The Number of people is 12 when time taken is 2 hours.
According to the statement
Time taken when 10 people works is 3 hours
Time taken when 5 people works is 8 hours
Then we have to find the number of peoples when time taken is 2 hours.
So, average time that for which single person works is 180 min/ 10 = 18 min.
It means the average time for single person works is 18 min in case of 10 people.
and one thing is clear that the number of people is greater than 10 people when time taken is 2 hours.
So, The Number of people is 12 when time taken is 2 hours.
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Elimination was used to solve a system of equations.
One of the intermediate steps led to the equation 9x = 27.
Which of the following systems could have led to this equation?
O
9x + 2y = 21
-9x - 2y = 21
10x - y = 15
x+y = - 12
7x - 2y = 15
x + y = 6
4x + 3y = 24
-5x - 3y = 3
The system of equation that could have led to the equation 9x = 27 is
7x - 2y = 15
x + y = 6
The correct option is the third option
7x - 2y = 15
x + y = 6
Solving systems of equationsFrom the question, we are to determine the system that could have led to 9x = 27
1.
9x + 2y = 21
-9x - 2y = 21
Subtracting, we get
9x + 2y = 21
-9x - 2y = 21
-------------------
18x + 4y = 0
2.
10x - y = 15
x + y = - 12
Subtracting, we get
10x - y = 15
x + y = - 12
---------------------
9x -2y = 27
3.
7x - 2y = 15
x + y = 6
Here, multiply the second equation by 2
2 × [x + y = 6]
2x + 2y = 12
Now, add to the first equation
7x - 2y = 15
2x + 2y = 12
------------------
9x = 27
4.
4x + 3y = 24
-5x - 3y = 3
Subtracting, we get
4x + 3y = 24
-5x - 3y = 3
---------------------
9x + 6y = 21
Hence, the system of equation that could have led to the equation 9x = 27 is
7x - 2y = 15
x + y = 6
The correct option is the third option
7x - 2y = 15
x + y = 6
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Which of the following terms is defined as a set of all points in a plane that are a given distance from a point?
O Circle
O Line segment
O Parallel line
O Ray
Answer:
circle
Step-by-step explanation:
any point on the circumference of a circle is equidistant from the centre.
Instructions: Given the coordinate points of the preimage, use the transformation given
to provide the points of the image.
The rotation about 90 degrees clockwise from the origin would give H'( -2, 3) , I' (1 , -1) and J' (-4, 0)
How to determine the coordinates
Note that rotation about in clockwise 90 degrees direction when M(h , k) rotated about the origin, the new rotation coordinates would be in the form M' (k , -h)
Coordinates of the preimage were given as;
H ( -3, -2)
I ( 1, 1 )
J ( 0, -4)
The coordinates after a 90 degrees rotation about the origin, would be
For H ( -3, -2)
h = - (-3) = 3
k = -2
H' = ( -2, 3)
For I ( 1, 1)
h = - (1) = -1
k = 1
I' = ( 1, -1)
For J ( 0, -4)
h = - (0) = 0
k = -4
J' = ( -4, 0 )
Thus, the rotation about 90 degrees clockwise from the origin would give H'( -2, 3) , I' (1 , -1) and J' (-4, 0)
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Use a model to solve six multiplied by seven eighths. Leave your answer as an improper fraction.
A. forty two forty eighths
B. thirteen eighths
C. thirteen fourteenths
D. forty two eighths
Let's see
seven eighths means 7/8
So
6(7/8)42/821/4Forty two eighths
Nathan buys a bottle of water for $1.25, gum for $0.50, and a book for $3.95. the sales tax is 10%. what is the sales tax for the things he buys
Answer:
$0.75, which is
75 cents
Step-by-step explanation:
First add the cost of all the items.
1.25 + .50 + 3.95
= 5.70
To find 10% of 5.70, change the percent to a decimal and multiply.
10% is .10
5.70 × .10 = .57
The tax is 57 cents. This can be written as $0.57
These marbles are placed in a bag and two
of them are randomly drawn.
What is the probability of drawing two
yellow marbles if the first one is placed back
in the bag before the second draw?
Give your answer as a ratio, reduced to
Help
simplest terms.
Hint: Multiply the probability of the 1st Event by the
probability of the 2nd Event to get your answer.
The probability of drawing two yellow balls if they're not replaced exists 1/45.
What is probability?
The probability exists in the analysis of the possibilities of happening of an outcome, which exists accepted by the ratio between favorable cases and possible cases.
Number of yellow marbles be 2
Number of pink marbles be 3
Number of blue marbles be 5
Total number of marbles = 2+3+5 = 10
The probability of removing the first yellow ball = 2/10
Since the ball exists not replaced, that indicates there choice be 9 balls left and 1 yellow ball left.
Probability of drawing the second yellow ball = 1/9.
Probability of drawing two yellow balls if they're not replaced
= 2/10 × 1/9
= 2/90
= 1/45
The probability of drawing two yellow balls if they're not replaced exists 1/45.
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Which statement correctly describes the expression 19×4?
A. Both factors are negative, so the product will be positive.
B. One factor is positive and one factor is negative, so the product will be positive.
C. Both factors are positive, so the product will be negative.
D. Both factors are positive, so the product will be positive.
Answer:
D. Both factors are positive, so the product will be positive.
1. Find the Principal when S.l. = 100 Rate = 5% per annum Time = 2 years.
The principal is 1000
SI = PRT/100
Simple interest = 100
Rate = 5%
Time = 2 years.
SI = PRT/100
100 = (P × 5 × 2)/100
10000 = 10P
P = 10000/10
P = 1000
There are 5 different families of triplets at a triplets convention. Each triplet shook hands with all the other triplets, except his or her siblings. How many handshakes took place?
There is a total of 90 handshakes.
How many handshakes took place?
There are 5 sets of triplets.
If we select one of the sets, each of the triplets will have one handshake with the other 12 people. So we have 36 handshakes at this point.
Now we only care for the other 4 sets.
We select one set again, each triple on that set will have one handshake with the other 9 people, so for the 3 triplets, we have a total of 27 new handshakes.
For the remaining 3 sets we do the same, this time we add 18 handshakes.
Finally, there are 2 sets of triplets, this time we add 9 new handshakes.
To get the total number of handshakes we need to add them all:
36 + 27 + 18 + 9 = 90
There is a total of 90 handshakes.
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What is the -value in the solution to this system of linear equations?y
4 + 5 = −12xy
-2 + 3 = −16xy
The xy-value in the solution to the given system of linear equation shows that x = 2 and y = -4.
What is a system of linear equations?Whenever two or more linear equations operate simultaneously, we create a System of Linear Equations. These equations must contain one or more similar variables in order to operate together.
When solving a system of linear equations, our objective is to simplify two equations having two variables to a single equation having one variable. Because each equation in the system includes two variables, substituting an expression for a variable is one technique to minimize the number of variables in an equation.
From the given information:
4x + 5y = -12 --- (1)
-2x + 3y = -16 ----- (2)
From equation (1)
4x+5y+(−5y) = −12 + (−5y) (Add -5y to both sides)
4x = −5y − 12
Divide both sides by 4
[tex]\mathbf{\dfrac{4x}{4}= \dfrac{-5y-12}{4}}[/tex]
[tex]\mathbf{x= \dfrac{-5}{4}y-3}[/tex]
Replacing the value of x in [tex]\mathbf{ \dfrac{-5}{4}y-3}[/tex] into equation (2); we have:
[tex]=\mathbf{-2(\dfrac{-5}{4}y-3)+3y=-16}[/tex]
[tex]\mathbf{\dfrac{11}{2}y+6 =-16}[/tex]
Simplifying both sides of the equation, we have:
[tex]\mathbf{\dfrac{11}{2}y+6-6 =-16-6}[/tex]
[tex]\mathbf{\dfrac{11}{2}y=-22}[/tex]
Cross multiply
11y = -44
y = -4
Replace the value of y = -4 into [tex]\mathbf{x= \dfrac{-5}{4}y-3}[/tex]
[tex]\mathbf{x= \dfrac{-5}{4}(-4)-3}[/tex]
x = 2
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Using a table, find the range of the function for the given domain:
f(x) = 2x² -7 with domain: x = {-4, -2, 0, 3}
OA.y=(-5, 1, 11, 25}
OB. y = {4, 2, 0, -3)
OC. y =(-11,-9, -7,-4}
OD.y = (25, 1, -7, 11)
The range of the function f(x) = 2x² -7 with domain: x = {-4, -2, 0, 3} is y = (25, 1, -7, 11). Option D is the correct answer.
The range of values that we are permitted to enter into our function is known as the domain of a function.
The x values for a function like f make up this set (x).
A function's range is the collection of values it can take as input. After we substitute an x value, this set of values is what the function outputs. The y values are those.
In light of the query
x VS F(x) = 2x² -7
-4 F(4) = [tex]2(-4)^2 -7[/tex] = 25
-2 F(-2) = [tex]2(-2)^2 -7[/tex] = 1
0 F(0) = [tex]2(0)^2 -7[/tex] = -7
3 F(3) = [tex]2(3)^2 - 7[/tex] = 11
∴ Option D, y = (25, 1, -7, 11)
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The general term of a sequence is T(n)=n+2/n+3, find the value of T(1)*T(2)*T(3)*……….*T(100).
Answer:
T(1)=1+2(1)+3=6
T(2)=2+2(2)+3=9
T(3)=3+2(3)+3=12
T(100)=100+2(100)+3=303
A researcher randomly assigns participants to complete a crossword puzzle with or without music. The time it takes to complete the crossword puzzle is compared between groups. The experimental group in this example is:
Answer:
The music group
Step-by-step explanation:
The experiment group is the group where something is being modified, so the music group is the one having their environment modified.
Which could be the entire interval over which the function, f(x), is positive? a 2-column table with 8 rows. the first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2, 3, 4. the second column is labeled f of x with entries negative 2, 0, 2, 2, 0, negative 8, negative 10, negative 20.
The entire interval over which the function, f(x), is positive is (-∞,1).
What is a function?A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable. In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
Each element of X receives exactly one element of Y when a function from one set to the other is used. The set X is referred to as the function's domain, while the set Y is referred to as the function's codomain.
According to the question,
The function has positive values corresponding to the interval from negative infinity to one.
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Write the equation of the line that has a slope of -2 and passes through (-4, -5)
Answer: [tex]y+5=-2(x+4)[/tex]
Step-by-step explanation:
See attached image.
Sandy rakes and bags the leaves on her front lawn in 30 mins. Randy does the same job in 20 mins. How many fewer minutes will it take to complete the same job if sandy and randy work together than if sandy works alone?
The number of minutes it take to complete the same job if sandy and randy work together than if sandy works alone is 18mins.
How to calculate time?According to this question, Sandy rakes and bags the leaves on her front lawn in 30 mins while Randy does the same job in 20 mins.
To calculate the time it will take both of them to work together, we use the following expression;
1/30 + 1/20 = 1/x
x = 12mins
Therefore, it will take 30 - 12 = 18 mins, to complete the same job if sandy and randy work together than if sandy works alone.
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Aaron has a loan of 1250£ He pays simple intrest 0.5% per month for eight months Calculate the total amount of interest Aaron pays
when x=-1 what is the value of y?
Answer: y=3
Step-by-step explanation:
The x-axis is on the horizontal line, and the y-axis is on the vertical line. On the horizontal line at -1, just go up until you find where y is located.
By doing this, you can find that y=3.
Answer:
Step-by-step explanation:
All we have to do is find the point on the line where x = -1. If we know this, we can see how high the point is (i.e., find it's y-value). Then, we would know the value of y.
If we draw a vertical line from where x equals -1, we see that it crosses the line at point (-1, 3). This means that we can draw a line from the point to the number -1 on the x-axis and another line from the point to the number 3 on the y-axis.
Hence, the y-value when x=-1 would be 3.
A golfer’s arm rotates 1/2 of a revolution in 1/10 of a second. If the angular displacement is measured in radians, which statements are true?
Based on the calculations, the true statements are:
A. The angular velocity is 10π rad/sec.
E. The angular velocity is 600π rad/min.
How to calculate the angular velocity?Mathematically, angular velocity can be calculated by using this formula:
ω = θ/t
Where:
ω is the angular velocity.θ is the angle.t is the time.Note: 1/2 revolution = 0.5 × 2π = π radians.
Substituting the given parameters into the formula, we have;
ω = θ/t
ω = π/0.1
ω = 10π rad/s.
Next, we would convert the time in seconds to minutes:
ω = 10π × 60
ω = 600π rad/min.
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Complete Question:
A golfer’s arm rotates 1/2 of a revolution in 1/10 of a second. If the angular displacement is measured in radians, which statements are true? Check all that apply.
A. The angular velocity is 10π rad/sec.
B. The angular velocity is 10π rad/min.
C. The angular velocity is 60π rad/min.
D. The angular velocity is 600π rad/sec.
E. The angular velocity is 600π rad/min.
Answer:
A,
Step-by-step explanation:
Edge202
Quick Please
(order from least to greatest)
please and thank you
Answer:
√(3 , √(π , 2
Step-by-step explanation:
ascending order
Q.3. The slope of line is ¾ and the y - intercept is equal to 4 . Write the equation of the line and draw the graph of the line.
help me now!!
The equation of line with the given slope and y-intercept is y = (3/4)x + 4.
What is the equation of the line?Given that;
Slope = 3/4y-intercept b = 4Equation of the line y = ?We use the formula for equation of line to determine the equation.
y = mx + b
Where m is the slope and b is the y-intercept.
We plug in our values
y = mx + b
y = (3/4)x + 4
Therefore, the equation of line with the given slope and y-intercept is y = (3/4)x + 4.
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A cup holds 2\9 litre of water. How many cups of water can be filled with 3litre bottle
Answer:
the answer might be 13.5
FIRST CORRECT ANSWER WILL GET BRAINLIEST
Answer:
They are parallel.
Step-by-step explanation:
They have the same slope, 7, and different y-intercepts, 4, -1/4, so they are parallel.
3 is subtracted from the product of 8 and a number
Answer: (8 * x) -3
Step-by-step explanation:
The term product refers to multiplication, so let the unknown number be x and multiply it by 8. Then you can subtract 3 afterwards.
*= multiplication
Find the interval in which the function is negative.
f(x)=x²-3x - 4
1. (-∞0, -1)
II. (-1, 4)
HI. (4, ∞)
Oll only
III only
OLI
LIII
Answer: II only: (-1, 4)
Step-by-step explanation:
x^2 - 3x - 4 is a parabolic function. When you factor the equation, it comes out to f(x) = (x-4)(x+1). Thus, the function as zeros at -1 and 4. Since the a value is positive, the parabola points up. Therefore, if you graph the function, it is negative between -1 and 4, so the answer is II only
A set of twins, Andrea and Courtney, are initially 10 years old. While Courtney remains on Earth, Andrea rides on a spaceship that travels away from Earth at a speed of 0.60c for 10 years (as measured by Courtney). At the end of the trip, Courtney is 20 years old. How old is Andrea
The initial age of 10 years and the spaceship speed of 0.60•c, gives the Andrea's age at the end of the trip as 18 years.
How can Andrea's new age be calculated?The time dilation using the Lorentz transformation formula is presented as follows;
[tex]t' = \frac{t}{ \sqrt{1 - \frac{ {v}^{2} }{ {c}^{2} } } } [/tex]
From the question, we have;
The spaceship's speed, v = 0.6•c
∆t = Rest frame, Courtney's time, change = 10 years
Therefore;
[tex]\delta t' =\delta t \times \sqrt{1 - \frac{ {(0.6 \cdot c)}^{2} }{ {c}^{2} } } = 8[/tex]
The time that elapses as measured by Andrea = 8 years
Andrea's age, A, at the end of the trip is therefore;
A = 10 years + 8 years = 18 years
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Solve the linear equation
x/2 + 2y/3 = -1 and x - y/3 = 3
Multiply by 6
3x+4y=-6-»eq(1)And
x-y/3=3Multiply by 3
3x-y=9-»eq(2)eq(1)-eq(2)
5y=-15y=-3Then
3x+4(-3)=-63x-12=-63x=6x=2From Equation 1
[tex] \dfrac{x}{2} + \dfrac{2y}{3} = - 1 [/tex]
[tex] \dfrac{3x + 4y}{6} = - 1[/tex]
[tex]3x + 4y = - 6 [/tex]
From Equation 2
[tex]x - \dfrac{y}{3} = 3 [/tex]
[tex] \dfrac{3x - y}{3} = 3[/tex]
[tex]3x - y = 9[/tex]
By eliminating ;;
For that multiply equation 2 by 4
12x - 4y = 36 _(3)
By taking equation (1) and (3)
3x + 4y = -6
12x - 4y = 36
__________
15x = 30
x = 30/15
x = 2
Putting the value of x in 2
[tex]3(2) - y = 9[/tex]
[tex]6 - y = 9[/tex]
[tex]6 - 9 = y[/tex]
[tex]-3 = y[/tex]
So The value of x = 2 and y = -3
Mr. Omwoyo, the principal of Maili Mbili Secondary would wish to cover the floor of the new administration block using square tiles. The floor is a rectangle of sides 12.8m by 8.4m. Find the area of the largest tiles in cm² which can be used to fit exactly without cutting.
Answer:
hi play truth and dare to with me in g met
The probability of a student buying coffee before class is 30%. The probability of a student buying a muffin before class is 40%. The probability of a student buying tea before class is 20%. The probability a student buys coffee AND a muffin before class is 15%. The probability a student buys tea AND a muffin before class is 10%. What is the probability that a student buys coffee OR a muffin before class
The probability that a student buys coffee OR a muffin before class is 55%
How to determine the probability?The given parameters are:
P(Coffee) = 30%
P(Muffin) = 40%
P(Tea) = 20%
P(Coffee and Muffin) = 15%
P(Tea and Muffin) = 10%
The probability that a student buys coffee OR a muffin before class is
P(Coffee or Muffin) = P(Coffee) + P(Muffin) - P(Coffee and Muffin)
This gives
P(Coffee or Muffin) = 30% + 40% - 15%
Evaluate
P(Coffee or Muffin) = 55%
Hence, the probability that a student buys coffee OR a muffin before class is 55%
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What is the recursive formula for the geometric sequence with this explicit
formula?
The recursive formula for the geometric sequence is given as follows:
D.
[tex]a_1 = 9[/tex].[tex]a_n = a_{n-1} \times \left(-\frac{1}{3}\right)[/tex]What is a geometric sequence?A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
With a recursive formula, it is given by:
[tex]a_n = a_{n-1} \times q[/tex]
For this problem, the first term and the common ratio are:
[tex]a_1 = 9, q = -\frac{1}{3}[/tex]
Then the recursive formula is:
D.
[tex]a_1 = 9[/tex].[tex]a_n = a_{n-1} \times \left(-\frac{1}{3}\right)[/tex]More can be learned about geometric sequences at https://brainly.com/question/11847927
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