Each morning librarians place 560 books on a book shelf in the school library. Each student that visits library that day takes exactly 3 books from this shelf. Let s be the number of students which visit library on a particular day. Let b be the number of books left on the shelf at the end of that day. a How does the number of books left on the shelf depend on number of students visiting library? Find formula for the function b(s).
The relationship between the books and the students is an illustration of a linear function
The formula for the function is: [tex]b(s) = 560 - 3s[/tex]
From the question, we have:
[tex]b = 560[/tex] --- number of books in the morning
[tex]r = 3[/tex] ---- the number of books per students
So, the number of books as a function of number of students is:
[tex]b(s) = b - r \times s[/tex]
Substitute known values
[tex]b(s) = 560 - 3 \times s[/tex]
[tex]b(s) = 560 - 3s[/tex]
Hence, the formula for the function is:
[tex]b(s) = 560 - 3s[/tex]
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which is another way to write this number? (3 x 1,000) + (3 x 10) (3 x 1/100) + (3 x 1/1000)
The equivalent expression to (3 x 1,000) + (3 x 10) + (3 x 1/100) + (3 x 1/1000) is 3030.033. This result doesn't require simplification through Exponential or Scientific notation since it's not an especially large or small value.
Explanation:The student's question is asking for an alternative way to write the number produced by the mathematical operation: (3 x 1,000) + (3 x 10) + (3 x 1/100) + (3 x 1/1000). This is a combination of addition and multiplication involving decimal places. It can also be expressed in exponential notation:
First simplify and solve the individual operations: (3 x 1,000) = 3000, (3 x 10) = 30, (3 x 1/100) = 0.03, and (3 x 1/1000) = 0.003.Next, add your results: 3000 + 30 + 0.03 + 0.003 = 3030.033.So, another way to write the stated combination of multiplication and addition operations is 3030.033. The Exponential notation might not be an ideal replacement in this specific case since the result is not a large or small number which normally requires this notation. Scientific notation, (which uses powers of ten to express larger or smaller numbers), could most effectively be implemented if our final result was a very large or very small number.
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Find three points that solve the equation , -5x-3y=-7
What is a transformation and 3 types of transformations.
Name the triangle with the following characteristics. Sides: 5 cm, 5 cm, 7 cm.
A. scalene triangle B. acute triangle C. isosceles triangle D. right triangle
HELP ASAP
what is the exact of the expressions square root of 180 - square root of 125 + square root of 5
The exact value of the expression √180 - √125 + √5 simplifies to 2√5, by combining like terms after simplifying each square root separately.
The exact value of the expression [tex]\sqrt{180}[/tex] - [tex]\sqrt{125}[/tex] + [tex]\sqrt{5}[/tex] can be calculated by simplifying each square root separately. Firstly, the [tex]\sqrt{180}[/tex] can be simplified to 6√5, because 180 = 36 × 5, and 36 is a perfect square whose square root is 6. Similarly, the [tex]\sqrt{125}[/tex] simplifies to 5√5, since 125 = 25 × 5 and the [tex]\sqrt{25}[/tex] is 5. The [tex]\sqrt{5}[/tex] remains as it is because it cannot be simplified further.
The expression then becomes 6√5 - 5√5 + √5. Now, we combine like terms. Since all terms involve the [tex]\sqrt{5}[/tex], we can combine them as follows: (6 - 5 + 1)√5, which simplifies to 2√5. Therefore, the exact value of the expression is 2√5.
Area of 100 3/4 feet x 75 1/2 feet?
What's the Estimate of 615-342
Final answer:
To estimate the difference between 615 and 342, round each number to the nearest ten or hundred and subtract. Rounding to the nearest hundred gives an estimate of 300, while rounding to the nearest ten gives an estimate of 280.
Explanation:
To estimate the difference between 615 and 342, you can round each number to the nearest ten or hundred and then subtract the rounded numbers. Here's the step-by-step process:
Round 615 to the nearest hundred, which gives you 600.Round 342 to the nearest hundred, which gives you 300.Subtract the rounded numbers: 600 - 300 = 300.This gives an estimate of the difference between 615 and 342 as 300.
If you prefer to round to the nearest ten instead, you'd get:
Round 615 to the nearest ten, which gives you 620.Round 342 to the nearest ten, which gives you 340.Subtract the rounded numbers: 620 - 340 = 280.In this case, the estimate would be 280. You can choose the level of precision you want in your estimate based on how you round the numbers.
Is 7.38 a mixed decimal
The Fenton College Cougars made 40 field goals in a recent basketball game some 2 pointers and the rest 3 pointers. Altogether the 40 baskets counted for 89 points. how many of each type of field goal was made?
An audio cable is 15.7dm long. How long is the cable in meters?
a child is to receive a dose of 0.5 teaspoon of cough medicine every 4 hours. if the bottle contains 60 doses, how many days will the medicine last?
What is 5.8×2.4?
Show your work
What grade if u like this you will get 24 points
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Choose the best answer. Which of the following is not a type of savings account? A.passbook account
B.statement account
C.club account
D.automatic account
Answer with explanation:
Saving Account →A savings account is a type of bank account in which you can keep extra money possessed by you in an institution, which is most safest place,The money you get as an interest is proportional to amount of money deposited in that institution.
A. Passbook Account : A Passbook Savings account is also a saving account,in which you get interest for your deposit and also get a passbook for easy record keeping.
B.Statement account : It is also a saving account,in which you get statement for your credit and debit in your account.
C. Club Account: In this type of Saving account, you deposit money for your future investment or for any future purpose by a group.You have to deposit and withdraw money within a certain time frame.
D. Automatic account: In this type of account , money is transferred to it's customers automatically in their accounts by a certain process. It is not a saving Account.
Option 4→: Automatic Account : is the type of account which is not a saving Account.
Find the volume v of the described solid s. the base of s is an elliptical region with boundary curve 16x^22 + 9y^2 = 144. cross-sections perpendicular to the x-axis are isosceles right triangles with hypotenuse in the base.
When finding the length of the hypotenuse of a right triangle why might you approximate the answer
Sample Response:: If the square root is not a perfect square, then an approximation of the root often makes more sense in the context of the problem. For real-world problems, you would want an approximation, so you have an estimate of the length you are looking at.
w varies jointly as x and y and inversely as the square of z. If w=280 when x=30, y=12, and z=3, find w when x=20, y=10 and z=2
Can someone help me if anyone know. Please, thanks
which types of angels are not congruent?
Suppose θ is an angle in the fourth quadrant with cosθ=x/4. Find expressions for the other five trig functions in terms of x?
Cell phones can weigh as little as 2 ounces. How many pounds can the cell phone weigh?
A cell phone weighing 2 ounces translates to 0.125 pounds, since there are 16 ounces in one pound.
Explanation:Cell phones can weigh as little as 2 ounces. The first step in determining how much a cell phone can weigh in pounds is to know the conversion factor between ounces and pounds. Since there are 16 ounces in one pound, you can divide the weight of the cell phone in ounces by 16 to convert it to pounds. For a cell phone that weighs 2 ounces:
Divide the weight in ounces by 16 to convert to pounds: 2 ounces ÷ 16 = 0.125 pounds.Therefore, a cell phone that weighs 2 ounces is equivalent to 0.125 pounds.
The top of a 22-foot ladder rests against the top of an 18-foot wall. If the base of the ladder is on the same ground level as that of wall, what angle does the ladder form with the ground? Express your solution to the nearest degree.
Answer:
Step-by-step explanation:
Given that The top of a 22-foot ladder rests against the top of an 18-foot wall.
The ladder, the wall and the floor together make a right angled triangle with hypotenuse as ladder.
Thus we have a right triangle with hypotenuse = 22 ft
and the side of the wall = 18
The required angle is the angle the ladder form with the ground.
Hence we have if x is the angle
[tex]sin x =\frac{Opposite}{Hypotenuse} =\frac{18}{22}[/tex]
From this we can find the angle X
X = sin inverse of 18/22
X=54.9
Round it off to X=55 degrees
Take apart an addend to solve 35+27
write in logarithmic form
6^2=36
The conversion of the expression 6^2=36 into logarithmic form results in log6(36) = 2. This method involves identifying the base (6), the exponent (2), and the result (36) in the original exponential equation.
Explanation:In mathematics, you can interchange between an exponential form and a logarithmic form. Your given expression is 6^2=36, which is in exponential form.
To change this into logarithmic form, identify the base (which is 6 in this case), the exponent (which is 2), and the result (which is 36). The logarithmic form of the equation would then be 'log base 6 of 36 is 2'.
So, written in the usual mathematical notation, your answer would be log6(36) = 2. Here, 'log' stands for logarithm; the number following 'log' (6 in this case) is the base, the term within parentheses (36 in this case) is the number we're taking log of, and '2' is the value of the logarithm.
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A surveyor took the following measurements from two irregularly shaped pieces of land. Some of the lengths and angle measures are missing. Find all missing lengths and angle measures. Round lengths to the nearest tenth and angle measures to the nearest minute
To find the width of the river, use trigonometry and the tangent function. The width of the river is approximately 67.1 meters.
Explanation:To find the width of the river, we can use trigonometry. The surveyor measured an angle of 35° from the baseline to the tree on the opposite bank. We know the distance along the river is 100 m. Let's denote the width of the river as 'x'.
We can use the tangent function to solve for 'x'. The tangent of the angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is 'x' (the width of the river) and the adjacent side is 100 m (the distance along the river).
So, the equation becomes:
tan(35°) = x/100
To find the value of 'x', we can multiply both sides by 100:
x = 100 * tan(35°)
Using a calculator, we can find that x is approximately 67.1 m. Therefore, the width of the river is approximately 67.1 meters.
The depths of water, at the edge of a pier, at different times of day, are represented by the table below. Which of the following functions best models the depths of the water?
Which of these is equivalent to 3-23-2?
Answer:
-22
Step-by-step explanation:
This is a case of directed numbers. The numbers 23 and 2 carry negative signs like this:
- 23
- 2
Therefore, adding these negative numbers gives -23 - 2 = -25
Adding the sum to 3 gives: 3 - 25 = -22
For each lettered part, a through c, examine the two given sets of numbers. without doing any calculations, decide which set has the larger standard deviation and explain why. then check by finding the standard deviations by hand. set 1 set 2
a.4, 7, 7, 7, 10 4, 6, 7, 8, 10
b.100, 140, 150, 160, 200 10, 50, 60, 70, 110
c.10, 16, 18, 20, 22, 28 48, 56, 58, 60, 62, 70
a. Set 2 has larger standard deviation.
b. Set 1 and set 2 have same standard deviation.
c. Set 2 has larger standard deviation.
a. Set 1: 4, 7, 7, 7, 10
Set 2: 4, 6, 7, 8, 10
It seems like Set 2 might have a larger standard deviation because the numbers are more spread out from the mean (which appears to be around 7).
The set 3 has larger standard deviation.
For Set 1:
Mean = (4 + 7 + 7 + 7 + 10) / 5
= 7
Standard Deviation = ([tex]\sqrt{\frac{(4-7)^2 + (7-7)^2 + (7-7)^2 + (7-7)^2 + (10-7)^2)}{5}[/tex]]
= 1.89
For Set 2:
Mean = (4 + 6 + 7 + 8 + 10) / 5
=7
Standard Deviation = ([tex]\sqrt{\frac{(4-7)^2 + (6-7)^2 + (7-7)^2 + (8-7)^2 + (10-7)^2)}{5}[/tex]]
= 2
Hence, set 2 has larger standard deviation.
b. Set 1: 100, 140, 150, 160, 200
Set 2: 10, 50, 60, 70, 110
Here, Set 1 seems to have same standard deviation as set 2.
For set 1:
Mean = (100 + 140 + 150 + 160 + 200) / 5 = 150
Standard Deviation =[tex]\sqrt{\frac{(100-150)^2 + (140-150)^2 + (150-150)^2 + (160-150)^2 + (200-150)^2)}{5}}[/tex]
= 32.24
For set 2:
Mean = (10 + 50 + 60 + 70 + 110) / 5
= 60
Standard Deviation = [tex]\sqrt{\frac{(10-60)^2 + (50-60)^2 + (60-60)^2 + (70-60)^2 + (110-60)^2)}{5}}[/tex]
=32.24
Hence, set 1 and set 2 have same standard deviation.
c. Set 1: 10, 16, 18, 20, 22, 28
Set 2: 48, 56, 58, 60, 62, 70
Set 2 generally has larger values, suggesting that it could have a larger standard deviation because the mean is larger for set 2.
For Set 1:
Mean = (10 + 16 + 18 + 20 + 22 + 28) / 6
= 19
Standard Deviation = [tex]\sqrt{\frac{(10-19)^2 + (16-19)^2 + (18-19)^2 + (20-19)^2 + (22-19)^2 + (28-19)^2)}{6}}[/tex]
= 5.50
For Set 2:
Mean = (48 + 56 + 58 + 60 + 62 + 70) / 6
= 58.33
Standard Deviation = [tex]\sqrt{\frac{(48-58.33)^2 + (56-58.33)^2 + (58-58.33)^2 + (60-58.33)^2 + (62-58.33)^2 + (70-58.33)^2)}{6}}[/tex]
=6.641
Hence, the second set have the larger standard deviation.
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What is the differentiation of f(x) =2x^4/5?
What is the value of the 4 in 24,659
The value of 4 in the given number is 4000.
The given number is 24,659.
What is the place value?Place value can be defined as the value represented by a digit in a number on the basis of its position in the number.
In the given number 24,659, 4 is in thousands place.
So, the value of 4 is 4000
Therefore, the value of 4 in the given number is 4000.
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