What's the radius of a circle with an area of 123 square feet? A. 6.26 ft. B. 39.17 ft. C. 26.32 ft. D. 3.14 ft.

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:

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:

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.

The value of 4 in the given number is 4000.

The given number is 24,659.

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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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.

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 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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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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The algebraic expression for the word phrase '9 less than half a number' is x/2 - 9.

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.

0.73 =  0.7300 is our answer.

Given,

0.73 and 0.7300

We have to compare these decimal 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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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.

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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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

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.

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:

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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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.

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.

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.

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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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.

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.

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.