A map of Australia has a scale of 1cm : 110 km. If the distance between Darwin and Alice springs is 1444 kilometers, how far apart are they on the map, to the nearest tenth of a centimeter
Simplify completely quantity x squared minus 10 x minus 24 all over x squared minus 3 x minus 108 and find the restrictions on the variable.
x+2/x+9 is the simplified form of x squared minus 10 x minus 24 all over x squared minus 3 x minus 108 and x≠-2 and x≠-9 are the restrictions of the variable.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given sentence is x squared minus 10 x minus 24 all over x squared minus 3 x minus 108
(x²-10x-24)/(x²-3x-108)
We will simplify the given expression by factorisation we will get
(x²-12x+2x-24)/x²-12x+9x-108
Taking x as common from first two terms in numerator and 2 from last two terms in numerator
Similarly, take x common from first two terms and 9 from last two terms in denominator we will get
x(x-12)+2(x-12)/x(x-12)+9(x-12)
(x+2)(x-12)/(x+9)(x-12)
After simplifying we are left with x+2/x+9
the restrictions on the variable is x should not be equal to -9 and it should not be -2
Hence, x+2/x+9 is the simplified form of x squared minus 10 x minus 24 all over x squared minus 3 x minus 108 and x≠-2 and x≠-9 are the restrictions of the variable.
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How do you write 2.82 in words
7 more than 11 times a number increased by the quotient of y and z
Answer:
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Step-by-step explanation:
Which expression is equivalent to –21.8 – (–18.3)?
The equivalent expression of the expression -21.8 - (-18.3) will be -3.5.
What is an expression?
Expression in math is defined as the collection of the number, variables and functions by using operations like addition, subtraction, multiplication, and division.
The mathematical expression is given as;
⇒ - 21.8 - (- 18.3)
Now, Solve the expression as;
The mathematical expression is
⇒ - 21.8 - (- 18.3)
= -21.8 + 18.3
(Since, Two negative sign give positive sign after combine.)
After subtract the numbers we get;
= - 3.5
So, The equivalent expression is;
⇒ - 21.8 - (- 18.3) = - 3.5
Thus, The equivalent expression of the expression -21.8 - (-18.3) will be -3.5.
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I WILL GIVE BRAINLIEST please I really need the answer
Rounded to the nearest some, What is the greatest amount of money that rounds to $105.40? What is the least amount of money that rounds to $105.40?
The greatest amount of money that rounds to $105.40 is $105.41, while the least amount that rounds to $105.40 is $105.39.
Explanation:The greatest amount of money that rounds to $105.40 would be the amount slightly greater than $105.40. Since rounding to the nearest cent, we would look at the hundredths place. Any amount greater than $105.405 would round up to $105.41. So the greatest amount of money that rounds to $105.40 would be $105.41.
The least amount of money that rounds to $105.40 would be the amount slightly less than $105.40. Again, looking at the hundredths place, any amount less than $105.395 would round down to $105.39. So the least amount of money that rounds to $105.40 would be $105.39.
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Jay Miller insured his pizza shop for $200,000 for fire insurance at an annual rate per $100 of $.49. At the end of 10 months, Jay canceled the policy since his pizza shop went out of business. Using the tables in the Business Math Handbook that accompanies the course textbook, determine the refund to Jay.
A. $127.40
B. $980
C. $186.20
D. $852.60
The following table shows the data collected from a random sample of 100 middle school students on the number of hours they play outdoor games every week: Weekly Duration of Outdoor Games Time (in hours) 0-2 3-5 6-8 9-11 Number of Students 30 62 8 0 There are 1,200 students in the school. Based on the sample proportion, how many students in the school would be expected to play outdoor games for at least three hours every week?
Answer:
you been waiting for your answer since 2017 bru im so sorry LLMA O the answer is 840
Answer:
840
Step-by-step explanation:
30 + 62 + 8 = 100
100 x 12 = 1,200
70 people out of 100 do activities for at least three hours a week.
70 x 12 = 840
100 x 12 = 1,200
840/1,200 in the school are expected to play outdoor games for at least three hours every week.
oml you asked this question in 2017. THATS 5 YEARS AGO
sorry
how to solve for pie
Answer:
Use the formula.
The circumference of a circle is found with the formula C= π*d = 2*π*r. Thus pi equals a circle's circumference divided by its diameter. Plug your numbers into a calculator: the result should be roughly 3.14
Step-by-step explanation:
Who do you work out 5 Quarts.= ? Cups and 48cups = ? Gallons
For the quarts to cups:
First, you need to figure out how many cups are in 1 quart. This is 4 cups = 1 quart.
If you have 4 cups in one quart then you need to multiply 4 cups by 5 quarts which equals 20 cups.
For the cups to gallons, you first need to find out how many cups are in 1 gallon. This is 16 cups = 1 gallon.
If you have 16 cups in 1 gallon then you will need to multiply 48 cups by 16 to find out how many gallons you will have which equals 3 gallons.
Hope this helps.
Fathi wants to print out a PDF document that is 48 pages long. To save paper, he decides to print on both sides of each sheet and to print two pages on each side of the sheet.
Fathi will need 12 sheets of paper to print a 48 page PDF document by printing two pages on each side of the paper. The total page count is halved twice, once for each side of a sheet and again for each pages printed per side.
Explanation:Fathi has a PDF document that is 48 pages long and he wants to print it in a way that saves paper. This involves printing two pages on each side of a sheet of paper and then using both sides of the sheet. To find out how many sheets he will need, we can start by halving the total page count because printing two pages on each side means we effectively halve the number of pages. So, 48÷2 equals 24 'effective' pages. Then, because he's printing on both sides of each sheet, we halve that number again, giving us 24÷2 equal 12 sheets of paper. So Fathi will need 12 sheets of paper to print his 48-page document.
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Without subtracting 8.5 - 4.64, determine what digit will be in the hundredths place. Explain
PLEASE HELP PRONTO
What is the length of the segment of the number line consisting of the points that satisfy (x-4)^2 <= 9$?
The length of the number line segment satisfying the inequality (x-4)² ≤ 9 is 6 units, found by solving the inequality to get the range 1 <= x <= 7 and subtracting the lower endpoint from the higher endpoint.
To find the length of the segment of the number line for the points that satisfy the inequality (x-4)² ≤ 9, we first solve the inequality. Taking square roots of both sides gives us |x-4| ≤ 3.
This means that the distance from x to 4 on the number line is less than or equal to 3. We can express this as two separate inequalities: x-4 ≤ 3 and x-4 ≥ -3. Solving these gives us x ≤ 7 and x ≥ 1, which represent the endpoints of the segment on the number line.
The length of this segment is the difference between the endpoints, which is 7 - 1 = 6. So, the length of the number line segment that contains all points satisfying the original inequality is 6 units.
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Explain how complex fractions can be used to solve problems involving ratios
a team won 11 of its last 25 games.what percent of its games did the team win?
Evaluate this exponential expression. (0.125)2/3
You are given a rectangular sheet of cardboard that measures 11 in. by 8.5 in. (see the diagram below). A small square of the same size is cut from each corner, and each side folded up along the cuts to from a box with no lid. 1. Anya thinks the cut should be 1.5 inches to create the greatest volume, while Terrence thinks it should be 3 inches. Explain how both students can determine the formula for the volume of the box. Determine which student's suggestion would create the larger volume. Explain how there can be two different volumes when each student starts with the same size cardboard. 2. Why is the value of x limited to 0 in. < x < 4.25 in.?
We can solve for the value of x using the formula:
V = l w h
where,
h = x the size of the cut since it would form the walls of the rectangle
w = 8.5 – 2x = it is subtracted by 2x since two sides will be cut
l = 11 – 2x
Substituting:
V = x (8.5 − 2x) (11 − 2x)
Expanding the expression:
V = 93.5 x – 39 x^2 + 4 x^3
To solve the maxima, we have to get the 1st derivative dV / dx then equate to 0. dV / dx = 0:
dV / dx = 93.5 – 78 x + 12 x^2
0 = 93.5 – 78 x + 12 x^2
We get:
x ≈ 1.585 in and x ≈ 4.915 in
Therefore Anya’s suggestion of 1.5 inches would create the larger volume since it is nearer to 1.585 inches.
There can be different volumes since volume refers to the amount of space inside the rectangle. They can only have similar perimeter and surface area, but not volume.
It is restricted to 0 in. < x < 4.25 in. because our w is 8.5 – 2x. Going beyond that value will give negative dimensions.
Choose the linear inequality that describes the graph. The gray area represents the shaded region
Answer:
The required inequality that shown in the given graph is [tex]y\geq 2x-2[/tex].
Step-by-step explanation:
Consider the provided graph.
The y-intercept of the line is, (0,-2)
The x-intercept of the line is, (1,0)
To find the equation of line use the formula:
[tex](y-y_1)=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
Substitute [tex](x_1,y_1)=(0,-2)\text{and}(x_2,y_2)=(1,0)[/tex]
[tex]y-(-2)=\frac{0-(-2)}{1-0}(x-0)[/tex]
[tex]y+2=\frac{(2)}{1}(x)[/tex]
[tex]y+2=2x[/tex]
[tex]y=2x-2[/tex]
Therefore the equation of line is [tex]y=2x-2[/tex].
The graph is solid line and shaded region is above the line. So, use the inequality sign "≥".
Thus, the required inequality that shown in the given graph is [tex]y\geq 2x-2[/tex].
PLEASE HELP WITH MATH VOCAB THX!!
Find the probability of flipping a coin and it showing heads and drawing a diamond from a standard deck of cards.
The probability of flipping a coin and it showing heads and drawing a diamond from a standard deck of cards is 1/8.
What is the probability?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability = (number of sides with a head / number of sides of a coin) x (number of diamonds / number of cards)
1/2 x 13/54 = 1/8
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Final answer:
The probability of flipping a coin and getting heads followed by drawing a diamond from a standard deck of cards is 1/8 or 0.125.
Explanation:
The probability question involves two independent events: flipping a coin and drawing a card from a standard deck. For the coin toss, the probability of getting heads is 0.5 since a coin has two sides and both are equally likely. Now, for drawing a diamond from a standard deck of cards, there are 13 diamonds out of 52 cards, so the probability is 13/52 or 1/4.
To find the probability of both events happening, we multiply the probabilities of each event, because they are independent events. So, the probability of flipping a coin and getting heads and then drawing a diamond is (1/2) * (1/4) = 1/8 or 0.125.
If you spend $9.74 in how many ways can you receive change for a ten-dollar bill
Final answer:
To determine the ways to receive change for a ten-dollar bill when you have spent $9.74, you need to consider the coin denominations that sum up to the remaining $0.26. This is a combinatorial problem known as the 'coin changing problem,' which involves calculating the combinations of coins that can be used to make up the remaining change.
Explanation:
To calculate how many ways you can receive change for a ten-dollar bill, you would need to consider the different denominations of U.S. currency and how they could combine to total the difference between your purchase amount of $9.74 and a $10 bill, which is $0.26.
The ways you can receive change can include a combination of quarters, dimes, nickels, and pennies.
To model this as a mathematical problem, let's calculate the different combinations: You could receive one quarter and one penny, or two dimes and six pennies, or one dime, one nickel, and eleven pennies, and so on.
Since the question asks for the number of ways to receive change and not the specific combinations, we can use combinatorics to determine the total number of combinations.
Note:
Since the actual calculations for combinatorics can be complex and the question does not provide all the necessary details to give a definitive number, we can consider this as an example of a combinatorial problem in mathematics.
The coin changing problem is a classic example that could be applied here, where algorithms can be used to find the number of ways to make change for a certain amount using given denominations.
An average person in the United States throws away 4.5 × 10² g of trash per day. In 2013, there were about 3.2×106 people in the U.S.
About how many grams of trash was thrown away in the United States in 2013?
show the graphical representation of 2/3 using a pie chart.
To produce a pie chart reflecting 2/3, the pie must be divided into 3 equal parts, representing the whole. Two of these sections are then filled in or marked, representing the 2 in the fraction 2/3 or roughly 66.7% of the total pie chart.
Explanation:To create a pie chart representation of the fraction 2/3, you need to think of the pie as representing the whole or 1. From there, we split the pie into 3 equal parts (since your denominator is 3), then, you will shade in 2 of those parts (as your numerator is 2). That shaded area of the pie chart represents 2/3.
It's essential to remember that each slice of the pie in a pie graph represents a share of the total or percentage. Thus, if you consider your pie to be 100%, then each one-third piece would be roughly 33.3%, and two of these would give you approximately 66.7%, which is the decimal equivalent of 2/3.
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f (x)=4x^2+4x+8, g (x)=4x-7 find (g*f)(x)
find a8 of the sequence 10, 9.75, 9.5, 9.25
Using Euler’s Formula (F + V = E + 2), find the number of edges. Faces: 25 Vertices: 17 Edges: ?
This question is based on the concept of Euler’s Formula. Therefore, there are 40 edges.
Given:
Faces: 25 Vertices: 17
We need to determined the number of edges by using the Euler’s Formula (F + V = E + 2).
According to the question,
It is given that,
Faces: 25
Vertices: 17
By using Euler’s Formula ,
F + V = E + 2
Now put all the given values in the formula.
We get,
25 + 17 = E + 2
42 = E + 2
42 - 2 = E
E = 40
Therefore, there are 40 edges.
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7(h+3)=6(h-3) pls help
If p is a prime, which one of the following could be a prime also?
F) 23p + 45
G) 23p + 46
H) 23p + 47
J) 23p + 48
K) 23p + 49
Final answer:
The expression that could potentially yield a prime number when p is substituted with a prime number is 23p + 46, since it results in an odd number.
Explanation:
To determine which of the options could also be a prime number, we need to check each expression by substituting a prime number for p. Since we are looking for a possible prime number, we can start by excluding options that will always result in an even number (which can't be prime unless the value is 2).
We know that any prime number p (other than 2) will be odd, and hence 23p will also be odd. Adding an odd number (45, 47, 49) to an odd number results in an even number, which cannot be prime other than 2. On the other hand, adding an even number (46 or 48) to an odd number results in an odd number.
The answer could be 23p + 46 or 23p + 48. However, 48 is divisible by 2, which would make 23p + 48 even (hence not prime for any p greater than 2). Therefore, the only potential expression that could yield a prime is 23p + 46, as long as p is chosen such that the result is not divisible by any other number.