The least common multiple of 32, 48, and 16 is 96
How to calculate the least common multiple ?The first step is to get the prime factors of each number
The prime factors of 32 are 2, 2, 2, 2 and 2.
The prime factors of 48 are 2, 2, 2, 2 and 3
The prime factors of 16 are 2,2,2 and 2
The least common multiple of 32, 48 and 16 can be calculated as follows
2 × 2 × 2 × 2 × 2 × 3
= 32 × 3
= 96
Hence the least common multiple of 32, 48, and 16 is 96
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If you plot the point - 8.85 on a number line, would you place it to the left or right of -8.8? Explain
If you plot the point, - 8.85 on the number line you would put it left of -8.8
- 8.85 is left of -8.8
This is further explained below.
What is a number line?Generally, A image of a graded straight line is what is known as a number line, and its purpose is to provide a visual representation of the actual numbers. It is generally accepted that a real number may be assigned to each point on a number line, and that each point can be assigned to a real number.
In conclusion, The number line follows natural arithmetic rules, Hence
Since
-3,-2,-1,0,1,2,3 is the sequence of the natural arithmetic rules hence,
- 8.85 is left of -8.8
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The equation below represents Function A and the graph represents Function B: Function A f(x) = x − 9 Function B graph of line going through ordered pairs negative 1, negative 3 and 2, 3 Which equation best compares the slopes of the two functions? (1 point) Slope of Function B = 2 x Slope of Function A. Slope of Function A = Slope of Function B Slope of Function A = 2 x Slope of Function B Slope of Function B = − Slope of Function A
We will see that the slope of function B is 2, and the slope of function A is 1. This means that the correct equation is:
Slope of function B = 2*Slope of Function A
Which equation compares the slopes?
First, a general linear equation is:
y = a*x + b
Where a is the slope and b the y-intercept.
Here the function A is:
f(x) = x - 9
Then the slope is equal to 1.
We know that function B is a line that passes through (-1, -3) and (2, 3)
Then the slope is:
s = (3 + 3)/(2 + 1) = 6/3 = 2
So the slope of function B is 2, and the slope of function A is 1. Then the equation is:
Slope of function B = 2*Slope of Function A
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Solve y3 = 1.
y = −1
y = 1
y = ±1
y = 3
The value of the expression y³ = 1 is y = 1.
Expression:
An expression also known as algebraic expression consisting of variables, numbers and an arithmetic operation between them.
Given,
Here we have the expression y³ = 1.
Now, we need to find the value of y.
While we looking into the expression, when we have to find the value of y then we have to move the cube vale to the other side.
When we move the cube to the other side then it will be the cube root of the number.
While we simplify the cube root of the number then we get the result.
Therefore,
y³ = 1
Move the cube to the other side,
y = ∛1
We know that,
∛1 = 1
So, the value of y = 1.
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Please answer this question :) Need Help!
Answer:
Step 3, she forgot to square half of the middle term before adding it to both
sides.
Step-by-step explanation:
yw
Margo can purchase tile at a store for $0.89 per tile and rent a tile saw for $56. At another store she can
borrow the tile saw for free if she buys tiles there for $1.59 per tile. How many tiles must she buy for the
cost to be the same at both stores?
Marco must buy
tiles for the cost to be the same at both stores.
Answer:
80
Step-by-step explanation:
Use trial and error until you find a common multiple.
The art department is planning a trip to a museum. The bus costs $100 plus $7 per student. A professor donated $40 to defray the costs. If the school charges students 10$ each, how many students need to go on the trip not to lose money?
Total 20 students should go to the trip to not to lose money.
Cost of bus = 100 dollars
For students the charge is 7 dollars per student.
Amount professor donated to defray the cost is 40 dollars.
School is charging 10 dollars per student for the trip.
Therefore, reduced cost = 100 - 40 = 60 dollars
Profit earned from each student is 10 - 7 = 3 dollars.
Hence, minimum students should go to the trip will be 60 ÷ 3 = 20.
Since, 20 × 3 = 60, the cost is covered and no money is lost.
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Exploration: More Conversions
The other day you worked with converting meters, centimeters, and millimeters. Here are
some more unit conversions.
1. Use the equation F = C + 32, where F represents degrees Fahrenheit and C
represents degrees Celsius, to complete the table.
temperature (C)
20
3.
4
175
2. Use the equation c = 2.54n, where c represents the length in centimeters and n
represents the length in inches, to complete the table.
length (in)
10
8
temperature (F)
3-—-/-
length (cm)
I
Are these proportional relationships? Explain why or why not.
They have not a proportional relationship.
What is Comparing Relationships with Equations?The equation that represents a proportional relationship, or a line, is y = k x , where is the constant of proportionality. Use k = y x from either a table or a graph to find k and create the equation. Proportional relationships can be represented by tables, graphs and equations.
From table 1.
temperature ( ∘ C) temperature ( ∘ F)
20 68
4 39.2
175 347
converted by using equation F=[tex]\frac{9}{5}[/tex]C+32
From table 2.
length (in) length (cm)
10 25.4
8 20.32
[tex]3\frac{1}{2}[/tex] 8.89
Converted by using equation c = 2.54n where c represent length (in cm) and n represent length in inches.
Now,
we will check the proportionality by [tex]\frac{c}{F}[/tex] if all the values of this ratio is same for the tables then they are showing proportionality .
From the table they are not showing proportionality.
Hence, They have not a proportional relationship
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Expand
7(9- f)
How do I do it
Answer:
firstly we need multiply out the bracket.
7×9=63
7×f= 7f.
then you subtract 63-7f= 56
your answer is 56
2. Julian is cutting lengths of rope for a class project. Each rope length should be 10
inches long. The specifications allow for a difference of 0.5 inches. Which absolute
value inequality represents the difference between the rope lengths cut and the
specifications?
The absolute value inequality represents the difference between the rope lengths cut and the specifications are | x - 10 | ≤ 0.5.
What is the modulus value?Modulus value always outputs a positive value irrespective of the input value sign.
Julian needed to cut ropes for her school project and their length should be 10 inches long with a difference of 0.5 inches.
∴ The maximum allowable length of the rope should be (10 + 0.5) = 10.5 inches and the minimum allowable length of the rope should be
(10 -0.5) = 9.5 inches.
The absolute value of inequality that represents this condition is,
| x - 10 | ≤ 0.5.
x - 10 ≤ 0.5.
x ≤ 10.5, And
- ( x - 10) ≤ 0.5.
-x + 10 ≤ 0.5.
- x ≤ - 9.5. ( think of moving the terms on either side to make x positive).
x ≥ 9.5.
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which situation is best modeled by an exponential distribution? suppose that, in a strand of dna, mutations occur randomly and independently of other mutations at an average rate of one mutation per 12,400 a. a geneticist is examining a strand of dna. what is the probability that she will observe a mutation within the next 15,000 a? suppose that defects in electrical wire occur randomly and independently of other defects. the average rate is 0.001 defects per cm of wire. what is the probability that a 100 m long spool of wire will contain fewer than two defects? suppose that a traffic light is green for 30 s, yellow for 4 s, and red for 56 s. if cars arrive at the intersection randomly, what is the probability a car will arrive when the light is yellow?
By probability , An average rate of one mutation per 12,400 A.A geneticist is examining a strand of DNA .
Describe probability using an example?
By dividing the number of positive outcomes by the entire number of possible outcomes, probability—the likelihood that an event will occur—is determined. The most basic illustration is a coin toss. There are just two outcomes when you flip a coin: either it comes up heads or tails.The area of mathematics known as probability explores potential outcomes of events as well as their relative probabilities and distributions.The four most popular approaches to probability are classical, empirical, subjective, and axiomatic.Suppose that, in a strand f DNA ,mutations occur randomly and independently of other mutations .
at an average rate of one mutation per 12,400 A.A geneticist is examining a strand of DNA .
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2. Three times one number minus a second is 8, and the sum of
the numbers is 12. Find the numbers.
Answer:
8
Step-by-step explanation:
Let the number be “X"
Solution:
4 + (X/2) = 8
(X/2) = 8-4
(X/2) = 4
X = 4×2
X = 8
THEREFORE THE ANSWER IS “8”
Answer:
This is a simultaneous equation.
Step-by-step explanation:
let the first number be x and second be y
Lets make an equation first:
3x-y = 8 .....(1)
x+y = 12........(2)
Solve by elimination.
Dass
3x+x= 8+12
4x=20
x=5
find y
x+y=12
5+y=12
y=12-5
y= 7
Therefore the two numbers are 5 and 7
Q2 - Word problems.
Solve the problems and write the answers
A trifle recipe requires 1½ cups of sugar. A chocolate cake recipe requires twice as much sugar. How many cups of sugar go into the cake?___
[tex] \frac{?}{?} [/tex]
Answer:
The answer is 3, but here’s how I got that answer.
Step-by-step explanation:
As we know the trifle recipe requires 1 ½ cups of sugar, and the chocolate cake requires double the amount of sugar.
You have two options.
Multiply 1½ by 2
1½ x 2 = 3
———————————
Or add 1½ + 1½
1½ + 1½ = 3
———————————-
Wasn’t sure what you were asking for with this this question, but hope it helped.
Answer: 3
Step-by-step explanation:
Since the trifle cake uses 1 ½ cups of sugar and the chocolate twice as much sugar as the trifle cake you should multiply 1 ½ x 2 which would equal 3. So, 3 cups of sugar should go into the cake. (This is my first answer to a question so I'm sorry if I'm confusing)
Determine the x- and y-intercepts of the graph of x−4y=8
Then plot the intercepts to graph the equation.
Show a picture, please.
The x-intercept of the equation is: (8, 0)
The y-intercept is of the equation is: (0, -2)
How to Find the X-intercept and the Y-intercept of a Line?The x-intercept is the point on the x-axis where the line cuts across the x-axis, while the y-intercept is the point on the y-axis that the graph intercepts.
The value of the x-intercept is the value of x when the value of y is equal to zero, while the y-intercept of a graph is the value of y when the value of x is zero.
Given the equation of the linear graph as, x - 4y = 8, to find the x-intercept, substitute y = 0 into the equation:
x - 4(0) = 8
Solve for x:
x - 0 = 8
x = 8
The x-intercept is: 8.
(8, 0)
To find the y-intercept, substitute x = 0 into the equation, x - 4y = 8 and solve for the value of y:
0 - 4y = 8
-4y = 8
-4y/-4 = 8/-4
y = -2
The y-intercept is: -2.
(0, -2)
The graph for x - 4y = 8 is shown in the attachment.
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Jason was paid 10 cents for every golf ball he found and brought back to the shop.
Answer: C.
Step-by-step explanation:
X would represent the number of golf balls he brought back and .10 is the amount of money he makes for each of them.
Answer:
0.10x
Step-by-step explanation:
x stands for the amount of golf balls he brings back to the shop and 0.10 stands for the 10 cents he gets paid for each ball.
What is the next digit in the quotient?
5?
8)4184
-40
18
————
Answer: 2
Step-by-step explanation:
The greatest divisor of 8 that is less than 18 is 16, and 16 divided by 8 is 2.
The next digit of quotient is 16.
Here given that,
4184 is divisible by 8
since we know that,
Division is a process of repeated subtraction. It is the inverse action of multiplication. It is characterised as the formation of equal groupings. When we divide numbers, we split them down into smaller amounts so that the multiplication of those smaller numbers equals the larger number taken.
4184 is divisible by 8 we get,
⇒ 4148/8
⇒ 516
So, the quotient is 516
Hence,
The next digit is 16.
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I'm not sure , hellp
In the given parallelogram,
∠W = 85°
∠WXV = 59°
Since, VW is parallel to XY,
So,
∠YVX = ∠WXV ............... (Alternate interior angles)
⇒ ∠YVX = 59°
Now,
∠W = ∠Y .................. (Opposite angles of a parallelogram are equal)
⇒ ∠Y = 85°
As we know that opposite sides of a parallelogram are equal,
Therefore,
VW = YX
⇒ 2x = 6
⇒ x = 6/2 = 3 units
What is a Parallelogram?A parallelogram is a straightforward (non-self-intersecting) quadrilateral in Euclidean geometry that has two sets of parallel sides.In a parallelogram, the opposing or confronting sides are of equal length, and the opposing angles are of equal size. The Euclidean parallel postulate, or one of its equivalent formulations, is a necessary precondition for both the congruence of opposite sides and opposite angles, and neither condition can be demonstrated without using it.The parallelepiped is a parallelogram's three-dimensional equivalent.Order 2 rotational symmetry (through 180°) is present in a parallelogram (or order 4 if a square). The shape must be either a rhombus or an oblong if it also possesses precisely two lines of reflectional symmetry (a non-square rectangle). A square object is one with four lines of reflectional symmetry.
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How are the entries of the matrix named by position?
⎡⎣⎢071−1−8236−35−4−5−2−98⎤⎦⎥
Drag an answer into each box to match the matrix entry with its position in the matrix.
The most appropriate choice for matrix will be given by-
The position number of all the matrix entries are
[tex]a_{11} = 0\\a_{12} = -1\\a_{13} = 3\\a_{14} = 5\\a_{15} = -2\\a_{21} = 7\\a_{22} = -8\\a_{23} = 6\\a_{24} = -4\\a_{25} = -9\\a_{31} = 1\\a_{32} = 2\\a_{33} = -3\\a_{34} = -5\\a_{35} = 8[/tex]
What is a matrix?
Any arrangement of numbers in the form of rows and columns are called matrix. The numbers inside a matrix is known as elements of the matrix.
The position number of a matrix entry is denoted by [tex]a_{mn}[/tex] where m denotes the row position and n denotes the column position.
We can do addition, subtraction, multiplication on matrix but two matrices cannot be divided.
Here,
The position number of a matrix entry is denoted by [tex]a_{mn}[/tex] where m denotes the row position and n denotes the column position.
The given matrix is
[tex]\left[\begin{array}{ccccc}0 & -1 & 3 & 5 & -2\\7&-8&6&-4&9\\1&2&-3&-5&8\end{array}\right][/tex]
The position numbers of all the matrix entries are given below
[tex]a_{11} = 0\\a_{12} = -1\\a_{13} = 3\\a_{14} = 5\\a_{15} = -2\\a_{21} = 7\\a_{22} = -8\\a_{23} = 6\\a_{24} = -4\\a_{25} = -9\\a_{31} = 1\\a_{32} = 2\\a_{33} = -3\\a_{34} = -5\\a_{35} = 8[/tex]
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Complete the equation of the line through
10, 3) and
8, 8).
Use exact numbers.
[tex](\stackrel{x_1}{10}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{8}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{8}-\stackrel{y1}{3}}}{\underset{run} {\underset{x_2}{8}-\underset{x_1}{10}}} \implies \cfrac{ 5 }{ -2 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{3}=\stackrel{m}{-\cfrac{5}{2}}(x-\stackrel{x_1}{10}) \\\\\\ y-3=-\cfrac{5}{2}x+25\implies {\Large \begin{array}{llll} y=-\cfrac{5}{2}x+28 \end{array}}[/tex]
What are the domain and range of the function below?
The domain of the given function is (-∞,5) and the range is (5,∞).
What are domain and range?All the independent variable, x, for which y is defined, is the domain and range of a function. Every possible value of the dependent variable y comes within a function's range.
From the graph, we can see that x varies from -∞ to -5
So, the domain is the interval of (-∞,-5)
The function of f(x) varies from (5,∞)
So, the range is (5,∞).
Therefore, the domain of the given function is (-∞,-5) and the range is (5,∞).
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Data were collected on the distance a baseball will travel when hit by a baseball bat at a certain speed. the speed, s, is measured in miles per hour, and distance, y, is measured in yards. the line of fit is given by Å· = 3.98 53.59s. if the ball travels for a duration of 5 seconds, what is the predicted distance of the ball? 267.95 feet 271.93 feet 283.87 feet 287.85 feet
By evaluating the linear equation in t = 5 seconds, we will see that the distance traveled is 271.93 feet.
What is the predicted distance of the ball?
Here we know that the line that defines the distance traveled by the ball (y) as a function of time (t) is:
y = 3.98 + 53.59*t
Now we want to predict the distance traveled y the ball if it travels for 5 seconds, so we just need to evaluate the above linear equation in t = 5.
So we will get:
y = 3.98 + 53.59*5 = 271.93
So we conclude that the distance traveled in that time is 271.93 feet.
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Answer: 271.93 feet
Step-by-step explanation:
I took the test
adriel is younger than jevonte. There ages are consecutive odd integers. Find adriel’s age if the sum of the square of adriel’s age and 4 times jevonte’s age is 85
Answer:
Step-by-step explanation:
Adriel’s age if the sum of the square of adriel’s age and 4 times jevonte’s age is 85 is 7 years
How to calculate the value?Let the ages be x and x + 2 since they're consecutive odd integers.
We want to find Adriel’s age if the sum of the square of adriel’s age and 4 times jevonte’s age is 85. This will be illustrated as:
x² + 4(x + 2) = 85
x² + 4x + 8 = 85
Collect like terms
x² + 4x + 8 - 85
x² + 4x - 77 = 0
x² + 11x - 7x - 77 = 0
x(x + 12) - 7(x + 11) = 0
x - 7 = 0
x = 0 + 7
Therefore, the age is 7 years.
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3x + 6x = 45 solve for x
HELP PLS I NEED THIS DONE BY TOMORROW!!
PLS BE 100% CORRECT
The answer to the following verbal expressions of inequality are:
A: x ≤ 69;
B: The option that shows the graph of the inequality d<2 is Option C.
C: The option that shows the graph of the inequality of x ≤ 5 is option B.
D: represents the graph of the inequality given in option C that is x > -8
E: The inequality that describes the situation is ≥ 49 (Option B)
What is inequality?In mathematics, inequality is defined as a declaration of an order connection between two integers or algebraic expressions (greater than, greater than or equal to, less than, or less than or equal to).
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( Please help )
Answer the question in photo.
Keiko is trying to score in the “ryō” range in her math class which is above a 70. Her test scores so far are an 85, 57, and 78. What is the lowest score that she can get on her next test in order to stay in the ryō range when her scores are averaged?
What's the inequality for this story?
Write the steps to solve it
What is the solution?
When this inequality is graphed will the limit be an open or closed circle?
When this inequality is graphed will the line have an arrow pointing to the right or to the left
The lowest score that Keiko is trying to score to get in the "ryo" range is , the inequality to represent this story is (x+85+57+78)/4 > 70 .
In the question ,
it is given that
Keiko need to score average above 70 to get in the ryo range
let x be the marks that Keiko scores in the next test ,
so, the average = (x+85+57+78)/4
According to the question
Average > 70
Substituting the value of average , the inequality becomes
(x+85+57+78)/4 > 70
x+85+57+78 > 280
x+220 > 280
x > 280-220
x > 60
the lowest score that Keiko should get is greater than 60 .
When the inequality x > 60 , will be graphed then the limit will be an open circle as equal to sign is not included in the inequality .
as when the numbers increases , it move towards right side
So, When the inequality is graphed, the line will have an arrow pointing towards the right .
Therefore , the lowest score that Keiko is trying to score to get in the "ryo" range is , the inequality to represent this story is greater than 60 ,
the inequality to represent this story is (x+85+57+78)/4 > 70 ,
the limit of graph will be open circle and arrow will be pointing towards right .
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How do you solve this equation x²=36
You can see the following steps to know the solvation
x² = 36
x = √36
x = 6.
i) in a certain county there are two political parties, liberal and conservative. it has been observed that between elections a fixed percentage, 45% of liberals switch to the conservative party and a fixed percentage, 32% of conservatives switch to the liberal party. the other voters remain in the same party. assume that there are altogether 7700 eligible voters in the county.
In linear equation, Number of members in liberal party = 32 * 77 = 2464
What does the term "linear equation" mean?
A mathematical function where the variables only occur in the first degree, where the constants are multiplied, and where the only possible combinations are addition and subtraction.
45% Of liberals switch to the conservative party
total number of eligible votes in the country =7700
Number of members change to liberal to conservative = 45% of 7700
= 45/100 * 7700
= 45 * 77 = 3465
32% of conservative switch to the liberals party = 32 % of 7700
= 32/100 * 7700
Number of members in liberal party = 32 * 77 = 2464
An equilibrium in campain contributions one for the each party among the set of contribution to the party.
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The complete question is -
in a certain county there are two political parties, liberal and conservative. it has been observed that between elections a fixed percentage, 45% of liberals switch to the conservative party and a fixed percentage, 32% of conservatives switch to the liberal party. the other voters remain in the same party. assume that there are altogether 7700 eligible voters in the county. Find the equilibrium Values for the system if any?
I need help with this.
Answer:
2533 km/hr
Step-by-step explanation:
time = 8 hours 30 minutes
[tex]\sf = 8\dfrac{1}{2} \ hours\\\\ =\dfrac{17}{2} \ hours[/tex]
Distance = 298 km
[tex]\sf \boxed{\bf Average \ speed = Distance * time}[/tex]
[tex]\sf = 298 * \dfrac{17}{2}\\\\ = 149 * 17\\\\= 2533 \ km / hr[/tex]
21. Higher Order Thinking The product
of a factor and 0.1 is 8.35. What is the
factor? What is the product of the factor
and 0.01?
The product of factor 83.5 with 0.01 will be 0.835
What are mathematics operations?
• A mathematical operation is a function that converts a set of zero or more input values (also called "b" or "arguments") into a defined output value. The number of operands determines the operation's arity. Most commonly studied operations are binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive and multiplicative inverses.
• Zero-arity operations, or nullary operations, are constants, and mixed products are arity three operations, or ternary operations.
Here, the given statement is :
The product of a factor and 0.1 is 8.35
Let the factor be a then :
a x 0.1 = 8.35
a = 8.35/0.1
a = 83.5
The factor is 83.5
Now, the product of this with 0.01 will be :
83.5 x 0.01 = 0.835
Therefore, The product of factor 83.5 with 0.01 will be 0.835
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Gabril has a roll of tape that is 4 1/2 yd long.He cuts the tape into pieces that are each 3/2 yd long
The number of tapes cut is 3 pieces.
How to find the number of pieces of tape cut?He has a roll of tape that is 4 1/2 yard long.
He cuts the tape into pieces that are each 3/2 yard long.
Therefore, the number of roll of tape cut can be calculated as follows:
Initial length of the tape in yard = 4 1 / 2 = 9 / 2 yards
Length of the tape cut in yard = 3 /2 yards
Hence,
number of tape cut = 9 / 2 ÷ 3 / 2
number of tape cut = 9 / 2 × 2 / 3
number of tape cut = 9 / 3
number of tape cut = 3 pieces
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