20% = 0.20
multiply original price ( $0) by 0.20 for the amount of discount then subtract it
80*0.20 = 16.00
she will save $16
80-16 = 64
she will pay $64 after the discount
If the pattern continues, how many cups of milk does George need to make 6 batches of muffins? Explain how you found your answer.
To make 6 batches of muffins, George needs 3 cups of milk, which is found by multiplying the ratio of 1/2 cup of milk per batch by 6.
Explanation:The question is asking to determine the quantity of an ingredient needed for a recipe, specifically milk for pancakes, according to a given ratio. The question is based on a proportion where 1/2 cup of milk is needed for one batch of pancakes. To find out how many cups of milk are needed for 6 batches of muffins (assuming muffins and pancakes require the same amount of milk which appears to be a minor typo in the scenario), we multiply the 1/2 cup required for one batch by 6.
Thus, the calculation is: 1/2 cup of milk × 6 batches = 3 cups of milk.
To find out how many cups of milk George needs to make 6 batches of muffins, we first need to determine the number of cups needed for one batch. Let's assume that each batch requires 3 cups of milk. Therefore, to make 6 batches, George would need 3 cups x 6 batches = 18 cups of milk
Mr. River's car averages 25 3/4 miles per gallon. Express the miles per gallon as a decimal
The price of a technology stock was $ 9.69 yesterday. Today, the price fell to $ 9.58 . Find the percentage decrease.
Explain why you think slope-intercept form makes sense as a name for y = mx +
b. explain why you think point-slope form make sense as a name for y - y1 = m(x - x1)
The slope-intercept form y = mx + b shows how the slope and y-intercept values are used in the equation, while the point-slope form y - y₁ = m(x - x₁) defines a line using a point and the slope.
Explanation:The slope-intercept form, y = mx + b, makes sense as a name because it explicitly shows how the slope and y-intercept values are used in the equation.
The 'm' represents the slope, which describes the steepness of the line, and the 'b' represents the y-intercept, which indicates where the line intersects the y-axis.
For example, in the equation y = 2x + 3, the slope is 2 and the y-intercept is 3.
The point-slope form, y - y₁ = m(x - x₁), is called so because it defines a line using a single point (x₁, y₁) and the slope 'm'. This form makes it easier to determine the equation of a line when given a point and the slope.
For instance, in the equation y - 2 = -3(x - 4), the point (4, 2) and the slope -3 are used to specify the line equation.
What is the concentration of nitrate ions in a 0.125 M Mg(NO3)2 solution
We have that the concentration of the nitrate ions is mathematically given as
M= 0.250M
The concentration of the nitrate ionsQuestion Parameters:
Generally the equation for the Reaction is mathematically given as
Mg(NO₃)₂ --> Mg²⁺ + 2NO₃⁻
Each mole of the Mg(NO₃)₂ will dissociate into 2 moles of NO₃⁻.
the concentration of the nitrate ions is
M = (0.125M)(2)
M= 0.250M
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A cube has an edge if 4 feet. The edge is increasing at a rate of 2 feet per minute. Express the volume of the cube as a function
To find the volume of a cube with an edge length that is increasing with time, express the edge length as a function of time and substitute this into the volume formula. In the given problem, the edge length is increasing 2 feet per minute, thus the volume V of the cube at any given time can be expressed as V = (4 + 2t)³.
Explanation:The volume of a cube is calculated by raising the edge length to the power of three (V = e³). For this problem, we know that the edge e is increasing at a rate of 2 feet per minute. Therefore, we can express e as a function of time t, where e = 4 + 2t. Substituting this back into our volume equation, we receive the volume V of the cube as a function of time t: V = (4 + 2t)³.
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Which item would most likely appear on a culturally fair test?
Suppose an ant is sitting on the perimeter of the unit circle at the point (1,0). if the ant travels a distance of 2π3 in the counter-clockwise direction, then the coordinates of the point where the ant stops will be
After traveling a distance of 2π/3 on the unit circle in the counter-clockwise direction from (1,0), the ant stops at the coordinates (-1/2, √3/2), which are found using the unit circle's parametric equations.
Explanation:The question asks about finding the coordinates of a point on the unit circle after traveling a certain distance in the counter-clockwise direction. The distance given is 2π/3, which, when considering the circumference of the unit circle (2π), represents an arc that is a third of the full circle. The unit circle is centered at the origin (0,0) and has a radius of 1, with points on it defined by cos(θ) and sin(θ) for any angle θ measured in radians from the positive x-axis.
Traveling 2π/3 radians from (1,0) in the counter-clockwise direction lands us at an angle of 2π/3 radians from the positive x-axis. The coordinates of the point on the unit circle at this angle can be found using the circle's parametric equations x = cos(θ) and y = sin(θ). Substituting θ with 2π/3, we obtain:
x = cos(2π/3) = -1/2y = sin(2π/3) = √3/2Therefore, the coordinates of the point where the ant stops are (-1/2, √3/2).
Name the property of equality that justifies: If x = 3 and y = x + 5, then y = 8
Use this equation to find dy/dx. 9y cos(x) = x2 + y2
Final answer:
The derivative dy/dx for the equation 9y cos(x) = x² + y² is found by applying implicit differentiation. Rearranging terms after differentiation, dy/dx is obtained as the fraction (9y sin(x) + 2x) / (9 cos(x) - 2y).
Explanation:
The question asks for the derivative of dy/dx using the equation 9y cos(x) = x2 + y2. To find dy/dx, we can apply implicit differentiation, which implies taking the derivative of both sides with respect to x while treating y as a function of x (y(x)).
Let's differentiate both sides:
The left side: d/dx [9y cos(x)] = d/dx [9y] cos(x) + 9y d/dx[cos(x)] = 9(dy/dx) cos(x) - 9y sin(x)
The right side: d/dx [x2 + y2] = 2x + 2y(dy/dx)
Equating both the derivatives, we have:
9(dy/dx) cos(x) - 9y sin(x) = 2x + 2y(dy/dx)
Now, solving for dy/dx gives us:
dy/dx = (9y sin(x) + 2x) / (9 cos(x) - 2y)
The table shows the outputs y for different inputs x:
Input (x) 5 6 7 8
Output (y) 2 5 8 11
Part A: Do the data in this table represent a function? Justify your answer. (3 points)
Part B: Compare the data in the table with the relation f(x) = 2x + 13. Which relation has a greater value when x = 7? (2 points)
Part C: Using the relation in Part B, what is the value of x if f(x) = 75?
Answer:
A. yes...it is a function because there is no repeating x values.
B. (5,2)(6,5)...slope = (5 - 2) / (6 - 5) = 3
y = mx + b
slope(m) = 3
(5,2)...x = 5 and y = 2
now we sub
2 = 3(5) + b
2 = 15 + b
2 - 15 = b
-13 = b
so the equation is : y = 3x - 13
when x = 7
y = 3(7) - 13....y = 21 - 13....y = 8
f(x) = 2x + 13...when x = 7
f(7) = 2(7) + 13...f(7) = 14 + 13.....f(7) = 27
the function has a greater value
C. f(x) = 2x + 13....when f(x) = 75
75 = 2x + 13
75 - 13 = 2x
62 = 2x
62/2 = x
31 = x
Step-by-step explanation:
Suppose that in a population of 1000 there are 300 defective items and 700 items that are not defective. if you are selecting two items at random from this population, what is the probability they will both be defective?
two hundred eighty-four thousand, one hundred eighty-seven in expanded form
Let f(X)=1/x+1
Use the limit definition of the derivative to find:
i) f(-4)
ii) f(-3)
iii) f(1)
iv) f(3)
The sum of 3 less than 5 times a number and the number increased by 9 is 24. what is the number?
The lateral area of the right regular triangular prism is 18cm2. find the total surface area. give your answer in decimal form rounded to 2 decimal places
Effie's store has 10,908 more comic book than Brody's. Brody's store has 45,607 coming books. How many books do Effie's and Brody's store have together?
Show your work...
One 50 pound bag of fertilizer will cover 75 square feet of lawn.how many pounds of fertilizer will tawny need to cover 120 square feet of lawn
80 pounds of fertilizer will be needed to cover 120 square feet of lawn.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
To write a proportion.
50/75 = x/120.
Then Cross multiply to get;
6,000/75x.
Now, divide each side by 75 to isolate the “x”.
x = 80.
Therefore 80 pounds of fertilizer will cover 120 square feet of lawn.
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Farmer Jack needs 1,800 square feet of garden space to have enough corn for a year. His garden space is currently 10 5⁄6 feet by 18 feet. How much more land does farmer Jack need to plant the rest of his corn?
Farmer Jack needs an additional 1,602 2/3 square feet of land to plant the rest of his corn.
Explanation:To find out how much more land Farmer Jack needs to plant the rest of his corn, we need to calculate the area of his current garden and subtract it from the required area of 1,800 square feet. Farmer Jack's garden is 10 5/6 feet by 18 feet, so we can multiply these two dimensions to get the area of his current garden. Then, we subtract this area from 1,800 to find out how much more land he needs:
Area of Farmer Jack's garden: 10 5/6 feet * 18 feet = 197 1/3 square feet
More land needed by Farmer Jack: 1,800 square feet - 197 1/3 square feet = 1,602 2/3 square feet
Farm Jack needs an additional 1,602 2/3 square feet of land to plant the rest of his corn.
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which of the following are the factors of 4b^2-16?
380 students increase 5% what is the new amount of students
The local home improvement store wants to increase their inventory. Last year 40 lawn mowers cost them $4,776.
At the same cost, how much would 120 lawn mowers cost them this year?
Answer:14,328
Step-by-step explanation:
A picture has a width that is 17 inches shorter than the length, and its total area is 480 square inches. Find the dimensions of the picture.
Final answer:
To find the dimensions of the picture, set up an equation using the length and width. Solve the equation to find the dimensions: length = 32 inches, width = 15 inches.
Explanation:
To find the dimensions of the picture, let's assume the length is x inches. According to the problem, the width is 17 inches shorter than the length, so the width would be (x - 17) inches. The total area of the picture is given as 480 square inches. We can set up an equation using the length and width: x(x - 17) = 480. Solve this quadratic equation to find the dimensions of the picture.
Expanding the equation, we get x^2 - 17x - 480 = 0. Factoring the quadratic equation, we find (x + 15)(x - 32) = 0. Therefore, the possible values for x are -15 and 32. Since the length cannot be negative, we discard -15. Thus, the length of the picture is 32 inches and the width is (32 - 17) = 15 inches.
Final answer:
The dimensions of the picture are 32 inches in length and 15 inches in width.
Explanation:
To find the dimensions of the picture, we need to establish equations based on the information provided. Let the length of the picture be L inches and the width be W inches.
Given that:
The width is 17 inches shorter than the length: W = L - 17.The total area of the picture is 480 square inches: L × W = 480.Plug the width expression from step 1 into the area equation from step 2 to form a quadratic equation:
L(L - 17) = 480
Solving this quadratic equation will give us the value of L. Once we have L, we can use the first equation to get W. Let's solve the quadratic equation:
L² - 17L - 480 = 0
Factoring the quadratic, we find that (L - 32)(L + 15) = 0. So L can be either 32 or -15. Since a length cannot be negative, L must be 32 inches, and W, therefore, is 32 - 17 = 15 inches.
The dimensions of the picture are therefore 32 inches by 15 inches.
The width of a rectangle is 3 4 the length. The perimeter is 252 cm. What is the width of the rectangle? A) 36 cm B) 48 cm C) 54 cm D) 72 cm
Compare 249 and 271 write the greater number in word form
Ursula bought 9 dozen rolls of first aid tape for the health office. The rolls were divide equally into 4 boxes. How many rolls are in each box?
Z = x4 + x2y, x = s + 2t − u, y = stu2; ∂z ∂s , ∂z ∂t , ∂z ∂u when s = 1, t = 4, u = 5
A null hypothesis can only be rejected at the 5% significance level if and only if:
Brianna built a rectangular flower garden. The garden is 10 feet long and 8 feet wide. What is the area of Briannas flower garden?.
Keith has p pennies, n nickels, and d dimes in his pocket. The total number of coins is 9. The expression 0.01p+0.05n+0.10d represents the value of the coins, which is equal to $0.44. He has one more dime than nickels. How many pennies does Keith have? Keith has _____ pennies.
he has 4 pennies
2 nickels=10 cents
3 dime=30 cents
20 cents
40 +4 pennies =44 cents
Answer:
Keith has 4 pennies, 3 dimes and 2 nickels.
Step-by-step explanation:
Let the pennies be = p
Let the nickels be = n
Let the dimes be = d
Total coins Keith has = 9
So, 1st equation form :
[tex]p+n+d=9[/tex] ....(1)
Keith has one more dime than nickels, means [tex]d=n+1[/tex] .....(2)
Total value of these coins is $0.44
So, third equation forms:
[tex]0.01p+0.05n+0.10d=0.44[/tex] .....(3)
Substituting (2) in (1)
[tex]p+n+n+1=9[/tex]
[tex]p+2n=8[/tex] .....(4)
Similarly substitution (2) in (3)
[tex]0.01p+0.05n+0.10(n+1)=0.44[/tex]
[tex]0.01p+0.05n+0.10n+0.10=0.44[/tex]
[tex]0.01p+0.15n=0.34[/tex] ....(5)
Now multiplying (4) by 0.01 and subtracting by (5)
[tex]0.01p+0.02n=0.08[/tex] subtracting this from (5) we get
[tex]0.13n=0.26[/tex]
So, we get n = 2
[tex]p+2n=8[/tex]
[tex]p+2(2)=8[/tex]
[tex]p+4=8[/tex]
p = 4
[tex]p+n+d=9[/tex]
[tex]4+2+d=9[/tex]
[tex]6+d=9[/tex]
d = 3
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Therefore, Keith has 4 pennies, 3 dimes and 2 nickels.