Rotation of a point through 189° about the origin When a point C(h, k) is rotated through 180° in either an anticlockwise or clockwise direction about the origin O, it takes the new position D(-h, -k).
The rotation formula will give us the precise location of a point after a finite degree of rotation. The rotation formula is determined by the type of rotation applied to the point in relation to the origin. A geometric two-dimensional shape can undergo four major types of transformation.
The rotation formula describes how a point rotates with respect to the origin. The rotation formula is used to determine the position of a point after it has been rotated. A rotation is a circular motion around a specific axis or point of rotation. In general, rotation can be done in two ways: clockwise and anti-clockwise or counter-clockwise.
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can anyone help me with this I am stuck
Using integrals, the desired probabilities and measures are given as follows:
a) P(X < 6) = 0.84375 = 84.375%.
b) P(X < 13) = 1 = 100%.
c) P(6 < X < 8) = 0.15625 = 15.625%.
d) P(X > 5) = 0.31641 = 31.641%.
e) x = 6.434.
What is the probability distribution?The distribution is given as follows, simplifying the operations:
f(x) = 0.09375x - 0.01171875x², 0 ≤ x ≤ 8.
Hence the density function is:
[tex]\int_{a}^{b} f(x) dx[/tex]
[tex]\int_{a}^{b} (0.09375x - 0.01171875x^2) dx[/tex]
[tex]0.046875x^2 - 0.00390625x^3|_{x=a}^{x = b}[/tex]
Applying the Fundamental Theorem of Calculus:
P(a < X < b) = 0.046875b² - 0.00390625b³ - 0.046875a² + 0.00390625a³
Hence, for item a:
P(X < 6) = 0.046875(6)² - 0.00390625(6)³.
P(X < 6) = 0.84375 = 84.375%.
For item b, the entire distribution is below 13, hence:
P(X < 13) = 1 = 100%.
For item c:
P(6 < X < 8) = 0.046875(8)² - 0.00390625(8)³ - 0.046875(6)² + 0.00390625(6)³.
P(6 < X < 8) = 0.15625 = 15.625%.
For item d:
P(5 < X < 8) = 0.046875(8)² - 0.00390625(8)³ - 0.046875(5)² + 0.00390625(5)³.
P(X > 5) = 0.31641 = 31.641%.
For item e:
We have to find b when a = 0 and P(X < b) = 0.9, hence:
0.046875b² - 0.00390625b³ = 0.9.
Using a calculator, the solution in the range of the distribution is given by:
b = x = 6.434.
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Jared estimates that his houseplant is as heavy as a 5 kilogram bowling ball. Draw a tape diagram to estimate the weight of 3 houseplants.
3 houseplants will weigh 15 kg (Refer to the tape diagram below).
What is a tape diagram?A tape diagram is a visual model that looks like a piece of tape and is used to aid in the calculation of ratios, addition, subtraction, and, most commonly, multiplication. It is also referred to as a divided bar model, a fraction strip model, a length model, or a strip diagram. It is used in elementary school mathematics education to solve word problems.The weight of 3 household plants will be about 15 kg.
5 kg × 3 = 15 kg(Refer to the tape diagram given below)Therefore, the weight of 3 household plants will be about 15 kg (Refer to the tape diagram below).
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4. What is the probability of pulling either a fork or a spoon out of the bag?
We the Probability of pulling either fork or spoon as 1.
We are given that:
We have a fork and a spoon in a bag.
Total number of items in a bag = 1 + 1 = 2
Now, we need to tell the probability of either pulling a fork or a spoon.
Now,
Probability of pulling a fork = 1 / 2 = 0.5
Probability of pulling a spoon = 1 / 2 = 0.5
So, the Probability of pulling either of them will be = 1 / 2 + 1 / 2 = 1
Therefore, we the Probability of pulling either fork or spoon as 1.
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what set M is the set of months hauling 31 days?
The set of months having 31 days will be S = { January, March, May, July, August, October, December }.
A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.
We know that there are 12 months in a year.
From these months, we get that the months that have 31 days are:
January
March
May
July
August
October
December
The set of months having 31 days will be:
S = { January, March, May, July, August, October, December }
Therefore, we get that, the set of months having 31 days will be S = { January, March, May, July, August, October, December }.
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Find all the numbers that satisfy the fol-
lowing descriptions:
The number has seven digits.
The number is between 1,000 and
10,000.
The digit in the tenths place is 150%
of the digit in the thousandths place.
The digit in the hundredths place is
of the sum of the digit in the
tenths place and the digit in the
thousandths place.
The sum of all the digits in the num-
ber is 17.
None of the digits are zero.
There is no number which is satisfying the given conditions.
The first condition is that the number has seven digits.
The second condition is that the number lies between 1000 and 10000.
From these two conditions, we can conclude that there is no number which satisfies all the given conditions. Because there is no seven-digit number which is less than 10000.
Let us assume that the second condition is the number lies between 1000000 and 10000000.
And let the required number be "abcdefg".
The third condition is the digit in the tenth place is 150% of the digit in the thousandth place.
⇒ f = 150 × (d) / 100 = 1.5 × d
The fourth condition is the digit in the hundredth place is the sum of the digit in the tenth place and the digit in the thousandth place.
⇒ e = f + d = 1.5d + d = 2.5d
The fifth condition is the sum of all the digits in the number is 17.
⇒ a + b + c + d + e + f + g = 17
⇒ a + b + c + d + 2.5d + 1.5d + g = 17
⇒ a + b + c + 5d + g = 17
And the last condition is none of the digits is zero.
Using the last condition the possible values for d are either 1 or 2.
Because, if d is 3, then if we take the least possible digit(1) for others, the sum on the LHS is 19, which is greater than 17.
And d can not be 1. Because, if d is 1, then f and e are 1.5 and 2.5 respectively. 1.5 and 2.5 are not valid digits.
Therefore, the value of d = 2.
f = 1.5d = 3
e = 2.5d = 5
If d = 2, then we get a + b + c + g + 10 = 17
⇒ a + b + c + g = 17 - 10
⇒ a + b + c + g = 7
⇒ The possible values for (a, b, c, g) are (4, 1, 1, 1), (1, 4, 1, 1), (1, 1, 4, 1), (1, 1, 1, 4), (2, 2, 2, 1), (2, 2, 1, 2), (2, 1, 2, 2), (1, 2, 2, 2), (2, 3, 1, 1), (3, 2, 1, 1), (1, 1, 2, 3), and (1, 1, 3, 2)...
Therefore there are more than 12 possible answers that satisfy the assumption made.
411253114125311142531111253422225312212532212253212225322312531321253112325311322531Learn more about number here:
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What is the solution set of the quadratic inequality 4(x + 2)²(less than equal to)0
Answer:
{-2}
Step-by-step explanation:
You want the solution set for the inequality 4(x +2)² ≤ 0.
SolutionThe expression on the left cannot be negative, but it can be zero when ...
x +2 = 0 ⇒ x = -2
The only solution to this inequality is x = -2.
Expressed as a set of solutions, we have ...
x ∈ {-2}
Select the part of speech for the underlined words below. I WAS afraid of roller coasters when I was younger, but I AM a huge fan of them now. preposition, adverb, verb, adjective
Answer: I'm pretty sure its a verb
Step-by-step explanation:
The sum of an integer and 7 times the next consecutive odd integer is 6. Find the value of the greater integer.
The value of the integer number is -1
How to find the value of the greater integer?The statement is given as:
The sum of an integer and 7 times the next consecutive odd integer is 6
Let the integer value be x
So, the next consecutive odd integer is x + 2
When represented as an equation, we have
x + 7(x + 2) = 6
Open the bracket
x + 7x + 14 = 6
Evaluate the like terms
8x = -8
Divide both sides by 8
x = -1
Hence, the value of the integer number is -1
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find the area of the circle
The circle has an area of 28.26 ft².
It is assumed that the circle's radius is 3 feet.
The circle's area must be determined.
What is radius of a circle ?
A line segment from a circle's center to its perimeter is known as the radius.
As per the question ;
Radius of circle , r = 3 ft
Area of the circle is given by ;
A = πr²
A = π × 3²
A = 9π
or
A = 9 × 3.14
or
A = 28.26 ft²
Thus , the area of the circle will be 28.26 ft².
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in the grid below what is the distance between point a and b. round to the nearest tenth
12345678901234567890
Yes; The construction demonstrates how to bisect an angle correctly using technology because Circles D & E have the same radius
How to properly bisect an angle?
In construction of angles and lines, bisection means dividing either a given angle or line segment into two equal parts. This means after the construction, the two parts must have equal measure.
The steps to bisect a line segment are as follows;
1. Draw the required length of the line segment AB.
2. With point A and radius of the compass greater than half of AB, describe arcs above and below the segment.
3. With the same radius as in step 2 and point B, describe two arcs above and below the segment. These would intersect that of step 2 at C and D.
4. Join the points of intersection of the arcs with a straight line CD.
Now, in this given question with the circle, we can see that line AG is the line that bisects the angle EAD.
Now, we see that circles C and D have the same radius and as such the construction demonstrated is correct for that very reason.
Answer: yes
Step-by-step explanation: the construction correctly shows how to bisect an angle using technology because circles D and E have the same radius.
Find the domain and range of the function F(t) = sec(3.14t/4)
The domain of sec(3.14t/4) is all real numbers except 2+4n, where n is any integer and range of sec(3.14t/4) is [tex](\infty,-1] \cup [1,\infty)[/tex].
The Domain of a function f(x) is the set of all values for which the function is defined.
The Range of a function is the set of all values that f takes.
As, [tex]sec x=\frac{1}{cos x}[/tex] , so sec x is defined where [tex]cos x \neq 0[/tex].
It implies, sec(3.14t/4) is defined where [tex]cos(3.14t/4)\neq 0[/tex].
The cosine is 0 at [tex](2n+1)\frac{\pi }{2}[/tex] , where n is any integer.
Now, [tex]\frac{3.14t}{4} =\frac{(2n+1)\pi }{2}[/tex]
[tex]\frac{\pi t}{4} =\frac{(2n+1)\pi }{2}[/tex]
[tex]t=2(2n+1)\\t=2+4n[/tex]
Since, the range of cos x is [-1,1], so sec x will never be less than 1, but can grow infinitely large as cos x approaches 0.
Thus, The domain of sec(3.14t/4) is all real numbers except 2+4n, where n is any integer and range of sec(3.14t/4) is [tex](\infty,-1] \cup [1,\infty)[/tex].
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Find the sum of (6.9 × 106) and (5.9 × 105). Write the final answer in scientific notation.
The sum of (6.9 × 10^6) and (5.9 × 10^5) written in scientific notation is 12.8 × 10^11
Scientific notation(6.9 × 10^6) and (5.9 × 10^5)
Sum
= (6.9 × 10^6) + (5.9 × 10^5)
= (6.9 + 5.9) × 10^(6+5)
= 12.8 × 10^11
Therefore, the sum of (6.9 × 10^6) and (5.9 × 10^5) written in scientific notation is 12.8 × 10^11
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Rewrite as a simplified fraction 0.7 repeating
Answer:
7/10
Step-by-step explanation:
Rewriting 0.7 as a fraction would be 7/10. 0.7 can also be 0.70, and 70/100
(100 POINTS ASAP)
Triangle EFG is shown in the graph.
The triangle will be reflected across the x-axis and then dilated by a scale factor of 2 with respect to the origin, resulting in triangle E'F'G'.
What will be the coordinates of G'?
Answer:
The coordinates of G' will be (8, 4)Step-by-step explanation:
Point G has coordinates (4, -2).
After reflection across the x-axis it s coordinates will change as per rule:
(x, y) → (x, - y)Applied to point G:
(4, - 2) → (4, 2)After dilation by a scale factor of 2 the coordinates will change as per rule:
(x, y) → (2x, 2y)Applied to point G:
(4, 2) → (2*4 = 8, 2*2 = 4)G' = (8, 4)Josue is the youngest of three siblings whose ages are consecutive even integers. If
the sum of their ages is 78, find Josue's age.
Answer:
39 is the sum of their ages
Step-by-step explanation:
Hope this helps :)
Find the perimeter of the equilateral triangle.
9x16
8-3x
The perimeter is
The perimeter of the equilateral triangle will be 27x - 48.
How to calculate the perimeter?It should be noted that the perimeter of an equilateral triangle is the addition of all its sides or multiplying by three since they're equal.
Therefore, the perimeter of the equilateral triangle will be:
= 3(9x - 16)
= 27x - 48
Therefore, the perimeter of the equilateral triangle will be 27x - 48.
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Find the perimeter of the equilateral triangle.
9x - 16
Evaluate.
Remember Order of Operations!
(PEMDAS)
(-7+3²) × 8
Answer:
16
Step-by-step explanation:
[tex]-7+3^2\\3^2\\=9\\=-7+9\\=-7+9 = 2\\=2\times \:8\\2\times \:8=16\\\boxed{16}[/tex]
geometry someone help
Answer:
D. F
Step-by-step explanation:
Both F and G are not on plane P
100 points + first decent answer gets brainliest
The mean of a distribution of selected theme park admission prices is $59 with a standard deviation of $3.99. The mean cost of a distribution of a specific home stereo system sold at many different stores is $1,499 with a standard deviation of $4.
Which distribution has the lower standard deviation?
Which distribution is more spread out? Explain.
Answer:
See explanation
Step-by-step explanation:
Selected theme park admission prices has the lower standard deviation.
Specific home stereo system's distribution is more spread out since the ratio between the standard deviation and the mean is greater compared to that of selected theme park admission prices.
specific home stereo system: 3.99/59=0.0676.
selected theme park admission prices: 4/1499=0.002668
0.0676>0.002668
Answer:
The theme park ahs the lower standard deviation
Rory has 6 pounds of ground beef to make meatballs. He uses 5/8 pound per meatball to make 9 meatballs. How many 1/8 pound meatballs can Rory make with the remaining beef?
Rory can make 43 metaballs from the remaining beef.
What are maths operations?An operation is a function in mathematics that converts zero or more input values (also known as "operands" or "arguments") to a well-defined output value. The operation's arity is determined by the number of operands.Binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive inverse and multiplicative inverse, are the most commonly studied operations. A zero-arity operation, also known as a nullary operation, is a constant. The mixed product is an example of an arity 3 operation, also known as a ternary operation.Rory has 6 pounds of ground beef on hand for making meatballs.
He makes 9 meatballs with 5/8 pounds of meat per meatball.
We must subtract 5/8 from 6.
6 - 5/848-5/843/8There are 43/8 pounds of ground beef remaining.
As a result, the number of 1/8 pound meatballs produced from 21/8 pound ground beef can be calculated as follows:
43/8 ÷ 1/843/8 × 8/1= 43Therefore, Rory can make 43 metaballs from the remaining beef.
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need help with 36.01 x 0.06
Answer: 2.1606
Step-by-step explanation:
36.01 x 0.06 =
3601/100 x 6/100=
3601 x 6/(100 x 100)=
21606/10000=2.1606
Let f(x) = -3x+5 and g(x)=x²-2. Find the difference (g - f)(x).
(g-f)(x) =
Answer: f(x^2) = x^2 - 5
Zan needs 28 centimeters of ribbon for each bow she makes. What is the greatest number of bows Zan can make with 9 feet of ribbon?
Answer:
3
Step-by-step explanation:
i think its 3 because 28 divided by 9 is 3
Determine which integer in the solution set will make the equation true.
3s − 12 = −9
S: {−1, 0, 1, 2}
A: −1
B: 0
C: 1
D: 2
Answer:
c) 1
Step-by-step explanation:
Solving for the value of s,
→ 3s - 12 = -9
→ 3s = -9 + 12
→ s = 3/3
→ [ s = 1 ]
Thus, option (c) is correct.
The graph of f(x) is shown.
How many horizontal tangent lines does f(x) have?
0
1
2
3
4
Check the picture below.
beth and ann are joking that their combined ages equal sams age. if beth is twice anns age and sam is 69. what are beth and anns age
Answer: ann is 69 and beth is 138
Step-by-step explanation:
Just need these answers for an assignment help would be nice
Answer:
below
Step-by-step explanation:
25)-ab
=-(-1/2)(3/4)
=3/8
26)b÷c
=(3/4)×1/-6
=3/-24
=-1/8
27)c÷a
=-6÷-1/2
=6×2/1
=12
Write 4,000,000 in scientific notation
4 × 10 then put a 6 by the 10 as an exponent.
if a(x + 1) = 2x + 3a, and a ≠ 0, then what is x in terms of a
Answer:
[tex]x = \frac{2a}{a - 2} [/tex]