The robot will take 0.15 hours to complete one task.
What is the unitary method of problem solving?
A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary technique. The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. In the unitary method, the value of a unit quantity is determined before the values of other units are determined. Direct variation and inverse variation are its two different forms of variations. When there is a direct variation, an increase or decrease in one quantity will result in an equivalent rise or fall in the other. If we increase one quantity in inverse variation, the value of another quantity will drop.
Given, time taken by robot to complete five tasks = 0.75 hours
Thus, time taken by robot to complete one task = (0.75/5) = 0.15 hours
Therefore, the robot will take 0.15 hours to complete one task.
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Zach and Ginny are building model cars. Ginny's car is 2 more than 3 times the length of Zach's car. The sum of the lengths of both cars is 30 inches. Write an equation to determine the lengths of Zach's and Ginny's cars. A. 3x+2=30B. x+2+3x=30C. 2x+3=30D. x+2x+3=30
We can represent the length in Zach's car model by x
Since we have been given that Ginny's car is 2 more than 3 times the length of Zach's car, then we can get the expression as follow
[tex]\begin{gathered} 3\text{ times the length of Zach's car is} \\ 3\times x=3x \\ \end{gathered}[/tex][tex]\begin{gathered} 2\text{ more than 3 times the length of Zach's car will be} \\ 2+3x \end{gathered}[/tex]Therefore,
Ginny's model will be 2 + 3x
Next, we are told that the sum of the lengths of both cars is 30 inches
Then
[tex]\begin{gathered} Zach\text{+}Ginny=30 \\ x+2+3x=30 \end{gathered}[/tex]Therefore,
The answer is
[tex]x+2+3x=30[/tex]Thus, the answer is Option B
Create a division equation that represents the question: How many \frac{3}{8} are in \frac{5}{4} ?
The division equation that represents number of 3/8 in 5/4 is 10/3 = x.
Given,
Fractions : 3/8 and 5/4
We have to find a division equation for number of 3/8 in 5/4
Number of 3/8 in 5/4 = x
Now,
Number of a in b = b/a
So here,
Number of 3/8 in 5/4, x = 5/4 / 3/8
Number of 3/8 in 5/4, x = 5/ 3/2
Number of 3/8 in 5/4, x = 5 × 2 / 3
Number of 3/8 in 5/4, x = 10/3
That is,
The division equation that represents number of 3/8 in 5/4 is 10/3 = x.
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(1 × 10¹)(8 × 10^4) help
Answer:
800000
Step-by-step explanation:
(1 x 10^1) = 10
(8 x 10^4) = 80000
10 x 80000 = 800000
If a and b are the roots of 2x²+3x-1=0,find the values of a³-b³
Answer:
Step-by-step explanation:
Your equation has two complex roots, a=-3/4+sqrt(23)/4*i and b=-3/4-sqrt(23)/4*i. Calculate (x-a³/b³)*(x-b³/a³) and simplify it to get that expression. It will be a bit tedious, but the result is quite nice.
a³/b³=1001/1024+45*sqrt(23)/1024*i
b³/a³=1001/1024-45*sqrt(23)/1024*i
Notice that these are complex conjugates (which isn’t surprising, because a and b were complex conjugates). That’s why the result (x-a³/b³)*(x-b³/a³) will be a polynomial with real coefficients!
If you have complex conjugate roots c+di and c-di, you always get (x-(c+di))*(x-(c-di))=x²-2cx+c²+d², where c and d are real numbers.
It is -2c=-2*1001/1024=-1001/512, and
c²+d²=(1001/1024)²+(45*sqrt(23)/1024)²=1048576/1048576=1.
Solve it , I need help
y < 2
can't be y <= 2 or y<=1 because the dot is open meaning the point is not included.
the range is talking about the y value, the point is at y = 2. The graph is also negative; therefore, range will be anything less than y = 2
w=0.75f.
What does 0.75 tell us in this situation?
Answer:
it should be in the ratio of 3:4
Step-by-step explanation:
100w= 75f
w/f = 75/100
= 3/4
= 3:4
A group of friends wants to go to the amusement park. They have no more than $155 to spend on parking and admission. Parking is $18, and tickets cost $24 per person, including tax. What is the maximum number of people who can go to the amusement park?
Answer:
5
Step-by-step explanation:
155-18=137
137/24=5.70833333
5 people are able to join max
which best describes why you might want to rewrite a literal equation?
To solve for a different indicated variable.
To solve for the variable x.
To solve for a different number.
To solve for the variable y.
Sentence (A) "to solve for a different indicated variable" best describes why we might want to rewrite a literal equation.
What are literal equations?A literal equation is one that is mostly made up of letters. Examples of literal equations include formulas. Every variable in the equation "literally" represents a crucial aspect of the overall relationship that the equation expresses. Multiple letters or variables make up a literal equation. Examples include the formula for calculating speed (v = Dt) and the area of a circle (A = r₂).So, as in the description, it is given that A literal equation is one that is mostly made up of letters.
Therefore, sentence (A) "to solve for a different indicated variable" best describes why we might want to rewrite a literal equation.
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The correct question is given below:
Which best describes why you might want to rewrite a literal equation?
(A) To solve for a different indicated variable.
(B) To solve for the variable x.
(C) To solve for a different number.
(D) To solve for the variable y.
At the school 460 of the students walk to school.
1The number of students who take public transit is 20% of the number of students who walk. How many students take public transit?
2The number of students who bike to school is 5% of the number of students who walk. How many students bike to school
3The number of students who bike to school is 5% of the number of students who walk. How many students bike to school?
Answer:
92 public transit
23 bike
Step-by-step explanation:
460 / 5 = 92
460 / 20 = 23
a photocopy of a polygon was reduced to 30% of it's original size. Then, the copy was reduced again to 30% of it's size. What is the ratio of the corresponding sides of the second photo copy of the original? (round to four decimal places as needed)
Let's call a to the length of a side on the original polygon.
Let's call b to the length of the corresponding side to side a in the first photocopy. The length of b is: 0.3a (30% of a).
Similarly, c the length of the corresponding side in the second photocopy is: 0.3b = 0.3x0.3a = 0.09a
Then, the ratio of the corresponding sides of the second photocopy of the original to the sides of the original is 0.09:1
What is the value of x?
Answer:
x=27
Step-by-step explanation:
mathhhh helppp pleasee
not to intrude but is that big ideas math?
easy 8th grade math
with explanation pls
Answer:
x: (40,0)
y:(0,30)
Step-by-step explanation:
hope this helped
have a good day :)
A race car driver
travels 34 ft in the first second of a race.
If the driver travels 3.5 additional feet each
subsequent second, how many feet did the
driver travel in 52 s?
The number of distance in feet the driver travel in 52 seconds is 216 feet.
How to find the distance in feet the driver can travel in a particular time?The race car driver travels 34 feet in the first second of a race.
The driver travels 3.5 additional feet each subsequent second.
The number of feet the driver travel in 52 seconds can be solved as follows:
Therefore,
the distance travel = 34 + 3.5x
where
x = number of time in seconds the driver travelsTherefore,
the distance travel = 34 + 3.5(52)
the distance travel = 34 + 182
the distance travel = 216 feet
Therefore, if the driver travels 34 feet in the first seconds of the race and travels an additional 3.5 feet each subsequent second, the number of distance in feet the driver will travel in 52 seconds is 216 feet.
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What is the constant of proportionality in the equation y=3xy=3xy, equals, 3, x?
constant of proportionality ==equals
The constant proportionality is 3
What is Proportionality Constant ?
The proportionality constant is the ratio between two variables that varies directly . For directly proportional variables, their ratio is always a constant and this constant is the proportionality constant.
Now, We have the equation is:
y = 3xy
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form k = y/x or y = kx
To get the constant of proportionality,
we will derive both sides of the equation by x.
y/x = 3x/x
y/x = 3
Hence, The constant proportionality is 3
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Alan is ordering uniforms for his flag football team. Each uniform costs $14. All orders over $150 receive a 15% discount.
If Alan buys 12 uniforms, what will be the cost?
Answer:
$142.80
Step-by-step explanation:
smarts
how do i convert (x+3)(x-4) to standard form
Answer:
solving the bracket
x×x = x²
x×-4= -4x
3×x= 3x
3×-4= -12
x²-x-12=0
two trains leave the station at the same time, one heading west and the other east. the westbound train travels miles per hour slower than the eastbound train. if the two trains are miles apart after hours, what is the rate of the westbound train?
if the two trains are miles apart after hours, then the rate of the westbound train is 79 miles per hour
two trains leave the station at the same time, one heading west and the other east.
the westbound train travels miles per hour slower than the eastbound train. if the two trains are miles apart after hours,
what is the rate of the westbound train?
Allow the westbound train to be "w" and the eastbound train to be "e". We can make the following equation:
4 (e + (e - 12)) = 680
4 (2e + 12) = 680
8e - 48 = 680
8e = 728
e = 91 mph
e - 12 = w
91 - 12 = w
79 = w
Therefore, the westbound train travels at 79 miles per hour.
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Find the length of the missing side.
Answer:
13 cm
Step-by-step explanation:
You can use the pythagorean theorem to solve this problem. The pythagorean theorem states that [tex]a^2+b^2=c^2[/tex] where and b are the legs of a right triangle and c is the hypotenuse.
In the problem, we are given two legs, 12 and 5, so we can substitute them in for a and b and solve from there:
[tex]5^2+12^2=c^2[/tex]
[tex]25+144=c^2[/tex]
[tex]c^2=169[/tex]
[tex]c=13[/tex]
The missing side is 13 cm long
The mass of a textbook is approximately 0.0165 metric tons. If this number were written in scientific notation, what would the
exponent be?
If the number were written in scientific notation, the exponent will be -2.
What is scientific notation?Scientific notation is a method of expressing numbers that are either too large or too little to be represented in decimal form. In the United Kingdom, it is known as scientific form, standard index form, or standard form.
The number of times a number is multiplied by itself is referred to as its exponent.
In this case, the mass of a textbook is approximately 0.0165 metric tons. It should be noted that this will be 1.65 × 10^-2. The exponent is -2.
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look at attachment please MATHHHHHHHHHHHHHHHHH
Answer: 89%
[tex]\frac{0.89}{1}*\frac{100}{100} = \frac{89}{100}[/tex]
2y - 16 = 12 solve for y and simplify your answer as much as possible
Answer:
y = 14
Step-by-step explanation:
2y - 16 = 12
add 16 to both sides:
2y - 16 + 16 = 12 + 16
2y = 28
divide both sides by 2:
2y/2 = 28/2
y = 14
Answer: y = 14 is the solution.
Math for Homework
Question Help Challenge You buy 1.09 pounds of apples, 0.99pounds of grapes, and 1.29 pounds of oranges. What is your total bill?
Grocery Store Prices
Item
Cost
Apples
$0.99 per
pound
Grapes
$1.19 per
pound
$1.09 per
Oranges
Savvar Egge Rigid muiago
Your total bill is $
(Round to the nearest cent as needed.)
Clasroom Continks Schoonet: math
Work out the area of this semicircle.
Take to be 3.142 and write down all of the digits given by your calculator.
18 cm
Answer:
A = 127.251 cm²
Step-by-step explanation:
the area (A) of a circle is calculated as
A = πr² ( where r is the radius )
the area (A) of a semicircle is then
A = [tex]\frac{1}{2}[/tex] πr²
given diameter = 18 then r = 18 ÷ 2 = 9 cm , so
A = 0.5 × 3.142 × 9² = 0.5 × 3.142 × 81 = 127.251 cm²
8x-5x+21 = 36-6y
Write the equation so that y is a function of x.
The equation so that y is a function of x is y = [tex]\frac{-1}{2}[/tex]x + [tex]\frac{5}{2}[/tex].
What is equation?A formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign. Like this: 2x - 4 Equals 2. In the above example, the variable x exists. Equation: A declaration that two expressions with variables or integers are equal. In essence, equations are questions, and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics. Equations come in two varieties: identities and conditional equations. All possible values of the variables result in an identity. Only certain combinations of the variables' values make a conditional equation true. Two expressions joined by the equals symbol ("=") form an equation.
Given Data
Function
8x-5x+21 = 36-6y
6y = 36 - 21 - 8x +5x
6y = -3x + 15
y = [tex]\frac{-1}{2}[/tex]x + [tex]\frac{5}{2}[/tex]
The equation so that y is a function of x is y = [tex]\frac{-1}{2}[/tex]x + [tex]\frac{5}{2}[/tex]
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Aurora is planning to participate in an event at her school's field day that requires her to complete tasks at various stations in the fastest time possible. To prepare for the event, she is practicing and keeping track of her time to complete each station.
The x-coordinate is the station number, and the y-coordinate is the time in minutes since the start of the race that she completed the task.
(1, 3), (2, 6), (3, 12), (4, 24)
Part A: Is this data modeling an arithmetic sequence or a geometric sequence? Explain your answer. (2 points)
Part B: Use a recursive formula to determine the time she will complete station 5. Show your work. (4 points)
Part C: Use an explicit formula to find the time she will complete the 9th station. Show your work. (4 points)
From the given sequence, it is found that:
a) It is a geometric sequence, as the ratio between consecutive terms is the same.
b) Station 5 will be completed in 48 minutes.
c) Station 9 will be completed in 768 minutes.
What is a geometric sequence?In a geometric sequence, 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 the following rule:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
In the context of this problem, the ratio between consecutive terms is given by:
r = 24/12 = 12/6 = 6/3 = 2.
Hence it is a geometric sequence.
Applying the recursive formula, the time for Station 5 is the time for Station 4 multiplied by the common ratio of 2, hence:
24 x 2 = 48 minutes.
The first term of the sequence is of 3, hence the explicit formula is given by:
[tex]a_n = 3(2)^{n-1}[/tex]
Hence the time for the 9th station, in minutes, is given as follows:
[tex]a_9 = 3(2)^{8} = 768[/tex]
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A 12-sided die is rolled. The set of equally likely outcomes is {1,2,3,4,5,6,7,8,9,10,11,12). Find the probability of rolling a number less than 7.The probability of rolling a number less than 7 is
Probability is the quantitative measure of the likelihood of the occurrence of an event.
It is mathematically expressed as:
[tex]P=\frac{number\text{ of selected outcome}}{number\text{ of total outcome}}[/tex]We can decide to call the set of numbers below 7 "A".
A = {1, 2, 3, 4, 5, 6}
|A| = 6
We call the universal set, the set containing all the numbers rollable "U"
|U| = 12
Our probability is therefore:
[tex]undefined[/tex]When 4a-a is simplified it’s equivalent to
Answer: 3a
Step-by-step explanation: 4a - 1a = 3a
There are 20 balloons in Emma's hand. Four-fifths are red
balloons. How many red balloons are in Emma's hand?
Answer:
16
Step-by-step explanation:
4/5=0.8
20*0.8=16
axline computers manufactures personal computers at two plants, one in texas and the other in hawaii. the texas plant has 45 employees; the hawaii plant has 15. a random sample of 10 employees is to be asked to fill out a benefits questionnaire. (round your answers to four decimal places.) (a) what is the probability that none of the employees in the sample work at the plant in hawaii?
The probability that none of the employees in the sample work at the plant in hawai is 0.0112
Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.
PH= 20/60 = 1/3
P(T) = 2/3
It is hypergeometric distribution
P(X=k)={\frac {{\binom {K}{k}}{\binom {N-K}{n-k}}}{\binom {N}{n}}},
where
N = 60
K = 20 for Hawai; 40 for Texas
n = 10
P(X=0) = 0.0112
Hence The probability that none of the employees in the sample work at the plant in hawai is 0.0112
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