The probability that among these 11 people, the number passing the test is between 2 and 4 inclusive is 0.0665
What is Probability?
Probability gives us the information about how likely an event is going to occur
Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.
Probability of any event is greater than or equal to zero and less than or equal to 1.
Probability of sure event is 1 and probability of unsure event is 0.
Now
Binomial distribution of probability will be used
Here, n = 11, p = 0.63,
P(X = x) = [tex]{n\choose x} p^x(1-p)^{n-x}[/tex]
P(X= 2) = [tex]{11\choose 2} 0.63^2(1-0.63)^{11-2}[/tex]
= 0.0028
P(X = 3) = [tex]{11\choose 3} 0.63^3(1-0.63)^{11 - 3}\\[/tex]
= 0.0144
P(X = 4) = [tex]{11\choose 4} 0.63^4(1-0.63)^{11 - 4}\\\\[/tex]
= 0.0493
The probability that among these 11 people, the number passing the test is between 2 and 4 inclusive = 0.0028 + 0.0144 + 0.0493
= 0.0665
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Graph the following inequalitiesy ≥ -x/4 + 5
Solution
The graph of the inequality is shown below
Which of the following rational expressions has the domain restrictions X = -6 and x = 1?
The domain of the function is possible values of independant varaible such that function is defined or have real values.
So the expression
[tex]\frac{(x+2)(x-3)}{(x-1)(x+6)}[/tex]is not defined for x = -6 and for x = 1, as expression becomes undefined for this values of x (Denominator becomes 0).
So answer is,
[tex]\frac{(x+2)(x-3)}{(x-1)(x+6)}[/tex]Option B is correct.
solve the system by substitution type your stepsx=2y-53x-y=5
Answer:
The solution to the system of equations is
x = 3
y = 4
Explanation:
Given the pair of equations:
[tex]\begin{gathered} x=2y-5\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\text{.}(1) \\ 3x-y=5\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\text{.}(2) \end{gathered}[/tex]To solve these simultaneously, use the expression for x in equation (1) in equation (2)
[tex]\begin{gathered} 3(2y-5)-y=5 \\ 6y-15-y=5 \\ 6y-y-15=5 \\ 5y-15=5 \\ \\ \text{Add 15 to both sides} \\ 5y-15+15=5+15 \\ 5y=20 \\ \\ \text{Divide both sides by 5} \\ \frac{5y}{5}=\frac{20}{5} \\ \\ y=4 \end{gathered}[/tex]Using y = 4 in equation (1)
[tex]\begin{gathered} x=2(4)-5 \\ =8-5 \\ =3 \end{gathered}[/tex]Therefore, x = 3, and y = 4
Given the following data, find the diameter that represents the 69th percentile.AnswerHow to enter your answer (opens in new window)Diameters of Golf Balls1.531.36 1.69 1.68 1.701.601.601.361.34 1.531.32 1.401.39 1.391.44
Given that there is a Table given of diameters
15. Graph the rational function ya*-*Both branches of the rational function pass through which quadrant?Quadrant 2Quadrant 3Quadrant 1Quadrant 4
SOLUTION:
CONCLUSION:
Both branches of the rational function pass through Quadrant 1.
F (x)=x^2+4 what is f(-4)
ANSWER
f(-4) = 20
EXPLANATION
To find f(-4) we just have to replace x by -4 in function f(x):
[tex]f(-4)=(-4)^2+4[/tex]First solve the exponents. Remember that if the exponent is even and the result is always positive, either the base is positive or negative:
[tex]f(-4)=16+4=20[/tex]SOLVE PLEASE -2x^2+18x+____
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
- 2x² + 18x + _________
Step 02:
(a + b) = a² + 2ab + b²
a² = -2x²
[tex]a\text{ = }\sqrt[]{-2\cdot x^{2}}\text{ = x }\sqrt[]{-2}[/tex][tex]a\text{ = }\sqrt[]{2}i[/tex]2ab = 18x
[tex]2(x\sqrt[\text{ }]{-2)}\cdot\text{ b = 18 x}[/tex][tex]b\text{ = }\frac{18x}{2x\sqrt[]{-2}}=\frac{9}{\sqrt[]{-2}}=\frac{9}{\sqrt[]{2\text{ }}i}[/tex]Two ways to express the solution:
[tex]\begin{gathered} -2x^{2\text{ }}+\text{ 18x + 9/}\sqrt[]{-2} \\ -2x^2+18x\text{ + 9 / }\sqrt[]{2}i \end{gathered}[/tex]Last weekend, 5% of the tickets sold at Seaworldwere discount tickets. If Seaworld sold 60 tickets inall, howmany discount tickets did it sell? Use thepercent proportion.
Let:
N = Total tickets
d = discount tickets
r = percent of discount tickets sold
so:
[tex]\begin{gathered} d=N\cdot r \\ where\colon \\ N=60 \\ r=0.05 \\ so\colon \\ d=60\cdot0.05 \\ d=3 \end{gathered}[/tex]3 discount tickets were sold
If cos(0) = 24/25, and 0 is in Quadrant I, then what is cos(0/2)? Simplify your answer completely, rationalize the denominator, and enter it in fractional form.
The given information is:
[tex]\begin{gathered} \cos (\theta)=\frac{24}{25} \\ \theta\text{ is in quadrant I} \end{gathered}[/tex]cos (theta/2) is given by:
[tex]\cos (\frac{\theta}{2})=\pm\sqrt[]{\frac{1+\cos\theta}{2}}[/tex]In Quadrant I, cos (theta) is positive, then the answer is positive. By replacing the known values:
[tex]\begin{gathered} \cos (\frac{\theta}{2})=\sqrt[]{\frac{1+\frac{24}{25}}{2}} \\ \cos (\frac{\theta}{2})=\sqrt[]{\frac{\frac{25+24}{25}}{2}} \\ \cos (\frac{\theta}{2})=\sqrt[]{\frac{\frac{49}{25}}{2}} \\ \cos (\frac{\theta}{2})=\sqrt[]{\frac{49}{25\times2}} \\ \cos (\frac{\theta}{2})=\sqrt[]{\frac{49}{50}} \\ \cos (\frac{\theta}{2})=\frac{\sqrt[]{49}}{\sqrt[]{50}} \\ \cos (\frac{\theta}{2})=\frac{7}{\sqrt[]{50}} \\ \cos (\frac{\theta}{2})=\frac{7}{\sqrt[]{50}}\cdot\frac{\sqrt[]{50}}{\sqrt[]{50}} \\ \cos (\frac{\theta}{2})=\frac{7\sqrt[]{50}}{50} \\ \cos (\frac{\theta}{2})=\frac{7\sqrt[]{25\times2}}{50} \\ \cos (\frac{\theta}{2})=\frac{7\cdot\sqrt[]{25}\cdot\sqrt[]{2}}{50} \\ \cos (\frac{\theta}{2})=\frac{7\cdot5\cdot\sqrt[]{2}}{50} \\ \text{Simplify 5/50} \\ \cos (\frac{\theta}{2})=\frac{7\sqrt[]{2}}{10} \end{gathered}[/tex]For each ordered pair, determine whether it is a solution to the sytem of equations.
Given
We have the system of equations:
[tex]\begin{gathered} 3x\text{ - 2y = -4} \\ 2x\text{ + 5y = -9} \end{gathered}[/tex]The ordered pair that would be a solution to the given system of equations must satisfy both equations. There can only be one ordered pair and this can be obtained by solving the system of equations simultaneously
Using a graphing tool, the plot of the lines is shown below:
The point where the lines intercept is the solution to the system of equations.
Hence the ordered pair that is a solution is (-2, -1)
Answer:
(4,8) - No
(8, -5) - No
(0, 3) - No
(-2, -1) - Yes
What are all the ordered pairs that are solutions to the inequality 2x-3y>=12
To answer this question, we need to solve this inequality for y as follows:
[tex]2x-3y\ge12[/tex]Then, we have:
[tex]-3y\ge12-2x\Rightarrow\frac{-3y}{-3}\leq\frac{12}{-3}-\frac{2x}{-3}\Rightarrow y\leq-4+\frac{2x}{3}[/tex]As we can see the direction of the inequality changed because we multiplied it by a negative number.
Then, if we can see the inequality, we find that the values that make this inequality true
are infinite values (the values of y are in function of the values of x).
Then, since we have the values given in the options, we need to check which of these values make the inequality true or we can graph a line for this inequality.
We have that the line is given by:
y = 2x/3 - 4
The x-intercept for this line is:
[tex]undefined[/tex]How many people were using program 2 but not program 3?
Let Program 1, Program 2, and Program 3 be represented by P1, P2, and P3.
Given:
n(P1 n P2) = 6
n(P2 n P3) =8
n(P1 n P3) = 5
n(P1 n P2 n P3) = 2
n(P1 U P2' U P3') =18
n(P2) = 22
n(P3 U P1 U P2') = 16
n(P1 U P2 U P3)' = 17
Representing the information on a Venn diagram:
The number of people that were using Program 2 but not Program 3:
[tex]\begin{gathered} n(P_2UP_3^{\prime})=n(P_2)-n(P_2nP_3)\text{ } \\ =\text{ 22 - 8} \\ =\text{ 16} \end{gathered}[/tex]Number of people surveyed
The number of people surveyed is the sum of the individual subsets:
[tex]\begin{gathered} =\text{ 18 + 10 + 13 + 4 + 6 + 3 + }2\text{ + 17} \\ =\text{ 73} \end{gathered}[/tex]This is so hard I don’t understand this pls help
From the given question
There are given that the matrix.
Now,
To find the inverse of any matrix, first find their determinant.
Then,
According to the properties of the matrix:
If the determinant of any matrix is zero, then their inverse has undefined.
So,
From the determinant of the given matrix:
[tex]\begin{gathered} \begin{bmatrix}{4} & {8} & {} \\ {7} & {14} & \\ {} & {} & {}\end{bmatrix}=(14\times4)-(8\times7) \\ =56-56 \\ =0 \end{gathered}[/tex]The determinant of the given matrix is zero
So, their inverse has not been defined.
Hence, the correct option is A.
9. Find the volume of the triangular pyramid. (2pts)-10 mI9 m16 m
Answer:
240 m³
Explanation:
The volume of a pyramid is equal to:
[tex]V=\frac{1}{3}\times B\times H[/tex]Where B is the area of the base and H is the height of the pyramid.
Then, the base of the pyramid is a triangle, so the area of a triangle is equal to:
[tex]B=\frac{b\times h}{2}[/tex]Where b is the base of the triangle and h is the height of the triangle. So, replacing b by 16 m and h by 9 m, we get:
[tex]B=\frac{16\times9}{2}=\frac{144}{2}=72m^2[/tex]Finally, replacing B by 72 m² and H by 10 m, we get that the volume of the pyramid is equal to:
[tex]V=\frac{1}{3}\times72\times10=\frac{1}{3}\times720=240m^3[/tex]Therefore, the volume is 240 m³
8Suppose Z follows the standard normal distribution. Use the calculator provided, or this table, to determine the value of c so that the following is true.p=(-c ≤ Z ≤ c ) =0.9127Carry your intermediate computations to at least four decimal places. Round your answer to two decimal places.
The value of c such that [tex]P(-c\leq Z\leq c)=0.9127[/tex] is true is 0.0873 where Z follows the standard normal distribution.
It is given to us that -
[tex]P(-c\leq Z\leq c)=0.9127[/tex] is true
It is also given that Z follows the standard normal distribution.
We have to find out the value of c.
Since Z follows the standard normal distribution, so we can say that
Z ∼ N(0,1)
To find out c,
[tex]P(-c\leq Z\leq c)=0.9127\\= > P(Z\leq c)-P(Z\leq -c)=0.9127\\[/tex]
Since there is a symmetric z-distribution, the above equation can be represented as -
[tex][1-P(Z\leq -c)]-P(Z\leq -c) = 0.9127\\= > 1-P(Z\leq -c) - P(Z\leq -c) = 0.9127\\= > 1-2P(Z\leq -c)=0.9127\\= > 2P(Z\leq -c)=0.0873\\= > P(Z\leq -c)=0.04365[/tex]
=> -c ≈ 0.0873 (Using online calculator)
Therefore, the value of c such that [tex]P(-c\leq Z\leq c)=0.9127[/tex] is true is 0.0873 where Z follows the standard normal distribution.
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Answer:
The value of c such that is true is 0.0873 where Z follows the standard normal distribution.
Step-by-step explanation:
a bag contains 30 marbles. 8 are pink, 11 are blue, 4 are yellow and 7 are purple. Calculate the probability of randomly selecting a marble that is not blue .
In order to find the probability of a marble not being blue, we need to find how many marbles are not blue.
To do so, we just need to sum the number of pink, yellow and purple marbles:
[tex]8+4+7=19[/tex]Now, to find the probability, we just need to divide the number of non-blue marbles by the total number of marbles.
[tex]\frac{19}{30}=0.6333=63.33\text{\%}[/tex]Convert the radical to exponential form. Assume variables represent positive real numbers.
Exponential Form of Radicals
A radical can be expressed in exponential form by using the equivalence:
[tex]\sqrt[m]{x^n}=x^{\frac{n}{m}}[/tex]We are given the expression:
[tex]\sqrt[4]{16a^4b^3}[/tex]It can be separated into several radicals:
[tex]\sqrt[4]{16a^4b^3}=\sqrt[4]{16}\cdot\sqrt[4]{a^4}\cdot\sqrt[4]{b^3}[/tex]Now we apply the equivalence on each individual radical:
[tex]\begin{gathered} \sqrt[4]{16a^4b^3}=\sqrt[4]{2^4}\cdot\sqrt[4]{a^4}\cdot\sqrt[4]{b^3} \\ \sqrt[4]{16a^4b^3}=2^{\frac{4}{4}}\cdot a^{\frac{4}{4}}\cdot b^{\frac{3}{4}} \end{gathered}[/tex]Simplifying:
[tex]\sqrt[4]{16a^4b^3}=2ab^{\frac{3}{4}}[/tex]a square pyramid has a base height edge length of 3m and a slant height of 6m. find the lateral area and surface area of the pyramid
hello
given that the pyramid has the shape of a triangle, we can easily find the height of the pyramid using pythagoran's theorem
from triangle b, let's use the formula and solve for y
[tex]\begin{gathered} x^2=h^2+z^2 \\ 6^2=h^2+1.5^2 \\ 36=h^2+2.25 \\ \text{collect like terms} \\ h^2=36-2.25 \\ h^2=33.75 \\ \text{solve for h} \\ h=\sqrt[]{33.75} \\ h=5.809\approx5.81m \end{gathered}[/tex]having known the value of the heigh of the pyramid, we can now proceed to solve for the lateral area and surface area
for the lateral area, the formula is given as
[tex]\begin{gathered} A_l=l\sqrt[]{l^2+4h} \\ l=\text{edge length} \\ h=\text{height of pyramid} \end{gathered}[/tex][tex]\begin{gathered} A_l=l\sqrt[]{l^2+4h} \\ l=3m \\ h=5.81m \\ A_l=3\sqrt[]{3^2+4\times5.81_{}} \\ A_l=17.03m^2 \end{gathered}[/tex]the lateral area of the figure is 17.03 squared meter.
let's solve for the surface area
the formula for the surface area of a square pyramid is given as
[tex]\begin{gathered} A=l^2+2l\sqrt[]{\frac{l^2}{4}+4h^2} \\ l=3m \\ h=5.81 \\ A=3^2+2\times3\sqrt[]{\frac{3^2}{4}+4\times5.81^2} \\ A=9+6\sqrt[]{\frac{9}{4}+135.0244} \\ A=79.298\approx79.3m \end{gathered}[/tex](a) Find an angle between 0 and 2pi that is coterminal with 10pi/3.(b) Find an angle between 0° and 360° that is coterminal with -300°.Give exact values for your answers.(a) __ radians(b) __ °
To find a coterminal angle between 0 and 2pi, you can subtract 2pi from the given angle, like this
[tex]\frac{10\pi}{3}-2\pi\text{ }[/tex]To do the subtraction, you can convert 2pi into a fraction, like this
[tex]\frac{2\pi\cdot3}{3}=\frac{6\pi}{3}[/tex]So, you have
[tex]\frac{10\pi}{3}-2\pi=\frac{10\pi}{3}-\frac{6\pi}{3}=\frac{4\pi}{3}[/tex]Therefore, 4pi/3 is the angle between 0 and 2pi that y is coterminal with 10pi/3.
For point (b), you can add 360° at the angle given, like this
[tex]360+(-300)=360-300=60[/tex]Therefore, an angle between 0° and 360° that is coterminal with -300° is 60°.
Simplify. Final answer should be in standard form NUMBER 18
4(2 - 3w)(w^2 - 2w + 10) =
(8 - 12w)(w^2 - 2w + 10) =
8w^2 - 16w + 80 - 12w^3 + 24w^2 - 120w =
- 12w^3 + 32w^2 - 123w + 80
NEED ANSWER ASAP Solve this system of equations:3x - 2y = - 8y= 3/2x - 2I NEED ALL THE STEPS
Let's solve it by replacing in the first equation.
3x-2y=-8
y=3/2x-2
So,
3x-2(3/2x -2)=-8
3x-3x+4=-8
is it option one or two I don't need to work
From the options, the function has the next form
[tex]y=a\cdot b^x[/tex]where a and b are two constants.
The function pass through the point (0, 2), then:
[tex]\begin{gathered} 2=a\cdot b^0 \\ 2=a\cdot1 \\ 2=a \end{gathered}[/tex]The function pass through the point (1, 10), then:
[tex]\begin{gathered} 10=2\cdot b^1 \\ \frac{10}{2}=b \\ 5=b \end{gathered}[/tex]Therefore, the function is:
[tex]y=2\cdot5^x^{}[/tex](06.04)The line of best fit for a scatter plot is shown:A scatter plot and line of best fit are shown. Data points are located at 1 and 4, 2 and 6, 2 and 3, 4 and 3, 6 and 1, 4 and 5, 7 and 2, 0 and 6. A line of best fit passes through the y-axis at 6 and through the point 4 and 3.What is the equation of this line of best fit in slope-intercept form? (4 points)y = −6x + three fourthsy = 6x + three fourthsy = negative three fourthsx + 6y = three fourthsx + 6
Answer:
[tex]y\text{ = -}\frac{3}{4}x\text{ + 6}[/tex]Explanation:
Given the y-intercept and a point, we want to get the equation of the line of best fit
We have the slope-intercept form as:
[tex]y\text{ = mx + b}[/tex]where m is the slope and b is the y-intercept:
[tex]y\text{ = mx + 6}[/tex]Now, to get m, we substitute the point (4,3)
We substitute 3 for y and 4 for x
We have that as:
[tex]\begin{gathered} 3\text{ = 4m + 6} \\ 3-6\text{ = 4m} \\ 4m\text{ = -3} \\ m\text{ = -}\frac{3}{4} \end{gathered}[/tex]Thus, the equation of the line of best fit is:
[tex]y\text{ = -}\frac{3}{4}x\text{ + 6}[/tex]How does g(t) = 1/2t change over the interval t = 0 to t = 1?
we have the equation
[tex]g(t)=\frac{1}{3^t}[/tex]Find out the rate of change over the interval [0,1]
Remember that
the formula to calculate the rate of change is equal to
[tex]\frac{g(b)-g(a)}{b-a}[/tex]In this problem
a=0
b=1
g(a)=g(0)=1
g(b)=g(1)=1/3
therefore
the function decreases by a factor of 3PLEASE HELP 15 POINTS!! I'M GIVING BRAINLIEST
The value of sinα in the right angle triangle is [tex]\frac{16\sqrt{281} }{78961}[/tex]
What is a right-angle triangle?A right-angled triangle is a triangle, that has one of its interior angles equal to 90 degrees or any one angle is a right angle. Therefore, this triangle is also called the right triangle or 90-degree triangle. The right triangle plays an important role in trigonometry.
sin α = opposite/hypotenuse
opposite = 16, hypotenuse [tex]\sqrt{281}[/tex]
sin α = [tex]\frac{16}{\sqrt{281} }[/tex]
By rationalizing, the denominator which means multiply the fraction by [tex]\frac{\sqrt{281} }{\sqrt{281} }[/tex]
[tex]\frac{16}{\sqrt{281} }[/tex] x [tex]\frac{\sqrt{281} }{\sqrt{281} }[/tex] = [tex]\frac{16\sqrt{281} }{78961}[/tex]
sin [tex]\alpha[/tex] = [tex]\frac{16\sqrt{281} }{78961}[/tex]
In conclusion, the value of sin[tex]\alpha[/tex] = [tex]\frac{16\sqrt{281} }{78961}[/tex]
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Graph AABC with A(4, 7), B(0,0), and C(8, 1).a. Which sides of AABC are congruent? How do you know?b. Construct the bisector of ZB. Mark the intersection of the ray and AC as D.c. What do you notice about AD and CD?
a) Two sides of a triangle are concruent when they are the same length. First calculate the lenght of each side
[tex]\begin{gathered} AC^2=\text{ (X\_c-X\_a)}^2+(Y_a-Y_c)^2=(8-4)^2+(7-1)^2=\text{ 52} \\ AC=\sqrt{52}=7.2 \end{gathered}[/tex][tex]\begin{gathered} AB^2=(X_a-X_b)^2+(Y_a-Y_b)^2=(4-0)^2+(7-0)^2=\text{ 65} \\ AB=\sqrt{65}=8.06\approx8 \end{gathered}[/tex][tex]\begin{gathered} BC^2=(X_c-X_b)^2+(Y_c-Y_b)^2=(8-0)^2+(1-0)^2=\text{ 65 } \\ BC=\sqrt{65}=8.06\approx8 \end{gathered}[/tex]Sides AB and BC aren congruent.
b)
The bisector divides the triangle in exact halves.
The bisector is the blue line, in green you'll se the length of each side.
c)
What is the approximate diameter of the largest Circle she can make
We have that the circumference of a circle can be represented with the following equation:
[tex]C=\pi d[/tex]where d represents the diameter of the circle.
In this case, we have a circle of circumference C = 30 ft made with the lights, then, using the equation and solving for d, assuming that pi equals 3.14, we get:
[tex]\begin{gathered} 30=(3.14)d \\ \Rightarrow d=\frac{30}{3.14}=9.55\approx10ft \end{gathered}[/tex]therefore, the approximate diameter of the largest circle is 10 ft
A girl cycled a total of 15 kilometers by making 5 trips to work. How many trips will she have to make to cover a total of 24 kilometers? Solve using unit rates.
We need to find how many trips she will have to make to cover a total of 24 kilometers.
We know that she covered 15 kilometers by making 5 trips. Thus, the number of kilometers made on each trip is:
[tex]\frac{15\text{ kilometers}}{5\text{ trips}}=\frac{15\div5\text{ kilometers}}{5\div5\text{ trip}}=\frac{3\text{ kilometers}}{1\text{ trip}}[/tex]Then, she made 3 kilometers on 1 trip (unit rate).
Now, to cover 24 kilometers, she needs to make 8 trips, because:
[tex]\begin{gathered} 3\text{ kilometers }\times8=24\text{ kilometers} \\ \\ 1\text{ trip }\times8=8\text{ trips} \end{gathered}[/tex]Thus:
[tex]\frac{3\text{ kilometers}}{1\text{ trip}}=\frac{3\text{ kilometers}}{1\text{ trip}}\times\frac{8}{8}=\frac{3\times8\text{ kilometers}}{1\times8\text{ trips}}=\frac{24\text{ kilometers}}{8\text{ trips}}[/tex]Answer: She will have to make 8 trips.
Solve the following equation for x. (x - 5) -6 2 OX= -2 O x=2 x=-17 X=-7
You have teh following equation:
(x - 5)/2 = - 6
In order to find the solution to the previous equation, proceed as follow:
(x - 5)/2 = -6 multiply by 2 both sides
x - 5 = -6(2)
x - 5 = -12 add 5 both sides
x = -12 + 5 simlify
x = -7
Hence, the solution to the gicen equation is x = -7
A window had a length of 2ft & width of 3ft. What is the area of the window?
The formula used to calculate the area of the window will be
[tex]\begin{gathered} \text{Area}=l\times w \\ \text{where,} \\ l=2ft \\ w=3ft \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} \text{Area}=l\times w \\ \text{Area}=2ft\times3ft \\ \text{Area}=6ft^2 \end{gathered}[/tex]Hence,
The final answer = 6ft²