imath+f_2\,\vec\jmath+f_3\,\vec k[/tex]
The curl is
[tex]\nabla\cdot\vec f=(\partial_x\,\vec\imath+\partial_y\,\vec\jmath+\partial_z\,\vec k)\times(f_1\,\vec\imath+f_2\,\vec\jmath+f_3\,\vec k)[/tex]
where [tex]\partial_\xi[/tex] denotes the partial derivative operator with respect to [tex]\xi[/tex]. Recall that
[tex]\vec\imath\times\vec\jmath=\vec k[/tex]
[tex]\vec\jmath\times\vec k=\vec i[/tex]
[tex]\vec k\times\vec\imath=\vec\jmath[/tex]
and that for any two vectors [tex]\vec a[/tex] and [tex]\vec b[/tex], [tex]\vec a\times\vec b=-\vec b\times\vec a[/tex], and [tex]\vec a\times\vec a=\vec0[/tex].
The cross product reduces to
[tex]\nabla\times\vec f=(\partial_yf_3-\partial_zf_2)\,\vec\imath+(\partial_xf_3-\partial_zf_1)\,\vec\jmath+(\partial_xf_2-\partial_yf_1)\,\vec k[/tex]
When you compute the partial derivatives, you'll find that all the components reduce to 0 and
[tex]\nabla\times\vec f=\vec0[/tex]
which means [tex]\vec f[/tex] is indeed conservative and we can find [tex]f[/tex].
Integrate both sides of
[tex]\dfrac{\partial f}{\partial y}=2xze^{2xyz}[/tex]
with respect to [tex]y[/tex] and
[tex]\implies f(x,y,z)=e^{2xyz}+g(x,z)[/tex]
Differentiate both sides with respect to [tex]x[/tex] and
[tex]\dfrac{\partial f}{\partial x}=\dfrac{\partial(e^{2xyz})}{\partial x}+\dfrac{\partial g}{\partial x}[/tex]
[tex]2yze^{2xyz}+4z^2\cos(xz^2)=2yze^{2xyz}+\dfrac{\partial g}{\partial x}[/tex]
[tex]4z^2\cos(xz^2)=\dfrac{\partial g}{\partial x}[/tex]
[tex]\implies g(x,z)=4\sin(xz^2)+h(z)[/tex]
Now
[tex]f(x,y,z)=e^{2xyz}+4\sin(xz^2)+h(z)[/tex]
and differentiating with respect to [tex]z[/tex] gives
[tex]\dfrac{\partial f}{\partial z}=\dfrac{\partial(e^{2xyz}+4\sin(xz^2))}{\partial z}+\dfrac{\mathrm dh}{\mathrm dz}[/tex]
[tex]2xye^{2xyz}+8xz\cos(xz^2)=2xye^{2xyz}+8xz\cos(xz^2)+\dfrac{\mathrm dh}{\mathrm dz}[/tex]
[tex]\dfrac{\mathrm dh}{\mathrm dz}=0[/tex]
[tex]\implies h(z)=C[/tex]
for some constant [tex]C[/tex]. So
[tex]f(x,y,z)=e^{2xyz}+4\sin(xz^2)+C[/tex]
The curl of a vector field can be calculated by finding the determinant of a 3x3 matrix constructed from the unit vectors, partial derivatives, and the components of the vector field. The existence of a function f(x,y,z) such that f⃗ =∇f would imply that the vector field is conservative, meaning it has zero curl.
Explanation:In mathematics and vector calculus, the curl of a vector field is a vector operator that shows the rotation or the circular motion of the vectors in a vector field. It is denoted by ∇×F. The given vector field f⃗ (x,y,z)=(2yze^(2xyz)+4z²cos(xz²)î⃗ +(2xze^(2xyz)j⃗ +(2xye^(2xyz)+8xzcos(xz²))k). The curl can be obtained by finding the determinant of a matrix.
Consider a 3x3 matrix composed of î, ĵ, and k (in the first row), partial derivates (∂/∂x, ∂/∂y, ∂/∂z) (in the second row), and the vector field components (in the third row). Now, you need to calculate the determinant of this matrix to find the curl of the vector field.
The existence of function f(x,y,z) such that f⃗ =∇f would imply that the vector field is conservative. For a vector field to be conservative, it needs to have zero curl. So, once we have the curl, if it equates to zero, it implies the existence of such a function. Otherwise, no such function exists.
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The price of a gallon of milk was $2.65. The price rose y dollars after the last hurricane. Then the price dropped $0.15 and later rose again by $0.05. Which expression represents the current price of milk? A) 2.40 + y B) 2.45 + y C) 2.50 + y D) 2.55 + y
Answers
Answer:
D
Step-by-step explanation:
So you start with $2.65 and a variable y. What we will do is work without the dollar and keep it for the end as it quite disturbs and work our way while keeping the y. So first we have 2.65. Now it rose by y so. The price = 2.65 + y. Then it dropped by 0.15. So 2.65 + y - 0.15. Here you see we have like terms so we reduce and get 2.50 + y. Now it rose by 0.05. So 2.50 + y + 0.05. Again, like terms, reduce. 2.55 + y. There you go with the answer.
Final answer:
The current price of milk, after it first increased by an unknown amount y, then decreased by $0.15, and finally increased by $0.05, is represented by the expression $2.55 + y, which is Option D.
Explanation:
The question asks us to calculate the current price of a gallon of milk after a series of price changes. The original price was $2.65. After a hurricane, the price increased by y dollars. Subsequently, the price dropped by $0.15, and then again rose by $0.05.
To find the new price, we start with the original price and apply the changes step by step:
Original price: $2.65
Price after hurricane increase: $2.65 + y
Price after $0.15 drop: ($2.65 + y) - $0.15 = $2.50 + y
Price after $0.05 rise: ($2.50 + y) + $0.05 = $2.55 + y
Hence, the correct answer representing the current price of milk after these changes is Option D) $2.55 + y.
Determine the equation of the graph:
Answers
Answer:
Choice A
Step-by-step explanation:
In order to determine the equation of the graph, we can simply graph the four equations using an online graphing utility like desmos graphing tool and then run a comparison to identify the appropriate equation of the given graph.
Below are the graphs of the 4 given equations. The graphs were obtained using the desmos online graphing utility;
From the graphs below, the graph that matches the given graph is the one obtained from;
y = x cosx
This is the equation of the given graph
Given that sin θ = x/4. Which expression represents θ in terms of x?
arccos(x/4)
arcsin(x/4)
sin(x/4)
cos(x/4)
Answers
Answer:
arcsin(x/4)
Step-by-step explanation:
Sinθ =x/4
θ= sin-¹(x/4)
θ= arc sin (x/4)
The expression represents θ in terms of x will be θ = arcsin (x/4).
What is trigonometry?The connection between the lengths and angles of a triangular shape is the subject of trigonometry.
Given that sin θ = x/4.
Then the expression represents θ in terms of x will be
sin θ = x/4
θ = arcsin (x/4)
Thus, the correct option is B.
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Which of the following has the least steep graph?
A.y = 3x - 16
B. y= 2x + 7/15
C.y = x + 24
D. y= 1/2x +3
Answers
the answer for this question is ( d)
The least steep graph is y=1/2x+3.
What is a least steep graph?The greater the value of the slope, the "steeper" the slope is, and vice versa.So, the smallest value of the absolute value of these slopes is 1/2.The slope with the highest absolute value is the steepest.A positive slope means the function is ascending left to right.A negative slope means it is descending left to right.Hence, the least steep graph is y=1/2x+3.
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Use formulas to find the lateral area and surface area of the given prism. Round your answer to the nearest whole number.
A. 755 m2; 815 m2
B. 755 m2; 785 m2
C. 725 m2; 815 m2
D. 725 m2; 785 m2
Answers
Answer:
The answer is A. 755 m2; 815 m2
Step-by-step explanation:
The answer is A) 472m^2; 486 m^2.
Let a, b, and c be the sides of the base and h be the height of the prism
a = 2 m
b = 7 m
c = 7.28 m
h = 29 m
The lateral surface area is:
LA = a*h + b*h + c*h = h * (a + b + c)
LA = 29 * (2 + 7 + 7.28) = 29 * 16.28 ≈ 472 m²
The surface area is:
SA = LA + 2 * 1/2 * a * b
SA = 472 + 2 * 7 = 472 + 14 = 486 m²
Answer:
The lateral surface area is 755 sq.m. and total surface area is 785 sq.m.
Step-by-step explanation:
Let a, b, and c be the sides of the base and h be the height of the prism.
a = 5 m
b=6 m
c=11.21 m
h = 34 m
Lateral surface area of triangular prism = [tex](a+b+c)h[/tex]
= [tex](5+6+11.21)34[/tex]
=755.14 sq.m.
Total surface are of triangular prism = Lateral surface area + area of 2 triangles
=[tex]755.14+2 (\frac{1}{2} \times b\times h)[/tex]
=[tex]755.14+2 (\frac{1}{2} \times 5\times 6)[/tex]
=[tex]785.14[/tex]
Thus the lateral surface area is 755 sq.m. and total surface area is 785 sq.m.
Option B is correct.
Mikayla and her two friends made a pizza and cut it into 8 equal sized slices. Of makayla and her friends ate 5 slice of pizza what decimal represents the portion of pizza that remains
Answers
Answer:
0.375
Step-by-step explanation:
1/4= 0.25
0.25/2=1/8
0.125=1/8
0.125x3=3/8
0.375=3/8
The remaining portion of the pizza is 0.375.
What are decimals?A decimal is a number that consists of a whole and a fractional part.
Given that, Mikayla and her two friends made a pizza and cut it into 8 equal sized slices. Of which Makayla and her friends ate 5 slices of pizza,
The whole pizza be represented by 1,
Now, they sliced the pizza into 8 equal parts, and ate 5 of it,
Therefore,
Remaining = 1-5/8
= 3/8
= 0.375
Hence, the remaining portion of the pizza is 0.375.
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You're given two side lengths of 3 centimeters and 5 centimeters. Which measurement can you use for the length of the third side to construct a valid triangle? A. 8 centimeters B. 6 centimeters C. 4 centimeters D. 10 centimeters E. 2 centimeters Select all answersCorrect answers plezz
Answers
Answer: To find the third side of a triangle (there are two answers you could get), you need to use the Pythagorean formula: a^2+b^2=c^2. First answer, 3^2+5^2=c^2. Solve for c. c=5.83. The second answer, 3^2+b^2=5^2. Solve for b. b=4.
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Mags wants to know what the hottest hairstyle Trend in is in our town what is the best group to survey of to find this information
Answers
Answer:
You should choose the last option because it is the most random at choosing salons to ask and so will give the least biased answer.
Step-by-step explanation:
ask the hair salon and they will tell you what hairstyle is hottest
Fifteen points for an answer! Brainliest for a step-by-step/explanation!
What is the factored form of this expression?
3x-9
Answers
Answer:
3(x-3)
Step-by-step explanation:
First, we can see that both 3 and 9 are divisible by 3. So we know that 3/3=1 and 9/3=3.
When factoring equations, there have to be parenthesis so it's more organized. So we can put 3 outside of parenthesis:
3(x-3)
The reason we put the 3 outside of parenthesis is because when we multiply 3 by everything in the parenthesis, we will get the equation we originally started with, which is 3x-9.
So the answer is 3(x-3)
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Which expression is the factored form of −4.5n+3−4.5n+3 ?
−3(1.5n−1)−3(1.5n−1)
−1.5(−3n+2)−1.5(−3n+2)
−1.5(3n+2)−1.5(3n+2)
−3(1.5n+1)
Answers
Answer:
−3(1.5n−1)−3(1.5n−1)
Step-by-step explanation:
To factor the expression −4.5n+3−4.5n+3, find the GCF between each term. Using the GCF 3, divide each term by 3 and rewrite it as −3(1.5n−1)−3(1.5n−1).
The other options are not the factors because they give the wrong signs of at least one term in the expression.
−1.5(−3n+2)−1.5(−3n+2) = 4.5n -3 + 4.5n - 3
−1.5(3n+2)−1.5(3n+2) = -4.5n - 3 - 4.5n - 3
−3(1.5n+1) = -4.5n - 3
Consider a game in which a player rolls a number cube to determine the number of points earned. If a player rolls a number greater than or equal to 4, the number of the roll is added to the total points. Any other roll is deducted from the player's total. What is the expected value of the points earned on a single roll in this game?
Answers
Answer:
UR BAD AT SPELLING KID
Step-by-step explanation:
Answer:
The expected value would be a gain of 1,5
Step-by-step explanation:
For any calculation of expecte value you should multiply the probability of every chance with his value or gain, for example, for this dice
If your roll 1
p(1) = 1/6, and his gain is -1
If your roll 2
p(2) = 1/6, and his gain is -2
If your roll 3
p(3) = 1/6, and his gain is -3
If your roll 4
p(4) = 1/6, and his gain is 4
If your roll 5
p(5) = 1/6, and his gain is 5
If your roll 6
p(6) = 1/6, and his gain is 6
So the expecte value would be
E = p(1)*(-1) + p(2)*(-2)+p(3)*(-3)+p(4)*(4)+p(5)*5+p(6)*6
p(1)=p(2)=p(3)=p(4)=p(5)=p(6)=1/6 because this dice is a cube, with even chances to fall in any face.
E = (1/6)*(-1-2-3+4+5+6)
E=(1/6)*(-6+15)
E=(1/6)*(9)
E=1,5
The expected value would be a gain of 1,5
Find the derivative of f(x) = -2x2 + 11x at x = 9.
a) -25
b) -243
c) 63
d) 19
Answers
[tex]\bf f(x)=-2x^2+11x\implies \left. \cfrac{df}{dx}=-4x+11 \right|_{x=9}\implies -4(9)+11\implies -25[/tex]
Answer:
a) -25
Step-by-step explanation:
First you have to find the derivative of F(x):
[tex]f(x)=2x^{2} +11x\\Derivative=2(2x)+1(11)\\Derivative=4x+11[/tex]
Now you just have to calculate the vale of f(x) when x=9
[tex]-4x+11=\\-4(9)+11=\\-36+11=-25[/tex]
So when x=9, the derivative of [tex]f(x)=2x^{2} +11x[/tex] is equal to -25
Aidan rode his bike 2.3 km from home to the library.Then he biked to the park.When he left home, his odometer read 293.8 km.When he reached the park, it read 308.2 km.How far from the library is the park?
Answers
Answer:
308.2 - 293.8 = 14.4 km
14.4 - 2.3 = 12.1
So the library is 12.1 km from the park.
Library is 12.1 km far from the park.
What is Distance?Distance is the total movement of an object without any regard to direction.
Given that, Aidan rode his bike 2.3 km from home to the library. Then he biked to the park. When he left home, his odometer read 293.8 km. When he reached the park, it read 308.2 km.
Total Distance reading in Odometer after reaching Library =
293.8 + 2.3 = 296.1 km
Reading in Odometer after reaching park = 308.2 km
308.2 - 296.1 = 12.1 km
Hence, Library is 12.1 km far from the park.
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In a certain state, there are currently 5,902,060 acres of farmland. This area is decreasing at a rate of 4.3% every year. Select the correct equation that models the situation after t years.
Answers
Answer:
y=5,902,060*(.957)^t
Step-by-step explanation:
Since the original amount would be decreasing and it's an exponential one, hence the "every year", we can determine that it's an exponential decay equation.
The exponential delay equation is y=A*(1-r)^t. The y is the remaining amount, A is the original amount, r is the rate in decimal form, and t is for years. "1-r" is for decreasing rates and "1+r" is for increasing rates.
First thing we need to do is turn the rate, 4.3%, from a percentage to a decimal. You can do this by moving the decimal two places to the right, which gives you 0.043.
Now plug the numbers into the equation.
y=5,902,060*(1-0.043)^t
Simplify what's inside the parenthesis and get your final equation.
y=5,902,060*(.957)^t
Answer:
F = 5,902,060(0.957)[tex]F = 5,902,060(0.957)^{t}[/tex]
Step-by-step explanation:
Find the vertex, focus, directrix, and focal width of the parabola.
-1/16x^2 = y
a. Vertex: (0, 0); Focus: (0, -4); Directrix: y = 4; Focal width: 16
b. Vertex: (0, 0); Focus: (-8, 0); Directrix: x = 4; Focal width: 64
c. Vertex: (0, 0); Focus: (0, 4); Directrix: y = -4; Focal width: 4
d. Vertex: (0, 0); Focus: (0, -4); Directrix: y = 4; Focal width: 64
Answers
Answer:
Vertex: (0, 0); Focus: (0, -4); Directrix: y = 4; Focal width: 16 ⇒ answer (a)
Step-by-step explanation:
* Lets revise some facts about the parabola
- Standard form equation for a parabola of vertex at (0 , 0)
- If the equation is in the form x² = 4py, then
- The axis of symmetry is the y-axis, x = 0
- 4p equal to the coefficient of y in the given equation to
solve for p
- If p > 0, the parabola opens up.
- If p < 0, the parabola opens down.
- Use p to find the coordinates of the focus, (0 , p)
- Use p to find equation of the directri , y= − p
- Use p to find the endpoints of the focal diameter, (±2p , p)
* Now lets solve the problem
- The vertex of the parabola is (0 , 0)
∵ -1/16x² = y ⇒ multiply each side by -16
∴ x² = -16y
∴ 4p = -16 ⇒ ÷ 4 tbe both sides
∴ p = -4
∵ The focus is (0 , p)
∴ The focus is (0 , -4)
∵ The directrix is y = -p
∴ The directrix is y = -(-4) = 4 ⇒ y = 4
∵ The endpoints of the focal diameter, (±2p , p)
∴ The focal width = 2p - (-2p) = 4p
∴ The focal width = 4 × I-4I = 16
* Vertex: (0, 0); Focus: (0, -4); Directrix: y = 4; Focal width: 16
Answer:
A
Step-by-step explanation:
i just took the edg quiz
Please help me please
Answers
Answer:
60°
Step-by-step explanation:
The radius of the circle is given as 7 ( centre of circle to point C )
The other radius is also 7 ( from centre to point D)
CD = 7
The triangle is therefore equilateral ( all 3 sides = 7 )
The angles of an equilateral triangle are equal and measure 60°
Hence mCD = 60°
You usually buy a 5.4 ounce bottle of lotion. There is a new bottle that says it gives you 20% more free.
Use the drop-down menus to build an equation that could be used to find the size of the larger bottle, .
Answers
Answer: If you want to find out how much 20 percent of 5.4 is, you have to multiply, the equation would be
5.4 x .2 = 1.08, so it will give you 1.08 more
Step-by-step explanation:
Jordan made 3 cups of lemonade to sell at the dock street school back sale. She divided the lemonade into 2-ounces container. How many full containers were packaged for the sale?
Answers
Answer:
12
Step-by-step explanation:
There are 8 ounces in a cup
8*3=24
24/2(for 2 oz. containers)=12
Answer:
There were 12 full containers packaged for the sale.
Step By Step Explanation:
3 cups of lemonade equals 24 ounces. So take 24 divided by 2 and you get your answer of 12 full 2-ounce containers of lemonade packaged for the sale.
What is the function rule represented by the following mapping diagram?
y = -5x + 1
y = x + 1
y = -3x - 1
y = -4x
Answers
Answer:
i feel like the answer is y=-3x - 1 but at the same time i think its wrong.
Step-by-step explanation:
Answer:y=-3x - 1
Step-by-step explanation: