To solve this problem, we set up two linear equations based on the given information and solved them simultaneously. We found that Erin's age is 24 years.
Explanation:This problem is a classic example of a linear equation. We can set up two equations based on the information given:
Erin is 8 years younger than twice Paula’s age. This can be written as E = 2P - 8.The sum of their ages is 40. This can be written as E + P = 40.Upon substituting the value of E (Erin's age) from the first equation into the second, we get: 2P - 8 + P = 40. Simplifying this gives P = 16. Substituting P = 16 into the first equation, we find E = 24. Therefore, Erin is 24 years old.
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What is the side length of the smallest square plate on which a 30-cm chopstick can fit along a diagonal without any overhang?
Answer:
21.2
Step-by-step explanation:
math xl said so
The side length of the smallest square plate is 21.2 units.
What is the Pythagoras theorem?The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.
Given that, length of diagonal on the square is 30 cm.
Let the side of a square be x.
Now, x²+x²=30²
2x²=900
x²=450
x=√450
x=21.2 units
Therefore, the side length of the smallest square plate is 21.2 units.
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Angela lives in the United States. She went on a trip, flying first to London, then to Paris, then back to the United States. Assume that currency rates remained constant during her trip.a. If the currency rate was $1.67 per English pound, about how many pounds did she receive in exchange for $500 cash? Show your work or explain your reasoning.
The number of pounds that she received in exchange for $500 cash will be 299.40 pounds.
What are ratio and proportion?A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.
Angela lives in the United States. She went on a trip, flying first to London, then to Paris, then back to the United States. Assume that currency rates remained constant during her trip. If the currency rate was $1.67 per English pound.
The dollar is directly proportional to the pound.
Let p be the number of the pound.
p / 500 = 1 / 1.67
p = 500 / 1.67
p = 299.40 pounds.
The number of pounds that she received in exchange for $500 cash will be 299.40 pounds.
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The following is Michael Jordan’s baseball stats. Year Avg Gm AB R H TB 2B 3B HR 1994 0.202 127 436 46 88 116 17 1 3 Research baseball statistics online to determine what each label represent in the baseball world. How can you use the given information to determine how many singles Jordan hit during his baseball career?
Using mathematical operations, the total no. of singles Jordan hit during his baseball career = 67.
What are mathematical operations?Understanding the distinction between Operators and Operands will be made easier if we are aware of the differences between and purposes for Numbers/Values, Symbols, and Functions.
Understanding mathematical operations will be aided by being aware of the distinction between Operators and Operands as well as their function.
In the given statistics,
The number of Home Runs = 3
The number of Doubles = 17
The number of Triples = 1
The total no. of hits = 88
Now, to calculate the total no. of singles hit = 88 - (3+17+1)
= 67
Therefore, the total no. of singles Jordan hit during his baseball career = 67.
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are relations always functions
help help help please
You buy a bookshelf. The label on the box says the bookshelf is 5151 inches tall. How tall is it in feet?
1 foot = 12 inches
so 5151 inches divided by 12 = 429.25 feet tall
that is too tall for a normal house so hopefully you meant 51 inches
51 / 12 = 4.25 (4 1/4) feet tall
PLEASE HELP:::
Louise used this figure to model the expression 20/4.
Wyatt’s eye-level height is 120 ft above sea level, and Shawn’s eye-level height is 270 ft above sea level. How much farther can Shawn see to the horizon? Use the formula mc024-1.jpg, mc024-2.jpg with d being the distance they can see in miles and h being their eye-level height in feet.
Answer:
3 sqrt5
Step-by-step explanation:
Write and English phrase that would translate into the following mathematical expression. 5z-8.
Which of the following is equivalent to the expression 5z-8?
there are 40 girls on a softball team. 3 out of every 5 prefer chocolate over vanilla milkshakes .
how many girls prefer chocolate milkshakes
24 girls prefer chocolate milkshakes out of 40 girls.
Ratio and proportionsFrom the given information, you can see that we have a total of 40 girls
If 3 out of every 5 prefer chocolate over vanilla milkshakes, hen;
3girls = every 5 prefer chocolate
x = 40 girls
Cross multiply
5x = 3 * 40
5x = 120
x = 24
Hence 24 girls prefer chocolate milkshakes
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By default, the normal style places ____ points of blank space after each paragraph. 8 10 12 14
A hose fills a tank at a rate of 20 gallons per minute.
What is the rate in liters per hour?
(1 gallon ≈ 3.79 liters)
Answer:
[tex]\frac{4548}{1}[/tex] liters per hour.
Step-by-step explanation:
Given : A hose fills a tank at a rate of 20 gallons per minute.
To find : What is the rate in liters per hour?
Solution : We have given
A tank can fill hose in 1 minute = 20 gallon .
1 gallon = 3.79 liters.
20 gallon = 20 * 3.79 = 75.8 liters.
20 gallon = 75 .8 liters.
So,
A tank can fill hose in 1 minute = 75.8 liters.
A tank can fill hose in 60 minute = 75.8 * 60 liters = 4548 liters.
A tank can fill hose in 1 hour = 4548 liters.
Rate = [tex]\frac{4548}{1}[/tex] liters per hour.
Therefore, [tex]\frac{4548}{1}[/tex] liters per hour.
if 4x +5=9x-2,then x=
if f(x) = 2x-5, which expression represents f(x+1)
Answer: The required expression for f(x+1) is 2x-3.
Step-by-step explanation: We are given the following function :
[tex]f(x)=2x-5~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We are to find the expression for f(x+1).
To find the expression for f(x+1), we need to substitute x+1 in place of x in (i).
So, we get from expression (i) that
[tex]f(x+1)\\\\=2(x+1)-5\\\\=2x+2-5\\\\=2x-3.[/tex]
Thus, the required expression for f(x+1) is 2x-3.
I need help to figure this problem out
Which expression is the best estimate of the product of 7/8 and 1/10
Rotating a polygon in Quadrant II 270° clockwise is the same as
A) rotating it 90° clockwise.
B) rotating it 180° clockwise.
C) rotating it 90° counterclockwise.
D) rotating it 270° counterclockwise.
Answer:
90°
Step-by-step explanation:
Hi! A and B are definitely not the right answers, because that’s basically rotating it forward even more. Rotating a polygon in Quadrant II 370 degrees clockwise is like rotating it 99 degrees counterclockwise, because the next 90 degrees you were to rotate it, it would be in it’s original position. The answer is C.
The perimeter of a rectangle is 900 yards. what are the dimensions of the rectangle if the length is 70 yards more than the width?
if a number is a natural number, then it is also a whole number? what is the Inverse, the Converse, the Contrapositive, and the Bi-Conditional? and what is the Truth value for each one?
The original statement, 'If a number is a natural number, then it is also a whole number' is true because every natural number falls into the set of whole numbers. However, its converse is not true, as whole numbers include 0, which is not a natural number, making the inverse and the bi-conditional false. The contrapositive of the statement is true, maintaining logical consistency.
Explanation:If a number is a natural number, then it is indeed also a whole number. The relationship between natural numbers and whole numbers is an inclusive one, where all natural numbers (1, 2, 3, ...) are also whole numbers (0, 1, 2, 3, ...). The original statement can be expressed in logical form as: If P, then Q, where P is 'a number is a natural number,' and Q is 'it is also a whole number.'
Here is how the other forms of the statement look:
The inverse negates both the hypothesis and the conclusion: If not P, then not Q. So, 'If a number is not a natural number, then it is not a whole number.'
The converse switches the hypothesis and the conclusion: If Q, then P. For our statement, 'If a number is a whole number, then it is also a natural number.'
The contrapositive negates and switches the hypothesis and conclusion: If not Q, then not P. Therefore, 'If a number is not a whole number, then it is not a natural number.'
The bi-conditional states that P if and only if Q: A number is a natural number if and only if it is a whole number.'
The truth value of the original statement is true since all natural numbers are whole numbers. However, the converse is not true because whole numbers also include 0, which is not a natural number. Consequently, the inverse and the bi-conditional are false. The contrapositive is true because if it is not a whole number, then it can't be a natural number (considering that whole numbers include all natural numbers).
Devin brought his snail collection to school.He has 10 snails.How could he put them into 2 tanks so two classes could see them?Write equation for all the possible ways.One of the way is given. Explain how you have found all the ways.
Investigators at the scene of a crime strongly suspect that a handwritten promissory note for $10,000.00 has been altered to read $40,000.00. how might this be proven?
To prove that there is altering made on the promissory note, the investigators should test the ink on a piece of TLC. This would tell them when the ink was used and how long ago it was used so they can compare.
Which graph represents the solution set of the system of inequalities?
{−2x+y≤4
y>x+2
The correct graph is:
First graph
Step-by-step explanation:The first inequality is:
[tex]-2x+y\leq 4[/tex]
The graph of this inequality is a straight solid line ( since the inequality is a inequality with a equality sign i.e. not strict ) which passes through (-2,0) and (0,4) and the shaded region is towards the origin as it passes the zero point test.
The second inequality is:
[tex]y>x+2[/tex]
is a dotted straight line (since the inequality is strict) which passes through (-2,0) and (0,2) and the shaded region is away from the origin as it fails the zero point test.
Hence, the correct graph is the first graph.
Please calculate −0.5(7b−12a)−(8.4a−14b) if a=−10; b=−6.
Talia is packing a moving box. She has a square-framed poster with an area of 9 square feet. The cube-shaped box has a volume of 30 cubic feet. Will the posture lie flat in the box?
Answer: Yes, the posture will be lie flat in the box.
Step-by-step explanation:
since we have given that
Area of square framed poster = 9 sq. feet
Volume of cube shaped box = 30 cubic feet.
As we know the formula for "volume of cube":
[tex]Volume=30\\\\a^3=30\\\\a=\sqrt[3]{30}=3.10\ feet[/tex]
So, Area of cube shaped box would be
[tex]6a^2=6\times (3.1)^2=57.9\ ft^2[/tex]
Since the cube box is large enough so that the posture will lie flat in the box.
Find the area of the trapezoid.
144 square units
72 square units
88 square units
44 square units
area = 13+9=22
22/2 = 11
11x 4 = 44 square units
Answer:
44 square units
Step-by-step explanation:
Area of the trapezoid formula is [tex]\frac{base1 + base2}{2} \cdot height[/tex]
To find the base and the height we count the number of units in the graph
Base 1= 13
Base 2= 9 and height = 4
Now plug in all the values in the formula and find the area of the trapezoid
Area of the trapezoid=[tex]\frac{base1 + base2}{2} \cdot height[/tex]
=[tex]\frac{13+9}{2} \cdot 4[/tex]
=[tex]\frac{22}{2} \cdot 4[/tex]
=44 square units
The probability that concert tickets are available by telephone is 0.91. for the same event, the probability that tickets are available through a web site is 0.96. assume that these two ways to buy tickets are independent. what is the probability that someone who tries to buy tickets both through the internet and by the telephone will obtain at least one ticket? round your answer to four decimal places (e.g. 98.7654).
Final answer:
The probability of obtaining at least one concert ticket through both the internet and by telephone is 0.9984.
Explanation:
The probability that someone who tries to buy tickets both through the internet and by telephone will obtain at least one ticket is 0.9984.
To calculate this, we first find the probability of not getting any tickets through either method: P(no tickets) = P(no tickets by phone) * P(no tickets online). Then, subtract this probability from 1 to get the probability of obtaining at least one ticket: P(at least one ticket) = 1 - P(no tickets).
Julie owns a video store. Her monthly expenses, including rent, average $1,168. This year she made $34,416 in revenue. What is the difference between her average monthly revenue and her average monthly expenses?
You want to make five-letter codes that use the letters a, f, e, r, and m without repeating any letter. what is the probability that a randomly chosen code starts with a?0.100.150.200.25
Answer:
Option C is the right answer
Step-by-step explanation:
The probability that a randomly chosen code starts with A is 0.20
To mail a first class letter, the U.S Postal Service charges $.34 for the first ounce and $.21 for each additional ounce. It cost $1.18 to mail your letter. How many ounces does your letter weigh?
a food store makes a 11-pound mixture of peanuts, almonds, and raisians. The cost of peanuts is $1.50 per pounds, almonds cost $3.00 per pound, and raisins cost $1.50 per pound. The mixture calls for twice as many peanuts as almounds. The total cost of the mixture is $21.00. How much of each ingredient did the store use.