Solution
We want to solve
[tex]27x^2=9x\text{ using zero product thorem}[/tex]The zero product property states that if a⋅b=0 then either a or b equal zero. This basic property helps us solve equations like (x+2)(x-5)=0.
For the question,
[tex]\begin{gathered} 27x^2=9x \\ \text{Divide both sides by }9 \\ 3x^2=x \\ \text{Subtract x from both sides} \\ 3x^2-x=0 \\ \text{Factorize} \\ x(3x-1)=0 \\ \text{Applying the zero theroem, we have} \\ x=0\text{ or 3x-1=0} \\ x=0\text{ or 3x = 1} \\ x=0\text{ or x = }\frac{1}{3} \end{gathered}[/tex]The answer is x = 0 and x = 1/3
Charlotte has 41 m of fencing to build a three-sided fence around a rectangular plot of land that sits on a riverbank. (The fourth side of the enclosure would be the river.) The area of the land is 204 square meters. List each set of possible dimensions (length and width) of the field.
Answer:
L x W = 8.5 x 24 or 12 x 17
Step-by-step explanation:
x (41 -2x) =204
-2x^2 + 41x -204 = 0 Use Quadratic Formula to find x = 8.5 or 12
(x-8.5)(x-12) = 0
two sides = 8.5 and river/third side = 24
or two sides 12 and river/thirdside = 17
find the equatuon of the line y=_x+_
Answer: y = -2x + 5
Step-by-step explanation:
y = _x + 5
(5,0) (3,4)
(y2 - y1) / (x2 - x1)
(4 - 0 ) / (3 -5)
4 / -2
-2
y = -2x + 5
There are 100 centimeters (cm) in 1 meter (m) Choose the correct answers from the drop-downs lists to complete the sentence. To convert 4 m to centimeters Choose 4 by C
given: 100 cm = 1 meters
We need to convert 4 m to cm
so,
[tex]4m=4\cdot100\operatorname{cm}=400\operatorname{cm}[/tex]Suppose a basketball player has made 359 out of 449 free throws. If the player makes the next 3 free throws, I will pay you $39. Otherwise you pay me $43.
Step 1 of 2 : Find the expected value of the proposition
The expected value of the proposition is $22.6
How to determine the expected value?The given parameters are
Proportions of free throws = 359 out of 449Amount paid for making a throw = $39Amount collected for losing a throw = $43Represent the proportion as a fraction
So, we have
p = 359/449
The expected value is then calculated as
E(x) = p * Amount paid for making a throw - (1 - p) * Amount collected for losing a throw
Where p represents the proportion defined above
So, we have
E(x) = 359/449 * 39 - (1 - 359/449) * 43
Evaluate the difference
E(x) = 359/449 * 39 - 90/449 * 43
So, we have
E(x) = 22.6
Hence, the proposition has an expected value of $22.6
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Answer:
-1.09
The problem requires one to calculate the win payoff and win probability as well as the lose payoff and probability. You would then do a calculation like this:
[(Win Payoff) x (Win Probability)] + [(Lose Payoff) x (Lose Probability)]
First person to solve gets Brainliest!!!!
3. Select all expressions that are equivalent to (2n + 6)(n + 3)a. 2(n? + 6n +9)b. 2n? + 6n + 18c. 2n2 + 12n + 18d. 12n + 18e. 2(n + 3)(n + 3)f. 2(n + 3)?
Select all expressions that are equivalent to (2n + 6)(n + 3)
we have
(2n + 6)(n + 3)
apply distributive property
2n^2+6n+6n+18
2n^2+12n+18
Verify each option
option A
2(n^2 + 6n +9)=2n^2+12n+18 -------> is ok
option B
is not correct
option C
is correct
option D
is not correct
option E
2(n + 3)(n + 3)= (2n + 6)(n + 3) ------> is correct
option F
2(n + 3)^2=2(n^2+6n+9)=2n^2+12n+18 -----> is ok
therefore
answers areA, C, E, FYou wish to program an LED strip containing n LEDs . Each individual LED can be lit in red, green, blue, or white. How many length-n
colour sequences have at least one pair of adjacent LEDs that light up with the same colour?
Hint: Find a recurrence relation. Order matters, (GGR and RGG are different). Also need to consider for the intersection of probabilities.
Using the Fundamental Counting Theorem, the number of length-n sequences that have at least one pair of adjacent LEDs that light up with the same color is:
[tex]N = 4 - 4 \times 3^{n - 1}[/tex]
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n trials, each with [tex]n_1, n_2, \cdots, n_n[/tex] possible results, each thing independent of the other, the number of results is given as follows:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
In the context of this problem, there are n LEDs, each with 4 possible colors, hence he total number of sequences is:
[tex]T = 4^n[/tex]
For sequences with no repeating LEDs, we have that:
The first LED can have 4 outcomes.Any of the following LEDs can have 3 outcomes. (except the color of the previous one).Hence the number is:
[tex]T_n = 4 \times 3^{n-1}[/tex]
(n - 1) as the first LED is not included on those with 3 possibilities.
Having at least one repeating and no repeating are complementary events, hence the number of sequences is:
[tex]N = 4 - 4 \times 3^{n - 1}[/tex]
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The current in a resistor is inversely proportional to the resistance. By what factor will the current change if the resistance increases 10%.
The factor by which the current changes if the resistance increases 10% is; 90.9% reduction
How to Interpret Ohms' Law?
Ohm's law states that the electrical current (I) flowing in a circuit is directly proportional to the voltage (V) and inversely proportional to the resistance(R). Therefore, if the voltage is increased, the current will increase provided the resistance of the circuit does not change. Thus;
I = V/R
Now, we are told that the resistance increases by 10%.
Thus, New value of resistance = 1.1R
Thus, new current/old current = 1/1.1 = 0.909 = 90.9%
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Convert. 260 milliliters to centiliters.
Answer:
26 centilitres.
Explanation:
First, we start by recalling the standard conversion between millilitres and centilitres.
[tex]10\text{ milliliter = 1 centileter}[/tex]Let 260 milliliters = x centiliters
We express it as a ratio:
[tex]\frac{10\text{ }milliliters}{1\text{ centiliter}}=\frac{260milliliters}{x\text{ centiliters}}[/tex]Cross multiply to solve for x:
[tex]\begin{gathered} 10x=260\times1 \\ x=\frac{260}{10} \\ x=26\text{ centiliters} \end{gathered}[/tex]Therefore, 260 millilitres is 26 centiliters.
Circumference of 2 circles =220m and 286m find area!
Helppp!!!!
Every line through the center of a circle forms a line of reflection symmetry, and every angle has rotational symmetry around the center. The areas are 123.83 [tex]m^{2}[/tex] and[tex]209.07m^{2}[/tex]
What is a circle?The form having the greatest surface area for a given perimeter is a circle.
Every line through the center of a circle forms a line of reflection symmetry, and every angle has rotational symmetry around the center. The orthogonal group O is the symmetry group of it (2,R). Circle group T is the collection of rotations alone.
Every circle is comparable.The radius and circumference of a circle are proportionate.The ratio between the enclosed area and the square of its radius is one.2 and, respectively, serve as the proportionality constants.The unit circle is the circle with radius 1 and an origin center.It becomes the Riemannian circle when viewed as a large unit sphere circle.A distinct circle can be found through any three locations that are not all on the same line. It is feasible to express explicitly equations for the coordinates of the circle's center and radius in terms of the coordinates of the three specified points in Cartesian coordinates.
Circumference= [tex]2\pi r[/tex]= 220 and 286
[tex]2\pi r[/tex]= 220
2*3.14*r=220
r= 220/35.03= 6.28
area=[tex]\pi r^{2}[/tex]
= 3.14*6.28*6.28
= 123.83[tex]m^{2}[/tex]
[tex]2\pi r[/tex]= 286
2*3.14*r= 286
r= 286/35.03 = 8.16
area= [tex]\pi r^{2}[/tex]
= 209.07[tex]m^{2}[/tex]
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A group fitness gym classifies its fitness class attendees by class type and member status. The marketing team has gathered data from a random month, in which therewere 2153 class attendees. The data is summarized in the table below.Class Type and Member Status of ClassAttendeesClass TypeBarreBoot CampBoxingSpinningYogaMember207230291233239Non-Member196185180176216What is the probability that an attendee does not attend a barre class? Enter a fraction or round your answer to 4 decimal places, if necessary.
The total number associated to barre class is 207 + 196 = 403
Therefore, the probability that a attendee does not attend a barre class is given by 403/2153 = 0.1872
a line perpendicular to y = 2x +4 through (4.2) slope of the new line equationequation of the new line
y= 2x+4
Slope-intercept form
y=mx+b
Where:
m= slope
b= y-intercept
y=2x+4
Slope = m= 2
Perpendicular lines have negative reciprocal slopes.
So, the slope of the new line = -1/2
New equation:
y= -1/2x+b
Replace x,y by the point (4,2) and solve for b:
2 = -1/2(4)+b
2= -2 + b
2+2 = b
4 = b
New line equation:
y= -1/2x+4
the sum of the interior angles of an octagon is 1080 degrees. each angle is six degrees larger than the angle just smaller than it. what is the measure of the fourth angle?
The measure of the fourth angle that is x and the value is 133°
What is an octagon?A regular octagon will have all its sides equal in length. Each interior angle of a regular octagon is equal to 135°. Therefore, the measure of exterior angle becomes 180° – 135° = 45°. The sum of the interior angles of the octagon is 135 × 8 = 1080°.
Let the 8 interior angles of the octagon be:
x-12, x-8, x-4, x, x+4, x+8, x+12, x+16.
Their sum = 8x+16 = 1080, or
this implies 8x = 1080–16 = 1064
thus on further solving we get x = 133
Hence the sixth angle = x+8 =141 degrees.
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The side lengths in yards of a triangle and a square are shown in the diagram. (4x - 2) yd 2x yd 2(x + 7) yd 2.5x yd The perimeter of the triangle is equal to the perimeter of the square. What is the value of x?
(4x -2) yd, 2x yd, 2(x + 7) yd, 2.5x yd. The triangle's perimeter is the same as the square's perimeter. The value of x=6
Given that,
The graphic displays the yards-long sides of a triangle and a square. The triangle's perimeter is the same as the square's perimeter.
We have to find the value of x in the given side.
In the picture we can see the triangle and square.
The perimeter of the triangle is sum of the three sides of the triangle.
The perimeter of the square is 4 times the side of the square.
4x-2+2x+2(x+7)=4×2.5x
4x-2+2x+2x+14=10x
8x+12=10x
10x-8x=12
2x=12
x=12/2
x=6
Therefore, the value of x=6
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Montraie is going to invest in an account paying an interest rate of 4.6% compounded annually. How much would Montraie need to invest, to the nearest ten dollars, for the value of the account to reach $1,610 in 15 years?
If Montraie is going to invest in an account paying an interest rate of 4.6% compounded annually, then she has to invest $820.06 for the value of the account to reach $1610 in 15 years
The interest rate = 4.6%
The final amount = $1610
The time period = 15 years
The compound interest
A = [tex]P(1+\frac{r}{100})^{t}[/tex]
Where A is the final amount
P is the principal amount
r = interest rate
t is the time period
Substitute the values in the equation
1610 = [tex]P(1+\frac{4.6}{100})^{15}[/tex]
1610 = P×1.96
P = 1610/1.96
P = $820.06
Hence, if Montraie is going to invest in an account paying an interest rate of 4.6% compounded annually, then she has to invest $820.06 for the value of the account to reach $1610 in 15 years
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In a recent awards ceremony, the age of the winner for best actor was 38 and the age of the winner for best actress was 51. For all best actors, the mean age is 46.8 years and the standard deviation is 5.7 years. For all best actresses, the mean age is 31.9 years and the standard deviation is 10.8 years. (All ages are determined at the time of the awards ceremony.) Relative to their genders, who had the more extreme age when winning the award, the actor or the actress? Explain.
Given
the age of the winner for best actor was 38 and the age of the winner for best actress was 51.
For all best actors, the mean age is 46.8 years and the standard deviation is 5.7 years.
For all best actresses, the mean age is 31.9 years and the standard deviation is 10.8 years.
Find
who had the more extreme age when winning the award, the actor or the actress
Explanation
the Z- score is given by
[tex]Z=\frac{X-\mu}{\sigma}[/tex]Best Actor
X = 38
mean = 46.8 years
standard deviation = 5.7 years.
so ,
[tex]\begin{gathered} Z=\frac{38-46.8}{5.7} \\ \\ Z=-1.54385964912\approx-1.54 \end{gathered}[/tex]Best Actress
X = 51
mean = 31.9 years
standard deviation = 10.8 years.
so ,
[tex]\begin{gathered} Z=\frac{51-31.9}{10.8} \\ \\ Z=1.76851851852\approx1.77 \end{gathered}[/tex]the best actress's age is farther from the mean so he has the more extreme age when the winning the award.
Final Answer
Hence , the z- score for best actor is -1.54 and for best actress = 1.77
Actress has more extreme age
Below is the graph of y=3x".Translate it to make it the graph of y=3(x-4)3 +1.
There are two shiftments, 1 to the side along the x-axis and 1 vertical along the y-axis
Horizontal shifts:
[tex]y=(x\pm a)^n[/tex]Vertical shifts
[tex]y=x^n\pm a[/tex]Since the x is substracted 4 units, it means that the graph is translated 4 units to the right.
Since the function is completely added 1 unit its means that all the graph is shifted 1 unit up.
find the final amount of money in an account if $3,100 is deposited at 2.5% interest compounded quarterly and the money is left for 5 years
Given -
Money deposited in an account = $3,100
Interest rate = 2.5% compounded quarterly
Time = 5 years
To Find -
The final amount of money =?
Step-by-Step Explanation -
As we know there are 4 quarters in a year.
So,
In five years, there are 20 quarters.
On applying the formula:
Final Amount =
[tex]\begin{gathered} =\text{ }P\times(1+i)^n \\ \\ =\text{ 3100 }\times(1+\text{ 0.025/4})^{20} \\ \\ =\text{ 3100}\times(1\text{ + 0.00625})^{20} \\ \\ =\text{ 3100}\times(1.00625)^{20} \\ \\ =\text{ 3100}\times1.1327 \\ \\ =\text{ 3511.3939} \end{gathered}[/tex]Final Answer -
The final amount of money = $3511.4
Determine if it has a minimum of maximum and what that value is whilst also Identifying the domain and range
Hello!
First, let's rewrite the expression here:
[tex]f\mleft(x\mright)=-2x^2+12x-15[/tex]We will have to find the coefficients a, b and c:
• a ,= -2;
,• b ,= 12;
,• c ,= -15;
As we can see, coefficient a is negative. It means that the parabola will face downwards and have a maximum value.
We can obtain this point by using the two formulas below to calculate the coordinates (x, y) of this point, look:
[tex]\begin{gathered} X_V=\text{ }-\frac{b}{2\cdot a} \\ \\ Y_V=-\frac{b^2-4\cdot a\cdot c}{4\cdot a} \end{gathered}[/tex]As we know the coefficients, let's replace the values in the formulas:
Xv:
[tex]\begin{gathered} X_V=-\frac{b}{2\cdot a} \\ \\ X_V=-\frac{12}{2\cdot(-2)}=-\frac{12}{-4}=-(-3)=+3 \\ \\ X_V=3 \end{gathered}[/tex]Now let's find Yv:
[tex]\begin{gathered} Y_V=-\frac{b^2-4\cdot a\cdot c}{4\cdot a} \\ \\ Y_V=-\frac{12^2-4\cdot(-2)\cdot(-15)}{4\cdot(-2)}=-\frac{144-120}{-8}=-\frac{24}{-8}=-(-3)=+3 \\ \\ Y_V=3 \end{gathered}[/tex]Doing this, we obtained the coordinate of the maximum point (x, y) = (3, 3).
As it doesn't have any restrictions, the domain will be: [-∞, +∞].
[tex]-\infty\: We have one restriction in the range, do you remember which?The maximum value will be when y = 3, so the range is [-∞, 3].
Look at the graph of this function below:
Simplify 4 - 2y +(-8y) +7.3.4-2y+ ( 8y) +7.3=Q(Simplify your answer. Use integers or decimals for any numbers in theWhat is 4-2y+(-8y)+7.3
In order to simplify an equation we want to add all the terms with the same unkowns.
In the equation
4 - 2y + (-8y) + 7.3
we can see that there are terms with y and numbers alone.
We combine like terms:
Terms with y: -2y,
Jenna bought a coat on sale for $120 which was 2/3 of the original price what was the original price of the coat
Jenna bought a coat on sale for $120
The price of the coat is the 2/3of the original price
Let the original price is $x
So, the equation will be :
2/3 of x =120
[tex]\begin{gathered} \frac{2}{3}\text{ of x=120} \\ \frac{2}{3}\times x=120 \\ x=120\times\frac{3}{2} \\ x=60\times3 \\ x=180\text{ dollars} \end{gathered}[/tex]So, The original price of the coat is $180
I only need the answer
THANK YOU!!
Formula for the trigonometry is y = b sin ( πx/2 - π/2) + 4
y = A sin( ωx + δ) + b
period: t = 4
ω = 2π/t = 2π/4 = π/2
A = 10 -(-2)/ 2
= 6
b = (10-2)/2
= 4
y = b sin (πx/2 + δ) + 4
x = 0, y = bsinδ + 4 = -2
sinδ = -1 => δ = -π/2
y = b sin( πx/2 - π/2) + 4
Therefore the formula for the trigonometry function is y = b sin(πx/2 - π/2) + 4.
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For each relation, decide whether or not it is a function.
Top left: Yes, each input corresponds to only one output.
Top right: Yes, each input corresponds to only one output.
Bottom left: Yes, each input corresponds to only one output.
Bottom right: No, the input of -1 corresponds to three different outputs.
Malcolm's Bakery Shop sells gourment cupcakes. The shop's cost for making 3 cupcakes is $6.75, and the cost of making 5 cupcakes is $9.75 . What is the shop's cost per minute?
A. $1.50
B. $1.95
C. $2.25
D. $3.00
The average cost per minute which the shop runs is $1.50
Shop's Cost per MinuteTo find the shop's cost per minute, we can write down equations and proceed to solve.
In the given question, 3 cupcakes cost $6.75 and 5 cupcakes cost $9.75.
But we were not given the average cost per cupcake.
To do that, let's write an equation for this.
[tex]y = mx + c[/tex]
Let's find the slope to this equation which determines the average cost per minute.
[tex]m = \frac{y_2-y_1}{x_2-x_1} \\m = \frac{9.75 - 6.75}{5 - 3} \\m = 1.50[/tex]
The shop's cost per minute was calculated to be $1.50.
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3. Which of the following quadratic functions has a maximum point?
The general form of a quadratic equation is given by the expression:
[tex]ax^2+bx+c=0[/tex]A quadratic equation having a maximum value or point is one that has its value of a to be lesser than zero
(a < 0). Such a graph opens downwards
Therefore, any quadratic equation that has the a-value to be lesser than zero has a maximum point
Mathematically expressed as:
[tex]\begin{gathered} y=-x^2 \\ \Rightarrow a=-1 \end{gathered}[/tex]question is in image
The expresion for the correlation coefficient is :
[tex]r=\frac{n\Sigma xy-\Sigma x\Sigma y}{\sqrt[]{\mleft\lbrace n\Sigma x^2-(\Sigma x)^2\}\mleft\lbrace n\Sigma y^2-(\Sigma y)\mright?^2\mright\rbrace}}[/tex]summation of x = 5 + 7 + 10 + 15 + 19
Summation of x = 56
Summation of y = 19 + 17 + 16 + 12 + 7
Summation of y = 71
Summation of prodcut xy
[tex]\begin{gathered} \Sigma xy=5\times19+7\times17+10\times16+15\times12+19\times7 \\ \Sigma xy=687 \end{gathered}[/tex]Summation of x^2 = 25 + 49 + 100 + 225 + 361
Summation of x^2 = 760
Summation of y^2 = 361 + 289 + 256 + 144 + 49
Summation of y^2 = 1099
Substitute tha value in the expression of correlation coefficient
[tex]\begin{gathered} r=\frac{n\Sigma xy-\Sigma x\Sigma y}{\sqrt[]{\mleft\lbrace n\Sigma x^2-(\Sigma x)^2\}\mleft\lbrace n\Sigma y^2-(\Sigma y)\mright?^2\mright\rbrace}} \\ r=\frac{5(687)-56\times71}{\sqrt[]{\mleft\lbrace5(760)-(56)^2\}\mleft\lbrace5(1099\mright)-(71\mright)^2}} \\ r=\frac{541}{\sqrt[]{\begin{cases}3800-3136\}\mleft\lbrace5495-5042\mright\rbrace\end{cases}}} \\ r=\frac{541}{\sqrt[]{300792}} \\ r=\frac{541}{548.44} \\ r=0.985 \end{gathered}[/tex]Answer: A) Correlation coefficient is 0.985
Tonya spends 55% of her savings on a new dress. If she saved $120, how much was the dress? mathematical representation.
a50/23 = b
b.0.55 x 120 = d
c.190x = 45; change the decimal to a %
d.x/45 = 190; change the decimal to a %
e.55d = 120
f.23 x 50 = b
g.23/50 = b
h.2.50/45 = p
i.2.50p = 45
j..23 x 50 = b
k..45 x 190 = x
l..55d = 120
The coat of the dress based on the percentage is $66.
How to calculate the value?From the information, it was stated that Tonya spends 55% of her savings on a new dress and that she saved $120.
Let the cost of the dress be represented as x
Therefore, the appropriate information given I'll be expressed as:
= 55% × 120 = x
0.55 × 120 = x
Multiply
x = 66
The amount spent is $66.
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I need help with this practice problem from my ACT prep guideIt is trigonometry It asks to graph the function yourself, on paper, or on desmos
If we start with the parent function f(x) = cot(x), the transformation needed to go from this function to cot(x + π/6) is expressed as:
[tex]f(x)\to f(x+\frac{\pi}{6})[/tex]That is, we need to make a shift of π/6 units to the left, beginning with the cot(x) graph. The graph of cot(x + π/6) is:
At the bakery cupcakes are displayed in 12 rows with 6 cupcakes per row. If a
customer buys 24 cupcakes, how many cupcakes are left?
The width of a room is 7 feet, and the area of the room is 77 square feet. Find the room's length.
...
Answer:
11
Step-by-step explanation:
A = lw
l = A/w
l = 77/7
l = 11
Hope that helps