Answer:
D) 140
Step-by-step explanation:
5% = 5/100
100/5 = 20
7 times 20 = 140
HELP PLEASE
18 miles= how many feet
_________feet
Answer:
18 miles= how many feet
____95,040_____feet
Step-by-step explanation:
happy to help ya:)
I WILL GIVE BRAINIEST, PLEASE HELP
Answer:
A = (1, 10)
B = (4,10)
C = (4, 14)
D = (1, 16)
Step-by-step explanation:
Okay, so first, we move, or translate the quadrilateral PQRS down -8 spaces on the graph, turning old points:
P (1, -2) = (1, -10) Q (4, -2) = (4, - 10) S (1, -8) = (1, -16) and R (4, -6) = (4, -14)
Now, we need to rotate this new box into -x, y. So our new points are:
(1, -10) = (-1, 10) (4, -10) = (-4, 10) (1, -16) = (-1, 16) and (4,-14) = (-4, 14)
Now we're reflecting off the y-axis, making our x change. So for our final points:
A(1, 10) B (4,10) D(1, 16) and C(4, 14)
Hope this helps! Please check my math and comment wether this worked or not! :)
Answer:
hi
Step-by-step explanation:
How do I find x in this question?
Answer:
x = 8
Step-by-step explanation:
By Basic Proportionality Theorem:
\( \frac{3}{x - 2} = \frac{x}{x + 8} \\ \\ x(x - 2) = 3(x + 8) \\ \\ {x}^{2} - 2x = 3x + 24 \\ \\ {x}^{2} - 2x - 3x - 24 = 0 \\ \\ {x}^{2} - 5x - 24 = 0 \\ \\ {x}^{2} - 8x + 3x - 24 = 0 \\ \\ x (x - 8) + 3(x - 8) = 0 \\ \\ (x - 8)(x + 3) = 0 \\ \\ x - 8 = 0 \: \: or \: \: x + 3 = 0 \\ \\ x = 8 \: \: or \: \: x = - 3 \\ \\ \because \: length \: can \: not \: be \: - ve \\ \\ \implies \: x \neq - 3 \\ \\ \implies \: x = 8\)
Joe bought a cylindrical water tank for his garden, but he forgot to ask the seller what the diameter of the tank was. He needs to know the diameter of the tank so that he can build a platform for it to sit on. The seller told him the Volume and the height, calculate the diameter of the tank using the information below. The volume of the tank is 300π 〖ft〗^3 and its height is 10ft.
Answer:
1.7ft
Step-by-step explanation:
Given data
Volume of tank= 300π 〖ft〗^3
Height of tank= 10ft
The expression for the volume of a cylinder is given as
Volume= πr^2h
Substitute
300π = π *r^2*10
300= r^2*100
3= r^2
r= √3
r= 1.7 ft
Hence the radius of the cylinder is 1.7ft
What is the equation of the line with slope 3 through the point (5, 1) in point-slope form?
y-5=3(x-1)
y-1=3(x-5)
y=3x-14
y=3x+2
In AHIJ, ZH ZJ, JH = 10 and IJ = 14. Find the length of HI?
Answer:Its 1.3
Step-by-step explanation:
I took the test
what is the explicit rule for the nth term of the geometric sequence? 5, 20, 80, 320, 1,280, …
To determine the explicit rule for the nth term of the given geometric sequence 5, 20, 80, 320, 1,280, ..., use the formula:`an = a1 * r^(n - 1)`, where an represents the nth term of the sequence.`a1`represents the first term of the sequence.`r` represents the common ratio between terms of the sequence.
The given sequence is 5, 20, 80, 320, 1,280, ...Let's now apply the formula to find the explicit rule for the nth term of the given sequence.`an = a1 * r^(n - 1)`Where a1 = 5 (first term of the sequence)`r` can be found by dividing any term by the preceding term, as `r = (second term) / (first term)`In this case,`r = (20) / (5) = 4`
Substituting the values in the formula:`an = a1 * r^(n - 1)``an = 5 * 4^(n - 1)` Therefore, the explicit rule for the nth term of the given geometric sequence is `an = 5 * 4^(n - 1)`.You can use this formula to find the value of any term in the sequence, given its position (n) in the sequence.For example, to find the 150th term of the sequence, substitute n = 150 in the formula: `a150 = 5 * 4^(150 - 1)`. This simplifies to `a150 = 1.442 x 10^90`.
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PLZ HELP MEEE!!!
Sheila has sketched a net for a cylinder as shown below.
What is the closest to the total surface area of her cylinder?
A. 141 in2
B. 68 in2
C. 198 in2
D. 297 in2
Do number 12 pleasee
Answer:
114
Step-by-step explanation:
25% = 25/100 = 0.25
152 × 0.25 = 38
152 - 38 = 114
Answer:
$114
Step-by-step explanation:
152x0.75 = 114
Thomas has 12 more marbles than twice the number of marbles Andrew has. Andrew has x marbles. Which expression represents how many marbles Thomas has?
Answer:
2x + 12
Step-by-step explanation:
Let
x = number of marbles Andrew has
Number of marbles Thomas has = 2x + 12
The expression which represents number of marbles Thomas has = 2x + 12
If Andrew has 2 marbles, that is, x = 2
Then, 2x + 12 = 2(2) + 12
= 4 + 12 = 16
Thomas = 16 marbles
the face of a clock is divided into 12 equal parts. the radius of the clock face is 6 inches. assume the hands of the clock will form a central angle.the face of a clock is divided into 12 equal parts.which statements about the clock are accurate? check all that apply.
The clock's minute hand is longer than the hour hand.
We know that the face of a clock is divided into 12 equal parts, and the radius of the clock face is 6 inches. We also know that the hands of the clock will form a central angle. The accurate statements about the clock are:
The length of each hour's section is π inches, or 3.14 inches.
The central angle of each hour section is 30°.
The clock's minute hand is longer than the hour hand.
Since there are 12 divisions, 360°/12 = 30°. Therefore, the central angle of each hour section is 30°.
The length of each hour's section can be calculated as the circumference of the clock face (2πr) divided by 12. Therefore, the length of each hour's section is (2π × 6)/12 = π inches, or approximately 3.14 inches.
The clock's minute hand is longer than the hour hand because it needs to travel a greater distance in the same amount of time.
The minute hand travels 360° in 60 minutes, while the hour hand travels 360° in 12 hours. Therefore, the minute hand must be longer to cover more distance in the same amount of time.
Therefore, the accurate statements about the clock are:
The length of each hour's section is π inches, or 3.14 inches.
The central angle of each hour section is 30°.
The clock's minute hand is longer than the hour hand.
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6.+in+a+survey+conducted+on+an+srs+of+200+american+adults,+72%+of+them+said+they+believed+in+aliens.+give+a+95%+confidence+interval+for+percent+of+american+adults+who+believe+in+aliens.
We can conclude that we are 95% confident that the true proportion of American adults who believe in aliens lies between 0.63 and 0.81 is the answer.
In a survey conducted on an SRS of 200 American adults, 72% of them said they believed in aliens. We have to provide a 95% confidence interval for the percent of American adults who believe in aliens. A confidence interval is a range of values that estimates a population parameter with a specific level of confidence.
The formula for a confidence interval for a population proportion is: p ± zα/2 × √((p(1-p))/n) where, p is the sample proportion, zα/2 is the z-value for the level of confidence, and n is the sample size.
Here, p = 0.72, n = 200, α = 1 - 0.95 = 0.05/2 = 0.025 (for a 95% confidence interval), and zα/2 = 1.96 (from the z-table).
Now, let's plug in the values: p ± zα/2 × √((p(1-p))/n) = 0.72 ± 1.96 × √((0.72(1 - 0.72))/200)= 0.72 ± 0.0894
Thus, the 95% confidence interval for the percent of American adults who believe in aliens is (0.63, 0.81).
Therefore, we can conclude that we are 95% confident that the true proportion of American adults who believe in aliens lies between 0.63 and 0.81.
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The function f(x) = x^3 is transformed to f(x) = 4x^3. Which statement describes the graph of the transformed function?
A. The graph was translated up by 4 units.
B. The graph was stretched horizontally by a factor of 4.
C. The graph was translated down by 4 units.
D. The graph was stretched vertically by a factor of 4.
Answer: Option D.
Step-by-step explanation:
The translation is defined as
\(g(x)=kf(x)\)
Where, k is stretch factor.
If 0<k<1, then the graph compressed vertically by factor k and if k>1, then the graph stretch vertically by factor k.
It is given that,
\(f(x)=x^3\)
After transformation the function becomes
\(f(x)=4x^3\)
here, k=4>1, so the graph was stretched vertically by a factor of 4.
Therefore, the correct option is D.
determine whether the relation defines y as a function of x. Guve the domain.
Answer
Explanation
Given:
\(y=-\frac{5}{x}\)To determine whether the relation defines y as a function of x, we get the domain first.
Based on the given relation, when we plug in x=0, the value would be undefined. So the function domain is x<0 or x>0.
Hence, the interval notation is:
\((-\infty,0)\cup(0,-\infty)\)We can use vertical line test to determine if it is a function as shown in the graph below:
As we can see, there's only one point of intersection so the relation defines y as a function of x. Therefore, the answer is:
Function; domain
\((-\infty,0)\cup(0,-\infty)\)How to solve 3(x+3)=27
Answer:
x=6
Step-by-step explanation:
Basically you want to isolate x into a form x=... so you have to work your way backwards.
First, notice that there is an expression (x+3) that is multiplied by 3. Let's undo that. If we remove the 3, then the right hand side will also have to change. In fact, we can divide both sides by 3.
You then get (x+3) = 9.
Now, let's subtract 3 from both sides:
x+3 -3 = 9 -3
Which simplifies to x = 6.
So with the operations "divide left and right by the same" and "subtract the same left and right", you can simplify most equations.
Step-by-step explanation:
solving an equation is like finding out for a balance, why the contents of the 2 cups weigh the same.
to take away (or add) piece by piece the same weight from both sides to keep the balance, until you find the originally not obvious reason for the balance.
in our case e look for the value of x. everything else we know.
so, we try to sort between the types of terms (the ones with variables, the ones without variables, then maybe different variables if applicable and so on).
but we have to do it by keeping the balance.
so everything we change on one side, we also have change on the other.
3(x + 3) = 27
we could do now 2 different things.
we could multiply the bracket term and then see how to continue.
or we could divide both sides by 3 to get rid of the obscuring multiplication factor of the bracket term with the variable.
we still keep the variable on one side.
so, I suggest we do the second thing.
3(x + 3) = 27 | /3 both sides
x + 3 = 9
now we still have constant terms on both side.
let's get rid of the constants on the variable side.
how ? well, we need to subtract 3.
x + 3 = 9 | -3 on both sides
x = 6
hey, and we are finished !
x = 6 made the balance happen.
132÷1716 show your work
We will investigate the process of division and express a fraction in its simplest form.
We are given the following operation of division to be performed:
\(132\text{ / 1716}\)We can express the above operation in a form of a fraction as follows:
\(\frac{132}{1716}\)Whenever we are looking at the simplification process we try to determine the divisibility of both numerator an denominator with a common integer.
We see that both numerator and denominator are divisible by integer ( 3 ). Hence, we can go ahead and write down the divisibility of both numerator and denominator by 3 in the fraction form:
\(\begin{gathered} \frac{132}{1716}=\frac{44}{572}\ldots\text{ Divisibility of ( 3 )} \\ \\ \frac{44}{572} \end{gathered}\)We see that both numerator and denominator are divisible by integer ( 11 ). Hence, we can go ahead and write down the divisibility of both numerator and denominator by 11 in the fraction form:
\(\begin{gathered} \frac{44}{572}\text{ = }\frac{4}{52}\ldots\text{ Divisibility of ( 11 )} \\ \\ \frac{4}{52} \end{gathered}\)Next we see that we can further perform the divisibility operation by dividing both numerator and denominator by ( 4 ) and express in fraction in its simplest form:
\(\begin{gathered} \frac{4}{52}\text{ = }\frac{1}{13}\ldots\text{ Divisibility of ( 4 ) } \\ \\ \frac{1}{13} \end{gathered}\)The above result is expressed in its most simplest form. This means the numerator and denominator can not be further divided or divisible by any common integer other than ( 1 ). Hence, we have arrived at the simplest answer to the division operation:
\(\frac{1}{13}\ldots Answer\)NEED HELP PLZ I BEG U
Answer:
12.5 ft
Step-by-step explanation:
Ratio of shadow to person =
4:5
Ratio of shadow to tree =
10:x
Form an equation
4/5 = 10/x
4x = 50
x = 12.5
Answer = 12.5 ft
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In the diagram below, angle f is congruent to angle i. Enter segments in the blanks provided that would result in a true equation.
The segments in the blank provided is GH/FH=IH/JH so that the equation is true
What are the 4 characteristics of similar triangles?Similar triangles differ in size but have the same form. Corresponding angles are identical in comparable triangles. Similar triangles have corresponding sides that have the same ratio. The ratio of the square of any two of their corresponding sides to any identical triangle's area is the same.
What are the 3 types of triangle similarity?The triangle similarity criteria are:
AA (Angle-Angle)
SSS (Side-Side-Side)
SAS (Side-Angle-Side)
In the given question
<GHP=<IHJ (vertically opposite angles)
<JIH=<HPG (alternate angles)
From AA similarity critera
triangles JHI ~ triangle GHP
Hence
GH/FH=IH/JH
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2x+y=3
Зу = 18 -6x
On a graph please
Find an equation of the circle that has center (-5,3) and passes through (0,-2)
Let’s find the equation of a circle with
radius r and center (-5,3)=(h,k) and that passes through (0,-2):
By definition, an equation of the circle with center (h,k) and radius r is:
\((x-h)^2\text{ }+\text{ (}y-k)^2\text{ = }r^2\)This is called the standard form for the equation of the circle. So, in our case we would have:
\((x+5)^2\text{ }+\text{ (}y-3)^2\text{ = }r^2\)Now, if we have the point (x,y) = (0,-2), we resolve the above equation for radius r. That is:
\((0+5)^2\text{ }+\text{ (-2}-3)^2\text{ = }r^2\)that is equivalent to say:
\((5)^2\text{ }+\text{ (-5})^2\text{ = }r^2\)that is equivalent to
\(25^{}\text{ }+\text{ 25}^{}\text{ = }r^2\)that is:
\(50^{}\text{ = }r^2\)so, replacing the radius previously found, as well as the center of the circle, in the canonical equation of the circle we obtain:
\(r\text{ = }\sqrt[]{50}\text{ = 5}\sqrt[]{2}\)replacing the radius previously found, as well as the center of the circle, in the canonical equation of the circle we obtain:
\((x+5)^2\text{ }+\text{ (}y-3)^2\text{ = 50}^2\text{ = 5}\sqrt[]{2}\)so, the correct equation for the circle is
\((x+5)^2\text{ }+\text{ (}y-3)^2\text{ = 50}^2\text{ }\)Given the equation \( \mathrm{y}=2 \cos 3(x-30)+1 \) has a maximum when \( \mathrm{x}=30 \) degrees. Explain how to find other values of \( x \) when the same maximum value occurs.
The other values of \(\( x \)\) when the same maximum value occurs when we add or subtract multiples of \(\(\frac{14\pi}{15}\)\) from the given value of \(\( x \)\).
Understanding the properties of the cosine function and how it relates to the given equation.
The cosine function oscillates between its maximum value of 1 and its minimum value of -1. The value of \(\(a\)\) in the equation \(\(y = a\cos(bx - c) + d\)\)determines the amplitude of the oscillation. In given equation, the coefficient 2 before \(\(\cos3(x - 30)\)\) indicates that the amplitude is 2.
The \(\(b\)\) value in the equation determines the period of the oscillation. The period, denoted as \(\(T\)\), is calculated using the formula
\(\(T = \frac{2\pi}{|b|}\).\)
In the equation,\(\(b = 3\)\), so the period of the cosine function is
\(\(T = \frac{2\pi}{3}\)\).
Given that the maximum occurs at\(\(x = 30\)\) degrees, the equation is of the form \(\(y = a\cos(bx)\)\). The maximum value of the cosine function is achieved when\(\(bx\)\) is a multiple of \(\(2\pi\)\).
When \(\(x = 30\)\), we have \(\(30b = 2\pi k\)\),
where \(k\) is an integer. Rearranging the equation,
\(\(b = \frac{2\pi k}{30}\).\)
Since \(\(b = 3\)\) , substitute it to solve for \(\(k\)\).
\(\(\frac{2\pi k}{30} = 3\)\)
Simplifying the equation, we get:
\(\(2\pi k = 90\)\)
Dividing both sides by \(\(2\pi\)\), we find:
\(\(k = \frac{90}{2\pi}\)\)
Approximating the value of \(\(\pi\) to 3.14\), we can calculate \(\(k\)\):
\(\(k = \frac{90}{2 \times 3.14} \approx 14.33\)\)
Since \(\(k\)\) must be an integer, the closest integer to 14.33 is 14. Therefore, when the same maximum value occurs, the value of \(\(x\)\)will be given by:
\(\(x = \frac{2\pi \times 14}{30}\)\)
Simplifying the equation:
\(\(x = \frac{28\pi}{30}\)\)
Reducing the fraction:
\(\(x = \frac{14\pi}{15}\)\)
So, when the same maximum value occurs, other values of \(\(x\)\) will be multiples of \(\(\frac{14\pi}{15}\)\).
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A full tub of water weighs 3 1/8 pounds. If the tub is filled up only 1/7 full how much would it weigh?
Answer:
\(\frac{25}{56}\) pounds
Step-by-step explanation:
By using unitary method,
∵ 1 full tub of water weighs = \(3\frac{1}{8}\) pounds
∴ \(\frac{1}{7}\) of a water tub will weigh = \(3\frac{1}{8}\times \frac{1}{7}\)
= \(\frac{(24+1)}{8}\times \frac{1}{7}\)
= \(\frac{25}{56}\) pounds
Therefore, water filled in \(\frac{1}{7}\)th part of the tub will weigh \(\frac{25}{56}\) pounds.
The weight of the tub if filled up to 1/7 full is 25/56 pounds
How to find product of fractionGiven:
Full weight of tub = 31/8 poundsIf filled halfway:
= 1/7 × 3 1/8
= 1/7 × 25/8
= (1 × 25) / (7 × 8)
= 25/56 pounds
Therefore, the weight of the tub if filled to 1/7 of the capacity is 25/56 pounds
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The International Air Transport Association surveys business travelers to develop quality ratings for transatlantic gateway airports. The maximum possible rating is 10. Suppose a simple random sample of 50 business travelers is selected and each traveler is asked to provide a rating for the Miami International Airport. The ratings obtained from the sample of 50 business travelers follow.
1 5 6 7 8 8 8 9 9 9 9 10 3 4 5 5 7 6 8 9 10 5 4 6 5 7 3 1 9 8 8 9 9 10 7 6 4 8 10 2 5 1 8 6 9 6 8 8 10 10
Develop a 95% confidence interval estimating of the population mean rating for Miami.
CI = 6.76 ± 1.96 × (2.67/√50)
CI = 6.76 ± 0.96
Therefore, the 95% confidence interval for the population means rating for Miami is: (5.80, 7.72)
We can be 95% confident that the true mean rating for Miami International Airport falls within this interval.
To develop a 95% confidence interval for the population means rating for Miami International Airport, we need to follow these steps:
1. Calculate the sample mean (x) by adding up all the ratings and dividing by the sample size (n=50).
2. Calculate the sample standard deviation (s).
3. Use a t-distribution to find the t-score for a 95% confidence interval with (n-1) degrees of freedom.
4. Calculate the margin of error (ME) using the t-score, standard deviation, and sample size.
5. Add and subtract the margin of error from the sample mean to find the lower and upper limits of the confidence interval.
To calculate the 95% confidence interval, we need to use the formula:
CI = x ± Z' (s/√n)
Where:
x = sample mean
Z' = z-score for the desired confidence level (in this case, 95%, so
Z' = 1.96)
s = sample standard deviation
n = sample size
Step 1: Calculate the sample mean (x)
Sum of ratings = 346
Sample size (n) = 50
x = 346/50 = 6.92
Step 2: Calculate the sample standard deviation (s)
Variance = [(Sum of (rating - x)^2) / (n-1)] = 88.48
Standard deviation (s) = √(88.48) = 9.41
Step 3: Find the t-score
For a 95% confidence interval with 49 (n-1) degrees of freedom, the t-score is approximately 2.01.
Step 4: Calculate the margin of error (ME)
ME = t-score × (s / √n) = 2.01 × (9.41 / √50) = 2.01 × 1.33 = 2.67
Step 5: Find the confidence interval
Lower limit: x - ME = 6.92 - 2.67 = 5.80
Upper limit: x + ME = 6.92 + 2.67 = 7.72
Thus, the 95% confidence interval for the population mean rating for Miami International Airport is approximately
(5.80, 7.72)
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Answer the question right for brainliest
Answer:
3 to the power 9 is the answer
Answer:
\( 3^9 \)
Step-by-step explanation:
\( 3^8 \times 3 = 3^8 \times 3^1 = 3^{8 + 1} = 3^9 \)
Find f such that f'(x) = 7/√x , f(9) = 54.
f (x) = ...
To find a function given its derivative and an initial condition, we integrate the derivative and solve for the constant using the given condition. Example: \(f(x) = 14\sqrt{x} + 12\) satisfies \(f'(x) = 7/ \sqrt{x}\) and f(9) = 54.
The function f(x) can be found by integrating f'(x) with respect to x. Given \(f'(x) = 7/\sqrt{x}\), we can integrate it to obtain \(f(x) = 14\sqrt{x} + C\) , where C is an arbitrary constant.
To determine the value of C, we use the initial condition f(9) = 54, which gives us:
\(54 = 14\sqrt{9} + C\)
54 = 42 + C
C = 12
Substituting C into the expression for f(x), we get the final solution:
\(f(x) = 14\sqrt{x} + 12\)
Therefore, the function f(x) that satisfies \(f'(x) = 7/\sqrt{x}\) and f(9) = 54 is \(f(x) = 14\sqrt{x} + 12.\)
In summary, we can find a function given its derivative and an initial condition by integrating the derivative and solving for the arbitrary constant using the given condition. In this case, we found the function \(f(x) = 14\sqrt{x} + 12\) that satisfies \(f'(x) = 7/\sqrt{x}\) and f(9) = 54.
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Lloyd's account has a balance of −$53.50. If he owes the bank more than $40, his account gets closed. Which of the following is true about Lloyd's account?
It stays open, because |−53.50| > 40
It gets closed, because |−53.50| < 40
It stays open, because |−53.50| < 40
It gets closed, because |−53.50| > 40
Answer:
It stays open,because |−53.50| > 40
Step-by-step explanation:
His account has 53.50 dollars, so he can still pay it off. Don't get confused about the fact that he has 53.50 dollars, not owes.
Hope this helps!
Have a great day!
Consider isosceles ΔXYZ.
Answer:
n = 3
XY = 39 ft
XZ = 39 ft
Step-by-step explanation:
If we rotate the triangle 90° to the right we can see that the congruent angles are now on the bottom, making it the "more commonly seen isosceles triangle" we know.
This means that the two legs will be congruent to each other, so we can set them equal and solve for n:
(9n + 12) = (15n - 6)
9n + 12 = 15n - 6
9n + 18 = 15n
18 = 6n
6n = 18
n = 3
Now we can plug this value of n (3) into one of the expressions to solve for the legs. Since they will be the same length we only need to do one, but I will do both to make sure my work is as correct as possible:
XY
9n + 12
9(3) + 12
27 + 12 = 39
XZ
15n - 6
15(3) - 6
45 - 6 = 39
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly.
- Heather
Mia wants to purchase a pair of jeans that cost $36. They are on sale for 20% off. What are two ways that Mia can find the cost of the jeans? Write your answers in the blanks. Mia can find the difference of 36 and of 36 or she can multiply 36 by
please help
Answer:
multiply 36 by .20 and subtract that from 36
Step-by-step explanation:
20% is the amount off. if you multiply .20 and subtract it you'll get $7.20 so 36-7.20 which is $28.80.
Answer:
28.80 is 36 dollars 20 percent off.
Step-by-step explanation:
take the original price
divide the original price by 5
alternatively, divide the original price by 100 and multiply it by 20
subtract this new number from the original one
the number you calculated is the discounted value.
more simple steps:
1. subtract the final price from the original price
2. divide this number by the original price
3. multiply the result by 100
other explanation: a 20 percent discount is 0.20 in decimal format. secondly, multiply the decimal discount by the price of the item to determine the savings in dollars. for example: if the original price of the item equals 24$, y I u would multiply 0.2 by 24$ to GET $4.80
hope this helps!
translate the english phrase into an algebraic expression: the quotient of the product of 6 and 6r, and the product of 8s and 4.
This algebraic expression represents the same mathematical relationship as the original English phrase.
To translate the English phrase "the quotient of the product of 6 and 6r, and the product of 8s and 4" into an algebraic expression, we need to first identify the mathematical operations involved and then convert them into symbols.
The phrase is asking us to divide the product of 6 and 6r by the product of 8s and 4. In mathematical terms, we can represent this as:
(6 × 6r) / (8s ×4)
Here, the symbol "*" represents multiplication, and "/" represents division. We multiply 6 and 6r to get the product of 6 and 6r, and we multiply 8s and 4 to get the product of 8s and 4. Finally, we divide the product of 6 and 6r by the product of 8s and 4 to get the quotient.
We can simplify this expression by dividing both the numerator and denominator by the greatest common factor, which in this case is 4. This gives us the simplified expression:
(3r / 2s)
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The English phrase "the quotient of the product of 6 and 6r, and the product of 8s and 4" can be translated into an algebraic expression as follows: (6 * 6r) / (8s * 4)
Let's break down the expression:
The product of 6 and 6r is represented by "6 * 6r" or simply "36r".The product of 8s and 4 is represented by "8s * 4" or "32s".Therefore, the complete expression becomes: 36r / 32s
In this expression, the product of 6 and 6r is calculated first, which is 36r. Then the product of 8s and 4 is calculated, which is 32s. Finally, the quotient of 36r and 32s is calculated by dividing 36r by 32s.
This expression represents the quotient of the product of 6 and 6r and the product of 8s and 4. It signifies that we divide the product of 6 and 6r by the product of 8s and 4.
In algebra, it is important to accurately represent verbal descriptions or phrases using appropriate mathematical symbols and operations. Translating English phrases into algebraic expressions allows us to manipulate and solve mathematical problems more effectively.
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Ms. Jackson bought a new car. It cost $9,360. She paid 10% As a down payment. How much was her down payment?
Answer:
$936
Step-by-step explanation:
10% is just divided by 10 so 9360 divided by 10 is 936