A sweater is on sale for
20% off the regular price.
The sale price is $60.
What is the regular price of the sweater?
Answer:
$48
Step-by-step explanation:
List price = $60.00
Discount = 20% .
Hence the new price is (100-20)% = 80% of original price .
=> price = $ 60* 80/100
=> price = $ 48
Is it possible to construct a triangle with side lengths of 11 cm, 15 cm, and 21 cm? Why or why not?
mr. renato had $150 in his bank account. he deposited $50. acuple of days later he withdrew $20. a week later he deposited $75 .the next week he withdrew $100. what is mr. Renato balance after all the transactions
What is the value of mc009-1.jpg?
–34
–2
10
34
the pic is the .jpg
The value of the expression -4²+(5-2)(-6) is -34 when following the standard rules of arithmetic.
Explanation:The value of the expression −4²+(5−2)(−6) can be determined by first calculating the power and then performing the operations inside the parentheses, followed by the multiplication and addition/subtraction.
The power of −4² is 16 because the negative sign is not inside the parentheses, so it is not squared, and 16 will be considered as a negative number here (-16).
Next, we calculate the value within the parentheses (5−2), which gives us 3.
Then we multiply 3 by −6, which equates to −18. Finally, we add the two results: −16 + (−18) = −16 −18 = −(16 + 18) = −(34), resulting in the value −34.
Don tracked the price of gas for several months. In January gas cost $2.65, in February the price had risen $0.56, in March decreased $0.23, in April risen $1.02, and in May decreased $0.48. By how many dollars has the price of gas changed from January to May?
The solution is, By $.87 dollars has the price of gas changed from January to May
What is Subtraction?Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.
here, we have,
given that,
Starting price is 2.65, increased by .56
2.65+.56=3.21
Price is 3.21, decreased by .23
3.21-.23=2.98
Price is 2.98, increased by 1.02
2.98+1.02= 4
Price is 4, decreased by .48
4-.48=3.52
Now find the difference from the starting price (January) from the end price (May)
3.52-2.65=.87
The difference from gas prices is $.87.
Hence, The solution is, By $.87 dollars has the price of gas changed from January to May.
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Carlos has 7 times as many red toy cars as blue toy cars. He has 56 total cars. How many more red cars does he have?
let x = blue cars
so 7x = red cars
x +7x = 56
8x = 56
x = 56/8 =7 blue cars
7*7 =49 red cars
49-7 =42 more red cars
You are enrolled in a wellness course at your college. You achieved grades of 70, 86, 81, and 83 on the first four exams. The fina exam counts the same as an exam given during the semester. A.) If x represents the grade on the final exam, write an expression that represents your course average (arithmetic mean). B.) If your average is greater than or equal to 80 and less than 90, you will earn a B in the course. Using the expression from part A for your course average, write a compound inequality that must be satisfied to earn a B.
The answer provides an expression for the course average and a compound inequality to earn a B in a wellness course.
Expression representing the course average: 1/5(70 + 86 + 81 + 83 + x)
Compound inequality for earning a B: 80 ≤ 1/5(70 + 86 + 81 + 83 + x) < 90
the GCF of the following numbers. 32 and 40
Which BEST describes the construction of a triangle if given one side length of 10 cm and one right angle?
A)
Unique triangle
B)
More than one triangle
C)
Triangle not possible
D)
Cannot be determined
Answer:
b
Step-by-step explanation:
Twenty different books are to be put on five book shelves, each of which holds at least twenty books.
Given that the volume decreases at a rate of 3 cubic meters per minute, find the rate of change of an edge, in meters per minute, of the cube when the volume is exactly 64 cubic meters
a homeowner has 200 feet of fence to enclose an area for a pet.
(a) if the area is given by A(x)=X(100-x), what dimension maximize the area inside the fence?
(b) what is the maximum area?
(c) determine the domain and range of A in this application.
(a) The function describes a parabola that opens downward. The value of A(x) is zero when x=0 and when x=100. The vertex (maximum) is halfway between those zeros, at x=50. The dimensions are 50 and 100-50 = 50. The maximum area pen will be 50 ft square.
(b) A(50) = (50 ft)² = 2500 ft² . . . the maximum area
(c) A(x) will be negative if x < 0 or x > 100, so the domain is 0 ≤ x ≤ 100.
The value of A(x) ranges from 0 to its maximum, 2500. Hence the range is 0 ≤ A(x) ≤ 2500.
For a rectangular fenced area, the dimensions that maximize the area are 50 feet by 50 feet, given a total of 200 feet of fence. The maximum possible area is 2500 square feet. The domain for this function is [0, 100] and the range is [0, 2500].
Explanation:This problem deals with maximizing an area given a certain length of fencing. It is a part of optimization problems often encountered in calculus. Firstly, we understand that a rectangle will give maximum area for a fixed perimeter. Considering a rectangle, the dimensions would be x and 100-x, where x is one of the sides of the rectangle.
(a) To find the dimension that maximizes the area, we first need to find the derivative A'(x) of A(x), which equals to -2x + 100. Setting A'(x) to zero gives us x = 50. That means the dimensions that will give us maximum area are 50 feet by 50 feet.
(b) Substituting x = 50 back into the original function, we find that the maximum area is A(50)=50(100-50)=50*50=2500 square feet.
(c) For the domain of A in this application, it would be all possible values of x. So, x could be any number from 0 to 100 (both inclusive). The range of A would be from 0 to the maximum value, 2500 square feet.
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The median for the given set of 6 ordered data values is 32.5.
9, 12, 25, _, 41, 48
What is the missing value?
A= P(1+nr) ; solve for r
Which of the following is the simplified form of the seventh root of x times the seventh root of x times the seventh root of x ?
ABCD is a trapezoid. = 2.5 cm, and = 4 cm, and the area = 6.5 cm2. What is the altitude of the trapezoid?
Answer:
Altitude of the trapezoid is 2 cm.
Step-by-step explanation:
ABCD is a trapezoid. Since two bases of the trapezoid are
B1 = 2.5 cm and B2 = 4 cm.
Area given is 6.5 cm²
Then we have to calculated he altitude of the trapezoid.
Now we know the formula of area of the trapezoid = [tex]\frac{1}{2}[/tex] ( Base1 + Base2)
By putting the values in the formula
6.5 = [tex]\frac{1}{2}[/tex] ( 2.5 + 4 ) × h
6.5 = [tex]\frac{6.5}{2}[/tex] × h
h = \frac{2\times 6.5}{6.5} = 2 cm.
Answer is altitude of the trapezoid is 2 cm.
Consider the following equation:
f′(a)=limh→0 (f(a+h)−f(a))/h
Let f(x)=3√x If a≠0, use the above formula to find f′(a)=
Show that f′(0) does not exist and that f has a vertical tangent line at (0,0)
Final answer:
To find the derivative of f(x) = 3√x at a nonzero point, use the definition of the derivative with limits. The derivative at x=0 does not exist because the function has an infinite slope at this point, demonstrated by the absence of a limit, signifying a vertical tangent line at (0,0).
Explanation:
To find f'(a) for f(x) = 3√x when a ≠ 0, we can use the given definition of the derivative:
f'(a) = limh→0 (f(a+h) – f(a)) / h.
To show that f'(0) does not exist and that f has a vertical tangent line at (0,0), we need to evaluate the limit as h tends to zero for the derivative definition applied at a = 0. Since the square root function is not differentiable at 0 (due to the function having an infinite slope at this point), the limit will not exist, indicating that the derivative at 0 does not exist, and the graph of f exhibits a vertical tangent at that point.
Bart bought a digital camera with a list price of $219 from an online store offering a 6 percent discount. He needs to pay $7.50 for shipping. What was Bart's total cost?
$205.86
$211.50
$213.36
Which of the following is a sample of the population of bookstores on the West Coast of the United States? I. All book stores in California II. Randomly selected children's book stores III. Internet book stores A. I only B. II only C. I and III D. III only E. I and II
Answer:
It would be I - All bookstores in California
Step-by-step explanation:
Internet book stores and random children's bookstores do not specify that they're on the West Coast and could be taken from anywhere
Distribution with a mean of 100 and standard deviation of 15...
What is the percentile score of
112?
82?
The percentile scores for a distribution with a mean of 100 and a standard deviation of 15, the z-scores for 112 and 82 are 0.8 and -1.2, respectively.
Calculating Percentile Scores
To determine percentile scores for the values given in the original student question, we need to calculate the z-scores for 112 and 82 from a distribution with a mean of 100 and a standard deviation of 15.
To find the z-score, use the formula:
Z = (X - mu) / sigma
Where X is the raw score, \\mu is the mean, and \\sigma is the standard deviation.
For 112:
Z = (112 - 100) / 15
Z = 12 / 15
Z = 0.8
For 82:
Z = (82 - 100) / 15
Z = -18 / 15
Z = -1.2
Once the z-scores are calculated, we can look up the corresponding percentiles in a standard normal distribution table.
A z-score of 0.8 corresponds to approximately the 78.81st percentile, meaning about 78.81% of the scores are below 112.
A z-score of -1.2 corresponds to approximately the 11.54th percentile, meaning about 11.54% of the scores are below 82.
Translate the phrase to mathematical language. Then simplify the expression.
Subtract 81 from −55.
What is a numerical expression for the phrase?__
(Do not simplify.)
Simplify the expression.__
Shelly used exactly 1/ 3 of a cup of oil and 3/ 8 of a cup of water in a recipe. How many cups of liquid did Shelly use in all?
Answer: =[tex]\dfrac{17}{24}[/tex]
Step-by-step explanation:
Given : The amount of oil is used in a recipe. = [tex]\dfrac{1}{3}[/tex]
The amount of water used in a recipe = [tex]\dfrac{3}{8}[/tex]
The total number of cups of liquid used by Shelly:-
[tex]\dfrac{1}{3}+\dfrac{3}{8}=\dfrac{8+3\times3}{24}\\\\\=\dfrac{8+9}{24}=\dfrac{17}{24}[/tex]
Hence, the total number of cups of liquid used in all =[tex]\dfrac{17}{24}[/tex]
The volume of this rectangular prism is 6x3. What does the coefficient 6 mean in terms of the problem?
A. The total volume of the prism is 6 cubic units.
B. The length is 6 times the width.
C. The width is 6 times the height and the length.
D. The length of the prism is 6 units.
Answer:
B. The length is 6 times the width
Step-by-step explanation:
The proper solution is choice B. The length is 6 times the width.
How do you resolve rectangular prisms?
To find the quantity of a rectangular prism, multiply its 3 dimensions: duration x width x height. The volume is expressed in cubic gadgets.
What are examples of square prisms?Right rectangular prisms or cuboids are all around us. a few examples are books, packing containers, homes, bricks, forums, doorways, containers, cabinets, mobiles, and laptops.
What does the coefficient mean?Any of the elements of a product taken into consideration with regards to a specific element particularly: a constant thing of a term as outstanding from a variable.
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write the number 1,744,326 in expanded form
FREE POINTS!!!!!!!!!! 10 POINTS Len's recipe for blueberry muffins calls for 110.25 grams of brown sugar for the muffin batter and an additional 55.45 grams of brown sugar for the topping. Len wants to make 4.5 batches of muffins. Enter the total amount of brown sugar that Len will need
the answer is 745.65
hope i helped:)
katie and carol bought toys for charity toy drive.katie bought 125 dolls for 13$ each. carol bought 65 toy boats for 32$ each.who spent more money altogher
A soccer coach purchased one goal and some soccer balls for the team. The expression 180 + 15x represents the cost before tax. What do the different parts of the expression model? Drag the parts of the expression into the boxes to match each description.
The expression [tex]180+15x[/tex] consists of ONE CONSTANT [180] and another VARIABLE EXPRESSION [15x].
Since the coach purchased ONE GOAL, this corresponds to the CONSTANT, which is 180. 180 is the price of the goal.
Since coach purchased several soccer balls, but doesn't say how many, it is the variable part, 15x, where
either 15 is price of ball and x is the number of balls, OR15 is the number of balls and x is the price of eachANSWER:
180 represents the price of the goal
15x represents the total price of the soccer balls
Answer:
180 represents the price of the goal
15x represents the total price of the soccer balls
Step-by-step explanation:
Differentiate f and find the domain of f. (enter the domain in interval notation.)f(x) = ln(x2 − 12x)derivative f '(x) = 2x−12x2−12x correct: your answer is correct.domain
What is the interquartile range of 4 5 7 9 10 14 16 24
Answer:
The answer is 9
Step-by-step explanation: ? i did the the tetst or whatever and 9 is the correct answer.
YOUR WELCOME :}
Order these numbers from least to greatest. 14325 , 5.753 , 534 , 5.34