The number line which represents the solution bro the inequality y -2 < -5 is;
An open circle is at negative 3. Everything to the left of the circle is shaded.
First, we must solve the inequality so that it looks it's simplest form in order to be represented on a number line.
Solving the inequality is as follows;
y - 2 < -5
y < -5 +2
y < -3.
In essence, representation of the inequality, y < -3 on the number line is as follows;
An open circle is at negative 3. Everything to the left of the circle is shaded.
PS: It is only a closed circle if the inequality includes an equal to sign.
Does anybody know this? Evaluate the following expression using the correct order of operations.
Answer:
-4
Step-by-step explanation:
Wehn dealing with order of operations, we can remember the expression PEMDAS, which stands for parentheses, exponents, multiplication, division, addition, and subtraction.
So, our first step in the above problem is the parentheses:
[tex]2(3-5)^3+4(-4+7)\\2(-2)^3+4(3)[/tex]
The second step is exponents:
[tex]2(-2)^3+4(3)\\2(-8)+4(3)[/tex]
The third step is multiplication:
[tex]2(-8)+4(3)\\-16+12[/tex]
The fourth and final step is addition:
[tex]-16+12\\-4[/tex]
The volume of a cone is 1,782 cubic centimeters. a cylinder has the same radius and height as the cone. what is the volume of the cylinder?
The volume of the cylinder that has same height and radius with the given cone is 5,346 cm³
What are the 3-D figure?Pyramids and prisms are examples of three-dimensional shapes, as are shapes with curved surfaces. The three-dimensional prism shape has two bases that are parallel and congruent. Any polygon is acceptable for the bases, which are two of the faces. Rectangles make up the remaining faces.
What is the Volume of a Cylinder?Given that the cylinder and the cone have the same radius and height, the volume of a cylinder equals 3 times the volume of a cone.
According to the given figure:
Given, a cone that has a volume of 1,782 cubic cm, has the same radius and height with a cylinder,
therefore,
Volume of the cylinder = 3 x (1,782)
Volume of the cylinder = 5,346 cubic centimeters
Hence, the volume of the cylinder is 5,346 cubic centimeter.
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Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
Answer:
B {3/2, -5/3}
Step-by-step explanation:
6x² + x - 15 = 0
6x² + 10x - 9x - 15 = 0
2x(3x + 5) - 3(3x + 5) = 0
(3x + 5)(2x - 3) = 0
3x + 5 = 0 or 2x - 3 = 0
3x = -5 or 2x = 3
x = -5/3 or x = 3/2
Answer: B {3/2, -5/3}
Answer:
[tex]\left\{\dfrac{3}{2},\ -\dfrac{5}{3}\right\}[/tex]
Step-by-step explanation:
Given quadratic equation: [tex]6x^2+x-15=0[/tex]
[tex]\implies a=\textsf{6},b=\textsf{1},c=\textsf{-15}[/tex]
..................................................................................................................................................
[tex]{\large \textsf{ Quadratic Formula: }}x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\ \Bigg{\|}\ \textsf{when }ax^2+bx+c=0[/tex]
..................................................................................................................................................
Step 1: Substitute the given values into the formula and simplify.
[tex]\implies x=\dfrac{-{(\textsf1})\pm \sqrt{\textsf{(1)}^2-4(\textsf{6}){(\textsf{-15})}}}{2{(\textsf{6})}}[/tex]
[tex]\implies x=\dfrac{-1\pm \sqrt{1-4(-90)}}{12}[/tex]
[tex]\implies x=\dfrac{-1\pm \sqrt{1+360}}{12}[/tex]
[tex]\implies x=\dfrac{-1\pm \sqrt{361}}{12}[/tex]
[tex]\implies x=\dfrac{-1\pm 19}{12}[/tex]
Step 2: Separate into two cases.
[tex]x_1=\dfrac{-1+19}{2}[/tex]
[tex]x_2=\dfrac{-1-19}{2}[/tex]
Step 3: Solve both cases.
[tex]\implies x_1=\dfrac{-1+19}{12}=\dfrac{18}{12}=\dfrac{6\times3}{6\times2}=\boxed{\dfrac{3}{2}}[/tex]
[tex]\implies x_2=\dfrac{-1-19}{12}=\dfrac{-20}{12}=\dfrac{-4\times5}{4\times3}=\boxed{-\dfrac{5}{3}}[/tex]
The solutions to this quadratic are: [tex]x_1=\dfrac{3}{2},\ x_2=-\dfrac{5}{3}[/tex]
..................................................................................................................................................
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The two lines y = 2x + 8 and y = 2x - 12 intersect the x-axis at the P and Q.
Work out the distance PQ.
Answer:
PQ = 10 units
Step-by-step explanation:
to find where the lines cross the x- axis let y = 0 and solve for x , that is
2x + 8 = 0 ( subtract 8 from both sides )
2x = - 8 ( divide both sides by 2 )
x = - 4 ← point P
and
2x - 12 = 0 ( add 12 to both sides )
2x = 12 ( divide both sides by 2 )
x = 6 ← point Q
the lines cross the x- axis at x = - 4 and x = 6
using the absolute value of the difference , then
PQ = | - 4 - 6 | = | - 10 | = 10 units
or
PQ = | 6 - (- 4) | = | 6 + 4 | = | 10 | = 10 units
Answer: [tex]\Huge\boxed{Distance=10~units}[/tex]
Step-by-step explanation:
Find the point PGiven expression
y = 2x + 8
Substitute 0 for the y value to find the x value
This is the definition of x-intercepts
(0) = 2x + 8
Subtract 8 on both sides
0 - 8 = 2x + 8 - 8
-8 = 2x
Divide 2 on both sides
-8 / 2 = 2x / 2
x = -4
[tex]\large\boxed{P~(-4,0)}[/tex]
Find the point QGiven expression
y = 2x - 12
Substitute 0 for the y value to find the x value
(0) = 2x - 12
Add 12 on both sides
0 + 12 = 2x - 12 + 12
12 = 2x
Divide 2 on both sides
12 / 2 = 2x / 2
x = 6
[tex]\large\boxed{Q~(6,0)}[/tex]
Find the distance between PQGiven information
[tex](x_1,~y_1)=(-4,~0)[/tex]
[tex](x_2,~y_2)=(6,~0)[/tex]
Substitute values into the distance formula
[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]Distance=\sqrt{(6-(-4))^2+(0-0)^2}[/tex]
Simplify values in the parenthesis
[tex]Distance=\sqrt{(10)^2+(0)^2}[/tex]
Simplify values in the radical sign
[tex]Distance=\sqrt{100}[/tex]
[tex]\Huge\boxed{Distance=10~units}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Approximate the area under the
function between a and b using a
left-hand sum with the given
number of intervals.
f(x) = x² + 2
a = 0
b= 6
6 intervals
Answer:
67 square units
Step-by-step explanation:
The area using the left-hand sum is the sum of products of the function value at the left side of the interval and the width of the interval.
AreaThe attachment shows a table of the x-value at the left side of each interval, and the corresponding function value there. The interval width is 1 unit in every case, so the desired area is simply the sum of the function values.
The approximate area is 67 square units.
Split up the interval [0, 6] into 6 equally spaced subintervals of length [tex]\Delta x = \frac{6-0}6 = 1[/tex]. So we have the partition
[0, 1] U [1, 2] U [2, 3] U [3, 4] U [4, 5] U [5, 6]
where the left endpoint of the [tex]i[/tex]-th interval is
[tex]\ell_i = i - 1[/tex]
with [tex]i\in\{1,2,3,4,5,6\}[/tex].
The area under [tex]f(x)=x^2+2[/tex] on the interval [0, 6] is then given by the definite integral and approximated by the Riemann sum,
[tex]\displaystyle \int_0^6 f(x) \, dx \approx \sum_{i=1}^6 f(\ell_i) \Delta x \\\\ ~~~~~~~~ = \sum_{i=1}^6 \bigg((i-1)^2 + 2\bigg) \\\\ ~~~~~~~~ = \sum_{i=1}^6 \bigg(i^2 - 2i + 3\bigg) \\\\ ~~~~~~~~ = \frac{6\cdot7\cdot13}6 - 6\cdot7 + 3\cdot6 = \boxed{67}[/tex]
where we use the well-known sums,
[tex]\displaystyle \sum_{i=1}^n 1 = \underbrace{1 + 1 + \cdots + 1}_{n\,\rm times} = n[/tex]
[tex]\displaystyle \sum_{i=1}^n i = 1 + 2 + \cdots + n = \frac{n(n+1)}2[/tex]
[tex]\displaystyle \sum_{i=1}^n i^2 = 1 + 4 + \cdots + n^2 = \frac{n(n+1)(2n+1)}6[/tex]
Darlene is building a rectangular fence. the length is 8 feet longer than the width. the perimeter of the rectangle is 76 feet. what is the length of the rectangle?
Answer:8 feet
Step-by-step explanation:
Complete the proofs, ASAP!!! (Geometry)
1) [tex]\triangle ABC[/tex] with [tex]\overline{AC} \cong \overline{BC}[/tex], [tex]\overline{AB} \parallel \vec{CE}[/tex] (given)
2) [tex]\angle A \cong \angle B[/tex] (base angles theorem)
3) [tex]\angle A \cong \angle 1[/tex] (corresponding angles theorem)
4) [tex]\angle B \cong \angle 2[/tex] (alternate interior angles theorem)
5) [tex]\angle 1 \cong \angle 2[/tex] (transitive property of congruence)
6) [tex]\vec{CE}[/tex] bisects [tex]\angle BCD[/tex] (if a ray splits an angle into two congruent parts, it is a bisector)
What is the equation of the line that passes through (4, -1) and (-2, 3)?
a.) 2 x + 3 y - 5 = 0
b.) -2 x + 3 y - 5 = 0
c.) 2 x - 3 y - 5 = 0
Answer:
a
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (4, - 1 ) and (x₂, y₂ ) = (- 2, 3 )
m = [tex]\frac{3-(-1)}{-2-4}[/tex] = [tex]\frac{3+1}{-6}[/tex] = [tex]\frac{4}{-6}[/tex] = - [tex]\frac{2}{3}[/tex] , then
y = - [tex]\frac{2}{3}[/tex] x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (- 2, 3 ) , then
3 = [tex]\frac{4}{3}[/tex] + c ⇒ c = 3 - [tex]\frac{4}{3}[/tex] = [tex]\frac{5}{3}[/tex]
y = - [tex]\frac{2}{3}[/tex] x + [tex]\frac{5}{3}[/tex] ← in slope- intercept form
multiply through by 3 to clear the fractions
3y = - 2x + 5 ( subtract - 2x + 5 from both sides )
2x + 3y - 5 = 0 ← in general form
How many liters of water should be added to 18 liters of a 14% bleach solution so that the resulting solution contains only 10% bleach? original (l) added (l) new (l) amount of bleach 2.52 0 amount of solution 18 x 1.8 liters 7.2 liters 15.5 liters 25.2 liters
18 liters of 14% bleach contains 0.14×18 = 2.52 liters of bleach.
Adding [tex]x[/tex] liters of pure water to the solution increases the total volume to [tex]18+x[/tex] liters without changing the total amount of bleach.
To end up with a 10% bleach solution, we must add
[tex]\dfrac{2.52}{18+x} = 0.10 \implies 2.52 = 1.8 + 0.10x \implies 0.10x = 0.72 \implies x=\boxed{7.2}[/tex]
liters of water.
Answer:
b
Step-by-step explanation:
What is this expression in simplified form?
4/14 - 11/14
Answer:
baiBsiasbisvdxhsbhssj
Answer:
-1/7
is the answer of your question
pipe A can fill a tank in 3 hours. if pipe B can fill the same tank in 2 hours, how many minutes will it take both pipes to fill 2/3 of the tank
Answer:
pipe A =3. pipe B=2 find LCM of 3 and 2 . it will be 6 . Then take 6×2/3 it will give you 4 minutes as the answerAnswer:
48 minutes
Step-by-step explanation:
The rate of filling from both pipes is the sum of the rates in units of tanks per hour. We want the time for 2/3 of a tank.
Sum of ratesThe sum of the filling rates is ...
rate A + rate B = (1/3) tank/hour + (1/2) tank/hour = 5/6 tank/hour
Fill timeThe time to fill a tank or part thereof will be the number of tanks divided by the rate in tanks per hour:
time = (2/3 tank)/(5/6 tank/hour) = ((4/6)/(5/6)) hour = 4/5 hour
There are 60 minutes in an hour, so the fill time is ...
(4/5 hour)×(60 min/hour) = 48 min
It will take 48 minutes for both pipes to fill 2/3 of the tank.
Find the producer surplus at the equilibrium point. 3) s(x) = x 3, 0 k x k 3; x = 3
The producer surplus at the equilibrium point is 1.0146
An equilibrium (or equilibrium point) of a dynamical machine-generated via an autonomous machine of everyday differential equations (ODEs) is a solution that doesn't change with time.
Equilibrium is the country in which the marketplace delivers and calls for stability each different, and as a result, expenses turn out to be solid. usually, an over-deliver of products or services reasons charges to head down, which leads to higher demand—at the same time as a below-supply or scarcity reasons costs to head up resulting in fewer calls.
The equilibrium equations (balance of linear momentum) are given in index form as(1.4)σji,j+bi=ρu¨i, I,j=1,2,3where σij are additives of (Cauchy) stress, ρ is mass density, and bi is body force additives.
Producer Surplus = area of shadestportion
Area of shaded portion = free of rect minus area of OneD
Aves of OABO=Now serving from
"[3√74-3/5]
= √(x+3)" de
=2 (2√6-√5)
(Jon= √46 = Fure=456-255
(x+3)+1
Area of rectangle OA BC =316
= 3√6
producer surplus = 3√6 - (ure -2√5)
= 2√3-66
= 1.0146
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Quick algebra 1 question for 25 points!
Only answer if you know the answer, Tysm!
Answer:
d. 9
Step-by-step explanation:
y= 0.22x^2 - 1.76x +4.75
x is the time in months so we should replace x by 10
y = 0.22 (10)^2 - 1.76(10) + 4.75
0.22 (100) - 17.6 + 4.75
22 - 17.6 + 4.75
9.15
So the number of laptops that will be sold during month 10 is 9. (you can't have 0.15 of a computer)
Answer:
d. 9
Step-by-step explanation:
The equation: y = 0.22x^2 - 1.76x + 4.75
x: Time in months
y: Number of laptops sold
Since we need to predict the number of laptops that will be sold during month 10, we can replace the x with 10.
The new equation will be: y = 22 - 17.6 + 4.75
Then y will be 9.15
Since there cannot be 0.15 of a laptop, we round the number 9.15 to a whole number, which is 9.
D) 9 is our final answer to this question.
the value of digit 7 in 906.7
The answer is tenths
Step-by-step explanation:
According to the place value chart of decimals,the first number after the decimal point starts from tenths and continues.so the answer is tenths
Hi :)
Remember Place value in decimal numbers
———————————[tex]\large\boldsymbol{\hfill\stackrel{hundreds}{9}~\hfill\stackrel{tenths}0~\hfill\stackrel{ones}6.\hfill\stackrel{tenths}{7}}[/tex]
Then
The place-value of [tex]\boldsymbol{7}[/tex] is [tex]\boldsymbol{tenths}[/tex].
[tex]\tt{Learn~More;Work~Harder}[/tex]
:)
distance between −42 and −78
Answer:
36 units
Step-by-step explanation:
to find the distance take the absolute value of the difference, that is
| - 42 - (- 78) | = | - 42 + 78 | = | 36 | = 36
or
| - 78 - (- 42) | = | - 78 + 42 | = | - 36 | = 36
Answer:
-36
Step-by-step explanation:
-78 - (-42)
= -78 + 42
= -36
Select true or false to tell whether the following conditional p q is true or false. Use the truth table if needed.
If 3 + 2 = 5, Then 5 + 5 = 10
The given condition on the basis of truth table is true.
According to the statement
we have given that the some condition p and q. and we have to find that the given condition is true or false on the basis of the truth table.
So, The given conditions are:
If 3 + 2 = 5, Then 5 + 5 = 10
Now,
The Truth table is a tabular representation of all the combinations of values for inputs and their corresponding outputs. It is a mathematical table that shows all possible outcomes that would occur from all possible scenarios that are considered.
So, the given conditions are properly verified with the truth table. So, it is true.
So, The given condition on the basis of truth table is true.
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With tax included, a couch costs $315. What does the couch cost before tax?
The $315 cost of the couch after tax, gives the cost before tax, C, as the following equation;
[tex]Cost \: before \: tax, \: \: \mathbf {C} = \frac{315}{1 + t} [/tex]
How can the cost before tax be expressed?The cost of the couch with tax = $315
Let, t, represent the tax rate, and let C, represent the cost before tax, we have;
315 = C + C × t
315 = C × (1 + t)Which gives;
The cost of the couch before tax, C = 315/(1 + t)Mathematically, we have the following equation;
[tex]Cost \: before \: tax, \: \: \mathbf {C} = \frac{315}{1 + t} [/tex]
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Please help with this question asap!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
no solution
Step-by-step explanation:
We can think of an absolute value as the magnitude of the number. We can also define it as how far the number is from 0 on the number line. Thus, absolute value must always be positive (or 0).
Solve
Start by adding 1 to both sides:
[tex]\frac{|m|}{2}=-2[/tex]
Multiply both sides by 2:
[tex]|m|=-4[/tex]
The absolute value of a number is always positive (with the exception of 0), therefore there is no solution.
Additional CommentsNotice we can only add/multiply (or subtract/divide) an equation because of the Addition/Subtraction/Multiplication/Division Property of Equality which state that if you add/subtract/multiply/divide one side of the equation by a certain value, you must do the same to the other side of the equation.
pls pls help meee i dont understand the fundamental theorem of algebra
Answer:
Hey! I'm gonna go ahead and give ya the "meaning" of the fundamental theorem of algebra but not the answer to the A. B. and C.
Step-by-step explanation:
fundamental theorem of algebra, theorem of equations proved by Carl Friedrich Gauss in 1799. It states that every polynomial equation of degree n with complex number coefficients has n roots, or solutions, in the complex numbers. The roots can have a multiplicity greater than zero.
Michelle is purchasing fabric for two new sewing projects: a hat and a tote bag. The two projects each need red and black fabric. The hat requires 2 yards of red fabric and 1 yard of black fabric. The tote bag requires 2 yards of red fabric and 4 yards of black fabric. Michelle paid $14 for the hat’s fabric and $26 for the tote bag’s fabric. How much does one yard of each fabric cost?
The cost of one yard of black fabric is $4.
The cost of one yard of red fabric is $5.
What are the linear functions that represent the question?2r + b = 14 equation 1
2r + 4b = 26 equation 2
Where:
r = cost of one yard of red fabric
b = cost of one yard of black fabric
What is the cost of each type of fabric?
Subtract equation 1 from equation 2
3b = 12
b = 12 / 3
b = 4
Substitute for b in equation 1
2r + 4 = 14
2r = 14 - 4
2r = 10
r = 10 / 2
r = $5
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Write a polynomial of least degree with rational coefficients and with the root
–15+10[tex]\sqrt{6\\}[/tex]
Answer:
p(x) = x² +30x -375
Step-by-step explanation:
When a quadratic has real rational coefficients, any irrational or complex roots come in conjugate pairs.
Factored formA root of p means (x -p) is a factor of the polynomial. Here, we have roots of -15+10√6 and -15-10√6, so the factored form can be written ...
p(x) = (x -(-15 +10√6))(x -(-15 -10√6))
Using the factoring of the difference of squares, we can write this as ...
p(x) = (x +15)² -(10√6)²
Standard formExpanding the factored form, we can write the polynomial as ...
p(x) = x² +30x +225 -600
p(x) = x² +30x -375
The ratio of the triangle are in the ratio 1:2:3 Find the angles of this triangle?
Answer:
Step-by-step explanation:
let we suppose the ratios as x , 2x and 3x
we know that,
x + 2x + 3x = -----
6x= -------
x= -----/6
therefore x = ......
2x = 2 * x (value of x)
3x = 3 * x (value of x)
and the question is solved
Answer:
let the ratio be 1x,2x,3x
Now,
1x+2x+3x=180°(sum of angles of triangle are 180)
or,6x=180°
or,x=180/6
or,x=30°
Then,
1x=1*30
=30°
2x=2*30
=60°
3x=3*30
=90°
Miss a turn
Go forward
3 squares
Go back
2 squares
Go back
1 square
Go forward
2 squares
Go forward
3 squares
In a game, a fair spinner has six equal sections
as shown.
a) Noel spins the spinner.
Write down the probability he gets 'Miss a turn'.
Give your answer as a fraction.
(1)
b) The spinner lands on 'Go back 1 square'
four times in a row.
Steve is next to spin.
Write down the probability that he gets
'Go back 1 square'.
Give your answer as a fraction.
c) In one game there are 96 spins.
How many of these spins are expected
to be 'Go forward 3 squares'?
(1)
(2)
Total marks: 4
See below for the values of the probabilities
How to determine the probabilityThe complete question is added as an attachment
Write down the probability he gets 'Miss a turn'.
From the spinner, we have
Sections = 6
Miss a turn = 1
So, the probability that he gets 'Miss a turn is
P = 1/6
Write down the probability that he gets 'Go back 1 square'.
Here, we have:
Number of rows = 4
'Go back 1 square' = 4
The probability that he gets 'Go back 1 square' is
P = 'Go back 1 square'/Number of rows
This gives
P = 4/4
Evaluate
P = 1
How many of these spins are expected to be 'Go forward 3 squares'?
Here, we have
Spins = 96
From the spinner, the probability of 'Go forward 3 squares' is
P =1/6
So, the expected number is
E(x) = np
This gives
E(x) = 96 * 1/6
Evaluate
E(x) = 16
Hence, 16 spins are expected to be 'Go forward 3 squares'
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(x^2-6x+9)^2-15(x^2-6x+10)=1
Answer:
x = -1, 7, 3 + i, 3 - i.
Step-by-step explanation:
(x^2-6x+9)^2-15(x^2-6x+10)=1
(x^2 - 6x + 9)^2 - 15(x^2 - 6x + 9) - 15*1 = 1
(x^2 - 6x + 9)^2 - 15(x^2 - 6x + 9) - 16 = 0
Let Z = x^2 - 6x + 9, then we have:
Z^2 - 15Z - 16 = 0
(Z - 16)(Z + 1) = 0
Z = 16 or Z = -1
so x^2 - 6x + 9 = -1 or x^2 - 6x + 9 = 16
x^2 - 6x + 9 = -1
---> x^2 - 6x + 10 = 0
Using the Quadratic Formula:
---> x = [6 +/- √((-6)^2 - 4* 1* 10) / 2
---> x = 6/2 +/- √-4/2
---> x = 3 + i , 3 - i.
x^2 - 6x + 9 = 16
---> x^2 - 6x - 7 = 0
---> (x - 7)(x + 1) = 0
---> x = 7, -1.
Identify the elevation and the percentage of oxygen available at each elevation. 8,850 m 57% 33% 4,500 m 100%
1. Sea level (0 m) - 100%
2. Mid-level elevation (4,500 m) - 57%
3. Peak (8,850 m) - 33%
What does oxygen mean?Oxygen is a colorless, odorless, and tasteless gas necessary for all living things. Animals take it up and then change it into carbon dioxide, which plants then use as a carbon source to release oxygen back into the atmosphere.The energy-producing process that powers the metabolisms of most living organisms, respiration, depends heavily on oxygen. All living things, including humans, depend on oxygen in the air we breathe to survive. The process of photosynthesis is where plants and certain bacteria produce oxygen.Identify the elevation and the percentage of oxygen available at each elevation.
Elevation has a significant impact on the amount of oxygen in the atmosphere. The oxygen level increases with decreasing height and decreases with increasing elevation. Thus, we have a situation where the oxygen concentration is highest at sea level or 0 elevations. The oxygen level drops dramatically when we ascend to greater elevations, say 4,500 m, making breathing difficult. Even at higher altitudes, such as 8,850 m, the oxygen level will drop significantly, making it necessary for a person to undergo extensive training and carry oxygen to survive.
1. Sea level (0 m) - 100%
2. Mid-level elevation (4,500 m) - 57%
3. Peak (8,850 m) - 33%
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50 pupils in a sports centre are surveyed. the pupils can only use the swimming pool and the gym. 31 pupils use the swimming pool. 28 pupils use the gym. 7 pupils use neither the swimming pool nor the gym. find the probability to select a pupil that uses the swimming pool but not the gym.
Using it's concept, it is found that there is a 0.3 = 30% probability to select a pupil that uses the swimming pool but not the gym.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, we have that 50 - 7 = 43 pupils use at least one of the pool or the gym.
We use the following relation, considering the numbers of each:
Both = Pool + Gym - At least one
Hence:
Both = 31 + 28 - 43 = 16.
From this, we have that out of 50 pupils, there are 31 - 16 = 15 pupils who use the pool but not the gym, hence the probability is:
p = 15/50 = 0.3 = 30%.
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A pedestal for a statue is made with 405 cubic feet of concrete. a rectangular prism with a height of 9 feet. what is the area of the base of the pedestal? 6.7 square feet 22.5 square feet 45 square feet 3,645 square feet
45 square feet is the area of the base of the pedestal.
what is rectangular prism?
A rectangular prism is a 3D figure with 6 rectangular faces. To find the volume of a rectangular prism, multiply its 3 dimensions: length x width x height. The volume is expressed in cubic units.we know that
The volume of the pedestal (rectangular prism) is given by the formula
V = B × h
where
B is the area of the rectangular base of pedestal
V = 405 ft³
h = 9 ft
put the given values in the formula and solve for B
405 = B × 9
B = 405/9
B = 45 ft²
Therefore, 45 square feet is the area of the base of the pedestal.
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Jarred sells DVDs. His inventory shows that he has a total of 3,500 DVDs. He has 2,342 more contemporary titles than classic titles. Let x represent the number of contemporary titles and y represent the number of classic titles. The system of equations models the given information for both types of DVDs.
x + y = 3,500
x – y = 2,342
Solve the system of equations. How many contemporary titles does Jarred have?
The number of contemporary titles and classic titles in Jarred DVDs collection is 2,921 and 579 respectively.
Simultaneous equationSimultaneous equation is an equation which involves the solving for two unknown values at the same time.
number of contemporary titles = xnumber of classic titles = yx + y = 3,500
x – y = 2,342
Add both be equation
x + x = 3,500 + 2,342
2x = 5,842
x = 5,842 ÷ 2
x = 2,921
Substitute x = 2,921 into
x – y = 2,342
2,921 - y = 2, 342
-y = 2,342 - 2,921
-y = -579
y = 579
Therefore, the number of contemporary titles and classic titles in Jarred DVDs collection is 2,921 and 579 respectively.
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what is the sum of (6x^2-x+8) - (x^2+2)
Answer:
5x^2-x+6
Step-by-step explanation:
That should work
Solve the given differential equation by undetermined coefficients. y'' 4y' 4y = 2x 3
The solution of the differential equation is [tex]y = (C_{1} + C_{2} x)e^{-2x} +\frac{1}{2} [x^{3} -\frac{3}{2} x-6][/tex] .
According to the given question.
We have a differential equation
[tex]y^{"} + 4y^{'} + 4y = 2x^{3}[/tex]
The above differerntial equation acn be written as
[tex](D^{2} +4D+ 4)= 2x^{3}[/tex]
Now, the auxillary equation for the above differential equation is given by
[tex]m^{2} + 4m + 4 = 0[/tex]
[tex]\implies m^{2} + 2m + 2m + 4 = 0[/tex]
⇒ m (m + 2) + 2(m + 2) = 0
⇒ m(m + 2)(m + 2) = 0
Therefore,
[tex]C.F = (C_{1} + C_{2}x)e^{-2x}[/tex]
Now,
[tex]PI = \frac{1}{D^{2} +4D+4} 2x^{3}[/tex]
[tex]\implies PI = \frac{1}{4(1+\frac{D^{2}+4D }{4} )} 2x^{3}[/tex]
[tex]\implies PI = \frac{1}{4} [1+(\frac{D^{2}+4D }{4} )]^{-1} 2x^{3}[/tex]
[tex]\implies PI = \frac{1}{4} [ 1 - (\frac{D^{2} +4D}{4} )+(\frac{D^{2} +4D}{4} )^{2} -(\frac{D^{2}+4D }{4}) ^{3} ...]2x^{3}[/tex]
[tex]\implies PI =\frac{1}{2} [ x^{3} -\frac{1}{4} (6x)-3x^{2} +3x^{2} -6][/tex]
[tex]\implies PI = \frac{1}{2} [x^{3} -\frac{3}{2} x-6][/tex]
Therefore, the solution of the differential equation will be
y = CI + PI
[tex]y = (C_{1} + C_{2} x)e^{-2x} +\frac{1}{2} [x^{3} -\frac{3}{2} x-6][/tex]
Hence, the solution of the differential equation is [tex]y = (C_{1} + C_{2} x)e^{-2x} +\frac{1}{2} [x^{3} -\frac{3}{2} x-6][/tex] .
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