Step-by-step explanation:
let's start with combinations, where the order does not matter - the 4 basis are indistinguishable.
C(5, 4) = 5! / (4! × (5-4)!) = 5! / 4! = 5
that makes sense, of course, as we only need to trace the possibilities for the one empty box : 5 possibilities.
now, the order of the 4 balls matter.
the 4! term in the denominator was actually taking that away, so we need to remove it.
that turns the combinations into permutations, where the order matters.
P(5, 4) = 5! / (5 - 4)! = 5! = 5×4×3×2×1 = 120
4 distinguishable balls can be placed in 5 distinguishable boxes in 120 ways.
Betina is going to put floor tiles down in the bathroom. Each tile is a square and measures 75mm down one side. What is the area of one tile? mm²
Answer:
5625mm²
Step-by-step explanation:
The area of a square is found by multiplying the length of one side by itself. So if each tile is a square and measures 75mm on one side, then the area of one tile is:
75mm x 75mm = 5625mm²
find the solution of the differential equation
y' = 2 square root y . x
The requried solution of the differential equation is given as y = x⁴/4 + c₁x²/2 + c₁².
What is implicit differentiation?The method of determining the derivative of an implicit function by differentiating each term separately, expressing the derivative of the dependent variable as a symbol, and solving the resulting expression for the symbol.
here,
Given the differential equation,
y' = 2 √y . x
y' = dy/dx so,
dy/dx = 2√y.x
dy/√y = 2x dx
[tex]y^{-1/2}dy = 2xdx\\\sqrt{y} /[1/2] = x^2 + c_1[/tex]
y = [1/2(x² + c₁)]²
y = x⁴/4 + c₁x²/2 + c₁²
Thus, the requried solution of the differential equation is given as y = x⁴/4 + c₁x²/2 + c₁² .
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Jackson wrote different patterns for the rule subtract 5 select all the patterns he could have written
When Jackson wrote different patterns for the rule "subtract 5", the patterns that he could have written include
A. 27, 22, 17, 12, 7
D. 100, 95, 90, 85, 80
What is the expression regarding the pattern?It is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.
Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc. In this case, when Jackson wrote different patterns for the rule "subtract 5", the patterns that he could have written include 27, 22, 17, 12, 7 and 100, 95, 90, 85, 80. In this cases, there are difference of 5.
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Complete question
Jackson wrote different patterns for the rule "subtract 5". Select all of the patterns that he could have written.
27, 22, 17, 12, 7
5, 10, 15, 20, 25
55, 50, 35, 30, 25
100, 95, 90, 85, 80
75, 65, 55, 45, 35
Please help me with the following question.
If one order is selected, the probability of getting an order that is not accurate is 0.236.
What is probability in maths?Probability is a measure of the likelihood of an event occurring. The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. Scientific probability is built on the basis of probability theory.
The calculation is;
P(Not accurate ) is equal to [n(Not accurate) + (Not accurate)- n] /Total
Thus, we have;
P(Not accurate) is calculated as follows:
(60 + 32 + 12 + 38 + 122 + 12 - 12)/(280 + 245 + 122 + 331 + 60 + 32 + 12 + 38).
P(Not accurate) = 264/1120
P(Not accurate ) = 0.236
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what is the value of the expression below?
[9.75+(1/2)^2]÷2
Answer:
5
Step-by-step explanation:
{9.75 + [tex]\frac{1}{2} ^{2}[/tex]] ÷ 2
[9.75 + [tex]\frac{1}{4}[/tex]] ÷ 2 1/4 = .25
(9.75 + .25) /2
10/2 = 5
NO LINKS!!
Underline the hypothesis and circle the conclusion in the following conditional statement. Then write the converse, inverse, and contrapositive. Determine whether each statement is true or false.
Conditional: If the stars are visible, then it is night.
Converse:
Inverse:
Contrapositive:
The hypothesis is "the stars are visible".
The conclusion is "it is night".
This is because a conditional follows the format of "if hypothesis, then conclusion". It shortens to "If P, then Q".
It's fairly clear that the original conditional is true. There are some extremely rare exceptions, but mostly stars are only visible at night.
--------------------------
The converse is "If it is night, then the stars are visible".
Reason: The original "If P, then Q" format flips to "If Q, then P" when forming the converse.
The converse is false. The fact that it is night does not automatically lead to the stars being visible. For example, storm clouds at night can obscure the stars.
--------------------------
The inverse is "If the stars aren't visible, then it is not night".
We negate both the hypothesis and conclusion. The format of the inverse is "If not P, then not Q".
Like the previous statement, the inverse is false. Why? Because the stars not being visible doesn't automatically mean it's not night. We could have storm clouds covering up the stars. Or perhaps the city has a lot of light pollution to drown out the stars.
The converse and inverse have the same truth value, as they are equivalent statements (just phrased slightly different ways).
--------------------------
The contrapositive is "If it's not night, then the stars aren't visible".
The original conditional "If P, then Q" leads to the contrapositive "If not Q, then not P". We swap the positions of P and Q. Also, we negate each piece. In a sense, we combine both the inverse and converse operations to get a contrapositive.
The contrapositive is true because "not night" of course means "day", in which the stars aren't present in the sky. The contrapositive and original conditional have the same truth value. The contrapositive is a way to rephrase the original conditional.
Answer:
Hypothesis: "the stars are visible"
Conclusion: "it is night"
Converse: "If it is night, then the stars are visible" - false.
Inverse: "If the stars are not visible, then it is not night." - false.
Contrapositive: "If it is not night, then the stars are not visible" - true.
Step-by-step explanation:
Conditional statement
"If this happens, then that will happen."
Hypothesis: The part after the "if".Conclusion: The part after the "then".Given conditional statement:
"If the stars are visible, then it is night."Therefore:
Hypothesis: "the stars are visible"Conclusion: "it is night"Converse statement
The converse of a conditional statement is formed by switching the hypothesis and the conclusion.
Therefore, the converse of the given conditional statement is:
"If it is night, then the stars are visible"This is a false statement as the stars will not be visible if there is cloud cover at night.
Inverse statement
The inverse of a conditional statement is formed by negating the hypothesis and the conclusion.
Therefore, the inverse of the given conditional statement is:
"If the stars are not visible, then it is not night."This is a false statement as the stars will not be visible if there is cloud cover at night.
Contrapositive statement
The contrapositive of a conditional statement is when both the hypothesis and conclusion are negated and then switched.
Therefore, the contrapositive of the given conditional statement is:
"If it is not night, then the stars are not visible"It is difficult to say if this is a true or false statement without more information, as it is possible to see bright stars during the daytime through a telescope or a really powerful pair of binoculars.
If we are to assume that "visible" means "visible to the eye" without any magnification assistance, then the statement is true (if we exclude the sun, which is a star).
please do I need help
Answer:
W
Step-by-step explanation:
What are two things that are the same for an angle of elevation in an angle of depression
Answer:
sight line & horizontal line
Step-by-step explanation:
varsitytutrs
What is the justification for step 3 in the solution process?
0.8a − 0.1a = a − 2.5
Step 1: 0.7a = a − 2.5
Step 2: -0.3a = -2.5
Step 3: a = 8.3
A.
the division property of equality
B.
the addition property of equality
C.
the subtraction property of equality
D.
combining like terms
Answer:
Letter A
Step-by-step explanation:
The justification for step 3 in the solution process is the subtraction property of equality. This property states that if two numbers are subtracted from each other on both sides of an equation, the two sides remain equal. In this case, step 3 is subtracting -0.3a from both sides of the equation, which results in a = 8.3.
Answer: A
Step-by-step explanation:
Please help answer this !!!!
The area of the rectangle with a length of (x + 5) cm and width of (x + 2) cm is (x² + 7x + 10) cm²
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A rectangle is a quadrilateral (has four sides and four angles) in which opposite sides are equal and parallel. The area of a rectangle is the amount of space that it occupies. The area is calculated using:
Area = length * width
The rectangle shown has a length of (x + 5) cm and width of (x + 2) cm. Hence:
Area = length * width
Substituting:
Area = (x + 5)(x + 2)
Area = x² + 2x + 5x + 10
Area = (x² + 7x + 10) cm²
The area of the rectangle is (x² + 7x + 10) cm²
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What is the answer for these expressions
a) 5-5 is a numerical expression
b) c-5 is a variable expression where, variable is c
c) 8÷x+9 is a variable expression where, variable is x
d) 100·6 is a numerical expression
What is numerical and variable expression?When an expression can be converted into a number value, it is said to be a numerical expression.Examples include 5-5, which evaluates to 0, and 8/2, which evaluates to 4. An expression that contains one or more variables and can have a variety of values depending on the particular values given to the variables is known as a variable expression.Examples include x + 2 (where x is a variable), 3y (where y is a variable), and a - b. (where a and b are variables).To learn more about expression refer to:
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Find the perimeter of each polygon
The perimeter of polygon ABC = 67.4
The perimeter of polygon PQRS = 78.8
What is the Perimeter of a Polygon?The perimeter of a polygon is calculated by adding the lengths of all sides of the polygon together.
What is the Two-tangents Theorem?The Two-Tangent Theorem states that if two tangents are drawn to a circle from the same external point, then the tangents are congruent (have the same length).
Perimeter of polygon ABC = AB + BC + AC
AB = 10.5 + (23.2 - 11.2) = 22.5 [based on the Two-Tangent Theorem]
BC = 23.2
AC = 10.5 + 11.2 = 21.7
Perimeter of polygon ABC = 22.5 + 23.2 + 21.7 = 67.4
Perimeter of polygon PQRS = PQ + QR + RS + PS
PQ = 25
PS = 21.8
QR = 13 + 4.6 = 17.6
RS = 4.6 + 9.8 = 14.4
Perimeter of polygon PQRS = 25 + 21.8 + 17.6 + 14.4 = 78.8
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Let L1 be a line that passes through the points (–2, 9) and (1, 3), and let L2 be the line that passes through the points (–4, 10) and (3, –4). Determine whether L1 and L2 are parallel
The two lines L1 and L2 are parallel
How to identify if the lines are parallelFor two lines to be parallel the slope must be equal, hence we calculate the slope of the two lines
The slope, m of the linear function L1 is calculated using the points (–2, 9) and (1, 3)
m = (y₀ - y₁) / (x₀ - x₁)
m = (9 - 3) / (-2 - 1)
m = (6) / (-3)
m = -2
The slope, m of the linear function L2 is calculated using the points (–4, 10) and (3, –4)
m = (y₀ - y₁) / (x₀ - x₁)
m = (10 + 4) / (-4 - 3)
m = (14) / (-7)
m = -2
The lines are parallel
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Three numbers sum to 117. The second number is 10 less than the first. The third number is 2 more than half the first. What are the three numbers?
Answer:
Step-by-step explanation:
The three numbers are 50, 40, and 27.
We can solve this equation by setting up a system of equations.
Let x be the first number, y be the second number, and z be the third number.
x + y + z = 117
y = x - 10
z = (1/2)x + 2
Substituting the equation for y into the first equation, we get:
x + (x - 10) + (1/2)x + 2 = 117
2x - 8 = 117
2x = 125
x = 62.5
Substituting this value of x into the other equations, we get:
y = x - 10 = 62.5 - 10 = 52
z = (1/2)x + 2 = (1/2)62.5 + 2 = 32.5 + 2 = 34.5
Rounding these values, the three numbers are 50, 40, and 27.
C varies inversely as J. If we also know that C=7 when J=25 , determine C when J=15. Round your answer to two decimal places!
Answer:
1
Step-by-step explanation:
C•1/J
C•K/J
K=C×J
K=175
when J =15
then C is;
C=K/J
175/15
C=11.67
ANYONE GOOD AT MATH PLEASE HELP!! I BEF OF YOU, YOU WILL EARN POINTS IF SO
Answer:
1. 3 -1
2. 6-3
3. 20-8 adding the smallest and the highest#
(Answer accurately to a spreadsheet!)
You run a table at a flea market for 7 days. You sell sunglasses for $5.00 per pair. You buy them for $1.25 per pair. These are your sales for the week: Day 1, 8 pair. Day 2, 7 pair. Day 3, 15 pair. Day 4, 12 pair. Day 5, 31 pair. Day 6, 20 pair. Day 7, 35 pair. How much were your sales each day? What were your total sales for the week? What was your daily average of sales? What
was your total cost? How much profit did you make?
Answer:
Day 1: 8 pairs x $5.00/pair = $40.00
Day 2: 7 pairs x $5.00/pair = $35.00
Day 3: 15 pairs x $5.00/pair = $75.00
Day 4: 12 pairs x $5.00/pair = $60.00
Day 5: 31 pairs x $5.00/pair = $155.00
Day 6: 20 pairs x $5.00/pair = $100.00
Day 7: 35 pairs x $5.00/pair = $175.00
Total sales for the week: $40.00 + $35.00 + $75.00 + $60.00 + $155.00 + $100.00 + $175.00 = $605.00
Daily average of sales: $605.00 / 7 = $86.43
Total cost: 8 pairs + 7 pairs + 15 pairs + 12 pairs + 31 pairs + 20 pairs + 35 pairs = 128 pairs x $1.25/pair = $160.00
Profit: $605.00 - $160.00 = $445.00
So your total sales for the week were $605.00, your daily average of sales was $86.43, your total cost was $160.00 and your profit was $445.00
Find the equation of a line that is parallel to y=13x−5 and passes through the point (3,−2).
Give your answer in the form y=mx+b.
Answer:
y = 13x - 41
Step-by-step explanation:
Parallel lines always have the same slope since
[tex]m_{2}=m_{1}[/tex]
Thus, the slope of the second line is m = 13.
We can find the y-intercept of the line by plugging in the points for x and y, 13 for m, and solving for b:
[tex]-2=13(3)+b\\-2=39+b\\-41=b[/tex]
A mother changes her baby 6 times a day. How many diapers will be deeded in a year?
1 year = 365 days
1 day => 6 diapers
1 year => 365 × 6 = 2190 diapers changed per year
If a1=6 and an=an-1 -2
Answer:
a₄ = 0
Step-by-step explanation:
using the recursive rule [tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] - 2 and a₁ = 6 , then
a₂ = a₁ - 2 = 6 - 2 = 4
a₃ = a₂ - 2 = 4 - 2 = 2
a₄ = a₃ - 2 = 2 - 2 = 0
Elabora un dibujo libre en el que consideres figuras con distintas transformaciones
The production of congruent figures involves stiff rigid transformation Even if you could imagine them as forms that "appear exactly the same," congruent figures.
Rigid transformation: what is it?During accurate modification of a geometric object, distance between each point pair is maintained. In other words, precise transformations maintain an object's size and shape. For instance, the angles and lengths of a triangle are preserved throughout a rigid transformation. Imagine a stiff shape, such as one made of cardboard, distorting. Even when the shape is rotated, mirrored, and moved left and right, nothing changes.
Here,
When I used putty to create a mold, it was the opposite. After that, users can stretch and twist the objects.
These ratios are not exact though. The distance between every pair of points is altered when the shape is stretched.
Applying rotations, reflection, and translations—three different forms of transformations—can result in congruent shapes.
In reality, by mixing any or all of these three transformations, any congruent shape pairs can be matched to one another.
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The complete question is " Do rigid transformations make congruent figures?"
What is the area (in square centimeters) of a rectangle that is 6.5 centimeters long and 2.4 centimeters wide?
Answer:
Area = 15.6 cm²
Step-by-step explanation:
Area of a rectangle = long * wide
Then:
Area of a rectangle = 6.5 cms * 2.4 cm
Area of a rectangle = 15.6 cm²
Mr. Vivaldi is getting ready for the spring orchestra concert.
please help asap
• it would mean sm and make my day
The compound inequality for the graph given is -2 < x < 5.
How to find the compound inequality ?When a compound inequality is graphed such that there is an open circle instead of a filled - in circle over a number, then it means that x is either greater than this value, or less than this value. In other words, x is not equal to this value.
The circles over - 2 and 5 are not filled in which means that x is greater or less than - 2 and 5.
x is less than 5 because the arrow goes from 5 to infinity and x is greater than - 2 for the same reason.
The compound inequality is therefore:
-2 < x < 5
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Find an ordered pair (x, y) that is a solution to the equation.
4x-y=3
(x, y) = (_, _)
Answer:
(0, -3)
Step-by-step explanation:
You want a point on the graph of 4x -y = 3.
PointIt is often convenient to choose an intercept when looking for a point that will satisfy the equation. Here, it is convenient to set x=0 to obtain y=-3.
A solution ordered pair is (0, -3).
__
Additional comment
Here, it will be more convenient to choose a value for x. Choosing a value for y can result in fractions becoming involved for the values of x. We prefer to avoid that.
y = 4x -3 . . . . . . y=-3 when x=0; y=1 when x=1, so (1, 1) is another solution
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What percent is 40 out of 160?
Answer:
Step-by-step explanation:
57
Answer: 25%
Step-by-step explanation:
How would the following triangle be classified?
Answer:
scalene acute as its all sides length are not equall and its all angle are less than 90 degrees
HELP MEEEEEEEEEEEEEE
Answer:
B
Step-by-step explanation:
after 0 it's 1 and 4 is after 5
x+6y=-5
2x+12y=-10
Solve the system using elimination method
Answer:
The system has infinitely many solutions---------------------------------------
Given system:
x + 6y = - 52x + 12y = - 10First simplify the second equation by dividing all terms by 2:
x + 6y = - 5We got the same equation as the first one. It means the two lines overlap, so there are infinitely many solutions.
If we use elimination method, we will subtract the two equations then end up with equation 0 = 0.
you can perform 6 push ups in 24 seconds. wrote and graph an equation that represent the relationship between time and number of push up. at this rate how many pushups can you perform in 2 minutes
At the given rate, I can perform 480 pushups.
Your goal should be to complete 100 push-ups in 2 minutes (this is a standard for elite soldiers).
White defines that as 10 to 20 push-ups if your max is 25 reps, 2 sets of 10 to 20 if your max is 25 to 50 reps, and 2 to 3 sets of 10 to 20 if your max is greater than 50 push-ups. "If you're doing a lot of sets and hitting a lot of volume, I'd try to do them every other day.
24/6 = 4
meaning they are doing 4 push ups per second, this is your slope
the equation of your line is y = 4x, you can graph this using a table of values
2 minutes = 120s
y = 4(120)
y = 480 push ups
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