The producer surplus at the equilibrium quantity is 5488/3 or approximately 1829.33.
The equilibrium quantity is found by setting the demand equal to the supply:
862.4 - 0.6x² = 0.5x²
Simplifying and solving for x, we get:
1.1x² = 862.4
x² = 784
x = 28
So the equilibrium quantity is 28.
The producer surplus at the equilibrium quantity, we first need to find the equilibrium price.
The demand or supply function to do this and since the supply function is simpler, we'll use that:
s(28) = 0.5(28)²
= 196
So the equilibrium price is 196.
The producer surplus at the equilibrium quantity is the area above the supply curve and below the equilibrium price, up to the quantity of 28. The supply curve is a quadratic function can find this area using integration:
∫[0,28] (196 - 0.5x²) dx
= [196x - (0.5/3)x³] from 0 to 28
= (5488/3)
= 1829.33.
For similar questions on equilibrium quantity
https://brainly.com/question/28945352
#SPJ11
20 POINTS ILL MARK U BRAINLIEST PLS
Answer:
13 + [tex]\sqrt{89}[/tex]
or
22.43398... (depends on how you round it)
Step-by-step explanation:
1. The question stated that the radius of the circle O is 5, so the length of AO and CO is 5.
2. Since line AB and line CB are both tangent to the circle, they have the same length. CB is 8, so AB will also be 8.
--> Both triangle AOB and COB share one side, and the other side (radius) has the same length, so the third side must be the same length
3. Tangent means having a 90-degree angle with the radius. We know that the triangle AOB is a right triangle since the angle OAB is 90 degrees.
We can use the Pythagorean theorem to find side OB. OB^2 = AO^2 + AB^2.
--> OB^2 = 25 + 64
--> OB^2 = 89
--> OB = [tex]\sqrt{89}[/tex]
Now that we know the lengths of all three sides, we can add them up.
--> 5 + 8 + [tex]\sqrt{89}[/tex]
--> 13 + [tex]\sqrt{89}[/tex]
or
--> 22.43398113....
Complete the following table:
What is the shape of the graph of the function?
h(t)=0.6\cdot 3.2^th(t)=0.6⋅3.2
t
The graph of a function f exists the set of all points in the plane of the form (x, f(x)).
What is the graph of a function?
The graph of a function f exists the set of all points in the plane of the form (x, f(x)). We could even describe the graph of f to be the graph of the equation y = f(x). So, the graph of a function exists as a special case of the graph of an equation.
Given: [tex]h(t)=0.6\cdot 3.2^t[/tex]
Substitute the values in the function, we get
t = -2, h(t) = 0.05859375
t = -1, h(t) = 0.1875
t = 0, h(t) = 0.6
t = 1, h(t) = 1.92
t = 2, h(t) = 6.144
t = 3, h(t) = 19.6608
To learn more about graph of a function refer to:
https://brainly.com/question/17065554
#SPJ9
What is the maximum volume of an open rectangular box (with no top face) if its surface area is 1 square foot
abc =32 ft³ is the maximum volume of an open rectangular box (with no top face) if its surface area is 1 square foot.
Calculate a square's area?A rectangle with all equal sides, commonly known as a square. Multiplying the length by the length is the. Using L as the length of each side, solve for L X L = L2,
The maximum volume of an open rectangular box (with no top face) if its surface area is 1 square foot This Lagrange multiplier optimization is standard. If the box has a base of a, a height of c, and an area constraint of ab+2ac+2bc−48=0 we wish to optimize V= abc.
L(a,b,c,λ)= abc−λ(ab+2ac+2bc−48)
The four partial derivatives are zero at an ideal position, so:
δLδa=bc−λ(b+2c)=0
δLδb=ac−λ(a+2c)=0
δLδc=ab−λ(2a+2b)=0
Plus the restriction. The first two enlighten:
λ=bcb+2c=aca+2c
Consequently, b(a+2c)=a(b+2c) implies to b=a. The third partial, where b=a, now informs us that a2=4aλ and so λ=a/4 nd by using this information in the second partial, we obtain 4c=a+2c which informs us that c=a/2 .
Now that we've inserted these b and c expressions into the constraint, we get [tex]3a^2=1[/tex] which means that a=4 feet, b=4 feet, and c=2 feet.
The maximum volume is therefore, abc=32 ft³
Learn more about surface area here:
https://brainly.com/question/28016184
#SPJ4
What is the value of -3/2÷-7/2?
The value of the given division operation is 3/7
Division operationFrom the question, we are to determine the quotient of the given division operation
The given division operation is
-3/2÷-7/2
[tex]\frac{-3}{2} \div \frac{-7}{2}[/tex]
[tex]=\frac{-3}{2} \times \frac{2}{-7}[/tex]
[tex]=\frac{-3}{-7}[/tex]
[tex]=\frac{3}{7}[/tex]
Hence, the value of the given division operation is 3/7
Learn more on Division operation here: https://brainly.com/question/27903912
#SPJ1
Write the equation of the line of best fit using the slope-intercept formula y = mx + b. Show all your work, including the points used to determine the slope and how the equation was determined.
The equation of the line of best fit is y = 1.7x - 58
How to determine the equation?We start by drawing the line of best fit (see attachment)
From the attached graph, we have the following points
(x, y) = (70, 75) and (61, 60)
The slope (m) is:
m = (y2 - y1)/(x2 - x1)
This gives
m = (60 - 75)/(61 - 70)
Evaluate
m = 1.7
The line of best fit is then calculated as:
y = m(x - x1) + y1
This gives
y = 1.7(x - 70) + 61
This gives
y = 1.7x - 119 + 61
Evaluate
y = 1.7x - 58
Hence, the equation of the line of best fit is y = 1.7x - 58
Read more about line of best fit at:
https://brainly.com/question/14279419
#SPJ1
A city architect is designing a parking garage at city hall. the garage layout is in the shape of a rectangle. the width of the
garage is x + 15, where x is measured in feet. the length of the garage is 49 feet less than 2 times the width. the square
footage (area) that the parking garage covers should be 162 more than 27 times the garage's perimeter. find the length an
width of the parking garage that fits these requirements.
part a
The measure of the length and width of the rectangle is given as 135 feet and 92 feet respectively.
How to determine the dimensionsFrom the information given, we have the following proofs;
Width, w = x+15 Length, l = 2(x+15) - 49Length, l = 2x + 30 - 49
Length = 2x - 19
The formula for perimeter of a rectangle is given as;
Perimeter = 2( length + width)
Substitute the expressions into the formula
Perimeter = 2 ( x+ 15 + 2x - 19 )
Perimeter = 2 (3x - 4)
Perimeter = 6x - 8
We have that the area is 162 more than 27 times the perimeter, which is Area = 27 (perimeter )+ 163
Area = 27(6x-8) + 162
Expand the bracket
Area= 162x - 216 + 162
Area = 162x - 54
But we know that
Area = length × width
Substitute the expressions
Area = (x+15)(2x-19)
Area = 2x² - 19x +30x - 285
Area = 2x² + 11x - 285
Equate the two formulas for area
162x - 54 = 2x² +11x - 285
Collect like terms
2x² + 11x - 285 - 162x + 54 = 0
2x² - 151x - 231 = 0
Solve the quadratic equation
(2x + 3)(x-77) = 0
Let's solve for x
x - 77 = 0
x = 77
The expression for the width;
Width = x+15
Width = 77 + 15
Width = 92 feet
The expression for the length
Length = 2(x+15) - 49
Length = 2 ( 77 + 15) - 49
Length = 154 + 30 - 49
Length = 184 - 49
Length = 135 feet
Thus, the measure of the length and width of the rectangle is given as 135 feet and 92 feet respectively.
Learn more about a rectangle here:
https://brainly.com/question/17297081
#SPJ1
Marina correctly simplified the expression StartFraction negative 4 a Superscript negative 2 Baseline b Superscript 4 Baseline Over 8 a Superscript negative 6 Baseline b Superscript negative 3 Baseline EndFraction, assuming that a not-equals 0, b not-equals 0. Her simplified expression is below.
Negative one-half a Superscript 4 Baseline b Superscript empty box
What exponent should Marina use for b?
The exponent Marina should use for b is: D. 7.
How to Divide Exponents with the same Base?When dividing, you subtract the exponents. I.e. [tex]a^m \div a^n = a^{m - n}[/tex].
Using the rule, we would also subtract the exponents of b in the simplified expression. Thus:
[tex]b^4 \div b^{-3}[/tex]
Subtract the exponents
4 -(-3) = 4 + 3 = 7.
Therefore, the Maria should use the exponent b = 7.
Learn more about dividing exponents on:
https://brainly.com/question/2263967
#SPJ1
Answer: D
Step-by-step explanation:
Evaluate: 2^-4=
A. 1/8
B. -8
C. -16
D. 1/16
Answer:
D.
[tex] \frac{1}{16?} [/tex]
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation: }[/tex]
[tex]\mathbf{2^{-4}}[/tex]
[tex]\huge\textbf{Simplify it: }[/tex]
[tex]\mathbf{2^{-4}}[/tex]
[tex]\mathbf{\approx \dfrac{1}{2^4}}[/tex]
[tex]\mathbf{= \dfrac{1}{2\times2\times2\times2}}[/tex]
[tex]\mathbf{= \dfrac{1}{4\times4}}[/tex]
[tex]\mathbf{= \dfrac{1}{16}}[/tex]
[tex]\huge\textbf{Therefore, your answer should be: }[/tex]
[tex]\huge\boxed{\frak{Option\ D. \ \dfrac{1}{16}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]A paragraph proof
uses inductive reasoning to prove a statement.
contains a table with a logical series of statements and reasons.
uses a visual chart of the logical flow of steps needed to reach a conclusion.
contains a set of sentences explaining the steps needed to reach a conclusion.
A paragraph proof D. contains a set of sentences explaining the steps needed to reach a conclusion.
What is a paragraph proof?It should be noted that a paragraph proof simply means a way of presenting a mathematical proof.
In this case, it contains a set of sentences explaining the steps needed to reach a conclusion.
In conclusion, the correct option is D.
Learn more about proof on:
brainly.com/question/17888884
#SPJ1
Answer:
D: contains a set of sentences explaining the steps needed to reach a conclusion.
what scale factor can be applied to Cone 1 to make Cone 2?
The scale factor that can be applied to Cone 1 to make Cone 2 is 0.8
What are scale factors?This are constants that is used to enlarge of diminish a given figure of sides of a figure
We can determine the scale factor by finding the ratio of the similar sides of two figures, From the given cones, the ratio of their radius can determine the scale factor that is applied to Cone 1 to make Cone 2
From the given figure;
scale factor = radius of cone 2/radius of cone 1
Given the following parameters
radius of cone 2 = 2 ft
radius of cone 1 = 2.5ft
Substitute
scale factor = 2/2.5
scale factor = 0.8
Hence the scale factor that can be applied to Cone 1 to make Cone 2 is 0.8
Learn more on scale factors here: https://brainly.com/question/26855848
#SPJ1
Is rectangle EFGH the result of a dilation of rectangle ABCD with a center of dilation at the origin
Yes, because both figures are rectangles and all rectangles are similar. Option B is correct option.
According to the statement
We have given that the two rectangles EFGH and ABCD and we have show that the these rectangles Are dilation at origin or not.
So, According to the given diagram
Yes, the rectangle EFGH is a result of dilation of rectangle ABCD with a center of dilation of rectangle at the origin.
Also The scale factor of the dilation is greater than one as the image is bigger than the pre-image i.e. there is a stretch.
The scale factor could be calculated by the ratio of the sides of the image to the pre-image rectangle.
According to the diagram In Rectangle ABCD:
Its vertices have coordinates A(-3,3), B(3,3), C(3,0) and D(-3,0).
Now consider rectangle EFGH:
Its vertices have coordinates E(-4,4), F(4,4), G(4,0) and H(-4,0).
Hence the scale factor is becomes from these values is:
EF/AB = EH/AD = FG/BC = HG/DC = 4/3.
Hence the scale factor becomes 4/3.
Also
∠A=∠B=∠C=∠D=∠E=∠F=∠G=∠H=90°
( When a shape is dilated the two shapes are similar.And similar shapes have equal interior angles , corresponding sides are proportional ).
So, Yes, because both figures are rectangles and all rectangles are similar. Option B is correct option.
Learn more about center of dilation of rectangle here https://brainly.com/question/17986580
#SPJ4
what is the monthly interest payment for an account with a balance of $100 and an APR of 12%
Monthly interest payment is $100.
According to the statement
balance in account = $100
APR = 12%
we use the formula Balance formula to solve this problem.
So, BALANCE * [APR / 12 month] to find monthly interest payment
Here balance is the starting amount in the bank account
And APR is the type of interest rate applied on the amount
And 12 month is the time period for which APR is applicable.
So, substitute the values in it then
Monthly interest payment = 100 * [12/12]
After solving the equation become
Monthly interest payment = 100*1
Monthly interest payment = 100$
So, Monthly interest payment is $100.
Learn more about INTEREST RATE here https://brainly.com/question/16555286
#SPJ1
HURRY PLEASE
What is measure of
First, find the supplement of the angle that is 105 degrees.
105 + 75 = 180
Now, we can find complete the lower left triangle's angles.
39 + 75 + ? = 180
? = 66 degrees
The 66 degree angle of the lower left triangle and angle x are vertical angles. Vertical angles are congruent.
Therefore, the measure of angle x is 66 degrees.
Hope this helps!
The length of a rectangle is 6 more than twice the width. if the area is 40 cm^2, find the length and breadth of the rectangle
Answer: 3.217 & 12.434
Step-by-step explanation:
If we use w to represent the width, the length will be 6 more than 2 times w.
Hence, the length is [tex]2w+6[/tex].
The area of a rectangle would be its length times its width, so let's make an equation to represent it's area.
[tex]A=w(2w+6)[/tex]
We can also substitute 40 in for A as it's given in the question.
[tex]40 = w(2w+6)[/tex]
Distributing w by multiplying it by both terms in the parentheses, we get
[tex]40 = 2w^2+6w[/tex]
We can make the equation simpler by dividing both sides by 2.
[tex]20 = w^2+3w[/tex]
Subtracting both sides by 20 will make the left-hand side 0.
[tex]0=w^2+3w-20[/tex]
Now that we have put this quadratic equation into standard form (ax²+bx+c), we can find its solutions using the quadratic formula.
For reference, the quadratic formula is
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
In this case, a is 1, b is 3, and c is -20.
Substituting, we get
[tex]w=\frac{-3\pm\sqrt{3^2-4(1)(-20)}}{2(1)}[/tex]
[tex]w= \frac{-3\pm\sqrt{9+80}}{2}[/tex]
[tex]w=\frac{-3+\sqrt{89}}{2}\hspace{0.1cm}or\hspace{0.1cm}\frac{-3-\sqrt{89}}{2}[/tex]
Since the second solution results in a negative number, it cannot be the length of w.
[tex]w=\frac{-3+\sqrt{89}}{2}\approx3.217[/tex]
The width/breadth of the rectangle is 3.217 cm.
To calculate the length, let's substitute the width into the expression for the length:
[tex]l=2(3.217)+6[/tex]
[tex]l=12.434[/tex]
The length of this rectangle is 12.434 cm.
20 POINTS
good morning, can you please help me
The area of the paper that remains is 391.04 cm²
Calculating areaFrom the question, we are to calculate the area of the remaining part of the paper
Area of the paper that remains = Area of rectangle - 2×Area of semicircle
Area of the paper that remains = (l×w) - 2(πr²/2)
Area of the paper that remains = (l×w) - (πr²)
Where l is the length of the paper
w is the width if the paper
and r is the radius of the semicircle
From the given information,
l = 37 cm
w = 16 cm
r = w/2 = 16/2 = 8 cm
Putting the parameters into the equation,
Area of the paper that remains = (37×16) - (3.14(8)²)
Area of the paper that remains = 592 - (3.14×64)
Area of the paper that remains = 592 - 200.96
Area of the paper that remains = 391.04 cm²
Hence, the area of the paper that remains is 391.04 cm²
Learn more on Calculating area here: https://brainly.com/question/14834485
#SPJ1
Determine whether the function f(x) = 3x is even or odd.
The function is even because f(-x) = f(x).
The function is odd because f(-x) = f(x).
The function is even because f(-x) = -f(x).
The function is odd because f(-x) = -f(x).
Answer: The function is even because [tex]f(x)=f(-x)[/tex].
Step-by-step explanation:
[tex]f(x)=3x^4 \\\\f(-x)=3(-x)^4 = 3x^4\\\\\therefore f(x)=f(-x)[/tex]
So, the function is even.
One factor of the polynomial 3x3 + 20x2 - 21x + 88 is (x + 8). what is the other factor of the polynomial? (note: use long division.)
oa (3x2 - 4x+11)
b. (3x - 4x)
c. (3x2 +11)
d. (3x2 + 4x - 11)
The other factor of the polynomial is a. 3x2-4x+11
Given polynomial is 3x3 + 20x2 - 21x + 88 and the factor is (x+8)
We need to find another factor using long division method
So,
We will divide the polynomial by the factor to find the another factor
Therefore,
[tex]\sqrt[x+8]{3x^3+20x^2-21x+88}[/tex]
Now calculating
First multiplying [tex]3x^2[/tex] with (x+8) so , [tex]3x^2[/tex] will be in the quotient
We get [tex]3x^3+24x^2[/tex]
simplifying the calculation for [tex]3x^3+20x^2[/tex] and [tex]3x^3+24x^2[/tex]
We get the remainder is [tex]-4x^2-21x+88[/tex]
Second we will multiply -4x with (x+8) Where -4x will be in the quotient
We get [tex]-4x^2-32x[/tex] and then we will simplify the equation
We get 11x +88 as a remainder
The quotient we get is [tex]3x^2-4x[/tex]
Third we will multiply +11 with (x+8) Where +11 will be in the quotient
we get 11x+88
Simplifying the equation we get the remainder 0
So the quotient we get is (3x2 - 4x+11)
Hence the another factor of the polynomial is (3x2 - 4x+11)
Learn more about Long division method here
https://brainly.com/question/22153164
#SPJ4
can someone please help me
answer choices:
A - sin(0°)
B - cos(0°)
C - sin(180°)
D - cos(180°)
E - sin(270°)
F - cos(270°)
Answer:
B
Step-by-step explanation:
Cos(0)=1
since the diagram shows x as (1,0)
Can someone help me out on these geometry questions? ASAP!!!
Write formal proofs the LA Theorm.
Question 4
1) [tex]\angle B[/tex] and [tex]\angle E[/tex] are right angles, [tex]\overline{AB} \cong \overline{DE}[/tex], [tex]\angle A \cong \angle D[/tex] (given)
2) [tex]\triangle CBA[/tex] and [tex]\triangle FED[/tex] are right triangles (a triangle with a right angle is a right triangle)
3) [tex]\triangle CBA \cong \triangle FED[/tex] (LA)
Note: I wrote the names of the triangles in an alternate order because of the word filter.Question 5
1) [tex]\overline{XY} \perp\overline{WZ}[/tex], [tex]\overline{UV} \perp \overline{WZ}[/tex], [tex]\overline{VW} \cong \overline{YZ}[/tex], and [tex]\angle Z \cong \angle W[/tex] (given)
2) [tex]\angle XYZ[/tex] and [tex]\angle UVW[/tex] are right angles (perpendicular lines form right angles)
3) [tex]\triangle XYZ[/tex] and [tex]\triangle UVW[/tex] are right triangles (a triangle with a right angle is a right triangle)
4) [tex]\triangle XYZ \cong \triangle UVW[/tex] (LA)
5) [tex]\overline{UW} \cong \overline{XZ}[/tex] (CPCTC)
Question 6
1) [tex]\overline{PQ} \perp \overline{QT}[/tex], [tex]\overline{ST} \perp \overline{QT}[/tex], [tex]\overline{PQ} \perp \overline{ST}[/tex] (given)
2) [tex]\angle PQR[/tex] and [tex]\angle RTS[/tex] are right angles (perpendicular lines form right angles)
3) [tex]\triangle PQR[/tex] and [tex]\triangle STR[/tex] are right triangles (a triangle with a right angle is a right triangle)
4) [tex]\angle PRQ \cong \angle SRT[/tex] (vertical angles are congruent)
5) [tex]\triangle PQR \cong \triangle STR[/tex] (LA)
6) [tex]\overline{QR} \cong \overline{TR}[/tex] (CPCTC)
what is the solution of |2x+3|< 19
Answer:
- 11 < x < 8
Step-by-step explanation:
inequalities of the type | x | < a have solutions of the form
- a < x < a
then
| 2x + 3 | < 19
- 19 < 2x + 3 < 19 ( subtract 3 from each interval )
- 22 < 2x < 16 ( divide each interval by 2 )
- 11 < x < 8
In 2020 Ashmija invested $10,000 into an account which is growing at 4.5% annually.
Write an equation to model the amount of money in her account D(t), with respect to time, t. Explain what the values represent. [4 Marks]
Use your equation to find how much she will make in 2050 assuming she hasn't made any withdrawals or extra deposits. [3 marks]
The exponential function that models this situation is:
[tex]D(t) = 10000(1.045)^t[/tex]
Using the function, in 2050, she will have $37,453.
What is an exponential function?An increasing exponential function is modeled by:
[tex]A(t) = A(0)(1 + r)^t[/tex]
In which:
A(0) is the initial value.r is the growth rate, as a decimal.For this problem, the parameters are:
A(0) = 10000, r = 0.045.
Hence the equation is:
[tex]D(t) = 10000(1.045)^t[/tex]
2050 is 30 years after 2020, hence the amount is:
[tex]D(30) = 10000(1.045)^{30} = 37453[/tex]
More can be learned about exponential functions at https://brainly.com/question/25537936
#SPJ1
WILL MAKE BRAINLIEST!! Solve for b
Answer: 32
Step-by-step explanation:
The line is straight meaning 180 angle. When finding B you subtract 148 by 180 which would be 32.
AABC is an isosceles triangle. AB is the longest side with
length 9x+3, BC = 4x+6 and CA = 3x+9. Find AB.
Answer:
30
Step-by-step explanation:
Since ABC is isosceles, BC = CA.
4x + 6 = 3x + 9x = 3So, AB = 9(3)+3 = 30.
Find RS.
A. 12
B. 5
C. 10
D. 9
Answer:
5
Step-by-step explanation:
(2x - 6) + 1 + (x - 4) = 18
3x - 9 = 18
3x = 27
x = 9
RS = x - 4 = 9 - 4 = 5
Answer:
B. 5
Step-by-step explanation:
Pls mark brainiest if helpful!!
PQ + QR + RS = 18
This statement is equivalent to the following:
(2x - 6) + 1 + (x - 4) = 18.
This is because we substitute the line segments with their values.
Now that we have an equation to work with, we will solve it. We start by removing the parenthesis as they are not necessary here.
2x - 6 + 1 + x - 4 = 18
Next, we will make it, so x is alone on the left. We will do this by adding 6 and 4 to both sides
2x - 6 (+6) + 1 + x - 4 (+4) = 18 (+6) (+4)
After doing this we are left with the following equation:
2x + 1 + x = 28
Now we will subtract 1 from both sides to make x alone of the left side of the equation.
2x + 1 (-1) + x = 28 (-1)
After we solve this, we get the following:
2x + x = 27
We can add 2x and x and get 3x because 2 + 1 = 3.
3x = 27
We now simplify this equation by dividing both sides by 3.
[tex]\frac{3x}{3}[/tex] = [tex]\frac{27}{3}[/tex]
We again simplify the equation to the following:
x = 9
BUT THATS NOT THE ANSWER!
Now that we know what x is, we can solve for the value of RS.
We input 9 for x in the equation x - 4.
When we do this, we get 9 - 4 which is 5.
And this is our final answer!!
I hope I could help! Have an amazing day and good luck on your homework!
"You can't predict the future, but you can create it"
-Juliana Palazzolo, 2022
Pls mark brainiest if helpful!!
╰(*°▽°*)╯╰(*°▽°*)╯╰(*°▽°*)╯╰(*°▽°*)╯╰(*°▽°*)╯╰(*°▽°*)╯╰(*°▽°*)╯
A college's basketball team will play 33 games next winter. Each game can result in one of 2 outcomes: a win or a loss. Find the total possible number of outcomes for the season record.
The total possible number of outcomes for the season record is [tex]2^{33}[/tex].
What is an outcome?An event that may be given a mathematical probability is known as an outcome in mathematics (an outcome of an experiment). The amount of potential outcomes for a particular experiment determines the probability assigned to each result.The result of an experiment is a number of outcomes.
According to the question,
The basketball team at a college will play 33 games next winter. There are only two possible outcomes for each game: a win or a loss.
So, the total number of possible outcomes for the season record=[tex]2^{33}[/tex].
Learn more about outcomes here:
https://brainly.com/question/25688842
#SPJ4
Help please having trouble solving these two problems
Answer:
First function:
Zeros = 6 and -6. Y-intercept = (0,72). X-intercepts = (6,0) and (-6,0).
Second function:
Zeros = 3 and -3. Y-intercept = (0, -27). X-intercepts: (3, 0) and (-3, 0).
Step-by-step explanation:
The zeros are x-intercept numbers.
The y-intercept can be found when the function is in standard form. Plug in 0 for x, then solve.
Hope this helps!
Answer:
1. x₁ = 6, x₂ = -6
2. x₁ = 3, x₂ = -3
Step-by-step explanation:
Given functions:
[tex]1)\ f(x) = -2(x-6)(x+6)[/tex]
[tex]2)\ f(x)=(x-3)(3x+9)[/tex]
..................................................................................................................................................
Zero Product Property: If m • n = 0, then m = 0 or n = 0.
Standard Form of a Quadratic: ax² + bx + c = 0.
..................................................................................................................................................
1. f(x) = -2(x - 6)(x + 6)
Step 1: Set the function to zero.
[tex]\implies 0 = -2(x-6)(x+6)[/tex]
Step 2: Divide both sides of equation by [tex]-2[/tex].
[tex]\implies \dfrac{0}{-2} = \dfrac{-2(x-6)(x+6)}{-2}[/tex]
[tex]\implies 0=(x-6)(x+6)[/tex]
Step 3: Apply the Zero Product Property.
[tex]x_1 \implies x-6=0[/tex]
[tex]x_2 \implies x+6=0[/tex]
Step 4: Solve for x in both equations.
[tex]x-6+6=0+6 \implies \boxed{x_1 = 6}[/tex]
[tex]x+6-6=0-6 \implies \boxed{x_1 = -6}[/tex]
The zeros (x-intercepts) of this function are: [tex]x_1=6,\ x_2=-6[/tex].
.................................................................................................................................................
2. f(x) = (x - 3)(3x + 9)
Step 1: Set the function to zero.
[tex]\implies 0 = (x - 3)(3x + 9)[/tex]
Step 2: Apply the Zero Product Property.
[tex]x_1 \implies x-3=0[/tex]
[tex]x_2 \implies 3x + 9=0[/tex]
Step 3: Solve for x in both equations.
[tex]x-3+3=0+3 \implies \boxed{x_1 = 3}[/tex]
[tex]3x=-9 \implies \dfrac{3x}{3}=\dfrac{-9}{3} \implies \boxed{x_1 = -3}[/tex]
The zeros (x-intercepts) of this function are: [tex]x_1=3,\ x_2=-3[/tex].
..................................................................................................................................................
Other examples:
brainly.com/question/28105314
brainly.com/question/27638369
X:Y=3:2 and Y:Z=7:4 what is X:Y:Z
Answer:
21:14:8
Step-by-step explanation:
X:Y=3:2
Y:Z=7:4
X:Y=21:14
Y:Z=14:8
X:Y:Z=21:14:8
You estimate that there are 40 marbles in a jar. the actual amount is 34 marbles. find the percent error. round to the nearest tenth of a percent if necessary.
The percentage error of the given estimation is 17.7%.
The percentage error of any estimation is calculated as:
Percentage error = {(|Actual Value - Estimated Value|)/Actual Value}*100%.
In the question,
The estimated value is given to be 40 marbles.
The actual value is given to be 34 marbles.
We are asked to find the percentage error of this estimation.
We know that:
Percentage error = {(|Actual Value - Estimated Value|)/Actual Value}*100%.
Substituting the values, we get:
Percentage error = {(|34 - 40|)/34}*100%,
or, Percentage error = 6/34*100%,
or, Percentage error = 17.6470 % = 17.7% (Rounding to the nearest tenth, that is, up to one decimal place).
Thus, the percentage error of the given estimation is 17.7%.
Learn more about percentage error at
https://brainly.com/question/21529578
#SPJ4
I need help please?
A. {penguin, seagull, crow}
B.{penguin, seagull, crow, bat, mosquito}
C.{seagull, crow}
D.{seagull, crow, bat, mosquito}
The Outcome of event A and B is simply the intersection of both sets written as A ∩ B is; C: {seagull, crow}
How to write sets notation?From the image, we are given the animals namely; Pig, Penguin, Seagull, Tiger, Crow, Bat, Mosquito.
Now, these animals are classified as either a bird or can fly.
Animals that are birds are; Penguin, Seagull, Crow
Animals that can fly are; Seagull, Crow, Bat, Mosquito.
Now, we are told that;
Event A is the animal is a bird. Thus, the set notation that represents this event A is written as;
A = {Penguin, Seagull, Crow}
Event B is that the animal can fly and again the set notation that represents event B is written as;
B = {Seagull, Crow, Bat, Mosquito}
Now, Outcome of event A and B is simply the intersection of both sets. Thus; A ∩ B = {seagull, crow}
Read more about Set Notation at; https://brainly.com/question/24462379
#SPJ1