What is the solution to the system of equations 2x-5y=-5 and x+2y=11?
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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write an algebraic expression for the word phrase 9 less than half a number
The algebraic expression for the word phrase '9 less than half a number' is x/2 - 9.
Explanation:To write an algebraic expression for the word phrase '9 less than half a number,' we first need to define a variable to represent the number. Let's say the number is 'x.' Half of 'x' can be written as 'x/2.' Then, we subtract 9 from 'x/2,' which gives us the algebraic expression: x/2 - 9.
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The algebraic expression for '9 less than half a number' is written as 1/2n - 9, where 'n' stands for the number.
To write an algebraic expression for the word phrase '9 less than half a number', you need to break down the phrase into mathematical terms. Firstly, consider 'half a number'; this can be represented as 1/2n where 'n' is the variable representing the number. The phrase '9 less than' indicates a subtraction of '9' from 'half a number'. Therefore, the algebraic expression would be 1/2n - 9.
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
which types of angels are not congruent?
compare the decimals <, >, or = 0.73 ___ 0.7300
0.73 = 0.7300 is our answer.
Given,
0.73 and 0.7300
We have to compare these decimal numbers.
What is the inequality used to compare two numbers?< = less than
> = greater than
= means equal
≤ = less than or equal to
≥ = greater than or equal to
We have,
0.73 = 73 / 100
There are two numbers after the decimal point.
We divide it by 100.
0.7300 = 7300/1000 = 73/100
There are four numbers after the decimal point.
We divide it by 10000.
We see that both the decimal numbers are equal.
Thus 0.73 = 0.7300
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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
What is the differentiation of f(x) =2x^4/5?
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 statement is modeled by the expression?
A) 100/p The coach received 100 tokens for the amusement park rides. If there are p players on the team, each player will receive 100/p tokens.
B) One hundred more players signed up for soccer than the league had planned for. The league had p uniforms in stock. The number of uniforms the league needs to buy to make up the difference is 100/p.
C) After the league had supplied each player with a uniform, there were 100 uniforms left over. If there are p players in the league, 100/p is the number of uniforms the league had originally.
D) Each player in the league was given 100 tickets to sell. If there are p players in the league, the total number of tickets to sell is 100/p
Answer:
Option A is correct
Step-by-step explanation:
I know this because I am in k12 online school and it said it was: The coach received 100 tokens for the amusement park rides. If there are p players on the team, each player will receive 100p tokens. I hope this helps! Have a fantastic day!
the circle graph shows the result of a survey conducted on 700 people . how many of them liked apple pie the best
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'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.
Red and grey bricks were used to build a decorative wall. There were 140 bricks used in all. How many red bricks were used?
To find the number of red bricks used to build the decorative wall, we can set up a system of equations. By solving the equations, we find that all 140 bricks used were red bricks.
Explanation:To find the number of red bricks used, we can set up a system of equations.
Let r represent the number of red bricks and g represent the number of grey bricks.
We know that there were 140 bricks used in total, so we can write the equation: r + g = 140.
Since we specifically want to find the number of red bricks, we can write the equation: r = 140 - g.
By substituting this expression for r in the first equation, we get: 140 - g + g = 140.
Simplifying the equation, we find that 140 - g + g = 140 - g + g = 140.
Therefore, 140 - g = 140, and solving for g, we find that g = 0.
This means that no grey bricks were used and all 140 bricks used were red bricks.
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.
Find three points that solve the equation , -5x-3y=-7
Joan can type 50 letters in three hours. When Jill helps, they can do the job in one hour. How long would it have taken Jill to do the job alone?
Answer:50 in 1.5 hours.
Step-by-step explanation:
If Joan can do 50 in 3 hours, then in 1 hour, that’s 50/3.
Jill completes the rest of the 50, so 50-(50/3) is how many letters Jill can type in an hour.
50-(50/3)=(150/3)-(50/3)=100/3 letters in an hour. If Jill can write 100 letters in 3 hours, then she can write 50 in 1.5 hours.
Marty's cat weighs 10.4 pounds. This is 24.4 pounds less than the weight of his dog. Write and solve a subtraction equation to find the weight of Marty's dog
Is 7.38 a mixed decimal
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.
Mitchell found a job listed in the classified ads that pays a yearly salary of $57.300. what is the weekly salary based on this annual salary?
The weekly salary based on this annual salary will be $1.102.
What is Division method?
Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
Mitchell found a job listed in the classified ads that pays a yearly salary of $57.300.
Now,
Since, Mitchell found a job listed in the classified ads that pays a yearly salary of $57.300.
We know that;
In 1 yea, The number of weeks = 52
Hence, The weekly salary based on this annual salary = $57.300 ÷ 52
= $1.102
Thus, The weekly salary based on this annual salary will be $1.102.
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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?
Area of 100 3/4 feet x 75 1/2 feet?
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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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.
An audio cable is 15.7dm long. How long is the cable in meters?
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 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.
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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Anna is shopping for a new backpack. The probability that the backpack is pink is 0.7, and the probability that it is canvas is 0.7. The probability that it is pink and canvas is 0.5. What is the probability that it is pink or canvas.
Answer: The required probability is 0.9.
Step-by-step explanation: Given that Anna is shopping for a new backpack. The probability that the backpack is pink is 0.7, the probability that it is canvas is 0.7 and the probability that it is pink and canvas is 0.5.
We are to find the probability that the backpack is either pink or canvas.
Let, 'A' and 'B' be the events that the backpack is pink and canvas respectively.
Then, according to the given information, we have
[tex]P(A)=0.7,~~P(B)=0.7,~~P(A\cap B)=0.5,~~~P(A\cup B)=?[/tex]
From the law of probability, we have
[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)\\\\\Rightarrow P(A\cap B)=0.7+0.7-0.5\\\\\Rightarrow P(A\cap B)=1.4-0.5\\\\\Rightarrow P(A\cap B)=0.9.[/tex]
Therefore, the required probability that the backpack is either pink or canvas is 0.9.