Answers
The equation of the parabola that models the cross section of the reflector is: y = (1/32)x².
To model a cross section of the reflector as a parabola that opens upward and has its vertex at the origin,
We can use the standard equation for a parabola in vertex form:
y = a(x - h)² + k
In this equation, (h, k) represents the coordinates of the vertex.
Since we want the vertex to be at the origin (0, 0), the equation becomes:
y = ax²
To determine the value of 'a,' we can use the given information that the bulb is located 8 inches from the vertex.
Since the bulb is located at the focus, we know that the distance from the vertex to the focus (f) is also 8 inches.
In a parabola, the distance from the vertex to the focus is given by the formula f = 1/(4a).
Plugging in the value of f (8) into the formula, we can solve for 'a':
8 = 1/(4a)
32a = 1
a = 1/32
Therefore, the equation of the parabola that models the cross section of the reflector is: y = (1/32)x²
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Related Questions
PLEASE HELPPP IM CONFUSEDDDD
Answers
Answer: C: (-4,-3)
Step-by-step explanation:
You have the correct answer selected!
The solution of a system of equations is where the graphs of the two lines intersect. we can read that point to be (-4,-3), so thats the answer :)
The Question is in the Picture, use the Pythagorean theorem to solve and show your work please
Answers
Answer:
y=8
Step-by-step explanation:
Complete the square to put
y=3x²-24x + 56 in vertex form.
a) y = 3(x-8)² +4
b) y=3(x-7)² +5
c) y = 3(x-6)² +6
d) y = 3(x - 5)² +7
e) y = 3(x-4)² +8
Answers
Solve for X
20x+30
28x-10
Answers
Answer:
[tex]\huge\boxed{\sf x = 5}[/tex]
Step-by-step explanation:
Statement:Corresponding angles are equal.Solution:20x + 30 = 28x - 10 (Corresponding angles)
Add 10 to both sides20x + 30 + 10 = 28x
20x + 40 = 28x
Subtract 20x from both sides40 = 28x - 20x
40 = 8x
Divide both sides by 85 = x
OR
x = 5[tex]\rule[225]{225}{2}[/tex]
Define the term inflation
Answers
Answer: Inflation is the rise in general level of prices which is determined by the Consumer Price Index (CPI).
1.The volume of a triangular prism is 204cm3 . If its height is 17cm, then find the area of its base.
Answers
Answer:
12 cm ^2
Step-by-step explanation:
Using the formula
V=ABh
Solving forAB
AB=V
h=204
17=12cm²
i need help can someone help me
Answers
The value of the side labelled x is equal to 3.8 to the nearest tenth using the trigonometric ratio of sine.
What is trigonometric ratios?The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.
The basic trigonometric ratios includes;
sine, cosine and tangent.
Considering the sine of angle 41°
sin 41° = 2.5/x {opposite/hypotenuse}
x = 2.5/sin 41° {cross multiplication}
x = 3.8106
Therefore, the value of the side labelled x is equal to 3.8 to the nearest tenth using the trigonometric ratio of sine.
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need help with this please
Answers
The number that belongs in the green box is given as follows:
D. 2.
How to interpret the problem?A quadratic function is given according to the following rule:
y = ax² + bx + c
The solutions are given as follows:
[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a}[/tex][tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a}[/tex]In which the discriminant is given as follows:
[tex]\Delta = b^2 - 4ac[/tex]
The number that goes into the green box is then given as follows:
2a = 2(1) = 2.
Meaning that option D is the correct option in the context of this problem.
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In the following probability distribution, the random variable
represents the number of activities a parent of a 6th-8th grade student is involved in.
Please round to 2 decimal places for a-c, 3 decimal places for the probability in part d.
X 0 1 2 3 4
P(X) 0.053 0.117 0.258 0.312 0.26
a) Compute and the mean,
, of the random variable
.
2.610
Correct
b) Compute the variance,
, of the random variable
.
c) Compute the standard deviation,
, of the random variable
.
1.14
Correct
d) What is the probability that a randomly selected student has a parent involved in 4 activities?
Answers
a) The mean of the random variable is 2.610 (rounded to 2 decimal places).
b) The variance of the random variable is 1.880 (rounded to 3 decimal places).
c) The standard deviation of the random variable is 1.372 (rounded to 3 decimal places).
d) The probability that a randomly selected student has a parent involved in 4 activities is 0.260 (rounded to 3 decimal places).
To compute the variance of the random variable, we need to calculate the squared deviation of each value from the mean, weighted by their respective probabilities, and then sum them up.
b) Variance [tex](\sigma^2)[/tex] of the random variable:
Variance is given by the formula[tex]Var(X) = \sum [(X - \mu)^2 \times P(X)],[/tex] where X represents the values of the random variable, μ is the mean, and P(X) is the probability.
Using the given data:
X: 0 1 2 3 4
P(X): 0.053 0.117 0.258 0.312 0.26
μ (mean): 2.610
Calculating the squared deviations for each value:
[tex](0 - 2.610)^2 \times 0.053 = 14.152[/tex]
[tex](1 - 2.610)^2 \times 0.117 = 0.291[/tex]
[tex](2 - 2.610)^2 \times 0.258 = 0.148[/tex]
[tex](3 - 2.610)^2 \times 0.312 = 0.122[/tex]
[tex](4 - 2.610)^2 \times 0.26 = 1.429[/tex]
Summing up the squared deviations:
Var(X) = 14.152 + 0.291 + 0.148 + 0.122 + 1.429 = 16.142
Therefore, the variance of the random variable is 16.142.
c) Standard deviation (σ) of the random variable:
The standard deviation is the square root of the variance.
Taking the square root of the variance calculated above:
Standard deviation (σ) = √(16.142) ≈ 4.020 (rounded to 3 decimal places)
d) Probability of a randomly selected student having a parent involved in 4 activities:
The probability of a specific value occurring in a discrete probability distribution is given by the corresponding probability value.
From the given data:
P(X = 4) = 0.26
Therefore, the probability that a randomly selected student has a parent involved in 4 activities is 0.26 (rounded to 3 decimal places).
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i need help can everyone please help me
Answers
Since AC is the angle bisector of ∠BAD, the flowchart proof should be completed as follows;
Statement Reason
AC bisects ∠BAD Given
∠BAC ≅ ∠DAC Definition of an angle bisector.
∠BCA ≅ ∠DCA Congruent angles of a triangle (SAS).
AC ≅ AC Reflexive property
ΔABC ≅ ΔADC AAS postulate
What is an angle bisector?In Mathematics and Geometry, an angle bisector can be defined as a type of line, ray, or segment, that typically bisects or divides a line segment exactly into two (2) equal and congruent angles.
By applying the angle bisector theorem to the given triangle, we have the following statements and justifications:
AC bisects ∠BAD Given
∠BAC ≅ ∠DAC Definition of an angle bisector.
Based on side, angle, side (SA) and congruent angles of a triangle (SAS), we can reasonably infer and logically deduce that ∠BCA is congruent to ∠DCA i.e ∠BCA ≅ ∠DCA.
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Write the word
sentence as an
inequality.
A number w plus 4.6
is more than 6.
An inequality is answer:
Answers
The inequality that represents the number sentence is given as follows:
w + 4.6 > 6.
What are the inequality symbols?The four most common inequality symbols, and how to interpret them, are presented as follows:
> x: the amount is greater than x -> the number is to the right of x with an open dot at the number line. On the coordinate plane, these are the points above the dashed line y = x.< x: the amount is less than x. -> the number is to the left of x with an open dot at the number line. On the coordinate plane, these are the points below the dashed line y = x.≥ x: the amount is at least x. -> the number is to the right of x with a closed dot at the number line. On the coordinate plane, these are the points above the continuous line y = x.≤ the amount is at most x. -> the number is to the left of x with a closed dot at the number line. On the coordinate plane, these are the points below the continuous line y = x.A number w plus 4.6 is represented as follows:
w + 4.6.
The amount is more than 6, hence the inequality is given as follows:
w + 4.6 > 6.
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How do you find the length of an arc expressed in terms of pi?
Answers
Ratios are often represented by the symbol. For example, 5 : 4 might mean 5 eggs are needed for every 4 batches of cookies. Select all of the ratios that are equivalent to the ratio 12:3. 6:1 1:4 4:1 246 15:6 120 : 30
Answers
The ratios that are equivalent to the ratio 12:3 are 4:1 and 120:30.
We have,
To determine the ratios that are equivalent to the ratio 12:3, we need to find ratios that have the same value when simplified.
The ratio 12:3 can be simplified by dividing both numbers by their greatest common divisor (GCD), which in this case is 3.
Dividing 12 by 3 gives us 4, and dividing 3 by 3 gives us 1. Therefore, the simplified ratio is 4:1.
Now let's check the given options:
6:1 - This ratio is not equivalent because it is different from the simplified ratio 4:1.
1:4 - This ratio is not equivalent because the order of the numbers is reversed, and it is different from the simplified ratio 4:1.
4:1 - This ratio is equivalent to the original ratio 12:3. When simplified, both ratios result in 4:1.
246 - This is not a ratio and cannot be compared to the original ratio 12:3.
15:6 - This ratio is not equivalent because it is different from the simplified ratio 4:1.
120:30 - This ratio can be simplified by dividing both numbers by their GCD, which is 30.
Dividing 120 by 30 gives us 4, and dividing 30 by 30 gives us 1.
Therefore, the simplified ratio is 4:1, which is equivalent to the original ratio 12:3.
Thus,
The ratios that are equivalent to the ratio 12:3 are 4:1 and 120:30.
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Find the equation of the line.
Use exact numbers.
Answers
Answer:
y = 3x + 3
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]
with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (0, 3) ← 2 points on the line
m = [tex]\frac{3-0}{0-(-1)}[/tex] = [tex]\frac{3}{0+1}[/tex] = [tex]\frac{3}{1}[/tex] = 3
the line crosses the y- axis at (0, 3 ) ⇒ c = 3
y = 3x + 3 ← equation of line
Write the equation of the hyperbola
Answers
Using the center and distance between co-vertex and center, the equation of the hyperbola is written below
[tex]\frac{(y + 3)^2}{49} - \frac{(x - 10)^2}{144} = 1[/tex]
What is the equation of hyperbolaA hyperbola, in analytic geometry, is a conic section that is formed when a plane intersects a double right circular cone at an angle such that both halves of the cone are intersected.
The equation of hyperbola is given as;
[tex]\frac{(y - k)^2}{a^2} - \frac{(x - h)^2}{b^2} = 1[/tex]
where (h,k) is the center of the hyperbola, a is the distance between a vertex and the center, and b is the distance between a co-vertex and the center.
In this case, the center is (10,−3), a=7, and b=12. Therefore, the equation of the hyperbola is
The equation of the hyperbola is;
[tex]\frac{(y + 3)^2}{49} - \frac{(x - 10)^2}{144} = 1[/tex]
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PLEASE HELP
Which of the following graphs shows an angle that would have an equivalent cosine ratio to the graph shown?
Answers
Answer: 150 deg
Step-by-step explanation:
cosine is negative in quadrants 2 and 3. the current angle, 210, is in quad 3. It will have an equal cosine value in quad 2.
that angle will be -210 degrees. in positive terms that is 360-210 = 150 degrees.
thus the answer which shows 150 degrees is correct.
in general:
[tex]cos(x) = cos(-x)[/tex]
The accompanying diagram shows a revolving door with three panels, each of which is 4 feet long. What is the width, w, of the opening between x and y, to the nearest tenth of a foot?
Answers
The width, w, of the opening between x and y, is 6.9 ft.
We have,
From the diagram,
We have the radius of the circle and the angle subtended by the chord at the center of the circle.
So,
We can also use the formula.
= 2 x radius x sin(angle/2)
This is the length of the chord.
Now,
radius = 4 ft
angle = 360/3 = 120
Substituting the values.
= 2 x radius x sin(angle/2)
= 2 x 4 x sin (120/2)
= 2 x 4 x sin 60
= 2 x 4 x √3/2
= 4 x √3
= 4 x 1.732
= 6.928
Rounding to the nearest tenth.
= 6.9 ft
Thus,
The width, w, of the opening between x and y, is 6.9 ft.
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p: 10 > 7 q: 10 > 5
p →q
F F → T
T F → F
F T → T
T T → T
Answers
Answer: if it's true that 10 > 7 (P), then it's also true that 10 > 5 (Q).
Step-by-step explanation: In the context of logic and truth tables, p → q can be read as "if p then q." You've provided the truth values for the combinations of p and q, which I'll summarize here:
If p and q are both False (F), then p → q is True (T).
If p is True (T) and q is False (F), then p → q is False (F).
If p is False (F) and q is True (T), then p → q is True (T).
If p and q are both True (T), then p → q is True (T).
Given your propositions:
P: 10 > 7
Q: 10 > 5
P is True because 10 is indeed greater than 7. Q is also True because 10 is greater than 5.
Therefore, we're in the fourth case of your truth table: both p and q are True, so p → q is also True.
sin( 3pi/4 ) =
O A. 1/2
OB. -√2/2
O C. √3/2
O D. √2/2
Answers
Answer:
sin(3pi/4 ) = -√2/2
So, B.
I really need help doing this. please help me.
Answers
The bisector angle is angle PQT which is equal to angle RQT.
What is angle bisector?Angle bisector or a bisector angle is a type of angle obtained after dividing the initial angle into two equal parts.
The bisected angle can be obtained using a pair of compass and a pencil attached to it.
To bisect the given angle RQP; we will take the following steps;
place the compass on exactly point Qexpand the radius of the compass such that the pencil attached to the compass will be in between R and P.strike an arc with the pencil clock wisestrike another arc with the pencil anti clock wise such that the two arc intersects.draw a line from point Q to intersect the two arcs.label the point of intersection of the two arcs Tangle PQT is equal to angle RQTLearn more about bisector angles here: https://brainly.com/question/24334771
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If tanA = 60/11 and sinB = 45/53 and angles A and B are in Quadrant I, find the value of tan(A-B)
Answers
Based on the information, it should be noted that the value of tan(A-B) is 234/583.
How to calculate the valueGiven:
tanA = 60/11
sinB = 45/53
A and B are in Quadrant I
We can use the following identity to find tan(A-B):
tan(A-B) = (tanA - tanB)/(1 + tanA*tanB)
Substituting the given values, we get:
tan(A-B) = (60/11 - 45/53)/(1 + (60/11)*(45/53))
= (15/53)/(295/583)
= 234/583
Therefore, the value of tan(A-B) is 234/583.
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Quentin deposited $1,264 into a savings account that earns 2.75% simple interest annually. What will Quentin’s account balance be at the end of 2.5 years? Assume he makes no additional deposits during that time period.
Answers
Answer:
I love math
Step-by-step explanation:
The formula for simple interest is:
I = P * r * t
where:
I = interest earned
P = principal amount
r = interest rate (as a decimal)
t = time (in years)
In this case, we know that:
P = $1,264
r = 2.75% = 0.0275 (as a decimal)
t = 2.5 years
So, we can plug in these values and solve for I:
I = 1,264 * 0.0275 * 2.5 = $87.55
Therefore, the interest earned over 2.5 years is $87.55. To find the ending balance, we need to add the interest earned to the principal:
Ending balance = $1,264 + $87.55 = $1,351.55
So, Quentin's account balance will be $1,351.55 at the end of 2.5 years.
I WILL GIVE BRAINLIEST, square root of x, find the domain of x
Answers
The domain for the square root function is the set of all whole numbers
Calculating the domain of the square root functionFrom the question, we have the following parameters that can be used in our computation:
Function type = square root function
Equation: square root of x
This means that
f(x) = √x
The domain for x in the function is the set of input values the function can take
In this case, the square root function can take any whole number as its input
This means that the domain for f(x) is the set of all whole number
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Kendra's Tea Shop has caffeinated tea and decaffeinated tea. The tea shop served 87 caffeinated teas and 13 decaffeinated teas. What percentage of the teas served were caffeinated?
Answers
Answer:
Kendra's Tea Shop served 87 caffeinated teas and 13 decaffeinated teas. This means that 87 out of 100 teas served were caffeinated. Therefore, 87% of the teas served were caffeinated.
Sketch the region enclosed by
y
=
5
x
and
y
=
8
x
2
. Find the area of the region.
Answers
Answer:
125/384 ≈ 0.32552
Step-by-step explanation:
You want the area between the curves y = 5x and y = 8x².
AreaThe difference between the curves is ...
f(x) = 5x -8x² = x(5 -8x)
This difference is zero when ...
x = 0
5 -8x = 0 ⇒ x = 5/8
The area will be the integral of f(x) with the limits 0 and 5/8:
[tex]\displaystyle \text{area}=\int_0^\frac{5}{8}{(5x-8x^2)}\,dx=\dfrac{5}{2}\cdot\left(\dfrac{5}{8}\right)^2-\dfrac{8}{3}\cdot\left(\dfrac{5}{8}\right)^3\\\\\\\text{area}=\left(\dfrac{5}{8}\right)^2\left(\dfrac{5}{2}-\dfrac{8}{3}\cdot\dfrac{5}{8}\right)=\dfrac{25}{64}\cdot\dfrac{5}{6}=\boxed{\dfrac{125}{384}}[/tex]
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An isosceles right triangle has a third side measurement of 25 inches and a perimeter of 85 inches. The leg of the dilated triangle measures 6 inches. What is the perimeter of the dilated triangle?
Answers
Given that the third side of the original triangle measures 25 inches, we can set up the following equation based on the perimeter:
x + x + 25 = 85
Simplifying the equation:
2x + 25 = 85
Subtracting 25 from both sides:
2x = 60
Dividing both sides by 2:
x = 30
So, the length of each leg of the original triangle is 30 inches.
Now, let's consider the dilated triangle. We are told that the leg of the dilated triangle measures 6 inches. Let's assume the scale factor of the dilation is "k."
The length of each leg of the dilated triangle can be found by multiplying the length of the corresponding leg of the original triangle by the scale factor:
Leg of dilated triangle = k * Leg of original triangle
Leg of dilated triangle = k * 30
Given that the leg of the dilated triangle measures 6 inches, we can set up the following equation:
k * 30 = 6
Dividing both sides by 30:
k = 6/30
Simplifying:
k = 1/5
So, the scale factor of the dilation is 1/5.
Now, to find the perimeter of the dilated triangle, we need to multiply the length of each side of the original triangle by the scale factor and sum them up:
Perimeter of dilated triangle = 2 * (k * 30) + k * 25
Plugging in the values:
Perimeter of dilated triangle = 2 * (1/5 * 30) + 1/5 * 25
Simplifying:
Perimeter of dilated triangle = 2 * 6 + 5
Perimeter of dilated triangle = 12 + 5
Perimeter of dilated triangle = 17 inches
Therefore, the perimeter of the dilated triangle is 17 inches.
Name the quadrant in which angle 0 must lie for the following to be true.
Answers
Answer:
d
Step-by-step explanation:
f+90+42=180 what is the answer of this
Answers
Answer:
hello
the answer is:
f = 180 - 42 - 90 = 48
The PTO is selling raffle tickets to raise money for classroom supplies. There is 1 winning ticket out of the 150 tickets sold. The winner gets a prize worth $200.
Round your answers to the nearest cent.
Make a probability distribution table and find the expected winnings of one raffle ticket. $?
If a raffle ticket costs $4, what is the expected profit or loss of one raffle ticket? (Enter a negative number for a loss) $?
Answers
Answer:
Expected winnings = $1.33
Expected profit or loss = -$2.67
Step-by-step explanation:
Winning Probability Prize Value
Yes 1/150 $200
No 149/150 $0
Expected winnings of one raffle ticket:
Expected winnings = (Probability of winning x Prize value) + (Probability of losing x Prize value)
Expected winnings = (1/150 x $200) + (149/150 x $0)
Expected winnings = $1.33
If a raffle ticket costs $4, the expected profit or loss of one raffle ticket can be calculated as:
Expected profit or loss = Expected winnings - Cost of ticket
Expected profit or loss = $1.33 - $4
Expected profit or loss = -$2.67
A spherical boulder is 28 feet in diameter and weighs almost 8 tons. Find the volume Use 3.14 for pi
Answers
Answer:
V = (4/3) × 3.14 × 14³ = 11,310.08 cubic feet
Work Shown:
d = diameter = 28
r = radius = d/2 = 28/2 = 14
V = volume of a sphere
V = (4/3)*pi*r^3
V = (4/3)*3.14*(14)^3
V = 11,488.2133 cubic feet approximately
The info "weighs almost 8 tons" is never used. It is likely an intended distraction. All we need is the radius of the sphere to get its volume.