Answer:
7. 3/7
8. 5/7
9. 1/7
10. 6/7
11. 5/7
12. 4/7
Here is a list of numbers: 8.3, 3.2, 5.3, 8.5, 9.2, 2.9, 4.7, 7.6, 7.8 State the median. Give your answer as a decimal.
regarded as likely, probable, or certain.
Probable and certain both speak about something that may (or may not) happen in the future, but probable and possible speak about future possibilities in different ways.
What is Probable?‘Probable’ is high up on the scale of probability. If something is probable, then there is a high chance that something will happen. We can imagine that ‘probable’ is around 80% and up on the scale of probability.
If something is possible, it doesn’t mean it’s probable. However, if something is probable then it’s possible too. And if this confuses you then you’re probably in the right place.
Probable and certain are both on a scale of probability. Probability is the level of possibility or chance that something will happen or will be true in the present or future.
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Find a polar equation for the curve represented by the given Cartesian equation. x2+y2=25. x2+y2=−8y. y=√3x
The polar equation for this curve is: theta = pi/3 (or any angle that satisfies tan(theta) = sqrt(3))
To find the polar equation for the curve represented by the given Cartesian equations, we can use the conversion formulas between Cartesian and polar coordinates.
\(x^2 + y^2 = 25:\)
In polar coordinates, the conversion formulas are:
x = r cos(theta)
y = r sin(theta)
Substituting these values into the equation \(x^2 + y^2 = 25:\)
\((r cos(theta))^2 + (r sin(theta))^2 = 25\)
\(r^2 (cos^2(theta) + sin^2(theta)) = 25\)
\(r^2 = 25\)
The polar equation for this curve is simply:
r = 5
\(x^2 + y^2 = -8y:\)
In polar coordinates:
x = r cos(theta)
y = r sin(theta)
Substituting these values into the equation \(x^2 + y^2 = -8y:\)
\((r cos(theta))^2 + (r sin(theta))^2 = -8(r sin(theta))\)
\(r^2 (cos^2(theta) + sin^2(theta)) = -8r sin(theta)\)
\(r^2 = -8r sin(theta)\)
The polar equation for this curve is:
r = -8 sin(theta)
y = sqrt(3) x:
In polar coordinates:
x = r cos(theta)
y = r sin(theta)
Substituting these values into the equation y = sqrt(3) x:
r sin(theta) = sqrt(3) (r cos(theta))
r sin(theta) = sqrt(3) r cos(theta)
tan(theta) = sqrt(3)
The polar equation for this curve is:
theta = pi/3 (or any angle that satisfies tan(theta) = sqrt(3))
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A right triangle has two legs that measure b=4 and a=
✓ 84 , how long is the hypotenuse?
Answer:
Sides: a = 9.165 b = 4 c = 10
Step-by-step explanation:
Is that check mark supposed to be square root?
Answer:
\((4^{2} +(\sqrt{84} ^{2} )\\=100\)
Step-by-step explanation:
1. The cost of buying some books is partly constant and partly varies with the number of books bought. The cost is #4800 when 20 books are bought and #8000 when 40 are bought. Find the cost when 1000 books are bought
Answer:
Step-by-step explanation:
let the cost based on number of book bought be x and the constant be c:
4800 = 20x + c
8000 = 40x + c
c is common in both equations:
c =4800-20x
c = 8000-40x
equate the two:
4800-20x = 8000 - 40x
20x = 3200
x = 160
and c = 4800-20*160
c = 1600
Cost of 1000 books:
160*1000 + 1600
= 161600
determine the domain of the relation given by the graph below. enter you answer within braces { }.
The relation has a domain of { x | -4 ≤ x ≤ 4 }.
How do you determine the relation's domain?The domain is the set of all "x" values, whereas the range is the set of all "y" values in an ordered pair. Remember that the following symbols are used to denote ordered pairs: (x, y). reviewing a set of matched pairings in order.
Domain formula: What is it?The set of all possible inputs is the domain of a function. For instance, all real integers other than x=0 are in the domain of f(x)=x2 and g(x)=1/x, respectively.
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2.4 An experiment involves tossing a pair of dice, one green and one red, and recording the numbers that come up. If x equals the outcome on the green die and y the outcome on the red die, describe the sample space S (a) by listing the elements (x,y); (b) by using the rule method. 2.8 For the sample space of Exercise 2.4, (a) list the elements corresponding to the event A that the sum is greater than 8 ; (b) list the elements corresponding to the event B that a 2 occurs on either die; (c) list the elements corresponding to the event C that a number greater than 4 comes up on the green die; (d) list the elements corresponding to the event A∩C; (e) list the elements corresponding to the event A∩B; (f) list the elements corresponding to the event B∩C; (g) construct a Venn diagram to illustrate the intersections and unions of the events A,B, and C.
The sample space for the experiment of tossing a pair of dice consists of all possible outcomes of the two dice rolls. Using a rule method, we can represent the sample space as S = {(1,1), (1,2), (1,3), ..., (6,5), (6,6)}.
(a) The event A corresponds to the sum of the outcomes being greater than 8. The elements of event A are (3,6), (4,5), (4,6), (5,4), (5,5), (5,6), (6,3), (6,4), (6,5), (6,6).
(b) The event B corresponds to a 2 occurring on either die. The elements of event B are (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (1,2), (3,2), (4,2), (5,2), (6,2).
(c) The event C corresponds to a number greater than 4 appearing on the green die. The elements of event C are (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6).
(d) The event A∩C corresponds to the outcomes where both the sum is greater than 8 and a number greater than 4 appears on the green die. The elements of event A∩C are (5,4), (5,5), (5,6), (6,3), (6,4), (6,5), (6,6).
(e) The event A∩B corresponds to the outcomes where both the sum is greater than 8 and a 2 occurs on either die. There are no elements in this event.
(f) The event B∩C corresponds to the outcomes where both a 2 occurs on either die and a number greater than 4 appears on the green die. The elements of event B∩C are (5,2), (6,2).
(g) The Venn diagram illustrating the intersections and unions of the events A, B, and C would have three overlapping circles representing each event. The area where all three circles intersect represents the event A∩B∩C, which is empty in this case. The area where circles A and C intersect represents the event A∩C, and the area where circles B and C intersect represents the event B∩C. The unions of the events can also be represented by the combinations of overlapping areas.
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2.4
(a) Sample space S: {(1, 1), (1, 2), ... (6, 5), (6, 6)}
(b) Rule method: S = {(x, y) | x, y ∈ {1, 2, 3, 4, 5, 6}}
2.8
(a) A: {(3, 6), (4, 5), ... (6, 6)}
(b) B: {(1, 2), (2, 1), (2, 2)}
(c) C: {(5, 1), (5, 2), ... (6, 6)}
(d) A∩C: {(5, 4), ... (6, 6)}
(e) A∩B: {}
(f) B∩C: {}
2.4
(a) Sample space S by listing the elements (x, y):
S = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6),
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}
(b) Sample space S using the rule method:
S = {(x, y) | x, y ∈ {1, 2, 3, 4, 5, 6}}
2.8
(a) Elements corresponding to event A (the sum is greater than 8):
A = {(3, 6), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 3), (6, 4), (6, 5), (6, 6)}
(b) Elements corresponding to event B (a 2 occurs on either die):
B = {(1, 2), (2, 1), (2, 2)}
(c) Elements corresponding to event C (a number greater than 4 on the green die):
C = {(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6),
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}
(d) Elements corresponding to event A∩C:
A∩C = {(5, 4), (5, 5), (5, 6), (6, 3), (6, 4), (6, 5), (6, 6)}
(e) Elements corresponding to event A∩B:
A∩B = {} (No common elements between A and B)
(f) Elements corresponding to event B∩C:
B∩C = {} (No common elements between B and C)
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10. APPLICATION Inspector 47 at the Zap battery plant
keeps a record of which AA batteries she finds defective.
Although the battery numbers at right do not make an
exact sequence, she thinks they are close to an arithmetic
sequence
a. Write a recursive formula for an arithmetic sequence
that estimates which batteries are defective. Explain
your reasoning
b. Predict the numbers of the next five defective batteries.
c. How many batteries in 100,000 will be defective?
Defective
Batteries
255, 500, 773
998, 1227, 1510,
1721, 2010
To prepare for a bike race, rex rides his bike for 13 miles each day for 5 days. the app he uses only tracks distance in kilometers. if 1 mile = 1.61 kilometers, what is rex's distance in kilometers? round the answer to the nearest hundredth. 8.07 kilometers 104.65 kilometers 20.93 kilometers 26.19 kilometers
Rex's bike distance in kilometers is calculated to be 104.65 kilometers
How to solve for rex's distance in kilometers
Given that:
rex rides his bike for 13 miles each day for 5 days
1 mile = 1.61 kilometers
Rex's total ride in five days
13 miles * 5 days = 65miles
1 mile = 1.61 kilometers
65 miles = ? kilometers
cross multiply gives
? kilometers * 1 mile = 1.61 kilometers * 65 miles
? kilometers = 106.65 kilometers
Hence the unknown distance in kilometers represented as ? is solved to be 106.65 kilometers to the nearest hundredth
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Answer:
b 104.65
Step-by-step explanation:
i did the exam
Given the function f:{1}→{1}; f(x)=1, check which one(s) of the properties it has.
A. increasing
B. decreasing
C. strictly increasing
D. injective
E. surjective
F. strictly decreasing
G. None of the above
The function f has the property injective. (D)
An injective function is also known as a one-to-one function, which means that for every unique output, there is a unique input.
In this case, the function f maps the single element in the domain {1} to the single element in the codomain {1}, and there is only one possible output for the single input, so it is injective.
It does not have the properties of being increasing, decreasing, strictly increasing, strictly decreasing, or surjective because the function is a constant function mapping the single element in its domain to the single element in its codomain.
As a result, it does not change in value and cannot be classified as increasing or decreasing. Additionally, it is not surjective because the codomain contains one element that is not mapped to by the function.
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Is 5feet, 12feet, 13feet a right triangle or not a right triangle ?
Answer:
Yes, a right triangle can have side lengths 5, 12, and 13.
Step-by-step explanation:
What is the greastest number of acute angles that a triangle can contain?
Answer:
3 acute angles.
Step-by-step explanation:
Triangles have three angles. If any one angle is obtuse or right-angle, then the remaining two angles must be acute. Or else, all the 3 angles can be acute.
An example can be an equilateral triangle because it has 3 acute angles. Each angle is 60 degrees.
determine the values of x and y such that the points (1,2,3), 5(,7,1), and (x,y,2) are collinear (lie on a line).
the values of x and y that make the points (1,2,3), (5,7,1), and (x,y,2) collinear are x = 2 and y = 4.
Let's consider the direction ratios of the given points:
Point 1: (1, 2, 3)
Direction ratios: (1-0, 2-0, 3-0) = (1, 2, 3)
Point 2: (5, 7, 1)
Direction ratios: (5-1, 7-2, 1-3) = (4, 5, -2)
Point 3: (x, y, 2)
Direction ratios: (x-1, y-2, 2-1) = (x-1, y-2, 1)
Since the direction ratios should be proportional, we can set up the following proportion:
(1, 2, 3) / (4, 5, -2) = (x-1, y-2, 1) / (4, 5, -2)
This gives us the following ratios:
1/4 = (x-1)/4
2/5 = (y-2)/5
3/-2 = 1/-2
Simplifying these ratios, we get:
1 = x - 1
2 = y - 2
3 = 1
Solving these equations, we find:
x - 1 = 1
x = 2
y - 2 = 2
y = 4
Therefore, the values of x and y that make the points (1,2,3), (5,7,1), and (x,y,2) collinear are x = 2 and y = 4.
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what is 5*5+100-99*76
Answer:
-7399
Step-by-step explanation:
mark me brainiest please
Answer:
-7399
Step-by-step explanation:
5*5+100-99*76
25 + 100 - 7524
= -7399
Solve this problem , please
Answer:
1. 20.724 or 6.6π
2.3.14 or π
3. 15.7 or 5π
4. 9.42 or 3π
5. 25.12 or 8π
6. 18.84 or 6π
Step-by-step explanation:
just ask :)
if there were 20 dogs and 60 cats at a pet daycare, how many cats would there be if there were 40 dogs and the ratio stayed the same? do not put the unit.
Therefore, if there were 40 dogs and the ratio stayed the same, there would be 120 cats at the pet daycare.
If the ratio of dogs to cats stays the same, then the ratio of dogs to cats in the two situations will be equal.
The initial ratio of dogs to cats is:
dogs : cats = 20 : 60
= 1 : 3
To maintain the same ratio, the new number of cats (C) can be found by setting up the proportion:
dogs : cats = 40 : C
Using the initial ratio of dogs to cats, we can substitute and simplify:
1 : 3 = 40 : C
Cross-multiplying gives:
C = (3 x 40) / 1
= 120
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help please ill give brainliest
help with my geometry please
Answer:
x = 11
z = 86
Step-by-step explanation:
8x + 6 and 10x-16 are vertical angles
Vertical angles are pairs of angles that are opposite each other and have the same vertex, or point of intersection. They are formed when two lines intersect at a point, and are always congruent, or of equal measure.
To solve this equation, we need to isolate the variable x on one side of the equation. To do this, we can start by subtracting 6 from both sides of the equation:
8x + 6 - 6 = 10x - 16 - 6
8x = 10x - 22
Now we can subtract 8x from both sides of the equation:
8x - 8x = 10x - 22 - 8x
0 = 2x - 22
To solve for x, we can add 22 to both sides of the equation:
0 + 22 = 2x - 22 + 22
22 = 2x
Finally, we can divide both sides of the equation by 2 to find the value of x: 22 / 2 = 2x / 2
x = 11
Therefore, the solution to the equation is x = 11.
Now that we have x, z is a supplementary angle to 8x + 6 (or you could do 10x - 16)
Supplementary angles are pairs of angles that add up to 180 degrees. They are formed when two lines intersect at a point, and the angles formed at the intersection are supplementary.
First plug in x, 8x + 6 = 8(11) + 6 = 88 + 6 = 94
180 - 94 = z
z = 86
Work out the size of angle EAB.
You must give a reason for each stage of your working.
Need help with this pls
Answer:
num 1 is answer...
Can someone help me with this??
Answer:
yes
no
yes
yes
Answer:
nope
sorry lad
Step-by-step explanation:
. Doanh nghiệp dự tính đầu tư góp vốn liên doanh với số tiền ban đầu là 500 trđ, trong vòng 4 năm, lãi suất dự kiến là 12%/năm. Tính tổng số lãi của hoạt động đầu tư liên doanh thu được sau khi kết thúc liên doanh ?
A sample of n = 100 scores has a mean of 5. a second sample has n = 25 scores and m = 7. if the two samples are combined, the sample mean for the combined sample will be __________.
A sample of n = 100 scores has a mean of 5. A second sample has n = 25 scores and m = 7. if the two samples are combined, the sample mean for the combined sample will be 5.4.
We are given the sample mean of n = 100, is 5. Therefore, the sum of 100 observations is 100 x 5 = 500
The sample mean of n = 25, is 7. Therefore, the sum of 25 observations is
25 x 7 = 175
The sum of two samples is 500 + 175 = 675.
And the sum of two sample size is 100 + 25 = 125
Now, the combined mean is:
675125=5.4
What is mean?
A dataset's mean(also known as the arithmetic mean, which differs from the geometric mean) is calculated by dividing the sum of all values by the total number of values. It is frequently referred to as the "average" and is the most widely used measure of central tendency.
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Write an equation in point-slope form for the line that passes through the point with the given slope.
Answer:
Slope: 3
Equation: y + 2 = 3(x + 1)
Step-by-step explanation:
Find the slope using (-1, -2) and (0, 1):
\( slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - (-2)}{0 - (-1)} = \frac{3}{1} = 3 \)
Slope (m) = 3
The equation can be represented in point-slope form, y - b = m(x - a)
Where,
(-1, -2) = (a, b)
m = 3
Plug in the values into y - b = m(x - a)
y - (-2) = 3(x - (-1))
y + 2 = 3(x + 1)
Find the linear approximation to the function
at the point (x, y, z) = (1, -2,0)
L (x,y,z) = ______
The linear approximation to the function at the point (x, y, z) = (1, -2,0) is: L(x,y,z) = y - 4x + 4z + 4
The linear approximation to a function is essentially an approximation of the function in the vicinity of a given point using a tangent plane. This approximation is valid for small values of x, y, and z, and can be useful in many applications where precise values of the function are not necessary.
To find the linear approximation to the function at the point (x, y, z) = (1, -2,0), we need to first find the partial derivatives of the function with respect to x, y, and z. Let's assume that the function is denoted by f(x, y, z). Then, the partial derivatives can be calculated as follows:
fx(x, y, z) = 2xy - z
fy(x, y, z) = x^2 + 2z
fz(x, y, z) = -2xy
Now, we need to use these partial derivatives to find the equation of the tangent plane to the function at the point (1, -2, 0). The equation of the tangent plane can be given by:
f(x, y, z) ≈ f(1, -2, 0) + fx(1, -2, 0)(x-1) + fy(1, -2, 0)(y+2) + fz(1, -2, 0)(z-0)
Plugging in the values of the partial derivatives and the given point, we get:
f(x, y, z) ≈ -4 + (-4)(x-1) + 1(y+2) + 4(z-0)
Simplifying this equation, we get:
f(x, y, z) ≈ -4 - 4x + y + 4z + 8
f(x, y, z) ≈ y - 4x + 4z + 4
Consequently, L(x,y,z) = y - 4x + 4z + 4 is the linear approximation to the function at the point (x, y, z) = (1, -2, 0).
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PLZZZZZZZZZZ HLPPPPPPPPP MEEEEEEEEEEEE
Answer:
2 roots.
Step-by-step explanation:
The roots are the same things as the x-intercepts. From -4 to 3, there are two times when the polynomial intersects the x-axis. So, there are 2 roots.
Hope this helps!
Need help on surface area of this!
Answer:
Area = 1476 units^2
Step-by-step explanation:
(2)(12)(30) + (2)(9)(30) + (2)(9)(12) total area
Area = 1476 units^2
Answer:
1,476 units
Step-by-step explanation:
Formula of surface area (rectangular prism):
A = 2(wl + hl + hw)
2 · (12·9 + 30·9 + 30·12) = 1476
5. There are 30 rows of seats on a concert hall: 25 seats are in the1st row, 27 seats on the 2nd row, 29 seats on the 3rd row, and soon. If the price per ticket is $2,500, how much will be the totalsales for a one-night concert if all seats are taken?
First row = 25
Second row = 27
Third row = 29
This is 25, 27, 29...
there are 30 rows, this is n = 30
common difference = d = 27 - 25 = 2
then, we use the formula:
\(\begin{gathered} a_n=a_1+(n-1)d \\ a_n=25+(30-1)2 \\ a_n=25+(29)(2) \\ a_n=25+58 \\ a_n=83 \end{gathered}\)so, 83 is the last term:
\(S_n=\frac{n}{2}(a_1+a_n)=\frac{30}{2}(25+83)=15(108)=1620\)that mean 1620 total seats, therefore:
\(\text{total sales = }1620\times2500=4050000\)answer: $4,050,000
if you want to find a confidence interval for the mean weight loss, is it necessary to know that the population distribution of weight loss is normally distributed? explain why or why not.
No, It is not critical, to understand that population weight reduction is typically distributed. It is crucial to understand that the population's weight reduction is normally distributed.
What is central limit theorem?With a large sample size, the sampling distribution of the sample mean can be roughly compared to a normal distribution with mean and standard deviation for a random variable X with mean and standard deviation.
according to our question-
it is not necessary to know that the population distribution of weight loss is normally distributed.Because the sample size is greater than thirty, and according to the Central Limit Theorem, every sample with a size greater than thirty has a normally distributed behavior.Know more about Central Limit Theorem click here:
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Determine the measure of the interior angle at vertex e. a. 30 b. 50 c. 90 d. 150
the measure of the interior angle at the vertex is 90.
4x + 4x + 3x + 3x + 4x = 540
x = 30
Vertex E = 3x where x = 30
3x =?
3(30) = 90
Vertex E = 90*
A vertex angle is defined as the angle formed by two lines or rays that intersect at a point. These two rays form the sides of the angle. So the angle associated with a particular vertex is called the vertex angle and is measured in degrees.
In geometry, a vertex is an angle associated with a vertex of an n-dimensional polytope. In two dimensions, it refers to the angle formed by two intersecting lines: B. The "corners" of the polygon.
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