Answer:
8km /hr
1/ 8 of a litre.
Explanation:
We are told that Amelia drives 48 kilometres in 6 hours, this means the number of kilometres she drives per litre is
[tex]48\operatorname{km}\div6\text{litres}[/tex][tex]\frac{8\operatorname{km}}{\text{litre}}[/tex]Hence, Amelia drives 8 kilometres per litre.
The next question can be rephrased as, given that Amelia drives 8 km per litre, how many litres will it take to drive one kilometre?
To answer this question, we make use of the equation
[tex]\operatorname{km}\text{ travelled = 8km/litre }\cdot\text{ litres}[/tex]Now, we want
km travelled = 1 km
and the above equation gives
[tex]\begin{gathered} 1=\frac{8\operatorname{km}}{\text{litre}}\cdot\text{litres} \\ 1=8\cdot\text{litres} \end{gathered}[/tex]Dividing both sides by 8 gives
[tex]\text{litres}=\frac{1}{8}[/tex]Hence, it takes 1/8 of a litre to drive 1 kilometre.
During a baseball game, Diego thought his team would get 4 runs, and they actually got 7 runs. What was Diego's percent error? Make sure to include a percent sign. (Round to two decimal places)
Answer:
11 percent
Step-by-step explanation:
No idea to explain
Corbie earns $2750 paid once a month after taxes.
James gets paid every other week for tutoring at the
local library, and his smallest paycheck in the past six
months was $280.
Their monthly rent for their home is $925 and their most
expensive month for combined utilities last year cost
$325. Their smartphones cost $180 per month. They
spend $120 per week on groceries, $45 per week on
gas,and $620 per month for their car's payment,
insurance, and maintenance savings. James spends
$600 per semester (twice a year) for college tuition.
They each give themselves a $100 per week allowance
for personal expenses such as clothes, haircuts, dining
out, and entertainment.
Calculate their prorated monthly amounts, their monthly
totals, and their cash flow.
1. Corbie and James' total prorated monthly incomes are Corbie's $2,750 and James' $606.
2. Their combined monthly totals are:
Income = $3,356.
Expenses = $3,111.
3. Their monthly net cash flow is $245.
What is the net cash flow?The net cash flow is the cash surplus after paying all operating costs.
The net cash flow for Corbie and James is the difference between their total earnings per month and their total expenses per month.
For some income and expenses, there is a proration. Since 52 weeks make up the typical year, each month is considered 4.33 weeks.
1 year = 52 weeks
1 month = 4.33 weeks (52/12)
Monthly Income:
Corbie = $2,750
James = $606 ($280 x 26/52 x 4.333)
Total income = $3,356
Monthly Expenses:
Rent = $925
Utilities = $325
Phones = $180
Groceries = $520 ($120 x 4.33)
Gas = $195 ($45 x 4.33)
Tuition = $100 ($600 x 2)/12
Incidentals = $866 (200 x 4.33)
Total expenses = $3,111
Net Cash Flow = $245 ($3,356 - $3,111)
Thus, whereas, Corbie and James earn a combined and prorated monthly income of $3,356, their total monthly expenses of $3,111 leave them with a net cash flow of $245.
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which description compass the domains of function a and function be correctly rest of the information in the picture below please answer with the answer choices
Given:
Function A: f(x) = -3x + 2
And the graph of the function B
We will compare the domains of the functions
Function A is a linear function, the domain of the linear function is all real numbers
Function B: as shown in the figure the graph starts at x = 0 and the function is graphed for all positive real numbers So, Domain is x ≥ 0
So, the answer will be the last option
The domain of function A is the set of real numbers
The domain of function B: x ≥ 0
Kuta Software Infinie Algebra ? Absolute Value Inequalities Salve each inequality and graph its solution. 61 1 laulsis * -36043 3) m-2/
Prob 22
7 + | 6v + 7| ≤ 60
then
| 6v + 7| ≤ 53
now eliminate lines ||
6v + 7 ≤ 53
and
6v + 7 ≤ - 53,. 6v ≤ -60
Now solve for x
6v ≤ 47,. v≤ 46/6
also
6v ≥ -47,. v≥ -46/6
Then answer is
-10 ≤ v ≤ -46/6
Graph for problem 22
Section 5.2-4 Graph the following system of equations and find the solution. Plot the solution on the graph. Enter your answer as (x,y). -2x-3y = 0 x+3y = 3 1 2 3 4 5 -1 -2 -3 -4 -5 1 2 3 4 5 -1 -2 -3 -4 -5 Clear All Draw: LineDot Solution =
For finding y, we can replace the value of x in any equations.
Solution (-3,2)
Plot graphs
A linear equation written in the form y = mx + b is in ?
A linear equation is written in the form
[tex]y=mx+b[/tex]it is the Slope-intercept form
In the diagram, RSTU ~ ABC D. Find the ratio of their perimeterA А.24BR18S36TDCThe ratio of their perimeters is
The ratio of the perimeters of two similar shapes is equal to the ratio of their corresponding sides, then, by taking the top sides of these figures we can express the following ratio
18 : 24
by dividing both numbers by 2, we get:
9 : 12
Dividing by 3:
3 : 4
Then the ratio of their perimeters equals 3 : 4
Which sequence of transformations will map AABC onto AA' B'C'?A- reflection and translationB- rotation and reflectionC- translation and dilation D- dilation and rotation
For the given problem, we can observe that the image is bigger than the original diagram.
We can also observe that the image is rotated counterclockwise.
Hence, the sequence of transformation that maps triangle ABC onto triangle A'B'C' is a dilation and a rotation.
Answer: Option D
Quadrilateral TUVW is a rhombus and m∠SVU=4z+56°. What is the value of z?WTUVS26°z=°Submit
From the question, we were told:
TUVW is a rhombus
Angle SUV = 4z + 56˚
We are asked to find the value of z.
From the diagram, we can see that angle SVU is 90˚
So, to get the value of z, we equate the value of SVU to 90˚
4z + 56˚ = 90˚
subtract 56˚ from both sides:
4z + 56 - 56 = 90 - 56
4z = 34
divide both sides by 4 to make z the subject of formula:
z = 34/4
z = 8.5
Which answer choice shows 3.002 written in expanded form?A) 3 + 0.2B) 3 + 0.02C) 3 + 0.002D) 3+ 0.0002
SOLUTION
We want to know which answer choice shows 3.002 written in expanded form
To do this let us subtract 3.002 from 3, we have
We got 0.002
So the expanded form is
[tex]3+0.002[/tex]Hence the correct answer is option C
event a is the event that randomly selected students from your school is make event b is the event that randomly selected students from your school owns a bicycle which of the following do we know for certain correctly represents the probability of selecting a male students or selecting a student who owns a bicycle
The or probability in the context of this problem is represented as follows:
P(A U B).
Or probabilityThe or probability between two events A and B is the probability that at least one of the events happen.
The symbol of the or probability is given as follows:
U
In the context of this problem, the events are given as follows:
Event A: a randomly selected student is male.Event B: a randomly selected student owns a bike.Hence the probability of selecting a male students or selecting a student who owns a bicycle is represented as follows:
P(A or B) = P(A U B).
The other options are as follows:
P(A ∩ B): both male and own bike, representing the intersection operation of the events.P(A): male.P(B): own bike.Missing informationThe complete problem is given by the image at the end of the answer.
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the length of a screwdriver is 0.75 cm is how many screws can be placed to the end to make a road that's 18 cm long show yours
Length of screwdriver = 0.75
Length of road = 18cm
Number of screws that can be placed on a road
[tex]\begin{gathered} =\text{ }\frac{18}{0.75} \\ =\text{ 24} \end{gathered}[/tex]8You are asked to draw a triangle withside lengths of 10 inches, 7 inches, and2 inches. How many triangles like thiscan you draw?A. OneB. ThreeC. TwoD. Zero
ANSWER
D. Zero
EXPLANATION
The triangle inequality states that the sum of any two sides of a triangle is greater than the third side,
All these inequalities must be true to be able to form a triangle with the given sides,
[tex]\begin{gathered} 7+10>2\Rightarrow17>2\Rightarrow true \\ 2+10>7\Rightarrow12>7\Rightarrow true \\ 7+2>10\Rightarrow9>10\Rightarrow false \end{gathered}[/tex]Hence, no triangle can be formed with these side lengths.
Sara is 33 years younger than Rolando. The sum of their ages is 105. Select the system of equations if Sara’s age is represented by S and Rolando’s age is represented by R.
Given:
Sara's age is represented by S and Ronaldo's age is represented by R.
Since,
Sara is 33 years younger than Ronaldo, then;
S= R - 33
Now, the sum of ages of Sara and Ronaldo is 105 then
[tex]R+S=105[/tex]Hence, from above,
[tex]\begin{gathered} S+R=105 \\ S=R-33 \end{gathered}[/tex]Therefore, second option is correct.
27. Ava surveys teachers for how long it takes them to drive to school eachmorning. She records each response in the dot plot shown.5 10 15 20 25 30 35 40 45 50 55 60Length of Drive (minutes)Ava considers drives of 55 minutes or more as not typical. Given this,which measure of the entire data set represents the most typicaldriving time?meanrangemedianmean absolute deviation
EXPLANATION
The measure that represent the most typical driving time is the mean.
y=-5x+6y=-3x-2x=y= and the grap
y = -5x + 6 .................1
y = -3x - 2......................1
first equate the two equations to find x and y
-5x + 6 = -3x - 2
-5x +3x = -2 - 6
-2x = -8
x = -8/-2
x = 4
Next substitute x in equation 1
y = 5(4) + 6
y = 20 + 6
y = 26
Graphically,
y = -5x + 6
for x = 0
y = -5 x 0 + 6
y = 6
for y = 0
0 = -5x + 6
5x = 6
x = 6/5
x = 1.2
fiirst plot the coordinate (0,6) and (1.2,0) on the graph for the first equation to get the first straight line.
y = -3x - 2
x = 0
y = -3 x 0 - 2
y = -2
y = 0
0 = -3x - 2
3x = -2
x = -2/3
x = -0.67
plot the coordinate on the graph
solution for this question is (4,26)
If students only know the radius of a circle, what other measures could they determine? Explain how students would use the radius to find the other parts.
Radius of the circle : Radius is the distance from the center outwards.
With the help of radius we can determine the following terms:
1. Diameter : Diameter is the twice of radius and it is teh staright line that passes through the center. Expression for the diameter is :
[tex]\text{ Diameter= 2}\times Radius[/tex]2. Circumference: Circumference of the circle or perimeter of the circle is the measurement of the boundary of the circle. It express as:
[tex]\begin{gathered} \text{ Circumference of Circle=2}\Pi(Radius) \\ \text{ where }\Pi=3.14 \end{gathered}[/tex]3. Area of Circle: Area of a circle is the region occupied by the circle in a two-dimensional plane. It express as:
[tex]\begin{gathered} \text{ Area of Circle = }\Pi(radius)^2 \\ \text{where : }\Pi=3.14 \end{gathered}[/tex]4. Center Angle of the Sector: Central angles are subtended by an arc between those two points, and the arc length is the central angle of a circle of radius one. It express as :
[tex]\text{ Central Angle of sector=}\frac{Area\text{ of Sector}}{\Pi(radius)^2}\times360[/tex]5. Arc length : An arc of a circle is any portion of the circumference of a circle. It express as :
[tex]\text{ Arc Length = }Radius(\text{ Angle Substended by the arc from the centerof crircle)}[/tex]In the given figure the radius is AO & BO
The graph shows the relationship between pounds of grapes, g, and their cost, c.
A graph on a coordinate plane shows cost of grapes on the horizontal axis (c), numbered 2 to 6, and pounds of grapes on the vertical axis (g), numbered 1 to 4. Solid circles are at points (0, 0), (2, 1), (4, 2), (6, 3), and are connected by a solid line.
Use the graph to complete the statements.
For every dollar you spend, you can get
0.5
pounds of grapes.
For each pound of grapes, you would need $
.
For every dollar you spend, you can get 0.5 pounds of grapes.
For each pound of grapes, you would need $2.
How to interpret the graph?From the coordinates of this graph, we can reasonably infer and logically deduce that it models a straight line, shows a proportional relationship and can be represented by using a linear function.
Mathematically, a proportional relationship can be represented by the following equation:
g = kc
Where:
k is the constant of proportionality.g represent the pounds of grapes.c represent the cost of grapes in dollar.Next, we would determine the constant of proportionality (k) for the data points shown on this graph as follows:
k = g/c
k = 1/2 or 0.5
Therefore, the linear equation is given by g = 0.5c.
For the amount of dollar needed at g = 1, we have:
g = 0.5c
c = g/0.5
c = 1/0.5
c = $2.
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What 3D shape will be formed when the following are rotated around the axis
a)
A washer will be formed
b)
A cone will be formed
C)
A sphere will be formed
144 grapefruits in 4 boxes, How many grapefruits in 100 boxes?
Problem
144 grapefruits in 4 boxes, How many grapefruits in 100 boxes?
Solution
for this case we can do the following proportional rule:
4/144 = x/100
And solving for x we got:
x= 100 (4/144)= 2.77
So between 2 and 3 grape fruits are expected
Given A(-9, -12), B(-2, 2), C(x, 6).and D(-5, -2), find the value ofx so that AB || CD
1) Given these line segments, let's find the slope of them. Let's begin with AB
[tex]m=\frac{2-(-12)}{-2-(-9)}=\frac{14}{-2+9}=\frac{14}{7}=2[/tex]2) Parallel lines have the same slope, so let's set this slope formula so that we can get the slope m=2. Bearing in mind CD:
[tex]\begin{gathered} 2=\frac{-2-6}{-5-x} \\ 2=\frac{-8}{-5-x} \\ 2(-5-x)=-8 \\ -10-2x=-8 \\ -2x=-8+10 \\ -2x=2 \\ x=-1 \end{gathered}[/tex]Thus, x=-1
The points −−5, 11 and r, 9 lie on a line with slope 2. Find the missing coordinate r.
Solution
[tex]\begin{gathered} Let\text{ }(x_1,y_1),\text{ }(x_2,y_2) \\ Let\text{ }m=slope \\ m=\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex][tex]\begin{gathered} If(-5,-11)=\text{ }(x_1,y_1),then\text{ }x_1=-5,\text{ }y_1=-11 \\ (r,9)=\text{ }(x_2,y_2),then\text{ }x_2=r,\text{ }y_1=9 \end{gathered}[/tex]Using the Slope formula written above;
[tex]\begin{gathered} 2=\frac{9-(-11)}{r-(-5)} \\ 2=\frac{20}{r+5} \\ Cross\text{ }multiply \\ 2(r+5)=20 \\ Expansion\text{ }of\text{ }bracket \\ 2r+10=20 \\ 2r=20-10 \\ 2r=10 \\ Divide\text{ }both\text{ }sides\text{ }by\text{ }2 \\ \frac{2r}{2}=\frac{10}{5} \\ r=5 \end{gathered}[/tex]Therefore, the missing co-ordinate r is 5.
Which of the following is an equation of a line that is parallel to y = 4x - 5 and has a y-intercept of (0, 7)?
Answer:
Step-by-step explanation:
To start your equation is in the format y=mx+b.
For a line to be parallel it must have the same slope (m) so we know 4 must remain the same. x & y will not change since they represent the variables. y=4x (so far) then the point (0,7) as stated is the y intercept. 0 is the x value and 7 is the y we need to add 7 to our equation.
final equation y=4x+7
a lampshade has a radius of 9in what is the circumference of the top of the shade use 3.4 to approximate Pi round your answer to the nearest whole number
The top of the lampshade is circular in shape
[tex]\begin{gathered} \text{The circumference of a circle = 2}\pi r \\ \text{where }\pi=3.14,\text{ r= radius of the circle} \\ \text{The radius , r=9 in} \\ \text{Circumference = 2 x 3.14 x }9 \\ \text{Circumference = }56.52\text{ in} \end{gathered}[/tex]The circumference of the top of the shade is 56.52 inches
2. (02.01 LC)While researching the industry she is interested in, Charlize sees that the average employment rate is 97.3%. How many people, out of every 250, are employed? (1point)24.33O 234.66Ο Ο243.25O 256.93
EXPLANATION
We can compute the average by multiplying the average by 0.973, as shown follows:
[tex]\text{Amount of people}=250\cdot0.973=243.25[/tex]In conclusion, the amount of people is equal to 243.25
Margie uses 36 inches of lace to make one pillow. She makes 24 pillows for the school fair. How many total inches of lace does Margie use on the pillows?
Margie used a total of 264 inches of lace for the 24 pillows
How to calculate the total inches of lace used ?
Margie used 36 inches of lace for one pillow
She needs to make 24 pillows
The total inches of lace that was used for the 24 pillows can be calculated as follows
= 36 × 24
= 864
Hence Margie used 864 inches of lace for 24 pillows
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Hey everybody! Can somebody help me solve this problem? I don't need a big explanation just the answer and a brief explanation on how you get it! Look at photo for problem.
Given the ordered pairs:
(-12, -16), (-3, -4), (0, 0), (9, 12)
Let's say that the first coordinate corresponds to x, and the second one corresponds to y. Then, the constant of variation k relates x and y as:
[tex]y=k\cdot x[/tex]Using the ordered pairs:
[tex]\begin{gathered} -16=-12k\Rightarrow k=\frac{4}{3} \\ -4=-3k\Rightarrow k=\frac{4}{3} \\ 0=0\cdot k\text{ (this means that it is correct)} \\ 12=9k\Rightarrow k=\frac{4}{3} \end{gathered}[/tex]We conclude that the constant of variation is:
[tex]k=\frac{4}{3}[/tex]Which of the following logarithmic expressions have been evaluated correctly?
Given:
Logarithmic expressions in options.
Required:
Select correct calculated option.
Explanation:
1). ln 1 = 0
2).
[tex]log_29=3.1699250014[/tex]3)
[tex]log\frac{1}{100}=-2_[/tex]4).
[tex]log_3(-1)=NaN[/tex]5).
[tex]log_5\text{ }\frac{1}{125}=-3[/tex]Answer:
Hence, option A and E are correct.
can you help me with key attributes of quadratic function
The shape of a quadratic function is a parabola.
The domain of a quadratic function is the set of all real numbers.
The range of the quadratic function is the set of all y values at or above the vertex for a parabola open upwards.
In the given parabola, y=0 is the y coordinate of the vertex of the parabola.
Therefore, the range is R=[0, ∞).
The domain is (-∞, ∞).
10. A city has a population of 125,500 in the year 1989. In the year 2007, its population is 109, 185. A. Find the continuous growth/decay rate for this city. Be sure to show all your work.B. If the growth/decay rate continues, find the population of the city in the year 2021.C. In what year will the population of the city reach 97,890? Be sure to show all your work.
SOLUTION
A.
To solve this question, we will use the compound interest formula.
Which is:
[tex]\begin{gathered} A=P(1-\frac{r}{100})^{nt} \\ Since\text{ we are dealing with a yearly statistics, n = 1} \end{gathered}[/tex][tex]\begin{gathered} \text{From 1989 to 2007, there is a year difference of 18 years} \\ t=18 \\ A=109,185 \\ P=125,500 \\ We\text{ are looking for the continuous growth rate (r)} \\ \text{Now, we will substitute all these given parameters into the formula } \\ \text{above.} \end{gathered}[/tex][tex]\begin{gathered} 109,185=\text{ 125,500(1-}\frac{r}{100})^{18} \\ \frac{195185}{125500}=\frac{125500}{125500}(1-\frac{r}{100})^{18} \\ 0.87=(1-\frac{r}{100})^{18} \\ \text{take the natural logarithm of both sides:} \\ \ln 0.87=18\ln (1-\frac{r}{100}) \\ -0.1393=18\ln (1-\frac{r}{100}) \\ \frac{-0.1393}{18}=\ln (1-\frac{r}{100})_{}_{}_{}_{}_{} \\ -0.007737=\ln (1-\frac{r}{100}) \\ \end{gathered}[/tex][tex]\begin{gathered} e^{-0.007737}=(1-\frac{r}{100}) \\ 0.9922=1-\frac{r}{100} \\ \frac{r}{100}=1-0.9922 \\ \frac{r}{100}=0.007707 \\ r=100\times0.007707 \\ r=0.771\text{ \%} \end{gathered}[/tex]The continuous decay rate is 0.771%
B.
Using the same formula:
[tex]\begin{gathered} A=P(1-\frac{r}{100})^{nt} \\ t=2021-2007=14 \\ P=109,185 \\ n=1 \\ A=\text{?} \\ r=0.771 \\ \text{Substitute all the parameters into the formula above:} \end{gathered}[/tex][tex]\begin{gathered} A=P(1-\frac{r}{100})^{nt} \\ A=109,185(1-\frac{0.771}{100})^{1\times14} \\ A=109,185\times0.89730607 \\ A=97,972.36 \\ A=97,972\text{ (to the nearest person)} \end{gathered}[/tex]The population of the city in the year 2021 is 97,972.
C.
We will use the same formula:
[tex]\begin{gathered} A=P(1-\frac{r}{100})^{nt} \\ A=97,890 \\ P=125,500 \\ r=0.771 \\ t=\text{?} \\ \text{Substitute all these parameters into the formula above:} \\ \end{gathered}[/tex][tex]\begin{gathered} 97890=125,500(1-\frac{0.771}{100})^t^{} \\ \frac{97890}{125500}=\frac{125500}{125500}(0.99229)^t \\ 0.78=0.99229^t \\ \ln 0.78=t\ln 0.99229 \\ -\frac{0.2485}{\ln 0.99229}=t \\ t=32.101 \\ SO\text{ the year that the population will reach 97,890 will be:} \\ 1989+32.101=2021.101 \\ \text{Which is approximately year 2021.} \end{gathered}[/tex]