Division Property of Equality
16m = 160
divide both sides by 16 to find m
m = 160/16 = 10
Answer:
Property of equality for division.Step-by-step explanation:
The given expression is
[tex]16m=160[/tex]
So, we use one of the properties of equalities for division, which states that if we divide one side of the equation, we also must divide the other side by the same number, to not mess up the balance of the equation. Applying this property, we have
[tex]\frac{16m}{16}=\frac{160}{16}\\ m=10[/tex]
Cups are sold 5 to a package and plates are sold 10 to a package. If you want to have the same number of each item for the party, what is the least number of packages of each you need to buy?
1 package of plates = 10 plates and 2 package of cups = 10 cups
so 3 packages is least amount
One out of two people entering the grocery store purchase soda. how many people out of 20 purchase soda?
WHY is -2 3 8l9 1,476 -6.01 all rational numbers . have a separate explanation for each number
Michael has 4 lots of land to sell. He sells two of them at a loss of $1,200 each and sells the other two at a profit of $1,400 each. How much money does he make on his investment?
Michael makes a total of $400 from his land investment after calculating the total losses and gains from the lands sold.
Explanation:In order to find out the total money that Michael has made from his land investment, you need to calculate the losses and the gains individually. Michael sells two of his lands at a loss of $1,200 each, hence his total loss is 2 * $1,200 = $2,400. On the other hand, he sells the other two lands at a profit of $1,400 each, hence his total profit is 2 * $1,400 = $2,800.
To get the total money that he made on his investment, you subtract the total loss from the total profit. That is $2,800 (total profit) - $2,400 (total loss) = $400. Hence, Michael makes $400 on his investment.
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The number of boys in the chess club is 4 more than twice the number of girls.there are 38 boys in the chess club. How many girls are in the club?
Please can you help me
Answer:
5 : 1
Step-by-step explanation:
From your second-grade memorization of multiplication tables, you recognize that 15 = 3×5, so you know 3 is a factor of both numbers in the ratio. To reduce the ratio to simplest form, you divide out all common factors:
15 : 3 = (15/3) : (3/3) = 5 : 1
What is 39ft/min to yd/s?
Please explain using dimensional analysis.
Neil and Jean each choose a number at random from the set 1,2,3,4,5,6,7,9,10 their numbers are allowed to be the same. What is the probability that the product of those two numbers is even?
The probability that the product of the numbers selected by Neil and Jean is even is approximately 0.8889.
Explanation:To answer your question, let's first classify the numbers from the given set 1,2,3,4,5,6,7,9,10 into two categories: even numbers (2, 4, 6, 10) and odd numbers (1, 3, 5, 7, 9). Each of the people, Neil and Jean, can pick any number independently. Hence we have two scenarios which result in the product being even - either both pick even numbers or at least one of them picks even.
The probability of both picking an even number is (4/9)*(4/9) = 16/81. Also, there is no constraint on the second scenario, so, total probabilities = 1. Hence, the probability of at least one picking an even is 1 - probability(both picking odd) = 1 - (5/9)*(5/9) = 1 - 25/81 = 56/81.
Therefore, the total probability that the product of the numbers selected by Neil and Jean is even is the sum of the above two probabilities i.e., 16/81 + 56/81 = 72/81 = 0.8889 (approx).
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What kind of transformation does the graph show?
A) flip
B) reflection
C) rotation
D) slide
If y = 44 when x = –264, what is y when x = –486
The value of 'y' when x equals -486 using the same ratio (1:6) as given in the original input is -81.
Explanation:To solve this problem, we're given a ratio of y to x (1:6) when x is -264 and y is 44. This ratio implies that y is one-sixth of x. Utilizing this information, we can determine y for a different x value (-486). By maintaining the 1:6 ratio, we divide -486 by 6, resulting in -81. Therefore, when x is -486, y equals -81. This solution stems from understanding the proportional relationship between y and x, allowing us to calculate y for any given x value based on the established ratio. In this case, the ratio of 1:6 guides the computation, ensuring the accurate determination of y as -81 when x is -486.
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300 yards / 1 minute find unit rate feet per wonds
15 points!! The power P (measures in horsepower, hp) needed to propel a boat is directly proportional to the cube of the speed s. A 73-hp engine is needed to propel a certain boat at 10 knots. Find the power needed to drive the boat at 19 knots. (Round your answer to the nearest whole number.)
Is it true that |3-8| and |3+8|
To determine if |3-8| is equal to |3+8|, we calculate the absolute values: |3-8|=5 and |3+8|=11. Since 5 is not equal to 11, the statement is false.
To solve the given problem, we need to understand the properties of absolute values. Absolute value measures the distance of a number from zero on the number line, regardless of direction.
First, calculate the absolute value of each expression: |3-8| and |3+8|.For |3-8|:3 - 8 = -5, and the absolute value of -5 is 5. Therefore, |3-8| = 5.
For |3+8|:3 + 8 = 11, and the absolute value of 11 is 11. Therefore, |3+8| = 11.
In conclusion, it is not true that |3-8| equals |3+8|, as |3-8| = 5 and |3+8| = 11.
here is the full question-Is it true that |3-8| and |3+8| are equal?
Please help me .......
Answer:
[tex]9b+10u > 1,000[/tex]
If an exterior angle of a regular polygon measures 40°, how many sides does the polygon have?
Find dy/dx x^3+y^3=18xy
Final answer:
The student's question involves finding the derivative dy/dx for the equation [tex]x^3 + y^3 = 18xy[/tex]. This is done through implicit differentiation, resulting in dy/dx = [tex](18y - 3x^2) / (3y^2 - 18x).[/tex]
Explanation:
The student has presented an equation involving x and y and has asked for the derivative of y with respect to x (dy/dx). To find dy/dx, we use implicit differentiation because y is not isolated on one side of the equation. The given equation is [tex]x^3 + y^3 = 18xy.[/tex]
Start by differentiating both sides with respect to x:
The derivative of [tex]x^3[/tex] with respect to x is [tex]3x^2.[/tex]
The derivative of [tex]y^3[/tex] with respect to x is [tex]3y^2[/tex] times dy/dx (chain rule).
The derivative of 18xy with respect to x is 18y + 18x times dy/dx (product rule).
Bringing all terms involving dy/dx to one side gives:
[tex]3x^2 + 3y^2(dy/dx) = 18y + 18x(dy/dx)[/tex]
Solve for dy/dx:
[tex]3y^2(dy/dx) - 18x(dy/dx) = 18y - 3x^2[/tex]
Factor out dy/dx:
[tex]dy/dx (3y^2 - 18x) = 18y - 3x^2[/tex]
Finally, solve for dy/dx:
[tex]dy/dx = (18y - 3x^2) / (3y^2 - 18x)[/tex]
This expression represents the slope of the tangent to the curve at any point (x, y).
The number 3.141595... is called what?
An equilateral triangle is never or sometimes an isosceles triangle?
The commission of selling each iPhone is $30 and the commission of selling each iPad is $20. If you one day sold 4 more iPhones than iPads and earned a total commission of $520, how many iPhones and iPads did you sell respectively?
By solving the system of equations which includes the total commission and difference in quantity of iPhones and iPads sold, we determine that the salesperson sold 8 iPads and 12 iPhones.
The student is tasked with solving a system of linear equations to determine how many iPhones and iPads were sold based on the commission earned. Let's define the number of iPads sold as x and the number of iPhones as x + 4.
The total commission for iPhones is $30 per iPhone and the total commission for iPads is $20 per iPad. The total commission earned from selling these products is $520.
We can set up two equations based on the given information:
Commission from iPhones: 30(x + 4)
Commission from iPads: 20x
Total Commission: 30(x + 4) + 20x = 520
By solving the equation 30(x + 4) + 20x = 520, we find:
30x + 120 + 20x = 520
50x + 120 = 520
50x = 400
x = 8
So, the number of iPads sold is 8. Since the number of iPhones sold is 4 more than iPads, we have:
Number of iPhones sold = x + 4 = 8 + 4
Number of iPhones sold = 12
Therefore, the salesperson sold 8 iPads and 12 iPhones respectively.
Ivan is saving money to buy a game. so far he has saved $30 , which is two-thirds of the total cost of the game. how much does the game cost?
Answer:
45 :)
Step-by-step explanation:
How many terms are in the expression a3 + 3a2b - 4ab - 11b + 7?
7
4
5
6
the answer is 5
1: a^3
2: 3a^2b
3: 4ab
4: 11b
5: 7
anything seporated by a + or - is a term
If a line is perpendicular to a line segment, what angle do they form at their intersection
Which equation below represents a vertical line? y = x + 0, y = x – 0, y = 4, x = 4
Two ants walk on a line in a random fashion. they begin 10cm apart. at each time step, each ant has a probability of 1/2 to move 1cm to the left, and probability 1/2 to move 1cm to the right. what is the probability that after 7 time steps, the ants have met one another (i.e., passed through the same point)?
Simplify the expression. 23 · 16 + 24 ÷ 4
A. 80
B. 38
C. 134
38 is most likley the answer am i right?!
Final answer:
To simplify the expression 23 · 16 + 24 ÷ 4, we first perform the multiplication and division according to PEMDAS, resulting in 368 + 6, and then add those results to get the final answer, 374.
Explanation:
To simplify the expression 23 · 16 + 24 ÷ 4, we need to follow the order of operations, which is often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right).
First calculate the multiplication: 23 × 16 = 368.
Then, the division: 24 ÷ 4 = 6.
Finally, add the two results together: 368 + 6 = 374.
Therefore, the simplified expression equals 374.
A dish tv satellite dish is the shape of a paraboloid. the dish is 36 inches wide, and 8 inches deep. how many inches should the receiver be located from the vertex for optimal reception? (round to the nearest thousandth)
The receiver is situated 10.125 inches from the vertex, is the correct response.
What is Parabola?
The line perpendicular to the directrix and passing through the focus (that is, the line that splits the parabola through the middle) is called the "axis of symmetry". The point where the parabola intersects its axis of symmetry is called the "vertex" and is the point where the parabola is most sharply curved. The distance between the vertex and the focus, measured along the axis of symmetry, is the "focal length". The "latus rectum" is the chord of the parabola that is parallel to the directrix and passes through the focus. Parabolas can open up, down, left, right, or in some other arbitrary direction. Any parabola can be repositioned and rescaled to fit exactly on any other parabola—that is, all parabolas are geometrically similar.According to our question-
Make the origin of the parabola the vertex. Then, it has the equation y = bx^2.
The parabola crosses via (18,8), therefore 8 = b(182^) b = 0.02469 because
Its equation is y = 0.02469x2.
For best reception, the receiver should be positioned at the paraboloid's focus point.
The focus has a y-coordinate of
a = 1/(4b) = 1/0.098765
= 10.125 in
The receiver is situated 10.125 inches from the vertex, is the correct response.
Hence we can say that, the receiver is situated 10.125 inches from the vertex.
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Final answer:
Using the formula [tex]f = \(\frac{d^2}{16h}\)[/tex] for a parabolic dish, where the dish is 36 inches wide (diameter) and 8 inches deep, the optimal location of the receiver is calculated to be approximately 10.125 inches from the vertex for best reception.
Explanation:
The question asks where the receiver should be placed on a satellite dish that has the shape of a paraboloid for optimal reception. The given dimensions are that the dish is 36 inches wide and 8 inches deep. A parabolic dish reflects signals to a focal point where the receiver is typically placed for optimal signal reception. We can use the properties of a parabolic shape to find the location of the focal point, also known as the focus of the parabola.
To find the focal length (distance from the vertex to the focus) of a paraboloid, we use the formula [tex]f = \(\frac{d^2}{16h}\)[/tex], where d is the diameter and h is the depth. Substituting our values in (d = 36 inches, h = 8 inches) we get the focal length [tex]f = \(\frac{36^2}{16 \times 8}\) = \(\frac{1296}{128}\) \approx 10.125[/tex] inches. Therefore, the receiver should be located approximately 10.125 inches from the vertex of the satellite dish for optimal reception.
The receiver's optimal location, rounded to the nearest thousandth, is therefore 10.125 inches from the vertex.
A coin is flipped five times find the number of possible sets of heads and tails that have 0 heads
The number of possible sets with 0 heads when flipping a coin five times is 1, represented by five consecutive tails (TTTTT).
When flipping a coin five times, the number of possible sets that have 0 heads (meaning all tails) is just one. This single microstate is TTTTT.
The reason for this is that each coin flip is an independent event with two possible outcomes: heads (H) or tails (T). When we are only concerned with the total head and tail count and not the order in which they appear, the only set with 0 heads is the set where every coin lands on tails.
Simplify the Expression.
-1/8 - 2/7 =
A. -1/8
B. 23/56
C. -23/56
D. 1/5
Algebra Vocabulary Crossword help ?!
1. a relation described in word format? (17 letter)
9. a way to name a function identifying its input?
(16 letter)
The student is looking for the terms 'Verbal Description' and 'Function Notation' for their Algebra Vocabulary Crossword. These refer to a relation described in word format and a way to name a function identifying its input respectively.
Explanation:Based on the number of letters you've indicated, it looks like you're looking for two vocabulary items in the field of Algebra.
First, a relation described in a word format is typically called a Verbal Description, which has 17 letters.
Second, a way to name a function identifying its input is called Function Notation, which has 16 letters.
In Algebra, Verbal Description is when you describe a mathematical relationship using words. For example, 'the sum of a number and three is seven.' This could be translated to the equation x+3=7.
Function Notation, on the other hand, is a way to name a function that is dependent on one or more inputs. For example, f(x) = x^2 is function notation, since the output 'f(x)' is dependent on the input 'x'.
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At city high school,the sophomore class has 60 more students than the freshman class.the junior class has 50 fewer students than twice the students in the freshman class.the senior class is three times as large as the freshman class.if there are a total of 1,424 students at the city high school,how many students are in the freshman class?
The number of students in the freshman class are:
202
Step-by-step explanation:Let the number of students in Freshman class = x
The sophomore class has 60 more students than the freshman class.This means that the number of students in sophomore class = x+60
The junior class has 50 fewer students than twice the students in the freshman class.This means that the number of students in junior class= 2x-50
The senior class is three times as large as the freshman class.This means that the number of students in senior class are: 3x
There are a total of 1,424 students at the city high school.This means that:
[tex]x+x+60+2x-50+3x=1424\\\\x+x+2x+3x+60-50=1424\\\\7x+10=1424\\\\7x=1424-10\\\\7x=1414\\\\x=\dfrac{1414}{7}\\\\x=202[/tex]