the number of ways of selecting and matching nine banners with a country is 36.
What is combination?
A combination is a choice made in mathematics from a group of different elements when the order of the choices is irrelevant (unlike permutations). For instance, if three fruits, such as an apple, an orange, and a pear, are supplied, there are three possible pairings of the two: an apple and a pear. Formally speaking, a k-combination of a set S is a subset of S's k unique components. In other words, two combinations are the same if and only if they have the same members. (It is not important how the individuals in each set are arranged.) The quantity of k-combinations for a set with n components
Given, 9 of the 20 banners with the word “Hello” in different languages with the 9 countries
Toatl ways for arranging the 9 banners will be 9C2
And as the matching nine banner with the country is 9/20
So the number of ways of selecting is 9c2 = 36.
Hence the number of ways to select and matching the banner is 36.
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What is the answer to this question?
Find the value of X in the diagram.
The value of x is 10, in the diagram, Vertically opposed angles
What is Vertically opposed angles?
Two lines intersecting at a point create vertical angles. Every time they are on an equal footing. Alternatively stated, four angles are created anytime two lines cross or intersect. Two opposed angles are equal and are referred to as vertical angles, as we can see. Due to their position opposite one another, they are also known as "Vertically opposed angles."
Angles that are vertically opposed to one another at a certain vertex are formed by two straight lines intersecting. The equality of the vertically opposed angles has been established.
Here in the diagram 5x = 2y
y = 5X/2
We have 2y+2y+8x = 180 in a straight line.
So 4y+8x = 180
4(5x/2) +8x = 180
10x+8x = 180
x = 180/18
x = 10
Hence, the value of x is 10, in the diagram.
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A company receives medicine in 1-gallon (128-ounce) jars and then sells the medicine in vials that hold 3 ounces. What fraction of another vial could be filled with the leftover medicine? How do you know?
The fraction of another vial could be filled with the leftover medicine is 125 / 128.
What is a fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
In this case, the company receives medicine in 1-gallon (128-ounce) jars and then sells the medicine in vials that hold 3 ounces
The fraction left will be:
= 1 - Amount filled
= 1 - 3/128
= 125 / 128
The fraction left is 125 / 128.
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HELP ASAP!! 50 PNTS THANKS
Answer: 1st and 2nd
Step-by-step explanation:
An investment of $400 is compounded monthly at an interest rate of 7.6%. What will the
balance be in eight years? Round to the nearest hundredth.
Answer:
See below
Step-by-step explanation:
Present Value = 400
Period = 1 month 8 years is n = 96 periods
Interest per period in decimal form i = .076 / 12 = .0063333
Fv = PV ( 1 + i)^n
Fv = 400 ( 1 + .076/12)^96 = 733.29 dollars
Randi takes the stairs at work whenever possible instead of the elevator. She must climb 51 steps from her office to get to the accounting department. The human resources
department is 34 steps below her office. How many steps are there between human
resources and accounting?
The steps between the human resource department and accountant department are 85 steps.
What is Human Resource?
The group of individuals who work for a given organization, business sector, industry, or economy is referred to as its human resources.
As given in the question,
Randi must climb 51 steps from her office to get to the accounting department, and
The HR department is 34 steps below her office.
Since, the HR department is below her office and accountant department is above her office so, we need to add the steps taken from her office to reach both department.
So,
Steps between HR department and accountant department = Steps between her office and HR department + Steps between her office and accountant department
Steps between HR department and accountant department = 51 + 34
Therefore,
Steps between HR department and accountant department = 85 steps
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Please help! Thank you so much!
Answer:
x=14
Step-by-step explanation:
A fruit basket contains 3 apples, 1 orange, 3 grapefruits, and 2 bananas. How many
pieces of fruit are in the basket?
O 10
09
08
07
dembow needs to hire a mechanic to fix his car. Mechanic G charges $30 per hour of work while mechanic k charges $20 per hour of work plus a $30 reservation fee. Write equations for mechanic G and mechanic k where y is the cost in dollars and x is the hours of work.
The equations for Mechanic G is y = 30x and for mechanic K is y = 20x + 30
What is rate?Rate is a ratio that compares two different quantities which have different units. For example, if we say John types 50 words in a minute, then his rate of typing is 50 words per minute. The word "per" gives a clue that we are dealing with a rate.
for mechanic G since he charges 30 dollars per hour, for x hours his charge will be 30x
so that y = 30x
For K since he charges at rate of 20 dollars per hour, his charge after x hours will be 20x. if he takes 30 dollars reservation fee
then his total cost is y = 20x + 30
In conclusion, the equations for mechanic G and K are y = 30x and y = 20x + 30 respectively.
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The bulbs are incandescent bulb for a and fluorescent bulb is for b
A 0.3kwh in 3 hours and 1.0kWh in 10 hours and for b is 0.35Kwh in 3 hours and in 10 hours it’s 0.9 kWh usage (pls help brainlist)
The graph has been shown where lines A and B meet each other at the coordinates (0.51, 5.2).
What are graphs?In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.Bar graphs, circle graphs, and line graphs are the three most often used types of graphs. Different types of data can be displayed using different types of graphs.So, the coordinates where both lines meet are:
Coordinates for line A:
(0.3, 3)(1.0, 10)Coordinates for line B:
(0.35, 3)(0.9, 10)Now, plot the graph as follows:
(Refer to the graph attached below)
The coordinates where both lines meet are:
(0.51, 5.2)Therefore, the graph has been shown where lines A and B meet each other at the coordinates (0.51, 5.2).
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Which Trinomials are perfect square trinomials?
A) 25a^2-40a+64
B) x^2-6x-16
C) 16z^4+48z^2+36
D) 9m^2+36m+36
Trinomials that are perfect square trinomials are (C) [tex]16z^{4}+48z^{2}+36[/tex] and (D) [tex]9m^{2}+36m+36[/tex].
[tex](a+b)^{2}=a^{2}+2ab+b^{2}[/tex]
We will check every trinomials in given options.
(A) [tex]25a^{2}-40a+64[/tex]
[tex]25a^{2} = (5a)^{2}[/tex]
[tex]64 = 8^{2}[/tex]
[tex]-40a \neq 2(5a)(8)[/tex]
Hence, its not a perfect square.
(B) [tex]x^{2}-6x-16[/tex]
[tex]x^{2} = (x)^{2}[/tex]
[tex]-16 \neq 4^{2}[/tex]
[tex]-6x \neq 2(x)(4)[/tex]
Hence, its not a perfect square.
(C) [tex]16z^{4}+48z^{2} +36[/tex]
[tex]16z^{4} = (4z^{2} )^{2}[/tex]
[tex]36 = 6^{2}[/tex]
[tex]48z^{2}=2(4z^{2} )(6)[/tex]
[tex]16z^{4}+48z^{2} +36 = (4z^{2}+6 )^{2}[/tex]
Hence, its a perfect square.
(D) [tex]9m^{2}+36m+36[/tex]
[tex]9m^{2} = (3m)^{2}[/tex]
[tex]36 = 6^{2}[/tex]
[tex]36m=2(3m)(6)[/tex]
[tex]9m^{2}+36m+36 = (3m+6)^{2}[/tex]
Hence, its a perfect square.
Therefore, only (C) and (D) are perfect square.
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A fraction can easily be written as a percent when the denominator is _________________.
Group of answer choices
100
50
10
20
Answer:
100
Step-by-step explanation:
Example 33/ 100 = 33% 28/ 100= 28 % etc
Mr. Baker leaves the check-in counter at the airport and walks to a moving sidewalk, which takes him to his gate. Mr. Baker's distance (d), in meters, from the check-in counter while he has been standing on the moving sidewalk for s seconds, is described by the function d = 2s + 20.
Which statement is true?
A. Mr. Baker is 2 meters from the check-in counter after 22 seconds.
B. Mr. Baker is 20 meters from the check-in counter 24 seconds.
C. Mr. Baker moves 2 meters per second while standing on the moving sidewalk, and he walked 20 meters to get to the moving sidewalk.
D. Mr. Baker moves 20 meters per second while standing on the moving sidewalk, and he walked 2 meters to get to the moving sidewalk.
Mr. Baker moves 2 meters per second while standing on the moving sidewalk, and he walked 20 meters to get to the moving sidewalk. which is the correct answer would be an option (C).
What is the distance?Distance is defined as the product of speed and time.
The function shows Mr. Baker's distance (d), in meters, from the check-in counter while he has been standing on the moving sidewalk for s seconds. d = 2s + 20.
Here He travels at a speed of two meters per second while standing on the moving sidewalk, and he walked 20 meters to get there.
Thus, Mr. Baker moves 2 meters per second while standing on the moving sidewalk, and he walked 20 meters to get to the moving sidewalk.
Hence, the correct answer would be option (C).
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Plsssssssss helpppppppppppp
find the value of y when x=11. y--6x +5
Answer: 71
Step-by-step explanation:
First, plug 11 in for x: y=6(11)+5
Then, multiply 6 by 11: 6(11)=66
Finally, add 5: 66+5=71
Express
2x² + 20x + 7
in the form 2(x + p)² + q
The given expression is expressed in the form of 2(x + p)² + q as:
f(x) = (x + 5)² - 21.5
Given,
Express
2x² + 20x + 7
Step 1: Subtract both sides by 7
2x² + 20x = -7
Step: GCF and divide
2(x² + 10x) = -7
x² + 10x = -7/2
Step 3: Complete the Square
x² + 10x + 25 = -7/2 + 25
(x +5)² = 43/2
Step 4: Subtract 43/2 to both sides
(x + 5)² - 43/2
Hence we get the equation.
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Is this graph a function?
ANSWERS:
This is a function.
This cannot be determined from this graph.
This is not a function.
(C) This is not a function.
The equation x = 3 represents a vertical line and not a mapping from values of x to values of y.
Hence, its a equation not a function.
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The sum of 8 times a number and 2 equals 6. translate the sentence into an equation
Answer: (8x + 2) = 6
Step-by-step explanation:
Answer:
8(x) + 2 = 6
Step-by-step explanation:
What is the y-intercept of the linear equation x minus one-half y = negative 6? –6 –3 0 12
Answer:
The y-intercept is 12
Step-by-step explanation:
the equation is: x - 1/2y = -6
We need to find the y-intercept which is the y value when x=0.
Knowing that, we can just substitute 0 for x to get:
0 - 1/2y = -6
From there, it's just algebra so:
0 - 1/2y = -6
-1/2y = -6
-0.5y = -6
y = 12
College tuition: A simple random sample of 35 colleges and universities in the United States has a mean tuition of $19,300 with a standard deviation of
$10,800. Construct a 95% confidence interval for the mean tuition for all colleges and universities in the United States. Round the answers to the nearest whole
number.
A 95% confidence interval for the mean tuition for all colleges and universities is
Answer:
The 95% confidence interval for the mean tuition for all colleges and universities in the United States is between $15718 and $22882.
Step-by-step explanation:
Sample size greater than 30, which means that we use the normal distribution to find the interval.
We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:
α = (1 - 0.95) / 2
= 0.025
Now, we have to find z in the table as such z has a pvalue of . So it is z with a pvalue of 1 - 0.025 = 0.975.
So, z = 1.96
Now, find M as such
M = z * (σ / √n )
In which σ is the standard deviation of the population and n is the size of the sample.
M = 1.96 * ( 10800 / √35 )
M = 3581.72
M ≈ 3582
The lower end of the interval is the sample mean subtracted by M. So it is 19300 - 3582 = $15718.
The upper end of the interval is the sample mean added to M. So it is 19300 + 3582 = $22882.
The 95% confidence interval for the mean tuition for all colleges and universities in the United States is between $15718 and $22882.
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A toy rocket is shot vertically into the air from a launching pad 7 feet above the ground with an initial velocity of 72 feet per second. The height h, in feet, of the rocket above the ground at t seconds after launch is given by the function h(t)=-16 t²+72 t+7. How long will it take the rocket to reach its maximum height? What is the maximum height?
The rocket reaches its maximum height at ______ second(s) after launch.
(Simplify your answer.)
The maximum height reached by the object is ______feet.
(Simplify your answer.)
The maximum height of the object is 88 feet and the time is 2.25 second(s) after launch
Time to reach the maximum heightThe function is given as
h(t) = -16t² + 72t + 7
Differentiate the above function
So, we have the following representation
h'(t) = -32t + 72
Set to 0
-32t + 72 = 0
So, we have
32t = 72
Divide by 32
t = 2.25
Hence, the time is 2.25 seconds
The maximum heightIn (a), we have
t = 2.25
Substitute t = 2.25 in h(t) = -16t² + 72t + 7
h(2.25) = -16(2.25)² + 72(2.25) + 7
Evaluate
h(2.25) = 88
Hence, the maximum height is 88 feet
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Factorise 12xto the power of 3 -4xsquared
The factorized form of the given mathematical phrase 12x to the power of 3 - 4xsquared will be 4x²(3x - 1).
What is an algebraic factor?An algebraic factor is the multiplication of two algebraic terms.
The root of the quadratic equation formed by the algebraic factor is always real.
That term could be in form of summation multiplication or in subtraction.
As per the given phrase,
12x to the power of 3 - 4xsquared
12x³ - 4x²
Take x² as common,
x²(12x - 4)
Take 4 as common
4x²(3x - 1)
Hence "The factorized form of the given mathematical phrase 12x to the power of 3 - 4xsquared will be 4x²(3x - 1)".
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help me on this question (20pts)
The function with same rate of change as the function y = (7/4)x + 3 will be option C.
The rate of change for a function is nothing but rate of change of one thing over the second thing.
it can be calculated by [tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]
For a equation written in y = mx + c , m is nothing but the slope / rate of change of function.
So for function y = (7/4)x + 3
m = 7/4 which is the rate of change for this function.
Now let us find rate of change for each function.
For A rate of change will be = (-4 - 0) / (5 - 1)
= -4/3
For B it will be = ( 4 - 1) / (0 - (-1) )
= 3
For C it will be = (15 - 8) / (8 - 4)
= 7/4
For D it will be = (-2 - 0) / ( 0 - (-1) )
= -2
Therefore the rate of change which is same as the given function is of option C.
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Reasoning Solve the given equation and check your answer. Use pencil and paper. Is it possible to solve the equation using multiplication?
Explain your reasoning.
8x= (-16)
The value of x after solution of the equation 8x = -16 is -2 and it is not possible to solve this equation using multiplication.
According to the question,
We have the following equation:
8x = -16
Now, this equation can not be solved using multiplication because 8 is already in multiplication with x on the left hand side. If 8 would have been in division then it could be solved using multiplication.
So, dividing by 8 on both the sides:
x = -16/8
x = -2
Hence, the value of x after solution of the equation 8x = -16 is -2 and it is not possible to solve this equation using multiplication.
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Membership at a private arcade club costs a one-time initiation fee of $50 plus $10
per month.
Part A: Write a function expressing the total amount of money spent on membership
as a function of the number of months.
Part B: Identify the independent variable and the dependent variable in this
situation.
Part C: How much total money has been spent on membership after 12 months?
Answer:
600 is the answer to the question
Foster recently went on a weekend hiking trip and recorded the elevation changes at several checkpoints. Fosters elevation log can be seen in the table below. If the next checkpoint has a change in final elevation of 148.3 what is the change in elevation
4. The greatest change in elevation is on Checkpoint 4.
5. The change in elevation on the final checkpoint is of: -62.1 feet.
How to obtain the change in elevation for each checkpoint?The change in elevation for each checkpoint is given by the subtraction of the final elevation by the initial elevation. Both these elevations are given on the table.
Hence, for each checkpoint, the changes are given as follows:
Checkpoint 1: -78 - (-125.4) = 47.4 feet.Checkpoint 2: -101.6 - (-78) = -23.6 feet.Checkpoint 3: 14.7 - (-101.6) = 116.3 feetCheckpoint 4: 225.1 - 14.7 = 210.4 feetHence the greatest change is of 210.4 feet on checkpoint 4.
The final elevation is of 148.3 feet, hence the change in elevation on the final stage is obtained as follows:
148.3 - 210.4 = -62.1 feet.
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Solve #20 and show explanation
The next step is 4004 x 4004. So option(b) is correct
The process of making something less complicated and thus easier to do or understand, or the result of such a process is a simplification.
Reduce the expression to 3/4x + y/2 (4x + 7). The given expression can be written as 3/4x + y/2 (4x) + y/2 using the distributive property.
Given that
44 x 44 = 1936
404 x 404 = 163216
We have to find the next step
In the first step only fours are there
In the next step 0 is included in between the fours
If we follow the same sequence there will be two zeros coming between fours
= 4004 x 4004
= 16032016
Therefore the next step is 4004 x 4004
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Y is greater than or equal to 2
The given statement in mathematical notation is Y≥2.
Given that the statement is Y is greater than or equal to 2.
We want to write the given statement in the mathematical notation.
In algebra, statements basically consist of true or false statements. These mathematical statements can consist of words and symbols.
The greater than in symbolic form is > and greater than or equal to ≥.
As it is given that Y is greater than or equal to 2 can be rewritten as Y≥2.
Hence, the given statement Y is greater than or equal to 2 is Y≥2.
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Write an expression for the sequence of operations described below.
raise 3 to the 9th power, then add the result to j
Do not simplify any part of the expression.
An expression for given sequence of operations is: j + 3^9
In this question, we need to write an expression for the sequence of operations described below.
raise 3 to the 9th power, then add the result to j
Consider the part of given statement,
raise 3 to the 9th power
We write this as: 3^9
then we add this result to j.
So, we get an expression: 3^9 + j
Therefore, an expression for given sequence of operations is: j + 3^9
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What is the answer???
Answer:
-(x+1)²+4
Step-by-step explanation:
y = -x²-2x-3
= -[x²+2x+3]
= -[(x²+2x)+3]
{formulae to get the vertex form is add (b/2)² to the expression
(2/2)² = 1}
= -[(x²+2x+1)-1+3]
{we are adding so we have to subtract the same number as well}
= -[(x²+2x+1)+2]
thus vertex form,
y = -(x+1)²+2
When 14 is subtracted from the square of a number, the result is 5 times the number. Find the positive solution.
The positive solution for the given equation is 7 .
In the question ,
it is given that ,
when a number 14 is subtracted from the square of number ,
then the result is 5 times the number .
let that number be "x" .
So , the equation representing the amount statement is
x² - 14 = 5x
x² - 5x - 14 = 0
By using splitting the middle term method to find the solution.
we get ,
x² - 7x [tex]+[/tex] 2x - 14 [tex]=[/tex] 0
taking x common ,
x(x - 7) + 2(x - 7) = 0
(x + 2)(x - 7) = 0
we get , x + 2 = 0 and x - 7 = 0
the solution as x = -2 and x = 7 ,
Therefore , The positive solution for the given equation is 7 .
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Answer:7
Step-by-step explanation:
