The local park has 4 bike racks . Each bike rack can hold 15 bikes . There are 16 bikes in the bike racks.What expression shows the total number of empty spaces in the bike racks ?
A 250-kVA, three-phase, 480-volt transformer requires 75 gallons of insulating oil to keep it properly cooled. How many liters is this?
This problem can be directly solved by using a conversion factor. Simple research will tell us that 1 gallon contains about 3.78 Liter. Therefore the volume in Liter is:
volume = 75 gallons * (3.78 Liter / gallon)
volume = 283.5 Liters
nelda baked 2 kinds of pasta in pans. each pan was the same size. She sliced one pan of pasta into 6 equal pieces. She sliced the other pan into eight equal pieces. How can the pans of pasta now be sliced so that both pans have the same size pieces?
Answer:
The first pan has to be divided into 4 equal parts.
The second pan has to be divided into 3 equal parts.
Step-by-step explanation:
The first step to solve this problem is finding the least common multiple of 6 and 8.
The multiples of 6 are {0,6,12,18,24,30,36,42,...}
The multiples of 8 are {0,8,16,24,32,...}
The least common multiple of 6 and 8 is 24.
So both kinds of pasta have to be baked so after the second step they have 24 equal parts.
So:
First pan:
The first pan was sliced into 6 equal parts.
24/6 = 4.
So each of the 6 parts have to be divided into 4 equal parts.
After the second step, they have 6*4 = 24 equal parts.
Second pan:
The second pan was sliced into 8 equal parts
24/8 = 3
So each of the 8 parts have to be divided into 3 equal parts.
After the second step, they have 8*3 = 24 equal parts.
Zeno has to go a distance, d, to get to his destination. He claims he can never get there because he has to travel half that distance d, then half of half of distance d, and so on. He says that he has to do an infinite number of tasks and that it is impossible. Use an infinite geometric series to help Zeno. Identify a1 and r to form the infinite geometric series that represents the problem.
a1=1/2d
r=1/2
sup it needs twenty character apparently
The [tex]a_{1} =\frac{d}{2}[/tex] and [tex]r=\frac{1 }{2 }[/tex] are for the infinite Geometric sequence.
What is geometric sequence ?
Geometric sequence a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.
i.e. [tex]a+ar+ar^2+ar^3+......[/tex]
Here, [tex]a=[/tex] First term and [tex]r=[/tex] common ratio
Next term formula, [tex]a_{n} =a_{1}\ *\ r^{n-1}[/tex]
We have,
[tex]d=[/tex] distance to her destination,
Now,
According to the question;
Zeno has to travel half that distance i.e. [tex]\frac{d}{2}[/tex],
Then half of half of distance i.e. [tex]\frac{d}{4}[/tex],
Then half of [tex]\frac{d}{4}[/tex] distance i.e. [tex]\frac{d}{8}[/tex] and so on.
So,
Here, we have,
[tex]\frac{d}{2},\frac{d}{4},\frac{d}{8}, .........[/tex]
So,
We have Geometric Sequence,
Here,
[tex]a_{1} =\frac{d}{2}[/tex] and
Now,
[tex]r=[/tex] common ratio,
[tex]r=\frac{a_{2} }{a_{1} }[/tex]
[tex]r=\frac{\frac{d}{4} }{\frac{d}{2} }[/tex]
We get,
[tex]r=\frac{1 }{2 }[/tex]
So, These are [tex]a_{1} =\frac{d}{2}[/tex] and [tex]r=\frac{1 }{2 }[/tex] of the Geometric sequence.
Hence, we can say that he [tex]a_{1} =\frac{d}{2}[/tex] and [tex]r=\frac{1 }{2 }[/tex] are for the infinite Geometric sequence.
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HELP PLEASE IS URGENT NEED TO PASS CLASS
you visit a farm and notice that white chicken lay white eggs and colored chickens lay brown eggs, so you decide that only white chickens lay white eggs. wht type of reasoning is this
The type of reasoning demonstrated in the scenario is deductive reasoning.
Deductive reasoning starts with a general premise or statement and applies it to a specific case to reach a logical conclusion. In this case, the premise is that white chickens lay white eggs and colored chickens lay brown eggs. Therefore, when encountering a white chicken, the conclusion is drawn that it will lay white eggs.
To understand deductive reasoning, let's break it down:
Premise:
White chickens lay white eggs.
Colored chickens lay brown eggs.
Observation:
Encounter a white chicken.
Conclusion:
Therefore, the white chicken will lay white eggs.
This conclusion is based on the general premise about the egg-laying behavior of white and colored chickens. Deductive reasoning allows us to draw specific conclusions from general principles, assuming the premises are true.
A school bus uses 3/4 of a tank of gas to drive back and forth to school in a week with 5 school days. How much gas does the bus use to drive back and forth to school in a week with 4 school days? Write your answer in simplest form.
Write an inequality statement comparing m and n. Using complete sentences, explain how you know that your inequality is true.
Hello There!
It would me m > n.
As you can see, M is further along on the number line than n therefore meaning it has a higher value.
Hope This Helps You!
Good Luck :)
if the smaller of two consecutive even intergers is subtracted from 3 times the larger the result is 42
3(x-2)+2(x+1)=-14
plz show work
Conduct a hypothesis test for each sample at the .01 level of significance and determine what action, if any, should be take. provide the test statistic and p-value for each test.
In the equation below, variables X and Y represent two matrices. Which property of matrix addition is illustrated below? x+y=y+x
Answer:
Matrix addition is commutative.
Step-by-step explanation:
We know that if there are two matrices X and Y of same order(i.e. same number of the rows and columns) then the addition between the two matrix is commutative i.e.
X+Y=Y+X.
While in case of multiplication of two matrices commutativity may or may not hold true.
solving a mathematical problem without the use of paper and pencil,calculator, or computer is called using _________ math
Which of the following is less than 6.5 x 10^-5.
A. 1.4 x 10^-3
B. 2.5 x 10^-4
C. 7.8 x 10^-5
D. 4.6 x 10^-6
[tex]4.6\times10^{-6}[/tex] is less than [tex]6.5\times10^{-5}[/tex]. Therefore, option D is the correct answer.
Given that, [tex]6.5\times10^{-5}[/tex].
We need to find which is less than [tex]6.5\times10^{-5}[/tex].
What is scientific notation?The scientific notation helps us to represent the numbers that are very huge or very tiny in a form of multiplication of single-digit numbers and 10 raised to the power of the respective exponent. The exponent is positive if the number is very large and it is negative if the number is very small.
Now, [tex]6.5\times10^{-5}[/tex] =0.000065
[tex]1.4\times10^{-3}[/tex] =0.0014
[tex]2.5\times10^{-4}[/tex] =0.00025
[tex]7.8\times10^{-5}[/tex] =0.000078
[tex]4.6\times10^{-6}[/tex] =0.0000046
[tex]4.6\times10^{-6}[/tex] is less than [tex]6.5\times10^{-5}[/tex]. Therefore, option D is the correct answer.
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Olivia earned $250 a week plus 5% commission on all sales over $1,500. How much did she earn the week she sold $3,500 worth of merchandise?
how can the statement c(1.5)+9 be interpreted
Which is another way to check the sum of 52 + 23 + 10 + 78?
A. 78 + 10 + 23 + 52
B. 78 – 52 – 10 – 23
C. 163 – 52 + 23 + 10 + 78
D. 78 – 52 + 10 + 23
Answer:
A. 78 + 10 + 23 + 52
Step-by-step explanation:
We can solve the problem by using the commutative property: "in an addition, changing the order of the operands does not change the result.
The original addition is 52 + 23 + 10 + 78. We see that option A is exactly the same addition, only the order of the numbers has been changed:
78 + 10 + 23 + 52
Therefore, the two additions are equivalent.
The interior angles formed by the sides of a quadrilateral have measures that sum to 360°. What is the value of x? Enter your answer in the box. x =
The value of x is equal to 59°.
In Mathematics and Euclidean Geometry, a quadrilateral is a type of polygon that has four (4) sides, four (4) vertices, four (4) edges and four (4) angles.
Generally, the sum of the interior angles of any quadrilateral is equal to 360 degrees. In this context, we can logically deduce the following;
2x + 3 + x + 2x + 3 + x = 360°
6x + 6 = 360°
6x = 360° - 6
6x = 354°
x = 354/6
x = 59°.
Find the 80th percentile of the distribution of the average of 49 fly balls.
The 80th percentile of the distribution of the average of 49 fly balls is approximately 254.2 feet
The 80th percentile of the distribution of the average of 49 fly balls can be found using the formula for the sample mean and the Z-score. Given that the mean distance of fly balls hit is 250 feet, the standard deviation is 50 feet, and the sample size is 49, we can calculate the 80th percentile as follows:
Calculate the Z-score corresponding to the 80th percentile, which is 0.842
Use the Z-score formula to find the sample mean:
Sample Mean=Population Mean + Z × Standard Deviation/ Sample Size
Sample Mean=250+0.842× 50/ √49
Sample Mean=250+0.842×5
Sample Mean=250+4.2
Sample Mean=254.2
Therefore, the 80th percentile of the distribution of the average of 49 fly balls is approximately 254.2 feet
Complete question:
Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 250 feet and a standard deviation of 50 feet. We randomly sample 49 fly balls. Find the 80th percentile of the distribution of the average of 49 fly balls.
Each _____ on the coordinate plane has an address, called the _____ _____, (x,y).
Each point on the coordinate plane has an address, called the coordinates.
What is Coordinate Plane?The coordinate plane is a two-dimension surface formed by two number lines. One number line is horizontal and is called the x-axis. The other number line is vertical number line and is called the y-axis.
The coordinate plane is a two-dimension surface formed by two number lines.
A coordinate plane, also known as a rectangular coordinate plane grid, is a two-dimensional plane formed by the intersection of a vertical line called the Y-axis and a horizontal line called the X-axis.
One number line is horizontal and is called the x-axis.
The other number line is vertical number line and is called the y-axis.
The two axes meet at a point called the origin.
Hence, Each point on the coordinate plane has an address, called the coordinates.
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Hasan has 18 3/4 yards of fabric. It takes 3 1/6 yards to make a pillowcase. Hasan plans to make as many pillow cases as he can. How many yards of fabric is left over?
Answer:
[tex]\frac{35}{38}[/tex] yards of fabric is left over.
Step-by-step explanation:
Hasan has the total length of fabric = [tex]18\frac{3}{4}[/tex] yards
= [tex]\frac{75}{4}[/tex] yards
Hasan plans to make as many pillow cases as he can.
To make one pillow case the fabric will be needed = [tex]3\frac{1}{6}[/tex] yards = [tex]\frac{19}{6}[/tex] yards
Hasan can make the total number of pillowcases = [tex]\frac{\frac{75}{4} }{\frac{19}{6} }[/tex]
= [tex]\frac{75}{4}[/tex] × [tex]\frac{6}{19}[/tex]
= [tex]\frac{75}{2}[/tex] × [tex]\frac{3}{19}[/tex]
= [tex]\frac{225}{38}[/tex]
= [tex]5\frac{35}{38}[/tex]
He can make 5 pillow cases and [tex]\frac{35}{38}[/tex] yards of fabric would be left over.
3× 1,250 in expanded form and use distributive property
How many ones in 800?
Carmen needs at least 86 points to pass Karissa's score. Karissa has 631 points. How many points does Carmen have?
What system of linear inequalities is shown in the graph?
Enter your answers in the boxes.
(graph is in picture)
A ticket agency sells tickets to a basketball game.The agency charges $32.50 for each ticket, a convenience charge of $3.30 for each ticket and a processing fee of $5.90 for the entire order. The total charge for an order is $220.70. How many tickets were purchased?
Division is one of the four fundamental arithmetic operations. The number of tickets purchased is 6.
What is Division?Division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.
Given the following details as shown below.
The agency charges $32.50 for each ticket, A convenience charge of $3.30 for each ticket And a processing fee of $5.90 for the entire order. The total charge for an order is $220.70.Let M represent the number of tickets purchased. Therefore, we can write,
Total charge = cost of each ticket x M + convenience charge x M + processing fee
220.70 = 32.50M + 3.30M + 5.90
Subtract 5.90 on both sides
220.70 - 5.90 = 32.50M + 3.30M
214.8 = 35.8M
Divide both sides by 35.8
6 = M
This means the number of tickets purchased is 6.
Thus, the number of tickets purchased is 6.
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Phil has three times as many rocks as peter together they have 48 rocks how many more rocks does Phil have been Peter
Charlotte buys tickets to go to a baseball game the total includes a charge of 7% of the original price for extra fees. If Charlotte pays a total of $44.94 how much was the original price of the ticket
The original price of the ticket is $42.
Let the original cost of the ticket be represented by x
Based on the information given, the equation to solve the question will be:
x + (7% × x) = $44.94
x + (7/100 × x) = $44.94
x + (0.07 × x) = $44.94
x + 0.07x = $44.94
1.07x = $44.94
Divide both side by 1.07
1.07x/1.07 = $44.94/1.07
x = $42
Therefore, the original price of the ticket is $42.
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The original price of the ticket was $42.
Explanation:To find the original price of the ticket, we need to subtract the extra fees from the total amount Charlotte paid.
Let x be the original price of the ticket.
The extra fees would be 7% of x, which is 0.07x. Since the total paid is $44.94, we can set up the equation:
x + 0.07x = 44.94
Combining like terms on the left side gives us 1.07x = 44.94.
Next, we divide both sides by 1.07 to isolate x:
x = 44.94 / 1.07 = $42
Therefore, the original price of the ticket was $42.
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Sara tells Michael she is 160 centimeters tall, while Michael says he is 60 inches tall. If there are 2.54 centimeters in an inch, who is taller?
What are the seven steps needed to reconcile a bank statement?
1. Add Deposits
2. Bank Errors
3. Outstanding Checks
4. Check Register Reconciliation
5. Interest Earned
6. Check Register Errors
7. Compare Both Statements