The correct option c) 120; for the assignment of 7 students to 10 seats in a row.
What is referred as the combination?Combinations are mathematical techniques that count the number of potential arrangements for a set of elements only when order of the selections is irrelevant. You can choose the constituents of combos in any order.The procedure for determining how many arrangements are feasible when only a few items are selected from a set of items that are unique is as follows:The formula for finding the combination is-
ⁿCₓ = n!/ x!(n - x)!
Where,
n = total value.x = selected valueFor the given question.
Total students to be assigned a seat = 7.
Total seats in a classroom = 10.
Thus, Applying combination;
¹⁰C₇ = 10!/7!(10 - 7)!
¹⁰C₇ = 120
Thus, if there are 10 seats in a row, there are 120 different ways that 7 students could be seated in a classroom.
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a wooden cube nn units on a side is painted red on all six faces and then cut into n^3n 3 unit cubes. exactly one-fourth of the total number of faces of the unit cubes are red. what is nn?
After being painted red on all six faces, a hardwood cube with nn units on each side is chopped into n3n 3-unit cubes. The unit cubes have exactly one-fourth of their faces be red, therefore nn equals 4.
On each face of the large wooden cube, there are tiny faces that have been painted red.
There are few faces overall because each unit cube has faces.
Given that one-fourth of the little faces are red,
[tex]6n^2/6n^3[/tex] [tex]= 1/4[/tex]
[tex]1/n = 1/4[/tex]
[tex]N=4[/tex]
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DIMENSIONAL ANALYSIS (MATH) GIVING BRAINILIEST!
Q1: What is the speed of a horsefly in feet per second? Round to the nearest hundredth.
Q2: How many times does a dragonfly's wing beat per minute?
Q3: About how many times can a bumble bee travel in one minute?
Answer:
Q1 = 6.45f/s
Q2 = 0.633 times
Q3 = 0.107 miles
Step-by-step explanation:
Q1: Since
4.4 miles = 1 hour
and
1 mile = 5,280 feet
1 hour = 3600 seconds
Then 4.4 miles
= 5,280 feet × 4.4
= 23,232 feet / 3600 seconds
= 6.453f/s
= 6.45f/s
Q2: Wing beat per minute
= 38 ÷ 60
= 0.633 times
Q3: Miles per minute
Since 6.4 miles = 1 hour,
6.4 miles = 1 × 60
6.4 miles = 60 minutes
x miles = 1 minute
= 6.4/60
= 0.107 miles
Find the perimeter of this semi-circle
with diameter, d = 84cm.
Give your answer as an expression in
terms of π.
The perimeter of this semi-circle with diameter, d = 84cm the expression in terms of π are as follows:
= 48π + 42
What is the equation for a semicircle?The area of a circle, A, is calculated using the formula A = pi * r2, where r is the circle's radius. Since we already know that a semicircle is half of a circle, we can easily divide that equation by two to determine the area of a semicircle. As a result, A = pi * r2/2 is the formula for calculating the area of a semicircle.
How do you calculate the circumference of a half-semicircle?With the aid of the following formula, we can determine a semicircle's perimeter: The semicircle's perimeter is equal to r + 2r units, where r is the radius of the semicircle.
According to the given data:Diameter of the semi-circle = 84cm
Now,
the circumference of the semi-circle = πr + 2r
Substituting the value of r in the given formula:
the circumference of the semi-circle = πr + 2r
= πr + 2r
= 48π + 42
The perimeter of this semi-circle with diameter, d = 84cm the expression in terms of π are as follows:
= 48π + 42
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2. Maria earns a $50,000 salary plus a 10% commission on any sales over $20,000. Last year
Maria made $40,000 in sales. How much did Maria earn in salary plus commission?
Last year, Maria earned $54,000
In this question, we have been given Maria earns a $50,000 salary plus a 10% commission on any sales over $20,000.
Last year Maria made $40,000 in sales.
This means, she got 10% commission
We find the 10 percent of 40000.
40000 * (10/100) = 4000
Her total earning would be,
$50,000 + $4000(commission) = $54,000
Therefore, Maria earned $54,000
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the superintendent of schools in a small town in ohio made many policy changes to the way school administration worked in his district. a researcher at a nearby university wanted to look at what teachers in his district thought about the changes. the researcher made a list of all the schools in the district and used a random number generator to select a sample of five schools from the district. then the researcher interviewed every teacher at each of those five schools. which sampling method did the researcher use?
Answer:
The number to the ration
Step-by-step explanation:
Which equations are true for x = –2 and x = 2? Select two options x2 – 4 = 0 x2 = –4 3x2 + 12 = 0 4x2 = 16 2(x – 2)2 = 0
By using algebra properties, the quadratic equation y = x² - 4 contains the roots x = - 2 and x = 2.
How to derive a quadratic equation by factorizationIn this problem we need to derive the quadratic equation that contains two roots: r₁ = - 2, r₂ = 2. We need to replace all roots in the factor form of the quadratic equation and expand it by algebra properties. First, replace the roots of the factor form of the quadratic equation:
y = (x - r₁) · (x - r₂)
y = (x + 2) · (x - 2)
Second, expand the expression derived in the previous step by algebra properties:
y = (x + 2) · x - (x + 2) · 2
y = x² + 2 · x - 2 · x - 4
y = x² - 4
Third, write the resulting expression:
y = x² - 4
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Darius ran a total distance of 52 1/4 mile last month. Each day he went for * 1 pc
a run, he ran 2 3/4 miles. How many days did Darius run last
month?
Answer:
82 and 2/4 (if it was 30 days)
Step-by-step explanation:
you turn the fraction into a decimal and multiply it by the certain number of what you need to figure out.
12 mushrooms $3 How much for one
Answer:
4
Step-by-step explanation:
12÷3=4
Complete the proof that
With the help of angles we can say that ∠HJI=∠FJG.
What are angles?When two straight lines or rays intersect at a single endpoint, an angle is created.The vertex of an angle is the location where two points come together.The Latin word "angulus," which means "corner," is where the term "angle" originates.Vertex: The intersection of two lines or sides at an angle is called a vertex. In the diagram, O is the vertex.Arms: The angle's two sides linked at a single end. The arms of an angle are OA and OB.Initial Side: A straight line from which an angle is drawn, sometimes referred to as the reference line. The reference line is OB.The side that the angle measurement is done up to is known as the terminal side. OA is the terminal side in the diagram that is shown below.Acc to our question-
∠HJI=∠FJG=180 , they are forming linear pairs.due to transitive property of inequality we can say that-they both are equal and congruent.Hence, ∠HJI≅∠FJG are equal and congruent.
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the sum of the measures of the angles in the triangle is 180 degrees. what is the measure of each angle? write and solve an equation
If sum of the measures of the angles in the triangle is 180 degrees then
measures of each angle is 60 degrees.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Given,
The sum of the measures of the angles in the triangle is 180 degrees
By angle sum property, sum of the measures of the angles in the triangle is 180 degrees
Let the measure of angle be x
x+x+x= 180 degrees
3x=180
Divide both sides by 3
x=180/3
x=60
Hence each angle measures 60 degrees.
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What else must you know to prove the triangles congruent by SAS?
D
B
OA AB CD
OB. AD AC
O CAB DC
OD AD BC
As per the reference attachment attached thereby along with the question statement, to prove the triangles ABC and ADC are congruent by SAS property, proving either of (AB ≅ CD), (AB ≅ DC) or (AD ≅ BC) will suffice.
In the reference attachment attached thereby along with the question statement, we are provided with two triangles, (ADC and ABC),
And as per the question statement, we are required to determine the relation between the corresponding sides or angles of the concerned triangles which we will need to prove over the information already provided in the figure, to ascertain that triangles ABC and ADC are congruent by SAS property.
Now, for two triangles to be congruent by SAS property, they will need to have two pairs of equal corresponding sides, and one set of equal corresponding angles.
Among our concerned triangles, ΔABC and ΔADC, already given that,
(∠DAC = ∠BCA), i.e., one set of equal corresponding angles,
And, (AC) is a common side to both ΔABC and ΔADC, i.e., one set of equal corresponding sides.
At this point, for ΔABC and ΔADC to be congruent, we will need to prove another set of corresponding sides to be equal, to complete SAS property.
Therefore, proving either of (AB ≅ CD), (AB ≅ DC) or (AD ≅ BC) will complete the second set of corresponding sides being equal, and (ΔABC and ΔADC) can be proved to be congruent triangles.
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Over which of the following intervals would the function h(x)=|x-2|+6 be decreasing only?
We have an absolute value function that opens upwards. The interval where it is decreasing only is:
(-∞, 2)
Over which interval is the function decreasing only?All absolute value equations of the form:
y = |x - a| + b
have graphs that open upwards, and a vertex in the point (a, b).
While ones of the form:
y = -|x - a| + b
have graphs that open downwards, and again, a vertex in the point (a, b).
In this case we have one that open upwards:
h(x)=|x-2|+6
With a vertex at (2, 6)
The function will be decreasing on the left side of the vertex, so the interval where the function is only decreasing is:
(-∞, 2)
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2/7 x 2 1/4 write your answers in simpliest form
Answer:
the answer is 9/14
Step-by-step explanation:
2/7× 2 1/4 = 2/7× 9/4
= 2 × 9 / 7 × 4
= 18/28
= 9/14
What is the radical form of each of the given expressions? Drag the answer into the box to correctly match each expression.
2 2/3 -
3 1/3 -
3 3/2 -
2 1/2 -
The radical form of each of the given expressions are;
1) 2^(2/3) = ∛(2²)
2) 3^(1/3) = ∛3
3) 3^(3/2) = √3³
4) 2^(1/2) = √2
What is the radical form of the exponent form?The radical form of the expression [tex]a^{\frac{x}{y} }[/tex] is; [tex]\sqrt[y]{a^{x} }[/tex]
Thus, we can solve each of the given expressions;
1) We are given the expression as 2^(2/3).
Thus;
x = 2 and y = 3 and we have; ∛(2²)
2) We are given the expression as 3^(1/3).
Thus, x = 1 and y = 3 and so we have;
∛3
3) We are given the expression as 3^(3/2). Thus;
x = 3 and y = 2 and so we now have; √3³
4) We are given the expression as 2^(1/2). Thus;
x = 1 and y = 2 and so we now have; √2
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Read Zalika's number problem.
' I am thinking of a number N. Twice (N+10) is the same as four times (N-10) '
a. Write down an equation to show this.
b. Solve the equation to find the vale of N.
Part A
The equation that shows the statement is
2N + 20 = 4N - 40
Part B
The value of N = 30
The number that he is thinking = N
Twice (N+10) = 2(N+10)
= 2N + 20
Four times (N-10) = 4(N - 10)
= 4N - 40
Twice (N+10) is the same as four times (N-10)
The equation that represent the given statement is
2N + 20 = 4N - 40
Part B
Solve the equation
2N + 20 = 4N - 40
4N - 2N = 20 + 40
2N = 60
N = 60/2
Divide the terms
N =30
Hence,
Part A
The equation that shows the statement is
2N + 20 = 4N - 40
Part B
The value of N = 30
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A bus drove 265 miles from la to lv in 4 hours.if it traveled at a constant speed,how many hours will it take to travel from salt lake city to las vegas give the distance from las vegas to salt lake city is 425 miles
Time taken by bus to travel from Las Vegas to salt lake city is 6.41 hours.
Here it is given that bus travel from La to Lv in 4 hours and the distance between them is 265 miles.
We have to find the time taken to travel from Las Vegas to salt lake city whose distance between them is 425 miles.
Formula to find the speed is:
Speed = Distance / Time
Distance = 265 miles
Time = 4 hours
Speed = 265/4
= 66.25 miles/ hour
From this, we can find the time taken to travel from Las Vegas to salt lake city.
Distance = 425 miles
Speed = 66.25 miles/ hours
Speed = Distance/time
Time = Distance / Speed
= 425/ 66.25
= 6.41 hours
Therefore the time taken is 6.41 hours.
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in order to estimate attendance at a music festival, management counts the number of people entering the admissions gate in a 30-minute sample time. management assumes that there is a steady stream of people entering the festival for the 10 hours that the admissions gate is open. at a particular music festival, 2,250 people were counted entering the gate in a 30-minute sample time. what was the estimated attendance at this festival?
Answer:
45,000
Step-by-step explanation:
Given a 30 minute sample of a constant stream shows 2250 people entered the gate, you want an estimate of the total number of people through the gate in 10 hours.
AttendanceA half-hour period is 1/20 of the 10-hour period the gate was open. The rate is assumed constant, so the 2250 people entering in that half-hour period is presumed to be 1/20 of the total attendance.
20 · 2250 = 45000
The estimated festival attendance is 45,000 people.
a party rental company has chairs and tables for rent. the total cost to rent chairs and tables is . the total cost to rent chairs and tables is . what is the cost to rent each chair and each table?
If the total cost to rent 2 chairs and 12 tables is $107 and the total cost to rent 5 chairs and 3 tables is $38, then the costs to rent each chair and table are $2.5 and $8.5 respectively. We can solve this question using elimination and substitution methods.
How do you prove that?Elimination and substitution methods are involved in solving this problem. We're going to use the variables x for the cost of a chair and y for the cost of a table. The total cost to to rent 2 chairs and 12 tables is $107, so the equation can be written as 2x + 12y = 107. The total cost to rent 5 chairs and 3 tables is $38, so the equation can be written as 5x + 3y = 38.
To find the value for x, we need to eliminate the variable y first. Start by multiplying each term in the second equation by 4.
5x · 4 + 3y · 4 = 38 · 4
20x + 12y = 152
Then, subtract the terms in the second equation from their counterparts in the first equation.
2x + 12y = 107
20x + 12y = 152 -
-18x + 0 = -45
Finally, with a little bit of algebraic manipulation, we've got x = 2.5, hence $2.5 is the cost in to rent a chair.
-18x = -45
x = -45/-18
x = 2.5
What about the cost to rent a table? Well, we can substitute 2.5 for x in either of the equations to get the value for y. For instance, we can pick the equation 2x + 12y = 107 and substitute x with 2.5 to isolate the variable y, like this:
2(2.5) + 12y = 107
5 + 12y = 107
12y = 107 - 5 = 102
y = 8.5
The value for y turns out to be 8.5. So the cost to rent a table is $8.5.
Your question is incomplete, but it was most probably "A party rental company has chairs and tables for rent. The total cost to rent 2 chairs and 12 tables is $107. The total cost to rent 5 chairs and 3 tables is $38. What is the cost to rent each chair and each table?"
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The figure shows two parallel lines, j and k, cut by two transversals, t₁ and t₂.
What is the value of m<3, in degrees, if m<5 = 70° and m<2 = 60°?
the figure for m3 in the above question is 50
Parallelogram ABCD is a rectangle.
AC = 2y + 7
BD = 3y - 4
What's the value of Y?
The value of y is 11.
What is a parallelogram?That quadrilateral in which opposite sides are parallel is called a parallelogram.
Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.
Given that Parallelogram ABCD is a rectangle.
Consider that AC and BD are opposite sides. In a parallelogram, we know that opposite sides are congruent which means:
AC = BD
2y + 7 = 3y - 4
Solving;
2y - 3y = -4 - 7
-y = -11
y = 11
Hence, the value of y is 11.
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I NEED HELP ME PLEASE!!!
Answer:
I hope this is right
TG = 34 TG=34 inches
From the figure
PQR is a triangle
PS, QT are medians of the triangle
G is the centroid
Step 1: Calculate the segment of the median (TG = ? )
We know that
Each median is divided into segments with a 2:1 ratio by the triangle centroid.
\therefore \frac{TG}{GQ} = \frac{2}{1} ∴
GQ/TG = 1/2
TG = 2 GQ TG=2GQ
TG = 2 * 17 TG=2∗17
TG = 34 TG=34
Hence, segment of the median TG = 34 inches
A housepainter mixed 5 gal of blue paint with every 9 gal of yellow paint in order to make a green paint. Which ratio of gallons of blue paint to gallons of yellow paint will NOT make the same shade of green paint?
The ratio of gallons of blue paint to gallons of yellow paint will NOT make the same shade of green paint 4:9.
What is Ratio?A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol (:). As a result, the ratio a/b has no units and is represented by the notation a: b.
Given:
A housepainter mixed 5 gal of blue paint with every 9 gal of yellow paint.
So, the ratio of gallons of blue paint to gallons of yellow paint is
= 5 to 9 or 5:9
Now, ratio of gallons of blue paint to gallons of yellow paint will NOT make the same shade of green paint
= 1- 5/9
=4/9
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-3+x=7 show me the answer and problem
Answer:
x=10
Step-by-step explanation:
-3+x=7
Add 3 to both sides.
7+3=10
x=10
Answer:
x=10
Step-by-step explanation:
-3+x=7
You have to add 3 to both sides to cancel out the -3
x=10
That leaves you with x=10
The equation for line j can be written as y=1/2x-4. Parallel to line j is line k which passes through the point (-8, -5). What is the equation of line k?
The equation of line k is y = 1/2x - 1.
What is the equation of a line?The equation y = mx + c is the general equation of any straight line, where m is the gradient of the line and c is the y -intercept.
Given that, the equation for line j can be written as y=1/2x-4. Parallel to line j is line k which passes through the point (-8, -5)
When two lines are parallel their slope are equal, so solving for c,
-5 = 1/2*-8 + c
c = -1
The equation will be,
y = 1/2x - 1
Hence, The equation of line k is y = 1/2x - 1.
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bruce bought two books,one book equal 4 dollals more than three times the other book they both equal 72
what is x
The value of x in the equation is $55 and this represents the cost of the expensive book
How to determine the value of x?The variable x is not defined in the question
So, we represent x as the more expensive book and y to represent the less expensive book
Also, from the question we understand that
One book = $4 more than three times than the other.Both books = $72The above statements can be interpreted to the following equations
x = 4 + 3y
x + y = 72
Substitute x = 4 + 3y in the equation x + y = 72
So, the equation x + y = 72 is represented as
4 + 3y + y = 72
Evaluate the like terms in the above equation
4 + 4y = 72
Collect the like terms in the above equation
4y = 72 - 4
Evaluate
4y = 68
Divide both sides by 4
So, we have
y = 17
Substitute 17 for y in the equation x = 4 + 3y to solve for x
x = 4 + 3 * 17
Evaluate the products
x = 4 + 51
Evaluate the sum
This gives
x = 55
Hence, the cost of the more expensive book is $55
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Determine if the given sequence is an arithmetic sequence. If it is, identify the common difference.
5, 4, 3, 2, ...
Is this an arithmetic sequence?
Ο No
O Yes
Select the correct choice and fill in any answer boxes in your choice below.
O A. The common difference is
O B. There is no common difference.
Answer:
Is this an arithmetic sequence?
Yes.
Is there a common difference and if so, what is it?
Yes, there is a common difference : 1
The common difference is 1
Hershey’s Chocolate World is located in Hershey, PA. The cost, , for any large chocolate bars is per bar, . Write a rule to represent this relationship.
. Hershey’s Chocolate World is located in Hershey, PA. The cost, c, for any large chocolate bars is $ 2.25 per bar, b. Write a rule to represent this relationship.
The equation to represent the expression is C ( b ) = 2.25b , where C ( b ) is the cost of b number of chocolate bars
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the cost of b chocolate bars be = C
Let the cost of 1 bar of chocolate bar be = $ 2.25
Let the number of chocolate bar be = b
Now , the equation to find the cost of b number of chocolate bars is ,
The cost of b number of chocolate bar =
cost of 1 bar of chocolate bar x number of chocolate bar
So , the equation is
The cost of b number of chocolate bar = 2.25b
So , the equation to find the cost of b number of chocolate bars is ,
Cost of b chocolate bars C = cost of b number of chocolate bar
C ( b ) = 2.25b
Therefore , the expression is C ( b ) = 2.25b
Hence , The equation to represent the expression is C ( b ) = 2.25b , where C ( b ) is the cost of b number of chocolate bars
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Jackson has saved $174.
He wants to purchase an electric dirt bike that costs $459.
If he saves $15 each week from the money he earns doing yard work and another $4 each week from his allowance, how many weeks will it take Jackson to save enough money to buy the bike?
Answer:
15 weeks.
Step-by-step explanation:
Can someone please help me this is due tomorrow!
Answer:
I can use the given (algebraic expression) 24c+12 to find the total cost of the order
The expression has two (terms). They are 24c and 12
In 24c the number 24 is the (coefficient) and the letter c is the (variable).
The term 24c represents a (product)
To find the total cost of the order I can (evaluate) the given expression
I have to (substitute) the given value for the variable then I can follow the (order of operations) to simplify the expression
24c+12
24(6)+12
144+12
156
The total cost is 156
Hope this helps :)
Write the domain as an equality
The domain of the inequality is from zero to negative infinity
[ -∞, 0)How to determine the domain of the inequalityThe domain refers to the values in the input of a function, these values are in the x direction.
The domain says the extents the values of the input is therefore no all the input values must be in the domain
Examining the graph shows that the graph reached the point x = 0 and returned with an arrow.
The arrow means that the values continued limitlessly, such limitless values are represented by infinity with symbol ∞.
The infinity is in the negative direction
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