A solar oven uses a parabolic reflector to focus the sun's rays at a point 5 inches from the vertex of the
reflector (see figure). Write an equation for a cross section of the oven's reflector with its focus on the
positive y axis and its vertex at the origin.
Answers
Answer:
y = [tex]\frac{x^2}{20}[/tex]
The focus of the solar oven's reflector is (0,a)
Step-by-step explanation:
The missing figure( i.e diagram) from the question is attached below:
Now ; given that :
The focus of the sun's rays is at a point L = 5 inches away from the vertex of the reflector. Also the distance of the parabolic curve be a= L = 5
So the equation for a cross section of the oven's reflector with its focus on the
positive y axis and its vertex at the origin is expressed as:
x² = 4 L y
x² = 4 (5) y
x² = 20 y
y = [tex]\frac{x^2}{20}[/tex]
The focus of the solar oven's reflector is (0,a)
Related Questions
Find the equation of the line that is perpendicular to y = – 1 3 x + 2 and passes though the point (–5, 2)
A) y = 3x + 13
B) y = 3x + 17
C) y = –3x + 13
D) y = –3x + 17
Answers
Answer:
y = 3x + 17
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Two angles in a triangle measure 1020 and 670. What is the measure of the third angle?
O 110
O 78°
1130
1699
Answers
Answer:
A) 110°
Step-by-step explanation:
All triangles equal 180, so:
102 + 67 + x = 180
169 + x = 180
x = 11
Describe how the area of a rectangle will change if its width remains
constant but its length is doubled.
Answers
Answer:
its the 2nd one
Step-by-step explanation:
Choose the correct rule for the sequence: 2, 4, 8, 16,... *
Answers
Answer:
x2
1 x (N x 2)
2 x (1 x 2) = 4
2 x (4 x 2) = 16
Step-by-step explanation:
A prism has a length of 12 centimeters, height of 9 centimeters, and width of 2 centimeters.
The formula for volume of a rectangular prism is V = Bh.
The variable B stands for the .
area of the base / length/ width/ height
In this prism, B equals cm2.
2/9/12/24
The variable h stands for .
area of the base/length/height/width
In this prism, h equals cm.
2/9/12
The volume of the prism is cm3.
113/126/216/300
Answers
Volume of a Rectangular Prism:
V = lwh
Length: 12 centimeters
Height: 9 centimeters
Width: 2 centimeters
V = 12(9)2
V = 108 x 2
V = 216
V = 216cm^2
The volume of the prism is 216 cm³ with a length of 12 cm, a height of 9 cm, and a width of 2 cm. This is obtained by using the formula for the volume of a prism.
What is the formula for the volume of a prism?The volume of a prism is
V=B × h cm³
Where B is the base area of the prism and h is the height of the prism.
Calculating the volume for the given prism:For the given prism,
length l=12cm
width w=2cm and
height h=9cm
Calculating the base area:
Since the prism has length and width, it is a rectangular prism
Thus,
B = l × w sq.cm
Then, the volume of the prism becomes
V= l × w × h cm³
On substituting the values
V= 12 × 2 × 9
= 216 cm³
Therefore, the volume of the given prism is 216 cm³.
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Ahmed is riding the elevator in a building. The building has floors above and below ground level. Ahmed uses the expression below to describe his movement.
6 + (negative 8)
Which statement could describe Ahmed’s movement?
Answers
Final answer:
Ahmed's movement described by the expression 6 + (negative 8) suggests he moves from the sixth floor above ground level down to the second floor below ground level.
Explanation:
The expression Ahmed uses to describe his movement in the elevator is 6 + (negative 8). To understand this expression in the context of elevator movement, 6 could represent Ahmed starting on the sixth floor above ground level. The addition of negative 8 would signify moving 8 floors downward. Thus, the expression indicates that Ahmed moves from the sixth floor down to the second floor below ground level (since 6 - 8 equals -2). The negative result corresponds to floors below ground level. Therefore, the statement that could describe Ahmed's movement is: Ahmed moves from the sixth floor above ground level down to the second floor below ground level.
Find the critical value corresponding to a sample size of 3 and a confidence level of 95%.
7.378
0.0506
5.991
0.103
Answers
Answer:
0.103 is the correct answer give me brainliest pls
Step-by-step explanation:
Final answer:
To find the critical value for a sample size of 3 and a 95% confidence level, you use a statistical table with an alpha value of 0.05, obtaining 5.991 as the critical value.
Explanation:
The critical value corresponding to a sample size of 3 and a confidence level of 95% is 5.991.
To find this critical value, we use a standard statistical table where for a 95% confidence level, the alpha value (a) is 0.05. Look up a table of critical values for a significance level of 0.05 and a sample size of 3 to obtain 5.991 as the critical value for a two-tailed test.
-0.2=s+(-0.8)
can someone help me? Khan academy...
Answers
what is the awnser to x²=4/9
Answers
Answer:
x = ±2 /3
Step-by-step explanation:
x²=4/9
Take the square root of each side
sqrt(x²)=±sqrt(4/9)
We know sqrt( a/b) = sqrt(a) / sqrt(b)
x = ±sqrt(4/ sqrt(9)
x = ±2 /3
Mila has 7 stamps. Dante has 84 stamps.
Dante has how many times as many stamps as Mila? Enter the answer in the box.
Answers
Answer:
Dante has 12 times more stamps as Mila
Step-by-step explanation:
7 x 12 = 84
Answer:
12
Step-by-step explanation:
84 divided by 7 is 12
Name the values of the 4s in the number 3,441.
Answers
Answer:
the first 4's value in ''441" is 400 ( its in the hundreds place ) and the the second 4's value in ''441'' is 40 (its in the tens place)
Step-by-step explanation:
Find the surface area of the pyramid shown below. The base is a rectangle and the opposite
triangular faces are the same size and shape.
Answers
Answer:
SA = 397
Step-by-step explanation:
The area of the rectangle is L x W = 18 x 7 = 126
The area of the triangle[tex]\frac{1}{3}[/tex] face is
A = [tex]\frac{1}{2}[/tex]bh
A = [tex]\frac{1}{2}[/tex] 18 x 10
A = [tex]\frac{1}{2}[/tex] 180
A = 90
Since there are two triangles the same size we times by 2
90 x 2 = 180
The triangles on the left and right sides are two other sizes compared to the other two triangles
A = [tex]\frac{1}{2}[/tex]bh
A = [tex]\frac{1}{2}[/tex] 7 x 13
A = [tex]\frac{1}{2}[/tex] 91
A = 45.5
Since there are two triangles the same size we times by 2 again so it will be 91
Than we add them up
91 + 126 + 180 = 397
Sorry if its wrong
The ___ formula will give us the coordinates of the points of intersection of a line and a quadratic only when the value of the discriminant,
The ___ formula will give us the coordinates of the points of intersection of a line and a quadratic only when the value of the discriminant,
formula will give us the coordinates of the points of intersection of a line and a quadratic only when the value of the discriminant,
The _____ formula will give us the coordinates of the points of intersection of a line and a quadratic only when the value of the discriminant, is positive or zero.
A. Quadratic
B. No points
C. Conjugate
D. Division
Answers
Answer:
A. Quadratic
Step-by-step explanation:
your welcome and hope this helps
Final answer:
The Quadratic formula will give us the coordinates of the points of intersection of a line and a quadratic only when the value of the discriminant is positive or zero.
Explanation:
The Quadratic formula will give us the coordinates of the points of intersection of a line and a quadratic only when the value of the discriminant is positive or zero.
The quadratic formula is:
x = (-b ± √(b² -4ac)) / 2a
Where a, b, and c are the coefficients of the quadratic equation ax² + bx + c = 0.
The quadratic formula will give us the coordinates of the points of intersection of a line and a quadratic only when the value of the discriminant is positive or zero. The quadratic formula is derived from the standard form of a quadratic equation, which is ax² + bx + c = 0. To find the points of intersection between a line and a quadratic, we would substitute the y-component (or x-component, depending on the variable used) of the line equation into the quadratic equation and solve for the remaining variable using the quadratic formula.
2/7> b+5/7 what is “B”
Answers
Answer:
-3/7 > b
Step-by-step explanation:
2/7> b+5/7
Subtract 5/7 from each side
2/7-5/7> b+5/7-5/7
-3/7 > b
The officers of a high school senior class are planning to rent buses and vans for a class trip. Each bus can transport 80 students, requires 5
chaperones, and costs $1,400 to rent. Each van can transport 10 students requires 1 chaperone, and costs $100 to rent. Since there are 800 students
in the senior class that may be eligible to go on the trip, the officers must plan to accommodate at least 800 students. Since only 65 parents have
volunteered to serve as chaperones, the officers must plan to use at most 65 chaperones. How many vehicles of each type should the officers rent in
order to minimize the transportation costs? What are the minimal transportation costs?
The officers should rent
buses and
vans to minimize the transportation costs.
The minimal transportation costs are $1.
Answers
Answer:
this hard
Step-by-step explanation:
Please help me out! I have spent over 127 points on these circumference questions so far... :(
Anyone who is good at math, please go to my profile and answer my math questions! A lot of them are not/only halfway answered.
Answers
Answer:
The circumference of the green circle is about 138.23 meters.
The circumference of the blue circle is about 69.115 meters.
Step-by-step explanation:
Considering 22 m as the green circle radius and 11 m as the blue circle radius:
The circumference of the green circle is about:
[tex]C=2\pi r[/tex]
[tex]C=2\pi 22\\C=44\pi \\C=138.23 m[/tex]
The circumference of the blue circle is about:
[tex]C=2\pi r[/tex]
[tex]C=2\pi 11\\C=22\pi \\C=69.115 m[/tex]
9. Find the vertex of f(x) = –2x2 - 4x – 8
a. Vertex: (-1,-6) b. Vertex: (-6,-1) C. Vertex: (2,1)
d. Vertex: (1,6)
e. Vertex: (1,-6)
Answers
Answer:
A is the answer, (-1,-6) is the vertex.
Step-by-step explanation:
With any quadratic, the formula for the x coordinate of the vertex is -b/2a.
In this case it is -(-4) / 2(-2) = 4 / -4 = -1.
To find the y, simply substitute the x.
f(-1) = -2(-1)² – 4(-1) – 8 = -2 + 4 – 8 = 2 – 8 = -6
Which expression represents the volume, in cubic units, of the composite figure?
Answers
Answer:
11.17
Step-by-step explanation:
In a data set with a normal distribution, the mean is 59 and the standard deviation is 3.
Part A
About what percent of the data lie between 53 and 62?
A. 68%
B. 83.85%
C. 81.5%
D. 50%
Part B
Complete: About 95% of the data lie between
Answers
Answer:
a) [tex]P(53<X<62)=P(\frac{53-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{62-\mu}{\sigma})=P(\frac{53-59}{3}<Z<\frac{62-59}{3})=P(-2<z<2)[/tex]
[tex]P(-2<z<2)=P(z<2)-P(z<-2)[/tex]
[tex]P(-2<z<2)=P(z<2)-P(z<-2)=0.97725-0.02275=0.9545[/tex]
b) [tex]a=59 +1.96*3=64.88[/tex]
And for the other limit we have:
[tex]a=59 -1.96*3=53.12[/tex]
And we will have 95% of the values between (53.12, 64.88)
Step-by-step explanation:
Part a
Let X the random variable of interest of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(59,3)[/tex]
Where [tex]\mu=59[/tex] and [tex]\sigma=3[/tex]
We are interested on this probability :
[tex]P(53<X<62)[/tex]
And we can solve this using the z score:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Using the last formula we got:
[tex]P(53<X<62)=P(\frac{53-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{62-\mu}{\sigma})=P(\frac{53-59}{3}<Z<\frac{62-59}{3})=P(-2<z<2)[/tex]
And we can find this probability with this difference:
[tex]P(-2<z<2)=P(z<2)-P(z<-2)[/tex]
And uing the normal standard distribution or excel we got:
[tex]P(-2<z<2)=P(z<2)-P(z<-2)=0.97725-0.02275=0.9545[/tex]
Part b
For this part we want to find a value a, such that we satisfy this condition:
[tex]P(X>a)=0.025[/tex] (a)
[tex]P(X<a)=0.975[/tex] (b)
As we can see on the figure attached the z value that satisfy the condition with 0.95 of the area on the left and 0.05 of the area on the right it's z=1.96.
If we use condition (b) from previous we have this:
[tex]P(X<a)=P(\frac{X-\mu}{\sigma}<\frac{a-\mu}{\sigma})=0.975[/tex]
[tex]P(z<\frac{a-\mu}{\sigma})=0.975[/tex]
But we know which value of z satisfy the previous equation so then we can do this:
[tex]z=1.96<\frac{a-59}{3}[/tex]
And if we solve for a we got
[tex]a=59 +1.96*3=64.88[/tex]
And for the other limit we have:
[tex]a=59 -1.96*3=53.12[/tex]
And we will have 95% of the values between (53.12, 64.88)
In a normal distribution with mean 59 and standard deviation 3, approximately 81.85% of the data lie between 53 and 62. And about 95% of the data lie between 53 and 65, which is two standard deviations from the mean.
Explanation:In a normal distribution, about 68% of the data lie within one standard deviation of the mean, about 95% lie within two standard deviations, and about 99.7% within three standard deviations.
Part A:
The range from 53 to 62 in this case is from -2 standard deviations from the mean (56) to +1 standard deviation (62). Looking at the empirical rule, we find that about 34.13% of data fall between the mean and -1 standard deviation, and 13.59% fall between -1 and -2 standard deviations. Similarly, about 34.13% of the data fall between the mean and +1 standard deviation. Therefore, the total percentage of data lying between 53 and 62 would be
34.13% + 13.59% + 34.13% = 81.85%, so option B is the closest.
Part B:
About 95% of the data lie between two standard deviations from the mean. Therefore, you would add and subtract two times the standard deviation from the mean, which would yield 59 - 2(3) = 53 and 59 + 2(3) = 65. Thus, about 95% of the data lie between 53 and 65.
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1. Without solving, identify whether this equation has a solution that is positive, negative, or zero:
3x – 5 = -3
2. Solve the equation.
x - 5(x - 1) = x - (2x - 3)
Answers
Answer:
3
Step-by-step explanation:
The equation will have a positive solution and the value of x will be 2/3.
What is an equation?A mathematical statement that shows that two mathematical expressions are equal.
Given is an equation, x - 5(x - 1) = x - (2x - 3)
On solving,
x-5x+5 = x-2x+3
3x = 2
x = 2/3
Hence, The equation will have a positive solution and the value of x will be 2/3.
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What is the solution set of 6x2-24=0
Answers
Answer:
x=2
Step-by-step explanation:
Answer:
Step-by-step explanation:
What is the new equation when you distribute the 2?
2(6x+14)=40
Answers
Answer:
12x+28 = 40
Step-by-step explanation:
2(6x+14)=40
Distribute the 2
2*6x +2*14 = 40
12x+28 = 40
PLEASE HELP!! WILL GIVE BRAINLIEST !!!
Which of the following is true of the data represented by the box plot?
box plot with point at 15, min at 17, Q1 at 51, median at 65, Q3 at 74, max at 90
A) If the outlier is included in the data, the median would not significantly change.
B) If the outlier is included in the data, the mean would increase.
C) If the outlier is included in the data, the box plot would be significantly skewed.
D) If the outlier is included in the data, the length of the tails would change significantly.
Answers
Answer:
the outlier is the point at 15
the data is skewed to the bottom because the values below the median are far more spread out; there are more extreme values that are far below the median than above the median.
Step-by-step explanation:
A) If the outlier is included in the data, the median would not significantly change.
Box Plot is a pictorial way of denoting data's distribution on the basis of Quartile 1, Quartile 3, Minimum, Median and Maximum
Outliers are the data observations or points, lying at huge significant difference (distance) from other concentrated data observation points.
A data value below the Box Plot Minimum, or above the Box Plot Maximum is an Outlier.Median is a Positional average, the mid point of data. It divides the data into two equal halves, 50% below it & 50% above it.
Median is not effected by extreme values like Outliers. So, inclusion of outliers doesn't significantly change Median.Mean is an Arithmetic Average. It is effected by extreme values like outliers. However, in this case of presence of Lower Outlier, the mean would decrease rather than increasing.
Skewness or Tail in the data denotes concentration of values in either (lower or higher side). It is not related to outliers.
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Triangle ABC is similar to triangle DEF. What is EF?
Answers
Answer:
24
Step-by-step explanation:
First, divide 30.4 by 19 to get your factor.
You get 1.6
Then times 1.6 by 15 to get 24 for EF.
*WILL GIVE BRAINLIEST*
A typical bone is made up
of which of these three
parts?
A. Dense outer layer, spongy bone,
marrow
B. Soft outer layer, spongy bone, marrow
C. Marrow, dense inner layer, dense outer
layer
D. Dense outer layer, spongy bone,
muscle tissue
which one plz help :(
Answers
Answer:
d. Dense outer layer, spongy bone,
muscle tissue
Step-by-step explanation:
it makes sense
Someone please help
Answers
1.20 Euro
BruhBruhBruh
Answer:
£1.20
Step-by-step explanation:
2/5 on magazine and 1/3 on dance lesson then we need to add these together by converting them to same fraction multiples.
2/5 x 3 = 6/15
1/3 x 5 = 5/15
6/15 +5/15 = 11/15
11/15 of 4.50 is found by division of the multiplier (the denominator)= 15
4.50/15 = 0.3 nb/ 0.3 = 1/15 of the whole 11 we search for
We then can multiply 0.3 x 11 as we have 1/15 and want 11/15
0.3 x 11 = 3.3
£3.30 = value of spending on dance lesson and magazine
0.3 x 4 = 1.2 = value of left over money
£1.20 converted to monetary
2(b+c) (use the distributive property)
Answers
Answer:
2b + 2c
Step-by-step explanation:
when distributed, the 2 get multiplied by the b and the c, so you'd have 2b + 2c.
Answer:
Answer is 2b + 2c
Step-by-step explanation:
2(b+c) you multiply 2 with b and then with c
write the expressions
the prouduct of r and 15
Answers
Answer:
Can you provide a screenshot? I could help you better with a visual.
Answer: i believe it is 15n
Step-by-step explanation
what is -3+1/3=?
what is 5+6+7x+3=
Answers
Answer:
-3+1/3=-8/3 or-2.6, 5+6+7x+3=7x+14
Step-by-step explanation:
Answer:
-3+1/3= -2.66666666667
Step-by-step explanation:
How much would 300 invested at 5% interest compound monthly be worth after 8 years
Answers
The total compound interest is $147.18