Factor the common factor out of each expression: 30+6k+18k^5
In a game of chess, a player can either
win, draw or lose.
The probability that Vishi wins any
game of chess is 0.5
The probability that Vishi draws any
game of chess is 0.3
Vishi plays two games of chess.
Work out the probability that Vishi will
lose exactly one of the two games.
Pls answer fast
Answer:
3.4
Step-by-step explanation:
0.5x + 0.3=2
then I subtracted 0.3 from both sides which I got 1.7 then I divided by 0.5x and then I got 3.4
Using the diagram below, which of the following parts of the triangles are
congruent?
Answer:
C.
Step-by-step explanation:
ACE is a straight line that connects to line AB and line DE.
AB & ED have same gradient which mean that it is parallel.
The parts of triangles which are congruent is ∠A ≅ ∠E which is option (C)
What is congruent triangle?In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the otherCongruent triangles are triangles that have the same size and shape. This means that the corresponding sides are equal and the corresponding angles are equal. We can tell whether two triangles are congruent without testing all the sides and all the angles of the two triangles.How to solve this problem?The steps are as follow:
As ACE is a straight line which connects to line AB and DEAlso the line AB and ED are parallel because their gradient are sameSo from above mention two reasons we can say that their is congruence between angle A and angle ESo the parts of triangles which are congruent is ∠A ≅ ∠E which is option (C)
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Is each statement true for OA? Drag “true” or “false” below each statement
Answer:
true. true. false.
Step-by-step explanation: i’m in love with the shape of u. we push and pull like magnet whatever
Given csc(A) = 60/16 and that angle A is in Quadrant I, find the exact value of sec A in simplest radical form using a rational denominator . Someone please help me!
Answer:
[tex]\displaystyle \sec A=\frac{65}{63}[/tex]
Step-by-step explanation:
We are given that:
[tex]\displaystyle \csc A=\frac{65}{16}[/tex]
Where A is in QI.
And we want to find sec(A).
Recall that cosecant is the ratio of the hypotenuse to the opposite side. So, find the adjacent side using the Pythagorean Theorem:
[tex]a=\sqrt{65^2-16^2}=\sqrt{3969}=63[/tex]
So, with respect to A, our adjacent side is 63, our opposite side is 16, and our hypotenuse is 65.
Since A is in QI, all of our trigonometric ratios will be positive.
Secant is the ratio of the hypotenuse to the adjacent. Hence:
[tex]\displaystyle \sec A=\frac{65}{63}[/tex]
Answer:
Step-by-step explanation:
cosec A =60/16
hypotenuse/opposite = 60/16 =15/4 (in simplest form)
therefore hypotenuse = 15 , opposite = 4
then adjacent =? (let be x)
using pythagoras theorem to find adjacent
opposite^2 + adjacent^2 = hypotenuse^2
4^2 + x^2 = 15^2
16 + x^2 = 225
x^2 = 225 - 16
x^2 = 209
[tex]x=\sqrt{209}[/tex]
sec A =hypotenuse/adjacent
[tex]=\frac{15}{\sqrt{209} }[/tex]
[tex]=\frac{15}{\sqrt{209} } * \frac{\sqrt{209} }{\sqrt{209} }[/tex]
=[tex]\frac{15\sqrt{209} }{209}[/tex]
how many tons is 9,000 lbs?
Answer:
9000 Pounds (lbs) = 4.017859 Tons (t)
1 lbs = 0.000446 t
1 t = 2,240 lbs
Step-by-step explanation:
Find the area of the polygon
Answer:
[tex]it \: is \: a \: polygon \: having \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ base = 5cm \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ height = 3cm \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ area \: of \: polygon \: = base \times height \\ \\ area \: of \: polygon \: = (5 \times 3)cm \\ \\ area \: of \: polygon = 15cm ^{2} [/tex]
Determine the vertex of the quadratic relation y= 4x2 + 32x – 11
Answer:
vertex = (- 4, - 75 )
Step-by-step explanation:
Given a quadratic in standard form
y = ax² + bx + c ( a ≠ 0 )
Then the x- coordinate of the vertex is
x = - [tex]\frac{b}{2a}[/tex]
y = 4x² + 32x - 11 ← is in standard form
with a = 4, b = 32 , then
x = - [tex]\frac{32}{8}[/tex] = - 4
Substitute x = - 4 into the equation for corresponding y- coordinate
y = 4(- 4)² + 32(- 4) - 11
= 4(16) - 128 - 11
= 64 - 139
= - 75
vertex = (- 4, - 75 )
2.39 round to the nearest tenth
Answer:
2.4
Step-by-step explanation:
If I round 2.39 to the nearest tenth it will be 2.4.
Have a nice day!
A total of 937 people attended the play.
Admission was $2.00 for adults and $0.75
for students. The total ticket sales
amounted to $1,109. How many students
and adults attended the school play?
Answer:
612 adults & 361 students
Step-by-step explanation:
What is the product of 1.65 and 1.05 x 10^-2?
Answer:
0.017325
x
Step-by-step explanation:
6 yd
4 yd
7 yd
4 yd
Perimeter:
Area:
Help me find the area and the permiter
Step-by-step explanation:
Assuming figure to be trapezoid,
Perimeter=6+4+7+4yd
=21 yd
Area of trapezoid=((6+7)/2) x ((4)^2-(0.5)^2)
=(13/2)x(16-0.25)
=6.5 x 15.75
=102.375 Sq yards
Can somebody pls help
Answer:
A, c, d
Step-by-step explanation:
Answer:
C & D
Step-by-step explanation:
In order to find the perimeter, we would need to add all the sides. w+L+w+L would be adding the lengths and the widths. Simplifying this, we would get 2w, because there are 2 sides that are the same width, and 2 sides that are 2 lengths.
w+L+w+L or w+w+L+L or 2w+2L
Hope this helps!
--Applepi101
WILL GIVE BRANLIEST! pls help thank u sm!! :-) u are all amazing
Answer:
A.)
Step-by-step explanation:
A.)
Answer:
A :)
Step-by-step explanation:
Can some help me solve this.
Answer:
The fourth (last) function is the correct one.
Step-by-step explanation:
Look at the parent function y = √x, Its graph goes through (0, 0). On the other hand, if y = √(x - h), the graph goes through (h, 0) if h is positive, and the graph is translated h units to the right from the graph of y = √x. If h is negative, the graph is translated h units to the left.
In the four possible answers given, the values of h are {-4, 9, 5, -9}, in that order. h = -9 results in the graph that is positioned 9 units to the left of the graph of y = √x. This graph is furthest to the left. Thus the fourth choice is the correct one.
4. There are 10 people in a room. If everyone high fives everyone else exactly once, how many hig flves took place in the room?
Answer:
45
Step-by-step explanation:
Let's do it for smaller numbers first.
0 people -> 0 high fives
1 people -> 0 high fives
2 people -> 1 high fives
3 people -> person 1 high fives 2 then 3
And person 2 high fives 3
->2+1= 3 high fives
4 people -> person 1 high fives 2,3, then 4
And person 2 high fives 3 then 4
And 3 high fives 4
->3+2+1=6
5 people -> person 1 high fives 2,3,4, then 5
And person 2 high fives 3,4, 5
And 3 high fives 4,5
And 4 high fives 5
-> 4+3+2+1=10
So for n people there would be (n-1)+(n-2)+....+3+2+1 high fives or (n-1)n/2 people.
Test:
3 people -> (3-1)3/2=(2)3/2=3
4 people -> (4-1)4/2=(3)4/2=6
5 people -> (5-1)5/2=(4)5/2=10
10 people-> (10-1)10/2=(9)10/2=90/2=45
or you could do 9+8+7+6+5+4+3+2+1 which also gives 45.
The other person has a great answer. Here's another approach.
Let's say we're selecting 2 people to fill slots A and B.
Slot A has 10 choices and slot B has 9 choices (since we can't pick the same person again to fill both slots simultaneously).
We have 10*9 = 90 ways to do this if order mattered.
However, we don't care about the order so we actually have 90/2 = 45 ways
---------------------------
Put another way: we can form a table that has 10 rows and 10 columns.
This table has 10*10 = 100 cells inside it.
Cross off the main diagonal that runs from the upper left corner to the bottom right corner. Any of these cells represent a certain person handshaking with themself, which we don't consider.
We cross of 10 items along this diagonal so we have 100-10 = 90 cells leftover.
Now consider that person A shaking with B can be notated as AB. This is identical to BA because the order doesn't matter. So we have twice as many handshakes counted.
That's why we divide by 2 to go from 90 to 90/2 = 45
-----------------------------
Another way to find the answer is to use the nCr combination formula with n = 10 and r = 2.
Yet another way to find the answer is look at Pascal's triangle. Find the row that has 1,10,45... in it at the start. These values correspond to r = 0, 1 and 2 respectively. We can see that 45 is when r = 2, which means we have 2 people shaking hands and there are 45 ways to have ten people shake hands.
So there are many approaches you can take with this problem.
how do you do this?
Step-by-step explanation: 6 22 22 51
one orange box is 10 the other box looks like 15
the scale factor is 15/10 or 1.5
the smaller triangle blue box is a 4
multiply 4 by the scale factor 1.5
4 × 1.5 = 6
Simo scored 65 points in a game. Ella scored e points in the same game. If they scored a total of t points for the game, write an equation that expresses t in terms of e. You will not solve this equation, just write it.
Answer:
Step-by-step explanation:
Lucy=65
Eva= X points
Total:
Points = 65 + 65 = 130
MCR3U1 Culminating 2021.pdf
#7.
A colony of bacteria is introduced into a growth medium. Its initial population
size is 350 thousand. 12 hours later, the colony has grown to a size of
800 thousand. If its population size increases exponentially, determine:
(a)
the exponential growth model for the size of the population Alt), after
t hours.
(b)
the population size after (i) 8 hours and (ii) 24 hours.
(c)
the rate of increase in the population size as a %/hour
(d)
the doubling time of the bacteria population.
Answer:
(a) [tex]y = 350,000 \times (1 + 0.07132)^t[/tex]
(b) (i) The population after 8 hours is 607,325
(ii) The population after 24 hours is 1,828,643
(c) The rate of increase of the population as a percentage per hour is 7.132%
(d) The doubling time of the population is approximately, 10.06 hours
Step-by-step explanation:
(a) The initial population of the bacteria, y₁ = a = 350,000
The time the colony grows, t = 12 hours
The final population of bacteria in the colony, y₂ = 800,000
The exponential growth model, can be written as follows;
[tex]y = a \cdot (1 + r)^t[/tex]
Plugging in the values, we get;
[tex]800,000 = 350,000 \times (1 + r)^{12}[/tex]
Therefore;
(1 + r)¹² = 800,000/350,000 = 16/7
12·㏑(1 + r) = ㏑(16/7)
㏑(1 + r) = (㏑(16/7))/12
r = e^((㏑(16/7))/12) - 1 ≈ 0.07132
The model is therefore;
[tex]y = 350,000 \times (1 + 0.07132)^t[/tex]
(b) (i) The population after 8 hours is given as follows;
y = 350,000 × (1 + 0.07132)⁸ ≈ 607,325.82
By rounding down, we have;
The population after 8 hours, y = 607,325
(ii) The population after 24 hours is given as follows;
y = 350,000 × (1 + 0.07132)²⁴ ≈ 1,828,643.92571
By rounding down, we have;
The population after 24 hours, y = 1,828,643
(c) The rate of increase of the population as a percentage per hour = r × 100
∴ The rate of increase of the population as a percentage = 0.07132 × 100 = 7.132%
(d) The doubling time of the population is the time it takes the population to double, which is given as follows;
Initial population = y
Final population = 2·y
The doubling time of the population is therefore;
[tex]2 \cdot y = y \times (1 + 0.07132)^t[/tex]
Therefore, we have;
2·y/y =2 = [tex](1 + 0.07132)^t[/tex]
t = ln2/(ln(1 + 0.07132)) ≈ 10.06
The doubling time of the population is approximately, 10.06 hours.
Which of the following correctly maps figure ABCD onto figure EFGH? Select two that apply.
Answer:
Option A
Step-by-step explanation:
From the graph attached,
Distance of point A of rectangle ABCD = 5 units
Distance of point E of rectangle EFGH = 5 units
Similarly, all the vertices of the rectangles ABCD and EFGH are equidistant from the y-axis.
Therefore, rectangle ABCD and rectangle EFGH may overlap each other by reflecting each other across y-axis.
Let's check by the rule of reflection,
Rule for the reflection of a point (x, y) across y-axis is given by,
(x, y) → (-x, y)
Following this rule,
A(-5, 5) → E(5, 5)
B(-3, 4) → F(3, 4)
C(-4, 1) → G(4, 1)
D(-6, 2) → H(6, 2)
Therefore, rule for the reflection is applicable in this question.
Option A will be the answer.
A local chess tournament gives medals for first, second, and third place. There are five students from Midland High, three students from Leasburg High, and six students from Cassville High competing in the tournament.
Which statements are true? Check all that apply.
Order matters in this scenario.
There are 2,184 ways to select a first-place, second-place, and third-place winner.
The probability that all three winners are from Midland High is 0.0275.
The probability that all three winners are from Leasburg High is 0.0046.
The probability that all three winners are from Cassville High is 0.0549
Answer:
There are 2,184 ways to select a first-place, second-place, and third-place winner.
The probability that all three winners are from Midland High is 0.0275.
The probability that all three winners are from Cassville High is 0.0549
Step-by-step explanation:
Since a local chess tournament gives medals for first, second, and third place, and there are five students from Midland High, three students from Leasburg High, and six students from Cassville High competing in the tournament, to determine which of the following statements are true, the following calculations must be performed:
A) There are 2,184 ways to select a first-place, second-place, and third-place winner.
5 + 3 + 6 = 14
14 x 13 x 12 = X
182 x 12 = X
2.184 = X
B) The probability that all three winners are from Midland High is 0.0275.
5/14 x 4/13 x 3/12 = X
0.02747 = X
C) The probability that all three winners are from Leasburg High is 0.0046.
3/14 x 2/13 x 1/12 = X
0.00274 = X
D) The probability that all three winners are from Cassville High is 0.0549
6/14 x 5/13 x 4/12 = X
0.0549 = X
Answer:
A, B, C, E
Step-by-step explanation:
Edg 2021
Branliest?
!!URGENT PLEASE HELP!!
A line segment has endpoints A(-6, 1) and B(0, 7). When AB is reflected in the y-axis, triangle ABA’ is formed. Graph ABA’ , you will see and you will be able to prove it is a right triangle. Name the parts of the right triangle, identify the two legs and the hypotenuse. And, Explain how you would prove ABA' is a right triangle?
Answer:
im not sure i need points though
Step-by-step explanation:
The proof is given below
What is right angle triangle?A right triangle or right-angled triangle, or more formally an orthogonal triangle, formerly called a rectangled triangle, is a triangle in which one angle is a right angle or two sides are perpendicular. A right angled triangle is a triangle with one of the angles as 90 degreesHow to solve this problem?The steps are as follow:
Reflection about y-axisp(x,y) = p'(-x,y)
A(-6,1) = A'(6,1)
The longest side is AA' is the hypotenuseThe right angle of right triangle is opposite the hypotenuseAB and A'B are the two legs of triangleAB is opposite side
A'B is adjacent side
Length of AA' is 12 unitsThe vertical distance y=6ΔABC = ΔA'BC (both right angle)[tex]A'B=AB=\sqrt{6^{2}+6^{2} }=8.5[/tex]Sin∅=8.5/2∅ = 45° (Angle between AB and AA')Hence we can prove that triangle is right angle triangle
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Find the volume of the irregular
figure.
Answer:
59 cm^3
Step-by-step explanation:
You can split the shape into two rectangular prisms.
3*3*1=9
10*5*1=50
9+50=59
If 3x - 4y = 15 and -2x + 3y = 10, then x - y = ?
Answer:
x - y = 25
Step-by-step explanation:
3x - 4y = 15
-2x + 3y = 10
Add the two equations together
3x - 4y = 15
-2x + 3y = 10
----------------------
x - y = 25
Answer:
[tex]{\Huge{\underline{\underline{\textbf{\textsf{Answer}}}}}}[/tex]
>> 3x - 4y = 15
>> -2x + 3y = 10
Add the two equations together
>> 3x - 4y = 15
>> -2x + 3y = 10
----------------------
Hence, x - y = 25
Which line of best fit is the best choice for the data given below?
Answer:
B
Step-by-step explanation:
Points need to be above and below a line of best fit.
Name the set(s) of numbers to which –5 belongs. a. whole numbers, natural numbers, integers b. rational numbers whole numbers, integers, rational numbers d. integers, rational numbers c.
5 belong to whole number. b I don't know
Someone PLEASE HELP!!!!! it’s urgent please help ASAP
The line the puck traveled is the hypotenuse of a right triangle.
Using the Pythagorean theorem:
Travel = sqrt( 4^2 + 30^2)
Travel = sqrt( 16 + 900)
Travel = sqrt(916)
Travel = 30.265 feet ( round the answer as needed)
math help please 2 questions
Answer:
first one is the second choice
question 2 is correct, the answer is the 4th option
Step-by-step explanation:
no other words
what is the length is centimeters of line segment AD?
=========================================================
Explanation:
Focus solely on triangle ABD.
Let x be the length of AD. This is the unknown horizontal leg of the triangle. The vertical leg is known, so we'll say b = 16.
The hypotenuse is 20, so c = 20.
Use the pythagorean theorem to find x
a^2 + b^2 = c^2
x^2 + 16^2 = 20^2
x^2 + 256 = 400
x^2 = 400 - 256
x^2 = 144
x = sqrt(144)
x = 12
Segment AD is 12 cm long.
Assume that a cell is a sphere with a radius of 10-³ or 0.001 centimeters and that a cell’s density is 1.1 grams per cubic centimeter.
Koalas weigh 6 kilograms on average. How many cells are in the average koala?
Answer:
[tex]n=1.3\times 10^{12}[/tex]
Step-by-step explanation:
Given that,
The radius of a cell, r = 10⁻³ cm
The density of the cell, d = 1.1 g/cm³
The weight of the Koala, m = 6 kg = 6000 grams
The density of an object is given by:
[tex]d=\dfrac{m}{V}[/tex]
For n cells,
[tex]nd=\dfrac{m}{V}\\\\n=\dfrac{m}{dV}[/tex]
Put all the values,
[tex]n=\frac{6000}{\frac{4}{3}\cdot\pi\cdot\left(10^{-3}\right)^{3}\cdot1.1}\\\\n=1.3\times 10^{12}[/tex]
So, there are [tex]1.3\times 10^{12}[/tex]cells in the average koala.