The equivalent expression of [tex]7x^2 \sqrt{2x^4} \times 6 \sqrt {2x^{12 }[/tex] is [tex]84x^{10[/tex]
How to determine the equivalent expression?The expression is given as:
7x^2 sqrt 2x^4 times 6 sqrt 2x^12
Rewrite properly as:
[tex]7x^2 \sqrt{2x^4} \times 6 \sqrt {2x^{12 }[/tex]
Evaluate the product
[tex]7 * 6x^2 \sqrt{2x^4*2x^{12 }[/tex]
This gives
[tex]42x^2 \sqrt{4x^{16}[/tex]
Take the square root of 4
[tex]2*42x^2 \sqrt{x^{16}[/tex]
Take the square root of x^16
[tex]2*42x^2 *x^8[/tex]
So, we have:
[tex]84x^{10[/tex]
Hence, the equivalent expression of [tex]7x^2 \sqrt{2x^4} \times 6 \sqrt {2x^{12 }[/tex] is [tex]84x^{10[/tex]
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Answer:
Step-by-step explanation:
The equivalent expression of is
How to determine the equivalent expression?
The expression is given as:
7x^2 sqrt 2x^4 times 6 sqrt 2x^12
Rewrite properly as:
Evaluate the product
This gives
Take the square root of 4
Take the square root of x^16
So, we have:
Hence, the equivalent expression of is
Dave leaves his office in Padelford Hall on his way to teach in Gould Hall. Below are several different scenarios. Take distance units to be “feet” and time units to be “minutes.” Assume Dave’s path to Gould Hall is along a straight line which is 2400 feet long.
I. Dave leaves Padelford Hall and walks at a constant spend until he reaches Gould Hall 10 minutes later.
II. Dave leaves Padelford Hall and walks at a constant speed. It takes him 6 minutes to reach the halfway point. Then he gets confused and stops for 1 minute. He then continues on to Gould Hall at the same constant speed he had when he originally left Padelford Hall.
III. Dave leaves Padelford Hall and walks at a constant speed. It takes him 6 minutes to reach the half-way point. Then he gets confused and stops for 1 minute to figure out where he is. Dave then continues on to Gould Hall at twice the constant speed he had when he originally left Padelford Hall.
g. Using all three scenarios, represent each scenario as an algebraic function.
See below for the algebraic expressions of the scenarios.
How to represent the scenarios?The given parameters are:
Distance = 2400 feetUnit of time = MinutesScenario 1
Represent the speed with x.
So, we have:
Speed = Distance/Time
The time is given as:
Time = 10 minutes
Since he did not stop at all;
The speed is
x = 2400/10
Multiply both sides by 10
10x = 2400
The above expression represents the scenario 1.
Scenario 2
Represent the speed with x, and time with t
So, we have:
Speed = Distance/Time
The time to reach halfway is given as:
Time = 6 minutes
He stopped for 1 minute, before continuing at the same initial speed
So, the total time it 13 minutes
The speed is represented as:
x = 2400/13
Multiply both sides by 13
13x = 2400
The above expression represents the scenario 2.
Scenario 3
Represent the speed with x, and time with t
So, we have:
Speed = Distance/Time
The time to reach halfway is given as:
Time = 6 minutes
He stopped for 1 minute, before continuing at twice the initial speed
So, the total time is
t = 6 + 1 + 1/2 * 6 minutes
t = 10 minutes
The speed is represented as:
x = 2400/10
Multiply both sides by 10
10x = 2400
The above expression represents the scenario 3.
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Please help!!! 24 points!!!
Answer:
-24
Step-by-step explanation:
-6 × f(3) - 6 × g(-1) = ?
to answer this we need to find the functional values of the functions at the specified points.
f(3) = -2
we find this easily : we go to x = 3 on the x-axis, and then see there at what y value a vertical line is intersecting the functional graph. the intersection is below the x-axis, so the y value is negative.
g(-1) = 6
we go to x=-1, and we find that a vertical line there will intersect the g curve at y = 6.
and that's really it.
now we need to calculate it all in the main expression :
-6 × -2 - 6 × 6 = 12 - 36 = -24
you remember, that multiplications and divisions have to happen before any addition of subtraction ?
A study showed that low-intensity shock therapy reduces pain levels in patients with lupus. During each session, electrodes were placed on the pain site indicated by the patient. Pain reduction was measured through self-reporting after each session.
Another study is being designed to examine whether low-intensity shock therapy also reduces pain in patients suffering from bulging disks in the thoracic region of the back. Two hundred female patients are subjects in the new study.
Part A: What is an appropriate design for the new study? Include treatments used, method of treatment assignment, and variables that should be measured. (4 points)
Part B: If the study consisted of 100 male and 100 female patients instead of 200 female patients, would you change the study design? If so, how would you modify your design? If not, why not? (4 points)
Part C: Could your design be double-blind? Explain. (2 points)
The experiment is illustrated below.
How to explain the experiment?A. The type of experimental design is a completely randomized design experiment where experimental units of 200 female subjects which are allocated randomly to say 4 treatment groups with each treatment group consist of 50 female patients.
Here the treatment used is low-intensity shock therapy which is also factor or explanatory variable. After administrating above treatment for a period of say 2-3 weeks, the response in pain reduction can be measured among all patients in 4 treatment groups by comparing their earlier pain level for reduction in pain.
If the study consist of 100 male and female patients, the experimental design can be changed into randomized block design by blocking subjects by gender.
The above design can be double blinded by not letting either the patients or lab technicians aware about which treatment groups, each of these subjects are experimented against to keep the data confidential.
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What is the frequency of the function f (x). f (x) = -2sin x/4 +3
Answer: [tex]8\pi[/tex]
Step-by-step explanation:
The period is [tex]\frac{2\pi}{1/4}=8\pi[/tex].
A box contains 5 red marbles and 2 yellow marbles. Consider the two–stage experiment of randomly selecting a marble from a box, NOT replacing it, and then selecting a second marble. Determine the probabilities of the following events:
a. Selecting 2 red marbles.
P (red) =
b. Selecting a red marble on the first draw and a yellow marble on the second.
P (red then yellow) =
c. Selecting at least 1 yellow marble.
P (at least 1 yellow) =
Answer:
a) 10/21 b) 5/21 c)1/21
Step-by-step explanation:
a) your have 7 choice and 5 or them or red, 5/7. You do not replace the red marble, so for your second draw, you now only have 6 choices and of those 6 choices only 4 of them are now red or 4/6 or 2/3. We multiple these two numbers together:
5/7(2/3) = 10/21
b) For the first draw, you have 5 red marbles available out of a total 7 marbles or 5/7. The second draw now only has 6 marbles and 2 of them or yellow to make 2/6 or 1/3 (simplified). We multiply these together.
5/7(1/3) =5/21
c) I am assuming that you are still selecting 2 marbles. The first draw would be 2/7. This time I am selecting yellow and there are only 2 choices for yellow. My next draw will only have 6 marbles and only 1 of them will be yellow, so 1/6. We multiply these together
2/7(1/6) = 2/42 or 1/21
Solve for x.
x-2.13 = 5.3
Answer:
x = 7.43
Step-by-step explanation:
X - 2.13 = 5.3
add -2.13 to both sides
x -2.13+2.13 = 5.3 + 2.13
-2.13 + 2.13 cancel out and 5.3 +2.13 equals 7.43
therefore x =7.43
check your work by substituting 7.43 for x
7.43 - 2.13 = 5.3
The base of a triangle is twelve more than twice its height. If the area of the triangle is 43 square centimeters, find its base and height.
Answer:
B=37
H=66
Step-by-step explanation:
Use algebra and find the answer.
Simplify: Simplify: StartRoot StartFraction 27 x Superscript 12 Baseline Over 300 x Superscript 8 Baseline EndFraction EndRoot
The solution of the given expression is 9*[tex]x^{4}[/tex]/100.
GIven an expression equal to 27[tex]x^{12}[/tex]/300[tex]x^{8}[/tex].
We have to simplify the expression in which variable comes only once.
Expression is combination of numbers ,symbols, fraction, coefficients, indeterminants,determinants, etc. It is mostly not found in equal to form. It expresses a relationship between variables.
The given fraction is 27[tex]x^{12}[/tex]/300[tex]x^{8}[/tex].
When we observe we find that in numerator x has large power and denominator x has small power as compared to power in numerator. So we will deduct the powers so that they will give only one power to us.
=27[tex]x^{4}[/tex]/300
Now divide numerator an denominator by 3.
=9[tex]x^{4}[/tex]/300
Hence the expression 27[tex]x^{12} /300x^{8}[/tex] will look like [tex]9x^{4} /100[/tex] after simplifying.
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Answer:
[tex]Simplify:\sqrt\frac{27x^{12} }{300x^{8} }[/tex]
[tex]O \frac{9}{100}x^{4}[/tex]
✔ [tex]\frac{3}{10} x^{2}[/tex]
[tex]O \frac{27}{300} x^{4}[/tex]
[tex]O\frac{9}{10} x^{2}[/tex]
Instructions: Find the missing side of the triangle 27,36,x
Answer:
x = 117
Step-by-step explanation:
Foremost, we know that the three angles of the triangle always add up to 180 degrees.
So, there are two sides which are 27 degrees and 36 degrees, we need to find the third one's degree.
Add 27 and 36 (27 + 36 = 63)
Two sides equal 63.
Then, subtract 180 - 63 = 117
So the third angle's measurement is 117 degrees. The answer is 117.
To check, add 117 + 27 + 36 = 180
Hope it helps.
How do you classify the following polynomial?
-4x³ + 2x² - 5x+3x²
(I need de classification, no the result)
Imagine the center of the London Eye Ferris Wheel is located at (0, 0) on a coordinate grid, and the radius lies on the x-axis. Write an equation of a circle for the ferris wheel, and sketch an image of what the ferris wheel would look like on the grid. Now graph a circle that is similar to the Ferris Wheel. Discuss the transformations needed to show that both circles on your graph are similar.
answer
symbolic materials ?
Conveyor belts called grain elevators are used to move grain into a silo. Answer the following questions knowing that the lower end of the belt is 100 feet from the base of the silo and that the silo is 150 feet tall.
a. How long is the belt?
b. If we know the angle of elevation from the lower end of the belt to a window on the side of the silo is 45°, use special right triangle ratios to calculate the height of the window from the ground.
c. We need a ramp to the window. How long would it need to be?
From the given information,
a. The length of the belt is 180.28 ft
b. The height of the window from the ground is 100 ft
c. The length of the ramp needed is 141.42 ft
What is the Pythagorean theorem's formula?The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two legs of the triangle. I.e., (hypotenuse)² = (opposite)² + (adjacent)²
Calculation:It is given that,
The height of the silo is 150 feet
The distance from the belt to the silo is 100 feet
With the given measurements, a right-angled triangle is formed.
a. Finding the length of the belt:
From the diagram,
The height of the silo, sh = 150 ft
The base distance, sb = 100 ft
So, the length of the conveyor belt is the hypotenuse (bh) of the triangle formed.
On applying the Pythagorean theorem,
bh² = sb² + sh²
⇒ bh² = (100)² + (150)²
⇒ bh² = 32500
⇒ bh = √32500 = 50√13
∴ bh = 180.28 ft
Thus, the length of the belt is 180.28 ft.
b. Finding the height of the window from the ground:
It is given that the angle of elevation from the lower end of the belt(b) to a window(w) on the side of the silo is 45°.
This creates a special right-angled triangle. I.e.,
The angles of the new triangle are 90°- 45°. So, the third angle also becomes 45° (Since the sum of angles in a triangle is 180°)
So, the new triangle has angles of 90°- 45°- 45°
Thus, the new triangle is said to be an isosceles right angled triangle.
So, the two legs of the triangle are equal. I.e., sb = sw = 100 ft
Therefore, the height of the window from the ground(sw) is 100 ft
c. Finding the length of the ramp(bw) to the window:
Since we have
sw = 100 ft and sb = 100 ft
On applying Pythagora's theorem,
bw² = sb² + sw²
⇒ bw² = (100)² + (100)²
⇒ bw = √20000 = 141.42 ft
Therefore, the length of the ramp to the window is 141.42 ft.
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4. Identify a transformation of the function f(x) = x by observing the equation of the function g(x) = x - 16.
Answer: A shift 16 units down
Step-by-step explanation:
See attached image.
The transformation of the function f(x) = x is (x, y) → (x + 16, y). This transformation is said to be the translation rule and the translation is 16 units towards the right.
What is the translation rule of transformations?The translation rule for a function f(x) is given by
(x, y) → (x + a, y + b)
Where a, and b are constant.
(x, y) → (x + a, y); translation towards right
(x, y) → (x - a, y); translation towards left
Calculation:It is given that the function f(x) = x and g(x) = x - 16
So, the variation is
x - a = x - 16
⇒ - a = x - x - 16
∴ a = 16
Thus, the transformation is (x, y) → (x + 16, y)
Therefore, the transformation of the function f(x) = x is (x, y) → (x + 16, y) i.e., the translation of 16 units towards the right .
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The cost of b tickets at $20 a ticket algebraic expression
The algebraic expression is 20b
How to determine the algebraic expression?The statement is given as:
$20 a ticket
This means that the cost of 1 ticket is $20.
So, the cost of b tickets is
Cost = 20 * b
Evaluate
Cost = 20b
Hence, the algebraic expression is 20b
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Find the mode for the scores 3,760, 5,200, 8,750, 4,400, 5,250
The difference of the square of a number and 9 is equal to 8 times that number. Find the positive solution.
[tex]x {}^{2} - 9 = 8x \\ x {}^{2} - 8x - 9 = 0 \\ x = \frac{ - ( - 8) + \sqrt[]{( - 8) {}^{2} - 4(1)( - 9)} }{2( {1}^{}) } [/tex]
[tex]x = \frac{8 + \sqrt{64 + 36} }{2} = \frac{8 + \sqrt{100} }{2} = \frac{8 + 10}{2} = 9[/tex]
Answer: x = 9
Step-by-step explanation:
The difference of the square of a number and 9 is equal to 8 times that number. Find the positive solution.
let x = a number
[tex]x^2-9=8x\\x^2-8x-9\\(x-9)(x+1)\\x-9 = 0\\x=9\\x+1=0\\x=-1[/tex]
taking only the positive solution, we get x = 9
Complete the function for this graph.
-5
ertificati...
5
-5
y = |x|+ [?]
Hint: y = |x-h| + v
Answer:
-5
Step-by-step explanation:
The y coordinate of the vertex is -5.
Identify the vertices of the feasible region and use them to find the maximum and/or minimum value for the given linear programming constraints.
System of Linear Programming:
z=−3x+5y
x+y≥−2
3x−y≤2
x−y≥−4
Maximum value of z:
Minimum value of z
The maximum value of the objective function is 26 and the minimum is -10
How to determine the maximum and the minimum values?The objective function is given as:
z=−3x+5y
The constraints are
x+y≥−2
3x−y≤2
x−y≥−4
Start by plotting the constraints on a graph (see attachment)
From the attached graph, the vertices of the feasible region are
(3, 7), (0, -2), (-3, 1)
Substitute these values in the objective function
So, we have
z= −3 * 3 + 5 * 7 = 26
z= −3 * 0 + 5 * -2 = -10
z= −3 * -3 + 5 * 1 =14
Using the above values, we have:
The maximum value of the objective function is 26 and the minimum is -10
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Jermy deposited money into a savings account that pays a simple annual interest rate of 1.6%. He earned 55.04 in interest after 4 years. How much did he deposit?.
860
1376
2976
3440
Answer: THE ANSWER IS A) $860
Step-by-step explanation: I GOT A 100 ON THE TEST
The table shows preferences of dancing or playing sports for male and female students:
Do you prefer dancing or playing sports?
Playing sports Dancing Row totals
Male students 18 16 34
Female students 18 35 53
Column totals 36 51 87
Mason mistakenly calculated the conditional relative frequency for female students who prefer playing sports to be 21%. What statistic did Mason actually calculate, and what should he have done differently?
The conditional relative frequency for female students who prefer playing sports is 34%.
How to determine the statistic calculated?The table of values is given as:
Sports Dancing Row totals
Male students 18 16 34
Female students 18 35 53
Column totals 36 51 87
Mason's calculation is given as:
P = 21%
This is gotten by
18/87 = 21%
The above represents the joint relative frequency of female students who prefer playing sports.
To calculate the conditional relative frequency, he should divide 18 by the row total.
So, we have
18/53 = 34%
Hence, the conditional relative frequency for female students who prefer playing sports is 34%.
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Set B and the universal set U are defined as follows.
U={f,g,h,p,q,r}
B={g,q,r}
Find the following sets.
Write your answer in roster form or as Ø.
(a) B' U U =
(b) B ∩ Ø =
Answer:
(a) B' U U = { f,g,h,p,q,r}
(b) B ∩ U = {g,q,r}
Step-by-step explanation:
Greetings !
(a) B/c B'= {X: X∈U and X∉B}
thus,B'= {f,h,p}
B' U U= {f,h,p} U {f,g,h,p,q,r}
= {f,g,h,p,q,r}
(b) B ∩ U= {g,q,r}
guys can you help me with this i just dont understand how to plot it so u just have to tell me how
Answer:
no
Step-by-step explanation:
Answer:
Step-by-step explanation:
6(3x-5)≤2(9x+7)+10
divide by 2
3(3x-5)≤9x+7+5
3(3x-5)≤9x+12
divide by 3
3x-5≤3x+4
-5≤4
which is true.
Given square ERTN, what is the length of NT ?
Answer:
|NT| = 25
Step-by-step explanation:
The four sides of this square all have the same length. Thus, 5x = 10x - 25, which, in turn, becomes 25 = 5x, giving us x = 5. The length of NT is 5(x), or |NT| = 25.
7. (05.02 MC)
Luciana's laptop has 3,000 pictures. The size of the pictures is skewed to the right, with a mean of 3.7MB and a standard deviation of 0.78MB
Part A: Can you accurately calculate the probability that the mean picture size is more than 3.8MB for an SRS of 20 pictures? Explain.
Part B: If you take a random sample of 60 pictures instead of 20, explain how the Central Limit Theorem allows you to find the probability that the mean picture size is more than 3.8MB.
Considering the Central Limit Theorem, we have that:
a) The probability cannot be calculated, as the underlying distribution is not normal and the sample size is less than 30.
b) The probability can be calculated, as the sample size is greater than 30.
What does the Central Limit Theorem state?It states that the sampling distribution of sample means of size n is approximately normal has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex], as long as the underlying distribution is normal or the sample size is greater than 30.
In this problem, the underlying distribution is skewed right, that is, not normal, hence:
For item a, the probability cannot be calculated, as the underlying distribution is not normal and the sample size is less than 30.For item b, the probability can be calculated, as the sample size is greater than 30.More can be learned about the Central Limit Theorem at https://brainly.com/question/16695444
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A ladder 8 m long is leaning against a building. How high on the building will the ladder reach when the bottom of the ladder is x = 1m from the building?
Answer:
7.9
Step-by-step explanation:
this would just be sqrt (8^2 - 1^2) or sqrt 63 or about 7.9
The ladder reaches 7.9 meters when the bottom of the ladder is x = 1m from the building.
What is the Pythagoras theorem?The square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.
It is given that:
A ladder 8 m long is leaning against a building.
From the data given, a right angle triangle is formed:
Applying the Pythagoras theorem:
Building high² = 8² - 1²
Building high² = 63
Building high = 7.9 meters
Thus, the ladder reaches 7.9 meters when the bottom of the ladder is x = 1m from the building.
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Simplify the following fractions.
Answer =
[tex] \frac{9}{16 \\ \\ } [/tex]
Show me step by step
Answer:
Expressions with numerous operators must be simplified in "BODMAS" order only, from left to right. The brackets are solved first, followed by powers or roots,division, or multiplication (whatever comes first from the left side of the formula), and finally subtraction or addition. The BODMAS simplification of fractions is a solution for addressing fractions that include many operations such as addition (+), subtraction (-), multiplication (×),division(÷), and brackets ().[tex] \pink{\maltese{ \text{BODMAS \:Full \: Form \: }}}[/tex]
To make numerical equations easier to understand, operations must be performed according to the BODMAS rule, which involves division, multiplication, addition, and subtraction to be performed in the order brackets.For example,The expression (48-24)÷3×4 as per BODMAS rule.
(48-24)÷3×4
=24÷3×4
=8×4
=32
Now,
The given question is,
Simplify:
[tex] \displaystyle{ \frac{7}{8} \div 5 \frac{1}{3} \times \frac{24}{7} }[/tex]
[tex] \displaystyle{ = \frac{7}{8} \div \frac{16}{3} \times \frac{24}{7} }[/tex]
[tex] \displaystyle{ = \frac{ \cancel{7} \times 3 \times \cancel{24} \: {}^{3} }{ \cancel{8 } \times 16 \times \cancel{7}} }[/tex]
[tex] \displaystyle{ = \frac{3 \times 3}{16} }[/tex]
[tex] \displaystyle{} = \frac{9}{16} [/tex]
Thus,the final answer is 9/16.
Solution -:
[tex] \frac{7}{8} \div 5 \frac{1}{3} \times \frac{24}{7} [/tex]
Let's begin-
solve,,,
Now,,According to BODMAS rule fist we divide ,
[tex] \frac{7}{8} \times \frac{3}{16} \times \frac{24}{7} \\[/tex]
Now , we multiple
[tex] \frac{3 \times 3}{16} \\ \\ = \frac{9}{16} [/tex]
and this is our final answers
▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃
Division → Multiplication → Addition → Subtraction
B stand bracket O stand of D stand divisionM stand MultiplicationA stand for additionS stand for subtractionSets A, B, and C are subsets of the universal set U. These sets are defined as follows.
U= {f,g,h,p,q,r,x,y,z}
A={f,g,p,q}
B={g,h,q,x,y}
C={p.q.x.y.z}
Find (C ∪ B) ∩ A'.
Write your answer in roster form or as Ø.
Answer:
(C U B )=(q,x,y)
(C U B )n A=q
Factor the greatest common binomial factor from each polynomial
if A and B are events with P(A) = 0.2, P(B) = 0.8, P(A and B) = 0.07, find P(A or B)
Work Shown:
P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) = 0.2 + 0.8 - 0.07
P(A or B) = 0.93
answer me please as soon as possible plot the graph same as shown in the question using green orange and black colors
Due to length restrictions, we kindly invite to read the explanation of this question for further details about the table and graph of the function.
How to plot the graph of a function
In this problem we must plot the graph of a function on a Cartesian plane. The procedure is summarized below:
Create a table for a series of equally spaced x-values.Calculate the y-values for corresponding values and fill the table.Mark the points on the Cartesian plane.Match the points with line segments.After following the procedure, we have the following result:
Input, x x + 4 Output, y (x, y)
- 2 - 2 + 4 2 (- 2, 2)
0 0 + 4 4 (0, 4)
2 2 + 4 6 (2, 6)
4 4 + 4 8 (4, 8)
6 6 + 4 10 (6, 10)
8 8 + 4 12 (8, 12)
Lastly, we plot the graph of the linear function.
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