Answers
We are given a set of data with the employee number and the corresponding weekly wage.
Part 1.1 To determine the wage per hour we need to find the quotient between the weekly wage and the number of hours worked per week.
In the case of employee 1, we have that his weekly wage was 1680, therefore, the weekly payment per hour is:
[tex]p=\frac{1680}{42}=40\text{ per hour}[/tex]The weekly payment is $40 per hour.
Part 1.2 We have that employee number 4 work a total of 6 hours each day of the week. Since there are 7 days per week we have that the total number of hours during the week is:
[tex]h_4=(6day)(7)=42\text{ }hours[/tex]Now, we multiply by the rate of payment per week, therefore, his weekly pay must be:
[tex]p_4=(42hours)(40\text{ per hour\rparen}=1680[/tex]Therefore, the weekly wage of 4 is 1680.
Part 1.3 To determine the number of hours that employee 8 we must have into account that the number of hours per week by the rate of pay per hour is the total weekly wage, therefore:
[tex](40\text{ per hour\rparen}h_8=2000[/tex]Now, we divide both sides by 40:
[tex]h_8=\frac{2000}{40}=50hours[/tex]Therefore, employee 8 worked 50 hours.
Part 1.4 Since the weekly payment is proportional to the number of hours this means that the employee that worked the least number of hours is the one with the least weekly wage.
We have that employee 5 has the smaller wage, therefore, employee 5 worked the least number of hours.
Part 1.5 we are asked to identify the dependent variable between weekly wage and the number of hours worked.
Since the number of hours does not depend on any of the other considered variables this means that this is the independent variable. Therefore, the dependent variables is the weekly wage. The correct answer is A
Part 1.6 The modal value of a set of data is the value that is repeated the most. We have that the weekly wage that is repeated the most is 1600 since it is the wage of employees 2 and 7. Therefore, the modal value is 1600
Part 1.7 The range of a set of data is the difference between the maximum and minimum values. The maximum wage is 2000 and the minimum is 1160, therefore, the range is:
[tex]R=2000-1160=840[/tex]The range is 840
Related Questions
A parabola that passes through the point (8, 28) has vertex (-2, 8). Its line of symmetry is parallel to the y-
axis.
Find equation of the parabola: y =
When x 18, what is the value of y:
What is the average rate of change between x = -2 and x = 18:
Answers
The equation of the parabola is y = 1/5( x + 2 )² + 8.
When x = 18 the value of y is 88 and the average rate of change between x = - 2 and x = 18 is 4.
The general equation of the parabola is given as:
y = a(x – h)² + k where ( h, k ) is the vertex of the parabola.
We have, the vertex as ( - 2, 8 ) and the parabola passes through ( 8, 28 ).
Then,
y = a(x – h)² + k
28 = a( 8 - (-2) )² + 8
28 = a(10)² + 8
28 - 8 = a(10)²
100a = 20
a = 20/100 = 1/5
Therefore, the equation of the parabola will be:
y = a(x – h)² + k
y = 1/5( x + 2 )² + 8
Now, when x = 18:
y = 1/5( x + 2 )² + 8
y = 1/5( 18 + 2 )² + 8
y = 1/5( 20 )² + 8
y = 80 + 8 = 88
Now, the change between x = - 2 and x = 18:
Then,
y = f(18) = y = 1/5( 18 + 2 )² + 8 = 1/5(20)² + 8 = 88
And;
y = f( - 2) = 1/5( -2 + 2 )² + 8 = 1/5(0)² + 8 = 8
Therefore the average rate of change between x = - 2 and x = 18 will be:
= [ f(18) - f(-2) / ( 18 - (-2) ) ]
= ( 88 - 8 ) / 20
= 80/20
= 4
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A 43-inch piece of steel is cut into three pieces so that the second piece is twice as long as the first
piece, and the third piece is three inches more than five times the length of the first piece. Find the
lengths of the pieces.
What is the length of the first piece?
Answers
The length of the first piece is 5 inches when a 43-inch piece of steel is cut into three pieces.
According to the question,
We have the following information:
A 43-inch piece of steel is cut into three pieces so that the second piece is twice as long as the first piece, and the third piece is three inches more than five times the length of the first piece.
Now, let's take the length of the first piece to be x inches (as shown in the figure).
Length of second piece = 2x inches
Length of third piece = (3+5x) inches
Now, we have the following expression for addition:
x + 2x + 3 + 5x = 43
8x+3 = 43
8x = 43-3
8x = 40
x = 40/8
x = 5 inches
Hence, the length of the first piece is 5 inches.
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SKIPPYTHEWALRUS U CAN'T ANSWER THIS QUESTIONI NEED CORRECT ANSWER 100 POINTS ONLY ANSWER CORRECTLY
A line passes through the points (7,9) and (10,1). What is its equation in point-slope form?
Use one of the specified points in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
Answers
Answer:
y - 1 = -8/3(x - 10)
also valid:
y - 9 = -8/3(x - 7)
Step-by-step explanation:
Point-slope equation is a fill-in-the-blank formula that is sort of a shortcut for writing the equation of a line. Point-slope is named that bc you fill in a point and the slope.
Point-slope Eq:
y - Y = m(x - X)
fill in the slope for the m and fill in any point on the line for the X,Y.
First slope:
Slope is y-y over x-x
9-1 / 7-10
= 8/ -3
= -8/3
So slope is -8/3 fill that in for the m.
y -Y = -8/3(x-X)
Pick one of the points (either one it totally doesn't matter)
Let's use (10,1)
fill in 10 for X and 1 in place of Y.
the y in the very front stays a y and the first x in the parentheses stays an x, so there will be two variables in your completed answer.
y - 1 = -8/3(x - 10)
make sure the parentheses on the right is beside the -8/3 fraction and is NOT written on the bottom, beside the 3 only.
Which statement correctly describes the relationship between the graph of f(x) and g(x)=f(x+2)? Responses The graph of g(x) is the graph of f(x) translated 2 units right. The graph of , g begin argument x end argument, is the graph of , , f open argument x close argument, , translated 2 units right. The graph of g(x) is the graph of f(x) translated 2 units down. The graph of , g begin argument x end argument, is the graph of , , f open argument x close argument, , translated 2 units down. The graph of g(x) is the graph of f(x) translated 2 units up. The graph of , g begin argument x end argument, is the graph of , , f open argument x close argument, , translated 2 units up. The graph of g(x) is the graph of f(x) translated 2 units left.
Answers
The graph of g(x) is the graph of f(x) translated 2 units left by the operation g(x)=f(x+2) so option (D) is correct.
What is the transformation of a graph?Transformation is rearranging a graph by a given rule it could be either increment of coordinate or decrement or reflection.
If we reflect any graph about y = x then the coordinate will interchange it that (x,y) → (y,x).
If a function f(x) is transformed by funciton g(x) as shown,
g(x) = f(x+a)
For a>0, then the graph of f(x) shifts left by "a" unit, while if a<0, then the graph of f(x) shifts right side by "a"units.
As per the given function,
g(x) = f(x + 2)
Since 2 > 0 therefore the function will shift 2 units left.
Hence "The graph of g(x) is the graph of f(x) translated 2 units left by the operation g(x)=f(x+2)".
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State what additional information is required in order to know that the triangles are congruent for the
reason given.
SSS
C
D
Y
X
A) WX = ED or XY = DC
C) YW = CE
B) ZW
ZE
D) XY = DC
Answers
Answer:
C. YW≅CE
Step-by-step explanation:
SSS is used when three pairs of sides are congruent. Two pairs of congruent sides are given. YW≅CE would be the third pair and therefore prove the triangles are congruent by SSS.
Taylor has $430 in her savings account. The annual simple interest at the bank is 2%. How much intreast will she earn on her savings in 9 months?
Answers
we have the following equation
[tex]m(t)=430+430\cdot0.02\cdot t[/tex]where t is the time in years, as we have 9 months, we have to change to years
[tex]t=\frac{9}{12}=\frac{3}{4}=0.75[/tex]so after 9 months we get
[tex]430+430\cdot0.02\cdot0.75=430+6.45[/tex]So she will earn $6.45 in 9 month
Divide polynomial and monomial 49c^2 d^2 - 70c^3 d^3 - 35c^2d^4 /7cd^2
Answers
start separating the fraction into smaller fractions
[tex]\frac{49c^2d^2}{7cd^2}-\frac{70c^3d^3}{7cd^2}-\frac{35c^2d^4}{7cd^2}[/tex]then, divide each of the fractions
[tex]7c-10c^2d-5cd^2[/tex]RATIOS/UNIT RATESRead and answer the question.Jessica sold 4 out of 32 boxes of the cookies her Girl Scout troop sold onSaturday. Select ALL the choices that display an equivalent ratio to thenumber of boxes Jessica sold to the total boxes sold.8 to 641:80 11O 21602:15
Answers
Solve for a side in right triangles. AC = ?. Round to the nearest hundredth
Answers
The length of segment AC is 2.96 units
How to determine the side length AC?From the question, the given parameters are
Line segment AB = 7 units
Angle A = 65 degrees
The line segment AC can be calculated using the following cosine ratio
cos(Angle) = Adjacent/Hypotenuse
Where
Adjacent = Side length AC
Hypotenuse = Side length AB
So, we have
cos(65) = AC/AB
This gives
cos(65) = AC/7
Make AC the subject
AC =7 * cos(65)
Evaluate
AC = 2.96
Hence, the side length AC has a value of 2.96 units
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A group of 23 students want to see the show at the planetarium. Tickets cost $11 for each student who is a member of the planetarium’s frequent visitor program and $13 for each student who is not a member. The total cost of the students’ tickets is $261.
Answers
Out of 23 students 19 students are the member of planetarium's frequent visitor program and 4 students are not the members.
Given,
The total number of students in a group = 23
Cost of ticket for member of planetarium's frequent visitor program = $11
Cost of ticket for the student who is not a member = $13
The total cost of the students ticket = $261
Lets take,
The number of students with membership = x
The number of students without membership = y
Total number of students, x + y = 23 -----------(1)
Now,
Total cost for the tickets, 11x + 13y = 261
Now, Multiply 13 with (1)
We get,
13x + 13y = 299
Solve for x
13x + 13y = 299 -
11x + 13y = 261
2x + 0 = 38
2x = 38
x = 38/2
x = 19
Now, put x in (1)
19 + y = 23
y = 23 - 19
y = 4
That is,
The number of students with membership is 19 and the number of students without membership is 4.
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Two segments of Parallelogram ABCD are shown below.  Which coordinate pair BEST represents the location of Point D, the fourth vertex of Parallelogram ABCD? A. (6, 1) B. (7, 0) C. (8,2) D. (7,1)
Answers
Given coordinates of A(2,-1), B(1,3), C(6,5)
Let the coordinates of D(x,y)
Let join AC and BD:
SO by mid point rule:
Coordinates of midpoint by AC are:
[tex](\frac{2+6}{2},\text{ }\frac{-1+5}{2})\rightarrow(4,2)[/tex]And the midpoint of BD are same as AC:
[tex]\begin{gathered} \frac{1+x}{2}=4 \\ 1+x=8 \\ x=7 \end{gathered}[/tex][tex]\begin{gathered} \frac{3+y}{2}=2 \\ 3+y=4 \\ y=4-3 \\ y=1 \end{gathered}[/tex]hence the coordinates of D are (7,1)
Option D is correct.
6x + 14y what is the letter y in this problem?
Answers
The value of letter y in this problem is y = 6x / -14
How to solve the equationThe equation says that 6x + 14y
To solve the equation that we have here, we would have to equate to 0
such that we would have the equation as 6x + 14y = 0
6x + 14y = 0
then we would have
6x = - 14y
remember that when positives crosses over we would have it turn as negative.
Next we would have to divide through by - 14 in order to get the value of y
hence we would have
-14y / -14 = 6x / -14
then we would have y as
y = 6x / -14
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Alani want to buy a 3366 buycie She reconsidering e payment options. The image shows Option A, which consists of making an initial down payment then smallet. equesized weekly payments. Option consists of making 6 equal payments over a week WE Weekly Bike Payments A-What factors should Alanl take into consideration before deciding between Option A and Option B? B- Communicate Precisely Suppose Alani could modify Option A and still pay off the bike in 5 weeks. Describe the relationship between the down payment and the weekly payments.
Answers
Question 125 ptsA raffle sells 1000 tickets at $5 per ticket. The possible prizes are given below. Find the expectedvalue of each ticket (from the perspective of the person buying the ticket). Include signs in youranswer as appropriate.1 ticket wins $10005 tickets win $10010 tickets win $20
Answers
The answer is $0.5
Explanation:
⇒ Total amount of tickets sold = 1000 x $5 = $5000
⇒ Expected value E(X) =∑X.P(x)
⇒ 1 x (1000/5000) + 5 x (100/5000) + 10 x (20/1000)
= 0.2 + 0.1 + 0.2
= $0.5
a man pushes a car with a force of 127.5n along a straight horizontal road.he manages to increase the speed of the car from 1 m/s to 2.8 m/s in 12 seconds. find the mass of the car. figure out acceleration first.
Answers
In order to determine the mass of the car, you first calculate the acceleration of the car, by using the following formula:
[tex]a=\frac{v_2-v_1}{\Delta t}[/tex]where:
v2: final speed of the car = 2.8 m/s
v1: initial speed of the car = 1 m/s
Δt: time interval = 12 s
You replace the previoues values into th formula for the acceleration:
[tex]a=\frac{2.8m/s-1.0m/s}{12s}=0.15\frac{m}{s^2}[/tex]Next, you the Newton's second law to find the mass of the car. You proceed as follow;
[tex]F=ma[/tex]where:
m: mass of the car = ?
a: acceleration of the car = 0.15m/s²
F: force exerted on the car by the man = 127.5N
You solve for m in the formula for F, and you replace the values of the other parameters to obtain m, just as follow:
[tex]m=\frac{F}{a}=\frac{127.5N}{0.15m/s^2}=850\operatorname{kg}[/tex]Hence, the mass of the car is 850kg
the circumference of a circle is 18pi ft. what is the area in square feet.
Answers
We have first the formula of the circumference of a circle
[tex]C=2\pi r[/tex]In order to know the area we need to know the radius of the circle, it can be obtained using the formula above and the next information.
C=18pi
r is the radius
[tex]18\pi=2\pi r[/tex]then we isolate the r
[tex]\begin{gathered} r=\frac{18\pi}{2\pi} \\ r=9 \end{gathered}[/tex]the radius is 9 ft
then we can calculate the area using the next formula
[tex]A=\pi r^2[/tex]we substitute the value of the radius
[tex]\begin{gathered} A=\pi(9)^2 \\ A=81\pi ft^2 \\ A=254.47ft^2 \end{gathered}[/tex]What is 150% of 38.
Answers
We are asked to find 150% of 38
Step 1:
Convert the 150% to decimal by removing the % sign which means dividing by 100.
150/100 = 1.5
Step 2:
Now simply multiply the decimal percentage with the number 38
1.5×38 = 57
Therefore, 150% of 38 is found to be 57
identify the constant of proportionality in the following questions. 1) y= 2x + 32) y= -3x - 4
Answers
Answer:
0. k=2
,1. k=-3
Explanation:
The constant of proportionality is the number that is beside the variable x in both equations.
(1)For the equation:
[tex]y=2x+3[/tex]The constant of proportionality is 2.
(2)For the equation:
[tex]y=-3x-4[/tex]The constant of proportionality is -3.
mathematics assignment
Answers
Examining the function the graph that is correct is the graph in option C
What is graph ?A graph is a representation of data using accepted means of presentation.
The graph used in the question is in cartesian coordinate and it a parabolic graph
How to find the correct graphThe given data is h(x) = -x² - 4
Examining the given function
The term -x² is a negative term hence the graph opens downwards
The value of h(x) when x = 0 is -4. Therefore the graph will have an intercept at -4
The graph of option C is the one that meets the required criteria hence the nest option
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write the equation of the line in slope-intercept form given the follow[tex]slope = - \frac{5}{4} \: y - intercept \: (0 \: - 8)[/tex]
Answers
Let's begin by identifying key information given to us:
[tex]\begin{gathered} slope=-\frac{5}{4}\: \\ y-intercept\: (0\: -8) \end{gathered}[/tex]The point-slope equation is given by:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-intercept\: (0\: -8)\Rightarrow(x_1,y_1)=(0,-8) \\ (x_1,y_1)=(0,-8) \\ m=-\frac{5}{4} \\ y-\mleft(-8\mright)=-\frac{5}{4}(x-0) \\ y+8=-\frac{5}{4}x-0 \\ y=-\frac{5}{4}x-8 \\ \\ \therefore\text{The slope-intercept form is }y=-\frac{5}{4}x-8 \end{gathered}[/tex]Find the product of -0.6 and -2/5
Express your answer as a fraction or
mixed number in simplest form.
Answers
Answer:
6/25Step-by-step explanation:
1) -0.6 = -6/10
= -3/5
2) -0.6*-2/5 = (-3/5)*(-2/5)
=(-3*-2)/(5*5)
=6/25need help with this answer in a quick and clear response
Answers
ANSWER
Yes
EXPLANATION
The system of inequalities shows that y is greater than or equal to the first line and less than or equal to the second line. This means that any point on both lines is a solution to the system.
Hence, the intersection of the boundary lines is part of the solution.
The table gives a set of outcomes and their probabilities. Let A be the event "the outcome is less than 8". Find P(A). Outcome Probability 1 0.12 2 0.11 3 0.4 4 0.02 5 0.04 6 0.17 7 0.02 00 0.09 9 0.03
Answers
We want to calculate the probability of this event A: "the outcome is less than 8". To calculate this probability, we should first note that we have a total of 9 outcomes. So, we will first identify out of this outcomes cause the event A to happen.
Since the event A is saying that the outcome is less than 8, then the outcomes that would make the event A to happen would be the numbers from 1 to 7. However, to calculate this probabilty, we will use this property of probability.
Given an event A, we have the
1. What would you do with each problem in order to get it in its simplest properform? Use words to explain the specific details to why you used thatprocess/rule.Number 2 a and b
Answers
Given
[tex]-6y^0\text{ and \lparen-6y\rparen}^0[/tex]The solutions can be seen below.
Explanation
[tex]\begin{gathered} a)\text{ }-6y^0=-6\times y^0=-6\times1=-6 \\ b)\text{ }(-6y)^0=1 \end{gathered}[/tex]In "a," only the y-value is raised to the power of 1 hence, the reason why y^0 became 1 which then multiplies -6 to get -6. However, in "b", the entire expression is raised to the power of zero, which will then give 1 as the answer.
Solve 2/3 (6w+12) this equation
Answers
Answer:
4w+8
Step-by-step explanation:
Consider the complex number 2 = V17 (cos(104°) + i sin(104°)).Plot z in the complex plane below.If necessary, round the point's coordinates to the nearest integer.Im5+4+3+2+1 +ReA+-5+-4-3-2-112345-1+-2-3 +-4+-5 +
Answers
Recall that to plot a point in the complex plane we have to know its real part and its imaginary part.
The real part of the given number is
[tex]\sqrt[]{17}\cos 104^{\circ},[/tex]and its imaginary part is
[tex]\sqrt[]{17}\sin 104^{\circ}.[/tex]Simplifying the above expressions, and rounding to the nearest integer we get that:
[tex]\begin{gathered} \operatorname{Re}(z)=-1, \\ \operatorname{Im}(z)=4. \end{gathered}[/tex]Therefore, the point has coordinates (-1,4).
Answer:
how to calculate 1+2?
Answers
There are 17 girls at a party with 30 guests. What fraction
of the party guests are girls?
Answers
Answer:
17/30
Step-by-step explanation:
There are 17 girls at a party with 30 guests. What fraction of the party guests are girls?
17/30
HighByte Entertainment sells four types of products: video games, DVDs, CDs, and radios. The numbers sold for 2020 and 2021 are shown in the double bargraph below. Use this graph to answer the questions.
Answers
Solution
Use this graph to answer the questions below:
The numbers sold for 2020 and 2021 are shown in the double bar above
1. The number of radio sold in 2021 = 440
2. Which products sold more in 2021 than in 2020 :
The only products that sold more in 2021 than in 2020 is video games
3. Which products sold the least over the two years
The products that sold the least = DVDS
0896. Calculate the atomic mass of copper if copper-63 is 69.17% abundant and copper-65 is30.83% abundant.
Answers
The atomic mass of the copper is
[tex]63\times69.17\text{ \% + 65}\times30.83\text{ \%}[/tex]solve the above expression
[tex]63\times\frac{69.17}{100}+65\times\frac{30.83}{100}[/tex][tex]63\times\frac{6917}{10000}+65\times\frac{3083}{10000}[/tex][tex]46.35+20.03=66.38[/tex]So the atomic weight of the mixture is 66.36 .