The rate charged by first mechanic is $45 per hour and the rate charged by second mechanic is $50 per hour.
Given mechanic first worked 20 hours and mechanic second worked 15 hours and they charged $1650. The sum of rates of first mechanic and second mechanic is $95 per hour.
let the rate charged by first mechanic be x .
let the rate charged by second mechanic be y.
According to question
x +y=95-----------1
20x+15y=1650----------2
Multiply equation 1 by 20 and subtract equation 2 from 1.
20x+20y-20x-15y=1900-1650
5y=250
y=50
put the value of y=50 in 1 to get the value of x.
x +y=95
x+50=95
x=95-50
x=45
Hence the rate charged by first mechanic is $45 per hour and the rate charged by second mechanic is $50 per hour.
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Question is incomplete as it should be as under:
Two mechanics worked on a car, the first mechanic worked 20 hrs. and the second mechanic worked 15 hours together. They charged a total of $ 1650. What is the rate charged per hour for each mechanic if the sum of the two rates per hour was $95 per hour?
To prove that ΔAED ˜ ΔACB by SAS, Jose shows that StartFraction A E Over A C EndFraction = StartFraction A D Over A B EndFraction.
Triangle A E D is shown. Line segment B C is drawn from side A D to A E to form triangle A C B.
Jose also has to state that
The other equality which must be stated by Jose is that angles BAC and BAE are congruent and their measures are equal.
What other congruence statements must Jose state?It follows from the task content that Jose is trying to prove the congruence of both triangles by means of the Side-Angle-Side congruence theorem.
It therefore follows that since, Jose has identified that the ratio of corresponding sides are equal as indicated in the task content, the equality which Jose has to state is the angle congruence equality.
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Answer:a. angle A= angle A
Step-by-step explanation: i took edg
g Using the latest observation in a sequence of data to forecast the next period is an associative forecast. a regression analysis. a naive forecast. a moving average forecast. an exponentially smoothed forecast.
Using the latest observation in a sequence of data to forecast the next period is a naïve forecast. Option C
What is a naïve forecast?
A naïve forecast is a forecasting technique in which the last sequence of data are used for the next period's forecast without predictions or adjusting the factors that could affect it.
Forecasts that are produced using a naïve approach are equivalent to the final observed value gotten.
Thus, using the latest observation in a sequence of data to forecast the next period is a naïve forecast
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Determine the value of K that will cause f(x)=Kx^2+4x-3 to intersect the line g(x)=2x-7 at 2 points
By using the definition of second order polynomials and the discriminant from quadratic formula, we conclude that the values of k must be less than 1/4.
How to determine the value of k such that a line intersects a quadratic equation
In this question we must determine the set of values of k such that the function g(x), a linear function, intersects a quadratic function f(x) at two points. In this case, we must solve the following second order polynomial:
k · x² + 4 · x - 3 - g(x) = 0
k · x² + 4 · x - 3 - 2 · x + 7 = 0
k · x² + 2 · x + 4 = 0
In this case, the discriminant of the equation described above must be positive:
2² - 4 · k · 4 > 0
4 - 16 · k > 0
4 > 16 · k
16 · k < 4
k < 1/4
By using the definition of second order polynomials and the discriminant from quadratic formula, we conclude that the values of k must be less than 1/4.
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The figure below is painted on the street. It consists of a rectangle and an isosceles triangle.
Answer:
62 cmStep-by-step explanation:
add all sides, the top is the same as the bottom, (the side of 6 must be counted only once).
[2 * ( 18 + 3 + 7)] + 6 =
(2 * 28) + 6 =
56 + 6 =
62
62 m is the parameter of the given figure.
What is Perimeter?The perimeter of a two-dimensional form is the space surrounding it. It represents the total length of the shape's sides. The units used to measure the sides of the form, such as meters, centimeters, inches, or feet, determine the units used to measure the perimeter.
In a statistical context, parameters often refer to the unknown values of a probability distribution. In this case, parameters can be estimated using statistical methods such as maximum likelihood estimation or Bayesian inference.
Add all sides, the top is the same as the bottom, (the side of 6 must be counted only once).
[2 * ( 18 + 3 + 7)] + 6 =
(2 * 28) + 6 =
56 + 6 =
62
The perimeter of the given arrow is 62 m.
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Solve the system of equations 2x-y=132x−y=13 and 6x+5y=-336x+5y=−33 by combining the equations.
Answer: (2;-9).
Step-by-step explanation:
[tex]\left \{ {{2x-y=13\ |*(-3)} \atop {6x+5y=-33}} \right. \ \ \ \ \left \{ {{-6x+3y=-39} \atop {6x+5y=-33}} \right. .\\Summing\ up\ these\ equations:\\8y=-72\ |:8\\y=-9.\\2x-(-9)=13\\2x+9=13\\2x=4\ |:2\\x=2.[/tex]
Marlon jogs two miles to the park in 25 minutes, turns around, and takes another 55 minutes to walk the same path back to his house. What is his average speed for the round-trip?
Answer:
3 mph
Step-by-step explanation:
So the average speed is simply: [tex]\frac{distance}{time}[/tex]. In case, the total time is 25 minutes + 55 minutes which is a total of 80 minutes, or 1.33 hours. The total distance traveled is two miles + two miles, since he jogged two miles to the park, and then he turns around and walks the same path. So in total he traveled 4 miles. Plugging this in to the formula gives you the equation: [tex]\overline{v}=\frac{4 \text{ miles}}{\frac{4}{3}\text {hours}}=\frac{4\text{ miles}}{1}*\frac{3}{4}\text{ hours} = 3mph[/tex]
Consider the quadratic function f(x) = x² - 8x -4. What is the value of the leading coefficient?
-8
01
Answer:
1
Step-by-step explanation:
f(x) = x² - 8x - 4 ← is in standard form
with leading term x² and so
leading coefficient is the coefficient of the x² term, that is 1
I’m having issues with finding the restriction of the equation in the photo
Answer:
x = 9
Step-by-step explanation:
Restricted value of the expressionSimplify the equation.Set the denominator to 0.Solve and find the solution.The solution is the restricted value of the equation.[tex]\sf \dfrac{(x +7)(x+8)}{(x -9(x + 6)} \ \div \ \dfrac{(x+8)(x - 2)}{(x+ 6)(x - 2)} =\dfrac{(x +7)(x+8)}{(x -9)*(x +6)}*\dfrac{(x + 6)(x - 2)}{(x +8 )(x - 2)}[/tex]
[tex]\sf =\dfrac{x +7}{x - 9}[/tex]
x - 9 = 0
x = 9
If we plugin x = 9, then the denominator would become 0 and hence the expression will become undefined.
So, x = 9 is the restricted value of the expression.
Stuart wants to raise $100 for the Rainbow Club charity. He already has three donations of $30.20.
$10.50 and $5.00. How much does Stuart still need to raise?
Answer:
$54.30
Step-by-step explanation:
Given Total Donations already raised
= $30.20 + $10.50 + $5.00
= $45.70
Donations still required = Total Donations needed - Donations already raised
= $100 - $45.70 = $54.30
In the following exercises, multiply the binomials. Use any method.
252. (3r − 8)(11r + 1)
Answer:
Hence the expression [tex]$$(3r-8)(11r+1)=33r^2-85r-8$$[/tex].
Step-by-step explanation:
Explanation
The given expression is (3 r-8)(11 r+1).We have to multiply the given expression.Multiply the (3 r-8) by 1 , multiply the (3 r-8) by 11r then add like terms.[tex]$$\frac{\begin{matrix}{} & {} & 3r & - & 8 \\ \times & {} & 11r & + & 1 \\ \end{matrix}}[/tex]
___________
[tex]{\frac{\begin{matrix}{} & {} & 3r & - & 8 \\ 33{{r}^2} & - & 88r & {} & {} \\ \end{matrix}}{\begin{matrix}33{{r}^2} & - & 85r & - & 8 \\ \end{matrix}}}$$[/tex]
If EF = 2x – 12, FG = 3x – 15, and EG = 23, find the values of x, EF, and FG.
The values of x, EF, and FG from the line segment are 10, 8 and 15 respectively.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
EG = EF + FG (segment addition postulate)
Hence:
23 = (2x - 12) + (3x - 15)
x = 10
EF = 2(10) - 12 = 8
FG = 3(10) - 15 = 15
The values of x, EF, and FG from the line segment are 10, 8 and 15 respectively.
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5. Tom travels 60 miles per hour going to a neighboring city and 50 miles per hour coming back using the same road. He drove a total of 5 hours away and back. What is the distance from Tom's house to the city he visited?
Find the altitude of this equilateral triangle - geometry
Answer:
4√3.
Step-by-step explanation:
If the height is h then
tan 60 = h / (1/2*8)
tan 60 = h/4
h = 4 tan 60
= 4 * √3.
By definition, when a test or technique measures what it intends to, it is a. valid. b. reliable. c. significant. d. generalizable.
By definition, when a test or technique measures what it intends to, it is valid.
The answer is option A.
The criterion-related validity of a take-a-look is measured by the validity coefficient. Its miles said as a number between zero and 1.00 that indicates the significance of the relationship, "r," among the take a look at and a measure of task overall performance (criterion).
Reliability and validity are both approximately how nicely a technique measures something: Reliability refers to the consistency of a measure (whether or not the consequences can be reproduced below identical situations).
Validity refers back to the accuracy of a measure (whether or not the results really do constitute what they may be speculated to a degree).
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Using the following image, solve the problems below given that B is the midpoint of AC.
How would you set this problem up to find x? (Hint: Enter in the equation to find x.)
Using your setup, what are the values of x, AC, BC, and AC?
x=?
AB=?
BC=?
AC=?
(Giving 60 points and brainly!)
Answer:
AB = 4
BC = 4
AC = 8
Step-by-step explanation:
Given, B is the midpoint of AC which means it divided the AC into two equal parts. Using this information we can write the following equation:
5x - 6 = 2x add 6 to both sides
5x = 2x + 6 subtract 2x from both sides
3x = 6 divide both sides by 3
x = 2 to find the length of AB, AC, and BC replace x with 2
AB = 5*2 - 6
BC = 2*2
AC = 8 (sum of AB and BC)
[tex]\huge \boxed{\sf x=2}\\\\\huge \boxed{\sf AB=4}\\\\\huge \boxed{\sf BC=4}\\\\\huge \boxed{\sf AC=8}[/tex]
[tex]\displaystyle \sf AB=BC\\\\5x-6=2x\\\\Subtracting\ 2x\ and\ adding\ 6\ to\ each\ side \\\\5x-6+6-2x=2x-2x+6\\\\5x-2x=6\\\\3x=6\\\\Divide\ each\ side\ by\ 3\\\\\frac{3x}{3} =\frac{6}{3} \\\\x=2[/tex]
[tex]\sf Substituting\ x=2\\\\AB=5(2)-6=10-6=4 \\\\BC=2(2)=4\\\\AC=AB+BC=4+4=8[/tex]
Draw a tree diagram to represent the following scenario. You choose a random letter from the word SANDWICH. How many possible outcome are there?
Probability helps us to know the chances of an event occurring. There are 8 different scenarios possible.
What is Probability?Probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
For the given word SANDWICH, there are 8 different scenarios possible, which can be represented as shown below.
Hence, there are 8 different scenarios possible.
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which vectors are unit vectors?
The unit vectors are u = {1, 1}. Option C
What are unit vectors?Unit vectors can be defined as vector with magnitude of 1.
It is important to note that a unit vector is a vector quantity. Vector quantities are known to have magnitude and direction.
They are represented with the sign 'u'
Thus, the unit vectors are u = {1, 1}. Option C
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The volume of a rectangular prism is given by the expression 2x^4+2x^3-4x^2-4x. Write the volume as the product its dimensions. Remember, V = lwh.
=========================================================
Explanation:
First factor out the GCF 2x
2x^4+2x^3-4x^2-4x
2x*x^3+2x*x^2-2x*2x-2x*2
2x(x^3 + x^2 - 2x - 2)
Then let's factor the expression inside the parenthesis using the factor by grouping method
x^3 + x^2 - 2x - 2
(x^3 + x^2) + (- 2x - 2)
x^2(x + 1) - 2(x + 1)
(x^2 - 2)(x+1)
We see that x^3 + x^2 - 2x - 2 factors to (x^2-2)(x+1)
Overall, the original expression fully factors to 2x(x^2-2)(x+1)
length = 2x
width = x^2-2
height = x+1
The order of length, width, and height doesn't matter.
The volume as the product its dimensions 2x*( x²-2)*(x+1).
What is Volume?Volume is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface.
Given:
volume of a rectangular prism is given by the expression 2x^4+2x³-4x²-4x
=2x*x^3+2x*x^2-2x*2x-2x*2
=2x(x³ + x² - 2x - 2)
Now, we get the factor 2x(x³ + x² - 2x - 2).
Keeping aside 2x we will now focus on (x³ + x² - 2x - 2)
We already get the one factor 2x and now using (x³ + x² - 2x - 2) to get the other two factors.
Now solving x³ + x² - 2x - 2
=(x³ + x²) + (- 2x - 2)
= x²(x + 1) - 2(x + 1)
=( x² - 2)(x+1)
Now we get the two factors ( x² - 2)(x+1).
The expression for volume as the product its dimensions is 2x*( x²-2)*(x+1)
Hence, volume as the product its dimensions is 2x*( x²-2)*(x+1).
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What is the horizontal asympote of this graph?
Using it's concept, it is found that the graph has no horizontal asymptote.
What are the horizontal asymptotes of a function f(x)?The horizontal asymptote is the value of f(x) as x goes to infinity, as long as this value is different of infinity.
In this problem, we have that:
The function is undefined for x < 0, hence [tex]\lim_{x \rightarrow -\infty} f(x)[/tex] is undefined.For x > 0, the funciton goes to infinity, hence [tex]\lim_{x \rightarrow \infty} f(x) = \infty[/tex].Thus, the graph has no horizontal asymptote.
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There are 480 students in a school.
and
1
of the students wear glasses.
5
How many of the students do not wear glasses
Answer:
96 students
Step-by-step explanation:
I am not exactly sure if this question is talking about a 1:5 ratio, but that's what I am assuming. To get 96, you need to replace the 5 with 480 because the problem seems to mean 1 to every 5 people wear glasses. Next, you do 480/5 to get the number on the left side of the ratio. You get 96 when you do that. I am a little confused with the question because it isn't exactly formatted correctly, but this is what I am guessing. Hope this helps!
How long is the blue ribbon if the red ribbon is 12 inches?
Tyler has 3 times as many books as Mai.
How many books does Mai have if Tyler has:
The length of the blue ribbon given the length of red ribbon is 8 inches
AlgebraLength of red ribbon = 12 incheslength of blue ribbon = 2/3 of red ribbon
= 2/3 × 12
= (2×12)/3
= 24/3
= 8 inches
Let
Number of books Mai has = xNumber of books Tyler has = 3x = 15 books3x = 15
x = 15/3
x = 5 books
Therefore, the number of books Mai has is 5 books
Complete question:
The length of the blue ribbon is two-thirds the length of the red ribbon. How long is the blue ribbon if the red ribbon is 12 inches?
Tyler has 3 times as many books as Mai. How many books does Mai have if Tyler has 15 books?
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Which topic is this and how to solve ?
Answer:
Step-by-step explanation:
to be honest, I have no idea what topic this is anymore but to solve it plug in 5 for f(x) and then use -3 for x and then simplify for B.
I have a 79.43 and if I add 10% would it raise it to 80% grade wise
Answer:
87 grade
Step-by-step explanation:
if yo add a 10% overall grade to you 79.43 you will get an 87.373
79.43 x 10% = 7.943 (points added bc of your 10%added)
79.43 + 7.943 = 87.373
round it and you'll have 87 overall grade
Identify the segments that are parallel, if any, if
Answer:
The answer is C
Step-by-step explanation:
it is C because parallel lines don't intercept the go up or across but they don't touch, just imagine it isn't graphed.
simplify:
5 whole, 3 out of 10 + 2 whole, 1 out of 5.
Fractions are written as the ratio of two integers. The sum of 5 3/10 and 2 1/5 is 7 1/2
Sum of fractionsFractions are written as the ratio of two integers. Given the following expression
5 3/10 + 2 1/5
convert the mixed into improper fraction
53/10 + 11/5
Find the LCM
53+22/10
75/10
7.5
Hence the sum of 5 3/10 and 2 1/5 is 7 1/2
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OF
Fo
T
The first equation from the previous system of
equations is graphed. Graph the second equation to
find the solution of the system of equations
VH-2x+4
13-1
What is the solution to the system?
Answer:
(3,-2)
Step-by-step explanation:
See attached image.
which of the following of these numbers represents the three sides of a right triangle?
Answer:
3,4 and 5 is the ratio between the sides of a right triangle, therefore also the multiples (6-8-10 .... 9-12-15 etc.)
Step-by-step explanation:
3,4 and 5 is the ratio between the sides of a right triangle, therefore also the multiples (6-8-10 .... 9-12-15 etc.)
Suppose the population of a certain city increases at a rate proportional to the number of Inhabitants at any time. If the population doubles in 30 years, in how many years will it triple
Answer:
It will triple in approximately 48 years.
Step-by-step explanation:
t=30*ln3/ln2=30*1.5849= 48 years (approx.)
Answer the following questions that follow up with the picture.
The coordinates of the pint of tangency of the two circles is(_,_)
The radius of the circle with the center N has a length of ___ units.
The radius of the circle with center P has a length of ___ units.
The diameter of the circle with center N has a length of ___ units.
A team of 10 volunteers is visiting families in a local community to deliver canned goods. It takes one volunteer 24 hours to complete one visit. What is the capacity of the team over the course of an 8-hour workday?
1/3 of the volunteers can complete the 8-hour workday
How to determine the capacity of the team
Total number of volunteers = 10
If it takes 1 volunteer = 24 hours = 1 day
It would take x number of volunteers = 8 hours
To find 'x' , cross multiply
We have,
x * 24 hours = 8 hours * 1
24x = 8
Make 'x' the subject of formula
x = 8/ 24
x = 1/3
Therefore, 1/3 of the volunteers can complete the 8-hour workday
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