The father is with the son's mother.
Given that,
a mother is 21 years older than her son.
Let us consider M be the age of the mother and S be the age of the son
which implies that,
M = S + 21 ---------------(1)
and in 6 years, mother will be 5 times as old as her son
i.e. M + 6 = 5(S + 6)
M = 5S + 24 ------------- (2)
so equation (1) and (2) implies that,
S + 21 = 5S + 24
21 = 4S + 24
S = - 3/4
That means son is - 3/4 years old or - 9 months.
The time at which we know the father will be with son's mother.
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discrete 5 dice of different colors are rolled, and the number coming up on each die is recorded. how many different outcomes are possible?
The number of total different outcomes are, 7,776.
What is rolling dice?
Every face of a cube known as a dice has a unique number.
By throwing a dice into the air, players can advance in any game by getting a certain number. Typically, this dice or dice has numbers from 1 to 6 written on each face or side of the cube-like shape.
Given:
Discrete 5 dice of different colors are rolled, and the number coming up on each dice is recorded.
Since all the dice are of different colors.
So any combination of the numbers on the dice is unique.
Dice has numbers 1 to 6.
So, for each dice there are 6 possibilities.
Since number coming on a dice is independent to the number coming on the another dice.
So, total different outcomes are = 6 x 6 x 6 x 6 x 6 = 6^5 = 7776.
Hence, the number of total different outcomes are, 7,776.
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analyze the solution to the system to determine whether there is a catapult arm length that aiden and natalie can both use to launch their tennis balls the same distance. explain your reasoning.
There is no catapult arm length that Aiden and Natalie can both use to launch their tennis balls the same distance.
From the graph,
x axis represents the arm length of the catapult and the y axis represents the distance.
The point at which the catapult arm length that Aiden and Natalie can both use to launch their tennis balls the same distance is the intersecting point of the both line
The coordinates of the intersecting point = (-30, 90)
Here arm length represents -30, but the arm length cannot be a negative value
Therefore, there is no arm length that gives equal distance
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Answer:
There is no catapult arm length that Aiden and Natalie can both use to launch their tennis balls the same distance.
Step-by-step explanation:
if a fair coin is tossed 5 times, what is the probability, to the nearest thousandth, of getting exactly 0 heads?
The probability of getting exactly 0 heads is, 0.031.
What is probability?
The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a proposition to be true. A number between 0 and 1 is the probability of an event, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.
Given:
A fair coin is tossed 5 times.
So, the the total number of possibilities are,
[tex]2^5= 32[/tex]
We have to find the probability of getting exactly 0 heads.
The only possible set of flips that yields 0 heads is {T, T, T, T, T}.
So,
The probability is, [tex]\frac{1}{32}=0.03125[/tex]
Probability ≈ 0.031
Hence, the probability of getting exactly 0 heads is, 0.031.
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Sketch the region bounded by the curves, and visually estimate the location of the centroid. Y = ex, y = 0, x = 0, x = 3.
The centroid appears to be in the middle of the base and one-third of the way up the triangle, at (1.5, e^1).
The center of the object is represented by the centroid. The centroid of a triangle is the location where the triangle's three medians cross. The intersection of all three medians is another definition of it. The median is a line that connects the middle of a side to the opposite vertex of a triangle. The region bounded by the curves is a triangle with the tip at (0, e^0) and the base at (3, 0). The centroid appears to be in the middle of the base and one-third of the way up the triangle, at (1.5, e^1).
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Pls help me, Brainliest + 100 points if correct and well explained:
What are the vertex and range of y = |x − 5| + 4?
a: (5, 4); −∞ < y < ∞
b: (5, 4); 4 ≤ y < ∞
c: (−5, 4); −∞ < y < ∞
d: (−5, 4); 4 ≤ y < ∞
The vertex and range of the function y = |x - 5| + 5 is (5, 4) and [4, ∞) respectively
Vertex and RangeThe vertex of the function is located at (h,k) of its vertex form, and will be located at the peak or trough of the parabola on a graph. This is the highest or lowest point of the function, depending on its direction.
The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain.
In the given function;
y = |x - 5| + 4
Using a graph, the lowest point of the function is at x = 5 and y = 4 is the vertex of this function.
vertex = (5, 4)
Range = [4, ∞)
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Find the distance from line L to point P for each of the following: Line L contains points (-5,3) and (4,-6). Point P(2,4)
Answer and explanation in one:
(4+9)/(-2-1) = 13/-3 = -13/3
y=-13x/3 + b
4=26/3 + b
b = 4-26/3 = (12-26)/3 = -14/3
y=-13x/3 -14/3 is the line through the two given points
find the line perpendicular and through (14,-6)
y=3x/13 + b, plug in the point to find b
-6 = 3(14)/13 + b
b = -6 -42/13 = -78/13 - 42/13 = -120/3
y= 3x/13 - 120/13
find the intersection point of the two lines, set them equal
3x/13 -120/13 = -13x/3 - 14/3
multiply by 39
9x - 360 = -169x - 182
178x = 360-182 = 178
x = 1
y= -27/3=-9
the point is (1,-9)
calculate the distance from (1,-9) to (14,-6)
d^2 = 9+169 = 178
d = sqr178 = about 13.34
If you walk around a circular path twice which has a diameter of 100 m, how far did you walk in total?
The total distance Is
m.
Use π = 3.14 and round your answer to the nearest hundredth.
Answer:
628 m
Step-by-step explanation:
We need to find the circumference, C, of the circle.
C = πd
C = 3.14 × 100 m
C = 314 m
Walking around the circular path twice is twice the length of the circumference.
distance = 2C = 2 × 314 m = 628 m
Kelli walks no more than 25 dogs on Mondays. Ms. Lincdan has 5 dogs that Kelli walks. The inequality shown can be
used to find x, the number of dogs Kelli can walk on Monday in addition to Ms. Lincoln's dogs.
x + 5 ≤ 25
Which inequality represents all possible values of x?
A x ≥ 20
B x ≤ 20
C x ≥ 30
D x ≤ 30
(5+9i)+(4-5i) simplify
Answer:
9 + 4i
Step-by-step explanation:
5 + 4 + 9i - 5i
=> 9 + 4i
question professor liu gave the same quiz to the students in her morning class and in her afternoon class. the average (arithmetic mean) score for the two classes combined was 84. which class had more students?
From the given average the number of students are more in the afternoon quiz as compare to the morning quiz .
As given in the question,
Combined average score of the two classes = 84.
Average score of students in the morning quiz = 80
Let 'x' be the number of students in the morning quiz
80 = ( Sum of all number of students in the morning quiz) / x
⇒ Sum of all number of students in the morning quiz = 80x __(1)
Average score of students in the afternoon quiz = 86
Let 'y' be the number of students in the afternoon quiz
86 = ( Sum of all number of students in the afternoon quiz) / y
⇒ Sum of all number of students in the afternoon quiz = 86y __(2)
Average score of combined classes = ( 80x + 86y ) / (x + y)
⇒ 84 = ( 80x + 86y ) / (x + y)
⇒ 84x + 84y = 80x + 86y
⇒4x = 2y
⇒ y = 2x
Number of students in the afternoon are double the number of students in the morning.
Therefore, from the given averages afternoon class has more number of students than morning class
The complete question is :
Professor Liu gave the same quiz to the students in her morning class and in her afternoon class. The average (arithmetic mean) score for the two classes combined was 84. Which class had more students?(1) The average score for the students in the morning class was 80
(2) the average score for the students in the afternoon class was 86
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Write an equation of the line that passes through (-6, 0) and (0, -24) .
Answer: y= -4x -24
Step-by-step explanation:
The equation is y=mx + b
We know the b is -24 because it already tells us the coordinate of the y-intercept is (0, -24), so we only need to find x by looking at the rise over run.
The rise is -24, and the run is 6, so -24/6 = -4
So the equation is y= -4x -24
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Four small candies cost $.96 how much do six candies cost
Six candies would cost $1.44.
Answer:
$1.44
Step-by-step explanation:
We need to figure out how much one piece of candy costs. So you do .96/4, which is going to equal 0.24.
1 piece of candy = $0.24
So we do 0.24*6= 1.44
I hope this helps!!!
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A line join A (3,2) and B (3,-3) on a half centimetre grid. P i a point on the line AB uch that AP:PB =3:2
ue the x tool to plot point P
The co-ordinates of the point P that divides the line segment AB in the ratio 3:2 are (3,0)
What is Line Geometry?
A line is an endlessly long object with no breadth, depth, or curve in geometry. Lines are thus one-dimensional objects, even if they can exist in two, three, or higher dimensions. In ordinary language, the term line can also refer to a line segment with two points denoting its endpoints.
Solution:
To find the co-ordinates of point P we wil use section formula
(x,y) = (m*x2 + n*x1 / m+n), (m*y2 + n*y1 / m+n)
(x,y) = (3*3 + 2*3)/5 , (3*2 + 2*(-3))/5
(x,y) = 15/5 , 0/5
(x,y) = 3,0
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Of the 47 plays attributed to a playwright, 11 are comedies, 16 are tragedies, 20 are histories. If one play is selected at random, find the odds against selecting a
The odds against selecting a history are 31/16.
Define probability.Probability is the concept that describes the likelihood of an event occurring. In many situations, it is necessary to foresee how something will turn out in the actual world. We may be aware of the result of an event or not. When this occurs, we state that there is a possibility that the event will occur.
Probability is the ratio of the most likely outcomes to all other possible outcomes of an event. The number of successful outcomes for an experiment with 'n' outcomes may be expressed using the symbol x. The following formula can be used to determine the likelihood of an event.
Probability(Event) = favorable outcome/Total outcome = x/n
Number of playwrights = 47
Number of tragedies = 16
Therefore, the odds against selecting tragedies are
(47 - 16) / 16
= 31/16
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The complete question is:
Of the 47 plays attributed to a playwright, 11 are comedies, 16 are tragedies, 20 are histories. If one play is selected at random, find the odds against selecting a tragedy.
You begin the week with 30 units of orange juice. You purchase 50 units. Your ending inventory for the week is 30 units. How many units did you sell?.
Using simple mathematical operations, we know that we sold a total (D) of 50 units of orange juice.
What are mathematical operations?A mathematical function known as an operation converts zero or more input values into a precisely defined output value.
The quantity of operands affects the operation's arity.
The order of operations refers to the rules that define the sequence in which we should perform the operations necessary to solve an equation.
Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction are collectively referred to as PEMDAS.
So, we begin the week with 30 units of orange juice.
We purchase more than 50 units of orange juice.
Total: 30 + 50 = 80 units
Our ending inventory was 30 units.
Units of orange juice sold: 80 - 30 = 50 units
Therefore, using simple mathematical operations, we know that we sold a total (D) of 50 units of orange juice.
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Complete question:
You begin the week with 30 units of orange juice. You purchase 50 units. Your ending inventory for the week is 30 units. How many units did you sell?
a) 5
b) 15
c) 49
d) 50
Think about all of the ways in which a line and a parabola can intersect. Select all of the number of ways in which a line and a parabola can intersect. 0 1 2 3 4 infinitely many
Answer:3
Step-by-step explanation:3
0.5 power of 2 + 0.3 power of 2?
Answer:
8.9
Step-by-step explanation:
Answer:
0.34
Step-by-step explanation:
[tex] {0.5 }^{2} + {0.3}^{2} \\ 0.25 + 0.09 \\ = 0.34[/tex]
(I'm not sure if this is what you meant)
a rectangle is constructed with its base on the diameter of a semicircle with radius 12 and with its two other vertices on the semicircle. what are the dimensions of the rectangle with maximum area?
As describes in geometry the area of the rectangle = 288cm
what is geometry ?
The area of mathematics known as geometry is concerned with the characteristics of the surrounding space as well as the shapes of individual objects and their spatial relationships.
solution
radius of semicircle = 12
diameter will be = 24 and this is the length of rectangle s given in the question
area of the rectangle = l*b
= 24*12
area of the rectangle = 288cm
Hence the area of the rectangle = 288cm
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1. You'll find the glue and scissors in ___
*There
*Their
* They're
What was the beginning balance in the incomplete register shown? Date 10/21/03 Description of Transaction Payment Deposit Balance Beginning Balance Mike's Cafe 10/26/03 Sporting Goods Store Paycheck Amusement Park $38.25
The required balance at the beginning of the incomplete register is $38.25.
Given that,
To determine the beginning balance in the incomplete register.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
In the table, in the register, the balance starts with an entry of $38.25 paycheck. So, the 1 st entry of the register shows the balance in the beginning.
Thus, the required balance at the beginning of the incomplete register is $38.25.
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A new car is purchased for 22600 dollars. The value of the car depreciates at 11. 5% per year. To the nearest tenth of a year, how long will it be until the value of the car is 5200 dollars?.
When the car is acquired for $22600 and depreciates at an 11.5% rate, it will take 6.7 years for its worth to reach $5200.
What is percent?In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).
Here,
Cost of car=$22600
Rate of depreciation=11.5%
After n years, value of car=$5200
Annual depreciation expense=22600*11.5%
=$2599
Value of the Car = Purchase cost - (Annual depreciation expenses * n)
5200=22600-(2599*n)
2599n=22600-5200
2599n=17400
n=6.695
n=6.7 years
The number of years until the value of the car is 5200 dollars at depreciation rate of 11.5% when purchased at 22600 dollars will be 6.7 years.
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On a coordinate plane, 2 trapezoids are shown. Trapezoid 1 has points A (negative 4, 3), B (1, 3), C (0, 0), and D (negative 3, 0). Trapezoid 2 has points A prime (negative 1, 1), B prime (4, 1), C prime (3, negative 2), and D prime (0, negative 2).
Which rule describes the translation?
T–3, –2(x, y)
T–3, 2(x, y)
T3, –2(x, y)
T3, 2(x, y)
The rule of translation will be; Horizontal shift by 3 units right and vertical shift by 2 units down (x, y) → (x + 3, y -2)
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s range(involving values of y) or in it’s domain(involving values of x).
For the shift left, shift right, shift down, shift up, vertical stretching, horizontal stretching, vertical compression, horizontal compression, reflection over the x-axis, reflection over the y-axis, and rotations by a determined amount(in degrees). All these translations have predetermined rules that we apply to the figures.
Given that Trapezoid 1 with vertices
A(-4, 3), B(1, 3), C(0, 0), D(-3, 0)
Trapezoid 2 with vertices are;
A'(-1, 1), B'(4, 1), C'(3, -2), D'(0, -2)
It can be observed by comparison that the x-values have increased by 3 units and the y-values have decreased by 2 units
So the rule of translation will be; Horizontal shift by 3 units right and vertical shift by 2 units down (x, y) → (x + 3, y -2)
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Evaluate the surface integral. s (x + y + z) ds, s is the parallelogram with parametric equations x = u + v, y = u − v, z = 1 + 2u + v, 0 ≤ u ≤ 3, 0 ≤ v ≤ 2.
the surface integral. s (x + y + z) ds, s is the parallelogram with parametric equations x = u + v, y = u − v, z = 1 + 2u + v is 10[tex]\sqrt{14}[/tex]
The surface element is
dS = || ∂r/∂u x ∂r/dv || du dv
where
r (u, v) = x (u, v) i + y (u, v) j + z (u, v) k
r (u, v) = (u + v) i + (u - v) j + (1 + 2u + v) k
is the vector parameterization for the surface S.
The normal vector to the surface is
∂r/∂u x ∂r/dv
… = (i + j + 2 k) x (i - j + k)
… = 3 i + j - 2 k
and has norm
|| ∂r/∂u x ∂r/dv || = √(3² + 1² + (-2)²) = √(14)
Now compute the integral:
∫∫ (x + y + z) dS = √(14) ∫₀¹ ∫₀² ((u + v) + (u - v) + (1 + 2u + v)) du dv
… = √(14) ∫₀¹ ∫₀² (3u + v + 1) du dv
… = √(14) ∫₀¹ (3/2 u² + uv + u) |₀² dv
… = √(14) ∫₀¹ (8 + 2v) dv
… = √(14) (8v + 2v²) |₀¹
… = 10 √(14)
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Use the given zero to find the remaining zeros of each function.
Thank you!! :)
Answer:
remaining zeros: {-1/2, √3}
Step-by-step explanation:
Given the polynomial function f(x) = 2x³ +x² -6x -3 has one zero at x = -√3, you want the remaining zeros.
Conjugate zerosA polynomial with rational real coefficients and zeros that are roots or complex numbers will have all such roots in conjugate pairs.
The root that is the conjugate of -√3 is +√3.
Product of rootsThe product of the roots of an odd-degree polynomial will be the opposite of the ratio of the constant to the leading coefficient. Here, that means the product of roots is ...
-(-3/2) = 3/2
We already know that two of the three roots are ±√3, so their product is -3. The remaining root will be ...
(3/2)/(-3) = -1/2
The remaining zeros of f(x) are √3 and -1/2.
__
Additional comment
When the degree of the polynomial is even, the constant term will be the product of the roots. This odd/negative, even/positive behavior comes from the fact that each zero (q) corresponds to a factor (x -q).
The product of these binomial factor constants is the constant in the standard-form polynomial. It will have a negative sign if there are an odd number of factors.
An airplane is preparing to land at an airport. It is 40,600 feet above the ground and is descending at the rate of 3,300 feet per minute. At the same airport, another airplane is taking off and will ascend at the rate of 2,500 feet per minute. When will the two airplanes be at the same altitude and what will that altitude be?
" They will be at the same altitude in ? minutes, when their altitude will be ? feet. "
Answer:
2.5x103
Step-by-step explanation:
19. a television set is on sale for 15% off the original price. if the sale is $340, what was the original price of the televisions set?
Using the percentage method, we know that the original price of the TV set was $400.
What is the percentage?Percentages are just fractions with a denominator of 100.
To show that a number is a percentage, we place the percent sign (%) next to it.
For instance, if you properly answered 75 out of 100 questions on a test, you would have received a 75% grade (75/100).
So, we know that the percentage is always out of 100.
Then we automatically know that:
100% - 15% = 85%
We know:
85% = $340
15% = ?
Now, calculate the reduced price as follows:
85/340 = 15/x
85x = 15(340)
85x = 5,100
x = 5100/85
x = $60
Original price of the TV set:
Sold cost + Reduced cost
$340 + $60
$400
Therefore, using the percentage method, we know that the original price of the TV set was $400.
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given 2n letters, two of each of n types, how many arrangements are there with no pair of consecutive letters the same?
The arrangements are there with no pair of consecutive letters the same is ∑ₐⁿ(−1)^k2^k(2n−k)!C(n,k).
Explain arrangements are there with no pair of consecutive letters the same.The past step makes six void spots in which three Is might be sorted out, however just three spots should be picked. Request doesn't make any difference, as every one of the three Is are something similar. Along these lines, there are (63) approaches to picking those spots.
According to question:Given 2n letters, two of every one of n types. What number of courses of action of these letters are there without any sets of sequential letters something similar? Kindly look at my answer and let me know where my mix-up is!
So such plans where the sets of indistinguishable letters are discernable. Then, at that point, ∑ₐⁿ(−1)^k2^k(2n−k)!C(n,k) gives the quantity of such plans by incorporation avoidance (there are (2n−k)! ways for k given matches to be together (by combining the those sets into single components) and the rest randomly requested, 2k ways of requesting inside those given matches, and C(n,k) ways of picking those k pairs).So we can acquire the recipe
∑ₐⁿ(−1)^k2^k(2n−k)!C(n,k)
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PLEASE HELP ASAPPP. WILL GIVE BRAINLIEST AND 5.0 STAR RATING.
Answer:
0.40
Step-by-step explanation:
.04 x 10 = .40
Answer: $0.40
Step-by-step explanation: The sales tax will be 4% of the selling price
The end price will be 10.40
a country uses as currency coins with values of 1 peso, 2 pesos, 5 pesos, and 10 pesos and bills with values of 5 pesos, 10 pesos, 20 pesos, 50 pesos, and 100 pesos. find a recurrence relation for the number of ways to pay a bill of n pesos if the order in which the coins and bills are paid matters
when we pay n pesos, then recurrence relation for all the number are in a ways to pay a bill is in this order:[tex]a_{n} =a_{n-1}+a_{n-2}+2a_{n-5}+2a_{n-10}+ a_{n-20}+a_{n-50}+a_{n-100}[/tex]
A recurrence relation is an equation which represents a chain primarily based totally on a few rule. It enables in locating the following time period (subsequent time period) established upon the previous time period (preceding time period). If we recognise the preceding time period in a given series, then we will without difficulty decide the following time period.
Recurrence family members are used to lessen complex issues to an iterative procedure primarily based totally on less difficult variations of the trouble. An instance trouble wherein this technique may be used is the Tower of Hanoi puzzle. Recurrent is some thing that happens frequently or repeatedly. However, in case you are speakme approximately a recurrence relation, then you definitely have a mathematical shape which you are handling and it's miles really specific than a recursive formula. Recursion is the repeated use of a process or action.
pay 1 pesos coin , then n-1 pesos
pay 2 pesos coin , then n-2 pesos if n ≥ 2
pay 5 pesos coin , then n-5 pesos if n ≥ 5
pay 10 pesos coin , then n-10 pesos if n ≥ 10
pay 5 pesos bill , then n-5 pesos if n ≥ 5
pay 10 pesos bill , then n-10 pesos if n ≥ 10
pay 20 pesos bill , then n-20 pesos if n ≥ 20
pay 50 pesos bill , then n-50 pesos if n ≥ 50
pay 100 pesos bill , then n-100 pesos if n ≥ 100
a0=1
so i have recurrence relation as follows:
[tex]a_{n} =a_{n-1}+a_{n-2}+2a_{n-5}+2a_{n-10}+ a_{n-20}+a_{n-50}+a_{n-100}[/tex]
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Given the equation |x+10|=15
, x= 5 is one solution. What is the other solution?
Answer:
x = - 25
Step-by-step explanation:
the absolute value function always gives a positive value , however , the expression inside the bars can be positive or negative, that is
| - a | = | a | =a
given
| x + 10 | = 15 , then
x + 10 = 15 ( subtract 10 from both sides )
x = 5
OR
-(x + 10) = 15
- x - 10 = 15 ( add 10 to both sides )
- x = 25 ( multiply both sides by - 1 )
x = - 25
solutions are x = 5 , x = - 25
Answer: -25
Step-by-step explanation: