The answer is:
The father's step is 80 cm
The son's step is 60 cm.
Why?To solve the problem, we need to write equations in order to create a relation between the father's and son's steps, and the distance covered by them.
We know thay they covered 240 meters, and the father's step is 20 cm (0.2m)greater than his son's step, so, we can write the following relation:
[tex]NumberOfSteps_{Son}=\frac{240m}{x}[/tex]
and,
[tex]NumberOfSteps_{Father}=\frac{240m}{x+0.2m}[/tex]
Now, if the know that the father made 100 fewer steps than his son, we have:
[tex]NumberOfSteps_{Son}-100=\frac{240m}{x+0.2m}[/tex]
Then, substituting the first equation into the second equation, we have:
[tex]\frac{240m}{x}-\frac{240m}{x+0.2m}=100\\\\\frac{240m(x+0.2m)-240mx}{x(x+0.2m)}=100\\\\240mx+0.2m*240m-240mx=(x)(x+0.2m)*100\\\\48m^{2}=100*(x^{2}+0.2mx)=100x^{2} +20mx\\\\48m^{2}=100x^{2}+20mx\\\\100x^{2}+20mx-48m^{2}[/tex]
We have a quadratic equation:
[tex]100x^{2}+20mx-48m^{2}=0[/tex]
Where,
[tex]a=100\\b=20\\c=-48[/tex]
So, solving it applying the quadratic formula, we have:
[tex]\frac{-b+-\sqrt{b^{2} -4ac} }{2a}[/tex]
[tex]\frac{-20+-\sqrt{20^{2} -4*100*-48} }{2*100}=\frac{-20+-\sqrt{400+19200} }{200}\\\\\frac{-20+-\sqrt{400+19200} }{200}=\frac{-20+-\sqrt{19600} }{200}\\\\\frac{-20+-\sqrt{19600} }{200}=\frac{-20+-(140)}{200}\\\\x_{1}=\frac{-20+140}{200}=0.6\\\\x_{2}=\frac{-20-140}{200}=-0.8[/tex]
Then, since distance cannot be negative, we need to take the positive value, so, the son's step is 0.6m or 60 cm.
Now, calculating the father's step, we have:
[tex]FatherStep=SonStep+20cm\\\\FatherStep=60cm+20cm=80cm[/tex]
Hence, we have that the father's step is 80 cm.
Have a nice day!
The distance of the father and son will be 80cm and 60cm respectively.
How to calculate the distance?The number of son's step will be:
= 240/x
The number or father's step will be:
= 240/x + 0.2
Solving further, we'll have 100x² - 20mx - 48m² and using quadratic formula, this will be x1 = 0.6 and x2 = -0.8.
The son's step will be:
= 0.6 × 100 = 60cm
The father's step will be:
= 60cm + 20cm = 80cm
Learn more about distance on:
https://brainly.com/question/17273444
please help me with this geometry question
image attached
15/17. The value (ratio) of cos A is 15/17.
The trigonometric ratios of an acute angle are, basically, the sine, the cosine and the tangent. They are defined from an acute angle, α, of a right triangle, whose elements are the hypotenuse, the leg contiguous to the angle, and the leg opposite the angle.
-The sine of the angle is the opposite leg divided by the hypotenuse.
-The cosine of the angle is the adjacent leg divided by the hypotenuse.
-The tangent of the angle is the opposite leg divided by the adjacent leg or, which is the same, the sine of the angle divided by the cosine of the angle.
cos A = adjacent leg/hypothenuse = BC/AC = 15/17
Please help me with these 2
explain the step plz
thanks
1)when we know x+y=90* the sine of x is equal to cosine of y , so the solution of the first is 0.6 again!
Answer:
Left diagram cos(y) = 0.6
Right diagram x = 5 makes the equation true.
Step-by-step explanation:
Left diagram
Both the sin(x) and the Cos(y) use the same side as the non hypotenuse side.
Therefore they most be equal.
So if sin(x) = 0.6, then cos(y) = 0.6
=========================
Right diagram
You can factor this to get the answer.
From the first 2 terms, take out x^2. From terms 3 and 4 take out 2.
x^2(x - 5) + 2(x - 5) = 0
Take out the common factor of (x - 5)
(x^2 +2)(x - 5)
x^2 + 2 yields a complex answer (which doesn't matter for this question)
x - 5 = 0
x = 5
Please help me out!?????
Answer
[tex]\frac{121}{4} \pi mm^2[/tex]
Explanation
Find the radius
11/2 = 5.5
The formula to find the area of a circle is [tex]\pi r^2[/tex]
[tex]\pi 5.5^2[/tex] = [tex]30.25\pi[/tex]
Convert number into fraction.
[tex]30.25 \rightarrow \frac{121}{4} \pi[/tex]
Area = [tex]\frac{121}{4} \pi mm^2[/tex]
Answer:
30.25π mm²
Step-by-step explanation:
The area (A) of a circle is calculated using the formula
A = πr² ← r is the radius
here diameter = 11 and radius is half of the diameter. thus
r = 5.5
A = π × 5.5² = 30.25π mm²
What is the equation of the line that is perpendicular to the given line and passes through the point (2, 6)?
x = 2
x = 6
y = 2
y = 6
Answer:
Either x = 2 or y = 6, depending on the original line
Step-by-step explanation:
So, if the original line is horizontal, our new line is vertical, and all vertical lines in a graph is x = some number. To pass through the point (2, 6), x has to equal 2, since the point's x-coordinate is 2.
On the other hand, if the original line is vertical, our new line is horizontal, which is y = some number. Our point's y-coordinate is 6, so our line should be that y = 6.
It's A, x=2. I hope i helped!!
Find the value of the indicated angles. PLEASE HELP!!
Answer:
Part 1) The measure of the angle is 47°
Part 2) The measure of the angle is 52°
Step-by-step explanation:
Part 1)
we know that
The inscribed angle is half that of the arc it comprises.
we have that
(12y-1)°=(9y+11)° ----> because the arc that the inscribed angles comprise is the same
Solve for y
12y-9y=11+1
3y=12
y=4°
Find the measure of the angle
(12y-1)°=12(4)-1=47°
Part 2)
we know that
The inscribed angle is half that of the arc it comprises.
we have that
2(3m+2)°=(4m+20)° ----> because the arc that the inscribed angles comprise is the same
Solve for m
6m+4=4m+20
6m-4m=20-4
2m=16
m=8
Find the measure of the angle
(4m+20)°=4(8)+20=52°
Jon has 15 coins in nickels and dimes.he has 3 more dimes than nickels.how many nickels and dimes dose he have
Answer: 6 nickels and 9 dimes
Step-by-step explanation:
15 coins - 3 extra dimes = 12
12 / 2 = 6
6 nickels
6 + 3 = 9 dimes
Which function represents a translation of the graph of y = x^2 by 8 units to the right?
A. [tex]y=x^2+8[/tex]
B. [tex]y=8x^2[/tex]
C. [tex]y=(x-8)^2[/tex]
D. [tex]y=(x+8)^2[/tex]
Answer:
Option C. [tex]y = (x-8) ^ 2[/tex]
Step-by-step explanation:
If we have a parent function f(x) and we want to make a transformation that translates the graph of f(x) horizontally then we do
[tex]y = f (x + h)[/tex]
Where h is a constant such that:
If [tex]h> 0[/tex] then the graph of f(x) moves h units to the left
If [tex]h <0[/tex] then the graph of f(x) moves h units to the right.
In this case we have the function [tex]y = x ^ 2[/tex] and we know that 8 units are moved to the right. If you move 8 units to the right This means that
[tex]h <0[/tex] and [tex]h = -8[/tex]
So if [tex]f(x) = x ^ 2[/tex] the transformed function will be:
[tex]y = f(x -8)[/tex]
[tex]y = (x-8) ^ 2[/tex]
If a pair of two idenrcal dice are rolled n successive rmes, how many sequences of outcomes contain all six doubles (i.e., two 1's, two 2's, ... ,two 6's)?
I think the answer is six
(1,1) , (2,2) , (3,3) , (4,4) , (5,5) , (6,6)
If T: (x, y) → (x - 7, y + 2), then T -1: (x,y) → _____.
A.( -x/7 , y/2)
B.(-7x, 2y)
C.(x - 7, y - 2)
D.(x + 7, y - 2)
Answer:
D. (x + 7, y - 2)
Step-by-step explanation:
To get back the original after translating left 7 and up 2, you must translate right 7 and down 2. The transformation of choice D does that.
A pizza stand at an outdoor festival is going to sell slices of pizza. Last year the stand sold two kinds: cheese and sausage. The ratio of cheese slices sold to total slices sold was 9:16. The sold 288 cheese slices last year. How many sausage slices were sold?
There are 126 slices of sausage pizza sold
Help
What is the approximate area of a sector given Θ≈212 with a radius of 45 m?
Question 1 options:
2613.59 m²
3744.45 m²
3371.26 m²
2928.36 m
Answer:
[tex]3,744.45\ m^{2}[/tex]
Step-by-step explanation:
we know that
The area of a sector is equal to
[tex]A=\frac{\theta}{360\°}\pi r^{2}[/tex]
where
[tex]\theta[/tex] ------> is the angle in degrees
r is the radius of the circle
In this problem we have
[tex]r=45\ m[/tex]
[tex]\theta=212\°[/tex]
assume
[tex]\pi =3.14[/tex]
substitute the values
[tex]A=\frac{212\°}{360\°}(3.14)(45)^{2}[/tex]
[tex]A=3,744.45\ m^{2}[/tex]
It took Fran 2.7 hours to drive to her mother's house on Monday morning. On her return trip on Tuesday night, traffic was heavier, so the trip took her 3 hours. Her average speed on Tuesday was 6 mph slower than on Monday. What was her average speed on Tuesday.
Answer:
Step-by-step explanation:
Set up a table for a distance = rate × time problem. We are considering the trips taken on Monday and Tuesday.
d = r × t
Monday
Tuesday
Now let's start filling in what we know. First off, Fran went to her Mother's both days. Unless her Mother moved overnight from Monday to Tuesday, the distance from Fran to her mom is the same both days, even though we don't know how far it is. So we will just call that "d".
d = r × t
Monday d =
Tuesday d =
Now we are told about the times it took to get there on both days. Monday took 2.7 hours and Tuesday took 3 hours. Filling in that:
d = r × t
Monday d = × 2.7
Tuesday d = × 3
We're getting there. Now let's look at rates. Again, we don't know her rate (that's what we are solving for!) but we do know that she drove faster on Monday than Tuesday. Tuesday she was 6 miles per hour slower than Monday. Since we don't know Monday's rate, we will call it r. Since we don't know Tuesday's rate, but only that it is 6 mph slower than Monday, we will call it r - 6
d = r × t
Monday d = r × 2.7
Tuesday d = r-6 × 3
Now we have our equations. We know that d = rt. Since the distances are the same, d = d, by the transitive property of equality, we can set the 2 expressions equal to each other:
2.7r = 3(r - 6) and solve for r:
2.7r = 3r - 18
-.3r = -18
r = 60
If r = 60, then that r value goes in for Monday. That means that Tuesday is 60 - 6 which is 54
What was her average speed on Tuesday is 54 mph
Monday
Time = 2.7 hours
Date = r mph
Distance = 4.5r miles
Tuesday
Time = 3 hours
rate = r-6 mph
Distance = 3(r-6) miles
Hence:
Distance = distance
2.7r=3(r-6)
2.7r = 3r - 18
0.3r = 18
r =18/0.3
r 60 mph ( Monday rate)
r-6=60-3 (Tuesday rate)
r-6 = 54 mph (Tuesday rate)
Inconclusion What was her average speed on Tuesday is 54 mph.
Learn more here:
https://brainly.com/question/13238620
Kylie started basketball practice at 2:30 p.m and finished at 6:00 p.m how long was kylie at basketball practice
Answer:
3 hours and 30 minutes
Step-by-step explanation:
Since both of these times are in the P.M., each hour has 60 minutes and 2:30 is half, add 30 minutes to get 3:00 P.M. and then add 3 hours to get 6:00 P.M. . 3 hours and 30 minutes added to 2:30 P.M. equals 6:00 P.M. :)
Answer:
3 hours and 30 minutes
Step-by-step explanation:
Kylie started basketball practice at 2:30
Kylie finished basketball practice at 6:00
Time duration = 3 hours and 30 minutes
2 : 30 → 3 : 00
( 30 minutes )
3 : 00 → 6 : 00
( 3 hours )
3 hours + 30 minutes = 3 hours and 30 minutes
The relation between two expressions that are not equal
Answer:
an inequality
Step-by-step explanation:
An inequality is the relation between two expressions that are not equal. The symbols generally used are less than (<) or greater than (>), as in:
4 > 3 or 4 < 9
That means that each side of the symbol represents a value that is different from the other side. The relationship is described with the sign to indicate which side has a greater value.
If both sides have an equal value, then it's an equation.
Express the product as a sum containing only sines or cosines. 64) sin (5θ) cos (2θ)
[tex]\bf \textit{Product to Sum Identities} \\\\sin(\alpha)cos(\beta)=\cfrac{1}{2}[sin(\alpha+\beta)\quad +\quad sin(\alpha-\beta)] \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ sin(5\theta )cos(2\theta )\implies \cfrac{1}{2}[sin(5\theta +2\theta )+sin(5\theta -2\theta )]\implies \cfrac{sin(7\theta )+sin(3\theta )}{2}[/tex]
The required value of trigonometry expression is the product as a sum [sin(7θ) + sin(3θ)] / 2.
What is the product to sum Identities?The product-to-sum formulae are used to represent the sum of the sine and cosine functions. These are generated from trigonometry's sum and difference formulae.
sin A cos B = (1/2) [ sin (A + B) + sin (A - B) ]
The trigonometry expression is given in the question
sin (5θ) cos (2θ)
According to the product to sum Identities
sin A cos B = (1/2) [ sin (A + B) + sin (A - B) ]
Here A = 5θ and B = 2θ
sin (5θ) cos (2θ) = (1/2) [sin(5θ + 2θ) + sin(5θ - 2θ)]
sin (5θ) cos (2θ) = (1/2) [sin(7θ) + sin(3θ)]
sin (5θ) cos (2θ) = [sin(7θ) + sin(3θ)] / 2
Thus, the required value of trigonometry expression is the product as a sum [sin(7θ) + sin(3θ)] / 2.
Learn more about Trigonometric functions here:
brainly.com/question/6904750
#SPJ2
Two variables are correlated with r=−0.31.
Which answer best describes the strength and direction of the association between the variables?
weak positive
weak negative
strong negative
strong positive
Answer:
weak negative
Step-by-step explanation:
we know that
The correlation coefficient r measures the direction and strength of a linear relationship. It can take a range of values from +1 to -1.
Values between -0.5 and -1.0 or 0.5 and 1.0 indicate a strong negative/positive linear relationship
Values between -0.3 to -0.1 or 0.1 to 0.3 indicate a weak negative/positive linear relationship
In this problem
The correlation coefficient for the data is −0.31
therefore
Is a weak negative correlation
There are 24 members of a swim team. How many different combinations of 5 swimmers can be chosen to sit in the front row for a team photo?
Answer: 42,504
There Are 42,504 Different Combinations For The Swimmers
Answer:i dont
Step-by-step explanation:
Please help me with these 5 questions!
2.
A. No
B. yes; k = -1/2 and y = -1/4x
C. yes; k = 4 and y = 4x
D. yes; k = 1/4 and y = 1/4x
6.
A. y = 5x-1
B. y = 5/2x+5
C. y = -x+5
D. y = 1/5x-1
8.
A. line a
B. line d
C. line b
D. line c
11.
What is the slope of the line through the points (–2, –1) and (8, –3)?
A. 3/2
B. 1/5
C. -3/2
D. -1/5
15.
A. line a
B. line d
B. line b
C. line c
Answer:
Part 2) Option D. yes; k = 1/4 and y = 1/4x
Part 6) Option D. y = 1/5x-1
Part 8) Option C. line b
Part 11) Option D. -1/5
Part 15) Option A. line a
Step-by-step explanation:
Part 2) we know that
A relationship between two variables, x, and y, represent a directly variation if it can be expressed in the form [tex]y=kx[/tex]
In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin
In this problem the line passes through the origin
therefore
Yes. y varies directly with x
Let
A(4,1)
The constant k is equal to
[tex]k=y/x[/tex]
substitute
[tex]k=1/4[/tex]
the equation is equal to
[tex]y=(1/4)x[/tex]
Part 6) we know that
The y-intercept of the trend line is -1 (For x=0)
The slope of the trend line is positive
The x-intercept of the trend line is 5 (For y=0)
therefore
the equation is equal to
[tex]y=(1/5)x-1[/tex]
Part 8) we have
[tex]y+4=-\frac{2}{3}x[/tex]
This is the equation of a line into point slope form
The slope is negative [tex]m=-2/3[/tex]
Pass through the point (0,-4) ----> y-intercept
The x-intercept is equal to
[tex]0+4=-\frac{2}{3}x[/tex]
[tex]x=-4*3/2=-6[/tex]
therefore
Is the line b
Part 11)
What is the slope of the line through the points (–2, –1) and (8, –3)?
we know that
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute the values
[tex]m=\frac{-3+1}{8+2}[/tex]
[tex]m=\frac{-2}{10}[/tex]
simplify
[tex]m=-\frac{1}{5}[/tex]
Part 15) we have
[tex]y=3x-2[/tex]
The slope is positive [tex]m=3[/tex]
The y-intercept is -2 (For x=0)
The x-intercept is (For y=0)
[tex]0=3x-2[/tex]
[tex]3x=2[/tex]
[tex]x=2/3[/tex]
therefore the line is a
Help with this question, please!!
Answer:
(x +8)² +(y +1)² = 9
Step-by-step explanation:
The formula for a circle with center (h, k) and radius r is ...
(x -h)² +(y -k)² = r²
Filling in your given numbers gives ...
(x -(-8))² +(y -(-1))² = 3²
Simplifying that results in ...
(x +8)² +(y +1)² = 9
A souvenir of the Eiffel Tower is scaled at 1/80 inch to 1 foot. If the total height of the tower is 1,069 feet, the approximate height of the souvenir of the Eiffel Tower to the nearest tenth is _____.
A.14
B.15
C.13
D.12
Answer: Option C
the approximate height of the souvenir of the Eiffel Tower to the nearest tenth is __13 in___.
Step-by-step explanation:
We know that each foot of height of the Eiffel Tower is equivalent to 1/80 inch of height of the souvenir.
The Eiffel Tower is 1,069 feet high.
Then the height of the souvenir the 1,069 times 1/80 in
[tex]h = 1,069 *\frac{1}{80}\\\\h=13.3\ in[/tex]
The answer is the option C
Is the square root of 8 a rational number
Answer:
No.
Step-by-step explanation:
The square root of an integer is rational only if that integer is a square number. The closest squares to 8 are 2^2 = 4 and 3^2 = 9. 8 is not a square number, so has an irrational square root.
The square root of 8 is an irrational number.
Explanation:A square root is a mathematical operation that, when applied to a number, finds a value that, when multiplied by itself, equals the original number. For example, the square root of 25 is 5 because 5 x 5 = 25. It is denoted by the √ symbol. Whether the square root of 8 is a rational number or not can be determined by finding the square root and checking if it can be expressed as a fraction.
The square root of 8 is approximately 2.828, which is an irrational number because it cannot be expressed as a fraction. To further prove that it is irrational, we can use the prime factorization method and show that 8 does not have a perfect square factor.
Learn more about Square root:https://brainly.com/question/428672
Which figure shows how a shape can be rotated about an axis to form a cylinder?
Answer
the rectangle
Step-by-step explanation:
the cylinder folds like a circle but it is not a circle.
A rectangular shape can be rotated about an axis to form a cylinder.
What is the cylindrical shape?A cylindrical shape is a three-dimensional geometrical shape consisting of two parallel circular bases which are connected by some height h.
We know that cylinder has some height h and two base circles.
If we compare the curved part of the cylinder then we can see that its shape is similar to a rectangle.
The length of the rectangle is similar to the circumference of the circular base of a cylinder and the height of the cylinder with the breadth of the rectangle.
Thus, a rectangular shape can be rotated about an axis to form a cylinder.
Learn more about the cylindrical shape:
https://brainly.com/question/25103758
find the vertex : f(x)=3x^2-18x+10
f(x)=3x^2-18x+10
a = 3, b = -18 and c = 10
The vertex of a parabola is in form a(x+d)^2 + e
d = b/2a = -18/2(3) = -18/6 = -3
e = c-b^2/4a = 10 - -18^2/4(3) = 10-27 = -17
Now the vertex form of the parabola becomes 3(x-3)^2 -17
Use the vertex form of the parabola in the vertex form of y = a(x-h)^2 +k
Where a = 3, h = -3 and k = -17
Now you have y = 3(x-(-3))^2 +(-17)
Simplify: y = 3(x+3)^2 -17
The vertex becomes the h and k values of (3,-17)
70 POINTS!!!!!!!!!! Given: E, F, Q, D∈k(O),O ∈ ED, m∠DFQ = 10°, measure of arc EF = 28° Find: Angles of △EFQ
Answer:
The measures of angles of triangle EFQ are
1) [tex]m\angle EFQ=100\°[/tex]
2) [tex]m\angle FEQ=66\°[/tex]
3) [tex]m\angle EQF=14\°[/tex]
Step-by-step explanation:
step 1
Find the measure of arc QD
we know that
The inscribed angle is half that of the arc it comprises.
[tex]m\angle DFQ=\frac{1}{2}(arc\ QD)[/tex]
substitute the given value
[tex]10\°=\frac{1}{2}(arc\ QD)[/tex]
[tex]20\°=(arc\ QD)[/tex]
[tex]arc\ QD=20\°[/tex]
step 2
Find the measure of arc FQ
we know that
[tex]arc\ QD+arc\ FQ+arc\ EF=180\°[/tex] ---> because ED is a diameter (the diameter divide the circle into two equal parts)
substitute the given values
[tex]20\°+arc\ FQ+28\°=180\°[/tex]
[tex]arc\ FQ=180\°-48\°=132\°[/tex]
step 3
Find the measure of angle EFQ
we know that
The inscribed angle is half that of the arc it comprises.
[tex]m\angle EFQ=\frac{1}{2}(arc\ QD+arc\ ED)[/tex]
substitute the given value
[tex]m\angle EFQ=\frac{1}{2}(20\°+180\°)=100\°[/tex]
step 4
Find the measure of angle FEQ
we know that
The inscribed angle is half that of the arc it comprises.
[tex]m\angle FEQ=\frac{1}{2}(arc\ FQ)[/tex]
substitute the given value
[tex]m\angle FEQ=\frac{1}{2}(132\°)=66\°[/tex]
step 5
Find the measure of angle EQF
we know that
The inscribed angle is half that of the arc it comprises.
[tex]m\angle EQF=\frac{1}{2}(arc\ EF)[/tex]
substitute the given value
[tex]m\angle EQF=\frac{1}{2}(28\°)=14\°[/tex]
A collection of coins consists of dimes and nickels .The number of dimes is two more than the twice the number of nickels.The value of the collection is $2.70. How many dimes are in the collection ?
27 dimes for my answer
hope it works
Which two events have the same probability the spinner is divided into 8 equal sections
Answer:
N/A
Step-by-step explanation:
Not enough context is given for the problem.
Just remember, though:
And = Multiplication
Or = Addition
1/8 chance for each section
Answer:
(A) P(gray), P(green)
Step-by-step explanation:
Notice that there are 2 tiles in each, so it should be A as the answer.
Please mark me brainiest!
Hope you have a good day!
A bag contains 7 blue cards, 4 green cards, 6 red cards, and 8 yellow cards. You randomly choose a card. How many possible outcomes are there? In how many ways can choosing a card that is not red occur?
Answer:
25 possible outcomes
19 non-red outcomes
Step-by-step explanation:
there are 25 cards. if you remove the 6 red card outcomes you have 19.
During the player's career, the player attempted 1,507 free throws and made 1,213 of those free throws. What percentage of free throws has this player made?
The answer is 80%
Correct me if I’m wrong
Vanessa has two bags that contain slips of paper. One bag has 4 slips of paper that are numbered 2, 3, 4, and 5. The other bag has 4 slips of paper that are numbered 3, 4, 5, and 6.
Vanessa chooses one slip of paper from each bag without looking.
The random variable X is the product of the numbers on the slips of paper.
What is P(12 ≤ X ≤ 15)?
Enter your answer, in simplest fraction form, in the box.
Answer:
5/16
Step-by-step explanation:
If Vanessa pulls out a 2 from the first bag, then the possibilities based on the second bag are:
X = 2*3 = 6
X = 2*4 = 8
X = 2*5 = 10
X = 2*6 = 12
Repeat this for the other values from the first bag. If she pulls a 3, the possibilities are:
X = 3*3 = 9
X = 3*4 = 12
X = 3*5 = 15
X = 3*6 = 18
If she pulls a 4:
X = 4*3 = 12
X = 4*4 = 16
X = 4*5 = 20
X = 4*6 = 24
And finally, if she pulls a 5:
X = 5*3 = 15
X = 5*4 = 20
X = 5*5 = 25
X = 5*6 = 30
Of the 16 total combinations, 5 are greater than or equal to 12 and less than or equal to 15.
Therefore, P(12 ≤ X ≤ 15) = 5/16.
BRAINLIEST AND 30 POINTS FOR WHOEVER CAN EXPLAIN HOW TO GET THESE ANSWERS...
Given: △ACM, m∠C=90°, CP⊥ AM. AP=9 cm, PM=16 cm.
Explain how to get these answers: AC = 15, CM = 20, CP = 12
Step-by-step explanation:
Since m∠ACM = 90°, then by angle addition, m∠ACP + m∠PCM = 90°.Since CP⊥ AM, then by definition of perpendicular, m∠APC = 90°. Since angles of a triangle add up to 180°, that means m∠PAC + m∠ACP = 90°.By substitution, m∠PCM = m∠PAC.Since m∠PCM + m∠CMP = 90°, then by substitution, m∠CMP = m∠PAC.Therefore, by AAA, △ACP and △CMP are similar.Having proven that the triangles are similar, we can write the proportion:
AP / CP = CP / MP
9 / CP = CP / 16
CP² = 144
CP = 12
Now, we can simply use Pythagorean theorem to find the other sides.
AC² = AP² + CP²
AC² = 9² + 12²
AC = 15
CM² = CP² + PM²
CM² = 12² + 16²
CM = 20