To solve the system of equations using Gauss-Jordan elimination, we'll start by writing the augmented matrix for the system. The augmented matrix is formed by combining the coefficients of the variables and the constant terms on the right side of each equation:
[1 -4 1 | 0]
[2 2 -1 | -4]
[1 -2 -1 | -5]
Now, we'll apply row operations to transform the augmented matrix into reduced row-echelon form.
Let's perform row 2 - 2 * row 1 to eliminate the x term in the second row:
[1 -4 1 | 0]
[0 10 -3 | -4]
[1 -2 -1 | -5]
Next, perform row 3 - row 1 to eliminate the x term in the third row:
[1 -4 1 | 0]
[0 10 -3 | -4]
[0 2 -2 | -5]
To make the second element of the third row equal to zero, perform row 3 - (1/5) * row 2:
[1 -4 1 | 0]
[0 10 -3 | -4]
[0 0 -1 | -3/5]
We can multiply the third row by -1 to make the leading coefficient in the third row positive:
[1 -4 1 | 0]
[0 10 -3 | -4]
[0 0 1 | 3/5]
Now, let's perform row 2 - 3 * row 3 to eliminate the z term in the second row:
[1 -4 1 | 0]
[0 10 0 | -19/5]
[0 0 1 | 3/5]
Next, perform row 1 + 4 * row 3 to eliminate the z term in the first row:
[1 -4 0 | 12/5]
[0 10 0 | -19/5]
[0 0 1 | 3/5]
Finally, divide the second row by 10 and simplify:
[1 -4 0 | 12/5]
[0 1 0 | -19/50]
[0 0 1 | 3/5]
Divide the first row by -4 and simplify:
[-1/4 1 0 | -3/5]
[0 1 0 | -19/50]
[0 0 1 | 3/5]
The resulting matrix corresponds to the system:
-1/4x + y = -3/5
y = -19/50
z = 3/5
Therefore, the solution to the system of equations is:
x = -3/10
y = -19/50
z = 3/5
Given a quaternion with rotation of 90° about the x-axis and route point (1,0,1)
Find the following:
a. Scalar part
b. i, j, k components
c. Px, Py, Pz
Given the quaternion with rotation of 90° about the x-axis and route point (1,0,1), we have to find the scalar part, i, j, k components, Px, Py, Pz.
To find the scalar part, we need to use the formula: Scalar part = cos(θ/2)Where θ is the angle of rotation, which is 90° in this case. Scalar part = cos(90°/2) = cos(45°) = 0.7071To find the i, j, k components, we use the formula: qi = sin(θ/2) * ai where ai is the unit vector in the axis of rotation. i-component = sin(90°/2) * 1 = 1j-component = 0k-component = 0Therefore, the quaternion is (0.7071, 1i, 0j, 0k)To find Px, Py, Pz, we rotate the point (1,0,1) by the given quaternion using the formula: P' = qpq-1where q is the given quaternion, and P' is the new point.
Let's first find the inverse of the quaternion.q-1 = (0.7071, -1i, 0j, 0k) (Since the scalar part remains the same, only the vector part gets negated)Now, let's substitute the values and simplify: P' = (0.7071 + 1i)(1 + 0j + 0k)(0.7071 - 1i) = (0.7071 + 1i)(0.7071 - 1i) = 1 - 0.7071iTherefore, the new point is (1, 0, -0.7071)Hence, Px = 1, Py = 0, and Pz = -0.7071.
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-6,-5,-4,-3,...rule
What is answer
Answer:
[tex]a_{n}[/tex] = n - 7
Step-by-step explanation:
There is a common difference between consecutive terms in the sequence
d = - 5 - (- 6) = - 4 - (- 5) = - 3 - (- 4) = 1
This indicates the sequence is arithmetic with nth term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = - 6 and d = 1 , then
[tex]a_{n}[/tex] = - 6 + 1 (n - 1) = - 6 + n - 1 = n - 7
A room needs to be painted. The room is 15 ft by 23 ft by 8 ft high. A gallon
of paint covers 250 2 and costs $28.
a. Find the number of gallons to paint the room.
b. What is the cost of painting the room if you do the work yourself?
Answer:
First we know that the room is a rectangular prism with measures:
width = W = 15ft
length = L = 23ft
height = H = 8ft
We want to paint the room (i suppose that we paint the four walls and the roof)
The area of each two of the walls the width times the height:
A = (15ft)*8ft = 120ft^2
And we have two of these walls, then the total area is:
area = 2*120ft^2 = 240ft^2
The area of each one of the other two walls is the height times the length:
A = (23ft)*8ft = 184ft^2
And we have two of these walls, then the total area is:
A = 2*184ft^2 = 368ft^2
The area of the roof is equal to the length times the width.
A = 23ft*15ft = 276ft^2
Then the total area we need to paint is:
area = 240ft^2 + 368ft^2 + 276ft^2 = 884 ft^2
a) We know that one gallon can cover 250 ft^2
Then to cover 884 ft^2 we need:
N = (884 ft^2)/(250 ft^2) = 3.536 gallons of paint
b) Knowing that each gallon costs $28, and that we need 3.536 gallons of paint to paint the room, the total cost is:
3.54*$28 = $99.008 = $99.01
Now if for some reason you only can buy paint in whole numbers, then you can not buy exactly 3.536 gallons, then you need to buy 4 gallons, and in this case, the total cost will be 4 times $28
cost = 4*$28 = $112
Which situation CANNOT be represented by this equation? 6−7=29 6 x - 7 = 29 CLEAR CHECK Joel earns $7 $ 7 per hour to mow his aunt's lawn. If he spends $6 $ 6 on gas, how many hours, x , will he need to mow to have $29 $ 29 left? Joel mows his aunt's lawn for $6 $ 6 per hour. If he spends $7 $ 7 on gas, how many hours, x , will he need to spend mowing the lawn to have $29 $ 29 left? Joel takes 6 6 hours to mow his aunt's lawn. If he spends $7 $ 7 on gas, how much does he get paid per hour, x , to mow the lawn and still have $29 $ 29 left?
Answer:
Joel earns $7 per hour to mow his aunt's lawn. If he spends $6 on gas, how many hours, x , will he need to mow to have $ 29 left?
Step-by-step explanation:
The given equation is :
6x - 7 = 29
It is given that total hours be = x
Joel earns $7 per hour, so the total earning of Joel in x hours is = $ 7x
He spends $6 on gas, so = 7x - 6
He is left with $ 29 after spending on gas.
Therefore, the equation becomes :
7x - 6 = 29
Clearly, it can be seen that in this case, the given situation cannot be represented by the given equation, i.e. 6x - 7 = 29.
Raymond takes a 28-inch by 21-inch rectangle of plywood and uses a table saw to cut from one corner of the piece of plywood to the diagonally opposite corner. Now Raymond has two equally sized triangles of plywood. What is the perimeter of each triangle?
Step-by-step explanation:
just to fit characters ...........
John’s friend told him that he could earn $25 for handing out flyers at a local concert. John wants to calculate the hourly rate. If he works a total of 2 hours, the equation 2x=25 can be used to determine his hourly rate. What would John’s hourly rate be, in dollars?
A
$12.50
B
$23
C
$27
D
$50
Answer:
D
Step-by-step explanation:
Which is NOT true?
A 11 = 11
B 11 = 18 - 7
C 11 + 5 = 15 + 11
D 11 + 3 = 6 + 8
Answer:
C
Step-by-step explanation:
11+5=15
15+11=26
15 does not equal 26
Answer:C 11 + 5 = 15 + 11
Step-by-step explanation:
This is the only one that is false because the left side of the equation is equal to 16 and the right side of the equation is equal to 26
kam
A company's stock was selling at
$28 a share. A month later, it was
selling at $21 a share. What is the
percent loss?
[?]%
Answer:Im pretty sure it's 25% percent loss
Step-by-step explanation:
sorry if im wrong
Consider sample of 47 football games, where at of them were won by the bomo tam. Use a 0.01 significance level to test the claim that the probability that the home team wins is greater than one half. Identify the null and alternative hypothes for this test.
The null hypothesis for this test is that the probability that the home team wins is equal to or less than one half. The alternative hypothesis is that the probability that the home team wins is greater than one half.
1. Identify the null hypothesis (H0): The null hypothesis for this test is that the probability that the home team wins is equal to or less than one half (P ≤ 0.5).
2. Identify the alternative hypothesis (Ha): The alternative hypothesis is that the probability that the home team wins is greater than one half (P > 0.5).
3. Determine the significance level (α): The significance level, also known as the alpha level, is set at 0.01. This means that we are willing to accept a 1% chance of rejecting the null hypothesis when it is actually true.
4. Collect the sample data: In this case, we have a sample of 47 football games, where "at" of them were won by the home team (let's assume "at" to be a specific number).
5. Calculate the test statistic: To test the claim, we need to calculate the test statistic based on the sample data. Since we are comparing a proportion (probability), we can use the z-test. The test statistic formula is given by:
z = (p - P) / √(P * (1 - P) / n)
Where:
p is the proportion of games won by the home team in the sample,
P is the claimed probability that the home team wins (in this case, P = 0.5),
n is the sample size.
6. Determine the critical value: Since we have a one-tailed test (alternative hypothesis is directional), we need to find the critical value corresponding to the significance level of 0.01 in the standard normal distribution (z-distribution). Using a z-table or a statistical software, the critical value for a 0.01 significance level is approximately 2.33.
7. Compute the test statistic: Plug in the values from the sample data into the test statistic formula calculated in Step 5 to obtain the z-value.
8. Compare the test statistic with the critical value: If the test statistic is greater than the critical value, we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.
9. Make a decision: If the test statistic is greater than the critical value, we reject the null hypothesis, indicating that there is sufficient evidence to support the claim that the probability that the home team wins is greater than one half. If the test statistic is less than or equal to the critical value, we fail to reject the null hypothesis, indicating that there is not enough evidence to support the claim.
10. Provide a conclusion: Based on the decision made in Step 9, state the conclusion in the context of the problem. For example, if we reject the null hypothesis, we can conclude that there is significant evidence to suggest that the home team has a greater than 50% chance of winning in these football games.
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3(2w -4) equals what
Answer:
6W-12
Step-by-step explanation:
Answer:
6w-12
Step-by-step explanation:
distribute:
3(2w-4) = 6w-12
Explain, using an example, why you need to multiply when converting from a larger unit to a smaller unit
Answer:
This is often called scaling in math, used in ratios, fraction, percent's etc.
Step-by-step explanation:
Answer:
You can use similar processes when converting from smaller to larger units. When converting a larger unit to a smaller one, you multiply; when you convert a smaller unit to a larger one, you divide. Here is an example..
find the coordinate vector of a =[ 2 3 4 5] with respect to the basis = [e22, e21, e12, e11 ] of m22.
The coordinate vector of vector a = [2, 3, 4, 5] with respect to the basis B = [e22, e21, e12, e11] of M22 is [3, 4, 5, 2].
To find the coordinate vector, we need to express vector a as a linear combination of the basis vectors. The given basis B represents the standard basis for a 2x2 matrix.
Let's break down the process step by step:
Start with the basis vectors: e22, e21, e12, e11.
Express vector a as a linear combination of the basis vectors:
a = 2 * e22 + 3 * e21 + 4 * e12 + 5 * e11
The coefficients in front of each basis vector represent the coordinates of a with respect to the basis B.
Therefore, the coordinate vector of a with respect to B is [2, 3, 4, 5].
However, it's important to note that the given basis B is not the standard basis for a 2x2 matrix. The standard basis for a 2x2 matrix consists of the following vectors: e11 = [1, 0, 0, 0], e12 = [0, 1, 0, 0], e21 = [0, 0, 1, 0], e22 = [0, 0, 0, 1].
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find the surface area of the part of the cone z=sqrt(x^2 y^2) that lies between the plane y=x and the cylinder y=x^2
The surface area of the part of the cone z = sqrt(x^2 + y^2) that lies between the plane y = x and the cylinder y = x^2 is sqrt(2)/6.
To find the surface area of the part of the cone z = sqrt(x^2 + y^2) that lies between the plane y = x and the cylinder y = x^2, we can use a double integral to integrate the surface area element dS over the region of interest.
First, we need to parameterize the surface in terms of two variables (u, v) such that the surface is defined by x = f(u,v), y = g(u,v), and z = h(u,v). We can use cylindrical coordinates, with x = r cos(theta), y = r sin(theta), and z = sqrt(x^2 + y^2) = r. Then, the cone is given by r = h(u,v) = u, and the region bounded by y = x and y = x^2 is given by u^2 <= v <= u.
Next, we need to compute the partial derivatives of f, g, and h with respect to u and v:
f_u = cos(theta)
f_v = -u sin(theta)
g_u = sin(theta)
g_v = u cos(theta)
h_u = 1
h_v = 0
Then, the surface area element dS can be computed using the formula:
dS = sqrt(1 + (h_u)^2 + (h_v)^2) du dv
Substituting in the partial derivatives and simplifying, we get:
dS = sqrt(2) du dv
Finally, we can set up the double integral over the region of interest and integrate dS:
surface area = ∫∫ dS = ∫[0,1]∫[u^2,u] sqrt(2) dv du
Evaluating this integral using the limits of integration gives us:
surface area = ∫[0,1] sqrt(2) (u - u^2) du
= sqrt(2) (1/2 - 1/3)
= sqrt(2)/6
Therefore, the surface area of the part of the cone z = sqrt(x^2 + y^2) that lies between the plane y = x and the cylinder y = x^2 is sqrt(2)/6.
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Please help me with the question
90 degrees and right angle
Sandra needs a new bicycle tire. Her tire has a circumference of 26π inches. What is the radius of her tire?
Answer:
it should be by mult by 10 is 816.81
PLSSS HELPPPPP
On the following number line, point C represents the integer -1. Identify the integer that each of the other letters represent.
A:
B:
D:
E:
Answer: B is 0 A is 1 D 2 E 3
Step-by-step explanation:
Answer:
a: 1
b: 0
d:2
e:3
Step-by-step explanation:
Since you already know that C is -1, you can add or subtract along the numberline by ones to get the values of each letter
Diddy Corp. Stock has a beta of 1.2, the current risk-free rate is 6 percent, and the expected return on the market is 14.50 percent. What is Diddy's cost of equity?
Answer: 16.2%
Step-by-step explanation:
You can find the cost of equity using the Capital Asset Pricing Model (CAPM).
Cost of equity = Risk free rate + Beta * (Expected return on market - Risk free rate)
= 6% + 1.2 * (14.50 - 6%)
= 6% + 10.2%
= 16.2%
A certain reality TV show lost a total of 9,000 viewers over the past 3 months. It lost the same number of
viewers each month.
The following equation describes this situation.
-9,000 = 3 = -3,000
What does -3,000 tell us?
Answer:
Step-by-step explanation:
- 3, 000 tells the number of views loss in each month.
Please solve as soon as possible thank you I appreciate it!
What is the volume of a sphere with a radius of 6.3 cm, rounded to the nearest tenth of a cubic centimeter?
Answer:
1047.4 cm^3
Step-by-step explanation:
Answer:1047.4
Step-by-step explanation:
.
"Suppose X --> N(20,5)
(a) Find: (i) P(X> 18)
(ii) P(7 < X < 15)
(b) Find the value a such that P(20-a < X < 20+ a) = 0.99
(c) Find the value b such that P(20-b< X < 20+ b) = 0.95
a) i)P(X > 18)= 0.65542
ii)P(7 < X < 15)=0.154
b)The value of a using the standard normal table or a calculator is 12.875
c)the value of b using the standard normal table or a calculator is 9.8
a) Let X be the normal random variable with mean μ = 20 and standard deviation σ = 5. We have to find P(X > 18) and P(7 < X < 15).
(i) P(X > 18)
This can be calculated using the standard normal table or a calculator as follows:
z = (18 - μ)/σ
= (18 - 20)/5
= -0.4
P(X > 18) = P(Z > -0.4)
= 1 - P(Z ≤ -0.4).
Using the standard normal table or a calculator, P(Z ≤ -0.4) = 0.34458
Therefore, P(X > 18) = 1 - 0.34458 = 0.65542
(ii) P(7 < X < 15). This can be calculated using the standard normal table or a calculator as follows:
z₁ = (7 - μ)/σ
(7 - 20)/5 = -2.6z₂
(15 - μ)/σ = (15 - 20)/5
= -1
P(7 < X < 15) = P(-2.6 < Z < -1)
= P(Z < -1) - P(Z < -2.6)
Using the standard normal table or a calculator,
P(Z < -1) = 0.15866P(Z < -2.6) = 0.00466
Therefore, P(7 < X < 15) = 0.15866 - 0.00466 = 0.154
b) We have to find the value of a such that
P(20 - a < X < 20 + a) = 0.99.
This can be calculated as follows:
z₁ = (20 - a - μ)/σ
= (20 - a - 20)/5
= -a/5z₂ = (20 + a - μ)/σ
= (20 + a - 20)/5 = a/5
We need to find a such that
P(z₁ < Z < z₂) = 0.99
Using the standard normal table or a calculator,
P(Z < z₂) - P(Z < z₁) = 0.99P(Z < a/5) - P(Z < -a/5) = 0.99
This can be rewritten as
P(Z < a/5) - [1 - P(Z < a/5)] = 0.99P(Z < a/5) - P(Z < -a/5) = 0.995
From the standard normal table or a calculator,
P(Z < 2.575) = 0.995P(Z < -2.575) = 0.005
Therefore,
2.575 = a/5 or -2.575 = -a/5a = 12.875
Therefore, the value of a is 12.875.
c) We have to find the value of b such that P(20 - b < X < 20 + b) = 0.95.
This can be calculated as follows:
z₁ = (20 - b - μ)/σ
= (20 - b - 20)/5
= -b/5z₂
= (20 + b - μ)/σ
= (20 + b - 20)/5 = b/5
We need to find b such that
P(z₁ < Z < z₂) = 0.95
Using the standard normal table or a calculator,
P(Z < z₂) - P(Z < z₁) = 0.95P(Z < b/5) - P(Z < -b/5) = 0.95
This can be rewritten as
P(Z < b/5) - [1 - P(Z < b/5)] = 0.95P(Z < b/5) - P(Z < -b/5) = 0.975
From the standard normal table or a calculator,
P(Z < 1.96) = 0.975P(Z < -1.96) = 0.025
Therefore,1.96 = b/5 or -1.96 = -b/5b = 9.8
Therefore, the value of b is 9.8.
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Find the measure of each angles:
Answer:
10. 123º
13. 65º
Step-by-step explanation:
For number 10, a straight line is equal to 180º so all we have to do is subtract 57 (the number that we're given) from 180
For number 13, vertical angles are always congruent (the same) so we know that it's 65º
Compute Z, corresponding to P28 for standard normal curve. 5. Random variable X is normally distributed with mean 36 and standard deviation 3. Find the 80th percentile.
The 80th percentile of the normal distribution with a mean of 36 and a standard deviation of 3 is approximately 38.52.
To compute Z corresponding to P28 for the standard normal curve, we need to find the Z-score that corresponds to a cumulative probability of 0.28. This can be done using a standard normal distribution table or a statistical software.
Using a standard normal distribution table, we can look up the cumulative probability closest to 0.28, which is 0.2794. The corresponding Z-score is approximately -0.59.
Therefore, Z corresponding to P28 for the standard normal curve is approximately -0.59.
Regarding the second part of your question, to find the 80th percentile of a normal distribution with a mean of 36 and a standard deviation of 3, we can use the Z-table or a statistical software.
The 80th percentile corresponds to a cumulative probability of 0.80. Using the Z-table or a statistical software, we can find the Z-score that corresponds to a cumulative probability of 0.80, which is approximately 0.84.
To find the actual value, we can use the formula:
Value = Mean + (Z-score * Standard Deviation)
Plugging in the values:
Value = 36 + (0.84 * 3) = 38.52
Therefore, the 80th percentile of the normal distribution with a mean of 36 and a standard deviation of 3 is approximately 38.52.
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5. Write a function of the form f(x) = - + k with a vertical asymptote at x = -15 and a horizontal asymptote of y = -6.
Jason wants to create a box with the same volume as the one shown below. He wants the length to be 4 inches. What would be the measurements of the width and height?
Answer:
Width-6
height-3
I determinded the width and the height by counting how many cubic blocks there are up and down.
Step-by-step explanation:
The measurements of the width and height can 3 inches each or 1 and 9 inches.
What is volume of cuboid?The volume of the cuboid is defined as the measure of the space occupied within a cuboid. The cuboid is a three-dimensional shape that has length, breadth, and height. The volume of a cuboid is equal to the product of length, width and height of a cuboid.
Given data as :
Jason wants to create a box with the same volume as the one shown
To determine measurements of width and height of box
Volume of given box (cuboid) = 6 × 2 × 3
Volume of given box = 36
length to be 4 inches.
length × width × height = 36
⇒ 4 w × h = 36
⇒ w × h = 9
Now multiplication factors of 9 as
9 = 1 × 9
9 = 3 × 3
So, width and height can 3 inches each or 1 and 9 inches.
Hence, the measurements of the width and height can 3 inches each or 1 and 9 inches.
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a large population is bi modal samples of sixe 40 are drawn in a sampling distribution
The given statement mentions a large population that exhibits a bimodal distribution. Bimodal distribution means that the data has two distinct peaks or modes.
Additionally, it states that samples of size 40 are drawn from this population, resulting in a sampling distribution.
A sampling distribution refers to the distribution of a statistic, such as the mean or proportion, calculated from multiple samples drawn from the same population. In this case, samples of size 40 are drawn, which means that each sample consists of 40 observations from the population.
The statement does not provide specific details about the purpose or objective of analyzing the sampling distribution. However, studying the sampling distribution can provide valuable insights into the behavior and properties of the population. It allows researchers to make inferences about the population parameters based on the statistics calculated from the samples.
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Marie charges $8 for a dozen of her pineapple cupcakes. She sold 23 dozen at the street fair yesterday. How much money did
Marie collect?
A) $144
B) $164
C) $184
D) $194
Help please and I’ll I’ve BRAINLIEST
Answer:
c
Step-by-step explanation:
each dozen cost $8 so do the $8 times the 23 dozen she sold to get the answer
Answer:
C)$184
Step-by-step explanation:
8 times 23=$184
plz can i get brainliest:)
Francesca makes and sells jewelry. She uses the equation p = "285 + 45n to model the situation, where p is the amount of profit she
makes and n is the number of necklaces she sells. What does the y-intercept
The y-intercept for the given equation p = 285+45n is 285.
What is Y intercept?The Y-intercept is the point where the graph intersects the y-axis.
Y-intercept formulaTo find the y-intercept of a function y = f(x), substitute x=0 and solve for y.
According to the given question
we have an equation p = 285+45n
where,
p is the amount of profit
and, n is the number of necklaces
Let, p = y and n = x
then the given equation becomes y=285+45x
substitute, x = 0 in equation y = 285+45x
⇒ y = 285
Hence, the y-intercept of the equation p=285+45n is 285.
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NEED THIS DONE ASAP
If P(x) = -2(1 - x)2 +5, what is the value of
P(-3)?
Answer:
P(-3) = -1
Step-by-step explanation:
So just substitute the value of x in the equation:
Value of x is (-3)
So:
P(x) = -2(1 - x)2 +5
P(-3) = -2(1-(-3)) 2 + 5
P(-3) = -2(4) 2 + 5
P(-3) = -8 + 2 + 5
P(-3) = -6 + 5
P(-3) = -1
what's the answer !!
[tex] \sqrt{44 \times 2 \times 2 \times 11} [/tex]
Answer:
44
Step-by-step explanation:
[tex] \sqrt{44 \times 2 \times 2 \times 11} [/tex]
[tex] \sqrt{88 \times 2 \times 11} [/tex]
[tex] \sqrt{176 \times 11} [/tex]
[tex] \sqrt{1936}[/tex]
[tex] \sqrt{ {44}^{2} } [/tex]
Pull terms out from under the radical, assuming positive real numbers.
[tex]44[/tex]
Hope it is helpful.....Step-by-step explanation:
[tex] \sqrt{44 \times 2 \times 2 \times 11} \\ = \sqrt{11 \times 4 \times 4 \times 11} \\ = \sqrt{11 \times 11 \times 4 \times 4} \\ = 11 \times 4 \\ = 44[/tex]