First Question is boolean,
Question 35 is probably floating point ,
Question 36 is probably an integer, since it shows 1, 2, 3, and 1, 2, 3 are not fractions, and integers are whole numbers.
Im not 100% sure but I hope I helped,
Have a nice day/night :)
Lesson 1-1: The periodic comet named Johnson has been seen at every return since its discovery in 1949, as shown in the table below: Occurrence Year Seen 1- 1949 2 1956 3 1963 4 1970 Use the table for Items 1-5. Describe any pattern you see in the table. Write the values in the second column at the table as a sequence. Identify the common difference. If the pattern continues, in which of the following years will the comet be visible again? A. 2017 B. 2018 C. 2019 D. 2020 About how many times would the Johnson comet be visible during a typical person’s lifetime? Explain your reasoning. 5. Reason abstractly. A man was born during a year in which the Johnson comet was visible in the sky. The next time that the comet was visible after the man’s birth year was in 2005. In what year was the man born? The table to use is attached to the question.
Answer:
Step-by-step explanation:
Occurrence Year seen Difference
1 1949 -
2 1956 1956 - 1949 = 7
3 1963 1963 - 1956 = 7
4 1970 1970 - 1963 = 7
Difference between each successive term of year seen = 7 years
Therefore, there is a common difference of 7 years between each successive term.
Function defining the year seen will be a linear function and will increase in the same pattern. (multiple of 7 years)
2017 - 1970 = 47 (It's not the multiple of 7)
2018 - 1970 = 48 (It's not the multiple of 7)
2019 - 1970 = 49 (multiple of 7)
2020 - 1970 = 50 (It's not the multiple of 7)
Therefore, comet will be seen next in 2019.
Option (C) will be the answer.
If a person is born in 2005
Then difference between 2005 and 1949 = 56 years
Number of times comet seen after 1949 = \(\frac{56}{7}=8\) times
Total number of comet seen in the lifetime = 8 times
Solve the simultaneous equation :
4x+2y=17
3x+2y=14
Answer:
(x, y) = (3, 5/2)
Step-by-step explanation:
\(4x+2y=17\\3x+2y=14\)
I'll solve by elimination here. If you invert the second equation and add it to the first, 2y and -2y would cancel out.
\(4x+2y=17\\-(3x+2y=14)\)
Now just add those from top to bottom.
\(\rightarrow (4x-3x)+(2y-2y)=17-14\\\rightarrow x=3\)
Nothing else needs to be done for that part. Now, you can pick either equation and use the known value of x to solve for y.
\(4x+2y=17\\\rightarrow 4(3)+2y=17\\\rightarrow 12+2y=17\\\rightarrow 2y=5\\\rightarrow y=\frac{5}{2}\)
(x, y) = (3, 5/2)
What is the area of the figure below
10cm
Answer:
A= 100 + 20π. or 162.832
Step-by-step explanation:
you first need to find the radius of the half circles with would be half of 10
so r = 5
and the circumstance equation is
c = 2πr
c = 2π(5)
c=10π
but circumference is calculating for a whole circle and you have 4 half circles. 4 half circles make 2 full circles.
2(10π)= 20π
now find the area of the square
10 × 10 = 100
put them together
100 + 20π
Debra pumped 2 gallons of water into her pool each minute for 10 minutes. Whag was ths total change in the amount of water in the pool
Answer:
There would be 20 gallons in her pool
Step-by-step explanation:
alison, beatrice and chole each had some books. alison gave beatrice and chole some books that doubled the number of books they had, lastly chole gave alison and beatrice some books that doubled the number of books they had. each of them had 32 books at the end. how many books did each of them have at first?
alison, beatrice and chole each of them have at first 56, 8, 32 books.
alison, beatrice and chole each had some books. alison gave beatrice and chole some books that doubled the number of books they had, lastly chole gave alison and beatrice some books that doubled the number of books they had. each of them had 32 books at the end.
What is Working backward?Working backward is process in which calculation done in reverse direction.
let alison, beatrice and chole has x,y and z books initially,
alison gave beatrice and chole some books that doubled the number of books they had
alison, beatrice and chole has (96-2y-2z), (2y) , (2z)
chole gave alison and beatrice some books that doubled the number of books they had. each of them had 32 books at the end.
alison, beatrice and chole has 2(96-2y-2z), 2(2y) , (96-2(96-2y-2z)-4y)
at the end,
beatrice = 32
4y=32
y = 8
chole =32
96-2(96-2y-2z)-4y)=32
z=32
alison = 96-y-z
x=96-8-32
x=56
Thus the required alison, beatrice and chole each of them have at first 56, 8, 32 books.
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((-5) - 9+ (7+(-6)))*(-4)
Answer:
The answer to ((-5) - 9+ (7+(-6)))*(-4) is 52
\(\sf Answer: \)
\(52\)
\(\sf Step-By-Step~ Explanation: \)
\(Equation\)
\(((-5) - 9 + (7+(-6))) \times (-4)\)
\(Subtract~~9~~and~~-5 = -14.\)
\((-14 + 7 - 6)~(-4)\)
\(Add~~-14~~and~~7 = -7\)
\((-7-6)~(-4)\)
\(Subtract~~6~~and~~-7 = -13\)
\(-13~(-4)\)
\(Lastly,~~multiply~~-13~~and~~-4 = 52\)
\(52\)
\(\huge\boxed{\sf Answer \ 52}\)
The length of a rectangular field is twice its breadth. If the perimeter of the field is 150m . Find the dimensions of the rectangle.
Answer:
length=50m
width=25m
Step-by-step explanation:
perimeter is the distance all round,hence
2(l+w)=2(2x+x)=
4x+2x=6x=150
6x=150x
x=25
l=50m
w=25m
Which equation can be used to represent the statement? Half of a number minus Severn is one and five tenths.
Shari planted a rectangular garden with a perimeter of 100 feet. The length of the garden is 10 feet shorter than the width. Find the length and width of the garden.
Answer:
What is the slope of the line through (-5,-10)(−5,−10)left parenthesis, minus, 5, comma, minus, 10, right parenthesis and (-1,5)(−1,5)left parenthesis, minus, 1, comma, 5, right parenthesis?
Step-by-step explanation:What is the slope of the line through (-5,-10)(−5,−10)left parenthesis, minus, 5, comma, minus, 10, right parenthesis and (-1,5)(−1,5)left parenthesis, minus, 1, comma, 5, right parenthesis?
Find the value of R100−L100, which is the difference of the Right Riemann sum and the Left Riemann sum using 100 rectangles to estimate the (signed) area under the function f(x)=7x on [0, 10].
The value of R100−L100, which is the difference of the Right Riemann sum and the Left Riemann sum using 100 rectangles to estimate the (signed) area under the function f(x)=7x on [0, 10], is 70.
To find the value of R100−L100, we need to calculate the Right Riemann sum and the Left Riemann sum separately and then take their difference.
The width of each rectangle is given by Δx = (b-a)/n = (10-0)/100 = 0.1, where n is the number of rectangles used.
The height of each rectangle for the Right Riemann sum is given by the value of f(x) at the right endpoint of the subinterval, which is x_i+1 = a + (i+1)Δx, where i = 0, 1, 2, ..., n-1.
Thus, the Right Riemann sum is given by:
R100 = f(x1)Δx + f(x2)Δx + ... + f(x100)Δx
= 7(0.1) + 7(0.2) + ... + 7(10)
= 7(0.1 + 0.2 + ... + 10)
= 7(0.1)(1 + 2 + ... + 100)
= 7(0.1)(5050)
= 3535
Similarly, the height of each rectangle for the Left Riemann sum is given by the value of f(x) at the left endpoint of the subinterval, which is x_i = a + iΔx, where i = 0, 1, 2, ..., n-1.
Thus, the Left Riemann sum is given by:
L100 = f(x0)Δx + f(x1)Δx + ... + f(x99)Δx
= 7(0) + 7(0.1) + ... + 7(9.9)
= 7(0 + 0.1 + ... + 9.9)
= 7(0.1)(0 + 1 + ... + 99)
= 7(0.1)(4950)
= 3465
Therefore, the difference between the Right Riemann sum and the Left Riemann sum is:
R100−L100 = 3535 - 3465 = 70
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I also don't understand what the 's' is in this problem.
Solve the systemm { x1 -x2 +4x3 = -4
6x1 -5x2 +7x3 = -5
3x1 -39x3 = 45 }
[x1] = [ __ ] [ __] [x2] = [ __ ] +s [ __] [x3] = [ __ ] [ __]
's' and 't' represent free parameters that can take on any real values.
In the given system of equations:
x1 - x2 + 4x3 = -4
6x1 - 5x2 + 7x3 = -5
3x1 - 39x3 = 45
To solve this system, we can use the method of Gaussian elimination or matrix operations. Let's use Gaussian elimination:
Step 1: Write the augmented matrix for the system:
[1 -1 4 | -4]
[6 -5 7 | -5]
[3 0 -39 | 45]
Step 2: Perform row operations to transform the matrix into row-echelon form:
R2 = R2 - 6R1
R3 = R3 - 3R1
The updated matrix becomes:
[1 -1 4 | -4]
[0 1 -17 | 19]
[0 3 -51 | 57]
Step 3: Perform additional row operations to further simplify the matrix:
R3 = R3 - 3R2
The updated matrix becomes:
[1 -1 4 | -4]
[0 1 -17 | 19]
[0 0 0 | 0]
Step 4: Write the system of equations corresponding to the row-echelon form:
x1 - x2 + 4x3 = -4
x2 - 17x3 = 19
0 = 0
Step 5: Express the variables in terms of a parameter:
x1 = s
x2 = 19 + 17s
x3 = t
where s and t are parameters.
Therefore, the solution to the system is:
[x1] = [s]
[x2] = [19 + 17s]
[x3] = [t]
In the provided solution format:
[x1] = [s] []
[x2] = [19 + 17s] + s []
[x3] = [t] [__]
Here, 's' and 't' represent free parameters that can take on any real values.
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Four kids. Aaron, Bessy, Carl and Dawn play with beads. They start with 200 beads in all. Aaron gave Bessy 26 beads. Bessy gave Carl 36 beads. Carl gave Dawn 32 beads, and Dawn gave Aaron 4 beads. They end up with the same number of beads as each other. How many beads did Aaron, Bessy, Carl and Dawn have at the beginning?
Step-by-step explanation:
Aaron had 72 beads
Bessy had 60 beads
Carl had 46 beads
Dawn had 22 beads
Maria has a cube-shaped box that measures 9 inches along each edge. Can she fit 1,000 1-cubic-inch cubes inside the box?
Answer:
No
Step-by-step explanation:
She would be able to fit 729 cubes but not 1000.
Range of the function f(x)=2x^2/3x-x^2
The range of the function f(x) = 2x^2 / (3x - x^2) is (-∞, 2) U (2, +∞).
To find the range of the function f(x) = 2x^2 / (3x - x^2), we need to determine the set of all possible output values.
First, we observe that the function is undefined when the denominator (3x - x^2) equals zero. This occurs when x = 0 or x = 3. Therefore, we need to consider the range for x values excluding these points.
To analyze the behavior of the function, we can examine its limits as x approaches positive or negative infinity. Taking the limit as x approaches infinity, we find that the function approaches 2. As x approaches negative infinity, the function also approaches 2.
Based on the limits and the fact that the function is continuous for all other values of x, we can conclude that the range of f(x) is the interval (-∞, 2) U (2, +∞), where (-∞, 2) represents all values less than 2 and (2, +∞) represents all values greater than 2.
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If a_1=2a 1 =2 and a_n=a_{n-1} 5a n =a n−1 5 then find the value of a_5a 5
The fifth term of the sequence is 1250, if the formula for finding the general term of a sequence is \(a_{n} = a_{n -1} 5\).
According to the given question.
We have a formula for finding the general term of a sequence is
\(a_{n} = a_{n -1} 5\)
Also,
The first term of the sequence, \(a_{1} = 2\)
Therefore,
The fifth term of the sequence is given by
\(a_{5} = a_{5-1} 5\)
⇒ \(a_{5} = a_{4} 5\)
⇒ \(a_{5} = (a_{4-1}5) 5\)
⇒ \(a_{5} = a_{3}25\)
⇒ \(a_{5} = (a_{3-1}5) 25\)
⇒ \(a_{5} = a_{2} 125\)
⇒ \(a_{5} = a_{2 -1} (5)125\)
⇒ \(a_{5} = a_{1} 625\)
⇒ \(a_{5} = 2(625)\)
⇒ \(a_{5} = 1250\)
Hence, the fifth term of the sequence is 1250, if the formula for finding the general term of a sequence is \(a_{n} = a_{n -1} 5\).
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the probability of the union of two events occurring can never be more than the probability of the intersection of two events occurring. true/false
The given statement "the probability of the union of two events occurring can never be more than the probability of the intersection of two events occurring." is False.
The union of two events A and B represents the event that at least one of the events A or B occurs. The probability of the union of two events can be calculated using the formula:
P(A or B) = P(A) + P(B) - P(A and B)
On the other hand, the intersection of two events A and B represents the event that both events A and B occur. The probability of the intersection of two events can be calculated using the formula:
P(A and B) = P(A) * P(B|A)
where P(B|A) is the conditional probability of B given that A has occurred.
It is possible for the probability of the union of two events to be greater than the probability of the intersection of two events if the two events are not mutually exclusive.
In this case, the probability of both events occurring together (the intersection) may be relatively small, while the probability of at least one of the events occurring (the union) may be relatively high.
In summary, the probability of the union of two events occurring can sometimes be greater than the probability of the intersection of two events occurring, depending on the relationship between the events.
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First to give find the value of x in 96x * 5 = -6 gets brainliest.
Answer:
- 1/80
Step-by-step explanation:
HELP!!! I WILL GIVE BRAINLIEST!!!!
1.Find f(4) if f(x) = (1/2)x + 13
2.Find f(5) if f(x) = (3/5)x - 10
3.Find f(-1) if f(x) = x2 + 7
4.Find f(2) if f(x) = 3x3 -12x2
Answer:
15, - 7, 8, - 24
Step-by-step explanation:
1
f(4) = \(\frac{1}{2}\) × 4 + 13 = 2 + 13 = 15
2
f(5) = \(\frac{3}{5}\) × 5 - 10 = 3 - 10 = - 7
3
f(- 1) = (- 1)² + 7 = 1 + 7 = 8
4
f(2) = 3(2)³ - 12(2)² = 3(8) - 12(4) = 24 - 48 = - 24
solve: -12=24+6y y=2 y=-2
Answer:
this problem is false -12=2
Step-by-step explanation:
the sides are not equal
HELP PLS!!!
Is a triangle with side lengths of 33 inches, 56
inches, and 65 inches a right triangle? Explain your
reasoning.
A. Not a right triangle because a² + b2 + c2
B. Not a right triangle because 33 + 56 + 65
C. Is a right triangle because a2 + b2 = c2
D. Is a right triangle because 33 + 56 = 65
in PQR if m∠p is 14 less than five times x, m∠q is five less than x and m∠r is nine less than twice x find x and the measure of each angle.
x=
m∠p=
m∠q=
m∠r=
The value of x =26°, m∠p =116°, m∠q=21°, m∠r=43°
What is an angle?
An angle is formed when two lines meets at the same vertex. It is measured by degree. Based on the measurements angles are of three types.
Consider POR as a triangle.
Given that m∠p=5x-14, m∠q=x-5, m∠r=2x-9.
In triangle the sum of the angle is 180°, then
m∠p + m∠q +m∠r =180°
⇒5x-14+x-5+2x-9 = 180°
⇒8x-28=180°
⇒x=26°
then, m∠p=5x-14 = 5(26)-14 = 116°
m∠q=x-5 = 26-5=21°
m∠r=2x-9 = 2(26)-9=43°
Hence, the value of x =26°, m∠p =116°, m∠q=21°, m∠r=43°
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Can somebody help me with #14 ? I don’t know how to start it off and solve it
Given the function:
\(f(x)=(x-4)^2\)• You can graph it.
By definition, this is the graph of the Parent Function (the simplest form) of Quadratic Functions:
The equation of this Parent Function is:
\(y=x^2\)You can identify that the function given in the exercise is like the Parent Function graphed above, but translated 4 units to the right. Because, according to the Transformation Rules for Functions, when:
\(f(x-h)\)The function is shifted right "h" units.
Therefore, you can graph the function provided in the exercise:
According to the instruction given in the exercise, you have to find the domain on which the function is one-to-one and non-decreasing.
By analyzing the graph, you can determine that the function increases (goes up) on this interval:
\(\lbrack4,+\infty)\)In order for that portion (the portion on the right, which is the one increasing) to be one-to-one, it has two passes the Vertical Line Test. This states that if the vertical lines intersect the graph at more than one point, it is not a One-to-One Function.
In this case, you get:
Since all the lines intersect the graph at one point, then it is a One-to-one Function.
By definition, the Domain of a function is the set of x-values for which it is defined.
Therefore, you can determine that the domain on which the function is one-to-one and non-decreasing is:
\(Domain:\lbrack4,\infty)\)• In order to find an inverse of the function of this domain, you need to follow these steps:
1. Rewrite the function in this form:
\(y=(x-4)^2\)2. Solve for "x":
\(\begin{gathered} \sqrt{y}=\sqrt{(x-4)^2} \\ \\ y=x-4 \\ x=\sqrt{y}+4 \end{gathered}\)3. Swap the variables:
\(y=\sqrt{x}+4\)4. Rewrite it as:
\(f^{-1}(x)=\sqrt{x}+4\)Keeping in mind the definition of Domain, you need to remember that a square root is not defined when its Radicand (the value inside the root) is negative.
Therefore, the Domains are the same:
\(Domain:\lbrack4,\infty)\)Hence, the answer is:
• Domain on which the function is one-to-one and non-decreasing:
\(Domain:\lbrack4,\infty)\)• Inverse of function on that domain:
\(f^{-1}(x)=\sqrt{x}+4\)this maths question i don’t really understand
Answer:
I think it is straight forward, u just have to solve the problem
Step-by-step explanation:
so 35 x 586= 20510
3.5 x 5860=20510
36 x 586=21096
70 x 586=41020
The average rainfall in Annette, Alaska, in September is 0.31 inch per day. 1 point
How much rain falls over the course of an average September? (September
has 30 days.) *
903 inches
90.3 inches
9.3 inches
.93 inches
i just multiply the 0.31 by the number of days in September to get the average
A map has a key showing that every 3 centimeters = 5 kilometers. How far apart are
two cities if the map shows they are 81 centimeters apart?
Let's consider the information given to us:
3 centimeters = 5 kilometers ⇒ \(\frac{3 cm}{5 km}\)81 centimeters = x kilometers ⇒ \(\frac{81 cm}{x km}\)Now we know these proportions are equal, so:
\(\frac{3}{5}=\frac{81}{x}\\ 3x = 5 * 81\\3x = 405\\x = 135\)
Thus the two cities are 135 km apart
Answer: 135 km
Hope that helps!
Answer:
135 km
Step-by-step explanation:
5 km / 3cm * 81 cm = 135 km
( see how the 'cm' cancel and you are left with 'km' as your answer?)
Please helppppimalmost done with homework!!!!
The value of the given expression will be 3√5.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given expression c² = 45 will be solved as below:-
c² = 45
Take the square root of the number 45.
c = √45
c = √ 9 x √5
c = 3√5
Therefore, the value of the given expression will be 3√5.
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Okay so like for integers I use a number line to help me like negative on one side and positive on the other but how do I deal like with these problems? And please explain :)
Answer:
Step-by-step explanation:
remember this:-
if +,- comes: change sign to - (eg. 8+(-4)= 8-4=4)
if -,+ comes: change sign to - (eg. 8-(+4)= 8-4=4)
if -,- comes: change sign to + (eg. 8-(-4)=8+4=12)
if +,+ comes: change sign to + (eg. 8+(+4)=8+4=12)
pretty please can someone answer this for me????? ty
The value of the function f(1)-f(-7) = -11
What is a function?A function from a set X to a set Y assigns to each element of X exactly one element of Y.
Given are a function,
For x = 1, take -x²-3x
f(1) = -1²-3 = -4
For x = -7, take |x+5|-9
f(-7) = |-7+5|-9 = -7
f(1)-f(-7) = -7-4 = -11
Hence, The value of the function f(1)-f(-7) = -11
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Help help help help help help
Answer:
y=1/3x+-8
Step-by-step explanation:
I think
3
87. 8
98
-
8[?].
the question didn’t have enough letters for me to post so i’m using this to post it