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Recall that two terms are called like terms if they have the same variables with the same exponents, in simpler words, two terms are like terms if when adding them the result is a simplification of the sum.
Answer: 8 and 12, 1, and 15 are like terms.
Related Questions
Study the data given,Below are the weights of 6 randomly selectedblack bears and 6 randomly selected grizzly bearsliving on a wildlife refuge.Which type of bear had morevariation in weight?Black Bear Weights (lbs): 102, 151, 248, 342,453, 498A. Black BearsMean: 299MAD: 132B. Grizzly BearsC. Both showed the same amount ofvariation in weightHaven't learned this yet.Grizzly Bear Weights (lbs): 294, 302, 347, 422,553, 596Mean: 419MAD: 104 2/3
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The mean absolute deviation (MAD) is a statistical measure of how much the different data points "move away" from the mean of the data set. In this case the weights of the bears have been given, the mean has been calculated and the MAD is derived by deducting each data point from the mean. The MAD has been given already by the way. Some data points fall below the mean while some are above it. but whatever the difference is, you'll have to take the "absolute value" that is positive value only. For example, the mean weight of the black bears is 299, and the weight of the first black bear is 102, that gives you adifference of 197. note that the result should be negative 197 (-197) but we are interested in the absolute values only.
Same way you find the absolute deviation for the other data points and you have, 197, 148, 51, 43, 154, and 199. Sum up these numbers and divide by the number of observed data (number of black bears) and you have 792 divided by 6 which gives you 132. This means the mean absolute deviation of the observed data is 132 as compared to the mean which is 299.
If you compare the MAD of the black bears with that of the grizzly bears, you would see that the MAD of the grizzly bears is more varied, because 104 2/3 moves further away from 419 than the MAD of the black bears which is 132 moving away from 299.
2. Two baseball players were up to bat. Consider the parabolic paths of their two hits, represented in thegraph at right. One hit covers a horizontal distance of 4 feet and reaches a maximum height of 20 feet.The other hit covers a horizontal distance of 6 feet, but only reaches a maximum height of 9 feet.
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Explanation:
The equation of parabola can be founded using the following equation:
[tex]y=a(x-h)^2+k[/tex]Where the point (h, k) is the vertex. So, if the hit covers a horizontal distance of 4 feet and reaches a maximum height of 20 feet, we can say that the vertex will be located at (2, 20) because the maximum height of 20 ft is reached when the horizontal distance is half of the maximum horizontal distance 4 ft.
So, the equation for the first hit is:
[tex]undefined[/tex]Prove that these 3 equations are the same. There is more than one way to do this. Show in multipleways for a higher score.y = (x + 5)(x + 1)y = (x + 3)^2 - 4y = x^2 + 6x + 5
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For the first equation:
y = (x + 5)(x + 1)
apply distribution property:
y = (x + 5)(x) + (x + 5)(1)
y = x·x + 5·x + x·1 + 5·1
y = x² + 5x + x + 5
y = x² + 6x + 5
For the second equation:
y = (x + 3)² - 4
use the fact that (a + b)² = a² + 2ab + b², for the term (x + 3)², then, you have:
y = x² + 2·x·3 + 3² - 4
y = x² + 6x + 9 - 4
y = x² + 6x + 5
The third equation is already in the convenient form.
Then, you can notice that all three equations are the same equations.
Find each percent decrease. Rounf to thr nearest percent. The first one is done for you.From $60 to $40?
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So the 100% percent is equal to $60 and is decreasing $40 so is:
[tex]60-40=20[/tex]So is decreasing $20. now we can made a rule of 3 to finde the percentage so:
[tex]\begin{gathered} 60\to100 \\ 20\to x \end{gathered}[/tex]and the ecuation will be:
[tex]\begin{gathered} x=\frac{100\cdot20}{60} \\ x=33.33\approx33 \end{gathered}[/tex]So in total the decrese a 33%
I have a calculus question about linear approximation. It is a doozie. High school, 12th grade senior AP Calculus. Math, not physics.
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To get the linear approximation, we follow the equation below:
[tex]y=f(a)+f^{\prime}(a)(x-a)[/tex]where "a" is the given value of x and f'(a) is the slope of the function at a given value of "a".
In the given equation, the given value of "a" or x is 5.
Let's now solve for the linear approximation. Here are the steps:
1. Solve for f(a) by replacing the x-variable in the given function with 5.
[tex]f(5)=5^5[/tex][tex]f(a)=3125[/tex]The value of f(a) is 3125.
2. Solve for the first derivative of f(x) using the power rule.
[tex]f(x)=x^5\Rightarrow f^{\prime}(x)=5x^4[/tex]The first derivative is equal to 5x⁴.
3. Replace the "x" variable in the first derivative with 5 and solve.
[tex]f^{\prime}(5)=5(5)^4[/tex][tex]f^{\prime}(5)=5(625)[/tex][tex]f^{\prime}(5)=3125[/tex]The value of the first derivative at x = 5 is also 3,125.
4. Using the linear approximation formula above, let's now replace f(a) with 3125 and f'(a) with 3125 as well since those are the calculated value in steps 1 and 3. Replace "a' with 5 too.
[tex]y=3125+3125(x-5)[/tex][tex]y=3125+3125(x-5)[/tex]5. Simplify the equation above.
[tex]y=3125+3125x-15625[/tex][tex]y=3125x-12500[/tex]Hence, the equation of the tangent line to f(x) at x = 5 is y = 3,125x - 12500 where the slope m is 3,125 and the y-intercept b is -12,500.
Now, to find our approximation for 4.7⁵, replace the "x" variable in the equation of the tangent line with 4.7 and solve.
[tex]y=3,125x-12,500[/tex][tex]y=3,125(4.7)-12,500[/tex][tex]y=14,687.5-12,500[/tex][tex]y=2187.5[/tex]
Using the approximated linear equation, the approximated value of 4.7^5 is 2, 187.5.
Complex numbers are used to describe current. I voltage, E, and impedance, Z. These three quantities are related by the equation E = IZ. Given two ofthese quantities, solve the equation E = IZ for the missing variable.I = 4 + 4i, Z= 7+3iE=(Simplify your answer. Type your answer in the form a+b/. Use integers or fractions for any numbers in the expression.)
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We have the following equation to solve
[tex]E=I\cdot Z[/tex]Where E, I, and Z are complex numbers, therefore let's put it in numbers
[tex]E=(4+4i)(7+3i)[/tex]We can solve it directly into the rectangular form by doing the distrutive
Then
[tex](4+4i)(7+3i)=28+12i+28i+12i^2[/tex]Remember that
[tex]i^2=-1[/tex]Then
[tex]\begin{gathered} (4+4\imaginaryI)(7+3\imaginaryI)=28+12i+28i-12 \\ \\ (4+4\imaginaryI)(7+3\imaginaryI)=16+40i \end{gathered}[/tex]Now we have completely solved the problem!
[tex]E=16+40i[/tex]______________________
The second solution (usual)
When we have real engineering problems, we like to do multiplication and division with the polar form, then let's convert Z and I to the polar form
[tex]\begin{gathered} I=4+4i=4\sqrt{2}\angle45° \\ \\ Z=7+3i=\sqrt{58}\angle23.2° \end{gathered}[/tex]Now to do the multiplication we multiple the magnitude and sum the phases (angles)
[tex]\begin{gathered} ZI=4\sqrt{2}\cdot\sqrt{58}\angle45°+23.2° \\ \\ ZI=4\sqrt{116}\operatorname{\angle}68.2° \end{gathered}[/tex]We already have the result, now just put it in the rectangular form
[tex]\begin{gathered} ZI=4\sqrt{116}\cdot\cos(68.2)+i4\sqrt{116}\sin(68.2) \\ \\ E=16+40i \end{gathered}[/tex]Use the point-slope formula to write an equation of the line that passes through 4, 2 and 6,5.Write the answer in slope-intercept form (if possible).
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In this case, we'll have to carry out several steps to find the solution.
Step 01:
data:
point 01 (4 , 2)
point 02 (6 , 5)
Step 02:
equation of the line:
slope:
[tex]m=\frac{y2-y1}{x2-x1}=\frac{5-2}{6-4}=\frac{3}{2}[/tex]Point-slope form of the line
(y - y1) = m (x - x1)
[tex]\begin{gathered} (y-2)=\frac{3}{2}(x-4) \\ \\ (y-2)=\frac{3}{2}x\text{ -}\frac{12}{2} \\ \\ y-2=\frac{3}{2}x-6 \\ \\ y=\frac{3}{2}x-6+2 \\ \\ y=\frac{3}{2}x-4 \end{gathered}[/tex]The answer is:
y = 3/2 x - 4
Construct a truth table of the following statement. Jack will not play or Chris is hurtUse the symbolic representationp: Jack will playr: Chris is hurt
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ANSWER and EXPLANATION
We want to construct a truth table for the following statement:
Jack will not play or Chris is hurt
where p: Jack will play; r: Chris is hurt
"Jack will not play" will be represented by -p.
This implies that "Jack will not play or Chris is hurt" will be represented by - p v r.
Let us now construct the truth table:
That is the truth table for the statement.
I don't understandDescribe in words and by using function notation
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f(x) = 2(x +3)^2 + 1
1. Scale f(x) by 1/2 ==> (1/2) f(x) = (x + 3)^2 + 1
2. Reflect f(x) through x axis ==> -(x+3)^2 + 1
3. Shirt f(x) to the right by 5 units ==> -(x + 3)^2 - 4
4. Shift f(x) down by 5 units ==> -(x - 2) - 4 = g(x)
-14x > -3 all I have to do is simplify it
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The first step in simplifying the inequality is to divide both sides by -14:
[tex]\frac{1}{-14}\times-14x>-3\times\frac{1}{-14}[/tex]Since we are dividing both sides by a negative number, the inequality reverses direction, and hence it becomes
[tex]\textcolor{#FF7968}{x<\frac{3}{14}}\text{\textcolor{#FF7968}{.}}[/tex]This is the farthest we can go in simplifying the inequality; therefore, the above inequality is our answer
The engine in a airplane has a power curve approximated by x2 270 y = + 14 15000 44 where I is the RPin and y is the horsepower generated. - At what RPM is the engine putting out maximum horsepower?. Round your answer to three decimal places. RPM What is the maximum horsepower? Round your answer to three decimal places.
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A)For this question, we will use the first and second derivative criteria. First, we compute the first and second derivative of the given function:
[tex]\begin{gathered} \frac{dy}{dx}=-\frac{2x}{15000}+\frac{27}{44} \\ \frac{d^{2}y}{dx^{2}}=-\frac{2}{15000} \end{gathered}[/tex]Setting the first derivative equal to zero and solving for x we get:
[tex]\begin{gathered} -\frac{2x}{15000}+\frac{27}{44}=0 \\ \frac{2x}{15000}=\frac{27}{44} \\ x=\frac{27(15000)}{44(2)}=4602.273 \end{gathered}[/tex]Evaluating the first second derivative at x=4602.273 we get a negative number, therefore the function has a maximum value at x=4602.273. At 4602.273 RPM the engine puts out its maximum horsepower.
B) Now, to compute the maximum horsepower we evaluate the given function at x=4602.273:
[tex]\begin{gathered} y=-\frac{(4602.273)^{2}}{15000}+\frac{27}{44}(4602.273)-14 \\ y=1398.061 \end{gathered}[/tex]Therefore, the maximum horsepower is 1398.061.
Determine whether the ordered pair is a solution of linear equation.Y = x - 1/2, ( -5, -2 ) A- yes it is a solution B- no it is not a solution
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The ordered pair is (- 5, - 2)
This means that when x = - 5, y = - 2
To determine if the ordered pair is a solution of the linear equation, We would substitute the values into the equation. If we substitute x = - 5 into the equation and y gives us - 2, then it is a solution.
Therefore,
y = - 5 - 1/2 = - 5 - 0.5
y = - 5.5
Since it is not - 2, then the answer is B
B- no it is not a solution
ed pai
Solve for xx and graph the solution on the number line below. If possible, resolve your answer to a single inequality. In case of no solution (∅), leave the number line blank.45≥4x+5 and 53>4x+5
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Expression given:
[tex]45\ge4x+5[/tex][tex]53>4x+5[/tex]Procedure:
• Solving for ,x ,in first inequality
[tex]-4x\ge-45+5[/tex][tex]-4x\ge-40[/tex][tex]x\le\frac{-40}{-4}[/tex][tex]x\le10[/tex]• Solving for ,x ,in second inequality
[tex]-4x>-53+5[/tex][tex]x<\frac{-48}{-4}[/tex][tex]x<12[/tex]Thus, the graph would be:
If the solution is for both inequalities, then the answer is in which both are included:
[tex]x\le10[/tex]this composed figure is made up of three similar shapes what is the area of the figure
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Given data:
The given figure is shown.
The area of the composite figure is,
[tex]\begin{gathered} A=(10\text{ cm)}\times(5\text{ cm)+}(3\text{ cm)(6 cm)+}\frac{1}{2}(3\text{ cm)(4 cm)} \\ =50cm^2+18cm^2+6cm^2 \\ =74cm^2 \end{gathered}[/tex]Thus, the area of the composite figure is 74 square-cm.
Vector performed an experiment at a local farm to determine if the addition of bananas to his biomass cow menure recipe helps produce more or less energy. Me collected random samples of menure and benenes from the farm, prepared 15 bottles each of both matures, and placed oballeen on top of each bottle. Alter two weeks, he measured the circumference of each balloon in centimeters: the bigger the balloon grew, the more energy that was produced. The results of the experiment are displayed in the box plots below. Which description most accurately summarizes the sample results? 10. 11. 13. 13. 14. 15. 15. 15. 18. 18. 19 20. 22. 25. 26 22.22.26 29 30 31 36. 36 38. 39. 43 46. 46. 49. 50 MORE CONSISTENT LESS S OUT THE Autor behind ONE CON nece MORE
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Notice the smaller range and values of the experiment with cow manure (smaller box diagram and also located at smaller values of total energy.
The banana mixture clearly generates a wider box diagram (so less consistent) and also located at higher values (to the right).
Therefore, the answer we choose is the last one (bottom right) that says that the cow manure data is more consistent than the other one, and also, since the mashed banana data is so much higher, combined with the previous will clearly give larger amounts of biogas.
Please select the bottom right option.
If x+4 is a factor of this polynomial, what is the value of a ?
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Answer: -86
Given:
[tex]P(x)=2x^3-11x^2+ax-40[/tex]If we consider x+4 as a factor of the given polynomial, this would mean that x=-4. For an x- value to be a factor of a polynomial, P(x) must be equal to 0. With that, we will have:
[tex]\begin{gathered} P(-4)=0 \\ P(-4)=2x^3-11x^2+ax-40 \\ 0=2(-4)^3-11(-4)^2+a(-4)-40 \\ 0=-128-176-4a-40 \\ 4a=-128-176-40 \\ 4a=-344 \\ a=-86 \end{gathered}[/tex]Therefore, the answer is -86
find f^-1(f(x)) for f(x)=(x-3)/2
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After solving the given equation for f(x) the resultant answer is f(x)=1.
What are equations?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation. As in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others. The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.So, find f(x):
When f^-1(f(x)) in f(x)=(x-3)/2.Now, calculate as follows:
f(x)=(x-3)/2f(x)=(f⁻¹-3)/2f(x)=(1/f - 3)/2f(x)=(1 -3f/f)/2f(x)=(1-3)/2f(x)=2/2f(x) = 1Therefore, after solving the given equation for f(x) the resultant answer is f(x)=1.
Know more about equations here:
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Consider the following functions.Step 3 of 4: Find (f g)(-1). Simplify your answer.Answerf(x) = x² + 6 and g(x) = -x +5(-2)-1)=
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Solving for (f•g)(-1)
[tex]\begin{gathered} (f\cdot g)(x)=f(x)\cdot g(x) \\ (f\cdot g)(x)=(x^2+6)\cdot(-x+5) \\ (f\operatorname{\cdot}g)(-1)=((-1)^2+6)\operatorname{\cdot}(-(-1)+5) \\ (f\operatorname{\cdot}g)(-1)=(1+6)\cdot(1+5) \\ (f\operatorname{\cdot}g)(-1)=7\cdot6 \\ \\ \text{Therefore, }(f\operatorname{\cdot}g)(-1)=42 \end{gathered}[/tex]Please give me the correct answer.True or false.If a =b, then a +c = b+c.
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Answer
a = b
a + c = b + c (Addition Property of Equality)
This operation is True.
Explanation
If we are told that
a = b
Adding the same number to both sides of an equation is called the Addition Property of Equality.
And it produces the same number on both sides after this operation.
a = b
Add c to both sides
a = b
a + c = b + c (Addition Property of Equality)
This operation is True.
Hope this Helps!!!
please help due in 5 minutes would mean a lot
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Answer:
150 degrees
Explanation:
Given: m∠8=150 degrees
Angles 8 and 5 are vertically opposite angles.
Vertical angles are equal, therefore:
[tex]\begin{gathered} m\angle5=m\angle8 \\ m\angle5=150\degree \end{gathered}[/tex]Next, angles 1 and 5 are corresponding angles.
Corresponding angles are equal, therefore:
[tex]\begin{gathered} m\angle1=m\angle5 \\ m\angle1=150\degree \end{gathered}[/tex]The measure of angle 1 is 150 degrees.
Given that tan A= 5/12 and tan B= -4/3 such that A is an acute angle and B is an obtuse angle find the value of,a) tan (A-45°)b) tan (B+360°)
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Solve for tan(A-45°).
Recall that tan(45°) = 1
[tex]\begin{gathered} \tan (A-45\degree)=\frac{\tan A-\tan B}{1+\tan A\tan B} \\ \tan (A-45\degree)=\frac{\frac{5}{12}-1}{1+(\frac{5}{12})(1)} \\ \tan (A-45\degree)=\frac{-\frac{7}{12}}{1+\frac{5}{12}} \\ \tan (A-45\degree)=\frac{-\frac{7}{12}}{\frac{17}{12}} \\ \tan (A-45\degree)=-\frac{7}{17} \end{gathered}[/tex]Therefore, tan(A-45°) = -7/17.
Solve for tan(B+360°)
Recall that tan(360°) = 0
[tex]\begin{gathered} \tan (B+360\degree)=\frac{\tan A+\tan B}{1-\tan A\tan B} \\ \tan (B+360\degree)=\frac{\frac{5}{12}+0}{1-(\frac{5}{12})(0)} \\ \tan (B+360\degree)=\frac{\frac{5}{12}}{1-\frac{5}{12}} \\ \tan (B+360\degree)=\frac{\frac{5}{12}}{\frac{7}{12}} \\ \tan (B+360\degree)=\frac{5}{7} \end{gathered}[/tex]Therefore, tan(B+360°) = 5/7.
What is the difference between a rectangle and a rhombus?
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A rhombus is a two-dimensional shape and is also characterized as a special parallelogram. It has four equal sides, with the opposite angles being equal to each other, whereas its adjacent angles are supplementary.
A rectangle is a also two-dimensional shape. It has four equal angles and four vertices. All the four angles of a rectangle measure 90°.
Rhombuses and Rectangles have the following differences:
1) A rhombus has four equal sides while in a rectangle, the opposite sides are equal.
2) The diagonals of a rhombus bisect each other at 90° while the diagonals of a rectangle bisect each other at different angles.
2.A group of students in MATH 105 start a walking program. The chart below shows eachmember's self-reported walking time in minutes during May 2022.X-300A-325B-550C-400D - 900E-150F-60G-600H - 250By what percent did X exceed or fall below the mean? it’s number 2
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Given: 300, 400, 60, 325, 900, 600, 550, 150, 250
1st we find the mean or avaerage of all the numbers.
Mean:
[tex]\frac{300+400+60+325+900+600+550+150+250}{9}=\frac{3525}{9}\approx392.778[/tex]From here we can see that X=300 falls below the mean.
So we can use this formula:
[tex]\frac{mean-actual\text{ }value}{mean}*100\%\Rightarrow\frac{392.778-300}{392.778}*100\%\approx23.688\%[/tex]Answer: X falls below the mean by 23.688%
pls help with this. just the answer
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Answer:
Step-by-step explanation:
“y” should be the first step of the system.
It takes Jenny 8.4 minutes to sweep a porch.Mofor can sweep the same porch in 13.3minutes. If they worked together how longwould it take them?
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Rate of Jenny = 1/ 8.4 minutes
Rate of Mofor = 1/13.3 minutes
We know time and rate are inverses of each other.
So, if they work together, their rates would be:
[tex]\frac{1}{8.4}+\frac{1}{13.3}[/tex]The time they will take will be the inverse of this, thus:
[tex](\frac{1}{8.4}+\frac{1}{13.3})^{-1}[/tex]So, let's calculate it:
[tex]\begin{gathered} (\frac{1}{8.4}+\frac{1}{13.3})^{-1} \\ =5.1484 \end{gathered}[/tex]That is around 5.15 minutes.
Question 3X1127INXRewrite in simplest rational exponent form VxVx. Show each step of your process.
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Given
[tex]\sqrt[]{x}\cdot\sqrt[4]{x}[/tex]So, we have that
[tex]\begin{gathered} \sqrt[]{x}=x^{\frac{1}{2}} \\ \sqrt[4]{x}=x^{\frac{1}{4}} \end{gathered}[/tex]Therefore, the expression given is
[tex]x^{\frac{1}{2}}\cdot x^{\frac{1}{4}}[/tex]Apply the laws of exponents
[tex]x^{\frac{1}{2}+\frac{1}{4}}=x^{\frac{3}{4}}[/tex]Answer:
[tex]x^{\frac{3}{4}}[/tex]Which symbol is used to represent Integer Numbers?1. Z2. W3. Q4. N
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Answer: Letter Z.
The notation Z for the set of integers comes from the German word Zahlen, which means "numbers". Integers strictly larger than zero are positive integers and integers strictly less than zero are negative integers.
Find the percent of change and classify as a percent increase or decrease. Round to the nearest tenth of a percent when necessary. A $39 watch is now on clearance for $17.50.
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The percent of increase or decrease = change/original x 100%
Since the original price of the watch is $39
Since its price now is $17.50, then
The change of the price = 39 - 17.50 = 21.50 dollars
The percentage of decrease = 21.50/39 x 100%
The percentage of decrease = 55.1282
Round it to the nearest tenth
The percentage of decrease is 55.1%
pol: Practice & Problem Solving 2.PS-22 Question Help Three sisters are saving for a special trip. The ratio of Helga's savings to Maurice's savings is 8:3 and the ratio of Maurice's savings to Nora's savings is 3:4. Together all 3 sisters have saved $60. How much has each girl saved? Answer questions 3–4. IS 4 squares long. Then, use the diagrams to show $60. (Type whole numbers.) 4. Complete the table. Helga's savings Maurice's savings Nora's savings $8 $ $24 $32 $ $6 $ $ 12 $4 $ $ $16 + Vi 1 1,0 More Enter your answer in the edit fields and then click Check Answer. 1 pant Clear All Check Answer remaining
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Answer:
Explanation:
We know that the ratio of Helga's savings to Maurice's savings is 8:3 and the ratio of Maurice's savings to Nora's savings is 3:4.
It means that if Helga has $8, Maurice has $3 and Nora has $4
In the same way, we can multiply one quantity by 2, and all the quantities will be multiplied by 2, so if Helga has $16, Maurice has $6 and Nora has $8
Because:
$8 x 2 = $16
$3 x 2 = $6
$4 x 2 = $8
So, following the same logic, we can complete the table as:
Therefore, the complete table is:
please help me please please please please please please please please please please please please please please
Answers
EXPLANATION
The Area of a square shape is:
Area= side*side = s^2
If we have that:
Area = 121 yd^2, then:
121=s^2
Isolating s:
[tex]s=\sqrt[]{121}=11\text{ ---> The answer is 11}[/tex]