Part A
Her steps were
[tex]-2 \frac{5}{6} \div 1 \frac{1}{3}\\\\-\frac{17}{6} \div \frac{4}{3}\\\\-\frac{6}{17} \times \frac{3}{4}\\\\-\frac{6\times 3}{17\times4}\\\\-\frac{18}{68}\\\\-\frac{9}{34}\\\\[/tex]
Kelsey made a mistake on line 3. Note how the 17/6 flips to 6/17. This is not correct. You keep the first fraction the same, but you do flip the second fraction. This only applies when you divide two fractions.
The third step should look like [tex]-\frac{17}{6}\times \frac{3}{4}[/tex]
=======================================================
Part B
Here's what she should have written
[tex]-2 \frac{5}{6} \div 1 \frac{1}{3}\\\\-\frac{17}{6} \div \frac{4}{3}\\\\-\frac{17}{6} \times \frac{3}{4}\\\\-\frac{17\times 3}{6\times 4}\\\\-\frac{51}{24}\\\\-\frac{17}{8}\\\\[/tex]
If you want to convert that improper fraction to a mixed number, then you could do something like this
[tex]-\frac{17}{8} = -\frac{16+1}{8}\\\\-\frac{17}{8} = -\frac{16}{8}-\frac{1}{8}\\\\-\frac{17}{8} = -2 \frac{1}{8}\\\\[/tex]
Or you could divide 17 over 8 using long division to get 2 remainder 1. The 2 is the quotient that goes to the left of the 1/8. The remainder of 1 is the numerator of 1/8.
Show that the equations x^2-7x+6=0 and y^2-14y+40=0 form a rectangle.Also find the joint equations of diagonals.
Answer:
1) The region between the four lines x = 6, x = 1, y = 4 and y = 10 describing both equations is a rectangle
2) The joint equations of diagonals are;
5·y = 56 - 6·x and 5·y = 6·x + 14.
Step-by-step explanation:
The equations are;
x² - 7·x + 6 = 0......................(1)
y² - 14·y + 40 = 0.................(2)
Factorizing equation (1) and equation (2) , we get
x² - 7·x + 6 = (x - 6)·(x - 1) = 0
Which are vertical lines at points x = 6 and x = 1
For equation (2) , we get
y² - 14·y + 40 = (y - 10)·(y - 4) = 0
Which are horizontal lines at point y = 4 and y = 10
The region between the four lines x = 6, x = 1, y = 4 and y = 10 describing both equations is a rectangle
2) The points of intersection of the equations are;
(1, 4), (1, 10), (6, 4), and (6, 10)
The end point of the diagonals are;
(1, 10), (6, 4) and (1, 4), (6, 10)
The slope of the diagonals are;
(10 - 4)/(1 - 6) = -6/5 and (4 - 10)/(1 - 6) = 6/5
The equation of one of the diagonals are then, y - 10 = -6/5×(x - 1)
y = -6/5·x + 6/5 + 10 = -6/5·x + 56/5
5·y = 56 - 6·x
The other diagonal is therefore;
y - 4 = 6/5×(x - 1)
y = 6/5·x - 6/5 + 4 = 6/5·x + 14/5
5·y = 6·x + 14.
The joint equations of diagonals are therefore;
5·y = 56 - 6·x and 5·y = 6·x + 14.
Solve for h. 3/7=h/14-2/7
Answer:
h = 10
Step-by-step explanation:
Given
[tex]\frac{3}{7}[/tex] = [tex]\frac{h}{14}[/tex] - [tex]\frac{2}{7}[/tex]
Multiply through by 14 to clear the fractions
6 = h - 4 ( add 4 to both sides )
10 = h
Answer:
10
Step-by-step explanation:
We start out with 3/7 = h/14 - 2/7
add 2/7 to both sides:
(5/7) = h/14
Multiply both sides by 14 to get rid of the fraction:
h = 10
Please answer this question now
Answer:
298.3 square centimeters
Step-by-step explanation:
We are given
Slant height (l)= 14cm
Radius (r)= 5cm
Since we are given the slant height ,
the formula for surface area of a cone =
πrl + πr²
πr(l + r)
π = 3.14
Hence,
3.14 × 5(14 + 5)
3.14 × 5(19)
= 298.3 square centimeters
I NEED HELP PLEASE I GIVE 5 STARS !
Answer:
C. 2[tex]\sqrt{29}[/tex]
Step-by-step explanation:
Square root of 116 is 10.7703296
Square root of 29 is 5.38516481, but as it is multiplied by 2, it becomes 10.7703296
make u the subject of the formula
u-x/v-x=u/v²
Answer:
See below.
Step-by-step explanation:
[tex]\frac{u-x}{v-x}=\frac{u}{v^2} \\[/tex]
Cross multiply and distribute.
[tex]u(v-x)=v^2(u-x)\\uv-ux=uv^2-xv^2[/tex]
Move all the u to the left side:
[tex]uv-ux-uv^2=-xv^2[/tex]
Factor out a u:
[tex]u(v-x-v^2)=-xv^2[/tex]
Divide:
[tex]u=\frac{-xv^2}{v-x-v^2}=\frac{xv^2}{x+v^2-v}[/tex]
(I factored out a negative in the second term.)
The diagonal of rhombus measure 16 cm and 30 cm. Find it's perimeter
Answer:
P = 68 cmStep-by-step explanation:
The diagonals of the rhombus divide it into 4 congruent right triangles.
So we can use Pythagorean theorem to calculate side of a rhombus.
[tex](\frac e2)^2+(\frac f2)^2=s^2\\\\e=30\,cm\quad\implies\quad\frac e2=15\,cm\\\\f=16\,cm\quad\implies\quad\frac f2=8\,cm\\\\15^2+8^2=s^2\\\\s^2=225+64\\\\s^2=289\\\\s=17[/tex]
Perimeter:
P = 4s = 4•17 = 68 cm
On Wednesday at camp, Samuel went for a hike at 6:30 A.M. The hike took 2 hours and 15 minutes. As soon as he got back from the hike, Samuel played volleyball for 1 hour. What time did Samuel finish playing volleyball?
Answer:
9:45 A.M.
Step-by-step explanation:
First, add the time that took him to hike:
6:30 + 2 hours and 15 minutes = 8:45 A.M.
Next, add the 1 hour that he played volleyball for:
8:45 + 1 hour = 9:45 A.M.
So, he finished playing volleyball at 9:45 A.M.
Answer:
9:45 am
Step-by-step explanation:
He went at 6:30 am to a hike.
It took him 2 hours 15 minutes
=> 6 : 30
+ 2 15
=> 8 : 45
He came back from the Hike at 8:45 am
He played volleyball for 1 hour.
=> 8 : 45
+ 1
=> 9 : 45
He finished playing volleyball at 9:45 am
This table represents a quadratic function.
y
x
0
14
1
10.5
2
8
3
6.5
4
5
6.5
What is the value of a in the function's equation?
A.2
B.1/2
C.-1/2
D.1
Answer:
B. 1/2
Step-by-step explanation:
y = ax^2 + bx + c
14 = a(0)^2 + b(0) + c
c = 14
10.5 = a(1)^2 + b(1) + 14
10.5 = a + b + 14 ____(i)
8 = a(2)^2 + b(2) + 14
8 = 4a + 2b + 14
4 = 2a + b + 7 ___ (ii)
i - ii
10.5 - 4 = -a + 7
6.5 = -a + 7
a = 7- 6.5
a = 0.5
Value of a in the quadratic function is 0.5
What is Quadratic function?In algebra, a quadratic function, a quadratic polynomial, a polynomial of degree 2, or simply a quadratic, is a polynomial function with one or more variables in which the highest-degree term is of the second degree
Given,
Quadratic function
y = [tex]ax^{2}+bx+c[/tex]
Consider values in the table x= 0 and y =14
[tex]14=a(0)^{2}+b(0)+c\\ c=14[/tex]
Consider x=1 and y = 10.5
[tex]10.5=a(1^{2})+b(1)+c\\ a+b=10.5-14\\a+b=-3.5[/tex]
Consider x=2 and y =8
[tex]8=a(2^{2})+b(2)+c\\ a\\8=4a+2b+14\\4a+2b=-6\\2a+b=-3[/tex]
Subtract a + b= -3.5 from 2a + b= -3
a=-3--3.5=0.5
Hence, the Value of a in the quadratic function is 0.5
Learn more about Quadratic function here
https://brainly.com/question/5975436
#SPJ2
A bag contains 2
2
blue marbles, 2
2
red marbles, and 2
2
yellow marbles.
If Jenna randomly draws a marble from the bag (and puts it back) 15
15
times, how many times should she expect to pull a yellow marble?
Answer:
5 times
Step-by-step explanation:
Jenna wil most likely pull a yellow marble 1/3 of the time, because the total number of marbles is 6, and there are 2 yellow marbles, 2/6 which is 1/3. 1/3 times 15 is 5. So Jenna will most likely pull a yellow marble 5 times.
How to do this question plz answer me step by step plzz plz plz plz plz plz plz plz
Answer:
288.4m
Step-by-step explanation:
This track is split into a rectangle and two semi-circles.
We can find the length of the semi-circles by finding its circumference with the formula [tex]2\pi r[/tex].
[tex]2\cdot3.14\cdot30\\188.4[/tex]
However this is half a circle, so:
[tex]188.4\div2=94.2[/tex].
There are two semi-circles.
[tex]94.2\cdot2=188.4[/tex]
Since there are two legs of 50m each, we add 100 to 188.4
[tex]188.4+100=288.4[/tex]m
Hope this helped!
Answer:
Step-by-step explanation:
To solve for the perimeter, we first look at the rectangle in the middle. the length is 50m, and there are two sides to it, so: 50 * 2 = 100m for the top and bottom of the track.
For the circle, we can see the diameter is 30m. To solve for the circumference, we need to use the formula 2πr.
15 * 2π ≈ 94.2477796077
We add that to 100m and get:
194.2477796077
Which type(s) of symmetry does the following object have?
Select all that apply.
Answer: You are correct. There is only one answer and that is choice B) vertical line of symmetry.
We can draw a vertical line through the center to have one half mirror over this line to get the other half. We can't do the same with a horizontal line or any other kind of line.
We do not have rotational symmetry. Rotating the figure will produce an image different from the original. The angle of rotation is some angle x such that 0 < x < 360.
Answer:
Theres more than one answer so b and a
Step-by-step explanation:
5
What is the equation, in point-slope form, of the line that
is parallel to the given line and passes through the point
(-3, 1)?
4
3
2
(-3, 1)
42.27
1
5 4 3 2 1
2 3 4 5 x
y-1=-{(x+3)
y-1=-{(x + 3)
y-1= {(x + 3)
y-1= {(x + 3)
(-2, 4)
Answer: [tex]y-1=\dfrac32(x+3)[/tex]
Step-by-step explanation:
Slope of a line passes through (a,b) and (c,d) = [tex]\dfrac{d-b}{c-a}[/tex]
In graph(below) given line is passing through (-2,-4) and (2,2) .
Slope of the given line passing through (-2,-4) and (2,2) =[tex]\dfrac{-4-2}{-2-2}=\dfrac{-6}{-4}=\dfrac{3}{2}[/tex]
Since parallel lines have equal slope . That means slope of the required line would be .
Equation of a line passing through (a,b) and has slope m is given by :_
(y-b)=m(x-a)
Then, Equation of a line passing through(-3, 1) and has slope = is given by
[tex](y-1)=\dfrac32(x-(-3))\\\\\Rightarrow\ y-1=\dfrac32(x+3)[/tex]
Required equation: [tex]y-1=\dfrac32(x+3)[/tex]
PLEASE HELP Polynomial Graph Studies Polynomials are great functions to use for modeling real-world scenarios where different intervals of increase and decrease happen. But polynomial equations and graphs can be trickier to work with than other function types. In mathematical modeling, we often create an equation to summarize data and make predictions for information not shown on the original display. In this activity, you’ll create an equation to fit this graph of a polynomial function. Part A Describe the type of function shown in the graph. Part B What are the standard form and the factored form of the function? Part C What are the zeros of the function? Part D Use the zeros to find all of the linear factors of the polynomial function. Part E Write the equation of the graphed function f(x), where a is the leading coefficient. Use the factors found in part D. Express the function as the product of its leading coefficient and the expanded form of the equation in standard form. Part F Use the y-intercept of the graph and your equation from part E to calculate the value of a. Part G Given what you found in all of the previous parts, write the equation for the function shown in the graph.
Answer:
Here's what I get
Step-by-step explanation:
Part A
The graph shows a polynomial of odd degree. It is probably a third-degree polynomial — a cubic equation.
Part B
The standard form of a cubic equation is
y = ax³ + bx² + cx + d
The factored form of a cubic equation is
y = a(x - b₁)(x² + b₂x + b₃)
If you can factor the quadratic, the factored form becomes
y = a(x - c₁)(x - c₂)(x - c₃)
Part C
The zeros of the function are at x = -25, x = - 15, and x = 15.
Part D
The linear factors of the function are x + 25, x + 15, and x - 15.
Part E
y = a(x + 25)(x + 15)(x - 15) = a(x + 25)(x² - 225)
y = a(x³ + 25x² - 225x - 5625)
Part F
When x = 0, y = 1.
1 = a[0³ +25(0)² - 225(0) - 5625] = a(0 + 0 - 0 -5625) = -5625a
a = -1/5625
Part G
[tex]y = -\dfrac{1}{5625}( x^{3} + 25x^{2} - 225x - 5625)\\\\y = \mathbf{ -\dfrac{1}{5625} x^{3} - \dfrac{1}{225}x^{2} + \dfrac{1}{25} x + 1}[/tex]
Answer
Actually, the answer should be -0.0007(x+20)(x+5)(x-15)
Step-by-step explanation:
This is continuing off of the previous answer
PART C
The zeros should be (15,0), (-5,0), and (-20,0)
PART D
x - 15, x + 5, and x + 20
PART E
a(x - 15)(x + 5)(x + 20)
Standard: [tex]a(x^{3} + 10x^{2} -275x-1500)[/tex]
PART F
The y-intercept is at (0,1), so we replace the x's with 0:
1 =[tex][(0)x^{3} +10(0)x^{2} -275(0)-1500][/tex] and this gives us (0+0-0-1500) which also equals -1500
Then we do [tex]\frac{1}{-1500}[/tex] which gives us -0.0006 repeating which rounds to -0.0007
a= -0.0007
PART G
Just place the numbers where they should go and your answer is
y =-0.0007(x + 20)(x + 5)(x - 15)
the placement for (x + 20) (x + 5) and (x - 15) doesn't matter as long as they are behind -0.0007
what is the coefficient of the variable in the expression 4-3x
As per the question,
We have to find what's the coefficient.
Let's start to seperate the expression.
Here,
x is the variable,
4 is a number.
-3 is also a number.
4, -3x
The number with x here is -3 in (-3x) as the coefficient is (-3) in the given equation.
Answer:
Hey there!
Rearrange the expression to: -3x+4
The coefficient would be -3.
Let me know if this helps :)
PLEASE HELP ASAP!!
The image above shows two dilated figures with lines IJ and JK drawn. If the smaller figure was dilated by a scale factor of 2, what relationship do lines IJ and KL have?
Answer:
[tex] IJ = 2(KL) [/tex]
Step-by-step explanation:
From the information given, the smaller figure was dilated on a scale factor of 2, to produce the bigger figure. In essence, the bigger figure is times 2 of the smaller figure.
Therefore, line IJ would be twice the length of KL.
The relationship that both lines have can be represented as: [tex] IJ = 2(KL) [/tex]
20 POINTS! ***CORRECT*** ANSWER GETS BRAINLIEST!!!!
The fraction model below shows the steps that a student performed to find a quotient.
Which statement best interprets the quotient?
A. There are 5 1/6 three-fourths in 4 1/8
B. There are 5 1/6 three and one-eights in 3/4
C. There are 5 1/2 three and one-eights in 3/4
D. There are 5 1/2 three-fourths in 4 1/8
Answer:
(D) There are [tex]5 \frac{1}{2}[/tex] three-fourths in [tex]4 \frac{1}{8}[/tex]
Step-by-step explanation:
We can see that in this model, the student tried to put [tex]\frac{3}{4}[/tex] into [tex]4 \frac{1}{8}[/tex]. We know this because the top of Step 2 is [tex]4 \frac{1}{8}[/tex] and he is counting how many fourths in the bottom.
So this becomes the division statement:
[tex]4 \frac{1}{8} \div \frac{3}{4}[/tex].
We can convert [tex]4 \frac{1}{8}[/tex] into a mixed number by multiplying 8 and 4, then adding 1.
[tex]\frac{33}{8} \div \frac{3}{4}[/tex].
Multiply by the reciprocal:
[tex]\frac{33}{8} \cdot \frac{4}{3} = \frac{132}{24}[/tex]
Which simplifies down to
[tex]\frac{11}{2}[/tex], which is just [tex]5 \frac{1}{2}[/tex] in improper form.
Hope this helped!
Answer:
D
Step-by-step explanation:
The number of polynomials having zeros as -2 and 5 is a)1 b)2 c)3 d)more than 3
Answer:
d) More than 3.
Step-by-step explanation:
The polynomial (x - 5)(x + 2) ( = x^2 - 3x + 10) has zeros of -2 and 5 but so have the polynomials formed by multiplying this by any integer:
- for example 2(x - 5)(x + 2) , 4(x - 5)(x + 2) and so on.
every rational number is a
a. whole number b. natural number c. integer d. real number
Greetings from Brasil...
a - whole number
FALSE
3/5, for example isnt a whole number
b. natural number
FALSE
0,457888..., for example isnt a natural number
c. integer
FALSE - like a
d. real number
TRUE
The set of real numbers contains the set of rational numbers
ℝ ⊃ ℚ
HELP ASAP
[tex]Given that $33^{-1} \equiv 77 \pmod{508}$, find $11^{-1} \pmod{508}$ as a residue modulo 508. (Give an answer between 0 and 507, inclusive.)[/tex]
===================================================
Work Shown:
[tex]33^{-1} \equiv 77 \text{ (mod 508)}\\\\(3*11)^{-1} \equiv 77 \text{ (mod 508)}\\\\3^{-1}*11^{-1} \equiv 77 \text{ (mod 508)}\\\\3*3^{-1}*11^{-1} \equiv 3*77 \text{ (mod 508)}\\\\11^{-1} \equiv 231 \text{ (mod 508)}\\\\[/tex]
Notice how 33*77 = 2541 and 11*231 = 2541
[tex]2541 \equiv 1 \text{ (mod 508)}[/tex] since 2541/508 has a remainder of 1.
So effectively [tex]33*77 \equiv 1 \text{ (mod 508)}[/tex] and [tex]11*231 \equiv 1 \text{ (mod 508)}[/tex]
What is the factored form of 125x6 – 8?
Answer:
Step-by-step explanation:
125 = 5 *5 * 5 = 5³
8 = 2 * 2 *2 = 2³
125x⁶ - 8 = 5³(x²)³ - 2³
= (5x²)³ - 2³ { a³ - b³ = (a -b)(a² + ab + b²)
= (5x² - 2) ([5x²]² + 5x²*2 + 2²)
= (5x² - 2)(25x⁴ + 10x² + 4)
Hint: (5x²)² = 5² * (x²)² = 25* x²ˣ² = 25x⁴
If f(x) = 4x + 15, then f(-3) = ?
Answer:
[tex]\Huge \boxed{3}[/tex]
Step-by-step explanation:
The function is given :
f(x) = 4x + 15
For f(-3), the input for the function f(x) is -3.
Replace the x variable with -3.
f(-3) = 4(-3) + 15
Evaluate.
f(-3) = -12 + 15
f(-3) = 3
The output for f(-3) is 3.
Answer: f(-3) = 3
Step-by-step explanation: Notice that f is a function of x.
So we want to find f(-3).
We find f(-3) by plugging -3 in for x,
everywhere that x appears in the function.
So we have 4(-3) + 15.
4(-3) is -12 so we have -12 + 15 which is 3.
So f(-3) is 3.
Which graph solves the following system? x+2y=4 5x−2y=8
Answer:
elimination method
x+2y=4 1
5x-2y=8 2
1+2
6x=12
x=2
plug into x+2y=4
2+2y=4
2y=4-2
2y=2
y=1
(2,1)
so graph 1
Help with this find the image of (1 ,2) after a reflection about y=x followed by a reflection about y=-x
Answer: (-1, -2)
Step-by-step explanation:
so at first you have (1, 2)
then you were asked to reflect about y=x which is (x, y) = (y, -x)
(1, 2) = (2, -1)
then followed by y=-x which is (x, y) = (-y, -x)
(2, -1) = (-1, -2)
I hope this helps!
Find the amplitude of y = -2 sin x
Answer:
Amplitude = 2
Step-by-step explanation:
The amplitude of this sine wave is 2 denoted by the coefficient -2 in front of the sin(x). The negative of the coefficient denotes that the sine wave is the opposite of the standard sine wave.
Cheers.
please help me i offered all my points and this is really important!!! The question is attached.
Answer:
25[tex]\sqrt{3}[/tex] +60
Step-by-step explanation: The first thing you need to do is realize that, this figure is a isosceles trapezoid due to the markings on each side.
So now we know both sides are 10.
We also know the the top two angles are congruent to each other and so are the bottom two angles due to the trapezoid being isosceles.
So the top two angles are 120 degrees and bottom two angles are 60 degrees.
It seems like we can't find the sides, let's try drawing two lines from each top angle all the way down to form two right triangles.
Wow, these two triangles are special right triangles in the form of
30 - 60 - 90 degrees.
shorter side = n
longer side = n[tex]\sqrt{3}[/tex]
hypotenuse = 2n
So, 2n = 10
n = 5 for the short side
The bottom base is 4[tex]\sqrt{3}[/tex] + 5 + 5 = 10 + 4[tex]\sqrt{3}[/tex]
The longer side is 5[tex]\sqrt{3}[/tex].
The area of trapezoid = (base1 + base2)/2 * height
= (4[tex]\sqrt{3}[/tex] + 10 + 4[tex]\sqrt{3}[/tex])/2 * 5[tex]\sqrt{3}[/tex] = (10 + 8[tex]\sqrt{3}[/tex])/2 * 5[tex]\sqrt{3}[/tex] = (5+4[tex]\sqrt{3}[/tex])*5[tex]\sqrt{3}[/tex] = 25[tex]\sqrt{3}[/tex] +60
So, 25[tex]\sqrt{3}[/tex] + 60 is our answer.
Answer:
60 +25√3
Step-by-step explanation:
In the figure of the isosceles trapezoid below, the angles at C and D are supplementary to the given angle, so are 60°. That makes triangle BDE a 30°-60°-90° right triangle, which has side length ratios ...
DE : BE : BD = 1 : √3 : 2 = 5 : 5√3 : 10
Triangle BDE can be relocated to the other end of the figure to become triangle CAD'. Then the area of concern is that of the rectangle with height 5√3 and length 5+4√3. The area is then ...
Area = lh = (5√3)(5 +4√3) = 5·5√3 +5·4·3
Area = 60 +25√3 . . . square units
_____
In the figure, 6.93 = 4√3, and 8.66 = 5√3, 16.93 = 10+4√3.
Which statement correctly compares
1–201 and
1512
ol-201 = 151
ol-201 < 51
l-201 > 151
Answer:
Option B.
Step-by-step explanation:
Consider the correct question is "Which statement correctly compares
1. -201 and 151
-201 = 151
-201 < 51
-201 > 151"
The given numbers are -201 and 151. We need to compare these numbers.
We know that all negative numbers are less than positive numbers.
So,
-201 < 151
If both numbers are negative, then the larger negative number is the smaller number.
Therefore, the correct option is B.
Which of the following images shows a scale copy of the trapezoid using a scale factor of 1/2
PLEASE HELP
Answer:
1
Step-by-step explanation:
split the shape to triangle and a rectangle
the rectangle at the original trapezoid has 2 squares in width and 3 squares for height multiply those numbers by 1/2 you will get 1 square for width and 1.5 squares for the height which is showen in option 1
Ramona works in a clothing store where she earns a base salary of $140 per day plus 14% of her daily sales. She sold $600 in clothing on Saturday and $1200 in clothing on Sunday. How much did she earn over the two days? A. $252 B. $291 C. $392 D. $532
Answer:
I hope this helps!
Answer D
Step-by-step explanation:
Step-by-step explanation:
salary per day =$140
bonus on sales =14%
sales on Saturday =$600
bonus on Saturday sales=14/100*$600
=$84
sales on Sunday =$1200
bonus on Sunday sales=14/100*$1200
=$168
total amount she earned over the two days=$140+$84+$168
=$532
The sum of the ages of Noi's and Noy's is 26 years. The different between four times Noi's age and two times Noy's age is 28 years. Find the age of Noi and Noy.
WRITE AS AN EQUATION
Answer:
The age of Noi is 13.333 Years and the age of Noy is 12.67 years
Step-by-step explanation:
The given information are;
The sum of the ages of Noi and Noy = 26 years
Four times Noi's age - Two times Noy's age = 28
Let the age of Noi = X and let the age of Noy = Y
We have;
X + Y = 26 years.................(1)
4X - 2Y = 28 years.............(2)
Divide equation (2) by 2 to get;
(4X - 2Y)/2 = (28 years)/2 which gives;
2X - Y = 14 years.................(3)
Add equation (3) to equation (1), to get;
X + Y + 2X - Y = 26 years + 14 years
3X = 40 years
X = 40/3 = 13.333 Years
From equation (1), X + Y = 26 years, therefore;
Y = 26 - X = 26 - 13.33 = 12.67 years
Therefore, the age of Noi = 13.333 Years and the age of Noy = 12.67 years.
Find the missing probability. P(A)=720,P(B)=35,P(A∩B)=21100 ,P(A∪B)=?
The missing probability P(A∪B) will be 37/50.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
Given information;
P(A)= 7/20,
P(B)=3/5,
P(A∩B) =21/100 ,
We need to find the missing probability P(A∪B).
We know that
P(A∪B)= P(A) + P(B) + P(A∩B)
P(A∪B) = 7/20 + 3/5 + 21/100
P (A U B) = 37/50
Therefore, the missing probability P(A∪B) will be 37/50.
Learn more about probability here;
https://brainly.com/question/11234923
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