Answer:
Cookie monster needs to steal at least 6 cookies more.
Step-by-step explanation:
Given:
Number of cookies already stole = 4
Total number of cookies he wants to steal [tex]\geq 10[/tex]
We need to find how many cookie he needs to steal more.
Solution:
Let number of cookies he needs to steal more be 'x'.
Now we can say that;
Number of cookies already stole plus number of cookies he needs to steal more should be greater than or equal to Total number of cookies he wants to steal
framing in equation form we get;
[tex]4+x\geq 10[/tex]
Now using Subtraction property of Inequality we will subtract both side by 4 we get;
[tex]4+x-4\geq 10-4\\\\x\geq 6[/tex]
Hence Cookie monster needs to steal at least 6 cookies more.
The Cookie Monster needs to steal at least 6 more cookies after getting caught.
Explanation:The Cookie Monster stole 4 cookies initially before getting caught. If he steals no less than 10 cookies each time, we need to determine how many more cookies he needs to steal. Let's represent the number of cookies he needs to steal as x. The equation to represent this situation is: x >= 10 - 4.
Simplifying the equation, we have x >= 6. Therefore, the Cookie Monster needs to steal at least 6 more cookies after getting caught.
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Consider the following scenario: A student has prepared a series of analytical solutions to be run on an instrument in another room. The student has worn gloves throughout the preparation of the solutions, and has wiped up all drips and spills that occurred during that process. The student removes her gloves before leaving the lab room and carries her solutions in scintillation vials in a large clean beaker to the room where the instrument is located. Once in the new room, the student obtains a new pair of gloves before dispensing the solutions for analysis. Which of the following changes could improve the student's procedure?
Answer:
If it is possible for the student to wear a hand glove while transporting the chemicals to the other room, and use her other hand to open doors and use elevators.
It is also better if she could with her teammate and they could share responsibilities such that one of them carries the solutions while the other opens doors and uses the elevator.
A less breakable or plastic bin could have been used to convey the solutions to the other room to prevent the use of bare hand from contacting the glassware.
Step-by-step explanation:
If it is possible for the student to wear a hand glove while transporting the chemicals to the other room, and use her other hand to open doors and use elevators.
It is also better if she could with her teammate and they could share responsibilities such that one of them carries the solutions while the other opens doors and uses the elevator.
A less breakable or plastic bin could have been used to convey the solutions to the other room to prevent the use of bare hand from contacting the glassware.
What is the value of x?
Answer:
x=22.5
Step-by-step explanation:
BM||DT
Using Intercept theorem/Intercept theorem
[tex]\frac{6}{6+15} =\frac{9}{9+x}[/tex]
6(9+x)=9*21
54+6x=189
6x=135
x=22.5
At least I think so
Elizabeth made a scale drawing of her school's basketball court before devising a winning strategy for her team. The dimensions of the court are 15\text{ m}15 m by 27\text{ m}27 m. Move points to recreate Elizabeth's drawing on the grid below.
Answer:
the answer is 16ft
step-by-step explanation:
in order to make a triangle with non-zero area, the sum of the shorter two sides must be greater than the longest side.
here, 4 + 4 > 7, so the lengths can form a triangle.
The correct answer was given: Brain
7+8= 15
hope this
The correct answer was given: Brain
36 cm is the final : )
The Answer is
5 by 9
*Will Give Brainliest* Consider the Piece-Wise graph described by the following equation:
Determine the coordinates of the point on the graph where x=3.
A. (3, 1)
B. (3, 3)
C. (3, 5)
D. (3, 13)
The coordinates of the point on the graph when x=3 are C. (3, 5)
Step-by-step explanation:
Given piece-wise function is:
[tex]y = \left \{ {{4x+1\ \ \ x<3 } \atop {2x-1\ \ \ x\geq 3 }} \right.[/tex]
In order to determine the coordinates of the point on the graph where x=3 we will see which part of the function we have to consider as the function is in two pieces.
By observing we see that the second piece of function will be used as it is for x≥ 3 so it includes 3.
Putting x = 3 in y = 2x-1
[tex]y = 2(3) -1\\y = 6-1\\y = 5[/tex]
Hence,
The coordinates of the point on the graph when x=3 are C. (3, 5)
Keywords: Functions, graph
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A repair company's charge for repairing a certain type of copy machine fits the model y = 47.38 + 0.617x where y is the number of dollars charged and x is the number of minutes the repair person is on the job. How many minutes would it take for the cost of repair to reach $130? (Round to the nearest minute.)
a. 203
c. 134
b. 287
d. 13
Answer:c is the correct answer
Step-by-step explanation:
A repair company's charge for repairing a certain type of copy machine fits the model y = 47.38 + 0.617x
where y is the number of dollars charged and
x is the number of minutes the repair person is on the job.
Therefore, to determine the number of minutes that it would take for the cost of repair to reach $130, we would substitute y =130 into the given model. It becomes
130 = 47.38 + 0.617x
0.617x = 130 - 47.38 = 82.62
x = 82.62/0.617 = 134 minutes
PLEASE PLEASE HELP ME!!! WILL GIVE BRAINLIEST!!!!
The data to represent average test scores for a class of 19 students includes an outlier value of 81. If the mean, including the outlier of 81, equals 94, which statement is always true about the new data when the outlier is removed?
A. The median would increase.
B. The median would decrease.
C. The mean would increase.
D. The mean would decrease.
Answer:
the answer would be C. The mean would increase.
Step-by-step explanation:
The mean has increased, the correct option is C.
What is an Average?Average is the mean of the data set obtained by summing all the values of the data set and then dividing it by the number of data in the set.
The total number of students is 19.
The outlier is 81
An outlier is a number that is different from the other set of numbers, it is obtained due to variability in the observation or due to experimental error.
The mean including the outlier of 81 equals 94.
For the mean including the outlier, it can be observed that the outlier is the left outlier or the smallest number.
Let x represent the sum of all the test scores
x / 19 = 94
x = 94 * 19
x = 1786
The sum without the outlier is 1786 - 81 = 1705
The mean without the outlier is
= 1705 / 18
= 94 13 /18
This is greater than 94.
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A bus traveled 336 traveled 336 miles in 7 hours. If the continues at the same number of miles per hour, how many miles will the bus travel in 15 hours? Explain
Answer:
The bus traveled 720 miles with constant speed.
Step-by-step explanation:
Given,
Distance = 336 miles
time = 7 hrs
We have to find out the distance traveled by the bus in 15 hours with constant speed.
Solution,
Since we know that the speed is equal to distance divided by time.
So the equation can be framed as;
[tex]speed=\frac{336}{7}=48\ mi/h[/tex]
Now time = 15 hrs
Distance traveled is equal to speed multiplied with time.
So the equation can be framed as;
[tex]Distance\ traveled=48\times15=720\ miles[/tex]
Hence The bus traveled 720 miles with constant speed.
Alexa is a songwriter who collects royalties on her songs whenever they are played in a commercial or a movie. Alexa will earn $20 every time one of her songs is played in a commercial and she will earn $110 every time one of her songs is played in a movie. Alexa earned a total of $340 in royalties on 8 commercials and movies. Write a system of equations that could be used to determine the number of commercials and the number of movies on which Alexa's songs were played. Define the variables that you use to write the system.
Answer:the equations are
x + y = 8
20x + 110y = 340
Step-by-step explanation:
Let x represent the number of commercials on which Alexa's songs were played.
Let y represent the number of movies on which Alexa's songs were played.
The total number of movies and commercials on which Alexa earned is 8. It means that
x + y = 8 - - - - - - - - - - - -1
Alexa will earn $20 every time one of her songs is played in a commercial and $110 every time one of her songs is played in a movie. Alexa earned a total of $340 in royalties. This means that
20x + 110y = 340 - - - - - - - - - - - -2
Answer:
variables:
c= the number of commercials
m= number of movies
system of equations:
20c+110m= 340
c+m= 8
The sum of three guys ages is 62. Angelo is two years younger than Aaron and Alfred is four years older than twice Aaron's age. What are the ages of each guy?
Answer: Angelo is 13 years old.
Aaron is 15 years old
Alfred is 34 years old
Step-by-step explanation:
Let x represent the age of Angelo.
Let y represent the age of Aaron.
Let z represent the age of Alfred
The sum of three guys ages is 62. It means that
x + y + z = 62 - - - - - - - - - - -1
Angelo is two years younger than Aaron. It means that
x = y - 2
Alfred is four years older than twice Aaron's age. It means that
z = 2y + 4
Substituting x = y - 2 and z = 2y + 4 into equation 1, it becomes
y - 2 + y + 2y + 4 = 62
4y + 2 = 62
4y = 62 - 2 = 60
y = 60/4 = 15
x = y - 2 = 15 - 2
x = 13
z = 2y + 4 = 2 × 15 + 4
z = 34
A female bunny gained three pounds per week for six weeks. A male bunny gained 8 pounds per week for six weeks. How many more pounds did the male bunny gain than the female bunny?
Answer:
Step-by-step explanation:
A female bunny gained three pounds per. It means that the total number of pounds that the female bunny gained in 6 weeks would be
3 × 6 = 18 pounds.
A male bunny gained 8 pounds per week. It means that the total number of pounds that the male bunny gained in 6 weeks would be
8 × 6 = 48 pounds.
Therefore, the number of pounds that the male bunny gained more the female bunny would be
48 - 18 = 30 pounds
Step-by-step explanation:
Female Bunny: Doe
Male Bunny: Buck
A doe gained three lbs per week for six weeks.
3 x 6 = 18
A buck gained eight lbs per week for six weeks.
8 x 6 = 48
How many more lbs did the buck get than the doe?
48-18= 30
Answer:
The male bunny gained thirty more pounds than the female bunny.
The buck gained 30 more lbs than the doe.
The distance between (0,5) and (6,-1) is
Answer:
6sqrt(2) units (exact form)
= 8.49 units (3 sf)
Step-by-step explanation:
sqrt[(-1-5)²+(6-0)²]
sqrt[(-6)² + 6²]
sqrt(36 + 36)
sqrt(72)
= 6sqrt(2) units (exact form)
= 8.49 units (3 sf)
Determine whether the value given below is from a discrete or continuous data set. The volume of cola in a can is 12.1 oz?A. A discretediscrete data set because there are infinitely many possible values and those values can be countedvalues can be counted B. A continuouscontinuous data set because there are infinitely many possible values and thosethere are infinitely many possible values and those values cannot be countedvalues cannot be counted C. The data set is neither continuous nor discrete. D. A discretediscrete data set because there are a finite number of possible valuesthere are a finite number of possible values
Answer:
B. A continuous continuous data set because there are infinitely many possible values and those there are infinitely many possible values and those values cannot be counted values cannot be counted
Step-by-step explanation:
Given that the volume of cola in a can is 12.1 oz
We have to find out whether discrete or continuous.
We can say a random variable is discrete if it takes values which have one to one correspondence with the set of natural numbers.
continuous if a one to one correspondence with set of natural numbers cannot be established.
In our case, we have volume of cola as 12.1 oz. Between two readings say,12.1 oz and 12.15 oz. there may be infinite other values which the volume can take
i.e. this is a continuous data.
B. A continuous continuous data set because there are infinitely many possible values and those here are infinitely many possible values and those values cannot be counted values cannot be counted
is right answer
The volume of cola in a can, measured as 12.1 oz, is an example of continuous data because it could theoretically take any value in a certain range, unlike discrete data which can only have certain distinct values.
Explanation:The volume of cola in a can being 12.1 oz represents continuous data. This is because continuous data can take on any value within a certain range or interval. In this case, the volume of the cola in the can could theoretically have been any number between certain limits, for example, 0 to 12.2 oz. This differs from discrete data, which can only take certain distinct or separate values, such as the number of cans of cola you might buy (1,2,3, etc.).
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Allysa spent $35 to purchase 12 chickens . She bought two different types of chickens. Americana chickens cost $3.75 each and Delaware chickens cost $2.50 each
Final answer:
To solve the problem, set up a system of equations representing the total number of chickens and the total cost. Solve the system using substitution or elimination method to find the number of Americana and Delaware chickens that Allysa bought.
Explanation:
Allysa spent a total of $35 to purchase 12 chickens. Let's denote the number of Americana chickens as 'x' and the number of Delaware chickens as 'y'. The cost of Americana chickens is $3.75 each, while the cost of Delaware chickens is $2.50 each. Based on this information, we can establish two equations:
x + y = 12 (equation 1, representing the total number of chickens)
3.75x + 2.50y = 35 (equation 2, representing the total cost)We can solve this system of equations using substitution or elimination method. Let's use substitution:
From equation 1, we can express x in terms of y: x = 12 - ySubstitute the value of x in equation 2: 3.75(12 - y) + 2.50y = 35Simplify and solve for y: 45 - 3.75y + 2.50y = 35Combine like terms: -1.25y = -10Divide both sides by -1.25 to solve for y: y = 8Substitute the value of y back into equation 1 to find x: x = 12 - 8 = 4Therefore, Allysa bought 4 Americana chickens and 8 Delaware chickens.
Alyssa purchased 4 Americana chickens and 8 Delaware chickens. By solving the system of equations, we determined the number of each type of chicken. At the end of the first week, she expects to take in $22.5 from selling eggs.
To determine the number of Americana chickens, A, and the number of Delaware chickens, D, Alyssa purchased, we set up a system of equations based on the given information:
The total number of chickens purchased is 12: A + D = 12.The total cost of the chickens is $35: 3.75A + 2.5D = 35.Now, to solve the system, we can use substitution or elimination. Let's use substitution:
From the first equation, we can express A in terms of D: A = 12 - D.Substitute this expression for A into the second equation: 3.75 x (12 - D) + 2.5D = 35.Simplify and solve for D: 45 - 3.75D + 2.5D = 35, which simplifies to D = 8.Substitute D back into the expression for A: A = 12 - 8 = 4.So, Alyssa purchased 4 Americana and 8 Delaware chickens.
To determine Alyssa's expected income from selling eggs at the end of the first week:
Total eggs per day: 2×4 (Americana chickens)+1×8 (Delaware chickens) = 8+8=16Total eggs in a week: 16 eggs/day x 7 days = 112 eggs.She sells eggs by the dozen, so 112 eggs / 12 = 9 dozens (approximately) . Income from selling 9 dozens at $2.50 each: 9 x $2.50 = $22.5.Therefore, Alyssa expects to take in $22.5 at the end of the first week from selling eggs.
Complete Question:
Alyssa spent $35 to purchase 12 chickens. She bought two different types of chickens. Americana chickens cost $3.75 each and Delaware chickens cost $2.50 each. Write a system of equations that can be used to determine the number of Americana chickens, A, and the number of Delaware chickens, D, she purchased. Determine algebraically how many of each type of chicken Allysa purchased. Each Americana chicken lays 2 eggs per day and each Delaware chicken lays 1 egg per day. Allysa only sells eggs by the full dozen for $2.50. Determine how much money she expects to take in at the end of the first week with her 12 chickens.
A and B play a game in which they alternately toss a pair of dice. The one who is first to get a total of 7 wins the game. Find the probability that (a) the one who tosses first wins the game
Answer: the probability that the first toss wins is:
P = 1/6 or 0.1667
Step-by-step explanation:
A die has six sides (that is 6 outcome per die)
For a pair of dice:
The Total number of possible outcomes = 6 × 6 = 36
The possible outcomes of 7 is:
(1,6),(2,5),(3,4),(4,3),(5,2),(6,1)
= 6
The probability P of getting 7 is:
P = number of possible outcomes of 7/total number of possible outcomes
P = 6/36 = 1/6
The probability that the first toss wins
P = 1/6 or 0.1667
Company A rents copy machines for $300 a month plus $0.50 per copy. Company B charges $600 a month plus $0.01 per copy. For which number of companies do the two companies charge the same amount?
Answer:
For 612 copies both companies will charge the same amount.
Step-by-step explanation:
Consider the provided information.
let x represents the number of copies and y represents the total charge.
Company A rents copy machines for $300 a month plus $0.50 per copy.
[tex]y = 300 + 0.5x[/tex]
Company B charges $600 a month plus $0.01 per copy.
[tex]y=600 + 0.01x[/tex]
We need to determine the number of copies for which two companies charge the same amount, so equate the equations as shown.
[tex]300 + 0.50x = 600 + 0.01x\\0.49x=300\\x\approx612.244[/tex]
The Approximate value of x to nearest whole number is 612.
Hence, for 612 copies both companies will charge the same amount.
Find the sum -1/42+1/6=
Answer:
The answer is 1/7
To add fractions, find the LCD and then combine
Which graph represents g(x)=−(x−3)2−5 ?
Answer:
see below
Step-by-step explanation:
The leading minus sign tells you the graph opens downward. (x-3) in the squared term tells you the x-coordinate of the vertex is x=3. The graph that matches these characteristics is shown below.
Use the ten-frame and a crayon to show how to decompose the numbers into tens and ones
Answer:
1 Suppose these numbers are boxes and the dots 2 represent the crayon color to show that they are filled.3 If we have 1 ten frame we will use it one ten and if we have 4 5 ones then they will not be a ten. 2 tens would make a5 twenty similarly 3 tens would make a thirty.6789101 If we add a single 10 and 5 ones the answer would be 152 Other examples would adding two tens and 7 ones which 3 would make 27.45Another way to decompose the number would be
43 taking the 4 of the left with tens like 40 ( 4*10) and 3 of the right as three separate ones ( 3*1= 3) .Adding 10s four times with three one times would make 43
Final answer:
The student's question deals with decomposing numbers into tens and ones and relates to the concept of powers of ten in mathematics. Powers of ten notation is foundational in understanding place value, large, and small numbers. By breaking down numbers into tens and ones, students can grasp numerical values more effectively.
Explanation:
The question pertains to the mathematical concept of decomposing numbers into tens and ones using a ten-frame and involves powers of ten. In mathematics, numbers can be broken down into tens and ones to understand their value better. It's essential to note that each place in our numbering system is ten times greater than the place to the right of it. This is part of the reason we use powers-of-ten notation.
Decomposing Numbers
When decomposing a number like 24, for example, we can break it down into two tens (20) and four ones (4). If we used a ten-frame, we would fill in two full ten-frame grids to represent the tens and then add four individual marks to represent the ones.
Understanding Powers of Ten
When we discuss powers of ten, we're talking about how the counting system is structured, with each place value being ten times greater than the one before it. The digital numbering system got started because humans have ten fingers and counted with them, leading to an increase by tens.
A positive exponent, like 10³, tells us to multiply the base (10) by itself the number of times indicated by the exponent (3), which results in 1000. On the other hand, a negative number as the power indicates a division, so a power like 10⁻¹=0.1. If we have 10⁻⁴, it means 0.0001, which is ten times smaller than 0.001 (10⁻³).
When dividing by powers of ten, we move the decimal point to the left by the number of zeros indicated by the power. This process simplifies understanding large and small numbers by expressing them in terms of powers of ten or powers of one thousand for very large numbers.
at a movie theater, the size of popcorn bags decreased 20% . if the old bags held 15 cups of popcorn, how much do the new bags hold?
Answer:
12 cups
Step-by-step explanation:
If the size of the bag decreased by 20%, so will the number of cups held.
Number of cups held before the change = 15 cups
If the number of cups held after the 20% reduction in the size of the bag
= (100 - 20)% × 15
=80% × 15
= 12 cups
The new bags will hold 12 cups.
The old bags held 15 cups of popcorn so, the new bags holds 12 cups of popcorn and this can be determined by using the unitary method.
Given :
At a movie theater, the size of popcorn bags decreased 20%.The old bags held 15 cups of popcorn.The unitary method can be used to determine the total number of cups of popcorn the new bag can hold.
Given that the old bags held 15 cups of popcorn, so, it is 100% capacity of the old bag. So, according to this capacity, the new bag can 80% of cups of popcorns that is:
[tex]=\dfrac{80}{100}\times 15[/tex]
Multiply 80 by 15 in the above expression.
[tex]=\dfrac{1200}{100}[/tex]
Now, divide 1200 by 100 in the above expression.
= 12 cups of popcorn
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Help me Find the arc length of a circle in terms of pi
Answer:
3
Step-by-step explanation:
Recall that the full circumference of a circle can be represented by an angle of 360°.
In our case, we are asked to find the arc AB on the circumference of a circle that is represented by an angle of only 20°
hence the fraction of the circumference that is represented by arc AB
= 20° / 360°
= 1/18
we can thus say that the length of AB is 1/18 of the total circumference
Arc Length of AB
= (1/18) of total circumference
= (1/18) x 2π x radius
= (1/18) x 2π x 27
= 3π units
Answer:
3π Radian
Step-by-step explanation:
[tex]we \: have \: \: \: s = r \alpha \\ here \: s = arc \: length \\ r = radious \: of \: circle \\ \alpha = centre \: angle \: of \: current \: circle \\ so \\ s = 27 \times 20 \\ \: \: \: = 540 \\ \: \: \: \: \: = 540 \times \frac{\pi}{180} \\ \\ \: \: \: \: = 3\pi \: radian[/tex]
Two horses ran from the same place at the same time. One horse ran at a speed of 16 m/sec and the other ran at a speed of 18 m/sec. How far apart were they in 1 minute? In 5 minutes? In 8 minutes?
Answer:
1 minute = 1080 - 960 = 120 m
5 minutes = 5400 - 4800 = 600 m
8 minutes = 8640 - 7680 = 960 m
Step-by-step explanation:
I think the easiest way is to just see how far they get at each time. So I'm going to go one horse at a time.
16 m/s
1 minute = 60 seconds, every second is 16 meters so 16 m/s * 60 s = 960 m
5 minutes = 300 seconds so 16 m/s * 300 s = 4800 m
8 minutes = 480 seconds, 16 m/s * 480 s = 7680 m
I also want to point out that unites cancel out. m/s * s is kinda like variables so the seconds being multiplied by m/s cancels witht eh seconds in the denominator.
Now the next horse
18 m/s
1 minute totals to 1080 m
5 minutes = 5400 m
8 minutes = 8640 m
Now we take the differences of each time
1 minute = 1080 - 960 = 120 m
5 minutes = 5400 - 4800 = 600 m
8 minutes = 8640 - 7680 = 960 m
Another way to do this is to take the difference of speed and then multiply that by the time. so 18-16 = 2, then multiply each time by 2. For me it just makes more intuitive sense the way I showed.
During statistical analysis, the investigator may consider searching for statistical associations among various groups that may suggest a cause–effect relationship, without having generated prior hypotheses about these groups. This is known as ____.
.
Answer:
This is known as Data dredging.
Step-by-step explanation:
In order for any statistical analysis to be significant, a researcher has to first generate a hypothesis.
Data dredging is trying to uncover patterns in data that can be presented statistically without devising a clear hypothesis by use data mining. It is also referred to as data fishing or p-hacking.
In this case any correlation (relationship between cause-effect)will be purely by chance.
Therefore, the investigator is Data dredging
Mr.Kork sold his car for $8,400. This was $200 more than two fifths of what he had paid for the car originally. How much had Mr. Kork paid for the car?
Answer:
He paid = $20,500
Step-by-step explanation:
Let the amount he bought the car originally be X
so from the statement,
(2/5)*X + $200 = $8,400
(2/5)*X = $8,400 - $200
solving for X
X = $8200 * 5/2
X = $20,500
The diameters of bolts produced by a certain machine are normally distributed with a mean of 0.30 inches and a standard deviation of 0.01 inches. What percentage of bolts will have a diameter greater than 0.32 inches?a. 47.72%
b. 97.72%
c. 37.45%
d. 2.28%
e. 4.56%
A square that is 5yd on a side is placed inside a rectangle that has a width of 11yd and a length of 17 yd. What is the area of the region inside the rectangle that surrounds the square?
Answer: 162 sq. yds.
Step-by-step explanation:
Given : A square that is 5yd on a side is placed inside a rectangle that has a width of 11yd and a length of 17 yd.
Then , Area of rectangle = length x width
= 11 yd x 17 yd = 187 sq. yds.
Area of square = (side)²
= (5 yd)² = 25 sq. yds.
Now , the area of the region inside the rectangle that surrounds the square will be Area of rectangle - Area of square
= 187 sq. yds.- 25 sq. yds.
=162 sq. yds.
Hence, the area of the region inside the rectangle that surrounds the square is 162 sq. yds. .
Each peanut butter snack costs $2 each chocolate snack costs $3 how much does it cost to buy 6 peanut butter snacks and 8 chocolate snacks write an equation
These triangle are similar find the value of x
A. 2
B.6
C.4
D.3
Answer:
4
Step-by-step explanation:
in similarity the ratio of the similar sides is the same i.e
10/5 =8/x
2x=8
x= 4
Billy left home at 9 a.M. And rode his bicycle to the park at an average speed of 10 miles per hour here I got the park at 9:30 a.M. How many miles from the park is Billy's home so I explain how you got your answer
Answer:
Park is 5 miles from Billy's home.
Step-by-step explanation:
Given:
Billy left home at 9 a.m. And rode his bicycle to the park at an average speed of 10 miles per hour here and got the park at 9:30 a.m.
Now, to find the distance from park to Billy,s home.
Time it took Billy to rode his bicycle from park to home is from 9.30 a.m to 9.30 p.m.
So, the time = (9.30 - 9.00) = 30 minutes
[tex]=\frac{30}{60}[/tex] [tex]=0.5\ hour.[/tex]
Speed = 10 miles per hour.
Now, to get the distance from park to Billy's home we put formula:
[tex]Distance=Speed\times Time.[/tex]
[tex]Distance=10\times 0.5[/tex]
[tex]Distance=5\ miles.[/tex]
Therefore, park is 5 miles from Billy's home.
A phone company offers two monthly plans. In plan A, the customer pays a monthly fee of $35 and then an additional 9 cents per minute of use. In Plan B, the customer pays a monthly fee of $55.70 and then an additional 6 cents per minute of use. For what amounts of monthly phone use will Plan A cost less than Plan B? Use m for the number of minutes of phone use, and solve your inequality for m.
Answer:
Lesser than 6.9 minutes
Step-by-step explanation:
Let m represent the number of minutes of phone use with either plan A or plan B.
In plan A, the customer pays a monthly fee of $35 and then an additional 9 cents(9/100 = $0.09) per minute of use. This means that the total cost of m minutes would be
0.09m + 35
In Plan B, the customer pays a monthly fee of $55.70 and then an additional 6 cents(6/100 = $0.06) per minute of use. This means that the total cost of m minutes would be
0.06m + 55.70
Therefore, for the amounts of monthly phone use for which Plan A will cost less than Plan B, it becomes
0.09m + 35 < 0.06m + 55.70
0.09m - 0.06m < 55.70 - 35
0.03m < 20.7
m < 20.7/3
m < 6.9
A drive has a maximum speed of 10,000 revolutions per minute. If a disc has a diameter of 14 cm, what is the linear speed, in km/h, of a point 6 cm from the center if the disc is spinning at a rate of 6000 revolutions per minute?
The point 6 cm away from the center travels in a circle of circumference 2π*(6 cm) = 12π cm, so that it covers this distance per revolution, 12π cm/1 rev.
So the disk has a linear speed of
(6000 rev/min) * (12π cm/rev) = 72,000π cm/min
which is equivalent to
(72,000π cm/min) * (1/100,000 km/cm) * (60 min/h)
or approximately 135.7 km/h.