√180m^2
I have to solve this using perfect squares, is anyone familiar with those?
Answers
Given:
The expression is
\(\sqrt{180m^2}\)
To find:
The value of the given expression by using the perfect squares.
Solution:
We have,
\(\sqrt{180m^2}\)
It can be written as
\(=\sqrt{2\times 2\times 3\times 3\times 5\times m^2}\)
\(=\sqrt{(2)^2(3)^25m^2}\)
\(=\sqrt{(2\times 3\times m)^25}\)
\(=\sqrt{(6m)^25}\)
\(=6m\sqrt{5}\)
Therefore, the value of given expression is \(6m\sqrt{5}\).
Related Questions
How do you do this question?
Answers
The coordinates of point C are (x, y) = (9, 8).
How to find the location of the coordinates of a point within a system of four triangles
In this case we need to determine the coordinates of point C based on the dimensions of each block. These dimensions can be determined by solving the following equations:
2 · x - y = 11 - 3
y + 2 · x = 20 - 4
2 · x - 16 + 2 · x = 8
4 · x - 16 = 8
4 · x = 24
x = 6
y = 2 · x - 8
y = 2 · 6 - 8
y = 12 - 8
y = 4
Finally, we determine the coordinates of point C:
X = 3 + x = 9
Y = 4 + y = 8
The point C has the following coordinates: (x, y) = (9, 8).
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Solve the coordinate of the midpoint of the segment. Show your work and explain the steps you used
to solve.
12.44)
(108-16)
Answers
Answer:
(60, 14 )
Step-by-step explanation:
Given the endpoints of a segment (x₁, y₁ ) and (x₂, y₂ ) , then the midpoint is
( \(\frac{x_{1}+x_{2} }{2}\) , \(\frac{y_{1}+y_{2} }{2}\) )
here (x₁, y₁ ) = (12, 44 ) and (x₂, y₂ ) = (108, - 16 ) , then
midpoint = ( \(\frac{12+108}{2}\), \(\frac{44-16}{2}\) ) = ( \(\frac{120}{2}\), \(\frac{28}{2}\) ) = ( 60, 14 )
Milla and Luka are 3 kilometers apart and walking toward each other. Milla's average speed is 5 kilometers per hour and Luka's is 4 kilometers per hour.
A table showing Rate in kilometers per hour, Time in hours, and Distance in kilometers. The first row shows, Milla, and has 5, t, and 5 t. The second row shows, Luka, and has 4, t, and 4 t.
Which equation can be used to find t, the time it takes for Milla and Luka to meet?
5t + 4t = 1
5t + 4t = 3
5t – 4t = 0
5t – 4t = 3
Answers
Answer:
b
Step-by-step explanation:
Answer:
its b 5t + 4t =3
Step-by-step explanation:
Does the average Washington State University student drive more or less than 300 miles from Pullman to home? In a sample of 226 students, the sample mean mileage was 285 miles with a sample standard deviation of 50 miles. Plotting the data, we see that the sample is approximately normal. (a) (4 points) Determine if a one-sided or two-sided confidence interval is appropriate for this situation. Explain your reasoning. (b) (10 points) Compute a 95% confidence interval for. Write your solution in interval notation. Interpret the meaning of the interval in the context of the situation. (c) (4 points) Compared the the confidence interval calculated above, if the confidence level is decreased to 90%, the new confidence interval is If the confidence level is increased to 99%, the new confidence interval is __. A. wider, wider B. narrower, narrower C. wider, narrower D. narrower
Answers
A two-sided confidence interval is appropriate because the research question is about whether the average mileage is significantly different from 300 miles.
(a) To determine if a one-sided or two-sided confidence interval is appropriate for this situation, we need to consider the research question and the nature of the hypothesis being tested. If the research question is specifically focused on whether the average mileage is less than or greater than 300 miles, then a one-sided confidence interval would be appropriate. On the other hand, if the research question is broader and seeks to determine whether the average mileage is significantly different from 300 miles (i.e., it could be less or greater), then a two-sided confidence interval would be appropriate.
(b) To compute a 95% confidence interval, we can use the formula:
CI =X ± (Z * (σ/√n))
Where X is the sample mean, Z is the z-value corresponding to the desired confidence level (in this case, 95% corresponds to Z = 1.96 for a large enough sample), σ is the population standard deviation (unknown, so we use the sample standard deviation), and n is the sample size.
Plugging in the given values:
CI = 285 ± (1.96 * (50/√226))
Simplifying the expression:
CI = 285 ± (1.96 * 3.322)
CI = [278.15, 291.85]
Interpretation: The 95% confidence interval for the average mileage from Pullman to home is [278.15, 291.85]. This means that we are 95% confident that the true average mileage of all Washington State University students falls within this interval. It suggests that based on the sample data, the average mileage is likely to be between 278.15 and 291.85 miles.
(c) If the confidence level is decreased to 90%, the new confidence interval will be narrower since a smaller confidence level requires less certainty, resulting in a narrower interval. Conversely, if the confidence level is increased to 99%, the new confidence interval will be wider as a higher confidence level demands greater certainty, leading to a wider interval to capture a larger range of potential values. Therefore, the answer is D. narrower for a confidence level of 90% and A. wider for a confidence level of 99%.
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please help its do now
...
..
.
Answers
Answer:
21.
Step-by-step explanation:
what is the answer to 4x − 12 −x ≥ 3
Answers
34x=1234x=12
Multiply both sides of the equation by 4343.
43⋅34⋅x=43⋅1243⋅34⋅x=43⋅12
Simplify both sides of the equation.
Answer:
x ≥ 5
Step-by-step explanation:
4x - 12 - x ≥ 3
Combine like terms: 4x and -x
3x−12 ≥ 3
Add 12 to both sides
3x − 12 + 12 ≥ 3 + 12
3x ≥ 15
Divide both sides by 3
3 / 3x ≥ 15 / 3
x ≥ 5
Which function has a greater rate of change?
Function A:
x 1.5 2.5 3.5 4.5 5.5
y –5 0 5 10 15
Function B:
y = –4.5x + 15
Function A has a rate change of BLANK and Function B has a rate change of BLANK so Function BLANK has a greater rate of change
Answers
Answer:
5; -4.5; Function AStep-by-step explanation:
Rate of change for function A is:
(15 - 10)/(5.5 - 4.5) = 5/1 = 5Rate of change of function B is:
-4.5 as the slope is the rate of changeComparing the values:
5 > - 4.5Function A has a greater rate of change
Answer:
Answer:
5; -4.5; Function A
Step-by-step explanation:
Rate of change for function A is:
(15 - 10)/(5.5 - 4.5) = 5/1 = 5
Rate of change of function B is:
-4.5 as the slope is the rate of change
Comparing the values:
5 > - 4.5
Function A has a greater rate of change
y A functionf (x) is graphed on the coordinate plane. 4 What is the function rule in slope-intercept form? 3 2 11 Enter your answer in the box. -5 -4 -3 -2 -1 1 2 3 4 5 f(x) = = -27 -3 Basic -5+ 7 8 9 -- X Y 22 0 X 4 5 6 х PO 1 2 3 < V + $ 0 % (0)
Answers
ANSWER
f(x) = -4x - 2
EXPLANATION
The slope-intercept form of the equation of a line is:
\(f(x)=mx+b\)Where m is the slope and b is the y-intercept.
The first thing we can get from the graph is the y-intercept - which is the point where the line crosses the y-axis:
The y-intercept is -2.
To find the slope we can select another point on the line and use the formula:
\(m=\frac{y_1-y_2}{x_1-x_2}\)The slope is:
\(m=\frac{2-(-2)}{-1-0}=\frac{2+2}{-1}=\frac{4}{-1}=-4\)So the equation of the line is:
\(f(x)=-4x-2\)
2x + 3y = 12
2x - y = 4
Answers
Answer:
The point of intersection between 2x+3y=12 and 2x-y=4 is (3,2)
Step-by-step explanation:
In exactly one year, how many mice would there be at school? EXPLAIN FULLY AND SHOW ALL WORK:Equation: Y=a(4)^xWhere:a is the initial value (when the generation = 0)x is the generation.
Answers
We know that each generation takes approximately 3 weeks, then, we can estimate how many generations we do have in one year, remember that one year has
\(1\text{ year }\approx52.14286\text{ weeks}\)Then, in one year we have
\(\frac{52.14286}{3}=17.383\text{ generations}\)In the real world, we can't have half of a generation or a decimal generation, then, let's approximate it to the nearest integer, in that case, 17 generations.
We have the expression that predicts the number of mice, then we can use that equation to find the result for 17 generations:
\(\begin{gathered} \text{ Initial Mice:} \\ f(x)=2\cdot4^x \end{gathered}\)Evaluate that at x = 17
\(\begin{gathered} \text{ Initial Mice} \\ f(x)=2\cdot4^x\Rightarrow f(17)=2\cdot4^{17}\Rightarrow3.44×10^{10} \end{gathered}\)With an offspring of
\(\begin{gathered} \text{ Offspring} \\ f(x)=6\cdot4^x\Rightarrow f(17)=6\cdot4^{17}=1.03×10^{11} \end{gathered}\)And the ending mice
\(\begin{gathered} \text{ Ending Mice} \\ f(x)=8\cdot4^x\Rightarrow f(17)=8\cdot4^{17}=1.37×10^{11} \end{gathered}\)Therefore, the final answer is
\(\text{ Ending mice = }1.37\times10^{11}\)The manufacturer of a fertilizer guarantees that, with the aid of the fertilizer, 80%
of planted seeds will germinate. Suppose the manufacturer is correct. If 9
seeds planted with the fertilizer are randomly selected, what is the probability that at least of them germinate? Carry your intermediate computations to at least four decimal places, and round your answer to at least two decimal places.
Answers
The probability that at least one seed germinates is approximately 0.9997 or 99.97%.
To find the probability that at least one seed germinates, we can use the complement rule. The complement of "at least one seed germinating" is "no seeds germinating."
The probability that a single seed does not germinate is 1 - 0.8 = 0.2 (since the manufacturer guarantees an 80% germination rate).
The probability that none of the 9 seeds germinate is (0.2)^9, as each seed has a 0.2 probability of not germinating.
Therefore, the probability that at least one seed germinates is 1 - (0.2)^9 = 0.9997472 (rounded to seven decimal places).
Thus, the probability that at least one seed germinates is approximately 0.9997, or 99.97% (rounded to two decimal places).
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the problem is the Spanish Club begins the school year with a $50 balance in its account. To raise money for activities during the school year, the club has bake sales every Friday after school. The table shows the club’s balance after the bake sale. Write an equation to represent the Spanish Club’s account balance after x weeks.
Answers
Answer:
use a chart to solve the question
Answer:
y=18x+50
Step-by-step explanation:
We can use a graph to solve this. Using y=mx+b, we can replace these variables with numbers.
First, we need to find the y-coordinate. This can be solved with 50 because they begin with $50. So we have y=mx+50
Next, we need to find the slope. We can make points by choosing random balances. I'll choose (2,86) and (4,122). We can find the slope through rise/run, and get 36/2, which would be 18. Now we can put this here. y=18x+50
And that is our answer! You can also use f(x) in place of y.
Dan bought a new computer for $900. Each year, the value of the computer decreased by 25% of the previous year's value. At this rate, what can Dan expect the approximate value of the computer to be after 8 years?
Answers
Answer:
$90
Step-by-step explanation:
Given data
Price= $900
Rate= 25%
Time= 8 years
Let us apply the compounding formula
A= P(1-r)^t >>>>note that the negative sign is because of the depreciation
substitute
A= 900(1-0.25)^8
A= 900(0.75)^8
A= 900*0.100
A= $90
Hence the value of the car after 8 years will be $90
A wine taster claims that she can distinguish four vintages of a particular Caber- net. What is the probability that she can do this by merely guessing
Answers
Given that a wine taster claims that she can distinguish four vintages of a particular Cabernet. A vintage is a term used for the year a wine was produced in the context of wine. In simpler terms, the year in which the grapes were grown is known as a vintage.
The wine taster claims that she can distinguish four vintages of a particular Cabernet. What is the probability that she can do this by merely guessing?
Answer: Given that a wine taster claims that she can distinguish four vintages of a particular Cabernet. A vintage is a term used for the year a wine was produced in the context of wine. In simpler terms, the year in which the grapes were grown is known as a vintage. These grapes are then processed, fermented, and aged in oak barrels to produce wine. Each vintage year has a distinct taste profile that distinguishes it from others. The Cabernet Sauvignon is a red wine grape variety that is known for producing red wine. The wine taster claims that she can distinguish four vintages of a particular Cabernet. Since she has four distinct vintages of Cabernet to choose from, her probability of getting a correct guess on the first attempt is 1/4. The probability of guessing the correct vintage again is 1/4. Following the same logic, the probability of guessing the correct vintage four times in a row is 1/4 raised to the power of four.
P(A) = 1/4 × 1/4 × 1/4 × 1/4. Therefore, the probability of her guessing correctly on all four attempts is (1/4)4. Which is equal to 1/256. This means that if the wine taster were to guess on her own, her chances of correctly identifying all four vintages would be 1/256, or approximately 0.4 percent. If a wine taster is claiming that she can distinguish between four distinct vintages of Cabernet, we need to determine if it is possible for her to do so simply by guessing. A vintage is defined as the year in which grapes are harvested to make wine. In the context of wine, each vintage year has a unique flavor profile that distinguishes it from other vintages. Cabernet Sauvignon is a well-known red wine grape variety that is commonly used to make red wine.
The wine taster claims that she can distinguish four vintages of Cabernet, which means she has four choices to select from when tasting. The probability of the wine taster guessing the correct vintage on the first try is 1/4, since she has four distinct options to choose from. Similarly, the probability of the taster guessing the correct vintage a second time is also 1/4, and the same applies to the third and fourth times.The probability of the taster guessing the correct vintage all four times in a row is (1/4)4 or 1/256. This means that if the wine taster were to guess on her own, her chances of correctly identifying all four vintages would be 1/256, or approximately 0.4 percent. As a result, if the wine taster claims to have correctly identified all four vintages, it is unlikely that she did so by merely guessing.
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can someone help please
Answers
Answer:
1.6
Step-by-step explanation:
two people are in a boat that is capable of a maximum speed of 5 kilometers per hour in still water, and wish to cross a river 1 kilometer wide to a point directly across from their starting point. if the speed of the water in the river is 5 kilometers per hour, how much time is required for the crossing?
Answers
This is approximately 0.283 hours, or 17 minutes. Therefore, it will take the boat approximately 17 minutes to cross the river.
The key to solving this problem is to understand the concept of relative velocity. In this case, the boat's speed relative to the water is 5 km/hr, and the water's speed relative to the shore is also 5 km/hr. Therefore, the boat's speed relative to the shore is the vector sum of these two velocities, which is 0 km/hr. This means that the boat will not make any progress toward the other side of the river unless it angles its course slightly upstream.
To determine the angle required, we need to use trigonometry. Let θ be the angle the boat makes with the direction perpendicular to the river. Then sin θ = 5/5 = 1, so θ = 45 degrees. This means that the boat needs to head upstream at a 45-degree angle to make progress across the river.
Now we can use the Pythagorean theorem to find the distance the boat travels:
d = √(1² + 1²) = √(2) km
Since the boat's speed relative to the shore is 0 km/hr, the time required for the crossing is simply the distance divided by the boat's speed relative to the water:
t = d / 5 = √(2) / 5 hours
This is approximately 0.283 hours or 17 minutes. Therefore, it will take the boat approximately 17 minutes to cross the river.
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what is 12 times 1-10
Answers
The answer is 2.
Please see the attached picture
Hope it helps
Good luck on your assignment
Can anyone help me please
Answers
Answer:
noqijauaajajajajabbaababbaa
A bread recipe calls for 1/4 tsp of salt. How much salt is needed to make 6 loaves of bread?
Answers
Answer:
1 1/2 tsp
Step-by-step explanation:
Which of the following is true? 1) D 5
=P 5
=Q 5
2) D 50
=P 5
=Q 25
3) D 5
=P 50
=Q 2
4) D 50
=P 5
=Q 2
Answers
Out of the given options, the statement that is true is: D50 = P5 = Q25.Therefore, the correct option is 2) D50 = P5 = Q25.
Given below are the values of P, Q, and D. D refers to the number of days to make a product, P is the number of people required to make the product, and Q is the number of products that can be made.
D5 = P50 = Q2
D50 = P5 = Q25
As per the problem statement, we need to determine which of the given statements is true.
Therefore, on comparing all the given values of P, Q, and D we can observe that the only statement that is true is
"D50 = P5 = Q25" as it satisfies the given values of P, Q, and D for producing the product.
Therefore, the correct option is 2) D50 = P5 = Q25.
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Which function is the inverse of f Superscript negative 1 Baseline (x) = negative one-half x minus three-halves? f Superscript negative 1 Baseline (x) = one-half x minus three-halves g
Answers
The inverse function of\(f^{(-1)}(x) = (1/2)x - 3/2 is g(x) = 2x + 3\)
To find the inverse of a function, we typically swap the roles of the independent variable (x) and the dependent variable (y) and solve for y. In this case, we have\(f^{(-1)}(x) = (1/2)x - 3/2.\)
Let's follow the steps to find the inverse function:
Step 1: Swap x and y:
x = (1/2)y - 3/2
Step 2: Solve for y:
x + 3/2 = (1/2)y
2x + 3 = y
So, the inverse function g(x) is g(x) = 2x + 3.
To verify if g(x) is the inverse of f^(-1)(x), we can compose the functions:
\(f^{(-1)}(g(x)) = f^{(-1)}(2x + 3)\)
Using the definition of f^(-1)(x), we substitute (2x + 3) for x:
\(f^{(-1)}(2x + 3) = (1/2)(2x + 3) - 3/2\)
= x + (3/2) - (3/2)
= x
As we can see, \(f^{(-1)}(g(x))\) simplifies to x, which confirms that g(x) = 2x + 3 is indeed the inverse function of f^(-1)(x) = (1/2)x - 3/2.
In summary, the inverse function of \(f^{(-1)}(x) = (1/2)x - 3/2\) is g(x) = 2x + 3.
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Answer:
It's f-1(x)= 1/2x-3/2
Step-by-step explanation:
Edge 2020.
b) Taxi fares cost 30% more at night.
How much does a $9 daytime journey cost at night?
Answers
2 school bags cost $ 276 . Find the cost of 88 school bags
Answers
Answer:12144
Step-by-step explanation:
Answer : FROM THE TOP, MAKE IT DROP THAT'S A WET!!! THAT'S A WET #WAP!!!
The slope of a line is -1/5, and the y-intercept is 5. What is the equation of the line written in general form?
x - 5y - 5 = 0
x - 5y - 25 = 0
x + 5y - 25 = 0
Answers
Answer:
x + 5y - 25 = 0
Step-by-step explanation:
Equation of line in slope intercept form is given as:
\(y = mx + b \\ \\ plug \: m = - \frac{1}{5} \: \: and \: \: b = 5 \\ \\ y = - \frac{1}{5} x + 5 \\ \\ 5y = - x + 25 \\ \\ x + 5y - 25 = 0\)
Answer:
x + 5y - 25 = 0
John is 15 years older than Karen. Two years
ago, John was two times as old as Karen. How
old is John?
Answers
Given point Y is between X and Z, where XY = 12 and XZ = 48, What is YZ?
Answers
Answer: 36
Step-by-step explanation:
XZ=XY+YZ
48=12+YZ
48-12=12-12+YZ
YZ=48-12
YZ=36
What is 5/8 - 3/16?
Answer choices:
Answers
Answer:
\( \frac{7}{16} \)
Step-by-step explanation:
In this kind of questions we use the following steps to find the answer:
\( \frac{5}{8} - \frac{3}{16} \)
Multiply first fraction by 2.\( \frac{10}{16} - \frac{3}{16} \)
Now we can write them as a single fraction.\( \frac{10 - 3}{16} = \frac{7}{16} \)
Is the answer to the question.
Answer:
C
Step-by-step explanation:
5/8 becomes 10/16 and then subtract that result from 17/16
Amber walks from her house to Claire then to Betsy how many blocks amber walk
Answers
Help please!! It’s due tomorrow!
Answers
Answer: 119°
Step-by-step explanation:
The two angles are alternate interior angles, meaning they're congruent. If you need help understanding that, just search alternate interior angles. The lines are parallel so it works.
Which statement best explains whether △ABC is similar to △DEF?
a. The triangles are similar because ∠B≅∠E.
b. The triangles are not similar because AB≠DE.
c. The triangles are similar because BCEF=ACDF.
d. There is not enough information to determine whether the triangles are similar.
Answers
The statement which best describes the similarity of the two triangles is; Choice D; There is not enough information to determine whether the triangles are similar.
Which statement best explains whether △ABC is similar to △DEF?The two triangles given in the task content are expected to be assessed to determine if they are similar.
From the concept of congruence in triangles, two triangles are congruent only if all 3 angle measures in one are similar to that in the other, or if the ratio of all corresponding pairs of sides are equal.
Hence, since neither of the conditions is satisfied by the information given, it follows that Choice D is correct.
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