What is five and five eighths minus two and six sevenths minus five eighths?
A high school basketball player attempted 36 free throws in a season. An analyst determined that the player successfully made 5 out of 6 of these free throws. How many free throws did the player successfully make that season in total?
Answer: The number of successful throw made in that season in total is 30
Step-by-step explanation:
On average the player successfully made 5 out of 6 free throws .
Thus if number of free throws is x then number of successful throw will be [tex]\frac{5}{6}\times x[/tex] .
The basketball player attempted 36 free trials in a season .
Here x=36
Therefore No of successful throws [tex]=\frac{5}{6}\times 36=30[/tex]
Thus the number of successful throw made in that season in total is 30
To form 3 adjacent squares (as in the figure), 10 toothpicks are required. How many toothpicks are required to form 100 adjacent squares? ...?
To find out the number of toothpicks required to form 100 adjacent squares, one can use the formula 4 + 3(n - 1), resulting in 301 toothpicks.
Explanation:To determine how many toothpicks are required to form 100 adjacent squares, we must first understand the pattern established by the initial set of squares. When forming three adjacent squares, 10 toothpicks are used. This is because the first square requires 4 toothpicks, and each subsequent square shares a side with the previous square, thus requiring only 3 additional toothpicks for each new square.
For n adjacent squares, the number of toothpicks required can be calculated with the formula: 4 + 3(n - 1), since the first square uses 4 toothpicks and each additional square uses 3 more toothpicks.
Now, let's apply this to 100 adjacent squares:
Start with the formula: 4 + 3(n - 1).Substitute n with 100 to find the total toothpicks for 100 squares: 4 + 3(100 - 1).Simplify the equation: 4 + 3(99) = 4 + 297.Add the values together: 4 + 297 = 301 toothpicks.Therefore, 301 toothpicks are required to form 100 adjacent squares.
The relationship is that for each square, we need 4 toothpicks (1 new side for each square). So, for 100 adjacent squares, we require 400 toothpicks.
Let's analyze the pattern to determine the relationship between the number of squares and the toothpicks required. Consider the formation of 3 adjacent squares:
For the first square, we need 4 sides (4 toothpicks).
For the second square, we have 3 shared sides with the first square and 1 new side (3 + 1 = 4 toothpicks).
For the third square, we have 3 shared sides with the second square and 1 new side (3 + 1 = 4 toothpicks).
So, for 3 adjacent squares, we need a total of 12 toothpicks (4 + 4 + 4).
Now, let's generalize this pattern. For each additional square beyond the third, we are adding 4 toothpicks (1 new side for each square). Therefore, the toothpicks required to form n adjacent squares can be expressed as 4n.
For 100 adjacent squares:
Toothpicks=4×100=400
Hence, 400 toothpicks are required to form 100 adjacent squares.
The question probable may be:
To form 3 adjacent squares, 10 toothpicks are required. How many toothpicks are required to form 100 adjacent squares?
An insurance company charges a 35-year old non-smoker an annual premium of $118 for a $100,000 term life insurance policy. The premiums for 45-year olds and 55-year old no smokers are $218 and $563, respectively. Write a quadratic model for the premium p as a function of age a.
Answer:
[tex]p=\dfrac{49}{40}a^2-88a+\dfrac{13579}{8}[/tex]
Step-by-step explanation:
Let premium p for age of a , (p,a)
# An insurance company charges a 35-year old non-smoker an annual premium of $118 for a $100,000 term life insurance policy.
(35,118)
# An insurance company charges a 45-year old non-smoker an annual premium of $218 for a $100,000 term life insurance policy.
(45,218)
# An insurance company charges a 55-year old non-smoker an annual premium of $563 for a $100,000 term life insurance policy.
(55,563)
Let quadratic model be p=Aa²+Ba+C
Substitute the points into equation
For point, (35,118)[tex]118=35^2A+35B+C[/tex]
[tex]118=1225A+35B+C[/tex] -------------(1)
For point, (45,218)[tex]218=45^2A+45B+C[/tex]
[tex]218=2025A+45B+C[/tex] -------------(2)
For point, (55,563)[tex]563=55^2A+55B+C[/tex]
[tex]563=3025A+55B+C[/tex] -------------(3)
Solve system of equation and find out A, B and C using calculator.
[tex]A=\dfrac{49}{40},B=-88,C=\dfrac{13579}{8}[/tex]
Quadratic model:
[tex]p=\dfrac{49}{40}a^2-88a+\dfrac{13579}{8}[/tex]
f(x)=4x-1 and g(x)=x2-5 FInd (f-g)(x)
A kite has a perimeter of 108 feet. One of the longer sides measures 30 feet. What are the lengths of the other three sides?
Answer:
30 feet, 24 feet, 24 feet
Step-by-step explanation:
A kite is a quadrilateral with two pairs of congruent adjacent sides.
One of the longer sides measures 30 feet. According to the definition, the kite has two sides of length 30 feet. Let x feet be the length of another side.
The perimeter of the kite is
[tex]2\cdot 30+2\cdot x\ feet[/tex]
Since the kite has a perimeter of 108 feet, we have
[tex]2\cdot 30+2\cdot x=108\\ \\60+2x=108\\ \\2x=108-60\\ \\2x=48\\ \\x=24[/tex]
The length of two another sides is 24 feet. The kite has two sides of 30 feet and two sides of 24 feet.
Answer: Hello mate!
The kite has two equal-length long sides and two equal-length shorter sides. We also know that the perimeter is the addition of the four sides, where we have two long sides, L, and two short sides, S.
Then 2S + 2L = 108ft
S + L = 54 ft
if L = 30 feet
S + 30 ft = 54ft
S = 54ft - 30 ft = 24ft
Then the other long side also has 30ft length, and the two shorter sides have 24ft length.
The ratio of students to to teachers is 2:3 if there were 21 teacher how many students will there
be
Write 9 as a power of the base 3
The number 9 can be expressed as a power of 3 by finding the appropriate exponent that, when raised to the base 3, equals 9. This exponent is 2, making 9 written as a power of 3 to be 3².
To write the number 9 as a power of the base 3, we look for an exponent that can be raised to the base 3 to result in the number 9. This is achieved by recognizing that 3 squared (3²) equals 9. So, 9 expressed as a power of 3 is 3².
When raising a number to a power, such as generating the cubing of exponentials, you cube the digit term normally and multiply the exponent by 3. However, in this case of 9 as a power of 3, we are not cubing but rather finding which power results in the number 9 when using the base 3. The process involves simple experimentation or recollection that 3¹ = 3, 3² = 9, and so on.
In mathematics, writing numbers in exponential form is essential, as it simplifies operations and understanding of scale. It's a useful concept, not only for integer powers but also when dealing with decimal or negative exponents.
The graph shows the amount of gas remaining in the gas tank of mrs. lius car as she drives at a steady speed for 2 hours. How long can she drive before he car runs out of gas
To determine how long Mrs. Liu can drive before her car runs out of gas, one needs to analyze the slope of the graph that shows the rate of gasoline consumption, know the total capacity of the tank, and perform a calculation to estimate the remaining driving time assuming constant consumption.
Explanation:The question asks to determine how long Mrs. Liu can drive her car before the gas tank is empty, based on the graph showing the amount of gas left as she drives at a steady speed for 2 hours. To answer this, we need to find the rate at which the gas is being used and then use it to estimate the time until the tank reaches empty.
To find the rate of gasoline consumption, you would typically look at the slope of the graph, which shows the decrease in gas over time. If the graph shows a linear decrease, the slope will give you the rate (e.g., gallons per hour). Suppose the graph indicates that the tank started full and decreased to half over 2 hours. In that case, the consumption rate is half the tank's capacity divided by 2 hours. If you know the total capacity of the tank, you can calculate the driving time until empty.
However, since the actual graph and numerical data are not provided here, we can only guide you through the process hypothetically. With the actual graph, you would:
Find the slope of the graph (gasoline used per hour).Determine the total capacity of the car's gas tank.Divide the remaining gasoline by the consumption rate to calculate the remaining driving time.Remember, this calculation assumes a constant rate of consumption, which may not be accurate in real-life scenarios due to variations in driving conditions and car performances.
What method would you choose to solve the equation 2x2 – 7 = 9? Explain why you chose this method.
What are the approximate solutions of 7x^2 4x-9=0??
Write an equation with a variable on both sides of the equal sign that has infinitely many solutions. Solve the equation and explain why it has an infinite number of solutions.
I have no idea?
square root of 3400 please =]
for the sequencing of 3/16, 4/25, 5/36, 6/49
would it be (n+1)/(n^2)? ...?
Jane, Andre, and Maria pick apples.Andre pick three times as many pounds as maria. Jane picks two times as many pounds as Andre. The total weight of apples is 840 pounds. How many pounds does Andre pick?
Which of the following would offer proof that a relation is a function?
the graphed line overlaps itself
every output has only one input
vertical line test
the graphed line is straight
Answer:
C just did this
Step-by-step explanation:
Find the range.
3 –9 7 –1 5 –4 2
2
16
8
–1
Answer:
the answer is 16
What value of x satisfied the equation -4x - 2 / 3 = -6
Is -9 a rational or irrational number
The number -9 is a rational number as it can be written as a fraction of two integers, specifically -9/1.
The number -9 is a rational number because it can be expressed as a fraction of two integers: -9/1 where -9 is the numerator and 1 is the denominator. By definition, rational numbers include all integers, as each integer can be written as a fraction with a denominator of 1. This is different from irrational numbers, which cannot be written as a simple fraction. An example of an irrational number is the square root of 2, which cannot be precisely expressed as a fraction of two integers.
Coin can be tossed until a tail appears or until it has been tossed 3 times. Given that tail does not occur on the first toss, whats probability that the coin is tossed 3 times?
Suppose the sun casts a shadow off a 35-foot building. If the angle of elevation to the sun is 60 degrees, how long is the shadow to the nearest tenth of a foot?
PLEEEEEEEEEEEEEEEAAAAAAAAAAAAAAAASE HELP ME!!!!
Which is the equation of the given line?
A. x=-3
B. x=3
C. y=-3
D. y=3
An automobile maker has an order for 7,500 new cars to be delivered in one week. Each car must be fitted with a new hood ornament that requires 1 hour and 15 minutes to install. Assuming the factory operates on a standard workweek shift (8 hours per day for 5 days), how many workers must be assigned this job to meet the deadline?
...?
Answer:
235 workers
Step-by-step explanation:
Factory operates on a standard work week shift for 5 days = 8 hours per day
In one week working hours are = 8 × 5 = 40 hours.
Company has an order for 7,500 new cars to be delivered in one week.
One car requires time to be fitted with a new hood ornament that requires to install = 1 hour and 15 minutes ( 1.25 hours )
In 40 hours (one week) cars will install with one worker = [tex]\frac{40}{1.25}[/tex] = 32 cars
To fulfill the order of 7,500 cars, Company needs workers = 7,500 ÷ 32 = 234.375 ≈ 235 workers.
235 workers must be assigned this job to meet the deadline.
What is 3/16 plus 1/4?
Rapid rental car company charges a $40 rental fee $15 for gas, and $0.25 per mile driven. For the same car, Capital Cars charges $5 for a rental and gas and $0.35 per mile. Find the number of miles for which the companies' charges will be the same. How much will the rental be
The product of two numbers is 10 times the value of 9 and 8. which expression shows the two numbers?
Π is the ratio of _______________ to _______________.
what is the length of a rectangle with width of 10in. and area 45in.^2
how to solve sin(pi/2) without a calculator ...?
By the definition of the functions of trigonometry, the sine of is equal to the -coordinate of the point with polar coordinates , giving . Similarly, , since it is the -coordinate of this point. Filling out the rest trigonometric functions then gives
Write an expression for calculation add 8 to the sum of 23and 10
The expression for adding 8 to the sum of 23 and 10 is (23 + 10) + 8. This is due to the commutative property of addition, which states that the order in which you add numbers does not change the result.
Explanation:The question asks for an expression to calculate adding 8 to the sum of 23 and 10. The first step is to add 23 and 10 together, which equals 33. Then add 8 to that sum. You can represent this process mathematically as (23 + 10) + 8. So if you need to write an expression for adding 8 to the sum of 23 and 10, it would be (23 + 10) + 8. Remember, adding numbers together (a process called addition) is commutative, meaning you can add numbers in any order and still get the same result.
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